From 0202061e81045bfac52a02916979c303fca35ef0 Mon Sep 17 00:00:00 2001
From: krahets <krahets@163.com>
Date: Fri, 17 Oct 2025 05:33:28 +0800
Subject: [PATCH] deploy

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diff --git a/404.html b/404.html
index f1d8e0045..b3ad98c0c 100644
--- a/404.html
+++ b/404.html
@@ -188,6 +188,12 @@
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+        
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diff --git a/assets/javascripts/bundle.c18c5fb9.min.js b/assets/javascripts/bundle.c18c5fb9.min.js
index 4c12f21df..e6555c9f5 100644
--- a/assets/javascripts/bundle.c18c5fb9.min.js
+++ b/assets/javascripts/bundle.c18c5fb9.min.js
@@ -27,4 +27,4 @@ PERFORMANCE OF THIS SOFTWARE.
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circle{fill:var(--md-mermaid-label-bg-color)}.actor{fill:var(--md-mermaid-sequence-actor-bg-color);stroke:var(--md-mermaid-sequence-actor-border-color)}text.actor>tspan{fill:var(--md-mermaid-sequence-actor-fg-color);font-family:var(--md-mermaid-font-family)}line{stroke:var(--md-mermaid-sequence-actor-line-color)}.actor-man circle,.actor-man line{fill:var(--md-mermaid-sequence-actorman-bg-color);stroke:var(--md-mermaid-sequence-actorman-line-color)}.messageLine0,.messageLine1{stroke:var(--md-mermaid-sequence-message-line-color)}.note{fill:var(--md-mermaid-sequence-note-bg-color);stroke:var(--md-mermaid-sequence-note-border-color)}.loopText,.loopText>tspan,.messageText,.noteText>tspan{stroke:none;font-family:var(--md-mermaid-font-family)!important}.messageText{fill:var(--md-mermaid-sequence-message-fg-color)}.loopText,.loopText>tspan{fill:var(--md-mermaid-sequence-loop-fg-color)}.noteText>tspan{fill:var(--md-mermaid-sequence-note-fg-color)}#arrowhead 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Hn(e,{viewport$:t,target$:r,print$:o}){return T(...R(".annotate:not(.highlight)",e).map(n=>wn(n,{target$:r,print$:o})),...R("pre:not(.mermaid) > code",e).map(n=>On(n,{target$:r,print$:o})),...R("pre.mermaid",e).map(n=>_n(n)),...R("table:not([class])",e).map(n=>Cn(n)),...R("details",e).map(n=>Mn(n,{target$:r,print$:o})),...R("[data-tabs]",e).map(n=>kn(n,{viewport$:t,target$:r})),...R("[title]",e).filter(()=>G("content.tooltips")).map(n=>Ge(n)))}function Ra(e,{alert$:t}){return t.pipe(b(r=>T($(!0),$(!1).pipe(Ye(2e3))).pipe(m(o=>({message:r,active:o})))))}function $n(e,t){let r=P(".md-typeset",e);return H(()=>{let o=new v;return o.subscribe(({message:n,active:i})=>{e.classList.toggle("md-dialog--active",i),r.textContent=n}),Ra(e,t).pipe(y(n=>o.next(n)),_(()=>o.complete()),m(n=>F({ref:e},n)))})}function Pa({viewport$:e}){if(!G("header.autohide"))return $(!1);let 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v;r.subscribe({next({active:n}){e.classList.toggle("md-header__title--active",n)},complete(){e.classList.remove("md-header__title--active")}});let o=me(".md-content h1");return typeof o=="undefined"?L:Ia(o,t).pipe(y(n=>r.next(n)),_(()=>r.complete()),m(n=>F({ref:e},n)))})}function Fn(e,{viewport$:t,header$:r}){let o=r.pipe(m(({height:i})=>i),Y()),n=o.pipe(b(()=>Ee(e).pipe(m(({height:i})=>({top:e.offsetTop,bottom:e.offsetTop+i})),X("bottom"))));return Q([o,n,t]).pipe(m(([i,{top:s,bottom:a},{offset:{y:c},size:{height:p}}])=>(p=Math.max(0,p-Math.max(0,s-c,i)-Math.max(0,p+c-a)),{offset:s-i,height:p,active:s-i<=c})),Y((i,s)=>i.offset===s.offset&&i.height===s.height&&i.active===s.active))}function Fa(e){let t=__md_get("__palette")||{index:e.findIndex(o=>matchMedia(o.getAttribute("data-md-color-media")).matches)},r=Math.max(0,Math.min(t.index,e.length-1));return 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c=o.pipe(y(()=>a.innerHTML=""),b(({items:l})=>T($(...l.slice(0,10)),$(...l.slice(10)).pipe(Ke(4),jr(n),b(([f])=>f)))),m(hn),le());return c.subscribe(l=>a.appendChild(l)),c.pipe(re(l=>{let f=me("details",l);return typeof f=="undefined"?L:d(f,"toggle").pipe(U(o),m(()=>f))})).subscribe(l=>{l.open===!1&&l.offsetTop<=i.scrollTop&&i.scrollTo({top:l.offsetTop})}),t.pipe(g(fr),m(({data:l})=>l)).pipe(y(l=>o.next(l)),_(()=>o.complete()),m(l=>F({ref:e},l)))}function Qa(e,{query$:t}){return t.pipe(m(({value:r})=>{let o=ve();return o.hash="",r=r.replace(/\s+/g,"+").replace(/&/g,"%26").replace(/=/g,"%3D"),o.search=`q=${r}`,{url:o}}))}function Zn(e,t){let r=new v,o=r.pipe(ee(),oe(!0));return r.subscribe(({url:n})=>{e.setAttribute("data-clipboard-text",e.href),e.href=`${n}`}),d(e,"click").pipe(U(o)).subscribe(n=>n.preventDefault()),Qa(e,t).pipe(y(n=>r.next(n)),_(()=>r.complete()),m(n=>F({ref:e},n)))}function ei(e,{worker$:t,keyboard$:r}){let o=new v,n=Te("search-query"),i=T(d(n,"keydown"),d(n,"focus")).pipe(Oe(ie),m(()=>n.value),Y());return o.pipe(je(i),m(([{suggest:a},c])=>{let p=c.split(/([\s-]+)/);if(a!=null&&a.length&&p[p.length-1]){let l=a[a.length-1];l.startsWith(p[p.length-1])&&(p[p.length-1]=l)}else p.length=0;return p})).subscribe(a=>e.innerHTML=a.join("").replace(/\s/g,"&nbsp;")),r.pipe(g(({mode:a})=>a==="search")).subscribe(a=>{switch(a.type){case"ArrowRight":e.innerText.length&&n.selectionStart===n.value.length&&(n.value=e.innerText);break}}),t.pipe(g(fr),m(({data:a})=>a)).pipe(y(a=>o.next(a)),_(()=>o.complete()),m(()=>({ref:e})))}function ti(e,{index$:t,keyboard$:r}){let o=we();try{let n=Bn(o.search,t),i=Te("search-query",e),s=Te("search-result",e);d(e,"click").pipe(g(({target:c})=>c instanceof Element&&!!c.closest("a"))).subscribe(()=>Be("search",!1)),r.pipe(g(({mode:c})=>c==="search")).subscribe(c=>{let p=Re();switch(c.type){case"Enter":if(p===i){let l=new Map;for(let f of R(":first-child [href]",s)){let 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Q([t,r.pipe(q(ve()),g(o=>!!o.searchParams.get("h")))]).pipe(m(([o,n])=>Yn(o.config)(n.searchParams.get("h"))),m(o=>{var s;let n=new Map,i=document.createNodeIterator(e,NodeFilter.SHOW_TEXT);for(let a=i.nextNode();a;a=i.nextNode())if((s=a.parentElement)!=null&&s.offsetHeight){let c=a.textContent,p=o(c);p.length>c.length&&n.set(a,p)}for(let[a,c]of n){let{childNodes:p}=E("span",null,c);a.replaceWith(...Array.from(p))}return{ref:e,nodes:n}}))}function Ya(e,{viewport$:t,main$:r}){let o=e.closest(".md-grid"),n=o.offsetTop-o.parentElement.offsetTop;return Q([r,t]).pipe(m(([{offset:i,height:s},{offset:{y:a}}])=>(s=s+Math.min(n,Math.max(0,a-i))-n,{height:s,locked:a>=i+n})),Y((i,s)=>i.height===s.height&&i.locked===s.locked))}function Qr(e,o){var n=o,{header$:t}=n,r=to(n,["header$"]);let i=P(".md-sidebar__scrollwrap",e),{y:s}=Ue(i);return H(()=>{let a=new v,c=a.pipe(ee(),oe(!0)),p=a.pipe(Me(0,de));return p.pipe(ae(t)).subscribe({next([{height:l},{height:f}]){i.style.height=`${l-2*s}px`,e.style.top=`${f}px`},complete(){i.style.height="",e.style.top=""}}),p.pipe(He()).subscribe(()=>{for(let l of R(".md-nav__link--active[href]",e)){if(!l.clientHeight)continue;let f=l.closest(".md-sidebar__scrollwrap");if(typeof f!="undefined"){let u=l.offsetTop-f.offsetTop,{height:h}=pe(f);f.scrollTo({top:u-h/2})}}}),fe(R("label[tabindex]",e)).pipe(re(l=>d(l,"click").pipe(Oe(ie),m(()=>l),U(c)))).subscribe(l=>{let f=P(`[id="${l.htmlFor}"]`);P(`[aria-labelledby="${l.id}"]`).setAttribute("aria-expanded",`${f.checked}`)}),Ya(e,r).pipe(y(l=>a.next(l)),_(()=>a.complete()),m(l=>F({ref:e},l)))})}function oi(e,t){if(typeof t!="undefined"){let r=`https://api.github.com/repos/${e}/${t}`;return Lt(De(`${r}/releases/latest`).pipe(he(()=>L),m(o=>({version:o.tag_name})),Qe({})),De(r).pipe(he(()=>L),m(o=>({stars:o.stargazers_count,forks:o.forks_count})),Qe({}))).pipe(m(([o,n])=>F(F({},o),n)))}else{let r=`https://api.github.com/users/${e}`;return De(r).pipe(m(o=>({repositories:o.public_repos})),Qe({}))}}function ni(e,t){let r=`https://${e}/api/v4/projects/${encodeURIComponent(t)}`;return De(r).pipe(he(()=>L),m(({star_count:o,forks_count:n})=>({stars:o,forks:n})),Qe({}))}function ii(e){let t=e.match(/^.+github\.com\/([^/]+)\/?([^/]+)?/i);if(t){let[,r,o]=t;return oi(r,o)}if(t=e.match(/^.+?([^/]*gitlab[^/]+)\/(.+?)\/?$/i),t){let[,r,o]=t;return ni(r,o)}return L}var Ba;function Ga(e){return Ba||(Ba=H(()=>{let t=__md_get("__source",sessionStorage);if(t)return $(t);if(ne("consent").length){let o=__md_get("__consent");if(!(o&&o.github))return L}return ii(e.href).pipe(y(o=>__md_set("__source",o,sessionStorage)))}).pipe(he(()=>L),g(t=>Object.keys(t).length>0),m(t=>({facts:t})),B(1)))}function ai(e){let t=P(":scope > :last-child",e);return H(()=>{let r=new v;return 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t=this;e.touches.length<2&&(this.multipointEnd.dispatch(e,this.element),this.sx2=this.sy2=null),this.x2&&Math.abs(this.x1-this.x2)>30||this.y2&&Math.abs(this.y1-this.y2)>30?(e.direction=this._swipeDirection(this.x1,this.x2,this.y1,this.y2),this.swipeTimeout=setTimeout((function(){t.swipe.dispatch(e,t.element)}),0)):(this.tapTimeout=setTimeout((function(){t._preventTap||t.tap.dispatch(e,t.element),t.isDoubleTap&&(t.doubleTap.dispatch(e,t.element),t.isDoubleTap=!1)}),0),t.isDoubleTap||(t.singleTapTimeout=setTimeout((function(){t.singleTap.dispatch(e,t.element)}),250))),this.touchEnd.dispatch(e,this.element),this.preV.x=0,this.preV.y=0,this.zoom=1,this.pinchStartLen=null,this.x1=this.x2=this.y1=this.y2=null}}},{key:"cancelAll",value:function(){this._preventTap=!0,clearTimeout(this.singleTapTimeout),clearTimeout(this.tapTimeout),clearTimeout(this.longTapTimeout),clearTimeout(this.swipeTimeout)}},{key:"cancel",value:function(e){this.cancelAll(),this.touchCancel.dispatch(e,this.element)}},{key:"_cancelLongTap",value:function(){clearTimeout(this.longTapTimeout)}},{key:"_cancelSingleTap",value:function(){clearTimeout(this.singleTapTimeout)}},{key:"_swipeDirection",value:function(e,t,i,n){return Math.abs(e-t)>=Math.abs(i-n)?e-t>0?"Left":"Right":i-n>0?"Up":"Down"}},{key:"on",value:function(e,t){this[e]&&this[e].add(t)}},{key:"off",value:function(e,t){this[e]&&this[e].del(t)}},{key:"destroy",value:function(){return this.singleTapTimeout&&clearTimeout(this.singleTapTimeout),this.tapTimeout&&clearTimeout(this.tapTimeout),this.longTapTimeout&&clearTimeout(this.longTapTimeout),this.swipeTimeout&&clearTimeout(this.swipeTimeout),this.element.removeEventListener("touchstart",this.start),this.element.removeEventListener("touchmove",this.move),this.element.removeEventListener("touchend",this.end),this.element.removeEventListener("touchcancel",this.cancel),this.rotate.del(),this.touchStart.del(),this.multipointStart.del(),this.multipointEnd.del(),this.pinch.del(),this.swipe.del(),this.tap.del(),this.doubleTap.del(),this.longTap.del(),this.singleTap.del(),this.pressMove.del(),this.twoFingerPressMove.del(),this.touchMove.del(),this.touchEnd.del(),this.touchCancel.del(),this.preV=this.pinchStartLen=this.zoom=this.isDoubleTap=this.delta=this.last=this.now=this.tapTimeout=this.singleTapTimeout=this.longTapTimeout=this.swipeTimeout=this.x1=this.x2=this.y1=this.y2=this.preTapPosition=this.rotate=this.touchStart=this.multipointStart=this.multipointEnd=this.pinch=this.swipe=this.tap=this.doubleTap=this.longTap=this.singleTap=this.pressMove=this.touchMove=this.touchEnd=this.touchCancel=this.twoFingerPressMove=null,window.removeEventListener("scroll",this._cancelAllHandler),null}}]),e}();function W(e){var t=function(){var e,t=document.createElement("fakeelement"),i={transition:"transitionend",OTransition:"oTransitionEnd",MozTransition:"transitionend",WebkitTransition:"webkitTransitionEnd"};for(e in i)if(void 0!==t.style[e])return i[e]}(),i=window.innerWidth||document.documentElement.clientWidth||document.body.clientWidth,n=c(e,"gslide-media")?e:e.querySelector(".gslide-media"),s=u(n,".ginner-container"),l=e.querySelector(".gslide-description");i>769&&(n=s),h(n,"greset"),v(n,"translate3d(0, 0, 0)"),a(t,{onElement:n,once:!0,withCallback:function(e,t){d(n,"greset")}}),n.style.opacity="",l&&(l.style.opacity="")}function B(e){if(e.events.hasOwnProperty("touch"))return!1;var t,i,n,s=y(),l=s.width,o=s.height,r=!1,a=null,g=null,f=null,p=!1,m=1,x=1,b=!1,S=!1,w=null,T=null,C=null,k=null,E=0,A=0,L=!1,I=!1,O={},P={},M=0,z=0,X=document.getElementById("glightbox-slider"),Y=document.querySelector(".goverlay"),q=new _(X,{touchStart:function(t){if(r=!0,(c(t.targetTouches[0].target,"ginner-container")||u(t.targetTouches[0].target,".gslide-desc")||"a"==t.targetTouches[0].target.nodeName.toLowerCase())&&(r=!1),u(t.targetTouches[0].target,".gslide-inline")&&!c(t.targetTouches[0].target.parentNode,"gslide-inline")&&(r=!1),r){if(P=t.targetTouches[0],O.pageX=t.targetTouches[0].pageX,O.pageY=t.targetTouches[0].pageY,M=t.targetTouches[0].clientX,z=t.targetTouches[0].clientY,a=e.activeSlide,g=a.querySelector(".gslide-media"),n=a.querySelector(".gslide-inline"),f=null,c(g,"gslide-image")&&(f=g.querySelector("img")),(window.innerWidth||document.documentElement.clientWidth||document.body.clientWidth)>769&&(g=a.querySelector(".ginner-container")),d(Y,"greset"),t.pageX>20&&t.pageX<window.innerWidth-20)return;t.preventDefault()}},touchMove:function(s){if(r&&(P=s.targetTouches[0],!b&&!S)){if(n&&n.offsetHeight>o){var a=O.pageX-P.pageX;if(Math.abs(a)<=13)return!1}p=!0;var h,d=s.targetTouches[0].clientX,c=s.targetTouches[0].clientY,u=M-d,m=z-c;if(Math.abs(u)>Math.abs(m)?(L=!1,I=!0):(I=!1,L=!0),t=P.pageX-O.pageX,E=100*t/l,i=P.pageY-O.pageY,A=100*i/o,L&&f&&(h=1-Math.abs(i)/o,Y.style.opacity=h,e.settings.touchFollowAxis&&(E=0)),I&&(h=1-Math.abs(t)/l,g.style.opacity=h,e.settings.touchFollowAxis&&(A=0)),!f)return v(g,"translate3d(".concat(E,"%, 0, 0)"));v(g,"translate3d(".concat(E,"%, ").concat(A,"%, 0)"))}},touchEnd:function(){if(r){if(p=!1,S||b)return C=w,void(k=T);var t=Math.abs(parseInt(A)),i=Math.abs(parseInt(E));if(!(t>29&&f))return t<29&&i<25?(h(Y,"greset"),Y.style.opacity=1,W(g)):void 0;e.close()}},multipointEnd:function(){setTimeout((function(){b=!1}),50)},multipointStart:function(){b=!0,m=x||1},pinch:function(e){if(!f||p)return!1;b=!0,f.scaleX=f.scaleY=m*e.zoom;var t=m*e.zoom;if(S=!0,t<=1)return S=!1,t=1,k=null,C=null,w=null,T=null,void f.setAttribute("style","");t>4.5&&(t=4.5),f.style.transform="scale3d(".concat(t,", ").concat(t,", 1)"),x=t},pressMove:function(e){if(S&&!b){var t=P.pageX-O.pageX,i=P.pageY-O.pageY;C&&(t+=C),k&&(i+=k),w=t,T=i;var n="translate3d(".concat(t,"px, ").concat(i,"px, 0)");x&&(n+=" scale3d(".concat(x,", ").concat(x,", 1)")),v(f,n)}},swipe:function(t){if(!S)if(b)b=!1;else{if("Left"==t.direction){if(e.index==e.elements.length-1)return W(g);e.nextSlide()}if("Right"==t.direction){if(0==e.index)return W(g);e.prevSlide()}}}});e.events.touch=q}var H=function(){function e(i,n){var s=this,l=arguments.length>2&&void 0!==arguments[2]?arguments[2]:null;if(t(this,e),this.img=i,this.slide=n,this.onclose=l,this.img.setZoomEvents)return!1;this.active=!1,this.zoomedIn=!1,this.dragging=!1,this.currentX=null,this.currentY=null,this.initialX=null,this.initialY=null,this.xOffset=0,this.yOffset=0,this.img.addEventListener("mousedown",(function(e){return s.dragStart(e)}),!1),this.img.addEventListener("mouseup",(function(e){return s.dragEnd(e)}),!1),this.img.addEventListener("mousemove",(function(e){return s.drag(e)}),!1),this.img.addEventListener("click",(function(e){return s.slide.classList.contains("dragging-nav")?(s.zoomOut(),!1):s.zoomedIn?void(s.zoomedIn&&!s.dragging&&s.zoomOut()):s.zoomIn()}),!1),this.img.setZoomEvents=!0}return n(e,[{key:"zoomIn",value:function(){var e=this.widowWidth();if(!(this.zoomedIn||e<=768)){var t=this.img;if(t.setAttribute("data-style",t.getAttribute("style")),t.style.maxWidth=t.naturalWidth+"px",t.style.maxHeight=t.naturalHeight+"px",t.naturalWidth>e){var i=e/2-t.naturalWidth/2;this.setTranslate(this.img.parentNode,i,0)}this.slide.classList.add("zoomed"),this.zoomedIn=!0}}},{key:"zoomOut",value:function(){this.img.parentNode.setAttribute("style",""),this.img.setAttribute("style",this.img.getAttribute("data-style")),this.slide.classList.remove("zoomed"),this.zoomedIn=!1,this.currentX=null,this.currentY=null,this.initialX=null,this.initialY=null,this.xOffset=0,this.yOffset=0,this.onclose&&"function"==typeof this.onclose&&this.onclose()}},{key:"dragStart",value:function(e){e.preventDefault(),this.zoomedIn?("touchstart"===e.type?(this.initialX=e.touches[0].clientX-this.xOffset,this.initialY=e.touches[0].clientY-this.yOffset):(this.initialX=e.clientX-this.xOffset,this.initialY=e.clientY-this.yOffset),e.target===this.img&&(this.active=!0,this.img.classList.add("dragging"))):this.active=!1}},{key:"dragEnd",value:function(e){var t=this;e.preventDefault(),this.initialX=this.currentX,this.initialY=this.currentY,this.active=!1,setTimeout((function(){t.dragging=!1,t.img.isDragging=!1,t.img.classList.remove("dragging")}),100)}},{key:"drag",value:function(e){this.active&&(e.preventDefault(),"touchmove"===e.type?(this.currentX=e.touches[0].clientX-this.initialX,this.currentY=e.touches[0].clientY-this.initialY):(this.currentX=e.clientX-this.initialX,this.currentY=e.clientY-this.initialY),this.xOffset=this.currentX,this.yOffset=this.currentY,this.img.isDragging=!0,this.dragging=!0,this.setTranslate(this.img,this.currentX,this.currentY))}},{key:"onMove",value:function(e){if(this.zoomedIn){var t=e.clientX-this.img.naturalWidth/2,i=e.clientY-this.img.naturalHeight/2;this.setTranslate(this.img,t,i)}}},{key:"setTranslate",value:function(e,t,i){e.style.transform="translate3d("+t+"px, "+i+"px, 0)"}},{key:"widowWidth",value:function(){return window.innerWidth||document.documentElement.clientWidth||document.body.clientWidth}}]),e}(),V=function(){function e(){var i=this,n=arguments.length>0&&void 0!==arguments[0]?arguments[0]:{};t(this,e);var s=n.dragEl,l=n.toleranceX,o=void 0===l?40:l,r=n.toleranceY,a=void 0===r?65:r,h=n.slide,d=void 0===h?null:h,c=n.instance,u=void 0===c?null:c;this.el=s,this.active=!1,this.dragging=!1,this.currentX=null,this.currentY=null,this.initialX=null,this.initialY=null,this.xOffset=0,this.yOffset=0,this.direction=null,this.lastDirection=null,this.toleranceX=o,this.toleranceY=a,this.toleranceReached=!1,this.dragContainer=this.el,this.slide=d,this.instance=u,this.el.addEventListener("mousedown",(function(e){return i.dragStart(e)}),!1),this.el.addEventListener("mouseup",(function(e){return i.dragEnd(e)}),!1),this.el.addEventListener("mousemove",(function(e){return i.drag(e)}),!1)}return n(e,[{key:"dragStart",value:function(e){if(this.slide.classList.contains("zoomed"))this.active=!1;else{"touchstart"===e.type?(this.initialX=e.touches[0].clientX-this.xOffset,this.initialY=e.touches[0].clientY-this.yOffset):(this.initialX=e.clientX-this.xOffset,this.initialY=e.clientY-this.yOffset);var t=e.target.nodeName.toLowerCase();e.target.classList.contains("nodrag")||u(e.target,".nodrag")||-1!==["input","select","textarea","button","a"].indexOf(t)?this.active=!1:(e.preventDefault(),(e.target===this.el||"img"!==t&&u(e.target,".gslide-inline"))&&(this.active=!0,this.el.classList.add("dragging"),this.dragContainer=u(e.target,".ginner-container")))}}},{key:"dragEnd",value:function(e){var t=this;e&&e.preventDefault(),this.initialX=0,this.initialY=0,this.currentX=null,this.currentY=null,this.initialX=null,this.initialY=null,this.xOffset=0,this.yOffset=0,this.active=!1,this.doSlideChange&&(this.instance.preventOutsideClick=!0,"right"==this.doSlideChange&&this.instance.prevSlide(),"left"==this.doSlideChange&&this.instance.nextSlide()),this.doSlideClose&&this.instance.close(),this.toleranceReached||this.setTranslate(this.dragContainer,0,0,!0),setTimeout((function(){t.instance.preventOutsideClick=!1,t.toleranceReached=!1,t.lastDirection=null,t.dragging=!1,t.el.isDragging=!1,t.el.classList.remove("dragging"),t.slide.classList.remove("dragging-nav"),t.dragContainer.style.transform="",t.dragContainer.style.transition=""}),100)}},{key:"drag",value:function(e){if(this.active){e.preventDefault(),this.slide.classList.add("dragging-nav"),"touchmove"===e.type?(this.currentX=e.touches[0].clientX-this.initialX,this.currentY=e.touches[0].clientY-this.initialY):(this.currentX=e.clientX-this.initialX,this.currentY=e.clientY-this.initialY),this.xOffset=this.currentX,this.yOffset=this.currentY,this.el.isDragging=!0,this.dragging=!0,this.doSlideChange=!1,this.doSlideClose=!1;var t=Math.abs(this.currentX),i=Math.abs(this.currentY);if(t>0&&t>=Math.abs(this.currentY)&&(!this.lastDirection||"x"==this.lastDirection)){this.yOffset=0,this.lastDirection="x",this.setTranslate(this.dragContainer,this.currentX,0);var n=this.shouldChange();if(!this.instance.settings.dragAutoSnap&&n&&(this.doSlideChange=n),this.instance.settings.dragAutoSnap&&n)return this.instance.preventOutsideClick=!0,this.toleranceReached=!0,this.active=!1,this.instance.preventOutsideClick=!0,this.dragEnd(null),"right"==n&&this.instance.prevSlide(),void("left"==n&&this.instance.nextSlide())}if(this.toleranceY>0&&i>0&&i>=t&&(!this.lastDirection||"y"==this.lastDirection)){this.xOffset=0,this.lastDirection="y",this.setTranslate(this.dragContainer,0,this.currentY);var s=this.shouldClose();return!this.instance.settings.dragAutoSnap&&s&&(this.doSlideClose=!0),void(this.instance.settings.dragAutoSnap&&s&&this.instance.close())}}}},{key:"shouldChange",value:function(){var e=!1;if(Math.abs(this.currentX)>=this.toleranceX){var t=this.currentX>0?"right":"left";("left"==t&&this.slide!==this.slide.parentNode.lastChild||"right"==t&&this.slide!==this.slide.parentNode.firstChild)&&(e=t)}return e}},{key:"shouldClose",value:function(){var e=!1;return Math.abs(this.currentY)>=this.toleranceY&&(e=!0),e}},{key:"setTranslate",value:function(e,t,i){var n=arguments.length>3&&void 0!==arguments[3]&&arguments[3];e.style.transition=n?"all .2s ease":"",e.style.transform="translate3d(".concat(t,"px, ").concat(i,"px, 0)")}}]),e}();function j(e,t,i,n){var s=e.querySelector(".gslide-media"),l=new Image,o="gSlideTitle_"+i,r="gSlideDesc_"+i;l.addEventListener("load",(function(){T(n)&&n()}),!1),l.src=t.href,""!=t.sizes&&""!=t.srcset&&(l.sizes=t.sizes,l.srcset=t.srcset),l.alt="",I(t.alt)||""===t.alt||(l.alt=t.alt),""!==t.title&&l.setAttribute("aria-labelledby",o),""!==t.description&&l.setAttribute("aria-describedby",r),t.hasOwnProperty("_hasCustomWidth")&&t._hasCustomWidth&&(l.style.width=t.width),t.hasOwnProperty("_hasCustomHeight")&&t._hasCustomHeight&&(l.style.height=t.height),s.insertBefore(l,s.firstChild)}function F(e,t,i,n){var s=this,l=e.querySelector(".ginner-container"),o="gvideo"+i,r=e.querySelector(".gslide-media"),a=this.getAllPlayers();h(l,"gvideo-container"),r.insertBefore(m('<div class="gvideo-wrapper"></div>'),r.firstChild);var d=e.querySelector(".gvideo-wrapper");S(this.settings.plyr.css,"Plyr");var c=t.href,u=location.protocol.replace(":",""),g="",v="",f=!1;"file"==u&&(u="http"),r.style.maxWidth=t.width,S(this.settings.plyr.js,"Plyr",(function(){if(c.match(/vimeo\.com\/([0-9]*)/)){var l=/vimeo.*\/(\d+)/i.exec(c);g="vimeo",v=l[1]}if(c.match(/(youtube\.com|youtube-nocookie\.com)\/watch\?v=([a-zA-Z0-9\-_]+)/)||c.match(/youtu\.be\/([a-zA-Z0-9\-_]+)/)||c.match(/(youtube\.com|youtube-nocookie\.com)\/embed\/([a-zA-Z0-9\-_]+)/)){var r=function(e){var t="";t=void 0!==(e=e.replace(/(>|<)/gi,"").split(/(vi\/|v=|\/v\/|youtu\.be\/|\/embed\/)/))[2]?(t=e[2].split(/[^0-9a-z_\-]/i))[0]:e;return t}(c);g="youtube",v=r}if(null!==c.match(/\.(mp4|ogg|webm|mov)$/)){g="local";var u='<video id="'+o+'" ';u+='style="background:#000; max-width: '.concat(t.width,';" '),u+='preload="metadata" ',u+='x-webkit-airplay="allow" ',u+="playsinline ",u+="controls ",u+='class="gvideo-local">';var p=c.toLowerCase().split(".").pop(),y={mp4:"",ogg:"",webm:""};for(var x in y[p="mov"==p?"mp4":p]=c,y)if(y.hasOwnProperty(x)){var S=y[x];t.hasOwnProperty(x)&&(S=t[x]),""!==S&&(u+='<source src="'.concat(S,'" type="video/').concat(x,'">'))}f=m(u+="</video>")}var w=f||m('<div id="'.concat(o,'" data-plyr-provider="').concat(g,'" data-plyr-embed-id="').concat(v,'"></div>'));h(d,"".concat(g,"-video gvideo")),d.appendChild(w),d.setAttribute("data-id",o),d.setAttribute("data-index",i);var C=O(s.settings.plyr,"config")?s.settings.plyr.config:{},k=new Plyr("#"+o,C);k.on("ready",(function(e){var t=e.detail.plyr;a[o]=t,T(n)&&n()})),b((function(){return e.querySelector("iframe")&&"true"==e.querySelector("iframe").dataset.ready}),(function(){s.resize(e)})),k.on("enterfullscreen",R),k.on("exitfullscreen",R)}))}function R(e){var t=u(e.target,".gslide-media");"enterfullscreen"==e.type&&h(t,"fullscreen"),"exitfullscreen"==e.type&&d(t,"fullscreen")}function G(e,t,i,n){var s,l=this,o=e.querySelector(".gslide-media"),r=!(!O(t,"href")||!t.href)&&t.href.split("#").pop().trim(),d=!(!O(t,"content")||!t.content)&&t.content;if(d&&(C(d)&&(s=m('<div class="ginlined-content">'.concat(d,"</div>"))),k(d))){"none"==d.style.display&&(d.style.display="block");var c=document.createElement("div");c.className="ginlined-content",c.appendChild(d),s=c}if(r){var u=document.getElementById(r);if(!u)return!1;var g=u.cloneNode(!0);g.style.height=t.height,g.style.maxWidth=t.width,h(g,"ginlined-content"),s=g}if(!s)return console.error("Unable to append inline slide content",t),!1;o.style.height=t.height,o.style.width=t.width,o.appendChild(s),this.events["inlineclose"+r]=a("click",{onElement:o.querySelectorAll(".gtrigger-close"),withCallback:function(e){e.preventDefault(),l.close()}}),T(n)&&n()}function Z(e,t,i,n){var s=e.querySelector(".gslide-media"),l=function(e){var t=e.url,i=e.allow,n=e.callback,s=e.appendTo,l=document.createElement("iframe");return l.className="vimeo-video 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t=e;if(null!==(e=e.toLowerCase()).match(/\.(jpeg|jpg|jpe|gif|png|apn|webp|avif|svg)/))return"image";if(e.match(/(youtube\.com|youtube-nocookie\.com)\/watch\?v=([a-zA-Z0-9\-_]+)/)||e.match(/youtu\.be\/([a-zA-Z0-9\-_]+)/)||e.match(/(youtube\.com|youtube-nocookie\.com)\/embed\/([a-zA-Z0-9\-_]+)/))return"video";if(e.match(/vimeo\.com\/([0-9]*)/))return"video";if(null!==e.match(/\.(mp4|ogg|webm|mov)/))return"video";if(null!==e.match(/\.(mp3|wav|wma|aac|ogg)/))return"audio";if(e.indexOf("#")>-1&&""!==t.split("#").pop().trim())return"inline";return e.indexOf("goajax=true")>-1?"ajax":"external"}},{key:"parseConfig",value:function(e,t){var i=this,n=l({descPosition:t.descPosition},this.defaults);if(L(e)&&!k(e)){O(e,"type")||(O(e,"content")&&e.content?e.type="inline":O(e,"href")&&(e.type=this.sourceType(e.href)));var s=l(n,e);return this.setSize(s,t),s}var r="",a=e.getAttribute("data-glightbox"),h=e.nodeName.toLowerCase();if("a"===h&&(r=e.href),"img"===h&&(r=e.src,n.alt=e.alt),n.href=r,o(n,(function(s,l){O(t,l)&&"width"!==l&&(n[l]=t[l]);var o=e.dataset[l];I(o)||(n[l]=i.sanitizeValue(o))})),n.content&&(n.type="inline"),!n.type&&r&&(n.type=this.sourceType(r)),I(a)){if(!n.title&&"a"==h){var d=e.title;I(d)||""===d||(n.title=d)}if(!n.title&&"img"==h){var c=e.alt;I(c)||""===c||(n.title=c)}}else{var u=[];o(n,(function(e,t){u.push(";\\s?"+t)})),u=u.join("\\s?:|"),""!==a.trim()&&o(n,(function(e,t){var s=a,l=new RegExp("s?"+t+"s?:s?(.*?)("+u+"s?:|$)"),o=s.match(l);if(o&&o.length&&o[1]){var r=o[1].trim().replace(/;\s*$/,"");n[t]=i.sanitizeValue(r)}}))}if(n.description&&"."===n.description.substring(0,1)){var g;try{g=document.querySelector(n.description).innerHTML}catch(e){if(!(e instanceof DOMException))throw e}g&&(n.description=g)}if(!n.description){var v=e.querySelector(".glightbox-desc");v&&(n.description=v.innerHTML)}return this.setSize(n,t,e),this.slideConfig=n,n}},{key:"setSize",value:function(e,t){var i=arguments.length>2&&void 0!==arguments[2]?arguments[2]:null,n="video"==e.type?this.checkSize(t.videosWidth):this.checkSize(t.width),s=this.checkSize(t.height);return e.width=O(e,"width")&&""!==e.width?this.checkSize(e.width):n,e.height=O(e,"height")&&""!==e.height?this.checkSize(e.height):s,i&&"image"==e.type&&(e._hasCustomWidth=!!i.dataset.width,e._hasCustomHeight=!!i.dataset.height),e}},{key:"checkSize",value:function(e){return M(e)?"".concat(e,"px"):e}},{key:"sanitizeValue",value:function(e){return"true"!==e&&"false"!==e?e:"true"===e}}]),e}(),U=function(){function e(i,n,s){t(this,e),this.element=i,this.instance=n,this.index=s}return n(e,[{key:"setContent",value:function(){var e=this,t=arguments.length>0&&void 0!==arguments[0]?arguments[0]:null,i=arguments.length>1&&void 0!==arguments[1]&&arguments[1];if(c(t,"loaded"))return!1;var n=this.instance.settings,s=this.slideConfig,l=w();T(n.beforeSlideLoad)&&n.beforeSlideLoad({index:this.index,slide:t,player:!1});var o=s.type,r=s.descPosition,a=t.querySelector(".gslide-media"),d=t.querySelector(".gslide-title"),u=t.querySelector(".gslide-desc"),g=t.querySelector(".gdesc-inner"),v=i,f="gSlideTitle_"+this.index,p="gSlideDesc_"+this.index;if(T(n.afterSlideLoad)&&(v=function(){T(i)&&i(),n.afterSlideLoad({index:e.index,slide:t,player:e.instance.getSlidePlayerInstance(e.index)})}),""==s.title&&""==s.description?g&&g.parentNode.parentNode.removeChild(g.parentNode):(d&&""!==s.title?(d.id=f,d.innerHTML=s.title):d.parentNode.removeChild(d),u&&""!==s.description?(u.id=p,l&&n.moreLength>0?(s.smallDescription=this.slideShortDesc(s.description,n.moreLength,n.moreText),u.innerHTML=s.smallDescription,this.descriptionEvents(u,s)):u.innerHTML=s.description):u.parentNode.removeChild(u),h(a.parentNode,"desc-".concat(r)),h(g.parentNode,"description-".concat(r))),h(a,"gslide-".concat(o)),h(t,"loaded"),"video"!==o){if("external"!==o)return"inline"===o?(G.apply(this.instance,[t,s,this.index,v]),void(s.draggable&&new V({dragEl:t.querySelector(".gslide-inline"),toleranceX:n.dragToleranceX,toleranceY:n.dragToleranceY,slide:t,instance:this.instance}))):void("image"!==o?T(v)&&v():j(t,s,this.index,(function(){var i=t.querySelector("img");s.draggable&&new V({dragEl:i,toleranceX:n.dragToleranceX,toleranceY:n.dragToleranceY,slide:t,instance:e.instance}),s.zoomable&&i.naturalWidth>i.offsetWidth&&(h(i,"zoomable"),new H(i,t,(function(){e.instance.resize()}))),T(v)&&v()})));Z.apply(this,[t,s,this.index,v])}else F.apply(this.instance,[t,s,this.index,v])}},{key:"slideShortDesc",value:function(e){var t=arguments.length>1&&void 0!==arguments[1]?arguments[1]:50,i=arguments.length>2&&void 0!==arguments[2]&&arguments[2],n=document.createElement("div");n.innerHTML=e;var s=n.innerText,l=i;if((e=s.trim()).length<=t)return e;var o=e.substr(0,t-1);return l?(n=null,o+'... <a href="#" class="desc-more">'+i+"</a>"):o}},{key:"descriptionEvents",value:function(e,t){var i=this,n=e.querySelector(".desc-more");if(!n)return!1;a("click",{onElement:n,withCallback:function(e,n){e.preventDefault();var s=document.body,l=u(n,".gslide-desc");if(!l)return!1;l.innerHTML=t.description,h(s,"gdesc-open");var o=a("click",{onElement:[s,u(l,".gslide-description")],withCallback:function(e,n){"a"!==e.target.nodeName.toLowerCase()&&(d(s,"gdesc-open"),h(s,"gdesc-closed"),l.innerHTML=t.smallDescription,i.descriptionEvents(l,t),setTimeout((function(){d(s,"gdesc-closed")}),400),o.destroy())}})}})}},{key:"create",value:function(){return m(this.instance.settings.slideHTML)}},{key:"getConfig",value:function(){k(this.element)||this.element.hasOwnProperty("draggable")||(this.element.draggable=this.instance.settings.draggable);var e=new $(this.instance.settings.slideExtraAttributes);return this.slideConfig=e.parseConfig(this.element,this.instance.settings),this.slideConfig}}]),e}(),J=w(),K=null!==w()||void 0!==document.createTouch||"ontouchstart"in window||"onmsgesturechange"in window||navigator.msMaxTouchPoints,Q=document.getElementsByTagName("html")[0],ee={selector:".glightbox",elements:null,skin:"clean",theme:"clean",closeButton:!0,startAt:null,autoplayVideos:!0,autofocusVideos:!0,descPosition:"bottom",width:"900px",height:"506px",videosWidth:"960px",beforeSlideChange:null,afterSlideChange:null,beforeSlideLoad:null,afterSlideLoad:null,slideInserted:null,slideRemoved:null,slideExtraAttributes:null,onOpen:null,onClose:null,loop:!1,zoomable:!0,draggable:!0,dragAutoSnap:!1,dragToleranceX:40,dragToleranceY:65,preload:!0,oneSlidePerOpen:!1,touchNavigation:!0,touchFollowAxis:!0,keyboardNavigation:!0,closeOnOutsideClick:!0,plugins:!1,plyr:{css:"https://cdn.plyr.io/3.6.8/plyr.css",js:"https://cdn.plyr.io/3.6.8/plyr.js",config:{ratio:"16:9",fullscreen:{enabled:!0,iosNative:!0},youtube:{noCookie:!0,rel:0,showinfo:0,iv_load_policy:3},vimeo:{byline:!1,portrait:!1,title:!1,transparent:!1}}},openEffect:"zoom",closeEffect:"zoom",slideEffect:"slide",moreText:"See more",moreLength:60,cssEfects:{fade:{in:"fadeIn",out:"fadeOut"},zoom:{in:"zoomIn",out:"zoomOut"},slide:{in:"slideInRight",out:"slideOutLeft"},slideBack:{in:"slideInLeft",out:"slideOutRight"},none:{in:"none",out:"none"}},svg:{close:'<svg version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" x="0px" y="0px" viewBox="0 0 512 512" xml:space="preserve"><g><g><path d="M505.943,6.058c-8.077-8.077-21.172-8.077-29.249,0L6.058,476.693c-8.077,8.077-8.077,21.172,0,29.249C10.096,509.982,15.39,512,20.683,512c5.293,0,10.586-2.019,14.625-6.059L505.943,35.306C514.019,27.23,514.019,14.135,505.943,6.058z"/></g></g><g><g><path d="M505.942,476.694L35.306,6.059c-8.076-8.077-21.172-8.077-29.248,0c-8.077,8.076-8.077,21.171,0,29.248l470.636,470.636c4.038,4.039,9.332,6.058,14.625,6.058c5.293,0,10.587-2.019,14.624-6.057C514.018,497.866,514.018,484.771,505.942,476.694z"/></g></g></svg>',next:'<svg version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" x="0px" y="0px" viewBox="0 0 477.175 477.175" xml:space="preserve"> <g><path d="M360.731,229.075l-225.1-225.1c-5.3-5.3-13.8-5.3-19.1,0s-5.3,13.8,0,19.1l215.5,215.5l-215.5,215.5c-5.3,5.3-5.3,13.8,0,19.1c2.6,2.6,6.1,4,9.5,4c3.4,0,6.9-1.3,9.5-4l225.1-225.1C365.931,242.875,365.931,234.275,360.731,229.075z"/></g></svg>',prev:'<svg version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" x="0px" y="0px" viewBox="0 0 477.175 477.175" xml:space="preserve"><g><path d="M145.188,238.575l215.5-215.5c5.3-5.3,5.3-13.8,0-19.1s-13.8-5.3-19.1,0l-225.1,225.1c-5.3,5.3-5.3,13.8,0,19.1l225.1,225c2.6,2.6,6.1,4,9.5,4s6.9-1.3,9.5-4c5.3-5.3,5.3-13.8,0-19.1L145.188,238.575z"/></g></svg>'},slideHTML:'<div class="gslide">\n    <div class="gslide-inner-content">\n        <div class="ginner-container">\n            <div class="gslide-media">\n            </div>\n            <div class="gslide-description">\n                <div class="gdesc-inner">\n                    <h4 class="gslide-title"></h4>\n                    <div class="gslide-desc"></div>\n                </div>\n            </div>\n        </div>\n    </div>\n</div>',lightboxHTML:'<div id="glightbox-body" class="glightbox-container" tabindex="-1" role="dialog" aria-hidden="false">\n    <div class="gloader visible"></div>\n    <div class="goverlay"></div>\n    <div class="gcontainer">\n    <div id="glightbox-slider" class="gslider"></div>\n    <button class="gclose gbtn" aria-label="Close" data-taborder="3">{closeSVG}</button>\n    <button class="gprev gbtn" aria-label="Previous" data-taborder="2">{prevSVG}</button>\n    <button class="gnext gbtn" aria-label="Next" data-taborder="1">{nextSVG}</button>\n</div>\n</div>'},te=function(){function e(){var i=arguments.length>0&&void 0!==arguments[0]?arguments[0]:{};t(this,e),this.customOptions=i,this.settings=l(ee,i),this.effectsClasses=this.getAnimationClasses(),this.videoPlayers={},this.apiEvents=[],this.fullElementsList=!1}return n(e,[{key:"init",value:function(){var e=this,t=this.getSelector();t&&(this.baseEvents=a("click",{onElement:t,withCallback:function(t,i){t.preventDefault(),e.open(i)}})),this.elements=this.getElements()}},{key:"open",value:function(){var e=arguments.length>0&&void 0!==arguments[0]?arguments[0]:null,t=arguments.length>1&&void 0!==arguments[1]?arguments[1]:null;if(0==this.elements.length)return!1;this.activeSlide=null,this.prevActiveSlideIndex=null,this.prevActiveSlide=null;var i=M(t)?t:this.settings.startAt;if(k(e)){var n=e.getAttribute("data-gallery");n&&(this.fullElementsList=this.elements,this.elements=this.getGalleryElements(this.elements,n)),I(i)&&(i=this.getElementIndex(e))<0&&(i=0)}M(i)||(i=0),this.build(),g(this.overlay,"none"==this.settings.openEffect?"none":this.settings.cssEfects.fade.in);var s=document.body,l=window.innerWidth-document.documentElement.clientWidth;if(l>0){var o=document.createElement("style");o.type="text/css",o.className="gcss-styles",o.innerText=".gscrollbar-fixer {margin-right: ".concat(l,"px}"),document.head.appendChild(o),h(s,"gscrollbar-fixer")}h(s,"glightbox-open"),h(Q,"glightbox-open"),J&&(h(document.body,"glightbox-mobile"),this.settings.slideEffect="slide"),this.showSlide(i,!0),1==this.elements.length?(h(this.prevButton,"glightbox-button-hidden"),h(this.nextButton,"glightbox-button-hidden")):(d(this.prevButton,"glightbox-button-hidden"),d(this.nextButton,"glightbox-button-hidden")),this.lightboxOpen=!0,this.trigger("open"),T(this.settings.onOpen)&&this.settings.onOpen(),K&&this.settings.touchNavigation&&B(this),this.settings.keyboardNavigation&&X(this)}},{key:"openAt",value:function(){var e=arguments.length>0&&void 0!==arguments[0]?arguments[0]:0;this.open(null,e)}},{key:"showSlide",value:function(){var e=this,t=arguments.length>0&&void 0!==arguments[0]?arguments[0]:0,i=arguments.length>1&&void 0!==arguments[1]&&arguments[1];f(this.loader),this.index=parseInt(t);var n=this.slidesContainer.querySelector(".current");n&&d(n,"current"),this.slideAnimateOut();var s=this.slidesContainer.querySelectorAll(".gslide")[t];if(c(s,"loaded"))this.slideAnimateIn(s,i),p(this.loader);else{f(this.loader);var l=this.elements[t],o={index:this.index,slide:s,slideNode:s,slideConfig:l.slideConfig,slideIndex:this.index,trigger:l.node,player:null};this.trigger("slide_before_load",o),l.instance.setContent(s,(function(){p(e.loader),e.resize(),e.slideAnimateIn(s,i),e.trigger("slide_after_load",o)}))}this.slideDescription=s.querySelector(".gslide-description"),this.slideDescriptionContained=this.slideDescription&&c(this.slideDescription.parentNode,"gslide-media"),this.settings.preload&&(this.preloadSlide(t+1),this.preloadSlide(t-1)),this.updateNavigationClasses(),this.activeSlide=s}},{key:"preloadSlide",value:function(e){var t=this;if(e<0||e>this.elements.length-1)return!1;if(I(this.elements[e]))return!1;var i=this.slidesContainer.querySelectorAll(".gslide")[e];if(c(i,"loaded"))return!1;var n=this.elements[e],s=n.type,l={index:e,slide:i,slideNode:i,slideConfig:n.slideConfig,slideIndex:e,trigger:n.node,player:null};this.trigger("slide_before_load",l),"video"==s||"external"==s?setTimeout((function(){n.instance.setContent(i,(function(){t.trigger("slide_after_load",l)}))}),200):n.instance.setContent(i,(function(){t.trigger("slide_after_load",l)}))}},{key:"prevSlide",value:function(){this.goToSlide(this.index-1)}},{key:"nextSlide",value:function(){this.goToSlide(this.index+1)}},{key:"goToSlide",value:function(){var e=arguments.length>0&&void 0!==arguments[0]&&arguments[0];if(this.prevActiveSlide=this.activeSlide,this.prevActiveSlideIndex=this.index,!this.loop()&&(e<0||e>this.elements.length-1))return!1;e<0?e=this.elements.length-1:e>=this.elements.length&&(e=0),this.showSlide(e)}},{key:"insertSlide",value:function(){var e=arguments.length>0&&void 0!==arguments[0]?arguments[0]:{},t=arguments.length>1&&void 0!==arguments[1]?arguments[1]:-1;t<0&&(t=this.elements.length);var i=new U(e,this,t),n=i.getConfig(),s=l({},n),o=i.create(),r=this.elements.length-1;s.index=t,s.node=!1,s.instance=i,s.slideConfig=n,this.elements.splice(t,0,s);var a=null,h=null;if(this.slidesContainer){if(t>r)this.slidesContainer.appendChild(o);else{var d=this.slidesContainer.querySelectorAll(".gslide")[t];this.slidesContainer.insertBefore(o,d)}(this.settings.preload&&0==this.index&&0==t||this.index-1==t||this.index+1==t)&&this.preloadSlide(t),0==this.index&&0==t&&(this.index=1),this.updateNavigationClasses(),a=this.slidesContainer.querySelectorAll(".gslide")[t],h=this.getSlidePlayerInstance(t),s.slideNode=a}this.trigger("slide_inserted",{index:t,slide:a,slideNode:a,slideConfig:n,slideIndex:t,trigger:null,player:h}),T(this.settings.slideInserted)&&this.settings.slideInserted({index:t,slide:a,player:h})}},{key:"removeSlide",value:function(){var e=arguments.length>0&&void 0!==arguments[0]?arguments[0]:-1;if(e<0||e>this.elements.length-1)return!1;var t=this.slidesContainer&&this.slidesContainer.querySelectorAll(".gslide")[e];t&&(this.getActiveSlideIndex()==e&&(e==this.elements.length-1?this.prevSlide():this.nextSlide()),t.parentNode.removeChild(t)),this.elements.splice(e,1),this.trigger("slide_removed",e),T(this.settings.slideRemoved)&&this.settings.slideRemoved(e)}},{key:"slideAnimateIn",value:function(e,t){var i=this,n=e.querySelector(".gslide-media"),s=e.querySelector(".gslide-description"),l={index:this.prevActiveSlideIndex,slide:this.prevActiveSlide,slideNode:this.prevActiveSlide,slideIndex:this.prevActiveSlide,slideConfig:I(this.prevActiveSlideIndex)?null:this.elements[this.prevActiveSlideIndex].slideConfig,trigger:I(this.prevActiveSlideIndex)?null:this.elements[this.prevActiveSlideIndex].node,player:this.getSlidePlayerInstance(this.prevActiveSlideIndex)},o={index:this.index,slide:this.activeSlide,slideNode:this.activeSlide,slideConfig:this.elements[this.index].slideConfig,slideIndex:this.index,trigger:this.elements[this.index].node,player:this.getSlidePlayerInstance(this.index)};if(n.offsetWidth>0&&s&&(p(s),s.style.display=""),d(e,this.effectsClasses),t)g(e,this.settings.cssEfects[this.settings.openEffect].in,(function(){i.settings.autoplayVideos&&i.slidePlayerPlay(e),i.trigger("slide_changed",{prev:l,current:o}),T(i.settings.afterSlideChange)&&i.settings.afterSlideChange.apply(i,[l,o])}));else{var r=this.settings.slideEffect,a="none"!==r?this.settings.cssEfects[r].in:r;this.prevActiveSlideIndex>this.index&&"slide"==this.settings.slideEffect&&(a=this.settings.cssEfects.slideBack.in),g(e,a,(function(){i.settings.autoplayVideos&&i.slidePlayerPlay(e),i.trigger("slide_changed",{prev:l,current:o}),T(i.settings.afterSlideChange)&&i.settings.afterSlideChange.apply(i,[l,o])}))}setTimeout((function(){i.resize(e)}),100),h(e,"current")}},{key:"slideAnimateOut",value:function(){if(!this.prevActiveSlide)return!1;var e=this.prevActiveSlide;d(e,this.effectsClasses),h(e,"prev");var t=this.settings.slideEffect,i="none"!==t?this.settings.cssEfects[t].out:t;this.slidePlayerPause(e),this.trigger("slide_before_change",{prev:{index:this.prevActiveSlideIndex,slide:this.prevActiveSlide,slideNode:this.prevActiveSlide,slideIndex:this.prevActiveSlideIndex,slideConfig:I(this.prevActiveSlideIndex)?null:this.elements[this.prevActiveSlideIndex].slideConfig,trigger:I(this.prevActiveSlideIndex)?null:this.elements[this.prevActiveSlideIndex].node,player:this.getSlidePlayerInstance(this.prevActiveSlideIndex)},current:{index:this.index,slide:this.activeSlide,slideNode:this.activeSlide,slideIndex:this.index,slideConfig:this.elements[this.index].slideConfig,trigger:this.elements[this.index].node,player:this.getSlidePlayerInstance(this.index)}}),T(this.settings.beforeSlideChange)&&this.settings.beforeSlideChange.apply(this,[{index:this.prevActiveSlideIndex,slide:this.prevActiveSlide,player:this.getSlidePlayerInstance(this.prevActiveSlideIndex)},{index:this.index,slide:this.activeSlide,player:this.getSlidePlayerInstance(this.index)}]),this.prevActiveSlideIndex>this.index&&"slide"==this.settings.slideEffect&&(i=this.settings.cssEfects.slideBack.out),g(e,i,(function(){var t=e.querySelector(".ginner-container"),i=e.querySelector(".gslide-media"),n=e.querySelector(".gslide-description");t.style.transform="",i.style.transform="",d(i,"greset"),i.style.opacity="",n&&(n.style.opacity=""),d(e,"prev")}))}},{key:"getAllPlayers",value:function(){return this.videoPlayers}},{key:"getSlidePlayerInstance",value:function(e){var t="gvideo"+e,i=this.getAllPlayers();return!(!O(i,t)||!i[t])&&i[t]}},{key:"stopSlideVideo",value:function(e){if(k(e)){var t=e.querySelector(".gvideo-wrapper");t&&(e=t.getAttribute("data-index"))}console.log("stopSlideVideo is deprecated, use slidePlayerPause");var i=this.getSlidePlayerInstance(e);i&&i.playing&&i.pause()}},{key:"slidePlayerPause",value:function(e){if(k(e)){var t=e.querySelector(".gvideo-wrapper");t&&(e=t.getAttribute("data-index"))}var i=this.getSlidePlayerInstance(e);i&&i.playing&&i.pause()}},{key:"playSlideVideo",value:function(e){if(k(e)){var t=e.querySelector(".gvideo-wrapper");t&&(e=t.getAttribute("data-index"))}console.log("playSlideVideo is deprecated, use slidePlayerPlay");var i=this.getSlidePlayerInstance(e);i&&!i.playing&&i.play()}},{key:"slidePlayerPlay",value:function(e){if(k(e)){var t=e.querySelector(".gvideo-wrapper");t&&(e=t.getAttribute("data-index"))}var i=this.getSlidePlayerInstance(e);i&&!i.playing&&(i.play(),this.settings.autofocusVideos&&i.elements.container.focus())}},{key:"setElements",value:function(e){var t=this;this.settings.elements=!1;var i=[];e&&e.length&&o(e,(function(e,n){var s=new U(e,t,n),o=s.getConfig(),r=l({},o);r.slideConfig=o,r.instance=s,r.index=n,i.push(r)})),this.elements=i,this.lightboxOpen&&(this.slidesContainer.innerHTML="",this.elements.length&&(o(this.elements,(function(){var e=m(t.settings.slideHTML);t.slidesContainer.appendChild(e)})),this.showSlide(0,!0)))}},{key:"getElementIndex",value:function(e){var t=!1;return o(this.elements,(function(i,n){if(O(i,"node")&&i.node==e)return t=n,!0})),t}},{key:"getElements",value:function(){var e=this,t=[];this.elements=this.elements?this.elements:[],!I(this.settings.elements)&&E(this.settings.elements)&&this.settings.elements.length&&o(this.settings.elements,(function(i,n){var s=new U(i,e,n),o=s.getConfig(),r=l({},o);r.node=!1,r.index=n,r.instance=s,r.slideConfig=o,t.push(r)}));var i=!1;return this.getSelector()&&(i=document.querySelectorAll(this.getSelector())),i?(o(i,(function(i,n){var s=new U(i,e,n),o=s.getConfig(),r=l({},o);r.node=i,r.index=n,r.instance=s,r.slideConfig=o,r.gallery=i.getAttribute("data-gallery"),t.push(r)})),t):t}},{key:"getGalleryElements",value:function(e,t){return e.filter((function(e){return e.gallery==t}))}},{key:"getSelector",value:function(){return!this.settings.elements&&(this.settings.selector&&"data-"==this.settings.selector.substring(0,5)?"*[".concat(this.settings.selector,"]"):this.settings.selector)}},{key:"getActiveSlide",value:function(){return this.slidesContainer.querySelectorAll(".gslide")[this.index]}},{key:"getActiveSlideIndex",value:function(){return this.index}},{key:"getAnimationClasses",value:function(){var e=[];for(var t in this.settings.cssEfects)if(this.settings.cssEfects.hasOwnProperty(t)){var i=this.settings.cssEfects[t];e.push("g".concat(i.in)),e.push("g".concat(i.out))}return e.join(" ")}},{key:"build",value:function(){var e=this;if(this.built)return!1;var t=document.body.childNodes,i=[];o(t,(function(e){e.parentNode==document.body&&"#"!==e.nodeName.charAt(0)&&e.hasAttribute&&!e.hasAttribute("aria-hidden")&&(i.push(e),e.setAttribute("aria-hidden","true"))}));var n=O(this.settings.svg,"next")?this.settings.svg.next:"",s=O(this.settings.svg,"prev")?this.settings.svg.prev:"",l=O(this.settings.svg,"close")?this.settings.svg.close:"",r=this.settings.lightboxHTML;r=m(r=(r=(r=r.replace(/{nextSVG}/g,n)).replace(/{prevSVG}/g,s)).replace(/{closeSVG}/g,l)),document.body.appendChild(r);var d=document.getElementById("glightbox-body");this.modal=d;var g=d.querySelector(".gclose");this.prevButton=d.querySelector(".gprev"),this.nextButton=d.querySelector(".gnext"),this.overlay=d.querySelector(".goverlay"),this.loader=d.querySelector(".gloader"),this.slidesContainer=document.getElementById("glightbox-slider"),this.bodyHiddenChildElms=i,this.events={},h(this.modal,"glightbox-"+this.settings.skin),this.settings.closeButton&&g&&(this.events.close=a("click",{onElement:g,withCallback:function(t,i){t.preventDefault(),e.close()}})),g&&!this.settings.closeButton&&g.parentNode.removeChild(g),this.nextButton&&(this.events.next=a("click",{onElement:this.nextButton,withCallback:function(t,i){t.preventDefault(),e.nextSlide()}})),this.prevButton&&(this.events.prev=a("click",{onElement:this.prevButton,withCallback:function(t,i){t.preventDefault(),e.prevSlide()}})),this.settings.closeOnOutsideClick&&(this.events.outClose=a("click",{onElement:d,withCallback:function(t,i){e.preventOutsideClick||c(document.body,"glightbox-mobile")||u(t.target,".ginner-container")||u(t.target,".gbtn")||c(t.target,"gnext")||c(t.target,"gprev")||e.close()}})),o(this.elements,(function(t,i){e.slidesContainer.appendChild(t.instance.create()),t.slideNode=e.slidesContainer.querySelectorAll(".gslide")[i]})),K&&h(document.body,"glightbox-touch"),this.events.resize=a("resize",{onElement:window,withCallback:function(){e.resize()}}),this.built=!0}},{key:"resize",value:function(){var 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m=g.split(":"),x=this.settings.videosWidth,b=this.settings.videosWidth,S=(b=M(x)||-1!==x.indexOf("px")?parseInt(x):-1!==x.indexOf("vw")?l*parseInt(x)/100:-1!==x.indexOf("vh")?o*parseInt(x)/100:-1!==x.indexOf("%")?l*parseInt(x)/100:parseInt(i.clientWidth))/(parseInt(m[0])/parseInt(m[1]));if(S=Math.floor(S),r&&(o-=s.offsetHeight),b>l||S>o||o<S&&l>b){var w=i.offsetWidth,T=i.offsetHeight,C=o/T,k={width:w*C,height:T*C};i.parentNode.setAttribute("style","max-width: ".concat(k.width,"px")),r&&s.setAttribute("style","max-width: ".concat(k.width,"px;"))}else i.parentNode.style.maxWidth="".concat(x),r&&s.setAttribute("style","max-width: ".concat(x,";"))}}}}},{key:"reload",value:function(){this.init()}},{key:"updateNavigationClasses",value:function(){var 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this.events)this.events.hasOwnProperty(t)&&this.events[t].destroy();this.events=null}return!1}if(this.closing)return!1;this.closing=!0,this.slidePlayerPause(this.activeSlide),this.fullElementsList&&(this.elements=this.fullElementsList),this.bodyHiddenChildElms.length&&o(this.bodyHiddenChildElms,(function(e){e.removeAttribute("aria-hidden")})),h(this.modal,"glightbox-closing"),g(this.overlay,"none"==this.settings.openEffect?"none":this.settings.cssEfects.fade.out),g(this.activeSlide,this.settings.cssEfects[this.settings.closeEffect].out,(function(){if(e.activeSlide=null,e.prevActiveSlideIndex=null,e.prevActiveSlide=null,e.built=!1,e.events){for(var t in e.events)e.events.hasOwnProperty(t)&&e.events[t].destroy();e.events=null}var i=document.body;d(Q,"glightbox-open"),d(i,"glightbox-open touching gdesc-open glightbox-touch glightbox-mobile gscrollbar-fixer"),e.modal.parentNode.removeChild(e.modal),e.trigger("close"),T(e.settings.onClose)&&e.settings.onClose();var n=document.querySelector(".gcss-styles");n&&n.parentNode.removeChild(n),e.lightboxOpen=!1,e.closing=null}))}},{key:"destroy",value:function(){this.close(),this.clearAllEvents(),this.baseEvents&&this.baseEvents.destroy()}},{key:"on",value:function(e,t){var i=arguments.length>2&&void 0!==arguments[2]&&arguments[2];if(!e||!T(t))throw new TypeError("Event name and callback must be defined");this.apiEvents.push({evt:e,once:i,callback:t})}},{key:"once",value:function(e,t){this.on(e,t,!0)}},{key:"trigger",value:function(e){var t=this,i=arguments.length>1&&void 0!==arguments[1]?arguments[1]:null,n=[];o(this.apiEvents,(function(t,s){var l=t.evt,o=t.once,r=t.callback;l==e&&(r(i),o&&n.push(s))})),n.length&&o(n,(function(e){return t.apiEvents.splice(e,1)}))}},{key:"clearAllEvents",value:function(){this.apiEvents.splice(0,this.apiEvents.length)}},{key:"version",value:function(){return"3.1.1"}}]),e}();return function(){var e=arguments.length>0&&void 0!==arguments[0]?arguments[0]:{},t=new 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-/*! update cache: 20251007160224 */
+/*! update cache: 20251017052948 */
diff --git a/assets/stylesheets/glightbox.min.css b/assets/stylesheets/glightbox.min.css
index 74cfeb08d..e4ad4744f 100644
--- a/assets/stylesheets/glightbox.min.css
+++ b/assets/stylesheets/glightbox.min.css
@@ -1,2 +1,2 @@
 .glightbox-container{width:100%;height:100%;position:fixed;top:0;left:0;z-index:999999!important;overflow:hidden;-ms-touch-action:none;touch-action:none;-webkit-text-size-adjust:100%;-moz-text-size-adjust:100%;-ms-text-size-adjust:100%;text-size-adjust:100%;-webkit-backface-visibility:hidden;backface-visibility:hidden;outline:0}.glightbox-container.inactive{display:none}.glightbox-container .gcontainer{position:relative;width:100%;height:100%;z-index:9999;overflow:hidden}.glightbox-container .gslider{-webkit-transition:-webkit-transform .4s ease;transition:-webkit-transform .4s ease;transition:transform .4s ease;transition:transform .4s ease,-webkit-transform .4s 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.gslide-media{-webkit-box-shadow:none!important;box-shadow:none!important}.desc-bottom .gslide-media,.desc-top .gslide-media{margin:0 auto;-webkit-box-orient:vertical;-webkit-box-direction:normal;-ms-flex-direction:column;flex-direction:column}.gslide-description{position:relative;-webkit-box-flex:1;-ms-flex:1 0 100%;flex:1 0 100%}.gslide-description.description-left,.gslide-description.description-right{max-width:100%}.gslide-description.description-bottom,.gslide-description.description-top{margin:0 auto;width:100%}.gslide-description p{margin-bottom:12px}.gslide-description p:last-child{margin-bottom:0}.zoomed .gslide-description{display:none}.glightbox-button-hidden{display:none}.glightbox-mobile .glightbox-container .gslide-description{height:auto!important;width:100%;position:absolute;bottom:0;padding:19px 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diff --git a/assets/stylesheets/palette.06af60db.min.css b/assets/stylesheets/palette.06af60db.min.css
index 9a08d7973..9bd052be1 100644
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circle{fill:var(--md-mermaid-label-bg-color)}.actor{fill:var(--md-mermaid-sequence-actor-bg-color);stroke:var(--md-mermaid-sequence-actor-border-color)}text.actor>tspan{fill:var(--md-mermaid-sequence-actor-fg-color);font-family:var(--md-mermaid-font-family)}line{stroke:var(--md-mermaid-sequence-actor-line-color)}.actor-man circle,.actor-man line{fill:var(--md-mermaid-sequence-actorman-bg-color);stroke:var(--md-mermaid-sequence-actorman-line-color)}.messageLine0,.messageLine1{stroke:var(--md-mermaid-sequence-message-line-color)}.note{fill:var(--md-mermaid-sequence-note-bg-color);stroke:var(--md-mermaid-sequence-note-border-color)}.loopText,.loopText>tspan,.messageText,.noteText>tspan{stroke:none;font-family:var(--md-mermaid-font-family)!important}.messageText{fill:var(--md-mermaid-sequence-message-fg-color)}.loopText,.loopText>tspan{fill:var(--md-mermaid-sequence-loop-fg-color)}.noteText>tspan{fill:var(--md-mermaid-sequence-note-fg-color)}#arrowhead 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c=o.pipe(y(()=>a.innerHTML=""),b(({items:l})=>T($(...l.slice(0,10)),$(...l.slice(10)).pipe(Ke(4),jr(n),b(([f])=>f)))),m(hn),le());return c.subscribe(l=>a.appendChild(l)),c.pipe(re(l=>{let f=me("details",l);return typeof f=="undefined"?L:d(f,"toggle").pipe(U(o),m(()=>f))})).subscribe(l=>{l.open===!1&&l.offsetTop<=i.scrollTop&&i.scrollTo({top:l.offsetTop})}),t.pipe(g(fr),m(({data:l})=>l)).pipe(y(l=>o.next(l)),_(()=>o.complete()),m(l=>F({ref:e},l)))}function Qa(e,{query$:t}){return t.pipe(m(({value:r})=>{let o=ve();return o.hash="",r=r.replace(/\s+/g,"+").replace(/&/g,"%26").replace(/=/g,"%3D"),o.search=`q=${r}`,{url:o}}))}function Zn(e,t){let r=new v,o=r.pipe(ee(),oe(!0));return r.subscribe(({url:n})=>{e.setAttribute("data-clipboard-text",e.href),e.href=`${n}`}),d(e,"click").pipe(U(o)).subscribe(n=>n.preventDefault()),Qa(e,t).pipe(y(n=>r.next(n)),_(()=>r.complete()),m(n=>F({ref:e},n)))}function ei(e,{worker$:t,keyboard$:r}){let o=new 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p.pipe(ae(t)).subscribe({next([{height:l},{height:f}]){i.style.height=`${l-2*s}px`,e.style.top=`${f}px`},complete(){i.style.height="",e.style.top=""}}),p.pipe(He()).subscribe(()=>{for(let l of R(".md-nav__link--active[href]",e)){if(!l.clientHeight)continue;let f=l.closest(".md-sidebar__scrollwrap");if(typeof f!="undefined"){let u=l.offsetTop-f.offsetTop,{height:h}=pe(f);f.scrollTo({top:u-h/2})}}}),fe(R("label[tabindex]",e)).pipe(re(l=>d(l,"click").pipe(Oe(ie),m(()=>l),U(c)))).subscribe(l=>{let f=P(`[id="${l.htmlFor}"]`);P(`[aria-labelledby="${l.id}"]`).setAttribute("aria-expanded",`${f.checked}`)}),Ya(e,r).pipe(y(l=>a.next(l)),_(()=>a.complete()),m(l=>F({ref:e},l)))})}function oi(e,t){if(typeof t!="undefined"){let r=`https://api.github.com/repos/${e}/${t}`;return Lt(De(`${r}/releases/latest`).pipe(he(()=>L),m(o=>({version:o.tag_name})),Qe({})),De(r).pipe(he(()=>L),m(o=>({stars:o.stargazers_count,forks:o.forks_count})),Qe({}))).pipe(m(([o,n])=>F(F({},o),n)))}else{let 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t=this;e.touches.length<2&&(this.multipointEnd.dispatch(e,this.element),this.sx2=this.sy2=null),this.x2&&Math.abs(this.x1-this.x2)>30||this.y2&&Math.abs(this.y1-this.y2)>30?(e.direction=this._swipeDirection(this.x1,this.x2,this.y1,this.y2),this.swipeTimeout=setTimeout((function(){t.swipe.dispatch(e,t.element)}),0)):(this.tapTimeout=setTimeout((function(){t._preventTap||t.tap.dispatch(e,t.element),t.isDoubleTap&&(t.doubleTap.dispatch(e,t.element),t.isDoubleTap=!1)}),0),t.isDoubleTap||(t.singleTapTimeout=setTimeout((function(){t.singleTap.dispatch(e,t.element)}),250))),this.touchEnd.dispatch(e,this.element),this.preV.x=0,this.preV.y=0,this.zoom=1,this.pinchStartLen=null,this.x1=this.x2=this.y1=this.y2=null}}},{key:"cancelAll",value:function(){this._preventTap=!0,clearTimeout(this.singleTapTimeout),clearTimeout(this.tapTimeout),clearTimeout(this.longTapTimeout),clearTimeout(this.swipeTimeout)}},{key:"cancel",value:function(e){this.cancelAll(),this.touchCancel.dispatch(e,this.element)}},{key:"_cancelLongTap",value:function(){clearTimeout(this.longTapTimeout)}},{key:"_cancelSingleTap",value:function(){clearTimeout(this.singleTapTimeout)}},{key:"_swipeDirection",value:function(e,t,i,n){return Math.abs(e-t)>=Math.abs(i-n)?e-t>0?"Left":"Right":i-n>0?"Up":"Down"}},{key:"on",value:function(e,t){this[e]&&this[e].add(t)}},{key:"off",value:function(e,t){this[e]&&this[e].del(t)}},{key:"destroy",value:function(){return this.singleTapTimeout&&clearTimeout(this.singleTapTimeout),this.tapTimeout&&clearTimeout(this.tapTimeout),this.longTapTimeout&&clearTimeout(this.longTapTimeout),this.swipeTimeout&&clearTimeout(this.swipeTimeout),this.element.removeEventListener("touchstart",this.start),this.element.removeEventListener("touchmove",this.move),this.element.removeEventListener("touchend",this.end),this.element.removeEventListener("touchcancel",this.cancel),this.rotate.del(),this.touchStart.del(),this.multipointStart.del(),this.multipointEnd.del(),this.pinch.del(),this.swipe.del(),this.tap.del(),this.doubleTap.del(),this.longTap.del(),this.singleTap.del(),this.pressMove.del(),this.twoFingerPressMove.del(),this.touchMove.del(),this.touchEnd.del(),this.touchCancel.del(),this.preV=this.pinchStartLen=this.zoom=this.isDoubleTap=this.delta=this.last=this.now=this.tapTimeout=this.singleTapTimeout=this.longTapTimeout=this.swipeTimeout=this.x1=this.x2=this.y1=this.y2=this.preTapPosition=this.rotate=this.touchStart=this.multipointStart=this.multipointEnd=this.pinch=this.swipe=this.tap=this.doubleTap=this.longTap=this.singleTap=this.pressMove=this.touchMove=this.touchEnd=this.touchCancel=this.twoFingerPressMove=null,window.removeEventListener("scroll",this._cancelAllHandler),null}}]),e}();function W(e){var t=function(){var e,t=document.createElement("fakeelement"),i={transition:"transitionend",OTransition:"oTransitionEnd",MozTransition:"transitionend",WebkitTransition:"webkitTransitionEnd"};for(e in i)if(void 0!==t.style[e])return i[e]}(),i=window.innerWidth||document.documentElement.clientWidth||document.body.clientWidth,n=c(e,"gslide-media")?e:e.querySelector(".gslide-media"),s=u(n,".ginner-container"),l=e.querySelector(".gslide-description");i>769&&(n=s),h(n,"greset"),v(n,"translate3d(0, 0, 0)"),a(t,{onElement:n,once:!0,withCallback:function(e,t){d(n,"greset")}}),n.style.opacity="",l&&(l.style.opacity="")}function B(e){if(e.events.hasOwnProperty("touch"))return!1;var t,i,n,s=y(),l=s.width,o=s.height,r=!1,a=null,g=null,f=null,p=!1,m=1,x=1,b=!1,S=!1,w=null,T=null,C=null,k=null,E=0,A=0,L=!1,I=!1,O={},P={},M=0,z=0,X=document.getElementById("glightbox-slider"),Y=document.querySelector(".goverlay"),q=new _(X,{touchStart:function(t){if(r=!0,(c(t.targetTouches[0].target,"ginner-container")||u(t.targetTouches[0].target,".gslide-desc")||"a"==t.targetTouches[0].target.nodeName.toLowerCase())&&(r=!1),u(t.targetTouches[0].target,".gslide-inline")&&!c(t.targetTouches[0].target.parentNode,"gslide-inline")&&(r=!1),r){if(P=t.targetTouches[0],O.pageX=t.targetTouches[0].pageX,O.pageY=t.targetTouches[0].pageY,M=t.targetTouches[0].clientX,z=t.targetTouches[0].clientY,a=e.activeSlide,g=a.querySelector(".gslide-media"),n=a.querySelector(".gslide-inline"),f=null,c(g,"gslide-image")&&(f=g.querySelector("img")),(window.innerWidth||document.documentElement.clientWidth||document.body.clientWidth)>769&&(g=a.querySelector(".ginner-container")),d(Y,"greset"),t.pageX>20&&t.pageX<window.innerWidth-20)return;t.preventDefault()}},touchMove:function(s){if(r&&(P=s.targetTouches[0],!b&&!S)){if(n&&n.offsetHeight>o){var a=O.pageX-P.pageX;if(Math.abs(a)<=13)return!1}p=!0;var h,d=s.targetTouches[0].clientX,c=s.targetTouches[0].clientY,u=M-d,m=z-c;if(Math.abs(u)>Math.abs(m)?(L=!1,I=!0):(I=!1,L=!0),t=P.pageX-O.pageX,E=100*t/l,i=P.pageY-O.pageY,A=100*i/o,L&&f&&(h=1-Math.abs(i)/o,Y.style.opacity=h,e.settings.touchFollowAxis&&(E=0)),I&&(h=1-Math.abs(t)/l,g.style.opacity=h,e.settings.touchFollowAxis&&(A=0)),!f)return v(g,"translate3d(".concat(E,"%, 0, 0)"));v(g,"translate3d(".concat(E,"%, ").concat(A,"%, 0)"))}},touchEnd:function(){if(r){if(p=!1,S||b)return C=w,void(k=T);var t=Math.abs(parseInt(A)),i=Math.abs(parseInt(E));if(!(t>29&&f))return t<29&&i<25?(h(Y,"greset"),Y.style.opacity=1,W(g)):void 0;e.close()}},multipointEnd:function(){setTimeout((function(){b=!1}),50)},multipointStart:function(){b=!0,m=x||1},pinch:function(e){if(!f||p)return!1;b=!0,f.scaleX=f.scaleY=m*e.zoom;var t=m*e.zoom;if(S=!0,t<=1)return S=!1,t=1,k=null,C=null,w=null,T=null,void f.setAttribute("style","");t>4.5&&(t=4.5),f.style.transform="scale3d(".concat(t,", ").concat(t,", 1)"),x=t},pressMove:function(e){if(S&&!b){var t=P.pageX-O.pageX,i=P.pageY-O.pageY;C&&(t+=C),k&&(i+=k),w=t,T=i;var n="translate3d(".concat(t,"px, ").concat(i,"px, 0)");x&&(n+=" scale3d(".concat(x,", ").concat(x,", 1)")),v(f,n)}},swipe:function(t){if(!S)if(b)b=!1;else{if("Left"==t.direction){if(e.index==e.elements.length-1)return W(g);e.nextSlide()}if("Right"==t.direction){if(0==e.index)return W(g);e.prevSlide()}}}});e.events.touch=q}var H=function(){function e(i,n){var s=this,l=arguments.length>2&&void 0!==arguments[2]?arguments[2]:null;if(t(this,e),this.img=i,this.slide=n,this.onclose=l,this.img.setZoomEvents)return!1;this.active=!1,this.zoomedIn=!1,this.dragging=!1,this.currentX=null,this.currentY=null,this.initialX=null,this.initialY=null,this.xOffset=0,this.yOffset=0,this.img.addEventListener("mousedown",(function(e){return s.dragStart(e)}),!1),this.img.addEventListener("mouseup",(function(e){return s.dragEnd(e)}),!1),this.img.addEventListener("mousemove",(function(e){return s.drag(e)}),!1),this.img.addEventListener("click",(function(e){return s.slide.classList.contains("dragging-nav")?(s.zoomOut(),!1):s.zoomedIn?void(s.zoomedIn&&!s.dragging&&s.zoomOut()):s.zoomIn()}),!1),this.img.setZoomEvents=!0}return n(e,[{key:"zoomIn",value:function(){var e=this.widowWidth();if(!(this.zoomedIn||e<=768)){var t=this.img;if(t.setAttribute("data-style",t.getAttribute("style")),t.style.maxWidth=t.naturalWidth+"px",t.style.maxHeight=t.naturalHeight+"px",t.naturalWidth>e){var i=e/2-t.naturalWidth/2;this.setTranslate(this.img.parentNode,i,0)}this.slide.classList.add("zoomed"),this.zoomedIn=!0}}},{key:"zoomOut",value:function(){this.img.parentNode.setAttribute("style",""),this.img.setAttribute("style",this.img.getAttribute("data-style")),this.slide.classList.remove("zoomed"),this.zoomedIn=!1,this.currentX=null,this.currentY=null,this.initialX=null,this.initialY=null,this.xOffset=0,this.yOffset=0,this.onclose&&"function"==typeof this.onclose&&this.onclose()}},{key:"dragStart",value:function(e){e.preventDefault(),this.zoomedIn?("touchstart"===e.type?(this.initialX=e.touches[0].clientX-this.xOffset,this.initialY=e.touches[0].clientY-this.yOffset):(this.initialX=e.clientX-this.xOffset,this.initialY=e.clientY-this.yOffset),e.target===this.img&&(this.active=!0,this.img.classList.add("dragging"))):this.active=!1}},{key:"dragEnd",value:function(e){var t=this;e.preventDefault(),this.initialX=this.currentX,this.initialY=this.currentY,this.active=!1,setTimeout((function(){t.dragging=!1,t.img.isDragging=!1,t.img.classList.remove("dragging")}),100)}},{key:"drag",value:function(e){this.active&&(e.preventDefault(),"touchmove"===e.type?(this.currentX=e.touches[0].clientX-this.initialX,this.currentY=e.touches[0].clientY-this.initialY):(this.currentX=e.clientX-this.initialX,this.currentY=e.clientY-this.initialY),this.xOffset=this.currentX,this.yOffset=this.currentY,this.img.isDragging=!0,this.dragging=!0,this.setTranslate(this.img,this.currentX,this.currentY))}},{key:"onMove",value:function(e){if(this.zoomedIn){var t=e.clientX-this.img.naturalWidth/2,i=e.clientY-this.img.naturalHeight/2;this.setTranslate(this.img,t,i)}}},{key:"setTranslate",value:function(e,t,i){e.style.transform="translate3d("+t+"px, "+i+"px, 0)"}},{key:"widowWidth",value:function(){return window.innerWidth||document.documentElement.clientWidth||document.body.clientWidth}}]),e}(),V=function(){function e(){var i=this,n=arguments.length>0&&void 0!==arguments[0]?arguments[0]:{};t(this,e);var s=n.dragEl,l=n.toleranceX,o=void 0===l?40:l,r=n.toleranceY,a=void 0===r?65:r,h=n.slide,d=void 0===h?null:h,c=n.instance,u=void 0===c?null:c;this.el=s,this.active=!1,this.dragging=!1,this.currentX=null,this.currentY=null,this.initialX=null,this.initialY=null,this.xOffset=0,this.yOffset=0,this.direction=null,this.lastDirection=null,this.toleranceX=o,this.toleranceY=a,this.toleranceReached=!1,this.dragContainer=this.el,this.slide=d,this.instance=u,this.el.addEventListener("mousedown",(function(e){return i.dragStart(e)}),!1),this.el.addEventListener("mouseup",(function(e){return i.dragEnd(e)}),!1),this.el.addEventListener("mousemove",(function(e){return i.drag(e)}),!1)}return n(e,[{key:"dragStart",value:function(e){if(this.slide.classList.contains("zoomed"))this.active=!1;else{"touchstart"===e.type?(this.initialX=e.touches[0].clientX-this.xOffset,this.initialY=e.touches[0].clientY-this.yOffset):(this.initialX=e.clientX-this.xOffset,this.initialY=e.clientY-this.yOffset);var t=e.target.nodeName.toLowerCase();e.target.classList.contains("nodrag")||u(e.target,".nodrag")||-1!==["input","select","textarea","button","a"].indexOf(t)?this.active=!1:(e.preventDefault(),(e.target===this.el||"img"!==t&&u(e.target,".gslide-inline"))&&(this.active=!0,this.el.classList.add("dragging"),this.dragContainer=u(e.target,".ginner-container")))}}},{key:"dragEnd",value:function(e){var t=this;e&&e.preventDefault(),this.initialX=0,this.initialY=0,this.currentX=null,this.currentY=null,this.initialX=null,this.initialY=null,this.xOffset=0,this.yOffset=0,this.active=!1,this.doSlideChange&&(this.instance.preventOutsideClick=!0,"right"==this.doSlideChange&&this.instance.prevSlide(),"left"==this.doSlideChange&&this.instance.nextSlide()),this.doSlideClose&&this.instance.close(),this.toleranceReached||this.setTranslate(this.dragContainer,0,0,!0),setTimeout((function(){t.instance.preventOutsideClick=!1,t.toleranceReached=!1,t.lastDirection=null,t.dragging=!1,t.el.isDragging=!1,t.el.classList.remove("dragging"),t.slide.classList.remove("dragging-nav"),t.dragContainer.style.transform="",t.dragContainer.style.transition=""}),100)}},{key:"drag",value:function(e){if(this.active){e.preventDefault(),this.slide.classList.add("dragging-nav"),"touchmove"===e.type?(this.currentX=e.touches[0].clientX-this.initialX,this.currentY=e.touches[0].clientY-this.initialY):(this.currentX=e.clientX-this.initialX,this.currentY=e.clientY-this.initialY),this.xOffset=this.currentX,this.yOffset=this.currentY,this.el.isDragging=!0,this.dragging=!0,this.doSlideChange=!1,this.doSlideClose=!1;var t=Math.abs(this.currentX),i=Math.abs(this.currentY);if(t>0&&t>=Math.abs(this.currentY)&&(!this.lastDirection||"x"==this.lastDirection)){this.yOffset=0,this.lastDirection="x",this.setTranslate(this.dragContainer,this.currentX,0);var n=this.shouldChange();if(!this.instance.settings.dragAutoSnap&&n&&(this.doSlideChange=n),this.instance.settings.dragAutoSnap&&n)return this.instance.preventOutsideClick=!0,this.toleranceReached=!0,this.active=!1,this.instance.preventOutsideClick=!0,this.dragEnd(null),"right"==n&&this.instance.prevSlide(),void("left"==n&&this.instance.nextSlide())}if(this.toleranceY>0&&i>0&&i>=t&&(!this.lastDirection||"y"==this.lastDirection)){this.xOffset=0,this.lastDirection="y",this.setTranslate(this.dragContainer,0,this.currentY);var s=this.shouldClose();return!this.instance.settings.dragAutoSnap&&s&&(this.doSlideClose=!0),void(this.instance.settings.dragAutoSnap&&s&&this.instance.close())}}}},{key:"shouldChange",value:function(){var e=!1;if(Math.abs(this.currentX)>=this.toleranceX){var t=this.currentX>0?"right":"left";("left"==t&&this.slide!==this.slide.parentNode.lastChild||"right"==t&&this.slide!==this.slide.parentNode.firstChild)&&(e=t)}return e}},{key:"shouldClose",value:function(){var e=!1;return Math.abs(this.currentY)>=this.toleranceY&&(e=!0),e}},{key:"setTranslate",value:function(e,t,i){var n=arguments.length>3&&void 0!==arguments[3]&&arguments[3];e.style.transition=n?"all .2s ease":"",e.style.transform="translate3d(".concat(t,"px, ").concat(i,"px, 0)")}}]),e}();function j(e,t,i,n){var s=e.querySelector(".gslide-media"),l=new Image,o="gSlideTitle_"+i,r="gSlideDesc_"+i;l.addEventListener("load",(function(){T(n)&&n()}),!1),l.src=t.href,""!=t.sizes&&""!=t.srcset&&(l.sizes=t.sizes,l.srcset=t.srcset),l.alt="",I(t.alt)||""===t.alt||(l.alt=t.alt),""!==t.title&&l.setAttribute("aria-labelledby",o),""!==t.description&&l.setAttribute("aria-describedby",r),t.hasOwnProperty("_hasCustomWidth")&&t._hasCustomWidth&&(l.style.width=t.width),t.hasOwnProperty("_hasCustomHeight")&&t._hasCustomHeight&&(l.style.height=t.height),s.insertBefore(l,s.firstChild)}function F(e,t,i,n){var s=this,l=e.querySelector(".ginner-container"),o="gvideo"+i,r=e.querySelector(".gslide-media"),a=this.getAllPlayers();h(l,"gvideo-container"),r.insertBefore(m('<div class="gvideo-wrapper"></div>'),r.firstChild);var d=e.querySelector(".gvideo-wrapper");S(this.settings.plyr.css,"Plyr");var c=t.href,u=location.protocol.replace(":",""),g="",v="",f=!1;"file"==u&&(u="http"),r.style.maxWidth=t.width,S(this.settings.plyr.js,"Plyr",(function(){if(c.match(/vimeo\.com\/([0-9]*)/)){var l=/vimeo.*\/(\d+)/i.exec(c);g="vimeo",v=l[1]}if(c.match(/(youtube\.com|youtube-nocookie\.com)\/watch\?v=([a-zA-Z0-9\-_]+)/)||c.match(/youtu\.be\/([a-zA-Z0-9\-_]+)/)||c.match(/(youtube\.com|youtube-nocookie\.com)\/embed\/([a-zA-Z0-9\-_]+)/)){var r=function(e){var t="";t=void 0!==(e=e.replace(/(>|<)/gi,"").split(/(vi\/|v=|\/v\/|youtu\.be\/|\/embed\/)/))[2]?(t=e[2].split(/[^0-9a-z_\-]/i))[0]:e;return t}(c);g="youtube",v=r}if(null!==c.match(/\.(mp4|ogg|webm|mov)$/)){g="local";var u='<video id="'+o+'" ';u+='style="background:#000; max-width: '.concat(t.width,';" '),u+='preload="metadata" ',u+='x-webkit-airplay="allow" ',u+="playsinline ",u+="controls ",u+='class="gvideo-local">';var p=c.toLowerCase().split(".").pop(),y={mp4:"",ogg:"",webm:""};for(var x in y[p="mov"==p?"mp4":p]=c,y)if(y.hasOwnProperty(x)){var S=y[x];t.hasOwnProperty(x)&&(S=t[x]),""!==S&&(u+='<source src="'.concat(S,'" type="video/').concat(x,'">'))}f=m(u+="</video>")}var w=f||m('<div id="'.concat(o,'" data-plyr-provider="').concat(g,'" data-plyr-embed-id="').concat(v,'"></div>'));h(d,"".concat(g,"-video gvideo")),d.appendChild(w),d.setAttribute("data-id",o),d.setAttribute("data-index",i);var C=O(s.settings.plyr,"config")?s.settings.plyr.config:{},k=new Plyr("#"+o,C);k.on("ready",(function(e){var t=e.detail.plyr;a[o]=t,T(n)&&n()})),b((function(){return e.querySelector("iframe")&&"true"==e.querySelector("iframe").dataset.ready}),(function(){s.resize(e)})),k.on("enterfullscreen",R),k.on("exitfullscreen",R)}))}function R(e){var t=u(e.target,".gslide-media");"enterfullscreen"==e.type&&h(t,"fullscreen"),"exitfullscreen"==e.type&&d(t,"fullscreen")}function G(e,t,i,n){var s,l=this,o=e.querySelector(".gslide-media"),r=!(!O(t,"href")||!t.href)&&t.href.split("#").pop().trim(),d=!(!O(t,"content")||!t.content)&&t.content;if(d&&(C(d)&&(s=m('<div class="ginlined-content">'.concat(d,"</div>"))),k(d))){"none"==d.style.display&&(d.style.display="block");var c=document.createElement("div");c.className="ginlined-content",c.appendChild(d),s=c}if(r){var u=document.getElementById(r);if(!u)return!1;var g=u.cloneNode(!0);g.style.height=t.height,g.style.maxWidth=t.width,h(g,"ginlined-content"),s=g}if(!s)return console.error("Unable to append inline slide content",t),!1;o.style.height=t.height,o.style.width=t.width,o.appendChild(s),this.events["inlineclose"+r]=a("click",{onElement:o.querySelectorAll(".gtrigger-close"),withCallback:function(e){e.preventDefault(),l.close()}}),T(n)&&n()}function Z(e,t,i,n){var s=e.querySelector(".gslide-media"),l=function(e){var t=e.url,i=e.allow,n=e.callback,s=e.appendTo,l=document.createElement("iframe");return l.className="vimeo-video gvideo",l.src=t,l.style.width="100%",l.style.height="100%",i&&l.setAttribute("allow",i),l.onload=function(){h(l,"node-ready"),T(n)&&n()},s&&s.appendChild(l),l}({url:t.href,callback:n});s.parentNode.style.maxWidth=t.width,s.parentNode.style.height=t.height,s.appendChild(l)}var $=function(){function e(){var i=arguments.length>0&&void 0!==arguments[0]?arguments[0]:{};t(this,e),this.defaults={href:"",sizes:"",srcset:"",title:"",type:"",description:"",alt:"",descPosition:"bottom",effect:"",width:"",height:"",content:!1,zoomable:!0,draggable:!0},L(i)&&(this.defaults=l(this.defaults,i))}return n(e,[{key:"sourceType",value:function(e){var t=e;if(null!==(e=e.toLowerCase()).match(/\.(jpeg|jpg|jpe|gif|png|apn|webp|avif|svg)/))return"image";if(e.match(/(youtube\.com|youtube-nocookie\.com)\/watch\?v=([a-zA-Z0-9\-_]+)/)||e.match(/youtu\.be\/([a-zA-Z0-9\-_]+)/)||e.match(/(youtube\.com|youtube-nocookie\.com)\/embed\/([a-zA-Z0-9\-_]+)/))return"video";if(e.match(/vimeo\.com\/([0-9]*)/))return"video";if(null!==e.match(/\.(mp4|ogg|webm|mov)/))return"video";if(null!==e.match(/\.(mp3|wav|wma|aac|ogg)/))return"audio";if(e.indexOf("#")>-1&&""!==t.split("#").pop().trim())return"inline";return e.indexOf("goajax=true")>-1?"ajax":"external"}},{key:"parseConfig",value:function(e,t){var i=this,n=l({descPosition:t.descPosition},this.defaults);if(L(e)&&!k(e)){O(e,"type")||(O(e,"content")&&e.content?e.type="inline":O(e,"href")&&(e.type=this.sourceType(e.href)));var s=l(n,e);return this.setSize(s,t),s}var r="",a=e.getAttribute("data-glightbox"),h=e.nodeName.toLowerCase();if("a"===h&&(r=e.href),"img"===h&&(r=e.src,n.alt=e.alt),n.href=r,o(n,(function(s,l){O(t,l)&&"width"!==l&&(n[l]=t[l]);var o=e.dataset[l];I(o)||(n[l]=i.sanitizeValue(o))})),n.content&&(n.type="inline"),!n.type&&r&&(n.type=this.sourceType(r)),I(a)){if(!n.title&&"a"==h){var d=e.title;I(d)||""===d||(n.title=d)}if(!n.title&&"img"==h){var c=e.alt;I(c)||""===c||(n.title=c)}}else{var u=[];o(n,(function(e,t){u.push(";\\s?"+t)})),u=u.join("\\s?:|"),""!==a.trim()&&o(n,(function(e,t){var s=a,l=new RegExp("s?"+t+"s?:s?(.*?)("+u+"s?:|$)"),o=s.match(l);if(o&&o.length&&o[1]){var r=o[1].trim().replace(/;\s*$/,"");n[t]=i.sanitizeValue(r)}}))}if(n.description&&"."===n.description.substring(0,1)){var g;try{g=document.querySelector(n.description).innerHTML}catch(e){if(!(e instanceof DOMException))throw e}g&&(n.description=g)}if(!n.description){var v=e.querySelector(".glightbox-desc");v&&(n.description=v.innerHTML)}return this.setSize(n,t,e),this.slideConfig=n,n}},{key:"setSize",value:function(e,t){var i=arguments.length>2&&void 0!==arguments[2]?arguments[2]:null,n="video"==e.type?this.checkSize(t.videosWidth):this.checkSize(t.width),s=this.checkSize(t.height);return e.width=O(e,"width")&&""!==e.width?this.checkSize(e.width):n,e.height=O(e,"height")&&""!==e.height?this.checkSize(e.height):s,i&&"image"==e.type&&(e._hasCustomWidth=!!i.dataset.width,e._hasCustomHeight=!!i.dataset.height),e}},{key:"checkSize",value:function(e){return M(e)?"".concat(e,"px"):e}},{key:"sanitizeValue",value:function(e){return"true"!==e&&"false"!==e?e:"true"===e}}]),e}(),U=function(){function e(i,n,s){t(this,e),this.element=i,this.instance=n,this.index=s}return n(e,[{key:"setContent",value:function(){var e=this,t=arguments.length>0&&void 0!==arguments[0]?arguments[0]:null,i=arguments.length>1&&void 0!==arguments[1]&&arguments[1];if(c(t,"loaded"))return!1;var n=this.instance.settings,s=this.slideConfig,l=w();T(n.beforeSlideLoad)&&n.beforeSlideLoad({index:this.index,slide:t,player:!1});var o=s.type,r=s.descPosition,a=t.querySelector(".gslide-media"),d=t.querySelector(".gslide-title"),u=t.querySelector(".gslide-desc"),g=t.querySelector(".gdesc-inner"),v=i,f="gSlideTitle_"+this.index,p="gSlideDesc_"+this.index;if(T(n.afterSlideLoad)&&(v=function(){T(i)&&i(),n.afterSlideLoad({index:e.index,slide:t,player:e.instance.getSlidePlayerInstance(e.index)})}),""==s.title&&""==s.description?g&&g.parentNode.parentNode.removeChild(g.parentNode):(d&&""!==s.title?(d.id=f,d.innerHTML=s.title):d.parentNode.removeChild(d),u&&""!==s.description?(u.id=p,l&&n.moreLength>0?(s.smallDescription=this.slideShortDesc(s.description,n.moreLength,n.moreText),u.innerHTML=s.smallDescription,this.descriptionEvents(u,s)):u.innerHTML=s.description):u.parentNode.removeChild(u),h(a.parentNode,"desc-".concat(r)),h(g.parentNode,"description-".concat(r))),h(a,"gslide-".concat(o)),h(t,"loaded"),"video"!==o){if("external"!==o)return"inline"===o?(G.apply(this.instance,[t,s,this.index,v]),void(s.draggable&&new V({dragEl:t.querySelector(".gslide-inline"),toleranceX:n.dragToleranceX,toleranceY:n.dragToleranceY,slide:t,instance:this.instance}))):void("image"!==o?T(v)&&v():j(t,s,this.index,(function(){var i=t.querySelector("img");s.draggable&&new V({dragEl:i,toleranceX:n.dragToleranceX,toleranceY:n.dragToleranceY,slide:t,instance:e.instance}),s.zoomable&&i.naturalWidth>i.offsetWidth&&(h(i,"zoomable"),new H(i,t,(function(){e.instance.resize()}))),T(v)&&v()})));Z.apply(this,[t,s,this.index,v])}else F.apply(this.instance,[t,s,this.index,v])}},{key:"slideShortDesc",value:function(e){var t=arguments.length>1&&void 0!==arguments[1]?arguments[1]:50,i=arguments.length>2&&void 0!==arguments[2]&&arguments[2],n=document.createElement("div");n.innerHTML=e;var s=n.innerText,l=i;if((e=s.trim()).length<=t)return e;var o=e.substr(0,t-1);return l?(n=null,o+'... <a href="#" class="desc-more">'+i+"</a>"):o}},{key:"descriptionEvents",value:function(e,t){var i=this,n=e.querySelector(".desc-more");if(!n)return!1;a("click",{onElement:n,withCallback:function(e,n){e.preventDefault();var s=document.body,l=u(n,".gslide-desc");if(!l)return!1;l.innerHTML=t.description,h(s,"gdesc-open");var o=a("click",{onElement:[s,u(l,".gslide-description")],withCallback:function(e,n){"a"!==e.target.nodeName.toLowerCase()&&(d(s,"gdesc-open"),h(s,"gdesc-closed"),l.innerHTML=t.smallDescription,i.descriptionEvents(l,t),setTimeout((function(){d(s,"gdesc-closed")}),400),o.destroy())}})}})}},{key:"create",value:function(){return m(this.instance.settings.slideHTML)}},{key:"getConfig",value:function(){k(this.element)||this.element.hasOwnProperty("draggable")||(this.element.draggable=this.instance.settings.draggable);var e=new $(this.instance.settings.slideExtraAttributes);return this.slideConfig=e.parseConfig(this.element,this.instance.settings),this.slideConfig}}]),e}(),J=w(),K=null!==w()||void 0!==document.createTouch||"ontouchstart"in window||"onmsgesturechange"in window||navigator.msMaxTouchPoints,Q=document.getElementsByTagName("html")[0],ee={selector:".glightbox",elements:null,skin:"clean",theme:"clean",closeButton:!0,startAt:null,autoplayVideos:!0,autofocusVideos:!0,descPosition:"bottom",width:"900px",height:"506px",videosWidth:"960px",beforeSlideChange:null,afterSlideChange:null,beforeSlideLoad:null,afterSlideLoad:null,slideInserted:null,slideRemoved:null,slideExtraAttributes:null,onOpen:null,onClose:null,loop:!1,zoomable:!0,draggable:!0,dragAutoSnap:!1,dragToleranceX:40,dragToleranceY:65,preload:!0,oneSlidePerOpen:!1,touchNavigation:!0,touchFollowAxis:!0,keyboardNavigation:!0,closeOnOutsideClick:!0,plugins:!1,plyr:{css:"https://cdn.plyr.io/3.6.8/plyr.css",js:"https://cdn.plyr.io/3.6.8/plyr.js",config:{ratio:"16:9",fullscreen:{enabled:!0,iosNative:!0},youtube:{noCookie:!0,rel:0,showinfo:0,iv_load_policy:3},vimeo:{byline:!1,portrait:!1,title:!1,transparent:!1}}},openEffect:"zoom",closeEffect:"zoom",slideEffect:"slide",moreText:"See more",moreLength:60,cssEfects:{fade:{in:"fadeIn",out:"fadeOut"},zoom:{in:"zoomIn",out:"zoomOut"},slide:{in:"slideInRight",out:"slideOutLeft"},slideBack:{in:"slideInLeft",out:"slideOutRight"},none:{in:"none",out:"none"}},svg:{close:'<svg version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" x="0px" y="0px" viewBox="0 0 512 512" xml:space="preserve"><g><g><path d="M505.943,6.058c-8.077-8.077-21.172-8.077-29.249,0L6.058,476.693c-8.077,8.077-8.077,21.172,0,29.249C10.096,509.982,15.39,512,20.683,512c5.293,0,10.586-2.019,14.625-6.059L505.943,35.306C514.019,27.23,514.019,14.135,505.943,6.058z"/></g></g><g><g><path d="M505.942,476.694L35.306,6.059c-8.076-8.077-21.172-8.077-29.248,0c-8.077,8.076-8.077,21.171,0,29.248l470.636,470.636c4.038,4.039,9.332,6.058,14.625,6.058c5.293,0,10.587-2.019,14.624-6.057C514.018,497.866,514.018,484.771,505.942,476.694z"/></g></g></svg>',next:'<svg version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" x="0px" y="0px" viewBox="0 0 477.175 477.175" xml:space="preserve"> <g><path d="M360.731,229.075l-225.1-225.1c-5.3-5.3-13.8-5.3-19.1,0s-5.3,13.8,0,19.1l215.5,215.5l-215.5,215.5c-5.3,5.3-5.3,13.8,0,19.1c2.6,2.6,6.1,4,9.5,4c3.4,0,6.9-1.3,9.5-4l225.1-225.1C365.931,242.875,365.931,234.275,360.731,229.075z"/></g></svg>',prev:'<svg version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" x="0px" y="0px" viewBox="0 0 477.175 477.175" xml:space="preserve"><g><path d="M145.188,238.575l215.5-215.5c5.3-5.3,5.3-13.8,0-19.1s-13.8-5.3-19.1,0l-225.1,225.1c-5.3,5.3-5.3,13.8,0,19.1l225.1,225c2.6,2.6,6.1,4,9.5,4s6.9-1.3,9.5-4c5.3-5.3,5.3-13.8,0-19.1L145.188,238.575z"/></g></svg>'},slideHTML:'<div class="gslide">\n    <div class="gslide-inner-content">\n        <div class="ginner-container">\n            <div class="gslide-media">\n            </div>\n            <div class="gslide-description">\n                <div class="gdesc-inner">\n                    <h4 class="gslide-title"></h4>\n                    <div class="gslide-desc"></div>\n                </div>\n            </div>\n        </div>\n    </div>\n</div>',lightboxHTML:'<div id="glightbox-body" class="glightbox-container" tabindex="-1" role="dialog" aria-hidden="false">\n    <div class="gloader visible"></div>\n    <div class="goverlay"></div>\n    <div class="gcontainer">\n    <div id="glightbox-slider" class="gslider"></div>\n    <button class="gclose gbtn" aria-label="Close" data-taborder="3">{closeSVG}</button>\n    <button class="gprev gbtn" aria-label="Previous" data-taborder="2">{prevSVG}</button>\n    <button class="gnext gbtn" aria-label="Next" data-taborder="1">{nextSVG}</button>\n</div>\n</div>'},te=function(){function e(){var i=arguments.length>0&&void 0!==arguments[0]?arguments[0]:{};t(this,e),this.customOptions=i,this.settings=l(ee,i),this.effectsClasses=this.getAnimationClasses(),this.videoPlayers={},this.apiEvents=[],this.fullElementsList=!1}return n(e,[{key:"init",value:function(){var e=this,t=this.getSelector();t&&(this.baseEvents=a("click",{onElement:t,withCallback:function(t,i){t.preventDefault(),e.open(i)}})),this.elements=this.getElements()}},{key:"open",value:function(){var e=arguments.length>0&&void 0!==arguments[0]?arguments[0]:null,t=arguments.length>1&&void 0!==arguments[1]?arguments[1]:null;if(0==this.elements.length)return!1;this.activeSlide=null,this.prevActiveSlideIndex=null,this.prevActiveSlide=null;var i=M(t)?t:this.settings.startAt;if(k(e)){var n=e.getAttribute("data-gallery");n&&(this.fullElementsList=this.elements,this.elements=this.getGalleryElements(this.elements,n)),I(i)&&(i=this.getElementIndex(e))<0&&(i=0)}M(i)||(i=0),this.build(),g(this.overlay,"none"==this.settings.openEffect?"none":this.settings.cssEfects.fade.in);var s=document.body,l=window.innerWidth-document.documentElement.clientWidth;if(l>0){var o=document.createElement("style");o.type="text/css",o.className="gcss-styles",o.innerText=".gscrollbar-fixer {margin-right: ".concat(l,"px}"),document.head.appendChild(o),h(s,"gscrollbar-fixer")}h(s,"glightbox-open"),h(Q,"glightbox-open"),J&&(h(document.body,"glightbox-mobile"),this.settings.slideEffect="slide"),this.showSlide(i,!0),1==this.elements.length?(h(this.prevButton,"glightbox-button-hidden"),h(this.nextButton,"glightbox-button-hidden")):(d(this.prevButton,"glightbox-button-hidden"),d(this.nextButton,"glightbox-button-hidden")),this.lightboxOpen=!0,this.trigger("open"),T(this.settings.onOpen)&&this.settings.onOpen(),K&&this.settings.touchNavigation&&B(this),this.settings.keyboardNavigation&&X(this)}},{key:"openAt",value:function(){var e=arguments.length>0&&void 0!==arguments[0]?arguments[0]:0;this.open(null,e)}},{key:"showSlide",value:function(){var e=this,t=arguments.length>0&&void 0!==arguments[0]?arguments[0]:0,i=arguments.length>1&&void 0!==arguments[1]&&arguments[1];f(this.loader),this.index=parseInt(t);var n=this.slidesContainer.querySelector(".current");n&&d(n,"current"),this.slideAnimateOut();var s=this.slidesContainer.querySelectorAll(".gslide")[t];if(c(s,"loaded"))this.slideAnimateIn(s,i),p(this.loader);else{f(this.loader);var l=this.elements[t],o={index:this.index,slide:s,slideNode:s,slideConfig:l.slideConfig,slideIndex:this.index,trigger:l.node,player:null};this.trigger("slide_before_load",o),l.instance.setContent(s,(function(){p(e.loader),e.resize(),e.slideAnimateIn(s,i),e.trigger("slide_after_load",o)}))}this.slideDescription=s.querySelector(".gslide-description"),this.slideDescriptionContained=this.slideDescription&&c(this.slideDescription.parentNode,"gslide-media"),this.settings.preload&&(this.preloadSlide(t+1),this.preloadSlide(t-1)),this.updateNavigationClasses(),this.activeSlide=s}},{key:"preloadSlide",value:function(e){var t=this;if(e<0||e>this.elements.length-1)return!1;if(I(this.elements[e]))return!1;var i=this.slidesContainer.querySelectorAll(".gslide")[e];if(c(i,"loaded"))return!1;var n=this.elements[e],s=n.type,l={index:e,slide:i,slideNode:i,slideConfig:n.slideConfig,slideIndex:e,trigger:n.node,player:null};this.trigger("slide_before_load",l),"video"==s||"external"==s?setTimeout((function(){n.instance.setContent(i,(function(){t.trigger("slide_after_load",l)}))}),200):n.instance.setContent(i,(function(){t.trigger("slide_after_load",l)}))}},{key:"prevSlide",value:function(){this.goToSlide(this.index-1)}},{key:"nextSlide",value:function(){this.goToSlide(this.index+1)}},{key:"goToSlide",value:function(){var e=arguments.length>0&&void 0!==arguments[0]&&arguments[0];if(this.prevActiveSlide=this.activeSlide,this.prevActiveSlideIndex=this.index,!this.loop()&&(e<0||e>this.elements.length-1))return!1;e<0?e=this.elements.length-1:e>=this.elements.length&&(e=0),this.showSlide(e)}},{key:"insertSlide",value:function(){var e=arguments.length>0&&void 0!==arguments[0]?arguments[0]:{},t=arguments.length>1&&void 0!==arguments[1]?arguments[1]:-1;t<0&&(t=this.elements.length);var i=new U(e,this,t),n=i.getConfig(),s=l({},n),o=i.create(),r=this.elements.length-1;s.index=t,s.node=!1,s.instance=i,s.slideConfig=n,this.elements.splice(t,0,s);var a=null,h=null;if(this.slidesContainer){if(t>r)this.slidesContainer.appendChild(o);else{var d=this.slidesContainer.querySelectorAll(".gslide")[t];this.slidesContainer.insertBefore(o,d)}(this.settings.preload&&0==this.index&&0==t||this.index-1==t||this.index+1==t)&&this.preloadSlide(t),0==this.index&&0==t&&(this.index=1),this.updateNavigationClasses(),a=this.slidesContainer.querySelectorAll(".gslide")[t],h=this.getSlidePlayerInstance(t),s.slideNode=a}this.trigger("slide_inserted",{index:t,slide:a,slideNode:a,slideConfig:n,slideIndex:t,trigger:null,player:h}),T(this.settings.slideInserted)&&this.settings.slideInserted({index:t,slide:a,player:h})}},{key:"removeSlide",value:function(){var e=arguments.length>0&&void 0!==arguments[0]?arguments[0]:-1;if(e<0||e>this.elements.length-1)return!1;var t=this.slidesContainer&&this.slidesContainer.querySelectorAll(".gslide")[e];t&&(this.getActiveSlideIndex()==e&&(e==this.elements.length-1?this.prevSlide():this.nextSlide()),t.parentNode.removeChild(t)),this.elements.splice(e,1),this.trigger("slide_removed",e),T(this.settings.slideRemoved)&&this.settings.slideRemoved(e)}},{key:"slideAnimateIn",value:function(e,t){var i=this,n=e.querySelector(".gslide-media"),s=e.querySelector(".gslide-description"),l={index:this.prevActiveSlideIndex,slide:this.prevActiveSlide,slideNode:this.prevActiveSlide,slideIndex:this.prevActiveSlide,slideConfig:I(this.prevActiveSlideIndex)?null:this.elements[this.prevActiveSlideIndex].slideConfig,trigger:I(this.prevActiveSlideIndex)?null:this.elements[this.prevActiveSlideIndex].node,player:this.getSlidePlayerInstance(this.prevActiveSlideIndex)},o={index:this.index,slide:this.activeSlide,slideNode:this.activeSlide,slideConfig:this.elements[this.index].slideConfig,slideIndex:this.index,trigger:this.elements[this.index].node,player:this.getSlidePlayerInstance(this.index)};if(n.offsetWidth>0&&s&&(p(s),s.style.display=""),d(e,this.effectsClasses),t)g(e,this.settings.cssEfects[this.settings.openEffect].in,(function(){i.settings.autoplayVideos&&i.slidePlayerPlay(e),i.trigger("slide_changed",{prev:l,current:o}),T(i.settings.afterSlideChange)&&i.settings.afterSlideChange.apply(i,[l,o])}));else{var r=this.settings.slideEffect,a="none"!==r?this.settings.cssEfects[r].in:r;this.prevActiveSlideIndex>this.index&&"slide"==this.settings.slideEffect&&(a=this.settings.cssEfects.slideBack.in),g(e,a,(function(){i.settings.autoplayVideos&&i.slidePlayerPlay(e),i.trigger("slide_changed",{prev:l,current:o}),T(i.settings.afterSlideChange)&&i.settings.afterSlideChange.apply(i,[l,o])}))}setTimeout((function(){i.resize(e)}),100),h(e,"current")}},{key:"slideAnimateOut",value:function(){if(!this.prevActiveSlide)return!1;var e=this.prevActiveSlide;d(e,this.effectsClasses),h(e,"prev");var t=this.settings.slideEffect,i="none"!==t?this.settings.cssEfects[t].out:t;this.slidePlayerPause(e),this.trigger("slide_before_change",{prev:{index:this.prevActiveSlideIndex,slide:this.prevActiveSlide,slideNode:this.prevActiveSlide,slideIndex:this.prevActiveSlideIndex,slideConfig:I(this.prevActiveSlideIndex)?null:this.elements[this.prevActiveSlideIndex].slideConfig,trigger:I(this.prevActiveSlideIndex)?null:this.elements[this.prevActiveSlideIndex].node,player:this.getSlidePlayerInstance(this.prevActiveSlideIndex)},current:{index:this.index,slide:this.activeSlide,slideNode:this.activeSlide,slideIndex:this.index,slideConfig:this.elements[this.index].slideConfig,trigger:this.elements[this.index].node,player:this.getSlidePlayerInstance(this.index)}}),T(this.settings.beforeSlideChange)&&this.settings.beforeSlideChange.apply(this,[{index:this.prevActiveSlideIndex,slide:this.prevActiveSlide,player:this.getSlidePlayerInstance(this.prevActiveSlideIndex)},{index:this.index,slide:this.activeSlide,player:this.getSlidePlayerInstance(this.index)}]),this.prevActiveSlideIndex>this.index&&"slide"==this.settings.slideEffect&&(i=this.settings.cssEfects.slideBack.out),g(e,i,(function(){var t=e.querySelector(".ginner-container"),i=e.querySelector(".gslide-media"),n=e.querySelector(".gslide-description");t.style.transform="",i.style.transform="",d(i,"greset"),i.style.opacity="",n&&(n.style.opacity=""),d(e,"prev")}))}},{key:"getAllPlayers",value:function(){return this.videoPlayers}},{key:"getSlidePlayerInstance",value:function(e){var t="gvideo"+e,i=this.getAllPlayers();return!(!O(i,t)||!i[t])&&i[t]}},{key:"stopSlideVideo",value:function(e){if(k(e)){var t=e.querySelector(".gvideo-wrapper");t&&(e=t.getAttribute("data-index"))}console.log("stopSlideVideo is deprecated, use slidePlayerPause");var i=this.getSlidePlayerInstance(e);i&&i.playing&&i.pause()}},{key:"slidePlayerPause",value:function(e){if(k(e)){var t=e.querySelector(".gvideo-wrapper");t&&(e=t.getAttribute("data-index"))}var i=this.getSlidePlayerInstance(e);i&&i.playing&&i.pause()}},{key:"playSlideVideo",value:function(e){if(k(e)){var t=e.querySelector(".gvideo-wrapper");t&&(e=t.getAttribute("data-index"))}console.log("playSlideVideo is deprecated, use slidePlayerPlay");var i=this.getSlidePlayerInstance(e);i&&!i.playing&&i.play()}},{key:"slidePlayerPlay",value:function(e){if(k(e)){var t=e.querySelector(".gvideo-wrapper");t&&(e=t.getAttribute("data-index"))}var i=this.getSlidePlayerInstance(e);i&&!i.playing&&(i.play(),this.settings.autofocusVideos&&i.elements.container.focus())}},{key:"setElements",value:function(e){var t=this;this.settings.elements=!1;var i=[];e&&e.length&&o(e,(function(e,n){var s=new U(e,t,n),o=s.getConfig(),r=l({},o);r.slideConfig=o,r.instance=s,r.index=n,i.push(r)})),this.elements=i,this.lightboxOpen&&(this.slidesContainer.innerHTML="",this.elements.length&&(o(this.elements,(function(){var e=m(t.settings.slideHTML);t.slidesContainer.appendChild(e)})),this.showSlide(0,!0)))}},{key:"getElementIndex",value:function(e){var t=!1;return o(this.elements,(function(i,n){if(O(i,"node")&&i.node==e)return t=n,!0})),t}},{key:"getElements",value:function(){var e=this,t=[];this.elements=this.elements?this.elements:[],!I(this.settings.elements)&&E(this.settings.elements)&&this.settings.elements.length&&o(this.settings.elements,(function(i,n){var s=new U(i,e,n),o=s.getConfig(),r=l({},o);r.node=!1,r.index=n,r.instance=s,r.slideConfig=o,t.push(r)}));var i=!1;return this.getSelector()&&(i=document.querySelectorAll(this.getSelector())),i?(o(i,(function(i,n){var s=new U(i,e,n),o=s.getConfig(),r=l({},o);r.node=i,r.index=n,r.instance=s,r.slideConfig=o,r.gallery=i.getAttribute("data-gallery"),t.push(r)})),t):t}},{key:"getGalleryElements",value:function(e,t){return e.filter((function(e){return e.gallery==t}))}},{key:"getSelector",value:function(){return!this.settings.elements&&(this.settings.selector&&"data-"==this.settings.selector.substring(0,5)?"*[".concat(this.settings.selector,"]"):this.settings.selector)}},{key:"getActiveSlide",value:function(){return this.slidesContainer.querySelectorAll(".gslide")[this.index]}},{key:"getActiveSlideIndex",value:function(){return this.index}},{key:"getAnimationClasses",value:function(){var e=[];for(var t in this.settings.cssEfects)if(this.settings.cssEfects.hasOwnProperty(t)){var i=this.settings.cssEfects[t];e.push("g".concat(i.in)),e.push("g".concat(i.out))}return e.join(" ")}},{key:"build",value:function(){var e=this;if(this.built)return!1;var t=document.body.childNodes,i=[];o(t,(function(e){e.parentNode==document.body&&"#"!==e.nodeName.charAt(0)&&e.hasAttribute&&!e.hasAttribute("aria-hidden")&&(i.push(e),e.setAttribute("aria-hidden","true"))}));var n=O(this.settings.svg,"next")?this.settings.svg.next:"",s=O(this.settings.svg,"prev")?this.settings.svg.prev:"",l=O(this.settings.svg,"close")?this.settings.svg.close:"",r=this.settings.lightboxHTML;r=m(r=(r=(r=r.replace(/{nextSVG}/g,n)).replace(/{prevSVG}/g,s)).replace(/{closeSVG}/g,l)),document.body.appendChild(r);var d=document.getElementById("glightbox-body");this.modal=d;var g=d.querySelector(".gclose");this.prevButton=d.querySelector(".gprev"),this.nextButton=d.querySelector(".gnext"),this.overlay=d.querySelector(".goverlay"),this.loader=d.querySelector(".gloader"),this.slidesContainer=document.getElementById("glightbox-slider"),this.bodyHiddenChildElms=i,this.events={},h(this.modal,"glightbox-"+this.settings.skin),this.settings.closeButton&&g&&(this.events.close=a("click",{onElement:g,withCallback:function(t,i){t.preventDefault(),e.close()}})),g&&!this.settings.closeButton&&g.parentNode.removeChild(g),this.nextButton&&(this.events.next=a("click",{onElement:this.nextButton,withCallback:function(t,i){t.preventDefault(),e.nextSlide()}})),this.prevButton&&(this.events.prev=a("click",{onElement:this.prevButton,withCallback:function(t,i){t.preventDefault(),e.prevSlide()}})),this.settings.closeOnOutsideClick&&(this.events.outClose=a("click",{onElement:d,withCallback:function(t,i){e.preventOutsideClick||c(document.body,"glightbox-mobile")||u(t.target,".ginner-container")||u(t.target,".gbtn")||c(t.target,"gnext")||c(t.target,"gprev")||e.close()}})),o(this.elements,(function(t,i){e.slidesContainer.appendChild(t.instance.create()),t.slideNode=e.slidesContainer.querySelectorAll(".gslide")[i]})),K&&h(document.body,"glightbox-touch"),this.events.resize=a("resize",{onElement:window,withCallback:function(){e.resize()}}),this.built=!0}},{key:"resize",value:function(){var e=arguments.length>0&&void 0!==arguments[0]?arguments[0]:null;if((e=e||this.activeSlide)&&!c(e,"zoomed")){var t=y(),i=e.querySelector(".gvideo-wrapper"),n=e.querySelector(".gslide-image"),s=this.slideDescription,l=t.width,o=t.height;if(l<=768?h(document.body,"glightbox-mobile"):d(document.body,"glightbox-mobile"),i||n){var r=!1;if(s&&(c(s,"description-bottom")||c(s,"description-top"))&&!c(s,"gabsolute")&&(r=!0),n)if(l<=768)n.querySelector("img");else if(r){var a=s.offsetHeight,u=n.querySelector("img");u.setAttribute("style","max-height: calc(100vh - ".concat(a,"px)")),s.setAttribute("style","max-width: ".concat(u.offsetWidth,"px;"))}if(i){var g=O(this.settings.plyr.config,"ratio")?this.settings.plyr.config.ratio:"";if(!g){var v=i.clientWidth,f=i.clientHeight,p=v/f;g="".concat(v/p,":").concat(f/p)}var m=g.split(":"),x=this.settings.videosWidth,b=this.settings.videosWidth,S=(b=M(x)||-1!==x.indexOf("px")?parseInt(x):-1!==x.indexOf("vw")?l*parseInt(x)/100:-1!==x.indexOf("vh")?o*parseInt(x)/100:-1!==x.indexOf("%")?l*parseInt(x)/100:parseInt(i.clientWidth))/(parseInt(m[0])/parseInt(m[1]));if(S=Math.floor(S),r&&(o-=s.offsetHeight),b>l||S>o||o<S&&l>b){var w=i.offsetWidth,T=i.offsetHeight,C=o/T,k={width:w*C,height:T*C};i.parentNode.setAttribute("style","max-width: ".concat(k.width,"px")),r&&s.setAttribute("style","max-width: ".concat(k.width,"px;"))}else i.parentNode.style.maxWidth="".concat(x),r&&s.setAttribute("style","max-width: ".concat(x,";"))}}}}},{key:"reload",value:function(){this.init()}},{key:"updateNavigationClasses",value:function(){var e=this.loop();d(this.nextButton,"disabled"),d(this.prevButton,"disabled"),0==this.index&&this.elements.length-1==0?(h(this.prevButton,"disabled"),h(this.nextButton,"disabled")):0!==this.index||e?this.index!==this.elements.length-1||e||h(this.nextButton,"disabled"):h(this.prevButton,"disabled")}},{key:"loop",value:function(){var e=O(this.settings,"loopAtEnd")?this.settings.loopAtEnd:null;return e=O(this.settings,"loop")?this.settings.loop:e,e}},{key:"close",value:function(){var e=this;if(!this.lightboxOpen){if(this.events){for(var t in this.events)this.events.hasOwnProperty(t)&&this.events[t].destroy();this.events=null}return!1}if(this.closing)return!1;this.closing=!0,this.slidePlayerPause(this.activeSlide),this.fullElementsList&&(this.elements=this.fullElementsList),this.bodyHiddenChildElms.length&&o(this.bodyHiddenChildElms,(function(e){e.removeAttribute("aria-hidden")})),h(this.modal,"glightbox-closing"),g(this.overlay,"none"==this.settings.openEffect?"none":this.settings.cssEfects.fade.out),g(this.activeSlide,this.settings.cssEfects[this.settings.closeEffect].out,(function(){if(e.activeSlide=null,e.prevActiveSlideIndex=null,e.prevActiveSlide=null,e.built=!1,e.events){for(var t in e.events)e.events.hasOwnProperty(t)&&e.events[t].destroy();e.events=null}var i=document.body;d(Q,"glightbox-open"),d(i,"glightbox-open touching gdesc-open glightbox-touch glightbox-mobile gscrollbar-fixer"),e.modal.parentNode.removeChild(e.modal),e.trigger("close"),T(e.settings.onClose)&&e.settings.onClose();var n=document.querySelector(".gcss-styles");n&&n.parentNode.removeChild(n),e.lightboxOpen=!1,e.closing=null}))}},{key:"destroy",value:function(){this.close(),this.clearAllEvents(),this.baseEvents&&this.baseEvents.destroy()}},{key:"on",value:function(e,t){var i=arguments.length>2&&void 0!==arguments[2]&&arguments[2];if(!e||!T(t))throw new TypeError("Event name and callback must be defined");this.apiEvents.push({evt:e,once:i,callback:t})}},{key:"once",value:function(e,t){this.on(e,t,!0)}},{key:"trigger",value:function(e){var t=this,i=arguments.length>1&&void 0!==arguments[1]?arguments[1]:null,n=[];o(this.apiEvents,(function(t,s){var l=t.evt,o=t.once,r=t.callback;l==e&&(r(i),o&&n.push(s))})),n.length&&o(n,(function(e){return t.apiEvents.splice(e,1)}))}},{key:"clearAllEvents",value:function(){this.apiEvents.splice(0,this.apiEvents.length)}},{key:"version",value:function(){return"3.1.1"}}]),e}();return function(){var e=arguments.length>0&&void 0!==arguments[0]?arguments[0]:{},t=new te(e);return t.init(),t}}));
-/*! update cache: 20251007160243 */
+/*! update cache: 20251017053005 */
diff --git a/en/assets/stylesheets/glightbox.min.css b/en/assets/stylesheets/glightbox.min.css
index 8464ceafa..7641bb766 100644
--- a/en/assets/stylesheets/glightbox.min.css
+++ b/en/assets/stylesheets/glightbox.min.css
@@ -1,2 +1,2 @@
 .glightbox-container{width:100%;height:100%;position:fixed;top:0;left:0;z-index:999999!important;overflow:hidden;-ms-touch-action:none;touch-action:none;-webkit-text-size-adjust:100%;-moz-text-size-adjust:100%;-ms-text-size-adjust:100%;text-size-adjust:100%;-webkit-backface-visibility:hidden;backface-visibility:hidden;outline:0}.glightbox-container.inactive{display:none}.glightbox-container .gcontainer{position:relative;width:100%;height:100%;z-index:9999;overflow:hidden}.glightbox-container .gslider{-webkit-transition:-webkit-transform .4s ease;transition:-webkit-transform .4s ease;transition:transform .4s ease;transition:transform .4s ease,-webkit-transform .4s 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.ginner-container{position:relative;width:100%;display:-webkit-box;display:-ms-flexbox;display:flex;-webkit-box-pack:center;-ms-flex-pack:center;justify-content:center;-webkit-box-orient:vertical;-webkit-box-direction:normal;-ms-flex-direction:column;flex-direction:column;max-width:100%;margin:auto;height:100vh}.glightbox-container .ginner-container.gvideo-container{width:100%}.glightbox-container .ginner-container.desc-bottom,.glightbox-container .ginner-container.desc-top{-webkit-box-orient:vertical;-webkit-box-direction:normal;-ms-flex-direction:column;flex-direction:column}.glightbox-container .ginner-container.desc-left,.glightbox-container .ginner-container.desc-right{max-width:100%!important}.gslide iframe,.gslide video{outline:0!important;border:none;min-height:165px;-webkit-overflow-scrolling:touch;-ms-touch-action:auto;touch-action:auto}.gslide:not(.current){pointer-events:none}.gslide-image{-webkit-box-align:center;-ms-flex-align:center;align-items:center}.gslide-image img{max-height:100vh;display:block;padding:0;float:none;outline:0;border:none;-webkit-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none;max-width:100vw;width:auto;height:auto;-o-object-fit:cover;object-fit:cover;-ms-touch-action:none;touch-action:none;margin:auto;min-width:200px}.desc-bottom .gslide-image img,.desc-top .gslide-image img{width:auto}.desc-left .gslide-image img,.desc-right .gslide-image img{width:auto;max-width:100%}.gslide-image img.zoomable{position:relative}.gslide-image img.dragging{cursor:-webkit-grabbing!important;cursor:grabbing!important;-webkit-transition:none;transition:none}.gslide-video{position:relative;max-width:100vh;width:100%!important}.gslide-video .plyr__poster-enabled.plyr--loading .plyr__poster{display:none}.gslide-video .gvideo-wrapper{width:100%;margin:auto}.gslide-video::before{content:'';position:absolute;width:100%;height:100%;background:rgba(255,0,0,.34);display:none}.gslide-video.playing::before{display:none}.gslide-video.fullscreen{max-width:100%!important;min-width:100%;height:75vh}.gslide-video.fullscreen video{max-width:100%!important;width:100%!important}.gslide-inline{background:#fff;text-align:left;max-height:calc(100vh - 40px);overflow:auto;max-width:100%;margin:auto}.gslide-inline .ginlined-content{padding:20px;width:100%}.gslide-inline .dragging{cursor:-webkit-grabbing!important;cursor:grabbing!important;-webkit-transition:none;transition:none}.ginlined-content{overflow:auto;display:block!important;opacity:1}.gslide-external{display:-webkit-box;display:-ms-flexbox;display:flex;width:100%;min-width:100%;background:#fff;padding:0;overflow:auto;max-height:75vh;height:100%}.gslide-media{display:-webkit-box;display:-ms-flexbox;display:flex;width:auto}.zoomed .gslide-media{-webkit-box-shadow:none!important;box-shadow:none!important}.desc-bottom .gslide-media,.desc-top .gslide-media{margin:0 auto;-webkit-box-orient:vertical;-webkit-box-direction:normal;-ms-flex-direction:column;flex-direction:column}.gslide-description{position:relative;-webkit-box-flex:1;-ms-flex:1 0 100%;flex:1 0 100%}.gslide-description.description-left,.gslide-description.description-right{max-width:100%}.gslide-description.description-bottom,.gslide-description.description-top{margin:0 auto;width:100%}.gslide-description p{margin-bottom:12px}.gslide-description p:last-child{margin-bottom:0}.zoomed .gslide-description{display:none}.glightbox-button-hidden{display:none}.glightbox-mobile .glightbox-container .gslide-description{height:auto!important;width:100%;position:absolute;bottom:0;padding:19px 11px;max-width:100vw!important;-webkit-box-ordinal-group:3!important;-ms-flex-order:2!important;order:2!important;max-height:78vh;overflow:auto!important;background:-webkit-gradient(linear,left top,left bottom,from(rgba(0,0,0,0)),to(rgba(0,0,0,.75)));background:linear-gradient(to bottom,rgba(0,0,0,0) 0,rgba(0,0,0,.75) 100%);-webkit-transition:opacity .3s linear;transition:opacity .3s linear;padding-bottom:50px}.glightbox-mobile .glightbox-container .gslide-title{color:#fff;font-size:1em}.glightbox-mobile .glightbox-container .gslide-desc{color:#a1a1a1}.glightbox-mobile .glightbox-container .gslide-desc a{color:#fff;font-weight:700}.glightbox-mobile .glightbox-container .gslide-desc *{color:inherit}.glightbox-mobile .glightbox-container .gslide-desc .desc-more{color:#fff;opacity:.4}.gdesc-open .gslide-media{-webkit-transition:opacity .5s ease;transition:opacity .5s ease;opacity:.4}.gdesc-open .gdesc-inner{padding-bottom:30px}.gdesc-closed .gslide-media{-webkit-transition:opacity .5s ease;transition:opacity .5s ease;opacity:1}.greset{-webkit-transition:all .3s ease;transition:all .3s ease}.gabsolute{position:absolute}.grelative{position:relative}.glightbox-desc{display:none!important}.glightbox-open{overflow:hidden}.gloader{height:25px;width:25px;-webkit-animation:lightboxLoader .8s infinite linear;animation:lightboxLoader .8s infinite linear;border:2px solid #fff;border-right-color:transparent;border-radius:50%;position:absolute;display:block;z-index:9999;left:0;right:0;margin:0 auto;top:47%}.goverlay{width:100%;height:calc(100vh + 1px);position:fixed;top:-1px;left:0;background:#000;will-change:opacity}.glightbox-mobile 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index 402a2b4b4..9a8665f33 100644
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--- a/index.html
+++ b/index.html
@@ -85,6 +85,11 @@
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+                <li class="md-select__item">
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new file mode 100644
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+      
+        
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+        
+        
+        <link rel="preconnect" href="https://fonts.gstatic.com" crossorigin>
+        <link rel="stylesheet" href="https://fonts.googleapis.com/css?family=Noto+Sans+JP:300,300i,400,400i,700,700i%7CFira+Code:400,400i,700,700i&display=fallback">
+        <style>:root{--md-text-font:"Noto Sans JP";--md-code-font:"Fira Code"}</style>
+      
+    
+    
+      <link rel="stylesheet" href="/ja/stylesheets/extra.css">
+    
+    <script>__md_scope=new URL("/ja/",location),__md_hash=e=>[...e].reduce((e,_)=>(e<<5)-e+_.charCodeAt(0),0),__md_get=(e,_=localStorage,t=__md_scope)=>JSON.parse(_.getItem(t.pathname+"."+e)),__md_set=(e,_,t=localStorage,a=__md_scope)=>{try{t.setItem(a.pathname+"."+e,JSON.stringify(_))}catch(e){}}</script>
+    
+      
+
+    
+    
+    
+  </head>
+  
+  
+    
+    
+      
+    
+    
+    
+    
+    <body dir="ltr" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="teal">
+  
+    
+    <input class="md-toggle" data-md-toggle="drawer" type="checkbox" id="__drawer" autocomplete="off">
+    <input class="md-toggle" data-md-toggle="search" type="checkbox" id="__search" autocomplete="off">
+    <label class="md-overlay" for="__drawer"></label>
+    <div data-md-component="skip">
+      
+    </div>
+    <div data-md-component="announce">
+      
+        <aside class="md-banner">
+          <div class="md-banner__inner md-grid md-typeset">
+            
+            
+
+    
+
+<div class="banner-svg">
+    <svg xmlns="http://www.w3.org/2000/svg"
+        viewBox="0 0 512 512"><!--!Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free Copyright 2024 Fonticons, Inc.-->
+        <path
+            d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
+    </svg>
+    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+</div>
+
+          </div>
+          
+        </aside>
+      
+    </div>
+    
+    
+      
+
+  
+
+<header class="md-header md-header--shadow" data-md-component="header">
+  <nav class="md-header__inner md-grid" aria-label="ヘッダー">
+    <a href="/ja/." title="Hello アルゴリズム" class="md-header__button md-logo" aria-label="Hello アルゴリズム" data-md-component="logo">
+      
+  <img src="/ja/assets/images/logo.svg" alt="logo">
+
+    </a>
+    <label class="md-header__button md-icon" for="__drawer">
+      
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 6h18v2H3V6m0 5h18v2H3v-2m0 5h18v2H3v-2Z"/></svg>
+    </label>
+    <div class="md-header__title" data-md-component="header-title">
+      <div class="md-header__ellipsis">
+        <div class="md-header__topic">
+          <span class="md-ellipsis">
+            Hello アルゴリズム
+          </span>
+        </div>
+        <div class="md-header__topic" data-md-component="header-topic">
+          <span class="md-ellipsis">
+            
+              
+            
+          </span>
+        </div>
+      </div>
+    </div>
+    
+      
+        <form class="md-header__option" data-md-component="palette">
+  
+    
+    
+    
+    <input class="md-option" data-md-color-media="" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="teal"  aria-label="ダークモード"  type="radio" name="__palette" id="__palette_0">
+    
+      <label class="md-header__button md-icon" title="ダークモード" for="__palette_1" hidden>
+        <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07 19.07 3.5m-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13.51 1.67m-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87.4 1.31M19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35-2.53-2.2m4.33-2.7 1.15-2.77 2.2 2.54-3.35.23m1.15-4.96-1.14-2.78 3.34.24-2.2 2.54M9.63 18.93l2.77 1.15-2.53 2.19-.24-3.34Z"/></svg>
+      </label>
+    
+  
+    
+    
+    
+    <input class="md-option" data-md-color-media="" data-md-color-scheme="slate" data-md-color-primary="black" data-md-color-accent="teal"  aria-label="ライトモード"  type="radio" name="__palette" id="__palette_1">
+    
+      <label class="md-header__button md-icon" title="ライトモード" for="__palette_0" hidden>
+        <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07 19.07 3.5m-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13.51 1.67m-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87.4 1.31M19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35-2.53-2.2m4.33-2.7 1.15-2.77 2.2 2.54-3.35.23m1.15-4.96-1.14-2.78 3.34.24-2.2 2.54M9.63 18.93l2.77 1.15-2.53 2.19-.24-3.34Z"/></svg>
+      </label>
+    
+  
+</form>
+      
+    
+    
+      <script>var media,input,key,value,palette=__md_get("__palette");if(palette&&palette.color){"(prefers-color-scheme)"===palette.color.media&&(media=matchMedia("(prefers-color-scheme: light)"),input=document.querySelector(media.matches?"[data-md-color-media='(prefers-color-scheme: light)']":"[data-md-color-media='(prefers-color-scheme: dark)']"),palette.color.media=input.getAttribute("data-md-color-media"),palette.color.scheme=input.getAttribute("data-md-color-scheme"),palette.color.primary=input.getAttribute("data-md-color-primary"),palette.color.accent=input.getAttribute("data-md-color-accent"));for([key,value]of Object.entries(palette.color))document.body.setAttribute("data-md-color-"+key,value)}</script>
+    
+    
+      <div class="md-header__option">
+  <div class="md-select">
+    
+    <button class="md-header__button md-icon" aria-label="言語切り替え">
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12.87 15.07-2.54-2.51.03-.03A17.52 17.52 0 0 0 14.07 6H17V4h-7V2H8v2H1v2h11.17C11.5 7.92 10.44 9.75 9 11.35 8.07 10.32 7.3 9.19 6.69 8h-2c.73 1.63 1.73 3.17 2.98 4.56l-5.09 5.02L4 19l5-5 3.11 3.11.76-2.04M18.5 10h-2L12 22h2l1.12-3h4.75L21 22h2l-4.5-12m-2.62 7 1.62-4.33L19.12 17h-3.24Z"/></svg>
+    </button>
+    <div class="md-select__inner">
+      <ul class="md-select__list">
+        
+          <li class="md-select__item">
+            <a href="/" hreflang="zh" class="md-select__link">
+              简体中文
+            </a>
+          </li>
+        
+          <li class="md-select__item">
+            <a href="/zh-hant/" hreflang="zh-Hant" class="md-select__link">
+              繁體中文
+            </a>
+          </li>
+        
+          <li class="md-select__item">
+            <a href="/en/" hreflang="en" class="md-select__link">
+              English
+            </a>
+          </li>
+        
+          <li class="md-select__item">
+            <a href="/ja/" hreflang="ja" class="md-select__link">
+              日本語
+            </a>
+          </li>
+        
+      </ul>
+    </div>
+  </div>
+</div>
+    
+    
+      <label class="md-header__button md-icon" for="__search">
+        
+        <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.516 6.516 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5Z"/></svg>
+      </label>
+      <div class="md-search" data-md-component="search" role="dialog">
+  <label class="md-search__overlay" for="__search"></label>
+  <div class="md-search__inner" role="search">
+    <form class="md-search__form" name="search">
+      <input type="text" class="md-search__input" name="query" aria-label="検索" placeholder="検索" autocapitalize="off" autocorrect="off" autocomplete="off" spellcheck="false" data-md-component="search-query" required>
+      <label class="md-search__icon md-icon" for="__search">
+        
+        <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.516 6.516 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5Z"/></svg>
+        
+        <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M20 11v2H8l5.5 5.5-1.42 1.42L4.16 12l7.92-7.92L13.5 5.5 8 11h12Z"/></svg>
+      </label>
+      <nav class="md-search__options" aria-label="検索">
+        
+          <a href="javascript:void(0)" class="md-search__icon md-icon" title="共有" aria-label="共有" data-clipboard data-clipboard-text="" data-md-component="search-share" tabindex="-1">
+            
+            <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 16.08c-.76 0-1.44.3-1.96.77L8.91 12.7c.05-.23.09-.46.09-.7 0-.24-.04-.47-.09-.7l7.05-4.11c.54.5 1.25.81 2.04.81a3 3 0 0 0 3-3 3 3 0 0 0-3-3 3 3 0 0 0-3 3c0 .24.04.47.09.7L8.04 9.81C7.5 9.31 6.79 9 6 9a3 3 0 0 0-3 3 3 3 0 0 0 3 3c.79 0 1.5-.31 2.04-.81l7.12 4.15c-.05.21-.08.43-.08.66 0 1.61 1.31 2.91 2.92 2.91 1.61 0 2.92-1.3 2.92-2.91A2.92 2.92 0 0 0 18 16.08Z"/></svg>
+          </a>
+        
+        <button type="reset" class="md-search__icon md-icon" title="クリア" aria-label="クリア" tabindex="-1">
+          
+          <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 6.41 17.59 5 12 10.59 6.41 5 5 6.41 10.59 12 5 17.59 6.41 19 12 13.41 17.59 19 19 17.59 13.41 12 19 6.41Z"/></svg>
+        </button>
+      </nav>
+      
+        <div class="md-search__suggest" data-md-component="search-suggest"></div>
+      
+    </form>
+    <div class="md-search__output">
+      <div class="md-search__scrollwrap" data-md-scrollfix>
+        <div class="md-search-result" data-md-component="search-result">
+          <div class="md-search-result__meta">
+            検索を初期化
+          </div>
+          <ol class="md-search-result__list" role="presentation"></ol>
+        </div>
+      </div>
+    </div>
+  </div>
+</div>
+    
+    
+      <div class="md-header__source">
+        <a href="https://github.com/krahets/hello-algo" title="リポジトリへ" class="md-source" data-md-component="source">
+  <div class="md-source__icon md-icon">
+    
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 496 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"/></svg>
+  </div>
+  <div class="md-source__repository">
+    krahets/hello-algo
+  </div>
+</a>
+      </div>
+    
+  </nav>
+  
+</header>
+    
+    <div class="md-container" data-md-component="container">
+      
+      
+        
+          
+        
+      
+      <main class="md-main" data-md-component="main">
+        <div class="md-main__inner md-grid">
+          
+            
+              
+              <div class="md-sidebar md-sidebar--primary" data-md-component="sidebar" data-md-type="navigation" >
+                <div class="md-sidebar__scrollwrap">
+                  <div class="md-sidebar__inner">
+                    
+
+
+
+<nav class="md-nav md-nav--primary" aria-label="ナビゲーション" data-md-level="0">
+  <label class="md-nav__title" for="__drawer">
+    <a href="/ja/." title="Hello アルゴリズム" class="md-nav__button md-logo" aria-label="Hello アルゴリズム" data-md-component="logo">
+      
+  <img src="/ja/assets/images/logo.svg" alt="logo">
+
+    </a>
+    Hello アルゴリズム
+  </label>
+  
+    <div class="md-nav__source">
+      <a href="https://github.com/krahets/hello-algo" title="リポジトリへ" class="md-source" data-md-component="source">
+  <div class="md-source__icon md-icon">
+    
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 496 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"/></svg>
+  </div>
+  <div class="md-source__repository">
+    krahets/hello-algo
+  </div>
+</a>
+    </div>
+  
+  <ul class="md-nav__list" data-md-scrollfix>
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_1" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="/ja/chapter_hello_algo/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m13.13 22.19-1.63-3.83c1.57-.58 3.04-1.36 4.4-2.27l-2.77 6.1M5.64 12.5l-3.83-1.63 6.1-2.77C7 9.46 6.22 10.93 5.64 12.5M19.22 4c.28 0 .53 0 .74.05.17 1.39-.02 4.25-3.3 7.53-1.7 1.71-3.73 3.02-6.01 3.89l-2.15-2.1c.92-2.31 2.23-4.34 3.92-6.03C15.18 4.58 17.64 4 19.22 4m0-2c-1.98 0-4.98.69-8.22 3.93-2.19 2.19-3.5 4.6-4.35 6.71-.28.75-.09 1.57.46 2.13l2.13 2.12c.38.38.89.61 1.42.61.23 0 .47-.06.7-.15A19.1 19.1 0 0 0 18.07 13c5.66-5.66 3.54-10.61 3.54-10.61S20.7 2 19.22 2m-4.68 7.46c-.78-.78-.78-2.05 0-2.83s2.05-.78 2.83 0c.77.78.78 2.05 0 2.83-.78.78-2.05.78-2.83 0m-5.66 7.07-1.41-1.41 1.41 1.41M6.24 22l3.64-3.64c-.34-.09-.67-.24-.97-.45L4.83 22h1.41M2 22h1.41l4.77-4.76-1.42-1.41L2 20.59V22m0-2.83 4.09-4.08c-.21-.3-.36-.62-.45-.97L2 17.76v1.41Z"/></svg>
+  
+  <span class="md-ellipsis">
+    はじめに
+  </span>
+  
+
+            </a>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_1_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_1">
+            <span class="md-nav__icon md-icon"></span>
+            はじめに
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_2" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="/ja/chapter_preface/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M21 4H3a2 2 0 0 0-2 2v13a2 2 0 0 0 2 2h18a2 2 0 0 0 2-2V6a2 2 0 0 0-2-2M3 19V6h8v13H3m18 0h-8V6h8v13m-7-9.5h6V11h-6V9.5m0 2.5h6v1.5h-6V12m0 2.5h6V16h-6v-1.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 0 章 &nbsp; 前書き
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_2" id="__nav_2_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_2_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_2">
+            <span class="md-nav__icon md-icon"></span>
+            第 0 章 &nbsp; 前書き
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_preface/about_the_book/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.1 &nbsp; この本について
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_preface/suggestions/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.2 &nbsp; 本書の使い方
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_preface/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="/ja/chapter_introduction/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="/ja/chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="/ja/chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="/ja/chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="/ja/chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="/ja/chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="/ja/chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="/ja/chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="/ja/chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="/ja/chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="/ja/chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="/ja/chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="/ja/chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="/ja/chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="/ja/chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
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+      <a href="/ja/chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
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+  
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+    </li>
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+            
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+      <a href="/ja/chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
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+      <a href="/ja/chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
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+      <a href="/ja/chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
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+  
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+      <a href="/ja/chapter_dynamic_programming/summary/" class="md-nav__link">
+        
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+  
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+  
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new file mode 100644
index 000000000..e47a71d4c
--- /dev/null
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circle{fill:var(--md-mermaid-label-bg-color)}.actor{fill:var(--md-mermaid-sequence-actor-bg-color);stroke:var(--md-mermaid-sequence-actor-border-color)}text.actor>tspan{fill:var(--md-mermaid-sequence-actor-fg-color);font-family:var(--md-mermaid-font-family)}line{stroke:var(--md-mermaid-sequence-actor-line-color)}.actor-man circle,.actor-man line{fill:var(--md-mermaid-sequence-actorman-bg-color);stroke:var(--md-mermaid-sequence-actorman-line-color)}.messageLine0,.messageLine1{stroke:var(--md-mermaid-sequence-message-line-color)}.note{fill:var(--md-mermaid-sequence-note-bg-color);stroke:var(--md-mermaid-sequence-note-border-color)}.loopText,.loopText>tspan,.messageText,.noteText>tspan{stroke:none;font-family:var(--md-mermaid-font-family)!important}.messageText{fill:var(--md-mermaid-sequence-message-fg-color)}.loopText,.loopText>tspan{fill:var(--md-mermaid-sequence-loop-fg-color)}.noteText>tspan{fill:var(--md-mermaid-sequence-note-fg-color)}#arrowhead 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Hn(e,{viewport$:t,target$:r,print$:o}){return T(...R(".annotate:not(.highlight)",e).map(n=>wn(n,{target$:r,print$:o})),...R("pre:not(.mermaid) > code",e).map(n=>On(n,{target$:r,print$:o})),...R("pre.mermaid",e).map(n=>_n(n)),...R("table:not([class])",e).map(n=>Cn(n)),...R("details",e).map(n=>Mn(n,{target$:r,print$:o})),...R("[data-tabs]",e).map(n=>kn(n,{viewport$:t,target$:r})),...R("[title]",e).filter(()=>G("content.tooltips")).map(n=>Ge(n)))}function Ra(e,{alert$:t}){return t.pipe(b(r=>T($(!0),$(!1).pipe(Ye(2e3))).pipe(m(o=>({message:r,active:o})))))}function $n(e,t){let r=P(".md-typeset",e);return H(()=>{let o=new v;return o.subscribe(({message:n,active:i})=>{e.classList.toggle("md-dialog--active",i),r.textContent=n}),Ra(e,t).pipe(y(n=>o.next(n)),_(()=>o.complete()),m(n=>F({ref:e},n)))})}function Pa({viewport$:e}){if(!G("header.autohide"))return $(!1);let 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$(...e).pipe(re(o=>d(o,"change").pipe(m(()=>o))),q(e[r]),m(o=>({index:e.indexOf(o),color:{media:o.getAttribute("data-md-color-media"),scheme:o.getAttribute("data-md-color-scheme"),primary:o.getAttribute("data-md-color-primary"),accent:o.getAttribute("data-md-color-accent")}})),B(1))}function jn(e){let t=R("input",e),r=E("meta",{name:"theme-color"});document.head.appendChild(r);let o=E("meta",{name:"color-scheme"});document.head.appendChild(o);let n=At("(prefers-color-scheme: light)");return H(()=>{let i=new v;return i.subscribe(s=>{if(document.body.setAttribute("data-md-color-switching",""),s.color.media==="(prefers-color-scheme)"){let a=matchMedia("(prefers-color-scheme: light)"),c=document.querySelector(a.matches?"[data-md-color-media='(prefers-color-scheme: light)']":"[data-md-color-media='(prefers-color-scheme: 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Q([t,r.pipe(q(ve()),g(o=>!!o.searchParams.get("h")))]).pipe(m(([o,n])=>Yn(o.config)(n.searchParams.get("h"))),m(o=>{var s;let n=new Map,i=document.createNodeIterator(e,NodeFilter.SHOW_TEXT);for(let a=i.nextNode();a;a=i.nextNode())if((s=a.parentElement)!=null&&s.offsetHeight){let c=a.textContent,p=o(c);p.length>c.length&&n.set(a,p)}for(let[a,c]of n){let{childNodes:p}=E("span",null,c);a.replaceWith(...Array.from(p))}return{ref:e,nodes:n}}))}function Ya(e,{viewport$:t,main$:r}){let o=e.closest(".md-grid"),n=o.offsetTop-o.parentElement.offsetTop;return Q([r,t]).pipe(m(([{offset:i,height:s},{offset:{y:a}}])=>(s=s+Math.min(n,Math.max(0,a-i))-n,{height:s,locked:a>=i+n})),Y((i,s)=>i.height===s.height&&i.locked===s.locked))}function Qr(e,o){var n=o,{header$:t}=n,r=to(n,["header$"]);let i=P(".md-sidebar__scrollwrap",e),{y:s}=Ue(i);return H(()=>{let a=new v,c=a.pipe(ee(),oe(!0)),p=a.pipe(Me(0,de));return p.pipe(ae(t)).subscribe({next([{height:l},{height:f}]){i.style.height=`${l-2*s}px`,e.style.top=`${f}px`},complete(){i.style.height="",e.style.top=""}}),p.pipe(He()).subscribe(()=>{for(let l of R(".md-nav__link--active[href]",e)){if(!l.clientHeight)continue;let f=l.closest(".md-sidebar__scrollwrap");if(typeof f!="undefined"){let u=l.offsetTop-f.offsetTop,{height:h}=pe(f);f.scrollTo({top:u-h/2})}}}),fe(R("label[tabindex]",e)).pipe(re(l=>d(l,"click").pipe(Oe(ie),m(()=>l),U(c)))).subscribe(l=>{let f=P(`[id="${l.htmlFor}"]`);P(`[aria-labelledby="${l.id}"]`).setAttribute("aria-expanded",`${f.checked}`)}),Ya(e,r).pipe(y(l=>a.next(l)),_(()=>a.complete()),m(l=>F({ref:e},l)))})}function oi(e,t){if(typeof t!="undefined"){let r=`https://api.github.com/repos/${e}/${t}`;return Lt(De(`${r}/releases/latest`).pipe(he(()=>L),m(o=>({version:o.tag_name})),Qe({})),De(r).pipe(he(()=>L),m(o=>({stars:o.stargazers_count,forks:o.forks_count})),Qe({}))).pipe(m(([o,n])=>F(F({},o),n)))}else{let r=`https://api.github.com/users/${e}`;return De(r).pipe(m(o=>({repositories:o.public_repos})),Qe({}))}}function ni(e,t){let r=`https://${e}/api/v4/projects/${encodeURIComponent(t)}`;return De(r).pipe(he(()=>L),m(({star_count:o,forks_count:n})=>({stars:o,forks:n})),Qe({}))}function ii(e){let t=e.match(/^.+github\.com\/([^/]+)\/?([^/]+)?/i);if(t){let[,r,o]=t;return oi(r,o)}if(t=e.match(/^.+?([^/]*gitlab[^/]+)\/(.+?)\/?$/i),t){let[,r,o]=t;return ni(r,o)}return L}var Ba;function Ga(e){return Ba||(Ba=H(()=>{let t=__md_get("__source",sessionStorage);if(t)return $(t);if(ne("consent").length){let o=__md_get("__consent");if(!(o&&o.github))return L}return ii(e.href).pipe(y(o=>__md_set("__source",o,sessionStorage)))}).pipe(he(()=>L),g(t=>Object.keys(t).length>0),m(t=>({facts:t})),B(1)))}function ai(e){let t=P(":scope > :last-child",e);return H(()=>{let r=new v;return 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$([...o].reduce((p,[l,f])=>{for(;c.length&&o.get(c[c.length-1]).tagName>=f.tagName;)c.pop();let u=f.offsetTop;for(;!u&&f.parentElement;)f=f.parentElement,u=f.offsetTop;let h=f.offsetParent;for(;h;h=h.offsetParent)u+=h.offsetTop;return p.set([...c=[...c,l]].reverse(),u)},new Map))}).pipe(m(c=>new Map([...c].sort(([,p],[,l])=>p-l))),je(i),b(([c,p])=>t.pipe(Rr(([l,f],{offset:{y:u},size:h})=>{let w=u+h.height>=Math.floor(a.height);for(;f.length;){let[,A]=f[0];if(A-p<u||w)l=[...l,f.shift()];else break}for(;l.length;){let[,A]=l[l.length-1];if(A-p>=u&&!w)f=[l.pop(),...f];else break}return[l,f]},[[],[...c]]),Y((l,f)=>l[0]===f[0]&&l[1]===f[1])))))).pipe(m(([a,c])=>({prev:a.map(([p])=>p),next:c.map(([p])=>p)})),q({prev:[],next:[]}),Ke(2,1),m(([a,c])=>a.prev.length<c.prev.length?{prev:c.prev.slice(Math.max(0,a.prev.length-1),c.prev.length),next:[]}:{prev:c.prev.slice(-1),next:c.next.slice(0,c.next.length-a.next.length)}))}function ci(e,{viewport$:t,header$:r,main$:o,target$:n}){return H(()=>{let i=new v,s=i.pipe(ee(),oe(!0));if(i.subscribe(({prev:a,next:c})=>{for(let[p]of c)p.classList.remove("md-nav__link--passed"),p.classList.remove("md-nav__link--active");for(let[p,[l]]of a.entries())l.classList.add("md-nav__link--passed"),l.classList.toggle("md-nav__link--active",p===a.length-1)}),G("toc.follow")){let a=T(t.pipe(be(1),m(()=>{})),t.pipe(be(250),m(()=>"smooth")));i.pipe(g(({prev:c})=>c.length>0),je(o.pipe(Oe(ie))),ae(a)).subscribe(([[{prev:c}],p])=>{let[l]=c[c.length-1];if(l.offsetHeight){let f=sr(l);if(typeof f!="undefined"){let u=l.offsetTop-f.offsetTop,{height:h}=pe(f);f.scrollTo({top:u-h/2,behavior:p})}}})}return G("navigation.tracking")&&t.pipe(U(s),X("offset"),be(250),Le(1),U(n.pipe(Le(1))),at({delay:250}),ae(i)).subscribe(([,{prev:a}])=>{let c=ve(),p=a[a.length-1];if(p&&p.length){let[l]=p,{hash:f}=new URL(l.href);c.hash!==f&&(c.hash=f,history.replaceState({},"",`${c}`))}else 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li({document$:e}){e.pipe(b(()=>R(".md-ellipsis")),re(t=>yt(t).pipe(U(e.pipe(Le(1))),g(r=>r),m(()=>t),ye(1))),g(t=>t.offsetWidth<t.scrollWidth),re(t=>{let r=t.innerText,o=t.closest("a")||t;return o.title=r,Ge(o).pipe(U(e.pipe(Le(1))),_(()=>o.removeAttribute("title")))})).subscribe(),e.pipe(b(()=>R(".md-status")),re(t=>Ge(t))).subscribe()}function mi({document$:e,tablet$:t}){e.pipe(b(()=>R(".md-toggle--indeterminate")),y(r=>{r.indeterminate=!0,r.checked=!1}),re(r=>d(r,"change").pipe(Fr(()=>r.classList.contains("md-toggle--indeterminate")),m(()=>r))),ae(t)).subscribe(([r,o])=>{r.classList.remove("md-toggle--indeterminate"),o&&(r.checked=!1)})}function es(){return/(iPad|iPhone|iPod)/.test(navigator.userAgent)}function fi({document$:e}){e.pipe(b(()=>R("[data-md-scrollfix]")),y(t=>t.removeAttribute("data-md-scrollfix")),g(es),re(t=>d(t,"touchstart").pipe(m(()=>t)))).subscribe(t=>{let r=t.scrollTop;r===0?t.scrollTop=1:r+t.offsetHeight===t.scrollHeight&&(t.scrollTop=r-1)})}function ui({viewport$:e,tablet$:t}){Q([We("search"),t]).pipe(m(([r,o])=>r&&!o),b(r=>$(r).pipe(Ye(r?400:100))),ae(e)).subscribe(([r,{offset:{y:o}}])=>{if(r)document.body.setAttribute("data-md-scrolllock",""),document.body.style.top=`-${o}px`;else{let n=-1*parseInt(document.body.style.top,10);document.body.removeAttribute("data-md-scrolllock"),document.body.style.top="",n&&window.scrollTo(0,n)}})}Object.entries||(Object.entries=function(e){let t=[];for(let r of Object.keys(e))t.push([r,e[r]]);return t});Object.values||(Object.values=function(e){let t=[];for(let r of Object.keys(e))t.push(e[r]);return t});typeof Element!="undefined"&&(Element.prototype.scrollTo||(Element.prototype.scrollTo=function(e,t){typeof e=="object"?(this.scrollLeft=e.left,this.scrollTop=e.top):(this.scrollLeft=e,this.scrollTop=t)}),Element.prototype.replaceWith||(Element.prototype.replaceWith=function(...e){let t=this.parentNode;if(t){e.length===0&&t.removeChild(this);for(let r=e.length-1;r>=0;r--){let o=e[r];typeof o=="string"?o=document.createTextNode(o):o.parentNode&&o.parentNode.removeChild(o),r?t.insertBefore(this.previousSibling,o):t.replaceChild(o,this)}}}));function ts(){return location.protocol==="file:"?gt(`${new URL("search/search_index.js",Yr.base)}`).pipe(m(()=>__index),B(1)):De(new URL("search/search_index.json",Yr.base))}document.documentElement.classList.remove("no-js");document.documentElement.classList.add("js");var rt=No(),Rt=Jo(),wt=en(Rt),Br=Go(),_e=pn(),ur=At("(min-width: 960px)"),hi=At("(min-width: 1220px)"),bi=tn(),Yr=we(),vi=document.forms.namedItem("search")?ts():qe,Gr=new v;Wn({alert$:Gr});var Jr=new v;G("navigation.instant")&&zn({location$:Rt,viewport$:_e,progress$:Jr}).subscribe(rt);var di;((di=Yr.version)==null?void 0:di.provider)==="mike"&&Gn({document$:rt});T(Rt,wt).pipe(Ye(125)).subscribe(()=>{Be("drawer",!1),Be("search",!1)});Br.pipe(g(({mode:e})=>e==="global")).subscribe(e=>{switch(e.type){case"p":case",":let t=me("link[rel=prev]");typeof t!="undefined"&&st(t);break;case"n":case".":let r=me("link[rel=next]");typeof r!="undefined"&&st(r);break;case"Enter":let o=Re();o instanceof HTMLLabelElement&&o.click()}});li({document$:rt});mi({document$:rt,tablet$:ur});fi({document$:rt});ui({viewport$:_e,tablet$:ur});var tt=Rn(Te("header"),{viewport$:_e}),$t=rt.pipe(m(()=>Te("main")),b(e=>Fn(e,{viewport$:_e,header$:tt})),B(1)),rs=T(...ne("consent").map(e=>fn(e,{target$:wt})),...ne("dialog").map(e=>$n(e,{alert$:Gr})),...ne("header").map(e=>Pn(e,{viewport$:_e,header$:tt,main$:$t})),...ne("palette").map(e=>jn(e)),...ne("progress").map(e=>Un(e,{progress$:Jr})),...ne("search").map(e=>ti(e,{index$:vi,keyboard$:Br})),...ne("source").map(e=>ai(e))),os=H(()=>T(...ne("announce").map(e=>mn(e)),...ne("content").map(e=>Hn(e,{viewport$:_e,target$:wt,print$:bi})),...ne("content").map(e=>G("search.highlight")?ri(e,{index$:vi,location$:Rt}):L),...ne("header-title").map(e=>In(e,{viewport$:_e,header$:tt})),...ne("sidebar").map(e=>e.getAttribute("data-md-type")==="navigation"?Ur(hi,()=>Qr(e,{viewport$:_e,header$:tt,main$:$t})):Ur(ur,()=>Qr(e,{viewport$:_e,header$:tt,main$:$t}))),...ne("tabs").map(e=>si(e,{viewport$:_e,header$:tt})),...ne("toc").map(e=>ci(e,{viewport$:_e,header$:tt,main$:$t,target$:wt})),...ne("top").map(e=>pi(e,{viewport$:_e,header$:tt,main$:$t,target$:wt})))),gi=rt.pipe(b(()=>os),$e(rs),B(1));gi.subscribe();window.document$=rt;window.location$=Rt;window.target$=wt;window.keyboard$=Br;window.viewport$=_e;window.tablet$=ur;window.screen$=hi;window.print$=bi;window.alert$=Gr;window.progress$=Jr;window.component$=gi;})();
+//# sourceMappingURL=bundle.c18c5fb9.min.js.map
+
+/*! update cache: 20251017053011 */
diff --git a/ja/assets/javascripts/bundle.c18c5fb9.min.js.map b/ja/assets/javascripts/bundle.c18c5fb9.min.js.map
new file mode 100644
index 000000000..9ebf9cc9e
--- /dev/null
+++ b/ja/assets/javascripts/bundle.c18c5fb9.min.js.map
@@ -0,0 +1,7 @@
+{
+  "version": 3,
+  "sources": ["node_modules/focus-visible/dist/focus-visible.js", "node_modules/clipboard/dist/clipboard.js", "node_modules/escape-html/index.js", "src/templates/assets/javascripts/bundle.ts", "node_modules/rxjs/node_modules/tslib/tslib.es6.js", "node_modules/rxjs/src/internal/util/isFunction.ts", "node_modules/rxjs/src/internal/util/createErrorClass.ts", "node_modules/rxjs/src/internal/util/UnsubscriptionError.ts", "node_modules/rxjs/src/internal/util/arrRemove.ts", "node_modules/rxjs/src/internal/Subscription.ts", "node_modules/rxjs/src/internal/config.ts", "node_modules/rxjs/src/internal/scheduler/timeoutProvider.ts", "node_modules/rxjs/src/internal/util/reportUnhandledError.ts", "node_modules/rxjs/src/internal/util/noop.ts", "node_modules/rxjs/src/internal/NotificationFactories.ts", "node_modules/rxjs/src/internal/util/errorContext.ts", "node_modules/rxjs/src/internal/Subscriber.ts", "node_modules/rxjs/src/internal/symbol/observable.ts", "node_modules/rxjs/src/internal/util/identity.ts", "node_modules/rxjs/src/internal/util/pipe.ts", "node_modules/rxjs/src/internal/Observable.ts", "node_modules/rxjs/src/internal/util/lift.ts", "node_modules/rxjs/src/internal/operators/OperatorSubscriber.ts", "node_modules/rxjs/src/internal/scheduler/animationFrameProvider.ts", "node_modules/rxjs/src/internal/util/ObjectUnsubscribedError.ts", "node_modules/rxjs/src/internal/Subject.ts", "node_modules/rxjs/src/internal/scheduler/dateTimestampProvider.ts", "node_modules/rxjs/src/internal/ReplaySubject.ts", "node_modules/rxjs/src/internal/scheduler/Action.ts", "node_modules/rxjs/src/internal/scheduler/intervalProvider.ts", "node_modules/rxjs/src/internal/scheduler/AsyncAction.ts", "node_modules/rxjs/src/internal/Scheduler.ts", "node_modules/rxjs/src/internal/scheduler/AsyncScheduler.ts", "node_modules/rxjs/src/internal/scheduler/async.ts", "node_modules/rxjs/src/internal/scheduler/AnimationFrameAction.ts", "node_modules/rxjs/src/internal/scheduler/AnimationFrameScheduler.ts", "node_modules/rxjs/src/internal/scheduler/animationFrame.ts", "node_modules/rxjs/src/internal/observable/empty.ts", "node_modules/rxjs/src/internal/util/isScheduler.ts", "node_modules/rxjs/src/internal/util/args.ts", "node_modules/rxjs/src/internal/util/isArrayLike.ts", "node_modules/rxjs/src/internal/util/isPromise.ts", "node_modules/rxjs/src/internal/util/isInteropObservable.ts", "node_modules/rxjs/src/internal/util/isAsyncIterable.ts", "node_modules/rxjs/src/internal/util/throwUnobservableError.ts", "node_modules/rxjs/src/internal/symbol/iterator.ts", "node_modules/rxjs/src/internal/util/isIterable.ts", "node_modules/rxjs/src/internal/util/isReadableStreamLike.ts", "node_modules/rxjs/src/internal/observable/innerFrom.ts", "node_modules/rxjs/src/internal/util/executeSchedule.ts", "node_modules/rxjs/src/internal/operators/observeOn.ts", "node_modules/rxjs/src/internal/operators/subscribeOn.ts", "node_modules/rxjs/src/internal/scheduled/scheduleObservable.ts", "node_modules/rxjs/src/internal/scheduled/schedulePromise.ts", "node_modules/rxjs/src/internal/scheduled/scheduleArray.ts", "node_modules/rxjs/src/internal/scheduled/scheduleIterable.ts", "node_modules/rxjs/src/internal/scheduled/scheduleAsyncIterable.ts", "node_modules/rxjs/src/internal/scheduled/scheduleReadableStreamLike.ts", "node_modules/rxjs/src/internal/scheduled/scheduled.ts", "node_modules/rxjs/src/internal/observable/from.ts", "node_modules/rxjs/src/internal/observable/of.ts", "node_modules/rxjs/src/internal/observable/throwError.ts", "node_modules/rxjs/src/internal/util/EmptyError.ts", "node_modules/rxjs/src/internal/util/isDate.ts", "node_modules/rxjs/src/internal/operators/map.ts", "node_modules/rxjs/src/internal/util/mapOneOrManyArgs.ts", "node_modules/rxjs/src/internal/util/argsArgArrayOrObject.ts", "node_modules/rxjs/src/internal/util/createObject.ts", "node_modules/rxjs/src/internal/observable/combineLatest.ts", "node_modules/rxjs/src/internal/operators/mergeInternals.ts", "node_modules/rxjs/src/internal/operators/mergeMap.ts", "node_modules/rxjs/src/internal/operators/mergeAll.ts", "node_modules/rxjs/src/internal/operators/concatAll.ts", "node_modules/rxjs/src/internal/observable/concat.ts", "node_modules/rxjs/src/internal/observable/defer.ts", "node_modules/rxjs/src/internal/observable/fromEvent.ts", "node_modules/rxjs/src/internal/observable/fromEventPattern.ts", "node_modules/rxjs/src/internal/observable/timer.ts", "node_modules/rxjs/src/internal/observable/merge.ts", "node_modules/rxjs/src/internal/observable/never.ts", "node_modules/rxjs/src/internal/util/argsOrArgArray.ts", "node_modules/rxjs/src/internal/operators/filter.ts", "node_modules/rxjs/src/internal/observable/zip.ts", "node_modules/rxjs/src/internal/operators/audit.ts", "node_modules/rxjs/src/internal/operators/auditTime.ts", "node_modules/rxjs/src/internal/operators/bufferCount.ts", "node_modules/rxjs/src/internal/operators/catchError.ts", "node_modules/rxjs/src/internal/operators/scanInternals.ts", "node_modules/rxjs/src/internal/operators/combineLatest.ts", "node_modules/rxjs/src/internal/operators/combineLatestWith.ts", "node_modules/rxjs/src/internal/operators/debounceTime.ts", "node_modules/rxjs/src/internal/operators/defaultIfEmpty.ts", "node_modules/rxjs/src/internal/operators/take.ts", "node_modules/rxjs/src/internal/operators/ignoreElements.ts", "node_modules/rxjs/src/internal/operators/mapTo.ts", "node_modules/rxjs/src/internal/operators/delayWhen.ts", "node_modules/rxjs/src/internal/operators/delay.ts", "node_modules/rxjs/src/internal/operators/distinctUntilChanged.ts", "node_modules/rxjs/src/internal/operators/distinctUntilKeyChanged.ts", "node_modules/rxjs/src/internal/operators/throwIfEmpty.ts", "node_modules/rxjs/src/internal/operators/endWith.ts", "node_modules/rxjs/src/internal/operators/finalize.ts", "node_modules/rxjs/src/internal/operators/first.ts", "node_modules/rxjs/src/internal/operators/takeLast.ts", "node_modules/rxjs/src/internal/operators/merge.ts", "node_modules/rxjs/src/internal/operators/mergeWith.ts", "node_modules/rxjs/src/internal/operators/repeat.ts", "node_modules/rxjs/src/internal/operators/scan.ts", "node_modules/rxjs/src/internal/operators/share.ts", "node_modules/rxjs/src/internal/operators/shareReplay.ts", "node_modules/rxjs/src/internal/operators/skip.ts", "node_modules/rxjs/src/internal/operators/skipUntil.ts", "node_modules/rxjs/src/internal/operators/startWith.ts", "node_modules/rxjs/src/internal/operators/switchMap.ts", "node_modules/rxjs/src/internal/operators/takeUntil.ts", "node_modules/rxjs/src/internal/operators/takeWhile.ts", "node_modules/rxjs/src/internal/operators/tap.ts", "node_modules/rxjs/src/internal/operators/throttle.ts", "node_modules/rxjs/src/internal/operators/throttleTime.ts", "node_modules/rxjs/src/internal/operators/withLatestFrom.ts", "node_modules/rxjs/src/internal/operators/zip.ts", "node_modules/rxjs/src/internal/operators/zipWith.ts", "src/templates/assets/javascripts/browser/document/index.ts", "src/templates/assets/javascripts/browser/element/_/index.ts", "src/templates/assets/javascripts/browser/element/focus/index.ts", "src/templates/assets/javascripts/browser/element/hover/index.ts", "src/templates/assets/javascripts/browser/element/offset/_/index.ts", "src/templates/assets/javascripts/browser/element/offset/content/index.ts", "src/templates/assets/javascripts/utilities/h/index.ts", "src/templates/assets/javascripts/utilities/round/index.ts", "src/templates/assets/javascripts/browser/script/index.ts", "src/templates/assets/javascripts/browser/element/size/_/index.ts", "src/templates/assets/javascripts/browser/element/size/content/index.ts", "src/templates/assets/javascripts/browser/element/visibility/index.ts", "src/templates/assets/javascripts/browser/toggle/index.ts", "src/templates/assets/javascripts/browser/keyboard/index.ts", "src/templates/assets/javascripts/browser/location/_/index.ts", "src/templates/assets/javascripts/browser/location/hash/index.ts", "src/templates/assets/javascripts/browser/media/index.ts", "src/templates/assets/javascripts/browser/request/index.ts", "src/templates/assets/javascripts/browser/viewport/offset/index.ts", "src/templates/assets/javascripts/browser/viewport/size/index.ts", "src/templates/assets/javascripts/browser/viewport/_/index.ts", "src/templates/assets/javascripts/browser/viewport/at/index.ts", "src/templates/assets/javascripts/browser/worker/index.ts", "src/templates/assets/javascripts/_/index.ts", "src/templates/assets/javascripts/components/_/index.ts", "src/templates/assets/javascripts/components/announce/index.ts", "src/templates/assets/javascripts/components/consent/index.ts", "src/templates/assets/javascripts/templates/tooltip/index.tsx", "src/templates/assets/javascripts/templates/annotation/index.tsx", "src/templates/assets/javascripts/templates/clipboard/index.tsx", "src/templates/assets/javascripts/templates/search/index.tsx", "src/templates/assets/javascripts/templates/source/index.tsx", "src/templates/assets/javascripts/templates/tabbed/index.tsx", "src/templates/assets/javascripts/templates/table/index.tsx", "src/templates/assets/javascripts/templates/version/index.tsx", "src/templates/assets/javascripts/components/tooltip/index.ts", "src/templates/assets/javascripts/components/content/annotation/_/index.ts", "src/templates/assets/javascripts/components/content/annotation/list/index.ts", "src/templates/assets/javascripts/components/content/annotation/block/index.ts", "src/templates/assets/javascripts/components/content/code/_/index.ts", "src/templates/assets/javascripts/components/content/details/index.ts", "src/templates/assets/javascripts/components/content/mermaid/index.css", "src/templates/assets/javascripts/components/content/mermaid/index.ts", "src/templates/assets/javascripts/components/content/table/index.ts", "src/templates/assets/javascripts/components/content/tabs/index.ts", "src/templates/assets/javascripts/components/content/_/index.ts", "src/templates/assets/javascripts/components/dialog/index.ts", "src/templates/assets/javascripts/components/header/_/index.ts", "src/templates/assets/javascripts/components/header/title/index.ts", "src/templates/assets/javascripts/components/main/index.ts", "src/templates/assets/javascripts/components/palette/index.ts", "src/templates/assets/javascripts/components/progress/index.ts", "src/templates/assets/javascripts/integrations/clipboard/index.ts", "src/templates/assets/javascripts/integrations/sitemap/index.ts", "src/templates/assets/javascripts/integrations/instant/index.ts", "src/templates/assets/javascripts/integrations/search/highlighter/index.ts", "src/templates/assets/javascripts/integrations/search/worker/message/index.ts", "src/templates/assets/javascripts/integrations/search/worker/_/index.ts", "src/templates/assets/javascripts/integrations/version/index.ts", "src/templates/assets/javascripts/components/search/query/index.ts", "src/templates/assets/javascripts/components/search/result/index.ts", "src/templates/assets/javascripts/components/search/share/index.ts", "src/templates/assets/javascripts/components/search/suggest/index.ts", "src/templates/assets/javascripts/components/search/_/index.ts", "src/templates/assets/javascripts/components/search/highlight/index.ts", "src/templates/assets/javascripts/components/sidebar/index.ts", "src/templates/assets/javascripts/components/source/facts/github/index.ts", "src/templates/assets/javascripts/components/source/facts/gitlab/index.ts", "src/templates/assets/javascripts/components/source/facts/_/index.ts", "src/templates/assets/javascripts/components/source/_/index.ts", "src/templates/assets/javascripts/components/tabs/index.ts", "src/templates/assets/javascripts/components/toc/index.ts", "src/templates/assets/javascripts/components/top/index.ts", "src/templates/assets/javascripts/patches/ellipsis/index.ts", "src/templates/assets/javascripts/patches/indeterminate/index.ts", "src/templates/assets/javascripts/patches/scrollfix/index.ts", "src/templates/assets/javascripts/patches/scrolllock/index.ts", "src/templates/assets/javascripts/polyfills/index.ts"],
+  "sourcesContent": ["(function (global, factory) {\n  typeof exports === 'object' && typeof module !== 'undefined' ? factory() :\n  typeof define === 'function' && define.amd ? define(factory) :\n  (factory());\n}(this, (function () { 'use strict';\n\n  /**\n   * Applies the :focus-visible polyfill at the given scope.\n   * A scope in this case is either the top-level Document or a Shadow Root.\n   *\n   * @param {(Document|ShadowRoot)} scope\n   * @see https://github.com/WICG/focus-visible\n   */\n  function applyFocusVisiblePolyfill(scope) {\n    var hadKeyboardEvent = true;\n    var hadFocusVisibleRecently = false;\n    var hadFocusVisibleRecentlyTimeout = null;\n\n    var inputTypesAllowlist = {\n      text: true,\n      search: true,\n      url: true,\n      tel: true,\n      email: true,\n      password: true,\n      number: true,\n      date: true,\n      month: true,\n      week: true,\n      time: true,\n      datetime: true,\n      'datetime-local': true\n    };\n\n    /**\n     * Helper function for legacy browsers and iframes which sometimes focus\n     * elements like document, body, and non-interactive SVG.\n     * @param {Element} el\n     */\n    function isValidFocusTarget(el) {\n      if (\n        el &&\n        el !== document &&\n        el.nodeName !== 'HTML' &&\n        el.nodeName !== 'BODY' &&\n        'classList' in el &&\n        'contains' in el.classList\n      ) {\n        return true;\n      }\n      return false;\n    }\n\n    /**\n     * Computes whether the given element should automatically trigger the\n     * `focus-visible` class being added, i.e. whether it should always match\n     * `:focus-visible` when focused.\n     * @param {Element} el\n     * @return {boolean}\n     */\n    function focusTriggersKeyboardModality(el) {\n      var type = el.type;\n      var tagName = el.tagName;\n\n      if (tagName === 'INPUT' && inputTypesAllowlist[type] && !el.readOnly) {\n        return true;\n      }\n\n      if (tagName === 'TEXTAREA' && !el.readOnly) {\n        return true;\n      }\n\n      if (el.isContentEditable) {\n        return true;\n      }\n\n      return false;\n    }\n\n    /**\n     * Add the `focus-visible` class to the given element if it was not added by\n     * the author.\n     * @param {Element} el\n     */\n    function addFocusVisibleClass(el) {\n      if (el.classList.contains('focus-visible')) {\n        return;\n      }\n      el.classList.add('focus-visible');\n      el.setAttribute('data-focus-visible-added', '');\n    }\n\n    /**\n     * Remove the `focus-visible` class from the given element if it was not\n     * originally added by the author.\n     * @param {Element} el\n     */\n    function removeFocusVisibleClass(el) {\n      if (!el.hasAttribute('data-focus-visible-added')) {\n        return;\n      }\n      el.classList.remove('focus-visible');\n      el.removeAttribute('data-focus-visible-added');\n    }\n\n    /**\n     * If the most recent user interaction was via the keyboard;\n     * and the key press did not include a meta, alt/option, or control key;\n     * then the modality is keyboard. Otherwise, the modality is not keyboard.\n     * Apply `focus-visible` to any current active element and keep track\n     * of our keyboard modality state with `hadKeyboardEvent`.\n     * @param {KeyboardEvent} e\n     */\n    function onKeyDown(e) {\n      if (e.metaKey || e.altKey || e.ctrlKey) {\n        return;\n      }\n\n      if (isValidFocusTarget(scope.activeElement)) {\n        addFocusVisibleClass(scope.activeElement);\n      }\n\n      hadKeyboardEvent = true;\n    }\n\n    /**\n     * If at any point a user clicks with a pointing device, ensure that we change\n     * the modality away from keyboard.\n     * This avoids the situation where a user presses a key on an already focused\n     * element, and then clicks on a different element, focusing it with a\n     * pointing device, while we still think we're in keyboard modality.\n     * @param {Event} e\n     */\n    function onPointerDown(e) {\n      hadKeyboardEvent = false;\n    }\n\n    /**\n     * On `focus`, add the `focus-visible` class to the target if:\n     * - the target received focus as a result of keyboard navigation, or\n     * - the event target is an element that will likely require interaction\n     *   via the keyboard (e.g. a text box)\n     * @param {Event} e\n     */\n    function onFocus(e) {\n      // Prevent IE from focusing the document or HTML element.\n      if (!isValidFocusTarget(e.target)) {\n        return;\n      }\n\n      if (hadKeyboardEvent || focusTriggersKeyboardModality(e.target)) {\n        addFocusVisibleClass(e.target);\n      }\n    }\n\n    /**\n     * On `blur`, remove the `focus-visible` class from the target.\n     * @param {Event} e\n     */\n    function onBlur(e) {\n      if (!isValidFocusTarget(e.target)) {\n        return;\n      }\n\n      if (\n        e.target.classList.contains('focus-visible') ||\n        e.target.hasAttribute('data-focus-visible-added')\n      ) {\n        // To detect a tab/window switch, we look for a blur event followed\n        // rapidly by a visibility change.\n        // If we don't see a visibility change within 100ms, it's probably a\n        // regular focus change.\n        hadFocusVisibleRecently = true;\n        window.clearTimeout(hadFocusVisibleRecentlyTimeout);\n        hadFocusVisibleRecentlyTimeout = window.setTimeout(function() {\n          hadFocusVisibleRecently = false;\n        }, 100);\n        removeFocusVisibleClass(e.target);\n      }\n    }\n\n    /**\n     * If the user changes tabs, keep track of whether or not the previously\n     * focused element had .focus-visible.\n     * @param {Event} e\n     */\n    function onVisibilityChange(e) {\n      if (document.visibilityState === 'hidden') {\n        // If the tab becomes active again, the browser will handle calling focus\n        // on the element (Safari actually calls it twice).\n        // If this tab change caused a blur on an element with focus-visible,\n        // re-apply the class when the user switches back to the tab.\n        if (hadFocusVisibleRecently) {\n          hadKeyboardEvent = true;\n        }\n        addInitialPointerMoveListeners();\n      }\n    }\n\n    /**\n     * Add a group of listeners to detect usage of any pointing devices.\n     * These listeners will be added when the polyfill first loads, and anytime\n     * the window is blurred, so that they are active when the window regains\n     * focus.\n     */\n    function addInitialPointerMoveListeners() {\n      document.addEventListener('mousemove', onInitialPointerMove);\n      document.addEventListener('mousedown', onInitialPointerMove);\n      document.addEventListener('mouseup', onInitialPointerMove);\n      document.addEventListener('pointermove', onInitialPointerMove);\n      document.addEventListener('pointerdown', onInitialPointerMove);\n      document.addEventListener('pointerup', onInitialPointerMove);\n      document.addEventListener('touchmove', onInitialPointerMove);\n      document.addEventListener('touchstart', onInitialPointerMove);\n      document.addEventListener('touchend', onInitialPointerMove);\n    }\n\n    function removeInitialPointerMoveListeners() {\n      document.removeEventListener('mousemove', onInitialPointerMove);\n      document.removeEventListener('mousedown', onInitialPointerMove);\n      document.removeEventListener('mouseup', onInitialPointerMove);\n      document.removeEventListener('pointermove', onInitialPointerMove);\n      document.removeEventListener('pointerdown', onInitialPointerMove);\n      document.removeEventListener('pointerup', onInitialPointerMove);\n      document.removeEventListener('touchmove', onInitialPointerMove);\n      document.removeEventListener('touchstart', onInitialPointerMove);\n      document.removeEventListener('touchend', onInitialPointerMove);\n    }\n\n    /**\n     * When the polfyill first loads, assume the user is in keyboard modality.\n     * If any event is received from a pointing device (e.g. mouse, pointer,\n     * touch), turn off keyboard modality.\n     * This accounts for situations where focus enters the page from the URL bar.\n     * @param {Event} e\n     */\n    function onInitialPointerMove(e) {\n      // Work around a Safari quirk that fires a mousemove on <html> whenever the\n      // window blurs, even if you're tabbing out of the page. \u00AF\\_(\u30C4)_/\u00AF\n      if (e.target.nodeName && e.target.nodeName.toLowerCase() === 'html') {\n        return;\n      }\n\n      hadKeyboardEvent = false;\n      removeInitialPointerMoveListeners();\n    }\n\n    // For some kinds of state, we are interested in changes at the global scope\n    // only. For example, global pointer input, global key presses and global\n    // visibility change should affect the state at every scope:\n    document.addEventListener('keydown', onKeyDown, true);\n    document.addEventListener('mousedown', onPointerDown, true);\n    document.addEventListener('pointerdown', onPointerDown, true);\n    document.addEventListener('touchstart', onPointerDown, true);\n    document.addEventListener('visibilitychange', onVisibilityChange, true);\n\n    addInitialPointerMoveListeners();\n\n    // For focus and blur, we specifically care about state changes in the local\n    // scope. This is because focus / blur events that originate from within a\n    // shadow root are not re-dispatched from the host element if it was already\n    // the active element in its own scope:\n    scope.addEventListener('focus', onFocus, true);\n    scope.addEventListener('blur', onBlur, true);\n\n    // We detect that a node is a ShadowRoot by ensuring that it is a\n    // DocumentFragment and also has a host property. This check covers native\n    // implementation and polyfill implementation transparently. If we only cared\n    // about the native implementation, we could just check if the scope was\n    // an instance of a ShadowRoot.\n    if (scope.nodeType === Node.DOCUMENT_FRAGMENT_NODE && scope.host) {\n      // Since a ShadowRoot is a special kind of DocumentFragment, it does not\n      // have a root element to add a class to. So, we add this attribute to the\n      // host element instead:\n      scope.host.setAttribute('data-js-focus-visible', '');\n    } else if (scope.nodeType === Node.DOCUMENT_NODE) {\n      document.documentElement.classList.add('js-focus-visible');\n      document.documentElement.setAttribute('data-js-focus-visible', '');\n    }\n  }\n\n  // It is important to wrap all references to global window and document in\n  // these checks to support server-side rendering use cases\n  // @see https://github.com/WICG/focus-visible/issues/199\n  if (typeof window !== 'undefined' && typeof document !== 'undefined') {\n    // Make the polyfill helper globally available. This can be used as a signal\n    // to interested libraries that wish to coordinate with the polyfill for e.g.,\n    // applying the polyfill to a shadow root:\n    window.applyFocusVisiblePolyfill = applyFocusVisiblePolyfill;\n\n    // Notify interested libraries of the polyfill's presence, in case the\n    // polyfill was loaded lazily:\n    var event;\n\n    try {\n      event = new CustomEvent('focus-visible-polyfill-ready');\n    } catch (error) {\n      // IE11 does not support using CustomEvent as a constructor directly:\n      event = document.createEvent('CustomEvent');\n      event.initCustomEvent('focus-visible-polyfill-ready', false, false, {});\n    }\n\n    window.dispatchEvent(event);\n  }\n\n  if (typeof document !== 'undefined') {\n    // Apply the polyfill to the global document, so that no JavaScript\n    // coordination is required to use the polyfill in the top-level document:\n    applyFocusVisiblePolyfill(document);\n  }\n\n})));\n", "/*!\n * clipboard.js v2.0.11\n * https://clipboardjs.com/\n *\n * Licensed MIT \u00A9 Zeno Rocha\n */\n(function webpackUniversalModuleDefinition(root, factory) {\n\tif(typeof exports === 'object' && typeof module === 'object')\n\t\tmodule.exports = factory();\n\telse if(typeof define === 'function' && define.amd)\n\t\tdefine([], factory);\n\telse if(typeof exports === 'object')\n\t\texports[\"ClipboardJS\"] = factory();\n\telse\n\t\troot[\"ClipboardJS\"] = factory();\n})(this, function() {\nreturn /******/ (function() { // webpackBootstrap\n/******/ \tvar __webpack_modules__ = ({\n\n/***/ 686:\n/***/ (function(__unused_webpack_module, __webpack_exports__, __webpack_require__) {\n\n\"use strict\";\n\n// EXPORTS\n__webpack_require__.d(__webpack_exports__, {\n  \"default\": function() { return /* binding */ clipboard; }\n});\n\n// EXTERNAL MODULE: ./node_modules/tiny-emitter/index.js\nvar tiny_emitter = __webpack_require__(279);\nvar tiny_emitter_default = /*#__PURE__*/__webpack_require__.n(tiny_emitter);\n// EXTERNAL MODULE: ./node_modules/good-listener/src/listen.js\nvar listen = __webpack_require__(370);\nvar listen_default = /*#__PURE__*/__webpack_require__.n(listen);\n// EXTERNAL MODULE: ./node_modules/select/src/select.js\nvar src_select = __webpack_require__(817);\nvar select_default = /*#__PURE__*/__webpack_require__.n(src_select);\n;// CONCATENATED MODULE: ./src/common/command.js\n/**\n * Executes a given operation type.\n * @param {String} type\n * @return {Boolean}\n */\nfunction command(type) {\n  try {\n    return document.execCommand(type);\n  } catch (err) {\n    return false;\n  }\n}\n;// CONCATENATED MODULE: ./src/actions/cut.js\n\n\n/**\n * Cut action wrapper.\n * @param {String|HTMLElement} target\n * @return {String}\n */\n\nvar ClipboardActionCut = function ClipboardActionCut(target) {\n  var selectedText = select_default()(target);\n  command('cut');\n  return selectedText;\n};\n\n/* harmony default export */ var actions_cut = (ClipboardActionCut);\n;// CONCATENATED MODULE: ./src/common/create-fake-element.js\n/**\n * Creates a fake textarea element with a value.\n * @param {String} value\n * @return {HTMLElement}\n */\nfunction createFakeElement(value) {\n  var isRTL = document.documentElement.getAttribute('dir') === 'rtl';\n  var fakeElement = document.createElement('textarea'); // Prevent zooming on iOS\n\n  fakeElement.style.fontSize = '12pt'; // Reset box model\n\n  fakeElement.style.border = '0';\n  fakeElement.style.padding = '0';\n  fakeElement.style.margin = '0'; // Move element out of screen horizontally\n\n  fakeElement.style.position = 'absolute';\n  fakeElement.style[isRTL ? 'right' : 'left'] = '-9999px'; // Move element to the same position vertically\n\n  var yPosition = window.pageYOffset || document.documentElement.scrollTop;\n  fakeElement.style.top = \"\".concat(yPosition, \"px\");\n  fakeElement.setAttribute('readonly', '');\n  fakeElement.value = value;\n  return fakeElement;\n}\n;// CONCATENATED MODULE: ./src/actions/copy.js\n\n\n\n/**\n * Create fake copy action wrapper using a fake element.\n * @param {String} target\n * @param {Object} options\n * @return {String}\n */\n\nvar fakeCopyAction = function fakeCopyAction(value, options) {\n  var fakeElement = createFakeElement(value);\n  options.container.appendChild(fakeElement);\n  var selectedText = select_default()(fakeElement);\n  command('copy');\n  fakeElement.remove();\n  return selectedText;\n};\n/**\n * Copy action wrapper.\n * @param {String|HTMLElement} target\n * @param {Object} options\n * @return {String}\n */\n\n\nvar ClipboardActionCopy = function ClipboardActionCopy(target) {\n  var options = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : {\n    container: document.body\n  };\n  var selectedText = '';\n\n  if (typeof target === 'string') {\n    selectedText = fakeCopyAction(target, options);\n  } else if (target instanceof HTMLInputElement && !['text', 'search', 'url', 'tel', 'password'].includes(target === null || target === void 0 ? void 0 : target.type)) {\n    // If input type doesn't support `setSelectionRange`. Simulate it. https://developer.mozilla.org/en-US/docs/Web/API/HTMLInputElement/setSelectionRange\n    selectedText = fakeCopyAction(target.value, options);\n  } else {\n    selectedText = select_default()(target);\n    command('copy');\n  }\n\n  return selectedText;\n};\n\n/* harmony default export */ var actions_copy = (ClipboardActionCopy);\n;// CONCATENATED MODULE: ./src/actions/default.js\nfunction _typeof(obj) { \"@babel/helpers - typeof\"; if (typeof Symbol === \"function\" && typeof Symbol.iterator === \"symbol\") { _typeof = function _typeof(obj) { return typeof obj; }; } else { _typeof = function _typeof(obj) { return obj && typeof Symbol === \"function\" && obj.constructor === Symbol && obj !== Symbol.prototype ? \"symbol\" : typeof obj; }; } return _typeof(obj); }\n\n\n\n/**\n * Inner function which performs selection from either `text` or `target`\n * properties and then executes copy or cut operations.\n * @param {Object} options\n */\n\nvar ClipboardActionDefault = function ClipboardActionDefault() {\n  var options = arguments.length > 0 && arguments[0] !== undefined ? arguments[0] : {};\n  // Defines base properties passed from constructor.\n  var _options$action = options.action,\n      action = _options$action === void 0 ? 'copy' : _options$action,\n      container = options.container,\n      target = options.target,\n      text = options.text; // Sets the `action` to be performed which can be either 'copy' or 'cut'.\n\n  if (action !== 'copy' && action !== 'cut') {\n    throw new Error('Invalid \"action\" value, use either \"copy\" or \"cut\"');\n  } // Sets the `target` property using an element that will be have its content copied.\n\n\n  if (target !== undefined) {\n    if (target && _typeof(target) === 'object' && target.nodeType === 1) {\n      if (action === 'copy' && target.hasAttribute('disabled')) {\n        throw new Error('Invalid \"target\" attribute. Please use \"readonly\" instead of \"disabled\" attribute');\n      }\n\n      if (action === 'cut' && (target.hasAttribute('readonly') || target.hasAttribute('disabled'))) {\n        throw new Error('Invalid \"target\" attribute. You can\\'t cut text from elements with \"readonly\" or \"disabled\" attributes');\n      }\n    } else {\n      throw new Error('Invalid \"target\" value, use a valid Element');\n    }\n  } // Define selection strategy based on `text` property.\n\n\n  if (text) {\n    return actions_copy(text, {\n      container: container\n    });\n  } // Defines which selection strategy based on `target` property.\n\n\n  if (target) {\n    return action === 'cut' ? actions_cut(target) : actions_copy(target, {\n      container: container\n    });\n  }\n};\n\n/* harmony default export */ var actions_default = (ClipboardActionDefault);\n;// CONCATENATED MODULE: ./src/clipboard.js\nfunction clipboard_typeof(obj) { \"@babel/helpers - typeof\"; if (typeof Symbol === \"function\" && typeof Symbol.iterator === \"symbol\") { clipboard_typeof = function _typeof(obj) { return typeof obj; }; } else { clipboard_typeof = function _typeof(obj) { return obj && typeof Symbol === \"function\" && obj.constructor === Symbol && obj !== Symbol.prototype ? \"symbol\" : typeof obj; }; } return clipboard_typeof(obj); }\n\nfunction _classCallCheck(instance, Constructor) { if (!(instance instanceof Constructor)) { throw new TypeError(\"Cannot call a class as a function\"); } }\n\nfunction _defineProperties(target, props) { for (var i = 0; i < props.length; i++) { var descriptor = props[i]; descriptor.enumerable = descriptor.enumerable || false; descriptor.configurable = true; if (\"value\" in descriptor) descriptor.writable = true; Object.defineProperty(target, descriptor.key, descriptor); } }\n\nfunction _createClass(Constructor, protoProps, staticProps) { if (protoProps) _defineProperties(Constructor.prototype, protoProps); if (staticProps) _defineProperties(Constructor, staticProps); return Constructor; }\n\nfunction _inherits(subClass, superClass) { if (typeof superClass !== \"function\" && superClass !== null) { throw new TypeError(\"Super expression must either be null or a function\"); } subClass.prototype = Object.create(superClass && superClass.prototype, { constructor: { value: subClass, writable: true, configurable: true } }); if (superClass) _setPrototypeOf(subClass, superClass); }\n\nfunction _setPrototypeOf(o, p) { _setPrototypeOf = Object.setPrototypeOf || function _setPrototypeOf(o, p) { o.__proto__ = p; return o; }; return _setPrototypeOf(o, p); }\n\nfunction _createSuper(Derived) { var hasNativeReflectConstruct = _isNativeReflectConstruct(); return function _createSuperInternal() { var Super = _getPrototypeOf(Derived), result; if (hasNativeReflectConstruct) { var NewTarget = _getPrototypeOf(this).constructor; result = Reflect.construct(Super, arguments, NewTarget); } else { result = Super.apply(this, arguments); } return _possibleConstructorReturn(this, result); }; }\n\nfunction _possibleConstructorReturn(self, call) { if (call && (clipboard_typeof(call) === \"object\" || typeof call === \"function\")) { return call; } return _assertThisInitialized(self); }\n\nfunction _assertThisInitialized(self) { if (self === void 0) { throw new ReferenceError(\"this hasn't been initialised - super() hasn't been called\"); } return self; }\n\nfunction _isNativeReflectConstruct() { if (typeof Reflect === \"undefined\" || !Reflect.construct) return false; if (Reflect.construct.sham) return false; if (typeof Proxy === \"function\") return true; try { Date.prototype.toString.call(Reflect.construct(Date, [], function () {})); return true; } catch (e) { return false; } }\n\nfunction _getPrototypeOf(o) { _getPrototypeOf = Object.setPrototypeOf ? Object.getPrototypeOf : function _getPrototypeOf(o) { return o.__proto__ || Object.getPrototypeOf(o); }; return _getPrototypeOf(o); }\n\n\n\n\n\n\n/**\n * Helper function to retrieve attribute value.\n * @param {String} suffix\n * @param {Element} element\n */\n\nfunction getAttributeValue(suffix, element) {\n  var attribute = \"data-clipboard-\".concat(suffix);\n\n  if (!element.hasAttribute(attribute)) {\n    return;\n  }\n\n  return element.getAttribute(attribute);\n}\n/**\n * Base class which takes one or more elements, adds event listeners to them,\n * and instantiates a new `ClipboardAction` on each click.\n */\n\n\nvar Clipboard = /*#__PURE__*/function (_Emitter) {\n  _inherits(Clipboard, _Emitter);\n\n  var _super = _createSuper(Clipboard);\n\n  /**\n   * @param {String|HTMLElement|HTMLCollection|NodeList} trigger\n   * @param {Object} options\n   */\n  function Clipboard(trigger, options) {\n    var _this;\n\n    _classCallCheck(this, Clipboard);\n\n    _this = _super.call(this);\n\n    _this.resolveOptions(options);\n\n    _this.listenClick(trigger);\n\n    return _this;\n  }\n  /**\n   * Defines if attributes would be resolved using internal setter functions\n   * or custom functions that were passed in the constructor.\n   * @param {Object} options\n   */\n\n\n  _createClass(Clipboard, [{\n    key: \"resolveOptions\",\n    value: function resolveOptions() {\n      var options = arguments.length > 0 && arguments[0] !== undefined ? arguments[0] : {};\n      this.action = typeof options.action === 'function' ? options.action : this.defaultAction;\n      this.target = typeof options.target === 'function' ? options.target : this.defaultTarget;\n      this.text = typeof options.text === 'function' ? options.text : this.defaultText;\n      this.container = clipboard_typeof(options.container) === 'object' ? options.container : document.body;\n    }\n    /**\n     * Adds a click event listener to the passed trigger.\n     * @param {String|HTMLElement|HTMLCollection|NodeList} trigger\n     */\n\n  }, {\n    key: \"listenClick\",\n    value: function listenClick(trigger) {\n      var _this2 = this;\n\n      this.listener = listen_default()(trigger, 'click', function (e) {\n        return _this2.onClick(e);\n      });\n    }\n    /**\n     * Defines a new `ClipboardAction` on each click event.\n     * @param {Event} e\n     */\n\n  }, {\n    key: \"onClick\",\n    value: function onClick(e) {\n      var trigger = e.delegateTarget || e.currentTarget;\n      var action = this.action(trigger) || 'copy';\n      var text = actions_default({\n        action: action,\n        container: this.container,\n        target: this.target(trigger),\n        text: this.text(trigger)\n      }); // Fires an event based on the copy operation result.\n\n      this.emit(text ? 'success' : 'error', {\n        action: action,\n        text: text,\n        trigger: trigger,\n        clearSelection: function clearSelection() {\n          if (trigger) {\n            trigger.focus();\n          }\n\n          window.getSelection().removeAllRanges();\n        }\n      });\n    }\n    /**\n     * Default `action` lookup function.\n     * @param {Element} trigger\n     */\n\n  }, {\n    key: \"defaultAction\",\n    value: function defaultAction(trigger) {\n      return getAttributeValue('action', trigger);\n    }\n    /**\n     * Default `target` lookup function.\n     * @param {Element} trigger\n     */\n\n  }, {\n    key: \"defaultTarget\",\n    value: function defaultTarget(trigger) {\n      var selector = getAttributeValue('target', trigger);\n\n      if (selector) {\n        return document.querySelector(selector);\n      }\n    }\n    /**\n     * Allow fire programmatically a copy action\n     * @param {String|HTMLElement} target\n     * @param {Object} options\n     * @returns Text copied.\n     */\n\n  }, {\n    key: \"defaultText\",\n\n    /**\n     * Default `text` lookup function.\n     * @param {Element} trigger\n     */\n    value: function defaultText(trigger) {\n      return getAttributeValue('text', trigger);\n    }\n    /**\n     * Destroy lifecycle.\n     */\n\n  }, {\n    key: \"destroy\",\n    value: function destroy() {\n      this.listener.destroy();\n    }\n  }], [{\n    key: \"copy\",\n    value: function copy(target) {\n      var options = arguments.length > 1 && arguments[1] !== undefined ? arguments[1] : {\n        container: document.body\n      };\n      return actions_copy(target, options);\n    }\n    /**\n     * Allow fire programmatically a cut action\n     * @param {String|HTMLElement} target\n     * @returns Text cutted.\n     */\n\n  }, {\n    key: \"cut\",\n    value: function cut(target) {\n      return actions_cut(target);\n    }\n    /**\n     * Returns the support of the given action, or all actions if no action is\n     * given.\n     * @param {String} [action]\n     */\n\n  }, {\n    key: \"isSupported\",\n    value: function isSupported() {\n      var action = arguments.length > 0 && arguments[0] !== undefined ? arguments[0] : ['copy', 'cut'];\n      var actions = typeof action === 'string' ? [action] : action;\n      var support = !!document.queryCommandSupported;\n      actions.forEach(function (action) {\n        support = support && !!document.queryCommandSupported(action);\n      });\n      return support;\n    }\n  }]);\n\n  return Clipboard;\n}((tiny_emitter_default()));\n\n/* harmony default export */ var clipboard = (Clipboard);\n\n/***/ }),\n\n/***/ 828:\n/***/ (function(module) {\n\nvar DOCUMENT_NODE_TYPE = 9;\n\n/**\n * A polyfill for Element.matches()\n */\nif (typeof Element !== 'undefined' && !Element.prototype.matches) {\n    var proto = Element.prototype;\n\n    proto.matches = proto.matchesSelector ||\n                    proto.mozMatchesSelector ||\n                    proto.msMatchesSelector ||\n                    proto.oMatchesSelector ||\n                    proto.webkitMatchesSelector;\n}\n\n/**\n * Finds the closest parent that matches a selector.\n *\n * @param {Element} element\n * @param {String} selector\n * @return {Function}\n */\nfunction closest (element, selector) {\n    while (element && element.nodeType !== DOCUMENT_NODE_TYPE) {\n        if (typeof element.matches === 'function' &&\n            element.matches(selector)) {\n          return element;\n        }\n        element = element.parentNode;\n    }\n}\n\nmodule.exports = closest;\n\n\n/***/ }),\n\n/***/ 438:\n/***/ (function(module, __unused_webpack_exports, __webpack_require__) {\n\nvar closest = __webpack_require__(828);\n\n/**\n * Delegates event to a selector.\n *\n * @param {Element} element\n * @param {String} selector\n * @param {String} type\n * @param {Function} callback\n * @param {Boolean} useCapture\n * @return {Object}\n */\nfunction _delegate(element, selector, type, callback, useCapture) {\n    var listenerFn = listener.apply(this, arguments);\n\n    element.addEventListener(type, listenerFn, useCapture);\n\n    return {\n        destroy: function() {\n            element.removeEventListener(type, listenerFn, useCapture);\n        }\n    }\n}\n\n/**\n * Delegates event to a selector.\n *\n * @param {Element|String|Array} [elements]\n * @param {String} selector\n * @param {String} type\n * @param {Function} callback\n * @param {Boolean} useCapture\n * @return {Object}\n */\nfunction delegate(elements, selector, type, callback, useCapture) {\n    // Handle the regular Element usage\n    if (typeof elements.addEventListener === 'function') {\n        return _delegate.apply(null, arguments);\n    }\n\n    // Handle Element-less usage, it defaults to global delegation\n    if (typeof type === 'function') {\n        // Use `document` as the first parameter, then apply arguments\n        // This is a short way to .unshift `arguments` without running into deoptimizations\n        return _delegate.bind(null, document).apply(null, arguments);\n    }\n\n    // Handle Selector-based usage\n    if (typeof elements === 'string') {\n        elements = document.querySelectorAll(elements);\n    }\n\n    // Handle Array-like based usage\n    return Array.prototype.map.call(elements, function (element) {\n        return _delegate(element, selector, type, callback, useCapture);\n    });\n}\n\n/**\n * Finds closest match and invokes callback.\n *\n * @param {Element} element\n * @param {String} selector\n * @param {String} type\n * @param {Function} callback\n * @return {Function}\n */\nfunction listener(element, selector, type, callback) {\n    return function(e) {\n        e.delegateTarget = closest(e.target, selector);\n\n        if (e.delegateTarget) {\n            callback.call(element, e);\n        }\n    }\n}\n\nmodule.exports = delegate;\n\n\n/***/ }),\n\n/***/ 879:\n/***/ (function(__unused_webpack_module, exports) {\n\n/**\n * Check if argument is a HTML element.\n *\n * @param {Object} value\n * @return {Boolean}\n */\nexports.node = function(value) {\n    return value !== undefined\n        && value instanceof HTMLElement\n        && value.nodeType === 1;\n};\n\n/**\n * Check if argument is a list of HTML elements.\n *\n * @param {Object} value\n * @return {Boolean}\n */\nexports.nodeList = function(value) {\n    var type = Object.prototype.toString.call(value);\n\n    return value !== undefined\n        && (type === '[object NodeList]' || type === '[object HTMLCollection]')\n        && ('length' in value)\n        && (value.length === 0 || exports.node(value[0]));\n};\n\n/**\n * Check if argument is a string.\n *\n * @param {Object} value\n * @return {Boolean}\n */\nexports.string = function(value) {\n    return typeof value === 'string'\n        || value instanceof String;\n};\n\n/**\n * Check if argument is a function.\n *\n * @param {Object} value\n * @return {Boolean}\n */\nexports.fn = function(value) {\n    var type = Object.prototype.toString.call(value);\n\n    return type === '[object Function]';\n};\n\n\n/***/ }),\n\n/***/ 370:\n/***/ (function(module, __unused_webpack_exports, __webpack_require__) {\n\nvar is = __webpack_require__(879);\nvar delegate = __webpack_require__(438);\n\n/**\n * Validates all params and calls the right\n * listener function based on its target type.\n *\n * @param {String|HTMLElement|HTMLCollection|NodeList} target\n * @param {String} type\n * @param {Function} callback\n * @return {Object}\n */\nfunction listen(target, type, callback) {\n    if (!target && !type && !callback) {\n        throw new Error('Missing required arguments');\n    }\n\n    if (!is.string(type)) {\n        throw new TypeError('Second argument must be a String');\n    }\n\n    if (!is.fn(callback)) {\n        throw new TypeError('Third argument must be a Function');\n    }\n\n    if (is.node(target)) {\n        return listenNode(target, type, callback);\n    }\n    else if (is.nodeList(target)) {\n        return listenNodeList(target, type, callback);\n    }\n    else if (is.string(target)) {\n        return listenSelector(target, type, callback);\n    }\n    else {\n        throw new TypeError('First argument must be a String, HTMLElement, HTMLCollection, or NodeList');\n    }\n}\n\n/**\n * Adds an event listener to a HTML element\n * and returns a remove listener function.\n *\n * @param {HTMLElement} node\n * @param {String} type\n * @param {Function} callback\n * @return {Object}\n */\nfunction listenNode(node, type, callback) {\n    node.addEventListener(type, callback);\n\n    return {\n        destroy: function() {\n            node.removeEventListener(type, callback);\n        }\n    }\n}\n\n/**\n * Add an event listener to a list of HTML elements\n * and returns a remove listener function.\n *\n * @param {NodeList|HTMLCollection} nodeList\n * @param {String} type\n * @param {Function} callback\n * @return {Object}\n */\nfunction listenNodeList(nodeList, type, callback) {\n    Array.prototype.forEach.call(nodeList, function(node) {\n        node.addEventListener(type, callback);\n    });\n\n    return {\n        destroy: function() {\n            Array.prototype.forEach.call(nodeList, function(node) {\n                node.removeEventListener(type, callback);\n            });\n        }\n    }\n}\n\n/**\n * Add an event listener to a selector\n * and returns a remove listener function.\n *\n * @param {String} selector\n * @param {String} type\n * @param {Function} callback\n * @return {Object}\n */\nfunction listenSelector(selector, type, callback) {\n    return delegate(document.body, selector, type, callback);\n}\n\nmodule.exports = listen;\n\n\n/***/ }),\n\n/***/ 817:\n/***/ (function(module) {\n\nfunction select(element) {\n    var selectedText;\n\n    if (element.nodeName === 'SELECT') {\n        element.focus();\n\n        selectedText = element.value;\n    }\n    else if (element.nodeName === 'INPUT' || element.nodeName === 'TEXTAREA') {\n        var isReadOnly = element.hasAttribute('readonly');\n\n        if (!isReadOnly) {\n            element.setAttribute('readonly', '');\n        }\n\n        element.select();\n        element.setSelectionRange(0, element.value.length);\n\n        if (!isReadOnly) {\n            element.removeAttribute('readonly');\n        }\n\n        selectedText = element.value;\n    }\n    else {\n        if (element.hasAttribute('contenteditable')) {\n            element.focus();\n        }\n\n        var selection = window.getSelection();\n        var range = document.createRange();\n\n        range.selectNodeContents(element);\n        selection.removeAllRanges();\n        selection.addRange(range);\n\n        selectedText = selection.toString();\n    }\n\n    return selectedText;\n}\n\nmodule.exports = select;\n\n\n/***/ }),\n\n/***/ 279:\n/***/ (function(module) {\n\nfunction E () {\n  // Keep this empty so it's easier to inherit from\n  // (via https://github.com/lipsmack from https://github.com/scottcorgan/tiny-emitter/issues/3)\n}\n\nE.prototype = {\n  on: function (name, callback, ctx) {\n    var e = this.e || (this.e = {});\n\n    (e[name] || (e[name] = [])).push({\n      fn: callback,\n      ctx: ctx\n    });\n\n    return this;\n  },\n\n  once: function (name, callback, ctx) {\n    var self = this;\n    function listener () {\n      self.off(name, listener);\n      callback.apply(ctx, arguments);\n    };\n\n    listener._ = callback\n    return this.on(name, listener, ctx);\n  },\n\n  emit: function (name) {\n    var data = [].slice.call(arguments, 1);\n    var evtArr = ((this.e || (this.e = {}))[name] || []).slice();\n    var i = 0;\n    var len = evtArr.length;\n\n    for (i; i < len; i++) {\n      evtArr[i].fn.apply(evtArr[i].ctx, data);\n    }\n\n    return this;\n  },\n\n  off: function (name, callback) {\n    var e = this.e || (this.e = {});\n    var evts = e[name];\n    var liveEvents = [];\n\n    if (evts && callback) {\n      for (var i = 0, len = evts.length; i < len; i++) {\n        if (evts[i].fn !== callback && evts[i].fn._ !== callback)\n          liveEvents.push(evts[i]);\n      }\n    }\n\n    // Remove event from queue to prevent memory leak\n    // Suggested by https://github.com/lazd\n    // Ref: https://github.com/scottcorgan/tiny-emitter/commit/c6ebfaa9bc973b33d110a84a307742b7cf94c953#commitcomment-5024910\n\n    (liveEvents.length)\n      ? e[name] = liveEvents\n      : delete e[name];\n\n    return this;\n  }\n};\n\nmodule.exports = E;\nmodule.exports.TinyEmitter = E;\n\n\n/***/ })\n\n/******/ \t});\n/************************************************************************/\n/******/ \t// The module cache\n/******/ \tvar __webpack_module_cache__ = {};\n/******/ \t\n/******/ \t// The require function\n/******/ \tfunction __webpack_require__(moduleId) {\n/******/ \t\t// Check if module is in cache\n/******/ \t\tif(__webpack_module_cache__[moduleId]) {\n/******/ \t\t\treturn __webpack_module_cache__[moduleId].exports;\n/******/ \t\t}\n/******/ \t\t// Create a new module (and put it into the cache)\n/******/ \t\tvar module = __webpack_module_cache__[moduleId] = {\n/******/ \t\t\t// no module.id needed\n/******/ \t\t\t// no module.loaded needed\n/******/ \t\t\texports: {}\n/******/ \t\t};\n/******/ \t\n/******/ \t\t// Execute the module function\n/******/ \t\t__webpack_modules__[moduleId](module, module.exports, __webpack_require__);\n/******/ \t\n/******/ \t\t// Return the exports of the module\n/******/ \t\treturn module.exports;\n/******/ \t}\n/******/ \t\n/************************************************************************/\n/******/ \t/* webpack/runtime/compat get default export */\n/******/ \t!function() {\n/******/ \t\t// getDefaultExport function for compatibility with non-harmony modules\n/******/ \t\t__webpack_require__.n = function(module) {\n/******/ \t\t\tvar getter = module && module.__esModule ?\n/******/ \t\t\t\tfunction() { return module['default']; } :\n/******/ \t\t\t\tfunction() { return module; };\n/******/ \t\t\t__webpack_require__.d(getter, { a: getter });\n/******/ \t\t\treturn getter;\n/******/ \t\t};\n/******/ \t}();\n/******/ \t\n/******/ \t/* webpack/runtime/define property getters */\n/******/ \t!function() {\n/******/ \t\t// define getter functions for harmony exports\n/******/ \t\t__webpack_require__.d = function(exports, definition) {\n/******/ \t\t\tfor(var key in definition) {\n/******/ \t\t\t\tif(__webpack_require__.o(definition, key) && !__webpack_require__.o(exports, key)) {\n/******/ \t\t\t\t\tObject.defineProperty(exports, key, { enumerable: true, get: definition[key] });\n/******/ \t\t\t\t}\n/******/ \t\t\t}\n/******/ \t\t};\n/******/ \t}();\n/******/ \t\n/******/ \t/* webpack/runtime/hasOwnProperty shorthand */\n/******/ \t!function() {\n/******/ \t\t__webpack_require__.o = function(obj, prop) { return Object.prototype.hasOwnProperty.call(obj, prop); }\n/******/ \t}();\n/******/ \t\n/************************************************************************/\n/******/ \t// module exports must be returned from runtime so entry inlining is disabled\n/******/ \t// startup\n/******/ \t// Load entry module and return exports\n/******/ \treturn __webpack_require__(686);\n/******/ })()\n.default;\n});", "/*!\n * escape-html\n * Copyright(c) 2012-2013 TJ Holowaychuk\n * Copyright(c) 2015 Andreas Lubbe\n * Copyright(c) 2015 Tiancheng \"Timothy\" Gu\n * MIT Licensed\n */\n\n'use strict';\n\n/**\n * Module variables.\n * @private\n */\n\nvar matchHtmlRegExp = /[\"'&<>]/;\n\n/**\n * Module exports.\n * @public\n */\n\nmodule.exports = escapeHtml;\n\n/**\n * Escape special characters in the given string of html.\n *\n * @param  {string} string The string to escape for inserting into HTML\n * @return {string}\n * @public\n */\n\nfunction escapeHtml(string) {\n  var str = '' + string;\n  var match = matchHtmlRegExp.exec(str);\n\n  if (!match) {\n    return str;\n  }\n\n  var escape;\n  var html = '';\n  var index = 0;\n  var lastIndex = 0;\n\n  for (index = match.index; index < str.length; index++) {\n    switch (str.charCodeAt(index)) {\n      case 34: // \"\n        escape = '&quot;';\n        break;\n      case 38: // &\n        escape = '&amp;';\n        break;\n      case 39: // '\n        escape = '&#39;';\n        break;\n      case 60: // <\n        escape = '&lt;';\n        break;\n      case 62: // >\n        escape = '&gt;';\n        break;\n      default:\n        continue;\n    }\n\n    if (lastIndex !== index) {\n      html += str.substring(lastIndex, index);\n    }\n\n    lastIndex = index + 1;\n    html += escape;\n  }\n\n  return lastIndex !== index\n    ? html + str.substring(lastIndex, index)\n    : html;\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport \"focus-visible\"\n\nimport {\n  EMPTY,\n  NEVER,\n  Observable,\n  Subject,\n  defer,\n  delay,\n  filter,\n  map,\n  merge,\n  mergeWith,\n  shareReplay,\n  switchMap\n} from \"rxjs\"\n\nimport { configuration, feature } from \"./_\"\nimport {\n  at,\n  getActiveElement,\n  getOptionalElement,\n  requestJSON,\n  setLocation,\n  setToggle,\n  watchDocument,\n  watchKeyboard,\n  watchLocation,\n  watchLocationTarget,\n  watchMedia,\n  watchPrint,\n  watchScript,\n  watchViewport\n} from \"./browser\"\nimport {\n  getComponentElement,\n  getComponentElements,\n  mountAnnounce,\n  mountBackToTop,\n  mountConsent,\n  mountContent,\n  mountDialog,\n  mountHeader,\n  mountHeaderTitle,\n  mountPalette,\n  mountProgress,\n  mountSearch,\n  mountSearchHiglight,\n  mountSidebar,\n  mountSource,\n  mountTableOfContents,\n  mountTabs,\n  watchHeader,\n  watchMain\n} from \"./components\"\nimport {\n  SearchIndex,\n  setupClipboardJS,\n  setupInstantNavigation,\n  setupVersionSelector\n} from \"./integrations\"\nimport {\n  patchEllipsis,\n  patchIndeterminate,\n  patchScrollfix,\n  patchScrolllock\n} from \"./patches\"\nimport \"./polyfills\"\n\n/* ----------------------------------------------------------------------------\n * Functions - @todo refactor\n * ------------------------------------------------------------------------- */\n\n/**\n * Fetch search index\n *\n * @returns Search index observable\n */\nfunction fetchSearchIndex(): Observable<SearchIndex> {\n  if (location.protocol === \"file:\") {\n    return watchScript(\n      `${new URL(\"search/search_index.js\", config.base)}`\n    )\n      .pipe(\n        // @ts-ignore - @todo fix typings\n        map(() => __index),\n        shareReplay(1)\n      )\n  } else {\n    return requestJSON<SearchIndex>(\n      new URL(\"search/search_index.json\", config.base)\n    )\n  }\n}\n\n/* ----------------------------------------------------------------------------\n * Application\n * ------------------------------------------------------------------------- */\n\n/* Yay, JavaScript is available */\ndocument.documentElement.classList.remove(\"no-js\")\ndocument.documentElement.classList.add(\"js\")\n\n/* Set up navigation observables and subjects */\nconst document$ = watchDocument()\nconst location$ = watchLocation()\nconst target$   = watchLocationTarget(location$)\nconst keyboard$ = watchKeyboard()\n\n/* Set up media observables */\nconst viewport$ = watchViewport()\nconst tablet$   = watchMedia(\"(min-width: 960px)\")\nconst screen$   = watchMedia(\"(min-width: 1220px)\")\nconst print$    = watchPrint()\n\n/* Retrieve search index, if search is enabled */\nconst config = configuration()\nconst index$ = document.forms.namedItem(\"search\")\n  ? fetchSearchIndex()\n  : NEVER\n\n/* Set up Clipboard.js integration */\nconst alert$ = new Subject<string>()\nsetupClipboardJS({ alert$ })\n\n/* Set up progress indicator */\nconst progress$ = new Subject<number>()\n\n/* Set up instant navigation, if enabled */\nif (feature(\"navigation.instant\"))\n  setupInstantNavigation({ location$, viewport$, progress$ })\n    .subscribe(document$)\n\n/* Set up version selector */\nif (config.version?.provider === \"mike\")\n  setupVersionSelector({ document$ })\n\n/* Always close drawer and search on navigation */\nmerge(location$, target$)\n  .pipe(\n    delay(125)\n  )\n    .subscribe(() => {\n      setToggle(\"drawer\", false)\n      setToggle(\"search\", false)\n    })\n\n/* Set up global keyboard handlers */\nkeyboard$\n  .pipe(\n    filter(({ mode }) => mode === \"global\")\n  )\n    .subscribe(key => {\n      switch (key.type) {\n\n        /* Go to previous page */\n        case \"p\":\n        case \",\":\n          const prev = getOptionalElement<HTMLLinkElement>(\"link[rel=prev]\")\n          if (typeof prev !== \"undefined\")\n            setLocation(prev)\n          break\n\n        /* Go to next page */\n        case \"n\":\n        case \".\":\n          const next = getOptionalElement<HTMLLinkElement>(\"link[rel=next]\")\n          if (typeof next !== \"undefined\")\n            setLocation(next)\n          break\n\n        /* Expand navigation, see https://bit.ly/3ZjG5io */\n        case \"Enter\":\n          const active = getActiveElement()\n          if (active instanceof HTMLLabelElement)\n            active.click()\n      }\n    })\n\n/* Set up patches */\npatchEllipsis({ document$ })\npatchIndeterminate({ document$, tablet$ })\npatchScrollfix({ document$ })\npatchScrolllock({ viewport$, tablet$ })\n\n/* Set up header and main area observable */\nconst header$ = watchHeader(getComponentElement(\"header\"), { viewport$ })\nconst main$ = document$\n  .pipe(\n    map(() => getComponentElement(\"main\")),\n    switchMap(el => watchMain(el, { viewport$, header$ })),\n    shareReplay(1)\n  )\n\n/* Set up control component observables */\nconst control$ = merge(\n\n  /* Consent */\n  ...getComponentElements(\"consent\")\n    .map(el => mountConsent(el, { target$ })),\n\n  /* Dialog */\n  ...getComponentElements(\"dialog\")\n    .map(el => mountDialog(el, { alert$ })),\n\n  /* Header */\n  ...getComponentElements(\"header\")\n    .map(el => mountHeader(el, { viewport$, header$, main$ })),\n\n  /* Color palette */\n  ...getComponentElements(\"palette\")\n    .map(el => mountPalette(el)),\n\n  /* Progress bar */\n  ...getComponentElements(\"progress\")\n    .map(el => mountProgress(el, { progress$ })),\n\n  /* Search */\n  ...getComponentElements(\"search\")\n    .map(el => mountSearch(el, { index$, keyboard$ })),\n\n  /* Repository information */\n  ...getComponentElements(\"source\")\n    .map(el => mountSource(el))\n)\n\n/* Set up content component observables */\nconst content$ = defer(() => merge(\n\n  /* Announcement bar */\n  ...getComponentElements(\"announce\")\n    .map(el => mountAnnounce(el)),\n\n  /* Content */\n  ...getComponentElements(\"content\")\n    .map(el => mountContent(el, { viewport$, target$, print$ })),\n\n  /* Search highlighting */\n  ...getComponentElements(\"content\")\n    .map(el => feature(\"search.highlight\")\n      ? mountSearchHiglight(el, { index$, location$ })\n      : EMPTY\n    ),\n\n  /* Header title */\n  ...getComponentElements(\"header-title\")\n    .map(el => mountHeaderTitle(el, { viewport$, header$ })),\n\n  /* Sidebar */\n  ...getComponentElements(\"sidebar\")\n    .map(el => el.getAttribute(\"data-md-type\") === \"navigation\"\n      ? at(screen$, () => mountSidebar(el, { viewport$, header$, main$ }))\n      : at(tablet$, () => mountSidebar(el, { viewport$, header$, main$ }))\n    ),\n\n  /* Navigation tabs */\n  ...getComponentElements(\"tabs\")\n    .map(el => mountTabs(el, { viewport$, header$ })),\n\n  /* Table of contents */\n  ...getComponentElements(\"toc\")\n    .map(el => mountTableOfContents(el, {\n      viewport$, header$, main$, target$\n    })),\n\n  /* Back-to-top button */\n  ...getComponentElements(\"top\")\n    .map(el => mountBackToTop(el, { viewport$, header$, main$, target$ }))\n))\n\n/* Set up component observables */\nconst component$ = document$\n  .pipe(\n    switchMap(() => content$),\n    mergeWith(control$),\n    shareReplay(1)\n  )\n\n/* Subscribe to all components */\ncomponent$.subscribe()\n\n/* ----------------------------------------------------------------------------\n * Exports\n * ------------------------------------------------------------------------- */\n\nwindow.document$  = document$          /* Document observable */\nwindow.location$  = location$          /* Location subject */\nwindow.target$    = target$            /* Location target observable */\nwindow.keyboard$  = keyboard$          /* Keyboard observable */\nwindow.viewport$  = viewport$          /* Viewport observable */\nwindow.tablet$    = tablet$            /* Media tablet observable */\nwindow.screen$    = screen$            /* Media screen observable */\nwindow.print$     = print$             /* Media print observable */\nwindow.alert$     = alert$             /* Alert subject */\nwindow.progress$  = progress$          /* Progress indicator subject */\nwindow.component$ = component$         /* Component observable */\n", "/*! *****************************************************************************\r\nCopyright (c) Microsoft Corporation.\r\n\r\nPermission to use, copy, modify, and/or distribute this software for any\r\npurpose with or without fee is hereby granted.\r\n\r\nTHE SOFTWARE IS PROVIDED \"AS IS\" AND THE AUTHOR DISCLAIMS ALL WARRANTIES WITH\r\nREGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY\r\nAND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT,\r\nINDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM\r\nLOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR\r\nOTHER TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR\r\nPERFORMANCE OF THIS SOFTWARE.\r\n***************************************************************************** */\r\n/* global Reflect, Promise */\r\n\r\nvar extendStatics = function(d, b) {\r\n    extendStatics = Object.setPrototypeOf ||\r\n        ({ __proto__: [] } instanceof Array && function (d, b) { d.__proto__ = b; }) ||\r\n        function (d, b) { for (var p in b) if (Object.prototype.hasOwnProperty.call(b, p)) d[p] = b[p]; };\r\n    return extendStatics(d, b);\r\n};\r\n\r\nexport function __extends(d, b) {\r\n    if (typeof b !== \"function\" && b !== null)\r\n        throw new TypeError(\"Class extends value \" + String(b) + \" is not a constructor or null\");\r\n    extendStatics(d, b);\r\n    function __() { this.constructor = d; }\r\n    d.prototype = b === null ? Object.create(b) : (__.prototype = b.prototype, new __());\r\n}\r\n\r\nexport var __assign = function() {\r\n    __assign = Object.assign || function __assign(t) {\r\n        for (var s, i = 1, n = arguments.length; i < n; i++) {\r\n            s = arguments[i];\r\n            for (var p in s) if (Object.prototype.hasOwnProperty.call(s, p)) t[p] = s[p];\r\n        }\r\n        return t;\r\n    }\r\n    return __assign.apply(this, arguments);\r\n}\r\n\r\nexport function __rest(s, e) {\r\n    var t = {};\r\n    for (var p in s) if (Object.prototype.hasOwnProperty.call(s, p) && e.indexOf(p) < 0)\r\n        t[p] = s[p];\r\n    if (s != null && typeof Object.getOwnPropertySymbols === \"function\")\r\n        for (var i = 0, p = Object.getOwnPropertySymbols(s); i < p.length; i++) {\r\n            if (e.indexOf(p[i]) < 0 && Object.prototype.propertyIsEnumerable.call(s, p[i]))\r\n                t[p[i]] = s[p[i]];\r\n        }\r\n    return t;\r\n}\r\n\r\nexport function __decorate(decorators, target, key, desc) {\r\n    var c = arguments.length, r = c < 3 ? target : desc === null ? desc = Object.getOwnPropertyDescriptor(target, key) : desc, d;\r\n    if (typeof Reflect === \"object\" && typeof Reflect.decorate === \"function\") r = Reflect.decorate(decorators, target, key, desc);\r\n    else for (var i = decorators.length - 1; i >= 0; i--) if (d = decorators[i]) r = (c < 3 ? d(r) : c > 3 ? d(target, key, r) : d(target, key)) || r;\r\n    return c > 3 && r && Object.defineProperty(target, key, r), r;\r\n}\r\n\r\nexport function __param(paramIndex, decorator) {\r\n    return function (target, key) { decorator(target, key, paramIndex); }\r\n}\r\n\r\nexport function __metadata(metadataKey, metadataValue) {\r\n    if (typeof Reflect === \"object\" && typeof Reflect.metadata === \"function\") return Reflect.metadata(metadataKey, metadataValue);\r\n}\r\n\r\nexport function __awaiter(thisArg, _arguments, P, generator) {\r\n    function adopt(value) { return value instanceof P ? value : new P(function (resolve) { resolve(value); }); }\r\n    return new (P || (P = Promise))(function (resolve, reject) {\r\n        function fulfilled(value) { try { step(generator.next(value)); } catch (e) { reject(e); } }\r\n        function rejected(value) { try { step(generator[\"throw\"](value)); } catch (e) { reject(e); } }\r\n        function step(result) { result.done ? resolve(result.value) : adopt(result.value).then(fulfilled, rejected); }\r\n        step((generator = generator.apply(thisArg, _arguments || [])).next());\r\n    });\r\n}\r\n\r\nexport function __generator(thisArg, body) {\r\n    var _ = { label: 0, sent: function() { if (t[0] & 1) throw t[1]; return t[1]; }, trys: [], ops: [] }, f, y, t, g;\r\n    return g = { next: verb(0), \"throw\": verb(1), \"return\": verb(2) }, typeof Symbol === \"function\" && (g[Symbol.iterator] = function() { return this; }), g;\r\n    function verb(n) { return function (v) { return step([n, v]); }; }\r\n    function step(op) {\r\n        if (f) throw new TypeError(\"Generator is already executing.\");\r\n        while (_) try {\r\n            if (f = 1, y && (t = op[0] & 2 ? y[\"return\"] : op[0] ? y[\"throw\"] || ((t = y[\"return\"]) && t.call(y), 0) : y.next) && !(t = t.call(y, op[1])).done) return t;\r\n            if (y = 0, t) op = [op[0] & 2, t.value];\r\n            switch (op[0]) {\r\n                case 0: case 1: t = op; break;\r\n                case 4: _.label++; return { value: op[1], done: false };\r\n                case 5: _.label++; y = op[1]; op = [0]; continue;\r\n                case 7: op = _.ops.pop(); _.trys.pop(); continue;\r\n                default:\r\n                    if (!(t = _.trys, t = t.length > 0 && t[t.length - 1]) && (op[0] === 6 || op[0] === 2)) { _ = 0; continue; }\r\n                    if (op[0] === 3 && (!t || (op[1] > t[0] && op[1] < t[3]))) { _.label = op[1]; break; }\r\n                    if (op[0] === 6 && _.label < t[1]) { _.label = t[1]; t = op; break; }\r\n                    if (t && _.label < t[2]) { _.label = t[2]; _.ops.push(op); break; }\r\n                    if (t[2]) _.ops.pop();\r\n                    _.trys.pop(); continue;\r\n            }\r\n            op = body.call(thisArg, _);\r\n        } catch (e) { op = [6, e]; y = 0; } finally { f = t = 0; }\r\n        if (op[0] & 5) throw op[1]; return { value: op[0] ? op[1] : void 0, done: true };\r\n    }\r\n}\r\n\r\nexport var __createBinding = Object.create ? (function(o, m, k, k2) {\r\n    if (k2 === undefined) k2 = k;\r\n    Object.defineProperty(o, k2, { enumerable: true, get: function() { return m[k]; } });\r\n}) : (function(o, m, k, k2) {\r\n    if (k2 === undefined) k2 = k;\r\n    o[k2] = m[k];\r\n});\r\n\r\nexport function __exportStar(m, o) {\r\n    for (var p in m) if (p !== \"default\" && !Object.prototype.hasOwnProperty.call(o, p)) __createBinding(o, m, p);\r\n}\r\n\r\nexport function __values(o) {\r\n    var s = typeof Symbol === \"function\" && Symbol.iterator, m = s && o[s], i = 0;\r\n    if (m) return m.call(o);\r\n    if (o && typeof o.length === \"number\") return {\r\n        next: function () {\r\n            if (o && i >= o.length) o = void 0;\r\n            return { value: o && o[i++], done: !o };\r\n        }\r\n    };\r\n    throw new TypeError(s ? \"Object is not iterable.\" : \"Symbol.iterator is not defined.\");\r\n}\r\n\r\nexport function __read(o, n) {\r\n    var m = typeof Symbol === \"function\" && o[Symbol.iterator];\r\n    if (!m) return o;\r\n    var i = m.call(o), r, ar = [], e;\r\n    try {\r\n        while ((n === void 0 || n-- > 0) && !(r = i.next()).done) ar.push(r.value);\r\n    }\r\n    catch (error) { e = { error: error }; }\r\n    finally {\r\n        try {\r\n            if (r && !r.done && (m = i[\"return\"])) m.call(i);\r\n        }\r\n        finally { if (e) throw e.error; }\r\n    }\r\n    return ar;\r\n}\r\n\r\n/** @deprecated */\r\nexport function __spread() {\r\n    for (var ar = [], i = 0; i < arguments.length; i++)\r\n        ar = ar.concat(__read(arguments[i]));\r\n    return ar;\r\n}\r\n\r\n/** @deprecated */\r\nexport function __spreadArrays() {\r\n    for (var s = 0, i = 0, il = arguments.length; i < il; i++) s += arguments[i].length;\r\n    for (var r = Array(s), k = 0, i = 0; i < il; i++)\r\n        for (var a = arguments[i], j = 0, jl = a.length; j < jl; j++, k++)\r\n            r[k] = a[j];\r\n    return r;\r\n}\r\n\r\nexport function __spreadArray(to, from, pack) {\r\n    if (pack || arguments.length === 2) for (var i = 0, l = from.length, ar; i < l; i++) {\r\n        if (ar || !(i in from)) {\r\n            if (!ar) ar = Array.prototype.slice.call(from, 0, i);\r\n            ar[i] = from[i];\r\n        }\r\n    }\r\n    return to.concat(ar || Array.prototype.slice.call(from));\r\n}\r\n\r\nexport function __await(v) {\r\n    return this instanceof __await ? (this.v = v, this) : new __await(v);\r\n}\r\n\r\nexport function __asyncGenerator(thisArg, _arguments, generator) {\r\n    if (!Symbol.asyncIterator) throw new TypeError(\"Symbol.asyncIterator is not defined.\");\r\n    var g = generator.apply(thisArg, _arguments || []), i, q = [];\r\n    return i = {}, verb(\"next\"), verb(\"throw\"), verb(\"return\"), i[Symbol.asyncIterator] = function () { return this; }, i;\r\n    function verb(n) { if (g[n]) i[n] = function (v) { return new Promise(function (a, b) { q.push([n, v, a, b]) > 1 || resume(n, v); }); }; }\r\n    function resume(n, v) { try { step(g[n](v)); } catch (e) { settle(q[0][3], e); } }\r\n    function step(r) { r.value instanceof __await ? Promise.resolve(r.value.v).then(fulfill, reject) : settle(q[0][2], r); }\r\n    function fulfill(value) { resume(\"next\", value); }\r\n    function reject(value) { resume(\"throw\", value); }\r\n    function settle(f, v) { if (f(v), q.shift(), q.length) resume(q[0][0], q[0][1]); }\r\n}\r\n\r\nexport function __asyncDelegator(o) {\r\n    var i, p;\r\n    return i = {}, verb(\"next\"), verb(\"throw\", function (e) { throw e; }), verb(\"return\"), i[Symbol.iterator] = function () { return this; }, i;\r\n    function verb(n, f) { i[n] = o[n] ? function (v) { return (p = !p) ? { value: __await(o[n](v)), done: n === \"return\" } : f ? f(v) : v; } : f; }\r\n}\r\n\r\nexport function __asyncValues(o) {\r\n    if (!Symbol.asyncIterator) throw new TypeError(\"Symbol.asyncIterator is not defined.\");\r\n    var m = o[Symbol.asyncIterator], i;\r\n    return m ? m.call(o) : (o = typeof __values === \"function\" ? __values(o) : o[Symbol.iterator](), i = {}, verb(\"next\"), verb(\"throw\"), verb(\"return\"), i[Symbol.asyncIterator] = function () { return this; }, i);\r\n    function verb(n) { i[n] = o[n] && function (v) { return new Promise(function (resolve, reject) { v = o[n](v), settle(resolve, reject, v.done, v.value); }); }; }\r\n    function settle(resolve, reject, d, v) { Promise.resolve(v).then(function(v) { resolve({ value: v, done: d }); }, reject); }\r\n}\r\n\r\nexport function __makeTemplateObject(cooked, raw) {\r\n    if (Object.defineProperty) { Object.defineProperty(cooked, \"raw\", { value: raw }); } else { cooked.raw = raw; }\r\n    return cooked;\r\n};\r\n\r\nvar __setModuleDefault = Object.create ? (function(o, v) {\r\n    Object.defineProperty(o, \"default\", { enumerable: true, value: v });\r\n}) : function(o, v) {\r\n    o[\"default\"] = v;\r\n};\r\n\r\nexport function __importStar(mod) {\r\n    if (mod && mod.__esModule) return mod;\r\n    var result = {};\r\n    if (mod != null) for (var k in mod) if (k !== \"default\" && Object.prototype.hasOwnProperty.call(mod, k)) __createBinding(result, mod, k);\r\n    __setModuleDefault(result, mod);\r\n    return result;\r\n}\r\n\r\nexport function __importDefault(mod) {\r\n    return (mod && mod.__esModule) ? mod : { default: mod };\r\n}\r\n\r\nexport function __classPrivateFieldGet(receiver, state, kind, f) {\r\n    if (kind === \"a\" && !f) throw new TypeError(\"Private accessor was defined without a getter\");\r\n    if (typeof state === \"function\" ? receiver !== state || !f : !state.has(receiver)) throw new TypeError(\"Cannot read private member from an object whose class did not declare it\");\r\n    return kind === \"m\" ? f : kind === \"a\" ? f.call(receiver) : f ? f.value : state.get(receiver);\r\n}\r\n\r\nexport function __classPrivateFieldSet(receiver, state, value, kind, f) {\r\n    if (kind === \"m\") throw new TypeError(\"Private method is not writable\");\r\n    if (kind === \"a\" && !f) throw new TypeError(\"Private accessor was defined without a setter\");\r\n    if (typeof state === \"function\" ? receiver !== state || !f : !state.has(receiver)) throw new TypeError(\"Cannot write private member to an object whose class did not declare it\");\r\n    return (kind === \"a\" ? f.call(receiver, value) : f ? f.value = value : state.set(receiver, value)), value;\r\n}\r\n", "/**\n * Returns true if the object is a function.\n * @param value The value to check\n */\nexport function isFunction(value: any): value is (...args: any[]) => any {\n  return typeof value === 'function';\n}\n", "/**\n * Used to create Error subclasses until the community moves away from ES5.\n *\n * This is because compiling from TypeScript down to ES5 has issues with subclassing Errors\n * as well as other built-in types: https://github.com/Microsoft/TypeScript/issues/12123\n *\n * @param createImpl A factory function to create the actual constructor implementation. The returned\n * function should be a named function that calls `_super` internally.\n */\nexport function createErrorClass<T>(createImpl: (_super: any) => any): T {\n  const _super = (instance: any) => {\n    Error.call(instance);\n    instance.stack = new Error().stack;\n  };\n\n  const ctorFunc = createImpl(_super);\n  ctorFunc.prototype = Object.create(Error.prototype);\n  ctorFunc.prototype.constructor = ctorFunc;\n  return ctorFunc;\n}\n", "import { createErrorClass } from './createErrorClass';\n\nexport interface UnsubscriptionError extends Error {\n  readonly errors: any[];\n}\n\nexport interface UnsubscriptionErrorCtor {\n  /**\n   * @deprecated Internal implementation detail. Do not construct error instances.\n   * Cannot be tagged as internal: https://github.com/ReactiveX/rxjs/issues/6269\n   */\n  new (errors: any[]): UnsubscriptionError;\n}\n\n/**\n * An error thrown when one or more errors have occurred during the\n * `unsubscribe` of a {@link Subscription}.\n */\nexport const UnsubscriptionError: UnsubscriptionErrorCtor = createErrorClass(\n  (_super) =>\n    function UnsubscriptionErrorImpl(this: any, errors: (Error | string)[]) {\n      _super(this);\n      this.message = errors\n        ? `${errors.length} errors occurred during unsubscription:\n${errors.map((err, i) => `${i + 1}) ${err.toString()}`).join('\\n  ')}`\n        : '';\n      this.name = 'UnsubscriptionError';\n      this.errors = errors;\n    }\n);\n", "/**\n * Removes an item from an array, mutating it.\n * @param arr The array to remove the item from\n * @param item The item to remove\n */\nexport function arrRemove<T>(arr: T[] | undefined | null, item: T) {\n  if (arr) {\n    const index = arr.indexOf(item);\n    0 <= index && arr.splice(index, 1);\n  }\n}\n", "import { isFunction } from './util/isFunction';\nimport { UnsubscriptionError } from './util/UnsubscriptionError';\nimport { SubscriptionLike, TeardownLogic, Unsubscribable } from './types';\nimport { arrRemove } from './util/arrRemove';\n\n/**\n * Represents a disposable resource, such as the execution of an Observable. A\n * Subscription has one important method, `unsubscribe`, that takes no argument\n * and just disposes the resource held by the subscription.\n *\n * Additionally, subscriptions may be grouped together through the `add()`\n * method, which will attach a child Subscription to the current Subscription.\n * When a Subscription is unsubscribed, all its children (and its grandchildren)\n * will be unsubscribed as well.\n *\n * @class Subscription\n */\nexport class Subscription implements SubscriptionLike {\n  /** @nocollapse */\n  public static EMPTY = (() => {\n    const empty = new Subscription();\n    empty.closed = true;\n    return empty;\n  })();\n\n  /**\n   * A flag to indicate whether this Subscription has already been unsubscribed.\n   */\n  public closed = false;\n\n  private _parentage: Subscription[] | Subscription | null = null;\n\n  /**\n   * The list of registered finalizers to execute upon unsubscription. Adding and removing from this\n   * list occurs in the {@link #add} and {@link #remove} methods.\n   */\n  private _finalizers: Exclude<TeardownLogic, void>[] | null = null;\n\n  /**\n   * @param initialTeardown A function executed first as part of the finalization\n   * process that is kicked off when {@link #unsubscribe} is called.\n   */\n  constructor(private initialTeardown?: () => void) {}\n\n  /**\n   * Disposes the resources held by the subscription. May, for instance, cancel\n   * an ongoing Observable execution or cancel any other type of work that\n   * started when the Subscription was created.\n   * @return {void}\n   */\n  unsubscribe(): void {\n    let errors: any[] | undefined;\n\n    if (!this.closed) {\n      this.closed = true;\n\n      // Remove this from it's parents.\n      const { _parentage } = this;\n      if (_parentage) {\n        this._parentage = null;\n        if (Array.isArray(_parentage)) {\n          for (const parent of _parentage) {\n            parent.remove(this);\n          }\n        } else {\n          _parentage.remove(this);\n        }\n      }\n\n      const { initialTeardown: initialFinalizer } = this;\n      if (isFunction(initialFinalizer)) {\n        try {\n          initialFinalizer();\n        } catch (e) {\n          errors = e instanceof UnsubscriptionError ? e.errors : [e];\n        }\n      }\n\n      const { _finalizers } = this;\n      if (_finalizers) {\n        this._finalizers = null;\n        for (const finalizer of _finalizers) {\n          try {\n            execFinalizer(finalizer);\n          } catch (err) {\n            errors = errors ?? [];\n            if (err instanceof UnsubscriptionError) {\n              errors = [...errors, ...err.errors];\n            } else {\n              errors.push(err);\n            }\n          }\n        }\n      }\n\n      if (errors) {\n        throw new UnsubscriptionError(errors);\n      }\n    }\n  }\n\n  /**\n   * Adds a finalizer to this subscription, so that finalization will be unsubscribed/called\n   * when this subscription is unsubscribed. If this subscription is already {@link #closed},\n   * because it has already been unsubscribed, then whatever finalizer is passed to it\n   * will automatically be executed (unless the finalizer itself is also a closed subscription).\n   *\n   * Closed Subscriptions cannot be added as finalizers to any subscription. Adding a closed\n   * subscription to a any subscription will result in no operation. (A noop).\n   *\n   * Adding a subscription to itself, or adding `null` or `undefined` will not perform any\n   * operation at all. (A noop).\n   *\n   * `Subscription` instances that are added to this instance will automatically remove themselves\n   * if they are unsubscribed. Functions and {@link Unsubscribable} objects that you wish to remove\n   * will need to be removed manually with {@link #remove}\n   *\n   * @param teardown The finalization logic to add to this subscription.\n   */\n  add(teardown: TeardownLogic): void {\n    // Only add the finalizer if it's not undefined\n    // and don't add a subscription to itself.\n    if (teardown && teardown !== this) {\n      if (this.closed) {\n        // If this subscription is already closed,\n        // execute whatever finalizer is handed to it automatically.\n        execFinalizer(teardown);\n      } else {\n        if (teardown instanceof Subscription) {\n          // We don't add closed subscriptions, and we don't add the same subscription\n          // twice. Subscription unsubscribe is idempotent.\n          if (teardown.closed || teardown._hasParent(this)) {\n            return;\n          }\n          teardown._addParent(this);\n        }\n        (this._finalizers = this._finalizers ?? []).push(teardown);\n      }\n    }\n  }\n\n  /**\n   * Checks to see if a this subscription already has a particular parent.\n   * This will signal that this subscription has already been added to the parent in question.\n   * @param parent the parent to check for\n   */\n  private _hasParent(parent: Subscription) {\n    const { _parentage } = this;\n    return _parentage === parent || (Array.isArray(_parentage) && _parentage.includes(parent));\n  }\n\n  /**\n   * Adds a parent to this subscription so it can be removed from the parent if it\n   * unsubscribes on it's own.\n   *\n   * NOTE: THIS ASSUMES THAT {@link _hasParent} HAS ALREADY BEEN CHECKED.\n   * @param parent The parent subscription to add\n   */\n  private _addParent(parent: Subscription) {\n    const { _parentage } = this;\n    this._parentage = Array.isArray(_parentage) ? (_parentage.push(parent), _parentage) : _parentage ? [_parentage, parent] : parent;\n  }\n\n  /**\n   * Called on a child when it is removed via {@link #remove}.\n   * @param parent The parent to remove\n   */\n  private _removeParent(parent: Subscription) {\n    const { _parentage } = this;\n    if (_parentage === parent) {\n      this._parentage = null;\n    } else if (Array.isArray(_parentage)) {\n      arrRemove(_parentage, parent);\n    }\n  }\n\n  /**\n   * Removes a finalizer from this subscription that was previously added with the {@link #add} method.\n   *\n   * Note that `Subscription` instances, when unsubscribed, will automatically remove themselves\n   * from every other `Subscription` they have been added to. This means that using the `remove` method\n   * is not a common thing and should be used thoughtfully.\n   *\n   * If you add the same finalizer instance of a function or an unsubscribable object to a `Subscription` instance\n   * more than once, you will need to call `remove` the same number of times to remove all instances.\n   *\n   * All finalizer instances are removed to free up memory upon unsubscription.\n   *\n   * @param teardown The finalizer to remove from this subscription\n   */\n  remove(teardown: Exclude<TeardownLogic, void>): void {\n    const { _finalizers } = this;\n    _finalizers && arrRemove(_finalizers, teardown);\n\n    if (teardown instanceof Subscription) {\n      teardown._removeParent(this);\n    }\n  }\n}\n\nexport const EMPTY_SUBSCRIPTION = Subscription.EMPTY;\n\nexport function isSubscription(value: any): value is Subscription {\n  return (\n    value instanceof Subscription ||\n    (value && 'closed' in value && isFunction(value.remove) && isFunction(value.add) && isFunction(value.unsubscribe))\n  );\n}\n\nfunction execFinalizer(finalizer: Unsubscribable | (() => void)) {\n  if (isFunction(finalizer)) {\n    finalizer();\n  } else {\n    finalizer.unsubscribe();\n  }\n}\n", "import { Subscriber } from './Subscriber';\nimport { ObservableNotification } from './types';\n\n/**\n * The {@link GlobalConfig} object for RxJS. It is used to configure things\n * like how to react on unhandled errors.\n */\nexport const config: GlobalConfig = {\n  onUnhandledError: null,\n  onStoppedNotification: null,\n  Promise: undefined,\n  useDeprecatedSynchronousErrorHandling: false,\n  useDeprecatedNextContext: false,\n};\n\n/**\n * The global configuration object for RxJS, used to configure things\n * like how to react on unhandled errors. Accessible via {@link config}\n * object.\n */\nexport interface GlobalConfig {\n  /**\n   * A registration point for unhandled errors from RxJS. These are errors that\n   * cannot were not handled by consuming code in the usual subscription path. For\n   * example, if you have this configured, and you subscribe to an observable without\n   * providing an error handler, errors from that subscription will end up here. This\n   * will _always_ be called asynchronously on another job in the runtime. This is because\n   * we do not want errors thrown in this user-configured handler to interfere with the\n   * behavior of the library.\n   */\n  onUnhandledError: ((err: any) => void) | null;\n\n  /**\n   * A registration point for notifications that cannot be sent to subscribers because they\n   * have completed, errored or have been explicitly unsubscribed. By default, next, complete\n   * and error notifications sent to stopped subscribers are noops. However, sometimes callers\n   * might want a different behavior. For example, with sources that attempt to report errors\n   * to stopped subscribers, a caller can configure RxJS to throw an unhandled error instead.\n   * This will _always_ be called asynchronously on another job in the runtime. This is because\n   * we do not want errors thrown in this user-configured handler to interfere with the\n   * behavior of the library.\n   */\n  onStoppedNotification: ((notification: ObservableNotification<any>, subscriber: Subscriber<any>) => void) | null;\n\n  /**\n   * The promise constructor used by default for {@link Observable#toPromise toPromise} and {@link Observable#forEach forEach}\n   * methods.\n   *\n   * @deprecated As of version 8, RxJS will no longer support this sort of injection of a\n   * Promise constructor. If you need a Promise implementation other than native promises,\n   * please polyfill/patch Promise as you see appropriate. Will be removed in v8.\n   */\n  Promise?: PromiseConstructorLike;\n\n  /**\n   * If true, turns on synchronous error rethrowing, which is a deprecated behavior\n   * in v6 and higher. This behavior enables bad patterns like wrapping a subscribe\n   * call in a try/catch block. It also enables producer interference, a nasty bug\n   * where a multicast can be broken for all observers by a downstream consumer with\n   * an unhandled error. DO NOT USE THIS FLAG UNLESS IT'S NEEDED TO BUY TIME\n   * FOR MIGRATION REASONS.\n   *\n   * @deprecated As of version 8, RxJS will no longer support synchronous throwing\n   * of unhandled errors. All errors will be thrown on a separate call stack to prevent bad\n   * behaviors described above. Will be removed in v8.\n   */\n  useDeprecatedSynchronousErrorHandling: boolean;\n\n  /**\n   * If true, enables an as-of-yet undocumented feature from v5: The ability to access\n   * `unsubscribe()` via `this` context in `next` functions created in observers passed\n   * to `subscribe`.\n   *\n   * This is being removed because the performance was severely problematic, and it could also cause\n   * issues when types other than POJOs are passed to subscribe as subscribers, as they will likely have\n   * their `this` context overwritten.\n   *\n   * @deprecated As of version 8, RxJS will no longer support altering the\n   * context of next functions provided as part of an observer to Subscribe. Instead,\n   * you will have access to a subscription or a signal or token that will allow you to do things like\n   * unsubscribe and test closed status. Will be removed in v8.\n   */\n  useDeprecatedNextContext: boolean;\n}\n", "import type { TimerHandle } from './timerHandle';\ntype SetTimeoutFunction = (handler: () => void, timeout?: number, ...args: any[]) => TimerHandle;\ntype ClearTimeoutFunction = (handle: TimerHandle) => void;\n\ninterface TimeoutProvider {\n  setTimeout: SetTimeoutFunction;\n  clearTimeout: ClearTimeoutFunction;\n  delegate:\n    | {\n        setTimeout: SetTimeoutFunction;\n        clearTimeout: ClearTimeoutFunction;\n      }\n    | undefined;\n}\n\nexport const timeoutProvider: TimeoutProvider = {\n  // When accessing the delegate, use the variable rather than `this` so that\n  // the functions can be called without being bound to the provider.\n  setTimeout(handler: () => void, timeout?: number, ...args) {\n    const { delegate } = timeoutProvider;\n    if (delegate?.setTimeout) {\n      return delegate.setTimeout(handler, timeout, ...args);\n    }\n    return setTimeout(handler, timeout, ...args);\n  },\n  clearTimeout(handle) {\n    const { delegate } = timeoutProvider;\n    return (delegate?.clearTimeout || clearTimeout)(handle as any);\n  },\n  delegate: undefined,\n};\n", "import { config } from '../config';\nimport { timeoutProvider } from '../scheduler/timeoutProvider';\n\n/**\n * Handles an error on another job either with the user-configured {@link onUnhandledError},\n * or by throwing it on that new job so it can be picked up by `window.onerror`, `process.on('error')`, etc.\n *\n * This should be called whenever there is an error that is out-of-band with the subscription\n * or when an error hits a terminal boundary of the subscription and no error handler was provided.\n *\n * @param err the error to report\n */\nexport function reportUnhandledError(err: any) {\n  timeoutProvider.setTimeout(() => {\n    const { onUnhandledError } = config;\n    if (onUnhandledError) {\n      // Execute the user-configured error handler.\n      onUnhandledError(err);\n    } else {\n      // Throw so it is picked up by the runtime's uncaught error mechanism.\n      throw err;\n    }\n  });\n}\n", "/* tslint:disable:no-empty */\nexport function noop() { }\n", "import { CompleteNotification, NextNotification, ErrorNotification } from './types';\n\n/**\n * A completion object optimized for memory use and created to be the\n * same \"shape\" as other notifications in v8.\n * @internal\n */\nexport const COMPLETE_NOTIFICATION = (() => createNotification('C', undefined, undefined) as CompleteNotification)();\n\n/**\n * Internal use only. Creates an optimized error notification that is the same \"shape\"\n * as other notifications.\n * @internal\n */\nexport function errorNotification(error: any): ErrorNotification {\n  return createNotification('E', undefined, error) as any;\n}\n\n/**\n * Internal use only. Creates an optimized next notification that is the same \"shape\"\n * as other notifications.\n * @internal\n */\nexport function nextNotification<T>(value: T) {\n  return createNotification('N', value, undefined) as NextNotification<T>;\n}\n\n/**\n * Ensures that all notifications created internally have the same \"shape\" in v8.\n *\n * TODO: This is only exported to support a crazy legacy test in `groupBy`.\n * @internal\n */\nexport function createNotification(kind: 'N' | 'E' | 'C', value: any, error: any) {\n  return {\n    kind,\n    value,\n    error,\n  };\n}\n", "import { config } from '../config';\n\nlet context: { errorThrown: boolean; error: any } | null = null;\n\n/**\n * Handles dealing with errors for super-gross mode. Creates a context, in which\n * any synchronously thrown errors will be passed to {@link captureError}. Which\n * will record the error such that it will be rethrown after the call back is complete.\n * TODO: Remove in v8\n * @param cb An immediately executed function.\n */\nexport function errorContext(cb: () => void) {\n  if (config.useDeprecatedSynchronousErrorHandling) {\n    const isRoot = !context;\n    if (isRoot) {\n      context = { errorThrown: false, error: null };\n    }\n    cb();\n    if (isRoot) {\n      const { errorThrown, error } = context!;\n      context = null;\n      if (errorThrown) {\n        throw error;\n      }\n    }\n  } else {\n    // This is the general non-deprecated path for everyone that\n    // isn't crazy enough to use super-gross mode (useDeprecatedSynchronousErrorHandling)\n    cb();\n  }\n}\n\n/**\n * Captures errors only in super-gross mode.\n * @param err the error to capture\n */\nexport function captureError(err: any) {\n  if (config.useDeprecatedSynchronousErrorHandling && context) {\n    context.errorThrown = true;\n    context.error = err;\n  }\n}\n", "import { isFunction } from './util/isFunction';\nimport { Observer, ObservableNotification } from './types';\nimport { isSubscription, Subscription } from './Subscription';\nimport { config } from './config';\nimport { reportUnhandledError } from './util/reportUnhandledError';\nimport { noop } from './util/noop';\nimport { nextNotification, errorNotification, COMPLETE_NOTIFICATION } from './NotificationFactories';\nimport { timeoutProvider } from './scheduler/timeoutProvider';\nimport { captureError } from './util/errorContext';\n\n/**\n * Implements the {@link Observer} interface and extends the\n * {@link Subscription} class. While the {@link Observer} is the public API for\n * consuming the values of an {@link Observable}, all Observers get converted to\n * a Subscriber, in order to provide Subscription-like capabilities such as\n * `unsubscribe`. Subscriber is a common type in RxJS, and crucial for\n * implementing operators, but it is rarely used as a public API.\n *\n * @class Subscriber<T>\n */\nexport class Subscriber<T> extends Subscription implements Observer<T> {\n  /**\n   * A static factory for a Subscriber, given a (potentially partial) definition\n   * of an Observer.\n   * @param next The `next` callback of an Observer.\n   * @param error The `error` callback of an\n   * Observer.\n   * @param complete The `complete` callback of an\n   * Observer.\n   * @return A Subscriber wrapping the (partially defined)\n   * Observer represented by the given arguments.\n   * @nocollapse\n   * @deprecated Do not use. Will be removed in v8. There is no replacement for this\n   * method, and there is no reason to be creating instances of `Subscriber` directly.\n   * If you have a specific use case, please file an issue.\n   */\n  static create<T>(next?: (x?: T) => void, error?: (e?: any) => void, complete?: () => void): Subscriber<T> {\n    return new SafeSubscriber(next, error, complete);\n  }\n\n  /** @deprecated Internal implementation detail, do not use directly. Will be made internal in v8. */\n  protected isStopped: boolean = false;\n  /** @deprecated Internal implementation detail, do not use directly. Will be made internal in v8. */\n  protected destination: Subscriber<any> | Observer<any>; // this `any` is the escape hatch to erase extra type param (e.g. R)\n\n  /**\n   * @deprecated Internal implementation detail, do not use directly. Will be made internal in v8.\n   * There is no reason to directly create an instance of Subscriber. This type is exported for typings reasons.\n   */\n  constructor(destination?: Subscriber<any> | Observer<any>) {\n    super();\n    if (destination) {\n      this.destination = destination;\n      // Automatically chain subscriptions together here.\n      // if destination is a Subscription, then it is a Subscriber.\n      if (isSubscription(destination)) {\n        destination.add(this);\n      }\n    } else {\n      this.destination = EMPTY_OBSERVER;\n    }\n  }\n\n  /**\n   * The {@link Observer} callback to receive notifications of type `next` from\n   * the Observable, with a value. The Observable may call this method 0 or more\n   * times.\n   * @param {T} [value] The `next` value.\n   * @return {void}\n   */\n  next(value?: T): void {\n    if (this.isStopped) {\n      handleStoppedNotification(nextNotification(value), this);\n    } else {\n      this._next(value!);\n    }\n  }\n\n  /**\n   * The {@link Observer} callback to receive notifications of type `error` from\n   * the Observable, with an attached `Error`. Notifies the Observer that\n   * the Observable has experienced an error condition.\n   * @param {any} [err] The `error` exception.\n   * @return {void}\n   */\n  error(err?: any): void {\n    if (this.isStopped) {\n      handleStoppedNotification(errorNotification(err), this);\n    } else {\n      this.isStopped = true;\n      this._error(err);\n    }\n  }\n\n  /**\n   * The {@link Observer} callback to receive a valueless notification of type\n   * `complete` from the Observable. Notifies the Observer that the Observable\n   * has finished sending push-based notifications.\n   * @return {void}\n   */\n  complete(): void {\n    if (this.isStopped) {\n      handleStoppedNotification(COMPLETE_NOTIFICATION, this);\n    } else {\n      this.isStopped = true;\n      this._complete();\n    }\n  }\n\n  unsubscribe(): void {\n    if (!this.closed) {\n      this.isStopped = true;\n      super.unsubscribe();\n      this.destination = null!;\n    }\n  }\n\n  protected _next(value: T): void {\n    this.destination.next(value);\n  }\n\n  protected _error(err: any): void {\n    try {\n      this.destination.error(err);\n    } finally {\n      this.unsubscribe();\n    }\n  }\n\n  protected _complete(): void {\n    try {\n      this.destination.complete();\n    } finally {\n      this.unsubscribe();\n    }\n  }\n}\n\n/**\n * This bind is captured here because we want to be able to have\n * compatibility with monoid libraries that tend to use a method named\n * `bind`. In particular, a library called Monio requires this.\n */\nconst _bind = Function.prototype.bind;\n\nfunction bind<Fn extends (...args: any[]) => any>(fn: Fn, thisArg: any): Fn {\n  return _bind.call(fn, thisArg);\n}\n\n/**\n * Internal optimization only, DO NOT EXPOSE.\n * @internal\n */\nclass ConsumerObserver<T> implements Observer<T> {\n  constructor(private partialObserver: Partial<Observer<T>>) {}\n\n  next(value: T): void {\n    const { partialObserver } = this;\n    if (partialObserver.next) {\n      try {\n        partialObserver.next(value);\n      } catch (error) {\n        handleUnhandledError(error);\n      }\n    }\n  }\n\n  error(err: any): void {\n    const { partialObserver } = this;\n    if (partialObserver.error) {\n      try {\n        partialObserver.error(err);\n      } catch (error) {\n        handleUnhandledError(error);\n      }\n    } else {\n      handleUnhandledError(err);\n    }\n  }\n\n  complete(): void {\n    const { partialObserver } = this;\n    if (partialObserver.complete) {\n      try {\n        partialObserver.complete();\n      } catch (error) {\n        handleUnhandledError(error);\n      }\n    }\n  }\n}\n\nexport class SafeSubscriber<T> extends Subscriber<T> {\n  constructor(\n    observerOrNext?: Partial<Observer<T>> | ((value: T) => void) | null,\n    error?: ((e?: any) => void) | null,\n    complete?: (() => void) | null\n  ) {\n    super();\n\n    let partialObserver: Partial<Observer<T>>;\n    if (isFunction(observerOrNext) || !observerOrNext) {\n      // The first argument is a function, not an observer. The next\n      // two arguments *could* be observers, or they could be empty.\n      partialObserver = {\n        next: (observerOrNext ?? undefined) as (((value: T) => void) | undefined),\n        error: error ?? undefined,\n        complete: complete ?? undefined,\n      };\n    } else {\n      // The first argument is a partial observer.\n      let context: any;\n      if (this && config.useDeprecatedNextContext) {\n        // This is a deprecated path that made `this.unsubscribe()` available in\n        // next handler functions passed to subscribe. This only exists behind a flag\n        // now, as it is *very* slow.\n        context = Object.create(observerOrNext);\n        context.unsubscribe = () => this.unsubscribe();\n        partialObserver = {\n          next: observerOrNext.next && bind(observerOrNext.next, context),\n          error: observerOrNext.error && bind(observerOrNext.error, context),\n          complete: observerOrNext.complete && bind(observerOrNext.complete, context),\n        };\n      } else {\n        // The \"normal\" path. Just use the partial observer directly.\n        partialObserver = observerOrNext;\n      }\n    }\n\n    // Wrap the partial observer to ensure it's a full observer, and\n    // make sure proper error handling is accounted for.\n    this.destination = new ConsumerObserver(partialObserver);\n  }\n}\n\nfunction handleUnhandledError(error: any) {\n  if (config.useDeprecatedSynchronousErrorHandling) {\n    captureError(error);\n  } else {\n    // Ideal path, we report this as an unhandled error,\n    // which is thrown on a new call stack.\n    reportUnhandledError(error);\n  }\n}\n\n/**\n * An error handler used when no error handler was supplied\n * to the SafeSubscriber -- meaning no error handler was supplied\n * do the `subscribe` call on our observable.\n * @param err The error to handle\n */\nfunction defaultErrorHandler(err: any) {\n  throw err;\n}\n\n/**\n * A handler for notifications that cannot be sent to a stopped subscriber.\n * @param notification The notification being sent\n * @param subscriber The stopped subscriber\n */\nfunction handleStoppedNotification(notification: ObservableNotification<any>, subscriber: Subscriber<any>) {\n  const { onStoppedNotification } = config;\n  onStoppedNotification && timeoutProvider.setTimeout(() => onStoppedNotification(notification, subscriber));\n}\n\n/**\n * The observer used as a stub for subscriptions where the user did not\n * pass any arguments to `subscribe`. Comes with the default error handling\n * behavior.\n */\nexport const EMPTY_OBSERVER: Readonly<Observer<any>> & { closed: true } = {\n  closed: true,\n  next: noop,\n  error: defaultErrorHandler,\n  complete: noop,\n};\n", "/**\n * Symbol.observable or a string \"@@observable\". Used for interop\n *\n * @deprecated We will no longer be exporting this symbol in upcoming versions of RxJS.\n * Instead polyfill and use Symbol.observable directly *or* use https://www.npmjs.com/package/symbol-observable\n */\nexport const observable: string | symbol = (() => (typeof Symbol === 'function' && Symbol.observable) || '@@observable')();\n", "/**\n * This function takes one parameter and just returns it. Simply put,\n * this is like `<T>(x: T): T => x`.\n *\n * ## Examples\n *\n * This is useful in some cases when using things like `mergeMap`\n *\n * ```ts\n * import { interval, take, map, range, mergeMap, identity } from 'rxjs';\n *\n * const source$ = interval(1000).pipe(take(5));\n *\n * const result$ = source$.pipe(\n *   map(i => range(i)),\n *   mergeMap(identity) // same as mergeMap(x => x)\n * );\n *\n * result$.subscribe({\n *   next: console.log\n * });\n * ```\n *\n * Or when you want to selectively apply an operator\n *\n * ```ts\n * import { interval, take, identity } from 'rxjs';\n *\n * const shouldLimit = () => Math.random() < 0.5;\n *\n * const source$ = interval(1000);\n *\n * const result$ = source$.pipe(shouldLimit() ? take(5) : identity);\n *\n * result$.subscribe({\n *   next: console.log\n * });\n * ```\n *\n * @param x Any value that is returned by this function\n * @returns The value passed as the first parameter to this function\n */\nexport function identity<T>(x: T): T {\n  return x;\n}\n", "import { identity } from './identity';\nimport { UnaryFunction } from '../types';\n\nexport function pipe(): typeof identity;\nexport function pipe<T, A>(fn1: UnaryFunction<T, A>): UnaryFunction<T, A>;\nexport function pipe<T, A, B>(fn1: UnaryFunction<T, A>, fn2: UnaryFunction<A, B>): UnaryFunction<T, B>;\nexport function pipe<T, A, B, C>(fn1: UnaryFunction<T, A>, fn2: UnaryFunction<A, B>, fn3: UnaryFunction<B, C>): UnaryFunction<T, C>;\nexport function pipe<T, A, B, C, D>(\n  fn1: UnaryFunction<T, A>,\n  fn2: UnaryFunction<A, B>,\n  fn3: UnaryFunction<B, C>,\n  fn4: UnaryFunction<C, D>\n): UnaryFunction<T, D>;\nexport function pipe<T, A, B, C, D, E>(\n  fn1: UnaryFunction<T, A>,\n  fn2: UnaryFunction<A, B>,\n  fn3: UnaryFunction<B, C>,\n  fn4: UnaryFunction<C, D>,\n  fn5: UnaryFunction<D, E>\n): UnaryFunction<T, E>;\nexport function pipe<T, A, B, C, D, E, F>(\n  fn1: UnaryFunction<T, A>,\n  fn2: UnaryFunction<A, B>,\n  fn3: UnaryFunction<B, C>,\n  fn4: UnaryFunction<C, D>,\n  fn5: UnaryFunction<D, E>,\n  fn6: UnaryFunction<E, F>\n): UnaryFunction<T, F>;\nexport function pipe<T, A, B, C, D, E, F, G>(\n  fn1: UnaryFunction<T, A>,\n  fn2: UnaryFunction<A, B>,\n  fn3: UnaryFunction<B, C>,\n  fn4: UnaryFunction<C, D>,\n  fn5: UnaryFunction<D, E>,\n  fn6: UnaryFunction<E, F>,\n  fn7: UnaryFunction<F, G>\n): UnaryFunction<T, G>;\nexport function pipe<T, A, B, C, D, E, F, G, H>(\n  fn1: UnaryFunction<T, A>,\n  fn2: UnaryFunction<A, B>,\n  fn3: UnaryFunction<B, C>,\n  fn4: UnaryFunction<C, D>,\n  fn5: UnaryFunction<D, E>,\n  fn6: UnaryFunction<E, F>,\n  fn7: UnaryFunction<F, G>,\n  fn8: UnaryFunction<G, H>\n): UnaryFunction<T, H>;\nexport function pipe<T, A, B, C, D, E, F, G, H, I>(\n  fn1: UnaryFunction<T, A>,\n  fn2: UnaryFunction<A, B>,\n  fn3: UnaryFunction<B, C>,\n  fn4: UnaryFunction<C, D>,\n  fn5: UnaryFunction<D, E>,\n  fn6: UnaryFunction<E, F>,\n  fn7: UnaryFunction<F, G>,\n  fn8: UnaryFunction<G, H>,\n  fn9: UnaryFunction<H, I>\n): UnaryFunction<T, I>;\nexport function pipe<T, A, B, C, D, E, F, G, H, I>(\n  fn1: UnaryFunction<T, A>,\n  fn2: UnaryFunction<A, B>,\n  fn3: UnaryFunction<B, C>,\n  fn4: UnaryFunction<C, D>,\n  fn5: UnaryFunction<D, E>,\n  fn6: UnaryFunction<E, F>,\n  fn7: UnaryFunction<F, G>,\n  fn8: UnaryFunction<G, H>,\n  fn9: UnaryFunction<H, I>,\n  ...fns: UnaryFunction<any, any>[]\n): UnaryFunction<T, unknown>;\n\n/**\n * pipe() can be called on one or more functions, each of which can take one argument (\"UnaryFunction\")\n * and uses it to return a value.\n * It returns a function that takes one argument, passes it to the first UnaryFunction, and then\n * passes the result to the next one, passes that result to the next one, and so on.  \n */\nexport function pipe(...fns: Array<UnaryFunction<any, any>>): UnaryFunction<any, any> {\n  return pipeFromArray(fns);\n}\n\n/** @internal */\nexport function pipeFromArray<T, R>(fns: Array<UnaryFunction<T, R>>): UnaryFunction<T, R> {\n  if (fns.length === 0) {\n    return identity as UnaryFunction<any, any>;\n  }\n\n  if (fns.length === 1) {\n    return fns[0];\n  }\n\n  return function piped(input: T): R {\n    return fns.reduce((prev: any, fn: UnaryFunction<T, R>) => fn(prev), input as any);\n  };\n}\n", "import { Operator } from './Operator';\nimport { SafeSubscriber, Subscriber } from './Subscriber';\nimport { isSubscription, Subscription } from './Subscription';\nimport { TeardownLogic, OperatorFunction, Subscribable, Observer } from './types';\nimport { observable as Symbol_observable } from './symbol/observable';\nimport { pipeFromArray } from './util/pipe';\nimport { config } from './config';\nimport { isFunction } from './util/isFunction';\nimport { errorContext } from './util/errorContext';\n\n/**\n * A representation of any set of values over any amount of time. This is the most basic building block\n * of RxJS.\n *\n * @class Observable<T>\n */\nexport class Observable<T> implements Subscribable<T> {\n  /**\n   * @deprecated Internal implementation detail, do not use directly. Will be made internal in v8.\n   */\n  source: Observable<any> | undefined;\n\n  /**\n   * @deprecated Internal implementation detail, do not use directly. Will be made internal in v8.\n   */\n  operator: Operator<any, T> | undefined;\n\n  /**\n   * @constructor\n   * @param {Function} subscribe the function that is called when the Observable is\n   * initially subscribed to. This function is given a Subscriber, to which new values\n   * can be `next`ed, or an `error` method can be called to raise an error, or\n   * `complete` can be called to notify of a successful completion.\n   */\n  constructor(subscribe?: (this: Observable<T>, subscriber: Subscriber<T>) => TeardownLogic) {\n    if (subscribe) {\n      this._subscribe = subscribe;\n    }\n  }\n\n  // HACK: Since TypeScript inherits static properties too, we have to\n  // fight against TypeScript here so Subject can have a different static create signature\n  /**\n   * Creates a new Observable by calling the Observable constructor\n   * @owner Observable\n   * @method create\n   * @param {Function} subscribe? the subscriber function to be passed to the Observable constructor\n   * @return {Observable} a new observable\n   * @nocollapse\n   * @deprecated Use `new Observable()` instead. Will be removed in v8.\n   */\n  static create: (...args: any[]) => any = <T>(subscribe?: (subscriber: Subscriber<T>) => TeardownLogic) => {\n    return new Observable<T>(subscribe);\n  };\n\n  /**\n   * Creates a new Observable, with this Observable instance as the source, and the passed\n   * operator defined as the new observable's operator.\n   * @method lift\n   * @param operator the operator defining the operation to take on the observable\n   * @return a new observable with the Operator applied\n   * @deprecated Internal implementation detail, do not use directly. Will be made internal in v8.\n   * If you have implemented an operator using `lift`, it is recommended that you create an\n   * operator by simply returning `new Observable()` directly. See \"Creating new operators from\n   * scratch\" section here: https://rxjs.dev/guide/operators\n   */\n  lift<R>(operator?: Operator<T, R>): Observable<R> {\n    const observable = new Observable<R>();\n    observable.source = this;\n    observable.operator = operator;\n    return observable;\n  }\n\n  subscribe(observerOrNext?: Partial<Observer<T>> | ((value: T) => void)): Subscription;\n  /** @deprecated Instead of passing separate callback arguments, use an observer argument. Signatures taking separate callback arguments will be removed in v8. Details: https://rxjs.dev/deprecations/subscribe-arguments */\n  subscribe(next?: ((value: T) => void) | null, error?: ((error: any) => void) | null, complete?: (() => void) | null): Subscription;\n  /**\n   * Invokes an execution of an Observable and registers Observer handlers for notifications it will emit.\n   *\n   * <span class=\"informal\">Use it when you have all these Observables, but still nothing is happening.</span>\n   *\n   * `subscribe` is not a regular operator, but a method that calls Observable's internal `subscribe` function. It\n   * might be for example a function that you passed to Observable's constructor, but most of the time it is\n   * a library implementation, which defines what will be emitted by an Observable, and when it be will emitted. This means\n   * that calling `subscribe` is actually the moment when Observable starts its work, not when it is created, as it is often\n   * the thought.\n   *\n   * Apart from starting the execution of an Observable, this method allows you to listen for values\n   * that an Observable emits, as well as for when it completes or errors. You can achieve this in two\n   * of the following ways.\n   *\n   * The first way is creating an object that implements {@link Observer} interface. It should have methods\n   * defined by that interface, but note that it should be just a regular JavaScript object, which you can create\n   * yourself in any way you want (ES6 class, classic function constructor, object literal etc.). In particular, do\n   * not attempt to use any RxJS implementation details to create Observers - you don't need them. Remember also\n   * that your object does not have to implement all methods. If you find yourself creating a method that doesn't\n   * do anything, you can simply omit it. Note however, if the `error` method is not provided and an error happens,\n   * it will be thrown asynchronously. Errors thrown asynchronously cannot be caught using `try`/`catch`. Instead,\n   * use the {@link onUnhandledError} configuration option or use a runtime handler (like `window.onerror` or\n   * `process.on('error)`) to be notified of unhandled errors. Because of this, it's recommended that you provide\n   * an `error` method to avoid missing thrown errors.\n   *\n   * The second way is to give up on Observer object altogether and simply provide callback functions in place of its methods.\n   * This means you can provide three functions as arguments to `subscribe`, where the first function is equivalent\n   * of a `next` method, the second of an `error` method and the third of a `complete` method. Just as in case of an Observer,\n   * if you do not need to listen for something, you can omit a function by passing `undefined` or `null`,\n   * since `subscribe` recognizes these functions by where they were placed in function call. When it comes\n   * to the `error` function, as with an Observer, if not provided, errors emitted by an Observable will be thrown asynchronously.\n   *\n   * You can, however, subscribe with no parameters at all. This may be the case where you're not interested in terminal events\n   * and you also handled emissions internally by using operators (e.g. using `tap`).\n   *\n   * Whichever style of calling `subscribe` you use, in both cases it returns a Subscription object.\n   * This object allows you to call `unsubscribe` on it, which in turn will stop the work that an Observable does and will clean\n   * up all resources that an Observable used. Note that cancelling a subscription will not call `complete` callback\n   * provided to `subscribe` function, which is reserved for a regular completion signal that comes from an Observable.\n   *\n   * Remember that callbacks provided to `subscribe` are not guaranteed to be called asynchronously.\n   * It is an Observable itself that decides when these functions will be called. For example {@link of}\n   * by default emits all its values synchronously. Always check documentation for how given Observable\n   * will behave when subscribed and if its default behavior can be modified with a `scheduler`.\n   *\n   * #### Examples\n   *\n   * Subscribe with an {@link guide/observer Observer}\n   *\n   * ```ts\n   * import { of } from 'rxjs';\n   *\n   * const sumObserver = {\n   *   sum: 0,\n   *   next(value) {\n   *     console.log('Adding: ' + value);\n   *     this.sum = this.sum + value;\n   *   },\n   *   error() {\n   *     // We actually could just remove this method,\n   *     // since we do not really care about errors right now.\n   *   },\n   *   complete() {\n   *     console.log('Sum equals: ' + this.sum);\n   *   }\n   * };\n   *\n   * of(1, 2, 3) // Synchronously emits 1, 2, 3 and then completes.\n   *   .subscribe(sumObserver);\n   *\n   * // Logs:\n   * // 'Adding: 1'\n   * // 'Adding: 2'\n   * // 'Adding: 3'\n   * // 'Sum equals: 6'\n   * ```\n   *\n   * Subscribe with functions ({@link deprecations/subscribe-arguments deprecated})\n   *\n   * ```ts\n   * import { of } from 'rxjs'\n   *\n   * let sum = 0;\n   *\n   * of(1, 2, 3).subscribe(\n   *   value => {\n   *     console.log('Adding: ' + value);\n   *     sum = sum + value;\n   *   },\n   *   undefined,\n   *   () => console.log('Sum equals: ' + sum)\n   * );\n   *\n   * // Logs:\n   * // 'Adding: 1'\n   * // 'Adding: 2'\n   * // 'Adding: 3'\n   * // 'Sum equals: 6'\n   * ```\n   *\n   * Cancel a subscription\n   *\n   * ```ts\n   * import { interval } from 'rxjs';\n   *\n   * const subscription = interval(1000).subscribe({\n   *   next(num) {\n   *     console.log(num)\n   *   },\n   *   complete() {\n   *     // Will not be called, even when cancelling subscription.\n   *     console.log('completed!');\n   *   }\n   * });\n   *\n   * setTimeout(() => {\n   *   subscription.unsubscribe();\n   *   console.log('unsubscribed!');\n   * }, 2500);\n   *\n   * // Logs:\n   * // 0 after 1s\n   * // 1 after 2s\n   * // 'unsubscribed!' after 2.5s\n   * ```\n   *\n   * @param {Observer|Function} observerOrNext (optional) Either an observer with methods to be called,\n   * or the first of three possible handlers, which is the handler for each value emitted from the subscribed\n   * Observable.\n   * @param {Function} error (optional) A handler for a terminal event resulting from an error. If no error handler is provided,\n   * the error will be thrown asynchronously as unhandled.\n   * @param {Function} complete (optional) A handler for a terminal event resulting from successful completion.\n   * @return {Subscription} a subscription reference to the registered handlers\n   * @method subscribe\n   */\n  subscribe(\n    observerOrNext?: Partial<Observer<T>> | ((value: T) => void) | null,\n    error?: ((error: any) => void) | null,\n    complete?: (() => void) | null\n  ): Subscription {\n    const subscriber = isSubscriber(observerOrNext) ? observerOrNext : new SafeSubscriber(observerOrNext, error, complete);\n\n    errorContext(() => {\n      const { operator, source } = this;\n      subscriber.add(\n        operator\n          ? // We're dealing with a subscription in the\n            // operator chain to one of our lifted operators.\n            operator.call(subscriber, source)\n          : source\n          ? // If `source` has a value, but `operator` does not, something that\n            // had intimate knowledge of our API, like our `Subject`, must have\n            // set it. We're going to just call `_subscribe` directly.\n            this._subscribe(subscriber)\n          : // In all other cases, we're likely wrapping a user-provided initializer\n            // function, so we need to catch errors and handle them appropriately.\n            this._trySubscribe(subscriber)\n      );\n    });\n\n    return subscriber;\n  }\n\n  /** @internal */\n  protected _trySubscribe(sink: Subscriber<T>): TeardownLogic {\n    try {\n      return this._subscribe(sink);\n    } catch (err) {\n      // We don't need to return anything in this case,\n      // because it's just going to try to `add()` to a subscription\n      // above.\n      sink.error(err);\n    }\n  }\n\n  /**\n   * Used as a NON-CANCELLABLE means of subscribing to an observable, for use with\n   * APIs that expect promises, like `async/await`. You cannot unsubscribe from this.\n   *\n   * **WARNING**: Only use this with observables you *know* will complete. If the source\n   * observable does not complete, you will end up with a promise that is hung up, and\n   * potentially all of the state of an async function hanging out in memory. To avoid\n   * this situation, look into adding something like {@link timeout}, {@link take},\n   * {@link takeWhile}, or {@link takeUntil} amongst others.\n   *\n   * #### Example\n   *\n   * ```ts\n   * import { interval, take } from 'rxjs';\n   *\n   * const source$ = interval(1000).pipe(take(4));\n   *\n   * async function getTotal() {\n   *   let total = 0;\n   *\n   *   await source$.forEach(value => {\n   *     total += value;\n   *     console.log('observable -> ' + value);\n   *   });\n   *\n   *   return total;\n   * }\n   *\n   * getTotal().then(\n   *   total => console.log('Total: ' + total)\n   * );\n   *\n   * // Expected:\n   * // 'observable -> 0'\n   * // 'observable -> 1'\n   * // 'observable -> 2'\n   * // 'observable -> 3'\n   * // 'Total: 6'\n   * ```\n   *\n   * @param next a handler for each value emitted by the observable\n   * @return a promise that either resolves on observable completion or\n   *  rejects with the handled error\n   */\n  forEach(next: (value: T) => void): Promise<void>;\n\n  /**\n   * @param next a handler for each value emitted by the observable\n   * @param promiseCtor a constructor function used to instantiate the Promise\n   * @return a promise that either resolves on observable completion or\n   *  rejects with the handled error\n   * @deprecated Passing a Promise constructor will no longer be available\n   * in upcoming versions of RxJS. This is because it adds weight to the library, for very\n   * little benefit. If you need this functionality, it is recommended that you either\n   * polyfill Promise, or you create an adapter to convert the returned native promise\n   * to whatever promise implementation you wanted. Will be removed in v8.\n   */\n  forEach(next: (value: T) => void, promiseCtor: PromiseConstructorLike): Promise<void>;\n\n  forEach(next: (value: T) => void, promiseCtor?: PromiseConstructorLike): Promise<void> {\n    promiseCtor = getPromiseCtor(promiseCtor);\n\n    return new promiseCtor<void>((resolve, reject) => {\n      const subscriber = new SafeSubscriber<T>({\n        next: (value) => {\n          try {\n            next(value);\n          } catch (err) {\n            reject(err);\n            subscriber.unsubscribe();\n          }\n        },\n        error: reject,\n        complete: resolve,\n      });\n      this.subscribe(subscriber);\n    }) as Promise<void>;\n  }\n\n  /** @internal */\n  protected _subscribe(subscriber: Subscriber<any>): TeardownLogic {\n    return this.source?.subscribe(subscriber);\n  }\n\n  /**\n   * An interop point defined by the es7-observable spec https://github.com/zenparsing/es-observable\n   * @method Symbol.observable\n   * @return {Observable} this instance of the observable\n   */\n  [Symbol_observable]() {\n    return this;\n  }\n\n  /* tslint:disable:max-line-length */\n  pipe(): Observable<T>;\n  pipe<A>(op1: OperatorFunction<T, A>): Observable<A>;\n  pipe<A, B>(op1: OperatorFunction<T, A>, op2: OperatorFunction<A, B>): Observable<B>;\n  pipe<A, B, C>(op1: OperatorFunction<T, A>, op2: OperatorFunction<A, B>, op3: OperatorFunction<B, C>): Observable<C>;\n  pipe<A, B, C, D>(\n    op1: OperatorFunction<T, A>,\n    op2: OperatorFunction<A, B>,\n    op3: OperatorFunction<B, C>,\n    op4: OperatorFunction<C, D>\n  ): Observable<D>;\n  pipe<A, B, C, D, E>(\n    op1: OperatorFunction<T, A>,\n    op2: OperatorFunction<A, B>,\n    op3: OperatorFunction<B, C>,\n    op4: OperatorFunction<C, D>,\n    op5: OperatorFunction<D, E>\n  ): Observable<E>;\n  pipe<A, B, C, D, E, F>(\n    op1: OperatorFunction<T, A>,\n    op2: OperatorFunction<A, B>,\n    op3: OperatorFunction<B, C>,\n    op4: OperatorFunction<C, D>,\n    op5: OperatorFunction<D, E>,\n    op6: OperatorFunction<E, F>\n  ): Observable<F>;\n  pipe<A, B, C, D, E, F, G>(\n    op1: OperatorFunction<T, A>,\n    op2: OperatorFunction<A, B>,\n    op3: OperatorFunction<B, C>,\n    op4: OperatorFunction<C, D>,\n    op5: OperatorFunction<D, E>,\n    op6: OperatorFunction<E, F>,\n    op7: OperatorFunction<F, G>\n  ): Observable<G>;\n  pipe<A, B, C, D, E, F, G, H>(\n    op1: OperatorFunction<T, A>,\n    op2: OperatorFunction<A, B>,\n    op3: OperatorFunction<B, C>,\n    op4: OperatorFunction<C, D>,\n    op5: OperatorFunction<D, E>,\n    op6: OperatorFunction<E, F>,\n    op7: OperatorFunction<F, G>,\n    op8: OperatorFunction<G, H>\n  ): Observable<H>;\n  pipe<A, B, C, D, E, F, G, H, I>(\n    op1: OperatorFunction<T, A>,\n    op2: OperatorFunction<A, B>,\n    op3: OperatorFunction<B, C>,\n    op4: OperatorFunction<C, D>,\n    op5: OperatorFunction<D, E>,\n    op6: OperatorFunction<E, F>,\n    op7: OperatorFunction<F, G>,\n    op8: OperatorFunction<G, H>,\n    op9: OperatorFunction<H, I>\n  ): Observable<I>;\n  pipe<A, B, C, D, E, F, G, H, I>(\n    op1: OperatorFunction<T, A>,\n    op2: OperatorFunction<A, B>,\n    op3: OperatorFunction<B, C>,\n    op4: OperatorFunction<C, D>,\n    op5: OperatorFunction<D, E>,\n    op6: OperatorFunction<E, F>,\n    op7: OperatorFunction<F, G>,\n    op8: OperatorFunction<G, H>,\n    op9: OperatorFunction<H, I>,\n    ...operations: OperatorFunction<any, any>[]\n  ): Observable<unknown>;\n  /* tslint:enable:max-line-length */\n\n  /**\n   * Used to stitch together functional operators into a chain.\n   * @method pipe\n   * @return {Observable} the Observable result of all of the operators having\n   * been called in the order they were passed in.\n   *\n   * ## Example\n   *\n   * ```ts\n   * import { interval, filter, map, scan } from 'rxjs';\n   *\n   * interval(1000)\n   *   .pipe(\n   *     filter(x => x % 2 === 0),\n   *     map(x => x + x),\n   *     scan((acc, x) => acc + x)\n   *   )\n   *   .subscribe(x => console.log(x));\n   * ```\n   */\n  pipe(...operations: OperatorFunction<any, any>[]): Observable<any> {\n    return pipeFromArray(operations)(this);\n  }\n\n  /* tslint:disable:max-line-length */\n  /** @deprecated Replaced with {@link firstValueFrom} and {@link lastValueFrom}. Will be removed in v8. Details: https://rxjs.dev/deprecations/to-promise */\n  toPromise(): Promise<T | undefined>;\n  /** @deprecated Replaced with {@link firstValueFrom} and {@link lastValueFrom}. Will be removed in v8. Details: https://rxjs.dev/deprecations/to-promise */\n  toPromise(PromiseCtor: typeof Promise): Promise<T | undefined>;\n  /** @deprecated Replaced with {@link firstValueFrom} and {@link lastValueFrom}. Will be removed in v8. Details: https://rxjs.dev/deprecations/to-promise */\n  toPromise(PromiseCtor: PromiseConstructorLike): Promise<T | undefined>;\n  /* tslint:enable:max-line-length */\n\n  /**\n   * Subscribe to this Observable and get a Promise resolving on\n   * `complete` with the last emission (if any).\n   *\n   * **WARNING**: Only use this with observables you *know* will complete. If the source\n   * observable does not complete, you will end up with a promise that is hung up, and\n   * potentially all of the state of an async function hanging out in memory. To avoid\n   * this situation, look into adding something like {@link timeout}, {@link take},\n   * {@link takeWhile}, or {@link takeUntil} amongst others.\n   *\n   * @method toPromise\n   * @param [promiseCtor] a constructor function used to instantiate\n   * the Promise\n   * @return A Promise that resolves with the last value emit, or\n   * rejects on an error. If there were no emissions, Promise\n   * resolves with undefined.\n   * @deprecated Replaced with {@link firstValueFrom} and {@link lastValueFrom}. Will be removed in v8. Details: https://rxjs.dev/deprecations/to-promise\n   */\n  toPromise(promiseCtor?: PromiseConstructorLike): Promise<T | undefined> {\n    promiseCtor = getPromiseCtor(promiseCtor);\n\n    return new promiseCtor((resolve, reject) => {\n      let value: T | undefined;\n      this.subscribe(\n        (x: T) => (value = x),\n        (err: any) => reject(err),\n        () => resolve(value)\n      );\n    }) as Promise<T | undefined>;\n  }\n}\n\n/**\n * Decides between a passed promise constructor from consuming code,\n * A default configured promise constructor, and the native promise\n * constructor and returns it. If nothing can be found, it will throw\n * an error.\n * @param promiseCtor The optional promise constructor to passed by consuming code\n */\nfunction getPromiseCtor(promiseCtor: PromiseConstructorLike | undefined) {\n  return promiseCtor ?? config.Promise ?? Promise;\n}\n\nfunction isObserver<T>(value: any): value is Observer<T> {\n  return value && isFunction(value.next) && isFunction(value.error) && isFunction(value.complete);\n}\n\nfunction isSubscriber<T>(value: any): value is Subscriber<T> {\n  return (value && value instanceof Subscriber) || (isObserver(value) && isSubscription(value));\n}\n", "import { Observable } from '../Observable';\nimport { Subscriber } from '../Subscriber';\nimport { OperatorFunction } from '../types';\nimport { isFunction } from './isFunction';\n\n/**\n * Used to determine if an object is an Observable with a lift function.\n */\nexport function hasLift(source: any): source is { lift: InstanceType<typeof Observable>['lift'] } {\n  return isFunction(source?.lift);\n}\n\n/**\n * Creates an `OperatorFunction`. Used to define operators throughout the library in a concise way.\n * @param init The logic to connect the liftedSource to the subscriber at the moment of subscription.\n */\nexport function operate<T, R>(\n  init: (liftedSource: Observable<T>, subscriber: Subscriber<R>) => (() => void) | void\n): OperatorFunction<T, R> {\n  return (source: Observable<T>) => {\n    if (hasLift(source)) {\n      return source.lift(function (this: Subscriber<R>, liftedSource: Observable<T>) {\n        try {\n          return init(liftedSource, this);\n        } catch (err) {\n          this.error(err);\n        }\n      });\n    }\n    throw new TypeError('Unable to lift unknown Observable type');\n  };\n}\n", "import { Subscriber } from '../Subscriber';\n\n/**\n * Creates an instance of an `OperatorSubscriber`.\n * @param destination The downstream subscriber.\n * @param onNext Handles next values, only called if this subscriber is not stopped or closed. Any\n * error that occurs in this function is caught and sent to the `error` method of this subscriber.\n * @param onError Handles errors from the subscription, any errors that occur in this handler are caught\n * and send to the `destination` error handler.\n * @param onComplete Handles completion notification from the subscription. Any errors that occur in\n * this handler are sent to the `destination` error handler.\n * @param onFinalize Additional teardown logic here. This will only be called on teardown if the\n * subscriber itself is not already closed. This is called after all other teardown logic is executed.\n */\nexport function createOperatorSubscriber<T>(\n  destination: Subscriber<any>,\n  onNext?: (value: T) => void,\n  onComplete?: () => void,\n  onError?: (err: any) => void,\n  onFinalize?: () => void\n): Subscriber<T> {\n  return new OperatorSubscriber(destination, onNext, onComplete, onError, onFinalize);\n}\n\n/**\n * A generic helper for allowing operators to be created with a Subscriber and\n * use closures to capture necessary state from the operator function itself.\n */\nexport class OperatorSubscriber<T> extends Subscriber<T> {\n  /**\n   * Creates an instance of an `OperatorSubscriber`.\n   * @param destination The downstream subscriber.\n   * @param onNext Handles next values, only called if this subscriber is not stopped or closed. Any\n   * error that occurs in this function is caught and sent to the `error` method of this subscriber.\n   * @param onError Handles errors from the subscription, any errors that occur in this handler are caught\n   * and send to the `destination` error handler.\n   * @param onComplete Handles completion notification from the subscription. Any errors that occur in\n   * this handler are sent to the `destination` error handler.\n   * @param onFinalize Additional finalization logic here. This will only be called on finalization if the\n   * subscriber itself is not already closed. This is called after all other finalization logic is executed.\n   * @param shouldUnsubscribe An optional check to see if an unsubscribe call should truly unsubscribe.\n   * NOTE: This currently **ONLY** exists to support the strange behavior of {@link groupBy}, where unsubscription\n   * to the resulting observable does not actually disconnect from the source if there are active subscriptions\n   * to any grouped observable. (DO NOT EXPOSE OR USE EXTERNALLY!!!)\n   */\n  constructor(\n    destination: Subscriber<any>,\n    onNext?: (value: T) => void,\n    onComplete?: () => void,\n    onError?: (err: any) => void,\n    private onFinalize?: () => void,\n    private shouldUnsubscribe?: () => boolean\n  ) {\n    // It's important - for performance reasons - that all of this class's\n    // members are initialized and that they are always initialized in the same\n    // order. This will ensure that all OperatorSubscriber instances have the\n    // same hidden class in V8. This, in turn, will help keep the number of\n    // hidden classes involved in property accesses within the base class as\n    // low as possible. If the number of hidden classes involved exceeds four,\n    // the property accesses will become megamorphic and performance penalties\n    // will be incurred - i.e. inline caches won't be used.\n    //\n    // The reasons for ensuring all instances have the same hidden class are\n    // further discussed in this blog post from Benedikt Meurer:\n    // https://benediktmeurer.de/2018/03/23/impact-of-polymorphism-on-component-based-frameworks-like-react/\n    super(destination);\n    this._next = onNext\n      ? function (this: OperatorSubscriber<T>, value: T) {\n          try {\n            onNext(value);\n          } catch (err) {\n            destination.error(err);\n          }\n        }\n      : super._next;\n    this._error = onError\n      ? function (this: OperatorSubscriber<T>, err: any) {\n          try {\n            onError(err);\n          } catch (err) {\n            // Send any errors that occur down stream.\n            destination.error(err);\n          } finally {\n            // Ensure finalization.\n            this.unsubscribe();\n          }\n        }\n      : super._error;\n    this._complete = onComplete\n      ? function (this: OperatorSubscriber<T>) {\n          try {\n            onComplete();\n          } catch (err) {\n            // Send any errors that occur down stream.\n            destination.error(err);\n          } finally {\n            // Ensure finalization.\n            this.unsubscribe();\n          }\n        }\n      : super._complete;\n  }\n\n  unsubscribe() {\n    if (!this.shouldUnsubscribe || this.shouldUnsubscribe()) {\n      const { closed } = this;\n      super.unsubscribe();\n      // Execute additional teardown if we have any and we didn't already do so.\n      !closed && this.onFinalize?.();\n    }\n  }\n}\n", "import { Subscription } from '../Subscription';\n\ninterface AnimationFrameProvider {\n  schedule(callback: FrameRequestCallback): Subscription;\n  requestAnimationFrame: typeof requestAnimationFrame;\n  cancelAnimationFrame: typeof cancelAnimationFrame;\n  delegate:\n    | {\n        requestAnimationFrame: typeof requestAnimationFrame;\n        cancelAnimationFrame: typeof cancelAnimationFrame;\n      }\n    | undefined;\n}\n\nexport const animationFrameProvider: AnimationFrameProvider = {\n  // When accessing the delegate, use the variable rather than `this` so that\n  // the functions can be called without being bound to the provider.\n  schedule(callback) {\n    let request = requestAnimationFrame;\n    let cancel: typeof cancelAnimationFrame | undefined = cancelAnimationFrame;\n    const { delegate } = animationFrameProvider;\n    if (delegate) {\n      request = delegate.requestAnimationFrame;\n      cancel = delegate.cancelAnimationFrame;\n    }\n    const handle = request((timestamp) => {\n      // Clear the cancel function. The request has been fulfilled, so\n      // attempting to cancel the request upon unsubscription would be\n      // pointless.\n      cancel = undefined;\n      callback(timestamp);\n    });\n    return new Subscription(() => cancel?.(handle));\n  },\n  requestAnimationFrame(...args) {\n    const { delegate } = animationFrameProvider;\n    return (delegate?.requestAnimationFrame || requestAnimationFrame)(...args);\n  },\n  cancelAnimationFrame(...args) {\n    const { delegate } = animationFrameProvider;\n    return (delegate?.cancelAnimationFrame || cancelAnimationFrame)(...args);\n  },\n  delegate: undefined,\n};\n", "import { createErrorClass } from './createErrorClass';\n\nexport interface ObjectUnsubscribedError extends Error {}\n\nexport interface ObjectUnsubscribedErrorCtor {\n  /**\n   * @deprecated Internal implementation detail. Do not construct error instances.\n   * Cannot be tagged as internal: https://github.com/ReactiveX/rxjs/issues/6269\n   */\n  new (): ObjectUnsubscribedError;\n}\n\n/**\n * An error thrown when an action is invalid because the object has been\n * unsubscribed.\n *\n * @see {@link Subject}\n * @see {@link BehaviorSubject}\n *\n * @class ObjectUnsubscribedError\n */\nexport const ObjectUnsubscribedError: ObjectUnsubscribedErrorCtor = createErrorClass(\n  (_super) =>\n    function ObjectUnsubscribedErrorImpl(this: any) {\n      _super(this);\n      this.name = 'ObjectUnsubscribedError';\n      this.message = 'object unsubscribed';\n    }\n);\n", "import { Operator } from './Operator';\nimport { Observable } from './Observable';\nimport { Subscriber } from './Subscriber';\nimport { Subscription, EMPTY_SUBSCRIPTION } from './Subscription';\nimport { Observer, SubscriptionLike, TeardownLogic } from './types';\nimport { ObjectUnsubscribedError } from './util/ObjectUnsubscribedError';\nimport { arrRemove } from './util/arrRemove';\nimport { errorContext } from './util/errorContext';\n\n/**\n * A Subject is a special type of Observable that allows values to be\n * multicasted to many Observers. Subjects are like EventEmitters.\n *\n * Every Subject is an Observable and an Observer. You can subscribe to a\n * Subject, and you can call next to feed values as well as error and complete.\n */\nexport class Subject<T> extends Observable<T> implements SubscriptionLike {\n  closed = false;\n\n  private currentObservers: Observer<T>[] | null = null;\n\n  /** @deprecated Internal implementation detail, do not use directly. Will be made internal in v8. */\n  observers: Observer<T>[] = [];\n  /** @deprecated Internal implementation detail, do not use directly. Will be made internal in v8. */\n  isStopped = false;\n  /** @deprecated Internal implementation detail, do not use directly. Will be made internal in v8. */\n  hasError = false;\n  /** @deprecated Internal implementation detail, do not use directly. Will be made internal in v8. */\n  thrownError: any = null;\n\n  /**\n   * Creates a \"subject\" by basically gluing an observer to an observable.\n   *\n   * @nocollapse\n   * @deprecated Recommended you do not use. Will be removed at some point in the future. Plans for replacement still under discussion.\n   */\n  static create: (...args: any[]) => any = <T>(destination: Observer<T>, source: Observable<T>): AnonymousSubject<T> => {\n    return new AnonymousSubject<T>(destination, source);\n  };\n\n  constructor() {\n    // NOTE: This must be here to obscure Observable's constructor.\n    super();\n  }\n\n  /** @deprecated Internal implementation detail, do not use directly. Will be made internal in v8. */\n  lift<R>(operator: Operator<T, R>): Observable<R> {\n    const subject = new AnonymousSubject(this, this);\n    subject.operator = operator as any;\n    return subject as any;\n  }\n\n  /** @internal */\n  protected _throwIfClosed() {\n    if (this.closed) {\n      throw new ObjectUnsubscribedError();\n    }\n  }\n\n  next(value: T) {\n    errorContext(() => {\n      this._throwIfClosed();\n      if (!this.isStopped) {\n        if (!this.currentObservers) {\n          this.currentObservers = Array.from(this.observers);\n        }\n        for (const observer of this.currentObservers) {\n          observer.next(value);\n        }\n      }\n    });\n  }\n\n  error(err: any) {\n    errorContext(() => {\n      this._throwIfClosed();\n      if (!this.isStopped) {\n        this.hasError = this.isStopped = true;\n        this.thrownError = err;\n        const { observers } = this;\n        while (observers.length) {\n          observers.shift()!.error(err);\n        }\n      }\n    });\n  }\n\n  complete() {\n    errorContext(() => {\n      this._throwIfClosed();\n      if (!this.isStopped) {\n        this.isStopped = true;\n        const { observers } = this;\n        while (observers.length) {\n          observers.shift()!.complete();\n        }\n      }\n    });\n  }\n\n  unsubscribe() {\n    this.isStopped = this.closed = true;\n    this.observers = this.currentObservers = null!;\n  }\n\n  get observed() {\n    return this.observers?.length > 0;\n  }\n\n  /** @internal */\n  protected _trySubscribe(subscriber: Subscriber<T>): TeardownLogic {\n    this._throwIfClosed();\n    return super._trySubscribe(subscriber);\n  }\n\n  /** @internal */\n  protected _subscribe(subscriber: Subscriber<T>): Subscription {\n    this._throwIfClosed();\n    this._checkFinalizedStatuses(subscriber);\n    return this._innerSubscribe(subscriber);\n  }\n\n  /** @internal */\n  protected _innerSubscribe(subscriber: Subscriber<any>) {\n    const { hasError, isStopped, observers } = this;\n    if (hasError || isStopped) {\n      return EMPTY_SUBSCRIPTION;\n    }\n    this.currentObservers = null;\n    observers.push(subscriber);\n    return new Subscription(() => {\n      this.currentObservers = null;\n      arrRemove(observers, subscriber);\n    });\n  }\n\n  /** @internal */\n  protected _checkFinalizedStatuses(subscriber: Subscriber<any>) {\n    const { hasError, thrownError, isStopped } = this;\n    if (hasError) {\n      subscriber.error(thrownError);\n    } else if (isStopped) {\n      subscriber.complete();\n    }\n  }\n\n  /**\n   * Creates a new Observable with this Subject as the source. You can do this\n   * to create custom Observer-side logic of the Subject and conceal it from\n   * code that uses the Observable.\n   * @return {Observable} Observable that the Subject casts to\n   */\n  asObservable(): Observable<T> {\n    const observable: any = new Observable<T>();\n    observable.source = this;\n    return observable;\n  }\n}\n\n/**\n * @class AnonymousSubject<T>\n */\nexport class AnonymousSubject<T> extends Subject<T> {\n  constructor(\n    /** @deprecated Internal implementation detail, do not use directly. Will be made internal in v8. */\n    public destination?: Observer<T>,\n    source?: Observable<T>\n  ) {\n    super();\n    this.source = source;\n  }\n\n  next(value: T) {\n    this.destination?.next?.(value);\n  }\n\n  error(err: any) {\n    this.destination?.error?.(err);\n  }\n\n  complete() {\n    this.destination?.complete?.();\n  }\n\n  /** @internal */\n  protected _subscribe(subscriber: Subscriber<T>): Subscription {\n    return this.source?.subscribe(subscriber) ?? EMPTY_SUBSCRIPTION;\n  }\n}\n", "import { TimestampProvider } from '../types';\n\ninterface DateTimestampProvider extends TimestampProvider {\n  delegate: TimestampProvider | undefined;\n}\n\nexport const dateTimestampProvider: DateTimestampProvider = {\n  now() {\n    // Use the variable rather than `this` so that the function can be called\n    // without being bound to the provider.\n    return (dateTimestampProvider.delegate || Date).now();\n  },\n  delegate: undefined,\n};\n", "import { Subject } from './Subject';\nimport { TimestampProvider } from './types';\nimport { Subscriber } from './Subscriber';\nimport { Subscription } from './Subscription';\nimport { dateTimestampProvider } from './scheduler/dateTimestampProvider';\n\n/**\n * A variant of {@link Subject} that \"replays\" old values to new subscribers by emitting them when they first subscribe.\n *\n * `ReplaySubject` has an internal buffer that will store a specified number of values that it has observed. Like `Subject`,\n * `ReplaySubject` \"observes\" values by having them passed to its `next` method. When it observes a value, it will store that\n * value for a time determined by the configuration of the `ReplaySubject`, as passed to its constructor.\n *\n * When a new subscriber subscribes to the `ReplaySubject` instance, it will synchronously emit all values in its buffer in\n * a First-In-First-Out (FIFO) manner. The `ReplaySubject` will also complete, if it has observed completion; and it will\n * error if it has observed an error.\n *\n * There are two main configuration items to be concerned with:\n *\n * 1. `bufferSize` - This will determine how many items are stored in the buffer, defaults to infinite.\n * 2. `windowTime` - The amount of time to hold a value in the buffer before removing it from the buffer.\n *\n * Both configurations may exist simultaneously. So if you would like to buffer a maximum of 3 values, as long as the values\n * are less than 2 seconds old, you could do so with a `new ReplaySubject(3, 2000)`.\n *\n * ### Differences with BehaviorSubject\n *\n * `BehaviorSubject` is similar to `new ReplaySubject(1)`, with a couple of exceptions:\n *\n * 1. `BehaviorSubject` comes \"primed\" with a single value upon construction.\n * 2. `ReplaySubject` will replay values, even after observing an error, where `BehaviorSubject` will not.\n *\n * @see {@link Subject}\n * @see {@link BehaviorSubject}\n * @see {@link shareReplay}\n */\nexport class ReplaySubject<T> extends Subject<T> {\n  private _buffer: (T | number)[] = [];\n  private _infiniteTimeWindow = true;\n\n  /**\n   * @param bufferSize The size of the buffer to replay on subscription\n   * @param windowTime The amount of time the buffered items will stay buffered\n   * @param timestampProvider An object with a `now()` method that provides the current timestamp. This is used to\n   * calculate the amount of time something has been buffered.\n   */\n  constructor(\n    private _bufferSize = Infinity,\n    private _windowTime = Infinity,\n    private _timestampProvider: TimestampProvider = dateTimestampProvider\n  ) {\n    super();\n    this._infiniteTimeWindow = _windowTime === Infinity;\n    this._bufferSize = Math.max(1, _bufferSize);\n    this._windowTime = Math.max(1, _windowTime);\n  }\n\n  next(value: T): void {\n    const { isStopped, _buffer, _infiniteTimeWindow, _timestampProvider, _windowTime } = this;\n    if (!isStopped) {\n      _buffer.push(value);\n      !_infiniteTimeWindow && _buffer.push(_timestampProvider.now() + _windowTime);\n    }\n    this._trimBuffer();\n    super.next(value);\n  }\n\n  /** @internal */\n  protected _subscribe(subscriber: Subscriber<T>): Subscription {\n    this._throwIfClosed();\n    this._trimBuffer();\n\n    const subscription = this._innerSubscribe(subscriber);\n\n    const { _infiniteTimeWindow, _buffer } = this;\n    // We use a copy here, so reentrant code does not mutate our array while we're\n    // emitting it to a new subscriber.\n    const copy = _buffer.slice();\n    for (let i = 0; i < copy.length && !subscriber.closed; i += _infiniteTimeWindow ? 1 : 2) {\n      subscriber.next(copy[i] as T);\n    }\n\n    this._checkFinalizedStatuses(subscriber);\n\n    return subscription;\n  }\n\n  private _trimBuffer() {\n    const { _bufferSize, _timestampProvider, _buffer, _infiniteTimeWindow } = this;\n    // If we don't have an infinite buffer size, and we're over the length,\n    // use splice to truncate the old buffer values off. Note that we have to\n    // double the size for instances where we're not using an infinite time window\n    // because we're storing the values and the timestamps in the same array.\n    const adjustedBufferSize = (_infiniteTimeWindow ? 1 : 2) * _bufferSize;\n    _bufferSize < Infinity && adjustedBufferSize < _buffer.length && _buffer.splice(0, _buffer.length - adjustedBufferSize);\n\n    // Now, if we're not in an infinite time window, remove all values where the time is\n    // older than what is allowed.\n    if (!_infiniteTimeWindow) {\n      const now = _timestampProvider.now();\n      let last = 0;\n      // Search the array for the first timestamp that isn't expired and\n      // truncate the buffer up to that point.\n      for (let i = 1; i < _buffer.length && (_buffer[i] as number) <= now; i += 2) {\n        last = i;\n      }\n      last && _buffer.splice(0, last + 1);\n    }\n  }\n}\n", "import { Scheduler } from '../Scheduler';\nimport { Subscription } from '../Subscription';\nimport { SchedulerAction } from '../types';\n\n/**\n * A unit of work to be executed in a `scheduler`. An action is typically\n * created from within a {@link SchedulerLike} and an RxJS user does not need to concern\n * themselves about creating and manipulating an Action.\n *\n * ```ts\n * class Action<T> extends Subscription {\n *   new (scheduler: Scheduler, work: (state?: T) => void);\n *   schedule(state?: T, delay: number = 0): Subscription;\n * }\n * ```\n *\n * @class Action<T>\n */\nexport class Action<T> extends Subscription {\n  constructor(scheduler: Scheduler, work: (this: SchedulerAction<T>, state?: T) => void) {\n    super();\n  }\n  /**\n   * Schedules this action on its parent {@link SchedulerLike} for execution. May be passed\n   * some context object, `state`. May happen at some point in the future,\n   * according to the `delay` parameter, if specified.\n   * @param {T} [state] Some contextual data that the `work` function uses when\n   * called by the Scheduler.\n   * @param {number} [delay] Time to wait before executing the work, where the\n   * time unit is implicit and defined by the Scheduler.\n   * @return {void}\n   */\n  public schedule(state?: T, delay: number = 0): Subscription {\n    return this;\n  }\n}\n", "import type { TimerHandle } from './timerHandle';\ntype SetIntervalFunction = (handler: () => void, timeout?: number, ...args: any[]) => TimerHandle;\ntype ClearIntervalFunction = (handle: TimerHandle) => void;\n\ninterface IntervalProvider {\n  setInterval: SetIntervalFunction;\n  clearInterval: ClearIntervalFunction;\n  delegate:\n    | {\n        setInterval: SetIntervalFunction;\n        clearInterval: ClearIntervalFunction;\n      }\n    | undefined;\n}\n\nexport const intervalProvider: IntervalProvider = {\n  // When accessing the delegate, use the variable rather than `this` so that\n  // the functions can be called without being bound to the provider.\n  setInterval(handler: () => void, timeout?: number, ...args) {\n    const { delegate } = intervalProvider;\n    if (delegate?.setInterval) {\n      return delegate.setInterval(handler, timeout, ...args);\n    }\n    return setInterval(handler, timeout, ...args);\n  },\n  clearInterval(handle) {\n    const { delegate } = intervalProvider;\n    return (delegate?.clearInterval || clearInterval)(handle as any);\n  },\n  delegate: undefined,\n};\n", "import { Action } from './Action';\nimport { SchedulerAction } from '../types';\nimport { Subscription } from '../Subscription';\nimport { AsyncScheduler } from './AsyncScheduler';\nimport { intervalProvider } from './intervalProvider';\nimport { arrRemove } from '../util/arrRemove';\nimport { TimerHandle } from './timerHandle';\n\nexport class AsyncAction<T> extends Action<T> {\n  public id: TimerHandle | undefined;\n  public state?: T;\n  // @ts-ignore: Property has no initializer and is not definitely assigned\n  public delay: number;\n  protected pending: boolean = false;\n\n  constructor(protected scheduler: AsyncScheduler, protected work: (this: SchedulerAction<T>, state?: T) => void) {\n    super(scheduler, work);\n  }\n\n  public schedule(state?: T, delay: number = 0): Subscription {\n    if (this.closed) {\n      return this;\n    }\n\n    // Always replace the current state with the new state.\n    this.state = state;\n\n    const id = this.id;\n    const scheduler = this.scheduler;\n\n    //\n    // Important implementation note:\n    //\n    // Actions only execute once by default, unless rescheduled from within the\n    // scheduled callback. This allows us to implement single and repeat\n    // actions via the same code path, without adding API surface area, as well\n    // as mimic traditional recursion but across asynchronous boundaries.\n    //\n    // However, JS runtimes and timers distinguish between intervals achieved by\n    // serial `setTimeout` calls vs. a single `setInterval` call. An interval of\n    // serial `setTimeout` calls can be individually delayed, which delays\n    // scheduling the next `setTimeout`, and so on. `setInterval` attempts to\n    // guarantee the interval callback will be invoked more precisely to the\n    // interval period, regardless of load.\n    //\n    // Therefore, we use `setInterval` to schedule single and repeat actions.\n    // If the action reschedules itself with the same delay, the interval is not\n    // canceled. If the action doesn't reschedule, or reschedules with a\n    // different delay, the interval will be canceled after scheduled callback\n    // execution.\n    //\n    if (id != null) {\n      this.id = this.recycleAsyncId(scheduler, id, delay);\n    }\n\n    // Set the pending flag indicating that this action has been scheduled, or\n    // has recursively rescheduled itself.\n    this.pending = true;\n\n    this.delay = delay;\n    // If this action has already an async Id, don't request a new one.\n    this.id = this.id ?? this.requestAsyncId(scheduler, this.id, delay);\n\n    return this;\n  }\n\n  protected requestAsyncId(scheduler: AsyncScheduler, _id?: TimerHandle, delay: number = 0): TimerHandle {\n    return intervalProvider.setInterval(scheduler.flush.bind(scheduler, this), delay);\n  }\n\n  protected recycleAsyncId(_scheduler: AsyncScheduler, id?: TimerHandle, delay: number | null = 0): TimerHandle | undefined {\n    // If this action is rescheduled with the same delay time, don't clear the interval id.\n    if (delay != null && this.delay === delay && this.pending === false) {\n      return id;\n    }\n    // Otherwise, if the action's delay time is different from the current delay,\n    // or the action has been rescheduled before it's executed, clear the interval id\n    if (id != null) {\n      intervalProvider.clearInterval(id);\n    }\n\n    return undefined;\n  }\n\n  /**\n   * Immediately executes this action and the `work` it contains.\n   * @return {any}\n   */\n  public execute(state: T, delay: number): any {\n    if (this.closed) {\n      return new Error('executing a cancelled action');\n    }\n\n    this.pending = false;\n    const error = this._execute(state, delay);\n    if (error) {\n      return error;\n    } else if (this.pending === false && this.id != null) {\n      // Dequeue if the action didn't reschedule itself. Don't call\n      // unsubscribe(), because the action could reschedule later.\n      // For example:\n      // ```\n      // scheduler.schedule(function doWork(counter) {\n      //   /* ... I'm a busy worker bee ... */\n      //   var originalAction = this;\n      //   /* wait 100ms before rescheduling the action */\n      //   setTimeout(function () {\n      //     originalAction.schedule(counter + 1);\n      //   }, 100);\n      // }, 1000);\n      // ```\n      this.id = this.recycleAsyncId(this.scheduler, this.id, null);\n    }\n  }\n\n  protected _execute(state: T, _delay: number): any {\n    let errored: boolean = false;\n    let errorValue: any;\n    try {\n      this.work(state);\n    } catch (e) {\n      errored = true;\n      // HACK: Since code elsewhere is relying on the \"truthiness\" of the\n      // return here, we can't have it return \"\" or 0 or false.\n      // TODO: Clean this up when we refactor schedulers mid-version-8 or so.\n      errorValue = e ? e : new Error('Scheduled action threw falsy error');\n    }\n    if (errored) {\n      this.unsubscribe();\n      return errorValue;\n    }\n  }\n\n  unsubscribe() {\n    if (!this.closed) {\n      const { id, scheduler } = this;\n      const { actions } = scheduler;\n\n      this.work = this.state = this.scheduler = null!;\n      this.pending = false;\n\n      arrRemove(actions, this);\n      if (id != null) {\n        this.id = this.recycleAsyncId(scheduler, id, null);\n      }\n\n      this.delay = null!;\n      super.unsubscribe();\n    }\n  }\n}\n", "import { Action } from './scheduler/Action';\nimport { Subscription } from './Subscription';\nimport { SchedulerLike, SchedulerAction } from './types';\nimport { dateTimestampProvider } from './scheduler/dateTimestampProvider';\n\n/**\n * An execution context and a data structure to order tasks and schedule their\n * execution. Provides a notion of (potentially virtual) time, through the\n * `now()` getter method.\n *\n * Each unit of work in a Scheduler is called an `Action`.\n *\n * ```ts\n * class Scheduler {\n *   now(): number;\n *   schedule(work, delay?, state?): Subscription;\n * }\n * ```\n *\n * @class Scheduler\n * @deprecated Scheduler is an internal implementation detail of RxJS, and\n * should not be used directly. Rather, create your own class and implement\n * {@link SchedulerLike}. Will be made internal in v8.\n */\nexport class Scheduler implements SchedulerLike {\n  public static now: () => number = dateTimestampProvider.now;\n\n  constructor(private schedulerActionCtor: typeof Action, now: () => number = Scheduler.now) {\n    this.now = now;\n  }\n\n  /**\n   * A getter method that returns a number representing the current time\n   * (at the time this function was called) according to the scheduler's own\n   * internal clock.\n   * @return {number} A number that represents the current time. May or may not\n   * have a relation to wall-clock time. May or may not refer to a time unit\n   * (e.g. milliseconds).\n   */\n  public now: () => number;\n\n  /**\n   * Schedules a function, `work`, for execution. May happen at some point in\n   * the future, according to the `delay` parameter, if specified. May be passed\n   * some context object, `state`, which will be passed to the `work` function.\n   *\n   * The given arguments will be processed an stored as an Action object in a\n   * queue of actions.\n   *\n   * @param {function(state: ?T): ?Subscription} work A function representing a\n   * task, or some unit of work to be executed by the Scheduler.\n   * @param {number} [delay] Time to wait before executing the work, where the\n   * time unit is implicit and defined by the Scheduler itself.\n   * @param {T} [state] Some contextual data that the `work` function uses when\n   * called by the Scheduler.\n   * @return {Subscription} A subscription in order to be able to unsubscribe\n   * the scheduled work.\n   */\n  public schedule<T>(work: (this: SchedulerAction<T>, state?: T) => void, delay: number = 0, state?: T): Subscription {\n    return new this.schedulerActionCtor<T>(this, work).schedule(state, delay);\n  }\n}\n", "import { Scheduler } from '../Scheduler';\nimport { Action } from './Action';\nimport { AsyncAction } from './AsyncAction';\nimport { TimerHandle } from './timerHandle';\n\nexport class AsyncScheduler extends Scheduler {\n  public actions: Array<AsyncAction<any>> = [];\n  /**\n   * A flag to indicate whether the Scheduler is currently executing a batch of\n   * queued actions.\n   * @type {boolean}\n   * @internal\n   */\n  public _active: boolean = false;\n  /**\n   * An internal ID used to track the latest asynchronous task such as those\n   * coming from `setTimeout`, `setInterval`, `requestAnimationFrame`, and\n   * others.\n   * @type {any}\n   * @internal\n   */\n  public _scheduled: TimerHandle | undefined;\n\n  constructor(SchedulerAction: typeof Action, now: () => number = Scheduler.now) {\n    super(SchedulerAction, now);\n  }\n\n  public flush(action: AsyncAction<any>): void {\n    const { actions } = this;\n\n    if (this._active) {\n      actions.push(action);\n      return;\n    }\n\n    let error: any;\n    this._active = true;\n\n    do {\n      if ((error = action.execute(action.state, action.delay))) {\n        break;\n      }\n    } while ((action = actions.shift()!)); // exhaust the scheduler queue\n\n    this._active = false;\n\n    if (error) {\n      while ((action = actions.shift()!)) {\n        action.unsubscribe();\n      }\n      throw error;\n    }\n  }\n}\n", "import { AsyncAction } from './AsyncAction';\nimport { AsyncScheduler } from './AsyncScheduler';\n\n/**\n *\n * Async Scheduler\n *\n * <span class=\"informal\">Schedule task as if you used setTimeout(task, duration)</span>\n *\n * `async` scheduler schedules tasks asynchronously, by putting them on the JavaScript\n * event loop queue. It is best used to delay tasks in time or to schedule tasks repeating\n * in intervals.\n *\n * If you just want to \"defer\" task, that is to perform it right after currently\n * executing synchronous code ends (commonly achieved by `setTimeout(deferredTask, 0)`),\n * better choice will be the {@link asapScheduler} scheduler.\n *\n * ## Examples\n * Use async scheduler to delay task\n * ```ts\n * import { asyncScheduler } from 'rxjs';\n *\n * const task = () => console.log('it works!');\n *\n * asyncScheduler.schedule(task, 2000);\n *\n * // After 2 seconds logs:\n * // \"it works!\"\n * ```\n *\n * Use async scheduler to repeat task in intervals\n * ```ts\n * import { asyncScheduler } from 'rxjs';\n *\n * function task(state) {\n *   console.log(state);\n *   this.schedule(state + 1, 1000); // `this` references currently executing Action,\n *                                   // which we reschedule with new state and delay\n * }\n *\n * asyncScheduler.schedule(task, 3000, 0);\n *\n * // Logs:\n * // 0 after 3s\n * // 1 after 4s\n * // 2 after 5s\n * // 3 after 6s\n * ```\n */\n\nexport const asyncScheduler = new AsyncScheduler(AsyncAction);\n\n/**\n * @deprecated Renamed to {@link asyncScheduler}. Will be removed in v8.\n */\nexport const async = asyncScheduler;\n", "import { AsyncAction } from './AsyncAction';\nimport { AnimationFrameScheduler } from './AnimationFrameScheduler';\nimport { SchedulerAction } from '../types';\nimport { animationFrameProvider } from './animationFrameProvider';\nimport { TimerHandle } from './timerHandle';\n\nexport class AnimationFrameAction<T> extends AsyncAction<T> {\n  constructor(protected scheduler: AnimationFrameScheduler, protected work: (this: SchedulerAction<T>, state?: T) => void) {\n    super(scheduler, work);\n  }\n\n  protected requestAsyncId(scheduler: AnimationFrameScheduler, id?: TimerHandle, delay: number = 0): TimerHandle {\n    // If delay is greater than 0, request as an async action.\n    if (delay !== null && delay > 0) {\n      return super.requestAsyncId(scheduler, id, delay);\n    }\n    // Push the action to the end of the scheduler queue.\n    scheduler.actions.push(this);\n    // If an animation frame has already been requested, don't request another\n    // one. If an animation frame hasn't been requested yet, request one. Return\n    // the current animation frame request id.\n    return scheduler._scheduled || (scheduler._scheduled = animationFrameProvider.requestAnimationFrame(() => scheduler.flush(undefined)));\n  }\n\n  protected recycleAsyncId(scheduler: AnimationFrameScheduler, id?: TimerHandle, delay: number = 0): TimerHandle | undefined {\n    // If delay exists and is greater than 0, or if the delay is null (the\n    // action wasn't rescheduled) but was originally scheduled as an async\n    // action, then recycle as an async action.\n    if (delay != null ? delay > 0 : this.delay > 0) {\n      return super.recycleAsyncId(scheduler, id, delay);\n    }\n    // If the scheduler queue has no remaining actions with the same async id,\n    // cancel the requested animation frame and set the scheduled flag to\n    // undefined so the next AnimationFrameAction will request its own.\n    const { actions } = scheduler;\n    if (id != null && actions[actions.length - 1]?.id !== id) {\n      animationFrameProvider.cancelAnimationFrame(id as number);\n      scheduler._scheduled = undefined;\n    }\n    // Return undefined so the action knows to request a new async id if it's rescheduled.\n    return undefined;\n  }\n}\n", "import { AsyncAction } from './AsyncAction';\nimport { AsyncScheduler } from './AsyncScheduler';\n\nexport class AnimationFrameScheduler extends AsyncScheduler {\n  public flush(action?: AsyncAction<any>): void {\n    this._active = true;\n    // The async id that effects a call to flush is stored in _scheduled.\n    // Before executing an action, it's necessary to check the action's async\n    // id to determine whether it's supposed to be executed in the current\n    // flush.\n    // Previous implementations of this method used a count to determine this,\n    // but that was unsound, as actions that are unsubscribed - i.e. cancelled -\n    // are removed from the actions array and that can shift actions that are\n    // scheduled to be executed in a subsequent flush into positions at which\n    // they are executed within the current flush.\n    const flushId = this._scheduled;\n    this._scheduled = undefined;\n\n    const { actions } = this;\n    let error: any;\n    action = action || actions.shift()!;\n\n    do {\n      if ((error = action.execute(action.state, action.delay))) {\n        break;\n      }\n    } while ((action = actions[0]) && action.id === flushId && actions.shift());\n\n    this._active = false;\n\n    if (error) {\n      while ((action = actions[0]) && action.id === flushId && actions.shift()) {\n        action.unsubscribe();\n      }\n      throw error;\n    }\n  }\n}\n", "import { AnimationFrameAction } from './AnimationFrameAction';\nimport { AnimationFrameScheduler } from './AnimationFrameScheduler';\n\n/**\n *\n * Animation Frame Scheduler\n *\n * <span class=\"informal\">Perform task when `window.requestAnimationFrame` would fire</span>\n *\n * When `animationFrame` scheduler is used with delay, it will fall back to {@link asyncScheduler} scheduler\n * behaviour.\n *\n * Without delay, `animationFrame` scheduler can be used to create smooth browser animations.\n * It makes sure scheduled task will happen just before next browser content repaint,\n * thus performing animations as efficiently as possible.\n *\n * ## Example\n * Schedule div height animation\n * ```ts\n * // html: <div style=\"background: #0ff;\"></div>\n * import { animationFrameScheduler } from 'rxjs';\n *\n * const div = document.querySelector('div');\n *\n * animationFrameScheduler.schedule(function(height) {\n *   div.style.height = height + \"px\";\n *\n *   this.schedule(height + 1);  // `this` references currently executing Action,\n *                               // which we reschedule with new state\n * }, 0, 0);\n *\n * // You will see a div element growing in height\n * ```\n */\n\nexport const animationFrameScheduler = new AnimationFrameScheduler(AnimationFrameAction);\n\n/**\n * @deprecated Renamed to {@link animationFrameScheduler}. Will be removed in v8.\n */\nexport const animationFrame = animationFrameScheduler;\n", "import { Observable } from '../Observable';\nimport { SchedulerLike } from '../types';\n\n/**\n * A simple Observable that emits no items to the Observer and immediately\n * emits a complete notification.\n *\n * <span class=\"informal\">Just emits 'complete', and nothing else.</span>\n *\n * ![](empty.png)\n *\n * A simple Observable that only emits the complete notification. It can be used\n * for composing with other Observables, such as in a {@link mergeMap}.\n *\n * ## Examples\n *\n * Log complete notification\n *\n * ```ts\n * import { EMPTY } from 'rxjs';\n *\n * EMPTY.subscribe({\n *   next: () => console.log('Next'),\n *   complete: () => console.log('Complete!')\n * });\n *\n * // Outputs\n * // Complete!\n * ```\n *\n * Emit the number 7, then complete\n *\n * ```ts\n * import { EMPTY, startWith } from 'rxjs';\n *\n * const result = EMPTY.pipe(startWith(7));\n * result.subscribe(x => console.log(x));\n *\n * // Outputs\n * // 7\n * ```\n *\n * Map and flatten only odd numbers to the sequence `'a'`, `'b'`, `'c'`\n *\n * ```ts\n * import { interval, mergeMap, of, EMPTY } from 'rxjs';\n *\n * const interval$ = interval(1000);\n * const result = interval$.pipe(\n *   mergeMap(x => x % 2 === 1 ? of('a', 'b', 'c') : EMPTY),\n * );\n * result.subscribe(x => console.log(x));\n *\n * // Results in the following to the console:\n * // x is equal to the count on the interval, e.g. (0, 1, 2, 3, ...)\n * // x will occur every 1000ms\n * // if x % 2 is equal to 1, print a, b, c (each on its own)\n * // if x % 2 is not equal to 1, nothing will be output\n * ```\n *\n * @see {@link Observable}\n * @see {@link NEVER}\n * @see {@link of}\n * @see {@link throwError}\n */\nexport const EMPTY = new Observable<never>((subscriber) => subscriber.complete());\n\n/**\n * @param scheduler A {@link SchedulerLike} to use for scheduling\n * the emission of the complete notification.\n * @deprecated Replaced with the {@link EMPTY} constant or {@link scheduled} (e.g. `scheduled([], scheduler)`). Will be removed in v8.\n */\nexport function empty(scheduler?: SchedulerLike) {\n  return scheduler ? emptyScheduled(scheduler) : EMPTY;\n}\n\nfunction emptyScheduled(scheduler: SchedulerLike) {\n  return new Observable<never>((subscriber) => scheduler.schedule(() => subscriber.complete()));\n}\n", "import { SchedulerLike } from '../types';\nimport { isFunction } from './isFunction';\n\nexport function isScheduler(value: any): value is SchedulerLike {\n  return value && isFunction(value.schedule);\n}\n", "import { SchedulerLike } from '../types';\nimport { isFunction } from './isFunction';\nimport { isScheduler } from './isScheduler';\n\nfunction last<T>(arr: T[]): T | undefined {\n  return arr[arr.length - 1];\n}\n\nexport function popResultSelector(args: any[]): ((...args: unknown[]) => unknown) | undefined {\n  return isFunction(last(args)) ? args.pop() : undefined;\n}\n\nexport function popScheduler(args: any[]): SchedulerLike | undefined {\n  return isScheduler(last(args)) ? args.pop() : undefined;\n}\n\nexport function popNumber(args: any[], defaultValue: number): number {\n  return typeof last(args) === 'number' ? args.pop()! : defaultValue;\n}\n", "export const isArrayLike = (<T>(x: any): x is ArrayLike<T> => x && typeof x.length === 'number' && typeof x !== 'function');", "import { isFunction } from \"./isFunction\";\n\n/**\n * Tests to see if the object is \"thennable\".\n * @param value the object to test\n */\nexport function isPromise(value: any): value is PromiseLike<any> {\n  return isFunction(value?.then);\n}\n", "import { InteropObservable } from '../types';\nimport { observable as Symbol_observable } from '../symbol/observable';\nimport { isFunction } from './isFunction';\n\n/** Identifies an input as being Observable (but not necessary an Rx Observable) */\nexport function isInteropObservable(input: any): input is InteropObservable<any> {\n  return isFunction(input[Symbol_observable]);\n}\n", "import { isFunction } from './isFunction';\n\nexport function isAsyncIterable<T>(obj: any): obj is AsyncIterable<T> {\n  return Symbol.asyncIterator && isFunction(obj?.[Symbol.asyncIterator]);\n}\n", "/**\n * Creates the TypeError to throw if an invalid object is passed to `from` or `scheduled`.\n * @param input The object that was passed.\n */\nexport function createInvalidObservableTypeError(input: any) {\n  // TODO: We should create error codes that can be looked up, so this can be less verbose.\n  return new TypeError(\n    `You provided ${\n      input !== null && typeof input === 'object' ? 'an invalid object' : `'${input}'`\n    } where a stream was expected. You can provide an Observable, Promise, ReadableStream, Array, AsyncIterable, or Iterable.`\n  );\n}\n", "export function getSymbolIterator(): symbol {\n  if (typeof Symbol !== 'function' || !Symbol.iterator) {\n    return '@@iterator' as any;\n  }\n\n  return Symbol.iterator;\n}\n\nexport const iterator = getSymbolIterator();\n", "import { iterator as Symbol_iterator } from '../symbol/iterator';\nimport { isFunction } from './isFunction';\n\n/** Identifies an input as being an Iterable */\nexport function isIterable(input: any): input is Iterable<any> {\n  return isFunction(input?.[Symbol_iterator]);\n}\n", "import { ReadableStreamLike } from '../types';\nimport { isFunction } from './isFunction';\n\nexport async function* readableStreamLikeToAsyncGenerator<T>(readableStream: ReadableStreamLike<T>): AsyncGenerator<T> {\n  const reader = readableStream.getReader();\n  try {\n    while (true) {\n      const { value, done } = await reader.read();\n      if (done) {\n        return;\n      }\n      yield value!;\n    }\n  } finally {\n    reader.releaseLock();\n  }\n}\n\nexport function isReadableStreamLike<T>(obj: any): obj is ReadableStreamLike<T> {\n  // We don't want to use instanceof checks because they would return\n  // false for instances from another Realm, like an <iframe>.\n  return isFunction(obj?.getReader);\n}\n", "import { isArrayLike } from '../util/isArrayLike';\nimport { isPromise } from '../util/isPromise';\nimport { Observable } from '../Observable';\nimport { ObservableInput, ObservedValueOf, ReadableStreamLike } from '../types';\nimport { isInteropObservable } from '../util/isInteropObservable';\nimport { isAsyncIterable } from '../util/isAsyncIterable';\nimport { createInvalidObservableTypeError } from '../util/throwUnobservableError';\nimport { isIterable } from '../util/isIterable';\nimport { isReadableStreamLike, readableStreamLikeToAsyncGenerator } from '../util/isReadableStreamLike';\nimport { Subscriber } from '../Subscriber';\nimport { isFunction } from '../util/isFunction';\nimport { reportUnhandledError } from '../util/reportUnhandledError';\nimport { observable as Symbol_observable } from '../symbol/observable';\n\nexport function innerFrom<O extends ObservableInput<any>>(input: O): Observable<ObservedValueOf<O>>;\nexport function innerFrom<T>(input: ObservableInput<T>): Observable<T> {\n  if (input instanceof Observable) {\n    return input;\n  }\n  if (input != null) {\n    if (isInteropObservable(input)) {\n      return fromInteropObservable(input);\n    }\n    if (isArrayLike(input)) {\n      return fromArrayLike(input);\n    }\n    if (isPromise(input)) {\n      return fromPromise(input);\n    }\n    if (isAsyncIterable(input)) {\n      return fromAsyncIterable(input);\n    }\n    if (isIterable(input)) {\n      return fromIterable(input);\n    }\n    if (isReadableStreamLike(input)) {\n      return fromReadableStreamLike(input);\n    }\n  }\n\n  throw createInvalidObservableTypeError(input);\n}\n\n/**\n * Creates an RxJS Observable from an object that implements `Symbol.observable`.\n * @param obj An object that properly implements `Symbol.observable`.\n */\nexport function fromInteropObservable<T>(obj: any) {\n  return new Observable((subscriber: Subscriber<T>) => {\n    const obs = obj[Symbol_observable]();\n    if (isFunction(obs.subscribe)) {\n      return obs.subscribe(subscriber);\n    }\n    // Should be caught by observable subscribe function error handling.\n    throw new TypeError('Provided object does not correctly implement Symbol.observable');\n  });\n}\n\n/**\n * Synchronously emits the values of an array like and completes.\n * This is exported because there are creation functions and operators that need to\n * make direct use of the same logic, and there's no reason to make them run through\n * `from` conditionals because we *know* they're dealing with an array.\n * @param array The array to emit values from\n */\nexport function fromArrayLike<T>(array: ArrayLike<T>) {\n  return new Observable((subscriber: Subscriber<T>) => {\n    // Loop over the array and emit each value. Note two things here:\n    // 1. We're making sure that the subscriber is not closed on each loop.\n    //    This is so we don't continue looping over a very large array after\n    //    something like a `take`, `takeWhile`, or other synchronous unsubscription\n    //    has already unsubscribed.\n    // 2. In this form, reentrant code can alter that array we're looping over.\n    //    This is a known issue, but considered an edge case. The alternative would\n    //    be to copy the array before executing the loop, but this has\n    //    performance implications.\n    for (let i = 0; i < array.length && !subscriber.closed; i++) {\n      subscriber.next(array[i]);\n    }\n    subscriber.complete();\n  });\n}\n\nexport function fromPromise<T>(promise: PromiseLike<T>) {\n  return new Observable((subscriber: Subscriber<T>) => {\n    promise\n      .then(\n        (value) => {\n          if (!subscriber.closed) {\n            subscriber.next(value);\n            subscriber.complete();\n          }\n        },\n        (err: any) => subscriber.error(err)\n      )\n      .then(null, reportUnhandledError);\n  });\n}\n\nexport function fromIterable<T>(iterable: Iterable<T>) {\n  return new Observable((subscriber: Subscriber<T>) => {\n    for (const value of iterable) {\n      subscriber.next(value);\n      if (subscriber.closed) {\n        return;\n      }\n    }\n    subscriber.complete();\n  });\n}\n\nexport function fromAsyncIterable<T>(asyncIterable: AsyncIterable<T>) {\n  return new Observable((subscriber: Subscriber<T>) => {\n    process(asyncIterable, subscriber).catch((err) => subscriber.error(err));\n  });\n}\n\nexport function fromReadableStreamLike<T>(readableStream: ReadableStreamLike<T>) {\n  return fromAsyncIterable(readableStreamLikeToAsyncGenerator(readableStream));\n}\n\nasync function process<T>(asyncIterable: AsyncIterable<T>, subscriber: Subscriber<T>) {\n  for await (const value of asyncIterable) {\n    subscriber.next(value);\n    // A side-effect may have closed our subscriber,\n    // check before the next iteration.\n    if (subscriber.closed) {\n      return;\n    }\n  }\n  subscriber.complete();\n}\n", "import { Subscription } from '../Subscription';\nimport { SchedulerAction, SchedulerLike } from '../types';\n\nexport function executeSchedule(\n  parentSubscription: Subscription,\n  scheduler: SchedulerLike,\n  work: () => void,\n  delay: number,\n  repeat: true\n): void;\nexport function executeSchedule(\n  parentSubscription: Subscription,\n  scheduler: SchedulerLike,\n  work: () => void,\n  delay?: number,\n  repeat?: false\n): Subscription;\n\nexport function executeSchedule(\n  parentSubscription: Subscription,\n  scheduler: SchedulerLike,\n  work: () => void,\n  delay = 0,\n  repeat = false\n): Subscription | void {\n  const scheduleSubscription = scheduler.schedule(function (this: SchedulerAction<any>) {\n    work();\n    if (repeat) {\n      parentSubscription.add(this.schedule(null, delay));\n    } else {\n      this.unsubscribe();\n    }\n  }, delay);\n\n  parentSubscription.add(scheduleSubscription);\n\n  if (!repeat) {\n    // Because user-land scheduler implementations are unlikely to properly reuse\n    // Actions for repeat scheduling, we can't trust that the returned subscription\n    // will control repeat subscription scenarios. So we're trying to avoid using them\n    // incorrectly within this library.\n    return scheduleSubscription;\n  }\n}\n", "/** @prettier */\nimport { MonoTypeOperatorFunction, SchedulerLike } from '../types';\nimport { executeSchedule } from '../util/executeSchedule';\nimport { operate } from '../util/lift';\nimport { createOperatorSubscriber } from './OperatorSubscriber';\n\n/**\n * Re-emits all notifications from source Observable with specified scheduler.\n *\n * <span class=\"informal\">Ensure a specific scheduler is used, from outside of an Observable.</span>\n *\n * `observeOn` is an operator that accepts a scheduler as a first parameter, which will be used to reschedule\n * notifications emitted by the source Observable. It might be useful, if you do not have control over\n * internal scheduler of a given Observable, but want to control when its values are emitted nevertheless.\n *\n * Returned Observable emits the same notifications (nexted values, complete and error events) as the source Observable,\n * but rescheduled with provided scheduler. Note that this doesn't mean that source Observables internal\n * scheduler will be replaced in any way. Original scheduler still will be used, but when the source Observable emits\n * notification, it will be immediately scheduled again - this time with scheduler passed to `observeOn`.\n * An anti-pattern would be calling `observeOn` on Observable that emits lots of values synchronously, to split\n * that emissions into asynchronous chunks. For this to happen, scheduler would have to be passed into the source\n * Observable directly (usually into the operator that creates it). `observeOn` simply delays notifications a\n * little bit more, to ensure that they are emitted at expected moments.\n *\n * As a matter of fact, `observeOn` accepts second parameter, which specifies in milliseconds with what delay notifications\n * will be emitted. The main difference between {@link delay} operator and `observeOn` is that `observeOn`\n * will delay all notifications - including error notifications - while `delay` will pass through error\n * from source Observable immediately when it is emitted. In general it is highly recommended to use `delay` operator\n * for any kind of delaying of values in the stream, while using `observeOn` to specify which scheduler should be used\n * for notification emissions in general.\n *\n * ## Example\n *\n * Ensure values in subscribe are called just before browser repaint\n *\n * ```ts\n * import { interval, observeOn, animationFrameScheduler } from 'rxjs';\n *\n * const someDiv = document.createElement('div');\n * someDiv.style.cssText = 'width: 200px;background: #09c';\n * document.body.appendChild(someDiv);\n * const intervals = interval(10);      // Intervals are scheduled\n *                                      // with async scheduler by default...\n * intervals.pipe(\n *   observeOn(animationFrameScheduler) // ...but we will observe on animationFrame\n * )                                    // scheduler to ensure smooth animation.\n * .subscribe(val => {\n *   someDiv.style.height = val + 'px';\n * });\n * ```\n *\n * @see {@link delay}\n *\n * @param scheduler Scheduler that will be used to reschedule notifications from source Observable.\n * @param delay Number of milliseconds that states with what delay every notification should be rescheduled.\n * @return A function that returns an Observable that emits the same\n * notifications as the source Observable, but with provided scheduler.\n */\nexport function observeOn<T>(scheduler: SchedulerLike, delay = 0): MonoTypeOperatorFunction<T> {\n  return operate((source, subscriber) => {\n    source.subscribe(\n      createOperatorSubscriber(\n        subscriber,\n        (value) => executeSchedule(subscriber, scheduler, () => subscriber.next(value), delay),\n        () => executeSchedule(subscriber, scheduler, () => subscriber.complete(), delay),\n        (err) => executeSchedule(subscriber, scheduler, () => subscriber.error(err), delay)\n      )\n    );\n  });\n}\n", "import { MonoTypeOperatorFunction, SchedulerLike } from '../types';\nimport { operate } from '../util/lift';\n\n/**\n * Asynchronously subscribes Observers to this Observable on the specified {@link SchedulerLike}.\n *\n * With `subscribeOn` you can decide what type of scheduler a specific Observable will be using when it is subscribed to.\n *\n * Schedulers control the speed and order of emissions to observers from an Observable stream.\n *\n * ![](subscribeOn.png)\n *\n * ## Example\n *\n * Given the following code:\n *\n * ```ts\n * import { of, merge } from 'rxjs';\n *\n * const a = of(1, 2, 3);\n * const b = of(4, 5, 6);\n *\n * merge(a, b).subscribe(console.log);\n *\n * // Outputs\n * // 1\n * // 2\n * // 3\n * // 4\n * // 5\n * // 6\n * ```\n *\n * Both Observable `a` and `b` will emit their values directly and synchronously once they are subscribed to.\n *\n * If we instead use the `subscribeOn` operator declaring that we want to use the {@link asyncScheduler} for values emitted by Observable `a`:\n *\n * ```ts\n * import { of, subscribeOn, asyncScheduler, merge } from 'rxjs';\n *\n * const a = of(1, 2, 3).pipe(subscribeOn(asyncScheduler));\n * const b = of(4, 5, 6);\n *\n * merge(a, b).subscribe(console.log);\n *\n * // Outputs\n * // 4\n * // 5\n * // 6\n * // 1\n * // 2\n * // 3\n * ```\n *\n * The reason for this is that Observable `b` emits its values directly and synchronously like before\n * but the emissions from `a` are scheduled on the event loop because we are now using the {@link asyncScheduler} for that specific Observable.\n *\n * @param scheduler The {@link SchedulerLike} to perform subscription actions on.\n * @param delay A delay to pass to the scheduler to delay subscriptions\n * @return A function that returns an Observable modified so that its\n * subscriptions happen on the specified {@link SchedulerLike}.\n */\nexport function subscribeOn<T>(scheduler: SchedulerLike, delay: number = 0): MonoTypeOperatorFunction<T> {\n  return operate((source, subscriber) => {\n    subscriber.add(scheduler.schedule(() => source.subscribe(subscriber), delay));\n  });\n}\n", "import { innerFrom } from '../observable/innerFrom';\nimport { observeOn } from '../operators/observeOn';\nimport { subscribeOn } from '../operators/subscribeOn';\nimport { InteropObservable, SchedulerLike } from '../types';\n\nexport function scheduleObservable<T>(input: InteropObservable<T>, scheduler: SchedulerLike) {\n  return innerFrom(input).pipe(subscribeOn(scheduler), observeOn(scheduler));\n}\n", "import { innerFrom } from '../observable/innerFrom';\nimport { observeOn } from '../operators/observeOn';\nimport { subscribeOn } from '../operators/subscribeOn';\nimport { SchedulerLike } from '../types';\n\nexport function schedulePromise<T>(input: PromiseLike<T>, scheduler: SchedulerLike) {\n  return innerFrom(input).pipe(subscribeOn(scheduler), observeOn(scheduler));\n}\n", "import { Observable } from '../Observable';\nimport { SchedulerLike } from '../types';\n\nexport function scheduleArray<T>(input: ArrayLike<T>, scheduler: SchedulerLike) {\n  return new Observable<T>((subscriber) => {\n    // The current array index.\n    let i = 0;\n    // Start iterating over the array like on a schedule.\n    return scheduler.schedule(function () {\n      if (i === input.length) {\n        // If we have hit the end of the array like in the\n        // previous job, we can complete.\n        subscriber.complete();\n      } else {\n        // Otherwise let's next the value at the current index,\n        // then increment our index.\n        subscriber.next(input[i++]);\n        // If the last emission didn't cause us to close the subscriber\n        // (via take or some side effect), reschedule the job and we'll\n        // make another pass.\n        if (!subscriber.closed) {\n          this.schedule();\n        }\n      }\n    });\n  });\n}\n", "import { Observable } from '../Observable';\nimport { SchedulerLike } from '../types';\nimport { iterator as Symbol_iterator } from '../symbol/iterator';\nimport { isFunction } from '../util/isFunction';\nimport { executeSchedule } from '../util/executeSchedule';\n\n/**\n * Used in {@link scheduled} to create an observable from an Iterable.\n * @param input The iterable to create an observable from\n * @param scheduler The scheduler to use\n */\nexport function scheduleIterable<T>(input: Iterable<T>, scheduler: SchedulerLike) {\n  return new Observable<T>((subscriber) => {\n    let iterator: Iterator<T, T>;\n\n    // Schedule the initial creation of the iterator from\n    // the iterable. This is so the code in the iterable is\n    // not called until the scheduled job fires.\n    executeSchedule(subscriber, scheduler, () => {\n      // Create the iterator.\n      iterator = (input as any)[Symbol_iterator]();\n\n      executeSchedule(\n        subscriber,\n        scheduler,\n        () => {\n          let value: T;\n          let done: boolean | undefined;\n          try {\n            // Pull the value out of the iterator\n            ({ value, done } = iterator.next());\n          } catch (err) {\n            // We got an error while pulling from the iterator\n            subscriber.error(err);\n            return;\n          }\n\n          if (done) {\n            // If it is \"done\" we just complete. This mimics the\n            // behavior of JavaScript's `for..of` consumption of\n            // iterables, which will not emit the value from an iterator\n            // result of `{ done: true: value: 'here' }`.\n            subscriber.complete();\n          } else {\n            // The iterable is not done, emit the value.\n            subscriber.next(value);\n          }\n        },\n        0,\n        true\n      );\n    });\n\n    // During finalization, if we see this iterator has a `return` method,\n    // then we know it is a Generator, and not just an Iterator. So we call\n    // the `return()` function. This will ensure that any `finally { }` blocks\n    // inside of the generator we can hit will be hit properly.\n    return () => isFunction(iterator?.return) && iterator.return();\n  });\n}\n", "import { SchedulerLike } from '../types';\nimport { Observable } from '../Observable';\nimport { executeSchedule } from '../util/executeSchedule';\n\nexport function scheduleAsyncIterable<T>(input: AsyncIterable<T>, scheduler: SchedulerLike) {\n  if (!input) {\n    throw new Error('Iterable cannot be null');\n  }\n  return new Observable<T>((subscriber) => {\n    executeSchedule(subscriber, scheduler, () => {\n      const iterator = input[Symbol.asyncIterator]();\n      executeSchedule(\n        subscriber,\n        scheduler,\n        () => {\n          iterator.next().then((result) => {\n            if (result.done) {\n              // This will remove the subscriptions from\n              // the parent subscription.\n              subscriber.complete();\n            } else {\n              subscriber.next(result.value);\n            }\n          });\n        },\n        0,\n        true\n      );\n    });\n  });\n}\n", "import { SchedulerLike, ReadableStreamLike } from '../types';\nimport { Observable } from '../Observable';\nimport { scheduleAsyncIterable } from './scheduleAsyncIterable';\nimport { readableStreamLikeToAsyncGenerator } from '../util/isReadableStreamLike';\n\nexport function scheduleReadableStreamLike<T>(input: ReadableStreamLike<T>, scheduler: SchedulerLike): Observable<T> {\n  return scheduleAsyncIterable(readableStreamLikeToAsyncGenerator(input), scheduler);\n}\n", "import { scheduleObservable } from './scheduleObservable';\nimport { schedulePromise } from './schedulePromise';\nimport { scheduleArray } from './scheduleArray';\nimport { scheduleIterable } from './scheduleIterable';\nimport { scheduleAsyncIterable } from './scheduleAsyncIterable';\nimport { isInteropObservable } from '../util/isInteropObservable';\nimport { isPromise } from '../util/isPromise';\nimport { isArrayLike } from '../util/isArrayLike';\nimport { isIterable } from '../util/isIterable';\nimport { ObservableInput, SchedulerLike } from '../types';\nimport { Observable } from '../Observable';\nimport { isAsyncIterable } from '../util/isAsyncIterable';\nimport { createInvalidObservableTypeError } from '../util/throwUnobservableError';\nimport { isReadableStreamLike } from '../util/isReadableStreamLike';\nimport { scheduleReadableStreamLike } from './scheduleReadableStreamLike';\n\n/**\n * Converts from a common {@link ObservableInput} type to an observable where subscription and emissions\n * are scheduled on the provided scheduler.\n *\n * @see {@link from}\n * @see {@link of}\n *\n * @param input The observable, array, promise, iterable, etc you would like to schedule\n * @param scheduler The scheduler to use to schedule the subscription and emissions from\n * the returned observable.\n */\nexport function scheduled<T>(input: ObservableInput<T>, scheduler: SchedulerLike): Observable<T> {\n  if (input != null) {\n    if (isInteropObservable(input)) {\n      return scheduleObservable(input, scheduler);\n    }\n    if (isArrayLike(input)) {\n      return scheduleArray(input, scheduler);\n    }\n    if (isPromise(input)) {\n      return schedulePromise(input, scheduler);\n    }\n    if (isAsyncIterable(input)) {\n      return scheduleAsyncIterable(input, scheduler);\n    }\n    if (isIterable(input)) {\n      return scheduleIterable(input, scheduler);\n    }\n    if (isReadableStreamLike(input)) {\n      return scheduleReadableStreamLike(input, scheduler);\n    }\n  }\n  throw createInvalidObservableTypeError(input);\n}\n", "import { Observable } from '../Observable';\nimport { ObservableInput, SchedulerLike, ObservedValueOf } from '../types';\nimport { scheduled } from '../scheduled/scheduled';\nimport { innerFrom } from './innerFrom';\n\nexport function from<O extends ObservableInput<any>>(input: O): Observable<ObservedValueOf<O>>;\n/** @deprecated The `scheduler` parameter will be removed in v8. Use `scheduled`. Details: https://rxjs.dev/deprecations/scheduler-argument */\nexport function from<O extends ObservableInput<any>>(input: O, scheduler: SchedulerLike | undefined): Observable<ObservedValueOf<O>>;\n\n/**\n * Creates an Observable from an Array, an array-like object, a Promise, an iterable object, or an Observable-like object.\n *\n * <span class=\"informal\">Converts almost anything to an Observable.</span>\n *\n * ![](from.png)\n *\n * `from` converts various other objects and data types into Observables. It also converts a Promise, an array-like, or an\n * <a href=\"https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Iteration_protocols#iterable\" target=\"_blank\">iterable</a>\n * object into an Observable that emits the items in that promise, array, or iterable. A String, in this context, is treated\n * as an array of characters. Observable-like objects (contains a function named with the ES2015 Symbol for Observable) can also be\n * converted through this operator.\n *\n * ## Examples\n *\n * Converts an array to an Observable\n *\n * ```ts\n * import { from } from 'rxjs';\n *\n * const array = [10, 20, 30];\n * const result = from(array);\n *\n * result.subscribe(x => console.log(x));\n *\n * // Logs:\n * // 10\n * // 20\n * // 30\n * ```\n *\n * Convert an infinite iterable (from a generator) to an Observable\n *\n * ```ts\n * import { from, take } from 'rxjs';\n *\n * function* generateDoubles(seed) {\n *    let i = seed;\n *    while (true) {\n *      yield i;\n *      i = 2 * i; // double it\n *    }\n * }\n *\n * const iterator = generateDoubles(3);\n * const result = from(iterator).pipe(take(10));\n *\n * result.subscribe(x => console.log(x));\n *\n * // Logs:\n * // 3\n * // 6\n * // 12\n * // 24\n * // 48\n * // 96\n * // 192\n * // 384\n * // 768\n * // 1536\n * ```\n *\n * With `asyncScheduler`\n *\n * ```ts\n * import { from, asyncScheduler } from 'rxjs';\n *\n * console.log('start');\n *\n * const array = [10, 20, 30];\n * const result = from(array, asyncScheduler);\n *\n * result.subscribe(x => console.log(x));\n *\n * console.log('end');\n *\n * // Logs:\n * // 'start'\n * // 'end'\n * // 10\n * // 20\n * // 30\n * ```\n *\n * @see {@link fromEvent}\n * @see {@link fromEventPattern}\n *\n * @param {ObservableInput<T>} A subscription object, a Promise, an Observable-like,\n * an Array, an iterable, or an array-like object to be converted.\n * @param {SchedulerLike} An optional {@link SchedulerLike} on which to schedule the emission of values.\n * @return {Observable<T>}\n */\nexport function from<T>(input: ObservableInput<T>, scheduler?: SchedulerLike): Observable<T> {\n  return scheduler ? scheduled(input, scheduler) : innerFrom(input);\n}\n", "import { SchedulerLike, ValueFromArray } from '../types';\nimport { Observable } from '../Observable';\nimport { popScheduler } from '../util/args';\nimport { from } from './from';\n\n// Devs are more likely to pass null or undefined than they are a scheduler\n// without accompanying values. To make things easier for (naughty) devs who\n// use the `strictNullChecks: false` TypeScript compiler option, these\n// overloads with explicit null and undefined values are included.\n\nexport function of(value: null): Observable<null>;\nexport function of(value: undefined): Observable<undefined>;\n\n/** @deprecated The `scheduler` parameter will be removed in v8. Use `scheduled`. Details: https://rxjs.dev/deprecations/scheduler-argument */\nexport function of(scheduler: SchedulerLike): Observable<never>;\n/** @deprecated The `scheduler` parameter will be removed in v8. Use `scheduled`. Details: https://rxjs.dev/deprecations/scheduler-argument */\nexport function of<A extends readonly unknown[]>(...valuesAndScheduler: [...A, SchedulerLike]): Observable<ValueFromArray<A>>;\n\nexport function of(): Observable<never>;\n/** @deprecated Do not specify explicit type parameters. Signatures with type parameters that cannot be inferred will be removed in v8. */\nexport function of<T>(): Observable<T>;\nexport function of<T>(value: T): Observable<T>;\nexport function of<A extends readonly unknown[]>(...values: A): Observable<ValueFromArray<A>>;\n\n/**\n * Converts the arguments to an observable sequence.\n *\n * <span class=\"informal\">Each argument becomes a `next` notification.</span>\n *\n * ![](of.png)\n *\n * Unlike {@link from}, it does not do any flattening and emits each argument in whole\n * as a separate `next` notification.\n *\n * ## Examples\n *\n * Emit the values `10, 20, 30`\n *\n * ```ts\n * import { of } from 'rxjs';\n *\n * of(10, 20, 30)\n *   .subscribe({\n *     next: value => console.log('next:', value),\n *     error: err => console.log('error:', err),\n *     complete: () => console.log('the end'),\n *   });\n *\n * // Outputs\n * // next: 10\n * // next: 20\n * // next: 30\n * // the end\n * ```\n *\n * Emit the array `[1, 2, 3]`\n *\n * ```ts\n * import { of } from 'rxjs';\n *\n * of([1, 2, 3])\n *   .subscribe({\n *     next: value => console.log('next:', value),\n *     error: err => console.log('error:', err),\n *     complete: () => console.log('the end'),\n *   });\n *\n * // Outputs\n * // next: [1, 2, 3]\n * // the end\n * ```\n *\n * @see {@link from}\n * @see {@link range}\n *\n * @param {...T} values A comma separated list of arguments you want to be emitted\n * @return {Observable} An Observable that emits the arguments\n * described above and then completes.\n */\nexport function of<T>(...args: Array<T | SchedulerLike>): Observable<T> {\n  const scheduler = popScheduler(args);\n  return from(args as T[], scheduler);\n}\n", "import { Observable } from '../Observable';\nimport { Subscriber } from '../Subscriber';\nimport { SchedulerLike } from '../types';\nimport { isFunction } from '../util/isFunction';\n\n/**\n * Creates an observable that will create an error instance and push it to the consumer as an error\n * immediately upon subscription.\n *\n * <span class=\"informal\">Just errors and does nothing else</span>\n *\n * ![](throw.png)\n *\n * This creation function is useful for creating an observable that will create an error and error every\n * time it is subscribed to. Generally, inside of most operators when you might want to return an errored\n * observable, this is unnecessary. In most cases, such as in the inner return of {@link concatMap},\n * {@link mergeMap}, {@link defer}, and many others, you can simply throw the error, and RxJS will pick\n * that up and notify the consumer of the error.\n *\n * ## Example\n *\n * Create a simple observable that will create a new error with a timestamp and log it\n * and the message every time you subscribe to it\n *\n * ```ts\n * import { throwError } from 'rxjs';\n *\n * let errorCount = 0;\n *\n * const errorWithTimestamp$ = throwError(() => {\n *   const error: any = new Error(`This is error number ${ ++errorCount }`);\n *   error.timestamp = Date.now();\n *   return error;\n * });\n *\n * errorWithTimestamp$.subscribe({\n *   error: err => console.log(err.timestamp, err.message)\n * });\n *\n * errorWithTimestamp$.subscribe({\n *   error: err => console.log(err.timestamp, err.message)\n * });\n *\n * // Logs the timestamp and a new error message for each subscription\n * ```\n *\n * ### Unnecessary usage\n *\n * Using `throwError` inside of an operator or creation function\n * with a callback, is usually not necessary\n *\n * ```ts\n * import { of, concatMap, timer, throwError } from 'rxjs';\n *\n * const delays$ = of(1000, 2000, Infinity, 3000);\n *\n * delays$.pipe(\n *   concatMap(ms => {\n *     if (ms < 10000) {\n *       return timer(ms);\n *     } else {\n *       // This is probably overkill.\n *       return throwError(() => new Error(`Invalid time ${ ms }`));\n *     }\n *   })\n * )\n * .subscribe({\n *   next: console.log,\n *   error: console.error\n * });\n * ```\n *\n * You can just throw the error instead\n *\n * ```ts\n * import { of, concatMap, timer } from 'rxjs';\n *\n * const delays$ = of(1000, 2000, Infinity, 3000);\n *\n * delays$.pipe(\n *   concatMap(ms => {\n *     if (ms < 10000) {\n *       return timer(ms);\n *     } else {\n *       // Cleaner and easier to read for most folks.\n *       throw new Error(`Invalid time ${ ms }`);\n *     }\n *   })\n * )\n * .subscribe({\n *   next: console.log,\n *   error: console.error\n * });\n * ```\n *\n * @param errorFactory A factory function that will create the error instance that is pushed.\n */\nexport function throwError(errorFactory: () => any): Observable<never>;\n\n/**\n * Returns an observable that will error with the specified error immediately upon subscription.\n *\n * @param error The error instance to emit\n * @deprecated Support for passing an error value will be removed in v8. Instead, pass a factory function to `throwError(() => new Error('test'))`. This is\n * because it will create the error at the moment it should be created and capture a more appropriate stack trace. If\n * for some reason you need to create the error ahead of time, you can still do that: `const err = new Error('test'); throwError(() => err);`.\n */\nexport function throwError(error: any): Observable<never>;\n\n/**\n * Notifies the consumer of an error using a given scheduler by scheduling it at delay `0` upon subscription.\n *\n * @param errorOrErrorFactory An error instance or error factory\n * @param scheduler A scheduler to use to schedule the error notification\n * @deprecated The `scheduler` parameter will be removed in v8.\n * Use `throwError` in combination with {@link observeOn}: `throwError(() => new Error('test')).pipe(observeOn(scheduler));`.\n * Details: https://rxjs.dev/deprecations/scheduler-argument\n */\nexport function throwError(errorOrErrorFactory: any, scheduler: SchedulerLike): Observable<never>;\n\nexport function throwError(errorOrErrorFactory: any, scheduler?: SchedulerLike): Observable<never> {\n  const errorFactory = isFunction(errorOrErrorFactory) ? errorOrErrorFactory : () => errorOrErrorFactory;\n  const init = (subscriber: Subscriber<never>) => subscriber.error(errorFactory());\n  return new Observable(scheduler ? (subscriber) => scheduler.schedule(init as any, 0, subscriber) : init);\n}\n", "import { createErrorClass } from './createErrorClass';\n\nexport interface EmptyError extends Error {}\n\nexport interface EmptyErrorCtor {\n  /**\n   * @deprecated Internal implementation detail. Do not construct error instances.\n   * Cannot be tagged as internal: https://github.com/ReactiveX/rxjs/issues/6269\n   */\n  new (): EmptyError;\n}\n\n/**\n * An error thrown when an Observable or a sequence was queried but has no\n * elements.\n *\n * @see {@link first}\n * @see {@link last}\n * @see {@link single}\n * @see {@link firstValueFrom}\n * @see {@link lastValueFrom}\n *\n * @class EmptyError\n */\nexport const EmptyError: EmptyErrorCtor = createErrorClass((_super) => function EmptyErrorImpl(this: any) {\n  _super(this);\n  this.name = 'EmptyError';\n  this.message = 'no elements in sequence';\n});\n", "/**\n * Checks to see if a value is not only a `Date` object,\n * but a *valid* `Date` object that can be converted to a\n * number. For example, `new Date('blah')` is indeed an\n * `instanceof Date`, however it cannot be converted to a\n * number.\n */\nexport function isValidDate(value: any): value is Date {\n  return value instanceof Date && !isNaN(value as any);\n}\n", "import { OperatorFunction } from '../types';\nimport { operate } from '../util/lift';\nimport { createOperatorSubscriber } from './OperatorSubscriber';\n\nexport function map<T, R>(project: (value: T, index: number) => R): OperatorFunction<T, R>;\n/** @deprecated Use a closure instead of a `thisArg`. Signatures accepting a `thisArg` will be removed in v8. */\nexport function map<T, R, A>(project: (this: A, value: T, index: number) => R, thisArg: A): OperatorFunction<T, R>;\n\n/**\n * Applies a given `project` function to each value emitted by the source\n * Observable, and emits the resulting values as an Observable.\n *\n * <span class=\"informal\">Like [Array.prototype.map()](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array/map),\n * it passes each source value through a transformation function to get\n * corresponding output values.</span>\n *\n * ![](map.png)\n *\n * Similar to the well known `Array.prototype.map` function, this operator\n * applies a projection to each value and emits that projection in the output\n * Observable.\n *\n * ## Example\n *\n * Map every click to the `clientX` position of that click\n *\n * ```ts\n * import { fromEvent, map } from 'rxjs';\n *\n * const clicks = fromEvent<PointerEvent>(document, 'click');\n * const positions = clicks.pipe(map(ev => ev.clientX));\n *\n * positions.subscribe(x => console.log(x));\n * ```\n *\n * @see {@link mapTo}\n * @see {@link pluck}\n *\n * @param {function(value: T, index: number): R} project The function to apply\n * to each `value` emitted by the source Observable. The `index` parameter is\n * the number `i` for the i-th emission that has happened since the\n * subscription, starting from the number `0`.\n * @param {any} [thisArg] An optional argument to define what `this` is in the\n * `project` function.\n * @return A function that returns an Observable that emits the values from the\n * source Observable transformed by the given `project` function.\n */\nexport function map<T, R>(project: (value: T, index: number) => R, thisArg?: any): OperatorFunction<T, R> {\n  return operate((source, subscriber) => {\n    // The index of the value from the source. Used with projection.\n    let index = 0;\n    // Subscribe to the source, all errors and completions are sent along\n    // to the consumer.\n    source.subscribe(\n      createOperatorSubscriber(subscriber, (value: T) => {\n        // Call the projection function with the appropriate this context,\n        // and send the resulting value to the consumer.\n        subscriber.next(project.call(thisArg, value, index++));\n      })\n    );\n  });\n}\n", "import { OperatorFunction } from \"../types\";\nimport { map } from \"../operators/map\";\n\nconst { isArray } = Array;\n\nfunction callOrApply<T, R>(fn: ((...values: T[]) => R), args: T|T[]): R {\n    return isArray(args) ? fn(...args) : fn(args);\n}\n\n/**\n * Used in several -- mostly deprecated -- situations where we need to \n * apply a list of arguments or a single argument to a result selector.\n */\nexport function mapOneOrManyArgs<T, R>(fn: ((...values: T[]) => R)): OperatorFunction<T|T[], R> {\n    return map(args => callOrApply(fn, args))\n}", "const { isArray } = Array;\nconst { getPrototypeOf, prototype: objectProto, keys: getKeys } = Object;\n\n/**\n * Used in functions where either a list of arguments, a single array of arguments, or a\n * dictionary of arguments can be returned. Returns an object with an `args` property with\n * the arguments in an array, if it is a dictionary, it will also return the `keys` in another\n * property.\n */\nexport function argsArgArrayOrObject<T, O extends Record<string, T>>(args: T[] | [O] | [T[]]): { args: T[]; keys: string[] | null } {\n  if (args.length === 1) {\n    const first = args[0];\n    if (isArray(first)) {\n      return { args: first, keys: null };\n    }\n    if (isPOJO(first)) {\n      const keys = getKeys(first);\n      return {\n        args: keys.map((key) => first[key]),\n        keys,\n      };\n    }\n  }\n\n  return { args: args as T[], keys: null };\n}\n\nfunction isPOJO(obj: any): obj is object {\n  return obj && typeof obj === 'object' && getPrototypeOf(obj) === objectProto;\n}\n", "export function createObject(keys: string[], values: any[]) {\n  return keys.reduce((result, key, i) => ((result[key] = values[i]), result), {} as any);\n}\n", "import { Observable } from '../Observable';\nimport { ObservableInput, SchedulerLike, ObservedValueOf, ObservableInputTuple } from '../types';\nimport { argsArgArrayOrObject } from '../util/argsArgArrayOrObject';\nimport { Subscriber } from '../Subscriber';\nimport { from } from './from';\nimport { identity } from '../util/identity';\nimport { Subscription } from '../Subscription';\nimport { mapOneOrManyArgs } from '../util/mapOneOrManyArgs';\nimport { popResultSelector, popScheduler } from '../util/args';\nimport { createObject } from '../util/createObject';\nimport { createOperatorSubscriber } from '../operators/OperatorSubscriber';\nimport { AnyCatcher } from '../AnyCatcher';\nimport { executeSchedule } from '../util/executeSchedule';\n\n// combineLatest(any)\n// We put this first because we need to catch cases where the user has supplied\n// _exactly `any`_ as the argument. Since `any` literally matches _anything_,\n// we don't want it to randomly hit one of the other type signatures below,\n// as we have no idea at build-time what type we should be returning when given an any.\n\n/**\n * You have passed `any` here, we can't figure out if it is\n * an array or an object, so you're getting `unknown`. Use better types.\n * @param arg Something typed as `any`\n */\nexport function combineLatest<T extends AnyCatcher>(arg: T): Observable<unknown>;\n\n// combineLatest([a, b, c])\nexport function combineLatest(sources: []): Observable<never>;\nexport function combineLatest<A extends readonly unknown[]>(sources: readonly [...ObservableInputTuple<A>]): Observable<A>;\n/** @deprecated The `scheduler` parameter will be removed in v8. Use `scheduled` and `combineLatestAll`. Details: https://rxjs.dev/deprecations/scheduler-argument */\nexport function combineLatest<A extends readonly unknown[], R>(\n  sources: readonly [...ObservableInputTuple<A>],\n  resultSelector: (...values: A) => R,\n  scheduler: SchedulerLike\n): Observable<R>;\nexport function combineLatest<A extends readonly unknown[], R>(\n  sources: readonly [...ObservableInputTuple<A>],\n  resultSelector: (...values: A) => R\n): Observable<R>;\n/** @deprecated The `scheduler` parameter will be removed in v8. Use `scheduled` and `combineLatestAll`. Details: https://rxjs.dev/deprecations/scheduler-argument */\nexport function combineLatest<A extends readonly unknown[]>(\n  sources: readonly [...ObservableInputTuple<A>],\n  scheduler: SchedulerLike\n): Observable<A>;\n\n// combineLatest(a, b, c)\n/** @deprecated Pass an array of sources instead. The rest-parameters signature will be removed in v8. Details: https://rxjs.dev/deprecations/array-argument */\nexport function combineLatest<A extends readonly unknown[]>(...sources: [...ObservableInputTuple<A>]): Observable<A>;\n/** @deprecated The `scheduler` parameter will be removed in v8. Use `scheduled` and `combineLatestAll`. Details: https://rxjs.dev/deprecations/scheduler-argument */\nexport function combineLatest<A extends readonly unknown[], R>(\n  ...sourcesAndResultSelectorAndScheduler: [...ObservableInputTuple<A>, (...values: A) => R, SchedulerLike]\n): Observable<R>;\n/** @deprecated Pass an array of sources instead. The rest-parameters signature will be removed in v8. Details: https://rxjs.dev/deprecations/array-argument */\nexport function combineLatest<A extends readonly unknown[], R>(\n  ...sourcesAndResultSelector: [...ObservableInputTuple<A>, (...values: A) => R]\n): Observable<R>;\n/** @deprecated The `scheduler` parameter will be removed in v8. Use `scheduled` and `combineLatestAll`. Details: https://rxjs.dev/deprecations/scheduler-argument */\nexport function combineLatest<A extends readonly unknown[]>(\n  ...sourcesAndScheduler: [...ObservableInputTuple<A>, SchedulerLike]\n): Observable<A>;\n\n// combineLatest({a, b, c})\nexport function combineLatest(sourcesObject: { [K in any]: never }): Observable<never>;\nexport function combineLatest<T extends Record<string, ObservableInput<any>>>(\n  sourcesObject: T\n): Observable<{ [K in keyof T]: ObservedValueOf<T[K]> }>;\n\n/**\n * Combines multiple Observables to create an Observable whose values are\n * calculated from the latest values of each of its input Observables.\n *\n * <span class=\"informal\">Whenever any input Observable emits a value, it\n * computes a formula using the latest values from all the inputs, then emits\n * the output of that formula.</span>\n *\n * ![](combineLatest.png)\n *\n * `combineLatest` combines the values from all the Observables passed in the\n * observables array. This is done by subscribing to each Observable in order and,\n * whenever any Observable emits, collecting an array of the most recent\n * values from each Observable. So if you pass `n` Observables to this operator,\n * the returned Observable will always emit an array of `n` values, in an order\n * corresponding to the order of the passed Observables (the value from the first Observable\n * will be at index 0 of the array and so on).\n *\n * Static version of `combineLatest` accepts an array of Observables. Note that an array of\n * Observables is a good choice, if you don't know beforehand how many Observables\n * you will combine. Passing an empty array will result in an Observable that\n * completes immediately.\n *\n * To ensure the output array always has the same length, `combineLatest` will\n * actually wait for all input Observables to emit at least once,\n * before it starts emitting results. This means if some Observable emits\n * values before other Observables started emitting, all these values but the last\n * will be lost. On the other hand, if some Observable does not emit a value but\n * completes, resulting Observable will complete at the same moment without\n * emitting anything, since it will now be impossible to include a value from the\n * completed Observable in the resulting array. Also, if some input Observable does\n * not emit any value and never completes, `combineLatest` will also never emit\n * and never complete, since, again, it will wait for all streams to emit some\n * value.\n *\n * If at least one Observable was passed to `combineLatest` and all passed Observables\n * emitted something, the resulting Observable will complete when all combined\n * streams complete. So even if some Observable completes, the result of\n * `combineLatest` will still emit values when other Observables do. In case\n * of a completed Observable, its value from now on will always be the last\n * emitted value. On the other hand, if any Observable errors, `combineLatest`\n * will error immediately as well, and all other Observables will be unsubscribed.\n *\n * ## Examples\n *\n * Combine two timer Observables\n *\n * ```ts\n * import { timer, combineLatest } from 'rxjs';\n *\n * const firstTimer = timer(0, 1000); // emit 0, 1, 2... after every second, starting from now\n * const secondTimer = timer(500, 1000); // emit 0, 1, 2... after every second, starting 0,5s from now\n * const combinedTimers = combineLatest([firstTimer, secondTimer]);\n * combinedTimers.subscribe(value => console.log(value));\n * // Logs\n * // [0, 0] after 0.5s\n * // [1, 0] after 1s\n * // [1, 1] after 1.5s\n * // [2, 1] after 2s\n * ```\n *\n * Combine a dictionary of Observables\n *\n * ```ts\n * import { of, delay, startWith, combineLatest } from 'rxjs';\n *\n * const observables = {\n *   a: of(1).pipe(delay(1000), startWith(0)),\n *   b: of(5).pipe(delay(5000), startWith(0)),\n *   c: of(10).pipe(delay(10000), startWith(0))\n * };\n * const combined = combineLatest(observables);\n * combined.subscribe(value => console.log(value));\n * // Logs\n * // { a: 0, b: 0, c: 0 } immediately\n * // { a: 1, b: 0, c: 0 } after 1s\n * // { a: 1, b: 5, c: 0 } after 5s\n * // { a: 1, b: 5, c: 10 } after 10s\n * ```\n *\n * Combine an array of Observables\n *\n * ```ts\n * import { of, delay, startWith, combineLatest } from 'rxjs';\n *\n * const observables = [1, 5, 10].map(\n *   n => of(n).pipe(\n *     delay(n * 1000), // emit 0 and then emit n after n seconds\n *     startWith(0)\n *   )\n * );\n * const combined = combineLatest(observables);\n * combined.subscribe(value => console.log(value));\n * // Logs\n * // [0, 0, 0] immediately\n * // [1, 0, 0] after 1s\n * // [1, 5, 0] after 5s\n * // [1, 5, 10] after 10s\n * ```\n *\n * Use map operator to dynamically calculate the Body-Mass Index\n *\n * ```ts\n * import { of, combineLatest, map } from 'rxjs';\n *\n * const weight = of(70, 72, 76, 79, 75);\n * const height = of(1.76, 1.77, 1.78);\n * const bmi = combineLatest([weight, height]).pipe(\n *   map(([w, h]) => w / (h * h)),\n * );\n * bmi.subscribe(x => console.log('BMI is ' + x));\n *\n * // With output to console:\n * // BMI is 24.212293388429753\n * // BMI is 23.93948099205209\n * // BMI is 23.671253629592222\n * ```\n *\n * @see {@link combineLatestAll}\n * @see {@link merge}\n * @see {@link withLatestFrom}\n *\n * @param {ObservableInput} [observables] An array of input Observables to combine with each other.\n * An array of Observables must be given as the first argument.\n * @param {function} [project] An optional function to project the values from\n * the combined latest values into a new value on the output Observable.\n * @param {SchedulerLike} [scheduler=null] The {@link SchedulerLike} to use for subscribing to\n * each input Observable.\n * @return {Observable} An Observable of projected values from the most recent\n * values from each input Observable, or an array of the most recent values from\n * each input Observable.\n */\nexport function combineLatest<O extends ObservableInput<any>, R>(...args: any[]): Observable<R> | Observable<ObservedValueOf<O>[]> {\n  const scheduler = popScheduler(args);\n  const resultSelector = popResultSelector(args);\n\n  const { args: observables, keys } = argsArgArrayOrObject(args);\n\n  if (observables.length === 0) {\n    // If no observables are passed, or someone has passed an empty array\n    // of observables, or even an empty object POJO, we need to just\n    // complete (EMPTY), but we have to honor the scheduler provided if any.\n    return from([], scheduler as any);\n  }\n\n  const result = new Observable<ObservedValueOf<O>[]>(\n    combineLatestInit(\n      observables as ObservableInput<ObservedValueOf<O>>[],\n      scheduler,\n      keys\n        ? // A handler for scrubbing the array of args into a dictionary.\n          (values) => createObject(keys, values)\n        : // A passthrough to just return the array\n          identity\n    )\n  );\n\n  return resultSelector ? (result.pipe(mapOneOrManyArgs(resultSelector)) as Observable<R>) : result;\n}\n\nexport function combineLatestInit(\n  observables: ObservableInput<any>[],\n  scheduler?: SchedulerLike,\n  valueTransform: (values: any[]) => any = identity\n) {\n  return (subscriber: Subscriber<any>) => {\n    // The outer subscription. We're capturing this in a function\n    // because we may have to schedule it.\n    maybeSchedule(\n      scheduler,\n      () => {\n        const { length } = observables;\n        // A store for the values each observable has emitted so far. We match observable to value on index.\n        const values = new Array(length);\n        // The number of currently active subscriptions, as they complete, we decrement this number to see if\n        // we are all done combining values, so we can complete the result.\n        let active = length;\n        // The number of inner sources that still haven't emitted the first value\n        // We need to track this because all sources need to emit one value in order\n        // to start emitting values.\n        let remainingFirstValues = length;\n        // The loop to kick off subscription. We're keying everything on index `i` to relate the observables passed\n        // in to the slot in the output array or the key in the array of keys in the output dictionary.\n        for (let i = 0; i < length; i++) {\n          maybeSchedule(\n            scheduler,\n            () => {\n              const source = from(observables[i], scheduler as any);\n              let hasFirstValue = false;\n              source.subscribe(\n                createOperatorSubscriber(\n                  subscriber,\n                  (value) => {\n                    // When we get a value, record it in our set of values.\n                    values[i] = value;\n                    if (!hasFirstValue) {\n                      // If this is our first value, record that.\n                      hasFirstValue = true;\n                      remainingFirstValues--;\n                    }\n                    if (!remainingFirstValues) {\n                      // We're not waiting for any more\n                      // first values, so we can emit!\n                      subscriber.next(valueTransform(values.slice()));\n                    }\n                  },\n                  () => {\n                    if (!--active) {\n                      // We only complete the result if we have no more active\n                      // inner observables.\n                      subscriber.complete();\n                    }\n                  }\n                )\n              );\n            },\n            subscriber\n          );\n        }\n      },\n      subscriber\n    );\n  };\n}\n\n/**\n * A small utility to handle the couple of locations where we want to schedule if a scheduler was provided,\n * but we don't if there was no scheduler.\n */\nfunction maybeSchedule(scheduler: SchedulerLike | undefined, execute: () => void, subscription: Subscription) {\n  if (scheduler) {\n    executeSchedule(subscription, scheduler, execute);\n  } else {\n    execute();\n  }\n}\n", "import { Observable } from '../Observable';\nimport { innerFrom } from '../observable/innerFrom';\nimport { Subscriber } from '../Subscriber';\nimport { ObservableInput, SchedulerLike } from '../types';\nimport { executeSchedule } from '../util/executeSchedule';\nimport { createOperatorSubscriber } from './OperatorSubscriber';\n\n/**\n * A process embodying the general \"merge\" strategy. This is used in\n * `mergeMap` and `mergeScan` because the logic is otherwise nearly identical.\n * @param source The original source observable\n * @param subscriber The consumer subscriber\n * @param project The projection function to get our inner sources\n * @param concurrent The number of concurrent inner subscriptions\n * @param onBeforeNext Additional logic to apply before nexting to our consumer\n * @param expand If `true` this will perform an \"expand\" strategy, which differs only\n * in that it recurses, and the inner subscription must be schedule-able.\n * @param innerSubScheduler A scheduler to use to schedule inner subscriptions,\n * this is to support the expand strategy, mostly, and should be deprecated\n */\nexport function mergeInternals<T, R>(\n  source: Observable<T>,\n  subscriber: Subscriber<R>,\n  project: (value: T, index: number) => ObservableInput<R>,\n  concurrent: number,\n  onBeforeNext?: (innerValue: R) => void,\n  expand?: boolean,\n  innerSubScheduler?: SchedulerLike,\n  additionalFinalizer?: () => void\n) {\n  // Buffered values, in the event of going over our concurrency limit\n  const buffer: T[] = [];\n  // The number of active inner subscriptions.\n  let active = 0;\n  // An index to pass to our accumulator function\n  let index = 0;\n  // Whether or not the outer source has completed.\n  let isComplete = false;\n\n  /**\n   * Checks to see if we can complete our result or not.\n   */\n  const checkComplete = () => {\n    // If the outer has completed, and nothing is left in the buffer,\n    // and we don't have any active inner subscriptions, then we can\n    // Emit the state and complete.\n    if (isComplete && !buffer.length && !active) {\n      subscriber.complete();\n    }\n  };\n\n  // If we're under our concurrency limit, just start the inner subscription, otherwise buffer and wait.\n  const outerNext = (value: T) => (active < concurrent ? doInnerSub(value) : buffer.push(value));\n\n  const doInnerSub = (value: T) => {\n    // If we're expanding, we need to emit the outer values and the inner values\n    // as the inners will \"become outers\" in a way as they are recursively fed\n    // back to the projection mechanism.\n    expand && subscriber.next(value as any);\n\n    // Increment the number of active subscriptions so we can track it\n    // against our concurrency limit later.\n    active++;\n\n    // A flag used to show that the inner observable completed.\n    // This is checked during finalization to see if we should\n    // move to the next item in the buffer, if there is on.\n    let innerComplete = false;\n\n    // Start our inner subscription.\n    innerFrom(project(value, index++)).subscribe(\n      createOperatorSubscriber(\n        subscriber,\n        (innerValue) => {\n          // `mergeScan` has additional handling here. For example\n          // taking the inner value and updating state.\n          onBeforeNext?.(innerValue);\n\n          if (expand) {\n            // If we're expanding, then just recurse back to our outer\n            // handler. It will emit the value first thing.\n            outerNext(innerValue as any);\n          } else {\n            // Otherwise, emit the inner value.\n            subscriber.next(innerValue);\n          }\n        },\n        () => {\n          // Flag that we have completed, so we know to check the buffer\n          // during finalization.\n          innerComplete = true;\n        },\n        // Errors are passed to the destination.\n        undefined,\n        () => {\n          // During finalization, if the inner completed (it wasn't errored or\n          // cancelled), then we want to try the next item in the buffer if\n          // there is one.\n          if (innerComplete) {\n            // We have to wrap this in a try/catch because it happens during\n            // finalization, possibly asynchronously, and we want to pass\n            // any errors that happen (like in a projection function) to\n            // the outer Subscriber.\n            try {\n              // INNER SOURCE COMPLETE\n              // Decrement the active count to ensure that the next time\n              // we try to call `doInnerSub`, the number is accurate.\n              active--;\n              // If we have more values in the buffer, try to process those\n              // Note that this call will increment `active` ahead of the\n              // next conditional, if there were any more inner subscriptions\n              // to start.\n              while (buffer.length && active < concurrent) {\n                const bufferedValue = buffer.shift()!;\n                // Particularly for `expand`, we need to check to see if a scheduler was provided\n                // for when we want to start our inner subscription. Otherwise, we just start\n                // are next inner subscription.\n                if (innerSubScheduler) {\n                  executeSchedule(subscriber, innerSubScheduler, () => doInnerSub(bufferedValue));\n                } else {\n                  doInnerSub(bufferedValue);\n                }\n              }\n              // Check to see if we can complete, and complete if so.\n              checkComplete();\n            } catch (err) {\n              subscriber.error(err);\n            }\n          }\n        }\n      )\n    );\n  };\n\n  // Subscribe to our source observable.\n  source.subscribe(\n    createOperatorSubscriber(subscriber, outerNext, () => {\n      // Outer completed, make a note of it, and check to see if we can complete everything.\n      isComplete = true;\n      checkComplete();\n    })\n  );\n\n  // Additional finalization (for when the destination is torn down).\n  // Other finalization is added implicitly via subscription above.\n  return () => {\n    additionalFinalizer?.();\n  };\n}\n", "import { ObservableInput, OperatorFunction, ObservedValueOf } from '../types';\nimport { map } from './map';\nimport { innerFrom } from '../observable/innerFrom';\nimport { operate } from '../util/lift';\nimport { mergeInternals } from './mergeInternals';\nimport { isFunction } from '../util/isFunction';\n\n/* tslint:disable:max-line-length */\nexport function mergeMap<T, O extends ObservableInput<any>>(\n  project: (value: T, index: number) => O,\n  concurrent?: number\n): OperatorFunction<T, ObservedValueOf<O>>;\n/** @deprecated The `resultSelector` parameter will be removed in v8. Use an inner `map` instead. Details: https://rxjs.dev/deprecations/resultSelector */\nexport function mergeMap<T, O extends ObservableInput<any>>(\n  project: (value: T, index: number) => O,\n  resultSelector: undefined,\n  concurrent?: number\n): OperatorFunction<T, ObservedValueOf<O>>;\n/** @deprecated The `resultSelector` parameter will be removed in v8. Use an inner `map` instead. Details: https://rxjs.dev/deprecations/resultSelector */\nexport function mergeMap<T, R, O extends ObservableInput<any>>(\n  project: (value: T, index: number) => O,\n  resultSelector: (outerValue: T, innerValue: ObservedValueOf<O>, outerIndex: number, innerIndex: number) => R,\n  concurrent?: number\n): OperatorFunction<T, R>;\n/* tslint:enable:max-line-length */\n\n/**\n * Projects each source value to an Observable which is merged in the output\n * Observable.\n *\n * <span class=\"informal\">Maps each value to an Observable, then flattens all of\n * these inner Observables using {@link mergeAll}.</span>\n *\n * ![](mergeMap.png)\n *\n * Returns an Observable that emits items based on applying a function that you\n * supply to each item emitted by the source Observable, where that function\n * returns an Observable, and then merging those resulting Observables and\n * emitting the results of this merger.\n *\n * ## Example\n *\n * Map and flatten each letter to an Observable ticking every 1 second\n *\n * ```ts\n * import { of, mergeMap, interval, map } from 'rxjs';\n *\n * const letters = of('a', 'b', 'c');\n * const result = letters.pipe(\n *   mergeMap(x => interval(1000).pipe(map(i => x + i)))\n * );\n *\n * result.subscribe(x => console.log(x));\n *\n * // Results in the following:\n * // a0\n * // b0\n * // c0\n * // a1\n * // b1\n * // c1\n * // continues to list a, b, c every second with respective ascending integers\n * ```\n *\n * @see {@link concatMap}\n * @see {@link exhaustMap}\n * @see {@link merge}\n * @see {@link mergeAll}\n * @see {@link mergeMapTo}\n * @see {@link mergeScan}\n * @see {@link switchMap}\n *\n * @param {function(value: T, ?index: number): ObservableInput} project A function\n * that, when applied to an item emitted by the source Observable, returns an\n * Observable.\n * @param {number} [concurrent=Infinity] Maximum number of input\n * Observables being subscribed to concurrently.\n * @return A function that returns an Observable that emits the result of\n * applying the projection function (and the optional deprecated\n * `resultSelector`) to each item emitted by the source Observable and merging\n * the results of the Observables obtained from this transformation.\n */\nexport function mergeMap<T, R, O extends ObservableInput<any>>(\n  project: (value: T, index: number) => O,\n  resultSelector?: ((outerValue: T, innerValue: ObservedValueOf<O>, outerIndex: number, innerIndex: number) => R) | number,\n  concurrent: number = Infinity\n): OperatorFunction<T, ObservedValueOf<O> | R> {\n  if (isFunction(resultSelector)) {\n    // DEPRECATED PATH\n    return mergeMap((a, i) => map((b: any, ii: number) => resultSelector(a, b, i, ii))(innerFrom(project(a, i))), concurrent);\n  } else if (typeof resultSelector === 'number') {\n    concurrent = resultSelector;\n  }\n\n  return operate((source, subscriber) => mergeInternals(source, subscriber, project, concurrent));\n}\n", "import { mergeMap } from './mergeMap';\nimport { identity } from '../util/identity';\nimport { OperatorFunction, ObservableInput, ObservedValueOf } from '../types';\n\n/**\n * Converts a higher-order Observable into a first-order Observable which\n * concurrently delivers all values that are emitted on the inner Observables.\n *\n * <span class=\"informal\">Flattens an Observable-of-Observables.</span>\n *\n * ![](mergeAll.png)\n *\n * `mergeAll` subscribes to an Observable that emits Observables, also known as\n * a higher-order Observable. Each time it observes one of these emitted inner\n * Observables, it subscribes to that and delivers all the values from the\n * inner Observable on the output Observable. The output Observable only\n * completes once all inner Observables have completed. Any error delivered by\n * a inner Observable will be immediately emitted on the output Observable.\n *\n * ## Examples\n *\n * Spawn a new interval Observable for each click event, and blend their outputs as one Observable\n *\n * ```ts\n * import { fromEvent, map, interval, mergeAll } from 'rxjs';\n *\n * const clicks = fromEvent(document, 'click');\n * const higherOrder = clicks.pipe(map(() => interval(1000)));\n * const firstOrder = higherOrder.pipe(mergeAll());\n *\n * firstOrder.subscribe(x => console.log(x));\n * ```\n *\n * Count from 0 to 9 every second for each click, but only allow 2 concurrent timers\n *\n * ```ts\n * import { fromEvent, map, interval, take, mergeAll } from 'rxjs';\n *\n * const clicks = fromEvent(document, 'click');\n * const higherOrder = clicks.pipe(\n *   map(() => interval(1000).pipe(take(10)))\n * );\n * const firstOrder = higherOrder.pipe(mergeAll(2));\n *\n * firstOrder.subscribe(x => console.log(x));\n * ```\n *\n * @see {@link combineLatestAll}\n * @see {@link concatAll}\n * @see {@link exhaustAll}\n * @see {@link merge}\n * @see {@link mergeMap}\n * @see {@link mergeMapTo}\n * @see {@link mergeScan}\n * @see {@link switchAll}\n * @see {@link switchMap}\n * @see {@link zipAll}\n *\n * @param {number} [concurrent=Infinity] Maximum number of inner\n * Observables being subscribed to concurrently.\n * @return A function that returns an Observable that emits values coming from\n * all the inner Observables emitted by the source Observable.\n */\nexport function mergeAll<O extends ObservableInput<any>>(concurrent: number = Infinity): OperatorFunction<O, ObservedValueOf<O>> {\n  return mergeMap(identity, concurrent);\n}\n", "import { mergeAll } from './mergeAll';\nimport { OperatorFunction, ObservableInput, ObservedValueOf } from '../types';\n\n/**\n * Converts a higher-order Observable into a first-order Observable by\n * concatenating the inner Observables in order.\n *\n * <span class=\"informal\">Flattens an Observable-of-Observables by putting one\n * inner Observable after the other.</span>\n *\n * ![](concatAll.svg)\n *\n * Joins every Observable emitted by the source (a higher-order Observable), in\n * a serial fashion. It subscribes to each inner Observable only after the\n * previous inner Observable has completed, and merges all of their values into\n * the returned observable.\n *\n * __Warning:__ If the source Observable emits Observables quickly and\n * endlessly, and the inner Observables it emits generally complete slower than\n * the source emits, you can run into memory issues as the incoming Observables\n * collect in an unbounded buffer.\n *\n * Note: `concatAll` is equivalent to `mergeAll` with concurrency parameter set\n * to `1`.\n *\n * ## Example\n *\n * For each click event, tick every second from 0 to 3, with no concurrency\n *\n * ```ts\n * import { fromEvent, map, interval, take, concatAll } from 'rxjs';\n *\n * const clicks = fromEvent(document, 'click');\n * const higherOrder = clicks.pipe(\n *   map(() => interval(1000).pipe(take(4)))\n * );\n * const firstOrder = higherOrder.pipe(concatAll());\n * firstOrder.subscribe(x => console.log(x));\n *\n * // Results in the following:\n * // (results are not concurrent)\n * // For every click on the \"document\" it will emit values 0 to 3 spaced\n * // on a 1000ms interval\n * // one click = 1000ms-> 0 -1000ms-> 1 -1000ms-> 2 -1000ms-> 3\n * ```\n *\n * @see {@link combineLatestAll}\n * @see {@link concat}\n * @see {@link concatMap}\n * @see {@link concatMapTo}\n * @see {@link exhaustAll}\n * @see {@link mergeAll}\n * @see {@link switchAll}\n * @see {@link switchMap}\n * @see {@link zipAll}\n *\n * @return A function that returns an Observable emitting values from all the\n * inner Observables concatenated.\n */\nexport function concatAll<O extends ObservableInput<any>>(): OperatorFunction<O, ObservedValueOf<O>> {\n  return mergeAll(1);\n}\n", "import { Observable } from '../Observable';\nimport { ObservableInputTuple, SchedulerLike } from '../types';\nimport { concatAll } from '../operators/concatAll';\nimport { popScheduler } from '../util/args';\nimport { from } from './from';\n\nexport function concat<T extends readonly unknown[]>(...inputs: [...ObservableInputTuple<T>]): Observable<T[number]>;\nexport function concat<T extends readonly unknown[]>(\n  ...inputsAndScheduler: [...ObservableInputTuple<T>, SchedulerLike]\n): Observable<T[number]>;\n\n/**\n * Creates an output Observable which sequentially emits all values from the first given\n * Observable and then moves on to the next.\n *\n * <span class=\"informal\">Concatenates multiple Observables together by\n * sequentially emitting their values, one Observable after the other.</span>\n *\n * ![](concat.png)\n *\n * `concat` joins multiple Observables together, by subscribing to them one at a time and\n * merging their results into the output Observable. You can pass either an array of\n * Observables, or put them directly as arguments. Passing an empty array will result\n * in Observable that completes immediately.\n *\n * `concat` will subscribe to first input Observable and emit all its values, without\n * changing or affecting them in any way. When that Observable completes, it will\n * subscribe to then next Observable passed and, again, emit its values. This will be\n * repeated, until the operator runs out of Observables. When last input Observable completes,\n * `concat` will complete as well. At any given moment only one Observable passed to operator\n * emits values. If you would like to emit values from passed Observables concurrently, check out\n * {@link merge} instead, especially with optional `concurrent` parameter. As a matter of fact,\n * `concat` is an equivalent of `merge` operator with `concurrent` parameter set to `1`.\n *\n * Note that if some input Observable never completes, `concat` will also never complete\n * and Observables following the one that did not complete will never be subscribed. On the other\n * hand, if some Observable simply completes immediately after it is subscribed, it will be\n * invisible for `concat`, which will just move on to the next Observable.\n *\n * If any Observable in chain errors, instead of passing control to the next Observable,\n * `concat` will error immediately as well. Observables that would be subscribed after\n * the one that emitted error, never will.\n *\n * If you pass to `concat` the same Observable many times, its stream of values\n * will be \"replayed\" on every subscription, which means you can repeat given Observable\n * as many times as you like. If passing the same Observable to `concat` 1000 times becomes tedious,\n * you can always use {@link repeat}.\n *\n * ## Examples\n *\n * Concatenate a timer counting from 0 to 3 with a synchronous sequence from 1 to 10\n *\n * ```ts\n * import { interval, take, range, concat } from 'rxjs';\n *\n * const timer = interval(1000).pipe(take(4));\n * const sequence = range(1, 10);\n * const result = concat(timer, sequence);\n * result.subscribe(x => console.log(x));\n *\n * // results in:\n * // 0 -1000ms-> 1 -1000ms-> 2 -1000ms-> 3 -immediate-> 1 ... 10\n * ```\n *\n * Concatenate 3 Observables\n *\n * ```ts\n * import { interval, take, concat } from 'rxjs';\n *\n * const timer1 = interval(1000).pipe(take(10));\n * const timer2 = interval(2000).pipe(take(6));\n * const timer3 = interval(500).pipe(take(10));\n *\n * const result = concat(timer1, timer2, timer3);\n * result.subscribe(x => console.log(x));\n *\n * // results in the following:\n * // (Prints to console sequentially)\n * // -1000ms-> 0 -1000ms-> 1 -1000ms-> ... 9\n * // -2000ms-> 0 -2000ms-> 1 -2000ms-> ... 5\n * // -500ms-> 0 -500ms-> 1 -500ms-> ... 9\n * ```\n *\n * Concatenate the same Observable to repeat it\n *\n * ```ts\n * import { interval, take, concat } from 'rxjs';\n *\n * const timer = interval(1000).pipe(take(2));\n *\n * concat(timer, timer) // concatenating the same Observable!\n *   .subscribe({\n *     next: value => console.log(value),\n *     complete: () => console.log('...and it is done!')\n *   });\n *\n * // Logs:\n * // 0 after 1s\n * // 1 after 2s\n * // 0 after 3s\n * // 1 after 4s\n * // '...and it is done!' also after 4s\n * ```\n *\n * @see {@link concatAll}\n * @see {@link concatMap}\n * @see {@link concatMapTo}\n * @see {@link startWith}\n * @see {@link endWith}\n *\n * @param args Input Observables to concatenate.\n */\nexport function concat(...args: any[]): Observable<unknown> {\n  return concatAll()(from(args, popScheduler(args)));\n}\n", "import { Observable } from '../Observable';\nimport { ObservedValueOf, ObservableInput } from '../types';\nimport { innerFrom } from './innerFrom';\n\n/**\n * Creates an Observable that, on subscribe, calls an Observable factory to\n * make an Observable for each new Observer.\n *\n * <span class=\"informal\">Creates the Observable lazily, that is, only when it\n * is subscribed.\n * </span>\n *\n * ![](defer.png)\n *\n * `defer` allows you to create an Observable only when the Observer\n * subscribes. It waits until an Observer subscribes to it, calls the given\n * factory function to get an Observable -- where a factory function typically\n * generates a new Observable -- and subscribes the Observer to this Observable.\n * In case the factory function returns a falsy value, then EMPTY is used as\n * Observable instead. Last but not least, an exception during the factory\n * function call is transferred to the Observer by calling `error`.\n *\n * ## Example\n *\n * Subscribe to either an Observable of clicks or an Observable of interval, at random\n *\n * ```ts\n * import { defer, fromEvent, interval } from 'rxjs';\n *\n * const clicksOrInterval = defer(() => {\n *   return Math.random() > 0.5\n *     ? fromEvent(document, 'click')\n *     : interval(1000);\n * });\n * clicksOrInterval.subscribe(x => console.log(x));\n *\n * // Results in the following behavior:\n * // If the result of Math.random() is greater than 0.5 it will listen\n * // for clicks anywhere on the \"document\"; when document is clicked it\n * // will log a MouseEvent object to the console. If the result is less\n * // than 0.5 it will emit ascending numbers, one every second(1000ms).\n * ```\n *\n * @see {@link Observable}\n *\n * @param {function(): ObservableInput} observableFactory The Observable\n * factory function to invoke for each Observer that subscribes to the output\n * Observable. May also return a Promise, which will be converted on the fly\n * to an Observable.\n * @return {Observable} An Observable whose Observers' subscriptions trigger\n * an invocation of the given Observable factory function.\n */\nexport function defer<R extends ObservableInput<any>>(observableFactory: () => R): Observable<ObservedValueOf<R>> {\n  return new Observable<ObservedValueOf<R>>((subscriber) => {\n    innerFrom(observableFactory()).subscribe(subscriber);\n  });\n}\n", "import { innerFrom } from '../observable/innerFrom';\nimport { Observable } from '../Observable';\nimport { mergeMap } from '../operators/mergeMap';\nimport { isArrayLike } from '../util/isArrayLike';\nimport { isFunction } from '../util/isFunction';\nimport { mapOneOrManyArgs } from '../util/mapOneOrManyArgs';\n\n// These constants are used to create handler registry functions using array mapping below.\nconst nodeEventEmitterMethods = ['addListener', 'removeListener'] as const;\nconst eventTargetMethods = ['addEventListener', 'removeEventListener'] as const;\nconst jqueryMethods = ['on', 'off'] as const;\n\nexport interface NodeStyleEventEmitter {\n  addListener(eventName: string | symbol, handler: NodeEventHandler): this;\n  removeListener(eventName: string | symbol, handler: NodeEventHandler): this;\n}\n\nexport type NodeEventHandler = (...args: any[]) => void;\n\n// For APIs that implement `addListener` and `removeListener` methods that may\n// not use the same arguments or return EventEmitter values\n// such as React Native\nexport interface NodeCompatibleEventEmitter {\n  addListener(eventName: string, handler: NodeEventHandler): void | {};\n  removeListener(eventName: string, handler: NodeEventHandler): void | {};\n}\n\n// Use handler types like those in @types/jquery. See:\n// https://github.com/DefinitelyTyped/DefinitelyTyped/blob/847731ba1d7fa6db6b911c0e43aa0afe596e7723/types/jquery/misc.d.ts#L6395\nexport interface JQueryStyleEventEmitter<TContext, T> {\n  on(eventName: string, handler: (this: TContext, t: T, ...args: any[]) => any): void;\n  off(eventName: string, handler: (this: TContext, t: T, ...args: any[]) => any): void;\n}\n\nexport interface EventListenerObject<E> {\n  handleEvent(evt: E): void;\n}\n\nexport interface HasEventTargetAddRemove<E> {\n  addEventListener(\n    type: string,\n    listener: ((evt: E) => void) | EventListenerObject<E> | null,\n    options?: boolean | AddEventListenerOptions\n  ): void;\n  removeEventListener(\n    type: string,\n    listener: ((evt: E) => void) | EventListenerObject<E> | null,\n    options?: EventListenerOptions | boolean\n  ): void;\n}\n\nexport interface EventListenerOptions {\n  capture?: boolean;\n  passive?: boolean;\n  once?: boolean;\n}\n\nexport interface AddEventListenerOptions extends EventListenerOptions {\n  once?: boolean;\n  passive?: boolean;\n}\n\nexport function fromEvent<T>(target: HasEventTargetAddRemove<T> | ArrayLike<HasEventTargetAddRemove<T>>, eventName: string): Observable<T>;\nexport function fromEvent<T, R>(\n  target: HasEventTargetAddRemove<T> | ArrayLike<HasEventTargetAddRemove<T>>,\n  eventName: string,\n  resultSelector: (event: T) => R\n): Observable<R>;\nexport function fromEvent<T>(\n  target: HasEventTargetAddRemove<T> | ArrayLike<HasEventTargetAddRemove<T>>,\n  eventName: string,\n  options: EventListenerOptions\n): Observable<T>;\nexport function fromEvent<T, R>(\n  target: HasEventTargetAddRemove<T> | ArrayLike<HasEventTargetAddRemove<T>>,\n  eventName: string,\n  options: EventListenerOptions,\n  resultSelector: (event: T) => R\n): Observable<R>;\n\nexport function fromEvent(target: NodeStyleEventEmitter | ArrayLike<NodeStyleEventEmitter>, eventName: string): Observable<unknown>;\n/** @deprecated Do not specify explicit type parameters. Signatures with type parameters that cannot be inferred will be removed in v8. */\nexport function fromEvent<T>(target: NodeStyleEventEmitter | ArrayLike<NodeStyleEventEmitter>, eventName: string): Observable<T>;\nexport function fromEvent<R>(\n  target: NodeStyleEventEmitter | ArrayLike<NodeStyleEventEmitter>,\n  eventName: string,\n  resultSelector: (...args: any[]) => R\n): Observable<R>;\n\nexport function fromEvent(\n  target: NodeCompatibleEventEmitter | ArrayLike<NodeCompatibleEventEmitter>,\n  eventName: string\n): Observable<unknown>;\n/** @deprecated Do not specify explicit type parameters. Signatures with type parameters that cannot be inferred will be removed in v8. */\nexport function fromEvent<T>(target: NodeCompatibleEventEmitter | ArrayLike<NodeCompatibleEventEmitter>, eventName: string): Observable<T>;\nexport function fromEvent<R>(\n  target: NodeCompatibleEventEmitter | ArrayLike<NodeCompatibleEventEmitter>,\n  eventName: string,\n  resultSelector: (...args: any[]) => R\n): Observable<R>;\n\nexport function fromEvent<T>(\n  target: JQueryStyleEventEmitter<any, T> | ArrayLike<JQueryStyleEventEmitter<any, T>>,\n  eventName: string\n): Observable<T>;\nexport function fromEvent<T, R>(\n  target: JQueryStyleEventEmitter<any, T> | ArrayLike<JQueryStyleEventEmitter<any, T>>,\n  eventName: string,\n  resultSelector: (value: T, ...args: any[]) => R\n): Observable<R>;\n\n/**\n * Creates an Observable that emits events of a specific type coming from the\n * given event target.\n *\n * <span class=\"informal\">Creates an Observable from DOM events, or Node.js\n * EventEmitter events or others.</span>\n *\n * ![](fromEvent.png)\n *\n * `fromEvent` accepts as a first argument event target, which is an object with methods\n * for registering event handler functions. As a second argument it takes string that indicates\n * type of event we want to listen for. `fromEvent` supports selected types of event targets,\n * which are described in detail below. If your event target does not match any of the ones listed,\n * you should use {@link fromEventPattern}, which can be used on arbitrary APIs.\n * When it comes to APIs supported by `fromEvent`, their methods for adding and removing event\n * handler functions have different names, but they all accept a string describing event type\n * and function itself, which will be called whenever said event happens.\n *\n * Every time resulting Observable is subscribed, event handler function will be registered\n * to event target on given event type. When that event fires, value\n * passed as a first argument to registered function will be emitted by output Observable.\n * When Observable is unsubscribed, function will be unregistered from event target.\n *\n * Note that if event target calls registered function with more than one argument, second\n * and following arguments will not appear in resulting stream. In order to get access to them,\n * you can pass to `fromEvent` optional project function, which will be called with all arguments\n * passed to event handler. Output Observable will then emit value returned by project function,\n * instead of the usual value.\n *\n * Remember that event targets listed below are checked via duck typing. It means that\n * no matter what kind of object you have and no matter what environment you work in,\n * you can safely use `fromEvent` on that object if it exposes described methods (provided\n * of course they behave as was described above). So for example if Node.js library exposes\n * event target which has the same method names as DOM EventTarget, `fromEvent` is still\n * a good choice.\n *\n * If the API you use is more callback then event handler oriented (subscribed\n * callback function fires only once and thus there is no need to manually\n * unregister it), you should use {@link bindCallback} or {@link bindNodeCallback}\n * instead.\n *\n * `fromEvent` supports following types of event targets:\n *\n * **DOM EventTarget**\n *\n * This is an object with `addEventListener` and `removeEventListener` methods.\n *\n * In the browser, `addEventListener` accepts - apart from event type string and event\n * handler function arguments - optional third parameter, which is either an object or boolean,\n * both used for additional configuration how and when passed function will be called. When\n * `fromEvent` is used with event target of that type, you can provide this values\n * as third parameter as well.\n *\n * **Node.js EventEmitter**\n *\n * An object with `addListener` and `removeListener` methods.\n *\n * **JQuery-style event target**\n *\n * An object with `on` and `off` methods\n *\n * **DOM NodeList**\n *\n * List of DOM Nodes, returned for example by `document.querySelectorAll` or `Node.childNodes`.\n *\n * Although this collection is not event target in itself, `fromEvent` will iterate over all Nodes\n * it contains and install event handler function in every of them. When returned Observable\n * is unsubscribed, function will be removed from all Nodes.\n *\n * **DOM HtmlCollection**\n *\n * Just as in case of NodeList it is a collection of DOM nodes. Here as well event handler function is\n * installed and removed in each of elements.\n *\n *\n * ## Examples\n *\n * Emit clicks happening on the DOM document\n *\n * ```ts\n * import { fromEvent } from 'rxjs';\n *\n * const clicks = fromEvent(document, 'click');\n * clicks.subscribe(x => console.log(x));\n *\n * // Results in:\n * // MouseEvent object logged to console every time a click\n * // occurs on the document.\n * ```\n *\n * Use `addEventListener` with capture option\n *\n * ```ts\n * import { fromEvent } from 'rxjs';\n *\n * const div = document.createElement('div');\n * div.style.cssText = 'width: 200px; height: 200px; background: #09c;';\n * document.body.appendChild(div);\n *\n * // note optional configuration parameter which will be passed to addEventListener\n * const clicksInDocument = fromEvent(document, 'click', { capture: true });\n * const clicksInDiv = fromEvent(div, 'click');\n *\n * clicksInDocument.subscribe(() => console.log('document'));\n * clicksInDiv.subscribe(() => console.log('div'));\n *\n * // By default events bubble UP in DOM tree, so normally\n * // when we would click on div in document\n * // \"div\" would be logged first and then \"document\".\n * // Since we specified optional `capture` option, document\n * // will catch event when it goes DOWN DOM tree, so console\n * // will log \"document\" and then \"div\".\n * ```\n *\n * @see {@link bindCallback}\n * @see {@link bindNodeCallback}\n * @see {@link fromEventPattern}\n *\n * @param {FromEventTarget<T>} target The DOM EventTarget, Node.js\n * EventEmitter, JQuery-like event target, NodeList or HTMLCollection to attach the event handler to.\n * @param {string} eventName The event name of interest, being emitted by the\n * `target`.\n * @param {EventListenerOptions} [options] Options to pass through to addEventListener\n * @return {Observable<T>}\n */\nexport function fromEvent<T>(\n  target: any,\n  eventName: string,\n  options?: EventListenerOptions | ((...args: any[]) => T),\n  resultSelector?: (...args: any[]) => T\n): Observable<T> {\n  if (isFunction(options)) {\n    resultSelector = options;\n    options = undefined;\n  }\n  if (resultSelector) {\n    return fromEvent<T>(target, eventName, options as EventListenerOptions).pipe(mapOneOrManyArgs(resultSelector));\n  }\n\n  // Figure out our add and remove methods. In order to do this,\n  // we are going to analyze the target in a preferred order, if\n  // the target matches a given signature, we take the two \"add\" and \"remove\"\n  // method names and apply them to a map to create opposite versions of the\n  // same function. This is because they all operate in duplicate pairs,\n  // `addListener(name, handler)`, `removeListener(name, handler)`, for example.\n  // The call only differs by method name, as to whether or not you're adding or removing.\n  const [add, remove] =\n    // If it is an EventTarget, we need to use a slightly different method than the other two patterns.\n    isEventTarget(target)\n      ? eventTargetMethods.map((methodName) => (handler: any) => target[methodName](eventName, handler, options as EventListenerOptions))\n      : // In all other cases, the call pattern is identical with the exception of the method names.\n      isNodeStyleEventEmitter(target)\n      ? nodeEventEmitterMethods.map(toCommonHandlerRegistry(target, eventName))\n      : isJQueryStyleEventEmitter(target)\n      ? jqueryMethods.map(toCommonHandlerRegistry(target, eventName))\n      : [];\n\n  // If add is falsy, it's because we didn't match a pattern above.\n  // Check to see if it is an ArrayLike, because if it is, we want to\n  // try to apply fromEvent to all of it's items. We do this check last,\n  // because there are may be some types that are both ArrayLike *and* implement\n  // event registry points, and we'd rather delegate to that when possible.\n  if (!add) {\n    if (isArrayLike(target)) {\n      return mergeMap((subTarget: any) => fromEvent(subTarget, eventName, options as EventListenerOptions))(\n        innerFrom(target)\n      ) as Observable<T>;\n    }\n  }\n\n  // If add is falsy and we made it here, it's because we didn't\n  // match any valid target objects above.\n  if (!add) {\n    throw new TypeError('Invalid event target');\n  }\n\n  return new Observable<T>((subscriber) => {\n    // The handler we are going to register. Forwards the event object, by itself, or\n    // an array of arguments to the event handler, if there is more than one argument,\n    // to the consumer.\n    const handler = (...args: any[]) => subscriber.next(1 < args.length ? args : args[0]);\n    // Do the work of adding the handler to the target.\n    add(handler);\n    // When we finalize, we want to remove the handler and free up memory.\n    return () => remove!(handler);\n  });\n}\n\n/**\n * Used to create `add` and `remove` functions to register and unregister event handlers\n * from a target in the most common handler pattern, where there are only two arguments.\n * (e.g.  `on(name, fn)`, `off(name, fn)`, `addListener(name, fn)`, or `removeListener(name, fn)`)\n * @param target The target we're calling methods on\n * @param eventName The event name for the event we're creating register or unregister functions for\n */\nfunction toCommonHandlerRegistry(target: any, eventName: string) {\n  return (methodName: string) => (handler: any) => target[methodName](eventName, handler);\n}\n\n/**\n * Checks to see if the target implements the required node-style EventEmitter methods\n * for adding and removing event handlers.\n * @param target the object to check\n */\nfunction isNodeStyleEventEmitter(target: any): target is NodeStyleEventEmitter {\n  return isFunction(target.addListener) && isFunction(target.removeListener);\n}\n\n/**\n * Checks to see if the target implements the required jQuery-style EventEmitter methods\n * for adding and removing event handlers.\n * @param target the object to check\n */\nfunction isJQueryStyleEventEmitter(target: any): target is JQueryStyleEventEmitter<any, any> {\n  return isFunction(target.on) && isFunction(target.off);\n}\n\n/**\n * Checks to see if the target implements the required EventTarget methods\n * for adding and removing event handlers.\n * @param target the object to check\n */\nfunction isEventTarget(target: any): target is HasEventTargetAddRemove<any> {\n  return isFunction(target.addEventListener) && isFunction(target.removeEventListener);\n}\n", "import { Observable } from '../Observable';\nimport { isFunction } from '../util/isFunction';\nimport { NodeEventHandler } from './fromEvent';\nimport { mapOneOrManyArgs } from '../util/mapOneOrManyArgs';\n\n/* tslint:disable:max-line-length */\nexport function fromEventPattern<T>(\n  addHandler: (handler: NodeEventHandler) => any,\n  removeHandler?: (handler: NodeEventHandler, signal?: any) => void\n): Observable<T>;\nexport function fromEventPattern<T>(\n  addHandler: (handler: NodeEventHandler) => any,\n  removeHandler?: (handler: NodeEventHandler, signal?: any) => void,\n  resultSelector?: (...args: any[]) => T\n): Observable<T>;\n/* tslint:enable:max-line-length */\n\n/**\n * Creates an Observable from an arbitrary API for registering event handlers.\n *\n * <span class=\"informal\">When that method for adding event handler was something {@link fromEvent}\n * was not prepared for.</span>\n *\n * ![](fromEventPattern.png)\n *\n * `fromEventPattern` allows you to convert into an Observable any API that supports registering handler functions\n * for events. It is similar to {@link fromEvent}, but far\n * more flexible. In fact, all use cases of {@link fromEvent} could be easily handled by\n * `fromEventPattern` (although in slightly more verbose way).\n *\n * This operator accepts as a first argument an `addHandler` function, which will be injected with\n * handler parameter. That handler is actually an event handler function that you now can pass\n * to API expecting it. `addHandler` will be called whenever Observable\n * returned by the operator is subscribed, so registering handler in API will not\n * necessarily happen when `fromEventPattern` is called.\n *\n * After registration, every time an event that we listen to happens,\n * Observable returned by `fromEventPattern` will emit value that event handler\n * function was called with. Note that if event handler was called with more\n * than one argument, second and following arguments will not appear in the Observable.\n *\n * If API you are using allows to unregister event handlers as well, you can pass to `fromEventPattern`\n * another function - `removeHandler` - as a second parameter. It will be injected\n * with the same handler function as before, which now you can use to unregister\n * it from the API. `removeHandler` will be called when consumer of resulting Observable\n * unsubscribes from it.\n *\n * In some APIs unregistering is actually handled differently. Method registering an event handler\n * returns some kind of token, which is later used to identify which function should\n * be unregistered or it itself has method that unregisters event handler.\n * If that is the case with your API, make sure token returned\n * by registering method is returned by `addHandler`. Then it will be passed\n * as a second argument to `removeHandler`, where you will be able to use it.\n *\n * If you need access to all event handler parameters (not only the first one),\n * or you need to transform them in any way, you can call `fromEventPattern` with optional\n * third parameter - project function which will accept all arguments passed to\n * event handler when it is called. Whatever is returned from project function will appear on\n * resulting stream instead of usual event handlers first argument. This means\n * that default project can be thought of as function that takes its first parameter\n * and ignores the rest.\n *\n * ## Examples\n *\n * Emits clicks happening on the DOM document\n *\n * ```ts\n * import { fromEventPattern } from 'rxjs';\n *\n * function addClickHandler(handler) {\n *   document.addEventListener('click', handler);\n * }\n *\n * function removeClickHandler(handler) {\n *   document.removeEventListener('click', handler);\n * }\n *\n * const clicks = fromEventPattern(\n *   addClickHandler,\n *   removeClickHandler\n * );\n * clicks.subscribe(x => console.log(x));\n *\n * // Whenever you click anywhere in the browser, DOM MouseEvent\n * // object will be logged.\n * ```\n *\n * Use with API that returns cancellation token\n *\n * ```ts\n * import { fromEventPattern } from 'rxjs';\n *\n * const token = someAPI.registerEventHandler(function() {});\n * someAPI.unregisterEventHandler(token); // this APIs cancellation method accepts\n *                                        // not handler itself, but special token.\n *\n * const someAPIObservable = fromEventPattern(\n *   function(handler) { return someAPI.registerEventHandler(handler); }, // Note that we return the token here...\n *   function(handler, token) { someAPI.unregisterEventHandler(token); }  // ...to then use it here.\n * );\n * ```\n *\n * Use with project function\n *\n * ```ts\n * import { fromEventPattern } from 'rxjs';\n *\n * someAPI.registerEventHandler((eventType, eventMessage) => {\n *   console.log(eventType, eventMessage); // Logs 'EVENT_TYPE' 'EVENT_MESSAGE' to console.\n * });\n *\n * const someAPIObservable = fromEventPattern(\n *   handler => someAPI.registerEventHandler(handler),\n *   handler => someAPI.unregisterEventHandler(handler)\n *   (eventType, eventMessage) => eventType + ' --- ' + eventMessage // without that function only 'EVENT_TYPE'\n * );                                                                // would be emitted by the Observable\n *\n * someAPIObservable.subscribe(value => console.log(value));\n *\n * // Logs:\n * // 'EVENT_TYPE --- EVENT_MESSAGE'\n * ```\n *\n * @see {@link fromEvent}\n * @see {@link bindCallback}\n * @see {@link bindNodeCallback}\n *\n * @param {function(handler: Function): any} addHandler A function that takes\n * a `handler` function as argument and attaches it somehow to the actual\n * source of events.\n * @param {function(handler: Function, token?: any): void} [removeHandler] A function that\n * takes a `handler` function as an argument and removes it from the event source. If `addHandler`\n * returns some kind of token, `removeHandler` function will have it as a second parameter.\n * @param {function(...args: any): T} [project] A function to\n * transform results. It takes the arguments from the event handler and\n * should return a single value.\n * @return {Observable<T>} Observable which, when an event happens, emits first parameter\n * passed to registered event handler. Alternatively it emits whatever project function returns\n * at that moment.\n */\nexport function fromEventPattern<T>(\n  addHandler: (handler: NodeEventHandler) => any,\n  removeHandler?: (handler: NodeEventHandler, signal?: any) => void,\n  resultSelector?: (...args: any[]) => T\n): Observable<T | T[]> {\n  if (resultSelector) {\n    return fromEventPattern<T>(addHandler, removeHandler).pipe(mapOneOrManyArgs(resultSelector));\n  }\n\n  return new Observable<T | T[]>((subscriber) => {\n    const handler = (...e: T[]) => subscriber.next(e.length === 1 ? e[0] : e);\n    const retValue = addHandler(handler);\n    return isFunction(removeHandler) ? () => removeHandler(handler, retValue) : undefined;\n  });\n}\n", "import { Observable } from '../Observable';\nimport { SchedulerLike } from '../types';\nimport { async as asyncScheduler } from '../scheduler/async';\nimport { isScheduler } from '../util/isScheduler';\nimport { isValidDate } from '../util/isDate';\n\n/**\n * Creates an observable that will wait for a specified time period, or exact date, before\n * emitting the number 0.\n *\n * <span class=\"informal\">Used to emit a notification after a delay.</span>\n *\n * This observable is useful for creating delays in code, or racing against other values\n * for ad-hoc timeouts.\n *\n * The `delay` is specified by default in milliseconds, however providing a custom scheduler could\n * create a different behavior.\n *\n * ## Examples\n *\n * Wait 3 seconds and start another observable\n *\n * You might want to use `timer` to delay subscription to an\n * observable by a set amount of time. Here we use a timer with\n * {@link concatMapTo} or {@link concatMap} in order to wait\n * a few seconds and start a subscription to a source.\n *\n * ```ts\n * import { of, timer, concatMap } from 'rxjs';\n *\n * // This could be any observable\n * const source = of(1, 2, 3);\n *\n * timer(3000)\n *   .pipe(concatMap(() => source))\n *   .subscribe(console.log);\n * ```\n *\n * Take all values until the start of the next minute\n *\n * Using a `Date` as the trigger for the first emission, you can\n * do things like wait until midnight to fire an event, or in this case,\n * wait until a new minute starts (chosen so the example wouldn't take\n * too long to run) in order to stop watching a stream. Leveraging\n * {@link takeUntil}.\n *\n * ```ts\n * import { interval, takeUntil, timer } from 'rxjs';\n *\n * // Build a Date object that marks the\n * // next minute.\n * const currentDate = new Date();\n * const startOfNextMinute = new Date(\n *   currentDate.getFullYear(),\n *   currentDate.getMonth(),\n *   currentDate.getDate(),\n *   currentDate.getHours(),\n *   currentDate.getMinutes() + 1\n * );\n *\n * // This could be any observable stream\n * const source = interval(1000);\n *\n * const result = source.pipe(\n *   takeUntil(timer(startOfNextMinute))\n * );\n *\n * result.subscribe(console.log);\n * ```\n *\n * ### Known Limitations\n *\n * - The {@link asyncScheduler} uses `setTimeout` which has limitations for how far in the future it can be scheduled.\n *\n * - If a `scheduler` is provided that returns a timestamp other than an epoch from `now()`, and\n * a `Date` object is passed to the `dueTime` argument, the calculation for when the first emission\n * should occur will be incorrect. In this case, it would be best to do your own calculations\n * ahead of time, and pass a `number` in as the `dueTime`.\n *\n * @param due If a `number`, the amount of time in milliseconds to wait before emitting.\n * If a `Date`, the exact time at which to emit.\n * @param scheduler The scheduler to use to schedule the delay. Defaults to {@link asyncScheduler}.\n */\nexport function timer(due: number | Date, scheduler?: SchedulerLike): Observable<0>;\n\n/**\n * Creates an observable that starts an interval after a specified delay, emitting incrementing numbers -- starting at `0` --\n * on each interval after words.\n *\n * The `delay` and `intervalDuration` are specified by default in milliseconds, however providing a custom scheduler could\n * create a different behavior.\n *\n * ## Example\n *\n * ### Start an interval that starts right away\n *\n * Since {@link interval} waits for the passed delay before starting,\n * sometimes that's not ideal. You may want to start an interval immediately.\n * `timer` works well for this. Here we have both side-by-side so you can\n * see them in comparison.\n *\n * Note that this observable will never complete.\n *\n * ```ts\n * import { timer, interval } from 'rxjs';\n *\n * timer(0, 1000).subscribe(n => console.log('timer', n));\n * interval(1000).subscribe(n => console.log('interval', n));\n * ```\n *\n * ### Known Limitations\n *\n * - The {@link asyncScheduler} uses `setTimeout` which has limitations for how far in the future it can be scheduled.\n *\n * - If a `scheduler` is provided that returns a timestamp other than an epoch from `now()`, and\n * a `Date` object is passed to the `dueTime` argument, the calculation for when the first emission\n * should occur will be incorrect. In this case, it would be best to do your own calculations\n * ahead of time, and pass a `number` in as the `startDue`.\n * @param startDue If a `number`, is the time to wait before starting the interval.\n * If a `Date`, is the exact time at which to start the interval.\n * @param intervalDuration The delay between each value emitted in the interval. Passing a\n * negative number here will result in immediate completion after the first value is emitted, as though\n * no `intervalDuration` was passed at all.\n * @param scheduler The scheduler to use to schedule the delay. Defaults to {@link asyncScheduler}.\n */\nexport function timer(startDue: number | Date, intervalDuration: number, scheduler?: SchedulerLike): Observable<number>;\n\n/**\n * @deprecated The signature allowing `undefined` to be passed for `intervalDuration` will be removed in v8. Use the `timer(dueTime, scheduler?)` signature instead.\n */\nexport function timer(dueTime: number | Date, unused: undefined, scheduler?: SchedulerLike): Observable<0>;\n\nexport function timer(\n  dueTime: number | Date = 0,\n  intervalOrScheduler?: number | SchedulerLike,\n  scheduler: SchedulerLike = asyncScheduler\n): Observable<number> {\n  // Since negative intervalDuration is treated as though no\n  // interval was specified at all, we start with a negative number.\n  let intervalDuration = -1;\n\n  if (intervalOrScheduler != null) {\n    // If we have a second argument, and it's a scheduler,\n    // override the scheduler we had defaulted. Otherwise,\n    // it must be an interval.\n    if (isScheduler(intervalOrScheduler)) {\n      scheduler = intervalOrScheduler;\n    } else {\n      // Note that this *could* be negative, in which case\n      // it's like not passing an intervalDuration at all.\n      intervalDuration = intervalOrScheduler;\n    }\n  }\n\n  return new Observable((subscriber) => {\n    // If a valid date is passed, calculate how long to wait before\n    // executing the first value... otherwise, if it's a number just schedule\n    // that many milliseconds (or scheduler-specified unit size) in the future.\n    let due = isValidDate(dueTime) ? +dueTime - scheduler!.now() : dueTime;\n\n    if (due < 0) {\n      // Ensure we don't schedule in the future.\n      due = 0;\n    }\n\n    // The incrementing value we emit.\n    let n = 0;\n\n    // Start the timer.\n    return scheduler.schedule(function () {\n      if (!subscriber.closed) {\n        // Emit the next value and increment.\n        subscriber.next(n++);\n\n        if (0 <= intervalDuration) {\n          // If we have a interval after the initial timer,\n          // reschedule with the period.\n          this.schedule(undefined, intervalDuration);\n        } else {\n          // We didn't have an interval. So just complete.\n          subscriber.complete();\n        }\n      }\n    }, due);\n  });\n}\n", "import { Observable } from '../Observable';\nimport { ObservableInput, ObservableInputTuple, SchedulerLike } from '../types';\nimport { mergeAll } from '../operators/mergeAll';\nimport { innerFrom } from './innerFrom';\nimport { EMPTY } from './empty';\nimport { popNumber, popScheduler } from '../util/args';\nimport { from } from './from';\n\nexport function merge<A extends readonly unknown[]>(...sources: [...ObservableInputTuple<A>]): Observable<A[number]>;\nexport function merge<A extends readonly unknown[]>(...sourcesAndConcurrency: [...ObservableInputTuple<A>, number?]): Observable<A[number]>;\n/** @deprecated The `scheduler` parameter will be removed in v8. Use `scheduled` and `mergeAll`. Details: https://rxjs.dev/deprecations/scheduler-argument */\nexport function merge<A extends readonly unknown[]>(\n  ...sourcesAndScheduler: [...ObservableInputTuple<A>, SchedulerLike?]\n): Observable<A[number]>;\n/** @deprecated The `scheduler` parameter will be removed in v8. Use `scheduled` and `mergeAll`. Details: https://rxjs.dev/deprecations/scheduler-argument */\nexport function merge<A extends readonly unknown[]>(\n  ...sourcesAndConcurrencyAndScheduler: [...ObservableInputTuple<A>, number?, SchedulerLike?]\n): Observable<A[number]>;\n\n/**\n * Creates an output Observable which concurrently emits all values from every\n * given input Observable.\n *\n * <span class=\"informal\">Flattens multiple Observables together by blending\n * their values into one Observable.</span>\n *\n * ![](merge.png)\n *\n * `merge` subscribes to each given input Observable (as arguments), and simply\n * forwards (without doing any transformation) all the values from all the input\n * Observables to the output Observable. The output Observable only completes\n * once all input Observables have completed. Any error delivered by an input\n * Observable will be immediately emitted on the output Observable.\n *\n * ## Examples\n *\n * Merge together two Observables: 1s interval and clicks\n *\n * ```ts\n * import { merge, fromEvent, interval } from 'rxjs';\n *\n * const clicks = fromEvent(document, 'click');\n * const timer = interval(1000);\n * const clicksOrTimer = merge(clicks, timer);\n * clicksOrTimer.subscribe(x => console.log(x));\n *\n * // Results in the following:\n * // timer will emit ascending values, one every second(1000ms) to console\n * // clicks logs MouseEvents to console every time the \"document\" is clicked\n * // Since the two streams are merged you see these happening\n * // as they occur.\n * ```\n *\n * Merge together 3 Observables, but run only 2 concurrently\n *\n * ```ts\n * import { interval, take, merge } from 'rxjs';\n *\n * const timer1 = interval(1000).pipe(take(10));\n * const timer2 = interval(2000).pipe(take(6));\n * const timer3 = interval(500).pipe(take(10));\n *\n * const concurrent = 2; // the argument\n * const merged = merge(timer1, timer2, timer3, concurrent);\n * merged.subscribe(x => console.log(x));\n *\n * // Results in the following:\n * // - First timer1 and timer2 will run concurrently\n * // - timer1 will emit a value every 1000ms for 10 iterations\n * // - timer2 will emit a value every 2000ms for 6 iterations\n * // - after timer1 hits its max iteration, timer2 will\n * //   continue, and timer3 will start to run concurrently with timer2\n * // - when timer2 hits its max iteration it terminates, and\n * //   timer3 will continue to emit a value every 500ms until it is complete\n * ```\n *\n * @see {@link mergeAll}\n * @see {@link mergeMap}\n * @see {@link mergeMapTo}\n * @see {@link mergeScan}\n *\n * @param {...ObservableInput} observables Input Observables to merge together.\n * @param {number} [concurrent=Infinity] Maximum number of input\n * Observables being subscribed to concurrently.\n * @param {SchedulerLike} [scheduler=null] The {@link SchedulerLike} to use for managing\n * concurrency of input Observables.\n * @return {Observable} an Observable that emits items that are the result of\n * every input Observable.\n */\nexport function merge(...args: (ObservableInput<unknown> | number | SchedulerLike)[]): Observable<unknown> {\n  const scheduler = popScheduler(args);\n  const concurrent = popNumber(args, Infinity);\n  const sources = args as ObservableInput<unknown>[];\n  return !sources.length\n    ? // No source provided\n      EMPTY\n    : sources.length === 1\n    ? // One source? Just return it.\n      innerFrom(sources[0])\n    : // Merge all sources\n      mergeAll(concurrent)(from(sources, scheduler));\n}\n", "import { Observable } from '../Observable';\nimport { noop } from '../util/noop';\n\n/**\n * An Observable that emits no items to the Observer and never completes.\n *\n * ![](never.png)\n *\n * A simple Observable that emits neither values nor errors nor the completion\n * notification. It can be used for testing purposes or for composing with other\n * Observables. Please note that by never emitting a complete notification, this\n * Observable keeps the subscription from being disposed automatically.\n * Subscriptions need to be manually disposed.\n *\n * ##  Example\n *\n * Emit the number 7, then never emit anything else (not even complete)\n *\n * ```ts\n * import { NEVER, startWith } from 'rxjs';\n *\n * const info = () => console.log('Will not be called');\n *\n * const result = NEVER.pipe(startWith(7));\n * result.subscribe({\n *   next: x => console.log(x),\n *   error: info,\n *   complete: info\n * });\n * ```\n *\n * @see {@link Observable}\n * @see {@link EMPTY}\n * @see {@link of}\n * @see {@link throwError}\n */\nexport const NEVER = new Observable<never>(noop);\n\n/**\n * @deprecated Replaced with the {@link NEVER} constant. Will be removed in v8.\n */\nexport function never() {\n  return NEVER;\n}\n", "const { isArray } = Array;\n\n/**\n * Used in operators and functions that accept either a list of arguments, or an array of arguments\n * as a single argument.\n */\nexport function argsOrArgArray<T>(args: (T | T[])[]): T[] {\n  return args.length === 1 && isArray(args[0]) ? args[0] : (args as T[]);\n}\n", "import { OperatorFunction, MonoTypeOperatorFunction, TruthyTypesOf } from '../types';\nimport { operate } from '../util/lift';\nimport { createOperatorSubscriber } from './OperatorSubscriber';\n\n/** @deprecated Use a closure instead of a `thisArg`. Signatures accepting a `thisArg` will be removed in v8. */\nexport function filter<T, S extends T, A>(predicate: (this: A, value: T, index: number) => value is S, thisArg: A): OperatorFunction<T, S>;\nexport function filter<T, S extends T>(predicate: (value: T, index: number) => value is S): OperatorFunction<T, S>;\nexport function filter<T>(predicate: BooleanConstructor): OperatorFunction<T, TruthyTypesOf<T>>;\n/** @deprecated Use a closure instead of a `thisArg`. Signatures accepting a `thisArg` will be removed in v8. */\nexport function filter<T, A>(predicate: (this: A, value: T, index: number) => boolean, thisArg: A): MonoTypeOperatorFunction<T>;\nexport function filter<T>(predicate: (value: T, index: number) => boolean): MonoTypeOperatorFunction<T>;\n\n/**\n * Filter items emitted by the source Observable by only emitting those that\n * satisfy a specified predicate.\n *\n * <span class=\"informal\">Like\n * [Array.prototype.filter()](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array/filter),\n * it only emits a value from the source if it passes a criterion function.</span>\n *\n * ![](filter.png)\n *\n * Similar to the well-known `Array.prototype.filter` method, this operator\n * takes values from the source Observable, passes them through a `predicate`\n * function and only emits those values that yielded `true`.\n *\n * ## Example\n *\n * Emit only click events whose target was a DIV element\n *\n * ```ts\n * import { fromEvent, filter } from 'rxjs';\n *\n * const div = document.createElement('div');\n * div.style.cssText = 'width: 200px; height: 200px; background: #09c;';\n * document.body.appendChild(div);\n *\n * const clicks = fromEvent(document, 'click');\n * const clicksOnDivs = clicks.pipe(filter(ev => (<HTMLElement>ev.target).tagName === 'DIV'));\n * clicksOnDivs.subscribe(x => console.log(x));\n * ```\n *\n * @see {@link distinct}\n * @see {@link distinctUntilChanged}\n * @see {@link distinctUntilKeyChanged}\n * @see {@link ignoreElements}\n * @see {@link partition}\n * @see {@link skip}\n *\n * @param predicate A function that\n * evaluates each value emitted by the source Observable. If it returns `true`,\n * the value is emitted, if `false` the value is not passed to the output\n * Observable. The `index` parameter is the number `i` for the i-th source\n * emission that has happened since the subscription, starting from the number\n * `0`.\n * @param thisArg An optional argument to determine the value of `this`\n * in the `predicate` function.\n * @return A function that returns an Observable that emits items from the\n * source Observable that satisfy the specified `predicate`.\n */\nexport function filter<T>(predicate: (value: T, index: number) => boolean, thisArg?: any): MonoTypeOperatorFunction<T> {\n  return operate((source, subscriber) => {\n    // An index passed to our predicate function on each call.\n    let index = 0;\n\n    // Subscribe to the source, all errors and completions are\n    // forwarded to the consumer.\n    source.subscribe(\n      // Call the predicate with the appropriate `this` context,\n      // if the predicate returns `true`, then send the value\n      // to the consumer.\n      createOperatorSubscriber(subscriber, (value) => predicate.call(thisArg, value, index++) && subscriber.next(value))\n    );\n  });\n}\n", "import { Observable } from '../Observable';\nimport { ObservableInputTuple } from '../types';\nimport { innerFrom } from './innerFrom';\nimport { argsOrArgArray } from '../util/argsOrArgArray';\nimport { EMPTY } from './empty';\nimport { createOperatorSubscriber } from '../operators/OperatorSubscriber';\nimport { popResultSelector } from '../util/args';\n\nexport function zip<A extends readonly unknown[]>(sources: [...ObservableInputTuple<A>]): Observable<A>;\nexport function zip<A extends readonly unknown[], R>(\n  sources: [...ObservableInputTuple<A>],\n  resultSelector: (...values: A) => R\n): Observable<R>;\nexport function zip<A extends readonly unknown[]>(...sources: [...ObservableInputTuple<A>]): Observable<A>;\nexport function zip<A extends readonly unknown[], R>(\n  ...sourcesAndResultSelector: [...ObservableInputTuple<A>, (...values: A) => R]\n): Observable<R>;\n\n/**\n * Combines multiple Observables to create an Observable whose values are calculated from the values, in order, of each\n * of its input Observables.\n *\n * If the last parameter is a function, this function is used to compute the created value from the input values.\n * Otherwise, an array of the input values is returned.\n *\n * ## Example\n *\n * Combine age and name from different sources\n *\n * ```ts\n * import { of, zip, map } from 'rxjs';\n *\n * const age$ = of(27, 25, 29);\n * const name$ = of('Foo', 'Bar', 'Beer');\n * const isDev$ = of(true, true, false);\n *\n * zip(age$, name$, isDev$).pipe(\n *   map(([age, name, isDev]) => ({ age, name, isDev }))\n * )\n * .subscribe(x => console.log(x));\n *\n * // Outputs\n * // { age: 27, name: 'Foo', isDev: true }\n * // { age: 25, name: 'Bar', isDev: true }\n * // { age: 29, name: 'Beer', isDev: false }\n * ```\n *\n * @param sources\n * @return {Observable<R>}\n */\nexport function zip(...args: unknown[]): Observable<unknown> {\n  const resultSelector = popResultSelector(args);\n\n  const sources = argsOrArgArray(args) as Observable<unknown>[];\n\n  return sources.length\n    ? new Observable<unknown[]>((subscriber) => {\n        // A collection of buffers of values from each source.\n        // Keyed by the same index with which the sources were passed in.\n        let buffers: unknown[][] = sources.map(() => []);\n\n        // An array of flags of whether or not the sources have completed.\n        // This is used to check to see if we should complete the result.\n        // Keyed by the same index with which the sources were passed in.\n        let completed = sources.map(() => false);\n\n        // When everything is done, release the arrays above.\n        subscriber.add(() => {\n          buffers = completed = null!;\n        });\n\n        // Loop over our sources and subscribe to each one. The index `i` is\n        // especially important here, because we use it in closures below to\n        // access the related buffers and completion properties\n        for (let sourceIndex = 0; !subscriber.closed && sourceIndex < sources.length; sourceIndex++) {\n          innerFrom(sources[sourceIndex]).subscribe(\n            createOperatorSubscriber(\n              subscriber,\n              (value) => {\n                buffers[sourceIndex].push(value);\n                // if every buffer has at least one value in it, then we\n                // can shift out the oldest value from each buffer and emit\n                // them as an array.\n                if (buffers.every((buffer) => buffer.length)) {\n                  const result: any = buffers.map((buffer) => buffer.shift()!);\n                  // Emit the array. If theres' a result selector, use that.\n                  subscriber.next(resultSelector ? resultSelector(...result) : result);\n                  // If any one of the sources is both complete and has an empty buffer\n                  // then we complete the result. This is because we cannot possibly have\n                  // any more values to zip together.\n                  if (buffers.some((buffer, i) => !buffer.length && completed[i])) {\n                    subscriber.complete();\n                  }\n                }\n              },\n              () => {\n                // This source completed. Mark it as complete so we can check it later\n                // if we have to.\n                completed[sourceIndex] = true;\n                // But, if this complete source has nothing in its buffer, then we\n                // can complete the result, because we can't possibly have any more\n                // values from this to zip together with the other values.\n                !buffers[sourceIndex].length && subscriber.complete();\n              }\n            )\n          );\n        }\n\n        // When everything is done, release the arrays above.\n        return () => {\n          buffers = completed = null!;\n        };\n      })\n    : EMPTY;\n}\n", "import { Subscriber } from '../Subscriber';\nimport { MonoTypeOperatorFunction, ObservableInput } from '../types';\n\nimport { operate } from '../util/lift';\nimport { innerFrom } from '../observable/innerFrom';\nimport { createOperatorSubscriber } from './OperatorSubscriber';\n\n/**\n * Ignores source values for a duration determined by another Observable, then\n * emits the most recent value from the source Observable, then repeats this\n * process.\n *\n * <span class=\"informal\">It's like {@link auditTime}, but the silencing\n * duration is determined by a second Observable.</span>\n *\n * ![](audit.svg)\n *\n * `audit` is similar to `throttle`, but emits the last value from the silenced\n * time window, instead of the first value. `audit` emits the most recent value\n * from the source Observable on the output Observable as soon as its internal\n * timer becomes disabled, and ignores source values while the timer is enabled.\n * Initially, the timer is disabled. As soon as the first source value arrives,\n * the timer is enabled by calling the `durationSelector` function with the\n * source value, which returns the \"duration\" Observable. When the duration\n * Observable emits a value, the timer is disabled, then the most\n * recent source value is emitted on the output Observable, and this process\n * repeats for the next source value.\n *\n * ## Example\n *\n * Emit clicks at a rate of at most one click per second\n *\n * ```ts\n * import { fromEvent, audit, interval } from 'rxjs';\n *\n * const clicks = fromEvent(document, 'click');\n * const result = clicks.pipe(audit(ev => interval(1000)));\n * result.subscribe(x => console.log(x));\n * ```\n *\n * @see {@link auditTime}\n * @see {@link debounce}\n * @see {@link delayWhen}\n * @see {@link sample}\n * @see {@link throttle}\n *\n * @param durationSelector A function\n * that receives a value from the source Observable, for computing the silencing\n * duration, returned as an Observable or a Promise.\n * @return A function that returns an Observable that performs rate-limiting of\n * emissions from the source Observable.\n */\nexport function audit<T>(durationSelector: (value: T) => ObservableInput<any>): MonoTypeOperatorFunction<T> {\n  return operate((source, subscriber) => {\n    let hasValue = false;\n    let lastValue: T | null = null;\n    let durationSubscriber: Subscriber<any> | null = null;\n    let isComplete = false;\n\n    const endDuration = () => {\n      durationSubscriber?.unsubscribe();\n      durationSubscriber = null;\n      if (hasValue) {\n        hasValue = false;\n        const value = lastValue!;\n        lastValue = null;\n        subscriber.next(value);\n      }\n      isComplete && subscriber.complete();\n    };\n\n    const cleanupDuration = () => {\n      durationSubscriber = null;\n      isComplete && subscriber.complete();\n    };\n\n    source.subscribe(\n      createOperatorSubscriber(\n        subscriber,\n        (value) => {\n          hasValue = true;\n          lastValue = value;\n          if (!durationSubscriber) {\n            innerFrom(durationSelector(value)).subscribe(\n              (durationSubscriber = createOperatorSubscriber(subscriber, endDuration, cleanupDuration))\n            );\n          }\n        },\n        () => {\n          isComplete = true;\n          (!hasValue || !durationSubscriber || durationSubscriber.closed) && subscriber.complete();\n        }\n      )\n    );\n  });\n}\n", "import { asyncScheduler } from '../scheduler/async';\nimport { audit } from './audit';\nimport { timer } from '../observable/timer';\nimport { MonoTypeOperatorFunction, SchedulerLike } from '../types';\n\n/**\n * Ignores source values for `duration` milliseconds, then emits the most recent\n * value from the source Observable, then repeats this process.\n *\n * <span class=\"informal\">When it sees a source value, it ignores that plus\n * the next ones for `duration` milliseconds, and then it emits the most recent\n * value from the source.</span>\n *\n * ![](auditTime.png)\n *\n * `auditTime` is similar to `throttleTime`, but emits the last value from the\n * silenced time window, instead of the first value. `auditTime` emits the most\n * recent value from the source Observable on the output Observable as soon as\n * its internal timer becomes disabled, and ignores source values while the\n * timer is enabled. Initially, the timer is disabled. As soon as the first\n * source value arrives, the timer is enabled. After `duration` milliseconds (or\n * the time unit determined internally by the optional `scheduler`) has passed,\n * the timer is disabled, then the most recent source value is emitted on the\n * output Observable, and this process repeats for the next source value.\n * Optionally takes a {@link SchedulerLike} for managing timers.\n *\n * ## Example\n *\n * Emit clicks at a rate of at most one click per second\n *\n * ```ts\n * import { fromEvent, auditTime } from 'rxjs';\n *\n * const clicks = fromEvent(document, 'click');\n * const result = clicks.pipe(auditTime(1000));\n * result.subscribe(x => console.log(x));\n * ```\n *\n * @see {@link audit}\n * @see {@link debounceTime}\n * @see {@link delay}\n * @see {@link sampleTime}\n * @see {@link throttleTime}\n *\n * @param {number} duration Time to wait before emitting the most recent source\n * value, measured in milliseconds or the time unit determined internally\n * by the optional `scheduler`.\n * @param {SchedulerLike} [scheduler=async] The {@link SchedulerLike} to use for\n * managing the timers that handle the rate-limiting behavior.\n * @return A function that returns an Observable that performs rate-limiting of\n * emissions from the source Observable.\n */\nexport function auditTime<T>(duration: number, scheduler: SchedulerLike = asyncScheduler): MonoTypeOperatorFunction<T> {\n  return audit(() => timer(duration, scheduler));\n}\n", "import { OperatorFunction } from '../types';\nimport { operate } from '../util/lift';\nimport { createOperatorSubscriber } from './OperatorSubscriber';\nimport { arrRemove } from '../util/arrRemove';\n\n/**\n * Buffers the source Observable values until the size hits the maximum\n * `bufferSize` given.\n *\n * <span class=\"informal\">Collects values from the past as an array, and emits\n * that array only when its size reaches `bufferSize`.</span>\n *\n * ![](bufferCount.png)\n *\n * Buffers a number of values from the source Observable by `bufferSize` then\n * emits the buffer and clears it, and starts a new buffer each\n * `startBufferEvery` values. If `startBufferEvery` is not provided or is\n * `null`, then new buffers are started immediately at the start of the source\n * and when each buffer closes and is emitted.\n *\n * ## Examples\n *\n * Emit the last two click events as an array\n *\n * ```ts\n * import { fromEvent, bufferCount } from 'rxjs';\n *\n * const clicks = fromEvent(document, 'click');\n * const buffered = clicks.pipe(bufferCount(2));\n * buffered.subscribe(x => console.log(x));\n * ```\n *\n * On every click, emit the last two click events as an array\n *\n * ```ts\n * import { fromEvent, bufferCount } from 'rxjs';\n *\n * const clicks = fromEvent(document, 'click');\n * const buffered = clicks.pipe(bufferCount(2, 1));\n * buffered.subscribe(x => console.log(x));\n * ```\n *\n * @see {@link buffer}\n * @see {@link bufferTime}\n * @see {@link bufferToggle}\n * @see {@link bufferWhen}\n * @see {@link pairwise}\n * @see {@link windowCount}\n *\n * @param {number} bufferSize The maximum size of the buffer emitted.\n * @param {number} [startBufferEvery] Interval at which to start a new buffer.\n * For example if `startBufferEvery` is `2`, then a new buffer will be started\n * on every other value from the source. A new buffer is started at the\n * beginning of the source by default.\n * @return A function that returns an Observable of arrays of buffered values.\n */\nexport function bufferCount<T>(bufferSize: number, startBufferEvery: number | null = null): OperatorFunction<T, T[]> {\n  // If no `startBufferEvery` value was supplied, then we're\n  // opening and closing on the bufferSize itself.\n  startBufferEvery = startBufferEvery ?? bufferSize;\n\n  return operate((source, subscriber) => {\n    let buffers: T[][] = [];\n    let count = 0;\n\n    source.subscribe(\n      createOperatorSubscriber(\n        subscriber,\n        (value) => {\n          let toEmit: T[][] | null = null;\n\n          // Check to see if we need to start a buffer.\n          // This will start one at the first value, and then\n          // a new one every N after that.\n          if (count++ % startBufferEvery! === 0) {\n            buffers.push([]);\n          }\n\n          // Push our value into our active buffers.\n          for (const buffer of buffers) {\n            buffer.push(value);\n            // Check to see if we're over the bufferSize\n            // if we are, record it so we can emit it later.\n            // If we emitted it now and removed it, it would\n            // mutate the `buffers` array while we're looping\n            // over it.\n            if (bufferSize <= buffer.length) {\n              toEmit = toEmit ?? [];\n              toEmit.push(buffer);\n            }\n          }\n\n          if (toEmit) {\n            // We have found some buffers that are over the\n            // `bufferSize`. Emit them, and remove them from our\n            // buffers list.\n            for (const buffer of toEmit) {\n              arrRemove(buffers, buffer);\n              subscriber.next(buffer);\n            }\n          }\n        },\n        () => {\n          // When the source completes, emit all of our\n          // active buffers.\n          for (const buffer of buffers) {\n            subscriber.next(buffer);\n          }\n          subscriber.complete();\n        },\n        // Pass all errors through to consumer.\n        undefined,\n        () => {\n          // Clean up our memory when we finalize\n          buffers = null!;\n        }\n      )\n    );\n  });\n}\n", "import { Observable } from '../Observable';\n\nimport { ObservableInput, OperatorFunction, ObservedValueOf } from '../types';\nimport { Subscription } from '../Subscription';\nimport { innerFrom } from '../observable/innerFrom';\nimport { createOperatorSubscriber } from './OperatorSubscriber';\nimport { operate } from '../util/lift';\n\n/* tslint:disable:max-line-length */\nexport function catchError<T, O extends ObservableInput<any>>(\n  selector: (err: any, caught: Observable<T>) => O\n): OperatorFunction<T, T | ObservedValueOf<O>>;\n/* tslint:enable:max-line-length */\n\n/**\n * Catches errors on the observable to be handled by returning a new observable or throwing an error.\n *\n * <span class=\"informal\">\n * It only listens to the error channel and ignores notifications.\n * Handles errors from the source observable, and maps them to a new observable.\n * The error may also be rethrown, or a new error can be thrown to emit an error from the result.\n * </span>\n *\n * ![](catch.png)\n *\n * This operator handles errors, but forwards along all other events to the resulting observable.\n * If the source observable terminates with an error, it will map that error to a new observable,\n * subscribe to it, and forward all of its events to the resulting observable.\n *\n * ## Examples\n *\n * Continue with a different Observable when there's an error\n *\n * ```ts\n * import { of, map, catchError } from 'rxjs';\n *\n * of(1, 2, 3, 4, 5)\n *   .pipe(\n *     map(n => {\n *       if (n === 4) {\n *         throw 'four!';\n *       }\n *       return n;\n *     }),\n *     catchError(err => of('I', 'II', 'III', 'IV', 'V'))\n *   )\n *   .subscribe(x => console.log(x));\n *   // 1, 2, 3, I, II, III, IV, V\n * ```\n *\n * Retry the caught source Observable again in case of error, similar to `retry()` operator\n *\n * ```ts\n * import { of, map, catchError, take } from 'rxjs';\n *\n * of(1, 2, 3, 4, 5)\n *   .pipe(\n *     map(n => {\n *       if (n === 4) {\n *         throw 'four!';\n *       }\n *       return n;\n *     }),\n *     catchError((err, caught) => caught),\n *     take(30)\n *   )\n *   .subscribe(x => console.log(x));\n *   // 1, 2, 3, 1, 2, 3, ...\n * ```\n *\n * Throw a new error when the source Observable throws an error\n *\n * ```ts\n * import { of, map, catchError } from 'rxjs';\n *\n * of(1, 2, 3, 4, 5)\n *   .pipe(\n *     map(n => {\n *       if (n === 4) {\n *         throw 'four!';\n *       }\n *       return n;\n *     }),\n *     catchError(err => {\n *       throw 'error in source. Details: ' + err;\n *     })\n *   )\n *   .subscribe({\n *     next: x => console.log(x),\n *     error: err => console.log(err)\n *   });\n *   // 1, 2, 3, error in source. Details: four!\n * ```\n *\n * @see {@link onErrorResumeNext}\n * @see {@link repeat}\n * @see {@link repeatWhen}\n * @see {@link retry }\n * @see {@link retryWhen}\n *\n * @param {function} selector a function that takes as arguments `err`, which is the error, and `caught`, which\n * is the source observable, in case you'd like to \"retry\" that observable by returning it again. Whatever observable\n * is returned by the `selector` will be used to continue the observable chain.\n * @return A function that returns an Observable that originates from either\n * the source or the Observable returned by the `selector` function.\n */\nexport function catchError<T, O extends ObservableInput<any>>(\n  selector: (err: any, caught: Observable<T>) => O\n): OperatorFunction<T, T | ObservedValueOf<O>> {\n  return operate((source, subscriber) => {\n    let innerSub: Subscription | null = null;\n    let syncUnsub = false;\n    let handledResult: Observable<ObservedValueOf<O>>;\n\n    innerSub = source.subscribe(\n      createOperatorSubscriber(subscriber, undefined, undefined, (err) => {\n        handledResult = innerFrom(selector(err, catchError(selector)(source)));\n        if (innerSub) {\n          innerSub.unsubscribe();\n          innerSub = null;\n          handledResult.subscribe(subscriber);\n        } else {\n          // We don't have an innerSub yet, that means the error was synchronous\n          // because the subscribe call hasn't returned yet.\n          syncUnsub = true;\n        }\n      })\n    );\n\n    if (syncUnsub) {\n      // We have a synchronous error, we need to make sure to\n      // finalize right away. This ensures that callbacks in the `finalize` operator are called\n      // at the right time, and that finalization occurs at the expected\n      // time between the source error and the subscription to the\n      // next observable.\n      innerSub.unsubscribe();\n      innerSub = null;\n      handledResult!.subscribe(subscriber);\n    }\n  });\n}\n", "import { Observable } from '../Observable';\nimport { Subscriber } from '../Subscriber';\nimport { createOperatorSubscriber } from './OperatorSubscriber';\n\n/**\n * A basic scan operation. This is used for `scan` and `reduce`.\n * @param accumulator The accumulator to use\n * @param seed The seed value for the state to accumulate\n * @param hasSeed Whether or not a seed was provided\n * @param emitOnNext Whether or not to emit the state on next\n * @param emitBeforeComplete Whether or not to emit the before completion\n */\n\nexport function scanInternals<V, A, S>(\n  accumulator: (acc: V | A | S, value: V, index: number) => A,\n  seed: S,\n  hasSeed: boolean,\n  emitOnNext: boolean,\n  emitBeforeComplete?: undefined | true\n) {\n  return (source: Observable<V>, subscriber: Subscriber<any>) => {\n    // Whether or not we have state yet. This will only be\n    // false before the first value arrives if we didn't get\n    // a seed value.\n    let hasState = hasSeed;\n    // The state that we're tracking, starting with the seed,\n    // if there is one, and then updated by the return value\n    // from the accumulator on each emission.\n    let state: any = seed;\n    // An index to pass to the accumulator function.\n    let index = 0;\n\n    // Subscribe to our source. All errors and completions are passed through.\n    source.subscribe(\n      createOperatorSubscriber(\n        subscriber,\n        (value) => {\n          // Always increment the index.\n          const i = index++;\n          // Set the state\n          state = hasState\n            ? // We already have state, so we can get the new state from the accumulator\n              accumulator(state, value, i)\n            : // We didn't have state yet, a seed value was not provided, so\n\n              // we set the state to the first value, and mark that we have state now\n              ((hasState = true), value);\n\n          // Maybe send it to the consumer.\n          emitOnNext && subscriber.next(state);\n        },\n        // If an onComplete was given, call it, otherwise\n        // just pass through the complete notification to the consumer.\n        emitBeforeComplete &&\n          (() => {\n            hasState && subscriber.next(state);\n            subscriber.complete();\n          })\n      )\n    );\n  };\n}\n", "import { combineLatestInit } from '../observable/combineLatest';\nimport { ObservableInput, ObservableInputTuple, OperatorFunction } from '../types';\nimport { operate } from '../util/lift';\nimport { argsOrArgArray } from '../util/argsOrArgArray';\nimport { mapOneOrManyArgs } from '../util/mapOneOrManyArgs';\nimport { pipe } from '../util/pipe';\nimport { popResultSelector } from '../util/args';\n\n/** @deprecated Replaced with {@link combineLatestWith}. Will be removed in v8. */\nexport function combineLatest<T, A extends readonly unknown[], R>(\n  sources: [...ObservableInputTuple<A>],\n  project: (...values: [T, ...A]) => R\n): OperatorFunction<T, R>;\n/** @deprecated Replaced with {@link combineLatestWith}. Will be removed in v8. */\nexport function combineLatest<T, A extends readonly unknown[], R>(sources: [...ObservableInputTuple<A>]): OperatorFunction<T, [T, ...A]>;\n\n/** @deprecated Replaced with {@link combineLatestWith}. Will be removed in v8. */\nexport function combineLatest<T, A extends readonly unknown[], R>(\n  ...sourcesAndProject: [...ObservableInputTuple<A>, (...values: [T, ...A]) => R]\n): OperatorFunction<T, R>;\n/** @deprecated Replaced with {@link combineLatestWith}. Will be removed in v8. */\nexport function combineLatest<T, A extends readonly unknown[], R>(...sources: [...ObservableInputTuple<A>]): OperatorFunction<T, [T, ...A]>;\n\n/**\n * @deprecated Replaced with {@link combineLatestWith}. Will be removed in v8.\n */\nexport function combineLatest<T, R>(...args: (ObservableInput<any> | ((...values: any[]) => R))[]): OperatorFunction<T, unknown> {\n  const resultSelector = popResultSelector(args);\n  return resultSelector\n    ? pipe(combineLatest(...(args as Array<ObservableInput<any>>)), mapOneOrManyArgs(resultSelector))\n    : operate((source, subscriber) => {\n        combineLatestInit([source, ...argsOrArgArray(args)])(subscriber);\n      });\n}\n", "import { ObservableInputTuple, OperatorFunction, Cons } from '../types';\nimport { combineLatest } from './combineLatest';\n\n/**\n * Create an observable that combines the latest values from all passed observables and the source\n * into arrays and emits them.\n *\n * Returns an observable, that when subscribed to, will subscribe to the source observable and all\n * sources provided as arguments. Once all sources emit at least one value, all of the latest values\n * will be emitted as an array. After that, every time any source emits a value, all of the latest values\n * will be emitted as an array.\n *\n * This is a useful operator for eagerly calculating values based off of changed inputs.\n *\n * ## Example\n *\n * Simple concatenation of values from two inputs\n *\n * ```ts\n * import { fromEvent, combineLatestWith, map } from 'rxjs';\n *\n * // Setup: Add two inputs to the page\n * const input1 = document.createElement('input');\n * document.body.appendChild(input1);\n * const input2 = document.createElement('input');\n * document.body.appendChild(input2);\n *\n * // Get streams of changes\n * const input1Changes$ = fromEvent(input1, 'change');\n * const input2Changes$ = fromEvent(input2, 'change');\n *\n * // Combine the changes by adding them together\n * input1Changes$.pipe(\n *   combineLatestWith(input2Changes$),\n *   map(([e1, e2]) => (<HTMLInputElement>e1.target).value + ' - ' + (<HTMLInputElement>e2.target).value)\n * )\n * .subscribe(x => console.log(x));\n * ```\n *\n * @param otherSources the other sources to subscribe to.\n * @return A function that returns an Observable that emits the latest\n * emissions from both source and provided Observables.\n */\nexport function combineLatestWith<T, A extends readonly unknown[]>(\n  ...otherSources: [...ObservableInputTuple<A>]\n): OperatorFunction<T, Cons<T, A>> {\n  return combineLatest(...otherSources);\n}\n", "import { asyncScheduler } from '../scheduler/async';\nimport { Subscription } from '../Subscription';\nimport { MonoTypeOperatorFunction, SchedulerAction, SchedulerLike } from '../types';\nimport { operate } from '../util/lift';\nimport { createOperatorSubscriber } from './OperatorSubscriber';\n\n/**\n * Emits a notification from the source Observable only after a particular time span\n * has passed without another source emission.\n *\n * <span class=\"informal\">It's like {@link delay}, but passes only the most\n * recent notification from each burst of emissions.</span>\n *\n * ![](debounceTime.png)\n *\n * `debounceTime` delays notifications emitted by the source Observable, but drops\n * previous pending delayed emissions if a new notification arrives on the source\n * Observable. This operator keeps track of the most recent notification from the\n * source Observable, and emits that only when `dueTime` has passed\n * without any other notification appearing on the source Observable. If a new value\n * appears before `dueTime` silence occurs, the previous notification will be dropped\n * and will not be emitted and a new `dueTime` is scheduled.\n * If the completing event happens during `dueTime` the last cached notification\n * is emitted before the completion event is forwarded to the output observable.\n * If the error event happens during `dueTime` or after it only the error event is\n * forwarded to the output observable. The cache notification is not emitted in this case.\n *\n * This is a rate-limiting operator, because it is impossible for more than one\n * notification to be emitted in any time window of duration `dueTime`, but it is also\n * a delay-like operator since output emissions do not occur at the same time as\n * they did on the source Observable. Optionally takes a {@link SchedulerLike} for\n * managing timers.\n *\n * ## Example\n *\n * Emit the most recent click after a burst of clicks\n *\n * ```ts\n * import { fromEvent, debounceTime } from 'rxjs';\n *\n * const clicks = fromEvent(document, 'click');\n * const result = clicks.pipe(debounceTime(1000));\n * result.subscribe(x => console.log(x));\n * ```\n *\n * @see {@link audit}\n * @see {@link auditTime}\n * @see {@link debounce}\n * @see {@link sample}\n * @see {@link sampleTime}\n * @see {@link throttle}\n * @see {@link throttleTime}\n *\n * @param {number} dueTime The timeout duration in milliseconds (or the time\n * unit determined internally by the optional `scheduler`) for the window of\n * time required to wait for emission silence before emitting the most recent\n * source value.\n * @param {SchedulerLike} [scheduler=async] The {@link SchedulerLike} to use for\n * managing the timers that handle the timeout for each value.\n * @return A function that returns an Observable that delays the emissions of\n * the source Observable by the specified `dueTime`, and may drop some values\n * if they occur too frequently.\n */\nexport function debounceTime<T>(dueTime: number, scheduler: SchedulerLike = asyncScheduler): MonoTypeOperatorFunction<T> {\n  return operate((source, subscriber) => {\n    let activeTask: Subscription | null = null;\n    let lastValue: T | null = null;\n    let lastTime: number | null = null;\n\n    const emit = () => {\n      if (activeTask) {\n        // We have a value! Free up memory first, then emit the value.\n        activeTask.unsubscribe();\n        activeTask = null;\n        const value = lastValue!;\n        lastValue = null;\n        subscriber.next(value);\n      }\n    };\n    function emitWhenIdle(this: SchedulerAction<unknown>) {\n      // This is called `dueTime` after the first value\n      // but we might have received new values during this window!\n\n      const targetTime = lastTime! + dueTime;\n      const now = scheduler.now();\n      if (now < targetTime) {\n        // On that case, re-schedule to the new target\n        activeTask = this.schedule(undefined, targetTime - now);\n        subscriber.add(activeTask);\n        return;\n      }\n\n      emit();\n    }\n\n    source.subscribe(\n      createOperatorSubscriber(\n        subscriber,\n        (value: T) => {\n          lastValue = value;\n          lastTime = scheduler.now();\n\n          // Only set up a task if it's not already up\n          if (!activeTask) {\n            activeTask = scheduler.schedule(emitWhenIdle, dueTime);\n            subscriber.add(activeTask);\n          }\n        },\n        () => {\n          // Source completed.\n          // Emit any pending debounced values then complete\n          emit();\n          subscriber.complete();\n        },\n        // Pass all errors through to consumer.\n        undefined,\n        () => {\n          // Finalization.\n          lastValue = activeTask = null;\n        }\n      )\n    );\n  });\n}\n", "import { OperatorFunction } from '../types';\nimport { operate } from '../util/lift';\nimport { createOperatorSubscriber } from './OperatorSubscriber';\n\n/**\n * Emits a given value if the source Observable completes without emitting any\n * `next` value, otherwise mirrors the source Observable.\n *\n * <span class=\"informal\">If the source Observable turns out to be empty, then\n * this operator will emit a default value.</span>\n *\n * ![](defaultIfEmpty.png)\n *\n * `defaultIfEmpty` emits the values emitted by the source Observable or a\n * specified default value if the source Observable is empty (completes without\n * having emitted any `next` value).\n *\n * ## Example\n *\n * If no clicks happen in 5 seconds, then emit 'no clicks'\n *\n * ```ts\n * import { fromEvent, takeUntil, interval, defaultIfEmpty } from 'rxjs';\n *\n * const clicks = fromEvent(document, 'click');\n * const clicksBeforeFive = clicks.pipe(takeUntil(interval(5000)));\n * const result = clicksBeforeFive.pipe(defaultIfEmpty('no clicks'));\n * result.subscribe(x => console.log(x));\n * ```\n *\n * @see {@link empty}\n * @see {@link last}\n *\n * @param defaultValue The default value used if the source\n * Observable is empty.\n * @return A function that returns an Observable that emits either the\n * specified `defaultValue` if the source Observable emits no items, or the\n * values emitted by the source Observable.\n */\nexport function defaultIfEmpty<T, R>(defaultValue: R): OperatorFunction<T, T | R> {\n  return operate((source, subscriber) => {\n    let hasValue = false;\n    source.subscribe(\n      createOperatorSubscriber(\n        subscriber,\n        (value) => {\n          hasValue = true;\n          subscriber.next(value);\n        },\n        () => {\n          if (!hasValue) {\n            subscriber.next(defaultValue!);\n          }\n          subscriber.complete();\n        }\n      )\n    );\n  });\n}\n", "import { MonoTypeOperatorFunction } from '../types';\nimport { EMPTY } from '../observable/empty';\nimport { operate } from '../util/lift';\nimport { createOperatorSubscriber } from './OperatorSubscriber';\n\n/**\n * Emits only the first `count` values emitted by the source Observable.\n *\n * <span class=\"informal\">Takes the first `count` values from the source, then\n * completes.</span>\n *\n * ![](take.png)\n *\n * `take` returns an Observable that emits only the first `count` values emitted\n * by the source Observable. If the source emits fewer than `count` values then\n * all of its values are emitted. After that, it completes, regardless if the\n * source completes.\n *\n * ## Example\n *\n * Take the first 5 seconds of an infinite 1-second interval Observable\n *\n * ```ts\n * import { interval, take } from 'rxjs';\n *\n * const intervalCount = interval(1000);\n * const takeFive = intervalCount.pipe(take(5));\n * takeFive.subscribe(x => console.log(x));\n *\n * // Logs:\n * // 0\n * // 1\n * // 2\n * // 3\n * // 4\n * ```\n *\n * @see {@link takeLast}\n * @see {@link takeUntil}\n * @see {@link takeWhile}\n * @see {@link skip}\n *\n * @param count The maximum number of `next` values to emit.\n * @return A function that returns an Observable that emits only the first\n * `count` values emitted by the source Observable, or all of the values from\n * the source if the source emits fewer than `count` values.\n */\nexport function take<T>(count: number): MonoTypeOperatorFunction<T> {\n  return count <= 0\n    ? // If we are taking no values, that's empty.\n      () => EMPTY\n    : operate((source, subscriber) => {\n        let seen = 0;\n        source.subscribe(\n          createOperatorSubscriber(subscriber, (value) => {\n            // Increment the number of values we have seen,\n            // then check it against the allowed count to see\n            // if we are still letting values through.\n            if (++seen <= count) {\n              subscriber.next(value);\n              // If we have met or passed our allowed count,\n              // we need to complete. We have to do <= here,\n              // because re-entrant code will increment `seen` twice.\n              if (count <= seen) {\n                subscriber.complete();\n              }\n            }\n          })\n        );\n      });\n}\n", "import { OperatorFunction } from '../types';\nimport { operate } from '../util/lift';\nimport { createOperatorSubscriber } from './OperatorSubscriber';\nimport { noop } from '../util/noop';\n\n/**\n * Ignores all items emitted by the source Observable and only passes calls of `complete` or `error`.\n *\n * ![](ignoreElements.png)\n *\n * The `ignoreElements` operator suppresses all items emitted by the source Observable,\n * but allows its termination notification (either `error` or `complete`) to pass through unchanged.\n *\n * If you do not care about the items being emitted by an Observable, but you do want to be notified\n * when it completes or when it terminates with an error, you can apply the `ignoreElements` operator\n * to the Observable, which will ensure that it will never call its observers\u2019 `next` handlers.\n *\n * ## Example\n *\n * Ignore all `next` emissions from the source\n *\n * ```ts\n * import { of, ignoreElements } from 'rxjs';\n *\n * of('you', 'talking', 'to', 'me')\n *   .pipe(ignoreElements())\n *   .subscribe({\n *     next: word => console.log(word),\n *     error: err => console.log('error:', err),\n *     complete: () => console.log('the end'),\n *   });\n *\n * // result:\n * // 'the end'\n * ```\n *\n * @return A function that returns an empty Observable that only calls\n * `complete` or `error`, based on which one is called by the source\n * Observable.\n */\nexport function ignoreElements(): OperatorFunction<unknown, never> {\n  return operate((source, subscriber) => {\n    source.subscribe(createOperatorSubscriber(subscriber, noop));\n  });\n}\n", "import { OperatorFunction } from '../types';\nimport { map } from './map';\n\n/** @deprecated To be removed in v9. Use {@link map} instead: `map(() => value)`. */\nexport function mapTo<R>(value: R): OperatorFunction<unknown, R>;\n/**\n * @deprecated Do not specify explicit type parameters. Signatures with type parameters\n * that cannot be inferred will be removed in v8. `mapTo` itself will be removed in v9,\n * use {@link map} instead: `map(() => value)`.\n * */\nexport function mapTo<T, R>(value: R): OperatorFunction<T, R>;\n\n/**\n * Emits the given constant value on the output Observable every time the source\n * Observable emits a value.\n *\n * <span class=\"informal\">Like {@link map}, but it maps every source value to\n * the same output value every time.</span>\n *\n * ![](mapTo.png)\n *\n * Takes a constant `value` as argument, and emits that whenever the source\n * Observable emits a value. In other words, ignores the actual source value,\n * and simply uses the emission moment to know when to emit the given `value`.\n *\n * ## Example\n *\n * Map every click to the string `'Hi'`\n *\n * ```ts\n * import { fromEvent, mapTo } from 'rxjs';\n *\n * const clicks = fromEvent(document, 'click');\n * const greetings = clicks.pipe(mapTo('Hi'));\n *\n * greetings.subscribe(x => console.log(x));\n * ```\n *\n * @see {@link map}\n *\n * @param value The value to map each source value to.\n * @return A function that returns an Observable that emits the given `value`\n * every time the source Observable emits.\n * @deprecated To be removed in v9. Use {@link map} instead: `map(() => value)`.\n */\nexport function mapTo<R>(value: R): OperatorFunction<unknown, R> {\n  return map(() => value);\n}\n", "import { Observable } from '../Observable';\nimport { MonoTypeOperatorFunction, ObservableInput } from '../types';\nimport { concat } from '../observable/concat';\nimport { take } from './take';\nimport { ignoreElements } from './ignoreElements';\nimport { mapTo } from './mapTo';\nimport { mergeMap } from './mergeMap';\nimport { innerFrom } from '../observable/innerFrom';\n\n/** @deprecated The `subscriptionDelay` parameter will be removed in v8. */\nexport function delayWhen<T>(\n  delayDurationSelector: (value: T, index: number) => ObservableInput<any>,\n  subscriptionDelay: Observable<any>\n): MonoTypeOperatorFunction<T>;\nexport function delayWhen<T>(delayDurationSelector: (value: T, index: number) => ObservableInput<any>): MonoTypeOperatorFunction<T>;\n\n/**\n * Delays the emission of items from the source Observable by a given time span\n * determined by the emissions of another Observable.\n *\n * <span class=\"informal\">It's like {@link delay}, but the time span of the\n * delay duration is determined by a second Observable.</span>\n *\n * ![](delayWhen.png)\n *\n * `delayWhen` operator shifts each emitted value from the source Observable by\n * a time span determined by another Observable. When the source emits a value,\n * the `delayDurationSelector` function is called with the value emitted from\n * the source Observable as the first argument to the `delayDurationSelector`.\n * The `delayDurationSelector` function should return an {@link ObservableInput},\n * that is internally converted to an Observable that is called the \"duration\"\n * Observable.\n *\n * The source value is emitted on the output Observable only when the \"duration\"\n * Observable emits ({@link guide/glossary-and-semantics#next next}s) any value.\n * Upon that, the \"duration\" Observable gets unsubscribed.\n *\n * Before RxJS V7, the {@link guide/glossary-and-semantics#complete completion}\n * of the \"duration\" Observable would have been triggering the emission of the\n * source value to the output Observable, but with RxJS V7, this is not the case\n * anymore.\n *\n * Only next notifications (from the \"duration\" Observable) trigger values from\n * the source Observable to be passed to the output Observable. If the \"duration\"\n * Observable only emits the complete notification (without next), the value\n * emitted by the source Observable will never get to the output Observable - it\n * will be swallowed. If the \"duration\" Observable errors, the error will be\n * propagated to the output Observable.\n *\n * Optionally, `delayWhen` takes a second argument, `subscriptionDelay`, which\n * is an Observable. When `subscriptionDelay` emits its first value or\n * completes, the source Observable is subscribed to and starts behaving like\n * described in the previous paragraph. If `subscriptionDelay` is not provided,\n * `delayWhen` will subscribe to the source Observable as soon as the output\n * Observable is subscribed.\n *\n * ## Example\n *\n * Delay each click by a random amount of time, between 0 and 5 seconds\n *\n * ```ts\n * import { fromEvent, delayWhen, interval } from 'rxjs';\n *\n * const clicks = fromEvent(document, 'click');\n * const delayedClicks = clicks.pipe(\n *   delayWhen(() => interval(Math.random() * 5000))\n * );\n * delayedClicks.subscribe(x => console.log(x));\n * ```\n *\n * @see {@link delay}\n * @see {@link throttle}\n * @see {@link throttleTime}\n * @see {@link debounce}\n * @see {@link debounceTime}\n * @see {@link sample}\n * @see {@link sampleTime}\n * @see {@link audit}\n * @see {@link auditTime}\n *\n * @param delayDurationSelector A function that returns an `ObservableInput` for\n * each `value` emitted by the source Observable, which is then used to delay the\n * emission of that `value` on the output Observable until the `ObservableInput`\n * returned from this function emits a next value. When called, beside `value`,\n * this function receives a zero-based `index` of the emission order.\n * @param subscriptionDelay An Observable that triggers the subscription to the\n * source Observable once it emits any value.\n * @return A function that returns an Observable that delays the emissions of\n * the source Observable by an amount of time specified by the Observable\n * returned by `delayDurationSelector`.\n */\nexport function delayWhen<T>(\n  delayDurationSelector: (value: T, index: number) => ObservableInput<any>,\n  subscriptionDelay?: Observable<any>\n): MonoTypeOperatorFunction<T> {\n  if (subscriptionDelay) {\n    // DEPRECATED PATH\n    return (source: Observable<T>) =>\n      concat(subscriptionDelay.pipe(take(1), ignoreElements()), source.pipe(delayWhen(delayDurationSelector)));\n  }\n\n  return mergeMap((value, index) => innerFrom(delayDurationSelector(value, index)).pipe(take(1), mapTo(value)));\n}\n", "import { asyncScheduler } from '../scheduler/async';\nimport { MonoTypeOperatorFunction, SchedulerLike } from '../types';\nimport { delayWhen } from './delayWhen';\nimport { timer } from '../observable/timer';\n\n/**\n * Delays the emission of items from the source Observable by a given timeout or\n * until a given Date.\n *\n * <span class=\"informal\">Time shifts each item by some specified amount of\n * milliseconds.</span>\n *\n * ![](delay.svg)\n *\n * If the delay argument is a Number, this operator time shifts the source\n * Observable by that amount of time expressed in milliseconds. The relative\n * time intervals between the values are preserved.\n *\n * If the delay argument is a Date, this operator time shifts the start of the\n * Observable execution until the given date occurs.\n *\n * ## Examples\n *\n * Delay each click by one second\n *\n * ```ts\n * import { fromEvent, delay } from 'rxjs';\n *\n * const clicks = fromEvent(document, 'click');\n * const delayedClicks = clicks.pipe(delay(1000)); // each click emitted after 1 second\n * delayedClicks.subscribe(x => console.log(x));\n * ```\n *\n * Delay all clicks until a future date happens\n *\n * ```ts\n * import { fromEvent, delay } from 'rxjs';\n *\n * const clicks = fromEvent(document, 'click');\n * const date = new Date('March 15, 2050 12:00:00'); // in the future\n * const delayedClicks = clicks.pipe(delay(date)); // click emitted only after that date\n * delayedClicks.subscribe(x => console.log(x));\n * ```\n *\n * @see {@link delayWhen}\n * @see {@link throttle}\n * @see {@link throttleTime}\n * @see {@link debounce}\n * @see {@link debounceTime}\n * @see {@link sample}\n * @see {@link sampleTime}\n * @see {@link audit}\n * @see {@link auditTime}\n *\n * @param {number|Date} due The delay duration in milliseconds (a `number`) or\n * a `Date` until which the emission of the source items is delayed.\n * @param {SchedulerLike} [scheduler=async] The {@link SchedulerLike} to use for\n * managing the timers that handle the time-shift for each item.\n * @return A function that returns an Observable that delays the emissions of\n * the source Observable by the specified timeout or Date.\n */\nexport function delay<T>(due: number | Date, scheduler: SchedulerLike = asyncScheduler): MonoTypeOperatorFunction<T> {\n  const duration = timer(due, scheduler);\n  return delayWhen(() => duration);\n}\n", "import { MonoTypeOperatorFunction } from '../types';\nimport { identity } from '../util/identity';\nimport { operate } from '../util/lift';\nimport { createOperatorSubscriber } from './OperatorSubscriber';\n\nexport function distinctUntilChanged<T>(comparator?: (previous: T, current: T) => boolean): MonoTypeOperatorFunction<T>;\nexport function distinctUntilChanged<T, K>(\n  comparator: (previous: K, current: K) => boolean,\n  keySelector: (value: T) => K\n): MonoTypeOperatorFunction<T>;\n\n/**\n * Returns a result {@link Observable} that emits all values pushed by the source observable if they\n * are distinct in comparison to the last value the result observable emitted.\n *\n * When provided without parameters or with the first parameter (`{@link distinctUntilChanged#comparator comparator}`),\n * it behaves like this:\n *\n * 1. It will always emit the first value from the source.\n * 2. For all subsequent values pushed by the source, they will be compared to the previously emitted values\n *    using the provided `comparator` or an `===` equality check.\n * 3. If the value pushed by the source is determined to be unequal by this check, that value is emitted and\n *    becomes the new \"previously emitted value\" internally.\n *\n * When the second parameter (`{@link distinctUntilChanged#keySelector keySelector}`) is provided, the behavior\n * changes:\n *\n * 1. It will always emit the first value from the source.\n * 2. The `keySelector` will be run against all values, including the first value.\n * 3. For all values after the first, the selected key will be compared against the key selected from\n *    the previously emitted value using the `comparator`.\n * 4. If the keys are determined to be unequal by this check, the value (not the key), is emitted\n *    and the selected key from that value is saved for future comparisons against other keys.\n *\n * ## Examples\n *\n * A very basic example with no `{@link distinctUntilChanged#comparator comparator}`. Note that `1` is emitted more than once,\n * because it's distinct in comparison to the _previously emitted_ value,\n * not in comparison to _all other emitted values_.\n *\n * ```ts\n * import { of, distinctUntilChanged } from 'rxjs';\n *\n * of(1, 1, 1, 2, 2, 2, 1, 1, 3, 3)\n *   .pipe(distinctUntilChanged())\n *   .subscribe(console.log);\n * // Logs: 1, 2, 1, 3\n * ```\n *\n * With a `{@link distinctUntilChanged#comparator comparator}`, you can do custom comparisons. Let's say\n * you only want to emit a value when all of its components have\n * changed:\n *\n * ```ts\n * import { of, distinctUntilChanged } from 'rxjs';\n *\n * const totallyDifferentBuilds$ = of(\n *   { engineVersion: '1.1.0', transmissionVersion: '1.2.0' },\n *   { engineVersion: '1.1.0', transmissionVersion: '1.4.0' },\n *   { engineVersion: '1.3.0', transmissionVersion: '1.4.0' },\n *   { engineVersion: '1.3.0', transmissionVersion: '1.5.0' },\n *   { engineVersion: '2.0.0', transmissionVersion: '1.5.0' }\n * ).pipe(\n *   distinctUntilChanged((prev, curr) => {\n *     return (\n *       prev.engineVersion === curr.engineVersion ||\n *       prev.transmissionVersion === curr.transmissionVersion\n *     );\n *   })\n * );\n *\n * totallyDifferentBuilds$.subscribe(console.log);\n *\n * // Logs:\n * // { engineVersion: '1.1.0', transmissionVersion: '1.2.0' }\n * // { engineVersion: '1.3.0', transmissionVersion: '1.4.0' }\n * // { engineVersion: '2.0.0', transmissionVersion: '1.5.0' }\n * ```\n *\n * You can also provide a custom `{@link distinctUntilChanged#comparator comparator}` to check that emitted\n * changes are only in one direction. Let's say you only want to get\n * the next record temperature:\n *\n * ```ts\n * import { of, distinctUntilChanged } from 'rxjs';\n *\n * const temps$ = of(30, 31, 20, 34, 33, 29, 35, 20);\n *\n * const recordHighs$ = temps$.pipe(\n *   distinctUntilChanged((prevHigh, temp) => {\n *     // If the current temp is less than\n *     // or the same as the previous record,\n *     // the record hasn't changed.\n *     return temp <= prevHigh;\n *   })\n * );\n *\n * recordHighs$.subscribe(console.log);\n * // Logs: 30, 31, 34, 35\n * ```\n *\n * Selecting update events only when the `updatedBy` field shows\n * the account changed hands.\n *\n * ```ts\n * import { of, distinctUntilChanged } from 'rxjs';\n *\n * // A stream of updates to a given account\n * const accountUpdates$ = of(\n *   { updatedBy: 'blesh', data: [] },\n *   { updatedBy: 'blesh', data: [] },\n *   { updatedBy: 'ncjamieson', data: [] },\n *   { updatedBy: 'ncjamieson', data: [] },\n *   { updatedBy: 'blesh', data: [] }\n * );\n *\n * // We only want the events where it changed hands\n * const changedHands$ = accountUpdates$.pipe(\n *   distinctUntilChanged(undefined, update => update.updatedBy)\n * );\n *\n * changedHands$.subscribe(console.log);\n * // Logs:\n * // { updatedBy: 'blesh', data: Array[0] }\n * // { updatedBy: 'ncjamieson', data: Array[0] }\n * // { updatedBy: 'blesh', data: Array[0] }\n * ```\n *\n * @see {@link distinct}\n * @see {@link distinctUntilKeyChanged}\n *\n * @param comparator A function used to compare the previous and current keys for\n * equality. Defaults to a `===` check.\n * @param keySelector Used to select a key value to be passed to the `comparator`.\n *\n * @return A function that returns an Observable that emits items from the\n * source Observable with distinct values.\n */\nexport function distinctUntilChanged<T, K>(\n  comparator?: (previous: K, current: K) => boolean,\n  keySelector: (value: T) => K = identity as (value: T) => K\n): MonoTypeOperatorFunction<T> {\n  // We've been allowing `null` do be passed as the `compare`, so we can't do\n  // a default value for the parameter, because that will only work\n  // for `undefined`.\n  comparator = comparator ?? defaultCompare;\n\n  return operate((source, subscriber) => {\n    // The previous key, used to compare against keys selected\n    // from new arrivals to determine \"distinctiveness\".\n    let previousKey: K;\n    // Whether or not this is the first value we've gotten.\n    let first = true;\n\n    source.subscribe(\n      createOperatorSubscriber(subscriber, (value) => {\n        // We always call the key selector.\n        const currentKey = keySelector(value);\n\n        // If it's the first value, we always emit it.\n        // Otherwise, we compare this key to the previous key, and\n        // if the comparer returns false, we emit.\n        if (first || !comparator!(previousKey, currentKey)) {\n          // Update our state *before* we emit the value\n          // as emission can be the source of re-entrant code\n          // in functional libraries like this. We only really\n          // need to do this if it's the first value, or if the\n          // key we're tracking in previous needs to change.\n          first = false;\n          previousKey = currentKey;\n\n          // Emit the value!\n          subscriber.next(value);\n        }\n      })\n    );\n  });\n}\n\nfunction defaultCompare(a: any, b: any) {\n  return a === b;\n}\n", "import { distinctUntilChanged } from './distinctUntilChanged';\nimport { MonoTypeOperatorFunction } from '../types';\n\n/* tslint:disable:max-line-length */\nexport function distinctUntilKeyChanged<T>(key: keyof T): MonoTypeOperatorFunction<T>;\nexport function distinctUntilKeyChanged<T, K extends keyof T>(key: K, compare: (x: T[K], y: T[K]) => boolean): MonoTypeOperatorFunction<T>;\n/* tslint:enable:max-line-length */\n\n/**\n * Returns an Observable that emits all items emitted by the source Observable that are distinct by comparison from the previous item,\n * using a property accessed by using the key provided to check if the two items are distinct.\n *\n * If a comparator function is provided, then it will be called for each item to test for whether or not that value should be emitted.\n *\n * If a comparator function is not provided, an equality check is used by default.\n *\n * ## Examples\n *\n * An example comparing the name of persons\n *\n * ```ts\n * import { of, distinctUntilKeyChanged } from 'rxjs';\n *\n * of(\n *   { age: 4, name: 'Foo' },\n *   { age: 7, name: 'Bar' },\n *   { age: 5, name: 'Foo' },\n *   { age: 6, name: 'Foo' }\n * ).pipe(\n *   distinctUntilKeyChanged('name')\n * )\n * .subscribe(x => console.log(x));\n *\n * // displays:\n * // { age: 4, name: 'Foo' }\n * // { age: 7, name: 'Bar' }\n * // { age: 5, name: 'Foo' }\n * ```\n *\n * An example comparing the first letters of the name\n *\n * ```ts\n * import { of, distinctUntilKeyChanged } from 'rxjs';\n *\n * of(\n *   { age: 4, name: 'Foo1' },\n *   { age: 7, name: 'Bar' },\n *   { age: 5, name: 'Foo2' },\n *   { age: 6, name: 'Foo3' }\n * ).pipe(\n *   distinctUntilKeyChanged('name', (x, y) => x.substring(0, 3) === y.substring(0, 3))\n * )\n * .subscribe(x => console.log(x));\n *\n * // displays:\n * // { age: 4, name: 'Foo1' }\n * // { age: 7, name: 'Bar' }\n * // { age: 5, name: 'Foo2' }\n * ```\n *\n * @see {@link distinct}\n * @see {@link distinctUntilChanged}\n *\n * @param {string} key String key for object property lookup on each item.\n * @param {function} [compare] Optional comparison function called to test if an item is distinct from the previous item in the source.\n * @return A function that returns an Observable that emits items from the\n * source Observable with distinct values based on the key specified.\n */\nexport function distinctUntilKeyChanged<T, K extends keyof T>(key: K, compare?: (x: T[K], y: T[K]) => boolean): MonoTypeOperatorFunction<T> {\n  return distinctUntilChanged((x: T, y: T) => compare ? compare(x[key], y[key]) : x[key] === y[key]);\n}\n", "import { EmptyError } from '../util/EmptyError';\nimport { MonoTypeOperatorFunction } from '../types';\nimport { operate } from '../util/lift';\nimport { createOperatorSubscriber } from './OperatorSubscriber';\n\n/**\n * If the source observable completes without emitting a value, it will emit\n * an error. The error will be created at that time by the optional\n * `errorFactory` argument, otherwise, the error will be {@link EmptyError}.\n *\n * ![](throwIfEmpty.png)\n *\n * ## Example\n *\n * Throw an error if the document wasn't clicked within 1 second\n *\n * ```ts\n * import { fromEvent, takeUntil, timer, throwIfEmpty } from 'rxjs';\n *\n * const click$ = fromEvent(document, 'click');\n *\n * click$.pipe(\n *   takeUntil(timer(1000)),\n *   throwIfEmpty(() => new Error('The document was not clicked within 1 second'))\n * )\n * .subscribe({\n *   next() {\n *    console.log('The document was clicked');\n *   },\n *   error(err) {\n *     console.error(err.message);\n *   }\n * });\n * ```\n *\n * @param errorFactory A factory function called to produce the\n * error to be thrown when the source observable completes without emitting a\n * value.\n * @return A function that returns an Observable that throws an error if the\n * source Observable completed without emitting.\n */\nexport function throwIfEmpty<T>(errorFactory: () => any = defaultErrorFactory): MonoTypeOperatorFunction<T> {\n  return operate((source, subscriber) => {\n    let hasValue = false;\n    source.subscribe(\n      createOperatorSubscriber(\n        subscriber,\n        (value) => {\n          hasValue = true;\n          subscriber.next(value);\n        },\n        () => (hasValue ? subscriber.complete() : subscriber.error(errorFactory()))\n      )\n    );\n  });\n}\n\nfunction defaultErrorFactory() {\n  return new EmptyError();\n}\n", "/** prettier */\nimport { Observable } from '../Observable';\nimport { concat } from '../observable/concat';\nimport { of } from '../observable/of';\nimport { MonoTypeOperatorFunction, SchedulerLike, OperatorFunction, ValueFromArray } from '../types';\n\n/** @deprecated The `scheduler` parameter will be removed in v8. Use `scheduled` and `concatAll`. Details: https://rxjs.dev/deprecations/scheduler-argument */\nexport function endWith<T>(scheduler: SchedulerLike): MonoTypeOperatorFunction<T>;\n/** @deprecated The `scheduler` parameter will be removed in v8. Use `scheduled` and `concatAll`. Details: https://rxjs.dev/deprecations/scheduler-argument */\nexport function endWith<T, A extends unknown[] = T[]>(\n  ...valuesAndScheduler: [...A, SchedulerLike]\n): OperatorFunction<T, T | ValueFromArray<A>>;\n\nexport function endWith<T, A extends unknown[] = T[]>(...values: A): OperatorFunction<T, T | ValueFromArray<A>>;\n\n/**\n * Returns an observable that will emit all values from the source, then synchronously emit\n * the provided value(s) immediately after the source completes.\n *\n * NOTE: Passing a last argument of a Scheduler is _deprecated_, and may result in incorrect\n * types in TypeScript.\n *\n * This is useful for knowing when an observable ends. Particularly when paired with an\n * operator like {@link takeUntil}\n *\n * ![](endWith.png)\n *\n * ## Example\n *\n * Emit values to know when an interval starts and stops. The interval will\n * stop when a user clicks anywhere on the document.\n *\n * ```ts\n * import { interval, map, fromEvent, startWith, takeUntil, endWith } from 'rxjs';\n *\n * const ticker$ = interval(5000).pipe(\n *   map(() => 'tick')\n * );\n *\n * const documentClicks$ = fromEvent(document, 'click');\n *\n * ticker$.pipe(\n *   startWith('interval started'),\n *   takeUntil(documentClicks$),\n *   endWith('interval ended by click')\n * )\n * .subscribe(x => console.log(x));\n *\n * // Result (assuming a user clicks after 15 seconds)\n * // 'interval started'\n * // 'tick'\n * // 'tick'\n * // 'tick'\n * // 'interval ended by click'\n * ```\n *\n * @see {@link startWith}\n * @see {@link concat}\n * @see {@link takeUntil}\n *\n * @param values Items you want the modified Observable to emit last.\n * @return A function that returns an Observable that emits all values from the\n * source, then synchronously emits the provided value(s) immediately after the\n * source completes.\n */\nexport function endWith<T>(...values: Array<T | SchedulerLike>): MonoTypeOperatorFunction<T> {\n  return (source: Observable<T>) => concat(source, of(...values)) as Observable<T>;\n}\n", "import { MonoTypeOperatorFunction } from '../types';\nimport { operate } from '../util/lift';\n\n/**\n * Returns an Observable that mirrors the source Observable, but will call a specified function when\n * the source terminates on complete or error.\n * The specified function will also be called when the subscriber explicitly unsubscribes.\n *\n * ## Examples\n *\n * Execute callback function when the observable completes\n *\n * ```ts\n * import { interval, take, finalize } from 'rxjs';\n *\n * // emit value in sequence every 1 second\n * const source = interval(1000);\n * const example = source.pipe(\n *   take(5), //take only the first 5 values\n *   finalize(() => console.log('Sequence complete')) // Execute when the observable completes\n * );\n * const subscribe = example.subscribe(val => console.log(val));\n *\n * // results:\n * // 0\n * // 1\n * // 2\n * // 3\n * // 4\n * // 'Sequence complete'\n * ```\n *\n * Execute callback function when the subscriber explicitly unsubscribes\n *\n * ```ts\n * import { interval, finalize, tap, noop, timer } from 'rxjs';\n *\n * const source = interval(100).pipe(\n *   finalize(() => console.log('[finalize] Called')),\n *   tap({\n *     next: () => console.log('[next] Called'),\n *     error: () => console.log('[error] Not called'),\n *     complete: () => console.log('[tap complete] Not called')\n *   })\n * );\n *\n * const sub = source.subscribe({\n *   next: x => console.log(x),\n *   error: noop,\n *   complete: () => console.log('[complete] Not called')\n * });\n *\n * timer(150).subscribe(() => sub.unsubscribe());\n *\n * // results:\n * // '[next] Called'\n * // 0\n * // '[finalize] Called'\n * ```\n *\n * @param {function} callback Function to be called when source terminates.\n * @return A function that returns an Observable that mirrors the source, but\n * will call the specified function on termination.\n */\nexport function finalize<T>(callback: () => void): MonoTypeOperatorFunction<T> {\n  return operate((source, subscriber) => {\n    // TODO: This try/finally was only added for `useDeprecatedSynchronousErrorHandling`.\n    // REMOVE THIS WHEN THAT HOT GARBAGE IS REMOVED IN V8.\n    try {\n      source.subscribe(subscriber);\n    } finally {\n      subscriber.add(callback);\n    }\n  });\n}\n", "import { Observable } from '../Observable';\nimport { EmptyError } from '../util/EmptyError';\nimport { OperatorFunction, TruthyTypesOf } from '../types';\nimport { filter } from './filter';\nimport { take } from './take';\nimport { defaultIfEmpty } from './defaultIfEmpty';\nimport { throwIfEmpty } from './throwIfEmpty';\nimport { identity } from '../util/identity';\n\nexport function first<T, D = T>(predicate?: null, defaultValue?: D): OperatorFunction<T, T | D>;\nexport function first<T>(predicate: BooleanConstructor): OperatorFunction<T, TruthyTypesOf<T>>;\nexport function first<T, D>(predicate: BooleanConstructor, defaultValue: D): OperatorFunction<T, TruthyTypesOf<T> | D>;\nexport function first<T, S extends T>(\n  predicate: (value: T, index: number, source: Observable<T>) => value is S,\n  defaultValue?: S\n): OperatorFunction<T, S>;\nexport function first<T, S extends T, D>(\n  predicate: (value: T, index: number, source: Observable<T>) => value is S,\n  defaultValue: D\n): OperatorFunction<T, S | D>;\nexport function first<T, D = T>(\n  predicate: (value: T, index: number, source: Observable<T>) => boolean,\n  defaultValue?: D\n): OperatorFunction<T, T | D>;\n\n/**\n * Emits only the first value (or the first value that meets some condition)\n * emitted by the source Observable.\n *\n * <span class=\"informal\">Emits only the first value. Or emits only the first\n * value that passes some test.</span>\n *\n * ![](first.png)\n *\n * If called with no arguments, `first` emits the first value of the source\n * Observable, then completes. If called with a `predicate` function, `first`\n * emits the first value of the source that matches the specified condition. Throws an error if\n * `defaultValue` was not provided and a matching element is not found.\n *\n * ## Examples\n *\n * Emit only the first click that happens on the DOM\n *\n * ```ts\n * import { fromEvent, first } from 'rxjs';\n *\n * const clicks = fromEvent(document, 'click');\n * const result = clicks.pipe(first());\n * result.subscribe(x => console.log(x));\n * ```\n *\n * Emits the first click that happens on a DIV\n *\n * ```ts\n * import { fromEvent, first } from 'rxjs';\n *\n * const div = document.createElement('div');\n * div.style.cssText = 'width: 200px; height: 200px; background: #09c;';\n * document.body.appendChild(div);\n *\n * const clicks = fromEvent(document, 'click');\n * const result = clicks.pipe(first(ev => (<HTMLElement>ev.target).tagName === 'DIV'));\n * result.subscribe(x => console.log(x));\n * ```\n *\n * @see {@link filter}\n * @see {@link find}\n * @see {@link take}\n *\n * @throws {EmptyError} Delivers an EmptyError to the Observer's `error`\n * callback if the Observable completes before any `next` notification was sent.\n * This is how `first()` is different from {@link take}(1) which completes instead.\n *\n * @param {function(value: T, index: number, source: Observable<T>): boolean} [predicate]\n * An optional function called with each item to test for condition matching.\n * @param {D} [defaultValue] The default value emitted in case no valid value\n * was found on the source.\n * @return A function that returns an Observable that emits the first item that\n * matches the condition.\n */\nexport function first<T, D>(\n  predicate?: ((value: T, index: number, source: Observable<T>) => boolean) | null,\n  defaultValue?: D\n): OperatorFunction<T, T | D> {\n  const hasDefaultValue = arguments.length >= 2;\n  return (source: Observable<T>) =>\n    source.pipe(\n      predicate ? filter((v, i) => predicate(v, i, source)) : identity,\n      take(1),\n      hasDefaultValue ? defaultIfEmpty(defaultValue!) : throwIfEmpty(() => new EmptyError())\n    );\n}\n", "import { EMPTY } from '../observable/empty';\nimport { MonoTypeOperatorFunction } from '../types';\nimport { operate } from '../util/lift';\nimport { createOperatorSubscriber } from './OperatorSubscriber';\n\n/**\n * Waits for the source to complete, then emits the last N values from the source,\n * as specified by the `count` argument.\n *\n * ![](takeLast.png)\n *\n * `takeLast` results in an observable that will hold values up to `count` values in memory,\n * until the source completes. It then pushes all values in memory to the consumer, in the\n * order they were received from the source, then notifies the consumer that it is\n * complete.\n *\n * If for some reason the source completes before the `count` supplied to `takeLast` is reached,\n * all values received until that point are emitted, and then completion is notified.\n *\n * **Warning**: Using `takeLast` with an observable that never completes will result\n * in an observable that never emits a value.\n *\n * ## Example\n *\n * Take the last 3 values of an Observable with many values\n *\n * ```ts\n * import { range, takeLast } from 'rxjs';\n *\n * const many = range(1, 100);\n * const lastThree = many.pipe(takeLast(3));\n * lastThree.subscribe(x => console.log(x));\n * ```\n *\n * @see {@link take}\n * @see {@link takeUntil}\n * @see {@link takeWhile}\n * @see {@link skip}\n *\n * @param count The maximum number of values to emit from the end of\n * the sequence of values emitted by the source Observable.\n * @return A function that returns an Observable that emits at most the last\n * `count` values emitted by the source Observable.\n */\nexport function takeLast<T>(count: number): MonoTypeOperatorFunction<T> {\n  return count <= 0\n    ? () => EMPTY\n    : operate((source, subscriber) => {\n        // This buffer will hold the values we are going to emit\n        // when the source completes. Since we only want to take the\n        // last N values, we can't emit until we're sure we're not getting\n        // any more values.\n        let buffer: T[] = [];\n        source.subscribe(\n          createOperatorSubscriber(\n            subscriber,\n            (value) => {\n              // Add the most recent value onto the end of our buffer.\n              buffer.push(value);\n              // If our buffer is now larger than the number of values we\n              // want to take, we remove the oldest value from the buffer.\n              count < buffer.length && buffer.shift();\n            },\n            () => {\n              // The source completed, we now know what are last values\n              // are, emit them in the order they were received.\n              for (const value of buffer) {\n                subscriber.next(value);\n              }\n              subscriber.complete();\n            },\n            // Errors are passed through to the consumer\n            undefined,\n            () => {\n              // During finalization release the values in our buffer.\n              buffer = null!;\n            }\n          )\n        );\n      });\n}\n", "import { ObservableInput, ObservableInputTuple, OperatorFunction, SchedulerLike } from '../types';\nimport { operate } from '../util/lift';\nimport { argsOrArgArray } from '../util/argsOrArgArray';\nimport { mergeAll } from './mergeAll';\nimport { popNumber, popScheduler } from '../util/args';\nimport { from } from '../observable/from';\n\n/** @deprecated Replaced with {@link mergeWith}. Will be removed in v8. */\nexport function merge<T, A extends readonly unknown[]>(...sources: [...ObservableInputTuple<A>]): OperatorFunction<T, T | A[number]>;\n/** @deprecated Replaced with {@link mergeWith}. Will be removed in v8. */\nexport function merge<T, A extends readonly unknown[]>(\n  ...sourcesAndConcurrency: [...ObservableInputTuple<A>, number]\n): OperatorFunction<T, T | A[number]>;\n/** @deprecated Replaced with {@link mergeWith}. Will be removed in v8. */\nexport function merge<T, A extends readonly unknown[]>(\n  ...sourcesAndScheduler: [...ObservableInputTuple<A>, SchedulerLike]\n): OperatorFunction<T, T | A[number]>;\n/** @deprecated Replaced with {@link mergeWith}. Will be removed in v8. */\nexport function merge<T, A extends readonly unknown[]>(\n  ...sourcesAndConcurrencyAndScheduler: [...ObservableInputTuple<A>, number, SchedulerLike]\n): OperatorFunction<T, T | A[number]>;\n\nexport function merge<T>(...args: unknown[]): OperatorFunction<T, unknown> {\n  const scheduler = popScheduler(args);\n  const concurrent = popNumber(args, Infinity);\n  args = argsOrArgArray(args);\n\n  return operate((source, subscriber) => {\n    mergeAll(concurrent)(from([source, ...(args as ObservableInput<T>[])], scheduler)).subscribe(subscriber);\n  });\n}\n", "import { ObservableInputTuple, OperatorFunction } from '../types';\nimport { merge } from './merge';\n\n/**\n * Merge the values from all observables to a single observable result.\n *\n * Creates an observable, that when subscribed to, subscribes to the source\n * observable, and all other sources provided as arguments. All values from\n * every source are emitted from the resulting subscription.\n *\n * When all sources complete, the resulting observable will complete.\n *\n * When any source errors, the resulting observable will error.\n *\n * ## Example\n *\n * Joining all outputs from multiple user input event streams\n *\n * ```ts\n * import { fromEvent, map, mergeWith } from 'rxjs';\n *\n * const clicks$ = fromEvent(document, 'click').pipe(map(() => 'click'));\n * const mousemoves$ = fromEvent(document, 'mousemove').pipe(map(() => 'mousemove'));\n * const dblclicks$ = fromEvent(document, 'dblclick').pipe(map(() => 'dblclick'));\n *\n * mousemoves$\n *   .pipe(mergeWith(clicks$, dblclicks$))\n *   .subscribe(x => console.log(x));\n *\n * // result (assuming user interactions)\n * // 'mousemove'\n * // 'mousemove'\n * // 'mousemove'\n * // 'click'\n * // 'click'\n * // 'dblclick'\n * ```\n *\n * @see {@link merge}\n *\n * @param otherSources the sources to combine the current source with.\n * @return A function that returns an Observable that merges the values from\n * all given Observables.\n */\nexport function mergeWith<T, A extends readonly unknown[]>(\n  ...otherSources: [...ObservableInputTuple<A>]\n): OperatorFunction<T, T | A[number]> {\n  return merge(...otherSources);\n}\n", "import { Subscription } from '../Subscription';\nimport { EMPTY } from '../observable/empty';\nimport { operate } from '../util/lift';\nimport { MonoTypeOperatorFunction, ObservableInput } from '../types';\nimport { createOperatorSubscriber } from './OperatorSubscriber';\nimport { innerFrom } from '../observable/innerFrom';\nimport { timer } from '../observable/timer';\n\nexport interface RepeatConfig {\n  /**\n   * The number of times to repeat the source. Defaults to `Infinity`.\n   */\n  count?: number;\n\n  /**\n   * If a `number`, will delay the repeat of the source by that number of milliseconds.\n   * If a function, it will provide the number of times the source has been subscribed to,\n   * and the return value should be a valid observable input that will notify when the source\n   * should be repeated. If the notifier observable is empty, the result will complete.\n   */\n  delay?: number | ((count: number) => ObservableInput<any>);\n}\n\n/**\n * Returns an Observable that will resubscribe to the source stream when the source stream completes.\n *\n * <span class=\"informal\">Repeats all values emitted on the source. It's like {@link retry}, but for non error cases.</span>\n *\n * ![](repeat.png)\n *\n * Repeat will output values from a source until the source completes, then it will resubscribe to the\n * source a specified number of times, with a specified delay. Repeat can be particularly useful in\n * combination with closing operators like {@link take}, {@link takeUntil}, {@link first}, or {@link takeWhile},\n * as it can be used to restart a source again from scratch.\n *\n * Repeat is very similar to {@link retry}, where {@link retry} will resubscribe to the source in the error case, but\n * `repeat` will resubscribe if the source completes.\n *\n * Note that `repeat` will _not_ catch errors. Use {@link retry} for that.\n *\n * - `repeat(0)` returns an empty observable\n * - `repeat()` will repeat forever\n * - `repeat({ delay: 200 })` will repeat forever, with a delay of 200ms between repetitions.\n * - `repeat({ count: 2, delay: 400 })` will repeat twice, with a delay of 400ms between repetitions.\n * - `repeat({ delay: (count) => timer(count * 1000) })` will repeat forever, but will have a delay that grows by one second for each repetition.\n *\n * ## Example\n *\n * Repeat a message stream\n *\n * ```ts\n * import { of, repeat } from 'rxjs';\n *\n * const source = of('Repeat message');\n * const result = source.pipe(repeat(3));\n *\n * result.subscribe(x => console.log(x));\n *\n * // Results\n * // 'Repeat message'\n * // 'Repeat message'\n * // 'Repeat message'\n * ```\n *\n * Repeat 3 values, 2 times\n *\n * ```ts\n * import { interval, take, repeat } from 'rxjs';\n *\n * const source = interval(1000);\n * const result = source.pipe(take(3), repeat(2));\n *\n * result.subscribe(x => console.log(x));\n *\n * // Results every second\n * // 0\n * // 1\n * // 2\n * // 0\n * // 1\n * // 2\n * ```\n *\n * Defining two complex repeats with delays on the same source.\n * Note that the second repeat cannot be called until the first\n * repeat as exhausted it's count.\n *\n * ```ts\n * import { defer, of, repeat } from 'rxjs';\n *\n * const source = defer(() => {\n *    return of(`Hello, it is ${new Date()}`)\n * });\n *\n * source.pipe(\n *    // Repeat 3 times with a delay of 1 second between repetitions\n *    repeat({\n *      count: 3,\n *      delay: 1000,\n *    }),\n *\n *    // *Then* repeat forever, but with an exponential step-back\n *    // maxing out at 1 minute.\n *    repeat({\n *      delay: (count) => timer(Math.min(60000, 2 ^ count * 1000))\n *    })\n * )\n * ```\n *\n * @see {@link repeatWhen}\n * @see {@link retry}\n *\n * @param count The number of times the source Observable items are repeated, a count of 0 will yield\n * an empty Observable.\n */\nexport function repeat<T>(countOrConfig?: number | RepeatConfig): MonoTypeOperatorFunction<T> {\n  let count = Infinity;\n  let delay: RepeatConfig['delay'];\n\n  if (countOrConfig != null) {\n    if (typeof countOrConfig === 'object') {\n      ({ count = Infinity, delay } = countOrConfig);\n    } else {\n      count = countOrConfig;\n    }\n  }\n\n  return count <= 0\n    ? () => EMPTY\n    : operate((source, subscriber) => {\n        let soFar = 0;\n        let sourceSub: Subscription | null;\n\n        const resubscribe = () => {\n          sourceSub?.unsubscribe();\n          sourceSub = null;\n          if (delay != null) {\n            const notifier = typeof delay === 'number' ? timer(delay) : innerFrom(delay(soFar));\n            const notifierSubscriber = createOperatorSubscriber(subscriber, () => {\n              notifierSubscriber.unsubscribe();\n              subscribeToSource();\n            });\n            notifier.subscribe(notifierSubscriber);\n          } else {\n            subscribeToSource();\n          }\n        };\n\n        const subscribeToSource = () => {\n          let syncUnsub = false;\n          sourceSub = source.subscribe(\n            createOperatorSubscriber(subscriber, undefined, () => {\n              if (++soFar < count) {\n                if (sourceSub) {\n                  resubscribe();\n                } else {\n                  syncUnsub = true;\n                }\n              } else {\n                subscriber.complete();\n              }\n            })\n          );\n\n          if (syncUnsub) {\n            resubscribe();\n          }\n        };\n\n        subscribeToSource();\n      });\n}\n", "import { OperatorFunction } from '../types';\nimport { operate } from '../util/lift';\nimport { scanInternals } from './scanInternals';\n\nexport function scan<V, A = V>(accumulator: (acc: A | V, value: V, index: number) => A): OperatorFunction<V, V | A>;\nexport function scan<V, A>(accumulator: (acc: A, value: V, index: number) => A, seed: A): OperatorFunction<V, A>;\nexport function scan<V, A, S>(accumulator: (acc: A | S, value: V, index: number) => A, seed: S): OperatorFunction<V, A>;\n\n// TODO: link to a \"redux pattern\" section in the guide (location TBD)\n\n/**\n * Useful for encapsulating and managing state. Applies an accumulator (or \"reducer function\")\n * to each value from the source after an initial state is established -- either via\n * a `seed` value (second argument), or from the first value from the source.\n *\n * <span class=\"informal\">It's like {@link reduce}, but emits the current\n * accumulation state after each update</span>\n *\n * ![](scan.png)\n *\n * This operator maintains an internal state and emits it after processing each value as follows:\n *\n * 1. First value arrives\n *   - If a `seed` value was supplied (as the second argument to `scan`), let `state = seed` and `value = firstValue`.\n *   - If NO `seed` value was supplied (no second argument), let `state = firstValue` and go to 3.\n * 2. Let `state = accumulator(state, value)`.\n *   - If an error is thrown by `accumulator`, notify the consumer of an error. The process ends.\n * 3. Emit `state`.\n * 4. Next value arrives, let `value = nextValue`, go to 2.\n *\n * ## Examples\n *\n * An average of previous numbers. This example shows how\n * not providing a `seed` can prime the stream with the\n * first value from the source.\n *\n * ```ts\n * import { of, scan, map } from 'rxjs';\n *\n * const numbers$ = of(1, 2, 3);\n *\n * numbers$\n *   .pipe(\n *     // Get the sum of the numbers coming in.\n *     scan((total, n) => total + n),\n *     // Get the average by dividing the sum by the total number\n *     // received so far (which is 1 more than the zero-based index).\n *     map((sum, index) => sum / (index + 1))\n *   )\n *   .subscribe(console.log);\n * ```\n *\n * The Fibonacci sequence. This example shows how you can use\n * a seed to prime accumulation process. Also... you know... Fibonacci.\n * So important to like, computers and stuff that its whiteboarded\n * in job interviews. Now you can show them the Rx version! (Please don't, haha)\n *\n * ```ts\n * import { interval, scan, map, startWith } from 'rxjs';\n *\n * const firstTwoFibs = [0, 1];\n * // An endless stream of Fibonacci numbers.\n * const fibonacci$ = interval(1000).pipe(\n *   // Scan to get the fibonacci numbers (after 0, 1)\n *   scan(([a, b]) => [b, a + b], firstTwoFibs),\n *   // Get the second number in the tuple, it's the one you calculated\n *   map(([, n]) => n),\n *   // Start with our first two digits :)\n *   startWith(...firstTwoFibs)\n * );\n *\n * fibonacci$.subscribe(console.log);\n * ```\n *\n * @see {@link expand}\n * @see {@link mergeScan}\n * @see {@link reduce}\n * @see {@link switchScan}\n *\n * @param accumulator A \"reducer function\". This will be called for each value after an initial state is\n * acquired.\n * @param seed The initial state. If this is not provided, the first value from the source will\n * be used as the initial state, and emitted without going through the accumulator. All subsequent values\n * will be processed by the accumulator function. If this is provided, all values will go through\n * the accumulator function.\n * @return A function that returns an Observable of the accumulated values.\n */\nexport function scan<V, A, S>(accumulator: (acc: V | A | S, value: V, index: number) => A, seed?: S): OperatorFunction<V, V | A> {\n  // providing a seed of `undefined` *should* be valid and trigger\n  // hasSeed! so don't use `seed !== undefined` checks!\n  // For this reason, we have to check it here at the original call site\n  // otherwise inside Operator/Subscriber we won't know if `undefined`\n  // means they didn't provide anything or if they literally provided `undefined`\n  return operate(scanInternals(accumulator, seed as S, arguments.length >= 2, true));\n}\n", "import { innerFrom } from '../observable/innerFrom';\nimport { Subject } from '../Subject';\nimport { SafeSubscriber } from '../Subscriber';\nimport { Subscription } from '../Subscription';\nimport { MonoTypeOperatorFunction, SubjectLike, ObservableInput } from '../types';\nimport { operate } from '../util/lift';\n\nexport interface ShareConfig<T> {\n  /**\n   * The factory used to create the subject that will connect the source observable to\n   * multicast consumers.\n   */\n  connector?: () => SubjectLike<T>;\n  /**\n   * If `true`, the resulting observable will reset internal state on error from source and return to a \"cold\" state. This\n   * allows the resulting observable to be \"retried\" in the event of an error.\n   * If `false`, when an error comes from the source it will push the error into the connecting subject, and the subject\n   * will remain the connecting subject, meaning the resulting observable will not go \"cold\" again, and subsequent retries\n   * or resubscriptions will resubscribe to that same subject. In all cases, RxJS subjects will emit the same error again, however\n   * {@link ReplaySubject} will also push its buffered values before pushing the error.\n   * It is also possible to pass a notifier factory returning an `ObservableInput` instead which grants more fine-grained\n   * control over how and when the reset should happen. This allows behaviors like conditional or delayed resets.\n   */\n  resetOnError?: boolean | ((error: any) => ObservableInput<any>);\n  /**\n   * If `true`, the resulting observable will reset internal state on completion from source and return to a \"cold\" state. This\n   * allows the resulting observable to be \"repeated\" after it is done.\n   * If `false`, when the source completes, it will push the completion through the connecting subject, and the subject\n   * will remain the connecting subject, meaning the resulting observable will not go \"cold\" again, and subsequent repeats\n   * or resubscriptions will resubscribe to that same subject.\n   * It is also possible to pass a notifier factory returning an `ObservableInput` instead which grants more fine-grained\n   * control over how and when the reset should happen. This allows behaviors like conditional or delayed resets.\n   */\n  resetOnComplete?: boolean | (() => ObservableInput<any>);\n  /**\n   * If `true`, when the number of subscribers to the resulting observable reaches zero due to those subscribers unsubscribing, the\n   * internal state will be reset and the resulting observable will return to a \"cold\" state. This means that the next\n   * time the resulting observable is subscribed to, a new subject will be created and the source will be subscribed to\n   * again.\n   * If `false`, when the number of subscribers to the resulting observable reaches zero due to unsubscription, the subject\n   * will remain connected to the source, and new subscriptions to the result will be connected through that same subject.\n   * It is also possible to pass a notifier factory returning an `ObservableInput` instead which grants more fine-grained\n   * control over how and when the reset should happen. This allows behaviors like conditional or delayed resets.\n   */\n  resetOnRefCountZero?: boolean | (() => ObservableInput<any>);\n}\n\nexport function share<T>(): MonoTypeOperatorFunction<T>;\n\nexport function share<T>(options: ShareConfig<T>): MonoTypeOperatorFunction<T>;\n\n/**\n * Returns a new Observable that multicasts (shares) the original Observable. As long as there is at least one\n * Subscriber this Observable will be subscribed and emitting data. When all subscribers have unsubscribed it will\n * unsubscribe from the source Observable. Because the Observable is multicasting it makes the stream `hot`.\n * This is an alias for `multicast(() => new Subject()), refCount()`.\n *\n * The subscription to the underlying source Observable can be reset (unsubscribe and resubscribe for new subscribers),\n * if the subscriber count to the shared observable drops to 0, or if the source Observable errors or completes. It is\n * possible to use notifier factories for the resets to allow for behaviors like conditional or delayed resets. Please\n * note that resetting on error or complete of the source Observable does not behave like a transparent retry or restart\n * of the source because the error or complete will be forwarded to all subscribers and their subscription will be\n * closed. Only new subscribers after a reset on error or complete happened will cause a fresh subscription to the\n * source. To achieve transparent retries or restarts pipe the source through appropriate operators before sharing.\n *\n * ![](share.png)\n *\n * ## Example\n *\n * Generate new multicast Observable from the `source` Observable value\n *\n * ```ts\n * import { interval, tap, map, take, share } from 'rxjs';\n *\n * const source = interval(1000).pipe(\n *   tap(x => console.log('Processing: ', x)),\n *   map(x => x * x),\n *   take(6),\n *   share()\n * );\n *\n * source.subscribe(x => console.log('subscription 1: ', x));\n * source.subscribe(x => console.log('subscription 2: ', x));\n *\n * // Logs:\n * // Processing: 0\n * // subscription 1: 0\n * // subscription 2: 0\n * // Processing: 1\n * // subscription 1: 1\n * // subscription 2: 1\n * // Processing: 2\n * // subscription 1: 4\n * // subscription 2: 4\n * // Processing: 3\n * // subscription 1: 9\n * // subscription 2: 9\n * // Processing: 4\n * // subscription 1: 16\n * // subscription 2: 16\n * // Processing: 5\n * // subscription 1: 25\n * // subscription 2: 25\n * ```\n *\n * ## Example with notifier factory: Delayed reset\n *\n * ```ts\n * import { interval, take, share, timer } from 'rxjs';\n *\n * const source = interval(1000).pipe(\n *   take(3),\n *   share({\n *     resetOnRefCountZero: () => timer(1000)\n *   })\n * );\n *\n * const subscriptionOne = source.subscribe(x => console.log('subscription 1: ', x));\n * setTimeout(() => subscriptionOne.unsubscribe(), 1300);\n *\n * setTimeout(() => source.subscribe(x => console.log('subscription 2: ', x)), 1700);\n *\n * setTimeout(() => source.subscribe(x => console.log('subscription 3: ', x)), 5000);\n *\n * // Logs:\n * // subscription 1:  0\n * // (subscription 1 unsubscribes here)\n * // (subscription 2 subscribes here ~400ms later, source was not reset)\n * // subscription 2:  1\n * // subscription 2:  2\n * // (subscription 2 unsubscribes here)\n * // (subscription 3 subscribes here ~2000ms later, source did reset before)\n * // subscription 3:  0\n * // subscription 3:  1\n * // subscription 3:  2\n * ```\n *\n * @see {@link shareReplay}\n *\n * @return A function that returns an Observable that mirrors the source.\n */\nexport function share<T>(options: ShareConfig<T> = {}): MonoTypeOperatorFunction<T> {\n  const { connector = () => new Subject<T>(), resetOnError = true, resetOnComplete = true, resetOnRefCountZero = true } = options;\n  // It's necessary to use a wrapper here, as the _operator_ must be\n  // referentially transparent. Otherwise, it cannot be used in calls to the\n  // static `pipe` function - to create a partial pipeline.\n  //\n  // The _operator function_ - the function returned by the _operator_ - will\n  // not be referentially transparent - as it shares its source - but the\n  // _operator function_ is called when the complete pipeline is composed via a\n  // call to a source observable's `pipe` method - not when the static `pipe`\n  // function is called.\n  return (wrapperSource) => {\n    let connection: SafeSubscriber<T> | undefined;\n    let resetConnection: Subscription | undefined;\n    let subject: SubjectLike<T> | undefined;\n    let refCount = 0;\n    let hasCompleted = false;\n    let hasErrored = false;\n\n    const cancelReset = () => {\n      resetConnection?.unsubscribe();\n      resetConnection = undefined;\n    };\n    // Used to reset the internal state to a \"cold\"\n    // state, as though it had never been subscribed to.\n    const reset = () => {\n      cancelReset();\n      connection = subject = undefined;\n      hasCompleted = hasErrored = false;\n    };\n    const resetAndUnsubscribe = () => {\n      // We need to capture the connection before\n      // we reset (if we need to reset).\n      const conn = connection;\n      reset();\n      conn?.unsubscribe();\n    };\n\n    return operate<T, T>((source, subscriber) => {\n      refCount++;\n      if (!hasErrored && !hasCompleted) {\n        cancelReset();\n      }\n\n      // Create the subject if we don't have one yet. Grab a local reference to\n      // it as well, which avoids non-null assertions when using it and, if we\n      // connect to it now, then error/complete need a reference after it was\n      // reset.\n      const dest = (subject = subject ?? connector());\n\n      // Add the finalization directly to the subscriber - instead of returning it -\n      // so that the handling of the subscriber's unsubscription will be wired\n      // up _before_ the subscription to the source occurs. This is done so that\n      // the assignment to the source connection's `closed` property will be seen\n      // by synchronous firehose sources.\n      subscriber.add(() => {\n        refCount--;\n\n        // If we're resetting on refCount === 0, and it's 0, we only want to do\n        // that on \"unsubscribe\", really. Resetting on error or completion is a different\n        // configuration.\n        if (refCount === 0 && !hasErrored && !hasCompleted) {\n          resetConnection = handleReset(resetAndUnsubscribe, resetOnRefCountZero);\n        }\n      });\n\n      // The following line adds the subscription to the subscriber passed.\n      // Basically, `subscriber === dest.subscribe(subscriber)` is `true`.\n      dest.subscribe(subscriber);\n\n      if (\n        !connection &&\n        // Check this shareReplay is still activate - it can be reset to 0\n        // and be \"unsubscribed\" _before_ it actually subscribes.\n        // If we were to subscribe then, it'd leak and get stuck.\n        refCount > 0\n      ) {\n        // We need to create a subscriber here - rather than pass an observer and\n        // assign the returned subscription to connection - because it's possible\n        // for reentrant subscriptions to the shared observable to occur and in\n        // those situations we want connection to be already-assigned so that we\n        // don't create another connection to the source.\n        connection = new SafeSubscriber({\n          next: (value) => dest.next(value),\n          error: (err) => {\n            hasErrored = true;\n            cancelReset();\n            resetConnection = handleReset(reset, resetOnError, err);\n            dest.error(err);\n          },\n          complete: () => {\n            hasCompleted = true;\n            cancelReset();\n            resetConnection = handleReset(reset, resetOnComplete);\n            dest.complete();\n          },\n        });\n        innerFrom(source).subscribe(connection);\n      }\n    })(wrapperSource);\n  };\n}\n\nfunction handleReset<T extends unknown[] = never[]>(\n  reset: () => void,\n  on: boolean | ((...args: T) => ObservableInput<any>),\n  ...args: T\n): Subscription | undefined {\n  if (on === true) {\n    reset();\n    return;\n  }\n\n  if (on === false) {\n    return;\n  }\n\n  const onSubscriber = new SafeSubscriber({\n    next: () => {\n      onSubscriber.unsubscribe();\n      reset();\n    },\n  });\n\n  return innerFrom(on(...args)).subscribe(onSubscriber);\n}\n", "import { ReplaySubject } from '../ReplaySubject';\nimport { MonoTypeOperatorFunction, SchedulerLike } from '../types';\nimport { share } from './share';\n\nexport interface ShareReplayConfig {\n  bufferSize?: number;\n  windowTime?: number;\n  refCount: boolean;\n  scheduler?: SchedulerLike;\n}\n\nexport function shareReplay<T>(config: ShareReplayConfig): MonoTypeOperatorFunction<T>;\nexport function shareReplay<T>(bufferSize?: number, windowTime?: number, scheduler?: SchedulerLike): MonoTypeOperatorFunction<T>;\n\n/**\n * Share source and replay specified number of emissions on subscription.\n *\n * This operator is a specialization of `replay` that connects to a source observable\n * and multicasts through a `ReplaySubject` constructed with the specified arguments.\n * A successfully completed source will stay cached in the `shareReplay`ed observable forever,\n * but an errored source can be retried.\n *\n * ## Why use `shareReplay`?\n *\n * You generally want to use `shareReplay` when you have side-effects or taxing computations\n * that you do not wish to be executed amongst multiple subscribers.\n * It may also be valuable in situations where you know you will have late subscribers to\n * a stream that need access to previously emitted values.\n * This ability to replay values on subscription is what differentiates {@link share} and `shareReplay`.\n *\n * ## Reference counting\n *\n * By default `shareReplay` will use `refCount` of false, meaning that it will _not_ unsubscribe the\n * source when the reference counter drops to zero, i.e. the inner `ReplaySubject` will _not_ be unsubscribed\n * (and potentially run for ever).\n * This is the default as it is expected that `shareReplay` is often used to keep around expensive to setup\n * observables which we want to keep running instead of having to do the expensive setup again.\n *\n * As of RXJS version 6.4.0 a new overload signature was added to allow for manual control over what\n * happens when the operators internal reference counter drops to zero.\n * If `refCount` is true, the source will be unsubscribed from once the reference count drops to zero, i.e.\n * the inner `ReplaySubject` will be unsubscribed. All new subscribers will receive value emissions from a\n * new `ReplaySubject` which in turn will cause a new subscription to the source observable.\n *\n * ## Examples\n *\n * Example with a third subscriber coming late to the party\n *\n * ```ts\n * import { interval, take, shareReplay } from 'rxjs';\n *\n * const shared$ = interval(2000).pipe(\n *   take(6),\n *   shareReplay(3)\n * );\n *\n * shared$.subscribe(x => console.log('sub A: ', x));\n * shared$.subscribe(y => console.log('sub B: ', y));\n *\n * setTimeout(() => {\n *   shared$.subscribe(y => console.log('sub C: ', y));\n * }, 11000);\n *\n * // Logs:\n * // (after ~2000 ms)\n * // sub A: 0\n * // sub B: 0\n * // (after ~4000 ms)\n * // sub A: 1\n * // sub B: 1\n * // (after ~6000 ms)\n * // sub A: 2\n * // sub B: 2\n * // (after ~8000 ms)\n * // sub A: 3\n * // sub B: 3\n * // (after ~10000 ms)\n * // sub A: 4\n * // sub B: 4\n * // (after ~11000 ms, sub C gets the last 3 values)\n * // sub C: 2\n * // sub C: 3\n * // sub C: 4\n * // (after ~12000 ms)\n * // sub A: 5\n * // sub B: 5\n * // sub C: 5\n * ```\n *\n * Example for `refCount` usage\n *\n * ```ts\n * import { Observable, tap, interval, shareReplay, take } from 'rxjs';\n *\n * const log = <T>(name: string, source: Observable<T>) => source.pipe(\n *   tap({\n *     subscribe: () => console.log(`${ name }: subscribed`),\n *     next: value => console.log(`${ name }: ${ value }`),\n *     complete: () => console.log(`${ name }: completed`),\n *     finalize: () => console.log(`${ name }: unsubscribed`)\n *   })\n * );\n *\n * const obs$ = log('source', interval(1000));\n *\n * const shared$ = log('shared', obs$.pipe(\n *   shareReplay({ bufferSize: 1, refCount: true }),\n *   take(2)\n * ));\n *\n * shared$.subscribe(x => console.log('sub A: ', x));\n * shared$.subscribe(y => console.log('sub B: ', y));\n *\n * // PRINTS:\n * // shared: subscribed <-- reference count = 1\n * // source: subscribed\n * // shared: subscribed <-- reference count = 2\n * // source: 0\n * // shared: 0\n * // sub A: 0\n * // shared: 0\n * // sub B: 0\n * // source: 1\n * // shared: 1\n * // sub A: 1\n * // shared: completed <-- take(2) completes the subscription for sub A\n * // shared: unsubscribed <-- reference count = 1\n * // shared: 1\n * // sub B: 1\n * // shared: completed <-- take(2) completes the subscription for sub B\n * // shared: unsubscribed <-- reference count = 0\n * // source: unsubscribed <-- replaySubject unsubscribes from source observable because the reference count dropped to 0 and refCount is true\n *\n * // In case of refCount being false, the unsubscribe is never called on the source and the source would keep on emitting, even if no subscribers\n * // are listening.\n * // source: 2\n * // source: 3\n * // source: 4\n * // ...\n * ```\n *\n * @see {@link publish}\n * @see {@link share}\n * @see {@link publishReplay}\n *\n * @param configOrBufferSize Maximum element count of the replay buffer or {@link ShareReplayConfig configuration}\n * object.\n * @param windowTime Maximum time length of the replay buffer in milliseconds.\n * @param scheduler Scheduler where connected observers within the selector function\n * will be invoked on.\n * @return A function that returns an Observable sequence that contains the\n * elements of a sequence produced by multicasting the source sequence within a\n * selector function.\n */\nexport function shareReplay<T>(\n  configOrBufferSize?: ShareReplayConfig | number,\n  windowTime?: number,\n  scheduler?: SchedulerLike\n): MonoTypeOperatorFunction<T> {\n  let bufferSize: number;\n  let refCount = false;\n  if (configOrBufferSize && typeof configOrBufferSize === 'object') {\n    ({ bufferSize = Infinity, windowTime = Infinity, refCount = false, scheduler } = configOrBufferSize);\n  } else {\n    bufferSize = (configOrBufferSize ?? Infinity) as number;\n  }\n  return share<T>({\n    connector: () => new ReplaySubject(bufferSize, windowTime, scheduler),\n    resetOnError: true,\n    resetOnComplete: false,\n    resetOnRefCountZero: refCount,\n  });\n}\n", "import { MonoTypeOperatorFunction } from '../types';\nimport { filter } from './filter';\n\n/**\n * Returns an Observable that skips the first `count` items emitted by the source Observable.\n *\n * ![](skip.png)\n *\n * Skips the values until the sent notifications are equal or less than provided skip count. It raises\n * an error if skip count is equal or more than the actual number of emits and source raises an error.\n *\n * ## Example\n *\n * Skip the values before the emission\n *\n * ```ts\n * import { interval, skip } from 'rxjs';\n *\n * // emit every half second\n * const source = interval(500);\n * // skip the first 10 emitted values\n * const result = source.pipe(skip(10));\n *\n * result.subscribe(value => console.log(value));\n * // output: 10...11...12...13...\n * ```\n *\n * @see {@link last}\n * @see {@link skipWhile}\n * @see {@link skipUntil}\n * @see {@link skipLast}\n *\n * @param {Number} count - The number of times, items emitted by source Observable should be skipped.\n * @return A function that returns an Observable that skips the first `count`\n * values emitted by the source Observable.\n */\nexport function skip<T>(count: number): MonoTypeOperatorFunction<T> {\n  return filter((_, index) => count <= index);\n}\n", "import { MonoTypeOperatorFunction, ObservableInput } from '../types';\nimport { operate } from '../util/lift';\nimport { createOperatorSubscriber } from './OperatorSubscriber';\nimport { innerFrom } from '../observable/innerFrom';\nimport { noop } from '../util/noop';\n\n/**\n * Returns an Observable that skips items emitted by the source Observable until a second Observable emits an item.\n *\n * The `skipUntil` operator causes the observable stream to skip the emission of values until the passed in observable\n * emits the first value. This can be particularly useful in combination with user interactions, responses of HTTP\n * requests or waiting for specific times to pass by.\n *\n * ![](skipUntil.png)\n *\n * Internally, the `skipUntil` operator subscribes to the passed in `notifier` `ObservableInput` (which gets converted\n * to an Observable) in order to recognize the emission of its first value. When `notifier` emits next, the operator\n * unsubscribes from it and starts emitting the values of the *source* observable until it completes or errors. It\n * will never let the *source* observable emit any values if the `notifier` completes or throws an error without\n * emitting a value before.\n *\n * ## Example\n *\n * In the following example, all emitted values of the interval observable are skipped until the user clicks anywhere\n * within the page\n *\n * ```ts\n * import { interval, fromEvent, skipUntil } from 'rxjs';\n *\n * const intervalObservable = interval(1000);\n * const click = fromEvent(document, 'click');\n *\n * const emitAfterClick = intervalObservable.pipe(\n *   skipUntil(click)\n * );\n * // clicked at 4.6s. output: 5...6...7...8........ or\n * // clicked at 7.3s. output: 8...9...10..11.......\n * emitAfterClick.subscribe(value => console.log(value));\n * ```\n *\n * @see {@link last}\n * @see {@link skip}\n * @see {@link skipWhile}\n * @see {@link skipLast}\n *\n * @param notifier An `ObservableInput` that has to emit an item before the source Observable elements begin to\n * be mirrored by the resulting Observable.\n * @return A function that returns an Observable that skips items from the\n * source Observable until the `notifier` Observable emits an item, then emits the\n * remaining items.\n */\nexport function skipUntil<T>(notifier: ObservableInput<any>): MonoTypeOperatorFunction<T> {\n  return operate((source, subscriber) => {\n    let taking = false;\n\n    const skipSubscriber = createOperatorSubscriber(\n      subscriber,\n      () => {\n        skipSubscriber?.unsubscribe();\n        taking = true;\n      },\n      noop\n    );\n\n    innerFrom(notifier).subscribe(skipSubscriber);\n\n    source.subscribe(createOperatorSubscriber(subscriber, (value) => taking && subscriber.next(value)));\n  });\n}\n", "import { concat } from '../observable/concat';\nimport { OperatorFunction, SchedulerLike, ValueFromArray } from '../types';\nimport { popScheduler } from '../util/args';\nimport { operate } from '../util/lift';\n\n// Devs are more likely to pass null or undefined than they are a scheduler\n// without accompanying values. To make things easier for (naughty) devs who\n// use the `strictNullChecks: false` TypeScript compiler option, these\n// overloads with explicit null and undefined values are included.\n\nexport function startWith<T>(value: null): OperatorFunction<T, T | null>;\nexport function startWith<T>(value: undefined): OperatorFunction<T, T | undefined>;\n\n/** @deprecated The `scheduler` parameter will be removed in v8. Use `scheduled` and `concatAll`. Details: https://rxjs.dev/deprecations/scheduler-argument */\nexport function startWith<T, A extends readonly unknown[] = T[]>(\n  ...valuesAndScheduler: [...A, SchedulerLike]\n): OperatorFunction<T, T | ValueFromArray<A>>;\nexport function startWith<T, A extends readonly unknown[] = T[]>(...values: A): OperatorFunction<T, T | ValueFromArray<A>>;\n\n/**\n * Returns an observable that, at the moment of subscription, will synchronously emit all\n * values provided to this operator, then subscribe to the source and mirror all of its emissions\n * to subscribers.\n *\n * This is a useful way to know when subscription has occurred on an existing observable.\n *\n * <span class=\"informal\">First emits its arguments in order, and then any\n * emissions from the source.</span>\n *\n * ![](startWith.png)\n *\n * ## Examples\n *\n * Emit a value when a timer starts.\n *\n * ```ts\n * import { timer, map, startWith } from 'rxjs';\n *\n * timer(1000)\n *   .pipe(\n *     map(() => 'timer emit'),\n *     startWith('timer start')\n *   )\n *   .subscribe(x => console.log(x));\n *\n * // results:\n * // 'timer start'\n * // 'timer emit'\n * ```\n *\n * @param values Items you want the modified Observable to emit first.\n * @return A function that returns an Observable that synchronously emits\n * provided values before subscribing to the source Observable.\n *\n * @see {@link endWith}\n * @see {@link finalize}\n * @see {@link concat}\n */\nexport function startWith<T, D>(...values: D[]): OperatorFunction<T, T | D> {\n  const scheduler = popScheduler(values);\n  return operate((source, subscriber) => {\n    // Here we can't pass `undefined` as a scheduler, because if we did, the\n    // code inside of `concat` would be confused by the `undefined`, and treat it\n    // like an invalid observable. So we have to split it two different ways.\n    (scheduler ? concat(values, source, scheduler) : concat(values, source)).subscribe(subscriber);\n  });\n}\n", "import { Subscriber } from '../Subscriber';\nimport { ObservableInput, OperatorFunction, ObservedValueOf } from '../types';\nimport { innerFrom } from '../observable/innerFrom';\nimport { operate } from '../util/lift';\nimport { createOperatorSubscriber } from './OperatorSubscriber';\n\n/* tslint:disable:max-line-length */\nexport function switchMap<T, O extends ObservableInput<any>>(\n  project: (value: T, index: number) => O\n): OperatorFunction<T, ObservedValueOf<O>>;\n/** @deprecated The `resultSelector` parameter will be removed in v8. Use an inner `map` instead. Details: https://rxjs.dev/deprecations/resultSelector */\nexport function switchMap<T, O extends ObservableInput<any>>(\n  project: (value: T, index: number) => O,\n  resultSelector: undefined\n): OperatorFunction<T, ObservedValueOf<O>>;\n/** @deprecated The `resultSelector` parameter will be removed in v8. Use an inner `map` instead. Details: https://rxjs.dev/deprecations/resultSelector */\nexport function switchMap<T, R, O extends ObservableInput<any>>(\n  project: (value: T, index: number) => O,\n  resultSelector: (outerValue: T, innerValue: ObservedValueOf<O>, outerIndex: number, innerIndex: number) => R\n): OperatorFunction<T, R>;\n/* tslint:enable:max-line-length */\n\n/**\n * Projects each source value to an Observable which is merged in the output\n * Observable, emitting values only from the most recently projected Observable.\n *\n * <span class=\"informal\">Maps each value to an Observable, then flattens all of\n * these inner Observables using {@link switchAll}.</span>\n *\n * ![](switchMap.png)\n *\n * Returns an Observable that emits items based on applying a function that you\n * supply to each item emitted by the source Observable, where that function\n * returns an (so-called \"inner\") Observable. Each time it observes one of these\n * inner Observables, the output Observable begins emitting the items emitted by\n * that inner Observable. When a new inner Observable is emitted, `switchMap`\n * stops emitting items from the earlier-emitted inner Observable and begins\n * emitting items from the new one. It continues to behave like this for\n * subsequent inner Observables.\n *\n * ## Example\n *\n * Generate new Observable according to source Observable values\n *\n * ```ts\n * import { of, switchMap } from 'rxjs';\n *\n * const switched = of(1, 2, 3).pipe(switchMap(x => of(x, x ** 2, x ** 3)));\n * switched.subscribe(x => console.log(x));\n * // outputs\n * // 1\n * // 1\n * // 1\n * // 2\n * // 4\n * // 8\n * // 3\n * // 9\n * // 27\n * ```\n *\n * Restart an interval Observable on every click event\n *\n * ```ts\n * import { fromEvent, switchMap, interval } from 'rxjs';\n *\n * const clicks = fromEvent(document, 'click');\n * const result = clicks.pipe(switchMap(() => interval(1000)));\n * result.subscribe(x => console.log(x));\n * ```\n *\n * @see {@link concatMap}\n * @see {@link exhaustMap}\n * @see {@link mergeMap}\n * @see {@link switchAll}\n * @see {@link switchMapTo}\n *\n * @param {function(value: T, index: number): ObservableInput} project A function\n * that, when applied to an item emitted by the source Observable, returns an\n * Observable.\n * @return A function that returns an Observable that emits the result of\n * applying the projection function (and the optional deprecated\n * `resultSelector`) to each item emitted by the source Observable and taking\n * only the values from the most recently projected inner Observable.\n */\nexport function switchMap<T, R, O extends ObservableInput<any>>(\n  project: (value: T, index: number) => O,\n  resultSelector?: (outerValue: T, innerValue: ObservedValueOf<O>, outerIndex: number, innerIndex: number) => R\n): OperatorFunction<T, ObservedValueOf<O> | R> {\n  return operate((source, subscriber) => {\n    let innerSubscriber: Subscriber<ObservedValueOf<O>> | null = null;\n    let index = 0;\n    // Whether or not the source subscription has completed\n    let isComplete = false;\n\n    // We only complete the result if the source is complete AND we don't have an active inner subscription.\n    // This is called both when the source completes and when the inners complete.\n    const checkComplete = () => isComplete && !innerSubscriber && subscriber.complete();\n\n    source.subscribe(\n      createOperatorSubscriber(\n        subscriber,\n        (value) => {\n          // Cancel the previous inner subscription if there was one\n          innerSubscriber?.unsubscribe();\n          let innerIndex = 0;\n          const outerIndex = index++;\n          // Start the next inner subscription\n          innerFrom(project(value, outerIndex)).subscribe(\n            (innerSubscriber = createOperatorSubscriber(\n              subscriber,\n              // When we get a new inner value, next it through. Note that this is\n              // handling the deprecate result selector here. This is because with this architecture\n              // it ends up being smaller than using the map operator.\n              (innerValue) => subscriber.next(resultSelector ? resultSelector(value, innerValue, outerIndex, innerIndex++) : innerValue),\n              () => {\n                // The inner has completed. Null out the inner subscriber to\n                // free up memory and to signal that we have no inner subscription\n                // currently.\n                innerSubscriber = null!;\n                checkComplete();\n              }\n            ))\n          );\n        },\n        () => {\n          isComplete = true;\n          checkComplete();\n        }\n      )\n    );\n  });\n}\n", "import { MonoTypeOperatorFunction, ObservableInput } from '../types';\nimport { operate } from '../util/lift';\nimport { createOperatorSubscriber } from './OperatorSubscriber';\nimport { innerFrom } from '../observable/innerFrom';\nimport { noop } from '../util/noop';\n\n/**\n * Emits the values emitted by the source Observable until a `notifier`\n * Observable emits a value.\n *\n * <span class=\"informal\">Lets values pass until a second Observable,\n * `notifier`, emits a value. Then, it completes.</span>\n *\n * ![](takeUntil.png)\n *\n * `takeUntil` subscribes and begins mirroring the source Observable. It also\n * monitors a second Observable, `notifier` that you provide. If the `notifier`\n * emits a value, the output Observable stops mirroring the source Observable\n * and completes. If the `notifier` doesn't emit any value and completes\n * then `takeUntil` will pass all values.\n *\n * ## Example\n *\n * Tick every second until the first click happens\n *\n * ```ts\n * import { interval, fromEvent, takeUntil } from 'rxjs';\n *\n * const source = interval(1000);\n * const clicks = fromEvent(document, 'click');\n * const result = source.pipe(takeUntil(clicks));\n * result.subscribe(x => console.log(x));\n * ```\n *\n * @see {@link take}\n * @see {@link takeLast}\n * @see {@link takeWhile}\n * @see {@link skip}\n *\n * @param {Observable} notifier The Observable whose first emitted value will\n * cause the output Observable of `takeUntil` to stop emitting values from the\n * source Observable.\n * @return A function that returns an Observable that emits the values from the\n * source Observable until `notifier` emits its first value.\n */\nexport function takeUntil<T>(notifier: ObservableInput<any>): MonoTypeOperatorFunction<T> {\n  return operate((source, subscriber) => {\n    innerFrom(notifier).subscribe(createOperatorSubscriber(subscriber, () => subscriber.complete(), noop));\n    !subscriber.closed && source.subscribe(subscriber);\n  });\n}\n", "import { OperatorFunction, MonoTypeOperatorFunction, TruthyTypesOf } from '../types';\nimport { operate } from '../util/lift';\nimport { createOperatorSubscriber } from './OperatorSubscriber';\n\nexport function takeWhile<T>(predicate: BooleanConstructor, inclusive: true): MonoTypeOperatorFunction<T>;\nexport function takeWhile<T>(predicate: BooleanConstructor, inclusive: false): OperatorFunction<T, TruthyTypesOf<T>>;\nexport function takeWhile<T>(predicate: BooleanConstructor): OperatorFunction<T, TruthyTypesOf<T>>;\nexport function takeWhile<T, S extends T>(predicate: (value: T, index: number) => value is S): OperatorFunction<T, S>;\nexport function takeWhile<T, S extends T>(predicate: (value: T, index: number) => value is S, inclusive: false): OperatorFunction<T, S>;\nexport function takeWhile<T>(predicate: (value: T, index: number) => boolean, inclusive?: boolean): MonoTypeOperatorFunction<T>;\n\n/**\n * Emits values emitted by the source Observable so long as each value satisfies\n * the given `predicate`, and then completes as soon as this `predicate` is not\n * satisfied.\n *\n * <span class=\"informal\">Takes values from the source only while they pass the\n * condition given. When the first value does not satisfy, it completes.</span>\n *\n * ![](takeWhile.png)\n *\n * `takeWhile` subscribes and begins mirroring the source Observable. Each value\n * emitted on the source is given to the `predicate` function which returns a\n * boolean, representing a condition to be satisfied by the source values. The\n * output Observable emits the source values until such time as the `predicate`\n * returns false, at which point `takeWhile` stops mirroring the source\n * Observable and completes the output Observable.\n *\n * ## Example\n *\n * Emit click events only while the clientX property is greater than 200\n *\n * ```ts\n * import { fromEvent, takeWhile } from 'rxjs';\n *\n * const clicks = fromEvent<PointerEvent>(document, 'click');\n * const result = clicks.pipe(takeWhile(ev => ev.clientX > 200));\n * result.subscribe(x => console.log(x));\n * ```\n *\n * @see {@link take}\n * @see {@link takeLast}\n * @see {@link takeUntil}\n * @see {@link skip}\n *\n * @param {function(value: T, index: number): boolean} predicate A function that\n * evaluates a value emitted by the source Observable and returns a boolean.\n * Also takes the (zero-based) index as the second argument.\n * @param {boolean} inclusive When set to `true` the value that caused\n * `predicate` to return `false` will also be emitted.\n * @return A function that returns an Observable that emits values from the\n * source Observable so long as each value satisfies the condition defined by\n * the `predicate`, then completes.\n */\nexport function takeWhile<T>(predicate: (value: T, index: number) => boolean, inclusive = false): MonoTypeOperatorFunction<T> {\n  return operate((source, subscriber) => {\n    let index = 0;\n    source.subscribe(\n      createOperatorSubscriber(subscriber, (value) => {\n        const result = predicate(value, index++);\n        (result || inclusive) && subscriber.next(value);\n        !result && subscriber.complete();\n      })\n    );\n  });\n}\n", "import { MonoTypeOperatorFunction, Observer } from '../types';\nimport { isFunction } from '../util/isFunction';\nimport { operate } from '../util/lift';\nimport { createOperatorSubscriber } from './OperatorSubscriber';\nimport { identity } from '../util/identity';\n\n/**\n * An extension to the {@link Observer} interface used only by the {@link tap} operator.\n *\n * It provides a useful set of callbacks a user can register to do side-effects in\n * cases other than what the usual {@link Observer} callbacks are\n * ({@link guide/glossary-and-semantics#next next},\n * {@link guide/glossary-and-semantics#error error} and/or\n * {@link guide/glossary-and-semantics#complete complete}).\n *\n * ## Example\n *\n * ```ts\n * import { fromEvent, switchMap, tap, interval, take } from 'rxjs';\n *\n * const source$ = fromEvent(document, 'click');\n * const result$ = source$.pipe(\n *   switchMap((_, i) => i % 2 === 0\n *     ? fromEvent(document, 'mousemove').pipe(\n *         tap({\n *           subscribe: () => console.log('Subscribed to the mouse move events after click #' + i),\n *           unsubscribe: () => console.log('Mouse move events #' + i + ' unsubscribed'),\n *           finalize: () => console.log('Mouse move events #' + i + ' finalized')\n *         })\n *       )\n *     : interval(1_000).pipe(\n *         take(5),\n *         tap({\n *           subscribe: () => console.log('Subscribed to the 1-second interval events after click #' + i),\n *           unsubscribe: () => console.log('1-second interval events #' + i + ' unsubscribed'),\n *           finalize: () => console.log('1-second interval events #' + i + ' finalized')\n *         })\n *       )\n *   )\n * );\n *\n * const subscription = result$.subscribe({\n *   next: console.log\n * });\n *\n * setTimeout(() => {\n *   console.log('Unsubscribe after 60 seconds');\n *   subscription.unsubscribe();\n * }, 60_000);\n * ```\n */\nexport interface TapObserver<T> extends Observer<T> {\n  /**\n   * The callback that `tap` operator invokes at the moment when the source Observable\n   * gets subscribed to.\n   */\n  subscribe: () => void;\n  /**\n   * The callback that `tap` operator invokes when an explicit\n   * {@link guide/glossary-and-semantics#unsubscription unsubscribe} happens. It won't get invoked on\n   * `error` or `complete` events.\n   */\n  unsubscribe: () => void;\n  /**\n   * The callback that `tap` operator invokes when any kind of\n   * {@link guide/glossary-and-semantics#finalization finalization} happens - either when\n   * the source Observable `error`s or `complete`s or when it gets explicitly unsubscribed\n   * by the user. There is no difference in using this callback or the {@link finalize}\n   * operator, but if you're already using `tap` operator, you can use this callback\n   * instead. You'd get the same result in either case.\n   */\n  finalize: () => void;\n}\nexport function tap<T>(observerOrNext?: Partial<TapObserver<T>> | ((value: T) => void)): MonoTypeOperatorFunction<T>;\n/** @deprecated Instead of passing separate callback arguments, use an observer argument. Signatures taking separate callback arguments will be removed in v8. Details: https://rxjs.dev/deprecations/subscribe-arguments */\nexport function tap<T>(\n  next?: ((value: T) => void) | null,\n  error?: ((error: any) => void) | null,\n  complete?: (() => void) | null\n): MonoTypeOperatorFunction<T>;\n\n/**\n * Used to perform side-effects for notifications from the source observable\n *\n * <span class=\"informal\">Used when you want to affect outside state with a notification without altering the notification</span>\n *\n * ![](tap.png)\n *\n * Tap is designed to allow the developer a designated place to perform side effects. While you _could_ perform side-effects\n * inside of a `map` or a `mergeMap`, that would make their mapping functions impure, which isn't always a big deal, but will\n * make it so you can't do things like memoize those functions. The `tap` operator is designed solely for such side-effects to\n * help you remove side-effects from other operations.\n *\n * For any notification, next, error, or complete, `tap` will call the appropriate callback you have provided to it, via a function\n * reference, or a partial observer, then pass that notification down the stream.\n *\n * The observable returned by `tap` is an exact mirror of the source, with one exception: Any error that occurs -- synchronously -- in a handler\n * provided to `tap` will be emitted as an error from the returned observable.\n *\n * > Be careful! You can mutate objects as they pass through the `tap` operator's handlers.\n *\n * The most common use of `tap` is actually for debugging. You can place a `tap(console.log)` anywhere\n * in your observable `pipe`, log out the notifications as they are emitted by the source returned by the previous\n * operation.\n *\n * ## Examples\n *\n * Check a random number before it is handled. Below is an observable that will use a random number between 0 and 1,\n * and emit `'big'` or `'small'` depending on the size of that number. But we wanted to log what the original number\n * was, so we have added a `tap(console.log)`.\n *\n * ```ts\n * import { of, tap, map } from 'rxjs';\n *\n * of(Math.random()).pipe(\n *   tap(console.log),\n *   map(n => n > 0.5 ? 'big' : 'small')\n * ).subscribe(console.log);\n * ```\n *\n * Using `tap` to analyze a value and force an error. Below is an observable where in our system we only\n * want to emit numbers 3 or less we get from another source. We can force our observable to error\n * using `tap`.\n *\n * ```ts\n * import { of, tap } from 'rxjs';\n *\n * const source = of(1, 2, 3, 4, 5);\n *\n * source.pipe(\n *   tap(n => {\n *     if (n > 3) {\n *       throw new TypeError(`Value ${ n } is greater than 3`);\n *     }\n *   })\n * )\n * .subscribe({ next: console.log, error: err => console.log(err.message) });\n * ```\n *\n * We want to know when an observable completes before moving on to the next observable. The system\n * below will emit a random series of `'X'` characters from 3 different observables in sequence. The\n * only way we know when one observable completes and moves to the next one, in this case, is because\n * we have added a `tap` with the side effect of logging to console.\n *\n * ```ts\n * import { of, concatMap, interval, take, map, tap } from 'rxjs';\n *\n * of(1, 2, 3).pipe(\n *   concatMap(n => interval(1000).pipe(\n *     take(Math.round(Math.random() * 10)),\n *     map(() => 'X'),\n *     tap({ complete: () => console.log(`Done with ${ n }`) })\n *   ))\n * )\n * .subscribe(console.log);\n * ```\n *\n * @see {@link finalize}\n * @see {@link TapObserver}\n *\n * @param observerOrNext A next handler or partial observer\n * @param error An error handler\n * @param complete A completion handler\n * @return A function that returns an Observable identical to the source, but\n * runs the specified Observer or callback(s) for each item.\n */\nexport function tap<T>(\n  observerOrNext?: Partial<TapObserver<T>> | ((value: T) => void) | null,\n  error?: ((e: any) => void) | null,\n  complete?: (() => void) | null\n): MonoTypeOperatorFunction<T> {\n  // We have to check to see not only if next is a function,\n  // but if error or complete were passed. This is because someone\n  // could technically call tap like `tap(null, fn)` or `tap(null, null, fn)`.\n  const tapObserver =\n    isFunction(observerOrNext) || error || complete\n      ? // tslint:disable-next-line: no-object-literal-type-assertion\n        ({ next: observerOrNext as Exclude<typeof observerOrNext, Partial<TapObserver<T>>>, error, complete } as Partial<TapObserver<T>>)\n      : observerOrNext;\n\n  return tapObserver\n    ? operate((source, subscriber) => {\n        tapObserver.subscribe?.();\n        let isUnsub = true;\n        source.subscribe(\n          createOperatorSubscriber(\n            subscriber,\n            (value) => {\n              tapObserver.next?.(value);\n              subscriber.next(value);\n            },\n            () => {\n              isUnsub = false;\n              tapObserver.complete?.();\n              subscriber.complete();\n            },\n            (err) => {\n              isUnsub = false;\n              tapObserver.error?.(err);\n              subscriber.error(err);\n            },\n            () => {\n              if (isUnsub) {\n                tapObserver.unsubscribe?.();\n              }\n              tapObserver.finalize?.();\n            }\n          )\n        );\n      })\n    : // Tap was called with no valid tap observer or handler\n      // (e.g. `tap(null, null, null)` or `tap(null)` or `tap()`)\n      // so we're going to just mirror the source.\n      identity;\n}\n", "import { Subscription } from '../Subscription';\n\nimport { MonoTypeOperatorFunction, ObservableInput } from '../types';\nimport { operate } from '../util/lift';\nimport { createOperatorSubscriber } from './OperatorSubscriber';\nimport { innerFrom } from '../observable/innerFrom';\n\n/**\n * An object interface used by {@link throttle} or {@link throttleTime} that ensure\n * configuration options of these operators.\n *\n * @see {@link throttle}\n * @see {@link throttleTime}\n */\nexport interface ThrottleConfig {\n  /**\n   * If `true`, the resulting Observable will emit the first value from the source\n   * Observable at the **start** of the \"throttling\" process (when starting an\n   * internal timer that prevents other emissions from the source to pass through).\n   * If `false`, it will not emit the first value from the source Observable at the\n   * start of the \"throttling\" process.\n   *\n   * If not provided, defaults to: `true`.\n   */\n  leading?: boolean;\n  /**\n   * If `true`, the resulting Observable will emit the last value from the source\n   * Observable at the **end** of the \"throttling\" process (when ending an internal\n   * timer that prevents other emissions from the source to pass through).\n   * If `false`, it will not emit the last value from the source Observable at the\n   * end of the \"throttling\" process.\n   *\n   * If not provided, defaults to: `false`.\n   */\n  trailing?: boolean;\n}\n\n/**\n * Emits a value from the source Observable, then ignores subsequent source\n * values for a duration determined by another Observable, then repeats this\n * process.\n *\n * <span class=\"informal\">It's like {@link throttleTime}, but the silencing\n * duration is determined by a second Observable.</span>\n *\n * ![](throttle.svg)\n *\n * `throttle` emits the source Observable values on the output Observable\n * when its internal timer is disabled, and ignores source values when the timer\n * is enabled. Initially, the timer is disabled. As soon as the first source\n * value arrives, it is forwarded to the output Observable, and then the timer\n * is enabled by calling the `durationSelector` function with the source value,\n * which returns the \"duration\" Observable. When the duration Observable emits a\n * value, the timer is disabled, and this process repeats for the\n * next source value.\n *\n * ## Example\n *\n * Emit clicks at a rate of at most one click per second\n *\n * ```ts\n * import { fromEvent, throttle, interval } from 'rxjs';\n *\n * const clicks = fromEvent(document, 'click');\n * const result = clicks.pipe(throttle(() => interval(1000)));\n *\n * result.subscribe(x => console.log(x));\n * ```\n *\n * @see {@link audit}\n * @see {@link debounce}\n * @see {@link delayWhen}\n * @see {@link sample}\n * @see {@link throttleTime}\n *\n * @param durationSelector A function that receives a value from the source\n * Observable, for computing the silencing duration for each source value,\n * returned as an `ObservableInput`.\n * @param config A configuration object to define `leading` and `trailing`\n * behavior. Defaults to `{ leading: true, trailing: false }`.\n * @return A function that returns an Observable that performs the throttle\n * operation to limit the rate of emissions from the source.\n */\nexport function throttle<T>(durationSelector: (value: T) => ObservableInput<any>, config?: ThrottleConfig): MonoTypeOperatorFunction<T> {\n  return operate((source, subscriber) => {\n    const { leading = true, trailing = false } = config ?? {};\n    let hasValue = false;\n    let sendValue: T | null = null;\n    let throttled: Subscription | null = null;\n    let isComplete = false;\n\n    const endThrottling = () => {\n      throttled?.unsubscribe();\n      throttled = null;\n      if (trailing) {\n        send();\n        isComplete && subscriber.complete();\n      }\n    };\n\n    const cleanupThrottling = () => {\n      throttled = null;\n      isComplete && subscriber.complete();\n    };\n\n    const startThrottle = (value: T) =>\n      (throttled = innerFrom(durationSelector(value)).subscribe(createOperatorSubscriber(subscriber, endThrottling, cleanupThrottling)));\n\n    const send = () => {\n      if (hasValue) {\n        // Ensure we clear out our value and hasValue flag\n        // before we emit, otherwise reentrant code can cause\n        // issues here.\n        hasValue = false;\n        const value = sendValue!;\n        sendValue = null;\n        // Emit the value.\n        subscriber.next(value);\n        !isComplete && startThrottle(value);\n      }\n    };\n\n    source.subscribe(\n      createOperatorSubscriber(\n        subscriber,\n        // Regarding the presence of throttled.closed in the following\n        // conditions, if a synchronous duration selector is specified - weird,\n        // but legal - an already-closed subscription will be assigned to\n        // throttled, so the subscription's closed property needs to be checked,\n        // too.\n        (value) => {\n          hasValue = true;\n          sendValue = value;\n          !(throttled && !throttled.closed) && (leading ? send() : startThrottle(value));\n        },\n        () => {\n          isComplete = true;\n          !(trailing && hasValue && throttled && !throttled.closed) && subscriber.complete();\n        }\n      )\n    );\n  });\n}\n", "import { asyncScheduler } from '../scheduler/async';\nimport { throttle, ThrottleConfig } from './throttle';\nimport { MonoTypeOperatorFunction, SchedulerLike } from '../types';\nimport { timer } from '../observable/timer';\n\n/**\n * Emits a value from the source Observable, then ignores subsequent source\n * values for `duration` milliseconds, then repeats this process.\n *\n * <span class=\"informal\">Lets a value pass, then ignores source values for the\n * next `duration` milliseconds.</span>\n *\n * ![](throttleTime.png)\n *\n * `throttleTime` emits the source Observable values on the output Observable\n * when its internal timer is disabled, and ignores source values when the timer\n * is enabled. Initially, the timer is disabled. As soon as the first source\n * value arrives, it is forwarded to the output Observable, and then the timer\n * is enabled. After `duration` milliseconds (or the time unit determined\n * internally by the optional `scheduler`) has passed, the timer is disabled,\n * and this process repeats for the next source value. Optionally takes a\n * {@link SchedulerLike} for managing timers.\n *\n * ## Examples\n *\n * ### Limit click rate\n *\n * Emit clicks at a rate of at most one click per second\n *\n * ```ts\n * import { fromEvent, throttleTime } from 'rxjs';\n *\n * const clicks = fromEvent(document, 'click');\n * const result = clicks.pipe(throttleTime(1000));\n *\n * result.subscribe(x => console.log(x));\n * ```\n *\n * @see {@link auditTime}\n * @see {@link debounceTime}\n * @see {@link delay}\n * @see {@link sampleTime}\n * @see {@link throttle}\n *\n * @param duration Time to wait before emitting another value after\n * emitting the last value, measured in milliseconds or the time unit determined\n * internally by the optional `scheduler`.\n * @param scheduler The {@link SchedulerLike} to use for\n * managing the timers that handle the throttling. Defaults to {@link asyncScheduler}.\n * @param config A configuration object to define `leading` and\n * `trailing` behavior. Defaults to `{ leading: true, trailing: false }`.\n * @return A function that returns an Observable that performs the throttle\n * operation to limit the rate of emissions from the source.\n */\nexport function throttleTime<T>(\n  duration: number,\n  scheduler: SchedulerLike = asyncScheduler,\n  config?: ThrottleConfig\n): MonoTypeOperatorFunction<T> {\n  const duration$ = timer(duration, scheduler);\n  return throttle(() => duration$, config);\n}\n", "import { OperatorFunction, ObservableInputTuple } from '../types';\nimport { operate } from '../util/lift';\nimport { createOperatorSubscriber } from './OperatorSubscriber';\nimport { innerFrom } from '../observable/innerFrom';\nimport { identity } from '../util/identity';\nimport { noop } from '../util/noop';\nimport { popResultSelector } from '../util/args';\n\nexport function withLatestFrom<T, O extends unknown[]>(...inputs: [...ObservableInputTuple<O>]): OperatorFunction<T, [T, ...O]>;\n\nexport function withLatestFrom<T, O extends unknown[], R>(\n  ...inputs: [...ObservableInputTuple<O>, (...value: [T, ...O]) => R]\n): OperatorFunction<T, R>;\n\n/**\n * Combines the source Observable with other Observables to create an Observable\n * whose values are calculated from the latest values of each, only when the\n * source emits.\n *\n * <span class=\"informal\">Whenever the source Observable emits a value, it\n * computes a formula using that value plus the latest values from other input\n * Observables, then emits the output of that formula.</span>\n *\n * ![](withLatestFrom.png)\n *\n * `withLatestFrom` combines each value from the source Observable (the\n * instance) with the latest values from the other input Observables only when\n * the source emits a value, optionally using a `project` function to determine\n * the value to be emitted on the output Observable. All input Observables must\n * emit at least one value before the output Observable will emit a value.\n *\n * ## Example\n *\n * On every click event, emit an array with the latest timer event plus the click event\n *\n * ```ts\n * import { fromEvent, interval, withLatestFrom } from 'rxjs';\n *\n * const clicks = fromEvent(document, 'click');\n * const timer = interval(1000);\n * const result = clicks.pipe(withLatestFrom(timer));\n * result.subscribe(x => console.log(x));\n * ```\n *\n * @see {@link combineLatest}\n *\n * @param {ObservableInput} other An input Observable to combine with the source\n * Observable. More than one input Observables may be given as argument.\n * @param {Function} [project] Projection function for combining values\n * together. Receives all values in order of the Observables passed, where the\n * first parameter is a value from the source Observable. (e.g.\n * `a.pipe(withLatestFrom(b, c), map(([a1, b1, c1]) => a1 + b1 + c1))`). If this is not\n * passed, arrays will be emitted on the output Observable.\n * @return A function that returns an Observable of projected values from the\n * most recent values from each input Observable, or an array of the most\n * recent values from each input Observable.\n */\nexport function withLatestFrom<T, R>(...inputs: any[]): OperatorFunction<T, R | any[]> {\n  const project = popResultSelector(inputs) as ((...args: any[]) => R) | undefined;\n\n  return operate((source, subscriber) => {\n    const len = inputs.length;\n    const otherValues = new Array(len);\n    // An array of whether or not the other sources have emitted. Matched with them by index.\n    // TODO: At somepoint, we should investigate the performance implications here, and look\n    // into using a `Set()` and checking the `size` to see if we're ready.\n    let hasValue = inputs.map(() => false);\n    // Flipped true when we have at least one value from all other sources and\n    // we are ready to start emitting values.\n    let ready = false;\n\n    // Other sources. Note that here we are not checking `subscriber.closed`,\n    // this causes all inputs to be subscribed to, even if nothing can be emitted\n    // from them. This is an important distinction because subscription constitutes\n    // a side-effect.\n    for (let i = 0; i < len; i++) {\n      innerFrom(inputs[i]).subscribe(\n        createOperatorSubscriber(\n          subscriber,\n          (value) => {\n            otherValues[i] = value;\n            if (!ready && !hasValue[i]) {\n              // If we're not ready yet, flag to show this observable has emitted.\n              hasValue[i] = true;\n              // Intentionally terse code.\n              // If all of our other observables have emitted, set `ready` to `true`,\n              // so we know we can start emitting values, then clean up the `hasValue` array,\n              // because we don't need it anymore.\n              (ready = hasValue.every(identity)) && (hasValue = null!);\n            }\n          },\n          // Completing one of the other sources has\n          // no bearing on the completion of our result.\n          noop\n        )\n      );\n    }\n\n    // Source subscription\n    source.subscribe(\n      createOperatorSubscriber(subscriber, (value) => {\n        if (ready) {\n          // We have at least one value from the other sources. Go ahead and emit.\n          const values = [value, ...otherValues];\n          subscriber.next(project ? project(...values) : values);\n        }\n      })\n    );\n  });\n}\n", "import { zip as zipStatic } from '../observable/zip';\nimport { ObservableInput, ObservableInputTuple, OperatorFunction, Cons } from '../types';\nimport { operate } from '../util/lift';\n\n/** @deprecated Replaced with {@link zipWith}. Will be removed in v8. */\nexport function zip<T, A extends readonly unknown[]>(otherInputs: [...ObservableInputTuple<A>]): OperatorFunction<T, Cons<T, A>>;\n/** @deprecated Replaced with {@link zipWith}. Will be removed in v8. */\nexport function zip<T, A extends readonly unknown[], R>(\n  otherInputsAndProject: [...ObservableInputTuple<A>],\n  project: (...values: Cons<T, A>) => R\n): OperatorFunction<T, R>;\n/** @deprecated Replaced with {@link zipWith}. Will be removed in v8. */\nexport function zip<T, A extends readonly unknown[]>(...otherInputs: [...ObservableInputTuple<A>]): OperatorFunction<T, Cons<T, A>>;\n/** @deprecated Replaced with {@link zipWith}. Will be removed in v8. */\nexport function zip<T, A extends readonly unknown[], R>(\n  ...otherInputsAndProject: [...ObservableInputTuple<A>, (...values: Cons<T, A>) => R]\n): OperatorFunction<T, R>;\n\n/**\n * @deprecated Replaced with {@link zipWith}. Will be removed in v8.\n */\nexport function zip<T, R>(...sources: Array<ObservableInput<any> | ((...values: Array<any>) => R)>): OperatorFunction<T, any> {\n  return operate((source, subscriber) => {\n    zipStatic(source as ObservableInput<any>, ...(sources as Array<ObservableInput<any>>)).subscribe(subscriber);\n  });\n}\n", "import { ObservableInputTuple, OperatorFunction, Cons } from '../types';\nimport { zip } from './zip';\n\n/**\n * Subscribes to the source, and the observable inputs provided as arguments, and combines their values, by index, into arrays.\n *\n * What is meant by \"combine by index\": The first value from each will be made into a single array, then emitted,\n * then the second value from each will be combined into a single array and emitted, then the third value\n * from each will be combined into a single array and emitted, and so on.\n *\n * This will continue until it is no longer able to combine values of the same index into an array.\n *\n * After the last value from any one completed source is emitted in an array, the resulting observable will complete,\n * as there is no way to continue \"zipping\" values together by index.\n *\n * Use-cases for this operator are limited. There are memory concerns if one of the streams is emitting\n * values at a much faster rate than the others. Usage should likely be limited to streams that emit\n * at a similar pace, or finite streams of known length.\n *\n * In many cases, authors want `combineLatestWith` and not `zipWith`.\n *\n * @param otherInputs other observable inputs to collate values from.\n * @return A function that returns an Observable that emits items by index\n * combined from the source Observable and provided Observables, in form of an\n * array.\n */\nexport function zipWith<T, A extends readonly unknown[]>(...otherInputs: [...ObservableInputTuple<A>]): OperatorFunction<T, Cons<T, A>> {\n  return zip(...otherInputs);\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  ReplaySubject,\n  Subject,\n  fromEvent\n} from \"rxjs\"\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Watch document\n *\n * Documents are implemented as subjects, so all downstream observables are\n * automatically updated when a new document is emitted.\n *\n * @returns Document subject\n */\nexport function watchDocument(): Subject<Document> {\n  const document$ = new ReplaySubject<Document>(1)\n  fromEvent(document, \"DOMContentLoaded\", { once: true })\n    .subscribe(() => document$.next(document))\n\n  /* Return document */\n  return document$\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Retrieve all elements matching the query selector\n *\n * @template T - Element type\n *\n * @param selector - Query selector\n * @param node - Node of reference\n *\n * @returns Elements\n */\nexport function getElements<T extends keyof HTMLElementTagNameMap>(\n  selector: T, node?: ParentNode\n): HTMLElementTagNameMap[T][]\n\nexport function getElements<T extends HTMLElement>(\n  selector: string, node?: ParentNode\n): T[]\n\nexport function getElements<T extends HTMLElement>(\n  selector: string, node: ParentNode = document\n): T[] {\n  return Array.from(node.querySelectorAll<T>(selector))\n}\n\n/**\n * Retrieve an element matching a query selector or throw a reference error\n *\n * Note that this function assumes that the element is present. If unsure if an\n * element is existent, use the `getOptionalElement` function instead.\n *\n * @template T - Element type\n *\n * @param selector - Query selector\n * @param node - Node of reference\n *\n * @returns Element\n */\nexport function getElement<T extends keyof HTMLElementTagNameMap>(\n  selector: T, node?: ParentNode\n): HTMLElementTagNameMap[T]\n\nexport function getElement<T extends HTMLElement>(\n  selector: string, node?: ParentNode\n): T\n\nexport function getElement<T extends HTMLElement>(\n  selector: string, node: ParentNode = document\n): T {\n  const el = getOptionalElement<T>(selector, node)\n  if (typeof el === \"undefined\")\n    throw new ReferenceError(\n      `Missing element: expected \"${selector}\" to be present`\n    )\n\n  /* Return element */\n  return el\n}\n\n/* ------------------------------------------------------------------------- */\n\n/**\n * Retrieve an optional element matching the query selector\n *\n * @template T - Element type\n *\n * @param selector - Query selector\n * @param node - Node of reference\n *\n * @returns Element or nothing\n */\nexport function getOptionalElement<T extends keyof HTMLElementTagNameMap>(\n  selector: T, node?: ParentNode\n): HTMLElementTagNameMap[T] | undefined\n\nexport function getOptionalElement<T extends HTMLElement>(\n  selector: string, node?: ParentNode\n): T | undefined\n\nexport function getOptionalElement<T extends HTMLElement>(\n  selector: string, node: ParentNode = document\n): T | undefined {\n  return node.querySelector<T>(selector) || undefined\n}\n\n/**\n * Retrieve the currently active element\n *\n * @returns Element or nothing\n */\nexport function getActiveElement(): HTMLElement | undefined {\n  return (\n    document.activeElement?.shadowRoot?.activeElement as HTMLElement ??\n    document.activeElement as HTMLElement ??\n    undefined\n  )\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  Observable,\n  debounceTime,\n  distinctUntilChanged,\n  fromEvent,\n  map,\n  merge,\n  shareReplay,\n  startWith\n} from \"rxjs\"\n\nimport { getActiveElement } from \"../_\"\n\n/* ----------------------------------------------------------------------------\n * Data\n * ------------------------------------------------------------------------- */\n\n/**\n * Focus observable\n *\n * Previously, this observer used `focus` and `blur` events to determine whether\n * an element is focused, but this doesn't work if there are focusable elements\n * within the elements itself. A better solutions are `focusin` and `focusout`\n * events, which bubble up the tree and allow for more fine-grained control.\n *\n * `debounceTime` is necessary, because when a focus change happens inside an\n * element, the observable would first emit `false` and then `true` again.\n */\nconst observer$ = merge(\n  fromEvent(document.body, \"focusin\"),\n  fromEvent(document.body, \"focusout\")\n)\n  .pipe(\n    debounceTime(1),\n    startWith(undefined),\n    map(() => getActiveElement() || document.body),\n    shareReplay(1)\n  )\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Watch element focus\n *\n * @param el - Element\n *\n * @returns Element focus observable\n */\nexport function watchElementFocus(\n  el: HTMLElement\n): Observable<boolean> {\n  return observer$\n    .pipe(\n      map(active => el.contains(active)),\n      distinctUntilChanged()\n    )\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  Observable,\n  debounceTime,\n  fromEvent,\n  identity,\n  map,\n  merge,\n  startWith\n} from \"rxjs\"\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Watch element hover\n *\n * @param el - Element\n * @param duration - Debounce duration\n *\n * @returns Element hover observable\n */\nexport function watchElementHover(\n  el: HTMLElement, duration?: number\n): Observable<boolean> {\n  return merge(\n    fromEvent(el, \"mouseenter\").pipe(map(() => true)),\n    fromEvent(el, \"mouseleave\").pipe(map(() => false))\n  )\n    .pipe(\n      duration ? debounceTime(duration) : identity,\n      startWith(false)\n    )\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  Observable,\n  animationFrameScheduler,\n  auditTime,\n  fromEvent,\n  map,\n  merge,\n  startWith\n} from \"rxjs\"\n\n/* ----------------------------------------------------------------------------\n * Types\n * ------------------------------------------------------------------------- */\n\n/**\n * Element offset\n */\nexport interface ElementOffset {\n  x: number                            /* Horizontal offset */\n  y: number                            /* Vertical offset */\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Retrieve element offset\n *\n * @param el - Element\n *\n * @returns Element offset\n */\nexport function getElementOffset(\n  el: HTMLElement\n): ElementOffset {\n  return {\n    x: el.offsetLeft,\n    y: el.offsetTop\n  }\n}\n\n/* ------------------------------------------------------------------------- */\n\n/**\n * Watch element offset\n *\n * @param el - Element\n *\n * @returns Element offset observable\n */\nexport function watchElementOffset(\n  el: HTMLElement\n): Observable<ElementOffset> {\n  return merge(\n    fromEvent(window, \"load\"),\n    fromEvent(window, \"resize\")\n  )\n    .pipe(\n      auditTime(0, animationFrameScheduler),\n      map(() => getElementOffset(el)),\n      startWith(getElementOffset(el))\n    )\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  Observable,\n  animationFrameScheduler,\n  auditTime,\n  fromEvent,\n  map,\n  merge,\n  startWith\n} from \"rxjs\"\n\nimport { ElementOffset } from \"../_\"\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Retrieve element content offset (= scroll offset)\n *\n * @param el - Element\n *\n * @returns Element content offset\n */\nexport function getElementContentOffset(\n  el: HTMLElement\n): ElementOffset {\n  return {\n    x: el.scrollLeft,\n    y: el.scrollTop\n  }\n}\n\n/* ------------------------------------------------------------------------- */\n\n/**\n * Watch element content offset\n *\n * @param el - Element\n *\n * @returns Element content offset observable\n */\nexport function watchElementContentOffset(\n  el: HTMLElement\n): Observable<ElementOffset> {\n  return merge(\n    fromEvent(el, \"scroll\"),\n    fromEvent(window, \"resize\")\n  )\n    .pipe(\n      auditTime(0, animationFrameScheduler),\n      map(() => getElementContentOffset(el)),\n      startWith(getElementContentOffset(el))\n    )\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport { JSX as JSXInternal } from \"preact\"\n\n/* ----------------------------------------------------------------------------\n * Helper types\n * ------------------------------------------------------------------------- */\n\n/**\n * HTML attributes\n */\ntype Attributes =\n  & JSXInternal.HTMLAttributes\n  & JSXInternal.SVGAttributes\n  & Record<string, any>\n\n/**\n * Child element\n */\ntype Child =\n  | ChildNode\n  | HTMLElement\n  | Text\n  | string\n  | number\n\n/* ----------------------------------------------------------------------------\n * Helper functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Append a child node to an element\n *\n * @param el - Element\n * @param child - Child node(s)\n */\nfunction appendChild(el: HTMLElement, child: Child | Child[]): void {\n\n  /* Handle primitive types (including raw HTML) */\n  if (typeof child === \"string\" || typeof child === \"number\") {\n    el.innerHTML += child.toString()\n\n  /* Handle nodes */\n  } else if (child instanceof Node) {\n    el.appendChild(child)\n\n  /* Handle nested children */\n  } else if (Array.isArray(child)) {\n    for (const node of child)\n      appendChild(el, node)\n  }\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * JSX factory\n *\n * @template T - Element type\n *\n * @param tag - HTML tag\n * @param attributes - HTML attributes\n * @param children - Child elements\n *\n * @returns Element\n */\nexport function h<T extends keyof HTMLElementTagNameMap>(\n  tag: T, attributes?: Attributes | null, ...children: Child[]\n): HTMLElementTagNameMap[T]\n\nexport function h<T extends h.JSX.Element>(\n  tag: string, attributes?: Attributes | null, ...children: Child[]\n): T\n\nexport function h<T extends h.JSX.Element>(\n  tag: string, attributes?: Attributes | null, ...children: Child[]\n): T {\n  const el = document.createElement(tag)\n\n  /* Set attributes, if any */\n  if (attributes)\n    for (const attr of Object.keys(attributes)) {\n      if (typeof attributes[attr] === \"undefined\")\n        continue\n\n      /* Set default attribute or boolean */\n      if (typeof attributes[attr] !== \"boolean\")\n        el.setAttribute(attr, attributes[attr])\n      else\n        el.setAttribute(attr, \"\")\n    }\n\n  /* Append child nodes */\n  for (const child of children)\n    appendChild(el, child)\n\n  /* Return element */\n  return el as T\n}\n\n/* ----------------------------------------------------------------------------\n * Namespace\n * ------------------------------------------------------------------------- */\n\nexport declare namespace h {\n  namespace JSX {\n    type Element = HTMLElement\n    type IntrinsicElements = JSXInternal.IntrinsicElements\n  }\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Round a number for display with repository facts\n *\n * This is a reverse-engineered version of GitHub's weird rounding algorithm\n * for stars, forks and all other numbers. While all numbers below `1,000` are\n * returned as-is, bigger numbers are converted to fixed numbers:\n *\n * - `1,049` => `1k`\n * - `1,050` => `1.1k`\n * - `1,949` => `1.9k`\n * - `1,950` => `2k`\n *\n * @param value - Original value\n *\n * @returns Rounded value\n */\nexport function round(value: number): string {\n  if (value > 999) {\n    const digits = +((value - 950) % 1000 > 99)\n    return `${((value + 0.000001) / 1000).toFixed(digits)}k`\n  } else {\n    return value.toString()\n  }\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  Observable,\n  defer,\n  finalize,\n  fromEvent,\n  map,\n  merge,\n  switchMap,\n  take,\n  throwError\n} from \"rxjs\"\n\nimport { h } from \"~/utilities\"\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Create and load a `script` element\n *\n * This function returns an observable that will emit when the script was\n * successfully loaded, or throw an error if it wasn't.\n *\n * @param src - Script URL\n *\n * @returns Script observable\n */\nexport function watchScript(src: string): Observable<void> {\n  const script = h(\"script\", { src })\n  return defer(() => {\n    document.head.appendChild(script)\n    return merge(\n      fromEvent(script, \"load\"),\n      fromEvent(script, \"error\")\n        .pipe(\n          switchMap(() => (\n            throwError(() => new ReferenceError(`Invalid script: ${src}`))\n          ))\n        )\n    )\n      .pipe(\n        map(() => undefined),\n        finalize(() => document.head.removeChild(script)),\n        take(1)\n      )\n  })\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  NEVER,\n  Observable,\n  Subject,\n  defer,\n  filter,\n  finalize,\n  map,\n  merge,\n  of,\n  shareReplay,\n  startWith,\n  switchMap,\n  tap\n} from \"rxjs\"\n\nimport { watchScript } from \"../../../script\"\n\n/* ----------------------------------------------------------------------------\n * Types\n * ------------------------------------------------------------------------- */\n\n/**\n * Element offset\n */\nexport interface ElementSize {\n  width: number                        /* Element width */\n  height: number                       /* Element height */\n}\n\n/* ----------------------------------------------------------------------------\n * Data\n * ------------------------------------------------------------------------- */\n\n/**\n * Resize observer entry subject\n */\nconst entry$ = new Subject<ResizeObserverEntry>()\n\n/**\n * Resize observer observable\n *\n * This observable will create a `ResizeObserver` on the first subscription\n * and will automatically terminate it when there are no more subscribers.\n * It's quite important to centralize observation in a single `ResizeObserver`,\n * as the performance difference can be quite dramatic, as the link shows.\n *\n * If the browser doesn't have a `ResizeObserver` implementation available, a\n * polyfill is automatically downloaded from unpkg.com. This is also compatible\n * with the built-in privacy plugin, which will download the polyfill and put\n * it alongside the built site for self-hosting.\n *\n * @see https://bit.ly/3iIYfEm - Google Groups on performance\n */\nconst observer$ = defer(() => (\n  typeof ResizeObserver === \"undefined\"\n    ? watchScript(\"https://unpkg.com/resize-observer-polyfill\")\n    : of(undefined)\n))\n  .pipe(\n    map(() => new ResizeObserver(entries => {\n      for (const entry of entries)\n        entry$.next(entry)\n    })),\n    switchMap(observer => merge(NEVER, of(observer))\n      .pipe(\n        finalize(() => observer.disconnect())\n      )\n    ),\n    shareReplay(1)\n  )\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Retrieve element size\n *\n * @param el - Element\n *\n * @returns Element size\n */\nexport function getElementSize(\n  el: HTMLElement\n): ElementSize {\n  return {\n    width:  el.offsetWidth,\n    height: el.offsetHeight\n  }\n}\n\n/* ------------------------------------------------------------------------- */\n\n/**\n * Watch element size\n *\n * This function returns an observable that subscribes to a single internal\n * instance of `ResizeObserver` upon subscription, and emit resize events until\n * termination. Note that this function should not be called with the same\n * element twice, as the first unsubscription will terminate observation.\n *\n * Sadly, we can't use the `DOMRect` objects returned by the observer, because\n * we need the emitted values to be consistent with `getElementSize`, which will\n * return the used values (rounded) and not actual values (unrounded). Thus, we\n * use the `offset*` properties. See the linked GitHub issue.\n *\n * @see https://bit.ly/3m0k3he - GitHub issue\n *\n * @param el - Element\n *\n * @returns Element size observable\n */\nexport function watchElementSize(\n  el: HTMLElement\n): Observable<ElementSize> {\n  return observer$\n    .pipe(\n      tap(observer => observer.observe(el)),\n      switchMap(observer => entry$\n        .pipe(\n          filter(({ target }) => target === el),\n          finalize(() => observer.unobserve(el)),\n          map(() => getElementSize(el))\n        )\n      ),\n      startWith(getElementSize(el))\n    )\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport { ElementSize } from \"../_\"\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Retrieve element content size (= scroll width and height)\n *\n * @param el - Element\n *\n * @returns Element content size\n */\nexport function getElementContentSize(\n  el: HTMLElement\n): ElementSize {\n  return {\n    width:  el.scrollWidth,\n    height: el.scrollHeight\n  }\n}\n\n/**\n * Retrieve the overflowing container of an element, if any\n *\n * @param el - Element\n *\n * @returns Overflowing container or nothing\n */\nexport function getElementContainer(\n  el: HTMLElement\n): HTMLElement | undefined {\n  let parent = el.parentElement\n  while (parent)\n    if (\n      el.scrollWidth  <= parent.scrollWidth &&\n      el.scrollHeight <= parent.scrollHeight\n    )\n      parent = (el = parent).parentElement\n    else\n      break\n\n  /* Return overflowing container */\n  return parent ? el : undefined\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  NEVER,\n  Observable,\n  Subject,\n  defer,\n  distinctUntilChanged,\n  filter,\n  finalize,\n  map,\n  merge,\n  of,\n  shareReplay,\n  switchMap,\n  tap\n} from \"rxjs\"\n\nimport {\n  getElementContentSize,\n  getElementSize,\n  watchElementContentOffset\n} from \"~/browser\"\n\n/* ----------------------------------------------------------------------------\n * Data\n * ------------------------------------------------------------------------- */\n\n/**\n * Intersection observer entry subject\n */\nconst entry$ = new Subject<IntersectionObserverEntry>()\n\n/**\n * Intersection observer observable\n *\n * This observable will create an `IntersectionObserver` on first subscription\n * and will automatically terminate it when there are no more subscribers.\n *\n * @see https://bit.ly/3iIYfEm - Google Groups on performance\n */\nconst observer$ = defer(() => of(\n  new IntersectionObserver(entries => {\n    for (const entry of entries)\n      entry$.next(entry)\n  }, {\n    threshold: 0\n  })\n))\n  .pipe(\n    switchMap(observer => merge(NEVER, of(observer))\n      .pipe(\n        finalize(() => observer.disconnect())\n      )\n    ),\n    shareReplay(1)\n  )\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Watch element visibility\n *\n * @param el - Element\n *\n * @returns Element visibility observable\n */\nexport function watchElementVisibility(\n  el: HTMLElement\n): Observable<boolean> {\n  return observer$\n    .pipe(\n      tap(observer => observer.observe(el)),\n      switchMap(observer => entry$\n        .pipe(\n          filter(({ target }) => target === el),\n          finalize(() => observer.unobserve(el)),\n          map(({ isIntersecting }) => isIntersecting)\n        )\n      )\n    )\n}\n\n/**\n * Watch element boundary\n *\n * This function returns an observable which emits whether the bottom content\n * boundary (= scroll offset) of an element is within a certain threshold.\n *\n * @param el - Element\n * @param threshold - Threshold\n *\n * @returns Element boundary observable\n */\nexport function watchElementBoundary(\n  el: HTMLElement, threshold = 16\n): Observable<boolean> {\n  return watchElementContentOffset(el)\n    .pipe(\n      map(({ y }) => {\n        const visible = getElementSize(el)\n        const content = getElementContentSize(el)\n        return y >= (\n          content.height - visible.height - threshold\n        )\n      }),\n      distinctUntilChanged()\n    )\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  Observable,\n  fromEvent,\n  map,\n  startWith\n} from \"rxjs\"\n\nimport { getElement } from \"../element\"\n\n/* ----------------------------------------------------------------------------\n * Types\n * ------------------------------------------------------------------------- */\n\n/**\n * Toggle\n */\nexport type Toggle =\n  | \"drawer\"                           /* Toggle for drawer */\n  | \"search\"                           /* Toggle for search */\n\n/* ----------------------------------------------------------------------------\n * Data\n * ------------------------------------------------------------------------- */\n\n/**\n * Toggle map\n */\nconst toggles: Record<Toggle, HTMLInputElement> = {\n  drawer: getElement(\"[data-md-toggle=drawer]\"),\n  search: getElement(\"[data-md-toggle=search]\")\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Retrieve the value of a toggle\n *\n * @param name - Toggle\n *\n * @returns Toggle value\n */\nexport function getToggle(name: Toggle): boolean {\n  return toggles[name].checked\n}\n\n/**\n * Set toggle\n *\n * Simulating a click event seems to be the most cross-browser compatible way\n * of changing the value while also emitting a `change` event. Before, Material\n * used `CustomEvent` to programmatically change the value of a toggle, but this\n * is a much simpler and cleaner solution which doesn't require a polyfill.\n *\n * @param name - Toggle\n * @param value - Toggle value\n */\nexport function setToggle(name: Toggle, value: boolean): void {\n  if (toggles[name].checked !== value)\n    toggles[name].click()\n}\n\n/* ------------------------------------------------------------------------- */\n\n/**\n * Watch toggle\n *\n * @param name - Toggle\n *\n * @returns Toggle value observable\n */\nexport function watchToggle(name: Toggle): Observable<boolean> {\n  const el = toggles[name]\n  return fromEvent(el, \"change\")\n    .pipe(\n      map(() => el.checked),\n      startWith(el.checked)\n    )\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  EMPTY,\n  Observable,\n  filter,\n  fromEvent,\n  map,\n  merge,\n  share,\n  startWith,\n  switchMap\n} from \"rxjs\"\n\nimport { getActiveElement } from \"../element\"\nimport { getToggle } from \"../toggle\"\n\n/* ----------------------------------------------------------------------------\n * Types\n * ------------------------------------------------------------------------- */\n\n/**\n * Keyboard mode\n */\nexport type KeyboardMode =\n  | \"global\"                           /* Global */\n  | \"search\"                           /* Search is open */\n\n/* ------------------------------------------------------------------------- */\n\n/**\n * Keyboard\n */\nexport interface Keyboard {\n  mode: KeyboardMode                   /* Keyboard mode */\n  type: string                         /* Key type */\n  claim(): void                        /* Key claim */\n}\n\n/* ----------------------------------------------------------------------------\n * Helper functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Check whether an element may receive keyboard input\n *\n * @param el - Element\n * @param type - Key type\n *\n * @returns Test result\n */\nfunction isSusceptibleToKeyboard(\n  el: HTMLElement, type: string\n): boolean {\n  switch (el.constructor) {\n\n    /* Input elements */\n    case HTMLInputElement:\n      /* @ts-expect-error - omit unnecessary type cast */\n      if (el.type === \"radio\")\n        return /^Arrow/.test(type)\n      else\n        return true\n\n    /* Select element and textarea */\n    case HTMLSelectElement:\n    case HTMLTextAreaElement:\n      return true\n\n    /* Everything else */\n    default:\n      return el.isContentEditable\n  }\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Watch composition events\n *\n * @returns Composition observable\n */\nexport function watchComposition(): Observable<boolean> {\n  return merge(\n    fromEvent(window, \"compositionstart\").pipe(map(() => true)),\n    fromEvent(window, \"compositionend\").pipe(map(() => false))\n  )\n    .pipe(\n      startWith(false)\n    )\n}\n\n/**\n * Watch keyboard\n *\n * @returns Keyboard observable\n */\nexport function watchKeyboard(): Observable<Keyboard> {\n  const keyboard$ = fromEvent<KeyboardEvent>(window, \"keydown\")\n    .pipe(\n      filter(ev => !(ev.metaKey || ev.ctrlKey)),\n      map(ev => ({\n        mode: getToggle(\"search\") ? \"search\" : \"global\",\n        type: ev.key,\n        claim() {\n          ev.preventDefault()\n          ev.stopPropagation()\n        }\n      } as Keyboard)),\n      filter(({ mode, type }) => {\n        if (mode === \"global\") {\n          const active = getActiveElement()\n          if (typeof active !== \"undefined\")\n            return !isSusceptibleToKeyboard(active, type)\n        }\n        return true\n      }),\n      share()\n    )\n\n  /* Don't emit during composition events - see https://bit.ly/3te3Wl8 */\n  return watchComposition()\n    .pipe(\n      switchMap(active => !active ? keyboard$ : EMPTY)\n    )\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport { Subject } from \"rxjs\"\n\nimport { feature } from \"~/_\"\nimport { h } from \"~/utilities\"\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Retrieve location\n *\n * This function returns a `URL` object (and not `Location`) to normalize the\n * typings across the application. Furthermore, locations need to be tracked\n * without setting them and `Location` is a singleton which represents the\n * current location.\n *\n * @returns URL\n */\nexport function getLocation(): URL {\n  return new URL(location.href)\n}\n\n/**\n * Set location\n *\n * If instant navigation is enabled, this function creates a temporary anchor\n * element, sets the `href` attribute, appends it to the body, clicks it, and\n * then removes it again. The event will bubble up the DOM and trigger be\n * intercepted by the instant loading business logic.\n *\n * Note that we must append and remove the anchor element, or the event will\n * not bubble up the DOM, making it impossible to intercept it.\n *\n * @param url - URL to navigate to\n * @param navigate - Force navigation\n */\nexport function setLocation(\n  url: URL | HTMLLinkElement, navigate = false\n): void {\n  if (feature(\"navigation.instant\") && !navigate) {\n    const el = h(\"a\", { href: url.href })\n    document.body.appendChild(el)\n    el.click()\n    el.remove()\n\n  // If we're not using instant navigation, and the page should not be reloaded\n  // just instruct the browser to navigate to the given URL\n  } else {\n    location.href = url.href\n  }\n}\n\n/* ------------------------------------------------------------------------- */\n\n/**\n * Watch location\n *\n * @returns Location subject\n */\nexport function watchLocation(): Subject<URL> {\n  return new Subject<URL>()\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  Observable,\n  filter,\n  fromEvent,\n  map,\n  merge,\n  shareReplay,\n  startWith\n} from \"rxjs\"\n\nimport { getOptionalElement } from \"~/browser\"\nimport { h } from \"~/utilities\"\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Retrieve location hash\n *\n * @returns Location hash\n */\nexport function getLocationHash(): string {\n  return location.hash.slice(1)\n}\n\n/**\n * Set location hash\n *\n * Setting a new fragment identifier via `location.hash` will have no effect\n * if the value doesn't change. When a new fragment identifier is set, we want\n * the browser to target the respective element at all times, which is why we\n * use this dirty little trick.\n *\n * @param hash - Location hash\n */\nexport function setLocationHash(hash: string): void {\n  const el = h(\"a\", { href: hash })\n  el.addEventListener(\"click\", ev => ev.stopPropagation())\n  el.click()\n}\n\n/* ------------------------------------------------------------------------- */\n\n/**\n * Watch location hash\n *\n * @param location$ - Location observable\n *\n * @returns Location hash observable\n */\nexport function watchLocationHash(\n  location$: Observable<URL>\n): Observable<string> {\n  return merge(\n    fromEvent<HashChangeEvent>(window, \"hashchange\"),\n    location$\n  )\n    .pipe(\n      map(getLocationHash),\n      startWith(getLocationHash()),\n      filter(hash => hash.length > 0),\n      shareReplay(1)\n    )\n}\n\n/**\n * Watch location target\n *\n * @param location$ - Location observable\n *\n * @returns Location target observable\n */\nexport function watchLocationTarget(\n  location$: Observable<URL>\n): Observable<HTMLElement> {\n  return watchLocationHash(location$)\n    .pipe(\n      map(id => getOptionalElement(`[id=\"${id}\"]`)!),\n      filter(el => typeof el !== \"undefined\")\n    )\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  EMPTY,\n  Observable,\n  fromEvent,\n  fromEventPattern,\n  map,\n  merge,\n  startWith,\n  switchMap\n} from \"rxjs\"\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Watch media query\n *\n * Note that although `MediaQueryList.addListener` is deprecated we have to\n * use it, because it's the only way to ensure proper downward compatibility.\n *\n * @see https://bit.ly/3dUBH2m - GitHub issue\n *\n * @param query - Media query\n *\n * @returns Media observable\n */\nexport function watchMedia(query: string): Observable<boolean> {\n  const media = matchMedia(query)\n  return fromEventPattern<boolean>(next => (\n    media.addListener(() => next(media.matches))\n  ))\n    .pipe(\n      startWith(media.matches)\n    )\n}\n\n/**\n * Watch print mode\n *\n * @returns Print observable\n */\nexport function watchPrint(): Observable<boolean> {\n  const media = matchMedia(\"print\")\n  return merge(\n    fromEvent(window, \"beforeprint\").pipe(map(() => true)),\n    fromEvent(window, \"afterprint\").pipe(map(() => false))\n  )\n    .pipe(\n      startWith(media.matches)\n    )\n}\n\n/* ------------------------------------------------------------------------- */\n\n/**\n * Toggle an observable with a media observable\n *\n * @template T - Data type\n *\n * @param query$ - Media observable\n * @param factory - Observable factory\n *\n * @returns Toggled observable\n */\nexport function at<T>(\n  query$: Observable<boolean>, factory: () => Observable<T>\n): Observable<T> {\n  return query$\n    .pipe(\n      switchMap(active => active ? factory() : EMPTY)\n    )\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  Observable,\n  Subject,\n  map,\n  shareReplay,\n  switchMap\n} from \"rxjs\"\n\n/* ----------------------------------------------------------------------------\n * Helper types\n * ------------------------------------------------------------------------- */\n\n/**\n * Options\n */\ninterface Options {\n  progress$?: Subject<number>          // Progress subject\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Fetch the given URL\n *\n * This function returns an observable that emits the response as a blob and\n * completes, or emits an error if the request failed. The caller can cancel\n * the request by unsubscribing at any time, which will automatically abort\n * the inflight request and complete the observable.\n *\n * Note that we use `XMLHTTPRequest` not because we're nostalgic, but because\n * it's the only way to get progress events for downloads and also allow for\n * cancellation of requests, as the official Fetch API does not support this\n * yet, even though we're already in 2024.\n *\n * @param url - Request URL\n * @param options - Options\n *\n * @returns Data observable\n */\nexport function request(\n  url: URL | string, options?: Options\n): Observable<Blob> {\n  return new Observable<Blob>(observer => {\n    const req = new XMLHttpRequest()\n    req.open(\"GET\", `${url}`)\n    req.responseType = \"blob\"\n\n    // Handle response\n    req.addEventListener(\"load\", () => {\n      if (req.status >= 200 && req.status < 300) {\n        observer.next(req.response)\n        observer.complete()\n\n      // Every response that is not in the 2xx range is considered an error\n      } else {\n        observer.error(new Error(req.statusText))\n      }\n    })\n\n    // Handle network errors\n    req.addEventListener(\"error\", () => {\n      observer.error(new Error(\"Network error\"))\n    })\n\n    // Handle aborted requests\n    req.addEventListener(\"abort\", () => {\n      observer.complete()\n    })\n\n    // Handle download progress\n    if (typeof options?.progress$ !== \"undefined\") {\n      req.addEventListener(\"progress\", event => {\n        if (event.lengthComputable) {\n          options.progress$!.next((event.loaded / event.total) * 100)\n\n        // Hack: Chromium doesn't report the total number of bytes if content\n        // is compressed, so we need this fallback - see https://t.ly/ZXofI\n        } else {\n          const length = req.getResponseHeader(\"Content-Length\") ?? 0\n          options.progress$!.next((event.loaded / +length) * 100)\n        }\n      })\n\n      // Immediately set progress to 5% to indicate that we're loading\n      options.progress$.next(5)\n    }\n\n    // Send request and automatically abort request upon unsubscription\n    req.send()\n    return () => req.abort()\n  })\n}\n\n/* ------------------------------------------------------------------------- */\n\n/**\n * Fetch JSON from the given URL\n *\n * @template T - Data type\n *\n * @param url - Request URL\n * @param options - Options\n *\n * @returns Data observable\n */\nexport function requestJSON<T>(\n  url: URL | string, options?: Options\n): Observable<T> {\n  return request(url, options)\n    .pipe(\n      switchMap(res => res.text()),\n      map(body => JSON.parse(body) as T),\n      shareReplay(1)\n    )\n}\n\n/**\n * Fetch HTML from the given URL\n *\n * @param url - Request URL\n * @param options - Options\n *\n * @returns Data observable\n */\nexport function requestHTML(\n  url: URL | string, options?: Options\n): Observable<Document> {\n  const dom = new DOMParser()\n  return request(url, options)\n    .pipe(\n      switchMap(res => res.text()),\n      map(res => dom.parseFromString(res, \"text/html\")),\n      shareReplay(1)\n    )\n}\n\n/**\n * Fetch XML from the given URL\n *\n * @param url - Request URL\n * @param options - Options\n *\n * @returns Data observable\n */\nexport function requestXML(\n  url: URL | string, options?: Options\n): Observable<Document> {\n  const dom = new DOMParser()\n  return request(url, options)\n    .pipe(\n      switchMap(res => res.text()),\n      map(res => dom.parseFromString(res, \"text/xml\")),\n      shareReplay(1)\n    )\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  Observable,\n  fromEvent,\n  map,\n  merge,\n  startWith\n} from \"rxjs\"\n\n/* ----------------------------------------------------------------------------\n * Types\n * ------------------------------------------------------------------------- */\n\n/**\n * Viewport offset\n */\nexport interface ViewportOffset {\n  x: number                            /* Horizontal offset */\n  y: number                            /* Vertical offset */\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Retrieve viewport offset\n *\n * On iOS Safari, viewport offset can be negative due to overflow scrolling.\n * As this may induce strange behaviors downstream, we'll just limit it to 0.\n *\n * @returns Viewport offset\n */\nexport function getViewportOffset(): ViewportOffset {\n  return {\n    x: Math.max(0, scrollX),\n    y: Math.max(0, scrollY)\n  }\n}\n\n/* ------------------------------------------------------------------------- */\n\n/**\n * Watch viewport offset\n *\n * @returns Viewport offset observable\n */\nexport function watchViewportOffset(): Observable<ViewportOffset> {\n  return merge(\n    fromEvent(window, \"scroll\", { passive: true }),\n    fromEvent(window, \"resize\", { passive: true })\n  )\n    .pipe(\n      map(getViewportOffset),\n      startWith(getViewportOffset())\n    )\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  Observable,\n  fromEvent,\n  map,\n  startWith\n} from \"rxjs\"\n\n/* ----------------------------------------------------------------------------\n * Types\n * ------------------------------------------------------------------------- */\n\n/**\n * Viewport size\n */\nexport interface ViewportSize {\n  width: number                        /* Viewport width */\n  height: number                       /* Viewport height */\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Retrieve viewport size\n *\n * @returns Viewport size\n */\nexport function getViewportSize(): ViewportSize {\n  return {\n    width:  innerWidth,\n    height: innerHeight\n  }\n}\n\n/* ------------------------------------------------------------------------- */\n\n/**\n * Watch viewport size\n *\n * @returns Viewport size observable\n */\nexport function watchViewportSize(): Observable<ViewportSize> {\n  return fromEvent(window, \"resize\", { passive: true })\n    .pipe(\n      map(getViewportSize),\n      startWith(getViewportSize())\n    )\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  Observable,\n  combineLatest,\n  map,\n  shareReplay\n} from \"rxjs\"\n\nimport {\n  ViewportOffset,\n  watchViewportOffset\n} from \"../offset\"\nimport {\n  ViewportSize,\n  watchViewportSize\n} from \"../size\"\n\n/* ----------------------------------------------------------------------------\n * Types\n * ------------------------------------------------------------------------- */\n\n/**\n * Viewport\n */\nexport interface Viewport {\n  offset: ViewportOffset               /* Viewport offset */\n  size: ViewportSize                   /* Viewport size */\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Watch viewport\n *\n * @returns Viewport observable\n */\nexport function watchViewport(): Observable<Viewport> {\n  return combineLatest([\n    watchViewportOffset(),\n    watchViewportSize()\n  ])\n    .pipe(\n      map(([offset, size]) => ({ offset, size })),\n      shareReplay(1)\n    )\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  Observable,\n  combineLatest,\n  distinctUntilKeyChanged,\n  map\n} from \"rxjs\"\n\nimport { Header } from \"~/components\"\n\nimport { getElementOffset } from \"../../element\"\nimport { Viewport } from \"../_\"\n\n/* ----------------------------------------------------------------------------\n * Helper types\n * ------------------------------------------------------------------------- */\n\n/**\n * Watch options\n */\ninterface WatchOptions {\n  viewport$: Observable<Viewport>      /* Viewport observable */\n  header$: Observable<Header>          /* Header observable */\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Watch viewport relative to element\n *\n * @param el - Element\n * @param options - Options\n *\n * @returns Viewport observable\n */\nexport function watchViewportAt(\n  el: HTMLElement, { viewport$, header$ }: WatchOptions\n): Observable<Viewport> {\n  const size$ = viewport$\n    .pipe(\n      distinctUntilKeyChanged(\"size\")\n    )\n\n  /* Compute element offset */\n  const offset$ = combineLatest([size$, header$])\n    .pipe(\n      map(() => getElementOffset(el))\n    )\n\n  /* Compute relative viewport, return hot observable */\n  return combineLatest([header$, viewport$, offset$])\n    .pipe(\n      map(([{ height }, { offset, size }, { x, y }]) => ({\n        offset: {\n          x: offset.x - x,\n          y: offset.y - y + height\n        },\n        size\n      }))\n    )\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  Observable,\n  Subject,\n  endWith,\n  fromEvent,\n  ignoreElements,\n  mergeWith,\n  share,\n  takeUntil\n} from \"rxjs\"\n\n/* ----------------------------------------------------------------------------\n * Types\n * ------------------------------------------------------------------------- */\n\n/**\n * Worker message\n */\nexport interface WorkerMessage {\n  type: unknown                        /* Message type */\n  data?: unknown                       /* Message data */\n}\n\n/* ----------------------------------------------------------------------------\n * Helper functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Create an observable for receiving from a web worker\n *\n * @template T - Data type\n *\n * @param worker - Web worker\n *\n * @returns Message observable\n */\nfunction recv<T>(worker: Worker): Observable<T> {\n  return fromEvent<MessageEvent<T>, T>(worker, \"message\", ev => ev.data)\n}\n\n/**\n * Create a subject for sending to a web worker\n *\n * @template T - Data type\n *\n * @param worker - Web worker\n *\n * @returns Message subject\n */\nfunction send<T>(worker: Worker): Subject<T> {\n  const send$ = new Subject<T>()\n  send$.subscribe(data => worker.postMessage(data))\n\n  /* Return message subject */\n  return send$\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Create a bidirectional communication channel to a web worker\n *\n * @template T - Data type\n *\n * @param url - Worker URL\n * @param worker - Worker\n *\n * @returns Worker subject\n */\nexport function watchWorker<T extends WorkerMessage>(\n  url: string, worker = new Worker(url)\n): Subject<T> {\n  const recv$ = recv<T>(worker)\n  const send$ = send<T>(worker)\n\n  /* Create worker subject and forward messages */\n  const worker$ = new Subject<T>()\n  worker$.subscribe(send$)\n\n  /* Return worker subject */\n  const done$ = send$.pipe(ignoreElements(), endWith(true))\n  return worker$\n    .pipe(\n      ignoreElements(),\n      mergeWith(recv$.pipe(takeUntil(done$))),\n      share()\n    ) as Subject<T>\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport { getElement, getLocation } from \"~/browser\"\n\n/* ----------------------------------------------------------------------------\n * Types\n * ------------------------------------------------------------------------- */\n\n/**\n * Feature flag\n */\nexport type Flag =\n  | \"announce.dismiss\"                 /* Dismissable announcement bar */\n  | \"content.code.annotate\"            /* Code annotations */\n  | \"content.code.copy\"                /* Code copy button */\n  | \"content.lazy\"                     /* Lazy content elements */\n  | \"content.tabs.link\"                /* Link content tabs */\n  | \"content.tooltips\"                 /* Tooltips */\n  | \"header.autohide\"                  /* Hide header */\n  | \"navigation.expand\"                /* Automatic expansion */\n  | \"navigation.indexes\"               /* Section pages */\n  | \"navigation.instant\"               /* Instant navigation */\n  | \"navigation.instant.progress\"      /* Instant navigation progress */\n  | \"navigation.sections\"              /* Section navigation */\n  | \"navigation.tabs\"                  /* Tabs navigation */\n  | \"navigation.tabs.sticky\"           /* Tabs navigation (sticky) */\n  | \"navigation.top\"                   /* Back-to-top button */\n  | \"navigation.tracking\"              /* Anchor tracking */\n  | \"search.highlight\"                 /* Search highlighting */\n  | \"search.share\"                     /* Search sharing */\n  | \"search.suggest\"                   /* Search suggestions */\n  | \"toc.follow\"                       /* Following table of contents */\n  | \"toc.integrate\"                    /* Integrated table of contents */\n\n/* ------------------------------------------------------------------------- */\n\n/**\n * Translation\n */\nexport type Translation =\n  | \"clipboard.copy\"                   /* Copy to clipboard */\n  | \"clipboard.copied\"                 /* Copied to clipboard */\n  | \"search.result.placeholder\"        /* Type to start searching */\n  | \"search.result.none\"               /* No matching documents */\n  | \"search.result.one\"                /* 1 matching document */\n  | \"search.result.other\"              /* # matching documents */\n  | \"search.result.more.one\"           /* 1 more on this page */\n  | \"search.result.more.other\"         /* # more on this page */\n  | \"search.result.term.missing\"       /* Missing */\n  | \"select.version\"                   /* Version selector */\n\n/**\n * Translations\n */\nexport type Translations =\n  Record<Translation, string>\n\n/* ------------------------------------------------------------------------- */\n\n/**\n * Versioning\n */\nexport interface Versioning {\n  provider: \"mike\"                     /* Version provider */\n  default?: string | string[]          /* Default version */\n}\n\n/**\n * Configuration\n */\nexport interface Config {\n  base: string                         /* Base URL */\n  features: Flag[]                     /* Feature flags */\n  translations: Translations           /* Translations */\n  search: string                       /* Search worker URL */\n  tags?: Record<string, string>        /* Tags mapping */\n  version?: Versioning                 /* Versioning */\n}\n\n/* ----------------------------------------------------------------------------\n * Data\n * ------------------------------------------------------------------------- */\n\n/**\n * Retrieve global configuration and make base URL absolute\n */\nconst script = getElement(\"#__config\")\nconst config: Config = JSON.parse(script.textContent!)\nconfig.base = `${new URL(config.base, getLocation())}`\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Retrieve global configuration\n *\n * @returns Global configuration\n */\nexport function configuration(): Config {\n  return config\n}\n\n/**\n * Check whether a feature flag is enabled\n *\n * @param flag - Feature flag\n *\n * @returns Test result\n */\nexport function feature(flag: Flag): boolean {\n  return config.features.includes(flag)\n}\n\n/**\n * Retrieve the translation for the given key\n *\n * @param key - Key to be translated\n * @param value - Positional value, if any\n *\n * @returns Translation\n */\nexport function translation(\n  key: Translation, value?: string | number\n): string {\n  return typeof value !== \"undefined\"\n    ? config.translations[key].replace(\"#\", value.toString())\n    : config.translations[key]\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport { getElement, getElements } from \"~/browser\"\n\n/* ----------------------------------------------------------------------------\n * Types\n * ------------------------------------------------------------------------- */\n\n/**\n * Component type\n */\nexport type ComponentType =\n  | \"announce\"                         /* Announcement bar */\n  | \"container\"                        /* Container */\n  | \"consent\"                          /* Consent */\n  | \"content\"                          /* Content */\n  | \"dialog\"                           /* Dialog */\n  | \"header\"                           /* Header */\n  | \"header-title\"                     /* Header title */\n  | \"header-topic\"                     /* Header topic */\n  | \"main\"                             /* Main area */\n  | \"outdated\"                         /* Version warning */\n  | \"palette\"                          /* Color palette */\n  | \"progress\"                         /* Progress indicator */\n  | \"search\"                           /* Search */\n  | \"search-query\"                     /* Search input */\n  | \"search-result\"                    /* Search results */\n  | \"search-share\"                     /* Search sharing */\n  | \"search-suggest\"                   /* Search suggestions */\n  | \"sidebar\"                          /* Sidebar */\n  | \"skip\"                             /* Skip link */\n  | \"source\"                           /* Repository information */\n  | \"tabs\"                             /* Navigation tabs */\n  | \"toc\"                              /* Table of contents */\n  | \"top\"                              /* Back-to-top button */\n\n/**\n * Component\n *\n * @template T - Component type\n * @template U - Reference type\n */\nexport type Component<\n  T extends {} = {},\n  U extends HTMLElement = HTMLElement\n> =\n  T & {\n    ref: U                             /* Component reference */\n  }\n\n/* ----------------------------------------------------------------------------\n * Helper types\n * ------------------------------------------------------------------------- */\n\n/**\n * Component type map\n */\ninterface ComponentTypeMap {\n  \"announce\": HTMLElement              /* Announcement bar */\n  \"container\": HTMLElement             /* Container */\n  \"consent\": HTMLElement               /* Consent */\n  \"content\": HTMLElement               /* Content */\n  \"dialog\": HTMLElement                /* Dialog */\n  \"header\": HTMLElement                /* Header */\n  \"header-title\": HTMLElement          /* Header title */\n  \"header-topic\": HTMLElement          /* Header topic */\n  \"main\": HTMLElement                  /* Main area */\n  \"outdated\": HTMLElement              /* Version warning */\n  \"palette\": HTMLElement               /* Color palette */\n  \"progress\": HTMLElement              /* Progress indicator */\n  \"search\": HTMLElement                /* Search */\n  \"search-query\": HTMLInputElement     /* Search input */\n  \"search-result\": HTMLElement         /* Search results */\n  \"search-share\": HTMLAnchorElement    /* Search sharing */\n  \"search-suggest\": HTMLElement        /* Search suggestions */\n  \"sidebar\": HTMLElement               /* Sidebar */\n  \"skip\": HTMLAnchorElement            /* Skip link */\n  \"source\": HTMLAnchorElement          /* Repository information */\n  \"tabs\": HTMLElement                  /* Navigation tabs */\n  \"toc\": HTMLElement                   /* Table of contents */\n  \"top\": HTMLAnchorElement             /* Back-to-top button */\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Retrieve the element for a given component or throw a reference error\n *\n * @template T - Component type\n *\n * @param type - Component type\n * @param node - Node of reference\n *\n * @returns Element\n */\nexport function getComponentElement<T extends ComponentType>(\n  type: T, node: ParentNode = document\n): ComponentTypeMap[T] {\n  return getElement(`[data-md-component=${type}]`, node)\n}\n\n/**\n * Retrieve all elements for a given component\n *\n * @template T - Component type\n *\n * @param type - Component type\n * @param node - Node of reference\n *\n * @returns Elements\n */\nexport function getComponentElements<T extends ComponentType>(\n  type: T, node: ParentNode = document\n): ComponentTypeMap[T][] {\n  return getElements(`[data-md-component=${type}]`, node)\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  EMPTY,\n  Observable,\n  Subject,\n  defer,\n  finalize,\n  fromEvent,\n  map,\n  tap\n} from \"rxjs\"\n\nimport { feature } from \"~/_\"\nimport { getElement } from \"~/browser\"\n\nimport { Component } from \"../_\"\n\n/* ----------------------------------------------------------------------------\n * Types\n * ------------------------------------------------------------------------- */\n\n/**\n * Announcement bar\n */\nexport interface Announce {\n  hash: number                        /* Content hash */\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Watch announcement bar\n *\n * @param el - Announcement bar element\n *\n * @returns Announcement bar observable\n */\nexport function watchAnnounce(\n  el: HTMLElement\n): Observable<Announce> {\n  const button = getElement(\".md-typeset > :first-child\", el)\n  return fromEvent(button, \"click\", { once: true })\n    .pipe(\n      map(() => getElement(\".md-typeset\", el)),\n      map(content => ({ hash: __md_hash(content.innerHTML) }))\n    )\n}\n\n/**\n * Mount announcement bar\n *\n * @param el - Announcement bar element\n *\n * @returns Announcement bar component observable\n */\nexport function mountAnnounce(\n  el: HTMLElement\n): Observable<Component<Announce>> {\n  if (!feature(\"announce.dismiss\") || !el.childElementCount)\n    return EMPTY\n\n  /* Support instant navigation - see https://t.ly/3FTme */\n  if (!el.hidden) {\n    const content = getElement(\".md-typeset\", el)\n    if (__md_hash(content.innerHTML) === __md_get(\"__announce\"))\n      el.hidden = true\n  }\n\n  /* Mount component on subscription */\n  return defer(() => {\n    const push$ = new Subject<Announce>()\n    push$.subscribe(({ hash }) => {\n      el.hidden = true\n\n      /* Persist preference in local storage */\n      __md_set<number>(\"__announce\", hash)\n    })\n\n    /* Create and return component */\n    return watchAnnounce(el)\n      .pipe(\n        tap(state => push$.next(state)),\n        finalize(() => push$.complete()),\n        map(state => ({ ref: el, ...state }))\n      )\n  })\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  Observable,\n  Subject,\n  finalize,\n  map,\n  tap\n} from \"rxjs\"\n\nimport { Component } from \"../_\"\n\n/* ----------------------------------------------------------------------------\n * Types\n * ------------------------------------------------------------------------- */\n\n/**\n * Consent\n */\nexport interface Consent {\n  hidden: boolean                      /* Consent is hidden */\n}\n\n/**\n * Consent defaults\n */\nexport interface ConsentDefaults {\n  analytics?: boolean                  /* Consent for Analytics */\n  github?: boolean                     /* Consent for GitHub */\n}\n\n/* ----------------------------------------------------------------------------\n * Helper types\n * ------------------------------------------------------------------------- */\n\n/**\n * Watch options\n */\ninterface WatchOptions {\n  target$: Observable<HTMLElement>     /* Target observable */\n}\n\n/**\n * Mount options\n */\ninterface MountOptions {\n  target$: Observable<HTMLElement>     /* Target observable */\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Watch consent\n *\n * @param el - Consent element\n * @param options - Options\n *\n * @returns Consent observable\n */\nexport function watchConsent(\n  el: HTMLElement, { target$ }: WatchOptions\n): Observable<Consent> {\n  return target$\n    .pipe(\n      map(target => ({ hidden: target !== el }))\n    )\n}\n\n/* ------------------------------------------------------------------------- */\n\n/**\n * Mount consent\n *\n * @param el - Consent element\n * @param options - Options\n *\n * @returns Consent component observable\n */\nexport function mountConsent(\n  el: HTMLElement, options: MountOptions\n): Observable<Component<Consent>> {\n  const internal$ = new Subject<Consent>()\n  internal$.subscribe(({ hidden }) => {\n    el.hidden = hidden\n  })\n\n  /* Create and return component */\n  return watchConsent(el, options)\n    .pipe(\n      tap(state => internal$.next(state)),\n      finalize(() => internal$.complete()),\n      map(state => ({ ref: el, ...state }))\n    )\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport { h } from \"~/utilities\"\n\n/* ----------------------------------------------------------------------------\n * Types\n * ------------------------------------------------------------------------- */\n\n/**\n * Tooltip style\n */\nexport type TooltipStyle =\n  | \"inline\"\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Render a tooltip\n *\n * @param id - Tooltip identifier\n * @param style - Tooltip style\n *\n * @returns Element\n */\nexport function renderTooltip(\n  id?: string, style?: TooltipStyle\n): HTMLElement {\n  if (style === \"inline\") { // @todo refactor control flow\n    return (\n      <div class=\"md-tooltip md-tooltip--inline\" id={id} role=\"tooltip\">\n        <div class=\"md-tooltip__inner md-typeset\"></div>\n      </div>\n    )\n  } else {\n    return (\n      <div class=\"md-tooltip\" id={id} role=\"tooltip\">\n        <div class=\"md-tooltip__inner md-typeset\"></div>\n      </div>\n    )\n  }\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport { h } from \"~/utilities\"\n\nimport { renderTooltip } from \"../tooltip\"\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Render an annotation\n *\n * @param id - Annotation identifier\n * @param prefix - Tooltip identifier prefix\n *\n * @returns Element\n */\nexport function renderAnnotation(\n  id: string | number, prefix?: string\n): HTMLElement {\n  prefix = prefix ? `${prefix}_annotation_${id}` : undefined\n\n  /* Render tooltip with anchor, if given */\n  if (prefix) {\n    const anchor = prefix ? `#${prefix}` : undefined\n    return (\n      <aside class=\"md-annotation\" tabIndex={0}>\n        {renderTooltip(prefix)}\n        <a href={anchor} class=\"md-annotation__index\" tabIndex={-1}>\n          <span data-md-annotation-id={id}></span>\n        </a>\n      </aside>\n    )\n  } else {\n    return (\n      <aside class=\"md-annotation\" tabIndex={0}>\n        {renderTooltip(prefix)}\n        <span class=\"md-annotation__index\" tabIndex={-1}>\n          <span data-md-annotation-id={id}></span>\n        </span>\n      </aside>\n    )\n  }\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport { translation } from \"~/_\"\nimport { h } from \"~/utilities\"\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Render a 'copy-to-clipboard' button\n *\n * @param id - Unique identifier\n *\n * @returns Element\n */\nexport function renderClipboardButton(id: string): HTMLElement {\n  return (\n    <button\n      class=\"md-clipboard md-icon\"\n      title={translation(\"clipboard.copy\")}\n      data-clipboard-target={`#${id} > code`}\n    ></button>\n  )\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport { ComponentChild } from \"preact\"\n\nimport { configuration, feature, translation } from \"~/_\"\nimport { SearchItem } from \"~/integrations/search\"\nimport { h } from \"~/utilities\"\n\n/* ----------------------------------------------------------------------------\n * Helper types\n * ------------------------------------------------------------------------- */\n\n/**\n * Render flag\n */\nconst enum Flag {\n  TEASER = 1,                          /* Render teaser */\n  PARENT = 2                           /* Render as parent */\n}\n\n/* ----------------------------------------------------------------------------\n * Helper function\n * ------------------------------------------------------------------------- */\n\n/**\n * Render a search document\n *\n * @param document - Search document\n * @param flag - Render flags\n *\n * @returns Element\n */\nfunction renderSearchDocument(\n  document: SearchItem, flag: Flag\n): HTMLElement {\n  const parent = flag & Flag.PARENT\n  const teaser = flag & Flag.TEASER\n\n  /* Render missing query terms */\n  const missing = Object.keys(document.terms)\n    .filter(key => !document.terms[key])\n    .reduce<ComponentChild[]>((list, key) => [\n      ...list, <del>{key}</del>, \" \"\n    ], [])\n    .slice(0, -1)\n\n  /* Assemble query string for highlighting */\n  const config = configuration()\n  const url = new URL(document.location, config.base)\n  if (feature(\"search.highlight\"))\n    url.searchParams.set(\"h\", Object.entries(document.terms)\n      .filter(([, match]) => match)\n      .reduce((highlight, [value]) => `${highlight} ${value}`.trim(), \"\")\n    )\n\n  /* Render article or section, depending on flags */\n  const { tags } = configuration()\n  return (\n    <a href={`${url}`} class=\"md-search-result__link\" tabIndex={-1}>\n      <article\n        class=\"md-search-result__article md-typeset\"\n        data-md-score={document.score.toFixed(2)}\n      >\n        {parent > 0 && <div class=\"md-search-result__icon md-icon\"></div>}\n        {parent > 0 && <h1>{document.title}</h1>}\n        {parent <= 0 && <h2>{document.title}</h2>}\n        {teaser > 0 && document.text.length > 0 &&\n          document.text\n        }\n        {document.tags && document.tags.map(tag => {\n          const type = tags\n            ? tag in tags\n              ? `md-tag-icon md-tag--${tags[tag]}`\n              : \"md-tag-icon\"\n            : \"\"\n          return (\n            <span class={`md-tag ${type}`}>{tag}</span>\n          )\n        })}\n        {teaser > 0 && missing.length > 0 &&\n          <p class=\"md-search-result__terms\">\n            {translation(\"search.result.term.missing\")}: {...missing}\n          </p>\n        }\n      </article>\n    </a>\n  )\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Render a search result\n *\n * @param result - Search result\n *\n * @returns Element\n */\nexport function renderSearchResultItem(\n  result: SearchItem[]\n): HTMLElement {\n  const threshold = result[0].score\n  const docs = [...result]\n\n  const config = configuration()\n\n  /* Find and extract parent article */\n  const parent = docs.findIndex(doc => {\n    const l = `${new URL(doc.location, config.base)}` // @todo hacky\n    return !l.includes(\"#\")\n  })\n  const [article] = docs.splice(parent, 1)\n\n  /* Determine last index above threshold */\n  let index = docs.findIndex(doc => doc.score < threshold)\n  if (index === -1)\n    index = docs.length\n\n  /* Partition sections */\n  const best = docs.slice(0, index)\n  const more = docs.slice(index)\n\n  /* Render children */\n  const children = [\n    renderSearchDocument(article, Flag.PARENT | +(!parent && index === 0)),\n    ...best.map(section => renderSearchDocument(section, Flag.TEASER)),\n    ...more.length ? [\n      <details class=\"md-search-result__more\">\n        <summary tabIndex={-1}>\n          <div>\n            {more.length > 0 && more.length === 1\n              ? translation(\"search.result.more.one\")\n              : translation(\"search.result.more.other\", more.length)\n            }\n          </div>\n        </summary>\n        {...more.map(section => renderSearchDocument(section, Flag.TEASER))}\n      </details>\n    ] : []\n  ]\n\n  /* Render search result */\n  return (\n    <li class=\"md-search-result__item\">\n      {children}\n    </li>\n  )\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport { SourceFacts } from \"~/components\"\nimport { h, round } from \"~/utilities\"\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Render repository facts\n *\n * @param facts - Repository facts\n *\n * @returns Element\n */\nexport function renderSourceFacts(facts: SourceFacts): HTMLElement {\n  return (\n    <ul class=\"md-source__facts\">\n      {Object.entries(facts).map(([key, value]) => (\n        <li class={`md-source__fact md-source__fact--${key}`}>\n          {typeof value === \"number\" ? round(value) : value}\n        </li>\n      ))}\n    </ul>\n  )\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport { h } from \"~/utilities\"\n\n/* ----------------------------------------------------------------------------\n * Helper types\n * ------------------------------------------------------------------------- */\n\n/**\n * Tabbed control type\n */\ntype TabbedControlType =\n  | \"prev\"\n  | \"next\"\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Render control for content tabs\n *\n * @param type - Control type\n *\n * @returns Element\n */\nexport function renderTabbedControl(\n  type: TabbedControlType\n): HTMLElement {\n  const classes = `tabbed-control tabbed-control--${type}`\n  return (\n    <div class={classes} hidden>\n      <button class=\"tabbed-button\" tabIndex={-1} aria-hidden=\"true\"></button>\n    </div>\n  )\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport { h } from \"~/utilities\"\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Render a table inside a wrapper to improve scrolling on mobile\n *\n * @param table - Table element\n *\n * @returns Element\n */\nexport function renderTable(table: HTMLElement): HTMLElement {\n  return (\n    <div class=\"md-typeset__scrollwrap\">\n      <div class=\"md-typeset__table\">\n        {table}\n      </div>\n    </div>\n  )\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport { configuration, translation } from \"~/_\"\nimport { h } from \"~/utilities\"\n\n/* ----------------------------------------------------------------------------\n * Types\n * ------------------------------------------------------------------------- */\n\n/**\n * Version\n */\nexport interface Version {\n  version: string                      /* Version identifier */\n  title: string                        /* Version title */\n  aliases: string[]                    /* Version aliases */\n}\n\n/* ----------------------------------------------------------------------------\n * Helper functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Render a version\n *\n * @param version - Version\n *\n * @returns Element\n */\nfunction renderVersion(version: Version): HTMLElement {\n  const config = configuration()\n\n  /* Ensure trailing slash - see https://bit.ly/3rL5u3f */\n  const url = new URL(`../${version.version}/`, config.base)\n  return (\n    <li class=\"md-version__item\">\n      <a href={`${url}`} class=\"md-version__link\">\n        {version.title}\n      </a>\n    </li>\n  )\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Render a version selector\n *\n * @param versions - Versions\n * @param active - Active version\n *\n * @returns Element\n */\nexport function renderVersionSelector(\n  versions: Version[], active: Version\n): HTMLElement {\n  return (\n    <div class=\"md-version\">\n      <button\n        class=\"md-version__current\"\n        aria-label={translation(\"select.version\")}\n      >\n        {active.title}\n      </button>\n      <ul class=\"md-version__list\">\n        {versions.map(renderVersion)}\n      </ul>\n    </div>\n  )\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  EMPTY,\n  Observable,\n  Subject,\n  animationFrameScheduler,\n  asyncScheduler,\n  auditTime,\n  combineLatest,\n  debounceTime,\n  defer,\n  distinctUntilChanged,\n  filter,\n  finalize,\n  map,\n  merge,\n  of,\n  subscribeOn,\n  tap,\n  throttleTime\n} from \"rxjs\"\n\nimport {\n  ElementOffset,\n  getElement,\n  getElementContainer,\n  getElementOffset,\n  getElementSize,\n  watchElementContentOffset,\n  watchElementFocus,\n  watchElementHover\n} from \"~/browser\"\nimport { renderTooltip } from \"~/templates\"\n\nimport { Component } from \"../_\"\n\n/* ----------------------------------------------------------------------------\n * Types\n * ------------------------------------------------------------------------- */\n\n/**\n * Tooltip\n */\nexport interface Tooltip {\n  active: boolean                      /* Tooltip is active */\n  offset: ElementOffset                /* Tooltip offset */\n}\n\n/* ----------------------------------------------------------------------------\n * Data\n * ------------------------------------------------------------------------- */\n\n/**\n * Global sequence number for tooltips\n */\nlet sequence = 0\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Watch tooltip\n *\n * This function will append the tooltip temporarily to compute its width,\n * which is necessary for correct centering, and then removing it again.\n *\n * @param el - Tooltip element\n * @param host - Host element\n *\n * @returns Tooltip observable\n */\nexport function watchTooltip(\n  el: HTMLElement, host: HTMLElement\n): Observable<Tooltip> {\n  document.body.append(el)\n\n  /* Compute width and remove tooltip immediately */\n  const { width } = getElementSize(el)\n  el.style.setProperty(\"--md-tooltip-width\", `${width}px`)\n  el.remove()\n\n  /* Retrieve and watch containing element */\n  const container = getElementContainer(host)\n  const scroll$ =\n    typeof container !== \"undefined\"\n      ? watchElementContentOffset(container)\n      : of({ x: 0, y: 0 })\n\n  /* Compute tooltip visibility */\n  const active$ = merge(\n    watchElementFocus(host),\n    watchElementHover(host)\n  )\n    .pipe(\n      distinctUntilChanged()\n    )\n\n  /* Compute tooltip offset */\n  return combineLatest([active$, scroll$])\n    .pipe(\n      map(([active, scroll]) => {\n        let { x, y } = getElementOffset(host)\n        const size = getElementSize(host)\n\n        /**\n         * Experimental: fix handling of tables - see https://bit.ly/3TQEj5O\n         *\n         * If this proves to be a viable fix, we should refactor tooltip\n         * positioning and somehow streamline the current process. This might\n         * also fix positioning for annotations inside tables, which is another\n         * limitation.\n         */\n        const table = host.closest(\"table\")\n        if (table && host.parentElement) {\n          x += table.offsetLeft + host.parentElement.offsetLeft\n          y += table.offsetTop  + host.parentElement.offsetTop\n        }\n        return {\n          active,\n          offset: {\n            x: x - scroll.x + size.width  / 2 - width / 2,\n            y: y - scroll.y + size.height + 8\n          }\n        }\n      })\n    )\n}\n\n/**\n * Mount tooltip\n *\n * @param el - Host element\n *\n * @returns Tooltip component observable\n */\nexport function mountTooltip(\n  el: HTMLElement\n): Observable<Component<Tooltip>> {\n  const title = el.title\n  if (!title.length)\n    return EMPTY\n\n  /* Render tooltip and set title from host element */\n  const id = `__tooltip_${sequence++}`\n  const tooltip = renderTooltip(id, \"inline\")\n  const typeset = getElement(\".md-typeset\", tooltip)\n  typeset.innerHTML = title\n\n  /* Mount component on subscription */\n  return defer(() => {\n    const push$ = new Subject<Tooltip>()\n    push$.subscribe({\n\n      /* Handle emission */\n      next({ offset }) {\n        tooltip.style.setProperty(\"--md-tooltip-x\", `${offset.x}px`)\n        tooltip.style.setProperty(\"--md-tooltip-y\", `${offset.y}px`)\n      },\n\n      /* Handle complete */\n      complete() {\n        tooltip.style.removeProperty(\"--md-tooltip-x\")\n        tooltip.style.removeProperty(\"--md-tooltip-y\")\n      }\n    })\n\n    /* Toggle tooltip presence to mitigate empty lines when copying */\n    merge(\n      push$.pipe(filter(({ active }) => active)),\n      push$.pipe(debounceTime(250), filter(({ active }) => !active))\n    )\n      .subscribe({\n\n        /* Handle emission */\n        next({ active }) {\n          if (active) {\n            el.insertAdjacentElement(\"afterend\", tooltip)\n            el.setAttribute(\"aria-describedby\", id)\n            el.removeAttribute(\"title\")\n          } else {\n            tooltip.remove()\n            el.removeAttribute(\"aria-describedby\")\n            el.setAttribute(\"title\", title)\n          }\n        },\n\n        /* Handle complete */\n        complete() {\n          tooltip.remove()\n          el.removeAttribute(\"aria-describedby\")\n          el.setAttribute(\"title\", title)\n        }\n      })\n\n    /* Toggle tooltip visibility */\n    push$\n      .pipe(\n        auditTime(16, animationFrameScheduler)\n      )\n        .subscribe(({ active }) => {\n          tooltip.classList.toggle(\"md-tooltip--active\", active)\n        })\n\n    // @todo - refactor positioning together with annotations \u2013 there are\n    // several things that overlap and are identical in handling\n\n    /* Track relative origin of tooltip */\n    push$\n      .pipe(\n        throttleTime(125, animationFrameScheduler),\n        filter(() => !!el.offsetParent),\n        map(() => el.offsetParent!.getBoundingClientRect()),\n        map(({ x }) => x)\n      )\n      .subscribe({\n\n        /* Handle emission */\n        next(origin) {\n          if (origin)\n            tooltip.style.setProperty(\"--md-tooltip-0\", `${-origin}px`)\n          else\n            tooltip.style.removeProperty(\"--md-tooltip-0\")\n        },\n\n        /* Handle complete */\n        complete() {\n          tooltip.style.removeProperty(\"--md-tooltip-0\")\n        }\n      })\n\n    /* Create and return component */\n    return watchTooltip(tooltip, el)\n      .pipe(\n        tap(state => push$.next(state)),\n        finalize(() => push$.complete()),\n        map(state => ({ ref: el, ...state }))\n      )\n  })\n    .pipe(\n      subscribeOn(asyncScheduler)\n    )\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  Observable,\n  Subject,\n  animationFrameScheduler,\n  auditTime,\n  combineLatest,\n  debounceTime,\n  defer,\n  delay,\n  endWith,\n  filter,\n  finalize,\n  fromEvent,\n  ignoreElements,\n  map,\n  merge,\n  switchMap,\n  take,\n  takeUntil,\n  tap,\n  throttleTime,\n  withLatestFrom\n} from \"rxjs\"\n\nimport {\n  ElementOffset,\n  getActiveElement,\n  getElementSize,\n  watchElementContentOffset,\n  watchElementFocus,\n  watchElementOffset,\n  watchElementVisibility\n} from \"~/browser\"\n\nimport { Component } from \"../../../_\"\n\n/* ----------------------------------------------------------------------------\n * Types\n * ------------------------------------------------------------------------- */\n\n/**\n * Annotation\n */\nexport interface Annotation {\n  active: boolean                      /* Annotation is active */\n  offset: ElementOffset                /* Annotation offset */\n}\n\n/* ----------------------------------------------------------------------------\n * Helper types\n * ------------------------------------------------------------------------- */\n\n/**\n * Mount options\n */\ninterface MountOptions {\n  target$: Observable<HTMLElement>     /* Location target observable */\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Watch annotation\n *\n * @param el - Annotation element\n * @param container - Containing element\n *\n * @returns Annotation observable\n */\nexport function watchAnnotation(\n  el: HTMLElement, container: HTMLElement\n): Observable<Annotation> {\n  const offset$ = defer(() => combineLatest([\n    watchElementOffset(el),\n    watchElementContentOffset(container)\n  ]))\n    .pipe(\n      map(([{ x, y }, scroll]): ElementOffset => {\n        const { width, height } = getElementSize(el)\n        return ({\n          x: x - scroll.x + width  / 2,\n          y: y - scroll.y + height / 2\n        })\n      })\n    )\n\n  /* Actively watch annotation on focus */\n  return watchElementFocus(el)\n    .pipe(\n      switchMap(active => offset$\n        .pipe(\n          map(offset => ({ active, offset })),\n          take(+!active || Infinity)\n        )\n      )\n    )\n}\n\n/**\n * Mount annotation\n *\n * @param el - Annotation element\n * @param container - Containing element\n * @param options - Options\n *\n * @returns Annotation component observable\n */\nexport function mountAnnotation(\n  el: HTMLElement, container: HTMLElement, { target$ }: MountOptions\n): Observable<Component<Annotation>> {\n  const [tooltip, index] = Array.from(el.children)\n\n  /* Mount component on subscription */\n  return defer(() => {\n    const push$ = new Subject<Annotation>()\n    const done$ = push$.pipe(ignoreElements(), endWith(true))\n    push$.subscribe({\n\n      /* Handle emission */\n      next({ offset }) {\n        el.style.setProperty(\"--md-tooltip-x\", `${offset.x}px`)\n        el.style.setProperty(\"--md-tooltip-y\", `${offset.y}px`)\n      },\n\n      /* Handle complete */\n      complete() {\n        el.style.removeProperty(\"--md-tooltip-x\")\n        el.style.removeProperty(\"--md-tooltip-y\")\n      }\n    })\n\n    /* Start animation only when annotation is visible */\n    watchElementVisibility(el)\n      .pipe(\n        takeUntil(done$)\n      )\n        .subscribe(visible => {\n          el.toggleAttribute(\"data-md-visible\", visible)\n        })\n\n    /* Toggle tooltip presence to mitigate empty lines when copying */\n    merge(\n      push$.pipe(filter(({ active }) => active)),\n      push$.pipe(debounceTime(250), filter(({ active }) => !active))\n    )\n      .subscribe({\n\n        /* Handle emission */\n        next({ active }) {\n          if (active)\n            el.prepend(tooltip)\n          else\n            tooltip.remove()\n        },\n\n        /* Handle complete */\n        complete() {\n          el.prepend(tooltip)\n        }\n      })\n\n    /* Toggle tooltip visibility */\n    push$\n      .pipe(\n        auditTime(16, animationFrameScheduler)\n      )\n        .subscribe(({ active }) => {\n          tooltip.classList.toggle(\"md-tooltip--active\", active)\n        })\n\n    /* Track relative origin of tooltip */\n    push$\n      .pipe(\n        throttleTime(125, animationFrameScheduler),\n        filter(() => !!el.offsetParent),\n        map(() => el.offsetParent!.getBoundingClientRect()),\n        map(({ x }) => x)\n      )\n        .subscribe({\n\n          /* Handle emission */\n          next(origin) {\n            if (origin)\n              el.style.setProperty(\"--md-tooltip-0\", `${-origin}px`)\n            else\n              el.style.removeProperty(\"--md-tooltip-0\")\n          },\n\n          /* Handle complete */\n          complete() {\n            el.style.removeProperty(\"--md-tooltip-0\")\n          }\n        })\n\n    /* Allow to copy link without scrolling to anchor */\n    fromEvent<MouseEvent>(index, \"click\")\n      .pipe(\n        takeUntil(done$),\n        filter(ev => !(ev.metaKey || ev.ctrlKey))\n      )\n        .subscribe(ev => {\n          ev.stopPropagation()\n          ev.preventDefault()\n        })\n\n    /* Allow to open link in new tab or blur on close */\n    fromEvent<MouseEvent>(index, \"mousedown\")\n      .pipe(\n        takeUntil(done$),\n        withLatestFrom(push$)\n      )\n        .subscribe(([ev, { active }]) => {\n\n          /* Open in new tab */\n          if (ev.button !== 0 || ev.metaKey || ev.ctrlKey) {\n            ev.preventDefault()\n\n          /* Close annotation */\n          } else if (active) {\n            ev.preventDefault()\n\n            /* Focus parent annotation, if any */\n            const parent = el.parentElement!.closest(\".md-annotation\")\n            if (parent instanceof HTMLElement)\n              parent.focus()\n            else\n              getActiveElement()?.blur()\n          }\n        })\n\n    /* Open and focus annotation on location target */\n    target$\n      .pipe(\n        takeUntil(done$),\n        filter(target => target === tooltip),\n        delay(125)\n      )\n        .subscribe(() => el.focus())\n\n    /* Create and return component */\n    return watchAnnotation(el, container)\n      .pipe(\n        tap(state => push$.next(state)),\n        finalize(() => push$.complete()),\n        map(state => ({ ref: el, ...state }))\n      )\n  })\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  EMPTY,\n  Observable,\n  Subject,\n  defer,\n  endWith,\n  finalize,\n  ignoreElements,\n  merge,\n  share,\n  takeUntil\n} from \"rxjs\"\n\nimport {\n  getElement,\n  getElements,\n  getOptionalElement\n} from \"~/browser\"\nimport { renderAnnotation } from \"~/templates\"\n\nimport { Component } from \"../../../_\"\nimport {\n  Annotation,\n  mountAnnotation\n} from \"../_\"\n\n/* ----------------------------------------------------------------------------\n * Helper types\n * ------------------------------------------------------------------------- */\n\n/**\n * Mount options\n */\ninterface MountOptions {\n  target$: Observable<HTMLElement>     /* Location target observable */\n  print$: Observable<boolean>          /* Media print observable */\n}\n\n/* ----------------------------------------------------------------------------\n * Helper functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Find all annotation hosts in the containing element\n *\n * @param container - Containing element\n *\n * @returns Annotation hosts\n */\nfunction findHosts(container: HTMLElement): HTMLElement[] {\n  return container.tagName === \"CODE\"\n    ? getElements(\".c, .c1, .cm\", container)\n    : [container]\n}\n\n/**\n * Find all annotation markers in the containing element\n *\n * @param container - Containing element\n *\n * @returns Annotation markers\n */\nfunction findMarkers(container: HTMLElement): Text[] {\n  const markers: Text[] = []\n  for (const el of findHosts(container)) {\n    const nodes: Text[] = []\n\n    /* Find all text nodes in current element */\n    const it = document.createNodeIterator(el, NodeFilter.SHOW_TEXT)\n    for (let node = it.nextNode(); node; node = it.nextNode())\n      nodes.push(node as Text)\n\n    /* Find all markers in each text node */\n    for (let text of nodes) {\n      let match: RegExpExecArray | null\n\n      /* Split text at marker and add to list */\n      while ((match = /(\\(\\d+\\))(!)?/.exec(text.textContent!))) {\n        const [, id, force] = match\n        if (typeof force === \"undefined\") {\n          const marker = text.splitText(match.index)\n          text = marker.splitText(id.length)\n          markers.push(marker)\n\n        /* Replace entire text with marker */\n        } else {\n          text.textContent = id\n          markers.push(text)\n          break\n        }\n      }\n    }\n  }\n  return markers\n}\n\n/**\n * Swap the child nodes of two elements\n *\n * @param source - Source element\n * @param target - Target element\n */\nfunction swap(source: HTMLElement, target: HTMLElement): void {\n  target.append(...Array.from(source.childNodes))\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Mount annotation list\n *\n * This function analyzes the containing code block and checks for markers\n * referring to elements in the given annotation list. If no markers are found,\n * the list is left untouched. Otherwise, list elements are rendered as\n * annotations inside the code block.\n *\n * @param el - Annotation list element\n * @param container - Containing element\n * @param options - Options\n *\n * @returns Annotation component observable\n */\nexport function mountAnnotationList(\n  el: HTMLElement, container: HTMLElement, { target$, print$ }: MountOptions\n): Observable<Component<Annotation>> {\n\n  /* Compute prefix for tooltip anchors */\n  const parent = container.closest(\"[id]\")\n  const prefix = parent?.id\n\n  /* Find and replace all markers with empty annotations */\n  const annotations = new Map<string, HTMLElement>()\n  for (const marker of findMarkers(container)) {\n    const [, id] = marker.textContent!.match(/\\((\\d+)\\)/)!\n    if (getOptionalElement(`:scope > li:nth-child(${id})`, el)) {\n      annotations.set(id, renderAnnotation(id, prefix))\n      marker.replaceWith(annotations.get(id)!)\n    }\n  }\n\n  /* Keep list if there are no annotations to render */\n  if (annotations.size === 0)\n    return EMPTY\n\n  /* Mount component on subscription */\n  return defer(() => {\n    const push$ = new Subject()\n    const done$ = push$.pipe(ignoreElements(), endWith(true))\n\n    /* Retrieve container pairs for swapping */\n    const pairs: [HTMLElement, HTMLElement][] = []\n    for (const [id, annotation] of annotations)\n      pairs.push([\n        getElement(\".md-typeset\", annotation),\n        getElement(`:scope > li:nth-child(${id})`, el)\n      ])\n\n    /* Handle print mode - see https://bit.ly/3rgPdpt */\n    print$.pipe(takeUntil(done$))\n      .subscribe(active => {\n        el.hidden = !active\n\n        /* Add class to discern list element */\n        el.classList.toggle(\"md-annotation-list\", active)\n\n        /* Show annotations in code block or list (print) */\n        for (const [inner, child] of pairs)\n          if (!active)\n            swap(child, inner)\n          else\n            swap(inner, child)\n      })\n\n    /* Create and return component */\n    return merge(...[...annotations]\n      .map(([, annotation]) => (\n        mountAnnotation(annotation, container, { target$ })\n      ))\n    )\n      .pipe(\n        finalize(() => push$.complete()),\n        share()\n      )\n  })\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport { EMPTY, Observable, defer } from \"rxjs\"\n\nimport { Component } from \"../../../_\"\nimport { Annotation } from \"../_\"\nimport { mountAnnotationList } from \"../list\"\n\n/* ----------------------------------------------------------------------------\n * Helper types\n * ------------------------------------------------------------------------- */\n\n/**\n * Mount options\n */\ninterface MountOptions {\n  target$: Observable<HTMLElement>     /* Location target observable */\n  print$: Observable<boolean>          /* Media print observable */\n}\n\n/* ----------------------------------------------------------------------------\n * Helper functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Find list element directly following a block\n *\n * @param el - Annotation block element\n *\n * @returns List element or nothing\n */\nfunction findList(el: HTMLElement): HTMLElement | undefined {\n  if (el.nextElementSibling) {\n    const sibling = el.nextElementSibling as HTMLElement\n    if (sibling.tagName === \"OL\")\n      return sibling\n\n    /* Skip empty paragraphs - see https://bit.ly/3r4ZJ2O */\n    else if (sibling.tagName === \"P\" && !sibling.children.length)\n      return findList(sibling)\n  }\n\n  /* Everything else */\n  return undefined\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Mount annotation block\n *\n * @param el - Annotation block element\n * @param options - Options\n *\n * @returns Annotation component observable\n */\nexport function mountAnnotationBlock(\n  el: HTMLElement, options: MountOptions\n): Observable<Component<Annotation>> {\n  return defer(() => {\n    const list = findList(el)\n    return typeof list !== \"undefined\"\n      ? mountAnnotationList(list, el, options)\n      : EMPTY\n  })\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport ClipboardJS from \"clipboard\"\nimport {\n  EMPTY,\n  Observable,\n  Subject,\n  defer,\n  distinctUntilChanged,\n  distinctUntilKeyChanged,\n  filter,\n  finalize,\n  map,\n  mergeWith,\n  switchMap,\n  take,\n  takeLast,\n  takeUntil,\n  tap\n} from \"rxjs\"\n\nimport { feature } from \"~/_\"\nimport {\n  getElementContentSize,\n  watchElementSize,\n  watchElementVisibility\n} from \"~/browser\"\nimport { renderClipboardButton } from \"~/templates\"\n\nimport { Component } from \"../../../_\"\nimport {\n  Tooltip,\n  mountTooltip\n} from \"../../../tooltip\"\nimport {\n  Annotation,\n  mountAnnotationList\n} from \"../../annotation\"\n\n/* ----------------------------------------------------------------------------\n * Types\n * ------------------------------------------------------------------------- */\n\n/**\n * Code block overflow\n */\nexport interface Overflow {\n  scrollable: boolean                  /* Code block overflows */\n}\n\n/**\n * Code block\n */\nexport type CodeBlock =\n  | Overflow\n  | Annotation\n  | Tooltip\n\n/* ----------------------------------------------------------------------------\n * Helper types\n * ------------------------------------------------------------------------- */\n\n/**\n * Mount options\n */\ninterface MountOptions {\n  target$: Observable<HTMLElement>     /* Location target observable */\n  print$: Observable<boolean>          /* Media print observable */\n}\n\n/* ----------------------------------------------------------------------------\n * Data\n * ------------------------------------------------------------------------- */\n\n/**\n * Global sequence number for code blocks\n */\nlet sequence = 0\n\n/* ----------------------------------------------------------------------------\n * Helper functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Find candidate list element directly following a code block\n *\n * @param el - Code block element\n *\n * @returns List element or nothing\n */\nfunction findCandidateList(el: HTMLElement): HTMLElement | undefined {\n  if (el.nextElementSibling) {\n    const sibling = el.nextElementSibling as HTMLElement\n    if (sibling.tagName === \"OL\")\n      return sibling\n\n    /* Skip empty paragraphs - see https://bit.ly/3r4ZJ2O */\n    else if (sibling.tagName === \"P\" && !sibling.children.length)\n      return findCandidateList(sibling)\n  }\n\n  /* Everything else */\n  return undefined\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Watch code block\n *\n * This function monitors size changes of the viewport, as well as switches of\n * content tabs with embedded code blocks, as both may trigger overflow.\n *\n * @param el - Code block element\n *\n * @returns Code block observable\n */\nexport function watchCodeBlock(\n  el: HTMLElement\n): Observable<Overflow> {\n  return watchElementSize(el)\n    .pipe(\n      map(({ width }) => {\n        const content = getElementContentSize(el)\n        return {\n          scrollable: content.width > width\n        }\n      }),\n      distinctUntilKeyChanged(\"scrollable\")\n    )\n}\n\n/**\n * Mount code block\n *\n * This function ensures that an overflowing code block is focusable through\n * keyboard, so it can be scrolled without a mouse to improve on accessibility.\n * Furthermore, if code annotations are enabled, they are mounted if and only\n * if the code block is currently visible, e.g., not in a hidden content tab.\n *\n * Note that code blocks may be mounted eagerly or lazily. If they're mounted\n * lazily (on first visibility), code annotation anchor links will not work,\n * as they are evaluated on initial page load, and code annotations in general\n * might feel a little bumpier.\n *\n * @param el - Code block element\n * @param options - Options\n *\n * @returns Code block and annotation component observable\n */\nexport function mountCodeBlock(\n  el: HTMLElement, options: MountOptions\n): Observable<Component<CodeBlock>> {\n  const { matches: hover } = matchMedia(\"(hover)\")\n\n  /* Defer mounting of code block - see https://bit.ly/3vHVoVD */\n  const factory$ = defer(() => {\n    const push$ = new Subject<Overflow>()\n    const done$ = push$.pipe(takeLast(1))\n    push$.subscribe(({ scrollable }) => {\n      if (scrollable && hover)\n        el.setAttribute(\"tabindex\", \"0\")\n      else\n        el.removeAttribute(\"tabindex\")\n    })\n\n    /* Render button for Clipboard.js integration */\n    const content$: Array<Observable<Component<CodeBlock>>> = []\n    if (ClipboardJS.isSupported()) {\n      if (el.closest(\".copy\") || (\n        feature(\"content.code.copy\") && !el.closest(\".no-copy\")\n      )) {\n        const parent = el.closest(\"pre\")!\n        parent.id = `__code_${sequence++}`\n\n        /* Mount tooltip, if enabled */\n        const button = renderClipboardButton(parent.id)\n        parent.insertBefore(button, el)\n        if (feature(\"content.tooltips\"))\n          content$.push(mountTooltip(button))\n      }\n    }\n\n    /* Handle code annotations */\n    const container = el.closest(\".highlight\")\n    if (container instanceof HTMLElement) {\n      const list = findCandidateList(container)\n\n      /* Mount code annotations, if enabled */\n      if (typeof list !== \"undefined\" && (\n        container.classList.contains(\"annotate\") ||\n        feature(\"content.code.annotate\")\n      )) {\n        const annotations$ = mountAnnotationList(list, el, options)\n        content$.push(\n          watchElementSize(container)\n            .pipe(\n              takeUntil(done$),\n              map(({ width, height }) => width && height),\n              distinctUntilChanged(),\n              switchMap(active => active ? annotations$ : EMPTY)\n            )\n        )\n      }\n    }\n\n    /* Create and return component */\n    return watchCodeBlock(el)\n      .pipe(\n        tap(state => push$.next(state)),\n        finalize(() => push$.complete()),\n        map(state => ({ ref: el, ...state })),\n        mergeWith(...content$)\n      )\n  })\n\n  /* Mount code block lazily */\n  if (feature(\"content.lazy\"))\n    return watchElementVisibility(el)\n      .pipe(\n        filter(visible => visible),\n        take(1),\n        switchMap(() => factory$)\n      )\n\n  /* Mount code block */\n  return factory$\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  Observable,\n  Subject,\n  defer,\n  filter,\n  finalize,\n  map,\n  merge,\n  tap\n} from \"rxjs\"\n\nimport { Component } from \"../../_\"\n\n/* ----------------------------------------------------------------------------\n * Types\n * ------------------------------------------------------------------------- */\n\n/**\n * Details\n */\nexport interface Details {\n  action: \"open\" | \"close\"             /* Details state */\n  reveal?: boolean                     /* Details is revealed */\n}\n\n/* ----------------------------------------------------------------------------\n * Helper types\n * ------------------------------------------------------------------------- */\n\n/**\n * Watch options\n */\ninterface WatchOptions {\n  target$: Observable<HTMLElement>     /* Location target observable */\n  print$: Observable<boolean>          /* Media print observable */\n}\n\n/**\n * Mount options\n */\ninterface MountOptions {\n  target$: Observable<HTMLElement>     /* Location target observable */\n  print$: Observable<boolean>          /* Media print observable */\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Watch details\n *\n * @param el - Details element\n * @param options - Options\n *\n * @returns Details observable\n */\nexport function watchDetails(\n  el: HTMLDetailsElement, { target$, print$ }: WatchOptions\n): Observable<Details> {\n  let open = true\n  return merge(\n\n    /* Open and focus details on location target */\n    target$\n      .pipe(\n        map(target => target.closest(\"details:not([open])\")!),\n        filter(details => el === details),\n        map(() => ({\n          action: \"open\", reveal: true\n        }) as Details)\n      ),\n\n    /* Open details on print and close afterwards */\n    print$\n      .pipe(\n        filter(active => active || !open),\n        tap(() => open = el.open),\n        map(active => ({\n          action: active ? \"open\" : \"close\"\n        }) as Details)\n      )\n  )\n}\n\n/**\n * Mount details\n *\n * This function ensures that `details` tags are opened on anchor jumps and\n * prior to printing, so the whole content of the page is visible.\n *\n * @param el - Details element\n * @param options - Options\n *\n * @returns Details component observable\n */\nexport function mountDetails(\n  el: HTMLDetailsElement, options: MountOptions\n): Observable<Component<Details>> {\n  return defer(() => {\n    const push$ = new Subject<Details>()\n    push$.subscribe(({ action, reveal }) => {\n      el.toggleAttribute(\"open\", action === \"open\")\n      if (reveal)\n        el.scrollIntoView()\n    })\n\n    /* Create and return component */\n    return watchDetails(el, options)\n      .pipe(\n        tap(state => push$.next(state)),\n        finalize(() => push$.complete()),\n        map(state => ({ ref: el, ...state }))\n      )\n  })\n}\n", ".node circle,.node ellipse,.node path,.node polygon,.node rect{fill:var(--md-mermaid-node-bg-color);stroke:var(--md-mermaid-node-fg-color)}marker{fill:var(--md-mermaid-edge-color)!important}.edgeLabel .label rect{fill:#0000}.label{color:var(--md-mermaid-label-fg-color);font-family:var(--md-mermaid-font-family)}.label foreignObject{line-height:normal;overflow:visible}.label div .edgeLabel{color:var(--md-mermaid-label-fg-color)}.edgeLabel,.edgeLabel rect,.label div .edgeLabel{background-color:var(--md-mermaid-label-bg-color)}.edgeLabel,.edgeLabel rect{fill:var(--md-mermaid-label-bg-color);color:var(--md-mermaid-edge-color)}.edgePath .path,.flowchart-link{stroke:var(--md-mermaid-edge-color);stroke-width:.05rem}.edgePath .arrowheadPath{fill:var(--md-mermaid-edge-color);stroke:none}.cluster rect{fill:var(--md-default-fg-color--lightest);stroke:var(--md-default-fg-color--lighter)}.cluster span{color:var(--md-mermaid-label-fg-color);font-family:var(--md-mermaid-font-family)}g #flowchart-circleEnd,g #flowchart-circleStart,g #flowchart-crossEnd,g #flowchart-crossStart,g #flowchart-pointEnd,g #flowchart-pointStart{stroke:none}g.classGroup line,g.classGroup rect{fill:var(--md-mermaid-node-bg-color);stroke:var(--md-mermaid-node-fg-color)}g.classGroup text{fill:var(--md-mermaid-label-fg-color);font-family:var(--md-mermaid-font-family)}.classLabel .box{fill:var(--md-mermaid-label-bg-color);background-color:var(--md-mermaid-label-bg-color);opacity:1}.classLabel .label{fill:var(--md-mermaid-label-fg-color);font-family:var(--md-mermaid-font-family)}.node .divider{stroke:var(--md-mermaid-node-fg-color)}.relation{stroke:var(--md-mermaid-edge-color)}.cardinality{fill:var(--md-mermaid-label-fg-color);font-family:var(--md-mermaid-font-family)}.cardinality text{fill:inherit!important}defs #classDiagram-compositionEnd,defs #classDiagram-compositionStart,defs #classDiagram-dependencyEnd,defs #classDiagram-dependencyStart,defs #classDiagram-extensionEnd,defs #classDiagram-extensionStart{fill:var(--md-mermaid-edge-color)!important;stroke:var(--md-mermaid-edge-color)!important}defs #classDiagram-aggregationEnd,defs #classDiagram-aggregationStart{fill:var(--md-mermaid-label-bg-color)!important;stroke:var(--md-mermaid-edge-color)!important}g.stateGroup rect{fill:var(--md-mermaid-node-bg-color);stroke:var(--md-mermaid-node-fg-color)}g.stateGroup .state-title{fill:var(--md-mermaid-label-fg-color)!important;font-family:var(--md-mermaid-font-family)}g.stateGroup .composit{fill:var(--md-mermaid-label-bg-color)}.nodeLabel{color:var(--md-mermaid-label-fg-color);font-family:var(--md-mermaid-font-family)}.node circle.state-end,.node circle.state-start,.start-state{fill:var(--md-mermaid-edge-color);stroke:none}.end-state-inner,.end-state-outer{fill:var(--md-mermaid-edge-color)}.end-state-inner,.node circle.state-end{stroke:var(--md-mermaid-label-bg-color)}.transition{stroke:var(--md-mermaid-edge-color)}[id^=state-fork] rect,[id^=state-join] rect{fill:var(--md-mermaid-edge-color)!important;stroke:none!important}.statediagram-cluster.statediagram-cluster .inner{fill:var(--md-default-bg-color)}.statediagram-cluster rect{fill:var(--md-mermaid-node-bg-color);stroke:var(--md-mermaid-node-fg-color)}.statediagram-state rect.divider{fill:var(--md-default-fg-color--lightest);stroke:var(--md-default-fg-color--lighter)}defs #statediagram-barbEnd{stroke:var(--md-mermaid-edge-color)}.attributeBoxEven,.attributeBoxOdd{fill:var(--md-mermaid-node-bg-color);stroke:var(--md-mermaid-node-fg-color)}.entityBox{fill:var(--md-mermaid-label-bg-color);stroke:var(--md-mermaid-node-fg-color)}.entityLabel{fill:var(--md-mermaid-label-fg-color);font-family:var(--md-mermaid-font-family)}.relationshipLabelBox{fill:var(--md-mermaid-label-bg-color);fill-opacity:1;background-color:var(--md-mermaid-label-bg-color);opacity:1}.relationshipLabel{fill:var(--md-mermaid-label-fg-color)}.relationshipLine{stroke:var(--md-mermaid-edge-color)}defs #ONE_OR_MORE_END *,defs #ONE_OR_MORE_START *,defs #ONLY_ONE_END *,defs #ONLY_ONE_START *,defs #ZERO_OR_MORE_END *,defs #ZERO_OR_MORE_START *,defs #ZERO_OR_ONE_END *,defs #ZERO_OR_ONE_START *{stroke:var(--md-mermaid-edge-color)!important}defs #ZERO_OR_MORE_END circle,defs #ZERO_OR_MORE_START circle{fill:var(--md-mermaid-label-bg-color)}.actor{fill:var(--md-mermaid-sequence-actor-bg-color);stroke:var(--md-mermaid-sequence-actor-border-color)}text.actor>tspan{fill:var(--md-mermaid-sequence-actor-fg-color);font-family:var(--md-mermaid-font-family)}line{stroke:var(--md-mermaid-sequence-actor-line-color)}.actor-man circle,.actor-man line{fill:var(--md-mermaid-sequence-actorman-bg-color);stroke:var(--md-mermaid-sequence-actorman-line-color)}.messageLine0,.messageLine1{stroke:var(--md-mermaid-sequence-message-line-color)}.note{fill:var(--md-mermaid-sequence-note-bg-color);stroke:var(--md-mermaid-sequence-note-border-color)}.loopText,.loopText>tspan,.messageText,.noteText>tspan{stroke:none;font-family:var(--md-mermaid-font-family)!important}.messageText{fill:var(--md-mermaid-sequence-message-fg-color)}.loopText,.loopText>tspan{fill:var(--md-mermaid-sequence-loop-fg-color)}.noteText>tspan{fill:var(--md-mermaid-sequence-note-fg-color)}#arrowhead path{fill:var(--md-mermaid-sequence-message-line-color);stroke:none}.loopLine{fill:var(--md-mermaid-sequence-loop-bg-color);stroke:var(--md-mermaid-sequence-loop-border-color)}.labelBox{fill:var(--md-mermaid-sequence-label-bg-color);stroke:none}.labelText,.labelText>span{fill:var(--md-mermaid-sequence-label-fg-color);font-family:var(--md-mermaid-font-family)}.sequenceNumber{fill:var(--md-mermaid-sequence-number-fg-color)}rect.rect{fill:var(--md-mermaid-sequence-box-bg-color);stroke:none}rect.rect+text.text{fill:var(--md-mermaid-sequence-box-fg-color)}defs #sequencenumber{fill:var(--md-mermaid-sequence-number-bg-color)!important}", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  Observable,\n  map,\n  of,\n  shareReplay,\n  tap\n} from \"rxjs\"\n\nimport { watchScript } from \"~/browser\"\nimport { h } from \"~/utilities\"\n\nimport { Component } from \"../../_\"\n\nimport themeCSS from \"./index.css\"\n\n/* ----------------------------------------------------------------------------\n * Types\n * ------------------------------------------------------------------------- */\n\n/**\n * Mermaid diagram\n */\nexport interface Mermaid {}\n\n/* ----------------------------------------------------------------------------\n * Data\n * ------------------------------------------------------------------------- */\n\n/**\n * Mermaid instance observable\n */\nlet mermaid$: Observable<void>\n\n/**\n * Global sequence number for diagrams\n */\nlet sequence = 0\n\n/* ----------------------------------------------------------------------------\n * Helper functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Fetch Mermaid script\n *\n * @returns Mermaid scripts observable\n */\nfunction fetchScripts(): Observable<void> {\n  return typeof mermaid === \"undefined\" || mermaid instanceof Element\n    ? watchScript(\"https://unpkg.com/mermaid@10.7.0/dist/mermaid.min.js\")\n    : of(undefined)\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Mount Mermaid diagram\n *\n * @param el - Code block element\n *\n * @returns Mermaid diagram component observable\n */\nexport function mountMermaid(\n  el: HTMLElement\n): Observable<Component<Mermaid>> {\n  el.classList.remove(\"mermaid\") // Hack: mitigate https://bit.ly/3CiN6Du\n  mermaid$ ||= fetchScripts()\n    .pipe(\n      tap(() => mermaid.initialize({\n        startOnLoad: false,\n        themeCSS,\n        sequence: {\n          actorFontSize: \"16px\", // Hack: mitigate https://bit.ly/3y0NEi3\n          messageFontSize: \"16px\",\n          noteFontSize: \"16px\"\n        }\n      })),\n      map(() => undefined),\n      shareReplay(1)\n    )\n\n  /* Render diagram */\n  mermaid$.subscribe(async () => {\n    el.classList.add(\"mermaid\") // Hack: mitigate https://bit.ly/3CiN6Du\n    const id = `__mermaid_${sequence++}`\n\n    /* Create host element to replace code block */\n    const host = h(\"div\", { class: \"mermaid\" })\n    const text = el.textContent\n\n    /* Render and inject diagram */\n    const { svg, fn } = await mermaid.render(id, text)\n\n    /* Create a shadow root and inject diagram */\n    const shadow = host.attachShadow({ mode: \"closed\" })\n    shadow.innerHTML = svg\n\n    /* Replace code block with diagram and bind functions */\n    el.replaceWith(host)\n    fn?.(shadow)\n  })\n\n  /* Create and return component */\n  return mermaid$\n    .pipe(\n      map(() => ({ ref: el }))\n    )\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport { Observable, of } from \"rxjs\"\n\nimport { renderTable } from \"~/templates\"\nimport { h } from \"~/utilities\"\n\nimport { Component } from \"../../_\"\n\n/* ----------------------------------------------------------------------------\n * Types\n * ------------------------------------------------------------------------- */\n\n/**\n * Data table\n */\nexport interface DataTable {}\n\n/* ----------------------------------------------------------------------------\n * Data\n * ------------------------------------------------------------------------- */\n\n/**\n * Sentinel for replacement\n */\nconst sentinel = h(\"table\")\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Mount data table\n *\n * This function wraps a data table in another scrollable container, so it can\n * be smoothly scrolled on smaller screen sizes and won't break the layout.\n *\n * @param el - Data table element\n *\n * @returns Data table component observable\n */\nexport function mountDataTable(\n  el: HTMLElement\n): Observable<Component<DataTable>> {\n  el.replaceWith(sentinel)\n  sentinel.replaceWith(renderTable(el))\n\n  /* Create and return component */\n  return of({ ref: el })\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  Observable,\n  Subject,\n  animationFrameScheduler,\n  asyncScheduler,\n  auditTime,\n  combineLatest,\n  defer,\n  endWith,\n  filter,\n  finalize,\n  fromEvent,\n  ignoreElements,\n  map,\n  merge,\n  skip,\n  startWith,\n  subscribeOn,\n  takeUntil,\n  tap,\n  withLatestFrom\n} from \"rxjs\"\n\nimport { feature } from \"~/_\"\nimport {\n  Viewport,\n  getElement,\n  getElementContentOffset,\n  getElementContentSize,\n  getElementOffset,\n  getElementSize,\n  getElements,\n  watchElementContentOffset,\n  watchElementSize\n} from \"~/browser\"\nimport { renderTabbedControl } from \"~/templates\"\nimport { h } from \"~/utilities\"\n\nimport { Component } from \"../../_\"\n\n/* ----------------------------------------------------------------------------\n * Types\n * ------------------------------------------------------------------------- */\n\n/**\n * Content tabs\n */\nexport interface ContentTabs {\n  active: HTMLLabelElement             /* Active tab label */\n}\n\n/* ----------------------------------------------------------------------------\n * Helper types\n * ------------------------------------------------------------------------- */\n\n/**\n * Mount options\n */\ninterface MountOptions {\n  viewport$: Observable<Viewport>      /* Viewport observable */\n  target$: Observable<HTMLElement>     /* Location target observable */\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Watch content tabs\n *\n * @param inputs - Content tabs input elements\n *\n * @returns Content tabs observable\n */\nexport function watchContentTabs(\n  inputs: HTMLInputElement[]\n): Observable<ContentTabs> {\n  const initial = inputs.find(input => input.checked) || inputs[0]\n  return merge(...inputs.map(input => fromEvent(input, \"change\")\n    .pipe(\n      map(() => getElement<HTMLLabelElement>(`label[for=\"${input.id}\"]`))\n    )\n  ))\n    .pipe(\n      startWith(getElement<HTMLLabelElement>(`label[for=\"${initial.id}\"]`)),\n      map(active => ({ active }))\n    )\n}\n\n/**\n * Mount content tabs\n *\n * @param el - Content tabs element\n * @param options - Options\n *\n * @returns Content tabs component observable\n */\nexport function mountContentTabs(\n  el: HTMLElement, { viewport$, target$ }: MountOptions\n): Observable<Component<ContentTabs>> {\n  const container = getElement(\".tabbed-labels\", el)\n  const inputs = getElements<HTMLInputElement>(\":scope > input\", el)\n\n  /* Render content tab previous button for pagination */\n  const prev = renderTabbedControl(\"prev\")\n  el.append(prev)\n\n  /* Render content tab next button for pagination */\n  const next = renderTabbedControl(\"next\")\n  el.append(next)\n\n  /* Mount component on subscription */\n  return defer(() => {\n    const push$ = new Subject<ContentTabs>()\n    const done$ = push$.pipe(ignoreElements(), endWith(true))\n    combineLatest([push$, watchElementSize(el)])\n      .pipe(\n        takeUntil(done$),\n        auditTime(1, animationFrameScheduler)\n      )\n        .subscribe({\n\n          /* Handle emission */\n          next([{ active }, size]) {\n            const offset = getElementOffset(active)\n            const { width } = getElementSize(active)\n\n            /* Set tab indicator offset and width */\n            el.style.setProperty(\"--md-indicator-x\", `${offset.x}px`)\n            el.style.setProperty(\"--md-indicator-width\", `${width}px`)\n\n            /* Scroll container to active content tab */\n            const content = getElementContentOffset(container)\n            if (\n              offset.x         < content.x              ||\n              offset.x + width > content.x + size.width\n            )\n              container.scrollTo({\n                left: Math.max(0, offset.x - 16),\n                behavior: \"smooth\"\n              })\n          },\n\n          /* Handle complete */\n          complete() {\n            el.style.removeProperty(\"--md-indicator-x\")\n            el.style.removeProperty(\"--md-indicator-width\")\n          }\n        })\n\n    /* Hide content tab buttons on borders */\n    combineLatest([\n      watchElementContentOffset(container),\n      watchElementSize(container)\n    ])\n      .pipe(\n        takeUntil(done$)\n      )\n        .subscribe(([offset, size]) => {\n          const content = getElementContentSize(container)\n          prev.hidden = offset.x < 16\n          next.hidden = offset.x > content.width - size.width - 16\n        })\n\n    /* Paginate content tab container on click */\n    merge(\n      fromEvent(prev, \"click\").pipe(map(() => -1)),\n      fromEvent(next, \"click\").pipe(map(() => +1))\n    )\n      .pipe(\n        takeUntil(done$)\n      )\n        .subscribe(direction => {\n          const { width } = getElementSize(container)\n          container.scrollBy({\n            left: width * direction,\n            behavior: \"smooth\"\n          })\n        })\n\n    /* Switch to content tab target */\n    target$\n      .pipe(\n        takeUntil(done$),\n        filter(input => inputs.includes(input as HTMLInputElement))\n      )\n        .subscribe(input => input.click())\n\n    /* Add link to each content tab label */\n    container.classList.add(\"tabbed-labels--linked\")\n    for (const input of inputs) {\n      const label = getElement<HTMLLabelElement>(`label[for=\"${input.id}\"]`)\n      label.replaceChildren(h(\"a\", {\n        href: `#${label.htmlFor}`,\n        tabIndex: -1\n      }, ...Array.from(label.childNodes)))\n\n      /* Allow to copy link without scrolling to anchor */\n      fromEvent<MouseEvent>(label.firstElementChild!, \"click\")\n        .pipe(\n          takeUntil(done$),\n          filter(ev => !(ev.metaKey || ev.ctrlKey)),\n          tap(ev => {\n            ev.preventDefault()\n            ev.stopPropagation()\n          })\n        )\n          // @todo we might need to remove the anchor link on complete\n          .subscribe(() => {\n            history.replaceState({}, \"\", `#${label.htmlFor}`)\n            label.click()\n          })\n    }\n\n    /* Set up linking of content tabs, if enabled */\n    if (feature(\"content.tabs.link\"))\n      push$.pipe(\n        skip(1),\n        withLatestFrom(viewport$)\n      )\n        .subscribe(([{ active }, { offset }]) => {\n          const tab = active.innerText.trim()\n          if (active.hasAttribute(\"data-md-switching\")) {\n            active.removeAttribute(\"data-md-switching\")\n\n          /* Determine viewport offset of active tab */\n          } else {\n            const y = el.offsetTop - offset.y\n\n            /* Passively activate other tabs */\n            for (const set of getElements(\"[data-tabs]\"))\n              for (const input of getElements<HTMLInputElement>(\n                \":scope > input\", set\n              )) {\n                const label = getElement(`label[for=\"${input.id}\"]`)\n                if (\n                  label !== active &&\n                  label.innerText.trim() === tab\n                ) {\n                  label.setAttribute(\"data-md-switching\", \"\")\n                  input.click()\n                  break\n                }\n              }\n\n            /* Bring active tab into view */\n            window.scrollTo({\n              top: el.offsetTop - y\n            })\n\n            /* Persist active tabs in local storage */\n            const tabs = __md_get<string[]>(\"__tabs\") || []\n            __md_set(\"__tabs\", [...new Set([tab, ...tabs])])\n          }\n        })\n\n    /* Pause media (audio, video) on switch - see https://bit.ly/3Bk6cel */\n    push$.pipe(takeUntil(done$))\n      .subscribe(() => {\n        for (const media of getElements<HTMLAudioElement>(\"audio, video\", el))\n          media.pause()\n      })\n\n    /* Create and return component */\n    return watchContentTabs(inputs)\n      .pipe(\n        tap(state => push$.next(state)),\n        finalize(() => push$.complete()),\n        map(state => ({ ref: el, ...state }))\n      )\n  })\n    .pipe(\n      subscribeOn(asyncScheduler)\n    )\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport { Observable, merge } from \"rxjs\"\n\nimport { feature } from \"~/_\"\nimport { Viewport, getElements } from \"~/browser\"\n\nimport { Component } from \"../../_\"\nimport {\n  Tooltip,\n  mountTooltip\n} from \"../../tooltip\"\nimport {\n  Annotation,\n  mountAnnotationBlock\n} from \"../annotation\"\nimport {\n  CodeBlock,\n  mountCodeBlock\n} from \"../code\"\nimport {\n  Details,\n  mountDetails\n} from \"../details\"\nimport {\n  Mermaid,\n  mountMermaid\n} from \"../mermaid\"\nimport {\n  DataTable,\n  mountDataTable\n} from \"../table\"\nimport {\n  ContentTabs,\n  mountContentTabs\n} from \"../tabs\"\n\n/* ----------------------------------------------------------------------------\n * Types\n * ------------------------------------------------------------------------- */\n\n/**\n * Content\n */\nexport type Content =\n  | Annotation\n  | CodeBlock\n  | ContentTabs\n  | DataTable\n  | Details\n  | Mermaid\n  | Tooltip\n\n/* ----------------------------------------------------------------------------\n * Helper types\n * ------------------------------------------------------------------------- */\n\n/**\n * Mount options\n */\ninterface MountOptions {\n  viewport$: Observable<Viewport>      /* Viewport observable */\n  target$: Observable<HTMLElement>     /* Location target observable */\n  print$: Observable<boolean>          /* Media print observable */\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Mount content\n *\n * This function mounts all components that are found in the content of the\n * actual article, including code blocks, data tables and details.\n *\n * @param el - Content element\n * @param options - Options\n *\n * @returns Content component observable\n */\nexport function mountContent(\n  el: HTMLElement, { viewport$, target$, print$ }: MountOptions\n): Observable<Component<Content>> {\n  return merge(\n\n    /* Annotations */\n    ...getElements(\".annotate:not(.highlight)\", el)\n      .map(child => mountAnnotationBlock(child, { target$, print$ })),\n\n    /* Code blocks */\n    ...getElements(\"pre:not(.mermaid) > code\", el)\n      .map(child => mountCodeBlock(child, { target$, print$ })),\n\n    /* Mermaid diagrams */\n    ...getElements(\"pre.mermaid\", el)\n      .map(child => mountMermaid(child)),\n\n    /* Data tables */\n    ...getElements(\"table:not([class])\", el)\n      .map(child => mountDataTable(child)),\n\n    /* Details */\n    ...getElements(\"details\", el)\n      .map(child => mountDetails(child, { target$, print$ })),\n\n    /* Content tabs */\n    ...getElements(\"[data-tabs]\", el)\n      .map(child => mountContentTabs(child, { viewport$, target$ })),\n\n    /* Tooltips */\n    ...getElements(\"[title]\", el)\n      .filter(() => feature(\"content.tooltips\"))\n      .map(child => mountTooltip(child))\n  )\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  Observable,\n  Subject,\n  defer,\n  delay,\n  finalize,\n  map,\n  merge,\n  of,\n  switchMap,\n  tap\n} from \"rxjs\"\n\nimport { getElement } from \"~/browser\"\n\nimport { Component } from \"../_\"\n\n/* ----------------------------------------------------------------------------\n * Types\n * ------------------------------------------------------------------------- */\n\n/**\n * Dialog\n */\nexport interface Dialog {\n  message: string                      /* Dialog message */\n  active: boolean                      /* Dialog is active */\n}\n\n/* ----------------------------------------------------------------------------\n * Helper types\n * ------------------------------------------------------------------------- */\n\n/**\n * Watch options\n */\ninterface WatchOptions {\n  alert$: Subject<string>              /* Alert subject */\n}\n\n/**\n * Mount options\n */\ninterface MountOptions {\n  alert$: Subject<string>              /* Alert subject */\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Watch dialog\n *\n * @param _el - Dialog element\n * @param options - Options\n *\n * @returns Dialog observable\n */\nexport function watchDialog(\n  _el: HTMLElement, { alert$ }: WatchOptions\n): Observable<Dialog> {\n  return alert$\n    .pipe(\n      switchMap(message => merge(\n        of(true),\n        of(false).pipe(delay(2000))\n      )\n        .pipe(\n          map(active => ({ message, active }))\n        )\n      )\n    )\n}\n\n/**\n * Mount dialog\n *\n * This function reveals the dialog in the right corner when a new alert is\n * emitted through the subject that is passed as part of the options.\n *\n * @param el - Dialog element\n * @param options - Options\n *\n * @returns Dialog component observable\n */\nexport function mountDialog(\n  el: HTMLElement, options: MountOptions\n): Observable<Component<Dialog>> {\n  const inner = getElement(\".md-typeset\", el)\n  return defer(() => {\n    const push$ = new Subject<Dialog>()\n    push$.subscribe(({ message, active }) => {\n      el.classList.toggle(\"md-dialog--active\", active)\n      inner.textContent = message\n    })\n\n    /* Create and return component */\n    return watchDialog(el, options)\n      .pipe(\n        tap(state => push$.next(state)),\n        finalize(() => push$.complete()),\n        map(state => ({ ref: el, ...state }))\n      )\n  })\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  Observable,\n  Subject,\n  bufferCount,\n  combineLatest,\n  combineLatestWith,\n  defer,\n  distinctUntilChanged,\n  distinctUntilKeyChanged,\n  endWith,\n  filter,\n  from,\n  ignoreElements,\n  map,\n  mergeMap,\n  mergeWith,\n  of,\n  shareReplay,\n  startWith,\n  switchMap,\n  takeUntil\n} from \"rxjs\"\n\nimport { feature } from \"~/_\"\nimport {\n  Viewport,\n  getElements,\n  watchElementSize,\n  watchToggle\n} from \"~/browser\"\n\nimport { Component } from \"../../_\"\nimport { Main } from \"../../main\"\nimport {\n  Tooltip,\n  mountTooltip\n} from \"../../tooltip\"\n\n/* ----------------------------------------------------------------------------\n * Types\n * ------------------------------------------------------------------------- */\n\n/**\n * Header\n */\nexport interface Header {\n  height: number                       /* Header visible height */\n  hidden: boolean                      /* Header is hidden */\n}\n\n/* ----------------------------------------------------------------------------\n * Helper types\n * ------------------------------------------------------------------------- */\n\n/**\n * Watch options\n */\ninterface WatchOptions {\n  viewport$: Observable<Viewport>      /* Viewport observable */\n}\n\n/**\n * Mount options\n */\ninterface MountOptions {\n  viewport$: Observable<Viewport>      /* Viewport observable */\n  header$: Observable<Header>          /* Header observable */\n  main$: Observable<Main>              /* Main area observable */\n}\n\n/* ----------------------------------------------------------------------------\n * Helper functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Compute whether the header is hidden\n *\n * If the user scrolls past a certain threshold, the header can be hidden when\n * scrolling down, and shown when scrolling up.\n *\n * @param options - Options\n *\n * @returns Toggle observable\n */\nfunction isHidden({ viewport$ }: WatchOptions): Observable<boolean> {\n  if (!feature(\"header.autohide\"))\n    return of(false)\n\n  /* Compute direction and turning point */\n  const direction$ = viewport$\n    .pipe(\n      map(({ offset: { y } }) => y),\n      bufferCount(2, 1),\n      map(([a, b]) => [a < b, b] as const),\n      distinctUntilKeyChanged(0)\n    )\n\n  /* Compute whether header should be hidden */\n  const hidden$ = combineLatest([viewport$, direction$])\n    .pipe(\n      filter(([{ offset }, [, y]]) => Math.abs(y - offset.y) > 100),\n      map(([, [direction]]) => direction),\n      distinctUntilChanged()\n    )\n\n  /* Compute threshold for hiding */\n  const search$ = watchToggle(\"search\")\n  return combineLatest([viewport$, search$])\n    .pipe(\n      map(([{ offset }, search]) => offset.y > 400 && !search),\n      distinctUntilChanged(),\n      switchMap(active => active ? hidden$ : of(false)),\n      startWith(false)\n    )\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Watch header\n *\n * @param el - Header element\n * @param options - Options\n *\n * @returns Header observable\n */\nexport function watchHeader(\n  el: HTMLElement, options: WatchOptions\n): Observable<Header> {\n  return defer(() => combineLatest([\n    watchElementSize(el),\n    isHidden(options)\n  ]))\n    .pipe(\n      map(([{ height }, hidden]) => ({\n        height,\n        hidden\n      })),\n      distinctUntilChanged((a, b) => (\n        a.height === b.height &&\n        a.hidden === b.hidden\n      )),\n      shareReplay(1)\n    )\n}\n\n/**\n * Mount header\n *\n * This function manages the different states of the header, i.e. whether it's\n * hidden or rendered with a shadow. This depends heavily on the main area.\n *\n * @param el - Header element\n * @param options - Options\n *\n * @returns Header component observable\n */\nexport function mountHeader(\n  el: HTMLElement, { header$, main$ }: MountOptions\n): Observable<Component<Header | Tooltip>> {\n  return defer(() => {\n    const push$ = new Subject<Main>()\n    const done$ = push$.pipe(ignoreElements(), endWith(true))\n    push$\n      .pipe(\n        distinctUntilKeyChanged(\"active\"),\n        combineLatestWith(header$)\n      )\n        .subscribe(([{ active }, { hidden }]) => {\n          el.classList.toggle(\"md-header--shadow\", active && !hidden)\n          el.hidden = hidden\n        })\n\n    /* Mount tooltips, if enabled */\n    const tooltips = from(getElements(\"[title]\", el))\n      .pipe(\n        filter(() => feature(\"content.tooltips\")),\n        mergeMap(child => mountTooltip(child))\n      )\n\n    /* Link to main area */\n    main$.subscribe(push$)\n\n    /* Create and return component */\n    return header$\n      .pipe(\n        takeUntil(done$),\n        map(state => ({ ref: el, ...state })),\n        mergeWith(tooltips.pipe(takeUntil(done$)))\n      )\n  })\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  EMPTY,\n  Observable,\n  Subject,\n  defer,\n  distinctUntilKeyChanged,\n  finalize,\n  map,\n  tap\n} from \"rxjs\"\n\nimport {\n  Viewport,\n  getElementSize,\n  getOptionalElement,\n  watchViewportAt\n} from \"~/browser\"\n\nimport { Component } from \"../../_\"\nimport { Header } from \"../_\"\n\n/* ----------------------------------------------------------------------------\n * Types\n * ------------------------------------------------------------------------- */\n\n/**\n * Header\n */\nexport interface HeaderTitle {\n  active: boolean                      /* Header title is active */\n}\n\n/* ----------------------------------------------------------------------------\n * Helper types\n * ------------------------------------------------------------------------- */\n\n/**\n * Watch options\n */\ninterface WatchOptions {\n  viewport$: Observable<Viewport>      /* Viewport observable */\n  header$: Observable<Header>          /* Header observable */\n}\n\n/**\n * Mount options\n */\ninterface MountOptions {\n  viewport$: Observable<Viewport>      /* Viewport observable */\n  header$: Observable<Header>          /* Header observable */\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Watch header title\n *\n * @param el - Heading element\n * @param options - Options\n *\n * @returns Header title observable\n */\nexport function watchHeaderTitle(\n  el: HTMLElement, { viewport$, header$ }: WatchOptions\n): Observable<HeaderTitle> {\n  return watchViewportAt(el, { viewport$, header$ })\n    .pipe(\n      map(({ offset: { y } }) => {\n        const { height } = getElementSize(el)\n        return {\n          active: y >= height\n        }\n      }),\n      distinctUntilKeyChanged(\"active\")\n    )\n}\n\n/**\n * Mount header title\n *\n * This function swaps the header title from the site title to the title of the\n * current page when the user scrolls past the first headline.\n *\n * @param el - Header title element\n * @param options - Options\n *\n * @returns Header title component observable\n */\nexport function mountHeaderTitle(\n  el: HTMLElement, options: MountOptions\n): Observable<Component<HeaderTitle>> {\n  return defer(() => {\n    const push$ = new Subject<HeaderTitle>()\n    push$.subscribe({\n\n      /* Handle emission */\n      next({ active }) {\n        el.classList.toggle(\"md-header__title--active\", active)\n      },\n\n      /* Handle complete */\n      complete() {\n        el.classList.remove(\"md-header__title--active\")\n      }\n    })\n\n    /* Obtain headline, if any */\n    const heading = getOptionalElement(\".md-content h1\")\n    if (typeof heading === \"undefined\")\n      return EMPTY\n\n    /* Create and return component */\n    return watchHeaderTitle(heading, options)\n      .pipe(\n        tap(state => push$.next(state)),\n        finalize(() => push$.complete()),\n        map(state => ({ ref: el, ...state }))\n      )\n  })\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  Observable,\n  combineLatest,\n  distinctUntilChanged,\n  distinctUntilKeyChanged,\n  map,\n  switchMap\n} from \"rxjs\"\n\nimport {\n  Viewport,\n  watchElementSize\n} from \"~/browser\"\n\nimport { Header } from \"../header\"\n\n/* ----------------------------------------------------------------------------\n * Types\n * ------------------------------------------------------------------------- */\n\n/**\n * Main area\n */\nexport interface Main {\n  offset: number                       /* Main area top offset */\n  height: number                       /* Main area visible height */\n  active: boolean                      /* Main area is active */\n}\n\n/* ----------------------------------------------------------------------------\n * Helper types\n * ------------------------------------------------------------------------- */\n\n/**\n * Watch options\n */\ninterface WatchOptions {\n  viewport$: Observable<Viewport>      /* Viewport observable */\n  header$: Observable<Header>          /* Header observable */\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Watch main area\n *\n * This function returns an observable that computes the visual parameters of\n * the main area which depends on the viewport vertical offset and height, as\n * well as the height of the header element, if the header is fixed.\n *\n * @param el - Main area element\n * @param options - Options\n *\n * @returns Main area observable\n */\nexport function watchMain(\n  el: HTMLElement, { viewport$, header$ }: WatchOptions\n): Observable<Main> {\n\n  /* Compute necessary adjustment for header */\n  const adjust$ = header$\n    .pipe(\n      map(({ height }) => height),\n      distinctUntilChanged()\n    )\n\n  /* Compute the main area's top and bottom borders */\n  const border$ = adjust$\n    .pipe(\n      switchMap(() => watchElementSize(el)\n        .pipe(\n          map(({ height }) => ({\n            top:    el.offsetTop,\n            bottom: el.offsetTop + height\n          })),\n          distinctUntilKeyChanged(\"bottom\")\n        )\n      )\n    )\n\n  /* Compute the main area's offset, visible height and if we scrolled past */\n  return combineLatest([adjust$, border$, viewport$])\n    .pipe(\n      map(([header, { top, bottom }, { offset: { y }, size: { height } }]) => {\n        height = Math.max(0, height\n          - Math.max(0, top    - y,  header)\n          - Math.max(0, height + y - bottom)\n        )\n        return {\n          offset: top - header,\n          height,\n          active: top - header <= y\n        }\n      }),\n      distinctUntilChanged((a, b) => (\n        a.offset === b.offset &&\n        a.height === b.height &&\n        a.active === b.active\n      ))\n    )\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  Observable,\n  Subject,\n  asyncScheduler,\n  defer,\n  finalize,\n  fromEvent,\n  map,\n  mergeMap,\n  observeOn,\n  of,\n  repeat,\n  shareReplay,\n  skip,\n  startWith,\n  takeUntil,\n  tap\n} from \"rxjs\"\n\nimport { getElements, watchMedia } from \"~/browser\"\nimport { h } from \"~/utilities\"\n\nimport {\n  Component,\n  getComponentElement\n} from \"../_\"\n\n/* ----------------------------------------------------------------------------\n * Types\n * ------------------------------------------------------------------------- */\n\n/**\n * Palette colors\n */\nexport interface PaletteColor {\n  media?: string                       /* Media query */\n  scheme?: string                      /* Color scheme */\n  primary?: string                     /* Primary color */\n  accent?: string                      /* Accent color */\n}\n\n/**\n * Palette\n */\nexport interface Palette {\n  index: number                        /* Palette index */\n  color: PaletteColor                  /* Palette colors */\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Watch color palette\n *\n * @param inputs - Color palette element\n *\n * @returns Color palette observable\n */\nexport function watchPalette(\n  inputs: HTMLInputElement[]\n): Observable<Palette> {\n  const current = __md_get<Palette>(\"__palette\") || {\n    index: inputs.findIndex(input => matchMedia(\n      input.getAttribute(\"data-md-color-media\")!\n    ).matches)\n  }\n\n  /* Emit changes in color palette */\n  const index = Math.max(0, Math.min(current.index, inputs.length - 1))\n  return of(...inputs)\n    .pipe(\n      mergeMap(input => fromEvent(input, \"change\").pipe(map(() => input))),\n      startWith(inputs[index]),\n      map(input => ({\n        index: inputs.indexOf(input),\n        color: {\n          media:   input.getAttribute(\"data-md-color-media\"),\n          scheme:  input.getAttribute(\"data-md-color-scheme\"),\n          primary: input.getAttribute(\"data-md-color-primary\"),\n          accent:  input.getAttribute(\"data-md-color-accent\")\n        }\n      } as Palette)),\n      shareReplay(1)\n    )\n}\n\n/**\n * Mount color palette\n *\n * @param el - Color palette element\n *\n * @returns Color palette component observable\n */\nexport function mountPalette(\n  el: HTMLElement\n): Observable<Component<Palette>> {\n  const inputs = getElements<HTMLInputElement>(\"input\", el)\n  const meta = h(\"meta\", { name: \"theme-color\" })\n  document.head.appendChild(meta)\n\n  // Add color scheme meta tag\n  const scheme = h(\"meta\", { name: \"color-scheme\" })\n  document.head.appendChild(scheme)\n\n  /* Mount component on subscription */\n  const media$ = watchMedia(\"(prefers-color-scheme: light)\")\n  return defer(() => {\n    const push$ = new Subject<Palette>()\n    push$.subscribe(palette => {\n      document.body.setAttribute(\"data-md-color-switching\", \"\")\n\n      /* Retrieve color palette for system preference */\n      if (palette.color.media === \"(prefers-color-scheme)\") {\n        const media = matchMedia(\"(prefers-color-scheme: light)\")\n        const input = document.querySelector(media.matches\n          ? \"[data-md-color-media='(prefers-color-scheme: light)']\"\n          : \"[data-md-color-media='(prefers-color-scheme: dark)']\"\n        )!\n\n        /* Retrieve colors for system preference */\n        palette.color.scheme  = input.getAttribute(\"data-md-color-scheme\")!\n        palette.color.primary = input.getAttribute(\"data-md-color-primary\")!\n        palette.color.accent  = input.getAttribute(\"data-md-color-accent\")!\n      }\n\n      /* Set color palette */\n      for (const [key, value] of Object.entries(palette.color))\n        document.body.setAttribute(`data-md-color-${key}`, value)\n\n      /* Set toggle visibility */\n      for (let index = 0; index < inputs.length; index++) {\n        const label = inputs[index].nextElementSibling\n        if (label instanceof HTMLElement)\n          label.hidden = palette.index !== index\n      }\n\n      /* Persist preference in local storage */\n      __md_set(\"__palette\", palette)\n    })\n\n    /* Update theme-color meta tag */\n    push$\n      .pipe(\n        map(() => {\n          const header = getComponentElement(\"header\")\n          const style  = window.getComputedStyle(header)\n\n          // Set color scheme\n          scheme.content = style.colorScheme\n\n          /* Return color in hexadecimal format */\n          return style.backgroundColor.match(/\\d+/g)!\n            .map(value => (+value).toString(16).padStart(2, \"0\"))\n            .join(\"\")\n        })\n      )\n        .subscribe(color => meta.content = `#${color}`)\n\n    /* Revert transition durations after color switch */\n    push$.pipe(observeOn(asyncScheduler))\n      .subscribe(() => {\n        document.body.removeAttribute(\"data-md-color-switching\")\n      })\n\n    /* Create and return component */\n    return watchPalette(inputs)\n      .pipe(\n        takeUntil(media$.pipe(skip(1))),\n        repeat(),\n        tap(state => push$.next(state)),\n        finalize(() => push$.complete()),\n        map(state => ({ ref: el, ...state }))\n      )\n  })\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  Observable,\n  Subject,\n  defer,\n  finalize,\n  map,\n  tap\n} from \"rxjs\"\n\nimport { Component } from \"../_\"\n\n/* ----------------------------------------------------------------------------\n * Types\n * ------------------------------------------------------------------------- */\n\n/**\n * Progress indicator\n */\nexport interface Progress {\n  value: number                        // Progress value\n}\n\n/* ----------------------------------------------------------------------------\n * Helper types\n * ------------------------------------------------------------------------- */\n\n/**\n * Mount options\n */\ninterface MountOptions {\n  progress$: Subject<number>           // Progress subject\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Mount progress indicator\n *\n * @param el - Progress indicator element\n * @param options - Options\n *\n * @returns Progress indicator component observable\n */\nexport function mountProgress(\n  el: HTMLElement, { progress$ }: MountOptions\n): Observable<Component<Progress>> {\n\n  // Mount component on subscription\n  return defer(() => {\n    const push$ = new Subject<Progress>()\n    push$.subscribe(({ value }) => {\n      el.style.setProperty(\"--md-progress-value\", `${value}`)\n    })\n\n    // Create and return component\n    return progress$\n      .pipe(\n        tap(value => push$.next({ value })),\n        finalize(() => push$.complete()),\n        map(value => ({ ref: el, value }))\n      )\n  })\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport ClipboardJS from \"clipboard\"\nimport {\n  Observable,\n  Subject,\n  map,\n  tap\n} from \"rxjs\"\n\nimport { translation } from \"~/_\"\nimport { getElement } from \"~/browser\"\n\n/* ----------------------------------------------------------------------------\n * Helper types\n * ------------------------------------------------------------------------- */\n\n/**\n * Setup options\n */\ninterface SetupOptions {\n  alert$: Subject<string>              /* Alert subject */\n}\n\n/* ----------------------------------------------------------------------------\n * Helper functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Extract text to copy\n *\n * @param el - HTML element\n *\n * @returns Extracted text\n */\nfunction extract(el: HTMLElement): string {\n  el.setAttribute(\"data-md-copying\", \"\")\n  const copy = el.closest(\"[data-copy]\")\n  const text = copy\n    ? copy.getAttribute(\"data-copy\")!\n    : el.innerText\n  el.removeAttribute(\"data-md-copying\")\n  return text.trimEnd()\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Set up Clipboard.js integration\n *\n * @param options - Options\n */\nexport function setupClipboardJS(\n  { alert$ }: SetupOptions\n): void {\n  if (ClipboardJS.isSupported()) {\n    new Observable<ClipboardJS.Event>(subscriber => {\n      new ClipboardJS(\"[data-clipboard-target], [data-clipboard-text]\", {\n        text: el => (\n          el.getAttribute(\"data-clipboard-text\")! ||\n          extract(getElement(\n            el.getAttribute(\"data-clipboard-target\")!\n          ))\n        )\n      })\n        .on(\"success\", ev => subscriber.next(ev))\n    })\n      .pipe(\n        tap(ev => {\n          const trigger = ev.trigger as HTMLElement\n          trigger.focus()\n        }),\n        map(() => translation(\"clipboard.copied\"))\n      )\n        .subscribe(alert$)\n  }\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  Observable,\n  catchError,\n  map,\n  of\n} from \"rxjs\"\n\nimport {\n  getElement,\n  getElements,\n  requestXML\n} from \"~/browser\"\n\n/* ----------------------------------------------------------------------------\n * Types\n * ------------------------------------------------------------------------- */\n\n/**\n * Sitemap, i.e. a list of URLs\n */\nexport type Sitemap = Map<string, URL[]>\n\n/* ----------------------------------------------------------------------------\n * Helper functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Resolve URL to the given base URL\n *\n * When serving the site with instant navigation, MkDocs will set the hostname\n * to the value as specified in `dev_addr`, but the browser allows for several\n * hostnames to be used: `localhost`, `127.0.0.1` or even `0.0.0.0`, depending\n * on configuration. This function resolves the URL to the given hostname.\n *\n * @param url - URL\n * @param base - Base URL\n *\n * @returns Resolved URL\n */\nfunction resolve(url: URL, base: URL) {\n  url.protocol = base.protocol\n  url.hostname = base.hostname\n  return url\n}\n\n/**\n * Extract sitemap from document\n *\n * This function extracts the URLs and alternate links from the document, and\n * associates alternate links to the original URL as found in `loc`, allowing\n * the browser to navigate to the correct page when switching languages. The\n * format of the sitemap is expected to adhere to:\n *\n * ``` xml\n * <urlset>\n *   <url>\n *     <loc>...</loc>\n *     <xhtml:link rel=\"alternate\" hreflang=\"en\" href=\"...\"/>\n *     <xhtml:link rel=\"alternate\" hreflang=\"de\" href=\"...\"/>\n *     ...\n *   </url>\n *   ...\n * </urlset>\n * ```\n *\n * @param document - Document\n * @param base - Base URL\n *\n * @returns Sitemap\n */\nfunction extract(document: Document, base: URL): Sitemap {\n  const sitemap: Sitemap = new Map()\n  for (const el of getElements(\"url\", document)) {\n    const url = getElement(\"loc\", el)\n\n    // Create entry for location and add it to the list of links\n    const links = [resolve(new URL(url.textContent!), base)]\n    sitemap.set(`${links[0]}`, links)\n\n    // Attach alternate links to current entry\n    for (const link of getElements(\"[rel=alternate]\", el)) {\n      const href = link.getAttribute(\"href\")\n      if (href != null)\n        links.push(resolve(new URL(href), base))\n    }\n  }\n\n  // Return sitemap\n  return sitemap\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Fetch the sitemap for the given base URL\n *\n * If a network or parsing error occurs, we just default to an empty sitemap,\n * which means the caller should fall back to regular navigation.\n *\n * @param base - Base URL\n *\n * @returns Sitemap observable\n */\nexport function fetchSitemap(base: URL | string): Observable<Sitemap> {\n  return requestXML(new URL(\"sitemap.xml\", base))\n    .pipe(\n      map(document => extract(document, new URL(base))),\n      catchError(() => of(new Map())),\n    )\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  EMPTY,\n  Observable,\n  Subject,\n  catchError,\n  combineLatestWith,\n  concat,\n  debounceTime,\n  distinctUntilChanged,\n  distinctUntilKeyChanged,\n  endWith,\n  fromEvent,\n  ignoreElements,\n  map,\n  merge,\n  of,\n  share,\n  switchMap,\n  tap,\n  withLatestFrom\n} from \"rxjs\"\n\nimport { configuration, feature } from \"~/_\"\nimport {\n  Viewport,\n  getElements,\n  getLocation,\n  getOptionalElement,\n  requestHTML,\n  setLocation,\n  setLocationHash\n} from \"~/browser\"\nimport { getComponentElement } from \"~/components\"\n\nimport { Sitemap, fetchSitemap } from \"../sitemap\"\n\n/* ----------------------------------------------------------------------------\n * Helper types\n * ------------------------------------------------------------------------- */\n\n/**\n * Setup options\n */\ninterface SetupOptions {\n  location$: Subject<URL>              // Location subject\n  viewport$: Observable<Viewport>      // Viewport observable\n  progress$: Subject<number>           // Progress subject\n}\n\n/* ----------------------------------------------------------------------------\n * Helper functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Handle clicks on internal URLs while skipping external URLs\n *\n * @param ev - Mouse event\n * @param sitemap - Sitemap\n *\n * @returns URL observable\n */\nfunction handle(\n  ev: MouseEvent, sitemap: Sitemap\n): Observable<URL> {\n  if (!(ev.target instanceof Element))\n    return EMPTY\n\n  // Skip, as target is not within a link - clicks on non-link elements are\n  // also captured, which we need to exclude from processing\n  const el = ev.target.closest(\"a\")\n  if (el === null)\n    return EMPTY\n\n  // Skip, as link opens in new window - we now know we have captured a click\n  // on a link, but the link either has a `target` property defined, or the\n  // user pressed the `meta` or `ctrl` key to open it in a new window. Thus,\n  // we need to filter this event as well.\n  if (el.target || ev.metaKey || ev.ctrlKey)\n    return EMPTY\n\n  // Next, we must check if the URL is relevant for us, i.e., if it's an\n  // internal link to a page that is managed by MkDocs. Only then we can be\n  // sure that the structure of the page to be loaded adheres to the current\n  // document structure and can subsequently be injected into it without doing\n  // a full reload. For this reason, we must canonicalize the URL by removing\n  // all search parameters and hash fragments.\n  const url = new URL(el.href)\n  url.search = url.hash = \"\"\n\n  // Skip, if URL is not included in the sitemap - this could be the case when\n  // linking between versions or languages, or to another page that the author\n  // included as part of the build, but that is not managed by MkDocs. In that\n  // case we must not continue with instant navigation.\n  if (!sitemap.has(`${url}`))\n    return EMPTY\n\n  // We now know that we have a link to an internal page, so we prevent the\n  // browser from navigation and emit the URL for instant navigation. Note that\n  // this also includes anchor links, which means we need to implement anchor\n  // positioning ourselves. The reason for this is that if we wouldn't manage\n  // anchor links as well, scroll restoration will not work correctly (e.g.\n  // following an anchor link and scrolling).\n  ev.preventDefault()\n  return of(new URL(el.href))\n}\n\n/**\n * Create a map of head elements for lookup and replacement\n *\n * @param document - Document\n *\n * @returns Tag map\n */\nfunction head(document: Document): Map<string, HTMLElement> {\n  const tags = new Map<string, HTMLElement>()\n  for (const el of getElements(\":scope > *\", document.head))\n    tags.set(el.outerHTML, el)\n\n  // Return tag map\n  return tags\n}\n\n/**\n * Resolve relative URLs in the given document\n *\n * @param document - Document\n *\n * @returns Document observable\n */\nfunction resolve(document: Document): Observable<Document> {\n  for (const el of getElements<HTMLLinkElement>(\"[href], [src]\", document))\n    for (const key in [\"href\", \"src\"]) {\n      const value = el.getAttribute(key)\n      if (!/^(?:[a-z]+:)?\\/\\//i.test(value!))\n        el.href = el.href\n    }\n\n  // Return document observable\n  return of(document)\n}\n\n/**\n * Create a map of head elements for lookup and replacement\n *\n * @param next - Next document\n *\n * @returns Document observable\n */\nfunction inject(next: Document): Observable<Document> {\n  for (const selector of [\n    \"[data-md-component=announce]\",\n    \"[data-md-component=container]\",\n    \"[data-md-component=header-topic]\",\n    \"[data-md-component=outdated]\",\n    \"[data-md-component=logo]\",\n    \"[data-md-component=skip]\",\n    ...feature(\"navigation.tabs.sticky\")\n      ? [\"[data-md-component=tabs]\"]\n      : []\n  ]) {\n    const source = getOptionalElement(selector)\n    const target = getOptionalElement(selector, next)\n    if (\n      typeof source !== \"undefined\" &&\n      typeof target !== \"undefined\"\n    ) {\n      source.replaceWith(target)\n    }\n  }\n\n  // Update meta tags\n  const tags = head(document)\n  for (const [html, el] of head(next))\n    if (tags.has(html))\n      tags.delete(html)\n    else\n      document.head.appendChild(el)\n\n  // Remove meta tags that are not present in the new document\n  for (const el of tags.values())\n    el.remove()\n\n  // After components and meta tags were replaced, re-evaluate scripts\n  // that were provided by the author as part of Markdown files\n  const container = getComponentElement(\"container\")\n  return concat(getElements(\"script\", container))\n    .pipe(\n      switchMap(el => {\n        const script = next.createElement(\"script\")\n        if (el.src) {\n          for (const name of el.getAttributeNames())\n            script.setAttribute(name, el.getAttribute(name)!)\n          el.replaceWith(script)\n\n          // Complete when script is loaded\n          return new Observable(observer => {\n            script.onload = () => observer.complete()\n          })\n\n        // Complete immediately\n        } else {\n          script.textContent = el.textContent\n          el.replaceWith(script)\n          return EMPTY\n        }\n      }),\n      ignoreElements(),\n      endWith(next)\n    )\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Set up instant navigation\n *\n * This is a heavily orchestrated operation - see inline comments to learn how\n * this works with Material for MkDocs, and how you can hook into it.\n *\n * @param options - Options\n *\n * @returns Document observable\n */\nexport function setupInstantNavigation(\n  { location$, viewport$, progress$ }: SetupOptions\n): Observable<Document> {\n  const config = configuration()\n  if (location.protocol === \"file:\")\n    return EMPTY\n\n  // Load sitemap immediately, so we have it available when the user initiates\n  // the first navigation request, so there's no perceived delay.\n  const sitemap$ = fetchSitemap(config.base)\n\n  // Since we might be on a slow connection, the user might trigger multiple\n  // instant navigation events that overlap. MkDocs produces relative URLs for\n  // all internal links, which becomes a problem in this case, because we need\n  // to change the base URL the moment the user clicks a link that should be\n  // intercepted in order to be consistent with popstate, which means that the\n  // base URL would now be incorrect when resolving another relative link from\n  // the same site. For this reason we always resolve all relative links to\n  // absolute links, so we can be sure this never happens.\n  of(document)\n    .subscribe(resolve)\n\n  // --------------------------------------------------------------------------\n  // Navigation interception\n  // --------------------------------------------------------------------------\n\n  // Intercept navigation - to keep the number of event listeners down we use\n  // the fact that uncaptured events bubble up to the body. This has the nice\n  // property that we don't need to detach and then re-attach event listeners\n  // when the document is replaced after a navigation event.\n  const instant$ =\n    fromEvent<MouseEvent>(document.body, \"click\")\n      .pipe(\n        combineLatestWith(sitemap$),\n        switchMap(([ev, sitemap]) => handle(ev, sitemap)),\n        share()\n      )\n\n  // Intercept history change events, e.g. when the user uses the browser's\n  // back or forward buttons, and emit new location for fetching and parsing\n  const history$ =\n    fromEvent<PopStateEvent>(window, \"popstate\")\n      .pipe(\n        map(getLocation),\n        share()\n      )\n\n  // While it would be better UX to defer navigation events until the document\n  // is fully fetched and parsed, we must schedule it here to synchronize with\n  // popstate events, as they are emitted immediately. Moreover we need to\n  // store the current viewport offset for scroll restoration later on.\n  instant$.pipe(withLatestFrom(viewport$))\n    .subscribe(([url, { offset }]) => {\n      history.replaceState(offset, \"\")\n      history.pushState(null, \"\", url)\n    })\n\n  // Emit URLs that should be fetched via instant navigation on location subject\n  // which was passed into this function. The state of instant navigation can be\n  // intercepted by other parts of the application, which can synchronously back\n  // up or restore state before or after instant navigation happens.\n  merge(instant$, history$)\n    .subscribe(location$)\n\n  // --------------------------------------------------------------------------\n  // Fetching and parsing\n  // --------------------------------------------------------------------------\n\n  // Fetch document - we deduplicate requests to the same location, so we don't\n  // end up with multiple requests for the same page. We use `switchMap`, since\n  // we want to cancel the previous request when a new one is triggered, which\n  // is automatically handled by the observable returned by `request`. This is\n  // essential to ensure a good user experience, as we don't want to load pages\n  // that are not needed anymore, e.g., when the user clicks multiple links in\n  // quick succession or on slow connections. If the request fails for some\n  // reason, we fall back and use regular navigation, forcing a reload.\n  const document$ = location$\n    .pipe(\n      distinctUntilKeyChanged(\"pathname\"),\n      switchMap(url => requestHTML(url, { progress$ })\n        .pipe(\n          catchError(() => {\n            setLocation(url, true)\n            return EMPTY\n          })\n        )\n      ),\n\n      // The document was successfully fetched and parsed, so we can inject its\n      // contents into the currently active document\n      switchMap(resolve),\n      switchMap(inject),\n      share()\n    )\n\n  // --------------------------------------------------------------------------\n  // Scroll restoration\n  // --------------------------------------------------------------------------\n\n  // Handle scroll restoration - we must restore the viewport offset after the\n  // document has been fetched and injected, and every time the user clicks an\n  // anchor that leads to an element on the same page, which might also happen\n  // when the user uses the back or forward button.\n  merge(\n    document$.pipe(withLatestFrom(location$, (_, url) => url)),\n\n    // Handle instant navigation events that are triggered by the user clicking\n    // on an anchor link with a hash fragment different from the current one, as\n    // well as from popstate events, which are emitted when the user navigates\n    // back and forth between pages. We use a two-layered subscription to scope\n    // the scroll restoration to the current page, as we don't need to restore\n    // the viewport offset when the user navigates to a different page, as this\n    // is already handled by the previous observable.\n    location$.pipe(\n      distinctUntilKeyChanged(\"pathname\"),\n      switchMap(() => location$),\n      distinctUntilKeyChanged(\"hash\"),\n    ),\n\n    // Handle instant navigation events that are triggered by the user clicking\n    // on an anchor link with the same hash fragment as the current one in the\n    // URL. Is is essential that we only intercept those from instant navigation\n    // events and not from history change events, or we'll end up in and endless\n    // loop. The top-level history entry must be removed, as it will be replaced\n    // with a new one, which would otherwise lead to a duplicate entry.\n    location$.pipe(\n      distinctUntilChanged((a, b) => (\n        a.pathname === b.pathname &&\n        a.hash     === b.hash\n      )),\n      switchMap(() => instant$),\n      tap(() => history.back())\n    )\n  )\n    .subscribe(url => {\n\n      // Check if the current history entry has a state, which happens when the\n      // user presses the back or forward button to visit a page we've already\n      // seen. If there's no state, it means a new page was visited and we must\n      // scroll to the top, unless an anchor is given.\n      if (history.state !== null || !url.hash) {\n        window.scrollTo(0, history.state?.y ?? 0)\n      } else {\n        history.scrollRestoration = \"auto\"\n        setLocationHash(url.hash)\n        history.scrollRestoration = \"manual\"\n      }\n    })\n\n  // Disable scroll restoration when an instant navigation event occurs, so the\n  // browser does not immediately set the viewport offset to the prior history\n  // entry, scrolling to the position on the same page, which would look odd.\n  // Instead, we manually restore the position once the page has loaded.\n  location$.subscribe(() => {\n    history.scrollRestoration = \"manual\"\n  })\n\n  // Enable scroll restoration before window unloads - this is essential to\n  // ensure that full reloads (F5) restore the viewport offset correctly. If\n  // only popstate events wouldn't reset the viewport offset prior to their\n  // emission, we could just reset this in popstate. Meh.\n  fromEvent(window, \"beforeunload\")\n    .subscribe(() => {\n      history.scrollRestoration = \"auto\"\n    })\n\n  // Track viewport offset, so we can restore it when the user navigates back\n  // and forth between pages. Note that this must be debounced and cannot be\n  // done in popstate, as popstate has already removed the entry from the\n  // history, which means it is too late.\n  viewport$\n    .pipe(\n      distinctUntilKeyChanged(\"offset\"),\n      debounceTime(100)\n    )\n      .subscribe(({ offset }) => {\n        history.replaceState(offset, \"\")\n      })\n\n  // Return document\n  return document$\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport escapeHTML from \"escape-html\"\n\nimport { SearchConfig } from \"../config\"\n\n/* ----------------------------------------------------------------------------\n * Types\n * ------------------------------------------------------------------------- */\n\n/**\n * Search highlight function\n *\n * @param value - Value\n *\n * @returns Highlighted value\n */\nexport type SearchHighlightFn = (value: string) => string\n\n/**\n * Search highlight factory function\n *\n * @param query - Query value\n *\n * @returns Search highlight function\n */\nexport type SearchHighlightFactoryFn = (query: string) => SearchHighlightFn\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Create a search highlighter\n *\n * @param config - Search configuration\n *\n * @returns Search highlight factory function\n */\nexport function setupSearchHighlighter(\n  config: SearchConfig\n): SearchHighlightFactoryFn {\n  // Hack: temporarily remove pure lookaheads and lookbehinds\n  const regex = config.separator.split(\"|\").map(term => {\n    const temp = term.replace(/(\\(\\?[!=<][^)]+\\))/g, \"\")\n    return temp.length === 0 ? \"\uFFFD\" : term\n  })\n    .join(\"|\")\n\n  const separator = new RegExp(regex, \"img\")\n  const highlight = (_: unknown, data: string, term: string) => {\n    return `${data}<mark data-md-highlight>${term}</mark>`\n  }\n\n  /* Return factory function */\n  return (query: string) => {\n    query = query\n      .replace(/[\\s*+\\-:~^]+/g, \" \")\n      .trim()\n\n    /* Create search term match expression */\n    const match = new RegExp(`(^|${config.separator}|)(${\n      query\n        .replace(/[|\\\\{}()[\\]^$+*?.-]/g, \"\\\\$&\")\n        .replace(separator, \"|\")\n    })`, \"img\")\n\n    /* Highlight string value */\n    return value => escapeHTML(value)\n      .replace(match, highlight)\n      .replace(/<\\/mark>(\\s+)<mark[^>]*>/img, \"$1\")\n  }\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A RTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport { SearchResult } from \"../../_\"\nimport { SearchIndex } from \"../../config\"\n\n/* ----------------------------------------------------------------------------\n * Types\n * ------------------------------------------------------------------------- */\n\n/**\n * Search message type\n */\nexport const enum SearchMessageType {\n  SETUP,                               /* Search index setup */\n  READY,                               /* Search index ready */\n  QUERY,                               /* Search query */\n  RESULT                               /* Search results */\n}\n\n/* ------------------------------------------------------------------------- */\n\n/**\n * Message containing the data necessary to setup the search index\n */\nexport interface SearchSetupMessage {\n  type: SearchMessageType.SETUP        /* Message type */\n  data: SearchIndex                    /* Message data */\n}\n\n/**\n * Message indicating the search index is ready\n */\nexport interface SearchReadyMessage {\n  type: SearchMessageType.READY        /* Message type */\n}\n\n/**\n * Message containing a search query\n */\nexport interface SearchQueryMessage {\n  type: SearchMessageType.QUERY        /* Message type */\n  data: string                         /* Message data */\n}\n\n/**\n * Message containing results for a search query\n */\nexport interface SearchResultMessage {\n  type: SearchMessageType.RESULT       /* Message type */\n  data: SearchResult                   /* Message data */\n}\n\n/* ------------------------------------------------------------------------- */\n\n/**\n * Message exchanged with the search worker\n */\nexport type SearchMessage =\n  | SearchSetupMessage\n  | SearchReadyMessage\n  | SearchQueryMessage\n  | SearchResultMessage\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Type guard for search ready messages\n *\n * @param message - Search worker message\n *\n * @returns Test result\n */\nexport function isSearchReadyMessage(\n  message: SearchMessage\n): message is SearchReadyMessage {\n  return message.type === SearchMessageType.READY\n}\n\n/**\n * Type guard for search result messages\n *\n * @param message - Search worker message\n *\n * @returns Test result\n */\nexport function isSearchResultMessage(\n  message: SearchMessage\n): message is SearchResultMessage {\n  return message.type === SearchMessageType.RESULT\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A RTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  ObservableInput,\n  Subject,\n  first,\n  merge,\n  of,\n  switchMap\n} from \"rxjs\"\n\nimport { feature } from \"~/_\"\nimport { watchToggle, watchWorker } from \"~/browser\"\n\nimport { SearchIndex } from \"../../config\"\nimport {\n  SearchMessage,\n  SearchMessageType\n} from \"../message\"\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Set up search worker\n *\n * This function creates and initializes a web worker that is used for search,\n * so that the user interface doesn't freeze. In general, the application does\n * not care how search is implemented, as long as the web worker conforms to\n * the format expected by the application as defined in `SearchMessage`. This\n * allows the author to implement custom search functionality, by providing a\n * custom web worker via configuration.\n *\n * Material for MkDocs' built-in search implementation makes use of Lunr.js, an\n * efficient and fast implementation for client-side search. Leveraging a tiny\n * iframe-based web worker shim, search is even supported for the `file://`\n * protocol, enabling search for local non-hosted builds.\n *\n * If the protocol is `file://`, search initialization is deferred to mitigate\n * freezing, as it's now synchronous by design - see https://bit.ly/3C521EO\n *\n * @see https://bit.ly/3igvtQv - How to implement custom search\n *\n * @param url - Worker URL\n * @param index$ - Search index observable input\n *\n * @returns Search worker\n */\nexport function setupSearchWorker(\n  url: string, index$: ObservableInput<SearchIndex>\n): Subject<SearchMessage> {\n  const worker$ = watchWorker<SearchMessage>(url)\n  merge(\n    of(location.protocol !== \"file:\"),\n    watchToggle(\"search\")\n  )\n    .pipe(\n      first(active => active),\n      switchMap(() => index$)\n    )\n      .subscribe(({ config, docs }) => worker$.next({\n        type: SearchMessageType.SETUP,\n        data: {\n          config,\n          docs,\n          options: {\n            suggest: feature(\"search.suggest\")\n          }\n        }\n      }))\n\n  /* Return search worker */\n  return worker$\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  EMPTY,\n  Subject,\n  catchError,\n  combineLatest,\n  filter,\n  fromEvent,\n  map,\n  of,\n  switchMap,\n  withLatestFrom\n} from \"rxjs\"\n\nimport { configuration } from \"~/_\"\nimport {\n  getElement,\n  getLocation,\n  requestJSON,\n  setLocation\n} from \"~/browser\"\nimport { getComponentElements } from \"~/components\"\nimport {\n  Version,\n  renderVersionSelector\n} from \"~/templates\"\n\nimport { fetchSitemap } from \"../sitemap\"\n\n/* ----------------------------------------------------------------------------\n * Helper types\n * ------------------------------------------------------------------------- */\n\n/**\n * Setup options\n */\ninterface SetupOptions {\n  document$: Subject<Document>         /* Document subject */\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Set up version selector\n *\n * @param options - Options\n */\nexport function setupVersionSelector(\n  { document$ }: SetupOptions\n): void {\n  const config = configuration()\n  const versions$ = requestJSON<Version[]>(\n    new URL(\"../versions.json\", config.base)\n  )\n    .pipe(\n      catchError(() => EMPTY) // @todo refactor instant loading\n    )\n\n  /* Determine current version */\n  const current$ = versions$\n    .pipe(\n      map(versions => {\n        const [, current] = config.base.match(/([^/]+)\\/?$/)!\n        return versions.find(({ version, aliases }) => (\n          version === current || aliases.includes(current)\n        )) || versions[0]\n      })\n    )\n\n  /* Intercept inter-version navigation */\n  versions$\n    .pipe(\n      map(versions => new Map(versions.map(version => [\n        `${new URL(`../${version.version}/`, config.base)}`,\n        version\n      ]))),\n      switchMap(urls => fromEvent<MouseEvent>(document.body, \"click\")\n        .pipe(\n          filter(ev => !ev.metaKey && !ev.ctrlKey),\n          withLatestFrom(current$),\n          switchMap(([ev, current]) => {\n            if (ev.target instanceof Element) {\n              const el = ev.target.closest(\"a\")\n              if (el && !el.target && urls.has(el.href)) {\n                const url = el.href\n                // This is a temporary hack to detect if a version inside the\n                // version selector or on another part of the site was clicked.\n                // If we're inside the version selector, we definitely want to\n                // find the same page, as we might have different deployments\n                // due to aliases. However, if we're outside the version\n                // selector, we must abort here, because we might otherwise\n                // interfere with instant navigation. We need to refactor this\n                // at some point together with instant navigation.\n                //\n                // See https://github.com/squidfunk/mkdocs-material/issues/4012\n                if (!ev.target.closest(\".md-version\")) {\n                  const version = urls.get(url)!\n                  if (version === current)\n                    return EMPTY\n                }\n                ev.preventDefault()\n                return of(url)\n              }\n            }\n            return EMPTY\n          }),\n          switchMap(url => {\n            const { version } = urls.get(url)!\n            return fetchSitemap(new URL(url))\n              .pipe(\n                map(sitemap => {\n                  const location = getLocation()\n                  const path = location.href.replace(config.base, \"\")\n                  return sitemap.has(path.split(\"#\")[0])\n                    ? new URL(`../${version}/${path}`, config.base)\n                    : new URL(url)\n                })\n              )\n          })\n        )\n      )\n    )\n      .subscribe(url => setLocation(url, true))\n\n  /* Render version selector and warning */\n  combineLatest([versions$, current$])\n    .subscribe(([versions, current]) => {\n      const topic = getElement(\".md-header__topic\")\n      topic.appendChild(renderVersionSelector(versions, current))\n    })\n\n  /* Integrate outdated version banner with instant navigation */\n  document$.pipe(switchMap(() => current$))\n    .subscribe(current => {\n\n      /* Check if version state was already determined */\n      let outdated = __md_get(\"__outdated\", sessionStorage)\n      if (outdated === null) {\n        outdated = true\n\n        /* Obtain and normalize default versions */\n        let ignored = config.version?.default || \"latest\"\n        if (!Array.isArray(ignored))\n          ignored = [ignored]\n\n        /* Check if version is considered a default */\n        main: for (const ignore of ignored)\n          for (const version of current.aliases.concat(current.version))\n            if (new RegExp(ignore, \"i\").test(version)) {\n              outdated = false\n              break main\n            }\n\n        /* Persist version state in session storage */\n        __md_set(\"__outdated\", outdated, sessionStorage)\n      }\n\n      /* Unhide outdated version banner */\n      if (outdated)\n        for (const warning of getComponentElements(\"outdated\"))\n          warning.hidden = false\n    })\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  Observable,\n  Subject,\n  combineLatest,\n  distinctUntilChanged,\n  distinctUntilKeyChanged,\n  endWith,\n  finalize,\n  first,\n  fromEvent,\n  ignoreElements,\n  map,\n  merge,\n  shareReplay,\n  takeUntil,\n  tap\n} from \"rxjs\"\n\nimport {\n  getElement,\n  getLocation,\n  setToggle,\n  watchElementFocus,\n  watchToggle\n} from \"~/browser\"\nimport {\n  SearchMessage,\n  SearchMessageType,\n  isSearchReadyMessage\n} from \"~/integrations\"\n\nimport { Component } from \"../../_\"\n\n/* ----------------------------------------------------------------------------\n * Types\n * ------------------------------------------------------------------------- */\n\n/**\n * Search query\n */\nexport interface SearchQuery {\n  value: string                        /* Query value */\n  focus: boolean                       /* Query focus */\n}\n\n/* ----------------------------------------------------------------------------\n * Helper types\n * ------------------------------------------------------------------------- */\n\n/**\n * Watch options\n */\ninterface WatchOptions {\n  worker$: Subject<SearchMessage>      /* Search worker */\n}\n\n/**\n * Mount options\n */\ninterface MountOptions {\n  worker$: Subject<SearchMessage>      /* Search worker */\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Watch search query\n *\n * Note that the focus event which triggers re-reading the current query value\n * is delayed by `1ms` so the input's empty state is allowed to propagate.\n *\n * @param el - Search query element\n * @param options - Options\n *\n * @returns Search query observable\n */\nexport function watchSearchQuery(\n  el: HTMLInputElement, { worker$ }: WatchOptions\n): Observable<SearchQuery> {\n\n  /* Support search deep linking */\n  const { searchParams } = getLocation()\n  if (searchParams.has(\"q\")) {\n    setToggle(\"search\", true)\n\n    /* Set query from parameter */\n    el.value = searchParams.get(\"q\")!\n    el.focus()\n\n    /* Remove query parameter on close */\n    watchToggle(\"search\")\n      .pipe(\n        first(active => !active)\n      )\n        .subscribe(() => {\n          const url = getLocation()\n          url.searchParams.delete(\"q\")\n          history.replaceState({}, \"\", `${url}`)\n        })\n  }\n\n  /* Intercept focus and input events */\n  const focus$ = watchElementFocus(el)\n  const value$ = merge(\n    worker$.pipe(first(isSearchReadyMessage)),\n    fromEvent(el, \"keyup\"),\n    focus$\n  )\n    .pipe(\n      map(() => el.value),\n      distinctUntilChanged()\n    )\n\n  /* Combine into single observable */\n  return combineLatest([value$, focus$])\n    .pipe(\n      map(([value, focus]) => ({ value, focus })),\n      shareReplay(1)\n    )\n}\n\n/**\n * Mount search query\n *\n * @param el - Search query element\n * @param options - Options\n *\n * @returns Search query component observable\n */\nexport function mountSearchQuery(\n  el: HTMLInputElement, { worker$ }: MountOptions\n): Observable<Component<SearchQuery, HTMLInputElement>> {\n  const push$ = new Subject<SearchQuery>()\n  const done$ = push$.pipe(ignoreElements(), endWith(true))\n\n  /* Handle value change */\n  combineLatest([\n    worker$.pipe(first(isSearchReadyMessage)),\n    push$\n  ], (_, query) => query)\n    .pipe(\n      distinctUntilKeyChanged(\"value\")\n    )\n      .subscribe(({ value }) => worker$.next({\n        type: SearchMessageType.QUERY,\n        data: value\n      }))\n\n  /* Handle focus change */\n  push$\n    .pipe(\n      distinctUntilKeyChanged(\"focus\")\n    )\n      .subscribe(({ focus }) => {\n        if (focus)\n          setToggle(\"search\", focus)\n      })\n\n  /* Handle reset */\n  fromEvent(el.form!, \"reset\")\n    .pipe(\n      takeUntil(done$)\n    )\n      .subscribe(() => el.focus())\n\n  // Focus search query on label click - note that this is necessary to bring\n  // up the keyboard on iOS and other mobile platforms, as the search dialog is\n  // not visible at first, and programatically focusing an input element must\n  // be triggered by a user interaction - see https://t.ly/Cb30n\n  const label = getElement(\"header [for=__search]\")\n  fromEvent(label, \"click\")\n    .subscribe(() => el.focus())\n\n  /* Create and return component */\n  return watchSearchQuery(el, { worker$ })\n    .pipe(\n      tap(state => push$.next(state)),\n      finalize(() => push$.complete()),\n      map(state => ({ ref: el, ...state })),\n      shareReplay(1)\n    )\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  EMPTY,\n  Observable,\n  Subject,\n  bufferCount,\n  filter,\n  finalize,\n  first,\n  fromEvent,\n  map,\n  merge,\n  mergeMap,\n  of,\n  share,\n  skipUntil,\n  switchMap,\n  takeUntil,\n  tap,\n  withLatestFrom,\n  zipWith\n} from \"rxjs\"\n\nimport { translation } from \"~/_\"\nimport {\n  getElement,\n  getOptionalElement,\n  watchElementBoundary,\n  watchToggle\n} from \"~/browser\"\nimport {\n  SearchMessage,\n  SearchResult,\n  isSearchReadyMessage,\n  isSearchResultMessage\n} from \"~/integrations\"\nimport { renderSearchResultItem } from \"~/templates\"\nimport { round } from \"~/utilities\"\n\nimport { Component } from \"../../_\"\nimport { SearchQuery } from \"../query\"\n\n/* ----------------------------------------------------------------------------\n * Helper types\n * ------------------------------------------------------------------------- */\n\n/**\n * Mount options\n */\ninterface MountOptions {\n  query$: Observable<SearchQuery>      /* Search query observable */\n  worker$: Subject<SearchMessage>      /* Search worker */\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Mount search result list\n *\n * This function performs a lazy rendering of the search results, depending on\n * the vertical offset of the search result container.\n *\n * @param el - Search result list element\n * @param options - Options\n *\n * @returns Search result list component observable\n */\nexport function mountSearchResult(\n  el: HTMLElement, { worker$, query$ }: MountOptions\n): Observable<Component<SearchResult>> {\n  const push$ = new Subject<SearchResult>()\n  const boundary$ = watchElementBoundary(el.parentElement!)\n    .pipe(\n      filter(Boolean)\n    )\n\n  /* Retrieve container */\n  const container = el.parentElement!\n\n  /* Retrieve nested components */\n  const meta = getElement(\":scope > :first-child\", el)\n  const list = getElement(\":scope > :last-child\", el)\n\n  /* Reveal to accessibility tree \u2013 see https://bit.ly/3iAA7t8 */\n  watchToggle(\"search\")\n    .subscribe(active => list.setAttribute(\n      \"role\", active ? \"list\" : \"presentation\"\n    ))\n\n  /* Update search result metadata */\n  push$\n    .pipe(\n      withLatestFrom(query$),\n      skipUntil(worker$.pipe(first(isSearchReadyMessage)))\n    )\n      .subscribe(([{ items }, { value }]) => {\n        switch (items.length) {\n\n          /* No results */\n          case 0:\n            meta.textContent = value.length\n              ? translation(\"search.result.none\")\n              : translation(\"search.result.placeholder\")\n            break\n\n          /* One result */\n          case 1:\n            meta.textContent = translation(\"search.result.one\")\n            break\n\n          /* Multiple result */\n          default:\n            const count = round(items.length)\n            meta.textContent = translation(\"search.result.other\", count)\n        }\n      })\n\n  /* Render search result item */\n  const render$ = push$\n    .pipe(\n      tap(() => list.innerHTML = \"\"),\n      switchMap(({ items }) => merge(\n        of(...items.slice(0, 10)),\n        of(...items.slice(10))\n          .pipe(\n            bufferCount(4),\n            zipWith(boundary$),\n            switchMap(([chunk]) => chunk)\n          )\n      )),\n      map(renderSearchResultItem),\n      share()\n    )\n\n  /* Update search result list */\n  render$.subscribe(item => list.appendChild(item))\n  render$\n    .pipe(\n      mergeMap(item => {\n        const details = getOptionalElement(\"details\", item)\n        if (typeof details === \"undefined\")\n          return EMPTY\n\n        /* Keep position of details element stable */\n        return fromEvent(details, \"toggle\")\n          .pipe(\n            takeUntil(push$),\n            map(() => details)\n          )\n      })\n    )\n      .subscribe(details => {\n        if (\n          details.open === false &&\n          details.offsetTop <= container.scrollTop\n        )\n          container.scrollTo({ top: details.offsetTop })\n      })\n\n  /* Filter search result message */\n  const result$ = worker$\n    .pipe(\n      filter(isSearchResultMessage),\n      map(({ data }) => data)\n    )\n\n  /* Create and return component */\n  return result$\n    .pipe(\n      tap(state => push$.next(state)),\n      finalize(() => push$.complete()),\n      map(state => ({ ref: el, ...state }))\n    )\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  Observable,\n  Subject,\n  endWith,\n  finalize,\n  fromEvent,\n  ignoreElements,\n  map,\n  takeUntil,\n  tap\n} from \"rxjs\"\n\nimport { getLocation } from \"~/browser\"\n\nimport { Component } from \"../../_\"\nimport { SearchQuery } from \"../query\"\n\n/* ----------------------------------------------------------------------------\n * Types\n * ------------------------------------------------------------------------- */\n\n/**\n * Search sharing\n */\nexport interface SearchShare {\n  url: URL                             /* Deep link for sharing */\n}\n\n/* ----------------------------------------------------------------------------\n * Helper types\n * ------------------------------------------------------------------------- */\n\n/**\n * Watch options\n */\ninterface WatchOptions {\n  query$: Observable<SearchQuery>      /* Search query observable */\n}\n\n/**\n * Mount options\n */\ninterface MountOptions {\n  query$: Observable<SearchQuery>      /* Search query observable */\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Mount search sharing\n *\n * @param _el - Search sharing element\n * @param options - Options\n *\n * @returns Search sharing observable\n */\nexport function watchSearchShare(\n  _el: HTMLElement, { query$ }: WatchOptions\n): Observable<SearchShare> {\n  return query$\n    .pipe(\n      map(({ value }) => {\n        const url = getLocation()\n        url.hash = \"\"\n\n        /* Compute readable query strings */\n        value = value\n          .replace(/\\s+/g, \"+\")        /* Collapse whitespace */\n          .replace(/&/g, \"%26\")        /* Escape '&' character */\n          .replace(/=/g, \"%3D\")        /* Escape '=' character */\n\n        /* Replace query string */\n        url.search = `q=${value}`\n        return { url }\n      })\n    )\n}\n\n/**\n * Mount search sharing\n *\n * @param el - Search sharing element\n * @param options - Options\n *\n * @returns Search sharing component observable\n */\nexport function mountSearchShare(\n  el: HTMLAnchorElement, options: MountOptions\n): Observable<Component<SearchShare>> {\n  const push$ = new Subject<SearchShare>()\n  const done$ = push$.pipe(ignoreElements(), endWith(true))\n  push$.subscribe(({ url }) => {\n    el.setAttribute(\"data-clipboard-text\", el.href)\n    el.href = `${url}`\n  })\n\n  /* Prevent following of link */\n  fromEvent(el, \"click\")\n    .pipe(\n      takeUntil(done$)\n    )\n      .subscribe(ev => ev.preventDefault())\n\n  /* Create and return component */\n  return watchSearchShare(el, options)\n    .pipe(\n      tap(state => push$.next(state)),\n      finalize(() => push$.complete()),\n      map(state => ({ ref: el, ...state }))\n    )\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  Observable,\n  Subject,\n  asyncScheduler,\n  combineLatestWith,\n  distinctUntilChanged,\n  filter,\n  finalize,\n  fromEvent,\n  map,\n  merge,\n  observeOn,\n  tap\n} from \"rxjs\"\n\nimport { Keyboard } from \"~/browser\"\nimport {\n  SearchMessage,\n  SearchResult,\n  isSearchResultMessage\n} from \"~/integrations\"\n\nimport { Component, getComponentElement } from \"../../_\"\n\n/* ----------------------------------------------------------------------------\n * Types\n * ------------------------------------------------------------------------- */\n\n/**\n * Search suggestions\n */\nexport interface SearchSuggest {}\n\n/* ----------------------------------------------------------------------------\n * Helper types\n * ------------------------------------------------------------------------- */\n\n/**\n * Mount options\n */\ninterface MountOptions {\n  keyboard$: Observable<Keyboard>      /* Keyboard observable */\n  worker$: Subject<SearchMessage>      /* Search worker */\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Mount search suggestions\n *\n * This function will perform a lazy rendering of the search results, depending\n * on the vertical offset of the search result container.\n *\n * @param el - Search result list element\n * @param options - Options\n *\n * @returns Search result list component observable\n */\nexport function mountSearchSuggest(\n  el: HTMLElement, { worker$, keyboard$ }: MountOptions\n): Observable<Component<SearchSuggest>> {\n  const push$ = new Subject<SearchResult>()\n\n  /* Retrieve query component and track all changes */\n  const query  = getComponentElement(\"search-query\")\n  const query$ = merge(\n    fromEvent(query, \"keydown\"),\n    fromEvent(query, \"focus\")\n  )\n    .pipe(\n      observeOn(asyncScheduler),\n      map(() => query.value),\n      distinctUntilChanged(),\n    )\n\n  /* Update search suggestions */\n  push$\n    .pipe(\n      combineLatestWith(query$),\n      map(([{ suggest }, value]) => {\n        const words = value.split(/([\\s-]+)/)\n        if (suggest?.length && words[words.length - 1]) {\n          const last = suggest[suggest.length - 1]\n          if (last.startsWith(words[words.length - 1]))\n            words[words.length - 1] = last\n        } else {\n          words.length = 0\n        }\n        return words\n      })\n    )\n      .subscribe(words => el.innerHTML = words\n        .join(\"\")\n        .replace(/\\s/g, \"&nbsp;\")\n      )\n\n  /* Set up search keyboard handlers */\n  keyboard$\n    .pipe(\n      filter(({ mode }) => mode === \"search\")\n    )\n      .subscribe(key => {\n        switch (key.type) {\n\n          /* Right arrow: accept current suggestion */\n          case \"ArrowRight\":\n            if (\n              el.innerText.length &&\n              query.selectionStart === query.value.length\n            )\n              query.value = el.innerText\n            break\n        }\n      })\n\n  /* Filter search result message */\n  const result$ = worker$\n    .pipe(\n      filter(isSearchResultMessage),\n      map(({ data }) => data)\n    )\n\n  /* Create and return component */\n  return result$\n    .pipe(\n      tap(state => push$.next(state)),\n      finalize(() => push$.complete()),\n      map(() => ({ ref: el }))\n    )\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  NEVER,\n  Observable,\n  ObservableInput,\n  filter,\n  fromEvent,\n  merge,\n  mergeWith\n} from \"rxjs\"\n\nimport { configuration } from \"~/_\"\nimport {\n  Keyboard,\n  getActiveElement,\n  getElements,\n  setToggle\n} from \"~/browser\"\nimport {\n  SearchIndex,\n  SearchResult,\n  setupSearchWorker\n} from \"~/integrations\"\n\nimport {\n  Component,\n  getComponentElement,\n  getComponentElements\n} from \"../../_\"\nimport {\n  SearchQuery,\n  mountSearchQuery\n} from \"../query\"\nimport { mountSearchResult } from \"../result\"\nimport {\n  SearchShare,\n  mountSearchShare\n} from \"../share\"\nimport {\n  SearchSuggest,\n  mountSearchSuggest\n} from \"../suggest\"\n\n/* ----------------------------------------------------------------------------\n * Types\n * ------------------------------------------------------------------------- */\n\n/**\n * Search\n */\nexport type Search =\n  | SearchQuery\n  | SearchResult\n  | SearchShare\n  | SearchSuggest\n\n/* ----------------------------------------------------------------------------\n * Helper types\n * ------------------------------------------------------------------------- */\n\n/**\n * Mount options\n */\ninterface MountOptions {\n  index$: ObservableInput<SearchIndex> /* Search index observable */\n  keyboard$: Observable<Keyboard>      /* Keyboard observable */\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Mount search\n *\n * This function sets up the search functionality, including the underlying\n * web worker and all keyboard bindings.\n *\n * @param el - Search element\n * @param options - Options\n *\n * @returns Search component observable\n */\nexport function mountSearch(\n  el: HTMLElement, { index$, keyboard$ }: MountOptions\n): Observable<Component<Search>> {\n  const config = configuration()\n  try {\n    const worker$ = setupSearchWorker(config.search, index$)\n\n    /* Retrieve query and result components */\n    const query  = getComponentElement(\"search-query\", el)\n    const result = getComponentElement(\"search-result\", el)\n\n    /* Always close search on result selection */\n    fromEvent<PointerEvent>(el, \"click\")\n      .pipe(\n        filter(({ target }) => (\n          target instanceof Element && !!target.closest(\"a\")\n        ))\n      )\n        .subscribe(() => setToggle(\"search\", false))\n\n    /* Set up search keyboard handlers */\n    keyboard$\n      .pipe(\n        filter(({ mode }) => mode === \"search\")\n      )\n        .subscribe(key => {\n          const active = getActiveElement()\n          switch (key.type) {\n\n            /* Enter: go to first (best) result */\n            case \"Enter\":\n              if (active === query) {\n                const anchors = new Map<HTMLAnchorElement, number>()\n                for (const anchor of getElements<HTMLAnchorElement>(\n                  \":first-child [href]\", result\n                )) {\n                  const article = anchor.firstElementChild!\n                  anchors.set(anchor, parseFloat(\n                    article.getAttribute(\"data-md-score\")!\n                  ))\n                }\n\n                /* Go to result with highest score, if any */\n                if (anchors.size) {\n                  const [[best]] = [...anchors].sort(([, a], [, b]) => b - a)\n                  best.click()\n                }\n\n                /* Otherwise omit form submission */\n                key.claim()\n              }\n              break\n\n            /* Escape or Tab: close search */\n            case \"Escape\":\n            case \"Tab\":\n              setToggle(\"search\", false)\n              query.blur()\n              break\n\n            /* Vertical arrows: select previous or next search result */\n            case \"ArrowUp\":\n            case \"ArrowDown\":\n              if (typeof active === \"undefined\") {\n                query.focus()\n              } else {\n                const els = [query, ...getElements(\n                  \":not(details) > [href], summary, details[open] [href]\",\n                  result\n                )]\n                const i = Math.max(0, (\n                  Math.max(0, els.indexOf(active)) + els.length + (\n                    key.type === \"ArrowUp\" ? -1 : +1\n                  )\n                ) % els.length)\n                els[i].focus()\n              }\n\n              /* Prevent scrolling of page */\n              key.claim()\n              break\n\n            /* All other keys: hand to search query */\n            default:\n              if (query !== getActiveElement())\n                query.focus()\n          }\n        })\n\n    /* Set up global keyboard handlers */\n    keyboard$\n      .pipe(\n        filter(({ mode }) => mode === \"global\")\n      )\n        .subscribe(key => {\n          switch (key.type) {\n\n            /* Open search and select query */\n            case \"f\":\n            case \"s\":\n            case \"/\":\n              query.focus()\n              query.select()\n\n              /* Prevent scrolling of page */\n              key.claim()\n              break\n          }\n        })\n\n    /* Create and return component */\n    const query$ = mountSearchQuery(query, { worker$ })\n    return merge(\n      query$,\n      mountSearchResult(result, { worker$, query$ })\n    )\n      .pipe(\n        mergeWith(\n\n          /* Search sharing */\n          ...getComponentElements(\"search-share\", el)\n            .map(child => mountSearchShare(child, { query$ })),\n\n          /* Search suggestions */\n          ...getComponentElements(\"search-suggest\", el)\n            .map(child => mountSearchSuggest(child, { worker$, keyboard$ }))\n        )\n      )\n\n  /* Gracefully handle broken search */\n  } catch (err) {\n    el.hidden = true\n    return NEVER\n  }\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  Observable,\n  ObservableInput,\n  combineLatest,\n  filter,\n  map,\n  startWith\n} from \"rxjs\"\n\nimport { getLocation } from \"~/browser\"\nimport {\n  SearchIndex,\n  setupSearchHighlighter\n} from \"~/integrations\"\nimport { h } from \"~/utilities\"\n\nimport { Component } from \"../../_\"\n\n/* ----------------------------------------------------------------------------\n * Types\n * ------------------------------------------------------------------------- */\n\n/**\n * Search highlighting\n */\nexport interface SearchHighlight {\n  nodes: Map<ChildNode, string>        /* Map of replacements */\n}\n\n/* ----------------------------------------------------------------------------\n * Helper types\n * ------------------------------------------------------------------------- */\n\n/**\n * Mount options\n */\ninterface MountOptions {\n  index$: ObservableInput<SearchIndex> /* Search index observable */\n  location$: Observable<URL>           /* Location observable */\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Mount search highlighting\n *\n * @param el - Content element\n * @param options - Options\n *\n * @returns Search highlighting component observable\n */\nexport function mountSearchHiglight(\n  el: HTMLElement, { index$, location$ }: MountOptions\n): Observable<Component<SearchHighlight>> {\n  return combineLatest([\n    index$,\n    location$\n      .pipe(\n        startWith(getLocation()),\n        filter(url => !!url.searchParams.get(\"h\"))\n      )\n  ])\n    .pipe(\n      map(([index, url]) => setupSearchHighlighter(index.config)(\n        url.searchParams.get(\"h\")!\n      )),\n      map(fn => {\n        const nodes = new Map<ChildNode, string>()\n\n        /* Traverse text nodes and collect matches */\n        const it = document.createNodeIterator(el, NodeFilter.SHOW_TEXT)\n        for (let node = it.nextNode(); node; node = it.nextNode()) {\n          if (node.parentElement?.offsetHeight) {\n            const original = node.textContent!\n            const replaced = fn(original)\n            if (replaced.length > original.length)\n              nodes.set(node as ChildNode, replaced)\n          }\n        }\n\n        /* Replace original nodes with matches */\n        for (const [node, text] of nodes) {\n          const { childNodes } = h(\"span\", null, text)\n          node.replaceWith(...Array.from(childNodes))\n        }\n\n        /* Return component */\n        return { ref: el, nodes }\n      })\n    )\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  Observable,\n  Subject,\n  animationFrameScheduler,\n  asyncScheduler,\n  auditTime,\n  combineLatest,\n  defer,\n  distinctUntilChanged,\n  endWith,\n  finalize,\n  first,\n  from,\n  fromEvent,\n  ignoreElements,\n  map,\n  mergeMap,\n  observeOn,\n  takeUntil,\n  tap,\n  withLatestFrom\n} from \"rxjs\"\n\nimport {\n  Viewport,\n  getElement,\n  getElementOffset,\n  getElementSize,\n  getElements\n} from \"~/browser\"\n\nimport { Component } from \"../_\"\nimport { Header } from \"../header\"\nimport { Main } from \"../main\"\n\n/* ----------------------------------------------------------------------------\n * Types\n * ------------------------------------------------------------------------- */\n\n/**\n * Sidebar\n */\nexport interface Sidebar {\n  height: number                       /* Sidebar height */\n  locked: boolean                      /* Sidebar is locked */\n}\n\n/* ----------------------------------------------------------------------------\n * Helper types\n * ------------------------------------------------------------------------- */\n\n/**\n * Watch options\n */\ninterface WatchOptions {\n  viewport$: Observable<Viewport>      /* Viewport observable */\n  main$: Observable<Main>              /* Main area observable */\n}\n\n/**\n * Mount options\n */\ninterface MountOptions {\n  viewport$: Observable<Viewport>      /* Viewport observable */\n  header$: Observable<Header>          /* Header observable */\n  main$: Observable<Main>              /* Main area observable */\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Watch sidebar\n *\n * This function returns an observable that computes the visual parameters of\n * the sidebar which depends on the vertical viewport offset, as well as the\n * height of the main area. When the page is scrolled beyond the header, the\n * sidebar is locked and fills the remaining space.\n *\n * @param el - Sidebar element\n * @param options - Options\n *\n * @returns Sidebar observable\n */\nexport function watchSidebar(\n  el: HTMLElement, { viewport$, main$ }: WatchOptions\n): Observable<Sidebar> {\n  const parent = el.closest<HTMLElement>(\".md-grid\")!\n  const adjust =\n    parent.offsetTop -\n    parent.parentElement!.offsetTop\n\n  /* Compute the sidebar's available height and if it should be locked */\n  return combineLatest([main$, viewport$])\n    .pipe(\n      map(([{ offset, height }, { offset: { y } }]) => {\n        height = height\n          + Math.min(adjust, Math.max(0, y - offset))\n          - adjust\n        return {\n          height,\n          locked: y >= offset + adjust\n        }\n      }),\n      distinctUntilChanged((a, b) => (\n        a.height === b.height &&\n        a.locked === b.locked\n      ))\n    )\n}\n\n/**\n * Mount sidebar\n *\n * This function doesn't set the height of the actual sidebar, but of its first\n * child \u2013 the `.md-sidebar__scrollwrap` element in order to mitigiate jittery\n * sidebars when the footer is scrolled into view. At some point we switched\n * from `absolute` / `fixed` positioning to `sticky` positioning, significantly\n * reducing jitter in some browsers (respectively Firefox and Safari) when\n * scrolling from the top. However, top-aligned sticky positioning means that\n * the sidebar snaps to the bottom when the end of the container is reached.\n * This is what leads to the mentioned jitter, as the sidebar's height may be\n * updated too slowly.\n *\n * This behaviour can be mitigiated by setting the height of the sidebar to `0`\n * while preserving the padding, and the height on its first element.\n *\n * @param el - Sidebar element\n * @param options - Options\n *\n * @returns Sidebar component observable\n */\nexport function mountSidebar(\n  el: HTMLElement, { header$, ...options }: MountOptions\n): Observable<Component<Sidebar>> {\n  const inner = getElement(\".md-sidebar__scrollwrap\", el)\n  const { y } = getElementOffset(inner)\n  return defer(() => {\n    const push$ = new Subject<Sidebar>()\n    const done$ = push$.pipe(ignoreElements(), endWith(true))\n    const next$ = push$\n      .pipe(\n        auditTime(0, animationFrameScheduler)\n      )\n\n    /* Update sidebar height and offset */\n    next$.pipe(withLatestFrom(header$))\n      .subscribe({\n\n        /* Handle emission */\n        next([{ height }, { height: offset }]) {\n          inner.style.height = `${height - 2 * y}px`\n          el.style.top       = `${offset}px`\n        },\n\n        /* Handle complete */\n        complete() {\n          inner.style.height = \"\"\n          el.style.top       = \"\"\n        }\n      })\n\n    /* Bring active item into view on initial load */\n    next$.pipe(first())\n      .subscribe(() => {\n        for (const item of getElements(\".md-nav__link--active[href]\", el)) {\n          if (!item.clientHeight) // skip invisible toc in left sidebar\n            continue\n          const container = item.closest<HTMLElement>(\".md-sidebar__scrollwrap\")!\n          if (typeof container !== \"undefined\") {\n            const offset = item.offsetTop - container.offsetTop\n            const { height } = getElementSize(container)\n            container.scrollTo({\n              top: offset - height / 2\n            })\n          }\n        }\n      })\n\n    /* Handle accessibility for expandable items, see https://bit.ly/3jaod9p */\n    from(getElements<HTMLLabelElement>(\"label[tabindex]\", el))\n      .pipe(\n        mergeMap(label => fromEvent(label, \"click\")\n          .pipe(\n            observeOn(asyncScheduler),\n            map(() => label),\n            takeUntil(done$)\n          )\n        )\n      )\n        .subscribe(label => {\n          const input = getElement<HTMLInputElement>(`[id=\"${label.htmlFor}\"]`)\n          const nav = getElement(`[aria-labelledby=\"${label.id}\"]`)\n          nav.setAttribute(\"aria-expanded\", `${input.checked}`)\n        })\n\n    /* Create and return component */\n    return watchSidebar(el, options)\n      .pipe(\n        tap(state => push$.next(state)),\n        finalize(() => push$.complete()),\n        map(state => ({ ref: el, ...state }))\n      )\n  })\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport { Repo, User } from \"github-types\"\nimport {\n  EMPTY,\n  Observable,\n  catchError,\n  defaultIfEmpty,\n  map,\n  zip\n} from \"rxjs\"\n\nimport { requestJSON } from \"~/browser\"\n\nimport { SourceFacts } from \"../_\"\n\n/* ----------------------------------------------------------------------------\n * Helper types\n * ------------------------------------------------------------------------- */\n\n/**\n * GitHub release (partial)\n */\ninterface Release {\n  tag_name: string                     /* Tag name */\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Fetch GitHub repository facts\n *\n * @param user - GitHub user or organization\n * @param repo - GitHub repository\n *\n * @returns Repository facts observable\n */\nexport function fetchSourceFactsFromGitHub(\n  user: string, repo?: string\n): Observable<SourceFacts> {\n  if (typeof repo !== \"undefined\") {\n    const url = `https://api.github.com/repos/${user}/${repo}`\n    return zip(\n\n      /* Fetch version */\n      requestJSON<Release>(`${url}/releases/latest`)\n        .pipe(\n          catchError(() => EMPTY), // @todo refactor instant loading\n          map(release => ({\n            version: release.tag_name\n          })),\n          defaultIfEmpty({})\n        ),\n\n      /* Fetch stars and forks */\n      requestJSON<Repo>(url)\n        .pipe(\n          catchError(() => EMPTY), // @todo refactor instant loading\n          map(info => ({\n            stars: info.stargazers_count,\n            forks: info.forks_count\n          })),\n          defaultIfEmpty({})\n        )\n    )\n      .pipe(\n        map(([release, info]) => ({ ...release, ...info }))\n      )\n\n  /* User or organization */\n  } else {\n    const url = `https://api.github.com/users/${user}`\n    return requestJSON<User>(url)\n      .pipe(\n        map(info => ({\n          repositories: info.public_repos\n        })),\n        defaultIfEmpty({})\n      )\n  }\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport { ProjectSchema } from \"gitlab\"\nimport {\n  EMPTY,\n  Observable,\n  catchError,\n  defaultIfEmpty,\n  map\n} from \"rxjs\"\n\nimport { requestJSON } from \"~/browser\"\n\nimport { SourceFacts } from \"../_\"\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Fetch GitLab repository facts\n *\n * @param base - GitLab base\n * @param project - GitLab project\n *\n * @returns Repository facts observable\n */\nexport function fetchSourceFactsFromGitLab(\n  base: string, project: string\n): Observable<SourceFacts> {\n  const url = `https://${base}/api/v4/projects/${encodeURIComponent(project)}`\n  return requestJSON<ProjectSchema>(url)\n    .pipe(\n      catchError(() => EMPTY), // @todo refactor instant loading\n      map(({ star_count, forks_count }) => ({\n        stars: star_count,\n        forks: forks_count\n      })),\n      defaultIfEmpty({})\n    )\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport { EMPTY, Observable } from \"rxjs\"\n\nimport { fetchSourceFactsFromGitHub } from \"../github\"\nimport { fetchSourceFactsFromGitLab } from \"../gitlab\"\n\n/* ----------------------------------------------------------------------------\n * Types\n * ------------------------------------------------------------------------- */\n\n/**\n * Repository facts for repositories\n */\nexport interface RepositoryFacts {\n  stars?: number                       /* Number of stars */\n  forks?: number                       /* Number of forks */\n  version?: string                     /* Latest version */\n}\n\n/**\n * Repository facts for organizations\n */\nexport interface OrganizationFacts {\n  repositories?: number                /* Number of repositories */\n}\n\n/* ------------------------------------------------------------------------- */\n\n/**\n * Repository facts\n */\nexport type SourceFacts =\n  | RepositoryFacts\n  | OrganizationFacts\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Fetch repository facts\n *\n * @param url - Repository URL\n *\n * @returns Repository facts observable\n */\nexport function fetchSourceFacts(\n  url: string\n): Observable<SourceFacts> {\n\n  /* Try to match GitHub repository */\n  let match = url.match(/^.+github\\.com\\/([^/]+)\\/?([^/]+)?/i)\n  if (match) {\n    const [, user, repo] = match\n    return fetchSourceFactsFromGitHub(user, repo)\n  }\n\n  /* Try to match GitLab repository */\n  match = url.match(/^.+?([^/]*gitlab[^/]+)\\/(.+?)\\/?$/i)\n  if (match) {\n    const [, base, slug] = match\n    return fetchSourceFactsFromGitLab(base, slug)\n  }\n\n  /* Fallback */\n  return EMPTY\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  EMPTY,\n  Observable,\n  Subject,\n  catchError,\n  defer,\n  filter,\n  finalize,\n  map,\n  of,\n  shareReplay,\n  tap\n} from \"rxjs\"\n\nimport { getElement } from \"~/browser\"\nimport { ConsentDefaults } from \"~/components/consent\"\nimport { renderSourceFacts } from \"~/templates\"\n\nimport {\n  Component,\n  getComponentElements\n} from \"../../_\"\nimport {\n  SourceFacts,\n  fetchSourceFacts\n} from \"../facts\"\n\n/* ----------------------------------------------------------------------------\n * Types\n * ------------------------------------------------------------------------- */\n\n/**\n * Repository information\n */\nexport interface Source {\n  facts: SourceFacts                   /* Repository facts */\n}\n\n/* ----------------------------------------------------------------------------\n * Data\n * ------------------------------------------------------------------------- */\n\n/**\n * Repository information observable\n */\nlet fetch$: Observable<Source>\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Watch repository information\n *\n * This function tries to read the repository facts from session storage, and\n * if unsuccessful, fetches them from the underlying provider.\n *\n * @param el - Repository information element\n *\n * @returns Repository information observable\n */\nexport function watchSource(\n  el: HTMLAnchorElement\n): Observable<Source> {\n  return fetch$ ||= defer(() => {\n    const cached = __md_get<SourceFacts>(\"__source\", sessionStorage)\n    if (cached) {\n      return of(cached)\n    } else {\n\n      /* Check if consent is configured and was given */\n      const els = getComponentElements(\"consent\")\n      if (els.length) {\n        const consent = __md_get<ConsentDefaults>(\"__consent\")\n        if (!(consent && consent.github))\n          return EMPTY\n      }\n\n      /* Fetch repository facts */\n      return fetchSourceFacts(el.href)\n        .pipe(\n          tap(facts => __md_set(\"__source\", facts, sessionStorage))\n        )\n    }\n  })\n    .pipe(\n      catchError(() => EMPTY),\n      filter(facts => Object.keys(facts).length > 0),\n      map(facts => ({ facts })),\n      shareReplay(1)\n    )\n}\n\n/**\n * Mount repository information\n *\n * @param el - Repository information element\n *\n * @returns Repository information component observable\n */\nexport function mountSource(\n  el: HTMLAnchorElement\n): Observable<Component<Source>> {\n  const inner = getElement(\":scope > :last-child\", el)\n  return defer(() => {\n    const push$ = new Subject<Source>()\n    push$.subscribe(({ facts }) => {\n      inner.appendChild(renderSourceFacts(facts))\n      inner.classList.add(\"md-source__repository--active\")\n    })\n\n    /* Create and return component */\n    return watchSource(el)\n      .pipe(\n        tap(state => push$.next(state)),\n        finalize(() => push$.complete()),\n        map(state => ({ ref: el, ...state }))\n      )\n  })\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  Observable,\n  Subject,\n  defer,\n  distinctUntilKeyChanged,\n  finalize,\n  map,\n  of,\n  switchMap,\n  tap\n} from \"rxjs\"\n\nimport { feature } from \"~/_\"\nimport {\n  Viewport,\n  watchElementSize,\n  watchViewportAt\n} from \"~/browser\"\n\nimport { Component } from \"../_\"\nimport { Header } from \"../header\"\n\n/* ----------------------------------------------------------------------------\n * Types\n * ------------------------------------------------------------------------- */\n\n/**\n * Navigation tabs\n */\nexport interface Tabs {\n  hidden: boolean                      /* Navigation tabs are hidden */\n}\n\n/* ----------------------------------------------------------------------------\n * Helper types\n * ------------------------------------------------------------------------- */\n\n/**\n * Watch options\n */\ninterface WatchOptions {\n  viewport$: Observable<Viewport>      /* Viewport observable */\n  header$: Observable<Header>          /* Header observable */\n}\n\n/**\n * Mount options\n */\ninterface MountOptions {\n  viewport$: Observable<Viewport>      /* Viewport observable */\n  header$: Observable<Header>          /* Header observable */\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Watch navigation tabs\n *\n * @param el - Navigation tabs element\n * @param options - Options\n *\n * @returns Navigation tabs observable\n */\nexport function watchTabs(\n  el: HTMLElement, { viewport$, header$ }: WatchOptions\n): Observable<Tabs> {\n  return watchElementSize(document.body)\n    .pipe(\n      switchMap(() => watchViewportAt(el, { header$, viewport$ })),\n      map(({ offset: { y } }) => {\n        return {\n          hidden: y >= 10\n        }\n      }),\n      distinctUntilKeyChanged(\"hidden\")\n    )\n}\n\n/**\n * Mount navigation tabs\n *\n * This function hides the navigation tabs when scrolling past the threshold\n * and makes them reappear in a nice CSS animation when scrolling back up.\n *\n * @param el - Navigation tabs element\n * @param options - Options\n *\n * @returns Navigation tabs component observable\n */\nexport function mountTabs(\n  el: HTMLElement, options: MountOptions\n): Observable<Component<Tabs>> {\n  return defer(() => {\n    const push$ = new Subject<Tabs>()\n    push$.subscribe({\n\n      /* Handle emission */\n      next({ hidden }) {\n        el.hidden = hidden\n      },\n\n      /* Handle complete */\n      complete() {\n        el.hidden = false\n      }\n    })\n\n    /* Create and return component */\n    return (\n      feature(\"navigation.tabs.sticky\")\n        ? of({ hidden: false })\n        : watchTabs(el, options)\n    )\n      .pipe(\n        tap(state => push$.next(state)),\n        finalize(() => push$.complete()),\n        map(state => ({ ref: el, ...state }))\n      )\n  })\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  Observable,\n  Subject,\n  asyncScheduler,\n  bufferCount,\n  combineLatestWith,\n  debounceTime,\n  defer,\n  distinctUntilChanged,\n  distinctUntilKeyChanged,\n  endWith,\n  filter,\n  finalize,\n  ignoreElements,\n  map,\n  merge,\n  observeOn,\n  of,\n  repeat,\n  scan,\n  share,\n  skip,\n  startWith,\n  switchMap,\n  takeUntil,\n  tap,\n  withLatestFrom\n} from \"rxjs\"\n\nimport { feature } from \"~/_\"\nimport {\n  Viewport,\n  getElement,\n  getElementContainer,\n  getElementSize,\n  getElements,\n  getLocation,\n  getOptionalElement,\n  watchElementSize\n} from \"~/browser\"\n\nimport {\n  Component,\n  getComponentElement\n} from \"../_\"\nimport { Header } from \"../header\"\nimport { Main } from \"../main\"\n\n/* ----------------------------------------------------------------------------\n * Types\n * ------------------------------------------------------------------------- */\n\n/**\n * Table of contents\n */\nexport interface TableOfContents {\n  prev: HTMLAnchorElement[][]          /* Anchors (previous) */\n  next: HTMLAnchorElement[][]          /* Anchors (next) */\n}\n\n/* ----------------------------------------------------------------------------\n * Helper types\n * ------------------------------------------------------------------------- */\n\n/**\n * Watch options\n */\ninterface WatchOptions {\n  viewport$: Observable<Viewport>      /* Viewport observable */\n  header$: Observable<Header>          /* Header observable */\n}\n\n/**\n * Mount options\n */\ninterface MountOptions {\n  viewport$: Observable<Viewport>      /* Viewport observable */\n  header$: Observable<Header>          /* Header observable */\n  main$: Observable<Main>              /* Main area observable */\n  target$: Observable<HTMLElement>     /* Location target observable */\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Watch table of contents\n *\n * This is effectively a scroll spy implementation which will account for the\n * fixed header and automatically re-calculate anchor offsets when the viewport\n * is resized. The returned observable will only emit if the table of contents\n * needs to be repainted.\n *\n * This implementation tracks an anchor element's entire path starting from its\n * level up to the top-most anchor element, e.g. `[h3, h2, h1]`. Although the\n * Material theme currently doesn't make use of this information, it enables\n * the styling of the entire hierarchy through customization.\n *\n * Note that the current anchor is the last item of the `prev` anchor list.\n *\n * @param el - Table of contents element\n * @param options - Options\n *\n * @returns Table of contents observable\n */\nexport function watchTableOfContents(\n  el: HTMLElement, { viewport$, header$ }: WatchOptions\n): Observable<TableOfContents> {\n  const table = new Map<HTMLAnchorElement, HTMLElement>()\n\n  /* Compute anchor-to-target mapping */\n  const anchors = getElements<HTMLAnchorElement>(\"[href^=\\\\#]\", el)\n  for (const anchor of anchors) {\n    const id = decodeURIComponent(anchor.hash.substring(1))\n    const target = getOptionalElement(`[id=\"${id}\"]`)\n    if (typeof target !== \"undefined\")\n      table.set(anchor, target)\n  }\n\n  /* Compute necessary adjustment for header */\n  const adjust$ = header$\n    .pipe(\n      distinctUntilKeyChanged(\"height\"),\n      map(({ height }) => {\n        const main = getComponentElement(\"main\")\n        const grid = getElement(\":scope > :first-child\", main)\n        return height + 0.8 * (\n          grid.offsetTop -\n          main.offsetTop\n        )\n      }),\n      share()\n    )\n\n  /* Compute partition of previous and next anchors */\n  const partition$ = watchElementSize(document.body)\n    .pipe(\n      distinctUntilKeyChanged(\"height\"),\n\n      /* Build index to map anchor paths to vertical offsets */\n      switchMap(body => defer(() => {\n        let path: HTMLAnchorElement[] = []\n        return of([...table].reduce((index, [anchor, target]) => {\n          while (path.length) {\n            const last = table.get(path[path.length - 1])!\n            if (last.tagName >= target.tagName) {\n              path.pop()\n            } else {\n              break\n            }\n          }\n\n          /* If the current anchor is hidden, continue with its parent */\n          let offset = target.offsetTop\n          while (!offset && target.parentElement) {\n            target = target.parentElement\n            offset = target.offsetTop\n          }\n\n          /* Fix anchor offsets in tables - see https://bit.ly/3CUFOcn */\n          let parent = target.offsetParent as HTMLElement\n          for (; parent; parent = parent.offsetParent as HTMLElement)\n            offset += parent.offsetTop\n\n          /* Map reversed anchor path to vertical offset */\n          return index.set(\n            [...path = [...path, anchor]].reverse(),\n            offset\n          )\n        }, new Map<HTMLAnchorElement[], number>()))\n      })\n        .pipe(\n\n          /* Sort index by vertical offset (see https://bit.ly/30z6QSO) */\n          map(index => new Map([...index].sort(([, a], [, b]) => a - b))),\n          combineLatestWith(adjust$),\n\n          /* Re-compute partition when viewport offset changes */\n          switchMap(([index, adjust]) => viewport$\n            .pipe(\n              scan(([prev, next], { offset: { y }, size }) => {\n                const last = y + size.height >= Math.floor(body.height)\n\n                /* Look forward */\n                while (next.length) {\n                  const [, offset] = next[0]\n                  if (offset - adjust < y || last) {\n                    prev = [...prev, next.shift()!]\n                  } else {\n                    break\n                  }\n                }\n\n                /* Look backward */\n                while (prev.length) {\n                  const [, offset] = prev[prev.length - 1]\n                  if (offset - adjust >= y && !last) {\n                    next = [prev.pop()!, ...next]\n                  } else {\n                    break\n                  }\n                }\n\n                /* Return partition */\n                return [prev, next]\n              }, [[], [...index]]),\n              distinctUntilChanged((a, b) => (\n                a[0] === b[0] &&\n                a[1] === b[1]\n              ))\n            )\n          )\n        )\n      )\n    )\n\n  /* Compute and return anchor list migrations */\n  return partition$\n    .pipe(\n      map(([prev, next]) => ({\n        prev: prev.map(([path]) => path),\n        next: next.map(([path]) => path)\n      })),\n\n      /* Extract anchor list migrations */\n      startWith({ prev: [], next: [] }),\n      bufferCount(2, 1),\n      map(([a, b]) => {\n\n        /* Moving down */\n        if (a.prev.length < b.prev.length) {\n          return {\n            prev: b.prev.slice(Math.max(0, a.prev.length - 1), b.prev.length),\n            next: []\n          }\n\n        /* Moving up */\n        } else {\n          return {\n            prev: b.prev.slice(-1),\n            next: b.next.slice(0, b.next.length - a.next.length)\n          }\n        }\n      })\n    )\n}\n\n/* ------------------------------------------------------------------------- */\n\n/**\n * Mount table of contents\n *\n * @param el - Table of contents element\n * @param options - Options\n *\n * @returns Table of contents component observable\n */\nexport function mountTableOfContents(\n  el: HTMLElement, { viewport$, header$, main$, target$ }: MountOptions\n): Observable<Component<TableOfContents>> {\n  return defer(() => {\n    const push$ = new Subject<TableOfContents>()\n    const done$ = push$.pipe(ignoreElements(), endWith(true))\n    push$.subscribe(({ prev, next }) => {\n\n      /* Look forward */\n      for (const [anchor] of next) {\n        anchor.classList.remove(\"md-nav__link--passed\")\n        anchor.classList.remove(\"md-nav__link--active\")\n      }\n\n      /* Look backward */\n      for (const [index, [anchor]] of prev.entries()) {\n        anchor.classList.add(\"md-nav__link--passed\")\n        anchor.classList.toggle(\n          \"md-nav__link--active\",\n          index === prev.length - 1\n        )\n      }\n    })\n\n    /* Set up following, if enabled */\n    if (feature(\"toc.follow\")) {\n\n      /* Toggle smooth scrolling only for anchor clicks */\n      const smooth$ = merge(\n        viewport$.pipe(debounceTime(1), map(() => undefined)),\n        viewport$.pipe(debounceTime(250), map(() => \"smooth\" as const))\n      )\n\n      /* Bring active anchor into view */ // @todo: refactor\n      push$\n        .pipe(\n          filter(({ prev }) => prev.length > 0),\n          combineLatestWith(main$.pipe(observeOn(asyncScheduler))),\n          withLatestFrom(smooth$)\n        )\n          .subscribe(([[{ prev }], behavior]) => {\n            const [anchor] = prev[prev.length - 1]\n            if (anchor.offsetHeight) {\n\n              /* Retrieve overflowing container and scroll */\n              const container = getElementContainer(anchor)\n              if (typeof container !== \"undefined\") {\n                const offset = anchor.offsetTop - container.offsetTop\n                const { height } = getElementSize(container)\n                container.scrollTo({\n                  top: offset - height / 2,\n                  behavior\n                })\n              }\n            }\n          })\n    }\n\n    /* Set up anchor tracking, if enabled */\n    if (feature(\"navigation.tracking\"))\n      viewport$\n        .pipe(\n          takeUntil(done$),\n          distinctUntilKeyChanged(\"offset\"),\n          debounceTime(250),\n          skip(1),\n          takeUntil(target$.pipe(skip(1))),\n          repeat({ delay: 250 }),\n          withLatestFrom(push$)\n        )\n          .subscribe(([, { prev }]) => {\n            const url = getLocation()\n\n            /* Set hash fragment to active anchor */\n            const anchor = prev[prev.length - 1]\n            if (anchor && anchor.length) {\n              const [active] = anchor\n              const { hash } = new URL(active.href)\n              if (url.hash !== hash) {\n                url.hash = hash\n                history.replaceState({}, \"\", `${url}`)\n              }\n\n            /* Reset anchor when at the top */\n            } else {\n              url.hash = \"\"\n              history.replaceState({}, \"\", `${url}`)\n            }\n          })\n\n    /* Create and return component */\n    return watchTableOfContents(el, { viewport$, header$ })\n      .pipe(\n        tap(state => push$.next(state)),\n        finalize(() => push$.complete()),\n        map(state => ({ ref: el, ...state }))\n      )\n  })\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  Observable,\n  Subject,\n  bufferCount,\n  combineLatest,\n  distinctUntilChanged,\n  distinctUntilKeyChanged,\n  endWith,\n  finalize,\n  fromEvent,\n  ignoreElements,\n  map,\n  repeat,\n  skip,\n  takeUntil,\n  tap\n} from \"rxjs\"\n\nimport { Viewport } from \"~/browser\"\n\nimport { Component } from \"../_\"\nimport { Header } from \"../header\"\nimport { Main } from \"../main\"\n\n/* ----------------------------------------------------------------------------\n * Types\n * ------------------------------------------------------------------------- */\n\n/**\n * Back-to-top button\n */\nexport interface BackToTop {\n  hidden: boolean                      /* Back-to-top button is hidden */\n}\n\n/* ----------------------------------------------------------------------------\n * Helper types\n * ------------------------------------------------------------------------- */\n\n/**\n * Watch options\n */\ninterface WatchOptions {\n  viewport$: Observable<Viewport>      /* Viewport observable */\n  main$: Observable<Main>              /* Main area observable */\n  target$: Observable<HTMLElement>     /* Location target observable */\n}\n\n/**\n * Mount options\n */\ninterface MountOptions {\n  viewport$: Observable<Viewport>      /* Viewport observable */\n  header$: Observable<Header>          /* Header observable */\n  main$: Observable<Main>              /* Main area observable */\n  target$: Observable<HTMLElement>     /* Location target observable */\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Watch back-to-top\n *\n * @param _el - Back-to-top element\n * @param options - Options\n *\n * @returns Back-to-top observable\n */\nexport function watchBackToTop(\n  _el: HTMLElement, { viewport$, main$, target$ }: WatchOptions\n): Observable<BackToTop> {\n\n  /* Compute direction */\n  const direction$ = viewport$\n    .pipe(\n      map(({ offset: { y } }) => y),\n      bufferCount(2, 1),\n      map(([a, b]) => a > b && b > 0),\n      distinctUntilChanged()\n    )\n\n  /* Compute whether main area is active */\n  const active$ = main$\n    .pipe(\n      map(({ active }) => active)\n    )\n\n  /* Compute threshold for hiding */\n  return combineLatest([active$, direction$])\n    .pipe(\n      map(([active, direction]) => !(active && direction)),\n      distinctUntilChanged(),\n      takeUntil(target$.pipe(skip(1))),\n      endWith(true),\n      repeat({ delay: 250 }),\n      map(hidden => ({ hidden }))\n    )\n}\n\n/* ------------------------------------------------------------------------- */\n\n/**\n * Mount back-to-top\n *\n * @param el - Back-to-top element\n * @param options - Options\n *\n * @returns Back-to-top component observable\n */\nexport function mountBackToTop(\n  el: HTMLElement, { viewport$, header$, main$, target$ }: MountOptions\n): Observable<Component<BackToTop>> {\n  const push$ = new Subject<BackToTop>()\n  const done$ = push$.pipe(ignoreElements(), endWith(true))\n  push$.subscribe({\n\n    /* Handle emission */\n    next({ hidden }) {\n      el.hidden = hidden\n      if (hidden) {\n        el.setAttribute(\"tabindex\", \"-1\")\n        el.blur()\n      } else {\n        el.removeAttribute(\"tabindex\")\n      }\n    },\n\n    /* Handle complete */\n    complete() {\n      el.style.top = \"\"\n      el.hidden = true\n      el.removeAttribute(\"tabindex\")\n    }\n  })\n\n  /* Watch header height */\n  header$\n    .pipe(\n      takeUntil(done$),\n      distinctUntilKeyChanged(\"height\")\n    )\n      .subscribe(({ height }) => {\n        el.style.top = `${height + 16}px`\n      })\n\n  /* Go back to top */\n  fromEvent(el, \"click\")\n    .subscribe(ev => {\n      ev.preventDefault()\n      window.scrollTo({ top: 0 })\n    })\n\n  /* Create and return component */\n  return watchBackToTop(el, { viewport$, main$, target$ })\n    .pipe(\n      tap(state => push$.next(state)),\n      finalize(() => push$.complete()),\n      map(state => ({ ref: el, ...state }))\n    )\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  Observable,\n  filter,\n  finalize,\n  map,\n  mergeMap,\n  skip,\n  switchMap,\n  take,\n  takeUntil\n} from \"rxjs\"\n\nimport {\n  getElements,\n  watchElementVisibility\n} from \"~/browser\"\nimport { mountTooltip } from \"~/components\"\n\n/* ----------------------------------------------------------------------------\n * Helper types\n * ------------------------------------------------------------------------- */\n\n/**\n * Patch options\n */\ninterface PatchOptions {\n  document$: Observable<Document>      /* Document observable */\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Patch ellipsis\n *\n * This function will fetch all elements that are shortened with ellipsis, and\n * filter those which are visible. Once they become visible, they stay in that\n * state, even though they may be hidden again. This optimization is necessary\n * to reduce pressure on the browser, with elements fading in and out of view.\n *\n * @param options - Options\n */\nexport function patchEllipsis(\n  { document$ }: PatchOptions\n): void {\n  document$\n    .pipe(\n      switchMap(() => getElements(\".md-ellipsis\")),\n      mergeMap(el => watchElementVisibility(el)\n        .pipe(\n          takeUntil(document$.pipe(skip(1))),\n          filter(visible => visible),\n          map(() => el),\n          take(1)\n        )\n      ),\n      filter(el => el.offsetWidth < el.scrollWidth),\n      mergeMap(el => {\n        const text = el.innerText\n        const host = el.closest(\"a\") || el\n        host.title = text\n\n        /* Mount tooltip */\n        return mountTooltip(host)\n          .pipe(\n            takeUntil(document$.pipe(skip(1))),\n            finalize(() => host.removeAttribute(\"title\"))\n          )\n      })\n    )\n      .subscribe()\n\n  // @todo move this outside of here and fix memleaks\n  document$\n    .pipe(\n      switchMap(() => getElements(\".md-status\")),\n      mergeMap(el => mountTooltip(el))\n    )\n      .subscribe()\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  Observable,\n  fromEvent,\n  map,\n  mergeMap,\n  switchMap,\n  takeWhile,\n  tap,\n  withLatestFrom\n} from \"rxjs\"\n\nimport { getElements } from \"~/browser\"\n\n/* ----------------------------------------------------------------------------\n * Helper types\n * ------------------------------------------------------------------------- */\n\n/**\n * Patch options\n */\ninterface PatchOptions {\n  document$: Observable<Document>      /* Document observable */\n  tablet$: Observable<boolean>         /* Media tablet observable */\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Patch indeterminate checkboxes\n *\n * This function replaces the indeterminate \"pseudo state\" with the actual\n * indeterminate state, which is used to keep navigation always expanded.\n *\n * @param options - Options\n */\nexport function patchIndeterminate(\n  { document$, tablet$ }: PatchOptions\n): void {\n  document$\n    .pipe(\n      switchMap(() => getElements<HTMLInputElement>(\n        \".md-toggle--indeterminate\"\n      )),\n      tap(el => {\n        el.indeterminate = true\n        el.checked = false\n      }),\n      mergeMap(el => fromEvent(el, \"change\")\n        .pipe(\n          takeWhile(() => el.classList.contains(\"md-toggle--indeterminate\")),\n          map(() => el)\n        )\n      ),\n      withLatestFrom(tablet$)\n    )\n      .subscribe(([el, tablet]) => {\n        el.classList.remove(\"md-toggle--indeterminate\")\n        if (tablet)\n          el.checked = false\n      })\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  Observable,\n  filter,\n  fromEvent,\n  map,\n  mergeMap,\n  switchMap,\n  tap\n} from \"rxjs\"\n\nimport { getElements } from \"~/browser\"\n\n/* ----------------------------------------------------------------------------\n * Helper types\n * ------------------------------------------------------------------------- */\n\n/**\n * Patch options\n */\ninterface PatchOptions {\n  document$: Observable<Document>      /* Document observable */\n}\n\n/* ----------------------------------------------------------------------------\n * Helper functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Check whether the given device is an Apple device\n *\n * @returns Test result\n */\nfunction isAppleDevice(): boolean {\n  return /(iPad|iPhone|iPod)/.test(navigator.userAgent)\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Patch all elements with `data-md-scrollfix` attributes\n *\n * This is a year-old patch which ensures that overflow scrolling works at the\n * top and bottom of containers on iOS by ensuring a `1px` scroll offset upon\n * the start of a touch event.\n *\n * @see https://bit.ly/2SCtAOO - Original source\n *\n * @param options - Options\n */\nexport function patchScrollfix(\n  { document$ }: PatchOptions\n): void {\n  document$\n    .pipe(\n      switchMap(() => getElements(\"[data-md-scrollfix]\")),\n      tap(el => el.removeAttribute(\"data-md-scrollfix\")),\n      filter(isAppleDevice),\n      mergeMap(el => fromEvent(el, \"touchstart\")\n        .pipe(\n          map(() => el)\n        )\n      )\n    )\n      .subscribe(el => {\n        const top = el.scrollTop\n\n        /* We're at the top of the container */\n        if (top === 0) {\n          el.scrollTop = 1\n\n        /* We're at the bottom of the container */\n        } else if (top + el.offsetHeight === el.scrollHeight) {\n          el.scrollTop = top - 1\n        }\n      })\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  Observable,\n  combineLatest,\n  delay,\n  map,\n  of,\n  switchMap,\n  withLatestFrom\n} from \"rxjs\"\n\nimport {\n  Viewport,\n  watchToggle\n} from \"~/browser\"\n\n/* ----------------------------------------------------------------------------\n * Helper types\n * ------------------------------------------------------------------------- */\n\n/**\n * Patch options\n */\ninterface PatchOptions {\n  viewport$: Observable<Viewport>      /* Viewport observable */\n  tablet$: Observable<boolean>         /* Media tablet observable */\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Patch the document body to lock when search is open\n *\n * For mobile and tablet viewports, the search is rendered full screen, which\n * leads to scroll leaking when at the top or bottom of the search result. This\n * function locks the body when the search is in full screen mode, and restores\n * the scroll position when leaving.\n *\n * @param options - Options\n */\nexport function patchScrolllock(\n  { viewport$, tablet$ }: PatchOptions\n): void {\n  combineLatest([watchToggle(\"search\"), tablet$])\n    .pipe(\n      map(([active, tablet]) => active && !tablet),\n      switchMap(active => of(active)\n        .pipe(\n          delay(active ? 400 : 100)\n        )\n      ),\n      withLatestFrom(viewport$)\n    )\n      .subscribe(([active, { offset: { y }}]) => {\n        if (active) {\n          document.body.setAttribute(\"data-md-scrolllock\", \"\")\n          document.body.style.top = `-${y}px`\n        } else {\n          const value = -1 * parseInt(document.body.style.top, 10)\n          document.body.removeAttribute(\"data-md-scrolllock\")\n          document.body.style.top = \"\"\n          if (value)\n            window.scrollTo(0, value)\n        }\n      })\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\n/* ----------------------------------------------------------------------------\n * Polyfills\n * ------------------------------------------------------------------------- */\n\n/* Polyfill `Object.entries` */\nif (!Object.entries)\n  Object.entries = function (obj: object) {\n    const data: [string, string][] = []\n    for (const key of Object.keys(obj))\n      // @ts-expect-error - ignore property access warning\n      data.push([key, obj[key]])\n\n    /* Return entries */\n    return data\n  }\n\n/* Polyfill `Object.values` */\nif (!Object.values)\n  Object.values = function (obj: object) {\n    const data: string[] = []\n    for (const key of Object.keys(obj))\n      // @ts-expect-error - ignore property access warning\n      data.push(obj[key])\n\n    /* Return values */\n    return data\n  }\n\n/* ------------------------------------------------------------------------- */\n\n/* Polyfills for `Element` */\nif (typeof Element !== \"undefined\") {\n\n  /* Polyfill `Element.scrollTo` */\n  if (!Element.prototype.scrollTo)\n    Element.prototype.scrollTo = function (\n      x?: ScrollToOptions | number, y?: number\n    ): void {\n      if (typeof x === \"object\") {\n        this.scrollLeft = x.left!\n        this.scrollTop = x.top!\n      } else {\n        this.scrollLeft = x!\n        this.scrollTop = y!\n      }\n    }\n\n  /* Polyfill `Element.replaceWith` */\n  if (!Element.prototype.replaceWith)\n    Element.prototype.replaceWith = function (\n      ...nodes: Array<string | Node>\n    ): void {\n      const parent = this.parentNode\n      if (parent) {\n        if (nodes.length === 0)\n          parent.removeChild(this)\n\n        /* Replace children and create text nodes */\n        for (let i = nodes.length - 1; i >= 0; i--) {\n          let node = nodes[i]\n          if (typeof node === \"string\")\n            node = document.createTextNode(node)\n          else if (node.parentNode)\n            node.parentNode.removeChild(node)\n\n          /* Replace child or insert before previous sibling */\n          if (!i)\n            parent.replaceChild(node, this)\n          else\n            parent.insertBefore(this.previousSibling!, node)\n        }\n      }\n    }\n}\n"],
+  "mappings": 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diff --git a/ja/assets/javascripts/glightbox.min.js b/ja/assets/javascripts/glightbox.min.js
new file mode 100644
index 000000000..0745380f7
--- /dev/null
+++ b/ja/assets/javascripts/glightbox.min.js
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W(e){var t=function(){var e,t=document.createElement("fakeelement"),i={transition:"transitionend",OTransition:"oTransitionEnd",MozTransition:"transitionend",WebkitTransition:"webkitTransitionEnd"};for(e in i)if(void 0!==t.style[e])return i[e]}(),i=window.innerWidth||document.documentElement.clientWidth||document.body.clientWidth,n=c(e,"gslide-media")?e:e.querySelector(".gslide-media"),s=u(n,".ginner-container"),l=e.querySelector(".gslide-description");i>769&&(n=s),h(n,"greset"),v(n,"translate3d(0, 0, 0)"),a(t,{onElement:n,once:!0,withCallback:function(e,t){d(n,"greset")}}),n.style.opacity="",l&&(l.style.opacity="")}function B(e){if(e.events.hasOwnProperty("touch"))return!1;var t,i,n,s=y(),l=s.width,o=s.height,r=!1,a=null,g=null,f=null,p=!1,m=1,x=1,b=!1,S=!1,w=null,T=null,C=null,k=null,E=0,A=0,L=!1,I=!1,O={},P={},M=0,z=0,X=document.getElementById("glightbox-slider"),Y=document.querySelector(".goverlay"),q=new _(X,{touchStart:function(t){if(r=!0,(c(t.targetTouches[0].target,"ginner-container")||u(t.targetTouches[0].target,".gslide-desc")||"a"==t.targetTouches[0].target.nodeName.toLowerCase())&&(r=!1),u(t.targetTouches[0].target,".gslide-inline")&&!c(t.targetTouches[0].target.parentNode,"gslide-inline")&&(r=!1),r){if(P=t.targetTouches[0],O.pageX=t.targetTouches[0].pageX,O.pageY=t.targetTouches[0].pageY,M=t.targetTouches[0].clientX,z=t.targetTouches[0].clientY,a=e.activeSlide,g=a.querySelector(".gslide-media"),n=a.querySelector(".gslide-inline"),f=null,c(g,"gslide-image")&&(f=g.querySelector("img")),(window.innerWidth||document.documentElement.clientWidth||document.body.clientWidth)>769&&(g=a.querySelector(".ginner-container")),d(Y,"greset"),t.pageX>20&&t.pageX<window.innerWidth-20)return;t.preventDefault()}},touchMove:function(s){if(r&&(P=s.targetTouches[0],!b&&!S)){if(n&&n.offsetHeight>o){var a=O.pageX-P.pageX;if(Math.abs(a)<=13)return!1}p=!0;var h,d=s.targetTouches[0].clientX,c=s.targetTouches[0].clientY,u=M-d,m=z-c;if(Math.abs(u)>Math.abs(m)?(L=!1,I=!0):(I=!1,L=!0),t=P.pageX-O.pageX,E=100*t/l,i=P.pageY-O.pageY,A=100*i/o,L&&f&&(h=1-Math.abs(i)/o,Y.style.opacity=h,e.settings.touchFollowAxis&&(E=0)),I&&(h=1-Math.abs(t)/l,g.style.opacity=h,e.settings.touchFollowAxis&&(A=0)),!f)return v(g,"translate3d(".concat(E,"%, 0, 0)"));v(g,"translate3d(".concat(E,"%, ").concat(A,"%, 0)"))}},touchEnd:function(){if(r){if(p=!1,S||b)return C=w,void(k=T);var t=Math.abs(parseInt(A)),i=Math.abs(parseInt(E));if(!(t>29&&f))return t<29&&i<25?(h(Y,"greset"),Y.style.opacity=1,W(g)):void 0;e.close()}},multipointEnd:function(){setTimeout((function(){b=!1}),50)},multipointStart:function(){b=!0,m=x||1},pinch:function(e){if(!f||p)return!1;b=!0,f.scaleX=f.scaleY=m*e.zoom;var t=m*e.zoom;if(S=!0,t<=1)return S=!1,t=1,k=null,C=null,w=null,T=null,void f.setAttribute("style","");t>4.5&&(t=4.5),f.style.transform="scale3d(".concat(t,", ").concat(t,", 1)"),x=t},pressMove:function(e){if(S&&!b){var t=P.pageX-O.pageX,i=P.pageY-O.pageY;C&&(t+=C),k&&(i+=k),w=t,T=i;var n="translate3d(".concat(t,"px, ").concat(i,"px, 0)");x&&(n+=" scale3d(".concat(x,", ").concat(x,", 1)")),v(f,n)}},swipe:function(t){if(!S)if(b)b=!1;else{if("Left"==t.direction){if(e.index==e.elements.length-1)return W(g);e.nextSlide()}if("Right"==t.direction){if(0==e.index)return W(g);e.prevSlide()}}}});e.events.touch=q}var H=function(){function e(i,n){var s=this,l=arguments.length>2&&void 0!==arguments[2]?arguments[2]:null;if(t(this,e),this.img=i,this.slide=n,this.onclose=l,this.img.setZoomEvents)return!1;this.active=!1,this.zoomedIn=!1,this.dragging=!1,this.currentX=null,this.currentY=null,this.initialX=null,this.initialY=null,this.xOffset=0,this.yOffset=0,this.img.addEventListener("mousedown",(function(e){return s.dragStart(e)}),!1),this.img.addEventListener("mouseup",(function(e){return s.dragEnd(e)}),!1),this.img.addEventListener("mousemove",(function(e){return s.drag(e)}),!1),this.img.addEventListener("click",(function(e){return s.slide.classList.contains("dragging-nav")?(s.zoomOut(),!1):s.zoomedIn?void(s.zoomedIn&&!s.dragging&&s.zoomOut()):s.zoomIn()}),!1),this.img.setZoomEvents=!0}return n(e,[{key:"zoomIn",value:function(){var e=this.widowWidth();if(!(this.zoomedIn||e<=768)){var t=this.img;if(t.setAttribute("data-style",t.getAttribute("style")),t.style.maxWidth=t.naturalWidth+"px",t.style.maxHeight=t.naturalHeight+"px",t.naturalWidth>e){var i=e/2-t.naturalWidth/2;this.setTranslate(this.img.parentNode,i,0)}this.slide.classList.add("zoomed"),this.zoomedIn=!0}}},{key:"zoomOut",value:function(){this.img.parentNode.setAttribute("style",""),this.img.setAttribute("style",this.img.getAttribute("data-style")),this.slide.classList.remove("zoomed"),this.zoomedIn=!1,this.currentX=null,this.currentY=null,this.initialX=null,this.initialY=null,this.xOffset=0,this.yOffset=0,this.onclose&&"function"==typeof this.onclose&&this.onclose()}},{key:"dragStart",value:function(e){e.preventDefault(),this.zoomedIn?("touchstart"===e.type?(this.initialX=e.touches[0].clientX-this.xOffset,this.initialY=e.touches[0].clientY-this.yOffset):(this.initialX=e.clientX-this.xOffset,this.initialY=e.clientY-this.yOffset),e.target===this.img&&(this.active=!0,this.img.classList.add("dragging"))):this.active=!1}},{key:"dragEnd",value:function(e){var t=this;e.preventDefault(),this.initialX=this.currentX,this.initialY=this.currentY,this.active=!1,setTimeout((function(){t.dragging=!1,t.img.isDragging=!1,t.img.classList.remove("dragging")}),100)}},{key:"drag",value:function(e){this.active&&(e.preventDefault(),"touchmove"===e.type?(this.currentX=e.touches[0].clientX-this.initialX,this.currentY=e.touches[0].clientY-this.initialY):(this.currentX=e.clientX-this.initialX,this.currentY=e.clientY-this.initialY),this.xOffset=this.currentX,this.yOffset=this.currentY,this.img.isDragging=!0,this.dragging=!0,this.setTranslate(this.img,this.currentX,this.currentY))}},{key:"onMove",value:function(e){if(this.zoomedIn){var t=e.clientX-this.img.naturalWidth/2,i=e.clientY-this.img.naturalHeight/2;this.setTranslate(this.img,t,i)}}},{key:"setTranslate",value:function(e,t,i){e.style.transform="translate3d("+t+"px, "+i+"px, 0)"}},{key:"widowWidth",value:function(){return window.innerWidth||document.documentElement.clientWidth||document.body.clientWidth}}]),e}(),V=function(){function e(){var i=this,n=arguments.length>0&&void 0!==arguments[0]?arguments[0]:{};t(this,e);var s=n.dragEl,l=n.toleranceX,o=void 0===l?40:l,r=n.toleranceY,a=void 0===r?65:r,h=n.slide,d=void 0===h?null:h,c=n.instance,u=void 0===c?null:c;this.el=s,this.active=!1,this.dragging=!1,this.currentX=null,this.currentY=null,this.initialX=null,this.initialY=null,this.xOffset=0,this.yOffset=0,this.direction=null,this.lastDirection=null,this.toleranceX=o,this.toleranceY=a,this.toleranceReached=!1,this.dragContainer=this.el,this.slide=d,this.instance=u,this.el.addEventListener("mousedown",(function(e){return i.dragStart(e)}),!1),this.el.addEventListener("mouseup",(function(e){return i.dragEnd(e)}),!1),this.el.addEventListener("mousemove",(function(e){return i.drag(e)}),!1)}return n(e,[{key:"dragStart",value:function(e){if(this.slide.classList.contains("zoomed"))this.active=!1;else{"touchstart"===e.type?(this.initialX=e.touches[0].clientX-this.xOffset,this.initialY=e.touches[0].clientY-this.yOffset):(this.initialX=e.clientX-this.xOffset,this.initialY=e.clientY-this.yOffset);var t=e.target.nodeName.toLowerCase();e.target.classList.contains("nodrag")||u(e.target,".nodrag")||-1!==["input","select","textarea","button","a"].indexOf(t)?this.active=!1:(e.preventDefault(),(e.target===this.el||"img"!==t&&u(e.target,".gslide-inline"))&&(this.active=!0,this.el.classList.add("dragging"),this.dragContainer=u(e.target,".ginner-container")))}}},{key:"dragEnd",value:function(e){var t=this;e&&e.preventDefault(),this.initialX=0,this.initialY=0,this.currentX=null,this.currentY=null,this.initialX=null,this.initialY=null,this.xOffset=0,this.yOffset=0,this.active=!1,this.doSlideChange&&(this.instance.preventOutsideClick=!0,"right"==this.doSlideChange&&this.instance.prevSlide(),"left"==this.doSlideChange&&this.instance.nextSlide()),this.doSlideClose&&this.instance.close(),this.toleranceReached||this.setTranslate(this.dragContainer,0,0,!0),setTimeout((function(){t.instance.preventOutsideClick=!1,t.toleranceReached=!1,t.lastDirection=null,t.dragging=!1,t.el.isDragging=!1,t.el.classList.remove("dragging"),t.slide.classList.remove("dragging-nav"),t.dragContainer.style.transform="",t.dragContainer.style.transition=""}),100)}},{key:"drag",value:function(e){if(this.active){e.preventDefault(),this.slide.classList.add("dragging-nav"),"touchmove"===e.type?(this.currentX=e.touches[0].clientX-this.initialX,this.currentY=e.touches[0].clientY-this.initialY):(this.currentX=e.clientX-this.initialX,this.currentY=e.clientY-this.initialY),this.xOffset=this.currentX,this.yOffset=this.currentY,this.el.isDragging=!0,this.dragging=!0,this.doSlideChange=!1,this.doSlideClose=!1;var t=Math.abs(this.currentX),i=Math.abs(this.currentY);if(t>0&&t>=Math.abs(this.currentY)&&(!this.lastDirection||"x"==this.lastDirection)){this.yOffset=0,this.lastDirection="x",this.setTranslate(this.dragContainer,this.currentX,0);var n=this.shouldChange();if(!this.instance.settings.dragAutoSnap&&n&&(this.doSlideChange=n),this.instance.settings.dragAutoSnap&&n)return this.instance.preventOutsideClick=!0,this.toleranceReached=!0,this.active=!1,this.instance.preventOutsideClick=!0,this.dragEnd(null),"right"==n&&this.instance.prevSlide(),void("left"==n&&this.instance.nextSlide())}if(this.toleranceY>0&&i>0&&i>=t&&(!this.lastDirection||"y"==this.lastDirection)){this.xOffset=0,this.lastDirection="y",this.setTranslate(this.dragContainer,0,this.currentY);var s=this.shouldClose();return!this.instance.settings.dragAutoSnap&&s&&(this.doSlideClose=!0),void(this.instance.settings.dragAutoSnap&&s&&this.instance.close())}}}},{key:"shouldChange",value:function(){var e=!1;if(Math.abs(this.currentX)>=this.toleranceX){var t=this.currentX>0?"right":"left";("left"==t&&this.slide!==this.slide.parentNode.lastChild||"right"==t&&this.slide!==this.slide.parentNode.firstChild)&&(e=t)}return e}},{key:"shouldClose",value:function(){var e=!1;return Math.abs(this.currentY)>=this.toleranceY&&(e=!0),e}},{key:"setTranslate",value:function(e,t,i){var n=arguments.length>3&&void 0!==arguments[3]&&arguments[3];e.style.transition=n?"all .2s ease":"",e.style.transform="translate3d(".concat(t,"px, ").concat(i,"px, 0)")}}]),e}();function j(e,t,i,n){var s=e.querySelector(".gslide-media"),l=new Image,o="gSlideTitle_"+i,r="gSlideDesc_"+i;l.addEventListener("load",(function(){T(n)&&n()}),!1),l.src=t.href,""!=t.sizes&&""!=t.srcset&&(l.sizes=t.sizes,l.srcset=t.srcset),l.alt="",I(t.alt)||""===t.alt||(l.alt=t.alt),""!==t.title&&l.setAttribute("aria-labelledby",o),""!==t.description&&l.setAttribute("aria-describedby",r),t.hasOwnProperty("_hasCustomWidth")&&t._hasCustomWidth&&(l.style.width=t.width),t.hasOwnProperty("_hasCustomHeight")&&t._hasCustomHeight&&(l.style.height=t.height),s.insertBefore(l,s.firstChild)}function F(e,t,i,n){var s=this,l=e.querySelector(".ginner-container"),o="gvideo"+i,r=e.querySelector(".gslide-media"),a=this.getAllPlayers();h(l,"gvideo-container"),r.insertBefore(m('<div class="gvideo-wrapper"></div>'),r.firstChild);var d=e.querySelector(".gvideo-wrapper");S(this.settings.plyr.css,"Plyr");var c=t.href,u=location.protocol.replace(":",""),g="",v="",f=!1;"file"==u&&(u="http"),r.style.maxWidth=t.width,S(this.settings.plyr.js,"Plyr",(function(){if(c.match(/vimeo\.com\/([0-9]*)/)){var l=/vimeo.*\/(\d+)/i.exec(c);g="vimeo",v=l[1]}if(c.match(/(youtube\.com|youtube-nocookie\.com)\/watch\?v=([a-zA-Z0-9\-_]+)/)||c.match(/youtu\.be\/([a-zA-Z0-9\-_]+)/)||c.match(/(youtube\.com|youtube-nocookie\.com)\/embed\/([a-zA-Z0-9\-_]+)/)){var r=function(e){var t="";t=void 0!==(e=e.replace(/(>|<)/gi,"").split(/(vi\/|v=|\/v\/|youtu\.be\/|\/embed\/)/))[2]?(t=e[2].split(/[^0-9a-z_\-]/i))[0]:e;return t}(c);g="youtube",v=r}if(null!==c.match(/\.(mp4|ogg|webm|mov)$/)){g="local";var u='<video id="'+o+'" ';u+='style="background:#000; max-width: '.concat(t.width,';" '),u+='preload="metadata" ',u+='x-webkit-airplay="allow" ',u+="playsinline ",u+="controls ",u+='class="gvideo-local">';var p=c.toLowerCase().split(".").pop(),y={mp4:"",ogg:"",webm:""};for(var x in y[p="mov"==p?"mp4":p]=c,y)if(y.hasOwnProperty(x)){var S=y[x];t.hasOwnProperty(x)&&(S=t[x]),""!==S&&(u+='<source src="'.concat(S,'" type="video/').concat(x,'">'))}f=m(u+="</video>")}var w=f||m('<div id="'.concat(o,'" data-plyr-provider="').concat(g,'" data-plyr-embed-id="').concat(v,'"></div>'));h(d,"".concat(g,"-video gvideo")),d.appendChild(w),d.setAttribute("data-id",o),d.setAttribute("data-index",i);var C=O(s.settings.plyr,"config")?s.settings.plyr.config:{},k=new Plyr("#"+o,C);k.on("ready",(function(e){var t=e.detail.plyr;a[o]=t,T(n)&&n()})),b((function(){return e.querySelector("iframe")&&"true"==e.querySelector("iframe").dataset.ready}),(function(){s.resize(e)})),k.on("enterfullscreen",R),k.on("exitfullscreen",R)}))}function R(e){var t=u(e.target,".gslide-media");"enterfullscreen"==e.type&&h(t,"fullscreen"),"exitfullscreen"==e.type&&d(t,"fullscreen")}function G(e,t,i,n){var s,l=this,o=e.querySelector(".gslide-media"),r=!(!O(t,"href")||!t.href)&&t.href.split("#").pop().trim(),d=!(!O(t,"content")||!t.content)&&t.content;if(d&&(C(d)&&(s=m('<div class="ginlined-content">'.concat(d,"</div>"))),k(d))){"none"==d.style.display&&(d.style.display="block");var c=document.createElement("div");c.className="ginlined-content",c.appendChild(d),s=c}if(r){var u=document.getElementById(r);if(!u)return!1;var g=u.cloneNode(!0);g.style.height=t.height,g.style.maxWidth=t.width,h(g,"ginlined-content"),s=g}if(!s)return console.error("Unable to append inline slide content",t),!1;o.style.height=t.height,o.style.width=t.width,o.appendChild(s),this.events["inlineclose"+r]=a("click",{onElement:o.querySelectorAll(".gtrigger-close"),withCallback:function(e){e.preventDefault(),l.close()}}),T(n)&&n()}function Z(e,t,i,n){var s=e.querySelector(".gslide-media"),l=function(e){var t=e.url,i=e.allow,n=e.callback,s=e.appendTo,l=document.createElement("iframe");return l.className="vimeo-video 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t=e;if(null!==(e=e.toLowerCase()).match(/\.(jpeg|jpg|jpe|gif|png|apn|webp|avif|svg)/))return"image";if(e.match(/(youtube\.com|youtube-nocookie\.com)\/watch\?v=([a-zA-Z0-9\-_]+)/)||e.match(/youtu\.be\/([a-zA-Z0-9\-_]+)/)||e.match(/(youtube\.com|youtube-nocookie\.com)\/embed\/([a-zA-Z0-9\-_]+)/))return"video";if(e.match(/vimeo\.com\/([0-9]*)/))return"video";if(null!==e.match(/\.(mp4|ogg|webm|mov)/))return"video";if(null!==e.match(/\.(mp3|wav|wma|aac|ogg)/))return"audio";if(e.indexOf("#")>-1&&""!==t.split("#").pop().trim())return"inline";return e.indexOf("goajax=true")>-1?"ajax":"external"}},{key:"parseConfig",value:function(e,t){var i=this,n=l({descPosition:t.descPosition},this.defaults);if(L(e)&&!k(e)){O(e,"type")||(O(e,"content")&&e.content?e.type="inline":O(e,"href")&&(e.type=this.sourceType(e.href)));var s=l(n,e);return this.setSize(s,t),s}var r="",a=e.getAttribute("data-glightbox"),h=e.nodeName.toLowerCase();if("a"===h&&(r=e.href),"img"===h&&(r=e.src,n.alt=e.alt),n.href=r,o(n,(function(s,l){O(t,l)&&"width"!==l&&(n[l]=t[l]);var o=e.dataset[l];I(o)||(n[l]=i.sanitizeValue(o))})),n.content&&(n.type="inline"),!n.type&&r&&(n.type=this.sourceType(r)),I(a)){if(!n.title&&"a"==h){var d=e.title;I(d)||""===d||(n.title=d)}if(!n.title&&"img"==h){var c=e.alt;I(c)||""===c||(n.title=c)}}else{var u=[];o(n,(function(e,t){u.push(";\\s?"+t)})),u=u.join("\\s?:|"),""!==a.trim()&&o(n,(function(e,t){var s=a,l=new RegExp("s?"+t+"s?:s?(.*?)("+u+"s?:|$)"),o=s.match(l);if(o&&o.length&&o[1]){var r=o[1].trim().replace(/;\s*$/,"");n[t]=i.sanitizeValue(r)}}))}if(n.description&&"."===n.description.substring(0,1)){var g;try{g=document.querySelector(n.description).innerHTML}catch(e){if(!(e instanceof DOMException))throw e}g&&(n.description=g)}if(!n.description){var v=e.querySelector(".glightbox-desc");v&&(n.description=v.innerHTML)}return this.setSize(n,t,e),this.slideConfig=n,n}},{key:"setSize",value:function(e,t){var i=arguments.length>2&&void 0!==arguments[2]?arguments[2]:null,n="video"==e.type?this.checkSize(t.videosWidth):this.checkSize(t.width),s=this.checkSize(t.height);return e.width=O(e,"width")&&""!==e.width?this.checkSize(e.width):n,e.height=O(e,"height")&&""!==e.height?this.checkSize(e.height):s,i&&"image"==e.type&&(e._hasCustomWidth=!!i.dataset.width,e._hasCustomHeight=!!i.dataset.height),e}},{key:"checkSize",value:function(e){return M(e)?"".concat(e,"px"):e}},{key:"sanitizeValue",value:function(e){return"true"!==e&&"false"!==e?e:"true"===e}}]),e}(),U=function(){function e(i,n,s){t(this,e),this.element=i,this.instance=n,this.index=s}return n(e,[{key:"setContent",value:function(){var e=this,t=arguments.length>0&&void 0!==arguments[0]?arguments[0]:null,i=arguments.length>1&&void 0!==arguments[1]&&arguments[1];if(c(t,"loaded"))return!1;var n=this.instance.settings,s=this.slideConfig,l=w();T(n.beforeSlideLoad)&&n.beforeSlideLoad({index:this.index,slide:t,player:!1});var o=s.type,r=s.descPosition,a=t.querySelector(".gslide-media"),d=t.querySelector(".gslide-title"),u=t.querySelector(".gslide-desc"),g=t.querySelector(".gdesc-inner"),v=i,f="gSlideTitle_"+this.index,p="gSlideDesc_"+this.index;if(T(n.afterSlideLoad)&&(v=function(){T(i)&&i(),n.afterSlideLoad({index:e.index,slide:t,player:e.instance.getSlidePlayerInstance(e.index)})}),""==s.title&&""==s.description?g&&g.parentNode.parentNode.removeChild(g.parentNode):(d&&""!==s.title?(d.id=f,d.innerHTML=s.title):d.parentNode.removeChild(d),u&&""!==s.description?(u.id=p,l&&n.moreLength>0?(s.smallDescription=this.slideShortDesc(s.description,n.moreLength,n.moreText),u.innerHTML=s.smallDescription,this.descriptionEvents(u,s)):u.innerHTML=s.description):u.parentNode.removeChild(u),h(a.parentNode,"desc-".concat(r)),h(g.parentNode,"description-".concat(r))),h(a,"gslide-".concat(o)),h(t,"loaded"),"video"!==o){if("external"!==o)return"inline"===o?(G.apply(this.instance,[t,s,this.index,v]),void(s.draggable&&new V({dragEl:t.querySelector(".gslide-inline"),toleranceX:n.dragToleranceX,toleranceY:n.dragToleranceY,slide:t,instance:this.instance}))):void("image"!==o?T(v)&&v():j(t,s,this.index,(function(){var i=t.querySelector("img");s.draggable&&new V({dragEl:i,toleranceX:n.dragToleranceX,toleranceY:n.dragToleranceY,slide:t,instance:e.instance}),s.zoomable&&i.naturalWidth>i.offsetWidth&&(h(i,"zoomable"),new H(i,t,(function(){e.instance.resize()}))),T(v)&&v()})));Z.apply(this,[t,s,this.index,v])}else F.apply(this.instance,[t,s,this.index,v])}},{key:"slideShortDesc",value:function(e){var t=arguments.length>1&&void 0!==arguments[1]?arguments[1]:50,i=arguments.length>2&&void 0!==arguments[2]&&arguments[2],n=document.createElement("div");n.innerHTML=e;var s=n.innerText,l=i;if((e=s.trim()).length<=t)return e;var o=e.substr(0,t-1);return l?(n=null,o+'... <a href="#" class="desc-more">'+i+"</a>"):o}},{key:"descriptionEvents",value:function(e,t){var i=this,n=e.querySelector(".desc-more");if(!n)return!1;a("click",{onElement:n,withCallback:function(e,n){e.preventDefault();var s=document.body,l=u(n,".gslide-desc");if(!l)return!1;l.innerHTML=t.description,h(s,"gdesc-open");var o=a("click",{onElement:[s,u(l,".gslide-description")],withCallback:function(e,n){"a"!==e.target.nodeName.toLowerCase()&&(d(s,"gdesc-open"),h(s,"gdesc-closed"),l.innerHTML=t.smallDescription,i.descriptionEvents(l,t),setTimeout((function(){d(s,"gdesc-closed")}),400),o.destroy())}})}})}},{key:"create",value:function(){return m(this.instance.settings.slideHTML)}},{key:"getConfig",value:function(){k(this.element)||this.element.hasOwnProperty("draggable")||(this.element.draggable=this.instance.settings.draggable);var e=new $(this.instance.settings.slideExtraAttributes);return this.slideConfig=e.parseConfig(this.element,this.instance.settings),this.slideConfig}}]),e}(),J=w(),K=null!==w()||void 0!==document.createTouch||"ontouchstart"in window||"onmsgesturechange"in window||navigator.msMaxTouchPoints,Q=document.getElementsByTagName("html")[0],ee={selector:".glightbox",elements:null,skin:"clean",theme:"clean",closeButton:!0,startAt:null,autoplayVideos:!0,autofocusVideos:!0,descPosition:"bottom",width:"900px",height:"506px",videosWidth:"960px",beforeSlideChange:null,afterSlideChange:null,beforeSlideLoad:null,afterSlideLoad:null,slideInserted:null,slideRemoved:null,slideExtraAttributes:null,onOpen:null,onClose:null,loop:!1,zoomable:!0,draggable:!0,dragAutoSnap:!1,dragToleranceX:40,dragToleranceY:65,preload:!0,oneSlidePerOpen:!1,touchNavigation:!0,touchFollowAxis:!0,keyboardNavigation:!0,closeOnOutsideClick:!0,plugins:!1,plyr:{css:"https://cdn.plyr.io/3.6.8/plyr.css",js:"https://cdn.plyr.io/3.6.8/plyr.js",config:{ratio:"16:9",fullscreen:{enabled:!0,iosNative:!0},youtube:{noCookie:!0,rel:0,showinfo:0,iv_load_policy:3},vimeo:{byline:!1,portrait:!1,title:!1,transparent:!1}}},openEffect:"zoom",closeEffect:"zoom",slideEffect:"slide",moreText:"See more",moreLength:60,cssEfects:{fade:{in:"fadeIn",out:"fadeOut"},zoom:{in:"zoomIn",out:"zoomOut"},slide:{in:"slideInRight",out:"slideOutLeft"},slideBack:{in:"slideInLeft",out:"slideOutRight"},none:{in:"none",out:"none"}},svg:{close:'<svg version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" x="0px" y="0px" viewBox="0 0 512 512" xml:space="preserve"><g><g><path d="M505.943,6.058c-8.077-8.077-21.172-8.077-29.249,0L6.058,476.693c-8.077,8.077-8.077,21.172,0,29.249C10.096,509.982,15.39,512,20.683,512c5.293,0,10.586-2.019,14.625-6.059L505.943,35.306C514.019,27.23,514.019,14.135,505.943,6.058z"/></g></g><g><g><path d="M505.942,476.694L35.306,6.059c-8.076-8.077-21.172-8.077-29.248,0c-8.077,8.076-8.077,21.171,0,29.248l470.636,470.636c4.038,4.039,9.332,6.058,14.625,6.058c5.293,0,10.587-2.019,14.624-6.057C514.018,497.866,514.018,484.771,505.942,476.694z"/></g></g></svg>',next:'<svg version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" x="0px" y="0px" viewBox="0 0 477.175 477.175" xml:space="preserve"> <g><path d="M360.731,229.075l-225.1-225.1c-5.3-5.3-13.8-5.3-19.1,0s-5.3,13.8,0,19.1l215.5,215.5l-215.5,215.5c-5.3,5.3-5.3,13.8,0,19.1c2.6,2.6,6.1,4,9.5,4c3.4,0,6.9-1.3,9.5-4l225.1-225.1C365.931,242.875,365.931,234.275,360.731,229.075z"/></g></svg>',prev:'<svg version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" x="0px" y="0px" viewBox="0 0 477.175 477.175" xml:space="preserve"><g><path d="M145.188,238.575l215.5-215.5c5.3-5.3,5.3-13.8,0-19.1s-13.8-5.3-19.1,0l-225.1,225.1c-5.3,5.3-5.3,13.8,0,19.1l225.1,225c2.6,2.6,6.1,4,9.5,4s6.9-1.3,9.5-4c5.3-5.3,5.3-13.8,0-19.1L145.188,238.575z"/></g></svg>'},slideHTML:'<div class="gslide">\n    <div class="gslide-inner-content">\n        <div class="ginner-container">\n            <div class="gslide-media">\n            </div>\n            <div class="gslide-description">\n                <div class="gdesc-inner">\n                    <h4 class="gslide-title"></h4>\n                    <div class="gslide-desc"></div>\n                </div>\n            </div>\n        </div>\n    </div>\n</div>',lightboxHTML:'<div id="glightbox-body" class="glightbox-container" tabindex="-1" role="dialog" aria-hidden="false">\n    <div class="gloader visible"></div>\n    <div class="goverlay"></div>\n    <div class="gcontainer">\n    <div id="glightbox-slider" class="gslider"></div>\n    <button class="gclose gbtn" aria-label="Close" data-taborder="3">{closeSVG}</button>\n    <button class="gprev gbtn" aria-label="Previous" data-taborder="2">{prevSVG}</button>\n    <button class="gnext gbtn" aria-label="Next" data-taborder="1">{nextSVG}</button>\n</div>\n</div>'},te=function(){function e(){var i=arguments.length>0&&void 0!==arguments[0]?arguments[0]:{};t(this,e),this.customOptions=i,this.settings=l(ee,i),this.effectsClasses=this.getAnimationClasses(),this.videoPlayers={},this.apiEvents=[],this.fullElementsList=!1}return n(e,[{key:"init",value:function(){var e=this,t=this.getSelector();t&&(this.baseEvents=a("click",{onElement:t,withCallback:function(t,i){t.preventDefault(),e.open(i)}})),this.elements=this.getElements()}},{key:"open",value:function(){var e=arguments.length>0&&void 0!==arguments[0]?arguments[0]:null,t=arguments.length>1&&void 0!==arguments[1]?arguments[1]:null;if(0==this.elements.length)return!1;this.activeSlide=null,this.prevActiveSlideIndex=null,this.prevActiveSlide=null;var i=M(t)?t:this.settings.startAt;if(k(e)){var n=e.getAttribute("data-gallery");n&&(this.fullElementsList=this.elements,this.elements=this.getGalleryElements(this.elements,n)),I(i)&&(i=this.getElementIndex(e))<0&&(i=0)}M(i)||(i=0),this.build(),g(this.overlay,"none"==this.settings.openEffect?"none":this.settings.cssEfects.fade.in);var s=document.body,l=window.innerWidth-document.documentElement.clientWidth;if(l>0){var o=document.createElement("style");o.type="text/css",o.className="gcss-styles",o.innerText=".gscrollbar-fixer {margin-right: ".concat(l,"px}"),document.head.appendChild(o),h(s,"gscrollbar-fixer")}h(s,"glightbox-open"),h(Q,"glightbox-open"),J&&(h(document.body,"glightbox-mobile"),this.settings.slideEffect="slide"),this.showSlide(i,!0),1==this.elements.length?(h(this.prevButton,"glightbox-button-hidden"),h(this.nextButton,"glightbox-button-hidden")):(d(this.prevButton,"glightbox-button-hidden"),d(this.nextButton,"glightbox-button-hidden")),this.lightboxOpen=!0,this.trigger("open"),T(this.settings.onOpen)&&this.settings.onOpen(),K&&this.settings.touchNavigation&&B(this),this.settings.keyboardNavigation&&X(this)}},{key:"openAt",value:function(){var e=arguments.length>0&&void 0!==arguments[0]?arguments[0]:0;this.open(null,e)}},{key:"showSlide",value:function(){var e=this,t=arguments.length>0&&void 0!==arguments[0]?arguments[0]:0,i=arguments.length>1&&void 0!==arguments[1]&&arguments[1];f(this.loader),this.index=parseInt(t);var n=this.slidesContainer.querySelector(".current");n&&d(n,"current"),this.slideAnimateOut();var s=this.slidesContainer.querySelectorAll(".gslide")[t];if(c(s,"loaded"))this.slideAnimateIn(s,i),p(this.loader);else{f(this.loader);var l=this.elements[t],o={index:this.index,slide:s,slideNode:s,slideConfig:l.slideConfig,slideIndex:this.index,trigger:l.node,player:null};this.trigger("slide_before_load",o),l.instance.setContent(s,(function(){p(e.loader),e.resize(),e.slideAnimateIn(s,i),e.trigger("slide_after_load",o)}))}this.slideDescription=s.querySelector(".gslide-description"),this.slideDescriptionContained=this.slideDescription&&c(this.slideDescription.parentNode,"gslide-media"),this.settings.preload&&(this.preloadSlide(t+1),this.preloadSlide(t-1)),this.updateNavigationClasses(),this.activeSlide=s}},{key:"preloadSlide",value:function(e){var t=this;if(e<0||e>this.elements.length-1)return!1;if(I(this.elements[e]))return!1;var i=this.slidesContainer.querySelectorAll(".gslide")[e];if(c(i,"loaded"))return!1;var n=this.elements[e],s=n.type,l={index:e,slide:i,slideNode:i,slideConfig:n.slideConfig,slideIndex:e,trigger:n.node,player:null};this.trigger("slide_before_load",l),"video"==s||"external"==s?setTimeout((function(){n.instance.setContent(i,(function(){t.trigger("slide_after_load",l)}))}),200):n.instance.setContent(i,(function(){t.trigger("slide_after_load",l)}))}},{key:"prevSlide",value:function(){this.goToSlide(this.index-1)}},{key:"nextSlide",value:function(){this.goToSlide(this.index+1)}},{key:"goToSlide",value:function(){var e=arguments.length>0&&void 0!==arguments[0]&&arguments[0];if(this.prevActiveSlide=this.activeSlide,this.prevActiveSlideIndex=this.index,!this.loop()&&(e<0||e>this.elements.length-1))return!1;e<0?e=this.elements.length-1:e>=this.elements.length&&(e=0),this.showSlide(e)}},{key:"insertSlide",value:function(){var e=arguments.length>0&&void 0!==arguments[0]?arguments[0]:{},t=arguments.length>1&&void 0!==arguments[1]?arguments[1]:-1;t<0&&(t=this.elements.length);var i=new U(e,this,t),n=i.getConfig(),s=l({},n),o=i.create(),r=this.elements.length-1;s.index=t,s.node=!1,s.instance=i,s.slideConfig=n,this.elements.splice(t,0,s);var a=null,h=null;if(this.slidesContainer){if(t>r)this.slidesContainer.appendChild(o);else{var d=this.slidesContainer.querySelectorAll(".gslide")[t];this.slidesContainer.insertBefore(o,d)}(this.settings.preload&&0==this.index&&0==t||this.index-1==t||this.index+1==t)&&this.preloadSlide(t),0==this.index&&0==t&&(this.index=1),this.updateNavigationClasses(),a=this.slidesContainer.querySelectorAll(".gslide")[t],h=this.getSlidePlayerInstance(t),s.slideNode=a}this.trigger("slide_inserted",{index:t,slide:a,slideNode:a,slideConfig:n,slideIndex:t,trigger:null,player:h}),T(this.settings.slideInserted)&&this.settings.slideInserted({index:t,slide:a,player:h})}},{key:"removeSlide",value:function(){var e=arguments.length>0&&void 0!==arguments[0]?arguments[0]:-1;if(e<0||e>this.elements.length-1)return!1;var t=this.slidesContainer&&this.slidesContainer.querySelectorAll(".gslide")[e];t&&(this.getActiveSlideIndex()==e&&(e==this.elements.length-1?this.prevSlide():this.nextSlide()),t.parentNode.removeChild(t)),this.elements.splice(e,1),this.trigger("slide_removed",e),T(this.settings.slideRemoved)&&this.settings.slideRemoved(e)}},{key:"slideAnimateIn",value:function(e,t){var i=this,n=e.querySelector(".gslide-media"),s=e.querySelector(".gslide-description"),l={index:this.prevActiveSlideIndex,slide:this.prevActiveSlide,slideNode:this.prevActiveSlide,slideIndex:this.prevActiveSlide,slideConfig:I(this.prevActiveSlideIndex)?null:this.elements[this.prevActiveSlideIndex].slideConfig,trigger:I(this.prevActiveSlideIndex)?null:this.elements[this.prevActiveSlideIndex].node,player:this.getSlidePlayerInstance(this.prevActiveSlideIndex)},o={index:this.index,slide:this.activeSlide,slideNode:this.activeSlide,slideConfig:this.elements[this.index].slideConfig,slideIndex:this.index,trigger:this.elements[this.index].node,player:this.getSlidePlayerInstance(this.index)};if(n.offsetWidth>0&&s&&(p(s),s.style.display=""),d(e,this.effectsClasses),t)g(e,this.settings.cssEfects[this.settings.openEffect].in,(function(){i.settings.autoplayVideos&&i.slidePlayerPlay(e),i.trigger("slide_changed",{prev:l,current:o}),T(i.settings.afterSlideChange)&&i.settings.afterSlideChange.apply(i,[l,o])}));else{var r=this.settings.slideEffect,a="none"!==r?this.settings.cssEfects[r].in:r;this.prevActiveSlideIndex>this.index&&"slide"==this.settings.slideEffect&&(a=this.settings.cssEfects.slideBack.in),g(e,a,(function(){i.settings.autoplayVideos&&i.slidePlayerPlay(e),i.trigger("slide_changed",{prev:l,current:o}),T(i.settings.afterSlideChange)&&i.settings.afterSlideChange.apply(i,[l,o])}))}setTimeout((function(){i.resize(e)}),100),h(e,"current")}},{key:"slideAnimateOut",value:function(){if(!this.prevActiveSlide)return!1;var e=this.prevActiveSlide;d(e,this.effectsClasses),h(e,"prev");var t=this.settings.slideEffect,i="none"!==t?this.settings.cssEfects[t].out:t;this.slidePlayerPause(e),this.trigger("slide_before_change",{prev:{index:this.prevActiveSlideIndex,slide:this.prevActiveSlide,slideNode:this.prevActiveSlide,slideIndex:this.prevActiveSlideIndex,slideConfig:I(this.prevActiveSlideIndex)?null:this.elements[this.prevActiveSlideIndex].slideConfig,trigger:I(this.prevActiveSlideIndex)?null:this.elements[this.prevActiveSlideIndex].node,player:this.getSlidePlayerInstance(this.prevActiveSlideIndex)},current:{index:this.index,slide:this.activeSlide,slideNode:this.activeSlide,slideIndex:this.index,slideConfig:this.elements[this.index].slideConfig,trigger:this.elements[this.index].node,player:this.getSlidePlayerInstance(this.index)}}),T(this.settings.beforeSlideChange)&&this.settings.beforeSlideChange.apply(this,[{index:this.prevActiveSlideIndex,slide:this.prevActiveSlide,player:this.getSlidePlayerInstance(this.prevActiveSlideIndex)},{index:this.index,slide:this.activeSlide,player:this.getSlidePlayerInstance(this.index)}]),this.prevActiveSlideIndex>this.index&&"slide"==this.settings.slideEffect&&(i=this.settings.cssEfects.slideBack.out),g(e,i,(function(){var t=e.querySelector(".ginner-container"),i=e.querySelector(".gslide-media"),n=e.querySelector(".gslide-description");t.style.transform="",i.style.transform="",d(i,"greset"),i.style.opacity="",n&&(n.style.opacity=""),d(e,"prev")}))}},{key:"getAllPlayers",value:function(){return this.videoPlayers}},{key:"getSlidePlayerInstance",value:function(e){var t="gvideo"+e,i=this.getAllPlayers();return!(!O(i,t)||!i[t])&&i[t]}},{key:"stopSlideVideo",value:function(e){if(k(e)){var t=e.querySelector(".gvideo-wrapper");t&&(e=t.getAttribute("data-index"))}console.log("stopSlideVideo is deprecated, use slidePlayerPause");var i=this.getSlidePlayerInstance(e);i&&i.playing&&i.pause()}},{key:"slidePlayerPause",value:function(e){if(k(e)){var t=e.querySelector(".gvideo-wrapper");t&&(e=t.getAttribute("data-index"))}var i=this.getSlidePlayerInstance(e);i&&i.playing&&i.pause()}},{key:"playSlideVideo",value:function(e){if(k(e)){var t=e.querySelector(".gvideo-wrapper");t&&(e=t.getAttribute("data-index"))}console.log("playSlideVideo is deprecated, use slidePlayerPlay");var i=this.getSlidePlayerInstance(e);i&&!i.playing&&i.play()}},{key:"slidePlayerPlay",value:function(e){if(k(e)){var t=e.querySelector(".gvideo-wrapper");t&&(e=t.getAttribute("data-index"))}var i=this.getSlidePlayerInstance(e);i&&!i.playing&&(i.play(),this.settings.autofocusVideos&&i.elements.container.focus())}},{key:"setElements",value:function(e){var t=this;this.settings.elements=!1;var i=[];e&&e.length&&o(e,(function(e,n){var s=new U(e,t,n),o=s.getConfig(),r=l({},o);r.slideConfig=o,r.instance=s,r.index=n,i.push(r)})),this.elements=i,this.lightboxOpen&&(this.slidesContainer.innerHTML="",this.elements.length&&(o(this.elements,(function(){var e=m(t.settings.slideHTML);t.slidesContainer.appendChild(e)})),this.showSlide(0,!0)))}},{key:"getElementIndex",value:function(e){var t=!1;return o(this.elements,(function(i,n){if(O(i,"node")&&i.node==e)return t=n,!0})),t}},{key:"getElements",value:function(){var e=this,t=[];this.elements=this.elements?this.elements:[],!I(this.settings.elements)&&E(this.settings.elements)&&this.settings.elements.length&&o(this.settings.elements,(function(i,n){var s=new U(i,e,n),o=s.getConfig(),r=l({},o);r.node=!1,r.index=n,r.instance=s,r.slideConfig=o,t.push(r)}));var i=!1;return this.getSelector()&&(i=document.querySelectorAll(this.getSelector())),i?(o(i,(function(i,n){var s=new U(i,e,n),o=s.getConfig(),r=l({},o);r.node=i,r.index=n,r.instance=s,r.slideConfig=o,r.gallery=i.getAttribute("data-gallery"),t.push(r)})),t):t}},{key:"getGalleryElements",value:function(e,t){return e.filter((function(e){return e.gallery==t}))}},{key:"getSelector",value:function(){return!this.settings.elements&&(this.settings.selector&&"data-"==this.settings.selector.substring(0,5)?"*[".concat(this.settings.selector,"]"):this.settings.selector)}},{key:"getActiveSlide",value:function(){return 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diff --git a/ja/assets/javascripts/lunr/min/lunr.ar.min.js b/ja/assets/javascripts/lunr/min/lunr.ar.min.js
new file mode 100644
index 000000000..9b06c26c1
--- /dev/null
+++ b/ja/assets/javascripts/lunr/min/lunr.ar.min.js
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l=new RegExp("("+e.suf.suf2.split(" ").join("|")+")$");e.word=e.word.replace(l,"")}return r!=e.word&&(e.sufRemoved=!0),!1},e.wordCheck=function(){for(var r=(e.word,[e.removeSuf432,e.removeSuf1,e.removePre1]),t=0,c=!1;e.word.length>=7&&!e.result&&t<r.length;)7!=e.word.length||c?(r[t](),t++,c=!1):(e.checkPattern73(),c=!0);var l=[e.checkPattern63,e.removeSuf432,e.removeSuf1,e.removePre1,e.checkPattern64];for(t=0;6==e.word.length&&!e.result&&t<l.length;)l[t](),t++;var n=[e.checkPattern53,e.removeSuf432,e.removeSuf1,e.removePre1,e.checkPattern54];for(t=0;5==e.word.length&&!e.result&&t<n.length;)n[t](),t++;var o=[e.checkPattern43,e.removeSuf1,e.removePre1,e.removeSuf432];for(t=0;4==e.word.length&&!e.result&&t<o.length;)o[t](),t++;return!0},e.checkPattern43=function(){e.patternCheck(e.patterns.pt43)},e.checkPattern53=function(){e.patternCheck(e.patterns.pt53)},e.checkPattern54=function(){e.patternCheck(e.patterns.pt54)},e.checkPattern63=function(){e.patternCheck(e.patterns.pt63)},e.checkPattern64=function(){e.patternCheck(e.patterns.pt64)},e.checkPattern73=function(){e.patternCheck(e.patterns.pt73)},function(r){return"function"==typeof r.update?r.update(function(r){return e.setCurrent(r),e.stem(),e.getCurrent()}):(e.setCurrent(r),e.stem(),e.getCurrent())}}(),e.Pipeline.registerFunction(e.ar.stemmer,"stemmer-ar"),e.ar.stopWordFilter=e.generateStopWordFilter("، اض امين اه اها اي ا اب اجل اجمع اخ اخذ اصبح اضحى اقبل اقل اكثر الا ام اما امامك امامك امسى اما ان انا انت انتم انتما انتن انت انشا انى او اوشك اولئك اولئكم اولاء اولالك اوه اي ايا اين اينما اي ان اي اف اذ اذا اذا اذما اذن الى اليكم اليكما اليكن اليك اليك الا اما ان انما اي اياك اياكم اياكما اياكن ايانا اياه اياها اياهم اياهما اياهن اياي ايه ان ا ابتدا اثر اجل احد اخرى اخلولق اذا اربعة ارتد استحال اطار اعادة اعلنت اف اكثر اكد الالاء الالى الا الاخيرة الان الاول الاولى التى التي الثاني الثانية الذاتي الذى الذي الذين السابق الف اللائي اللاتي اللتان اللتيا اللتين اللذان اللذين اللواتي الماضي المقبل الوقت الى اليوم اما امام امس ان انبرى انقلب انه انها او اول اي ايار ايام ايضا ب بات باسم بان بخ برس بسبب بس بشكل بضع بطان بعد بعض بك بكم بكما بكن بل بلى بما بماذا بمن بن بنا به بها بي بيد بين بس بله بئس تان تانك تبدل تجاه تحول تلقاء تلك تلكم تلكما تم تينك تين ته تي ثلاثة ثم ثم ثمة ثم جعل جلل جميع جير حار حاشا حاليا حاي حتى حرى حسب حم حوالى حول حيث حيثما حين حي حبذا حتى حذار خلا خلال دون دونك ذا ذات ذاك ذانك ذان ذلك ذلكم ذلكما ذلكن ذو ذوا ذواتا ذواتي ذيت ذينك ذين ذه ذي راح رجع رويدك ريث رب زيارة سبحان سرعان سنة سنوات سوف سوى ساء ساءما شبه شخصا شرع شتان صار صباح صفر صه صه ضد ضمن طاق طالما طفق طق ظل عاد عام عاما عامة عدا عدة عدد عدم عسى عشر عشرة علق على عليك عليه عليها عل عن عند عندما عوض عين عدس عما غدا غير  ف فان فلان فو فى في فيم فيما فيه فيها قال قام قبل قد قط قلما قوة كانما كاين كاي كاين كاد كان كانت كذا كذلك كرب كل كلا كلاهما كلتا كلم كليكما كليهما كلما كلا كم كما كي كيت كيف كيفما كان كخ لئن لا لات لاسيما لدن لدى لعمر لقاء لك لكم لكما لكن لكنما لكي لكيلا للامم لم لما لما لن لنا له لها لو لوكالة لولا لوما لي لست لست لستم لستما لستن لست لسن لعل لكن ليت ليس ليسا ليستا ليست ليسوا لسنا ما ماانفك مابرح مادام ماذا مازال مافتئ مايو متى مثل مذ مساء مع معاذ مقابل مكانكم مكانكما مكانكن مكانك مليار مليون مما ممن من منذ منها مه مهما من من نحن نحو نعم نفس نفسه نهاية نخ نعما نعم ها هاؤم هاك هاهنا هب هذا هذه هكذا هل هلم هلا هم هما هن هنا هناك هنالك هو هي هيا هيت هيا هؤلاء هاتان هاتين هاته هاتي هج هذا هذان هذين هذه هذي هيهات وا واحد واضاف واضافت واكد وان واها واوضح وراءك وفي وقال وقالت وقد وقف وكان وكانت ولا ولم ومن وهو وهي ويكان وي وشكان يكون يمكن يوم ايان".split(" ")),e.Pipeline.registerFunction(e.ar.stopWordFilter,"stopWordFilter-ar")}});
\ No newline at end of file
diff --git a/ja/assets/javascripts/lunr/min/lunr.da.min.js b/ja/assets/javascripts/lunr/min/lunr.da.min.js
new file mode 100644
index 000000000..b9d850986
--- /dev/null
+++ b/ja/assets/javascripts/lunr/min/lunr.da.min.js
@@ -0,0 +1,18 @@
+/*!
+ * Lunr languages, `Danish` language
+ * https://github.com/MihaiValentin/lunr-languages
+ *
+ * Copyright 2014, Mihai Valentin
+ * http://www.mozilla.org/MPL/
+ */
+/*!
+ * based on
+ * Snowball JavaScript Library v0.3
+ * http://code.google.com/p/urim/
+ * http://snowball.tartarus.org/
+ *
+ * Copyright 2010, Oleg Mazko
+ * http://www.mozilla.org/MPL/
+ */
+
+!function(e,r){"function"==typeof define&&define.amd?define(r):"object"==typeof exports?module.exports=r():r()(e.lunr)}(this,function(){return function(e){if(void 0===e)throw new Error("Lunr is not present. Please include / require Lunr before this script.");if(void 0===e.stemmerSupport)throw new Error("Lunr stemmer support is not present. Please include / require Lunr stemmer support before this script.");e.da=function(){this.pipeline.reset(),this.pipeline.add(e.da.trimmer,e.da.stopWordFilter,e.da.stemmer),this.searchPipeline&&(this.searchPipeline.reset(),this.searchPipeline.add(e.da.stemmer))},e.da.wordCharacters="A-Za-zªºÀ-ÖØ-öø-ʸˠ-ˤᴀ-ᴥᴬ-ᵜᵢ-ᵥᵫ-ᵷᵹ-ᶾḀ-ỿⁱⁿₐ-ₜKÅℲⅎⅠ-ↈⱠ-ⱿꜢ-ꞇꞋ-ꞭꞰ-ꞷꟷ-ꟿꬰ-ꭚꭜ-ꭤff-stＡ-Ｚａ-ｚ",e.da.trimmer=e.trimmerSupport.generateTrimmer(e.da.wordCharacters),e.Pipeline.registerFunction(e.da.trimmer,"trimmer-da"),e.da.stemmer=function(){var r=e.stemmerSupport.Among,i=e.stemmerSupport.SnowballProgram,n=new function(){function e(){var e,r=f.cursor+3;if(d=f.limit,0<=r&&r<=f.limit){for(a=r;;){if(e=f.cursor,f.in_grouping(w,97,248)){f.cursor=e;break}if(f.cursor=e,e>=f.limit)return;f.cursor++}for(;!f.out_grouping(w,97,248);){if(f.cursor>=f.limit)return;f.cursor++}d=f.cursor,d<a&&(d=a)}}function n(){var e,r;if(f.cursor>=d&&(r=f.limit_backward,f.limit_backward=d,f.ket=f.cursor,e=f.find_among_b(c,32),f.limit_backward=r,e))switch(f.bra=f.cursor,e){case 1:f.slice_del();break;case 2:f.in_grouping_b(p,97,229)&&f.slice_del()}}function t(){var e,r=f.limit-f.cursor;f.cursor>=d&&(e=f.limit_backward,f.limit_backward=d,f.ket=f.cursor,f.find_among_b(l,4)?(f.bra=f.cursor,f.limit_backward=e,f.cursor=f.limit-r,f.cursor>f.limit_backward&&(f.cursor--,f.bra=f.cursor,f.slice_del())):f.limit_backward=e)}function s(){var e,r,i,n=f.limit-f.cursor;if(f.ket=f.cursor,f.eq_s_b(2,"st")&&(f.bra=f.cursor,f.eq_s_b(2,"ig")&&f.slice_del()),f.cursor=f.limit-n,f.cursor>=d&&(r=f.limit_backward,f.limit_backward=d,f.ket=f.cursor,e=f.find_among_b(m,5),f.limit_backward=r,e))switch(f.bra=f.cursor,e){case 1:f.slice_del(),i=f.limit-f.cursor,t(),f.cursor=f.limit-i;break;case 2:f.slice_from("løs")}}function o(){var e;f.cursor>=d&&(e=f.limit_backward,f.limit_backward=d,f.ket=f.cursor,f.out_grouping_b(w,97,248)?(f.bra=f.cursor,u=f.slice_to(u),f.limit_backward=e,f.eq_v_b(u)&&f.slice_del()):f.limit_backward=e)}var a,d,u,c=[new r("hed",-1,1),new r("ethed",0,1),new r("ered",-1,1),new r("e",-1,1),new r("erede",3,1),new r("ende",3,1),new r("erende",5,1),new r("ene",3,1),new r("erne",3,1),new r("ere",3,1),new r("en",-1,1),new r("heden",10,1),new r("eren",10,1),new r("er",-1,1),new r("heder",13,1),new r("erer",13,1),new r("s",-1,2),new r("heds",16,1),new r("es",16,1),new r("endes",18,1),new r("erendes",19,1),new r("enes",18,1),new r("ernes",18,1),new r("eres",18,1),new r("ens",16,1),new r("hedens",24,1),new r("erens",24,1),new r("ers",16,1),new r("ets",16,1),new r("erets",28,1),new r("et",-1,1),new r("eret",30,1)],l=[new r("gd",-1,-1),new r("dt",-1,-1),new r("gt",-1,-1),new r("kt",-1,-1)],m=[new r("ig",-1,1),new r("lig",0,1),new r("elig",1,1),new r("els",-1,1),new r("løst",-1,2)],w=[17,65,16,1,0,0,0,0,0,0,0,0,0,0,0,0,48,0,128],p=[239,254,42,3,0,0,0,0,0,0,0,0,0,0,0,0,16],f=new i;this.setCurrent=function(e){f.setCurrent(e)},this.getCurrent=function(){return f.getCurrent()},this.stem=function(){var r=f.cursor;return e(),f.limit_backward=r,f.cursor=f.limit,n(),f.cursor=f.limit,t(),f.cursor=f.limit,s(),f.cursor=f.limit,o(),!0}};return function(e){return"function"==typeof e.update?e.update(function(e){return n.setCurrent(e),n.stem(),n.getCurrent()}):(n.setCurrent(e),n.stem(),n.getCurrent())}}(),e.Pipeline.registerFunction(e.da.stemmer,"stemmer-da"),e.da.stopWordFilter=e.generateStopWordFilter("ad af alle alt anden at blev blive bliver da de dem den denne der deres det dette dig din disse dog du efter eller en end er et for fra ham han hans har havde have hende hendes her hos hun hvad hvis hvor i ikke ind jeg jer jo kunne man mange med meget men mig min mine mit mod ned noget nogle nu når og også om op os over på selv sig sin sine sit skal skulle som sådan thi til ud under var vi vil ville vor være været".split(" ")),e.Pipeline.registerFunction(e.da.stopWordFilter,"stopWordFilter-da")}});
\ No newline at end of file
diff --git a/ja/assets/javascripts/lunr/min/lunr.de.min.js b/ja/assets/javascripts/lunr/min/lunr.de.min.js
new file mode 100644
index 000000000..f3b5c108c
--- /dev/null
+++ b/ja/assets/javascripts/lunr/min/lunr.de.min.js
@@ -0,0 +1,18 @@
+/*!
+ * Lunr languages, `German` language
+ * https://github.com/MihaiValentin/lunr-languages
+ *
+ * Copyright 2014, Mihai Valentin
+ * http://www.mozilla.org/MPL/
+ */
+/*!
+ * based on
+ * Snowball JavaScript Library v0.3
+ * http://code.google.com/p/urim/
+ * http://snowball.tartarus.org/
+ *
+ * Copyright 2010, Oleg Mazko
+ * http://www.mozilla.org/MPL/
+ */
+
+!function(e,r){"function"==typeof define&&define.amd?define(r):"object"==typeof exports?module.exports=r():r()(e.lunr)}(this,function(){return function(e){if(void 0===e)throw new Error("Lunr is not present. Please include / require Lunr before this script.");if(void 0===e.stemmerSupport)throw new Error("Lunr stemmer support is not present. Please include / require Lunr stemmer support before this script.");e.de=function(){this.pipeline.reset(),this.pipeline.add(e.de.trimmer,e.de.stopWordFilter,e.de.stemmer),this.searchPipeline&&(this.searchPipeline.reset(),this.searchPipeline.add(e.de.stemmer))},e.de.wordCharacters="A-Za-zªºÀ-ÖØ-öø-ʸˠ-ˤᴀ-ᴥᴬ-ᵜᵢ-ᵥᵫ-ᵷᵹ-ᶾḀ-ỿⁱⁿₐ-ₜKÅℲⅎⅠ-ↈⱠ-ⱿꜢ-ꞇꞋ-ꞭꞰ-ꞷꟷ-ꟿꬰ-ꭚꭜ-ꭤff-stＡ-Ｚａ-ｚ",e.de.trimmer=e.trimmerSupport.generateTrimmer(e.de.wordCharacters),e.Pipeline.registerFunction(e.de.trimmer,"trimmer-de"),e.de.stemmer=function(){var r=e.stemmerSupport.Among,n=e.stemmerSupport.SnowballProgram,i=new function(){function e(e,r,n){return!(!v.eq_s(1,e)||(v.ket=v.cursor,!v.in_grouping(p,97,252)))&&(v.slice_from(r),v.cursor=n,!0)}function i(){for(var r,n,i,s,t=v.cursor;;)if(r=v.cursor,v.bra=r,v.eq_s(1,"ß"))v.ket=v.cursor,v.slice_from("ss");else{if(r>=v.limit)break;v.cursor=r+1}for(v.cursor=t;;)for(n=v.cursor;;){if(i=v.cursor,v.in_grouping(p,97,252)){if(s=v.cursor,v.bra=s,e("u","U",i))break;if(v.cursor=s,e("y","Y",i))break}if(i>=v.limit)return void(v.cursor=n);v.cursor=i+1}}function s(){for(;!v.in_grouping(p,97,252);){if(v.cursor>=v.limit)return!0;v.cursor++}for(;!v.out_grouping(p,97,252);){if(v.cursor>=v.limit)return!0;v.cursor++}return!1}function t(){m=v.limit,l=m;var e=v.cursor+3;0<=e&&e<=v.limit&&(d=e,s()||(m=v.cursor,m<d&&(m=d),s()||(l=v.cursor)))}function o(){for(var e,r;;){if(r=v.cursor,v.bra=r,!(e=v.find_among(h,6)))return;switch(v.ket=v.cursor,e){case 1:v.slice_from("y");break;case 2:case 5:v.slice_from("u");break;case 3:v.slice_from("a");break;case 4:v.slice_from("o");break;case 6:if(v.cursor>=v.limit)return;v.cursor++}}}function c(){return m<=v.cursor}function u(){return l<=v.cursor}function a(){var e,r,n,i,s=v.limit-v.cursor;if(v.ket=v.cursor,(e=v.find_among_b(w,7))&&(v.bra=v.cursor,c()))switch(e){case 1:v.slice_del();break;case 2:v.slice_del(),v.ket=v.cursor,v.eq_s_b(1,"s")&&(v.bra=v.cursor,v.eq_s_b(3,"nis")&&v.slice_del());break;case 3:v.in_grouping_b(g,98,116)&&v.slice_del()}if(v.cursor=v.limit-s,v.ket=v.cursor,(e=v.find_among_b(f,4))&&(v.bra=v.cursor,c()))switch(e){case 1:v.slice_del();break;case 2:if(v.in_grouping_b(k,98,116)){var t=v.cursor-3;v.limit_backward<=t&&t<=v.limit&&(v.cursor=t,v.slice_del())}}if(v.cursor=v.limit-s,v.ket=v.cursor,(e=v.find_among_b(_,8))&&(v.bra=v.cursor,u()))switch(e){case 1:v.slice_del(),v.ket=v.cursor,v.eq_s_b(2,"ig")&&(v.bra=v.cursor,r=v.limit-v.cursor,v.eq_s_b(1,"e")||(v.cursor=v.limit-r,u()&&v.slice_del()));break;case 2:n=v.limit-v.cursor,v.eq_s_b(1,"e")||(v.cursor=v.limit-n,v.slice_del());break;case 3:if(v.slice_del(),v.ket=v.cursor,i=v.limit-v.cursor,!v.eq_s_b(2,"er")&&(v.cursor=v.limit-i,!v.eq_s_b(2,"en")))break;v.bra=v.cursor,c()&&v.slice_del();break;case 4:v.slice_del(),v.ket=v.cursor,e=v.find_among_b(b,2),e&&(v.bra=v.cursor,u()&&1==e&&v.slice_del())}}var d,l,m,h=[new r("",-1,6),new r("U",0,2),new r("Y",0,1),new r("ä",0,3),new r("ö",0,4),new r("ü",0,5)],w=[new r("e",-1,2),new r("em",-1,1),new r("en",-1,2),new r("ern",-1,1),new r("er",-1,1),new r("s",-1,3),new r("es",5,2)],f=[new r("en",-1,1),new r("er",-1,1),new r("st",-1,2),new r("est",2,1)],b=[new r("ig",-1,1),new r("lich",-1,1)],_=[new r("end",-1,1),new r("ig",-1,2),new r("ung",-1,1),new r("lich",-1,3),new r("isch",-1,2),new r("ik",-1,2),new r("heit",-1,3),new r("keit",-1,4)],p=[17,65,16,1,0,0,0,0,0,0,0,0,0,0,0,0,8,0,32,8],g=[117,30,5],k=[117,30,4],v=new n;this.setCurrent=function(e){v.setCurrent(e)},this.getCurrent=function(){return v.getCurrent()},this.stem=function(){var e=v.cursor;return i(),v.cursor=e,t(),v.limit_backward=e,v.cursor=v.limit,a(),v.cursor=v.limit_backward,o(),!0}};return function(e){return"function"==typeof e.update?e.update(function(e){return i.setCurrent(e),i.stem(),i.getCurrent()}):(i.setCurrent(e),i.stem(),i.getCurrent())}}(),e.Pipeline.registerFunction(e.de.stemmer,"stemmer-de"),e.de.stopWordFilter=e.generateStopWordFilter("aber alle allem allen aller alles als also am an ander andere anderem anderen anderer anderes anderm andern anderr anders auch auf aus bei bin bis bist da damit dann das dasselbe dazu daß dein deine deinem deinen deiner deines dem demselben den denn denselben der derer derselbe derselben des desselben dessen dich die dies diese dieselbe dieselben diesem diesen dieser dieses dir doch dort du durch ein eine einem einen einer eines einig einige einigem einigen einiger einiges einmal er es etwas euch euer eure eurem euren eurer eures für gegen gewesen hab habe haben hat hatte hatten hier hin hinter ich ihm ihn ihnen ihr ihre ihrem ihren ihrer ihres im in indem ins ist jede jedem jeden jeder jedes jene jenem jenen jener jenes jetzt kann kein keine keinem keinen keiner keines können könnte machen man manche manchem manchen mancher manches mein meine meinem meinen meiner meines mich mir mit muss musste nach nicht nichts noch nun nur ob oder ohne sehr sein seine seinem seinen seiner seines selbst sich sie sind so solche solchem solchen solcher solches soll sollte sondern sonst um und uns unse unsem unsen unser unses unter viel vom von vor war waren warst was weg weil weiter welche welchem welchen welcher welches wenn werde werden wie wieder will wir wird wirst wo wollen wollte während würde würden zu zum zur zwar zwischen über".split(" ")),e.Pipeline.registerFunction(e.de.stopWordFilter,"stopWordFilter-de")}});
\ No newline at end of file
diff --git a/ja/assets/javascripts/lunr/min/lunr.du.min.js b/ja/assets/javascripts/lunr/min/lunr.du.min.js
new file mode 100644
index 000000000..49a0f3f0a
--- /dev/null
+++ b/ja/assets/javascripts/lunr/min/lunr.du.min.js
@@ -0,0 +1,18 @@
+/*!
+ * Lunr languages, `Dutch` language
+ * https://github.com/MihaiValentin/lunr-languages
+ *
+ * Copyright 2014, Mihai Valentin
+ * http://www.mozilla.org/MPL/
+ */
+/*!
+ * based on
+ * Snowball JavaScript Library v0.3
+ * http://code.google.com/p/urim/
+ * http://snowball.tartarus.org/
+ *
+ * Copyright 2010, Oleg Mazko
+ * http://www.mozilla.org/MPL/
+ */
+
+!function(e,r){"function"==typeof define&&define.amd?define(r):"object"==typeof exports?module.exports=r():r()(e.lunr)}(this,function(){return function(e){if(void 0===e)throw new Error("Lunr is not present. Please include / require Lunr before this script.");if(void 0===e.stemmerSupport)throw new Error("Lunr stemmer support is not present. Please include / require Lunr stemmer support before this script.");console.warn('[Lunr Languages] Please use the "nl" instead of the "du". The "nl" code is the standard code for Dutch language, and "du" will be removed in the next major versions.'),e.du=function(){this.pipeline.reset(),this.pipeline.add(e.du.trimmer,e.du.stopWordFilter,e.du.stemmer),this.searchPipeline&&(this.searchPipeline.reset(),this.searchPipeline.add(e.du.stemmer))},e.du.wordCharacters="A-Za-zªºÀ-ÖØ-öø-ʸˠ-ˤᴀ-ᴥᴬ-ᵜᵢ-ᵥᵫ-ᵷᵹ-ᶾḀ-ỿⁱⁿₐ-ₜKÅℲⅎⅠ-ↈⱠ-ⱿꜢ-ꞇꞋ-ꞭꞰ-ꞷꟷ-ꟿꬰ-ꭚꭜ-ꭤff-stＡ-Ｚａ-ｚ",e.du.trimmer=e.trimmerSupport.generateTrimmer(e.du.wordCharacters),e.Pipeline.registerFunction(e.du.trimmer,"trimmer-du"),e.du.stemmer=function(){var r=e.stemmerSupport.Among,i=e.stemmerSupport.SnowballProgram,n=new function(){function e(){for(var e,r,i,o=C.cursor;;){if(C.bra=C.cursor,e=C.find_among(b,11))switch(C.ket=C.cursor,e){case 1:C.slice_from("a");continue;case 2:C.slice_from("e");continue;case 3:C.slice_from("i");continue;case 4:C.slice_from("o");continue;case 5:C.slice_from("u");continue;case 6:if(C.cursor>=C.limit)break;C.cursor++;continue}break}for(C.cursor=o,C.bra=o,C.eq_s(1,"y")?(C.ket=C.cursor,C.slice_from("Y")):C.cursor=o;;)if(r=C.cursor,C.in_grouping(q,97,232)){if(i=C.cursor,C.bra=i,C.eq_s(1,"i"))C.ket=C.cursor,C.in_grouping(q,97,232)&&(C.slice_from("I"),C.cursor=r);else if(C.cursor=i,C.eq_s(1,"y"))C.ket=C.cursor,C.slice_from("Y"),C.cursor=r;else if(n(r))break}else if(n(r))break}function n(e){return C.cursor=e,e>=C.limit||(C.cursor++,!1)}function o(){_=C.limit,f=_,t()||(_=C.cursor,_<3&&(_=3),t()||(f=C.cursor))}function t(){for(;!C.in_grouping(q,97,232);){if(C.cursor>=C.limit)return!0;C.cursor++}for(;!C.out_grouping(q,97,232);){if(C.cursor>=C.limit)return!0;C.cursor++}return!1}function s(){for(var e;;)if(C.bra=C.cursor,e=C.find_among(p,3))switch(C.ket=C.cursor,e){case 1:C.slice_from("y");break;case 2:C.slice_from("i");break;case 3:if(C.cursor>=C.limit)return;C.cursor++}}function u(){return _<=C.cursor}function c(){return f<=C.cursor}function a(){var e=C.limit-C.cursor;C.find_among_b(g,3)&&(C.cursor=C.limit-e,C.ket=C.cursor,C.cursor>C.limit_backward&&(C.cursor--,C.bra=C.cursor,C.slice_del()))}function l(){var e;w=!1,C.ket=C.cursor,C.eq_s_b(1,"e")&&(C.bra=C.cursor,u()&&(e=C.limit-C.cursor,C.out_grouping_b(q,97,232)&&(C.cursor=C.limit-e,C.slice_del(),w=!0,a())))}function m(){var e;u()&&(e=C.limit-C.cursor,C.out_grouping_b(q,97,232)&&(C.cursor=C.limit-e,C.eq_s_b(3,"gem")||(C.cursor=C.limit-e,C.slice_del(),a())))}function d(){var e,r,i,n,o,t,s=C.limit-C.cursor;if(C.ket=C.cursor,e=C.find_among_b(h,5))switch(C.bra=C.cursor,e){case 1:u()&&C.slice_from("heid");break;case 2:m();break;case 3:u()&&C.out_grouping_b(z,97,232)&&C.slice_del()}if(C.cursor=C.limit-s,l(),C.cursor=C.limit-s,C.ket=C.cursor,C.eq_s_b(4,"heid")&&(C.bra=C.cursor,c()&&(r=C.limit-C.cursor,C.eq_s_b(1,"c")||(C.cursor=C.limit-r,C.slice_del(),C.ket=C.cursor,C.eq_s_b(2,"en")&&(C.bra=C.cursor,m())))),C.cursor=C.limit-s,C.ket=C.cursor,e=C.find_among_b(k,6))switch(C.bra=C.cursor,e){case 1:if(c()){if(C.slice_del(),i=C.limit-C.cursor,C.ket=C.cursor,C.eq_s_b(2,"ig")&&(C.bra=C.cursor,c()&&(n=C.limit-C.cursor,!C.eq_s_b(1,"e")))){C.cursor=C.limit-n,C.slice_del();break}C.cursor=C.limit-i,a()}break;case 2:c()&&(o=C.limit-C.cursor,C.eq_s_b(1,"e")||(C.cursor=C.limit-o,C.slice_del()));break;case 3:c()&&(C.slice_del(),l());break;case 4:c()&&C.slice_del();break;case 5:c()&&w&&C.slice_del()}C.cursor=C.limit-s,C.out_grouping_b(j,73,232)&&(t=C.limit-C.cursor,C.find_among_b(v,4)&&C.out_grouping_b(q,97,232)&&(C.cursor=C.limit-t,C.ket=C.cursor,C.cursor>C.limit_backward&&(C.cursor--,C.bra=C.cursor,C.slice_del())))}var f,_,w,b=[new r("",-1,6),new r("á",0,1),new r("ä",0,1),new r("é",0,2),new r("ë",0,2),new r("í",0,3),new r("ï",0,3),new r("ó",0,4),new r("ö",0,4),new r("ú",0,5),new r("ü",0,5)],p=[new r("",-1,3),new r("I",0,2),new r("Y",0,1)],g=[new r("dd",-1,-1),new r("kk",-1,-1),new r("tt",-1,-1)],h=[new r("ene",-1,2),new r("se",-1,3),new r("en",-1,2),new r("heden",2,1),new r("s",-1,3)],k=[new r("end",-1,1),new r("ig",-1,2),new r("ing",-1,1),new r("lijk",-1,3),new r("baar",-1,4),new r("bar",-1,5)],v=[new r("aa",-1,-1),new r("ee",-1,-1),new r("oo",-1,-1),new r("uu",-1,-1)],q=[17,65,16,1,0,0,0,0,0,0,0,0,0,0,0,0,128],j=[1,0,0,17,65,16,1,0,0,0,0,0,0,0,0,0,0,0,0,128],z=[17,67,16,1,0,0,0,0,0,0,0,0,0,0,0,0,128],C=new i;this.setCurrent=function(e){C.setCurrent(e)},this.getCurrent=function(){return C.getCurrent()},this.stem=function(){var r=C.cursor;return e(),C.cursor=r,o(),C.limit_backward=r,C.cursor=C.limit,d(),C.cursor=C.limit_backward,s(),!0}};return function(e){return"function"==typeof e.update?e.update(function(e){return n.setCurrent(e),n.stem(),n.getCurrent()}):(n.setCurrent(e),n.stem(),n.getCurrent())}}(),e.Pipeline.registerFunction(e.du.stemmer,"stemmer-du"),e.du.stopWordFilter=e.generateStopWordFilter(" aan al alles als altijd andere ben bij daar dan dat de der deze die dit doch doen door dus een eens en er ge geen geweest haar had heb hebben heeft hem het hier hij hoe hun iemand iets ik in is ja je kan kon kunnen maar me meer men met mij mijn moet na naar niet niets nog nu of om omdat onder ons ook op over reeds te tegen toch toen tot u uit uw van veel voor want waren was wat werd wezen wie wil worden wordt zal ze zelf zich zij zijn zo zonder zou".split(" ")),e.Pipeline.registerFunction(e.du.stopWordFilter,"stopWordFilter-du")}});
\ No newline at end of file
diff --git a/ja/assets/javascripts/lunr/min/lunr.el.min.js b/ja/assets/javascripts/lunr/min/lunr.el.min.js
new file mode 100644
index 000000000..ace017bd6
--- /dev/null
+++ b/ja/assets/javascripts/lunr/min/lunr.el.min.js
@@ -0,0 +1 @@
+!function(e,t){"function"==typeof define&&define.amd?define(t):"object"==typeof exports?module.exports=t():t()(e.lunr)}(this,function(){return function(e){if(void 0===e)throw new Error("Lunr is not present. Please include / require Lunr before this script.");if(void 0===e.stemmerSupport)throw new Error("Lunr stemmer support is not present. Please include / require Lunr stemmer support before this script.");e.el=function(){this.pipeline.reset(),void 0===this.searchPipeline&&this.pipeline.add(e.el.trimmer,e.el.normilizer),this.pipeline.add(e.el.stopWordFilter,e.el.stemmer),this.searchPipeline&&(this.searchPipeline.reset(),this.searchPipeline.add(e.el.stemmer))},e.el.wordCharacters="A-Za-zΑαΒβΓγΔδΕεΖζΗηΘθΙιΚκΛλΜμΝνΞξΟοΠπΡρΣσςΤτΥυΦφΧχΨψΩωΆάΈέΉήΊίΌόΎύΏώΪΐΫΰΐΰ",e.el.trimmer=e.trimmerSupport.generateTrimmer(e.el.wordCharacters),e.Pipeline.registerFunction(e.el.trimmer,"trimmer-el"),e.el.stemmer=function(){function e(e){return s.test(e)}function t(e){return/[ΑΕΗΙΟΥΩ]$/.test(e)}function r(e){return/[ΑΕΗΙΟΩ]$/.test(e)}function n(n){var s=n;if(n.length<3)return s;if(!e(n))return s;if(i.indexOf(n)>=0)return s;var u=new RegExp("(.*)("+Object.keys(l).join("|")+")$"),o=u.exec(s);return null!==o&&(s=o[1]+l[o[2]]),null!==(o=/^(.+?)(ΑΔΕΣ|ΑΔΩΝ)$/.exec(s))&&(s=o[1],/(ΟΚ|ΜΑΜ|ΜΑΝ|ΜΠΑΜΠ|ΠΑΤΕΡ|ΓΙΑΓΙ|ΝΤΑΝΤ|ΚΥΡ|ΘΕΙ|ΠΕΘΕΡ|ΜΟΥΣΑΜ|ΚΑΠΛΑΜ|ΠΑΡ|ΨΑΡ|ΤΖΟΥΡ|ΤΑΜΠΟΥΡ|ΓΑΛΑΤ|ΦΑΦΛΑΤ)$/.test(o[1])||(s+="ΑΔ")),null!==(o=/^(.+?)(ΕΔΕΣ|ΕΔΩΝ)$/.exec(s))&&(s=o[1],/(ΟΠ|ΙΠ|ΕΜΠ|ΥΠ|ΓΗΠ|ΔΑΠ|ΚΡΑΣΠ|ΜΙΛ)$/.test(o[1])&&(s+="ΕΔ")),null!==(o=/^(.+?)(ΟΥΔΕΣ|ΟΥΔΩΝ)$/.exec(s))&&(s=o[1],/(ΑΡΚ|ΚΑΛΙΑΚ|ΠΕΤΑΛ|ΛΙΧ|ΠΛΕΞ|ΣΚ|Σ|ΦΛ|ΦΡ|ΒΕΛ|ΛΟΥΛ|ΧΝ|ΣΠ|ΤΡΑΓ|ΦΕ)$/.test(o[1])&&(s+="ΟΥΔ")),null!==(o=/^(.+?)(ΕΩΣ|ΕΩΝ|ΕΑΣ|ΕΑ)$/.exec(s))&&(s=o[1],/^(Θ|Δ|ΕΛ|ΓΑΛ|Ν|Π|ΙΔ|ΠΑΡ|ΣΤΕΡ|ΟΡΦ|ΑΝΔΡ|ΑΝΤΡ)$/.test(o[1])&&(s+="Ε")),null!==(o=/^(.+?)(ΕΙΟ|ΕΙΟΣ|ΕΙΟΙ|ΕΙΑ|ΕΙΑΣ|ΕΙΕΣ|ΕΙΟΥ|ΕΙΟΥΣ|ΕΙΩΝ)$/.exec(s))&&o[1].length>4&&(s=o[1]),null!==(o=/^(.+?)(ΙΟΥΣ|ΙΑΣ|ΙΕΣ|ΙΟΣ|ΙΟΥ|ΙΟΙ|ΙΩΝ|ΙΟΝ|ΙΑ|ΙΟ)$/.exec(s))&&(s=o[1],(t(s)||s.length<2||/^(ΑΓ|ΑΓΓΕΛ|ΑΓΡ|ΑΕΡ|ΑΘΛ|ΑΚΟΥΣ|ΑΞ|ΑΣ|Β|ΒΙΒΛ|ΒΥΤ|Γ|ΓΙΑΓ|ΓΩΝ|Δ|ΔΑΝ|ΔΗΛ|ΔΗΜ|ΔΟΚΙΜ|ΕΛ|ΖΑΧΑΡ|ΗΛ|ΗΠ|ΙΔ|ΙΣΚ|ΙΣΤ|ΙΟΝ|ΙΩΝ|ΚΙΜΩΛ|ΚΟΛΟΝ|ΚΟΡ|ΚΤΗΡ|ΚΥΡ|ΛΑΓ|ΛΟΓ|ΜΑΓ|ΜΠΑΝ|ΜΠΡ|ΝΑΥΤ|ΝΟΤ|ΟΠΑΛ|ΟΞ|ΟΡ|ΟΣ|ΠΑΝΑΓ|ΠΑΤΡ|ΠΗΛ|ΠΗΝ|ΠΛΑΙΣ|ΠΟΝΤ|ΡΑΔ|ΡΟΔ|ΣΚ|ΣΚΟΡΠ|ΣΟΥΝ|ΣΠΑΝ|ΣΤΑΔ|ΣΥΡ|ΤΗΛ|ΤΙΜ|ΤΟΚ|ΤΟΠ|ΤΡΟΧ|ΦΙΛ|ΦΩΤ|Χ|ΧΙΛ|ΧΡΩΜ|ΧΩΡ)$/.test(o[1]))&&(s+="Ι"),/^(ΠΑΛ)$/.test(o[1])&&(s+="ΑΙ")),null!==(o=/^(.+?)(ΙΚΟΣ|ΙΚΟΝ|ΙΚΕΙΣ|ΙΚΟΙ|ΙΚΕΣ|ΙΚΟΥΣ|ΙΚΗ|ΙΚΗΣ|ΙΚΟ|ΙΚΑ|ΙΚΟΥ|ΙΚΩΝ|ΙΚΩΣ)$/.exec(s))&&(s=o[1],(t(s)||/^(ΑΔ|ΑΛ|ΑΜΑΝ|ΑΜΕΡ|ΑΜΜΟΧΑΛ|ΑΝΗΘ|ΑΝΤΙΔ|ΑΠΛ|ΑΤΤ|ΑΦΡ|ΒΑΣ|ΒΡΩΜ|ΓΕΝ|ΓΕΡ|Δ|ΔΙΚΑΝ|ΔΥΤ|ΕΙΔ|ΕΝΔ|ΕΞΩΔ|ΗΘ|ΘΕΤ|ΚΑΛΛΙΝ|ΚΑΛΠ|ΚΑΤΑΔ|ΚΟΥΖΙΝ|ΚΡ|ΚΩΔ|ΛΟΓ|Μ|ΜΕΡ|ΜΟΝΑΔ|ΜΟΥΛ|ΜΟΥΣ|ΜΠΑΓΙΑΤ|ΜΠΑΝ|ΜΠΟΛ|ΜΠΟΣ|ΜΥΣΤ|Ν|ΝΙΤ|ΞΙΚ|ΟΠΤ|ΠΑΝ|ΠΕΤΣ|ΠΙΚΑΝΤ|ΠΙΤΣ|ΠΛΑΣΤ|ΠΛΙΑΤΣ|ΠΟΝΤ|ΠΟΣΤΕΛΝ|ΠΡΩΤΟΔ|ΣΕΡΤ|ΣΗΜΑΝΤ|ΣΤΑΤ|ΣΥΝΑΔ|ΣΥΝΟΜΗΛ|ΤΕΛ|ΤΕΧΝ|ΤΡΟΠ|ΤΣΑΜ|ΥΠΟΔ|Φ|ΦΙΛΟΝ|ΦΥΛΟΔ|ΦΥΣ|ΧΑΣ)$/.test(o[1])||/(ΦΟΙΝ)$/.test(o[1]))&&(s+="ΙΚ")),"ΑΓΑΜΕ"===s&&(s="ΑΓΑΜ"),null!==(o=/^(.+?)(ΑΓΑΜΕ|ΗΣΑΜΕ|ΟΥΣΑΜΕ|ΗΚΑΜΕ|ΗΘΗΚΑΜΕ)$/.exec(s))&&(s=o[1]),null!==(o=/^(.+?)(ΑΜΕ)$/.exec(s))&&(s=o[1],/^(ΑΝΑΠ|ΑΠΟΘ|ΑΠΟΚ|ΑΠΟΣΤ|ΒΟΥΒ|ΞΕΘ|ΟΥΛ|ΠΕΘ|ΠΙΚΡ|ΠΟΤ|ΣΙΧ|Χ)$/.test(o[1])&&(s+="ΑΜ")),null!==(o=/^(.+?)(ΑΓΑΝΕ|ΗΣΑΝΕ|ΟΥΣΑΝΕ|ΙΟΝΤΑΝΕ|ΙΟΤΑΝΕ|ΙΟΥΝΤΑΝΕ|ΟΝΤΑΝΕ|ΟΤΑΝΕ|ΟΥΝΤΑΝΕ|ΗΚΑΝΕ|ΗΘΗΚΑΝΕ)$/.exec(s))&&(s=o[1],/^(ΤΡ|ΤΣ)$/.test(o[1])&&(s+="ΑΓΑΝ")),null!==(o=/^(.+?)(ΑΝΕ)$/.exec(s))&&(s=o[1],(r(s)||/^(ΒΕΤΕΡ|ΒΟΥΛΚ|ΒΡΑΧΜ|Γ|ΔΡΑΔΟΥΜ|Θ|ΚΑΛΠΟΥΖ|ΚΑΣΤΕΛ|ΚΟΡΜΟΡ|ΛΑΟΠΛ|ΜΩΑΜΕΘ|Μ|ΜΟΥΣΟΥΛΜΑΝ|ΟΥΛ|Π|ΠΕΛΕΚ|ΠΛ|ΠΟΛΙΣ|ΠΟΡΤΟΛ|ΣΑΡΑΚΑΤΣ|ΣΟΥΛΤ|ΤΣΑΡΛΑΤ|ΟΡΦ|ΤΣΙΓΓ|ΤΣΟΠ|ΦΩΤΟΣΤΕΦ|Χ|ΨΥΧΟΠΛ|ΑΓ|ΟΡΦ|ΓΑΛ|ΓΕΡ|ΔΕΚ|ΔΙΠΛ|ΑΜΕΡΙΚΑΝ|ΟΥΡ|ΠΙΘ|ΠΟΥΡΙΤ|Σ|ΖΩΝΤ|ΙΚ|ΚΑΣΤ|ΚΟΠ|ΛΙΧ|ΛΟΥΘΗΡ|ΜΑΙΝΤ|ΜΕΛ|ΣΙΓ|ΣΠ|ΣΤΕΓ|ΤΡΑΓ|ΤΣΑΓ|Φ|ΕΡ|ΑΔΑΠ|ΑΘΙΓΓ|ΑΜΗΧ|ΑΝΙΚ|ΑΝΟΡΓ|ΑΠΗΓ|ΑΠΙΘ|ΑΤΣΙΓΓ|ΒΑΣ|ΒΑΣΚ|ΒΑΘΥΓΑΛ|ΒΙΟΜΗΧ|ΒΡΑΧΥΚ|ΔΙΑΤ|ΔΙΑΦ|ΕΝΟΡΓ|ΘΥΣ|ΚΑΠΝΟΒΙΟΜΗΧ|ΚΑΤΑΓΑΛ|ΚΛΙΒ|ΚΟΙΛΑΡΦ|ΛΙΒ|ΜΕΓΛΟΒΙΟΜΗΧ|ΜΙΚΡΟΒΙΟΜΗΧ|ΝΤΑΒ|ΞΗΡΟΚΛΙΒ|ΟΛΙΓΟΔΑΜ|ΟΛΟΓΑΛ|ΠΕΝΤΑΡΦ|ΠΕΡΗΦ|ΠΕΡΙΤΡ|ΠΛΑΤ|ΠΟΛΥΔΑΠ|ΠΟΛΥΜΗΧ|ΣΤΕΦ|ΤΑΒ|ΤΕΤ|ΥΠΕΡΗΦ|ΥΠΟΚΟΠ|ΧΑΜΗΛΟΔΑΠ|ΨΗΛΟΤΑΒ)$/.test(o[1]))&&(s+="ΑΝ")),null!==(o=/^(.+?)(ΗΣΕΤΕ)$/.exec(s))&&(s=o[1]),null!==(o=/^(.+?)(ΕΤΕ)$/.exec(s))&&(s=o[1],(r(s)||/(ΟΔ|ΑΙΡ|ΦΟΡ|ΤΑΘ|ΔΙΑΘ|ΣΧ|ΕΝΔ|ΕΥΡ|ΤΙΘ|ΥΠΕΡΘ|ΡΑΘ|ΕΝΘ|ΡΟΘ|ΣΘ|ΠΥΡ|ΑΙΝ|ΣΥΝΔ|ΣΥΝ|ΣΥΝΘ|ΧΩΡ|ΠΟΝ|ΒΡ|ΚΑΘ|ΕΥΘ|ΕΚΘ|ΝΕΤ|ΡΟΝ|ΑΡΚ|ΒΑΡ|ΒΟΛ|ΩΦΕΛ)$/.test(o[1])||/^(ΑΒΑΡ|ΒΕΝ|ΕΝΑΡ|ΑΒΡ|ΑΔ|ΑΘ|ΑΝ|ΑΠΛ|ΒΑΡΟΝ|ΝΤΡ|ΣΚ|ΚΟΠ|ΜΠΟΡ|ΝΙΦ|ΠΑΓ|ΠΑΡΑΚΑΛ|ΣΕΡΠ|ΣΚΕΛ|ΣΥΡΦ|ΤΟΚ|Υ|Δ|ΕΜ|ΘΑΡΡ|Θ)$/.test(o[1]))&&(s+="ΕΤ")),null!==(o=/^(.+?)(ΟΝΤΑΣ|ΩΝΤΑΣ)$/.exec(s))&&(s=o[1],/^ΑΡΧ$/.test(o[1])&&(s+="ΟΝΤ"),/ΚΡΕ$/.test(o[1])&&(s+="ΩΝΤ")),null!==(o=/^(.+?)(ΟΜΑΣΤΕ|ΙΟΜΑΣΤΕ)$/.exec(s))&&(s=o[1],/^ΟΝ$/.test(o[1])&&(s+="ΟΜΑΣΤ")),null!==(o=/^(.+?)(ΙΕΣΤΕ)$/.exec(s))&&(s=o[1],/^(Π|ΑΠ|ΣΥΜΠ|ΑΣΥΜΠ|ΑΚΑΤΑΠ|ΑΜΕΤΑΜΦ)$/.test(o[1])&&(s+="ΙΕΣΤ")),null!==(o=/^(.+?)(ΕΣΤΕ)$/.exec(s))&&(s=o[1],/^(ΑΛ|ΑΡ|ΕΚΤΕΛ|Ζ|Μ|Ξ|ΠΑΡΑΚΑΛ|ΠΡΟ|ΝΙΣ)$/.test(o[1])&&(s+="ΕΣΤ")),null!==(o=/^(.+?)(ΗΘΗΚΑ|ΗΘΗΚΕΣ|ΗΘΗΚΕ)$/.exec(s))&&(s=o[1]),null!==(o=/^(.+?)(ΗΚΑ|ΗΚΕΣ|ΗΚΕ)$/.exec(s))&&(s=o[1],(/(ΣΚΩΛ|ΣΚΟΥΛ|ΝΑΡΘ|ΣΦ|ΟΘ|ΠΙΘ)$/.test(o[1])||/^(ΔΙΑΘ|Θ|ΠΑΡΑΚΑΤΑΘ|ΠΡΟΣΘ|ΣΥΝΘ)$/.test(o[1]))&&(s+="ΗΚ")),null!==(o=/^(.+?)(ΟΥΣΑ|ΟΥΣΕΣ|ΟΥΣΕ)$/.exec(s))&&(s=o[1],(t(s)||/^(ΦΑΡΜΑΚ|ΧΑΔ|ΑΓΚ|ΑΝΑΡΡ|ΒΡΟΜ|ΕΚΛΙΠ|ΛΑΜΠΙΔ|ΛΕΧ|Μ|ΠΑΤ|Ρ|Λ|ΜΕΔ|ΜΕΣΑΖ|ΥΠΟΤΕΙΝ|ΑΜ|ΑΙΘ|ΑΝΗΚ|ΔΕΣΠΟΖ|ΕΝΔΙΑΦΕΡ)$/.test(o[1])||/(ΠΟΔΑΡ|ΒΛΕΠ|ΠΑΝΤΑΧ|ΦΡΥΔ|ΜΑΝΤΙΛ|ΜΑΛΛ|ΚΥΜΑΤ|ΛΑΧ|ΛΗΓ|ΦΑΓ|ΟΜ|ΠΡΩΤ)$/.test(o[1]))&&(s+="ΟΥΣ")),null!==(o=/^(.+?)(ΑΓΑ|ΑΓΕΣ|ΑΓΕ)$/.exec(s))&&(s=o[1],(/^(ΑΒΑΣΤ|ΠΟΛΥΦ|ΑΔΗΦ|ΠΑΜΦ|Ρ|ΑΣΠ|ΑΦ|ΑΜΑΛ|ΑΜΑΛΛΙ|ΑΝΥΣΤ|ΑΠΕΡ|ΑΣΠΑΡ|ΑΧΑΡ|ΔΕΡΒΕΝ|ΔΡΟΣΟΠ|ΞΕΦ|ΝΕΟΠ|ΝΟΜΟΤ|ΟΛΟΠ|ΟΜΟΤ|ΠΡΟΣΤ|ΠΡΟΣΩΠΟΠ|ΣΥΜΠ|ΣΥΝΤ|Τ|ΥΠΟΤ|ΧΑΡ|ΑΕΙΠ|ΑΙΜΟΣΤ|ΑΝΥΠ|ΑΠΟΤ|ΑΡΤΙΠ|ΔΙΑΤ|ΕΝ|ΕΠΙΤ|ΚΡΟΚΑΛΟΠ|ΣΙΔΗΡΟΠ|Λ|ΝΑΥ|ΟΥΛΑΜ|ΟΥΡ|Π|ΤΡ|Μ)$/.test(o[1])||/(ΟΦ|ΠΕΛ|ΧΟΡΤ|ΛΛ|ΣΦ|ΡΠ|ΦΡ|ΠΡ|ΛΟΧ|ΣΜΗΝ)$/.test(o[1])&&!/^(ΨΟΦ|ΝΑΥΛΟΧ)$/.test(o[1])||/(ΚΟΛΛ)$/.test(o[1]))&&(s+="ΑΓ")),null!==(o=/^(.+?)(ΗΣΕ|ΗΣΟΥ|ΗΣΑ)$/.exec(s))&&(s=o[1],/^(Ν|ΧΕΡΣΟΝ|ΔΩΔΕΚΑΝ|ΕΡΗΜΟΝ|ΜΕΓΑΛΟΝ|ΕΠΤΑΝ|Ι)$/.test(o[1])&&(s+="ΗΣ")),null!==(o=/^(.+?)(ΗΣΤΕ)$/.exec(s))&&(s=o[1],/^(ΑΣΒ|ΣΒ|ΑΧΡ|ΧΡ|ΑΠΛ|ΑΕΙΜΝ|ΔΥΣΧΡ|ΕΥΧΡ|ΚΟΙΝΟΧΡ|ΠΑΛΙΜΨ)$/.test(o[1])&&(s+="ΗΣΤ")),null!==(o=/^(.+?)(ΟΥΝΕ|ΗΣΟΥΝΕ|ΗΘΟΥΝΕ)$/.exec(s))&&(s=o[1],/^(Ν|Ρ|ΣΠΙ|ΣΤΡΑΒΟΜΟΥΤΣ|ΚΑΚΟΜΟΥΤΣ|ΕΞΩΝ)$/.test(o[1])&&(s+="ΟΥΝ")),null!==(o=/^(.+?)(ΟΥΜΕ|ΗΣΟΥΜΕ|ΗΘΟΥΜΕ)$/.exec(s))&&(s=o[1],/^(ΠΑΡΑΣΟΥΣ|Φ|Χ|ΩΡΙΟΠΛ|ΑΖ|ΑΛΛΟΣΟΥΣ|ΑΣΟΥΣ)$/.test(o[1])&&(s+="ΟΥΜ")),null!=(o=/^(.+?)(ΜΑΤΟΙ|ΜΑΤΟΥΣ|ΜΑΤΟ|ΜΑΤΑ|ΜΑΤΩΣ|ΜΑΤΩΝ|ΜΑΤΟΣ|ΜΑΤΕΣ|ΜΑΤΗ|ΜΑΤΗΣ|ΜΑΤΟΥ)$/.exec(s))&&(s=o[1]+"Μ",/^(ΓΡΑΜ)$/.test(o[1])?s+="Α":/^(ΓΕ|ΣΤΑ)$/.test(o[1])&&(s+="ΑΤ")),null!==(o=/^(.+?)(ΟΥΑ)$/.exec(s))&&(s=o[1]+"ΟΥ"),n.length===s.length&&null!==(o=/^(.+?)(Α|ΑΓΑΤΕ|ΑΓΑΝ|ΑΕΙ|ΑΜΑΙ|ΑΝ|ΑΣ|ΑΣΑΙ|ΑΤΑΙ|ΑΩ|Ε|ΕΙ|ΕΙΣ|ΕΙΤΕ|ΕΣΑΙ|ΕΣ|ΕΤΑΙ|Ι|ΙΕΜΑΙ|ΙΕΜΑΣΤΕ|ΙΕΤΑΙ|ΙΕΣΑΙ|ΙΕΣΑΣΤΕ|ΙΟΜΑΣΤΑΝ|ΙΟΜΟΥΝ|ΙΟΜΟΥΝΑ|ΙΟΝΤΑΝ|ΙΟΝΤΟΥΣΑΝ|ΙΟΣΑΣΤΑΝ|ΙΟΣΑΣΤΕ|ΙΟΣΟΥΝ|ΙΟΣΟΥΝΑ|ΙΟΤΑΝ|ΙΟΥΜΑ|ΙΟΥΜΑΣΤΕ|ΙΟΥΝΤΑΙ|ΙΟΥΝΤΑΝ|Η|ΗΔΕΣ|ΗΔΩΝ|ΗΘΕΙ|ΗΘΕΙΣ|ΗΘΕΙΤΕ|ΗΘΗΚΑΤΕ|ΗΘΗΚΑΝ|ΗΘΟΥΝ|ΗΘΩ|ΗΚΑΤΕ|ΗΚΑΝ|ΗΣ|ΗΣΑΝ|ΗΣΑΤΕ|ΗΣΕΙ|ΗΣΕΣ|ΗΣΟΥΝ|ΗΣΩ|Ο|ΟΙ|ΟΜΑΙ|ΟΜΑΣΤΑΝ|ΟΜΟΥΝ|ΟΜΟΥΝΑ|ΟΝΤΑΙ|ΟΝΤΑΝ|ΟΝΤΟΥΣΑΝ|ΟΣ|ΟΣΑΣΤΑΝ|ΟΣΑΣΤΕ|ΟΣΟΥΝ|ΟΣΟΥΝΑ|ΟΤΑΝ|ΟΥ|ΟΥΜΑΙ|ΟΥΜΑΣΤΕ|ΟΥΝ|ΟΥΝΤΑΙ|ΟΥΝΤΑΝ|ΟΥΣ|ΟΥΣΑΝ|ΟΥΣΑΤΕ|Υ||ΥΑ|ΥΣ|Ω|ΩΝ|ΟΙΣ)$/.exec(s))&&(s=o[1]),null!=(o=/^(.+?)(ΕΣΤΕΡ|ΕΣΤΑΤ|ΟΤΕΡ|ΟΤΑΤ|ΥΤΕΡ|ΥΤΑΤ|ΩΤΕΡ|ΩΤΑΤ)$/.exec(s))&&(/^(ΕΞ|ΕΣ|ΑΝ|ΚΑΤ|Κ|ΠΡ)$/.test(o[1])||(s=o[1]),/^(ΚΑ|Μ|ΕΛΕ|ΛΕ|ΔΕ)$/.test(o[1])&&(s+="ΥΤ")),s}var 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t.update(function(t){for(var r="",n=0;n<t.length;n++)r+=e[t.charAt(n)]||t.charAt(n);return r});for(var r="",n=0;n<t.length;n++)r+=e[t.charAt(n)]||t.charAt(n);return r}}(),e.Pipeline.registerFunction(e.el.normilizer,"normilizer-el")}});
\ No newline at end of file
diff --git a/ja/assets/javascripts/lunr/min/lunr.es.min.js b/ja/assets/javascripts/lunr/min/lunr.es.min.js
new file mode 100644
index 000000000..2989d3426
--- /dev/null
+++ b/ja/assets/javascripts/lunr/min/lunr.es.min.js
@@ -0,0 +1,18 @@
+/*!
+ * Lunr languages, `Spanish` language
+ * https://github.com/MihaiValentin/lunr-languages
+ *
+ * Copyright 2014, Mihai Valentin
+ * http://www.mozilla.org/MPL/
+ */
+/*!
+ * based on
+ * Snowball JavaScript Library v0.3
+ * http://code.google.com/p/urim/
+ * http://snowball.tartarus.org/
+ *
+ * Copyright 2010, Oleg Mazko
+ * http://www.mozilla.org/MPL/
+ */
+
+!function(e,s){"function"==typeof define&&define.amd?define(s):"object"==typeof exports?module.exports=s():s()(e.lunr)}(this,function(){return function(e){if(void 0===e)throw new Error("Lunr is not present. Please include / require Lunr before this script.");if(void 0===e.stemmerSupport)throw new Error("Lunr stemmer support is not present. 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\ No newline at end of file
diff --git a/ja/assets/javascripts/lunr/min/lunr.fi.min.js b/ja/assets/javascripts/lunr/min/lunr.fi.min.js
new file mode 100644
index 000000000..29f5dfcea
--- /dev/null
+++ b/ja/assets/javascripts/lunr/min/lunr.fi.min.js
@@ -0,0 +1,18 @@
+/*!
+ * Lunr languages, `Finnish` language
+ * https://github.com/MihaiValentin/lunr-languages
+ *
+ * Copyright 2014, Mihai Valentin
+ * http://www.mozilla.org/MPL/
+ */
+/*!
+ * based on
+ * Snowball JavaScript Library v0.3
+ * http://code.google.com/p/urim/
+ * http://snowball.tartarus.org/
+ *
+ * Copyright 2010, Oleg Mazko
+ * http://www.mozilla.org/MPL/
+ */
+
+!function(i,e){"function"==typeof define&&define.amd?define(e):"object"==typeof exports?module.exports=e():e()(i.lunr)}(this,function(){return function(i){if(void 0===i)throw new Error("Lunr is not present. Please include / require Lunr before this script.");if(void 0===i.stemmerSupport)throw new Error("Lunr stemmer support is not present. 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i(),k=!1,A.limit_backward=e,A.cursor=A.limit,s(),A.cursor=A.limit,o(),A.cursor=A.limit,u(),A.cursor=A.limit,c(),A.cursor=A.limit,k?(m(),A.cursor=A.limit):(A.cursor=A.limit,w(),A.cursor=A.limit),_(),!0}};return function(i){return"function"==typeof i.update?i.update(function(i){return n.setCurrent(i),n.stem(),n.getCurrent()}):(n.setCurrent(i),n.stem(),n.getCurrent())}}(),i.Pipeline.registerFunction(i.fi.stemmer,"stemmer-fi"),i.fi.stopWordFilter=i.generateStopWordFilter("ei eivät emme en et ette että he heidän heidät heihin heille heillä heiltä heissä heistä heitä hän häneen hänelle hänellä häneltä hänen hänessä hänestä hänet häntä itse ja johon joiden joihin joiksi joilla joille joilta joina joissa joista joita joka joksi jolla jolle jolta jona jonka jos jossa josta jota jotka kanssa keiden keihin keiksi keille keillä keiltä keinä keissä keistä keitä keneen keneksi kenelle kenellä keneltä kenen kenenä kenessä kenestä kenet ketkä ketkä ketä koska kuin kuka kun me meidän meidät meihin meille meillä meiltä meissä meistä meitä mihin miksi mikä mille millä miltä minkä minkä minua minulla minulle minulta minun minussa minusta minut minuun minä minä missä mistä mitkä mitä mukaan mutta ne niiden niihin niiksi niille niillä niiltä niin niin niinä niissä niistä niitä noiden noihin noiksi noilla noille noilta noin noina noissa noista noita nuo nyt näiden näihin näiksi näille näillä näiltä näinä näissä näistä näitä nämä ole olemme olen olet olette oli olimme olin olisi olisimme olisin olisit olisitte olisivat olit olitte olivat olla olleet ollut on ovat poikki se sekä sen siihen siinä siitä siksi sille sillä sillä siltä sinua sinulla sinulle sinulta sinun sinussa sinusta sinut sinuun sinä sinä sitä tai te teidän teidät teihin teille teillä teiltä teissä teistä teitä tuo tuohon tuoksi tuolla tuolle tuolta tuon tuona tuossa tuosta tuota tähän täksi tälle tällä tältä tämä tämän tänä tässä tästä tätä vaan vai vaikka yli".split(" ")),i.Pipeline.registerFunction(i.fi.stopWordFilter,"stopWordFilter-fi")}});
\ No newline at end of file
diff --git a/ja/assets/javascripts/lunr/min/lunr.fr.min.js b/ja/assets/javascripts/lunr/min/lunr.fr.min.js
new file mode 100644
index 000000000..68cd0094a
--- /dev/null
+++ b/ja/assets/javascripts/lunr/min/lunr.fr.min.js
@@ -0,0 +1,18 @@
+/*!
+ * Lunr languages, `French` language
+ * https://github.com/MihaiValentin/lunr-languages
+ *
+ * Copyright 2014, Mihai Valentin
+ * http://www.mozilla.org/MPL/
+ */
+/*!
+ * based on
+ * Snowball JavaScript Library v0.3
+ * http://code.google.com/p/urim/
+ * http://snowball.tartarus.org/
+ *
+ * Copyright 2010, Oleg Mazko
+ * http://www.mozilla.org/MPL/
+ */
+
+!function(e,r){"function"==typeof define&&define.amd?define(r):"object"==typeof exports?module.exports=r():r()(e.lunr)}(this,function(){return function(e){if(void 0===e)throw new Error("Lunr is not present. Please include / require Lunr before this script.");if(void 0===e.stemmerSupport)throw new Error("Lunr stemmer support is not present. 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\ No newline at end of file
diff --git a/ja/assets/javascripts/lunr/min/lunr.he.min.js b/ja/assets/javascripts/lunr/min/lunr.he.min.js
new file mode 100644
index 000000000..b863d3eae
--- /dev/null
+++ b/ja/assets/javascripts/lunr/min/lunr.he.min.js
@@ -0,0 +1 @@
+!function(e,r){"function"==typeof define&&define.amd?define(r):"object"==typeof exports?module.exports=r():r()(e.lunr)}(this,function(){return function(e){if(void 0===e)throw new Error("Lunr is not present. Please include / require Lunr before this script.");if(void 0===e.stemmerSupport)throw new Error("Lunr stemmer support is not present. Please include / require Lunr stemmer support before this script.");e.he=function(){this.pipeline.reset(),this.pipeline.add(e.he.trimmer,e.he.stopWordFilter,e.he.stemmer),this.searchPipeline&&(this.searchPipeline.reset(),this.searchPipeline.add(e.he.stemmer))},e.he.wordCharacters="֑-״א-תa-zA-Zａ-ｚＡ-Ｚ0-9０-９",e.he.trimmer=e.trimmerSupport.generateTrimmer(e.he.wordCharacters),e.Pipeline.registerFunction(e.he.trimmer,"trimmer-he"),e.he.stemmer=function(){var e=this;return e.result=!1,e.preRemoved=!1,e.sufRemoved=!1,e.pre={pre1:"ה ו י ת",pre2:"ב כ ל מ ש כש",pre3:"הב הכ הל המ הש בש לכ",pre4:"וב וכ ול ומ וש",pre5:"מה שה כל",pre6:"מב מכ מל ממ מש",pre7:"בה בו בי בת כה כו כי כת לה לו לי לת",pre8:"ובה ובו ובי ובת וכה וכו וכי וכת ולה ולו ולי ולת"},e.suf={suf1:"ך כ ם ן נ",suf2:"ים ות וך וכ ום ון ונ הם הן יכ יך ינ ים",suf3:"תי תך תכ תם תן תנ",suf4:"ותי ותך ותכ ותם ותן ותנ",suf5:"נו כם כן הם הן",suf6:"ונו וכם וכן והם והן",suf7:"תכם תכן תנו תהם תהן",suf8:"הוא היא הם הן אני אתה את אנו אתם אתן",suf9:"ני נו כי כו כם כן תי תך תכ תם תן",suf10:"י ך כ ם ן נ ת"},e.patterns=JSON.parse('{"hebrewPatterns": [{"pt1": [{"c": "ה", "l": 0}]}, {"pt2": [{"c": "ו", "l": 0}]}, {"pt3": [{"c": "י", "l": 0}]}, {"pt4": [{"c": "ת", "l": 0}]}, {"pt5": [{"c": "מ", "l": 0}]}, {"pt6": [{"c": "ל", "l": 0}]}, {"pt7": [{"c": "ב", "l": 0}]}, {"pt8": [{"c": "כ", "l": 0}]}, {"pt9": [{"c": "ש", "l": 0}]}, {"pt10": [{"c": "כש", "l": 0}]}, {"pt11": [{"c": "בה", "l": 0}]}, {"pt12": [{"c": "וב", "l": 0}]}, {"pt13": [{"c": "וכ", "l": 0}]}, {"pt14": [{"c": "ול", "l": 0}]}, {"pt15": [{"c": "ומ", "l": 0}]}, {"pt16": [{"c": "וש", "l": 0}]}, {"pt17": [{"c": "הב", "l": 0}]}, {"pt18": [{"c": "הכ", "l": 0}]}, {"pt19": [{"c": "הל", "l": 0}]}, {"pt20": [{"c": "המ", "l": 0}]}, {"pt21": [{"c": "הש", "l": 0}]}, {"pt22": [{"c": "מה", "l": 0}]}, {"pt23": [{"c": "שה", "l": 0}]}, {"pt24": [{"c": "כל", "l": 0}]}]}'),e.execArray=["cleanWord","removeDiacritics","removeStopWords","normalizeHebrewCharacters"],e.stem=function(){var r=0;for(e.result=!1,e.preRemoved=!1,e.sufRemoved=!1;r<e.execArray.length&&1!=e.result;)e.result=e[e.execArray[r]](),r++},e.setCurrent=function(r){e.word=r},e.getCurrent=function(){return e.word},e.cleanWord=function(){return!!new RegExp("[^֑-״א-ת]").test("")},e.removeDiacritics=function(){var r=new RegExp("[ְ-ֿ]","g");return e.word=e.word.replace(r,""),!1},e.removeStopWords=function(){if("אבל או אולי אותו אותי אותך אותם אותן אותנו אז אחר אחרות אחרי אחריכן אחרים אחרת אי איזה איך אין איפה אל אלה אלו אם אנחנו אני אף אפשר את אתה אתכם אתכן אתם אתן באיזה באיזו בגלל בין בלבד בעבור בעזרת בכל בכן בלי במידה במקום שבו ברוב בשביל בשעה ש בתוך גם דרך הוא היא היה היי היכן היתה היתי הם הן הנה הסיבה שבגללה הרי ואילו ואת זאת זה זות יהיה יוכל יוכלו יותר מדי יכול יכולה יכולות יכולים יכל יכלה יכלו יש כאן כאשר כולם כולן כזה כי כיצד כך כל כלל כמו כן כפי כש לא לאו לאיזותך לאן לבין לה להיות להם להן לו לזה לזות לי לך לכם לכן למה למעלה למעלה מ למטה למטה מ למעט למקום שבו למרות לנו לעבר לעיכן לפיכך לפני מאד מאחורי מאיזו סיבה מאין מאיפה מבלי מבעד מדוע מה מהיכן מול מחוץ מי מידע מכאן מכל מכן מלבד מן מנין מסוגל מעט מעטים מעל מצד מקום בו מתחת מתי נגד נגר נו עד עז על עלי עליו עליה עליהם עליך עלינו עם עצמה עצמהם עצמהן עצמו עצמי עצמם עצמן עצמנו פה רק שוב של שלה שלהם שלהן שלו שלי שלך שלכה שלכם שלכן שלנו שם תהיה תחת".split(" ").indexOf(e.word)>=0)return!0},e.normalizeHebrewCharacters=function(){return e.word=e.word.replace("ך","כ"),e.word=e.word.replace("ם","מ"),e.word=e.word.replace("ן","נ"),e.word=e.word.replace("ף","פ"),e.word=e.word.replace("ץ","צ"),!1},function(r){return"function"==typeof r.update?r.update(function(r){return e.setCurrent(r),e.stem(),e.getCurrent()}):(e.setCurrent(r),e.stem(),e.getCurrent())}}(),e.Pipeline.registerFunction(e.he.stemmer,"stemmer-he"),e.he.stopWordFilter=e.generateStopWordFilter("אבל או אולי אותו אותי אותך אותם אותן אותנו אז אחר אחרות אחרי אחריכן אחרים אחרת אי איזה איך אין איפה אל אלה אלו אם אנחנו אני אף אפשר את אתה אתכם אתכן אתם אתן באיזה באיזו בגלל בין בלבד בעבור בעזרת בכל בכן בלי במידה במקום שבו ברוב בשביל בשעה ש בתוך גם דרך הוא היא היה היי היכן היתה היתי הם הן הנה הסיבה שבגללה הרי ואילו ואת זאת זה זות יהיה יוכל יוכלו יותר מדי יכול יכולה יכולות יכולים יכל יכלה יכלו יש כאן כאשר כולם כולן כזה כי כיצד כך כל כלל כמו כן כפי כש לא לאו לאיזותך לאן לבין לה להיות להם להן לו לזה לזות לי לך לכם לכן למה למעלה למעלה מ למטה למטה מ למעט למקום שבו למרות לנו לעבר לעיכן לפיכך לפני מאד מאחורי מאיזו סיבה מאין מאיפה מבלי מבעד מדוע מה מהיכן מול מחוץ מי מידע מכאן מכל מכן מלבד מן מנין מסוגל מעט מעטים מעל מצד מקום בו מתחת מתי נגד נגר נו עד עז על עלי עליו עליה עליהם עליך עלינו עם עצמה עצמהם עצמהן עצמו עצמי עצמם עצמן עצמנו פה רק שוב של שלה שלהם שלהן שלו שלי שלך שלכה שלכם שלכן שלנו שם תהיה תחת".split(" ")),e.Pipeline.registerFunction(e.he.stopWordFilter,"stopWordFilter-he")}});
\ No newline at end of file
diff --git a/ja/assets/javascripts/lunr/min/lunr.hi.min.js b/ja/assets/javascripts/lunr/min/lunr.hi.min.js
new file mode 100644
index 000000000..7dbc41402
--- /dev/null
+++ b/ja/assets/javascripts/lunr/min/lunr.hi.min.js
@@ -0,0 +1 @@
+!function(e,r){"function"==typeof define&&define.amd?define(r):"object"==typeof exports?module.exports=r():r()(e.lunr)}(this,function(){return function(e){if(void 0===e)throw new Error("Lunr is not present. Please include / require Lunr before this script.");if(void 0===e.stemmerSupport)throw new Error("Lunr stemmer support is not present. Please include / require Lunr stemmer support before this script.");e.hi=function(){this.pipeline.reset(),this.pipeline.add(e.hi.trimmer,e.hi.stopWordFilter,e.hi.stemmer),this.searchPipeline&&(this.searchPipeline.reset(),this.searchPipeline.add(e.hi.stemmer))},e.hi.wordCharacters="ऀ-ःऄ-एऐ-टठ-यर-िी-ॏॐ-य़ॠ-९॰-ॿa-zA-Zａ-ｚＡ-Ｚ0-9０-９",e.hi.trimmer=e.trimmerSupport.generateTrimmer(e.hi.wordCharacters),e.Pipeline.registerFunction(e.hi.trimmer,"trimmer-hi"),e.hi.stopWordFilter=e.generateStopWordFilter("अत अपना अपनी अपने अभी अंदर आदि आप इत्यादि इन इनका इन्हीं इन्हें इन्हों इस इसका इसकी इसके इसमें इसी इसे उन उनका उनकी उनके उनको उन्हीं उन्हें उन्हों उस उसके उसी उसे एक एवं एस ऐसे और कई कर करता करते करना करने करें कहते कहा का काफ़ी कि कितना किन्हें किन्हों किया किर किस किसी किसे की कुछ कुल के को कोई कौन कौनसा गया घर जब जहाँ जा जितना जिन जिन्हें जिन्हों जिस जिसे जीधर जैसा जैसे जो तक तब तरह तिन तिन्हें तिन्हों तिस तिसे तो था थी थे दबारा दिया दुसरा दूसरे दो द्वारा न नके नहीं ना निहायत नीचे ने पर पहले पूरा पे फिर बनी बही बहुत बाद बाला बिलकुल भी भीतर मगर मानो मे में यदि यह यहाँ यही या यिह ये रखें रहा रहे ऱ्वासा लिए लिये लेकिन व वग़ैरह वर्ग वह वहाँ वहीं वाले वुह वे वो सकता सकते सबसे सभी साथ साबुत साभ सारा से सो संग ही हुआ हुई हुए है हैं हो होता होती होते होना होने".split(" ")),e.hi.stemmer=function(){return function(e){return"function"==typeof e.update?e.update(function(e){return e}):e}}();var r=e.wordcut;r.init(),e.hi.tokenizer=function(i){if(!arguments.length||null==i||void 0==i)return[];if(Array.isArray(i))return i.map(function(r){return isLunr2?new e.Token(r.toLowerCase()):r.toLowerCase()});var t=i.toString().toLowerCase().replace(/^\s+/,"");return r.cut(t).split("|")},e.Pipeline.registerFunction(e.hi.stemmer,"stemmer-hi"),e.Pipeline.registerFunction(e.hi.stopWordFilter,"stopWordFilter-hi")}});
\ No newline at end of file
diff --git a/ja/assets/javascripts/lunr/min/lunr.hu.min.js b/ja/assets/javascripts/lunr/min/lunr.hu.min.js
new file mode 100644
index 000000000..ed9d909f7
--- /dev/null
+++ b/ja/assets/javascripts/lunr/min/lunr.hu.min.js
@@ -0,0 +1,18 @@
+/*!
+ * Lunr languages, `Hungarian` language
+ * https://github.com/MihaiValentin/lunr-languages
+ *
+ * Copyright 2014, Mihai Valentin
+ * http://www.mozilla.org/MPL/
+ */
+/*!
+ * based on
+ * Snowball JavaScript Library v0.3
+ * http://code.google.com/p/urim/
+ * http://snowball.tartarus.org/
+ *
+ * Copyright 2010, Oleg Mazko
+ * http://www.mozilla.org/MPL/
+ */
+
+!function(e,n){"function"==typeof define&&define.amd?define(n):"object"==typeof exports?module.exports=n():n()(e.lunr)}(this,function(){return function(e){if(void 0===e)throw new Error("Lunr is not present. Please include / require Lunr before this script.");if(void 0===e.stemmerSupport)throw new Error("Lunr stemmer support is not present. Please include / require Lunr stemmer support before this script.");e.hu=function(){this.pipeline.reset(),this.pipeline.add(e.hu.trimmer,e.hu.stopWordFilter,e.hu.stemmer),this.searchPipeline&&(this.searchPipeline.reset(),this.searchPipeline.add(e.hu.stemmer))},e.hu.wordCharacters="A-Za-zªºÀ-ÖØ-öø-ʸˠ-ˤᴀ-ᴥᴬ-ᵜᵢ-ᵥᵫ-ᵷᵹ-ᶾḀ-ỿⁱⁿₐ-ₜKÅℲⅎⅠ-ↈⱠ-ⱿꜢ-ꞇꞋ-ꞭꞰ-ꞷꟷ-ꟿꬰ-ꭚꭜ-ꭤff-stＡ-Ｚａ-ｚ",e.hu.trimmer=e.trimmerSupport.generateTrimmer(e.hu.wordCharacters),e.Pipeline.registerFunction(e.hu.trimmer,"trimmer-hu"),e.hu.stemmer=function(){var n=e.stemmerSupport.Among,r=e.stemmerSupport.SnowballProgram,i=new function(){function e(){var e,n=L.cursor;if(d=L.limit,L.in_grouping(W,97,252))for(;;){if(e=L.cursor,L.out_grouping(W,97,252))return L.cursor=e,L.find_among(g,8)||(L.cursor=e,e<L.limit&&L.cursor++),void(d=L.cursor);if(L.cursor=e,e>=L.limit)return void(d=e);L.cursor++}if(L.cursor=n,L.out_grouping(W,97,252)){for(;!L.in_grouping(W,97,252);){if(L.cursor>=L.limit)return;L.cursor++}d=L.cursor}}function i(){return d<=L.cursor}function a(){var e;if(L.ket=L.cursor,(e=L.find_among_b(h,2))&&(L.bra=L.cursor,i()))switch(e){case 1:L.slice_from("a");break;case 2:L.slice_from("e")}}function t(){var e=L.limit-L.cursor;return!!L.find_among_b(p,23)&&(L.cursor=L.limit-e,!0)}function s(){if(L.cursor>L.limit_backward){L.cursor--,L.ket=L.cursor;var e=L.cursor-1;L.limit_backward<=e&&e<=L.limit&&(L.cursor=e,L.bra=e,L.slice_del())}}function c(){var e;if(L.ket=L.cursor,(e=L.find_among_b(_,2))&&(L.bra=L.cursor,i())){if((1==e||2==e)&&!t())return;L.slice_del(),s()}}function o(){L.ket=L.cursor,L.find_among_b(v,44)&&(L.bra=L.cursor,i()&&(L.slice_del(),a()))}function w(){var e;if(L.ket=L.cursor,(e=L.find_among_b(z,3))&&(L.bra=L.cursor,i()))switch(e){case 1:L.slice_from("e");break;case 2:case 3:L.slice_from("a")}}function l(){var e;if(L.ket=L.cursor,(e=L.find_among_b(y,6))&&(L.bra=L.cursor,i()))switch(e){case 1:case 2:L.slice_del();break;case 3:L.slice_from("a");break;case 4:L.slice_from("e")}}function u(){var e;if(L.ket=L.cursor,(e=L.find_among_b(j,2))&&(L.bra=L.cursor,i())){if((1==e||2==e)&&!t())return;L.slice_del(),s()}}function m(){var e;if(L.ket=L.cursor,(e=L.find_among_b(C,7))&&(L.bra=L.cursor,i()))switch(e){case 1:L.slice_from("a");break;case 2:L.slice_from("e");break;case 3:case 4:case 5:case 6:case 7:L.slice_del()}}function k(){var e;if(L.ket=L.cursor,(e=L.find_among_b(P,12))&&(L.bra=L.cursor,i()))switch(e){case 1:case 4:case 7:case 9:L.slice_del();break;case 2:case 5:case 8:L.slice_from("e");break;case 3:case 6:L.slice_from("a")}}function f(){var e;if(L.ket=L.cursor,(e=L.find_among_b(F,31))&&(L.bra=L.cursor,i()))switch(e){case 1:case 4:case 7:case 8:case 9:case 12:case 13:case 16:case 17:case 18:L.slice_del();break;case 2:case 5:case 10:case 14:case 19:L.slice_from("a");break;case 3:case 6:case 11:case 15:case 20:L.slice_from("e")}}function b(){var e;if(L.ket=L.cursor,(e=L.find_among_b(S,42))&&(L.bra=L.cursor,i()))switch(e){case 1:case 4:case 5:case 6:case 9:case 10:case 11:case 14:case 15:case 16:case 17:case 20:case 21:case 24:case 25:case 26:case 29:L.slice_del();break;case 2:case 7:case 12:case 18:case 22:case 27:L.slice_from("a");break;case 3:case 8:case 13:case 19:case 23:case 28:L.slice_from("e")}}var d,g=[new n("cs",-1,-1),new n("dzs",-1,-1),new n("gy",-1,-1),new n("ly",-1,-1),new n("ny",-1,-1),new n("sz",-1,-1),new n("ty",-1,-1),new n("zs",-1,-1)],h=[new n("á",-1,1),new n("é",-1,2)],p=[new n("bb",-1,-1),new n("cc",-1,-1),new n("dd",-1,-1),new n("ff",-1,-1),new n("gg",-1,-1),new n("jj",-1,-1),new n("kk",-1,-1),new n("ll",-1,-1),new n("mm",-1,-1),new n("nn",-1,-1),new n("pp",-1,-1),new n("rr",-1,-1),new n("ccs",-1,-1),new n("ss",-1,-1),new n("zzs",-1,-1),new n("tt",-1,-1),new n("vv",-1,-1),new n("ggy",-1,-1),new n("lly",-1,-1),new n("nny",-1,-1),new n("tty",-1,-1),new n("ssz",-1,-1),new n("zz",-1,-1)],_=[new n("al",-1,1),new n("el",-1,2)],v=[new n("ba",-1,-1),new n("ra",-1,-1),new n("be",-1,-1),new n("re",-1,-1),new n("ig",-1,-1),new n("nak",-1,-1),new n("nek",-1,-1),new n("val",-1,-1),new n("vel",-1,-1),new n("ul",-1,-1),new n("nál",-1,-1),new n("nél",-1,-1),new n("ból",-1,-1),new n("ról",-1,-1),new n("tól",-1,-1),new n("bõl",-1,-1),new n("rõl",-1,-1),new n("tõl",-1,-1),new n("ül",-1,-1),new n("n",-1,-1),new n("an",19,-1),new n("ban",20,-1),new n("en",19,-1),new n("ben",22,-1),new n("képpen",22,-1),new n("on",19,-1),new n("ön",19,-1),new n("képp",-1,-1),new n("kor",-1,-1),new n("t",-1,-1),new n("at",29,-1),new n("et",29,-1),new n("ként",29,-1),new n("anként",32,-1),new n("enként",32,-1),new n("onként",32,-1),new n("ot",29,-1),new n("ért",29,-1),new n("öt",29,-1),new n("hez",-1,-1),new n("hoz",-1,-1),new n("höz",-1,-1),new n("vá",-1,-1),new n("vé",-1,-1)],z=[new n("án",-1,2),new n("én",-1,1),new n("ánként",-1,3)],y=[new n("stul",-1,2),new n("astul",0,1),new n("ástul",0,3),new n("stül",-1,2),new n("estül",3,1),new n("éstül",3,4)],j=[new n("á",-1,1),new n("é",-1,2)],C=[new n("k",-1,7),new n("ak",0,4),new n("ek",0,6),new n("ok",0,5),new 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keressünk keresztül ki kívül között közül legalább legyen lehet lehetett lenne lenni lesz lett maga magát majd majd meg mellett mely melyek mert mi mikor milyen minden mindenki mindent mindig mint mintha mit mivel miért most már más másik még míg nagy nagyobb nagyon ne nekem neki nem nincs néha néhány nélkül olyan ott pedig persze rá s saját sem semmi sok sokat sokkal szemben szerint szinte számára talán tehát teljes tovább továbbá több ugyanis utolsó után utána vagy vagyis vagyok valaki valami valamint való van vannak vele vissza viszont volna volt voltak voltam voltunk által általában át én éppen és így õ õk õket össze úgy új újabb újra".split(" ")),e.Pipeline.registerFunction(e.hu.stopWordFilter,"stopWordFilter-hu")}});
\ No newline at end of file
diff --git a/ja/assets/javascripts/lunr/min/lunr.hy.min.js b/ja/assets/javascripts/lunr/min/lunr.hy.min.js
new file mode 100644
index 000000000..b37f79298
--- /dev/null
+++ b/ja/assets/javascripts/lunr/min/lunr.hy.min.js
@@ -0,0 +1 @@
+!function(e,r){"function"==typeof define&&define.amd?define(r):"object"==typeof exports?module.exports=r():r()(e.lunr)}(this,function(){return function(e){if(void 0===e)throw new Error("Lunr is not present. Please include / require Lunr before this script.");if(void 0===e.stemmerSupport)throw new Error("Lunr stemmer support is not present. Please include / require Lunr stemmer support before this script.");e.hy=function(){this.pipeline.reset(),this.pipeline.add(e.hy.trimmer,e.hy.stopWordFilter)},e.hy.wordCharacters="[A-Za-z԰-֏ff-ﭏ]",e.hy.trimmer=e.trimmerSupport.generateTrimmer(e.hy.wordCharacters),e.Pipeline.registerFunction(e.hy.trimmer,"trimmer-hy"),e.hy.stopWordFilter=e.generateStopWordFilter("դու և եք էիր էիք հետո նաև նրանք որը վրա է որ պիտի են այս մեջ ն իր ու ի այդ որոնք այն կամ էր մի ես համար այլ իսկ էին ենք հետ ին թ էինք մենք նրա նա դուք եմ էի ըստ որպես ում".split(" ")),e.Pipeline.registerFunction(e.hy.stopWordFilter,"stopWordFilter-hy"),e.hy.stemmer=function(){return function(e){return"function"==typeof e.update?e.update(function(e){return e}):e}}(),e.Pipeline.registerFunction(e.hy.stemmer,"stemmer-hy")}});
\ No newline at end of file
diff --git a/ja/assets/javascripts/lunr/min/lunr.it.min.js b/ja/assets/javascripts/lunr/min/lunr.it.min.js
new file mode 100644
index 000000000..344b6a3c0
--- /dev/null
+++ b/ja/assets/javascripts/lunr/min/lunr.it.min.js
@@ -0,0 +1,18 @@
+/*!
+ * Lunr languages, `Italian` language
+ * https://github.com/MihaiValentin/lunr-languages
+ *
+ * Copyright 2014, Mihai Valentin
+ * http://www.mozilla.org/MPL/
+ */
+/*!
+ * based on
+ * Snowball JavaScript Library v0.3
+ * http://code.google.com/p/urim/
+ * http://snowball.tartarus.org/
+ *
+ * Copyright 2010, Oleg Mazko
+ * http://www.mozilla.org/MPL/
+ */
+
+!function(e,r){"function"==typeof define&&define.amd?define(r):"object"==typeof exports?module.exports=r():r()(e.lunr)}(this,function(){return function(e){if(void 0===e)throw new Error("Lunr is not present. Please include / require Lunr before this script.");if(void 0===e.stemmerSupport)throw new Error("Lunr stemmer support is not present. 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r("evo",-1,1),new r("ivo",-1,1),new r("ar",-1,1),new r("ir",-1,1),new r("erà",-1,1),new r("irà",-1,1),new r("erò",-1,1),new r("irò",-1,1)],L=[17,65,16,0,0,0,0,0,0,0,0,0,0,0,0,128,128,8,2,1],y=[17,65,0,0,0,0,0,0,0,0,0,0,0,0,0,128,128,8,2],U=[17],x=new n;this.setCurrent=function(e){x.setCurrent(e)},this.getCurrent=function(){return x.getCurrent()},this.stem=function(){var e=x.cursor;return i(),x.cursor=e,u(),x.limit_backward=e,x.cursor=x.limit,f(),x.cursor=x.limit,v()||(x.cursor=x.limit,b()),x.cursor=x.limit,_(),x.cursor=x.limit_backward,c(),!0}};return function(e){return"function"==typeof e.update?e.update(function(e){return i.setCurrent(e),i.stem(),i.getCurrent()}):(i.setCurrent(e),i.stem(),i.getCurrent())}}(),e.Pipeline.registerFunction(e.it.stemmer,"stemmer-it"),e.it.stopWordFilter=e.generateStopWordFilter("a abbia abbiamo abbiano abbiate ad agl agli ai al all alla alle allo anche avemmo avendo avesse avessero avessi avessimo aveste avesti avete aveva avevamo avevano avevate avevi avevo avrai avranno avrebbe avrebbero avrei avremmo avremo avreste avresti avrete avrà avrò avuta avute avuti avuto c che chi ci coi col come con contro cui da dagl dagli dai dal dall dalla dalle dallo degl degli dei del dell della delle dello di dov dove e ebbe ebbero ebbi ed era erano eravamo eravate eri ero essendo faccia facciamo facciano facciate faccio facemmo facendo facesse facessero facessi facessimo faceste facesti faceva facevamo facevano facevate facevi facevo fai fanno farai faranno farebbe farebbero farei faremmo faremo fareste faresti farete farà farò fece fecero feci fosse fossero fossi fossimo foste fosti fu fui fummo furono gli ha hai hanno ho i il in io l la le lei li lo loro lui ma mi mia mie miei mio ne negl negli nei nel nell nella nelle nello noi non nostra nostre nostri nostro o per perché più quale quanta quante quanti quanto quella quelle quelli quello questa queste questi questo sarai saranno sarebbe sarebbero sarei saremmo saremo sareste saresti sarete sarà sarò se sei si sia siamo siano siate siete sono sta stai stando stanno starai staranno starebbe starebbero starei staremmo staremo stareste staresti starete starà starò stava stavamo stavano stavate stavi stavo stemmo stesse stessero stessi stessimo steste stesti stette stettero stetti stia stiamo stiano stiate sto su sua sue sugl sugli sui sul sull sulla sulle sullo suo suoi ti tra tu tua tue tuo tuoi tutti tutto un una uno vi voi vostra vostre vostri vostro è".split(" ")),e.Pipeline.registerFunction(e.it.stopWordFilter,"stopWordFilter-it")}});
\ No newline at end of file
diff --git a/ja/assets/javascripts/lunr/min/lunr.ja.min.js b/ja/assets/javascripts/lunr/min/lunr.ja.min.js
new file mode 100644
index 000000000..5f254ebe9
--- /dev/null
+++ b/ja/assets/javascripts/lunr/min/lunr.ja.min.js
@@ -0,0 +1 @@
+!function(e,r){"function"==typeof define&&define.amd?define(r):"object"==typeof exports?module.exports=r():r()(e.lunr)}(this,function(){return function(e){if(void 0===e)throw new Error("Lunr is not present. Please include / require Lunr before this script.");if(void 0===e.stemmerSupport)throw new Error("Lunr stemmer support is not present. Please include / require Lunr stemmer support before this script.");var r="2"==e.version[0];e.ja=function(){this.pipeline.reset(),this.pipeline.add(e.ja.trimmer,e.ja.stopWordFilter,e.ja.stemmer),r?this.tokenizer=e.ja.tokenizer:(e.tokenizer&&(e.tokenizer=e.ja.tokenizer),this.tokenizerFn&&(this.tokenizerFn=e.ja.tokenizer))};var t=new e.TinySegmenter;e.ja.tokenizer=function(i){var n,o,s,p,a,u,m,l,c,f;if(!arguments.length||null==i||void 0==i)return[];if(Array.isArray(i))return i.map(function(t){return r?new e.Token(t.toLowerCase()):t.toLowerCase()});for(o=i.toString().toLowerCase().replace(/^\s+/,""),n=o.length-1;n>=0;n--)if(/\S/.test(o.charAt(n))){o=o.substring(0,n+1);break}for(a=[],s=o.length,c=0,l=0;c<=s;c++)if(u=o.charAt(c),m=c-l,u.match(/\s/)||c==s){if(m>0)for(p=t.segment(o.slice(l,c)).filter(function(e){return!!e}),f=l,n=0;n<p.length;n++)r?a.push(new e.Token(p[n],{position:[f,p[n].length],index:a.length})):a.push(p[n]),f+=p[n].length;l=c+1}return a},e.ja.stemmer=function(){return function(e){return e}}(),e.Pipeline.registerFunction(e.ja.stemmer,"stemmer-ja"),e.ja.wordCharacters="一二三四五六七八九十百千万億兆一-龠々〆ヵヶぁ-んァ-ヴーｱ-ﾝﾞa-zA-Zａ-ｚＡ-Ｚ0-9０-９",e.ja.trimmer=e.trimmerSupport.generateTrimmer(e.ja.wordCharacters),e.Pipeline.registerFunction(e.ja.trimmer,"trimmer-ja"),e.ja.stopWordFilter=e.generateStopWordFilter("これ それ あれ この その あの ここ そこ あそこ こちら どこ だれ なに なん 何 私 貴方 貴方方 我々 私達 あの人 あのかた 彼女 彼 です あります おります います は が の に を で え から まで より も どの と し それで しかし".split(" ")),e.Pipeline.registerFunction(e.ja.stopWordFilter,"stopWordFilter-ja"),e.jp=e.ja,e.Pipeline.registerFunction(e.jp.stemmer,"stemmer-jp"),e.Pipeline.registerFunction(e.jp.trimmer,"trimmer-jp"),e.Pipeline.registerFunction(e.jp.stopWordFilter,"stopWordFilter-jp")}});
\ No newline at end of file
diff --git a/ja/assets/javascripts/lunr/min/lunr.jp.min.js b/ja/assets/javascripts/lunr/min/lunr.jp.min.js
new file mode 100644
index 000000000..c055ebaf3
--- /dev/null
+++ b/ja/assets/javascripts/lunr/min/lunr.jp.min.js
@@ -0,0 +1 @@
+module.exports=require("./lunr.ja");
\ No newline at end of file
diff --git a/ja/assets/javascripts/lunr/min/lunr.kn.min.js b/ja/assets/javascripts/lunr/min/lunr.kn.min.js
new file mode 100644
index 000000000..1cef9befd
--- /dev/null
+++ b/ja/assets/javascripts/lunr/min/lunr.kn.min.js
@@ -0,0 +1 @@
+!function(e,r){"function"==typeof define&&define.amd?define(r):"object"==typeof exports?module.exports=r():r()(e.lunr)}(this,function(){return function(e){if(void 0===e)throw new Error("Lunr is not present. Please include / require Lunr before this script.");if(void 0===e.stemmerSupport)throw new Error("Lunr stemmer support is not present. Please include / require Lunr stemmer support before this script.");e.kn=function(){this.pipeline.reset(),this.pipeline.add(e.kn.trimmer,e.kn.stopWordFilter,e.kn.stemmer),this.searchPipeline&&(this.searchPipeline.reset(),this.searchPipeline.add(e.kn.stemmer))},e.kn.wordCharacters="ಀ-಄ಅ-ಔಕ-ಹಾ-ೌ಼-ಽೕ-ೖೝ-ೞೠ-ೡೢ-ೣ೤೥೦-೯ೱ-ೳ",e.kn.trimmer=e.trimmerSupport.generateTrimmer(e.kn.wordCharacters),e.Pipeline.registerFunction(e.kn.trimmer,"trimmer-kn"),e.kn.stopWordFilter=e.generateStopWordFilter("ಮತ್ತು ಈ ಒಂದು ರಲ್ಲಿ ಹಾಗೂ ಎಂದು ಅಥವಾ ಇದು ರ ಅವರು ಎಂಬ ಮೇಲೆ ಅವರ ತನ್ನ ಆದರೆ ತಮ್ಮ ನಂತರ ಮೂಲಕ ಹೆಚ್ಚು ನ ಆ ಕೆಲವು ಅನೇಕ ಎರಡು ಹಾಗು ಪ್ರಮುಖ ಇದನ್ನು ಇದರ ಸುಮಾರು ಅದರ ಅದು ಮೊದಲ ಬಗ್ಗೆ ನಲ್ಲಿ ರಂದು ಇತರ ಅತ್ಯಂತ ಹೆಚ್ಚಿನ ಸಹ ಸಾಮಾನ್ಯವಾಗಿ ನೇ ಹಲವಾರು ಹೊಸ ದಿ ಕಡಿಮೆ ಯಾವುದೇ ಹೊಂದಿದೆ ದೊಡ್ಡ ಅನ್ನು ಇವರು ಪ್ರಕಾರ ಇದೆ ಮಾತ್ರ ಕೂಡ ಇಲ್ಲಿ ಎಲ್ಲಾ ವಿವಿಧ ಅದನ್ನು ಹಲವು ರಿಂದ ಕೇವಲ ದ ದಕ್ಷಿಣ ಗೆ ಅವನ ಅತಿ ನೆಯ ಬಹಳ ಕೆಲಸ ಎಲ್ಲ ಪ್ರತಿ ಇತ್ಯಾದಿ ಇವು ಬೇರೆ ಹೀಗೆ ನಡುವೆ ಇದಕ್ಕೆ ಎಸ್ ಇವರ ಮೊದಲು ಶ್ರೀ ಮಾಡುವ ಇದರಲ್ಲಿ ರೀತಿಯ ಮಾಡಿದ ಕಾಲ ಅಲ್ಲಿ ಮಾಡಲು ಅದೇ ಈಗ ಅವು ಗಳು ಎ ಎಂಬುದು ಅವನು ಅಂದರೆ ಅವರಿಗೆ ಇರುವ ವಿಶೇಷ ಮುಂದೆ ಅವುಗಳ ಮುಂತಾದ ಮೂಲ ಬಿ ಮೀ ಒಂದೇ ಇನ್ನೂ ಹೆಚ್ಚಾಗಿ ಮಾಡಿ ಅವರನ್ನು ಇದೇ ಯ ರೀತಿಯಲ್ಲಿ ಜೊತೆ ಅದರಲ್ಲಿ ಮಾಡಿದರು ನಡೆದ ಆಗ ಮತ್ತೆ ಪೂರ್ವ ಆತ ಬಂದ ಯಾವ ಒಟ್ಟು ಇತರೆ ಹಿಂದೆ ಪ್ರಮಾಣದ ಗಳನ್ನು ಕುರಿತು ಯು ಆದ್ದರಿಂದ ಅಲ್ಲದೆ ನಗರದ ಮೇಲಿನ ಏಕೆಂದರೆ ರಷ್ಟು ಎಂಬುದನ್ನು ಬಾರಿ ಎಂದರೆ ಹಿಂದಿನ ಆದರೂ ಆದ ಸಂಬಂಧಿಸಿದ ಮತ್ತೊಂದು ಸಿ ಆತನ ".split(" ")),e.kn.stemmer=function(){return function(e){return"function"==typeof e.update?e.update(function(e){return e}):e}}();var r=e.wordcut;r.init(),e.kn.tokenizer=function(t){if(!arguments.length||null==t||void 0==t)return[];if(Array.isArray(t))return t.map(function(r){return isLunr2?new e.Token(r.toLowerCase()):r.toLowerCase()});var n=t.toString().toLowerCase().replace(/^\s+/,"");return r.cut(n).split("|")},e.Pipeline.registerFunction(e.kn.stemmer,"stemmer-kn"),e.Pipeline.registerFunction(e.kn.stopWordFilter,"stopWordFilter-kn")}});
\ No newline at end of file
diff --git a/ja/assets/javascripts/lunr/min/lunr.ko.min.js b/ja/assets/javascripts/lunr/min/lunr.ko.min.js
new file mode 100644
index 000000000..eaf9dabf7
--- /dev/null
+++ b/ja/assets/javascripts/lunr/min/lunr.ko.min.js
@@ -0,0 +1 @@
+!function(e,r){"function"==typeof define&&define.amd?define(r):"object"==typeof exports?module.exports=r():r()(e.lunr)}(this,function(){return function(e){if(void 0===e)throw new Error("Lunr is not present. Please include / require Lunr before this script.");if(void 0===e.stemmerSupport)throw new Error("Lunr stemmer support is not present. Please include / require Lunr stemmer support before this script.");e.ko=function(){this.pipeline.reset(),this.pipeline.add(e.ko.trimmer,e.ko.stopWordFilter)},e.ko.wordCharacters="[A-Za-z가-힣]",e.ko.trimmer=e.trimmerSupport.generateTrimmer(e.ko.wordCharacters),e.Pipeline.registerFunction(e.ko.trimmer,"trimmer-ko"),e.ko.stopWordFilter=e.generateStopWordFilter("아 휴 아이구 아이쿠 아이고 어 나 우리 저희 따라 의해 을 를 에 의 가 으로 로 에게 뿐이다 의거하여 근거하여 입각하여 기준으로 예하면 예를 들면 예를 들자면 저 소인 소생 저희 지말고 하지마 하지마라 다른 물론 또한 그리고 비길수 없다 해서는 안된다 뿐만 아니라 만이 아니다 만은 아니다 막론하고 관계없이 그치지 않다 그러나 그런데 하지만 든간에 논하지 않다 따지지 않다 설사 비록 더라도 아니면 만 못하다 하는 편이 낫다 불문하고 향하여 향해서 향하다 쪽으로 틈타 이용하여 타다 오르다 제외하고 이 외에 이 밖에 하여야 비로소 한다면 몰라도 외에도 이곳 여기 부터 기점으로 따라서 할 생각이다 하려고하다 이리하여 그리하여 그렇게 함으로써 하지만 일때 할때 앞에서 중에서 보는데서 으로써 로써 까지 해야한다 일것이다 반드시 할줄알다 할수있다 할수있어 임에 틀림없다 한다면 등 등등 제 겨우 단지 다만 할뿐 딩동 댕그 대해서 대하여 대하면 훨씬 얼마나 얼마만큼 얼마큼 남짓 여 얼마간 약간 다소 좀 조금 다수 몇 얼마 지만 하물며 또한 그러나 그렇지만 하지만 이외에도 대해 말하자면 뿐이다 다음에 반대로 반대로 말하자면 이와 반대로 바꾸어서 말하면 바꾸어서 한다면 만약 그렇지않으면 까악 툭 딱 삐걱거리다 보드득 비걱거리다 꽈당 응당 해야한다 에 가서 각 각각 여러분 각종 각자 제각기 하도록하다 와 과 그러므로 그래서 고로 한 까닭에 하기 때문에 거니와 이지만 대하여 관하여 관한 과연 실로 아니나다를가 생각한대로 진짜로 한적이있다 하곤하였다 하 하하 허허 아하 거바 와 오 왜 어째서 무엇때문에 어찌 하겠는가 무슨 어디 어느곳 더군다나 하물며 더욱이는 어느때 언제 야 이봐 어이 여보시오 흐흐 흥 휴 헉헉 헐떡헐떡 영차 여차 어기여차 끙끙 아야 앗 아야 콸콸 졸졸 좍좍 뚝뚝 주룩주룩 솨 우르르 그래도 또 그리고 바꾸어말하면 바꾸어말하자면 혹은 혹시 답다 및 그에 따르는 때가 되어 즉 지든지 설령 가령 하더라도 할지라도 일지라도 지든지 몇 거의 하마터면 인젠 이젠 된바에야 된이상 만큼\t어찌됏든 그위에 게다가 점에서 보아 비추어 보아 고려하면 하게될것이다 일것이다 비교적 좀 보다더 비하면 시키다 하게하다 할만하다 의해서 연이서 이어서 잇따라 뒤따라 뒤이어 결국 의지하여 기대여 통하여 자마자 더욱더 불구하고 얼마든지 마음대로 주저하지 않고 곧 즉시 바로 당장 하자마자 밖에 안된다 하면된다 그래 그렇지 요컨대 다시 말하자면 바꿔 말하면 즉 구체적으로 말하자면 시작하여 시초에 이상 허 헉 허걱 바와같이 해도좋다 해도된다 게다가 더구나 하물며 와르르 팍 퍽 펄렁 동안 이래 하고있었다 이었다 에서 로부터 까지 예하면 했어요 해요 함께 같이 더불어 마저 마저도 양자 모두 습니다 가까스로 하려고하다 즈음하여 다른 다른 방면으로 해봐요 습니까 했어요 말할것도 없고 무릎쓰고 개의치않고 하는것만 못하다 하는것이 낫다 매 매번 들 모 어느것 어느 로써 갖고말하자면 어디 어느쪽 어느것 어느해 어느 년도 라 해도 언젠가 어떤것 어느것 저기 저쪽 저것 그때 그럼 그러면 요만한걸 그래 그때 저것만큼 그저 이르기까지 할 줄 안다 할 힘이 있다 너 너희 당신 어찌 설마 차라리 할지언정 할지라도 할망정 할지언정 구토하다 게우다 토하다 메쓰겁다 옆사람 퉤 쳇 의거하여 근거하여 의해 따라 힘입어 그 다음 버금 두번째로 기타 첫번째로 나머지는 그중에서 견지에서 형식으로 쓰여 입장에서 위해서 단지 의해되다 하도록시키다 뿐만아니라 반대로 전후 전자 앞의것 잠시 잠깐 하면서 그렇지만 다음에 그러한즉 그런즉 남들 아무거나 어찌하든지 같다 비슷하다 예컨대 이럴정도로 어떻게 만약 만일 위에서 서술한바와같이 인 듯하다 하지 않는다면 만약에 무엇 무슨 어느 어떤 아래윗 조차 한데 그럼에도 불구하고 여전히 심지어 까지도 조차도 하지 않도록 않기 위하여 때 시각 무렵 시간 동안 어때 어떠한 하여금 네 예 우선 누구 누가 알겠는가 아무도 줄은모른다 줄은 몰랏다 하는 김에 겸사겸사 하는바 그런 까닭에 한 이유는 그러니 그러니까 때문에 그 너희 그들 너희들 타인 것 것들 너 위하여 공동으로 동시에 하기 위하여 어찌하여 무엇때문에 붕붕 윙윙 나 우리 엉엉 휘익 윙윙 오호 아하 어쨋든 만 못하다\t하기보다는 차라리 하는 편이 낫다 흐흐 놀라다 상대적으로 말하자면 마치 아니라면 쉿 그렇지 않으면 그렇지 않다면 안 그러면 아니었다면 하든지 아니면 이라면 좋아 알았어 하는것도 그만이다 어쩔수 없다 하나 일 일반적으로 일단 한켠으로는 오자마자 이렇게되면 이와같다면 전부 한마디 한항목 근거로 하기에 아울러 하지 않도록 않기 위해서 이르기까지 이 되다 로 인하여 까닭으로 이유만으로 이로 인하여 그래서 이 때문에 그러므로 그런 까닭에 알 수 있다 결론을 낼 수 있다 으로 인하여 있다 어떤것 관계가 있다 관련이 있다 연관되다 어떤것들 에 대해 이리하여 그리하여 여부 하기보다는 하느니 하면 할수록 운운 이러이러하다 하구나 하도다 다시말하면 다음으로 에 있다 에 달려 있다 우리 우리들 오히려 하기는한데 어떻게 어떻해 어찌됏어 어때 어째서 본대로 자 이 이쪽 여기 이것 이번 이렇게말하자면 이런 이러한 이와 같은 요만큼 요만한 것 얼마 안 되는 것 이만큼 이 정도의 이렇게 많은 것 이와 같다 이때 이렇구나 것과 같이 끼익 삐걱 따위 와 같은 사람들 부류의 사람들 왜냐하면 중의하나 오직 오로지 에 한하다 하기만 하면 도착하다 까지 미치다 도달하다 정도에 이르다 할 지경이다 결과에 이르다 관해서는 여러분 하고 있다 한 후 혼자 자기 자기집 자신 우에 종합한것과같이 총적으로 보면 총적으로 말하면 총적으로 대로 하다 으로서 참 그만이다 할 따름이다 쿵 탕탕 쾅쾅 둥둥 봐 봐라 아이야 아니 와아 응 아이 참나 년 월 일 령 영 일 이 삼 사 오 육 륙 칠 팔 구 이천육 이천칠 이천팔 이천구 하나 둘 셋 넷 다섯 여섯 일곱 여덟 아홉 령 영".split(" ")),e.Pipeline.registerFunction(e.ko.stopWordFilter,"stopWordFilter-ko"),e.ko.stemmer=function(){return function(e){return"function"==typeof e.update?e.update(function(e){return e}):e}}(),e.Pipeline.registerFunction(e.ko.stemmer,"stemmer-ko")}});
\ No newline at end of file
diff --git a/ja/assets/javascripts/lunr/min/lunr.multi.min.js b/ja/assets/javascripts/lunr/min/lunr.multi.min.js
new file mode 100644
index 000000000..7debad096
--- /dev/null
+++ b/ja/assets/javascripts/lunr/min/lunr.multi.min.js
@@ -0,0 +1 @@
+!function(e,t){"function"==typeof define&&define.amd?define(t):"object"==typeof exports?module.exports=t():t()(e.lunr)}(this,function(){return function(e){e.multiLanguage=function(){for(var t=Array.prototype.slice.call(arguments),i=t.join("-"),r="",n=[],s=[],p=0;p<t.length;++p)"en"==t[p]?(r+="\\w",n.unshift(e.stopWordFilter),n.push(e.stemmer),s.push(e.stemmer)):(r+=e[t[p]].wordCharacters,e[t[p]].stopWordFilter&&n.unshift(e[t[p]].stopWordFilter),e[t[p]].stemmer&&(n.push(e[t[p]].stemmer),s.push(e[t[p]].stemmer)));var o=e.trimmerSupport.generateTrimmer(r);return e.Pipeline.registerFunction(o,"lunr-multi-trimmer-"+i),n.unshift(o),function(){this.pipeline.reset(),this.pipeline.add.apply(this.pipeline,n),this.searchPipeline&&(this.searchPipeline.reset(),this.searchPipeline.add.apply(this.searchPipeline,s))}}}});
\ No newline at end of file
diff --git a/ja/assets/javascripts/lunr/min/lunr.nl.min.js b/ja/assets/javascripts/lunr/min/lunr.nl.min.js
new file mode 100644
index 000000000..c4a253594
--- /dev/null
+++ b/ja/assets/javascripts/lunr/min/lunr.nl.min.js
@@ -0,0 +1,18 @@
+/*!
+ * Lunr languages, `Dutch` language
+ * https://github.com/MihaiValentin/lunr-languages
+ *
+ * Copyright 2014, Mihai Valentin
+ * http://www.mozilla.org/MPL/
+ */
+/*!
+ * based on
+ * Snowball JavaScript Library v0.3
+ * http://code.google.com/p/urim/
+ * http://snowball.tartarus.org/
+ *
+ * Copyright 2010, Oleg Mazko
+ * http://www.mozilla.org/MPL/
+ */
+
+!function(r,e){"function"==typeof define&&define.amd?define(e):"object"==typeof exports?module.exports=e():e()(r.lunr)}(this,function(){return function(r){if(void 0===r)throw new Error("Lunr is not present. Please include / require Lunr before this script.");if(void 0===r.stemmerSupport)throw new Error("Lunr stemmer support is not present. Please include / require Lunr stemmer support before this script.");r.nl=function(){this.pipeline.reset(),this.pipeline.add(r.nl.trimmer,r.nl.stopWordFilter,r.nl.stemmer),this.searchPipeline&&(this.searchPipeline.reset(),this.searchPipeline.add(r.nl.stemmer))},r.nl.wordCharacters="A-Za-zªºÀ-ÖØ-öø-ʸˠ-ˤᴀ-ᴥᴬ-ᵜᵢ-ᵥᵫ-ᵷᵹ-ᶾḀ-ỿⁱⁿₐ-ₜKÅℲⅎⅠ-ↈⱠ-ⱿꜢ-ꞇꞋ-ꞭꞰ-ꞷꟷ-ꟿꬰ-ꭚꭜ-ꭤff-stＡ-Ｚａ-ｚ",r.nl.trimmer=r.trimmerSupport.generateTrimmer(r.nl.wordCharacters),r.Pipeline.registerFunction(r.nl.trimmer,"trimmer-nl"),r.nl.stemmer=function(){var e=r.stemmerSupport.Among,i=r.stemmerSupport.SnowballProgram,n=new function(){function r(){for(var r,e,i,o=C.cursor;;){if(C.bra=C.cursor,r=C.find_among(b,11))switch(C.ket=C.cursor,r){case 1:C.slice_from("a");continue;case 2:C.slice_from("e");continue;case 3:C.slice_from("i");continue;case 4:C.slice_from("o");continue;case 5:C.slice_from("u");continue;case 6:if(C.cursor>=C.limit)break;C.cursor++;continue}break}for(C.cursor=o,C.bra=o,C.eq_s(1,"y")?(C.ket=C.cursor,C.slice_from("Y")):C.cursor=o;;)if(e=C.cursor,C.in_grouping(q,97,232)){if(i=C.cursor,C.bra=i,C.eq_s(1,"i"))C.ket=C.cursor,C.in_grouping(q,97,232)&&(C.slice_from("I"),C.cursor=e);else if(C.cursor=i,C.eq_s(1,"y"))C.ket=C.cursor,C.slice_from("Y"),C.cursor=e;else if(n(e))break}else if(n(e))break}function n(r){return C.cursor=r,r>=C.limit||(C.cursor++,!1)}function o(){_=C.limit,d=_,t()||(_=C.cursor,_<3&&(_=3),t()||(d=C.cursor))}function t(){for(;!C.in_grouping(q,97,232);){if(C.cursor>=C.limit)return!0;C.cursor++}for(;!C.out_grouping(q,97,232);){if(C.cursor>=C.limit)return!0;C.cursor++}return!1}function s(){for(var r;;)if(C.bra=C.cursor,r=C.find_among(p,3))switch(C.ket=C.cursor,r){case 1:C.slice_from("y");break;case 2:C.slice_from("i");break;case 3:if(C.cursor>=C.limit)return;C.cursor++}}function u(){return _<=C.cursor}function c(){return d<=C.cursor}function a(){var r=C.limit-C.cursor;C.find_among_b(g,3)&&(C.cursor=C.limit-r,C.ket=C.cursor,C.cursor>C.limit_backward&&(C.cursor--,C.bra=C.cursor,C.slice_del()))}function l(){var r;w=!1,C.ket=C.cursor,C.eq_s_b(1,"e")&&(C.bra=C.cursor,u()&&(r=C.limit-C.cursor,C.out_grouping_b(q,97,232)&&(C.cursor=C.limit-r,C.slice_del(),w=!0,a())))}function m(){var r;u()&&(r=C.limit-C.cursor,C.out_grouping_b(q,97,232)&&(C.cursor=C.limit-r,C.eq_s_b(3,"gem")||(C.cursor=C.limit-r,C.slice_del(),a())))}function f(){var r,e,i,n,o,t,s=C.limit-C.cursor;if(C.ket=C.cursor,r=C.find_among_b(h,5))switch(C.bra=C.cursor,r){case 1:u()&&C.slice_from("heid");break;case 2:m();break;case 3:u()&&C.out_grouping_b(j,97,232)&&C.slice_del()}if(C.cursor=C.limit-s,l(),C.cursor=C.limit-s,C.ket=C.cursor,C.eq_s_b(4,"heid")&&(C.bra=C.cursor,c()&&(e=C.limit-C.cursor,C.eq_s_b(1,"c")||(C.cursor=C.limit-e,C.slice_del(),C.ket=C.cursor,C.eq_s_b(2,"en")&&(C.bra=C.cursor,m())))),C.cursor=C.limit-s,C.ket=C.cursor,r=C.find_among_b(k,6))switch(C.bra=C.cursor,r){case 1:if(c()){if(C.slice_del(),i=C.limit-C.cursor,C.ket=C.cursor,C.eq_s_b(2,"ig")&&(C.bra=C.cursor,c()&&(n=C.limit-C.cursor,!C.eq_s_b(1,"e")))){C.cursor=C.limit-n,C.slice_del();break}C.cursor=C.limit-i,a()}break;case 2:c()&&(o=C.limit-C.cursor,C.eq_s_b(1,"e")||(C.cursor=C.limit-o,C.slice_del()));break;case 3:c()&&(C.slice_del(),l());break;case 4:c()&&C.slice_del();break;case 5:c()&&w&&C.slice_del()}C.cursor=C.limit-s,C.out_grouping_b(z,73,232)&&(t=C.limit-C.cursor,C.find_among_b(v,4)&&C.out_grouping_b(q,97,232)&&(C.cursor=C.limit-t,C.ket=C.cursor,C.cursor>C.limit_backward&&(C.cursor--,C.bra=C.cursor,C.slice_del())))}var d,_,w,b=[new e("",-1,6),new e("á",0,1),new e("ä",0,1),new e("é",0,2),new e("ë",0,2),new e("í",0,3),new e("ï",0,3),new e("ó",0,4),new e("ö",0,4),new e("ú",0,5),new e("ü",0,5)],p=[new e("",-1,3),new e("I",0,2),new e("Y",0,1)],g=[new e("dd",-1,-1),new e("kk",-1,-1),new e("tt",-1,-1)],h=[new e("ene",-1,2),new e("se",-1,3),new e("en",-1,2),new e("heden",2,1),new e("s",-1,3)],k=[new e("end",-1,1),new e("ig",-1,2),new e("ing",-1,1),new e("lijk",-1,3),new e("baar",-1,4),new e("bar",-1,5)],v=[new e("aa",-1,-1),new e("ee",-1,-1),new e("oo",-1,-1),new e("uu",-1,-1)],q=[17,65,16,1,0,0,0,0,0,0,0,0,0,0,0,0,128],z=[1,0,0,17,65,16,1,0,0,0,0,0,0,0,0,0,0,0,0,128],j=[17,67,16,1,0,0,0,0,0,0,0,0,0,0,0,0,128],C=new i;this.setCurrent=function(r){C.setCurrent(r)},this.getCurrent=function(){return C.getCurrent()},this.stem=function(){var e=C.cursor;return r(),C.cursor=e,o(),C.limit_backward=e,C.cursor=C.limit,f(),C.cursor=C.limit_backward,s(),!0}};return function(r){return"function"==typeof r.update?r.update(function(r){return n.setCurrent(r),n.stem(),n.getCurrent()}):(n.setCurrent(r),n.stem(),n.getCurrent())}}(),r.Pipeline.registerFunction(r.nl.stemmer,"stemmer-nl"),r.nl.stopWordFilter=r.generateStopWordFilter(" aan al alles als altijd andere ben bij daar dan dat de der deze die dit doch doen door dus een eens en er ge geen geweest haar had heb hebben heeft hem het hier hij hoe hun iemand iets ik in is ja je kan kon kunnen maar me meer men met mij mijn moet na naar niet niets nog nu of om omdat onder ons ook op over reeds te tegen toch toen tot u uit uw van veel voor want waren was wat werd wezen wie wil worden wordt zal ze zelf zich zij zijn zo zonder zou".split(" ")),r.Pipeline.registerFunction(r.nl.stopWordFilter,"stopWordFilter-nl")}});
\ No newline at end of file
diff --git a/ja/assets/javascripts/lunr/min/lunr.no.min.js b/ja/assets/javascripts/lunr/min/lunr.no.min.js
new file mode 100644
index 000000000..92bc7e4e8
--- /dev/null
+++ b/ja/assets/javascripts/lunr/min/lunr.no.min.js
@@ -0,0 +1,18 @@
+/*!
+ * Lunr languages, `Norwegian` language
+ * https://github.com/MihaiValentin/lunr-languages
+ *
+ * Copyright 2014, Mihai Valentin
+ * http://www.mozilla.org/MPL/
+ */
+/*!
+ * based on
+ * Snowball JavaScript Library v0.3
+ * http://code.google.com/p/urim/
+ * http://snowball.tartarus.org/
+ *
+ * Copyright 2010, Oleg Mazko
+ * http://www.mozilla.org/MPL/
+ */
+
+!function(e,r){"function"==typeof define&&define.amd?define(r):"object"==typeof exports?module.exports=r():r()(e.lunr)}(this,function(){return function(e){if(void 0===e)throw new Error("Lunr is not present. Please include / require Lunr before this script.");if(void 0===e.stemmerSupport)throw new Error("Lunr stemmer support is not present. Please include / require Lunr stemmer support before this script.");e.no=function(){this.pipeline.reset(),this.pipeline.add(e.no.trimmer,e.no.stopWordFilter,e.no.stemmer),this.searchPipeline&&(this.searchPipeline.reset(),this.searchPipeline.add(e.no.stemmer))},e.no.wordCharacters="A-Za-zªºÀ-ÖØ-öø-ʸˠ-ˤᴀ-ᴥᴬ-ᵜᵢ-ᵥᵫ-ᵷᵹ-ᶾḀ-ỿⁱⁿₐ-ₜKÅℲⅎⅠ-ↈⱠ-ⱿꜢ-ꞇꞋ-ꞭꞰ-ꞷꟷ-ꟿꬰ-ꭚꭜ-ꭤff-stＡ-Ｚａ-ｚ",e.no.trimmer=e.trimmerSupport.generateTrimmer(e.no.wordCharacters),e.Pipeline.registerFunction(e.no.trimmer,"trimmer-no"),e.no.stemmer=function(){var r=e.stemmerSupport.Among,n=e.stemmerSupport.SnowballProgram,i=new function(){function e(){var e,r=w.cursor+3;if(a=w.limit,0<=r||r<=w.limit){for(s=r;;){if(e=w.cursor,w.in_grouping(d,97,248)){w.cursor=e;break}if(e>=w.limit)return;w.cursor=e+1}for(;!w.out_grouping(d,97,248);){if(w.cursor>=w.limit)return;w.cursor++}a=w.cursor,a<s&&(a=s)}}function i(){var e,r,n;if(w.cursor>=a&&(r=w.limit_backward,w.limit_backward=a,w.ket=w.cursor,e=w.find_among_b(m,29),w.limit_backward=r,e))switch(w.bra=w.cursor,e){case 1:w.slice_del();break;case 2:n=w.limit-w.cursor,w.in_grouping_b(c,98,122)?w.slice_del():(w.cursor=w.limit-n,w.eq_s_b(1,"k")&&w.out_grouping_b(d,97,248)&&w.slice_del());break;case 3:w.slice_from("er")}}function t(){var e,r=w.limit-w.cursor;w.cursor>=a&&(e=w.limit_backward,w.limit_backward=a,w.ket=w.cursor,w.find_among_b(u,2)?(w.bra=w.cursor,w.limit_backward=e,w.cursor=w.limit-r,w.cursor>w.limit_backward&&(w.cursor--,w.bra=w.cursor,w.slice_del())):w.limit_backward=e)}function o(){var e,r;w.cursor>=a&&(r=w.limit_backward,w.limit_backward=a,w.ket=w.cursor,e=w.find_among_b(l,11),e?(w.bra=w.cursor,w.limit_backward=r,1==e&&w.slice_del()):w.limit_backward=r)}var s,a,m=[new r("a",-1,1),new r("e",-1,1),new r("ede",1,1),new r("ande",1,1),new r("ende",1,1),new r("ane",1,1),new r("ene",1,1),new r("hetene",6,1),new r("erte",1,3),new r("en",-1,1),new r("heten",9,1),new r("ar",-1,1),new r("er",-1,1),new r("heter",12,1),new r("s",-1,2),new r("as",14,1),new r("es",14,1),new r("edes",16,1),new r("endes",16,1),new r("enes",16,1),new r("hetenes",19,1),new r("ens",14,1),new r("hetens",21,1),new r("ers",14,1),new r("ets",14,1),new r("et",-1,1),new r("het",25,1),new r("ert",-1,3),new r("ast",-1,1)],u=[new r("dt",-1,-1),new r("vt",-1,-1)],l=[new r("leg",-1,1),new r("eleg",0,1),new r("ig",-1,1),new r("eig",2,1),new r("lig",2,1),new r("elig",4,1),new r("els",-1,1),new r("lov",-1,1),new r("elov",7,1),new r("slov",7,1),new r("hetslov",9,1)],d=[17,65,16,1,0,0,0,0,0,0,0,0,0,0,0,0,48,0,128],c=[119,125,149,1],w=new n;this.setCurrent=function(e){w.setCurrent(e)},this.getCurrent=function(){return w.getCurrent()},this.stem=function(){var r=w.cursor;return e(),w.limit_backward=r,w.cursor=w.limit,i(),w.cursor=w.limit,t(),w.cursor=w.limit,o(),!0}};return function(e){return"function"==typeof e.update?e.update(function(e){return i.setCurrent(e),i.stem(),i.getCurrent()}):(i.setCurrent(e),i.stem(),i.getCurrent())}}(),e.Pipeline.registerFunction(e.no.stemmer,"stemmer-no"),e.no.stopWordFilter=e.generateStopWordFilter("alle at av bare begge ble blei bli blir blitt både båe da de deg dei deim deira deires dem den denne der dere deres det dette di din disse ditt du dykk dykkar då eg ein eit eitt eller elles en enn er et ett etter for fordi fra før ha hadde han hans har hennar henne hennes her hjå ho hoe honom hoss hossen hun hva hvem hver hvilke hvilken hvis hvor hvordan hvorfor i ikke ikkje ikkje ingen ingi inkje inn inni ja jeg kan kom korleis korso kun kunne kva kvar kvarhelst kven kvi kvifor man mange me med medan meg meget mellom men mi min mine mitt mot mykje ned no noe noen noka noko nokon nokor nokre nå når og også om opp oss over på samme seg selv si si sia sidan siden sin sine sitt sjøl skal skulle slik so som som somme somt så sånn til um upp ut uten var vart varte ved vere verte vi vil ville vore vors vort vår være være vært å".split(" ")),e.Pipeline.registerFunction(e.no.stopWordFilter,"stopWordFilter-no")}});
\ No newline at end of file
diff --git a/ja/assets/javascripts/lunr/min/lunr.pt.min.js b/ja/assets/javascripts/lunr/min/lunr.pt.min.js
new file mode 100644
index 000000000..6c16996d6
--- /dev/null
+++ b/ja/assets/javascripts/lunr/min/lunr.pt.min.js
@@ -0,0 +1,18 @@
+/*!
+ * Lunr languages, `Portuguese` language
+ * https://github.com/MihaiValentin/lunr-languages
+ *
+ * Copyright 2014, Mihai Valentin
+ * http://www.mozilla.org/MPL/
+ */
+/*!
+ * based on
+ * Snowball JavaScript Library v0.3
+ * http://code.google.com/p/urim/
+ * http://snowball.tartarus.org/
+ *
+ * Copyright 2010, Oleg Mazko
+ * http://www.mozilla.org/MPL/
+ */
+
+!function(e,r){"function"==typeof define&&define.amd?define(r):"object"==typeof exports?module.exports=r():r()(e.lunr)}(this,function(){return function(e){if(void 0===e)throw new Error("Lunr is not present. Please include / require Lunr before this script.");if(void 0===e.stemmerSupport)throw new Error("Lunr stemmer support is not present. 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\ No newline at end of file
diff --git a/ja/assets/javascripts/lunr/min/lunr.ro.min.js b/ja/assets/javascripts/lunr/min/lunr.ro.min.js
new file mode 100644
index 000000000..727714018
--- /dev/null
+++ b/ja/assets/javascripts/lunr/min/lunr.ro.min.js
@@ -0,0 +1,18 @@
+/*!
+ * Lunr languages, `Romanian` language
+ * https://github.com/MihaiValentin/lunr-languages
+ *
+ * Copyright 2014, Mihai Valentin
+ * http://www.mozilla.org/MPL/
+ */
+/*!
+ * based on
+ * Snowball JavaScript Library v0.3
+ * http://code.google.com/p/urim/
+ * http://snowball.tartarus.org/
+ *
+ * Copyright 2010, Oleg Mazko
+ * http://www.mozilla.org/MPL/
+ */
+
+!function(e,i){"function"==typeof define&&define.amd?define(i):"object"==typeof exports?module.exports=i():i()(e.lunr)}(this,function(){return function(e){if(void 0===e)throw new Error("Lunr is not present. Please include / require Lunr before this script.");if(void 0===e.stemmerSupport)throw new Error("Lunr stemmer support is not present. 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dă ea ei el ele eram este eu eşti face fata fi fie fiecare fii fim fiu fiţi frumos fără graţie halbă iar ieri la le li lor lui lângă lîngă mai mea mei mele mereu meu mi mie mine mult multă mulţi mulţumesc mâine mîine mă ne nevoie nici nicăieri nimeni nimeri nimic nişte noastre noastră noi noroc nostru nouă noştri nu opt ori oricare orice oricine oricum oricând oricât oricînd oricît oriunde patra patru patrulea pe pentru peste pic poate pot prea prima primul prin puţin puţina puţină până pînă rog sa sale sau se spate spre sub sunt suntem sunteţi sută sînt sîntem sînteţi să săi său ta tale te timp tine toate toată tot totuşi toţi trei treia treilea tu tăi tău un una unde undeva unei uneia unele uneori unii unor unora unu unui unuia unul vi voastre voastră voi vostru vouă voştri vreme vreo vreun vă zece zero zi zice îi îl îmi împotriva în  înainte înaintea încotro încât încît între întrucât întrucît îţi ăla ălea ăsta ăstea ăştia şapte şase şi ştiu ţi ţie".split(" ")),e.Pipeline.registerFunction(e.ro.stopWordFilter,"stopWordFilter-ro")}});
\ No newline at end of file
diff --git a/ja/assets/javascripts/lunr/min/lunr.ru.min.js b/ja/assets/javascripts/lunr/min/lunr.ru.min.js
new file mode 100644
index 000000000..186cc485c
--- /dev/null
+++ b/ja/assets/javascripts/lunr/min/lunr.ru.min.js
@@ -0,0 +1,18 @@
+/*!
+ * Lunr languages, `Russian` language
+ * https://github.com/MihaiValentin/lunr-languages
+ *
+ * Copyright 2014, Mihai Valentin
+ * http://www.mozilla.org/MPL/
+ */
+/*!
+ * based on
+ * Snowball JavaScript Library v0.3
+ * http://code.google.com/p/urim/
+ * http://snowball.tartarus.org/
+ *
+ * Copyright 2010, Oleg Mazko
+ * http://www.mozilla.org/MPL/
+ */
+
+!function(e,n){"function"==typeof define&&define.amd?define(n):"object"==typeof exports?module.exports=n():n()(e.lunr)}(this,function(){return function(e){if(void 0===e)throw new Error("Lunr is not present. Please include / require Lunr before this script.");if(void 0===e.stemmerSupport)throw new Error("Lunr stemmer support is not present. 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n("ыло",24,2),new n("но",-1,1),new n("ено",27,2),new n("нно",27,1),new n("ет",-1,1),new n("ует",30,2),new n("ит",-1,2),new n("ыт",-1,2),new n("ют",-1,1),new n("уют",34,2),new n("ят",-1,2),new n("ны",-1,1),new n("ены",37,2),new n("ть",-1,1),new n("ить",39,2),new n("ыть",39,2),new n("ешь",-1,1),new n("ишь",-1,2),new n("ю",-1,2),new n("ую",44,2)],v=[new n("а",-1,1),new n("ев",-1,1),new n("ов",-1,1),new n("е",-1,1),new n("ие",3,1),new n("ье",3,1),new n("и",-1,1),new n("еи",6,1),new n("ии",6,1),new n("ами",6,1),new n("ями",6,1),new n("иями",10,1),new n("й",-1,1),new n("ей",12,1),new n("ией",13,1),new n("ий",12,1),new n("ой",12,1),new n("ам",-1,1),new n("ем",-1,1),new n("ием",18,1),new n("ом",-1,1),new n("ям",-1,1),new n("иям",21,1),new n("о",-1,1),new n("у",-1,1),new n("ах",-1,1),new n("ях",-1,1),new n("иях",26,1),new n("ы",-1,1),new n("ь",-1,1),new n("ю",-1,1),new n("ию",30,1),new n("ью",30,1),new n("я",-1,1),new n("ия",33,1),new n("ья",33,1)],F=[new n("ост",-1,1),new n("ость",-1,1)],q=[new n("ейше",-1,1),new n("н",-1,2),new n("ейш",-1,1),new n("ь",-1,3)],S=[33,65,8,232],W=new r;this.setCurrent=function(e){W.setCurrent(e)},this.getCurrent=function(){return W.getCurrent()},this.stem=function(){return w(),W.cursor=W.limit,!(W.cursor<b)&&(W.limit_backward=b,o()||(W.cursor=W.limit,f()||(W.cursor=W.limit),m()||(W.cursor=W.limit,l()||(W.cursor=W.limit,a()))),W.cursor=W.limit,W.ket=W.cursor,W.eq_s_b(1,"и")?(W.bra=W.cursor,W.slice_del()):W.cursor=W.limit,p(),W.cursor=W.limit,d(),!0)}};return function(e){return"function"==typeof e.update?e.update(function(e){return t.setCurrent(e),t.stem(),t.getCurrent()}):(t.setCurrent(e),t.stem(),t.getCurrent())}}(),e.Pipeline.registerFunction(e.ru.stemmer,"stemmer-ru"),e.ru.stopWordFilter=e.generateStopWordFilter("алло без близко более больше будем будет будете будешь будто буду будут будь бы бывает бывь был была были было быть в важная важное важные важный вам вами вас ваш ваша ваше ваши вверх вдали вдруг ведь везде весь вниз внизу во вокруг вон восемнадцатый восемнадцать восемь восьмой вот впрочем времени время все всегда всего всем всеми всему всех всею всю всюду вся всё второй вы г где говорил говорит год года году да давно даже далеко дальше даром два двадцатый двадцать две двенадцатый двенадцать двух девятнадцатый девятнадцать девятый девять действительно дел день десятый десять для до довольно долго должно другая другие других друго другое другой е его ее ей ему если есть еще ещё ею её ж же жизнь за занят занята занято заняты затем зато зачем здесь значит и из или им именно иметь ими имя иногда их к каждая каждое каждые каждый кажется как какая какой кем когда кого ком кому конечно которая которого которой которые который которых кроме кругом кто куда лет ли лишь лучше люди м мало между меля менее меньше меня миллионов мимо мира мне много многочисленная многочисленное многочисленные многочисленный мной мною мог могут мож может можно можхо мои мой мор мочь моя моё мы на наверху над надо назад наиболее наконец нам нами нас начала наш наша наше наши не него недавно недалеко нее ней нельзя нем немного нему непрерывно нередко несколько нет нею неё ни нибудь ниже низко никогда никуда ними них ничего но ну нужно нх о об оба обычно один одиннадцатый одиннадцать однажды однако одного одной около он она они оно опять особенно от отовсюду отсюда очень первый перед по под пожалуйста позже пока пор пора после посреди потом потому почему почти прекрасно при про просто против процентов пятнадцатый пятнадцать пятый пять раз разве рано раньше рядом с сам сама сами самим самими самих само самого самой самом самому саму свое своего своей свои своих свою сеаой себе себя сегодня седьмой сейчас семнадцатый семнадцать семь сих сказал сказала сказать сколько слишком сначала снова со собой собою совсем спасибо стал суть т та так такая также такие такое такой там твой твоя твоё те тебе тебя тем теми теперь тех то тобой тобою тогда того тоже только том тому тот тою третий три тринадцатый тринадцать ту туда тут ты тысяч у уж уже уметь хорошо хотеть хоть хотя хочешь часто чаще чего человек чем чему через четвертый четыре четырнадцатый четырнадцать что чтоб чтобы чуть шестнадцатый шестнадцать шестой шесть эта эти этим этими этих это этого этой этом этому этот эту я \ufeffа".split(" ")),e.Pipeline.registerFunction(e.ru.stopWordFilter,"stopWordFilter-ru")}});
\ No newline at end of file
diff --git a/ja/assets/javascripts/lunr/min/lunr.sa.min.js b/ja/assets/javascripts/lunr/min/lunr.sa.min.js
new file mode 100644
index 000000000..50ee56420
--- /dev/null
+++ b/ja/assets/javascripts/lunr/min/lunr.sa.min.js
@@ -0,0 +1 @@
+!function(e,r){"function"==typeof define&&define.amd?define(r):"object"==typeof exports?module.exports=r():r()(e.lunr)}(this,function(){return function(e){if(void 0===e)throw new Error("Lunr is not present. Please include / require Lunr before this script.");if(void 0===e.stemmerSupport)throw new Error("Lunr stemmer support is not present. Please include / require Lunr stemmer support before this script.");e.sa=function(){this.pipeline.reset(),this.pipeline.add(e.sa.trimmer,e.sa.stopWordFilter,e.sa.stemmer),this.searchPipeline&&(this.searchPipeline.reset(),this.searchPipeline.add(e.sa.stemmer))},e.sa.wordCharacters="ऀ-ःऄ-एऐ-टठ-यर-िी-ॏॐ-य़ॠ-९॰-ॿ꣠-꣱ꣲ-ꣷ꣸-ꣻ꣼-ꣽꣾ-ꣿᆰ0-ᆰ9",e.sa.trimmer=e.trimmerSupport.generateTrimmer(e.sa.wordCharacters),e.Pipeline.registerFunction(e.sa.trimmer,"trimmer-sa"),e.sa.stopWordFilter=e.generateStopWordFilter('तथा अयम्‌ एकम्‌ इत्यस्मिन्‌ तथा तत्‌ वा अयम्‌ इत्यस्य ते आहूत उपरि तेषाम्‌  किन्तु तेषाम्‌ तदा इत्यनेन अधिकः इत्यस्य तत्‌ केचन बहवः द्वि तथा महत्वपूर्णः अयम्‌ अस्य  विषये अयं अस्ति तत्‌ प्रथमः विषये इत्युपरि इत्युपरि इतर अधिकतमः अधिकः अपि सामान्यतया ठ इतरेतर नूतनम्‌ द  न्यूनम्‌ कश्चित्‌ वा विशालः द  सः अस्ति तदनुसारम् तत्र अस्ति केवलम्‌ अपि अत्र सर्वे विविधाः तत्‌ बहवः यतः इदानीम्‌ द  दक्षिण इत्यस्मै तस्य उपरि नथ अतीव कार्यम्‌ सर्वे एकैकम्‌ इत्यादि। एते सन्ति  उत इत्थम्‌ मध्ये एतदर्थं . स कस्य प्रथमः श्री. करोति अस्मिन् प्रकारः निर्मिता कालः तत्र कर्तुं  समान अधुना ते सन्ति स एकः अस्ति सः अर्थात् तेषां कृते . स्थितम्  विशेषः अग्रिम तेषाम्‌ समान स्रोतः ख म समान इदानीमपि अधिकतया करोतु ते समान इत्यस्य वीथी सह यस्मिन्  कृतवान्‌ धृतः तदा पुनः पूर्वं सः आगतः किम्‌ कुल इतर पुरा  मात्रा स विषये उ अतएव अपि नगरस्य  उपरि यतः प्रतिशतं  कतरः कालः साधनानि भूत तथापि जात सम्बन्धि अन्यत्‌ ग अतः अस्माकं स्वकीयाः अस्माकं इदानीं अन्तः इत्यादयः भवन्तः इत्यादयः एते एताः तस्य अस्य इदम् एते तेषां तेषां तेषां तान् तेषां तेषां तेषां समानः सः एकः च तादृशाः बहवः अन्ये च वदन्ति यत् कियत् कस्मै  कस्मै  यस्मै  यस्मै  यस्मै  यस्मै न अतिनीचः किन्तु प्रथमं सम्पूर्णतया  ततः चिरकालानन्तरं पुस्तकं सम्पूर्णतया अन्तः  किन्तु अत्र वा इह इव श्रद्धाय अवशिष्यते  परन्तु अन्ये वर्गाः सन्ति ते सन्ति शक्नुवन्ति सर्वे मिलित्वा सर्वे एकत्र"'.split(" ")),e.sa.stemmer=function(){return function(e){return"function"==typeof e.update?e.update(function(e){return e}):e}}();var r=e.wordcut;r.init(),e.sa.tokenizer=function(t){if(!arguments.length||null==t||void 0==t)return[];if(Array.isArray(t))return t.map(function(r){return isLunr2?new e.Token(r.toLowerCase()):r.toLowerCase()});var i=t.toString().toLowerCase().replace(/^\s+/,"");return r.cut(i).split("|")},e.Pipeline.registerFunction(e.sa.stemmer,"stemmer-sa"),e.Pipeline.registerFunction(e.sa.stopWordFilter,"stopWordFilter-sa")}});
\ No newline at end of file
diff --git a/ja/assets/javascripts/lunr/min/lunr.stemmer.support.min.js b/ja/assets/javascripts/lunr/min/lunr.stemmer.support.min.js
new file mode 100644
index 000000000..abd4475bb
--- /dev/null
+++ b/ja/assets/javascripts/lunr/min/lunr.stemmer.support.min.js
@@ -0,0 +1 @@
+!function(r,t){"function"==typeof define&&define.amd?define(t):"object"==typeof exports?module.exports=t():t()(r.lunr)}(this,function(){return function(r){r.stemmerSupport={Among:function(r,t,i,s){if(this.toCharArray=function(r){for(var t=r.length,i=new Array(t),s=0;s<t;s++)i[s]=r.charCodeAt(s);return i},!r&&""!=r||!t&&0!=t||!i)throw"Bad Among initialisation: s:"+r+", substring_i: "+t+", result: "+i;this.s_size=r.length,this.s=this.toCharArray(r),this.substring_i=t,this.result=i,this.method=s},SnowballProgram:function(){var r;return{bra:0,ket:0,limit:0,cursor:0,limit_backward:0,setCurrent:function(t){r=t,this.cursor=0,this.limit=t.length,this.limit_backward=0,this.bra=this.cursor,this.ket=this.limit},getCurrent:function(){var t=r;return r=null,t},in_grouping:function(t,i,s){if(this.cursor<this.limit){var e=r.charCodeAt(this.cursor);if(e<=s&&e>=i&&(e-=i,t[e>>3]&1<<(7&e)))return this.cursor++,!0}return!1},in_grouping_b:function(t,i,s){if(this.cursor>this.limit_backward){var e=r.charCodeAt(this.cursor-1);if(e<=s&&e>=i&&(e-=i,t[e>>3]&1<<(7&e)))return this.cursor--,!0}return!1},out_grouping:function(t,i,s){if(this.cursor<this.limit){var e=r.charCodeAt(this.cursor);if(e>s||e<i)return this.cursor++,!0;if(e-=i,!(t[e>>3]&1<<(7&e)))return this.cursor++,!0}return!1},out_grouping_b:function(t,i,s){if(this.cursor>this.limit_backward){var e=r.charCodeAt(this.cursor-1);if(e>s||e<i)return this.cursor--,!0;if(e-=i,!(t[e>>3]&1<<(7&e)))return this.cursor--,!0}return!1},eq_s:function(t,i){if(this.limit-this.cursor<t)return!1;for(var s=0;s<t;s++)if(r.charCodeAt(this.cursor+s)!=i.charCodeAt(s))return!1;return this.cursor+=t,!0},eq_s_b:function(t,i){if(this.cursor-this.limit_backward<t)return!1;for(var s=0;s<t;s++)if(r.charCodeAt(this.cursor-t+s)!=i.charCodeAt(s))return!1;return this.cursor-=t,!0},find_among:function(t,i){for(var s=0,e=i,n=this.cursor,u=this.limit,o=0,h=0,c=!1;;){for(var a=s+(e-s>>1),f=0,l=o<h?o:h,_=t[a],m=l;m<_.s_size;m++){if(n+l==u){f=-1;break}if(f=r.charCodeAt(n+l)-_.s[m])break;l++}if(f<0?(e=a,h=l):(s=a,o=l),e-s<=1){if(s>0||e==s||c)break;c=!0}}for(;;){var _=t[s];if(o>=_.s_size){if(this.cursor=n+_.s_size,!_.method)return _.result;var b=_.method();if(this.cursor=n+_.s_size,b)return _.result}if((s=_.substring_i)<0)return 0}},find_among_b:function(t,i){for(var s=0,e=i,n=this.cursor,u=this.limit_backward,o=0,h=0,c=!1;;){for(var a=s+(e-s>>1),f=0,l=o<h?o:h,_=t[a],m=_.s_size-1-l;m>=0;m--){if(n-l==u){f=-1;break}if(f=r.charCodeAt(n-1-l)-_.s[m])break;l++}if(f<0?(e=a,h=l):(s=a,o=l),e-s<=1){if(s>0||e==s||c)break;c=!0}}for(;;){var _=t[s];if(o>=_.s_size){if(this.cursor=n-_.s_size,!_.method)return _.result;var b=_.method();if(this.cursor=n-_.s_size,b)return _.result}if((s=_.substring_i)<0)return 0}},replace_s:function(t,i,s){var e=s.length-(i-t),n=r.substring(0,t),u=r.substring(i);return r=n+s+u,this.limit+=e,this.cursor>=i?this.cursor+=e:this.cursor>t&&(this.cursor=t),e},slice_check:function(){if(this.bra<0||this.bra>this.ket||this.ket>this.limit||this.limit>r.length)throw"faulty slice operation"},slice_from:function(r){this.slice_check(),this.replace_s(this.bra,this.ket,r)},slice_del:function(){this.slice_from("")},insert:function(r,t,i){var s=this.replace_s(r,t,i);r<=this.bra&&(this.bra+=s),r<=this.ket&&(this.ket+=s)},slice_to:function(){return this.slice_check(),r.substring(this.bra,this.ket)},eq_v_b:function(r){return this.eq_s_b(r.length,r)}}}},r.trimmerSupport={generateTrimmer:function(r){var t=new RegExp("^[^"+r+"]+"),i=new RegExp("[^"+r+"]+$");return function(r){return"function"==typeof r.update?r.update(function(r){return r.replace(t,"").replace(i,"")}):r.replace(t,"").replace(i,"")}}}}});
\ No newline at end of file
diff --git a/ja/assets/javascripts/lunr/min/lunr.sv.min.js b/ja/assets/javascripts/lunr/min/lunr.sv.min.js
new file mode 100644
index 000000000..3e5eb6400
--- /dev/null
+++ b/ja/assets/javascripts/lunr/min/lunr.sv.min.js
@@ -0,0 +1,18 @@
+/*!
+ * Lunr languages, `Swedish` language
+ * https://github.com/MihaiValentin/lunr-languages
+ *
+ * Copyright 2014, Mihai Valentin
+ * http://www.mozilla.org/MPL/
+ */
+/*!
+ * based on
+ * Snowball JavaScript Library v0.3
+ * http://code.google.com/p/urim/
+ * http://snowball.tartarus.org/
+ *
+ * Copyright 2010, Oleg Mazko
+ * http://www.mozilla.org/MPL/
+ */
+
+!function(e,r){"function"==typeof define&&define.amd?define(r):"object"==typeof exports?module.exports=r():r()(e.lunr)}(this,function(){return function(e){if(void 0===e)throw new Error("Lunr is not present. Please include / require Lunr before this script.");if(void 0===e.stemmerSupport)throw new Error("Lunr stemmer support is not present. Please include / require Lunr stemmer support before this script.");e.sv=function(){this.pipeline.reset(),this.pipeline.add(e.sv.trimmer,e.sv.stopWordFilter,e.sv.stemmer),this.searchPipeline&&(this.searchPipeline.reset(),this.searchPipeline.add(e.sv.stemmer))},e.sv.wordCharacters="A-Za-zªºÀ-ÖØ-öø-ʸˠ-ˤᴀ-ᴥᴬ-ᵜᵢ-ᵥᵫ-ᵷᵹ-ᶾḀ-ỿⁱⁿₐ-ₜKÅℲⅎⅠ-ↈⱠ-ⱿꜢ-ꞇꞋ-ꞭꞰ-ꞷꟷ-ꟿꬰ-ꭚꭜ-ꭤff-stＡ-Ｚａ-ｚ",e.sv.trimmer=e.trimmerSupport.generateTrimmer(e.sv.wordCharacters),e.Pipeline.registerFunction(e.sv.trimmer,"trimmer-sv"),e.sv.stemmer=function(){var r=e.stemmerSupport.Among,n=e.stemmerSupport.SnowballProgram,t=new function(){function e(){var e,r=w.cursor+3;if(o=w.limit,0<=r||r<=w.limit){for(a=r;;){if(e=w.cursor,w.in_grouping(l,97,246)){w.cursor=e;break}if(w.cursor=e,w.cursor>=w.limit)return;w.cursor++}for(;!w.out_grouping(l,97,246);){if(w.cursor>=w.limit)return;w.cursor++}o=w.cursor,o<a&&(o=a)}}function t(){var e,r=w.limit_backward;if(w.cursor>=o&&(w.limit_backward=o,w.cursor=w.limit,w.ket=w.cursor,e=w.find_among_b(u,37),w.limit_backward=r,e))switch(w.bra=w.cursor,e){case 1:w.slice_del();break;case 2:w.in_grouping_b(d,98,121)&&w.slice_del()}}function i(){var e=w.limit_backward;w.cursor>=o&&(w.limit_backward=o,w.cursor=w.limit,w.find_among_b(c,7)&&(w.cursor=w.limit,w.ket=w.cursor,w.cursor>w.limit_backward&&(w.bra=--w.cursor,w.slice_del())),w.limit_backward=e)}function s(){var e,r;if(w.cursor>=o){if(r=w.limit_backward,w.limit_backward=o,w.cursor=w.limit,w.ket=w.cursor,e=w.find_among_b(m,5))switch(w.bra=w.cursor,e){case 1:w.slice_del();break;case 2:w.slice_from("lös");break;case 3:w.slice_from("full")}w.limit_backward=r}}var a,o,u=[new r("a",-1,1),new r("arna",0,1),new r("erna",0,1),new r("heterna",2,1),new r("orna",0,1),new r("ad",-1,1),new r("e",-1,1),new r("ade",6,1),new r("ande",6,1),new r("arne",6,1),new r("are",6,1),new r("aste",6,1),new r("en",-1,1),new r("anden",12,1),new r("aren",12,1),new r("heten",12,1),new r("ern",-1,1),new r("ar",-1,1),new r("er",-1,1),new r("heter",18,1),new r("or",-1,1),new r("s",-1,2),new r("as",21,1),new r("arnas",22,1),new r("ernas",22,1),new r("ornas",22,1),new r("es",21,1),new r("ades",26,1),new r("andes",26,1),new r("ens",21,1),new r("arens",29,1),new r("hetens",29,1),new r("erns",21,1),new r("at",-1,1),new r("andet",-1,1),new r("het",-1,1),new r("ast",-1,1)],c=[new r("dd",-1,-1),new r("gd",-1,-1),new r("nn",-1,-1),new r("dt",-1,-1),new r("gt",-1,-1),new r("kt",-1,-1),new r("tt",-1,-1)],m=[new r("ig",-1,1),new r("lig",0,1),new r("els",-1,1),new r("fullt",-1,3),new r("löst",-1,2)],l=[17,65,16,1,0,0,0,0,0,0,0,0,0,0,0,0,24,0,32],d=[119,127,149],w=new n;this.setCurrent=function(e){w.setCurrent(e)},this.getCurrent=function(){return w.getCurrent()},this.stem=function(){var r=w.cursor;return e(),w.limit_backward=r,w.cursor=w.limit,t(),w.cursor=w.limit,i(),w.cursor=w.limit,s(),!0}};return function(e){return"function"==typeof e.update?e.update(function(e){return t.setCurrent(e),t.stem(),t.getCurrent()}):(t.setCurrent(e),t.stem(),t.getCurrent())}}(),e.Pipeline.registerFunction(e.sv.stemmer,"stemmer-sv"),e.sv.stopWordFilter=e.generateStopWordFilter("alla allt att av blev bli blir blivit de dem den denna deras dess dessa det detta dig din dina ditt du där då efter ej eller en er era ert ett från för ha hade han hans har henne hennes hon honom hur här i icke ingen inom inte jag ju kan kunde man med mellan men mig min mina mitt mot mycket ni nu när någon något några och om oss på samma sedan sig sin sina sitta själv skulle som så sådan sådana sådant till under upp ut utan vad var vara varför varit varje vars vart vem vi vid vilka vilkas vilken vilket vår våra vårt än är åt över".split(" ")),e.Pipeline.registerFunction(e.sv.stopWordFilter,"stopWordFilter-sv")}});
\ No newline at end of file
diff --git a/ja/assets/javascripts/lunr/min/lunr.ta.min.js b/ja/assets/javascripts/lunr/min/lunr.ta.min.js
new file mode 100644
index 000000000..a644bed22
--- /dev/null
+++ b/ja/assets/javascripts/lunr/min/lunr.ta.min.js
@@ -0,0 +1 @@
+!function(e,t){"function"==typeof define&&define.amd?define(t):"object"==typeof exports?module.exports=t():t()(e.lunr)}(this,function(){return function(e){if(void 0===e)throw new Error("Lunr is not present. Please include / require Lunr before this script.");if(void 0===e.stemmerSupport)throw new Error("Lunr stemmer support is not present. Please include / require Lunr stemmer support before this script.");e.ta=function(){this.pipeline.reset(),this.pipeline.add(e.ta.trimmer,e.ta.stopWordFilter,e.ta.stemmer),this.searchPipeline&&(this.searchPipeline.reset(),this.searchPipeline.add(e.ta.stemmer))},e.ta.wordCharacters="஀-உஊ-ஏஐ-ஙச-ட஠-னப-யர-ஹ஺-ிீ-௉ொ-௏ௐ-௙௚-௟௠-௩௪-௯௰-௹௺-௿a-zA-Zａ-ｚＡ-Ｚ0-9０-９",e.ta.trimmer=e.trimmerSupport.generateTrimmer(e.ta.wordCharacters),e.Pipeline.registerFunction(e.ta.trimmer,"trimmer-ta"),e.ta.stopWordFilter=e.generateStopWordFilter("அங்கு அங்கே அது அதை அந்த அவர் அவர்கள் அவள் அவன் அவை ஆக ஆகவே ஆகையால் ஆதலால் ஆதலினால் ஆனாலும் ஆனால் இங்கு இங்கே இது இதை இந்த இப்படி இவர் இவர்கள் இவள் இவன் இவை இவ்வளவு உனக்கு உனது உன் உன்னால் எங்கு எங்கே எது எதை எந்த எப்படி எவர் எவர்கள் எவள் எவன் எவை எவ்வளவு எனக்கு எனது எனவே என் என்ன என்னால் ஏது ஏன் தனது தன்னால் தானே தான் நாங்கள் நாம் நான் நீ நீங்கள்".split(" ")),e.ta.stemmer=function(){return function(e){return"function"==typeof e.update?e.update(function(e){return e}):e}}();var t=e.wordcut;t.init(),e.ta.tokenizer=function(r){if(!arguments.length||null==r||void 0==r)return[];if(Array.isArray(r))return r.map(function(t){return isLunr2?new e.Token(t.toLowerCase()):t.toLowerCase()});var i=r.toString().toLowerCase().replace(/^\s+/,"");return t.cut(i).split("|")},e.Pipeline.registerFunction(e.ta.stemmer,"stemmer-ta"),e.Pipeline.registerFunction(e.ta.stopWordFilter,"stopWordFilter-ta")}});
\ No newline at end of file
diff --git a/ja/assets/javascripts/lunr/min/lunr.te.min.js b/ja/assets/javascripts/lunr/min/lunr.te.min.js
new file mode 100644
index 000000000..9fa7a93b9
--- /dev/null
+++ b/ja/assets/javascripts/lunr/min/lunr.te.min.js
@@ -0,0 +1 @@
+!function(e,t){"function"==typeof define&&define.amd?define(t):"object"==typeof exports?module.exports=t():t()(e.lunr)}(this,function(){return function(e){if(void 0===e)throw new Error("Lunr is not present. Please include / require Lunr before this script.");if(void 0===e.stemmerSupport)throw new Error("Lunr stemmer support is not present. Please include / require Lunr stemmer support before this script.");e.te=function(){this.pipeline.reset(),this.pipeline.add(e.te.trimmer,e.te.stopWordFilter,e.te.stemmer),this.searchPipeline&&(this.searchPipeline.reset(),this.searchPipeline.add(e.te.stemmer))},e.te.wordCharacters="ఀ-ఄఅ-ఔక-హా-ౌౕ-ౖౘ-ౚౠ-ౡౢ-ౣ౦-౯౸-౿఼ఽ్ౝ౷౤౥",e.te.trimmer=e.trimmerSupport.generateTrimmer(e.te.wordCharacters),e.Pipeline.registerFunction(e.te.trimmer,"trimmer-te"),e.te.stopWordFilter=e.generateStopWordFilter("అందరూ అందుబాటులో అడగండి అడగడం అడ్డంగా అనుగుణంగా అనుమతించు అనుమతిస్తుంది అయితే ఇప్పటికే ఉన్నారు ఎక్కడైనా ఎప్పుడు ఎవరైనా ఎవరో ఏ ఏదైనా ఏమైనప్పటికి ఒక ఒకరు కనిపిస్తాయి కాదు కూడా గా గురించి చుట్టూ చేయగలిగింది తగిన తర్వాత దాదాపు దూరంగా నిజంగా పై ప్రకారం ప్రక్కన మధ్య మరియు మరొక మళ్ళీ మాత్రమే మెచ్చుకో వద్ద వెంట వేరుగా వ్యతిరేకంగా సంబంధం".split(" ")),e.te.stemmer=function(){return function(e){return"function"==typeof e.update?e.update(function(e){return e}):e}}();var t=e.wordcut;t.init(),e.te.tokenizer=function(r){if(!arguments.length||null==r||void 0==r)return[];if(Array.isArray(r))return r.map(function(t){return isLunr2?new e.Token(t.toLowerCase()):t.toLowerCase()});var i=r.toString().toLowerCase().replace(/^\s+/,"");return t.cut(i).split("|")},e.Pipeline.registerFunction(e.te.stemmer,"stemmer-te"),e.Pipeline.registerFunction(e.te.stopWordFilter,"stopWordFilter-te")}});
\ No newline at end of file
diff --git a/ja/assets/javascripts/lunr/min/lunr.th.min.js b/ja/assets/javascripts/lunr/min/lunr.th.min.js
new file mode 100644
index 000000000..dee3aac6e
--- /dev/null
+++ b/ja/assets/javascripts/lunr/min/lunr.th.min.js
@@ -0,0 +1 @@
+!function(e,r){"function"==typeof define&&define.amd?define(r):"object"==typeof exports?module.exports=r():r()(e.lunr)}(this,function(){return function(e){if(void 0===e)throw new Error("Lunr is not present. Please include / require Lunr before this script.");if(void 0===e.stemmerSupport)throw new Error("Lunr stemmer support is not present. Please include / require Lunr stemmer support before this script.");var r="2"==e.version[0];e.th=function(){this.pipeline.reset(),this.pipeline.add(e.th.trimmer),r?this.tokenizer=e.th.tokenizer:(e.tokenizer&&(e.tokenizer=e.th.tokenizer),this.tokenizerFn&&(this.tokenizerFn=e.th.tokenizer))},e.th.wordCharacters="[฀-๿]",e.th.trimmer=e.trimmerSupport.generateTrimmer(e.th.wordCharacters),e.Pipeline.registerFunction(e.th.trimmer,"trimmer-th");var t=e.wordcut;t.init(),e.th.tokenizer=function(i){if(!arguments.length||null==i||void 0==i)return[];if(Array.isArray(i))return i.map(function(t){return r?new e.Token(t):t});var n=i.toString().replace(/^\s+/,"");return t.cut(n).split("|")}}});
\ No newline at end of file
diff --git a/ja/assets/javascripts/lunr/min/lunr.tr.min.js b/ja/assets/javascripts/lunr/min/lunr.tr.min.js
new file mode 100644
index 000000000..563f6ec1f
--- /dev/null
+++ b/ja/assets/javascripts/lunr/min/lunr.tr.min.js
@@ -0,0 +1,18 @@
+/*!
+ * Lunr languages, `Turkish` language
+ * https://github.com/MihaiValentin/lunr-languages
+ *
+ * Copyright 2014, Mihai Valentin
+ * http://www.mozilla.org/MPL/
+ */
+/*!
+ * based on
+ * Snowball JavaScript Library v0.3
+ * http://code.google.com/p/urim/
+ * http://snowball.tartarus.org/
+ *
+ * Copyright 2010, Oleg Mazko
+ * http://www.mozilla.org/MPL/
+ */
+
+!function(r,i){"function"==typeof define&&define.amd?define(i):"object"==typeof exports?module.exports=i():i()(r.lunr)}(this,function(){return function(r){if(void 0===r)throw new Error("Lunr is not present. Please include / require Lunr before this script.");if(void 0===r.stemmerSupport)throw new Error("Lunr stemmer support is not present. Please include / require Lunr stemmer support before this script.");r.tr=function(){this.pipeline.reset(),this.pipeline.add(r.tr.trimmer,r.tr.stopWordFilter,r.tr.stemmer),this.searchPipeline&&(this.searchPipeline.reset(),this.searchPipeline.add(r.tr.stemmer))},r.tr.wordCharacters="A-Za-zªºÀ-ÖØ-öø-ʸˠ-ˤᴀ-ᴥᴬ-ᵜᵢ-ᵥᵫ-ᵷᵹ-ᶾḀ-ỿⁱⁿₐ-ₜKÅℲⅎⅠ-ↈⱠ-ⱿꜢ-ꞇꞋ-ꞭꞰ-ꞷꟷ-ꟿꬰ-ꭚꭜ-ꭤff-stＡ-Ｚａ-ｚ",r.tr.trimmer=r.trimmerSupport.generateTrimmer(r.tr.wordCharacters),r.Pipeline.registerFunction(r.tr.trimmer,"trimmer-tr"),r.tr.stemmer=function(){var i=r.stemmerSupport.Among,e=r.stemmerSupport.SnowballProgram,n=new function(){function r(r,i,e){for(;;){var n=Dr.limit-Dr.cursor;if(Dr.in_grouping_b(r,i,e)){Dr.cursor=Dr.limit-n;break}if(Dr.cursor=Dr.limit-n,Dr.cursor<=Dr.limit_backward)return!1;Dr.cursor--}return!0}function n(){var i,e;i=Dr.limit-Dr.cursor,r(Wr,97,305);for(var n=0;n<Br.length;n++){e=Dr.limit-Dr.cursor;var t=Br[n];if(Dr.eq_s_b(1,t[0])&&r(t[1],t[2],t[3]))return Dr.cursor=Dr.limit-i,!0;Dr.cursor=Dr.limit-e}return Dr.cursor=Dr.limit-e,!(!Dr.eq_s_b(1,"ü")||!r(Zr,246,252))&&(Dr.cursor=Dr.limit-i,!0)}function t(r,i){var e,n=Dr.limit-Dr.cursor;return r()&&(Dr.cursor=Dr.limit-n,Dr.cursor>Dr.limit_backward&&(Dr.cursor--,e=Dr.limit-Dr.cursor,i()))?(Dr.cursor=Dr.limit-e,!0):(Dr.cursor=Dr.limit-n,r()?(Dr.cursor=Dr.limit-n,!1):(Dr.cursor=Dr.limit-n,!(Dr.cursor<=Dr.limit_backward)&&(Dr.cursor--,!!i()&&(Dr.cursor=Dr.limit-n,!0))))}function u(r){return t(r,function(){return Dr.in_grouping_b(Wr,97,305)})}function o(){return u(function(){return Dr.eq_s_b(1,"n")})}function s(){return u(function(){return Dr.eq_s_b(1,"s")})}function c(){return u(function(){return Dr.eq_s_b(1,"y")})}function l(){return t(function(){return Dr.in_grouping_b(Lr,105,305)},function(){return Dr.out_grouping_b(Wr,97,305)})}function a(){return Dr.find_among_b(ur,10)&&l()}function m(){return n()&&Dr.in_grouping_b(Lr,105,305)&&s()}function d(){return Dr.find_among_b(or,2)}function f(){return n()&&Dr.in_grouping_b(Lr,105,305)&&c()}function b(){return n()&&Dr.find_among_b(sr,4)}function w(){return n()&&Dr.find_among_b(cr,4)&&o()}function _(){return n()&&Dr.find_among_b(lr,2)&&c()}function k(){return n()&&Dr.find_among_b(ar,2)}function p(){return n()&&Dr.find_among_b(mr,4)}function g(){return n()&&Dr.find_among_b(dr,2)}function y(){return n()&&Dr.find_among_b(fr,4)}function z(){return n()&&Dr.find_among_b(br,2)}function v(){return n()&&Dr.find_among_b(wr,2)&&c()}function h(){return Dr.eq_s_b(2,"ki")}function q(){return n()&&Dr.find_among_b(_r,2)&&o()}function C(){return n()&&Dr.find_among_b(kr,4)&&c()}function P(){return n()&&Dr.find_among_b(pr,4)}function F(){return n()&&Dr.find_among_b(gr,4)&&c()}function S(){return Dr.find_among_b(yr,4)}function W(){return n()&&Dr.find_among_b(zr,2)}function L(){return n()&&Dr.find_among_b(vr,4)}function x(){return n()&&Dr.find_among_b(hr,8)}function A(){return Dr.find_among_b(qr,2)}function E(){return n()&&Dr.find_among_b(Cr,32)&&c()}function j(){return Dr.find_among_b(Pr,8)&&c()}function T(){return n()&&Dr.find_among_b(Fr,4)&&c()}function Z(){return Dr.eq_s_b(3,"ken")&&c()}function B(){var r=Dr.limit-Dr.cursor;return!(T()||(Dr.cursor=Dr.limit-r,E()||(Dr.cursor=Dr.limit-r,j()||(Dr.cursor=Dr.limit-r,Z()))))}function D(){if(A()){var r=Dr.limit-Dr.cursor;if(S()||(Dr.cursor=Dr.limit-r,W()||(Dr.cursor=Dr.limit-r,C()||(Dr.cursor=Dr.limit-r,P()||(Dr.cursor=Dr.limit-r,F()||(Dr.cursor=Dr.limit-r))))),T())return!1}return!0}function G(){if(W()){Dr.bra=Dr.cursor,Dr.slice_del();var r=Dr.limit-Dr.cursor;return Dr.ket=Dr.cursor,x()||(Dr.cursor=Dr.limit-r,E()||(Dr.cursor=Dr.limit-r,j()||(Dr.cursor=Dr.limit-r,T()||(Dr.cursor=Dr.limit-r)))),nr=!1,!1}return!0}function H(){if(!L())return!0;var r=Dr.limit-Dr.cursor;return!E()&&(Dr.cursor=Dr.limit-r,!j())}function I(){var r,i=Dr.limit-Dr.cursor;return!(S()||(Dr.cursor=Dr.limit-i,F()||(Dr.cursor=Dr.limit-i,P()||(Dr.cursor=Dr.limit-i,C()))))||(Dr.bra=Dr.cursor,Dr.slice_del(),r=Dr.limit-Dr.cursor,Dr.ket=Dr.cursor,T()||(Dr.cursor=Dr.limit-r),!1)}function J(){var r,i=Dr.limit-Dr.cursor;if(Dr.ket=Dr.cursor,nr=!0,B()&&(Dr.cursor=Dr.limit-i,D()&&(Dr.cursor=Dr.limit-i,G()&&(Dr.cursor=Dr.limit-i,H()&&(Dr.cursor=Dr.limit-i,I()))))){if(Dr.cursor=Dr.limit-i,!x())return;Dr.bra=Dr.cursor,Dr.slice_del(),Dr.ket=Dr.cursor,r=Dr.limit-Dr.cursor,S()||(Dr.cursor=Dr.limit-r,W()||(Dr.cursor=Dr.limit-r,C()||(Dr.cursor=Dr.limit-r,P()||(Dr.cursor=Dr.limit-r,F()||(Dr.cursor=Dr.limit-r))))),T()||(Dr.cursor=Dr.limit-r)}Dr.bra=Dr.cursor,Dr.slice_del()}function K(){var r,i,e,n;if(Dr.ket=Dr.cursor,h()){if(r=Dr.limit-Dr.cursor,p())return Dr.bra=Dr.cursor,Dr.slice_del(),i=Dr.limit-Dr.cursor,Dr.ket=Dr.cursor,W()?(Dr.bra=Dr.cursor,Dr.slice_del(),K()):(Dr.cursor=Dr.limit-i,a()&&(Dr.bra=Dr.cursor,Dr.slice_del(),Dr.ket=Dr.cursor,W()&&(Dr.bra=Dr.cursor,Dr.slice_del(),K()))),!0;if(Dr.cursor=Dr.limit-r,w()){if(Dr.bra=Dr.cursor,Dr.slice_del(),Dr.ket=Dr.cursor,e=Dr.limit-Dr.cursor,d())Dr.bra=Dr.cursor,Dr.slice_del();else{if(Dr.cursor=Dr.limit-e,Dr.ket=Dr.cursor,!a()&&(Dr.cursor=Dr.limit-e,!m()&&(Dr.cursor=Dr.limit-e,!K())))return!0;Dr.bra=Dr.cursor,Dr.slice_del(),Dr.ket=Dr.cursor,W()&&(Dr.bra=Dr.cursor,Dr.slice_del(),K())}return!0}if(Dr.cursor=Dr.limit-r,g()){if(n=Dr.limit-Dr.cursor,d())Dr.bra=Dr.cursor,Dr.slice_del();else if(Dr.cursor=Dr.limit-n,m())Dr.bra=Dr.cursor,Dr.slice_del(),Dr.ket=Dr.cursor,W()&&(Dr.bra=Dr.cursor,Dr.slice_del(),K());else if(Dr.cursor=Dr.limit-n,!K())return!1;return!0}}return!1}function M(r){if(Dr.ket=Dr.cursor,!g()&&(Dr.cursor=Dr.limit-r,!k()))return!1;var i=Dr.limit-Dr.cursor;if(d())Dr.bra=Dr.cursor,Dr.slice_del();else if(Dr.cursor=Dr.limit-i,m())Dr.bra=Dr.cursor,Dr.slice_del(),Dr.ket=Dr.cursor,W()&&(Dr.bra=Dr.cursor,Dr.slice_del(),K());else if(Dr.cursor=Dr.limit-i,!K())return!1;return!0}function N(r){if(Dr.ket=Dr.cursor,!z()&&(Dr.cursor=Dr.limit-r,!b()))return!1;var i=Dr.limit-Dr.cursor;return!(!m()&&(Dr.cursor=Dr.limit-i,!d()))&&(Dr.bra=Dr.cursor,Dr.slice_del(),Dr.ket=Dr.cursor,W()&&(Dr.bra=Dr.cursor,Dr.slice_del(),K()),!0)}function O(){var r,i=Dr.limit-Dr.cursor;return Dr.ket=Dr.cursor,!(!w()&&(Dr.cursor=Dr.limit-i,!v()))&&(Dr.bra=Dr.cursor,Dr.slice_del(),r=Dr.limit-Dr.cursor,Dr.ket=Dr.cursor,!(!W()||(Dr.bra=Dr.cursor,Dr.slice_del(),!K()))||(Dr.cursor=Dr.limit-r,Dr.ket=Dr.cursor,!(a()||(Dr.cursor=Dr.limit-r,m()||(Dr.cursor=Dr.limit-r,K())))||(Dr.bra=Dr.cursor,Dr.slice_del(),Dr.ket=Dr.cursor,W()&&(Dr.bra=Dr.cursor,Dr.slice_del(),K()),!0)))}function Q(){var r,i,e=Dr.limit-Dr.cursor;if(Dr.ket=Dr.cursor,!p()&&(Dr.cursor=Dr.limit-e,!f()&&(Dr.cursor=Dr.limit-e,!_())))return!1;if(Dr.bra=Dr.cursor,Dr.slice_del(),Dr.ket=Dr.cursor,r=Dr.limit-Dr.cursor,a())Dr.bra=Dr.cursor,Dr.slice_del(),i=Dr.limit-Dr.cursor,Dr.ket=Dr.cursor,W()||(Dr.cursor=Dr.limit-i);else if(Dr.cursor=Dr.limit-r,!W())return!0;return Dr.bra=Dr.cursor,Dr.slice_del(),Dr.ket=Dr.cursor,K(),!0}function R(){var r,i,e=Dr.limit-Dr.cursor;if(Dr.ket=Dr.cursor,W())return Dr.bra=Dr.cursor,Dr.slice_del(),void K();if(Dr.cursor=Dr.limit-e,Dr.ket=Dr.cursor,q())if(Dr.bra=Dr.cursor,Dr.slice_del(),r=Dr.limit-Dr.cursor,Dr.ket=Dr.cursor,d())Dr.bra=Dr.cursor,Dr.slice_del();else{if(Dr.cursor=Dr.limit-r,Dr.ket=Dr.cursor,!a()&&(Dr.cursor=Dr.limit-r,!m())){if(Dr.cursor=Dr.limit-r,Dr.ket=Dr.cursor,!W())return;if(Dr.bra=Dr.cursor,Dr.slice_del(),!K())return}Dr.bra=Dr.cursor,Dr.slice_del(),Dr.ket=Dr.cursor,W()&&(Dr.bra=Dr.cursor,Dr.slice_del(),K())}else if(Dr.cursor=Dr.limit-e,!M(e)&&(Dr.cursor=Dr.limit-e,!N(e))){if(Dr.cursor=Dr.limit-e,Dr.ket=Dr.cursor,y())return Dr.bra=Dr.cursor,Dr.slice_del(),Dr.ket=Dr.cursor,i=Dr.limit-Dr.cursor,void(a()?(Dr.bra=Dr.cursor,Dr.slice_del(),Dr.ket=Dr.cursor,W()&&(Dr.bra=Dr.cursor,Dr.slice_del(),K())):(Dr.cursor=Dr.limit-i,W()?(Dr.bra=Dr.cursor,Dr.slice_del(),K()):(Dr.cursor=Dr.limit-i,K())));if(Dr.cursor=Dr.limit-e,!O()){if(Dr.cursor=Dr.limit-e,d())return Dr.bra=Dr.cursor,void Dr.slice_del();Dr.cursor=Dr.limit-e,K()||(Dr.cursor=Dr.limit-e,Q()||(Dr.cursor=Dr.limit-e,Dr.ket=Dr.cursor,(a()||(Dr.cursor=Dr.limit-e,m()))&&(Dr.bra=Dr.cursor,Dr.slice_del(),Dr.ket=Dr.cursor,W()&&(Dr.bra=Dr.cursor,Dr.slice_del(),K()))))}}}function U(){var r;if(Dr.ket=Dr.cursor,r=Dr.find_among_b(Sr,4))switch(Dr.bra=Dr.cursor,r){case 1:Dr.slice_from("p");break;case 2:Dr.slice_from("ç");break;case 3:Dr.slice_from("t");break;case 4:Dr.slice_from("k")}}function V(){for(;;){var r=Dr.limit-Dr.cursor;if(Dr.in_grouping_b(Wr,97,305)){Dr.cursor=Dr.limit-r;break}if(Dr.cursor=Dr.limit-r,Dr.cursor<=Dr.limit_backward)return!1;Dr.cursor--}return!0}function X(r,i,e){if(Dr.cursor=Dr.limit-r,V()){var n=Dr.limit-Dr.cursor;if(!Dr.eq_s_b(1,i)&&(Dr.cursor=Dr.limit-n,!Dr.eq_s_b(1,e)))return!0;Dr.cursor=Dr.limit-r;var t=Dr.cursor;return Dr.insert(Dr.cursor,Dr.cursor,e),Dr.cursor=t,!1}return!0}function Y(){var r=Dr.limit-Dr.cursor;(Dr.eq_s_b(1,"d")||(Dr.cursor=Dr.limit-r,Dr.eq_s_b(1,"g")))&&X(r,"a","ı")&&X(r,"e","i")&&X(r,"o","u")&&X(r,"ö","ü")}function $(){for(var r,i=Dr.cursor,e=2;;){for(r=Dr.cursor;!Dr.in_grouping(Wr,97,305);){if(Dr.cursor>=Dr.limit)return Dr.cursor=r,!(e>0)&&(Dr.cursor=i,!0);Dr.cursor++}e--}}function rr(r,i,e){for(;!Dr.eq_s(i,e);){if(Dr.cursor>=Dr.limit)return!0;Dr.cursor++}return(tr=i)!=Dr.limit||(Dr.cursor=r,!1)}function ir(){var r=Dr.cursor;return!rr(r,2,"ad")||(Dr.cursor=r,!rr(r,5,"soyad"))}function er(){var r=Dr.cursor;return!ir()&&(Dr.limit_backward=r,Dr.cursor=Dr.limit,Y(),Dr.cursor=Dr.limit,U(),!0)}var nr,tr,ur=[new i("m",-1,-1),new i("n",-1,-1),new i("miz",-1,-1),new i("niz",-1,-1),new i("muz",-1,-1),new i("nuz",-1,-1),new i("müz",-1,-1),new i("nüz",-1,-1),new i("mız",-1,-1),new i("nız",-1,-1)],or=[new i("leri",-1,-1),new i("ları",-1,-1)],sr=[new i("ni",-1,-1),new i("nu",-1,-1),new i("nü",-1,-1),new i("nı",-1,-1)],cr=[new i("in",-1,-1),new i("un",-1,-1),new i("ün",-1,-1),new i("ın",-1,-1)],lr=[new i("a",-1,-1),new i("e",-1,-1)],ar=[new i("na",-1,-1),new i("ne",-1,-1)],mr=[new i("da",-1,-1),new i("ta",-1,-1),new i("de",-1,-1),new i("te",-1,-1)],dr=[new i("nda",-1,-1),new i("nde",-1,-1)],fr=[new i("dan",-1,-1),new i("tan",-1,-1),new i("den",-1,-1),new i("ten",-1,-1)],br=[new i("ndan",-1,-1),new i("nden",-1,-1)],wr=[new i("la",-1,-1),new i("le",-1,-1)],_r=[new i("ca",-1,-1),new i("ce",-1,-1)],kr=[new i("im",-1,-1),new i("um",-1,-1),new i("üm",-1,-1),new i("ım",-1,-1)],pr=[new i("sin",-1,-1),new i("sun",-1,-1),new i("sün",-1,-1),new i("sın",-1,-1)],gr=[new i("iz",-1,-1),new i("uz",-1,-1),new i("üz",-1,-1),new i("ız",-1,-1)],yr=[new i("siniz",-1,-1),new i("sunuz",-1,-1),new i("sünüz",-1,-1),new i("sınız",-1,-1)],zr=[new i("lar",-1,-1),new i("ler",-1,-1)],vr=[new i("niz",-1,-1),new i("nuz",-1,-1),new i("nüz",-1,-1),new i("nız",-1,-1)],hr=[new i("dir",-1,-1),new i("tir",-1,-1),new i("dur",-1,-1),new i("tur",-1,-1),new i("dür",-1,-1),new i("tür",-1,-1),new i("dır",-1,-1),new i("tır",-1,-1)],qr=[new i("casına",-1,-1),new i("cesine",-1,-1)],Cr=[new i("di",-1,-1),new i("ti",-1,-1),new i("dik",-1,-1),new i("tik",-1,-1),new i("duk",-1,-1),new i("tuk",-1,-1),new i("dük",-1,-1),new i("tük",-1,-1),new i("dık",-1,-1),new i("tık",-1,-1),new i("dim",-1,-1),new i("tim",-1,-1),new i("dum",-1,-1),new i("tum",-1,-1),new i("düm",-1,-1),new i("tüm",-1,-1),new i("dım",-1,-1),new i("tım",-1,-1),new i("din",-1,-1),new i("tin",-1,-1),new i("dun",-1,-1),new i("tun",-1,-1),new i("dün",-1,-1),new i("tün",-1,-1),new i("dın",-1,-1),new i("tın",-1,-1),new i("du",-1,-1),new i("tu",-1,-1),new i("dü",-1,-1),new i("tü",-1,-1),new i("dı",-1,-1),new i("tı",-1,-1)],Pr=[new i("sa",-1,-1),new i("se",-1,-1),new i("sak",-1,-1),new i("sek",-1,-1),new i("sam",-1,-1),new i("sem",-1,-1),new i("san",-1,-1),new i("sen",-1,-1)],Fr=[new i("miş",-1,-1),new i("muş",-1,-1),new i("müş",-1,-1),new i("mış",-1,-1)],Sr=[new i("b",-1,1),new i("c",-1,2),new i("d",-1,3),new i("ğ",-1,4)],Wr=[17,65,16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,32,8,0,0,0,0,0,0,1],Lr=[1,16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,8,0,0,0,0,0,0,1],xr=[1,64,16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1],Ar=[17,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,130],Er=[1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1],jr=[17],Tr=[65],Zr=[65],Br=[["a",xr,97,305],["e",Ar,101,252],["ı",Er,97,305],["i",jr,101,105],["o",Tr,111,117],["ö",Zr,246,252],["u",Tr,111,117]],Dr=new e;this.setCurrent=function(r){Dr.setCurrent(r)},this.getCurrent=function(){return Dr.getCurrent()},this.stem=function(){return!!($()&&(Dr.limit_backward=Dr.cursor,Dr.cursor=Dr.limit,J(),Dr.cursor=Dr.limit,nr&&(R(),Dr.cursor=Dr.limit_backward,er())))}};return function(r){return"function"==typeof r.update?r.update(function(r){return n.setCurrent(r),n.stem(),n.getCurrent()}):(n.setCurrent(r),n.stem(),n.getCurrent())}}(),r.Pipeline.registerFunction(r.tr.stemmer,"stemmer-tr"),r.tr.stopWordFilter=r.generateStopWordFilter("acaba altmış altı ama ancak arada aslında ayrıca bana bazı belki ben benden beni benim beri beş bile bin bir biri birkaç birkez birçok birşey birşeyi biz bizden bize bizi bizim bu buna bunda bundan bunlar bunları bunların bunu bunun burada böyle böylece da daha dahi de defa değil diye diğer doksan dokuz dolayı dolayısıyla dört edecek eden ederek edilecek ediliyor edilmesi ediyor elli en etmesi etti ettiği ettiğini eğer gibi göre halen hangi hatta hem henüz hep hepsi her herhangi herkesin hiç hiçbir iki ile ilgili ise itibaren itibariyle için işte kadar karşın katrilyon kendi kendilerine kendini kendisi kendisine kendisini kez ki kim kimden kime kimi kimse kırk milyar milyon mu mü mı nasıl ne neden nedenle nerde nerede nereye niye niçin o olan olarak oldu olduklarını olduğu olduğunu olmadı olmadığı olmak olması olmayan olmaz olsa olsun olup olur olursa oluyor on ona ondan onlar onlardan onları onların onu onun otuz oysa pek rağmen sadece sanki sekiz seksen sen senden seni senin siz sizden sizi sizin tarafından trilyon tüm var vardı ve veya ya yani yapacak yapmak yaptı yaptıkları yaptığı yaptığını yapılan yapılması yapıyor yedi yerine yetmiş yine yirmi yoksa yüz zaten çok çünkü öyle üzere üç şey şeyden şeyi şeyler şu şuna şunda şundan şunları şunu şöyle".split(" ")),r.Pipeline.registerFunction(r.tr.stopWordFilter,"stopWordFilter-tr")}});
\ No newline at end of file
diff --git a/ja/assets/javascripts/lunr/min/lunr.vi.min.js b/ja/assets/javascripts/lunr/min/lunr.vi.min.js
new file mode 100644
index 000000000..22aed28c4
--- /dev/null
+++ b/ja/assets/javascripts/lunr/min/lunr.vi.min.js
@@ -0,0 +1 @@
+!function(e,r){"function"==typeof define&&define.amd?define(r):"object"==typeof exports?module.exports=r():r()(e.lunr)}(this,function(){return function(e){if(void 0===e)throw new Error("Lunr is not present. Please include / require Lunr before this script.");if(void 0===e.stemmerSupport)throw new Error("Lunr stemmer support is not present. Please include / require Lunr stemmer support before this script.");e.vi=function(){this.pipeline.reset(),this.pipeline.add(e.vi.stopWordFilter,e.vi.trimmer)},e.vi.wordCharacters="[A-Za-ẓ̀͐́͑̉̃̓ÂâÊêÔôĂ-ăĐ-đƠ-ơƯ-ư]",e.vi.trimmer=e.trimmerSupport.generateTrimmer(e.vi.wordCharacters),e.Pipeline.registerFunction(e.vi.trimmer,"trimmer-vi"),e.vi.stopWordFilter=e.generateStopWordFilter("là cái nhưng mà".split(" "))}});
\ No newline at end of file
diff --git a/ja/assets/javascripts/lunr/min/lunr.zh.min.js b/ja/assets/javascripts/lunr/min/lunr.zh.min.js
new file mode 100644
index 000000000..fda66e9c5
--- /dev/null
+++ b/ja/assets/javascripts/lunr/min/lunr.zh.min.js
@@ -0,0 +1 @@
+!function(e,r){"function"==typeof define&&define.amd?define(r):"object"==typeof exports?module.exports=r(require("@node-rs/jieba")):r()(e.lunr)}(this,function(e){return function(r,t){if(void 0===r)throw new Error("Lunr is not present. Please include / require Lunr before this script.");if(void 0===r.stemmerSupport)throw new Error("Lunr stemmer support is not present. Please include / require Lunr stemmer support before this script.");var i="2"==r.version[0];r.zh=function(){this.pipeline.reset(),this.pipeline.add(r.zh.trimmer,r.zh.stopWordFilter,r.zh.stemmer),i?this.tokenizer=r.zh.tokenizer:(r.tokenizer&&(r.tokenizer=r.zh.tokenizer),this.tokenizerFn&&(this.tokenizerFn=r.zh.tokenizer))},r.zh.tokenizer=function(n){if(!arguments.length||null==n||void 0==n)return[];if(Array.isArray(n))return n.map(function(e){return i?new r.Token(e.toLowerCase()):e.toLowerCase()});t&&e.load(t);var o=n.toString().trim().toLowerCase(),s=[];e.cut(o,!0).forEach(function(e){s=s.concat(e.split(" "))}),s=s.filter(function(e){return!!e});var u=0;return s.map(function(e,t){if(i){var n=o.indexOf(e,u),s={};return s.position=[n,e.length],s.index=t,u=n,new r.Token(e,s)}return e})},r.zh.wordCharacters="\\w一-龥",r.zh.trimmer=r.trimmerSupport.generateTrimmer(r.zh.wordCharacters),r.Pipeline.registerFunction(r.zh.trimmer,"trimmer-zh"),r.zh.stemmer=function(){return function(e){return e}}(),r.Pipeline.registerFunction(r.zh.stemmer,"stemmer-zh"),r.zh.stopWordFilter=r.generateStopWordFilter("的 一 不 在 人 有 是 为 為 以 于 於 上 他 而 后 後 之 来 來 及 了 因 下 可 到 由 这 這 与 與 也 此 但 并 並 个 個 其 已 无 無 小 我 们 們 起 最 再 今 去 好 只 又 或 很 亦 某 把 那 你 乃 它 吧 被 比 别 趁 当 當 从 從 得 打 凡 儿 兒 尔 爾 该 該 各 给 給 跟 和 何 还 還 即 几 幾 既 看 据 據 距 靠 啦 另 么 麽 每 嘛 拿 哪 您 凭 憑 且 却 卻 让 讓 仍 啥 如 若 使 谁 誰 虽 雖 随 隨 同 所 她 哇 嗡 往 些 向 沿 哟 喲 用 咱 则 則 怎 曾 至 致 着 著 诸 諸 自".split(" ")),r.Pipeline.registerFunction(r.zh.stopWordFilter,"stopWordFilter-zh")}});
\ No newline at end of file
diff --git a/ja/assets/javascripts/lunr/tinyseg.js b/ja/assets/javascripts/lunr/tinyseg.js
new file mode 100644
index 000000000..167fa6dd6
--- /dev/null
+++ b/ja/assets/javascripts/lunr/tinyseg.js
@@ -0,0 +1,206 @@
+/**
+ * export the module via AMD, CommonJS or as a browser global
+ * Export code from https://github.com/umdjs/umd/blob/master/returnExports.js
+ */
+;(function (root, factory) {
+    if (typeof define === 'function' && define.amd) {
+        // AMD. Register as an anonymous module.
+        define(factory)
+    } else if (typeof exports === 'object') {
+        /**
+         * Node. Does not work with strict CommonJS, but
+         * only CommonJS-like environments that support module.exports,
+         * like Node.
+         */
+        module.exports = factory()
+    } else {
+        // Browser globals (root is window)
+        factory()(root.lunr);
+    }
+}(this, function () {
+    /**
+     * Just return a value to define the module export.
+     * This example returns an object, but the module
+     * can return a function as the exported value.
+     */
+
+    return function(lunr) {
+        // TinySegmenter 0.1 -- Super compact Japanese tokenizer in Javascript
+        // (c) 2008 Taku Kudo <taku@chasen.org>
+        // TinySegmenter is freely distributable under the terms of a new BSD licence.
+        // For details, see http://chasen.org/~taku/software/TinySegmenter/LICENCE.txt
+
+        function TinySegmenter() {
+          var patterns = {
+            "[一二三四五六七八九十百千万億兆]":"M",
+            "[一-龠々〆ヵヶ]":"H",
+            "[ぁ-ん]":"I",
+            "[ァ-ヴーｱ-ﾝﾞｰ]":"K",
+            "[a-zA-Zａ-ｚＡ-Ｚ]":"A",
+            "[0-9０-９]":"N"
+          }
+          this.chartype_ = [];
+          for (var i in patterns) {
+            var regexp = new RegExp(i);
+            this.chartype_.push([regexp, patterns[i]]);
+          }
+
+          this.BIAS__ = -332
+          this.BC1__ = {"HH":6,"II":2461,"KH":406,"OH":-1378};
+          this.BC2__ = {"AA":-3267,"AI":2744,"AN":-878,"HH":-4070,"HM":-1711,"HN":4012,"HO":3761,"IA":1327,"IH":-1184,"II":-1332,"IK":1721,"IO":5492,"KI":3831,"KK":-8741,"MH":-3132,"MK":3334,"OO":-2920};
+          this.BC3__ = {"HH":996,"HI":626,"HK":-721,"HN":-1307,"HO":-836,"IH":-301,"KK":2762,"MK":1079,"MM":4034,"OA":-1652,"OH":266};
+          this.BP1__ = {"BB":295,"OB":304,"OO":-125,"UB":352};
+          this.BP2__ = {"BO":60,"OO":-1762};
+          this.BQ1__ = {"BHH":1150,"BHM":1521,"BII":-1158,"BIM":886,"BMH":1208,"BNH":449,"BOH":-91,"BOO":-2597,"OHI":451,"OIH":-296,"OKA":1851,"OKH":-1020,"OKK":904,"OOO":2965};
+          this.BQ2__ = {"BHH":118,"BHI":-1159,"BHM":466,"BIH":-919,"BKK":-1720,"BKO":864,"OHH":-1139,"OHM":-181,"OIH":153,"UHI":-1146};
+          this.BQ3__ = {"BHH":-792,"BHI":2664,"BII":-299,"BKI":419,"BMH":937,"BMM":8335,"BNN":998,"BOH":775,"OHH":2174,"OHM":439,"OII":280,"OKH":1798,"OKI":-793,"OKO":-2242,"OMH":-2402,"OOO":11699};
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+            if (str.match(this.chartype_[i][0])) {
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+        TinySegmenter.prototype.ts_ = function(v) {
+          if (v) { return v; }
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+        TinySegmenter.prototype.segment = function(input) {
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+          for (var i = 4; i < seg.length - 3; ++i) {
+            var score = this.BIAS__;
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+            var c5 = ctype[i+1];
+            var c6 = ctype[i+2];
+            score += this.ts_(this.UP1__[p1]);
+            score += this.ts_(this.UP2__[p2]);
+            score += this.ts_(this.UP3__[p3]);
+            score += this.ts_(this.BP1__[p1 + p2]);
+            score += this.ts_(this.BP2__[p2 + p3]);
+            score += this.ts_(this.UW1__[w1]);
+            score += this.ts_(this.UW2__[w2]);
+            score += this.ts_(this.UW3__[w3]);
+            score += this.ts_(this.UW4__[w4]);
+            score += this.ts_(this.UW5__[w5]);
+            score += this.ts_(this.UW6__[w6]);
+            score += this.ts_(this.BW1__[w2 + w3]);
+            score += this.ts_(this.BW2__[w3 + w4]);
+            score += this.ts_(this.BW3__[w4 + w5]);
+            score += this.ts_(this.TW1__[w1 + w2 + w3]);
+            score += this.ts_(this.TW2__[w2 + w3 + w4]);
+            score += this.ts_(this.TW3__[w3 + w4 + w5]);
+            score += this.ts_(this.TW4__[w4 + w5 + w6]);
+            score += this.ts_(this.UC1__[c1]);
+            score += this.ts_(this.UC2__[c2]);
+            score += this.ts_(this.UC3__[c3]);
+            score += this.ts_(this.UC4__[c4]);
+            score += this.ts_(this.UC5__[c5]);
+            score += this.ts_(this.UC6__[c6]);
+            score += this.ts_(this.BC1__[c2 + c3]);
+            score += this.ts_(this.BC2__[c3 + c4]);
+            score += this.ts_(this.BC3__[c4 + c5]);
+            score += this.ts_(this.TC1__[c1 + c2 + c3]);
+            score += this.ts_(this.TC2__[c2 + c3 + c4]);
+            score += this.ts_(this.TC3__[c3 + c4 + c5]);
+            score += this.ts_(this.TC4__[c4 + c5 + c6]);
+        //  score += this.ts_(this.TC5__[c4 + c5 + c6]);    
+            score += this.ts_(this.UQ1__[p1 + c1]);
+            score += this.ts_(this.UQ2__[p2 + c2]);
+            score += this.ts_(this.UQ3__[p3 + c3]);
+            score += this.ts_(this.BQ1__[p2 + c2 + c3]);
+            score += this.ts_(this.BQ2__[p2 + c3 + c4]);
+            score += this.ts_(this.BQ3__[p3 + c2 + c3]);
+            score += this.ts_(this.BQ4__[p3 + c3 + c4]);
+            score += this.ts_(this.TQ1__[p2 + c1 + c2 + c3]);
+            score += this.ts_(this.TQ2__[p2 + c2 + c3 + c4]);
+            score += this.ts_(this.TQ3__[p3 + c1 + c2 + c3]);
+            score += this.ts_(this.TQ4__[p3 + c2 + c3 + c4]);
+            var p = "O";
+            if (score > 0) {
+              result.push(word);
+              word = "";
+              p = "B";
+            }
+            p1 = p2;
+            p2 = p3;
+            p3 = p;
+            word += seg[i];
+          }
+          result.push(word);
+
+          return result;
+        }
+
+        lunr.TinySegmenter = TinySegmenter;
+    };
+
+}));
\ No newline at end of file
diff --git a/ja/assets/javascripts/lunr/wordcut.js b/ja/assets/javascripts/lunr/wordcut.js
new file mode 100644
index 000000000..0d898c9ed
--- /dev/null
+++ b/ja/assets/javascripts/lunr/wordcut.js
@@ -0,0 +1,6708 @@
+(function(f){if(typeof exports==="object"&&typeof module!=="undefined"){module.exports=f()}else if(typeof define==="function"&&define.amd){define([],f)}else{var g;if(typeof window!=="undefined"){g=window}else if(typeof global!=="undefined"){g=global}else if(typeof self!=="undefined"){g=self}else{g=this}(g.lunr || (g.lunr = {})).wordcut = f()}})(function(){var define,module,exports;return (function e(t,n,r){function s(o,u){if(!n[o]){if(!t[o]){var a=typeof require=="function"&&require;if(!u&&a)return a(o,!0);if(i)return i(o,!0);var f=new Error("Cannot find module '"+o+"'");throw f.code="MODULE_NOT_FOUND",f}var l=n[o]={exports:{}};t[o][0].call(l.exports,function(e){var n=t[o][1][e];return s(n?n:e)},l,l.exports,e,t,n,r)}return n[o].exports}var i=typeof require=="function"&&require;for(var o=0;o<r.length;o++)s(r[o]);return s})({1:[function(require,module,exports){
+var _ = require("underscore");
+
+var Acceptors = {
+  creators: null,
+  current: null,
+  tag: null,
+
+  init: function() {
+    this.creators = [];
+    this.current = [];
+    this.tag = {};
+  },
+
+  reset: function() {
+    this.current = [];
+    this.tag = {}
+  },
+
+  transit: function(ch) {
+    var self = this;
+
+    self.creators.forEach(function(creator) {
+      var acceptor = creator.createAcceptor(self.tag);
+      if (acceptor) 
+        self.current.push(acceptor);
+    });
+    
+    var _current = [];
+    self.tag = {};
+
+    for (var i = 0; i < self.current.length; i++) {
+      var _acceptor = self.current[i]
+        , acceptor = _acceptor.transit(ch);
+      
+      if (!acceptor.isError) {
+        _current.push(acceptor);
+        self.tag[acceptor.tag] = acceptor;
+      }
+    }
+    self.current = _current;
+
+  },
+
+  getFinalAcceptors: function() {    
+    return this.current.filter(function(acceptor) {
+      return acceptor.isFinal;
+    });
+  }
+};
+
+module.exports = function() {
+  var acceptors = _.clone(Acceptors);
+  acceptors.init();
+  return acceptors;
+};
+
+},{"underscore":25}],2:[function(require,module,exports){
+(function (__dirname){
+
+var LEFT = 0;
+var RIGHT = 1;
+var path = require("path");
+var glob = require("glob");
+
+var WordcutDict = {
+
+
+  init: function (dictPathFile, withDefault, words) {
+    withDefault = withDefault || false
+    var defaultDict = path.normalize(__dirname + "/..") + "/data/tdict-*.txt";
+    this.dict=[]
+    var dictPathIsDefined = dictPathFile !== undefined
+    var dictPath = (withDefault || !dictPathIsDefined) ? [defaultDict]: [];
+    var dictPathFile = dictPathFile || defaultDict
+
+    if(dictPathIsDefined){
+      if (Array.isArray(dictPathFile)) {
+        dictPath.concat.apply(dictPath, dictPathFile);
+      } else {
+        dictPath.push(dictPathFile)
+      }
+    }
+
+    this.addFiles(dictPath, false)
+
+    if(words!==undefined){
+      this.addWords(words, false)
+    }
+    this.finalizeDict();
+  },
+
+  addWords: function(words, finalize){
+    finalize = finalize===undefined || finalize;
+    this.dict.push.apply(this.dict, words)
+    if(finalize){
+      this.finalizeDict();
+    }
+  },
+
+  finalizeDict: function(){
+    this.dict = this.sortuniq(this.dict);
+  },
+
+  addFiles: function(files, finalize){
+    finalize = finalize===undefined || finalize;
+    
+    for (var i = 0; i < 1; i++) {
+      var words = "ก.ก.\nก.ก.น.\nก.ข.ค.\nก.ค.\nก.จ.\nก.ช.น.\nก.ฌ.\nก.ต.\nก.ต.ง.\nก.ต.ช.\nก.ตร.\nก.ท.\nก.น.ช.\nก.บช.\nก.บถ.\nก.ป.ส.\nก.พ.\nก.ม.\nก.ย.\nก.ร.\nก.ล.ต.\nก.ว.\nก.ศ.ว.\nก.ส.ท.\nก.ส.ธ.\nก.ส.อ.\nก.อ.\nกก.ตชด.\nกก.ตร.น.\nกก.ภ.จว.\nกก.รสช.\nกกบ.ขส.ทบ.\nกกล.รพน.\nกง.กห.\nกง.ทบ.\nกง.ทร.\nกซข.ป.\nกซม.ป.\nกทม.กรุงเทพมหานคร\nกบ.ทบ.\nกป.สป.\nกพ.ทบ.\nกพ.ทร.\nกพ.ทหาร\nกร.ทบ.\nกรป.กลาง\nกรอ.พอ.\nกศ.ด.\nกศ.บ.\nกศ.บป.\nกศ.ม.\nกษ.ด.\nกษ.บ.\nกษ.ม.\nกส.ด.\nกส.ทบ.\nกส.บ.\nกส.ม.\nกอ.ปค.\nกอ.รพน.\nกอ.รมน.\nกอ.รสต.\nข.ต.ว.\nขว.ทบ.\nขว.ทร.\nขว.ทหาร\nขส.ทบ.\nขส.ทร.\nขส.ทอ.\nค.ด.\nค.บ.\nค.พ.ศ.\nค.ม.\nค.ร.น.\nค.ร.ฟ.\nค.ร.ม.\nค.ศ.\nค.อ.ด.\nค.อ.บ.\nค.อ.ม.\nคศ.ด.\nคศ.บ.\nคศ.ม.\nง.ด.\nจ.จ.\nจ.จ.จ.\nจ.ช.\nจ.ต.\nจ.ท.\nจ.ป.ร.\nจ.ม.\nจ.ศ.\nจ.ส.ต.\nจ.ส.ท.\nจ.ส.อ.\nจ.อ.\nจ.อ.ร.\nจ.๑๘\nจก.ธน.\nจก.สน.\nช.ค.\nช.ค.บ.\nช.พ.ค.\nช.ส.\nช.ส.ค.\nฌ.ป.ค.\nฌ.ศ.ร.\nฌ.ส.อ.\nฐท.สห.\nด.ช.\nด.ญ.\nด.ต.\nด.ศ.ค.\nด.ศ.ร.\nดย.ทร.\nต.ก.\nต.ค.\nต.จ.\nต.จ.ว.\nต.ช.\nต.ต.\nต.บ.\nต.ม.\nต.ร.\nต.ศ.ร.\nต.ห.\nต.อ.\nต.อ.จ.\nตร.กม.\nตร.ซม.\nตร.ต.\nตร.ทล.\nตร.น.\nตร.ปม.\nตร.ภ.\nตร.ม.\nตร.รฟ.\nตร.ว.\nตร.ส.\nตร.สข.\nท.จ.\nท.จ.ว.\nท.ช.\nท.ญ.\nท.ด.\nท.ท.ท.\nท.ทบ.\nท.บ.\nท.พ.\nท.ม.\nท.ศ.\nทก.ด.\nทก.บ.\nทก.ม.\nทส.ปช.\nทส.รมว.กห.\nทุ.ส.นิ.ม.\nธ.ก.ส.\nธ.ค.\nธ.ญ\nธ.บ.\nน.ช.\nน.ญ.\nน.ด.\nน.ต.\nน.ท.\nน.น.\nน.บ.\nน.บ.ท.\nน.ป.ท.\nน.พ.\nน.ม.\nน.ร.\nน.ว.\nน.ศ.\nน.ส.\nน.ส.พ.\nน.ส.๓\nน.สพ.\nน.อ.\nนปพ.ภ.\nนศ.ด.\nนศ.บ.\nนศ.ม.\nบ.ก.\nบ.ข.ส.\nบ.ช.\nบ.ด.ท.\nบ.ตร.\nบ.ภ.\nบ.ม.\nบก.จร.\nบก.ตชด.\nบก.ตม.\nบก.ทล.\nบก.น.\nบก.ป.\nบก.ปค.\nบก.ปม.\nบก.ภ.เขต\nบก.รน.\nบก.รฟ.\nบก.ร้อย.ตชด.\nบก.ส.\nบกข.ป.\nบจพ.ป.\nบช.ก.\nบช.ด.\nบช.ตชด.\nบช.น.\nบช.บ.\nบช.ปส.\nบช.ภ.\nบช.ม.\nบชท.ป.\nบชน.ป.\nบชส.ป.\nบธ.ด.\nบธ.บ.\nบธ.ม.\nบนท.ป.\nบนอ.ป.\nบปช.ป.\nป.กท.\nป.กศ.\nป.กศ.สูง\nป.จ.\nป.จ.ว.\nป.ช.\nป.ธ.\nป.ป.\nป.ป.ก.\nป.ป.ช.\nป.ป.ป.\nป.ป.ร.\nป.ป.ส.\nป.พ.\nป.พ.พ.\nป.พย.\nป.ม.\nป.ม.ก.\nป.ม.ช.\nป.ม.ธ.\nป.ม.ศ.\nป.ม.อ.\nป.ร.ร.๔\nป.ร.ร.๕\nป.ร.ร.๖\nป.ล.\nป.ว.พ.\nป.วิ.อ.\nป.ส.ส.\nป.อ.\nป.อ.ร.ส.\nป.๑\nปม.วส.\nปอ.พ.\nผกก.ภ.\nผช.ผอ.\nผต.มท.\nผบ.ตร.\nผบ.ทบ.\nผบ.ทร.\nผบ.ทสส.\nผบ.ทอ.\nผบก.น.\nผบก.ป.\nผบก.ปค.\nผบก.ปม.\nผบก.ภ.\nผบช.ก.\nผบช.ตชด.\nผบช.น.\nผบช.ภ.\nผว.กทม.\nผอ.ปจ.\nพ.ก.ง.\nพ.กศ.\nพ.ข.ต.\nพ.ค.\nพ.ค.ช.\nพ.ค.ว.\nพ.ค.ศ.\nพ.จ.ต.\nพ.จ.ท.\nพ.จ.อ.\nพ.ช.\nพ.ช.ค.\nพ.ด.\nพ.ต.\nพ.ต.ต.\nพ.ต.ท.\nพ.ต.อ.\nพ.ต.อ.พิเศษ\nพ.ท.\nพ.บ.\nพ.ป.\nพ.ภ.ม.\nพ.ม.\nพ.ม.ช.\nพ.ย.\nพ.ร.ก.\nพ.ร.ฎ.\nพ.ร.ต.\nพ.ร.ธ.\nพ.ร.บ.\nพ.ศ.\nพ.ศ.บ.\nพ.ส.ร.\nพ.ส.ล.\nพ.อ.\nพ.อ.ต.\nพ.อ.ท.\nพ.อ.พิเศษ\nพ.อ.อ.\nพณ.ด.\nพณ.บ.\nพณ.ม.\nพธ.ด.\nพธ.บ.\nพธ.ม.\nพบ.ด.\nพบ.บ.\nพบ.ม.\nพย.ด.\nพย.บ.\nพย.ม.\nพล.จ.\nพล.ต.\nพล.ต.จ.\nพล.ต.ต.\nพล.ต.ท.\nพล.ต.อ.\nพล.ท.\nพล.ปตอ.\nพล.ม.\nพล.ม.๒\nพล.ร.จ.\nพล.ร.ต.\nพล.ร.ท.\nพล.ร.อ.\nพล.อ.\nพล.อ.จ.\nพล.อ.ต.\nพล.อ.ท.\nพล.อ.อ.\nพลา.ทร.\nพศ.ด.\nพศ.บ.\nพศ.ม.\nพอ.สว.\nภ.ง.ด.\nภ.ง.ด.๙\nภ.ด.\nภ.บ.\nภ.บ.ท.๕\nภ.ป.ร.\nภ.พ.\nภ.ม.\nภ.สถ.บ.\nม.ค.\nม.จ.\nม.ป.ท.\nม.ป.ป.\nม.ป.พ.\nม.ร.ว.\nม.ศ.\nม.อ.\nม.อ.ปัตตานี\nมิ.ย.\nมี.ค.\nยศ.ทบ.\nยศ.ทร.\nยศ.ทอ.\nร.ง.\nร.ด.\nร.ต.\nร.ต.ต.\nร.ต.ท.\nร.ต.อ.\nร.ท.\nร.น.\nร.บ.\nร.พ.\nร.ฟ.ล.\nร.ย.ล.\nร.ย.ส.ท.\nร.ล.\nร.ศ.\nร.ส.พ.\nร.อ.\nรป.ม.\nรร.จปร.\nรร.จอ.\nรร.ชท.\nรร.ตท.\nรร.นร.\nรร.นรต.\nรร.นอ.\nล.ญ.\nล.ว.\nลส.ชบ.\nว.ค.\nว.ฉ.\nว.ช.\nว.ด.ป.\nว.ป.ถ.\nวท.บ.\nศ.บ.\nศ.ป.ก.\nศ.ศ.ป.\nศฝร.ภ.\nศศ.บ.\nศษ.บ.\nศส.บ.\nส.ก.\nส.ก.ศ.ท.\nส.ค.\nส.ค.1\nส.ค.ร.\nส.ค.ส.\nส.ต.\nส.ต.ต.\nส.ต.ท.\nส.ต.อ.\nส.ท.\nส.ทร.\nส.ป.ช.\nส.ป.ส.ท.\nส.ป.อ.\nส.ร.\nส.ล.น.\nส.ว.\nส.ว.ท.\nส.ว.ส.ท.\nส.ส.\nส.ส.ท.\nส.ส.ร.\nส.ห.\nส.อ.\nสถ.บ.\nสนง.สสอ.\nสพ.ญ.\nสพ.บ.\nสว.จร.\nสว.ธร.\nสว.ส.\nสว.สป.\nสว.สส.\nสว.อก.\nสส.บ.\nสุ.จิ.ปุ.ลิ.\nห.ร.ม.\nอ.ก.ค.\nอ.ก.จ.\nอ.จ.\nอ.ช.พ.\nอ.ตร.\nอ.บ.\nอ.ส.ท.\nอ.ส.ม.ท.\nอ.ส.ย.\nอ.อ.ป.\nอส.รด.\nอุ.อา.ก.ส.\nฮ.จ.\nฮ.ท.\nฮ.ฝ.\nฮ.ล.\nฮ.ศ.\nเม.ย.\n\nกรีนิช\nกลันตัน\nกัลกัตตา\nกัวลาลัมเปอร์\nกัศมีร์\nกาฐมาณฑุ\nโกลกาตา\nควิเบก\nคอนเนตทิคัต\nคาบูล\nคุชราต\nคุนหมิง\nเคนตักกี\nเคนทักกี\nเคมบริดจ์\nแคชเมียร์\nแคนซัส\nแคนเบอร์รา\nแคโรไลนา\nแคลิฟอร์เนีย\nโคเปนเฮเกน\nโคลัมโบ\nโคโลราโด\nไครสต์เชิร์ช\nไคโร\nจาการ์ตา\nจำปาศักดิ์\nเจนไน\nเจนีวา\nเจ้อเจียง\nฉงชิ่ง\nเฉิงตู\nชานตง\nชิคาโก\nเชนไน\nเชอร์โนบิล\nซัปโปโร\nซานมารีโน\nซาบาห์\nซาราเยโว\nซาราวัก\nซิดนีย์\nซีอาน\nซีแอตเทิล\nซูริก\nซูริค\nเซเชลส์\nเซนได\nเซี่ยงไฮ้\nโซเฟีย\nโซล\nโซโลมอน\nไซ่ง่อน\nไซบีเรีย\nดัลลัส\nดาโคตา\nดานัง\nดีทรอยต์\nดูไบ\nเดนเวอร์\nเดลาแวร์\nเดียนเบียนฟู\nโดเวอร์\nโดฮา\nไดฟุกุ\nไดฟูกุ\nตรังกานู\nตริโปลี\nตูวาลู\nเตหะราน\nโตเกียว\nโตรอนโต\nทมิฬนาฑู\nทริโปลี\nทิเบต\nเทกซัส\nเท็กซัส\nเทนเนสซี\nเทลอาวีฟ\nแทสเมเนีย\nโทรอนโต\nไทเป\nธากา\nนางาซากิ\nนาริตะ\nนิวเจอร์ซีย์\nนิวเดลี\nนิวยอร์ก\nนิวยอร์ค\nนิวแฮมป์เชียร์\nเนบราสกา\nเนแบรสกา\nเนวาดา\nบรัสเซลส์\nบราซิเลีย\nบอมเบย์\nบอสตัน\nบังกาลอร์\nบังคาลอร์\nบูคาเรสต์\nบูดาเปสต์\nเบงกาซี\nเบนกาซี\nเบรุต\nเบลเกรด\nเบอร์ลิน\nแบกแดด\nปอยเปต\nปะลิส\nปะหัง\nปักกิ่ง\nปัญจาบ\nปัฏนา\nปารีส\nปีนัง\nเประ\nเปียงยาง\nพนมเปญ\nพระตะบอง\nพะโค\nพะสิม\nพาราณสี\nพิหารี\nเพนซิลวาเนีย\nเพนซิลเวเนีย\nฟรานซ์\nฟลอริดา\nฟิลาเดลเฟีย\nฟุกุชิมะ\nฟุกุชิมา\nฟุกุโอกะ\nฟูกูโอกะ\nแฟรงก์เฟิร์ต\nมอสโก\nมะนิลา\nมะละแหม่ง\nมัณฑะเลย์\nมัทราส\nมาดริด\nมิชิแกน\nมินนิโซตา\nมิยางิ\nมิลาน\nมิวนิก\nมิสซูรี\nมุมไบ\nเมน\nเมลเบิร์น\nเมาะตะมะ\nเมาะลำเลิง\nแมนจูเรีย\nแมนเชสเตอร์\nแมนฮัตตัน\nแมริแลนด์\nแมรีแลนด์\nแมสซาชูเซตส์\nยะไข่\nย่างกุ้ง\nยูทาห์\nยูนนาน\nเยรูซาเล็ม\nโยโกฮามา\nริยาด\nรีโอเดจาเนโร\nโรดไอแลนด์\nลอนดอน\nลอสแองเจลิส\nลาปาซ\nลาสเวกัส\nลิสบอน\nลุยเซียนา\nโลซาน\nโลซานน์\nวอชิงตัน\nวอร์ซอ\nวิสคอนซิน\nเวนิส\nเวลส์\nเวอร์จิเนีย\nเวอร์มอนต์\nเวียงจันทน์\nเวียนนา\nแวนคูเวอร์\nไวโอมิง\nสกอตแลนด์\nสก็อตแลนด์\nสตอกโฮล์ม\nสลังงอร์\nเสฉวน\nเสียมราฐ\nเสียมเรียบ\nหงสา\nหงสาวดี\nหนานไห่\nหลวงพระบาง\nหูเป่ย\nหูเป่ย์\nหูหนาน\nเหอเป่ย\nเหอเป่ย์\nเหอหนาน\nอชันตา\nอลาสกา\nอวันตี\nออริกอน\nออสโล\nอะแลสกา\nอัตตะปือ\nอัมมาน\nอัมสเตอร์ดัม\nอัสสัม\nอาบูดาบี\nอาร์คันซอ\nอินเดียนา\nอิบารากิ\nอิลลินอยส์\nอิสตันบูล\nอิสลามาบัด\nอุรุมชี\nอูลานบาตอร์\nเอดินบะระ\nเอเธนส์\nแอตแลนตา\nแอริโซนา\nแอลเจียร์\nโอคลาโฮมา\nโอค็อตสค์\nโอกินาวา\nโอซากา\nโอริสสา\nโอเรกอน\nโอไฮโอ\nไอดาโฮ\nไอโอวา\nฮอนโนลูลู\nฮานอย\nฮาเนดะ\nฮาราเร\nฮาวาย\nฮิโรชิมา\nฮุสตัน\nเฮลซิงกิ\n\nมกรา\nกุมภา\nมีนา\nเมษา\nพฤษภา\nมิถุนา\nกรกฎา\nสิงหา\nกันยา\nตุลา\nพฤศจิกา\nธันวา\nเอ\nบี\nซี\nดี\nอี\nเอฟ\nจี\nเอช\nไอ\nเจ\nเค\nแอล\nเอ็ม\nเอ็น\nโอ\nพี\nคิว\nอาร์\nเอส\nที\nยู\nวี\nดับเบิล\nดับบลิว\nเอ็กซ์\nเอ๊กซ์\nวาย\nแซด\nแอลฟา\nแอลฟ่า\nเบตา\nเบต้า\nแกมมา\nแกมม่า\nเดลตา\nเดลต้า\nโอเมกา\nโอเมก้า\nเมกะ\nกิกะ\nนาโน\nไมโคร\n\nกรรมาชน\nกรอบรูป\nกระดี๊กระด๊า\nกระบับ\nกราวนด์\nกรีน\nกรุ๊ป\nกฤษณ์\nกลาส\nก๊วน\nกษัตริยา\nกษัตริยาธิราช\nก่อนหน้า\nกะบับ\nกับดัก\nกัมมันตะ\nก๊าก\nก๋ากั่น\nกาญจน์\nกาญจนาภิเษก\nกามิกาเซ่\nการันตี\nกาหลิบ\nกิฟท์\nกิมจิ\nกีวี\nกึ๊ก\nกึ๋ย\nกุนซือ\nกุมภาพันธ์\nกู๋\nเกจิ\nเกมส์\nเกย์\nเกรด\nเกรย์\nเกสต์เฮาส์\nเก๊ะ\nเก๋ากี้\nเกิร์ล\nแกงค์\nแกรนด์\nแกสโซฮอล์\nแก๊สโซฮอล์\nโกเต็กซ์\nโกลด์\nโกะ\nโก๊ะ\nไกด์\nขั้นตอน\nเขวี้ยง\nคณาญาติ\nครัวซอง\nครัวซองต์\nคร่ำครวญ\nครีเอทีฟ\nครูเสด\nคลับ\nคลาสสิก\nคลิตอริส\nคลิป\nความหมาย\nควิก\nควีน\nคองเกรส\nคอนซูเมอร์\nคอนเซปต์\nคอนเซ็ปต์\nคอนโด\nคอนโดมิเนียม\nคอนเทนเนอร์\nคอนแทค\nคอนแท็ค\nคอนโทรล\nคอนเฟิร์ม\nคอปเตอร์\nคอมพ์\nคอมเพล็กซ์\nคอมมอนส์\nคอมเมนท์\nคอมเมนต์\nคอร์ป\nคอร์ปอเรชั่น\nคอร์รัปชัน\nคอร์รัปชั่น\nคอรัปชัน\nคอรัปชั่น\nคอร์ส\nคอลเล็กชั่น\nคอลัมน์\nคอลัมนิสต์\nคัตเอาต์\nคันคาก\nคันถธุระ\nคันธาระ\nคันยิ\nคัสตาร์ด\nคาราโอเกะ\nคีตกวี\nคีตปฏิภาณ\nคีตราชัน\nคาปูชิโน\nคามิคาเซ่\nคาเฟ่\nคาร์\nคาร์โก้\nคาราเมล\nคาแรกเตอร์\nคาแร็กเตอร์\nคาแรคเตอร์\nคาแร็คเตอร์\nคาวบอย\nคาสิโน\nคิกขุ\nคิวบิก\nคูลเลอร์\nเคบับ\nเครป\nเคลม\nเคลียร์\nเคลื่อนย้าย\nเคส\nเคอร์ฟิว\nแคชเชียร์\nแคทวอล์ค\nแคนดิเดต\nแคนตาลูป\nแคนยอน\nแคนู\nแคป\nแคมป์\nแคมปัส\nแคมเปญ\nแคร์\nแครกเกอร์\nแคร็กเกอร์\nแครอท\nแคสต์\nแคสติง\nแคสติ้ง\nโค้ก\nโค้ช\nโคโยตี\nโคโยตี้\nโครนา\nโคอะล่า\nโคอาลา\nโคอาล่า\nไคลแมกซ์\nไคลแม็กซ์\nงั้น\nง่าว\nงี้\nเง็ง\nโง่เขลา\nไง\nจตุคาม\nจ๊อกกี้\nจอหงวน\nจังโก้\nจัมโบ้\nจ๊าบ\nจารกรรม\nจารชน\nจิ๊ก\nจิ๊กโก๋\nจิ๊กซอว์\nจิตพิสัย\nจิตเภท\nจีดีพี\nจึ๊ก\nจุ๊ย\nจูน\nจูเนียร์\nเจ๊\nเจได\nเจ็ต\nเจล\nเจ๊าะแจ๊ะ\nเจี๊ยว\nแจ็กเก็ต\nแจ๊กเก็ต\nแจ็กพอต\nแจ็กพ็อต\nแจ๊กพอต\nแจ๊กพ็อต\nแจม\nแจ๊ส\nโจ๋\nฉลุย\nเฉิ่ม\nชนะเลิศ\nช็อค\nช็อต\nช็อป\nช็อปปิ้ง\nช็อปเปอร์\nชะโนด\nชัตเตอร์\nชัวร์\nชาร์จ\nชาร์ต\nชาร์ป\nชินบัญชร\nชิฟฟอน\nชีส\nชีอะห์\nเช็ก\nเช็งเม้ง\nเชฟ\nเชลียร์\nเชอร์รี่\nแชเชือน\nแช่แข็ง\nแชมป์\nแชมปิยอง\nแชมเปญ\nแชมเปี้ยน\nแชมพู\nโชว์รูม\nโชห่วย\nใช้งาน\nไชน่า\nซ้อ\nซอมบี้\nซะ\nซังเต\nซันตาคลอส\nซัพพลาย\nซัพพลายเออร์\nซัมเมอร์\nซากุระ\nซาดิสต์\nซาดิสม์\nซาตาน\nซานตาคลอส\nซาฟารี\nซาบะ\nซามูไร\nซาร์\nซาร์ดีน\nซาเล้ง\nซิง\nซิ่ง\nซิงเกิล\nซิตี\nซิตี้\nซินโดรม\nซิม\nซิ้ม\nซิมโฟนี\nซิมโฟนี่\nซิลเวอร์\nซี้\nซี้ซั้ว\nซีดาน\nซีน\nซีนีเพล็กซ์\nซีเนียร์\nซีร็อกซ์\nซีรีส์\nซีเรียส\nซีอีโอ\nซื่อบื้อ\nซุนหนี่\nซุปเปอร์\nซูชิ\nซูเปอร์\nซูม\nซูโม่\nซูเอี๋ย\nซูฮก\nเซ็กซ์\nเซ็กซี่\nเซ็กส์\nเซนเซอร์\nเซ็นเซอร์\nเซนเตอร์\nเซ็นเตอร์\nเซ็นทรัล\nเซนส์\nเซ่นไหว้\nเซฟตี้\nเซรามิก\nเซลส์\nเซลส์แมน\nเซอร์\nเซอร์ไพรส์\nเซอร์วิส\nเซาท์\nเซี้ยว\nแซ็ก\nแซกโซโฟน\nแซ็กโซโฟน\nแซนด์วิช\nแซมบ้า\nแซลมอน\nแซว\nโซเชียล\nโซน\nโซนี่\nโซลาร์\nโซโล\nโซโล่\nญาณทัสสนะ\nดยุก\nดยุค\nดร็อป\nดรัมเมเยอร์\nดรามา\nดราม่า\nดอกเตอร์\nด็อกเตอร์\nดัมพ์\nดั๊มพ์\nดาวน์\nดิกชันนารี\nดิสเครดิต\nดีกรี\nดีเจ\nดีไซน์\nดีไซน์เนอร์\nดีไซเนอร์\nดีเบต\nดีพาร์ตเมนต์\nดีพาร์ตเมนท์\nดีพาร์ทเมนต์\nดีพาร์ทเมนท์\nดีมานด์\nดีล\nดีลเลอร์\nดีเลย์\nเดชานุภาพ\nเดบิต\nเดโม\nเดย์\nเด้อ\nเดอะ\nเด๊ะ\nเดี้ยง\nเดี๊ยะ\nแดนซ์\nแดนเซอร์\nแดรี่\nโดนัท\nโดมิโน\nโดรายากิ\nไดเอ็ต\nตถตา\nตนเอง\nตรวจทาน\nตรวจสอบ\nตอกย้ำ\nต๊อง\nต่อยอด\nต่อรอง\nตะหงิด\nตังค์\nตันเถียน\nตัวตน\nตัวเอง\nตาปรือ\nต้าอ่วย\nติงต๊อง\nติ๋ม\nติ่มซำ\nติว\nติวเตอร์\nตี๋\nตื้บ\nตุ๊ก\nตุ๊กตุ๊ก\nตุ๊ด\nตุ๋ย\nตู้เซฟ\nเต๊ะ\nเตี๊ยม\nแตงกวา\nแตงโม\nแต๋ว\nโต๋เต๋\nโต๊ะจีน\nไตรมาส\nถ่ายทำ\nถูกต้อง\nทงคัตสึ\nทริป\nทรู\nทอม\nท็อป\nทอร์นาโด\nทอล์ค\nทักซิโด\nทันตกรรม\nทันตแพทยศาสตร์\nทับซ้อน\nทัวร์\nทัวร์นาเมนต์\nทัวร์นาเมนท์\nทัวริสต์\nทาเลนต์\nทาวน์\nทาวน์เฮาส์\nทำงาน\nทิป\nทิพยสมบัติ\nทิวลิป\nทีรามิสุ\nทีวี\nทูน่า\nเท็กซ์\nเทค\nเทคโน\nเทคโนแครต\nเทควันโด\nเทป\nเทรด\nเทรนด์\nเทรนเนอร์\nเทรลเลอร์\nเทรลเล่อร์\nเทเลกราฟ\nเทวบัญชา\nเทวบุตร\nเทวา\nเทวาธิราช\nเทโวโรหนะ\nเทอร์โบ\nเที่ยงคืน\nเที่ยงวัน\nเทียมทาน\nแทกติค\nแทคติค\nแทงกั๊ก\nแทงโก้\nโทมาฮอก\nโทมาฮอว์ก\nโทมาฮอว์ค\nโทร\nโทรโข่ง\nไทม์\nไทยแลนด์\nไทเฮา\nธรรมา\nธรรมาภิบาล\nธัมโม\nธีม\nธุรกรรม\nธุหร่ำ\nเธค\nนพมาศ\nนรีแพทย์\nน็อก\nน็อค\nน้องใหม่\nนอมินี\nนอร์ท\nน่ะ\nนางแบบ\nนาฏยศาลา\nนายแบบ\nนายพราน\nนินจา\nนิรันดร์\nนิว\nนิวส์\nนู้ด\nเนอะ\nเนิร์สเซอรี\nเนิร์สเซอรี่\nเนี้ยบ\nโนติส\nไนท์\nไนน์\nบรรพชน\nบร็อกโคลี\nบร็อคโคลี\nบรา\nบริกร\nบริวเวอรี่ส์\nบลอนด์\nบลูเบอร์รี\nบลูเบอร์รี่\nบ๊วย\nบอกซ์\nบ็อกซ์\nบ๊อกซ์\nบอดี้\nบอนด์\nบ๊อบ\nบอมบ์\nบ๋อย\nบอยคอต\nบอยคอตต์\nบอร์ด\nบังเกอร์\nบัตเตอร์\nบัลลาสต์\nบัส\nบาบูน\nบาร์บีคิว\nบาร์บี้\nบาลานซ์\nบิ๊ก\nบิล\nบึม\nบึ้ม\nบุญคุณ\nบุ๋น\nบุปผา\nบู๊\nบูชิโด\nบูติก\nบูติค\nบูม\nเบเกอรี่\nเบญจมบพิตร\nเบตาดีน\nเบนโตะ\nเบนโล\nเบบี้\nเบลอ\nเบอร์เกอร์\nเบอร์รี\nเบิร์ด\nเบิร์น\nแบ็กโฮ\nแบคโฮ\nแบด\nแบต\nแบนเนอร์\nแบรนด์\nแบล็ก\nแบล็ค\nไบโอ\nโบกี้\nโบตั๋น\nโบ้ย\nโบรกเกอร์\nโบรชัวร์\nโบว์\nโบว์ลิ่ง\nไบเบิล\nปฏิสัมพันธ์\nป๊อก\nปอดแหก\nป๊อป\nป๋อหลอ\nปักขคณนา\nปัจเจกชน\nปัจฉิมนิเทศ\nป๊า\nป๋า\nป่าไม้\nปาร์ตี้\nปาสกาล\nปาสคาล\nปาสเตอร์\nปิกอัพ\nปิ๊ง\nปิโตรเคมี\nปิยมิตร\nปึ้ก\nปูอัด\nเปโซ\nเป็นไง\nเปปเปอร์มินต์\nเปเปอร์\nเปราะบาง\nเป๊ะ\nเป่ายิงฉุบ\nเป่ายิ้งฉุบ\nเปียโน\nแป้ก\nแป๋ว\nแป๊ะเจี๊ยะ\nโปร\nโปรเจกต์\nโปรเจ็กต์\nโปรเจกเตอร์\nโปรเจ็กเตอร์\nโปรเจคท์\nโปรเจ็คท์\nโปรดักชั่น\nโปรดิวเซอร์\nโปรโมชั่น\nโปรโมต\nโปรโมเตอร์\nโปรโมท\nโปลิศ\nโปสเตอร์\nผลไม้\nผลักดัน\nผ้าห่ม\nผิดพลาด\nผู้นำ\nแผดเผา\nเฝอ\nพงษ์\nพริตตี้\nพรีเซนต์\nพรีเซ็นเตอร์\nพรีเมียม\nพรีเมียร์\nพฤหัส\nพล็อต\nพลาซ่า\nพลานุภาพ\nพ่อค้า\nพอเพียง\nพะเรอ\nพันธกิจ\nพันธุวิศวกรรม\nพาร์\nพาร์ตเนอร์\nพาร์ทเนอร์\nพาวเวอร์\nพาสเจอร์ไรส์\nพาสตา\nพาสต้า\nพาสปอร์ต\nพาเหรด\nพิซซ่า\nพีเรียด\nพุดดิ้ง\nพุทธภูมิ\nพุทธศตวรรษ\nพุทโธ\nพูล\nเพทนาการ\nเพนกวิน\nเพนตากอน\nเพรส\nเพรียวบาง\nเพลซ\nเพลท\nเพลย์บอย\nเพียบแปร้\nเพียว\nเพาเวอร์\nแพกเกจ\nแพ็ค\nแพตเทิร์น\nแพทเทิร์น\nแพทยสภา\nแพนงเชิญ\nแพนดา\nแพนด้า\nแพลน\nโพลล์\nโพลารอยด์\nโพสต์\nไพลิน\nฟยอร์ด\nฟรังก์\nฟรุต\nฟลอร์\nฟลุก\nฟลุค\nฟลุต\nฟลุท\nฟอยล์\nฟอร์ม\nฟันด์\nฟาวล์\nฟาสต์ฟู้ด\nฟินิกซ์\nฟิวเจอร์\nฟีด\nฟีเวอร์\nฟุตบาท\nเฟรช\nเฟรชชี่\nเฟรม\nเฟมินิสต์\nเฟส\nเฟอร์นิเจอร์\nเฟอร์รี่\nเฟิร์ม\nเฟี้ยวฟ้าว\nแฟกซ์\nแฟ็กซ์\nแฟนซี\nแฟนตาซี\nแฟ้บ\nแฟร์\nแฟรนไชส์\nแฟรี\nแฟรี่\nแฟลช\nแฟล็ต\nโฟน\nโฟม\nโฟล์ค\nไฟต์\nไฟแนนซ์\nไฟลต์\nไฟลท์\nภควัทคีตา\nภควัมบดี\nภควัมปติ\nภคันทลาพาธ\nภววิสัย\nภารตะ\nภูมิทัศน์\nม้ง\nมวลชน\nมยุราภิรมย์\nมลภาวะ\nมหภาค\nมหาอุปราชา\nมอคคา\nมอคค่า\nมอนสเตอร์\nม็อบ\nมอบตัว\nมอยส์เจอไรเซอร์\nมอลล์\nมะกัน\nมั้ง\nมัฟฟิน\nมั้ย\nม้านั่ง\nมาเฟีย\nมาม่า\nมายองเนส\nมายาคติ\nมาร์ก\nมาร์เก็ต\nมาร์เก็ตติ้ง\nมาร์ค\nมาร์จิน\nมาร์ช\nมาร์ต\nมาร์ท\nมาราธอน\nม้าหินอ่อน\nมินต์\nมินท์\nมินิ\nมิลค์\nมิวสิค\nมิสซัง\nมิสไซล์\nมิสเตอร์\nมือถือ\nมุมมอง\nเมคอัพ\nเมจิก\nเมจิค\nเมทัล\nเมเปิล\nเมาท์\nเมี่ยงคำ\nแมกกาซีน\nแม็กกาซีน\nแมคเคอเรล\nแม่ค้า\nแมชชีน\nแมชีน\nแมนชั่น\nแมมบ้า\nแมมโบ้\nโมจิ\nโมเดล\nโมเดิร์น\nโมเต็ล\nโมโนเรล\nโมหจริต\nไมค์\nไมเกรน\nยนตรกรรม\nยอมรับ\nยะเยือก\nยังไง\nยากูซ่า\nยาวี\nยิม\nยิว\nยุวทูต\nยูโทเปีย\nยูโร\nยูวี\nเยน\nเยลลี่\nเย้ว\nเยอบีรา\nเยอบีร่า\nเยอร์บีรา\nเยอร์บีร่า\nแยมโรล\nโยเกิร์ต\nโยโย่\nรวมมิตร\nร็อค\nร็อคเก็ต\nรองรับ\nรอมฎอน\nรอยัลตี้\nระโงก\nรันเวย์\nรัม\nรากหญ้า\nราชบัณฑิตยสถาน\nราชานุญาต\nราชานุสาวรีย์\nรามเทพ\nรามาธิบดี\nรามายณะ\nราเม็ง\nราเมน\nรายชื่อ\nราสเบอร์รี\nริกเตอร์\nริคเตอร์\nรีไซเคิล\nรีดไถ\nรีทัช\nรีเทิร์น\nรีไทร์\nรีแบรนด์\nรีพอร์ท\nรีโมต\nรีโมท\nรีวิว\nรีสอร์ต\nรีสอร์ท\nรีเสิร์ช\nรุมบ้า\nรุสโซ\nรูบิก\nรูบิค\nเรซิน\nเรซิ่น\nเรดิโอ\nเรต\nเรตติ้ง\nแรงใจ\nแรงดูด\nแรงผลัก\nแรลลี\nแรลลี่\nโรดแมป\nโรเนียว\nโรแมนติก\nโรแมนติค\nโรล\nโรลออน\nไรเฟิล\nล็อกเกอร์\nลอจิสติกส์\nล็อต\nล็อบบี้\nลอร์ด\nล้มเหลว\nละติน\nละอ่อน\nลาซานญ่า\nลาติน\nลาเต้\nลานีญา\nลามะ\nลิมิต\nลิมูซีน\nลิสต์\nลีก\nลีด\nลีดเดอร์\nลีเมอร์\nลีลาวดี\nลุค\nลูกชาย\nลูกสาว\nเลกเชอร์\nเลคเชอร์\nเลดี้\nเลสเบี้ยน\nเลิฟ\nแลนด์\nแล็บ\nโลโก้\nโลชั่น\nไลท์\nไลน์\nไลฟ์\nวนาราม\nวราราม\nวโรกาส\nว้อดก้า\nวอเตอร์\nวอฟเฟิล\nว้อย\nวอร์ม\nวอร์มอัพ\nวอร์รูม\nวอล์ก\nวอล์ค\nวอลซ์\nวอลนัต\nวอลนัท\nวอลล์\nว่ะ\nวันเวย์\nวัสสา\nวาซาบิ\nวาทกรรม\nวาทะ\nวานิลลา\nวานิลา\nวาฟเฟิล\nวาริชศาสตร์\nว้าว\nวัคค์\nวัจนะ\nวาไรตี้\nวิก\nวิดีโอ\nวิทย์\nวิน\nวิป\nวิปปิ้ง\nวิภัชภาค\nวิว\nวิลล์\nวิลเลจ\nวีเจ\nวีซ่า\nวีดิทัศน์\nวีน\nวีไอพี\nวืด\nเวณิกา\nเวเฟอร์\nเวสต์\nเวอร์\nเวิร์ก\nเวิร์กช็อป\nเวิร์ค\nเวิร์ลด์\nเวิลด์\nแวมไพร์\nไวกิ้ง\nไวเบรเตอร์\nไวอะกร้า\nไวอากร้า\nศากยบุตร\nศิรินทร์\nศิลปวัฒนธรรม\nศิลปากร\nศิวิไลซ์\nศึกษาศาสตร์\nสกรัม\nสกาย\nสกู๊ป\nสเกตช์\nสเก็ตช์\nสคริปต์\nสแควร์\nสงบสุข\nสจ๊วต\nสตรอเบอร์รี\nสตรอเบอรี\nสตรอว์เบอร์รี\nสตริง\nสต็อก\nสต๊อก\nสต็อค\nสต๊อค\nสตอรี\nสตาร์\nสตาร์ท\nสติกเกอร์\nสติ๊กเกอร์\nสตีล\nสตูดิโอ\nสเตชัน\nสเตชั่น\nสเตเดียม\nสเตนเลส\nสเต็ป\nสเตย์\nสเตริโอ\nสเตอริโอ\nสแตนดาร์ด\nสแตนเลส\nสโตน\nสโตร์\nสไตรค์\nสไตล์\nสถาปัตย์\nสไนเปอร์\nสปอต\nสป็อต\nสปอนเซอร์\nสปอร์ต\nสปา\nสปาย\nสปิริต\nสเปก\nสเปค\nสไปเดอร์\nสมณพราหมณ์\nสมาพันธ์\nสมิติเวช\nสโรชา\nสลัม\nสแล็ก\nสโลแกน\nสโลว์\nสไลด์\nสวีท\nสหรัฐ\nสหัชญาณ\nสหัสวรรษ\nสะกอม\nสะเด่า\nสะบึม\nสะบึมส์\nสะออน\nสังโฆ\nสะโหลสะเหล\nสันทนาการ\nสัมนา\nสามช่า\nสามแยก\nสารขัณฑ์\nสี่แยก\nสึนามิ\nสุนทรีย์\nสุริยยาตร\nสุริยยาตร์\nสุหนี่\nเสกสรรค์\nเสพติด\nเสือโคร่ง\nหงวน\nหน่อมแน้ม\nหมวย\nหมั่นโถว\nหม่านโถว\nหมายปอง\nหมิง\nหยวน\nหลวงตา\nหลวงปู่\nหลวงพี่\nหล่อฮังก้วย\nหลินจือ\nห่วย\nเห็นด้วย\nเหมย\nเห่ย\nเหี่ยวย่น\nแหม็บ\nแหวว\nโหงว\nโหงวเฮ้ง\nโหลน\nโหลยโท่ย\nไหง\nไหร่\nอพาร์ตเมนต์\nอพาร์ตเมนท์\nอพาร์ทเมนต์\nอพาร์ทเมนท์\nอมาตยาธิปไตย\nอยุติธรรม\nอริยสงฆ์\nอ่วม\nอวอร์ด\nออกแบบ\nออดิชั่น\nออดิทอเรียม\nออเดอร์\nออโต้\nออทิสติก\nอ่อนด้อย\nออฟ\nออยล์\nออร์แกน\nออร์แกนิก\nออร์แกนิค\nออร์เดอร์\nออรัล\nออสซี่\nอะ\nอัตลักษณ์\nอัตวิสัย\nอันเดอร์\nอันตรกิริยา\nอัลตรา\nอัลไซเมอร์\nอัลบัม\nอัลบั้ม\nอัลมอนด์\nอาข่า\nอาโนเนะ\nอาฟเตอร์\nอาร์ติสต์\nอาร์พีจี\nอาว์\nอาสวะ\nอิกัวนา\nอินดอร์\nอินดัสตรีส์\nอินเตอร์\nอิ่มแปร้\nอิมพีเรียล\nอิเล็กทริก\nอิเล็กทริค\nอิเลียด\nอิสรชน\nอิเหนา\nอิออน\nอีแต๋น\nอีโรติก\nอีเวนท์\nอีสต์\nอีสเตอร์\nอึ๊บ\nอึ้ม\nอึ๋ม\nอึมครึม\nอุด้ง\nอุตสาหการ\nอุเทน\nอุปการคุณ\nอุปทาน\nอุปนายก\nอุปนายิกา\nอุปสงค์\nอุปัทวเหตุ\nอุรังคธาตุ\nอูคูเลเล่\nอู้ฟู่\nเอ๋\nเอ็กซ์โป\nเอ็กซ์เพรส\nเอ็กโซเซต์\nเอ็กโซเซ่ต์\nเอเซีย\nเอ็นจีโอ\nเอ็นเตอร์เทน\nเอนทรานซ์\nเอ็นทรานซ์\nเอฟเฟ็กต์\nเอเยนต์\nเอลนีโญ\nเอสเปรสโซ\nเอสเพรสโซ\nเอ๋อ\nเอาต์\nเอาท์\nเอาท์ดอร์\nเอ๊าะ\nแอ็กชั่น\nแอ็คชั่น\nแอคทีฟ\nแอดมิชชั่น\nแอดมิสชัน\nแอนด์\nแอ๊บแบ๊ว\nแอปเปิล\nแอปเปิ้ล\nแอปพริคอท\nแอพพริคอท\nแอพริคอต\nแอร์\nแอโรบิก\nแอโรบิค\nแอลมอนด์\nแอสเตอร์\nโอเค\nโอเปอเรเตอร์\nโอเปร่า\nโอเพ่น\nโอ้ย\nโอยัวะ\nโอรสาธิราช\nโอเลี้ยง\nโอวัลติน\nโอเวอร์\nไอซ์\nไอซียู\nไอดอล\nไอเดีย\nไอติม\nฮวงจุ้ย\nฮ่องเต้\nฮองเฮา\nฮอต\nฮ็อต\nฮอตดอก\nฮ็อตด็อก\nฮันนีมูน\nฮัม\nฮัลโลวีน\nฮัลโหล\nฮากกา\nฮาร์ด\nฮาราคีรี\nฮาลาล\nฮาโลวีน\nฮิ\nฮิต\nฮิบรู\nฮิปโป\nฮิปฮอป\nฮีโร่\nฮูลาฮูป\nฮูล่าฮูป\nเฮฟวี\nเฮฟวี่\nเฮอร์ริเคน\nเฮีย\nแฮนด์\nแฮปปี้\nแฮมเบอร์เกอร์\nโฮป\nโฮม\nโฮลดิงส์\nโฮลวีต\nโฮสเตส\nไฮกุ\nไฮแจ็ค\nไฮโซ\nไฮเทค\nไฮบริด\nไฮเปอร์\nไฮไลต์\nไฮไลท์\nไฮเวย์\nไฮสคูล\nไฮเอนด์\n\nกรีซ\nกัมพูชา\nกัวเตมาลา\nกาตาร์\nกานา\nกาบอง\nกายอานา\nกินี\nเกรนาดีนส์\nเกรเนดา\nเกาหลี\nแกมเบีย\nโกตดิวัวร์\nคองโก\nคอโมโรส\nคอสตาริกา\nคาซัคสถาน\nคิตส์\nคิริบาตี\nคิริบาส\nคิวบา\nคีร์กีซสถาน\nคูเวต\nเคนยา\nเคปเวิร์ด\nเคย์แมน\nแคนาดา\nแคเมอรูน\nโครเอเชีย\nโคลอมเบีย\nจอร์เจีย\nจอร์แดน\nจาเมกา\nจิบูตี\nจีน\nชาด\nชิลี\nเช็ก\nซามัว\nซาอุ\nซิมบับเว\nซีเรีย\nซูดาน\nซูรินาเม\nเซนต์\nเซเนกัล\nเซอร์เบีย\nเซาตูเม\nเซียร์รา\nแซมเบีย\nโซมาเลีย\nโซเวียต\nไซปรัส\nญี่ปุ่น\nดารุสซาลาม\nเดนมาร์ก\nโดมินิกัน\nโดมินิกา\nตรินิแดด\nตองกา\nติมอร์\nตุรกี\nตูนิเซีย\nเติร์กเมนิสถาน\nโตโก\nโตเบโก\nไต้หวัน\nทาจิกิสถาน\nแทนซาเนีย\nนอร์เวย์\nนามิเบีย\nนาอูรู\nนิการากัว\nนิวซีแลนด์\nเนเธอร์แลนด์\nเนปาล\nเนวิส\nไนจีเรีย\nไนเจอร์\nบราซิล\nบริติช\nบริเตน\nบรูไน\nบอตสวานา\nบอสเนีย\nบังกลาเทศ\nบังคลาเทศ\nบัลแกเรีย\nบาร์บูดา\nบาร์เบโดส\nบาห์เรน\nบาฮามาส\nบิสเซา\nบุรุนดี\nบูร์กินาฟาโซ\nเบนิน\nเบลเยียม\nเบลารุส\nเบลีซ\nเบอร์มิวดา\nโบลิเวีย\nปรินซิปี\nปากีสถาน\nปานามา\nปาปัวนิวกินี\nปารากวัย\nปาเลสไตน์\nปาเลา\nเปรู\nเปอร์เซีย\nเปอร์โตริโก\nโปรตุเกส\nโปแลนด์\nฝรั่งเศส\nพม่า\nฟิจิ\nฟินแลนด์\nฟิลิปปินส์\nเฟรนช์\nภูฏาน\nภูฐาน\nมองโกเลีย\nมอนเตเนโกร\nมอนแทนา\nมอริเชียส\nมอริเตเนีย\nมอลโดวา\nมอลตา\nมัลดีฟส์\nมาเก๊า\nมาซิโดเนีย\nมาดากัสการ์\nมาร์แชลล์\nมาลาวี\nมาลี\nมาเลเซีย\nเม็กซิโก\nเมียนมาร์\nโมซัมบิก\nโมนาโก\nโมนาโค\nโมร็อกโก\nไมโครนีเซีย\nยูกันดา\nยูโกสลาเวีย\nยูเครน\nเยเมน\nเยอรมนี\nรวันดา\nรัสเซีย\nโรมาเนีย\nลักเซมเบิร์ก\nลัตเวีย\nลาว\nลิกเตนสไตน์\nลิทัวเนีย\nลิเบีย\nลีโอน\nลูเซีย\nเลโซโท\nเลบานอน\nเลสเต\nไลบีเรีย\nวาติกัน\nวานูอาตู\nวินเซนต์\nเวเนซุเอลา\nเวียดนาม\nศรีลังกา\nสเปน\nสโลวะเกีย\nสโลวัก\nสโลวีเนีย\nสวาซิแลนด์\nสวิตเซอร์แลนด์\nสวีเดน\nสหรัฐ\nสหราชอาณาจักร\nสิกขิม\nสิงคโปร์\nอเมริกา\nออสเตรเลีย\nออสเตรีย\nอันดอร์รา\nอัฟกานิสถาน\nอาเซอร์ไบจาน\nอาร์เจนตินา\nอาร์เมเนีย\nอาระเบีย\nอิเควทอเรียล\nอิตาลี\nอินเดีย\nอินโดนีเซีย\nอิรัก\nอิสราเอล\nอิหร่าน\nอียิปต์\nอุซเบกิสถาน\nอุรุกวัย\nเอกวาดอร์\nเอธิโอเปีย\nเอมิเรตส์\nเอริเทรีย\nเอลซัลวาดอร์\nเอสโตเนีย\nแองโกลา\nแอนติกา\nแอลจีเรีย\nแอลเบเนีย\nโอมาน\nไอซ์แลนด์\nไอร์แลนด์\nฮ่องกง\nฮอนดูรัส\nฮังการี\nเฮติ\nเฮอร์เซโกวีนา\n\nกระบี่\nกรุงเทพ\nกาญจนบุรี\nกาฬสินธุ์\nกำแพงเพชร\nขอนแก่น\nจันทบุรี\nฉะเชิงเทรา\nชลบุรี\nชัยนาท\nชัยภูมิ\nชุมพร\nเชียงราย\nเชียงใหม่\nตรัง\nตราด\nตาก\nนครนายก\nนครปฐม\nนครพนม\nนครราชสีมา\nนครศรีธรรมราช\nนครสวรรค์\nนนทบุรี\nนราธิวาส\nน่าน\nบึงกาฬ\nบุรีรัมย์\nปทุมธานี\nประจวบคีรีขันธ์\nปราจีนบุรี\nปัตตานี\nพะเยา\nพังงา\nพัทลุง\nพิจิตร\nพิษณุโลก\nเพชรบุรี\nเพชรบูรณ์\nแพร่\nภูเก็ต\nมหาสารคาม\nมุกดาหาร\nแม่ฮ่องสอน\nยโสธร\nยะลา\nร้อยเอ็ด\nระนอง\nระยอง\nราชบุรี\nลพบุรี\nลำปาง\nลำพูน\nเลย\nศรีสะเกษ\nสกลนคร\nสงขลา\nสตูล\nสมุทรปราการ\nสมุทรสงคราม\nสมุทรสาคร\nสระแก้ว\nสระบุรี\nสิงห์บุรี\nสุโขทัย\nสุพรรณบุรี\nสุราษฎร์\nสุราษฎร์ธานี\nสุรินทร์\nหนองคาย\nหนองบัวลำภู\nอยุธยา\nอ่างทอง\nอำนาจเจริญ\nอุดรธานี\nอุตรดิตถ์\nอุทัยธานี\nอุบลราชธานี\nกันทรลักษ์\nจตุจักร\nไชยา\nซีคอน\nดอนเมือง\nถลาง\nไทรโยค\nธนบุรี\nธัญบุรี\nบางกอก\nบางปะกง\nบางระจัน\nปะทิว\nปาย\nพญาไท\nพัฒน์พงษ์\nพัทยา\nพารากอน\nภูมิซรอล\nรัตนาธิเบศร์\nรังสิต\nลันตา\nลาดพร้าว\nวโรรส\nวิภาวดี\nสตึก\nสมุย\nสัตหีบ\nสิมิลัน\nสุขุมวิท\nสุไหง\nเสลภูมิ\nอังรีดูนังต์\nอ่างขาง\nอินทนนท์\nเอ็มโพเรียม\n\nคิวชู\nแคริบเบียน\nแคสเปียน\nดานูบ\nตะนาวศรี\nนอร์วีเจียน\nนิโคบาร์\nเนรัญชรา\nไนล์\nบอร์เนียว\nบอลติก\nเบงกอล\nปิง\nแปซิฟิก\nมะละกา\nมินดาเนา\nมิสซิสซิปปี\nเมดิเตอร์เรเนียน\nเมโสโปเตเมีย\nยมุนา\nยุโรป\nยูเรเชีย\nยูเรเซีย\nแยงซี\nแยงซีเกียง\nสแกนดิเนเวีย\nสะโตง\nสาละวิน\nสุมาตรา\nสุเอซ\nอะเมซอน\nอันดามัน\nอัลไต\nอาร์กติก\nอาหรับ\nอินโดจีน\nอิรวดี\nอิระวดี\nอีเจียน\nอุษาคเณย์\nอูราล\nเอเชีย\nเอเดรียติก\nเอเวอเรสต์\nแอตแลนติก\nแอนตาร์กติก\nแอนตาร์กติกา\nแอฟริกา\nโอลิมปัส\nไอโอเนียน\nฮวงโห\nฮอกไกโด\nฮอนชู\n\nกบิลพัสดุ์\nกุสินารา\nโกลิยะ\nโกสัมพี\nโคตรบอง\nโคตรบูรณ์\nตองอู\nทรอย\nทวารวดี\nทวาราวดี\nเทวทหะ\nไทรบุรี\nนาลันทา\nไบแซนไทน์\nปรัสเซีย\nปัลลวะ\nปาฏลีบุตร\nพุทธคยา\nมถุรา\nมายัน\nมิถิลา\nราชคฤห์\nล้านช้าง\nล้านนา\nลุมพินี\nวัชชี\nเวสาลี\nสารนาถ\nสาวัตถี\nหริภุญชัย\nอโยธยา\nออตโตมัน\nอังวะ\nอินทปัตถ์\nอุชเชนี\n\nกราฟิก\nกราฟิกส์\nกราฟิค\nกริด\nกิกะไบต์\nกูเกิล\nกูเกิ้ล\nเกตเวย์\nโกลบอล\nคลัสเตอร์\nคลาส\nคลิก\nคลิปอาร์ต\nคอนโซล\nคอนเทนต์\nคอมพิวติ้ง\nคอมไพล์\nคอมไพเลอร์\nคอมมูนิเคชั่น\nคอร์\nคีย์\nคีย์บอร์ด\nเครือข่าย\nเคอร์เซอร์\nเคอร์เนล\nแคช\nแคมฟรอก\nแคมฟร็อก\nแคร็ก\nโค้ด\nจาวา\nจีพีเอส\nชิป\nชิพ\nเชลล์\nแช็ต\nแชนเนล\nแชนแนล\nซ็อกเก็ต\nซอฟต์แวร์\nซอฟท์แวร์\nซอร์ส\nซัพพอร์ต\nซัพพอร์ท\nซีดี\nซีดีรอม\nซีเนอร์\nเซิร์ฟเวอร์\nโซลูชัน\nโซลูชั่น\nไซต์\nไซเบอร์\nทรานแซกชัน\nทรานแซกชั่น\nทรานแซ็กชัน\nทรานแซ็กชั่น\nทรานแซคชัน\nทรานแซคชั่น\nทรานแซ็คชัน\nทรานแซ็คชั่น\nทวิตเตอร์\nทวีต\nทัชแพด\nเทมเพลต\nเทอร์มินัล\nแท็ก\nแท็บ\nแทบเล็ต\nโทรจัน\nเน็ต\nเน็ตบุ๊ก\nเน็ตบุค\nเน็ตบุ๊ค\nเน็ตเวิร์ก\nเน็ตเวิร์ค\nโน้ตบุ๊ก\nโน้ตบุค\nโน้ตบุ๊ค\nดอส\nดาวน์เกรด\nดาวน์โหลด\nดิจิตอล\nดิจิทัล\nดีบั๊ก\nดีวีดี\nดีไวซ์\nเดเบียน\nเดลไฟ\nเดสก์ท็อป\nโดเมน\nไดรว์\nไดรเวอร์\nไดเรกทอรี\nไดโอด\nเทเลคอม\nบล็อกเกอร์\nบรอดแบนด์\nบราวเซอร์\nบลูทูท\nบลูทูธ\nบลูเรย์\nบั๊ก\nบัฟเฟอร์\nบิต\nบิท\nบูต\nเบราว์เซอร์\nแบนด์วิดท์\nไบต์\nไบนารี\nโปรแกรมเมอร์\nโปรเซส\nโปรเซสเซอร์\nโปรโตคอล\nพร็อกซี\nพอร์ต\nพอร์ท\nพาเนล\nพาร์ทิชัน\nพารามิเตอร์\nพาสเวิร์ด\nพิกเซล\nเพจ\nเพจเจอร์\nแพกเก็ต\nแพตช์\nแพลตฟอร์ม\nโพรเซส\nโพรเซสเซอร์\nโพรโทคอล\nไพธอน\nฟล็อปส์\nฟอนต์\nฟอร์แมต\nฟอร์เวิร์ด\nฟอรัม\nฟีเจอร์\nเฟซบุ๊ก\nเฟิร์มแวร์\nแฟล็ก\nโฟลเดอร์\nไฟร์ฟอกซ์\nไฟร์วอลล์\nไฟล์\nมอดูล\nมอนิเตอร์\nมัลติ\nมัลติทัช\nมัลติเพล็กซ์\nมัลแวร์\nมาสเตอร์\nมีเดีย\nเมนู\nเมมโมรี\nเมล\nเมาส์\nแมค\nโมดูล\nโมเด็ม\nโมบาย\nโมบายล์\nโมไบล์\nไมโครซอฟท์\nยูนิกซ์\nยูนิโคด\nยูนิโค้ด\nริงโทน\nรีเฟรช\nรีเลย์\nเราเตอร์\nเรียลไทม์\nลิงก์\nลินุกซ์\nลีนุกซ์\nลูป\nเลเยอร์\nแล็ปท็อป\nไลเซนส์\nไลบรารี\nวิกิ\nวิกิพีเดีย\nวินโดวส์\nวินโดว์ส\nเว็บ\nเวอร์ชวล\nเวอร์ชัน\nเวอร์ชั่น\nเวิร์กสเตชัน\nเวิร์กสเตชั่น\nเวิร์คสเตชัน\nเวิร์คสเตชั่น\nเวิร์ด\nเวิร์ม\nไวแมกซ์\nสกรีน\nสแกน\nสแกนเนอร์\nสแต็ก\nสนิฟเฟอร์\nสปายแวร์\nสเปซ\nสแปม\nสมาร์ท\nสล็อต\nเสิร์ช\nโหลด\nออนไลน์\nออปติก\nออปติคอล\nออปติคัล\nออฟไลน์\nออราเคิล\nอัพเกรด\nอัพเดต\nอัพโหลด\nอัปเกรด\nอัปเดต\nอัปโหลด\nอัลกอริทึม\nอาร์กิวเมนต์\nอินเตอร์เน็ต\nอินทิเกรเตอร์\nอินเทอร์เน็ต\nอินเทอร์เฟซ\nอินเทล\nอินพุต\nอินพุท\nอีเมล\nอีเมล์\nอูบุนตู\nอูบันตู\nเอนจิน\nเอ็นจิน\nเอาต์พุต\nเอาต์พุท\nเอาท์พุต\nเอาท์พุท\nแอนะล็อก\nแอนิเมชัน\nแอนิเมชั่น\nแอปพลิเคชัน\nแอปพลิเคชั่น\nแอพพลิเคชัน\nแอพพลิเคชั่น\nแอสเซมบลี\nแอสเซมเบลอร์\nโอเพน\nไอคอน\nไอซี\nไอพอด\nไอพ็อด\nไอแพด\nไอโฟน\nฮับ\nฮาร์ดดิสก์\nฮาร์ดแวร์\nแฮกเกอร์\nแฮ็กเกอร์\nแฮนด์เฮลด์\nโฮสต์\n\nกรีก\nกัณณาฑ\nกัศมีรี\nคันจิ\nคาตาคานะ\nคุชราตี\nคุรุมุขี\nซีริลลิก\nซูลู\nเซลติก\nเซิร์บ\nตากาล็อก\nเตลุคู\nเติร์ก\nทราวิฑ\nเบงกาลี\nปัญจาบี\nพินอิน\nมลยาฬัม\nมองโกล\nมาราฐี\nมาเลย์\nเม็กซิกัน\nแมนจู\nแมนดาริน\nไมถิลี\nเยอรมัน\nรัสเซียน\nสวาฮิลี\nสวิส\nสินธี\nอูรดู\nอัสสมี\nอารบิก\nอิตาเลียน\nอุยกูร์\nแอฟริกัน\nโอริยา\nไอริช\nฮันกึล\nฮินดี\nฮิรางานะ\nฮีบรู\n\nกรีนพีซ\nกรือเซะ\nกวนอิม\nกวนอู\nกัดดาฟี\nกัลยาณวัตร\nกัสสปะ\nกาลิเลโอ\nกินเนส\nกุมภกรรณ\nกูเตนเบิร์ก\nเกตส์\nเกษมณี\nโกณฑัญญะ\nขงเบ้ง\nคริสโตเฟอร์\nคองคอร์ด\nคอลเกต\nคานธี\nคาเบรียล\nคาร์ฟูร์\nคาร์สัน\nคาราบาว\nคาสิโอ\nคิริน\nคุนลุ้น\nคูโบต้า\nเครมลิน\nแคทรีนา\nโคตมะ\nโคตมี\nโคลัมบัส\nไคฟง\nไครสเลอร์\nง้อไบ๊\nจตุพร\nจ็อบส์\nจอห์น\nจิ้น\nจิม\nจิ๋ม\nจิว\nจุฬาภรณ์\nจุฬาลงกรณ์\nเจมส์\nแจ็กสัน\nโจเซฟ\nโจว\nชมัยมรุเชฐ\nชมัยมรุเชษฐ์\nชเวดากอง\nชาร์ลส์\nชินราช\nชินวัตร\nชุนชิว\nเช็ง\nเชตวัน\nเชฟรอน\nเชฟโรเลต\nเชลซี\nไชยานุชิต\nซ่ง\nซังฮี้\nซัดดัม\nซันซิล\nซัมซุง\nซัวเจ๋ง\nซินหัว\nซีซาร์\nซีแพค\nซูซาน\nซูซูกิ\nซูบารุ\nเซ็นทารา\nเซเวน\nเซเว่น\nโซฟิเทล\nโซยุซ\nโซยูซ\nณัฐวุฒิ\nดาร์ลี่\nดาวโจนส์\nดิสนีย์\nดีแทค\nดูปองท์\nเดโมแครต\nเดลล์\nเดลินิวส์\nเดวิด\nแดวู\nโดนัลด์\nโดราเอมอน\nโดเรมอน\nต๋อง\nตั๊กม้อ\nตากสิน\nตาเมือน\nตาลีบัน\nตูน\nเตมีย์\nโต๋\nโตชิบา\nโตโยต้า\nถังซัมจั๋ง\nถังซำจั๋ง\nทรพา\nทราเวล\nทรูมูฟ\nทีปังกร\nเทปโก\nเทพรัตน\nเทวทัต\nเทสโก้\nโทมัส\nไททานิก\nไททานิค\nไทยรัฐ\nธีออส\nนครินทรา\nนโปเลียน\nนพดล\nนราดูร\nนเรนทร\nนอสตราดามุส\nนาซา\nนาซ่า\nนาซี\nนาโต\nนาโต้\nนาลแก\nนิคอน\nนิโคลัส\nนิด้า\nนินเทนโด\nนิปปอน\nนิวตัน\nนิสสัน\nเนคเทค\nเนชั่น\nเนชันแนล\nเนชั่นแนล\nเนวิน\nเนสเล่\nเนสาด\nแนท\nแนสแดค\nโนเกีย\nโนเบล\nโนเวลล์\nโนโวเทล\nไนเม็กซ์\nบรอดเวย์\nบรัดเลย์\nบรู๊ซ\nบัลเมอร์\nบารัก\nบารัค\nบู๊ตึ๊ง\nเบญกาย\nเบนซ์\nเบ็นซ์\nเบนจามิน\nโบตัน\nไบโอเทค\nประชาธิปัตย์\nปวีณา\nปอเต็กตึ๊ง\nปอเต๊กตึ๊ง\nป่อเต็กตึ๊ง\nปัตตะโชติ\nปารุสก์\nปีเตอร์\nปูติน\nเป๊ปซี่\nเป้ย\nเปอร์โยต์\nเปาบุ้นจิ้น\nโปเกมอน\nโป๊ยก่าย\nพรหมทัต\nพลาโต\nพอลล่า\nพานาโซนิค\nพานาโซนิก\nพิทยานุกูล\nพิมพิสาร\nเพนแทกซ์\nเพลโต\nไพโอเนียร์\nฟรอยด์\nฟรังซิส\nฟรานซิส\nฟลอเรนซ์\nฟอร์ด\nฟิลิปส์\nฟูจิ\nแฟซ่า\nโฟร์โมสต์\nภูมิพล\nภูริทัต\nมงฟอร์ต\nมณโฑ\nมติชน\nมหิตลาธิเบศร\nมโหสถ\nมัจฉานุ\nมาร์กาเร็ต\nมาร์ติน\nมาสด้า\nมิตซูบิชิ\nมิราเคิล\nมุสโสลินี\nเม้ง\nเมจิ\nเมอร์ซีเดส\nเมอร์เซเดส\nแมกซ์เวลล์\nแมกไซไซ\nแมคอินทอช\nแมชีนเนอรี่\nโมคคัลลานะ\nโมโตโรลา\nโมโตโรล่า\nโมเนีย\nไมเคิล\nไมยราพณ์\nยโสธรา\nยะโฮวา\nยะโฮวาห์\nยามาฮ่า\nยาเวห์\nยาฮู\nยูนิเซฟ\nยูเนสโก\nยูไล\nเยโฮวาห์\nรอยเตอร์\nรอยัล\nรัชดา\nรัสปูติน\nราฟาเอล\nรามาวตาร\nราเมศวร\nราหุล\nริชาร์ด\nรีพับลิกัน\nรูนีย์\nเรนโบว์\nแรมโบ้\nโรตารี\nโรนัลโด\nโรนัลโด้\nโรบินสัน\nโรเบิร์ต\nล็อกซเล่ย์\nลิงคอล์น\nลิจฉวี\nลิไท\nลิไทย\nลินคอล์น\nลิเวอร์พูล\nเลโนโว\nเลียดก๊ก\nโลตัส\nวชิราลงกรณ์\nวลาดิเมียร์\nวอลล์สตรีท\nวาเลนไทน์\nวิกตอเรีย\nวิทยานุสรณ์\nวิทยายน\nวิมเบิลดัน\nวิลเลียม\nวีระ\nวุฒิชัย\nเวียดกง\nไวตามิลค์\nศกุนตลา\nศรีวิชัย\nศิริพงษ์\nศิริราช\nศุภชลาศัย\nสดกก๊อกธม\nสดายุ\nสตาลิน\nสตีฟ\nสแตนฟอร์ด\nสวรินทิรา\nสังกัจจายน์\nสาทิตย์\nสารีบุตร\nสิริกิติ์\nสิรินธร\nสิหิงค์\nสีวลี\nสีหนุ\nสีหมุนี\nสีหโมนี\nสุครีพ\nสุทโธทนะ\nสุเทพ\nสุนทราภรณ์\nสุนีย์\nสุรนารี\nสุรยุทธ์\nสุริยาสน์\nเส้าหลิน\nโสกราตีส\nโสภิต\nหนุมาน\nหลินฮุ่ย\nหลุยส์\nเห้งเจีย\nไหหม่า\nองคต\nองคุลิมาล\nอชาตศัตรู\nอดุลยเดช\nอพอลโล\nอริสโตเติล\nอริสมันต์\nอลิซาเบธ\nอ๋อม\nออร์คิด\nออสการ์\nอะพอลโล\nอับราฮัม\nอั้ม\nอัลกออิดะห์\nอัลคาเทล\nอัลจาซีราห์\nอัลเฟรด\nอัลเลาะห์\nอัสซุส\nอัสสชิ\nอัสสัมชัญ\nอาเซม\nอาเซ็ม\nอาเซียน\nอาฟต้า\nอาร์เซนอล\nอินทรชิต\nอินทราทิตย์\nอีซูซุ\nอีเลฟเวน\nอีเลฟเว่น\nอุณรุท\nอุบลรัตน์\nอุบาลี\nอุ๋ย\nเอกทัศน์\nเอเซอร์\nเอ็ดเวิร์ด\nเอดิสัน\nเอแบค\nเอลิซาเบธ\nเอสพลานาด\nเอสพลานาร์ด\nแอคคอร์\nแอคคอร์ด\nแองเจลิน่า\nแอตแลนติส\nแอน\nแอ๋ม\nแอมบาสซาเดอร์\nแอมบาสเดอร์\nแอมเวย์\nแอ๋ว\nโอดีสซีย์\nโอเดียน\nโอบามา\nโอรสาราม\nโอลิมเปีย\nโออิชิ\nไอน์สไตน์\nฮอนด้า\nฮอปกินส์\nฮอลลีวูด\nฮอลลีวู้ด\nฮานามิ\nฮามาส\nฮิตเลอร์\nฮิตาชิ\nฮุนเซน\nฮุนเซ็น\nฮุนได\nฮุสเซ็น\nเฮนรี\nเฮนรี่\nเฮเลน\nโฮจิมินห์\nโฮปเวลล์\nโฮเมอร์\n\nกลีเซอรีน\nกำทอน\nแกนีมีด\nครอส\nคริสตัล\nคลอโรพลาสต์\nคลอไรด์\nควอนตัม\nคอนดักเตอร์\nคอปเปอร์\nคอลลาเจน\nคอเลสเตอรอล\nคอสมิก\nคูลอมบ์\nเคอราติน\nแคโรทีน\nแคสสินี\nโครมาโทกราฟี\nไคโตซาน\nจีโนม\nจุลชีววิทยา\nชิคุนกุนยา\nซัลฟิวริก\nซัลเฟต\nซัลไฟด์\nซิงค์\nซิริอุส\nซิลิกา\nซิลิเกต\nซิลิโคน\nซีเทน\nซีเวิร์ต\nเซ็กเตอร์\nเซ็กเมนต์\nเซมิ\nโซนาร์\nไซบอร์ก\nดอปเปลอร์\nดอปเพลอร์\nไดนามิก\nไดนามิกส์\nไดนามิค\nไดนามิคส์\nไดออกไซด์\nทรานส์\nทามิฟลู\nเทฟลอน\nเทสโทสเตอโรน\nเทอร์โม\nแทนนิน\nไททัน\nไทฟอยด์\nไทรอยด์\nธาลัสซีเมีย\nเนกาตีฟ\nโนวา\nบอแรกซ์\nโบทอกซ์\nโบท็อกซ์\nไบโอติน\nปฏิยานุพันธ์\nโปรเจสเตอโรน\nพอลิเมอร์\nพันธุศาสตร์\nพัลซาร์\nพาร์กินสัน\nพาราเซตามอล\nพาราโบลา\nเพอร์ออกไซด์\nโพรเจสเทอโรน\nโพลาไรซ์\nโพลิเมอร์\nโพลีเอทิลีน\nไพรเมต\nฟลาโวนอยด์\nฟลูออเรสเซนซ์\nฟลูออไรด์\nฟอสซิล\nฟิชชัน\nฟิวชัน\nฟีโรโมน\nไฟเบอร์\nมอนอกไซด์\nมิราจ\nเมตริกซ์\nเมทริกซ์\nเมลานิน\nเมลามีน\nโมเมนตัม\nไมโตคอนเดรีย\nไมโทคอนเดรีย\nยีสต์\nยูริก\nยูเรีย\nรูมาตอยด์\nวีก้า\nเวกเตอร์\nเวก้า\nเวสิเคิล\nโวลต์\nสเกล\nสเกลาร์\nสเต็ม\nสเตียรอยด์\nสปีชีส์\nสเปิร์ม\nสัมพัทธภาพ\nสุริยจักรวาล\nออกเทน\nออโรรา\nออโรร่า\nอะคริลิก\nอะครีลิก\nอะซีติก\nอะซีโตน\nอะมิโน\nอะลูมินา\nอันโดรเมดา\nอัลคาไลน์\nอัลตราซาวด์\nอัลตราซาวนด์\nอัลลอยด์\nอินทิกรัล\nอินทิเกรต\nอีโบลา\nอีโบล่า\nเอ็กซ์โพเนนเชียล\nเอทานอล\nเอทิลีน\nเอนโทรปี\nเอสเตอร์\nเอสโตรเจน\nเอสโทรเจน\nแอนดรอยด์\nแอนแทร็กซ์\nแอมพลิจูด\nแอมโมเนียม\nแอลกอฮอลิซึม\nแอสพาร์แตม\nโอเซลทามิเวียร์\nฮับเบิล\nฮิวมัส\nไฮดรอกไซด์\nไฮดรอลิก\nไฮโดรลิก\nไฮเพอร์โบลา\n\nกงเต็ก\nกฎุมพี\nกฏ\nกฏหมาย\nกบฎ\nกราไฟต์\nก๊อปปี้\nกะทะ\nกังวาล\nกุฎฐัง\nกุฏุมพี\nฃวด\nคฑา\nคลินิค\nคลีนิก\nคลีนิค\nคาทอลิค\nคึ่นฉ่าย\nแคตตาล็อก\nโควต้า\nฅน\nจุมพฎ\nช็อคโกแลต\nแซ่ด\nดัทช์\nทนง\nทรมาณ\nทราก\nทะแยง\nทิฏฐิ\nบล็อค\nบ๊องแบ๊ว\nบัลเล่ต์\nเบรค\nแบงค์\nปรากฎ\nปัคคหะ\nปาฏิโมกข์\nปิติ\nปิรามิด\nโปรเตสแตนท์\nพนิช\nพยักเพยิด\nพริ้ว\nพลูโตเนียม\nพากษ์\nเฟิร์น\nยากี้\nเยภุยยสิกา\nรุสเซีย\nฤาษี\nล็อค\nล็อคเกอร์\nวันทยาหัตถ์\nวานิช\nวิญญาน\nวิศิษฐ์\nศรีษะ\nสเปกโทรสโคป\nสฤษฎ์\nสลิ่ม\nสัตตสดก\nสาราณียากร\nสุกี้\nสุกี้ยากี้\nสูญญากาศ\nหยอมแหยม\nหยอย\nหล่ะ\nอะดรีนาลีน\nอะหลั่ย\nอัตคัต\nอัฟริกา\nอานิสงค์\nอาฟริกา\nอิริยาบท\nอิเลคโทรนิคส์\nอีรุงตุงนัง\nอุตรายัน\nอุลตรา\nอุลตร้า\nโอกาศ\n\nกกหู\nกงการ\nกงจักร\nกฎเกณฑ์\nกฎบัตร\nกฎหมาย\nกฎหมู่\nกดขี่\nกดดัน\nก้นกบ\nก้นบึ้ง\nก้นปล่อง\nกนิษฐภคินี\nกนิษฐภาดา\nกรงเล็บ\nกรมการ\nกรมท่า\nกรมธรรม์\nกรมนา\nกรมวัง\nกรรมกร\nกรรมการ\nกรรมฐาน\nกรรมบถ\nกรรมพันธุ์\nกรรมวิธี\nกรรมสิทธิ์\nกระจกเงา\nกระจกตา\nกระจกนูน\nกระจกเว้า\nกระจอกชวา\nกระจอกเทศ\nกระจ้อยร่อย\nกระจับบก\nกระจับปิ้ง\nกระจับปี่\nกระโชกโฮกฮาก\nกระดานดำ\nกระดานหก\nกระดาษแก้ว\nกระดาษไข\nกระดาษทราย\nกระดาษสา\nกระดูกงู\nกระทาชาย\nกระเท่เร่\nกระบวนการ\nกระบองเพชร\nกระผีกริ้น\nกระยาทิพย์\nกระยาสารท\nกระยาหาร\nกระสอบทราย\nกระสุนปืน\nกระแสจิต\nกระแสน้ำ\nกระแสลม\nกรับคู่\nกรับพวง\nกรับเสภา\nกราดเกรี้ยว\nกราวรูด\nกริ่งเกรง\nกรีฑาสถาน\nกรีดกราย\nกรี๊ดกร๊าด\nกลไก\nกลบท\nกลเม็ด\nกลยุทธ์\nกลวิธี\nกลศาสตร์\nกลอักษร\nกลบเกลื่อน\nกลมกล่อม\nกลมกลืน\nกลมเกลียว\nกล้วยแขก\nกล้วยไม้\nกล่องเสียง\nกล่อมเกลา\nกล่อมเกลี้ยง\nกลัดกลุ้ม\nกลัดมัน\nกลั่นกรอง\nกลั่นแกล้ง\nกลับกลอก\nกลางคน\nกลางคัน\nกลางค่ำ\nกลางคืน\nกลางแจ้ง\nกลางแปลง\nกลางวัน\nกลาดเกลื่อน\nกล่าวขวัญ\nกล่าวโทษ\nกล่าวหา\nกล้ำกราย\nกล้ำกลืน\nกลิ้งกลอก\nกลิ้งเกลือก\nกลิ่นอาย\nกลียุค\nกวดขัน\nกวัดแกว่ง\nกวัดไกว\nกวีนิพนธ์\nก่อกวน\nก่อการ\nก่อตั้ง\nก่อสร้าง\nก่อหวอด\nก้อร่อก้อติก\nกองกลาง\nกองเกิน\nกองโจร\nกองทัพ\nกองทุน\nกองพล\nกองพัน\nกองฟอน\nกองร้อย\nกองหนุน\nกอบโกย\nกะเกณฑ์\nกะบังลม\nกักกัน\nกักขัง\nกักตัว\nกักตุน\nกัณฑ์เทศน์\nกัดฟัน\nกันชน\nกันท่า\nกันสาด\nกันเอง\nกับแกล้ม\nกับข้าว\nกับระเบิด\nกากเพชร\nกากหมู\nกาชาด\nกาญจนาภิเษก\nก้านคอ\nกาฝาก\nก้ามกราม\nกามกิจ\nกามคุณ\nกามเทพ\nกามโรค\nก้ามปู\nกายกรรม\nกายบริหาร\nกายภาพ\nกายวิภาค\nกายสิทธิ์\nก่ายกอง\nการคลัง\nการเงิน\nการบ้าน\nการเปรียญ\nการเมือง\nการเรือน\nการละเล่น\nกาลกิริยา\nกาลเทศะ\nก้าวก่าย\nก้าวร้าว\nก้าวหน้า\nกาสาวพัสตร์\nกาฬพฤกษ์\nกาฬโรค\nกำปั้น\nกำมือ\nกำแพงขาว\nกำลังใจ\nกำลังม้า\nกี่งอำเภอ\nกิจกรรม\nกิจการ\nกิจวัตร\nกิจจะลักษณะ\nกิตติคุณ\nกิตติศัพท์\nกินขาด\nกินใจ\nกินดอง\nกินโต๊ะ\nกินแบ่ง\nกินเปล่า\nกินเลี้ยง\nกินเส้น\nกินแหนง\nกิโลกรัม\nกิโลเมตร\nกิโลลิตร\nกิโลเฮิรตซ์\nกีดกัน\nกีดกั้น\nกีดขวาง\nกึกก้อง\nกึกกัก\nกึกกือ\nกึ่งกลาง\nกุกกัก\nกุ๊กกิ๊ก\nกุ้งฝอย\nกุ้งมังกร\nกุ้งแห้ง\nกุ้งเต้น\nกุ้งยิง\nกุญแจผี\nกุญแจมือ\nกุญแจเลื่อน\nกุญแจเสียง\nกุลธิดา\nกุลบุตร\nกุลสตรี\nกู้ยืม\nเก้งก้าง\nเก็บกวาด\nเก็บเกี่ยว\nเก็บงำ\nเก็บตก\nเกรงกลัว\nเกรงใจ\nเกรงขาม\nเกรียงไกร\nเกรียมกรม\nเกรี้ยวกราด\nเกล็ดเลือด\nเกลี้ยกล่อม\nเกลี้ยงเกลา\nเกลือกกลั้ว\nเกลือกกลิ้ง\nเกลื่อนกล่น\nเกลื่อนกลาด\nเกศธาตุ\nเกษตรกร\nเกษตรกรรม\nเกษตรศาสตร์\nเกษมสันต์\nเกษียรสมุทร\nเก้อเขิน\nเกาะแกะ\nเกี่ยงงอน\nเกียจคร้าน\nเกียรติคุณ\nเกียรตินิยม\nเกียรติประวัติ\nเกียรติภูมิ\nเกียรติยศ\nเกียรติศักดิ์\nเกียรติมุข\nเกี่ยวข้อง\nเกี่ยวดอง\nเกี่ยวพัน\nเกี่ยวโยง\nเกี้ยวพาน\nเกี้ยวพาราสี\nแก่แดด\nแก้ขัด\nแก้ไข\nแก้ตัว\nแก้เผ็ด\nแก้ลำ\nแกงคั่ว\nแกงจืด\nแกงบวด\nแกงป่า\nแกงเผ็ด\nแกงส้ม\nแก่งแย่ง\nแก่นแก้ว\nแก่นสาร\nแก้วตา\nแก้วหู\nแกว่งกวัด\nแกว่งไกว\nแกะรอย\nโก้เก๋\nโกรธเกรี้ยว\nโกรธขึ้ง\nไก่เขี่ย\nไก่ชน\nไก่บ้าน\nไก่ป่า\nไก่ฟ้า\nไกล่เกลี่ย\nขจัดขจาย\nขนเพชร\nขนสัตว์\nขนหนู\nขนส่ง\nขนมจีน\nขบขัน\nขบวนการ\nข่มขี่\nข่มขู่\nข่มขืน\nข่มเหง\nขมหิน\nขมิ้นชัน\nขมุบขมิบ\nขยะแขยง\nขยักขย่อน\nขยักขย้อน\nขยับขยาย\nขยับเขยื้อน\nขวดโหล\nขวยเขิน\nขวัญใจ\nขวัญตา\nขวัญอ่อน\nขวากหนาม\nขวางโลก\nของ้าว\nขอสับ\nขอขมา\nขอทาน\nขอโทษ\nขอร้อง\nขออภัย\nข้อเขียน\nข้อความ\nข้อเท็จจริง\nของกลาง\nของขวัญ\nของแข็ง\nของชำ\nของลับ\nของเล่น\nของว่าง\nของเหลว\nของไหล\nของไหว้\nข้องใจ\nข้องแวะ\nขอบข่าย\nขอบเขต\nขอบคุณ\nขอบใจ\nขอบพระคุณ\nข้อมูล\nข้อแม้\nข้อหา\nข้อสังเกต\nขัดข้อง\nขัดขืน\nขัดเขิน\nขัดจังหวะ\nขัดดอก\nขัดแตะ\nขัดยอก\nขัดแย้ง\nขัดสมาธิ\nขันหมาก\nขันอาสา\nขับขี่\nขับเคี่ยว\nขั้วโลก\nขาจร\nขาประจำ\nข้าราชการ\nข้าศึก\nข้าหลวง\nขาดแคลน\nขาดใจ\nขาดตอน\nขาดตัว\nขาดทุน\nขาดเหลือ\nขายหน้า\nข่าวกรอง\nข่าวคราว\nข่าวล่า\nข่าวลือ\nข่าวสาร\nข้าวเกรียบ\nข้าวแกง\nข้าวของ\nข้าวจี่\nข้าวเจ้า\nข้าวซอย\nข้าวต้ม\nข้าวตอก\nข้าวตัง\nข้าวแตน\nข้าวทิพย์\nข้าวบิณฑ์\nข้าวเปลือก\nข้าวโพด\nข้าวฟ่าง\nข้าวเม่า\nข้าวสวย\nข้าวสาร\nข้าวเหนียว\nข้าวหมาก\nข้าวหลาม\nขี้เกียจ\nขี้ข้า\nขี้ครอก\nขี้คร้าน\nขี้คุก\nขี้ไคล\nขี้เซา\nขีดขั้น\nขีดคร่อม\nขีดคั่น\nขีดฆ่า\nขี้ตา\nขี้ตืด\nขี้เถ้า\nขี้ทูด\nขี้ปะติ๋ว\nขี้ผึ้ง\nขี้มูก\nขี้ยา\nขี้แย\nขี้ริ้ว\nขี้เรื้อน\nขี้เล็บ\nขี้หู\nขี้หน้า\nขี้เหนียว\nขี้เหล็ก\nขี้เหร่\nขึงขัง\nขึงพืด\nขึ้งโกรธ\nขึ้นใจ\nขึ้นชื่อ\nขึ้นมือ\nขืนใจ\nขื่นขม\nขุดคุ้ย\nขุนทอง\nขุนนาง\nขุนพล\nขุนศึก\nขุนหลวง\nขูดรีด\nเข็มกลัด\nเข็มขัด\nเข้มข้น\nเข้มแข็ง\nเข้มงวด\nเข็มทิศ\nเข็มหมุด\nเข้าขา\nเข้าเค้า\nเข้าใจ\nเข้าชื่อ\nเข้าตัว\nเข้าถึง\nเข้าทรง\nเข้าท่า\nเข้าที\nเข้าเนื้อ\nเข้าเล่ม\nเขียวเสวย\nเขียวหวาน\nแขกเต้า\nแข็งกร้าว\nแข็งกล้า\nแข็งแกร่ง\nแข็งข้อ\nแข็งขัน\nแข่งขัน\nแข็งใจ\nแข็งตัว\nแข็งเมือง\nแข็งแรง\nแขวนลอย\nโขกสับ\nโขยกเขยก\nไขข้อ\nไขควง\nไขมัน\nไข่มุก\nไขว่ห้าง\nไขสันหลัง\nไขสือ\nไข่เค็ม\nไข่เยี่ยวม้า\nไข่หงส์\nไข่เหี้ย\nคงกระพัน\nคงตัว\nคงทน\nคงที่\nคชลักษณ์\nคชสาร\nคชสีห์\nคชราช\nคณิตศาสตร์\nคดเคี้ยว\nคติธรรม\nคติพจน์\nคนกลาง\nคนไข้\nคนใช้\nคนทรง\nคบไฟ\nคบเพลิง\nคบค้า\nคบคิด\nคบหา\nคมคาย\nครบครัน\nครบถ้วน\nครอบครอง\nครอบคลุม\nครอบครัว\nครอบงำ\nครอบจักรวาล\nคริสตกาล\nคริสตจักร\nคริสต์มาส\nคริสต์ศตวรรษ\nคริสต์ศักราช\nคริสตัง\nคริสเตียน\nครุกรรม\nครุภัณฑ์\nครุศาสตร์\nครุฑพ่าห์\nครุ่นคิด\nคลอเคลีย\nคล่องแคล่ว\nคล่องตัว\nคล่องมือ\nคลั่งไคล้\nคลาคล่ำ\nคลาไคล\nคลาดเคลื่อน\nคลาดแคล้ว\nคลี่คลาย\nคลึงเคล้น\nคลึงเคล้า\nคลื่นไส้\nคลื่นเหียน\nคลุกคลี\nคลุกคลาน\nคลุมเครือ\nคลุมโปง\nคลุ้มคลั่ง\nควงสว่าน\nควบคุม\nควบคู่\nควบแน่น\nควันหลง\nความคิด\nความหลัง\nความเห็น\nคอหอย\nคอห่าน\nคอแห้ง\nค่อนขอด\nค่อนแคะ\nค้อนควัก\nคั่งค้าง\nคั่งแค้น\nคัดค้าน\nคัดง้าง\nคัดท้าย\nคัดเลือก\nคันจาม\nคันฉ่อง\nคันฉาย\nคันชัก\nคันชั่ง\nคันไถ\nคันนา\nคันเร่ง\nคับขัน\nคับคั่ง\nคับแค้น\nคับแคบ\nคางทูม\nคางหมู\nค้างคืน\nค้างปี\nคาดคั้น\nคาดเชือก\nคาดโทษ\nคาดหมาย\nคานหาม\nคาบเกี่ยว\nคาบศิลา\nคาบสมุทร\nคำขาด\nคำนำ\nคิดค้น\nคืนดี\nคืนตัว\nคุกเข่า\nคุณค่า\nคุณชาย\nคุณธรรม\nคุณนาย\nคุณภาพ\nคุณลักษณะ\nคุณวุฒิ\nคุณศัพท์\nคุณสมบัติ\nคุณหญิง\nคุณากร\nคุณูปการ\nคุโณปการ\nคุมเชิง\nคุ้มกัน\nคุยเขื่อง\nคุยโต\nคุ้ยเขี่ย\nคุ้มครอง\nคู่กรณี\nคู่กัด\nคู่ขา\nคู่แข่ง\nคู่ครอง\nคู่ควร\nคู่คิด\nคู่คี่\nคู่ใจ\nคู่ชีพ\nคู่ชีวิต\nคู่บารมี\nคู่บุญ\nคู่ปรปักษ์\nคู่ปรับ\nคู่ผสม\nคู่มือ\nคู่รัก\nคู่ลำดับ\nคู่สาย\nคู่หมั้น\nคู่หู\nคู่อริ\nคู่อาฆาต\nเคมีภัณฑ์\nเคยตัว\nเคร่งขรึม\nเคร่งครัด\nเคร่งเครียด\nเครดิตฟองซิเอร์\nเครื่องกล\nเครื่องกัณฑ์\nเครื่องแกง\nเครื่องเขิน\nเครื่องครัว\nเครื่องเคียง\nเครื่องเงิน\nเครื่องจักร\nเครื่องเซ่น\nเครื่องดนตรี\nเครื่องต้น\nเครื่องทุ่นแรง\nเครื่องเทศ\nเครื่องใน\nเครื่องบิน\nเครื่องบูชา\nเครื่องแบบ\nเครื่องประดับ\nเครื่องปรุง\nเครื่องปรุงรส\nเครื่องมือ\nเครื่องยนต์\nเครื่องร่อน\nเครื่องราง\nเครื่องเรือน\nเครื่องล่าง\nเครื่องเล่น\nเครื่องสาย\nเครื่องสำอาง\nเครื่องสุกำศพ\nเครื่องหมาย\nเครือรัฐ\nเคลียคลอ\nเคลื่อนที่\nเคลื่อนไหว\nเคลือบแคลง\nเคลือบแฝง\nเคลือบฟัน\nเคว้งคว้าง\nเคหสถาน\nเค้าโครง\nเคียดแค้น\nเคี่ยวเข็ญ\nเคี้ยวเอื้อง\nเคืองขุ่น\nโคนม\nโคบาล\nโคมูตร\nโคมลอย\nโครงการ\nโครงเรื่อง\nโครงงาน\nโครงสร้าง\nโครมคราม\nโคลงเคลง\nฆ้องกระแต\nฆ้องชัย\nฆ้องวง\nฆ้องหุ่ย\nฆ้องเหม่ง\nฆ้องโหม่ง\nฆาตกร\nฆาตกรรม\nฆานประสาท\nงงงวย\nงงงัน\nงดเว้น\nงบดุล\nงบประมาณ\nงมโข่ง\nงมงาย\nง่วงงุน\nง่วงเหงา\nงอหาย\nง้องอน\nงอนง้อ\nงอมแงม\nงาช้าง\nง่าเงย\nงานการ\nง่ายดาย\nงึมงำ\nเงินเดือน\nเงินตรา\nเงินยวง\nเงียบกริบ\nเงียบเชียบ\nเงียบเหงา\nเงื่องหงอย\nเงื่อนไข\nเงื่อนงำ\nเงื่อนเวลา\nเงื้อมมือ\nแง่งอน\nจงใจ\nจงรัก\nจดจ่อ\nจดจำ\nจดหมาย\nจดหมายเหตุ\nจรจัด\nจรรยาบรรณ\nจริงจัง\nจริงใจ\nจอมขวัญ\nจอมใจ\nจอมทัพ\nจอมปลวก\nจอมพล\nจ๊ะเอ๋\nจักสาน\nจักรพรรดิ\nจักรภพ\nจักรยาน\nจักรยานยนต์\nจักรราศี\nจักรวรรดิ\nจักรวรรดินิยม\nจักรวาล\nจังหนับ\nจัดการ\nจัดจ้าน\nจัดเจน\nจัดแจง\nจัดตั้ง\nจัดสรร\nจับกุม\nจับจด\nจับเจ่า\nจ่าหน้า\nจาตุทสี\nจาตุมหาราช\nจาตุมหาราชิก\nจาตุมหาราชิกา\nจาตุรงคสันนิบาต\nจาตุรราชการ\nจานเชิง\nจานบิน\nจานผี\nจานเสียง\nจาบจ้วง\nจำเป็น\nจำพรรษา\nจำวัด\nจ้ำจี้จ้ำไช\nจำเลาะตา\nจิงโจ้น้ำ\nจิตใจ\nจิตตภาวนา\nจิตตัง\nจิตตานุปัสสนา\nจิตนิยม\nจิตบำบัด\nจิตแพทย์\nจิตวิสัย\nจิตรกร\nจิตรกรรม\nจิตรลดา\nจิตวิทยา\nจิตเวช\nจิตเวชศาสตร์\nจินตกวี\nจินตนา\nจินตนาการ\nจินตภาพ\nจุฑามณี\nจุฑามาศ\nจุฑารัตน์\nจุนเจือ\nจุ้นจ้าน\nจุลชีพ\nจุลชีวัน\nจุลชีวิน\nจุลทรรศน์\nจุลภาค\nจุลวรรค\nจุลศักราช\nจุลสาร\nจุลินทรีย์\nจุฬามณี\nจุฬาลักษณ์\nเจตคติ\nเจตจำนง\nเจตนารมณ์\nเจตภูต\nเจริญพร\nเจ้ากรม\nเจ้ากรรม\nเจ้าของ\nเจ้าขา\nเจ้าข้า\nเจ้าคณะ\nเจ้าค่ะ\nเจ้าจอม\nเจ้าชู้\nเจ้าตัว\nเจ้าถิ่น\nเจ้าท่า\nเจ้าที่\nเจ้าทุกข์\nเจ้านาย\nเจ้าเนื้อ\nเจ้าบ้าน\nเจ้าบ่าว\nเจ้าประคุณ\nเจ้าประคู้น\nเจ้าพนักงาน\nเจ้าพระคุณ\nเจ้าพระยา\nเจ้าพ่อ\nเจ้าพายุ\nเจ้าฟ้า\nเจ้าภาพ\nเจ้ามือ\nเจ้าแม่\nเจ้าเรือน\nเจ้าสังกัด\nเจ้าสัว\nเจ้าสาว\nเจ้าหน้าที่\nเจ้าหนี้\nเจ้าอาวาส\nเจาะจง\nเจือจาง\nเจือจาน\nเจือปน\nเจื้อยแจ้ว\nแจกจ่าย\nแจ่มแจ้ง\nแจ่มใส\nโจงกระเบน\nโจมตี\nโจรกรรม\nโจรสลัด\nใจความ\nใจคอ\nฉกฉวย\nฉกชิง\nฉลองได\nฉ้อฉล\nฉัตรมงคล\nฉันทลักษณ์\nฉายาลักษณ์\nฉิบหาย\nฉุกเฉิน\nฉุกละหุก\nฉุนเฉียว\nฉุปศาสตร์\nเฉไฉ\nเฉยเมย\nเฉาโฉด\nเฉิดฉัน\nเฉิดฉาย\nเฉิดฉิน\nเฉียบขาด\nเฉียบพลัน\nเฉียบแหลม\nเฉื่อยชา\nแฉะแบะ\nโฉดเฉา\nโฉมงาม\nโฉมฉาย\nโฉมเฉลา\nโฉมตรู\nโฉมยง\nโฉมศรี\nโฉมหน้า\nชดช้อย\nชดเชย\nชดใช้\nชนบท\nชนินทร์\nชนกกรรม\nชนมพรรษา\nชนมายุ\nชมเชย\nชมพูทวีป\nชมพูนท\nชมพูนุท\nชราธรรม\nชราภาพ\nชลจร\nชลธาร\nชลธี\nชลนัยน์\nชลนา\nชลเนตร\nชลประทาน\nชลมารค\nชลาธาร\nชลาลัย\nชลาศัย\nชลาสินธุ์\nชโลทร\nช่วงชิง\nช่วงใช้\nชวนชม\nชวนหัว\nช่วยเหลือ\nช่อฟ้า\nช่อม่วง\nชอกช้ำ\nช่องเขา\nช่องแคบ\nช่องไฟ\nช่องว่าง\nช้องนาง\nชอบกล\nชอบใจ\nชอบธรรม\nชอบพอ\nชักโครก\nชักเงา\nชักจูง\nชักชวน\nชักนำ\nชักเนื้อ\nชักพระ\nชักเย่อ\nชักใย\nชั่งใจ\nชังฆวิหาร\nชัดเจน\nชั้นเชิง\nชั่วคน\nชั่วคราว\nชั่วช้า\nชั่วโมง\nชั่วแล่น\nชาเย็น\nช้านาน\nช่างเครื่อง\nช่างฝีมือ\nช่างฟิต\nช่างไฟ\nช้างน้ำ\nช้างเผือก\nช้างพลาย\nช้างพัง\nช้างสาร\nช้างสีดอ\nชาติธรรม\nชาตินิยม\nชาติพันธุ์\nชาติพันธุ์วิทยา\nชาติภูมิ\nชานชาลา\nชายชาตรี\nชายคา\nชายฝั่ง\nชายทะเล\nชาวเล\nชาววัง\nช้ำใจ\nช้ำชอก\nชิงชัง\nชิงพลบ\nชินชา\nชินบุตร\nชิ้นเอก\nชิมลาง\nชีเปลือย\nชี้ขาด\nชี้แจง\nชี้นำ\nชี้แนะ\nชี้ฟ้า\nชีพจร\nชีพิตักษัย\nชื่นชม\nชื่นบาน\nชื่นมื่น\nชื่อย่อ\nชื่อรอง\nชื่อเล่น\nชื่อเสียง\nชุกชุม\nชุติมา\nชุบตัว\nชุบเลี้ยง\nชุมชน\nชุมทาง\nชุมสาย\nชุ่มใจ\nชุ่มชื่น\nชุ่มชื้น\nชุมนุมชน\nชูชีพ\nชูโรง\nชู้สาว\nเชยชม\nเชลยศักดิ์\nเชลยศึก\nเช่าซื้อ\nเช้าตรู่\nเช้ามืด\nเชิงกราน\nเชิงกล\nเชิงชั้น\nเชิงชาย\nเชิงซ้อน\nเชิงเดียว\nเชิงเดี่ยว\nเชิงตะกอน\nเชิงเทิน\nเชิงมุม\nเชิดชู\nเชิงอรรถ\nเชี่ยนหมาก\nเชี่ยวชาญ\nเชื่องช้า\nเชื่อใจ\nเชื่อถือ\nเชื่อฟัง\nเชื่อมือ\nเชื้อชาติ\nเชื้อเพลิง\nเชื้อไฟ\nเชื้อโรค\nเชื้อสาย\nเชื้อเชิญ\nเชื่องช้า\nเชือนแช\nเชื่อวัน\nแช่เย็น\nแช่อิ่ม\nแช่มช้อย\nแช่มชื่น\nโชกโชน\nโชติช่วง\nโชติรส\nใช้สอย\nซบเซา\nซมซาน\nซวนเซ\nซอกซอน\nซอกแซก\nซ่องสุม\nซ่องเสพ\nซ่องแซ่ง\nซ่อนรูป\nซ่อนเร้น\nซ่อนหา\nซ่อนกลิ่น\nซ่อนทราย\nซ่อมแซม\nซักค้าน\nซักซ้อม\nซักไซ้\nซักฟอก\nซักแห้ง\nซังกะตาย\nซังตาย\nซัดเซ\nซัดทอด\nซับซ้อน\nซับใน\nซับพระพักตร์\nซากศพ\nซ่านเซ็น\nซ้ำซ้อน\nซ้ำซาก\nซ้ำเติม\nซ้ำร้าย\nซี่โครง\nซีดเซียว\nซึมกะทือ\nซึมซาบ\nซึมเซา\nซึมทราบ\nซึมเศร้า\nซื่อตรง\nซื่อสัตย์\nซื้อขาย\nซุกซน\nซุกซ่อน\nซุบซิบ\nซู่ซ่า\nเซซัง\nเซ่อซ่า\nแซ่ซ้อง\nโซดาไฟ\nญาณทัสนะ\nญาณวิทยา\nญาณศาสตร์\nญาติกา\nฐานราก\nดกดื่น\nดงดิบ\nดลใจ\nดลบันดาล\nดวงแก้ว\nดวงใจ\nดวงเดือน\nดวงตรา\nดวงตา\nดวงสมร\nดอกจัน\nดอกจิก\nดอกบัว\nดอกเบี้ย\nดอกฟ้า\nดอกไม้\nดอกยาง\nดอกเล็บ\nดอกทอง\nดอกสร้อย\nดองยา\nดักคอ\nดักฟัง\nดังนั้น\nดังนี้\nดังหนึ่ง\nดั้งเดิม\nดัดจริต\nดัดแปลง\nดันทุรัง\nดับขันธ์\nดับจิต\nดับชีพ\nด่าทอ\nด่างทับทิม\nด่างพร้อย\nดาดฟ้า\nดาราศาสตร์\nดาลเดือด\nดาวกระจาย\nดาวเคราะห์\nดาวตก\nดาวเทียม\nดาวรุ่ง\nดาวเรือง\nดาวฤกษ์\nดาวหาง\nดาวเหนือ\nดาษดื่น\nดินขาว\nดินดาน\nดินดำ\nดินประสิว\nดินปืน\nดินระเบิด\nดินสอ\nดินสอพอง\nดิ้นรน\nดิบดี\nดีเกลือ\nดีใจ\nดีซ่าน\nดีดัก\nดีเดือด\nดีฝ่อ\nดีดดิ้น\nดึกดำบรรพ์\nดึกดื่น\nดึงดัน\nดึงดูด\nดื่มด่ำ\nดื้อด้าน\nดื้อดึง\nดื้อแพ่ง\nดื้อยา\nดื้อรั้น\nดุดัน\nดุเดือด\nดุร้าย\nดุลการค้า\nดุลพินิจ\nดุลภาค\nดุลยพินิจ\nดุลยภาพ\nดุษฎีนิพนธ์\nดุษฎีบัณฑิต\nดุษณีภาพ\nดูแคลน\nดูถูก\nดูดาย\nดูเบา\nดูแล\nดูหมิ่น\nดูเหมือน\nดูดดื่ม\nเด็ดขาด\nเด็ดดวง\nเด็ดเดี่ยว\nเดนตาย\nเดาสวด\nเดาสุ่ม\nเดินทาง\nเดินสะพัด\nเดินสาย\nเดินเหิน\nเดิมพัน\nเดียงสา\nเดียดฉันท์\nเดียวกัน\nเดียวดาย\nเดี๋ยวเดียว\nเดี๋ยวนี้\nเดือดดาล\nเดือดร้อน\nเดือนมืด\nเดือนหงาย\nแดดาล\nแดดิ้น\nแดกดัน\nโด่เด่\nโด่งดัง\nโดดเดี่ยว\nโดยสาร\nได้การ\nได้แก่\nได้ใจ\nได้ที\nได้ยิน\nได้เสีย\nตกเขียว\nตกค้าง\nตกใจ\nตกต่ำ\nตกแต่ง\nตกทอด\nตกฟาก\nตกมัน\nตกยาก\nตกลง\nตกหล่น\nต้นขั้ว\nต้นคิด\nต้นฉบับ\nต้นตอ\nต้นตำรับ\nต้นทุน\nต้นแบบ\nต้นเพลิง\nต้นมือ\nต้นไม้\nต้นร่าง\nต้นเรื่อง\nต้นสังกัด\nต้นหน\nต้นเหตุ\nตบตา\nตบแต่ง\nตบแผละ\nตบมือ\nต้มข่า\nต้มโคล้ง\nต้มยำ\nต้มส้ม\nตรมตรอม\nตรรกวิทยา\nตรรกศาสตร์\nตรวจการ\nตรวจการณ์\nตรวจตรา\nตระบัดสัตย์\nตรัสรู้\nตราตั้ง\nตราบาป\nตรายาง\nตราสาร\nตริตรอง\nตรีกฏุก\nตรีกาย\nตรีโกณ\nตรีโกณมิติ\nตรีคูณ\nตรีทูต\nตรีปิฎก\nตรีภพ\nตรีมูรติ\nตรึกตรอง\nตรึงตรา\nตรุษจีน\nตฤณชาติ\nตฤณมัย\nตลกบาตร\nตลบตะแลง\nตลบหลัง\nตลาดนัด\nตลาดน้ำ\nตลาดมืด\nตลาดสด\nต่อตี\nต่อเติม\nต่อว่า\nต่อสู้\nต่อกร\nต่อต้าน\nต่อแย้ง\nต้องการ\nต้องโทษ\nต้องหา\nต้อนรับ\nตอบโต้\nตอบแทน\nต่อยหอย\nตะพาบน้ำ\nตักตวง\nตักบาตร\nตั้งเข็ม\nตั้งไข่\nตั้งเค้า\nตั้งแง่\nตั้งใจ\nตั้งต้น\nตั้งแต่\nตั้งท้อง\nตัดขาด\nตัดใจ\nตัดเชือก\nตัดตอน\nตัดทอน\nตัดบท\nตัดพ้อ\nตัดรอน\nตัดสิน\nตับเต่า\nตับแลบ\nตับอ่อน\nตัวกลาง\nตัวการ\nตัวเก็ง\nตัวดี\nตัวตั้ง\nตัวเต็ง\nตัวถัง\nตัวแทน\nตัวประกอบ\nตัวประกัน\nตัวแปร\nตัวผู้\nตัวพิมพ์\nตัวเมีย\nตัวยืน\nตัวเลข\nตัวอย่าง\nตั๋วเงิน\nตั๋วแลกเงิน\nตากล้อง\nตาไก่\nตาข่าย\nตาชั่ง\nตาตุ่ม\nตาทวด\nตาปลา\nตาราง\nต่างหาก\nต้านทาน\nตามใจ\nตายใจ\nตายซาก\nตายด้าน\nตายตัว\nตายทั้งกลม\nตายห่า\nตายโหง\nตาลปัตร\nต่ำช้า\nต่ำต้อย\nตำส้ม\nติเตียน\nติณชาติ\nติดขัด\nติดใจ\nติดต่อ\nติดตั้ง\nติดตาม\nติดตื้น\nติดพัน\nติดลม\nติดอ่าง\nตีเกลียว\nตีขลุม\nตีความ\nตีคู่\nตีจาก\nตีตื้น\nตีแผ่\nตีรวน\nตีลังกา\nตีวง\nตีเสมอ\nตีนกา\nตีนคู้\nตีนจก\nตีนตะขาบ\nตีนผี\nตีนเหยียด\nตึกแถว\nตึกระฟ้า\nตึงเครียด\nตึงตัง\nตื้นตัน\nตื่นตัว\nตื่นตูม\nตื่นเต้น\nตุ๊ต๊ะ\nตุ้บตั้บ\nตุ้มหู\nตุลาการ\nตุลาคม\nตู้นิรภัย\nตูมตาม\nตู้เสบียง\nเตโชธาตุ\nเตร็ดเตร่\nเต้นรำ\nเตาแก๊ส\nเตาผิง\nเตาฟู่\nเตาไฟ\nเตารีด\nเตาสูบ\nเต่าทอง\nเต้ารับ\nเต้าส่วน\nเต้าเสียบ\nเต้าหู้ยี้\nแต่ละ\nแตกคอ\nแตกคอก\nแตกฉาน\nแตกดับ\nแตกตื่น\nแตกพาน\nแตกแยก\nแตกร้าว\nแตกหัก\nแต่งงาน\nแต่งตั้ง\nแต้มคู\nแต้มต่อ\nแตรงอน\nแตรเดี่ยว\nแตรฝรั่ง\nแตรฟันฟาร์\nแตรวง\nโต้ตอบ\nโต้เถียง\nโต้แย้ง\nโต๊ะหมู่\nโต๊ะอิหม่าม\nใต้ถุน\nไต้ก๋ง\nไต่คู้\nไต่เต้า\nไต่ถาม\nไต้ฝุ่น\nไตรจักร\nไตรจีวร\nไตรตรึงษ์\nไตรทวาร\nไตรปิฎก\nไตรเพท\nไตรภพ\nไตรภูมิ\nไตรภาคี\nไตรยางศ์\nไตรรงค์\nไตรรัตน์\nไตรลักษณ์\nไตรโลก\nไตรสรณคมน์\nไตรสิกขา\nไต่สวน\nถกเถียง\nถดถอย\nถนัดถนี่\nถนิมสร้อย\nถมถืด\nถมเถ\nถมไป\nถลากไถล\nถ้วนถี่\nถ้วยฟู\nถ่องแท้\nถอดถอน\nถ้อยคำ\nถ้อยแถลง\nถากถาง\nถ่านไฟฉาย\nถ่านหิน\nถามไถ่\nถ่ายทอด\nถ่ายทุกข์\nถ่ายเท\nถาวรวัตถุ\nถ้ำมอง\nถี่ถ้วน\nถึงใจ\nถูกใจ\nถูกชะตา\nเถรวาท\nเถ้าแก่\nเถ้าแก่เนี้ย\nแถมพก\nแถลงการณ์\nไถ่ถอน\nไถ่ถาม\nทดแทน\nทดรอง\nทดลอง\nทดสอบ\nทนทาน\nทนายความ\nทบทวน\nทแยงมุม\nทรงกลด\nทรงเครื่อง\nทรงเจ้า\nทรัพย์สิน\nทรามชม\nทรามเชย\nทรามวัย\nทรามสงวน\nทรามสวาท\nทรุดโทรม\nทฤษฎีบท\nท้วงติง\nท่วมท้น\nทวาทศ\nทวาทศมาส\nทวาบรยุค\nทวารบาล\nทวิบถ\nทวิบท\nทวิบาท\nทวิภาค\nทวิภาคี\nทวีคูณ\nทศกัณฐ์\nทศชาติ\nทศทิศ\nทศนิยม\nทศพร\nทศพล\nทศพิธราชธรรม\nทศมาส\nทศวรรษ\nท่อไอเสีย\nท้อถอย\nท้อแท้\nทองขาว\nทองคำ\nทองคำขาว\nทองคำเปลว\nทองเค\nทองแดง\nทองบรอนซ์\nทองม้วน\nทองย้อย\nทองสัมฤทธิ์\nทองหยอด\nทองหยิบ\nทองเหลือง\nทองเอก\nท่องเที่ยว\nท้องตรา\nท้องถิ่น\nท้องที่\nท้องน้อย\nท้องร่อง\nท้องเรื่อง\nทอดมัน\nทอดทิ้ง\nทอดน่อง\nทอดยอด\nทอดหุ่ย\nทอยกอง\nทะเบียนบ้าน\nทะเลทราย\nทะเลสาบ\nทะเลหลวง\nทักขิณาวัฏ\nทักท้วง\nทักทาย\nทักษิณาวรรต\nทักษิณาทาน\nทักษิณานุประทาน\nทั้งกลม\nทั้งคน\nทั้งดุ้น\nทั้งที\nทั้งนั้น\nทั้งนี้\nทั้งปวง\nทั้งผอง\nทั้งเพ\nทั้งมวล\nทั้งสิ้น\nทั้งหมด\nทั้งหลาย\nทัณฑ์บน\nทัดทาน\nทัดเทียม\nทันควัน\nทันใจ\nทันใด\nทันตา\nทันสมัย\nทันที\nทับถม\nทับทรวง\nทับศัพท์\nทั่วถึง\nทั่วไป\nท่าทาง\nท่าที\nท้าทาย\nทางการ\nทางข้าม\nทางด่วน\nทางเท้า\nทางโท\nทางใน\nทางผ่าน\nทางม้าลาย\nทางหลวง\nทางออก\nทางเอก\nทานกัณฑ์\nทานตะวัน\nท่านชาย\nทานบารมี\nท่านผู้หญิง\nท่านหญิง\nทาบทาม\nท้ายทอย\nทารุณกรรม\nทำคลอด\nทำใจ\nทำซ้ำ\nทำท่า\nทำที\nทำแท้ง\nทำโทษ\nทำบาป\nทำบุญ\nทำพิษ\nทำฟัน\nทำร้าย\nทำวัตร\nทำสาว\nทำเสน่ห์\nทำหมัน\nทำให้\nทิ้งขว้าง\nทิ้งทวน\nทิ้งท้าย\nทินกร\nทิพจักขุ\nทิพโสต\nทิพยจักษุ\nทิพยญาณ\nทิพยเนตร\nทิพยรส\nทิพากร\nทิ่มตำ\nทิ่มแทง\nทิวากร\nทิวากาล\nทิศทาง\nทีเด็ด\nทีท่า\nทีนี้\nทีหลัง\nทีฆนิกาย\nทีฆสระ\nที่ดิน\nที่นอน\nที่นั่ง\nที่ปรึกษา\nที่พึ่ง\nที่มั่น\nที่ราบ\nที่ว่าการ\nที่สุด\nที่หมาย\nที่ไหน\nทุกที\nทุกเมื่อ\nทุกข์สุข\nทุนทรัพย์\nทุนนิยม\nทุนรอน\nทุนสำรอง\nทุ่มเถียง\nทุ่มเท\nทูนหัว\nทูลกระหม่อม\nเทกระจาด\nเทครัว\nเทพเจ้า\nเทพดา\nเทพธิดา\nเทพนม\nเทพนิยม\nเทพนิยาย\nเทพบุตร\nเทพสังหรณ์\nเทศกาล\nเทศนาโวหาร\nเทศบัญญัติ\nเทศบาล\nเทศมนตรี\nเทห์ฟากฟ้า\nเท่ากับ\nเท่าใด\nเท่าตัว\nเท่าทัน\nเท่าทุน\nเท่าเทียม\nเท่านั้น\nเท่าไร\nเท้าช้าง\nเทิดทูน\nเที่ยงตรง\nเที่ยงแท้\nเที่ยงธรรม\nเทียนชนวน\nเทียนพรรษา\nเทียบเคียง\nเทียบเท่า\nเทือกเขา\nเทือกเถา\nแท็งก์น้ำ\nแท่นพิมพ์\nแท่นมณฑล\nแท่นหมึก\nแทรกซอน\nแทรกซ้อน\nแทรกซึม\nแทรกแซง\nแทะโลม\nไทยดำ\nไทยทาน\nไทยธรรม\nไทยน้อย\nไทยใหญ่\nธงชัย\nธงชาติ\nธงทิว\nธรณีวิทยา\nธรณีสงฆ์\nธรรมกาย\nธรรมการ\nธรรมเกษตร\nธรรมขันธ์\nธรรมคุณ\nธรรมจรรยา\nธรรมจริยา\nธรรมจักร\nธรรมจักษุ\nธรรมจาคะ\nธรรมจารี\nธรรมชาติ\nธรรมดา\nธรรมเนียม\nธรรมราชา\nธรรมศาสตร์\nธรรมสภา\nธรรมสังเวช\nธัญพืช\nธารพระกร\nธีรภาพ\nธีรราช\nนกเขา\nนกต่อ\nนกยูง\nนกรู้\nนกหวีด\nนครบาล\nนครรัฐ\nนงคราญ\nนงนุช\nนงพะงา\nนงเยาว์\nนงราม\nนงลักษณ์\nนบนอบ\nนพเก้า\nนพคุณ\nนพเคราะห์\nนพปฎล\nนพพล\nนพรัตน์\nนพศก\nนพศูล\nนมข้น\nนมผง\nนมไม้\nนมนาน\nนมหนู\nนมแมว\nนรีเวช\nนรีเวชวิทยา\nนวดฟั้น\nนวยนาด\nนวลระหง\nนวลลออ\nนวลละออง\nนวลจันทร์\nนอกครู\nนอกคอก\nนอกจาก\nนอกใจ\nนอกชาน\nนอกรีต\nนอกเหนือ\nนองเนือง\nนองเลือด\nนอนก้น\nนอนใจ\nนอบนบ\nนอนเล่น\nนอบน้อม\nน้อมนำ\nน้อยใจ\nน้อยหน้า\nนักการ\nนักการเมือง\nนักกีฬา\nนักข่าว\nนักท่องเที่ยว\nนักเทศน์\nนักโทษ\nนักธรรม\nนักบวช\nนักบิน\nนักบุญ\nนักปราชญ์\nนักพรต\nนักรบ\nนักเรียน\nนักเลง\nนักวิชาการ\nนักศึกษา\nนักสิทธิ์\nนักสืบ\nนักหนา\nนั่งเทียน\nนั่งร้าน\nนัดแนะ\nนัดหมาย\nนั่นแหละ\nนั่นเอง\nนับถือ\nนับประสา\nนัยน์ตา\nนาดำ\nนาปรัง\nนาปี\nนาสวน\nนาหว่าน\nนาคบาศ\nนาคปรก\nนาคราช\nนางกวัก\nนางกำนัล\nนางงาม\nนางใน\nนางบำเรอ\nนางแบบ\nนางพญา\nนางฟ้า\nนางไม้\nนางโลม\nนางสาว\nนางห้าม\nนางเอก\nนาฏกรรม\nนาฏดนตรี\nนาฏศิลป์\nนานนม\nน่านน้ำ\nน่านฟ้า\nนามกร\nนามธรรม\nนามไธย\nนามบัตร\nนามปากกา\nนามแฝง\nนามสกุล\nนามสงเคราะห์\nนามสมญา\nนายทะเบียน\nนายท่า\nนายท้าย\nนายทุน\nนายประกัน\nนายหน้า\nนายอำเภอ\nนารายณ์หัตถ์\nนารีผล\nนาวิกโยธิน\nนำจับ\nนำพา\nนำทาง\nนำร่อง\nนำสืบ\nนำแสดง\nน้ำกรด\nน้ำกาม\nน้ำเกลือ\nน้ำข้าว\nน้ำแข็ง\nน้ำแข็งไส\nน้ำแข็งแห้ง\nน้ำครำ\nน้ำคร่ำ\nน้ำค้าง\nน้ำค้างแข็ง\nน้ำคาวปลา\nน้ำคำ\nน้ำเค็ม\nน้ำเคย\nน้ำเงิน\nน้ำเงี้ยว\nน้ำจัณฑ์\nน้ำจิ้ม\nน้ำใจ\nน้ำเชื้อ\nน้ำเชื่อม\nน้ำซาวข้าว\nน้ำดอกไม้\nน้ำดี\nน้ำตก\nน้ำตา\nน้ำตาล\nน้ำท่า\nน้ำนม\nน้ำนวล\nน้ำบาดาล\nน้ำประสานทอง\nน้ำประปา\nน้ำปลา\nน้ำป่า\nน้ำผึ้ง\nน้ำพริก\nน้ำพริกเผา\nน้ำพี้\nน้ำพุ\nน้ำมนต์\nน้ำมนตร์\nน้ำมัน\nน้ำมือ\nน้ำมูก\nน้ำเมา\nน้ำย่อย\nน้ำยา\nน้ำรัก\nน้ำแร่\nน้ำลาย\nน้ำเลี้ยง\nน้ำสต๊อก\nน้ำส้ม\nน้ำส้มสายชู\nน้ำสังข์\nน้ำสาบาน\nน้ำเสียง\nน้ำหนวก\nน้ำหนอง\nน้ำหนัก\nน้ำหน้า\nน้ำหนึ่ง\nน้ำหมึก\nน้ำหอม\nน้ำเหลือง\nน้ำอบ\nน้ำอ้อย\nน้ำอัดลม\nนิ่งเฉย\nนิจศีล\nนิดเดียว\nนิดหน่อย\nนิติกร\nนิติกรรม\nนิติธรรม\nนิตินัย\nนิติบัญญัติ\nนิติบุคคล\nนิติภาวะ\nนิติวิทยาศาสตร์\nนิติเวช\nนิติเวชศาสตร์\nนิติศาสตร์\nนิเทศศาสตร์\nนิ่มนวล\nนิรุกติศาสตร์\nนิเวศวิทยา\nนิศากร\nนิศากาล\nนิศาชล\nนิศารัตน์\nนี่แน่ะ\nนี่แหละ\nนี่เอง\nนึกคิด\nนุงถุง\nนุ่งห่ม\nนุ่มนวล\nนุ่มนิ่ม\nเนตรนารี\nเนติบัณฑิต\nเนยเทียม\nเนยใส\nเนิ่นนาน\nเนิบนาบ\nเนื้อความ\nเนื้อคู่\nเนื้อเค็ม\nเนื้องอก\nเนื้อตัว\nเนื้อตาย\nเนื้อที่\nเนื้อแท้\nเนื้อเปื่อย\nเนื้อผ้า\nเนื้อเพลง\nเนื้อไม้\nเนื้อเยื่อ\nเนื้อร้อง\nเนื้อร้าย\nเนื้อเรื่อง\nเนื้อหา\nเนืองนอง\nเนืองนิตย์\nเนืองแน่น\nแน่ใจ\nแน่ชัด\nแน่แท้\nแน่นอน\nแน่นิ่ง\nแน่แน่ว\nแน่นแฟ้น\nแน่นหนา\nแนบเนียน\nแนบแน่น\nแนวคิด\nแนวทาง\nแนวโน้ม\nแนวป่า\nแนวรบ\nแนวร่วม\nแนวหน้า\nแนวหลัง\nแน่วแน่\nแนะนำ\nแนะแนว\nโน้มน้าว\nในหลวง\nบกพร่อง\nบงกช\nบงการ\nบดบัง\nบทกลอน\nบทกวี\nบทความ\nบทคัดย่อ\nบทเฉพาะกาล\nบทนำ\nบทบัญญัติ\nบทบาท\nบทประพันธ์\nบทเพลง\nบทร้อง\nบทเรียน\nบทลงโทษ\nบทสนทนา\nบทอัศจรรย์\nบทจร\nบทบงสุ์\nบทมาลย์\nบทรัช\nบทเรศ\nบทวลัญช์\nบนบาน\nบรมครู\nบรมธาตุ\nบรมบพิตร\nบรมวงศานุวงศ์\nบรมอัฐิ\nบรรณพิภพ\nบรรณศาลา\nบรรณาการ\nบรรณาธิการ\nบรรณานุกรม\nบรรณารักษ์\nบรรณารักษศาสตร์\nบรรดามี\nบรรดาศักดิ์\nบรรทัดฐาน\nบรรพบุรุษ\nบรรลัยกัลป์\nบรรลัยจักร\nบริคณห์สนธิ\nบวงสรวง\nบ่วงบาศ\nบ้วนพระโอษฐ์\nบ่อเกิด\nบอกกล่าว\nบอกบท\nบอกบุญ\nบอกใบ้\nบอกปัด\nบ้องกัญชา\nบ้องตื้น\nบ้องไฟ\nบ้องหู\nบอดสี\nบ่อนทำลาย\nบอบช้ำ\nบอบบาง\nบอบแบบ\nบังโกลน\nบังโคลน\nบังใบ\nบั้งไฟ\nบังคับการ\nบังคับบัญชา\nบัญชาการ\nบัณฑุกัมพล\nบัดดล\nบัดเดี๋ยว\nบัดนั้น\nบัดนี้\nบัดสีบัดเถลิง\nบัตรเครดิต\nบัตรพลี\nบัตรสนเท่ห์\nบัตรสินเชื่อ\nบั่นทอน\nบั้นท้าย\nบั้นปลาย\nบั้นพระองค์\nบั้นเอว\nบันไดลิง\nบันไดเลื่อน\nบันเทิงคดี\nบัวลอย\nบัวบก\nบ้าจี้\nบ้าดีเดือด\nบ้าน้ำลาย\nบ้าบิ่น\nบ้าระห่ำ\nบ้าเลือด\nบ้าหอบฟาง\nบากบั่น\nบากหน้า\nบางตา\nบางเบา\nบางที\nบาดเจ็บ\nบาดแผล\nบาดหมาง\nบาตรใหญ่\nบาทบงกช\nบาทบงสุ์\nบาทบริจาริกา\nบาทวิถี\nบานเกล็ด\nบานตะเกียง\nบานตะไท\nบานเบอะ\nบานปลาย\nบานแผละ\nบานพับ\nบ้านจัดสรร\nบ้านช่อง\nบ้านนอก\nบ้านพัก\nบ้านเมือง\nบ้านรับรอง\nบ้านเรือน\nบาปกรรม\nบายศรี\nบ่ายเบี่ยง\nบ่ายหน้า\nบ่าวไพร่\nบิดเบี้ยว\nบิดเบือน\nบิดพลิ้ว\nบี้แบน\nบีบคั้น\nบีบรัด\nบึ้งตึง\nบึ้งบูด\nบุกบั่น\nบุกเบิก\nบุกรุก\nบุคลิกภาพ\nบุคลิกลักษณะ\nบุญธรรม\nบุญนิธิ\nบุญฤทธิ์\nบุบสลาย\nบุ้ยใบ้\nบุรุษเพศ\nบุหงารำไป\nบู้บี้\nบูชายัญ\nบูดบึ้ง\nบูดเบี้ยว\nเบาความ\nเบาใจ\nเบาบาง\nเบาปัญญา\nเบามือ\nเบาแรง\nเบาสมอง\nเบาหวาน\nเบาโหวง\nเบ้าตา\nเบาะแส\nเบิกความ\nเบิกบาน\nเบี้ยล่าง\nเบี้ยเลี้ยง\nเบี้ยหวัด\nเบี่ยงบ่าย\nเบียดบัง\nเบียดเบียน\nเบียดเสียด\nเบื้องต้น\nเบื้องบน\nเบื้องหน้า\nเบื้องหลัง\nแบกะดิน\nแบเบาะ\nแบ่งเบา\nแบ่งปัน\nแบ่งแยก\nแบบฉบับ\nแบบแปลน\nแบบแผน\nแบบฝึกหัด\nแบบพิมพ์\nแบบสอบถาม\nแบบอย่าง\nแบะแฉะ\nแบะท่า\nโบแดง\nโบราณคดี\nโบราณวัตถุ\nโบราณสถาน\nใบขับขี่\nใบจอง\nใบตอง\nใบแทรก\nใบบอก\nใบบุญ\nใบเบิกทาง\nใบปลิว\nใบพัด\nใบโพ\nใบไม้\nใบระกา\nใบรับรอง\nใบลา\nใบเลี้ยง\nใบสั่ง\nใบสำคัญ\nใบสุทธิ\nใบเสร็จ\nใบหน้า\nใบอนุญาต\nใบระกา\nปกครอง\nปกคลุม\nปกป้อง\nปกปิด\nปฏิบัติการ\nปฏิบัติบูชา\nปฐพีวิทยา\nปฐมฌาน\nปฐมทัศน์\nปฐมเทศนา\nปฐมนิเทศ\nปฐมพยาบาล\nปฐมยาม\nปฐมฤกษ์\nปฐมวัย\nปฐมสมโพธิ\nปนเป\nป่นปี้\nปมเขื่อง\nปมเด่น\nปมด้อย\nปรนเปรอ\nปรบไก่\nปรบมือ\nปรสิตวิทยา\nประโปรย\nประพรม\nประกันชีวิต\nประกันภัย\nประจักษ์พยาน\nประจัญบาน\nประจันหน้า\nประจำการ\nประจำเดือน\nประจำเมือง\nประจำยาม\nประชดประชัน\nประชากร\nประชากรศาสตร์\nประชาคม\nประชาชน\nประชาราษฎร์\nประชาชาติ\nประชาชี\nประชาทัณฑ์\nประชาบาล\nประชาพิจารณ์\nประชาภิบาล\nประชามติ\nประชาสงเคราะห์\nประชาสัมพันธ์\nประดับประดา\nประดามี\nประดาน้ำ\nประเดี๋ยวเดียว\nประเดี๋ยวนี้\nประทับใจ\nประทุษร้าย\nประเทศราช\nประพาสต้น\nประเพณีนิยม\nประลัยกัลป์\nประวัติการณ์\nประวัติศาสตร์\nประสบการณ์\nประสบการณ์นิยม\nประสาทการ\nประสูติการ\nประสูติกาล\nประเส\nปรับทุกข์\nปรับโทษ\nปรับปรุง\nปรากฏการณ์\nปราดเปรียว\nปราดเปรื่อง\nปราบปราม\nปริญญาบัตร\nปรัยัติธรรม\nปรุโปร่ง\nปลงใจ\nปลงตก\nปลดทุกข์\nปลดปลง\nปลดปล่อย\nปลดเปลื้อง\nปลดระวาง\nปลดแอก\nปล้นสะดม\nปลอกกระสุน\nปลอกคอ\nปลอดโปร่ง\nปลอดภัย\nปลอมปน\nปลอมแปลง\nปลอบโยน\nปล่อยใจ\nปล่อยตัว\nปล่อยปละ\nปลั๊กไฟ\nปลากริม\nปลาเค็ม\nปลาจ่อม\nปลาเจ่า\nปลาแดก\nปลาตู้\nปลาทอง\nปลาร้า\nปลาส้ม\nปลาดาว\nปลาบิน\nปลาฝา\nปลาวาฬ\nปลาหมึก\nปลาบปลื้ม\nปลายข้าว\nปลายแถว\nปลายทาง\nปลิ้นปลอก\nปลิ้นปล้อน\nปลีกตัว\nปลีกย่อย\nปลุกใจ\nปลุกปล้ำ\nปลุกปั่น\nปลุกระดม\nปลุกเสก\nปลูกฝัง\nปลูกสร้าง\nปวดถ่วง\nปวดมวน\nปวดร้าว\nป่วนปั่น\nป่วยการ\nปอกลอก\nป้องกัน\nปักใจ\nปักดำ\nปักหลัก\nปัจเจกบุคคล\nปัจเจกพุทธะ\nปัจเจกโพธิ\nปัจฉิมชน\nปัจฉิมทิศ\nปัจฉิมภาค\nปัจฉิมยาม\nปัจฉิมลิขิต\nปัจฉิมวัย\nปัจฉิมวาจา\nปัญญาชน\nปัญญาวิมุติ\nปัญญาอ่อน\nปัดเป่า\nปันส่วน\nปั่นป่วน\nปั่นแปะ\nปั่นหัว\nปั้นจิ้ม\nปั้นเจ๋อ\nปั้นปึ่ง\nปั้นสิบ\nปั๊มน้ำมัน\nป่าช้า\nป่าชายเลน\nป่าดง\nป่าดงดิบ\nป่าดิบ\nป่าเถื่อน\nป่าเบญจพรรณ\nป่าละเมาะ\nปากกา\nปากขอ\nปากแข็ง\nปากคอ\nปากคำ\nปากคีบ\nปากจัด\nปากน้ำ\nปากเปล่า\nปากเสียง\nปานกลาง\nป่านนี้\nป้านลม\nป้ายสี\nป่าวร้อง\nปิดฉาก\nปิดบัง\nปิตุฆาต\nปิตุภูมิ\nปีมะโว้\nปีแสง\nปี่กลาง\nปี่ไฉน\nปี่ชวา\nปี่นอก\nปี่ใน\nปี่พาทย์\nปี่อ้อ\nปีกกา\nปีนเกลียว\nปีนป่าย\nปึกแผ่น\nปึงปัง\nปืนกล\nปืนครก\nปืนพก\nปืนยา\nปืนยาว\nปืนลม\nปืนเล็ก\nปืนเล็กยาว\nปืนสั้น\nปืนใหญ่\nปุบปับ\nปุ๊บปั๊บ\nปุ่มเปือก\nปุยฝ้าย\nปุ๋ยคอก\nปุ๋ยเคมี\nปุ๋ยวิทยาศาสตร์\nปุ๋ยหมัก\nปุ๋ยอินทรีย์\nปูจ๋า\nปูเสฉวน\nปู่เจ้า\nปู่ทวด\nปูนขาว\nปูนซีเมนต์\nปูนดิบ\nปูนแดง\nปูนปลาสเตอร์\nปูนปั้น\nเป็ดเทศ\nเป็ดน้ำ\nเป็นกลาง\nเป็นใจ\nเป็นต้น\nเป็นต่อ\nเป็นรอง\nเป็นไร\nเป็นลม\nเป็นห่วง\nเป็นอยู่\nเปรมปรีดิ์\nเปรอะเปื้อน\nเปรียบเทียบ\nเปรียบเปรย\nเปรี้ยวปาก\nเปรี้ยวหวาน\nเปรื่องปราด\nเปลญวน\nเปล่งปลั่ง\nเปล่าดาย\nเปล่าเปลี่ยว\nเปลี่ยนใจ\nเปลี่ยนตัว\nเปลี่ยนแปลง\nเปลี่ยนมือ\nเปลี่ยนหน้า\nเป๋อเหลอ\nเปะปะ\nเป่ากบ\nเป้านิ่ง\nเป้าหมาย\nเปิดฉาก\nเปิดเปิง\nเปิดโปง\nเปิดผนึก\nเปิดเผย\nเปียกปูน\nแป้งสาลี\nแป้งนวล\nแป้งเปียก\nแป้งมัน\nแป้งฝุ่น\nแป้งร่ำ\nแป้งสิงคโปร์\nแป้งหมี่\nแปดปน\nแปดเปื้อน\nแปรปรวน\nแปรผัน\nแปรพักตร์\nแปรรูป\nแปรอักษร\nแปลกปลอม\nแปะโป้ง\nโป้ปด\nโปร่งแสง\nโปร่งใส\nโปรดปราน\nโปรยทาน\nโปรยปราย\nโปโลน้ำ\nผกผัน\nผกากรอง\nผงขาว\nผงชูรส\nผงซักฟอก\nผงฟู\nผดุงครรภ์\nผมไฟ\nผลพลอยได้\nผลลัพธ์\nผลัดเปลี่ยน\nผลิตผล\nผลิตภัณฑ์\nผลุบโผล่\nผสมเทียม\nผสมผสาน\nผสมผเส\nผสมพันธุ์\nผสมโรง\nผสมเสร็จ\nผ่องแผ้ว\nผ่องใส\nผ่อนคลาย\nผ่อนชำระ\nผ่อนปรน\nผ่อนผัน\nผ่อนส่ง\nผอมโซ\nผอมแห้ง\nผักชี\nผักตบชวา\nผักบุ้ง\nผังเมือง\nผัดผ่อน\nผันแปร\nผันผวน\nผ่าตัด\nผ่าเผย\nผ่าหมาก\nผ่าเหล่า\nผ้าขนหนู\nผ้าขาวม้า\nผ้าขี้ริ้ว\nผ้าเช็ดตัว\nผ้าเช็ดปาก\nผ้าเช็ดมือ\nผ้าเช็ดหน้า\nผ้าดิบ\nผ้าต่วน\nผ้าไตร\nผ้าถุง\nผ้าแถบ\nผ้านวม\nผ้านุ่ง\nผ้าใบ\nผ้าป่า\nผ้าป่าน\nผ้าผ่อน\nผ้าพันคอ\nผ้าพันแผล\nผ้าแพร\nผ้าโพกหัว\nผ้ามัดหมี่\nผ้ายาง\nผ้าลูกไม้\nผ้าเหลือง\nผ้าอนามัย\nผ้าอ้อม\nผาดโผน\nผาติกรรม\nผิดหวัง\nผิวเผิน\nผิวพรรณ\nผิวหนัง\nผีกระสือ\nผีกระหัง\nผีกองกอย\nผีโขมด\nผีดิบ\nผีตองเหลือง\nผีถ้วยแก้ว\nผีแถน\nผีทะเล\nผีบุญ\nผีปอบ\nผีพุ่งไต้\nผีฟ้า\nผีเรือน\nผีสาง\nผีเสื้อ\nผีห่า\nผึ่งผาย\nผุดผ่อง\nผุดผาด\nผู้คน\nผู้คุม\nผู้จัดการ\nผู้ชาย\nผู้เชี่ยวชาญ\nผู้ดี\nผู้โดยสาร\nผู้ต้องขัง\nผู้ต้องหา\nผู้แทน\nผู้น้อย\nผู้บริโภค\nผู้บังคับบัญชา\nผู้ปกครอง\nผู้ประกอบการ\nผู้ป่วย\nผู้พิพากษา\nผู้เยาว์\nผู้ร้าย\nผู้วิเศษ\nผู้สื่อข่าว\nผู้เสียหาย\nผู้หญิง\nผู้ใหญ่\nผู้ใหญ่บ้าน\nผูกขวัญ\nผูกขาด\nผูกพัน\nผูกมัด\nเผชิญหน้า\nเผด็จการ\nเผด็จศึก\nเผยแผ่\nเผยแพร่\nเผละผละ\nเผ่าพันธุ์\nเผื่อแผ่\nแผงลอย\nแผนการ\nแผนงาน\nแผนที่\nแผนผัง\nแผนภาพ\nแผนภูมิ\nแผ่นดิน\nแผ่นเสียง\nแผ้วพาน\nโผงผาง\nฝนทอง\nฝอยทอง\nฝักแค\nฝักบัว\nฝักฝ่าย\nฝักใฝ่\nฝังใจ\nฝังหัว\nฝาชี\nฝาแฝด\nฝาละมี\nฝ่าพระบาท\nฝ่าฝืน\nฝ่าฟัน\nฝ้าฟาง\nฝากตัว\nฝากฝัง\nฝีดาษ\nฝีมะม่วง\nฝีจักร\nฝีเท้า\nฝีปาก\nฝีพาย\nฝีมือ\nฝีเย็บ\nฝึกงาน\nฝึกปรือ\nฝึกฝน\nฝึกสอน\nฝึกหัด\nฝืดเคือง\nใฝ่ฝัน\nพงพี\nพงศ์พันธุ์\nพญาโศก\nพญาไฟ\nพบปะ\nพบพาน\nพรสวรรค์\nพรมคด\nพรมแดน\nพรมมิ\nพรรคพวก\nพรรณราย\nพรวดพราด\nพรหมชาติ\nพรหมลิขิต\nพรหมโลก\nพรหมวิหาร\nพร้อมใจ\nพร้อมพรั่ง\nพร้อมเพรียง\nพร้อมมูล\nพร้อมสรรพ\nพร้อมหน้า\nพระครู\nพระคุณ\nพระเคราะห์\nพระเครื่อง\nพระเจ้า\nพระเจ้าอยู่หัว\nพระชายา\nพระทัย\nพระนาง\nพระนางเจ้า\nพระเป็นเจ้า\nพระผู้เป็นเจ้า\nพระพิมพ์\nพระพุทธเจ้า\nพระพุทธองค์\nพระภูมิ\nพระยา\nพระรอง\nพระสนม\nพระสนมเอก\nพระองค์\nพระองค์เจ้า\nพระเอก\nพรั่งพร้อม\nพรั่งพรู\nพรั่นพรึง\nพร่างพราว\nพรายน้ำ\nพรายแพรว\nพราวแพรว\nพร่ำพลอด\nพร่ำเพรื่อ\nพร่ำเพ้อ\nพริกไทย\nพริ้งพราย\nพริ้งเพรา\nพริ้งเพริศ\nพริบตา\nพริ้มพราย\nพริ้มเพรา\nพรุ่งนี้\nพฤติกรรม\nพฤติการณ์\nพฤตินัย\nพลการ\nพลขับ\nพลความ\nพลเมือง\nพลรบ\nพลร่ม\nพลเรือน\nพลโลก\nพลศึกษา\nพลบค่ำ\nพลอดรัก\nพลังงาน\nพลังเงียบ\nพลังจิต\nพลั้งปาก\nพลั้งเผลอ\nพลั้งพลาด\nพลัดถิ่น\nพลัดพราก\nพลาดท่า\nพลาดพลั้ง\nพลิกแพลง\nพลีกรรม\nพลุ่งพล่าน\nพวกพ้อง\nพวงมาลัย\nพวงมาลา\nพวงหรีด\nพวงคราม\nพวงชมพู\nพวงแสด\nพ่วงพี\nพวยน้ำ\nพวยพุ่ง\nพสกนิกร\nพหุคูณ\nพหุภาคี\nพหูพจน์\nพหูสูต\nพอควร\nพอใจ\nพอใช้\nพอใช้ได้\nพอดี\nพอตัว\nพอทำเนา\nพอประมาณ\nพอเพียง\nพอแรง\nพอสมควร\nพอเหมาะ\nพ่อขุน\nพ่อครัว\nพ่อตา\nพ่อบ้าน\nพ่อพันธุ์\nพ่อม่าย\nพ่อเมือง\nพ่อเลี้ยง\nพ่อสื่อ\nพอกพูน\nพ้องพาน\nพักผ่อน\nพักพิง\nพักฟื้น\nพักร้อน\nพักแรม\nพัดยศ\nพัดลม\nพันพัว\nพับฐาน\nพับเพียบ\nพัวพัน\nพาซื่อ\nพาดพิง\nพิณพาทย์\nพิธีกร\nพิธีกรรม\nพิธีการ\nพิธีรีตอง\nพิธีสาร\nพินัยกรรม\nพิมพ์เขียว\nพิมพ์ใจ\nพิมพ์ดีด\nพิษสง\nพี่น้อง\nพี่เบิ้ม\nพี่เลี้ยง\nพึงใจ\nพึงพอใจ\nพึ่งพา\nพึ่งพิง\nพืชพันธุ์\nพืชมงคล\nพื้นฐาน\nพื้นที่\nพื้นบ้าน\nพื้นเพ\nพื้นเมือง\nพื้นเสีย\nพุพอง\nพุทธกาล\nพุทธคุณ\nพุทธจักร\nพุทธเจดีย์\nพุทธฎีกา\nพุทธปฏิมา\nพุทธปฏิมากร\nพุทธมามกะ\nพุทธศักราช\nพุทธศาสนิกชน\nพุทธองค์\nพุทธชาด\nพุทธรักษา\nพุ่มพวง\nพุ่มไม้\nพู่กัน\nพูดจา\nเพ่งเล็ง\nเพดานบิน\nเพดานปาก\nเพริศพราย\nเพริศพริ้ง\nเพริศแพร้ว\nเพรียกพร้อง\nเพรียวลม\nเพลงเชิด\nเพลงยาว\nเพลิงกัลป์\nเพลินใจ\nเพลินตา\nเพลี่ยงพล้ำ\nเพ้อฝัน\nเพาะกาย\nเพาะชำ\nเพาะปลูก\nเพิกถอน\nเพิกเฉย\nเพิ่มเติม\nเพิ่มพูน\nเพียงตา\nเพียงพอ\nเพียบแประ\nเพียบพร้อม\nเพื่อนเกลอ\nเพื่อนตาย\nเพื่อนบ้าน\nเพื่อนฝูง\nเพื่อนยาก\nแพ้ท้อง\nแพร่หลาย\nแพร่งพราย\nแพรวพราว\nโพธิญาณ\nโพธิบัลลังก์\nโพธิสมภาร\nโพธิสัตว์\nโพ้นทะเล\nโพยภัย\nไพ่ตาย\nไพ่ป๊อก\nไพรวัน\nไพรสณฑ์\nไพรสัณฑ์\nไพร่พล\nไพร่ฟ้า\nไพร่สม\nไพร่ส่วย\nไพร่หลวง\nฟกช้ำ\nฟองเต้าหู้\nฟองน้ำ\nฟองมัน\nฟ้องกลับ\nฟ้องร้อง\nฟอนเฟะ\nฟักทอง\nฟัดเฟียด\nฟันดาบ\nฟันฝ่า\nฟันแท้\nฟันน้ำนม\nฟันปลา\nฟันฟาง\nฟันเฟือง\nฟันม้า\nฟันเลื่อย\nฟันหนู\nฟั่นเฝือ\nฟั่นเฟือน\nฟื้นตัว\nฟื้นฝอย\nฟื้นฟู\nฟุ้งซ่าน\nฟุ้งเฟ้อ\nฟุ้งเฟื่อง\nฟุตบอล\nฟูฟ่อง\nฟูเฟื่อง\nฟูมฟัก\nฟูมฟาย\nเฟะฟะ\nเฟื่องฟ้า\nเฟื่องฟุ้ง\nเฟื่องฟู\nไฟฉาย\nไฟแช็ก\nไฟธาตุ\nไฟฟ้า\nภัตกิจ\nภาคทัณฑ์\nภาคพื้น\nภาคเรียน\nภาคภูมิ\nภาพถ่าย\nภาพนิ่ง\nภาพประกอบ\nภาพพจน์\nภาพยนตร์\nภาพลวงตา\nภาพลักษณ์\nภายนอก\nภายใน\nภายหน้า\nภายหลัง\nภารกิจ\nภารธุระ\nภารโรง\nภารตวิทยา\nภาษาศาสตร์\nภาสกร\nภิญโญภาพ\nภินชาติ\nภูธร\nภูธเรศ\nภูบาล\nภูเบศ\nภูเบศวร์\nภูเขา\nภูเขาไฟ\nภูผา\nภูตคาม\nภูตบดี\nภูตรูป\nภูเตศวร\nภูมินทร์\nภูมิบาล\nภูมิประเทศ\nภูมิภาค\nภูมิรัฐศาสตร์\nภูมิลำเนา\nภูมิศาสตร์\nภูมิอากาศ\nภูมิธรรม\nภูมิปัญญา\nภูมิรู้\nภูมิใจ\nภูมิฐาน\nภูมิคุ้มกัน\nภูมิแพ้\nภูษาโยง\nเภทภัย\nเภสัชกร\nเภสัชกรรม\nเภสัชวิทยา\nเภสัชศาสตร์\nโภคทรัพย์\nโภคภัณฑ์\nโภชนากร\nโภชนาการ\nมกุฎราชกุมาร\nมงคลแฝด\nมงคลสูตร\nมงคลหัตถี\nมณเฑียรบาล\nมดดำ\nมดแดง\nมดเท็จ\nมดยอบ\nมดลูก\nมธุปายาส\nมธุรส\nมนเทียรบาล\nมนุษย์กบ\nมโนกรรม\nมโนคติ\nมโนทุจริต\nมโนธรรม\nมโนภาพ\nมโนมัย\nมโนรถ\nมโนรมย์\nมโนสุจริต\nมรรคนายก\nมรรคผล\nมฤคชาติ\nมฤคทายวัน\nมฤคราช\nมลทิน\nมลพิษ\nมลสาร\nมวกเหล็ก\nม้วนหน้า\nมวยไทย\nมวยปล้ำ\nมวยล้ม\nมวยวัด\nมวยสากล\nมวยหมู่\nมวลสาร\nมอคราม\nมอซอ\nมอหมึก\nมองเมียง\nมอบตัว\nมอบหมาย\nมอมเมา\nมะขามเทศ\nมะขามป้อม\nมะขามเปียก\nมะเขือเทศ\nมะเขือพวง\nมะพร้าวแก้ว\nมักคุ้น\nมักจี่\nมักง่าย\nมักน้อย\nมักมาก\nมักใหญ่\nมั่งคั่ง\nมั่งมี\nมัจจุราช\nมัชฌิมนิกาย\nมัชฌิมประเทศ\nมัชฌิมยาม\nมัชฌิมวัย\nมัดจำ\nมัดหมี่\nมัธยมกาล\nมัธยมศึกษา\nมันแกว\nมันเทศ\nมันฝรั่ง\nมันเปลว\nมันสมอง\nมั่นคง\nมั่นใจ\nมั่นหมาย\nมั่นเหมาะ\nมัวเมา\nมัวหมอง\nมั่วสุม\nม้าเทศ\nม้าน้ำ\nม้ามืด\nม้าเร็ว\nม้าล่อ\nม้าลาย\nมากมาย\nมาตรการ\nมาตรฐาน\nมาตราส่วน\nมาตุคาม\nมาตุฆาต\nมาตุภูมิ\nม่านตา\nม่านบังตา\nมายากร\nมายากล\nมายาการ\nมายาวี\nมารผจญ\nมารวิชัย\nมารสังคม\nมารหัวขน\nมาลาการ\nมิ่งขวัญ\nมิ่งมิตร\nมิจฉาจาร\nมิจฉาชีพ\nมิดชิด\nมิดเมี้ยน\nมิดหมี\nมิตรจิต\nมิตรภาพ\nมิตรสหาย\nมิน่า\nมีหน้า\nมีดโกน\nมีดดาบ\nมีดโต้\nมีดพก\nมีดพับ\nมีดสั้น\nมึนงง\nมึนชา\nมึนตึง\nมึนเมา\nมืดครึ้ม\nมืดมน\nมืดมัว\nมือจับ\nมือดี\nมือเติบ\nมือปืน\nมือเปล่า\nมือมืด\nมือสอง\nมือเสือ\nมือหนึ่ง\nมือใหม่\nมุกตลก\nมุขปาฐะ\nมุขมนตรี\nมุ่งมั่น\nมุ่งมาด\nมุ่งหน้า\nมุ่งหมาย\nมุ่งหวัง\nมุ้งลวด\nมุ้งสายบัว\nมุมก้ม\nมุมกลับ\nมุมเงย\nมุมฉาก\nมุมตรง\nมุมป้าน\nมุมมืด\nมุมแย้ง\nมุมสะท้อน\nมุมหักเห\nมุมแหลม\nมุสาวาท\nมูกเลือด\nมูกมัน\nมูกหลวง\nมูนดิน\nมูลฐาน\nมูลนาย\nมูลนิธิ\nมูลเหตุ\nมูลค่า\nมูลฝอย\nเม็ดเงิน\nเม็ดเลือด\nเม็ดโลหิต\nเม่นทะเล\nเมรุมาศ\nเมรุราช\nเมล์อากาศ\nเมาดิบ\nเมามัน\nเมามัว\nเมามาย\nเมินเฉย\nเมียน้อย\nเมียหลวง\nเมียงมอง\nเมี่ยงลาว\nเมี่ยงส้ม\nเมื่อกี้\nเมื่อตะกี้\nเมื่อใด\nเมื่อไร\nเมื่อไหร่\nเมื่อนั้น\nเมืองขึ้น\nเมืองท่า\nเมืองนอก\nเมืองหลวง\nเมื่อยขบ\nเมื่อยล้า\nแม่กอง\nแม่กุญแจ\nแม่คุณ\nแม่งาน\nแม่เจ้า\nแม่ชี\nแม่ทัพ\nแม่นม\nแม่น้ำ\nแม่บท\nแม่บ้าน\nแม่เบี้ย\nแม่พระ\nแม่พิมพ์\nแม่เพลง\nแม่มด\nแม่ม่าย\nแม่ไม้\nแม่ยก\nแม่ยาย\nแม่ร้าง\nแม่เรือน\nแม่แรง\nแม่เล้า\nแม่เลี้ยง\nแม่สี\nแม่สื่อ\nแม่เหล็ก\nแมงมุม\nแม่นยำ\nแมลงช้าง\nแมลงวัน\nแมลงปอ\nแมลงภู่\nแมลงเม่า\nแมวเซา\nแมวน้ำ\nแมวป่า\nแมวมอง\nไม้กลัด\nไม้กวาด\nไม้กางเขน\nไม้เกาหลัง\nไม้ขีดไฟ\nไม้จิ้มฟัน\nไม้เด็ด\nไม้ตาย\nไม้ตีพริก\nไม้ที\nไม้เท้า\nไม้บรรทัด\nไม้เมตร\nไม้ระแนง\nไม้เรียว\nไม้หมอน\nไม้อัด\nไม้จัตวา\nไม้ตรี\nไม้ไต่คู้\nไม้โท\nไม้ผัด\nไม้มลาย\nไม้ม้วน\nไม้ยมก\nไม้หน้า\nไม้หันอากาศ\nไม้เอก\nยกกลีบ\nยกครู\nยกเครื่อง\nยกเค้า\nยกทรง\nยกฟ้อง\nยกเมฆ\nยกยอ\nยกย่อง\nยกเลิก\nยกเว้น\nย่นย่อ\nยมทูต\nยมบาล\nยมราช\nยมโลก\nยวดยิ่ง\nยวดยาน\nยวนยี\nยวบยาบ\nย่อท้อ\nย่อส่วน\nย่อหน้า\nย่อหย่อน\nยอกย้อน\nยองใย\nย่องเบา\nย่องแย่ง\nยอดเยี่ยม\nยอดอก\nย้อนยอก\nย้อนรอย\nย้อนศร\nย้อนแสง\nย้อนหลัง\nยอบแยบ\nยอมความ\nย่อมเยา\nย่อยยับ\nยักยอก\nยักย้าย\nยักเยื้อง\nยัญกรรม\nยัญพิธี\nยัดเยียด\nยับเยิน\nยับยั้ง\nยั่วยวน\nยั่วยุ\nยั่วเย้า\nยากวาด\nยากันยุง\nยาเขียว\nยาใจ\nยาฉุน\nยาชา\nยาซัด\nยาดอง\nยาแดง\nยาถ่าย\nยาธาตุ\nยานัตถุ์\nยาเบื่อ\nยาโป๊\nยาแฝด\nยาพิษ\nยาระบาย\nยาสลบ\nยาสั่ง\nยาสีฟัน\nยาสูบ\nยาเส้น\nยาเสพติด\nยาหม่อง\nยาเหลือง\nย่าทวด\nย่านาง\nยากแค้น\nยากจน\nยากเย็น\nยากไร้\nยางนอก\nยางใน\nยางมะตอย\nยางมะตูม\nยางลบ\nยางสน\nยางอาย\nย่างกราย\nย่างเยื้อง\nย่างสด\nย่างสามขุม\nย่างเหยียบ\nยานเกราะ\nยานพาหนะ\nยานอวกาศ\nยานคาง\nยายทวด\nยาวเฟื้อย\nยาวยืด\nยาวเหยียด\nยำทวาย\nยำใหญ่\nยำเกรง\nยำเยง\nย่ำต๊อก\nย่ำยี\nย่ำแย่\nยิงเป้า\nยิ่งนัก\nยิ่งยวด\nยิ่งใหญ่\nยินดี\nยินยอม\nยินร้าย\nยิ้มกริ่ม\nยิ้มแฉ่ง\nยิ้มแต้\nยิ้มแป้น\nยิ้มเผล่\nยิ้มเยาะ\nยิ้มแย้ม\nยียวน\nยึดครอง\nยึดถือ\nยึดมั่น\nยึดเหนี่ยว\nยืดยาด\nยืดยาว\nยืดเยื้อ\nยืดหยุ่น\nยืดอก\nยืนกราน\nยืนต้น\nยืนพื้น\nยืนยง\nยืนยัน\nยืนหยัด\nยื้อยุด\nยุยง\nยุแยง\nยุแหย่\nยุคลบาท\nยุคเข็ญ\nยุคทอง\nยุคมืด\nยุ่งขิง\nยุ่งยาก\nยุ่งเหยิง\nยุติธรรม\nยุทธการ\nยุทธนาวี\nยุทธปัจจัย\nยุทธภัณฑ์\nยุทธภูมิ\nยุทธวิธี\nยุทธศาสตร์\nยุทธหัตถี\nยุทธนาการ\nยุทธนาธิการ\nยุบยับ\nยุบยิบ\nยุพราช\nยู่ยี่\nเย็นเจี๊ยบ\nเย็นใจ\nเย็นฉ่ำ\nเย็นเฉียบ\nเย็นชา\nเย็นชืด\nเย็นตา\nเย็นเยียบ\nเย็นเยือก\nเย็นวาบ\nเย็นวูบ\nเย็บกี่\nเย็บจักร\nเย็บด้าย\nเย้ยหยัน\nเย้าหยอก\nเยาะเย้ย\nเยี่ยมกราย\nเยี่ยมเยียน\nเยี่ยมเยือน\nเยี่ยมยอด\nเยื่อเคย\nเยื่อใย\nเยือกเย็น\nเยื้องกราย\nเยื้องยัก\nเยื้องย่าง\nแยกย้าย\nแยกแยะ\nแย่งชิง\nแยบคาย\nแยบยล\nแย้มพราย\nแย้มยิ้ม\nแย้มสรวล\nโยเย\nโย้เย้\nโยกโคลง\nโยกย้าย\nโยกโย้\nโยนกลอง\nใยหิน\nรกชัฏ\nรกร้าง\nรกเรี้ยว\nรกเรื้อ\nรกราก\nรงควัตถุ\nรชนีกร\nรถกระบะ\nรถเก๋ง\nรถเข็น\nรถแข่ง\nรถจักร\nรถจี๊ป\nรถตู้\nรถทัวร์\nรถบรรทุก\nรถพ่วง\nรถพยาบาล\nรถไฟ\nรถไฟฟ้า\nรถม้า\nรถเมล์\nรถยนต์\nรถราง\nรถลาก\nรถสปอร์ต\nรถสิบล้อ\nรบกวน\nรบรา\nรบเร้า\nรมดำ\nร่มเกล้า\nร่มชูชีพ\nร่มเย็น\nร่มรื่น\nร่วงโรย\nรวงผึ้ง\nรวงรัง\nรวดเร็ว\nรวนเร\nรวบยอด\nรวบรวม\nรวบรัด\nรวมพล\nรวมหัว\nร่วมใจ\nร่วมเพศ\nร่วมมือ\nร่วมรัก\nร่วมสมัย\nรวยริน\nรวยรื่น\nรสชาติ\nรสนิยม\nรองท้อง\nรองเท้า\nรองพื้น\nร่องน้ำ\nร่องรอย\nร้องขอ\nร้องทุกข์\nร้องเรียน\nร้องห่ม\nร้องไห้\nรองช้ำ\nรองทรง\nรอดชีวิต\nรอดตัว\nรอดตาย\nรอนแรม\nร่อนเร่\nร้อนใจ\nร้อนตัว\nร้อนรน\nร้อนรุ่ม\nร้อนวิชา\nร้อนอาสน์\nรอบจัด\nรอบเดือน\nรอบรู้\nรอยร้าว\nร่อยหรอ\nร้อยละ\nร้อยกรอง\nร้อยแก้ว\nร้อยหวาย\nระนาดทุ้ม\nระนาดเอก\nระเบิดขวด\nระเบิดมือ\nระเบียบการ\nรักใคร่\nรักษาการ\nรักษาการณ์\nรังไข่\nรังแตน\nรังนก\nรังผึ้ง\nรังเพลิง\nรังมด\nรังสรรค์\nรังสฤษฏ์\nรั้งรอ\nรังสีแพทย์\nรังสีวิทยา\nรัชกาล\nรัชทายาท\nรัชนีกร\nรัฐธรรมนูญ\nรัฐบาล\nรัฐบุรุษ\nรัฐประศาสน์\nรัฐประหาร\nรัฐพิธี\nรัฐมนตรี\nรัฐวิสาหกิจ\nรัฐศาสตร์\nรัฐสภา\nรัดกุม\nรัดเกล้า\nรัดตัว\nรัดประคด\nรัดรึง\nรัดรูป\nรัตติกาล\nรับขวัญ\nรับจ้าง\nรับช่วง\nรับใช้\nรับซื้อ\nรับทราบ\nรับประกัน\nรับประทาน\nรับปาก\nรับผิด\nรับผิดชอบ\nรับฟ้อง\nรับฟัง\nรับมือ\nรับรอง\nรับรู้\nรับสมัคร\nรับสั่ง\nรับหน้า\nรับเหมา\nรั่วไหล\nรามือ\nร่าเริง\nรากแก้ว\nรากขวัญ\nรากฐาน\nรากฟัน\nรากศัพท์\nรากเหง้า\nร่างกาย\nร่างแห\nร้างรา\nราชกรณียกิจ\nราชการ\nราชกิจ\nราชครู\nราชฐาน\nราชทัณฑ์\nราชทินนาม\nราชทูต\nราชธานี\nราชนาวี\nราชบัณฑิต\nราชบัลลังก์\nราชบาตร\nราชบุตร\nราชปะแตน\nราชภัฏ\nราชมัล\nราชยาน\nราชรถ\nราชลัญจกร\nราชเลขาธิการ\nราชเลขานุการ\nราชวงศ์\nราชวัติ\nราชสกุล\nราชสมบัติ\nราชสาส์น\nราชหัตถเลขา\nราชองครักษ์\nราชโองการ\nราชาคณะ\nราชาศัพท์\nราชินีนาถ\nร้านชำ\nร้านรวง\nราบคาบ\nราบรื่น\nราบเรียบ\nรายการ\nรายงาน\nรายจ่าย\nรายได้\nรายทาง\nรายรับ\nรายล้อม\nรายละเอียด\nรายวิชา\nร่ายยาว\nร่ายรำ\nร้ายกาจ\nร้ายแรง\nราวนม\nราวป่า\nร้าวฉาน\nร้าวราน\nรำพัด\nรำแพน\nรำวง\nร่ำไป\nร่ำร้อง\nร่ำเรียน\nร่ำไร\nร่ำลา\nร่ำไห้\nริเริ่ม\nริอ่าน\nริมฝีปาก\nริ้วรอย\nรีบร้อน\nรีบรุด\nรีบเร่ง\nรื่นรมย์\nรื่นเริง\nรื้อถอน\nรื้อฟื้น\nรุกฆาต\nรุกราน\nรุกล้ำ\nรุกไล่\nรุ่งขึ้น\nรุ่งแจ้ง\nรุ่งเช้า\nรุ่งเรือง\nรุ่งโรจน์\nรุ่งสว่าง\nรุ่งสาง\nรุ่งอรุณ\nรุจิเรข\nรุดหน้า\nรุนแรง\nรุมเร้า\nรุมล้อม\nรุ่มรวย\nรุ่มร้อน\nรุ่ยร่าย\nรู้แกว\nรู้ความ\nรู้คุณ\nรู้งาน\nรู้จัก\nรู้แจ้ง\nรู้ใจ\nรู้เชิง\nรู้ตัว\nรู้ทัน\nรู้เท่า\nรู้เรื่อง\nรู้สำนึก\nรู้สึก\nรู้เห็น\nรูปการณ์\nรูปโฉม\nรูปฌาน\nรูปถ่าย\nรูปทรง\nรูปธรรม\nรูปแบบ\nรูปพรรณ\nรูปพรหม\nรูปภพ\nรูปภาพ\nรูปร่าง\nรูปสมบัติ\nเร่ร่อน\nเร่งด่วน\nเร่งมือ\nเร่งรัด\nเร่งรีบ\nเร่งเร้า\nเร้นลับ\nเร่อร่า\nเร่าร้อน\nเราะราย\nเราะร้าย\nเริงใจ\nเริงรมย์\nเริดร้าง\nเริ่มต้น\nเริ่มแรก\nเรี่ยราด\nเรี่ยไร\nเรียกคืน\nเรียกตัว\nเรียกร้อง\nเรียกหา\nเรียบร้อย\nเรียงความ\nเรียงตัว\nเรียงเบอร์\nเรียงพิมพ์\nเรียงเม็ด\nเรียงราย\nเรียนรู้\nเรียบร้อย\nเรียบเรียง\nเรียบวุธ\nเรี่ยมเร้\nเรี่ยวแรง\nเรือกลไฟ\nเรือกอและ\nเรือกำปั่น\nเรือจ้าง\nเรือดำน้ำ\nเรือโดยสาร\nเรือตรวจการณ์\nเรือตังเก\nเรือธง\nเรือนำร่อง\nเรือบด\nเรือบิน\nเรือใบ\nเรือประมง\nเรือพ่วง\nเรือพิฆาต\nเรือยนต์\nเรือยาว\nเรือโยง\nเรือรบ\nเรือลากจูง\nเรือสำปั้น\nเรือสำเภา\nเรือหลวง\nเรือหางยาว\nเรืออีโปง\nเรือเอี้ยมจุ๊น\nเรื้อรัง\nเรือกสวน\nเรืองนาม\nเรืองรอง\nเรืองแสง\nเรื่องราว\nเรื่องสั้น\nเรือนแก้ว\nเรือนจำ\nเรือนเบี้ย\nเรือนแพ\nเรือนหอ\nเรื่อยเจื้อย\nเรื่อยเฉื่อย\nเรื่อยเปื่อย\nแรเงา\nแรกนา\nแรกนาขวัญ\nแรงงาน\nแรงดึงดูด\nแรงเทียน\nแรงม้า\nแรงเหวี่ยง\nแรมรอน\nแรมรา\nแรมโรย\nโรคจิต\nโรงครัว\nโรงงาน\nโรงเจ\nโรงเตี๊ยม\nโรงทาน\nโรงนา\nโรงพยาบาล\nโรงพัก\nโรงพิมพ์\nโรงเรียน\nโรงเรือน\nโรงแรม\nโรงเลี้ยง\nโรงเลื่อย\nโรงสี\nโรงสีข้าว\nโรงอาหาร\nโรมรัน\nโรยรา\nฤชากร\nฤดูกาล\nลงขัน\nลงแขก\nลงคอ\nลงตัว\nลงท้าย\nลงทุน\nลงโทษ\nลงพุง\nลงมือ\nลงรัก\nลงรอย\nลงแรง\nลงโรง\nลงเอย\nลดตัว\nลดละ\nลดเลี้ยว\nลดหย่อน\nลดหลั่น\nลนลาน\nล้นพ้น\nล้นหลาม\nล้นเหลือ\nลบล้าง\nลบเลือน\nลบหลู่\nลมกรด\nลมค้า\nลมงวง\nลมแดด\nลมทะเล\nลมบก\nลมบน\nลมบ้าหมู\nลมปราณ\nลมปาก\nลมพิษ\nลมว่าว\nลมเสีย\nลมหนาว\nลมหายใจ\nล่มจม\nล่มสลาย\nล้มละลาย\nล้มลุก\nล้มเลิก\nล่วงเกิน\nล่วงรู้\nล่วงละเมิด\nล่วงลับ\nล่วงล้ำ\nล่วงเลย\nล่วงหน้า\nลวดลาย\nลวดสปริง\nลวดหนาม\nล้วนแล้ว\nลหุโทษ\nล่อลวง\nล่อหลอก\nล่อแหลม\nล้อต๊อก\nล้อเลื่อน\nล้อเล่น\nล้อเลียน\nล้อหลอก\nลองเชิง\nลองดี\nลองภูมิ\nล่องหน\nลอดช่อง\nล่อนจ้อน\nลอบกัด\nล้อมวง\nลอยแก้ว\nลอยชาย\nลอยตัว\nลอยนวล\nลอยแพ\nลอยลำ\nละทิ้ง\nละเลย\nละเว้น\nละครนอก\nละครใน\nละครเพลง\nละครร้อง\nละครรำ\nละครลิง\nละครสัตว์\nละเอียดอ่อน\nลักไก่\nลักพา\nลักเพศ\nลักยิ้ม\nลักลอบ\nลักลั่น\nลักหลับ\nลัดเลาะ\nลับตา\nลับแล\nลับหลัง\nลาออก\nล่าช้า\nล่าทัพ\nล้าสมัย\nล้าหลัง\nลากข้าง\nล้างบาง\nล้างผลาญ\nลาดเขา\nลาดตระเวน\nลาดเท\nลาดยาง\nลานบิน\nลาภปาก\nลาภลอย\nลามปาม\nลามเลีย\nลายคราม\nลายเซ็น\nลายแทง\nลายน้ำ\nลายพร้อย\nลายมือ\nลายลักษณ์\nลายเส้น\nลำกล้อง\nลำแข้ง\nลำธาร\nลำแสง\nลำไส้\nลำตัด\nลำนำ\nล่ำสัน\nล้ำยุค\nล้ำสมัย\nล้ำลึก\nล้ำเลิศ\nล้ำเส้น\nล้ำหน้า\nลิงจุ่น\nลิงลม\nลิงโลด\nลิดรอน\nลิ้นไก่\nลิ้นชัก\nลิ้นปี่\nลิ้นควาย\nลิ้นงูเห่า\nลิ้นหมา\nลิบลับ\nลิบลิ่ว\nลิ่มเลือด\nลี้ภัย\nลี้ลับ\nลึกซึ้ง\nลึกลับ\nลึกล้ำ\nลืมตน\nลืมต้น\nลืมตัว\nลืมตา\nลืมเลือน\nลือชา\nลือชื่อ\nลือลั่น\nลุล่วง\nลุกลน\nลุกลาม\nลุกลี้ลุกลน\nลุกฮือ\nลุ่มน้ำ\nลุ่มลึก\nลุ่มหลง\nลุ่ทาง\nลูกกรง\nลูกกรอก\nลูกกรุง\nลูกกลอน\nลูกกลิ้ง\nลูกกวาด\nลูกกะจ๊อก\nลูกกุญแจ\nลูกเกด\nลูกแก้ว\nลูกขนไก่\nลูกข่าง\nลูกขุน\nลูกเขย\nลูกครึ่ง\nลูกคลื่น\nลูกความ\nลูกคอ\nลูกค้า\nลูกคิด\nลูกคู่\nลูกจ้าง\nลูกช้าง\nลูกชิด\nลูกชิ้น\nลูกชุบ\nลูกซอง\nลูกโซ่\nลูกดอก\nลูกดิ่ง\nลูกตะกั่ว\nลูกตุ้ม\nลูกเต้า\nลูกเต๋า\nลูกถ้วย\nลูกทุ่ง\nลูกเธอ\nลูกน้อง\nลูกน้ำ\nลูกนิมิต\nลูกบอล\nลูกบ้าน\nลูกบาศก์\nลูกบิด\nลูกเบี้ยว\nลูกประคบ\nลูกประคำ\nลูกปัด\nลูกปืน\nลูกโป่ง\nลูกผสม\nลูกผู้ชาย\nลูกผู้หญิง\nลูกพรรค\nลูกพี่\nลูกฟูก\nลูกไฟ\nลูกมือ\nลูกโม่\nลูกไม้\nลูกยาเธอ\nลูกรอก\nลูกรัง\nลูกเรือ\nลูกล้อ\nลูกลอย\nลูกเล่น\nลูกเลี้ยง\nลูกโลก\nลูกวัด\nลูกศร\nลูกศิษย์\nลูกสมุน\nลูกสะใภ้\nลูกสูบ\nลูกเสือ\nลูกหนัง\nลูกหนี้\nลูกหนู\nลูกหมาก\nลูกหลง\nลูกหลาน\nลูกหาบ\nลูกหิน\nลูกเห็บ\nลูกเหม็น\nลูกแหง่\nลูกอม\nลูกหม้อ\nลูบคม\nลูบคลำ\nลูบไล้\nเล็กน้อย\nเลขคณิต\nเลขผา\nเลขหมาย\nเล็ดลอด\nเล่นงาน\nเล่นแง่\nเล่นชู้\nเล่นตัว\nเล่นลิ้น\nเล่นหัว\nเลนส์นูน\nเลนส์เว้า\nเล็บครุฑ\nเลยเถิด\nเลศนัย\nเล่ห์กล\nเล่ห์เหลี่ยม\nเลอโฉม\nเลอมาน\nเลอเลิศ\nเลอสรวง\nเล่อล่า\nเลอะเลือน\nเล่าเรียน\nเล่าลือ\nเลาะลัด\nเลิกรา\nเลิกร้าง\nเลิกล้ม\nเลิศเลอ\nเลี้ยงชีพ\nเลี้ยงดู\nเลี้ยงต้อย\nเลียบเคียง\nเลี้ยวลด\nเลือกตั้ง\nเลือกเฟ้น\nเลือกสรร\nเลื่องลือ\nเลือดกำเดา\nเลือดเนื้อ\nเลือดฝาด\nเลือดเย็น\nเลือดร้อน\nเลือดหมู\nเลือดอุ่น\nเลือนราง\nเลื่อนเปื้อน\nเลื่อนลอย\nเลื่อมพราย\nเลื่อมใส\nเลื่อยฉลุ\nเลื่อยลันดา\nเลื่อยวงเดือน\nเลื้อยคลาน\nแลเหลียว\nแลกเปลี่ยน\nแล้วกัน\nและเล็ม\nโล่งใจ\nโล่งโถง\nโล่งอก\nโลดเต้น\nโลดโผน\nโลดลิ่ว\nโลดแล่น\nไล่ที่\nไล่เบี้ย\nไล่เลี่ย\nไล่เลียง\nไล่หลัง\nไล่ออก\nวกวน\nวงกบ\nวงกลม\nวงการ\nวงแขน\nวงเงิน\nวงจร\nวงนอก\nวงใน\nวงรี\nวงเล็บ\nวงเวียน\nวงแหวน\nวงศ์วาน\nวจีกรรม\nวจีเภท\nวจีภาค\nวนเวียน\nวอดวาย\nว็อบแว็บ\nวังวน\nวังหน้า\nวังหลวง\nวังหลัง\nวัดราษฎร์\nวัดวา\nวัดหลวง\nวัดผล\nวัดพื้น\nวัตถุนิยม\nวัตถุประสงค์\nวัตรปฏิบัติ\nวันโกน\nวันพระ\nวันเพ็ญ\nวัยรุ่น\nวัยวุฒิ\nว่ากล่าว\nว่าจ้าง\nว่าด้วย\nว่าที่\nวางก้าม\nวางใจ\nวางตัว\nวางตา\nวางโต\nวางท่า\nวางมวย\nวางมาด\nวางมือ\nวางวาย\nว่างเปล่า\nว่างเว้น\nวาดเขียน\nว่านเครือ\nวาบหวาม\nวายชนม์\nวายปราณ\nวายวาง\nวายวอด\nวายร้าย\nวายุภักษ์\nวาววับ\nวาววาม\nวาวแวว\nวาวแสง\nวิกฤตการณ์\nวิกฤติการณ์\nวิกฤตกาล\nวิกฤติกาล\nวิกลจริต\nวิงเวียน\nวิ่งเต้น\nวิ่งผลัด\nวิ่งรอก\nวิ่งราว\nวิจิตรศิลป์\nวิชาการ\nวิชาชีพ\nวิชาธร\nวิญญูชน\nวิดพื้น\nวิตกจริต\nวิถีทาง\nวิทยากร\nวิทยากล\nวิทยาการ\nวิทยาเขต\nวิทยาทาน\nวิทยาธร\nวิทยานิพนธ์\nวิทยาศาสตร์\nวิเทศสัมพันธ์\nวิธีการ\nวินัยธร\nวินัยปิฎก\nวินาศกรรม\nวินาศภัย\nวินาศสันตะโร\nวิภัชพยากรณ์\nวิภัชวาที\nวิไลวรรณ\nวิสัญญีแพทย์\nวิสัญญีภาพ\nวิสัญญีวิทยา\nวุฒิบัตร\nวุฒิสภา\nวุฒิสมาชิก\nวุ่นวาย\nวุ้นเส้น\nวูบวาบ\nเวจกุฎี\nเวจมรรค\nเวชกรรม\nเวชภัณฑ์\nเวชศาสตร์\nเวทมนตร์\nเวนคืน\nเวรกรรม\nเวฬุการ\nเวฬุวัน\nเว้าวอน\nเวิ้งว้าง\nเวียงวัง\nเวียนเทียน\nแว้งกัด\nแวดล้อม\nแวดวง\nแว่นขยาย\nแว่นแคว้น\nแว่นตา\nแวบวับ\nแววตา\nแวววาม\nแวววาว\nแวะเวียน\nโวยวาย\nไวไฟ\nไว้ใจ\nไว้ชื่อ\nไว้ตัว\nไว้ทุกข์\nไว้ลาย\nไว้หน้า\nไว้อาลัย\nศนิวาร\nศอกกลับ\nศอกกำ\nศอกกำมา\nศักดิ์ศรี\nศักดิ์สิทธิ์\nศารทวิษุวัติ\nศาลแขวง\nศาลจังหวัด\nศาลชั้นต้น\nศาลฎีกา\nศาลเตี้ย\nศาลทหาร\nศาลปกครอง\nศาลพระภูมิ\nศาลเพียงตา\nศาลแพ่ง\nศาลรัฐธรรมนูญ\nศาลแรงงาน\nศาลล้มละลาย\nศาลโลก\nศาลสูง\nศาลสูงสุด\nศาลอาญา\nศาลอุทธรณ์\nศาลากลาง\nศาลาดิน\nศาลาราย\nศาลาวัด\nศิลาฤกษ์\nศิลาแลง\nศิษย์เก่า\nศิษย์เอก\nศีลจุ่ม\nศีลธรรม\nศีลวัต\nศีลอด\nศูนย์กลาง\nศูนย์การค้า\nศูนย์ถ่วง\nศูนย์สูตร\nศูนย์หน้า\nเศร้าใจ\nเศร้าโศก\nเศร้าสร้อย\nเศร้าสลด\nเศร้าหมอง\nเศวตฉัตร\nเศษเกิน\nเศษซ้อน\nเศษวรรค\nเศษส่วน\nเศษเหล็ก\nโศกนาฏกรรม\nโศกศัลย์\nโศกเศร้า\nโศกสลด\nสกลโลก\nส่งเดช\nส่งท้าย\nส่งเสริม\nส่งเสีย\nส่งเสียง\nสงบเงียบ\nสงบเสงี่ยม\nสง่างาม\nสง่าราศี\nสดชื่น\nสดใส\nสตรีเพศ\nสติปัญญา\nสถลมารค\nสถานกงสุล\nสถานที่\nสถานทูต\nสถานการณ์\nสถานภาพ\nสถิติศาสตร์\nสนตะพาย\nสนใจ\nส้นตีน\nสนธิสัญญา\nสนนราคา\nสนับแข้ง\nสนับเพลา\nสนับมือ\nสนามบิน\nสนามเพลาะ\nสนิทสนม\nสนิมขุม\nสนิมสร้อย\nสนุกสนาน\nสบประมาท\nสบายใจ\nสภาพธรรม\nสมควร\nสมจริง\nสมใจ\nสมนัย\nสมน้ำหน้า\nสมประกอบ\nสมส่วน\nสมหวัง\nสมคบ\nสมทบ\nสมยอม\nสมรัก\nสมรู้\nสมสู่\nส้มฉุน\nส้มตำ\nส้มลิ้ม\nส้มกุ้ง\nส้มเช้า\nสมญานาม\nสมมติฐาน\nสมมุติฐาน\nสมมติเทพ\nสมรภูมิ\nสมัครใจ\nสมัยนิยม\nสมุทรศาสตร์\nสมุทรเสนา\nสยดสยอง\nสยองขวัญ\nสยามรัฐ\nสรรหา\nสรวมชีพ\nสรวลเส\nสร้อยเศร้า\nสร้างสรรค์\nสร้างเสริม\nสลดใจ\nสลบไสล\nสละสลวย\nสลาเหิน\nสลากภัต\nสวนครัว\nสวนป่า\nสวนสนุก\nสวนหย่อม\nส่วนกลาง\nส่วนเกิน\nส่วนตัว\nส่วนบุญ\nส่วนแบ่ง\nส่วนประกอบ\nส่วนพระองค์\nส่วนผสม\nส่วนรวม\nส่วนร่วม\nส่วนลด\nส่วนสัด\nสวมกอด\nสวมเขา\nสวมรอย\nสวยมภู\nสว่างไสว\nสวามิภักดิ์\nสวิงสวาย\nสสารนิยม\nส่อเสียด\nสอดคล้อง\nสอดแทรก\nสอดแนม\nสอบถาม\nสอบทาน\nสอบไล่\nสอบสวน\nส้อมเสียง\nสะสวย\nสะแกวัลย์\nสะแกแสง\nสะใจ\nสะเด็ดยาด\nสะเทือนใจ\nสะบัดช่อ\nสั่งสม\nสั่งสอน\nสั่งเสีย\nสังเกตการณ์\nสังคมนิยม\nสังคมวิทยา\nสังคมศาสตร์\nสังคมศึกษา\nสังคมสงเคราะห์\nสัญญาบัตร\nสัดส่วน\nสัตการ\nสัตบุรุษ\nสัตบริภัณฑ์\nสัตภัณฑ์\nสัตมหาสถาน\nสัตโลหะ\nสันเขา\nสันดอน\nสันหลัง\nสั่นเทา\nสั่นเทิ้ม\nสันติบาล\nสันติภาพ\nสันติวิธี\nสันติสุข\nสับเปลี่ยน\nสับสน\nสับหลีก\nสับหว่าง\nสัมมาคารวะ\nสัมมาชีพ\nส่าเหล้า\nสากกะเบือ\nสาทิสลักษณ์\nสาธุการ\nสาธุชน\nสาบเสือ\nสาปสรร\nสาปแช่ง\nสาปส่ง\nสามง่าม\nสามล้อ\nสามเหลี่ยม\nสามเวท\nสามัญชน\nสามัญสำนึก\nสายดิ่ง\nสายดิน\nสายตรวจ\nสายน้ำ\nสายบัว\nสายพาน\nสายฟ้า\nสายยาง\nสายยู\nสายใย\nสายรก\nสายรุ้ง\nสายล่อฟ้า\nสายลับ\nสายเลือด\nสายโลหิต\nสายวัด\nสายส่ง\nสายสวาท\nสายสะดือ\nสายสะพาย\nสายสัมพันธ์\nสายสิญจน์\nสายสืบ\nสายไหม\nสายอากาศ\nสายตา\nสายหยุด\nสารตรา\nสารประกอบ\nสารละลาย\nสารส้ม\nสารหนู\nสารทฤดู\nสาวใช้\nสาวน้อย\nสาวใหญ่\nสำนักงาน\nสำนักพิมพ์\nสำนักสงฆ์\nสำมะโนครัว\nสำเร็จรูป\nสิกขาบท\nสิงสถิต\nสิงสู่\nสิ่งก่อสร้าง\nสิ่งของ\nสิ่งปฏิกูล\nสิ่งพิมพ์\nสิ่งแวดล้อม\nสิ่งศักดิ์สิทธิ์\nสิทธิกร\nสิทธิ์ขาด\nสิทธิชัย\nสิทธิโชค\nสิทธิบัตร\nสินค้า\nสินจ้าง\nสินเชื่อ\nสินไถ่\nสินทรัพย์\nสินน้ำใจ\nสินบน\nสินแร่\nสินสมรส\nสินสอด\nสินไหม\nสิ้นเชิง\nสิ้นสุด\nสีผึ้ง\nสีลม\nสีชอล์ก\nสีถ่าน\nสีเทียน\nสีน้ำ\nสีน้ำมัน\nสีโปสเตอร์\nสีฝุ่น\nสี่เหลี่ยม\nสีหน้า\nสึกหรอ\nสืบทอด\nสืบค้น\nสืบสวน\nสืบสาว\nสืบเสาะ\nสื่อผสม\nสื่อมวลชน\nสื่อสาร\nสุกงอม\nสุกดิบ\nสุกปลั่ง\nสุกใส\nสุขนาฏกรรม\nสุขภัณฑ์\nสุขภาพ\nสุขลักษณะ\nสุขวิทยา\nสุขศาลา\nสุขศึกษา\nสุดท้าย\nสุตกวี\nสุนทรพจน์\nสุภาพชน\nสู่ขอ\nสู่รู้\nสู่สม\nสูงส่ง\nสูญเปล่า\nสูญสิ้น\nสูญเสีย\nสูญหาย\nเสสรวล\nเสแสร้ง\nเสกสรร\nเสถียรภาพ\nเส้นชัย\nเส้นตรง\nเส้นตาย\nเส้นทาง\nเส้นใย\nเส้นรุ้ง\nเส้นเลือด\nเส้นแวง\nเส้นสาย\nเส้นเสียง\nเส้นหมี่\nเส้นเอ็น\nเสบียงกรัง\nเสมอภาค\nเสมอหน้า\nเสมอเหมือน\nเสมียนตรา\nเสร็จสรรพ\nเสร็จสิ้น\nเสริมส่ง\nเสริมสร้าง\nเสริมสวย\nเสรีไทย\nเสรีธรรม\nเสรีนิยม\nเสรีภาพ\nเสาเข็ม\nเสาธง\nเสียใจ\nเสียเชิง\nเสียดาย\nเสียที\nเสียเที่ยว\nเสียเปรียบ\nเสียเปล่า\nเสียรู้\nเสียแรง\nเสียสละ\nเสียหลัก\nเสียหาย\nเสี่ยงทาย\nเสียดแทง\nเสียดแทรก\nเสียดสี\nเสี้ยนศึก\nเสี้ยนหนาม\nเสี้ยมสอน\nเสียวซ่าน\nเสียวไส้\nเสือดาว\nเสือดำ\nเสือปลา\nเสือป่า\nเสือไฟ\nเสื่อกก\nเสื่อกระจูด\nเสื่อน้ำมัน\nเสื่อลำแพน\nเสื้อกล้าม\nเสื้อกั๊ก\nเสื้อเกราะ\nเสื้อครุย\nเสื้อแสง\nเสื้อเมือง\nเสือกคลาน\nเสือกสน\nเสือกไส\nเสื่อมคลาย\nเสื่อมถอย\nเสื่อมทราม\nเสื่อมโทรม\nเสื่อมสลาย\nเสื่อมสูญ\nเสื่อมเสีย\nเสือหมอบ\nแสกหน้า\nแสดงออก\nแสเถา\nแสนกล\nแสนรู้\nแสร้งว่า\nใส่ความ\nใส่ไคล้\nใส่ใจ\nใส่ไฟ\nไส้กรอก\nไส้ไก่\nไส้ติ่ง\nไส้ศึก\nไส้อั่ว\nไส้เดือน\nไส้ตัน\nไสยเวท\nไสยศาสตร์\nหกล้ม\nหงส์หยก\nหงอนไก่\nหงอยก๋อย\nหงอยเหงา\nหงายท้อง\nหงายหลัง\nหงำเหงอะ\nหงำเหงือก\nหดหาย\nหดหู่\nหนทาง\nหนวกหู\nหน่วงเหนี่ยว\nหน่วยก้าน\nหน่อไม้\nหนองใน\nหนองแซง\nหนักข้อ\nหนักใจ\nหนักแน่น\nหนักหน่วง\nหนักหนา\nหนังกลับ\nหนังตะลุง\nหนังเรียด\nหนังสด\nหนังใหญ่\nหนังสือพิมพ์\nหนาแน่น\nหน้ากระดาน\nหน้ากาก\nหน้ากาฬ\nหน้าแข้ง\nหน้าจั่ว\nหน้าฉาน\nหน้าตัก\nหน้าตา\nหน้าต่าง\nหน้าท้อง\nหน้าทับ\nหน้าที่\nหน้าที่นั่ง\nหน้าบัน\nหน้าปัด\nหน้าผา\nหน้าผาก\nหน้าม้า\nหน้ามุข\nหน้าไม้\nหน้าเลือด\nหน้าอก\nหนามเตย\nหน่ายหนี\nหน่ายแหนง\nหนาวเหน็บ\nหนำใจ\nหนี้สิน\nหนี้ส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น\nกณิกนันต์\nกณิการ์\nกด\nกตเวทิตา\nกตเวที\nกตัญชลี\nกตัญญุตา\nกตัญญู\nกตาธิการ\nกตาภินิหาร\nกติกา\nกถา\nกถิกาจารย์\nกทลี\nกน\nก่น\nก้น\nกนก\nกนิษฐ์\nกนิษฐา\nกบ\nกบฏ\nกบดาน\nกบทู\nกบาล\nกบินทร์\nกบิล\nกบี่\nกบูร\nกเบนทร์\nกม\nก้ม\nกมณฑลาภิเษก\nกมณฑโลทก\nกมล\nกมลา\nกมลาศ\nกมลาสน์\nกมเลศ\nกมัณฑลุ\nกมุท\nกร\nกรกฎ\nกรกฎาคม\nกรกฏ\nกรง\nกรชกาย\nกรณฑ์\nกรณิการ์\nกรณี\nกรณีย์\nกรณียกิจ\nกรณียะ\nกรด\nกรน\nกรบ\nกรบูร\nกรพินธุ์\nกรม\nกรรกฎ\nกรรกศ\nกรรเกด\nกรรไกร\nกรรเจียก\nกรรชิง\nกรรเชียง\nกรรโชก\nกรรฐ์\nกรรฐา\nกรรณ\nกรรณา\nกรรณิกา\nกรรณิการ์\nกรรดิ\nกรรดิก\nกรรดึก\nกรรตุ\nกรรไตร\nกรรทบ\nกรรแทก\nกรรบิด\nกรรบูร\nกรรภิรมย์\nกรรม\nกรรม์\nกรรม์ภิรมย์\nกรรมชวาต\nกรรมัชวาต\nกรรมาชีพ\nกรรมาธิการ\nกรรมาร\nกรรษก\nกรรสะ\nกรรแสง\nกรวด\nกรวบ\nกรวม\nกร้วม\nกรวย\nกรวิก\nกรสาปน์\nกรสุทธิ์\nกรอ\nกร้อ\nกรอก\nกร็อกกร๋อย\nกรอกแกรก\nกรอง\nกรองกรอย\nกรอด\nกร่อน\nกรอบ\nกรอม\nกร่อย\nกระ\nกระกร\nกระกรุ่น\nกระกลับกลอก\nกระกี้\nกระเกรอก\nกระเกริก\nกระเกริ่น\nกระคน\nกระคาย\nกระงกกระเงิ่น\nกระง่องกระแง่ง\nกระง่อนกระแง่น\nกระเง้ากระงอด\nกระโงก\nกระจก\nกระจง\nกระจร\nกระจอก\nกระจองหง่อง\nกระจ๋องหง่อง\nกระจองอแง\nกระจ้อน\nกระจอนหู\nกระจ้อย\nกระจ๋อหวอ\nกระจะ\nกระจัก\nกระจัง\nกระจัด\nกระจับ\nกระจ่า\nกระจ่าง\nกระจาด\nกระจาน\nกระจาบ\nกระจาม\nกระจาย\nกระจาว\nกระจิก\nกระจิ๋ง\nกระจิด\nกระจิบ\nกระจิ๋ม\nกระจิริด\nกระจิ๋ว\nกระจี้\nกระจี๋\nกระจุก\nกระจุ๋งกระจิ๋ง\nกระจุบ\nกระจุ๊บ\nกระจุ๋มกระจิ๋ม\nกระจุย\nกระจู้\nกระจู๋กระจี๋\nกระจูด\nกระเจอะกระเจิง\nกระเจา\nกระเจ่า\nกระเจ้า\nกระเจาะ\nกระเจิง\nกระเจิดกระเจิง\nกระเจี้ยง\nกระเจี๊ยบ\nกระเจียว\nกระเจี๊ยว\nกระแจะ\nกระโจน\nกระโจม\nกระฉอก\nกระฉ่อน\nกระฉับกระเฉง\nกระฉิ่ง\nกระฉีก\nกระฉูด\nกระเฉก\nกระเฉด\nกระแฉก\nกระโฉกกระเฉก\nกระโฉม\nกระชดกระช้อย\nกระชอน\nกระชอมดอก\nกระช้อย\nกระชัง\nกระชั้น\nกระชับ\nกระชาก\nกระชาย\nกระชิง\nกระชิด\nกระชุ\nกระชุก\nกระชุ่มกระชวย\nกระเชอ\nกระเชา\nกระเช้า\nกระเชียง\nกระแชง\nกระแชะ\nกระโชก\nกระซ่องกระแซ่ง\nกระซับ\nกระซาบ\nกระซิก\nกระซิบ\nกระซี้\nกระซุง\nกระซุบกระซิบ\nกระซุ้ม\nกระซู่\nกระเซ็น\nกระเซอ\nกระเซอะกระเซอ\nกระเซอะกระเซิง\nกระเซ้า\nกระเซิง\nกระแซ\nกระแซะ\nกระโซกระเซ\nกระฎี\nกระฎุมพี\nกระดก\nกระด้ง\nกระดนโด่\nกระดวง\nกระดวน\nกระด้วมกระเดี้ยม\nกระดอ\nกระดอง\nกระดองหาย\nกระดอน\nกระดอม\nกระดักกระเดี้ย\nกระดังงัว\nกระดังงา\nกระดาก\nกระด้าง\nกระดางลาง\nกระดาด\nกระดาดขาว\nกระดาน\nกระดานพน\nกระดาษ\nกระดำกระด่าง\nกระดิก\nกระดิ่ง\nกระดิ้ง\nกระดิบ\nกระดี่\nกระดี้กระเดียม\nกระดึง\nกระดืบ\nกระดุ\nกระดุกกระดิก\nกระดุ้งกระดิ้ง\nกระดุบ\nกระดุบกระดิบ\nกระดุม\nกระดูก\nกระเดก\nกระเด้ง\nกระเด็น\nกระเด้า\nกระเดาะ\nกระเดิด\nกระเดี้ย\nกระเดียด\nกระเดือก\nกระเดื่อง\nกระแด็ก\nกระแด้ง\nกระแด้แร่\nกระแด่ว\nกระแดะ\nกระโดก\nกระโดง\nกระโดด\nกระโดน\nกระได\nกระตรับ\nกระตราก\nกระตรุด\nกระตรุม\nกระต้วมกระเตี้ยม\nกระต้อ\nกระต่องกระแต่ง\nกระต๊อบ\nกระต้อยตีวิด\nกระตัก\nกระตั้ว\nกระต่าย\nกระติก\nกระติ๊ด\nกระติบ\nกระตือรือร้น\nกระตุก\nกระตุ้งกระติ้ง\nกระตุ่น\nกระตุ้น\nกระตูบ\nกระเตง\nกระเต็น\nกระเตอะ\nกระเตาะ\nกระเตาะกระแตะ\nกระเตื้อง\nกระแต\nกระแตแต้แว้ด\nกระโตกกระตาก\nกระโตน\nกระถด\nกระถอบ\nกระถั่ว\nกระถาง\nกระถิก\nกระถิน\nกระเถิบ\nกระโถน\nกระทก\nกระทง\nกระทบ\nกระทรวง\nกระทอก\nกระท้อน\nกระท่อนกระแท่น\nกระท่อม\nกระท้อมกระแท้ม\nกระทะ\nกระทั่ง\nกระทั้น\nกระทา\nกระทาย\nกระทาสี\nกระทาหอง\nกระทำ\nกระทิกกระทวย\nกระทิง\nกระทึง\nกระทืบ\nกระทุ\nกระทุง\nกระทุ้ง\nกระทุ่ม\nกระทู้\nกระเท่\nกระเทียบ\nกระเทียม\nกระเทือน\nกระเทื้อม\nกระแทก\nกระแท่น\nกระแทะ\nกระไทชาย\nกระน่อง\nกระนั้น\nกระนี้\nกระแนะกระแหน\nกระโน้น\nกระไน\nกระบก\nกระบม\nกระบวน\nกระบวย\nกระบวร\nกระบอก\nกระบอง\nกระบะ\nกระบัด\nกระบั้วกระเบี้ย\nกระบ่า\nกระบ้า\nกระบาก\nกระบาย\nกระบาล\nกระบิ\nกระบิ้ง\nกระบิด\nกระบิล\nกระบี่\nกระบือ\nกระบุง\nกระบุ่มกระบ่าม\nกระบู้กระบี้\nกระบูน\nกระบูร\nกระเบง\nกระเบญ\nกระเบ็ดกระบวน\nกระเบน\nกระเบา\nกระเบิก\nกระเบียด\nกระเบียน\nกระเบื้อง\nกระแบก\nกระแบะ\nกระโบม\nกระปมกระปำ\nกระปมกระเปา\nกระปรอก\nกระปรอกว่าว\nกระปรี้กระเปร่า\nกระปอก\nกระป้อกระแป้\nกระป่อง\nกระป๋อง\nกระปอดกระแปด\nกระป๋อหลอ\nกระปั้วกระเปี้ย\nกระป่ำ\nกระปุก\nกระปุ๊กลุก\nกระปุ่ม\nกระปุ่มกระป่ำ\nกระปุ่มกระปิ่ม\nกระเป๋า\nกระเปาะ\nกระโปก\nกระโปรง\nกระผม\nกระผลีกระผลาม\nกระผาน\nกระผีก\nกระพรวน\nกระพริ้ม\nกระพอก\nกระพอง\nกระพ้อม\nกระพัก\nกระพัง\nกระพังเหิร\nกระพังโหม\nกระพัด\nกระพัตร\nกระพัน\nกระพั่น\nกระพา\nกระพาก\nกระพี้\nกระพือ\nกระพุ้ง\nกระพุ่ม\nกระเพาะ\nกระเพิง\nกระเพื่อม\nกระแพ้ง\nกระฟัดกระเฟียด\nกระฟูมกระฟาย\nกระมล\nกระมอบ\nกระมอมกระแมม\nกระมัง\nกระมัน\nกระมิดกระเมี้ยน\nกระมุท\nกระเมาะ\nกระย่อง\nกระย่องกระแย่ง\nกระย่อน\nกระย่อม\nกระยา\nกระยาง\nกระยาจก\nกระยาหงัน\nกระยิก\nกระยิ้มกระย่อง\nกระยึกกระยือ\nกระยืดกระยาด\nกระเย้อกระแหย่ง\nกระรอก\nกระเรียน\nกระโรกน้ำข้าว\nกระโรกใหญ่\nกระไร\nกระลด\nกระลบ\nกระลอก\nกระลอม\nกระละหล่ำ\nกระลัด\nกระลับ\nกระลัมพร\nกระลา\nกระลำ\nกระลำพัก\nกระลำพุก\nกระลิง\nกระลี\nกระลุมพาง\nกระลุมพุก\nกระลุมพู\nกระลูน\nกระลู่น์\nกระเล็น\nกระเลียด\nกระเลือก\nกระโลง\nกระวน\nกระวัด\nกระวาด\nกระวาน\nกระวาย\nกระวิน\nกระวี\nกระวีกระวาด\nกระวูดกระวาด\nกระเวน\nกระเวยกระวาย\nกระแวน\nกระโวยกระวาย\nกระษัย\nกระษาปณ์\nกระสง\nกระสบ\nกระสม\nกระสรวล\nกระสร้อย\nกระสวน\nกระสวย\nกระสอบ\nกระสะ\nกระสัง\nกระสัน\nกระสับกระส่าย\nกระสา\nกระสานติ์\nกระสาบ\nกระสาย\nกระสือ\nกระสุงกระสิง\nกระส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ทิง\nกากะเยีย\nกากี\nกาง\nก้าง\nกางเกง\nกางเขน\nก๊าซ\nกาซะลอง\nกาญจนา\nกาฐ\nกาด\nก๊าด\nกาน\nก่าน\nก้าน\nก๊าน\nกานดา\nกานต์\nกานน\nก้านพร้าว\nกานพลู\nกาน้า\nกาบ\nก้าบ\nกาบู\nกาพย์\nกาเฟอีน\nกาแฟ\nกาม\nก้าม\nกามารมณ์\nกามินี\nกาเมสุมิจฉาจาร\nกาย\nก่าย\nกาเยน\nการ\nการณ์\nการ์ด\nการ์ตูน\nการบูร\nการย์\nการวิก\nการเวก\nการะเกด\nการะบุหนิง\nการัณย์\nการันต์\nการางหัวขวาน\nการิตการก\nการิตวาจก\nการุญ\nการุณย์\nกาเรการ่อน\nกาล\nกาลกรรณี\nกาลกิณี\nกาลจักร\nกาลัญญุตา\nกาลัญญู\nกาลัด\nกาลานุกาล\nกาลิก\nกาลี\nกาแล\nกาแล็กซี\nกาแล็กโทส\nกาว\nก้าว\nกาววาว\nกาวาง\nกาแวน\nกาศิก\nกาษฐะ\nกาษา\nกาสร\nกาสะ\nกาสา\nกาสาร\nกาสาวะ\nกาสิโน\nกาหล\nกาหลง\nกาหลา\nกาเหว่า\nกาไหล่\nกาฬ\nกาฬาวก\nกาฮัง\nกำ\nก่ำ\nกำกวม\nกำกัด\nกำกับ\nก้ำกึ่ง\nกำกูน\nก้ำเกิน\nกำเกียง\nกำคูน\nกำจร\nกำจัด\nกำจาย\nกำชับ\nกำชำ\nกำซาบ\nกำซำ\nกำด้น\nกำดัด\nกำดาล\nกำเดา\nกำธร\nกำนล\nกำนัน\nกำนัล\nกำเนิด\nกำบัง\nก่ำบึ้ง\nกำเบ้อ\nกำปอ\nกำปั่น\nกำผลา\nกำพง\nกำพด\nกำพต\nกำพร้า\nกำพราก\nกำพวด\nกำพอง\nกำพืด\nกำพุด\nกำพู\nกำเพลิง\nกำแพง\nกำภู\nกำมลาศน์\nกำมเลศ\nกำมะถัน\nกำมะลอ\nกำมะหยี่\nกำมะหริด\nกำมังละการ\nกำมังวิลิต\nกำมัชพล\nกำยาน\nกำยำ\nกำรอ\nกำราบ\nกำราล\nกำเริบ\nกำไร\nกำลัง\nกำลุง\nกำเลา\nกำไล\nกำสรด\nกำสรวล\nกำหนด\nกำหนัด\nกำเหน็จ\nกำแหง\nกิก\nกิ๊ก\nกิ่ง\nกิ้งก่า\nกิ้งกือ\nกิ้งโครง\nกิจ\nกิจจะ\nกิจจา\nกิดาการ\nกิดาหยัน\nกิตติ\nกิตติมศักดิ์\nกิน\nกินนร\nกินปลี\nกินเปี้ยว\nกินริน\nกินรี\nกิ๊บ\nกิมตึ๋ง\nกิมิชาติ\nกิมิวิทยา\nกิโมโน\nกิโยตีน\nกิระ\nกิริณี\nกิรินท\nกิริเนศวร\nกิริยา\nกิเลน\nกิเลส\nกิโล\nกิโลมกะ\nกิ่ว\nกิ๋ว\nกี\nกี่\nกี้\nกี๊\nกี๋\nกีฏวิทยา\nกีด\nกีตาร์\nกีบ\nกีรติ\nกีฬา\nกึก\nกึง\nกึ่ง\nกึ๋น\nกุ\nกุก\nกุ๊ก\nกุกกุฏ\nกุกกุร\nกุกรรม\nกุ้ง\nกุงอน\nกุงาน\nกุโงก\nกุจี\nกุญแจ\nกุญชร\nกุฎ\nกุฎา\nกุฎี\nกุฎุมพี\nกุฏฐัง\nกุฏิ\nกุณฑ์\nกุณฑล\nกุณฑี\nกุณโฑ\nกุณาล\nกุณี\nกุด\nกุดัง\nกุดั่น\nกุดา\nกุทัณฑ์\nกุน\nกุ๊น\nกุนเชียง\nกุนที\nกุโนกามอ\nกุบ\nกุบกับ\nกุม\nกุ่ม\nกุมฝอย\nกุมภ์\nกุมภนิยา\nกุมภัณฑ์\nกุมภา\nกุมภิล\nกุมภีล์\nกุมเหง\nกุมาร\nกุมารา\nกุมารี\nกุมุท\nกุย\nกุ๊ย\nกุ๋ย\nกุยช่าย\nกุยเฮง\nกุรระ\nกุรุพินท์\nกุเรา\nกุล\nกุลา\nกุลาหล\nกุลี\nกุลีกุจอ\nกุเลา\nกุแล\nกุเวร\nกุศราช\nกุศล\nกุศโลบาย\nกุสุม\nกุสุมภ์\nกุสุมา\nกุสุมาลย์\nกุสุมิตลดาเวลลิตา\nกุหนี\nกุหนุง\nกุหร่า\nกุหล่า\nกุหลาบ\nกุแหละ\nกู\nกู่\nกู้\nกู๊ก\nกูฏ\nกูฏา\nกูณฑ์\nกูด\nกูบ\nกูปรี\nกูรมะ\nกูรมาวตาร\nเก\nเก้\nเก๊\nเก๋\nเกก\nเก๊ก\nเกกมะเหรก\nเก๊กฮวย\nเก้กัง\nเก็ง\nเก่ง\nเก้ง\nเก๋ง\nเกงกอย\nเก่งกาจ\nเกงเขง\nเก๋งเคง\nเก็จ\nเกจิอาจารย์\nเกชา\nเกณฑ์\nเกด\nเก็ด\nเกตุ\nเกน\nเก็บ\nเกม\nเกย\nเกยูร\nเกรง\nเกร็ง\nเกร็ด\nเกรน\nเกร่อ\nเกรอะ\nเกราะ\nเกริก\nเกริน\nเกริ่น\nเกรียก\nเกรียง\nเกรียด\nเกรียน\nเกรียบ\nเกรียม\nเกรียว\nเกรี้ยว\nเกเร\nเกล็ด\nเกลศ\nเกลอ\nเกลา\nเกล้า\nเกลาะ\nเกลี่ย\nเกลี้ย\nเกลียง\nเกลี้ยง\nเกลียด\nเกลียว\nเกลือ\nเกลื้อ\nเกลือก\nเกลื่อน\nเกลื้อน\nเกวัฏ\nเกวียน\nเกศ\nเกศว\nเกศวะ\nเกศา\nเกศินี\nเกศี\nเกษตร\nเกษม\nเกษียณ\nเกษียน\nเกษียร\nเกส\nเกสร\nเกสรี\nเกสา\nเกสี\nเก้อ\nเกอิชา\nเกะ\nเกะกะ\nเกา\nเก่า\nเก้า\nเก๋า\nเกาต์\nเกาทัณฑ์\nเกาบิล\nเกาลัด\nเกาลิน\nเกาไศย\nเกาหลี\nเกาเหลา\nเกาเหลียง\nเก้าอี้\nเกาะ\nเกิ้ง\nเกิด\nเกิน\nเกิบ\nเกีย\nเกียกกาย\nเกียง\nเกี่ยง\nเกี๋ยง\nเกียจ\nเกียด\nเกียน\nเกี้ยมไฉ่\nเกี้ยมอี๋\nเกียร์\nเกียรติ\nเกียรติ์\nเกี่ยว\nเกี้ยว\nเกี๊ยว\nเกี๊ยะ\nเกื้อ\nเกือก\nเกื้อกูล\nเกือบ\nแก\nแก่\nแก้\nแกง\nแก่ง\nแก้ง\nแก๊ง\nแกงได\nแกงแนง\nแกโดลิเนียม\nแกน\nแก่น\nแก๊ป\nแกม\nแก้ม\nแกมมา\nแกรก\nแกร่ง\nแกร็น\nแกรนิต\nแกรไฟต์\nแกร่ว\nแกระ\nแกล\nแกล้ง\nแกลน\nแกลบ\nแกล้ม\nแกลลอน\nแกลเลียม\nแกล้ว\nแกละ\nแกแล\nแกว\nแก้ว\nแกว่ง\nแก๊ส\nแกะ\nโก\nโก่\nโก้\nโก๋\nโกก\nโกกนุท\nโกกิลา\nโกโก้\nโกง\nโก่ง\nโกงกาง\nโก้งเก้ง\nโกงโก้\nโก้งโค้ง\nโกเชาว์\nโกญจนาท\nโกญจา\nโกฏิ\nโกฐ\nโกฐาส\nโกณะ\nโกดัง\nโกทัณฑ์\nโกน\nโก่น\nโก๋น\nโกมล\nโกมุท\nโกเมน\nโกเมศ\nโกย\nโกรก\nโกรกกราก\nโกรง\nโกร่ง\nโกร่งกร่าง\nโกรงเกรง\nโกร๋งเกร๋ง\nโกรญจ\nโกรต๋น\nโกรธ\nโกรธา\nโกร๋น\nโกรม\nโกรย\nโกรศ\nโกโรโกเต\nโกโรโกโรก\nโกโรโกโส\nโกลน\nโกลาหล\nโกไล\nโกวิท\nโกศ\nโกศล\nโกษม\nโกสน\nโกสัช\nโกสินทร์\nโกสีย์\nโกสุม\nโกไสย\nโกหก\nใกล้\nไก\nไก่\nไก๊\nไก๋\nไก่กอม\nไกพัล\nไกร\nไกรพ\nไกรลาส\nไกรศร\nไกรศรี\nไกรสร\nไกรสรี\nไกรสิทธิ\nไกล\nไกล่\nไกลาส\nไกว\nไกวัล\nขงจื๊อ\nขจร\nขจรจบ\nขจัด\nขจ่าง\nขจาย\nขจาว\nขจิต\nขจี\nขจุย\nขเจา\nขณะ\nขด\nขน\nข้น\nขนง\nขนด\nขนบ\nขนม\nขนอง\nขนอน\nขนอบ\nขนัด\nขนัน\nขนาก\nขนาง\nขนาด\nขนาน\nขนาบ\nขนาย\nขนำ\nขนิษฐ\nขนิษฐา\nขนุน\nขนุนนก\nขบ\nขบถ\nขบวน\nขบวร\nขม\nข่ม\nขมงโกรย\nขมวด\nขมวน\nขมอง\nขม่อม\nขมัง\nขมับ\nขมา\nขม้ำ\nขมิ้น\nขมิบ\nขมีขมัน\nขมึง\nขมึงทึง\nขมุ\nขมุกขมัว\nขมุบ\nขโมย\nขยด\nขยม\nขย่ม\nขยอก\nขยอง\nขย่อน\nขย้อน\nขยะ\nขยัก\nขยัน\nขยั้น\nขยับ\nขยาด\nขยาย\nขยำ\nขย้ำ\nขยิก\nขยิบ\nขยิ่ม\nขยี้\nขยุกขยิก\nขยุกขยุย\nขยุบ\nขยุบขยิบ\nขยุม\nขยุ้ม\nขยุย\nขรม\nขรรค์\nขรัว\nขริบ\nขรี\nขรึม\nขรุขระ\nขลบ\nขล้อ\nขลัง\nขลับ\nขลาด\nขลาย\nขลิบ\nขลุก\nขลุกขลัก\nขลุกขลิก\nขลุบ\nขลุม\nขลุ่ย\nขลู\nขลู่\nขวง\nข่วง\nขวด\nข่วน\nขวนขวาย\nขวบ\nขวย\nขวักไขว่\nขวัญ\nขวั้น\nขวับ\nขวับเขวียว\nขวา\nขวาก\nขวาง\nขว้าง\nขวาด\nขวาน\nขวายขวน\nขวาว\nขว้าว\nขวิด\nขอ\nข่อ\nข้อ\nของ\nข้อง\nขอด\nขอน\nข้อน\nขอบ\nขอม\nข่อย\nข้อย\nข่อยหยอง\nขะแจะ\nขะเน็ด\nขะมอมขะแมม\nขะมักเขม้น\nขะมุกขะมอม\nขะยิก\nขะยุก\nขะเย้อแขย่ง\nขัค\nขัง\nขังขอก\nขัช\nขัณฑสกร\nขัณฑสีมา\nขัด\nขัดมอน\nขัตติยมานะ\nขัน\nขั้น\nขันติ\nขันตี\nขันโตก\nขันที\nขันธ์\nขันธาวาร\nขับ\nขัว\nขั้ว\nขา\nข่า\nข้า\nขาก\nขาก๊วย\nขาง\nข่าง\nข้าง\nขาณุ\nขาด\nขาทนียะ\nขาน\nขาบ\nข้าพเจ้า\nขาม\nข่าม\nข้าม\nขาย\nข่าย\nขาล\nขาว\nข่าว\nข้าว\nข้าวอังกุลี\nขำ\nขิก\nขิง\nขิงแกลง\nขิงแครง\nขิด\nขิปสัทโท\nขิม\nขี่\nขี้\nขี้เข็บ\nขีณาสพ\nขีด\nขี้ตังนี\nขีปนาวุธ\nขี้ยอก\nขีระ\nขึง\nขึ้ง\nขึ้น\nขึ้นฉ่าย\nขืน\nขื่น\nขื่อ\nขุก\nขุด\nขุน\nขุ่น\nขุนเพ็ด\nขุม\nขุย\nขู่\nขูด\nเข\nเข้\nเขก\nเข็ง\nเข่ง\nเขจร\nเข็ญ\nเข็ด\nเขดา\nเขต\nเขน\nเข็น\nเข่น\nเขนง\nเขน็ด\nเขนย\nเขบ็จขบวน\nเขบ็ต\nเขม\nเข็ม\nเข้ม\nเข้มขาบ\nเขม็ง\nเขม็ดแขม่\nเขม่น\nเขม้น\nเขม้นขะมัก\nเขมร\nเขมา\nเขม่า\nเขมือบ\nเขย\nเขยก\nเขย่ง\nเขย้อแขย่ง\nเขย่า\nเขยิน\nเขยิบ\nเขยื้อน\nเขรอะ\nเขลง\nเขลอะ\nเขละ\nเขลา\nเขลาะ\nเขว\nเขษม\nเขฬะ\nเขะขะ\nเขา\nเข่า\nเข้า\nเขิง\nเขิน\nเขิบ\nเขี่ย\nเขียง\nเขียด\nเขียดตะปาด\nเขียน\nเขี่ยน\nเขียม\nเขียว\nเขี้ยว\nเขียะ\nเขือ\nเขือง\nเขื่อง\nเขื่อน\nเขือม\nแข\nแข้\nแขก\nแข็ง\nแข่ง\nแข้ง\nแขน\nแข่น\nแข้น\nแขนง\nแขม\nแขม็บ\nแขม่ว\nแขยง\nแขย่ง\nแขวก\nแขวง\nแขวน\nแขวะ\nโข\nโขก\nโขง\nโข่ง\nโขด\nโขดง\nโขน\nโขนง\nโขม\nโขมง\nโขมด\nโขยก\nโขยง\nโขย่ง\nโขยด\nโขลก\nโขลง\nโขลน\nโขษม\nไข\nไข่\nไข้\nไขว่\nไขว้\nคคนะ\nคคนัมพร\nคคนางค์\nคคนานต์\nคง\nคงคา\nคงไคย\nคช\nคชาชาติ\nคชาชีพ\nคชาธาร\nคชาภรณ์\nคณนา\nคณบดี\nคณะ\nคณาจารย์\nคณาธิการ\nคณาธิปไตย\nคณานับ\nคณิกา\nคณิต\nคเณศ\nคด\nคดี\nคติ\nคทา\nคน\nค้น\nคนทา\nคนทิสอ\nคนที\nคนโท\nคนธ์\nคันธ์\nคนธรรพ์\nคเนจร\nคบ\nคม\nคมน์\nคมนาการ\nคมนาคม\nคมิกภัต\nครก\nครบ\nครรชิต\nครรภ\nครรภ์\nครรลอง\nครรโลง\nครรไล\nครวญ\nครวี\nครหา\nครอก\nครอง\nครองแครง\nคร่อเงาะ\nคร่อเทียน\nครอบ\nคร่อม\nคระเมิม\nคระแลง\nคระไล\nคระแวง\nคระหน\nคระหวน\nคระหาย\nคระโหย\nครั่ง\nครั้ง\nครัดเคร่ง\nครัน\nครั่น\nครั้น\nครับ\nครัว\nครา\nคร่า\nคราก\nคราง\nคราญ\nคราด\nคร้าน\nคราบ\nคราม\nคร้าม\nครามครัน\nคราว\nคร่าว\nคราส\nครำ\nคร่ำ\nคร่ำเคร่ง\nคริปทอน\nคริสต์\nครีบ\nครีม\nครีษมายัน\nครึ\nครึกครื้น\nครึกโครม\nครึ่ง\nครึ่ด\nครึน\nครึ้ม\nครืด\nครืน\nครื้น\nครืนครั่น\nครื้นครั่น\nครื้นครึก\nครื้นเครง\nครือ\nครุ\nครุคระ\nครุฑ\nครุ่น\nครุมเครือ\nครุย\nครุวนา\nครู\nครู่\nครูด\nคฤโฆษ\nคฤนถ์\nคฤหบดี\nคฤหัสถ์\nคฤหาสน์\nคลวง\nคลอ\nคล้อ\nคลอก\nคลอง\nคล่อง\nคล้อง\nคลอด\nคลอน\nคล้อย\nคลอรีน\nคลอโรฟอร์ม\nคลอโรฟีลล์\nคละ\nคละคลุ้ง\nคลัก\nคลั่ก\nคลัง\nคลั่ง\nคลัตช์\nคลับคล้าย\nคลับคลา\nคลา\nคล้า\nคลางแคลง\nคลาด\nคลาน\nคลาย\nคล้าย\nคล้ายคลึง\nคล่าว\nคลำ\nคล่ำ\nคล้ำ\nคลิ้งโคลง\nคลิด\nคลินิก\nคลี\nคลี่\nคลึง\nคลื่น\nคลุก\nคลุ้ง\nคลุบ\nคลุม\nคลุ่ม\nคลุ้ม\nควง\nควณ\nควน\nควบ\nควย\nควร\nควัก\nควั่ก\nควั่งคว้าง\nควัน\nควั่น\nคว้า\nควาก\nคว้าง\nควาญ\nควาน\nคว้าน\nความ\nควาย\nคว่าว\nคว่ำ\nควินิน\nควิวคว่าง\nคหกรรม\nคหกรรมศาสตร์\nคหบดี\nคหัฐ\nคอ\nค้อ\nคอก\nค็อกคัส\nค็อกเทล\nคอเคซอยด์\nค่องอ้อย\nคอด\nคอแดง\nคอน\nค่อน\nค้อน\nคอนกรีต\nคอนเดนเซอร์\nคอนแวนต์\nคอนเสิร์ต\nคอม\nค่อม\nค้อม\nคอมพิวเตอร์\nคอมมานโด\nคอมมิวนิสต์\nคอย\nค่อย\nค้อย\nคอยล์\nคอร์ด\nคอแลน\nคอสติกโซดา\nคะ\nค่ะ\nคะไขว่\nคะค้อย\nคะคาน\nคะนน\nคะนอง\nคะน้า\nคะนึง\nคะเน\nคะเนงร้าย\nคะเน็ด\nคะแนน\nคะมำ\nคะยั้นคะยอ\nคะเยอ\nคัก\nคั่ก\nคัคนะ\nคัคนัมพร\nคัคนางค์\nคัคนานต์\nคั่ง\nคังไคย\nคัจฉ\nคัณฑมาลา\nคัณฑสูตร\nคัด\nคัดเค้า\nคัดมอน\nคัดเม็ง\nคัทลียา\nคัน\nคั่น\nคั้น\nคันถรจนาจารย์\nคันธกุฎี\nคันธมาทน์\nคันธารราษฎร์\nคับ\nคับค้อน\nคับคา\nคับแค\nคัพภ์\nคัมภีร์\nคัมภีรภาพ\nคัล\nคั่ว\nคา\nค่า\nค้า\nค่าคบ\nคาง\nค่าง\nค้าง\nคางคก\nค้างคาว\nคาด\nคาถา\nคาทอลิก\nคาน\nค้าน\nคาบ\nคาพยุต\nคาม\nคามวาสี\nคามณีย์\nคามภีร์\nคาย\nค่าย\nคาร์บอน\nคาร์บอเนต\nคาร์บอลิก\nคาร์บูเรเตอร์\nคาร์โบรันดัม\nคาร์โบไฮเดรต\nคารม\nคารวะ\nคาราเต้\nคาราวาน\nคาว\nค่าว\nค้าว\nคาวตอง\nคาวี\nคาวุต\nคาส\nคำ\nค่ำ\nค้ำ\nคำนวณ\nคำนวร\nคำนับ\nคำนัล\nคำนึง\nคำนูณ\nคำฝอย\nคำเพลิง\nคำรน\nคำรบ\nคำราม\nคำแสด\nคำแหง\nคำโอง\nคิก\nคิง\nคิด\nคิมหันต์\nคิรี\nคิลาน\nคิลานะ\nคิว\nคิ้ว\nคี่\nคีต\nคีบ\nคีม\nคีรี\nคีรีบูน\nคึก\nคึ่ก\nคึกคัก\nคืน\nคืบ\nคือ\nคุ\nคุก\nคุกกี้\nคุกคาม\nคุกพาทย์\nคุ้ง\nคุณ\nคุด\nคุดทะราด\nคุต\nคุตติ\nคุ่น\nคุ้น\nคุป\nคุปต์\nคุปติ\nคุม\nคุ่ม\nคุ้ม\nคุย\nคุ้ย\nคุยหฐาน\nคุยหประเทศ\nคุรุ\nคุลา\nคุลิก่า\nคุลีการ\nคุหา\nคู\nคู่\nคู้\nคูณ\nคูถ\nคูน\nคูปอง\nคูเรียม\nคูหา\nเค้ก\nเค้เก้\nเค้ง\nเคณฑะ\nเคด\nเค็ด\nเคน\nเค้น\nเคเบิล\nเค็ม\nเคมี\nเคย\nเครง\nเคร่ง\nเครงครา\nเครงครำ\nเครดิต\nเครน\nเครา\nเคร่า\nเคราหณี\nเคราะห์\nเครียด\nเครียว\nเครือ\nเครื่อง\nเคล้ง\nเคล็ด\nเคล้น\nเคล้า\nเคล่าคล่อง\nเคลิบเคลิ้ม\nเคลิ้ม\nเคลีย\nเคลื่อน\nเคลือบ\nเคว้ง\nเคหะ\nเคหา\nเคอะ\nเค้า\nเคาน์เตอร์\nเคารพ\nเคาะ\nเคาะแคะ\nเคียง\nเคียด\nเคียน\nเคียม\nเคี่ยม\nเคียร\nเคียว\nเคี่ยว\nเคี้ยว\nเคือง\nแค\nแค่\nแค้\nแคแล\nแคดเมียม\nแค็ตตาล็อก\nแคแตร\nแคโทด\nแคน\nแค่น\nแค้น\nแคบ\nแคบหมู\nแคปซูล\nแคม\nแคร่\nแครก\nแครง\nแคระ\nแคลคูลัส\nแคลง\nแคลเซียม\nแคลน\nแคล้ว\nแคล่วคล่อง\nแคลอรี\nแคลิฟอร์เนียม\nแคว\nแควก\nแคว้น\nแคแสด\nแคะ\nโค\nโคก\nโคเคน\nโค่ง\nโค้ง\nโคจร\nโคเซแคนต์\nโคไซน์\nโคตร\nโคแทนเจนต์\nโคธา\nโคน\nโค่น\nโคบอลต์\nโคปผกะ\nโคม\nโคม่า\nโครก\nโครกคราก\nโครง\nโคร่ง\nโคร่งคร่าง\nโครม\nโครเมียม\nโครโมโซม\nโคราช\nโครำ\nโคล\nโคลง\nโคลน\nโควตา\nโคออร์ดิเนต\nใคร\nใคร่\nใคร่ครวญ\nไค\nไค้\nไคร้\nไคร้เครือ\nไคล\nไคล้\nฆนะ\nฆราวาส\nฆ้อง\nฆ่า\nฆาต\nฆาน\nฆานินทรีย์\nเฆี่ยน\nโฆรวิส\nโฆษก\nโฆษณา\nโฆษะ\nโฆษ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nเฉ่ง\nเฉด\nเฉท\nเฉนียน\nเฉพาะ\nเฉย\nเฉลย\nเฉลว\nเฉลา\nเฉลิม\nเฉลี่ย\nเฉลียง\nเฉลี่ยง\nเฉลียบ\nเฉลียว\nเฉวียง\nเฉวียน\nเฉอะแฉะ\nเฉา\nเฉาก๊วย\nเฉาฮื้อ\nเฉาะ\nเฉิด\nเฉิบ\nเฉียง\nเฉียงพร้านางแอ\nเฉียด\nเฉียบ\nเฉียว\nเฉี่ยว\nเฉือน\nเฉื่อย\nแฉ\nแฉ่\nแฉก\nแฉง\nแฉ่ง\nแฉลบ\nแฉล้ม\nแฉะ\nโฉ\nโฉ่\nโฉเก\nโฉ่งฉ่าง\nโฉงเฉง\nโฉด\nโฉนด\nโฉบ\nโฉเบ๊\nโฉม\nโฉลก\nไฉน\nไฉไล\nชก\nชคัตตรัย\nชง\nชงโค\nชงฆ์\nชงฆา\nชงโลง\nชฎา\nชฎามังษี\nชฎามังสี\nชฎิล\nชด\nชน\nชนก\nชนนี\nชนม์\nชนวน\nชนะ\nชนัก\nชนา\nชนาง\nชนิด\nชเนตตี\nชบา\nชม\nชมดชม้อย\nชมนาด\nชมพู\nชมพู่\nชมรม\nชม้อย\nชม้าย\nชไม\nชยา\nชโย\nชรทึง\nชรริน\nชรอุ่ม\nชระล้ำ\nชระลุ\nชระอาบ\nชระเอม\nชรัด\nชรา\nชล\nชโลง\nชโลม\nช่วง\nชวด\nชวน\nชวย\nช่วย\nชวร\nชวลิต\nชวา\nชวาล\nชวาลา\nช่อ\nชอก\nช็อก\nช็อกโกเลต\nช็อกโกแลต\nชอง\nช่อง\nช้อง\nชองระอา\nชอน\nช่อน\nช้อน\nชอบ\nชอม\nช้อย\nชอล์ก\nชอ่ำ\nชอุ่ม\nชะ\nชะคราม\nชะงอก\nชะง่อน\nชะงัก\nชะงัด\nชะง้ำ\nชะงุ้ม\nชะเง้อ\nชะเงื้อม\nชะแง้\nชะโงก\nชะฉ่า\nชะช่อง\nชะชะ\nชะช้า\nชะโด\nชะตา\nชะต้า\nชะนี\nชะเนาะ\nชะเนียง\nชะพลู\nชะเพลิง\nชะมด\nชะมบ\nชะมวง\nชะมัง\nชะมัด\nชะแม่\nชะรอย\nชะลอ\nชะลอม\nชะล่า\nชะลาน\nชะลิน\nชะลูด\nชะเลง\nชะเลย\nชะแล็ก\nชะแลง\nชะวาก\nชะวาด\nชะเวิกชะวาก\nชะแวง\nชะอม\nชะอ้อน\nชะเอม\nชะโอน\nชัก\nชักคราม\nชักช้า\nชัง\nชั่ง\nชังคา\nชังฆ\nชัชวาล\nชัฏ\nชัด\nชัดช้า\nชัน\nชั้น\nชันกาด\nชันชี\nชันตุ\nชันนะตุ\nชันนุ\nชันโรง\nชันษา\nชันสูตร\nชัปนะ\nชัพ\nชัมพูนท\nชัย\nชัยพฤกษ์\nชัยภูมิ\nชัลลุกา\nชั่ว\nชั้ว\nชัวชม\nชา\nช้า\nชาคระ\nชาคริต\nชาคริยานุโยค\nช่าง\nช้าง\nช้าช่อน\nชาญ\nชาด\nชาดก\nชาต\nชาตบุษย์\nชาตรี\nชาตะ\nชาตา\nชาติ\nชาน\nชานุ\nช้าปี่\nชาปีไหน\nช้าแป้น\nช้าพลู\nชาม\nชามพูนท\nชามาดร\nชามาดา\nชามาตุ\nชาย\nชายา\nชาล\nชาลา\nชาลินี\nช้าเลือด\nชาว\nชาวี\nชำ\nช่ำ\nช้ำ\nชำงัด\nชำงาย\nช่ำชอง\nชำนะ\nชำนัญ\nชำนัน\nชำนาญ\nชำนิ\nชำเนียร\nชำมะนาด\nชำมะเลียง\nชำร่วย\nชำระ\nช้ำรั่ว\nชำรุด\nชำเรา\nชำเราะ\nชำแรก\nชำแระ\nชำเลือง\nชำแหละ\nชิ\nชิง\nชิ่ง\nชิงชัน\nชิงช้า\nชิงช้าชาลี\nชิงชี่\nชิงฮื้อ\nชิชะ\nชิชิ\nชิณณะ\nชิด\nชิเดนทรีย์\nชิต\nชิตินทรีย์\nชิน\nชิ้น\nชินโต\nชิโนรส\nชิม\nชิมแปนซี\nชิยา\nชิรณะ\nชิระ\nชิวหา\nชิสา\nชี\nชี่\nชี้\nชีปะขาว\nชีผะขาว\nชีผ้าขาว\nชีพ\nชีฟอง\nชีรณ\nชีระ\nชีวเคมี\nชีวประวัติ\nชีวภาพ\nชีววิทยา\nชีวะ\nชีวัน\nชีวา\nชีวาตม์\nชีวาลัย\nชีวิต\nชีวิตักษัย\nชีวิน\nชีวี\nชืด\nชื่น\nชื้น\nชื่อ\nชุก\nชุกชี\nชุ้ง\nชุณห\nชุด\nชุติ\nชุน\nชุบ\nชุม\nชุ่ม\nชุมนุม\nชุมพร\nชุมพา\nชุมแพรก\nชุมรุม\nชุมแสง\nชุมเห็ด\nชุ่ย\nชุลมุน\nชุลี\nชุษณะ\nชู\nชู้\nเช็ค\nเช้ง\nเช้งวับ\nเชงเลง\nเช็ด\nเชน\nเช่น\nเชย\nเชลง\nเชลย\nเชลแล็ก\nเชลียง\nเชวง\nเชษฐะ\nเชษฐา\nเชอ\nเช่า\nเช้า\nเชาว์\nเชาวน์\nเชิง\nเชิญ\nเชิด\nเชิ้ต\nเชียง\nเชี่ยน\nเชียบ\nเชี่ยม\nเชียร\nเชียร์\nเชียว\nเชี่ยว\nเชื่อ\nเชื้อ\nเชือก\nเชื่อง\nเชือด\nเชือน\nเชื่อม\nแช\nแช่\nแช่ง\nแชงมา\nแชบ๊วย\nแช่ม\nแชร์\nแชล่ม\nแชสซี\nแชะ\nโชก\nโชค\nโชงโลง\nโชดก\nโชดึก\nโชต\nโชตก\nโชติ\nโชติก\nโชน\nโชมโรม\nโชย\nโชยงการ\nโชยชาย\nโชยติส\nโชว์\nใช่\nใช้\nไช\nไชนะ\nไชย\nไชโย\nซก\nซ่ก\nซงดำ\nซ่งฮื้อ\nซด\nซน\nซ้น\nซบ\nซม\nซวดเซ\nซวน\nซวย\nซอ\nซอก\nซอง\nซ่อง\nซ้อง\nซองแมว\nซ้องแมว\nซอน\nซ่อน\nซ้อน\nซอม\nซ่อม\nซ้อม\nซอมซ่อ\nซอย\nซอส\nซัก\nซักส้าว\nซัง\nซั้ง\nซัด\nซับ\nซัลฟา\nซั้ว\nซา\nซ่า\nซาก\nซาง\nซ่าง\nซาด\nซาน\nซ่าน\nซาบซ่าน\nซาบซึ้ง\nซ่าโบะ\nซาแมเรียม\nซ้าย\nซาลาเปา\nซาว\nซ่าหริ่ม\nซำ\nซ้ำ\nซิ\nซี\nซิก\nซิกข์\nซิกซี้\nซิกแซ็ก\nซิการ์\nซิงโคนา\nซิ่น\nซินนามิก\nซินแส\nซิบ\nซิป\nซิฟิลิส\nซิลิคอน\nซิว\nซี่\nซีก\nซีเซียม\nซีด\nซี้ด\nซีนอน\nซีป่าย\nซีเมนต์\nซีเรียม\nซีลีเนียม\nซีอิ๊ว\nซึก\nซึง\nซึ่ง\nซึ้ง\nซึม\nซื่อ\nซื้อ\nซุก\nซุง\nซุน\nซุบ\nซุป\nซุ่ม\nซุ้ม\nซุ่มซ่าม\nซุย\nซู่\nซูโครส\nซูด\nซู้ด\nซูดซาด\nซูบ\nเซ\nเซ็ก\nเซแคนต์\nเซ็ง\nเซ่ง\nเซ้ง\nเซ็งแซ่\nเซต\nเซน\nเซ็น\nเซ่น\nเซนติกรัม\nเซนติเกรด\nเซนติเมตร\nเซนติลิตร\nเซปักตะกร้อ\nเซราะ\nเซรุ่ม\nเซลเซียส\nเซลล์\nเซลลูลอยด์\nเซลลูโลส\nเซ่อ\nเซอร์โคเนียม\nเซอะ\nเซา\nเซ้าซี้\nเซาะ\nเซิง\nเซิ้ง\nเซียน\nเซียบ\nเซียมซี\nเซียว\nเซี่ยว\nเซี่ยวกาง\nเซื่อง\nแซ\nแซ่\nแซ็กคาริน\nแซง\nแซงแซว\nแซด\nแซบ\nแซม\nแซยิด\nแซ่ว\nแซะ\nโซ\nโซ่\nโซก\nโซ่ง\nโซงโขดง\nโซเซ\nโซดา\nโซเดียม\nโซม\nโซรม\nโซลา\nไซ\nไซ้\nไซเกิล\nไซโคลน\nไซน์\nไซยาไนด์\nไซร้\nไซเรน\nไซโล\nฌาน\nฌาปน\nฌาปนกิจ\nฌาปนสถาน\nเฌอ\nเฌอเอม\nญวน\nญัตติ\nญาณ\nญาติ\nญานาซะฮ์\nญิบ\nญี่ปุ่น\nเญยธรรม\nไญยธรรม\nฎีกา\nฐกัด\nฐากูร\nฐาน\nฐานะ\nฐานันดร\nฐานานุกรม\nฐานานุรูป\nฐานานุศักดิ์\nฐานียะ\nฐาปน\nฐาปนา\nฐายี\nฐิต\nฐิติ\nฑาหก\nฑาหะ\nเฒ่า\nณรงค์\nเณร\nดก\nดง\nด้ง\nด้น\nดนโด่\nดนตรี\nดนัย\nดนุ\nดนู\nดบัสวิน\nดบัสวี\nดม\nดรงค์\nดรณี\nดรรชนี\nดราฟต์\nดรุณ\nดรุณี\nดล\nดวง\nด้วง\nดวด\nด่วน\nด้วน\nด้วย\nดอก\nดอง\nด่อง\nด้อง\nดองฉาย\nดองดึง\nดอด\nดอน\nด่อน\nดอม\nด้อม\nดอย\nด้อย\nดอลลาร์\nดะ\nดะโต๊ะ\nดะหมัง\nดัก\nดักดาน\nดักแด้\nดัง\nดั่ง\nดั้ง\nดัชนี\nดัด\nดัตช์\nดัน\nดั้น\nดับ\nดัมพ์\nดั้วเดี้ย\nดัสกร\nดา\nด่า\nดาก\nด่าง\nด้าง\nดาด\nดาน\nด่าน\nด้าน\nดาบ\nดาบส\nดาม\nด้าม\nด้ามจิ้ว\nดามพ์\nดาย\nด้าย\nดารกะ\nดารณี\nดารดาษ\nดาระ\nดารา\nดาล\nดาลัด\nดาว\nด่าว\nด้าว\nดาวดึงส์\nดาวบส\nดาษ\nดาษดา\nดำ\nด่ำ\nด้ำ\nดำกล\nดำเกิง\nดำแคง\nดำดง\nดำนาณ\nดำเนิน\nดำบล\nดำรง\nดำรวจ\nดำรัส\nดำริ\nดำรี\nดำรู\nดำฤษณา\nดำเลิง\nดิก\nดิ่ง\nดิฉัน\nดิฐ\nดิตถ์\nดิถี\nดิน\nดิ้น\nดิบ\nดิรัจฉาน\nดิลก\nดิ่ว\nดิ้ว\nดิ้วเดี้ยว\nดิษฐ์\nดิสโพรเซียม\nดี\nดีเซล\nดีด\nดีดีที\nดีบุก\nดีปลี\nดีเปรสชัน\nดีหมี\nดีหลี\nดึก\nดึง\nดึ่ง\nดึ่ม\nดื่น\nดื่ม\nดือ\nดื้อ\nดุ\nดุก\nดุกดิก\nดุกทะเล\nดุ้ง\nดุ้งดิ้ง\nดุจ\nดุด\nดุน\nดุ้น\nดุบ\nดุม\nดุ่ม\nดุ่ย\nดุรงค์\nดุริยะ\nดุริยางค์\nดุริยางคศาสตร์\nดุริยางคศิลป์\nดุล\nดุษฎี\nดุษณี\nดุษณีภาพ\nดุษิต\nดุสิต\nดุเหว่า\nดู\nดูกค่าง\nดูกร\nดูด\nดูรา\nดูแล\nเด\nเด่\nเดก\nเด็ก\nเดกซ์โทรส\nเดคากรัม\nเดคาเมตร\nเดคาลิตร\nเด้ง\nเด็จ\nเดช\nเดชน์\nเดชนะ\nเดชะ\nเดโช\nเดซิกรัม\nเดซิเมตร\nเดซิลิตร\nเด็ด\nเดน\nเด่น\nเดนมาร์ก\nเดรัจฉาน\nเด๋อ\nเด๋อด๋า\nเดา\nเด้า\nเดาะ\nเดิน\nเดิ่น\nเดิม\nเดียง\nเดียด\nเดียรดาษ\nเดียรถีย์\nเดียรัจฉาน\nเดียว\nเดี่ยว\nเดี๋ยว\nเดียะ\nเดื่อ\nเดือก\nเดื่อง\nเดือด\nเดือน\nเดือย\nแด\nแด่\nแดก\nแด็ก\nแดกงา\nแดกแด้\nแดง\nแดด\nแดน\nแด่น\nแด่ว\nแดะ\nแดะแด๋\nโด\nโด่\nโดกเดก\nโด่ง\nโดด\nโดน\nโดม\nโดมร\nโดย\nโดรณ\nใด\nได\nได้\nไดแซ็กคาไรด์\nไดนาโม\nไดนาไมต์\nไดโนเสาร์\nไดเรกตริกซ์\nตก\nต๊กโต\nตง\nต๋ง\nตงฉิน\nตงิด\nตงุ่น\nตด\nตติย\nตถาคต\nตน\nต้น\nตนัย\nตนุ\nตบ\nตบะ\nตปนียะ\nตม\nต้ม\nตมูก\nตยาคี\nตรง\nตรณี\nตรม\nตรรก\nตรรกะ\nตรลบ\nตรลอด\nตรลาด\nตรวจ\nตรวน\nตรอก\nตรอง\nตรอมใจ\nตรอมตรม\nตระ\nตระกล\nตระกวน\nตระกอง\nตระการ\nตระกูล\nตระคัร\nตระเตรียม\nตระนาว\nตระบก\nตระบอก\nตระบอง\nตระบัด\nตระบัน\nตระเบ็ง\nตระแบก\nตระแบง\nตระโบม\nตระพอง\nตระพัง\nตระลาการ\nตระวัน\nตระเว็ด\nตระเวน\nตระสัก\nตระหง่าน\nตระหนก\nตระหนัก\nตระหน่ำ\nตระหนี่\nตรัง\nตรังค์\nตรับ\nตรับฟัง\nตรัย\nตรัยตรึงศ์\nตรัส\nตรัสสา\nตรา\nตรากตรำ\nตราชู\nตราบ\nตราสัง\nตรำ\nตริ\nตริว\nตรี\nตรีปวาย\nตรีพิธพรรณ\nตรียัมปวาย\nตรึก\nตรึง\nตรุ\nตรุณ\nตรุณะ\nตรุษ\nตรู\nตรู่\nตฤณ\nตฤตีย\nตฤษณา\nตลก\nตลบ\nตลอด\nตลับ\nตลาด\nตลิ่ง\nตลึง\nตวง\nต่วน\nต้วมเตี้ยม\nตวัก\nตวัด\nตวาด\nตอ\nตอม่อ\nต่อ\nต้อ\nตอก\nต๊อก\nต๊อกต๋อย\nตอง\nต้อง\nตองกราย\nต้องเต\nตองแตก\nต่องแต่ง\nตองเหลือง\nตอด\nตอน\nต้อน\nตอบ\nตอเบา\nตอม\nต่อม\nต๋อม\nต่อย\nต้อย\nต้อยตริ่ง\nต้อยติ่ง\nต้อยตีวิด\nตอแย\nตอร์ปิโด\nต่อไส้\nตอแหล\nตะ\nตะกรน\nตะกร้อ\nตะกรัน\nตะกรับ\nตะกร้า\nตะกราม\nตะกรุด\nตะกรุม\nตะกรุมตะกราม\nตะกละ\nตะกลาม\nตะกวด\nตะกอ\nตะกอน\nตะกัง\nตะกั่ว\nตะกาง\nตะกาด\nตะกาย\nตะกาว\nตะกุกตะกัก\nตะกุย\nตะกู\nตะกูด\nตะเกียกตะกาย\nตะเกียง\nตะเกียบ\nตะแก\nตะแก่\nตะแกรง\nตะโก\nตะโก้\nตะโกก\nตะโกน\nตะโกรง\nตะโกรม\nตะไกร\nตะขบ\nตะขอ\nตะขาบ\nตะขิดตะขวง\nตะเข้\nตะเข็บ\nตะโขง\nตะคร้อ\nตะครอง\nตะครั่นตะครอ\nตะคร้ำ\nตะคริว\nตะคิว\nตะครุบ\nตะคอก\nตะคัน\nตะค้า\nตะคาก\nตะค้าน\nตะคุ่ม\nตะเครียว\nตะเคียว\nตะเคียน\nตะแคง\nตะไคร่\nตะไคร้\nตะเฆ่\nตะนอย\nตะนาว\nตะบม\nตะบอง\nตะบอย\nตะบัน\nตะบิ้ง\nตะบิด\nตะบิดตะบอย\nตะบี้ตะบัน\nตะบึง\nตะบูน\nตะเบ็ง\nตะเบ็งมาน\nตะเบ๊ะ\nตะแบก\nตะแบง\nตะโบม\nตะไบ\nตะปบ\nตะปลิง\nตะปิ้ง\nตะปุ่มตะป่ำ\nตะปู\nตะพง\nตะพด\nตะพอง\nตะพัก\nตะพัง\nตะพัด\nตะพั้น\nตะพาก\nตะพาน\nตะพาบ\nตะพาย\nตะพึด\nตะพึดตะพือ\nตะพุ่น\nตะเพรา\nตะเพิง\nตะเพิด\nตะเพียน\nตะโพก\nตะโพง\nตะโพน\nตะเภา\nตะใภ้\nตะม่อ\nตะมอย\nตะรังกะนู\nตะรังตังกวาง\nตะรังตังช้าง\nตะราง\nตะลอง\nตะลอน\nตะล่อม\nตะละ\nตะลาน\nตะลิงปลิง\nตะลิบ\nตะลีตะลาน\nตะลึง\nตะลึงพรึงเพริด\nตะลุง\nตะลุ่ม\nตะลุ่มนก\nตะลุมบอน\nตะลุ่มโปง\nตะลุมพอ\nตะลุมพุก\nตะลุย\nตะเลง\nตะแลงแกง\nตะไล\nตะวัน\nตะเวน\nตะหลิว\nตะหลุก\nตะหลุง\nตะแหง่ว\nตะแหมะแขะ\nตะโหงก\nตัก\nตักกะ\nตักเตือน\nตั๊กแตน\nตักษัย\nตัง\nตั่ง\nตั้ง\nตังเก\nตังฉ่าย\nตังเม\nตังวาย\nตังโอ๋\nตัจฉก\nตัจฉนี\nตัณฑุล\nตัณหา\nตัด\nตัน\nตันตระ\nตันติ\nตันหยง\nตับ\nตับปิ้ง\nตัว\nตั๋ว\nตัวจี๊ด\nตัวตืด\nตั้วโผ\nตั้วเหี่ย\nตา\nตาก\nตากวาง\nต่าง\nตาด\nตาน\nต่าน\nต้าน\nตานนกกด\nตานี\nตาบ\nตาม\nตามะแน\nตามิน\nตาย\nตาราไต\nตาล\nตาลุ\nต๋าว\nตาเสือ\nตาหนู\nตาฬ\nตำ\nต่ำ\nตำนาน\nตำบล\nตำแบ\nตำแย\nตำรวจ\nตำรับ\nตำรา\nตำรุ\nตำลึง\nตำเสา\nตำหนัก\nตำหนิ\nตำแหน่ง\nติ\nติก\nติ๊ก\nติกะ\nติกาหรัง\nติง\nติ่ง\nติ๋ง\nติ่งตั่ง\nติ๋งต่าง\nติงส\nติงสติ\nติณ\nติด\nติตติกะ\nติตติร\nติตถ\nติตถะ\nติถี\nติมิงคละ\nติรัจฉาน\nติลก\nติละ\nติ้ว\nตี\nตี่\nตีน\nตีบ\nตีรถะ\nตีระ\nตึ\nตึก\nตึ้ก\nตึ้กตั้ก\nตึง\nตึดตื๋อ\nตึ๊ดตื๋อ\nตืด\nตื่น\nตื้น\nตื้อ\nตื๊อ\nตื๋อ\nตุ\nตุ๊\nตุ๊กแก\nตุ๊กตา\nตุ๊กต่ำ\nตุกติก\nตุ๊กติ๊ก\nตุ๊กตุ่น\nตุ๊กตุ๋ย\nตุง\nตุ้งก่า\nตุ้งติ้ง\nตุ๊ดตู่\nตุน\nตุ่น\nตุ๋น\nตุนาหงัน\nตุบ\nตุ้บ\nตุ๊บป่อง\nตุปัดตุป่อง\nตุปัดตุเป๋\nตุ่ม\nตุ้ม\nตุ๋ม\nตุ้มกว้าว\nตุมกา\nตุ้มแซะ\nตุมตัง\nตุ้มเต๋น\nตุ้มปี่\nตุมพะ\nตุ่ย\nตุ้ย\nตุ๊ย\nตุ๋ยตุ่ย\nตุรคะ\nตุรงค์\nตุล\nตุลา\nตุหรัดตุเหร่\nตู\nตู่\nตู้\nตูก\nตูด\nตูบ\nตูม\nเต๊ก\nเต็ง\nเต่ง\nเตช\nเตโช\nเต้น\nเต็นท์\nเต็ม\nเตย\nเตร่\nเตร็ด\nเตรตา\nเตรียม\nเตรียมตรม\nเตละ\nเตลิด\nเตว็ด\nเต่อ\nเตอะ\nเตะ\nเตา\nเต่า\nเต้า\nเต๋า\nเต่าเกียด\nเต้าเจี้ยว\nเต้าทึง\nเต้าหู้\nเต้าฮวย\nเต๊าะ\nเตาะแตะ\nเติ่ง\nเติบ\nเติม\nเตี้ย\nเตียง\nเตียน\nเตียบ\nเตี๋ยม\nเตียรถ์\nเตียว\nเตี่ยว\nเตือน\nแต่\nแต้\nแตก\nแตง\nแต่ง\nแตงเม\nแต้จิ๋ว\nแตด\nแต๊ดแต๋\nแตน\nแต้ม\nแตร\nแตระ\nแต้ว\nแต้วแร้ว\nแต้วแล้ว\nแต่ว่า\nแต้แว้ด\nแตะ\nโต\nโต้\nโตก\nโต่ง\nโต้ง\nโตงเตง\nโตฎก\nโต๊ด\nโตน\nโตนด\nโต้โผ\nโตมร\nโตย\nโตรก\nโต๊ะ\nใต้\nไต\nไต่\nไต้\nไต๋\nไตร\nไตรกิศยา\nไตรดายุค\nไตร่ตรอง\nไตรย\nไต้หวัน\nถก\nถกล\nถงาด\nถด\nถนน\nถนอม\nถนัด\nถนัน\nถนำ\nถนิม\nถม\nถ่ม\nถมอ\nถมึงทึง\nถลก\nถลกบาตร\nถลน\nถล่ม\nถลอก\nถลัน\nถลา\nถลาก\nถลาย\nถลำ\nถลึงตา\nถลุง\nถ่วง\nถ้วน\nถ้วย\nถวัล\nถวัลย์\nถวาย\nถวิน\nถวิล\nถ่อ\nถ้อ\nถอก\nถอง\nถ่อง\nถ้อง\nถอด\nถอน\nถอบ\nถอบแถบ\nถ่อม\nถอย\nถ่อย\nถ้อย\nถะ\nถะถั่น\nถะมัดถะแมง\nถัก\nถัง\nถั่ง\nถัด\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นยา\nบิลเลียด\nบิวเรตต์\nบิสมัท\nบี้\nบีฑา\nบีตา\nบีบ\nบีเยศ\nบึก\nบึกบึน\nบึง\nบึ่ง\nบึ้ง\nบุ\nบุก\nบุคคล\nบุคลากร\nบุคลาธิษฐาน\nบุคลิก\nบุง\nบุ่ง\nบุ้ง\nบุ้งกี๋\nบุญ\nบุญญาธิการ\nบุญญานุภาพ\nบุญญาภินิหาร\nบุญญาภิสังขาร\nบุณฑริก\nบุณมี\nบุณย์\nบุตร\nบุตรี\nบุถุชน\nบุทคล\nบุนนาค\nบุบ\nบุบบิบ\nบุปผชาติ\nบุพกรรม\nบุพการี\nบุพกิจ\nบุพชาติ\nบุพทักษิณ\nบุพนิมิต\nบุพบท\nบุพพาจารย์\nบุพเพสันนิวาส\nบุพโพ\nบุ๋ม\nบุ่มบ่าม\nบุ้ย\nบุรณะ\nบุรพทิศ\nบุรพบท\nบุรพาจารย์\nบูรพาจารย์\nบุระ\nบุราณ\nบุรินทร์\nบุริมทิศ\nบุริมพรรษา\nบุริมสิทธิ\nบุรี\nบุรุษ\nบุโรทั่ง\nบุษกร\nบุษบก\nบุษบง\nบุษบัน\nบุษบา\nบุษบามินตรา\nบุษปราค\nบุษปะ\nบุษย์\nบุษย์น้ำทอง\nบุษยมาส\nบุษยะ\nบุษราคัม\nบุหงัน\nบุหงา\nบุหรง\nบุหรี่\nบุหลัน\nบู่\nบู้\nบูชนียสถาน\nบูชา\nบูชิต\nบูด\nบูดู\nบูร\nบูรณ์\nบูรณภาพ\nบูรณมี\nบูรณะ\nบูรณาการ\nบูรพ์\nบูรพะ\nบูรพา\nเบ้\nเบ่ง\nเบ๊จี๋\nเบญกานี\nเบญจกัลยาณี\nเบญจกามคุณ\nเบญจขันธ์\nเบญจดุริยางค์\nเบญจธรรม\nเบญจบรรพต\nเบญจพรรณ\nเบญจเพส\nเบญจมาศ\nเบญจรงค์\nเบญจศก\nเบญจศีล\nเบญจะ\nเบญจา\nเบญจางค์\nเบญจางคประดิษฐ์\nเบญญา\nเบญพาด\nเบ็ด\nเบ็ดเตล็ด\nเบ็ดเสร็จ\nเบน\nเบนซิน\nเบรก\nเบริลเลียม\nเบส\nเบ้อ\nเบอร์\nเบอร์คีเลียม\nเบ้อเร่อ\nเบ้อเร่อเท่อ\nเบ้อเริ่ม\nเบ้อเริ่มเทิ่ม\nเบอะ\nเบอะบะ\nเบะ\nเบา\nเบ้า\nเบาราณ\nเบาะ\nเบิก\nเบิ่ง\nเบี้ย\nเบี่ยง\nเบียด\nเบียน\nเบียร์\nเบี้ยว\nเบือ\nเบื่อ\nเบื้อ\nเบื้อง\nเบือน\nแบ\nแบ้\nแบก\nแบคทีเรีย\nแบ่ง\nแบงก์\nแบดมินตัน\nแบตเตอรี่\nแบน\nแบนโจ\nแบบ\nแบ็บ\nแบเรียม\nแบหลา\nแบะ\nโบ\nโบ้\nโบ๋\nโบก\nโบกขรณี\nโบกขรพรรษ\nโบชุก\nโบต\nโบนัส\nโบ๊เบ๊\nโบย\nโบรมีน\nโบรอน\nโบราณ\nโบสถ์\nใบ\nใบ้\nไบ่\nปก\nปกติ\nปกรณ์\nปกรณัม\nปกิณกะ\nปกีรณัม\nปโกฏิ\nปง\nป่ง\nปงช้าง\nปฎล\nปฏัก\nปฏิกรณ์\nปฏิกรรม\nปฏิการะ\nปฏิกิริยา\nปฏิกูล\nปฏิคม\nปฏิคหิต\nปฏิคาหก\nปฏิฆะ\nปฏิชีวนะ\nปฏิญญา\nปฏิญาณ\nปฏิทิน\nปฏิบถ\nปฏิบัติ\nปฏิปทา\nปฏิปักษ์\nปฏิปัน\nปฏิปุจฉาพยากรณ์\nปฏิปุจฉาวาที\nปฏิพัทธ์\nปฏิพากย์\nปฏิภาค\nปฏิภาณ\nปฏิมา\nปฏิมากร\nปฏิยุทธ์\nปฏิรพ\nปฏิรูป\nปฏิโลม\nปฏิวัติ\nปฏิวาต\nปฏิวาท\nปฏิเวธ\nปฏิสนธิ\nปฏิสวะ\nปฏิสังขรณ์\nปฏิสันถาร\nปฏิสัมภิทา\nปฏิเสธ\nปฐพี\nปฐม\nปฐวี\nปณต\nปณาม\nปณิธาน\nปณิธิ\nปณีต\nปด\nปดิวรัดา\nปติ\nปถพี\nปถมัง\nปถวี\nปทัฏฐาน\nปทัสถาน\nปทานุกรม\nปทีป\nปทุม\nปน\nป่น\nปนัดดา\nปปัญจะ\nปม\nปรนัย\nปรปักษ์\nปรโลก\nปรวาที\nปรก\nปรกติ\nปรง\nปรตยักษ์\nปรน\nปรนนิบัติ\nปรนิมมิตวสวัตดี\nปรบ\nปรปักษ์\nปรมัตถ์\nปรมาจารย์\nปรมาณู\nปรมาภิไธย\nปรมาภิเษก\nปรมินทร์\nบรเมนทร์\nปรเมศวร์\nปรเมษฐ์\nปรวด\nปรวนแปร\nปรศุ\nปรสิต\nปร๋อ\nปรองดอง\nปรอด\nปรอท\nปรอย\nประ\nประกบ\nประกฤต\nประกฤติ\nประกล\nประกวด\nประกวดประขัน\nประกอบ\nประกัน\nประกับ\nประกาย\nประกายพรึก\nประการ\nประกาศ\nประกาศนียบัตร\nประกาศิต\nประกำ\nประกิด\nประกิต\nประคด\nประคนธรรพ\nประคนธรรพ์\nประคบ\nประคบประหงม\nประคอง\nประคับประคอง\nประคัลภ์\nประคำ\nประคิ่น\nประคุณ\nประเคน\nประเคราะห์\nประโคน\nประโคนธรรพ\nประโคนธรรพ์\nประโคม\nประจง\nประจญ\nประจบ\nประจบประแจง\nประจวบ\nประจ๋อประแจ๋\nประจักษ์\nประจักษนิยม\nประจัญ\nประจัน\nประจาก\nประจาค\nประจาน\nประจำ\nประจิม\nประจิ้มประเจ๋อ\nประจุ\nประจุคมน์\nประจุบัน\nประเจก\nประเจิด\nประเจิดประเจ้อ\nประเจียด\nประแจ\nประชด\nประชน\nประชวม\nประชวร\nประชัน\nประชา\nประชาธิปไตย\nประชิด\nประชี\nประชุม\nประเชิญ\nประณต\nประณม\nประณาม\nประณิธาน\nประณิธิ\nประณีต\nประณุท\nประดง\nประดน\nประดวน\nประดอน\nประดอย\nประดัก\nประดักประเดิด\nประดัง\nประดับ\nประดา\nประดาก\nประดาป\nประดาษ\nประดิชญา\nประดิดประดอย\nประดิทิน\nประดิษฐ์\nประดิษฐกรรม\nประดิษฐาน\nประดุง\nประดุจ\nประดู่\nประเด\nประเด็น\nประเดิม\nประเดียง\nประเดี๋ยว\nประเดี๋ยวประด๋าว\nประแดง\nประแดะ\nประโดง\nประโดย\nประตง\nประตัก\nประตาป\nประติชญา\nประติญาณ\nประติทิน\nประติมากร\nประติมากรรม\nประติรพ\nประตู\nประถม\nประถมจินดา\nประทม\nประท้วง\nประทวน\nประทักษ์\nประทักษิณ\nประทัง\nประทัด\nประทับ\nประทาน\nประทาย\nประทาศี\nประทิน\nประทิ่น\nประทีป\nประทุฐ\nประทุน\nประทุษ\nประทุษฐ์\nประเทศ\nประเทา\nประเทียด\nประเทียบ\nประเทือง\nประธาน\nประธานาธิบดี\nประนม\nประนอ\nประนอม\nประนัง\nประนัปดา\nประนีประนอม\nประปราน\nประปราย\nประปา\nประเปรี้ยง\nประเปรียว\nประพจน์\nประพนธ์\nประพรม\nประพฤติ\nประพฤทธิ์\nประพัด\nประพัทธ์\nประพันธ์\nประพาต\nประพาส\nประพาสมหรณพ\nประพาฬ\nประพิณ\nประพิมพ์ประพาย\nประพุทธ์\nประเพณี\nประโพธ\nประไพ\nประไพร\nประภพ\nประภัสสร\nประภา\nประภาคาร\nประภาพ\nประภาษ\nประภาส\nประเภท\nประมง\nประมวล\nประมาณ\nประมาท\nประมุข\nประมุท\nประมูล\nประเมิน\nประโมง\nประโมทย์\nประยงค์\nประยุกต์\nประยุทธ์\nประยุร\nประยูร\nประโยค\nประโยชน์\nประโรหิต\nประลมพ์\nประลอง\nประลัย\nประลาต\nประลาย\nประลุ\nประเล่ห์\nประเล้าประโลม\nประโลม\nประวรรต\nประวรรตน์\nประวัติ\nประวาล\nประวาลปัทม์\nประวาส\nประวิง\nประวิช\nประวิตร\nประวิน\nประวีณ\nประเวณี\nประเวศ\nประเวศน์\nประศม\nประศาสน์\nประศุ\nประสก\nประสงค์\nประสบ\nประสพ\nประสม\nประสะ\nประสัก\nประสันนาการ\nประสัยห์\nประสา\nประสาท\nประสาธน์\nประสาน\nประสาร\nประสิทธิ์\nประสิทธิผล\nประสิทธิภาพ\nประสีประสา\nประสูต\nประสูติ\nประเสบัน\nประเสบันอากง\nประเสริฐ\nประหนึ่ง\nประหม่า\nประหยัด\nประหลาด\nประหล่ำ\nประหวัด\nประหวั่น\nประหัตประหาร\nประหาณ\nประหาร\nประเหล\nประเหส\nประไหมสุหรี\nประอบ\nประอร\nปรัก\nปรักปรำ\nปรักมะ\nปรัง\nปรัชญา\nปรัตถจริยา\nปรัตยุบัน\nปรัน\nปรับ\nปรัมปรา\nปรัศจิม\nปรัศนา\nปรัศนี\nปรัศว์\nปรัสสบท\nปร่า\nปรากฏ\nปรากรม\nปรากฤต\nปราการ\nปราง\nปรางค์\nปราจีน\nปราชญ์\nปราชญา\nปราชัย\nปราณ\nปราณี\nปราด\nปราน\nปรานี\nปราบ\nปราบดาภิเษก\nปราปต์\nปราม\nปรามาส\nปราโมช\nปราโมทย์\nปราย\nปรารถนา\nปรารภ\nปรารมภ์\nปราศ\nปราศจาก\nปราศรัย\nปราษณี\nปราษาณ\nปราสัย\nปราสาท\nปรำ\nปริ\nปริก\nปริกขาร\nปริกรรม\nปริกัป\nปริคณห์\nปริจาค\nปริจาริกา\nปริเฉท\nปริชน\nปริซึม\nปริญญา\nปริณาม\nปริณายก\nปริต\nปริตตะ\nปริตโตทก\nปริตร\nปริทรรศน์\nปริทัยหัคคี\nปริทัศน์\nปริเทพ\nปริเทวะ\nปรินิพพาน\nปริบ\nปริบท\nปริปันถ์\nปริพนธ์\nปริพัตร\nปริพันธ์\nปริพาชก\nปริภัณฑ์\nปริภาษ\nปริภูมิ\nปริโภค\nปริ่ม\nปริมณฑล\nปริมาณ\nปริมาตร\nปริยัติ\nปริยานุช\nปริยาย\nปริเยศ\nปริโยสาน\nปริวรรต\nปริวัตร\nปริวาร\nปริวาส\nปริวิตก\nปริเวณ\nปริศนา\nปริษัท\nปริสัญญู\nปริสุทธิ\nปริหาน\nปริหาร\nปรี่\nปรีชญา\nปรีชา\nปรี๊ด\nปรีดา\nปรีดิ\nปรีดิ์\nปรีดี\nปรีติ\nปรียะ\nปรียา\nปรึก\nปรึกษา\nปรึง\nปรือ\nปรื๋อ\nปรุ\nปรุง\nปรู\nปรู๋\nปรูด\nปรู๊ด\nปรู๊ดปร๊าด\nปรู๊ฟ\nปฤงคพ\nปฤจฉา\nปฤษฎางค์\nปฤษฐ\nปลก\nปลกเปลี้ย\nปลง\nปล่ง\nปลด\nปล้น\nปลวก\nปลอก\nปล่อง\nปล้อง\nปลอด\nปล้อน\nปลอบ\nปลอม\nปล่อย\nปละ\nปลัก\nปลั๊ก\nปลัง\nปลั่ง\nปลัด\nปลัดขิก\nปลา\nปลาต\nปลาบ\nปลาย\nปลาสเตอร์\nปลาสนาการ\nปล้ำ\nปลิง\nปลิด\nปลิ้น\nปลิโพธ\nปลิม\nปลิ่ม\nปลิว\nปลี\nปลีก\nปลื้ม\nปลุก\nปลูก\nปวกเปียก\nปวง\nป่วง\nปวด\nป่วน\nป้วน\nป้วนเปี้ยน\nป่วย\nปวัตน์\nปวารณา\nปวาล\nปวาส\nปวาฬ\nปวิช\nปวิตร\nปวิธ\nปวิเวก\nปวีณ\nปวุติ\nปเวณี\nปเวส\nปเวสน์\nปศุ\nปสันนะ\nปสันนาการ\nปสาท\nปสาน\nปสาสน์\nปสุ\nปสุต\nปสูติ\nปหังสนะ\nปหาน\nปหาร\nปหาส\nปอ\nป้อ\nป๋อ\nปอก\nปอง\nป่อง\nป้อง\nปอด\nปอน\nป้อน\nปอนด์\nปอเนาะ\nปอบ\nป้อแป้\nปอม\nป้อม\nป๋อม\nปอย\nป้อย\nป้อยอ\nปะ\nปะกน\nปะกัง\nปะการัง\nปะกำ\nปะขาว\nปะงาบ\nปะตาปา\nปะตาระกาหลา\nปะติดปะต่อ\nปะติยาน\nปะทะ\nปะทะปะทัง\nปะทุ\nปะทุน\nปะปน\nปะมง\nปะราลี\nปะรำ\nปะไร\nปะลอม\nปะเลง\nปะแล่ม\nปะโลง\nปะวะหล่ำ\nปะหงับ\nปะหนัน\nปะหัง\nปะเหลาะ\nปัก\nปักข์\nปักเป้า\nปักษ์\nปักษา\nปักษิน\nปักษี\nปัง\nปั๋ง\nปังสุ์\nปังสุกุล\nปัจจัตตะ\nปัจจันต์\nปัจจันตคาม\nปัจจันตชนบท\nปัจจันตประเทศ\nปัจจัย\nปัจจามิตร\nปัจจุคมน์\nปัจจุทธรณ์\nปัจจุบัน\nปัจจุสมัย\nปัจเจก\nปัจโจปการกิจ\nปัจฉา\nปัจฉิม\nปัจถรณ์\nปัจนึก\nปัจยาการ\nปัจเวกขณ์\nปัชชุน\nปัญจนที\nปัญจวัคคีย์\nปัญจก\nปัญจกะ\nปัญจมี\nปัญจวีสติ\nปัญญัติ\nปัญญา\nปัญหา\nปัฏ\nปัฏนะ\nปัฐยาวัต\nปัณฑรหัตถี\nปัณณะ\nปัณณาส\nปัณณาสก์\nปัณรสี\nปัณหิ\nปัด\nปัตคาด\nปัตตะ\nปัตตานึก\nปัตตานุโมทนา\nปัตตาเวีย\nปัตติ\nปัตติก\nปัตถร\nปัตถะ\nปัตนิ\nปัตนี\nปัตหล่า\nปัถพี\nปัถวี\nปัทม์\nปัทมะ\nปัทมาสน์\nปัน\nปั่น\nปั้น\nปั้นจั่น\nปันจุเหร็จ\nปั้นลม\nปั้นหยา\nปั้นเหน่ง\nปับ\nปั๊บ\nปัปผาสะ\nปัพพาชนียกรรม\nปัพภาระ\nปั๊ม\nปัยกา\nปัยยิกา\nปัวเปีย\nปัศจิม\nปัศตัน\nปัสสาวะ\nปัสสาสะ\nปา\nป่า\nป้า\nปาก\nปาง\nป้าง\nปาจรีย์\nปาจิตตีย์\nปาจีน\nปาฏลิ\nปาฏิบท\nปาฏิบุคลิก\nปาฏิโภค\nปาฏิหาริย์\nปาฐก\nปาฐกถา\nปาฐะ\nปาณกชาติ\nปาณะ\nปาณาติบาต\nปาณิ\nปาณี\nปาด\nปาติโมกข์\nปาตี\nปาเต๊ะ\nปาท่องโก๋\nปาทังกา\nปาทาน\nปาทุกา\nปาน\nป่าน\nป้าน\nปานะ\nปานียะ\nป้าบ\nป๊าบ\nปาพจน์\nปาม\nปาโมกข์\nป่าย\nป้าย\nปายาส\nปาร์เกต์\nปารมี\nปารเมศ\nปาราชิก\nปาริฉัตร\nปาริชาต\nปารุสกวัน\nปาล\nปาล์ม\nปาลิไลยก์\nปาลี\nปาว\nป่าว\nป๊าว\nปาวาร\nปาษาณ\nปาส\nปาสาณ\nปาสาทิกะ\nปาหนัน\nปาหี่\nปำ\nป้ำ\nป้ำเป๋อ\nปิกนิก\nปิ้ง\nปิงคละ\nปิงปอง\nปิฎก\nปิฏฐะ\nปิฐิ\nปิณฑะ\nปิด\nปิตตะ\nปิตา\nปิตามหัยกา\nปิตามหัยยิกา\nปิตุ\nปิตุจฉา\nปิตุภูมิ\nปิตุลา\nปิโตรเลียม\nปิ่น\nปิ่นแก้ว\nปิ่นโต\nปิปผลี\nปิ่ม\nปิ้ม\nปิยะ\nปิยังคุ\nปิโยรส\nปิลันธน์\nปิ๋ว\nปิศาจ\nปิหกะ\nปี\nปี่\nปี้\nปี๋\nปีก\nปีฐะ\nปี๊ด\nปีติ\nปีน\nปีบ\nปี๊บ\nปีศาจ\nปีฬกะ\nปึก\nปึง\nปึ่ง\nปึ๋ง\nปึ้ด\nปึมปื้อ\nปืน\nปื้น\nปือ\nปื้อ\nปื๋อ\nปุ\nปุ๊\nปุก\nปุกปุย\nปุคละ\nปุ้งกี๋\nปุงควะ\nปุงลิงค์\nปุงลึงค์\nปุจฉา\nปุฏะ\nปุณฑริก\nปุด\nปุตตะ\nปุถุชน\nปุนนาค\nปุนภพ\nปุนัพสุ\nปุบ\nปุ๊บ\nปุปผะ\nปุปะ\nปุพพะ\nปุ่ม\nปุ่มป่ำ\nปุ้ม\nปุ๋ม\nปุย\nปุ้ย\nปุ๋ย\nปุรณะ\nปุระ\nปุราณ\nปุราณะ\nปุริมพรรษา\nปุเรจาริก\nปุโรหิต\nปุลลิงค์\nปุลลึงค์\nปุลินท์\nปุโลปุเล\nปุษยะ\nปุสสะ\nปู\nปู่\nปูชกะ\nปูชนียบุคคล\nปูชนียวัตถุ\nปูชนียะ\nปูชา\nปูชิต\nปูด\nปูน\nปูม\nปู้ยี่ปู้ยำ\nปูระ\nปูลู\nเป้\nเป๋\nเปก\nเป๊ก\nเป่ง\nเป้ง\nเป๋ง\nเป็ด\nเปตพลี\nเปตอง\nเป็น\nเปยยาล\nเปร็ง\nเปรต\nเปรม\nเปรย\nเปรอ\nเปรอะ\nเปราะ\nเปรียง\nเปรี้ยง\nเปรี้ยงปร้าง\nเปรียญ\nเปรียบ\nเปรี่ยม\nเปรียว\nเปรี้ยว\nเปรียะ\nเปรี๊ยะ\nเปรื่อง\nเปรื้อย\nเปล\nเปล่ง\nเปลว\nเปลา\nเปล่า\nเปล้า\nเปลาะ\nเปลี้ย\nเปลี่ยน\nเปลี่ยม\nเปลี่ยว\nเปลือก\nเปลือง\nเปลื้อง\nเปลือย\nเปศะ\nเปศัส\nเปสการ\nเปสละ\nเปสุญวาท\nเป๋อ\nเป้อเย้อ\nเปอร์\nเปอร์เซ็นต์\nเปะ\nเปา\nเป่า\nเป้า\nเป๊า\nเป๋า\nเป๋าฮื้อ\nเปาะ\nเป๊าะ\nเปาะเปี๊ยะ\nเปาะแปะ\nเปิก\nเปิง\nเปิงมาง\nเปิด\nเปิ่น\nเปิบ\nเปิ๊บ\nเปีย\nเปียก\nเปี๊ยก\nเปี๊ยบ\nเปี่ยม\nเปี้ยว\nเปี๊ยว\nเปียะ\nเปี๊ยะ\nเปือก\nเปื้อน\nเปื่อย\nแป\nแป้ง\nแป๋ง\nแปด\nแป๊ด\nแปทู\nแป้น\nแป๊น\nแปบ\nแป๊บ\nแปม\nแปร\nแปร๋\nแปรก\nแปรง\nแปร่ง\nแปร๊ด\nแปร้น\nแปร๋น\nแปรปรวน\nแประ\nแปล\nแปล้\nแปลก\nแปลง\nแปลน\nแปลบ\nแปล๊บ\nแป้ว\nแป๊ว\nแปะ\nแป๊ะ\nแป๊ะซะ\nโป\nโป่\nโป้\nโป๊\nโปก\nโป๊ก\nโป๊กเกอร์\nโปกขรณี\nโปกขรพรรษ\nโปเก\nโปง\nโป่ง\nโป้ง\nโป่งข่าม\nโปงลาง\nโป่งวิด\nโปฐบท\nโปฐปทมาส\nโปดก\nโปตถกะ\nโปน\nโป๊ป\nโป๊ยเซียน\nโปรแกรม\nโปรง\nโปร่ง\nโปรด\nโปรตอน\nโปรตีน\nโปรเตสแตนต์\nโปรแทรกเตอร์\nโปรย\nโปล่ง\nโปลิโอ\nโปโล\nโปสก\nโปสต์การ์ด\nโปะ\nโป๊ะ\nโป๊ะจ้าย\nไป\nไป่\nไป๋\nไปยาล\nไปรษณีย์\nไปรษณียบัตร\nไปรษณียภัณฑ์\nไปรษณียากร\nไปล่\nไปศาจ\nผก\nผกา\nผกาย\nผคม\nผง\nผงก\nผงม\nผงะ\nผงาด\nผง่าน\nผจง\nผจญ\nผจัญ\nผจาน\nผชุม\nผณิน\nผณินทร\nผณิศวร\nผด\nผดุง\nผเดิน\nผทม\nผนวก\nผนวช\nผนัง\nผนิด\nผนึก\nผม\nผยอง\nผรณาปีติ\nผรสุ\nผริต\nผรุสวาท\nผล\nผลคุน\nผลคุนี\nผล็อย\nผละ\nผลัก\nผลัด\nผลับ\nผลัวะ\nผลา\nผลาญ\nผลานิสงส์\nผลาผล\nผลาหาร\nผลิ\nผลิกะ\nผลิต\nผลิน\nผลี\nผลีผลาม\nผลึก\nผลึ่ง\nผลือ\nผลุ\nผลุง\nผลุด\nผลุน\nผลุนผลัน\nผลุบ\nผลุบผลับ\nผลุย\nผลู\nผวน\nผวย\nผวา\nผสม\nผสาน\nผอง\nผ่อง\nผ่อน\nผอบ\nผอม\nผ็อย\nผอูน\nผะ\nผะดา\nผะสา\nผัก\nผัคคุณ\nผัคคุณี\nผัง\nผัด\nผัน\nผับ\nผัว\nผัวะ\nผัสสะ\nผัสสาหาร\nผา\nผ่า\nผ้า\nผาก\nผาง\nผ่าง\nผาณิต\nผาด\nผาติ\nผ่าน\nผาม\nผาย\nผ่ายผอม\nผาล\nผาลคุน\nผาลา\nผ่าว\nผาสุก\nผ้าฮาด\nผำ\nผ้ำ\nผิ\nผิง\nผิด\nผิตะ\nผิน\nผิว\nผี\nผี้ว์\nผึง\nผึ่ง\nผึ้ง\nผึ้งรวง\nผืน\nผื่น\nผุ\nผุด\nผุยผง\nผุสราคา\nผู้\nผูก\nเผ\nเผง\nเผชิญ\nเผ็ด\nเผด็จ\nเผดิม\nเผดียง\nเผ่น\nเผนิก\nเผย\nเผยอ\nเผยิบ\nเผยิบผยาบ\nเผล\nเผล่\nเผล็ด\nเผลอ\nเผลอไผล\nเผละ\nเผลาะ\nเผลาะแผละ\nเผลียง\nเผอเรอ\nเผอิญ\nเผอิล\nเผะ\nเผา\nเผ่า\nเผ้า\nเผาะ\nเผิ้ง\nเผิน\nเผียน\nเผือ\nเผื่อ\nเผือก\nเผือด\nเผือน\nเผื่อน\nแผ่\nแผก\nแผง\nแผด\nแผน\nแผ่น\nแผนก\nแผล\nแผลง\nแผล็บ\nแผล็ว\nแผละ\nแผ่ว\nแผ้ว\nโผ\nโผง\nโผฏฐัพพะ\nโผน\nโผเผ\nโผย\nโผล่\nโผลกเผลก\nโผละ\nโผอน\nโผะ\nไผ\nไผ่\nไผท\nฝน\nฝรั่ง\nฝรั่งเศส\nฝ่อ\nฝอย\nฝัก\nฝัง\nฝั่ง\nฝัด\nฝัน\nฝา\nฝ่า\nฝ้า\nฝาก\nฝาง\nฝาด\nฝาน\nฝาย\nฝ่าย\nฝ้าย\nฝิ่น\nฝี\nฝี่\nฝีก\nฝึก\nฝืด\nฝืน\nฝุ่น\nฝูง\nเฝ้า\nเฝือ\nเฝือก\nเฝือง\nเฝื่อน\nแฝก\nแฝง\nแฝด\nใฝ่\nไฝ\nพก\nพกุล\nพง\nพงศ์\nพงศกร\nพงศธร\nพงศา\nพงศาวดาร\nพจน์\nพจนา\nพจนานุกรม\nพจนารถ\nพจนีย์\nพจมาน\nพจี\nพชระ\nพญา\nพญาลอ\nพณิช\nพณิชย์\nพดด้วง\nพธู\nพนันดร\nพนาดร\nพนาดอน\nพนาราม\nพนาลัย\nพนาลี\nพนาวาส\nพนาเวศ\nพนาศรม\nพนาสณฑ์\nพนาสัณฑ์\nพเนจร\nพ่น\nพ้น\nพนม\nพนอง\nพนอม\nพนัก\nพนักงาน\nพนัง\nพนัน\nพนัส\nพนา\nพนาย\nพนิดา\nพนิต\nพบ\nพม่า\nพยนต์\nพยศ\nพยัก\nพยักพเยิด\nพยัคฆ์\nพยัคฆา\nพยัคฆิน\nพยัคฆี\nพยัชน์\nพยัญชนะ\nพยัต\nพยับ\nพยากรณ์\nพยาฆร์\nพยางค์\nพยาธิ\nพยาน\nพยาบาท\nพยาบาล\nพยาม\nพยามะ\nพยายาม\nพยุ\nพยุง\nพยุหยาตรา\nพยุหโยธา\nพยุหเสนา\nพยุหะ\nพยู่ห์\nพเยีย\nพร\nพรต\nพรม\nพรรค\nพรรค์\nพรรคานต์\nพรรณ\nพรรณนา\nพรรดึก\nพรรลาย\nพรรษ\nพรรษา\nพรรเอิญ\nพรวด\nพรวน\nพรหม\nพรหมจรรย์\nพรหมจาริณี\nพรหมจารี\nพรหมา\nพรหมาสตร์\nพรหมินทร์\nพรอก\nพร่อง\nพร้อง\nพรอด\nพร้อม\nพร้อมพรัก\nพร่อย\nพร้อย\nพระ\nพระนอม\nพระนาด\nพระฮาม\nพรักพร้อม\nพรั่ง\nพรัด\nพรั่น\nพรับ\nพร่า\nพร้า\nพราก\nพราง\nพร่าง\nพราด\nพราน\nพราย\nพราว\nพราหมณ์\nพราหมณะ\nพราหมณี\nพราหมี\nพรำ\nพร่ำ\nพริก\nพริ้ง\nพริบ\nพริ้ม\nพรึง\nพรึน\nพรึบ\nพรึ่บ\nพรืด\nพรุ\nพรุ่ง\nพรุน\nพรู\nพรูด\nพฤกษ์\nพฤกษชาติ\nพฤกษเทวดา\nพฤกษราช\nพฤกษศาสตร์\nพฤกษา\nพฤฒ\nพฤฒา\nพฤฒาจารย์\nพฤฒิ\nพฤต\nพฤติ\nพฤทธ์\nพฤทธิ์\nพฤนต์\nพฤนท์\nพฤศจิก\nพฤศจิกายน\nพฤษภ\nพฤษภาคม\nพฤหัสบดี\nพล\nพละ\nพลากร\nพลาดิศัย\nพลาธิการ\nพลานามัย\nพลบ\nพลวก\nพลวง\nพลวัต\nพลศาสตร์\nพลอ\nพล้อ\nพลอง\nพลอด\nพลอน\nพลอมแพลม\nพลอย\nพล่อย\nพลั่ก\nพลัง\nพลั่ง\nพลั้ง\nพลัด\nพลัน\nพลับ\nพลับพลา\nพลับพลึง\nพลั่ว\nพล่า\nพลาง\nพลาญ\nพลาด\nพล่าน\nพลาม\nพล่าม\nพลาย\nพลาสติก\nพลาสมา\nพลาหก\nพลำ\nพล้ำ\nพลำภัง\nพลิก\nพลิพัท\nพลิ้ว\nพลี\nพลุ\nพลุก\nพลุ่ก\nพลุกพล่าน\nพลุ่ง\nพลุ้ย\nพลู\nพลูโต\nพลูโทเนียม\nพวก\nพวง\nพ่วง\nพวน\nพวย\nพสก\nพสุ\nพสุธา\nพสุสงกรานต์\nพหล\nพหุ\nพหุล\nพหู\nพอ\nพ่อ\nพ้อ\nพอก\nพอง\nพ้อง\nพอน\nพ้อม\nพอโลเนียม\nพะ\nพะงา\nพะงาบ\nพะจง\nพะทำมะรง\nพะนอ\nพะเน้าพะนอ\nพะเนิน\nพะเนียง\nพะแนง\nพะพาน\nพะพิง\nพะเพิง\nพะยอม\nพ่ะย่ะค่ะ\nพะยูง\nพะยูน\nพะเยิบ\nพะเยิบพะยาบ\nพะรุงพะรัง\nพะโล้\nพะไล\nพะวง\nพะวักพะวน\nพะวา\nพะว้าพะวัง\nพะอง\nพะอากพะอำ\nพะอืดพะอม\nพัก\nพักตร์\nพักตรา\nพักร\nพัง\nพังกา\nพังงา\nพังผืด\nพังพวย\nพังพอน\nพังพาน\nพังพาบ\nพังเพย\nพัช\nพัชนี\nพัชระ\nพัญจน์\nพัฒนะ\nพัฒนา\nพัฒนากร\nพัฒนาการ\nพัด\nพัดชา\nพัดดึงส์\nพัตร\nพัทธ์\nพัทธยา\nพัทธสีมา\nพัทร\nพัน\nพันตู\nพันทาง\nพันธ์\nพันธะ\nพันธกรณี\nพันธบัตร\nพันธมิตร\nพันธนะ\nพันธนาคาร\nพันธนาการ\nพันธุ์\nพันธุกรรม\nพันลึก\nพันลือ\nพันเลิศ\nพันเอิญ\nพับ\nพัลลภ\nพัลวัน\nพัว\nพัวะ\nพัศดี\nพัสดุ\nพัสตร์\nพัสถาน\nพา\nพาก\nพากเพียร\nพากย์\nพาง\nพ่าง\nพาชี\nพาณิช\nพาณิชย์\nพาณิชยกรรม\nพาณิชยการ\nพาณิชยศาสตร์\nพาณิชยศิลป์\nพาณินี\nพาณี\nพาณีนี\nพาด\nพาท\nพาทย์\nพาธ\nพาธา\nพาน\nพ่าน\nพานร\nพานรินทร์\nพาม\nพาย\nพ่าย\nพายม้า\nพายัพ\nพายุ\nพาร์เซก\nพารณ\nพารา\nพาราฟิน\nพาล\nพาลา\nพาลี\nพาลุก\nพาโล\nพาไล\nพาส\nพาสน์\nพาสนา\nพาสุกรี\nพ่าห์\nพาหนะ\nพาหะ\nพาหา\nพาหิรกะ\nพาหิระ\nพาหุ\nพาหุรัด\nพาหุสัจจะ\nพาเหียร\nพาฬ\nพำ\nพำนัก\nพำพึม\nพำลา\nพิกล\nพิกสิต\nพิกัด\nพิกัติ\nพิกัน\nพิการ\nพิกุล\nพิเคราะห์\nพิฆน์\nพิฆเนศ\nพิฆเนศวร\nพิฆาต\nพิง\nพิจัย\nพิจาร\nพิจารณ์\nพิจารณา\nพิจิก\nพิจิต\nพิจิตร\nพิชญ์\nพิชัย\nพิชาน\nพิชิต\nพิเชฐ\nพิเชียร\nพิฑูรย์\nพิณ\nพิดทูล\nพิดาน\nพิโดร\nพิตร\nพิถี\nพิถีพิถัน\nพิทย\nพิทย์\nพิทยา\nพิทยาคม\nพิทยาคาร\nพิทยาธร\nพิทยาลัย\nพิทักษ์\nพิทูร\nพิเทศ\nพิธาน\nพิธี\nพิธุ\nพินทุ\nพินอบพิเทา\nพินัย\nพินาศ\nพินิจ\nพินิต\nพินิศ\nพินิศจัย\nพิเนต\nพิบัติ\nพิบุล\nพิบูล\nพิปริต\nพิปลาส\nพิพรรธ\nพิพรรธน์\nพิพักพิพ่วน\nพิพัฒ\nพิพัฒน์\nพิพากษ์\nพิพากษา\nพิพาท\nพิพิธ\nพิพิธภัณฑ์\nพิพิธภัณฑสถาน\nพิภพ\nพิภัช\nพิภาค\nพิภูษณะ\nพิเภก\nพิมปะการัง\nพิมพ์\nพิมพการัง\nพิมพา\nพิมพาภรณ์\nพิมล\nพิมเสน\nพิมาน\nพิมุข\nพิโมกข์\nพิโมกษ์\nพิโยกพิเกน\nพิโยค\nพิรอด\nพิระ\nพิรากล\nพิราบ\nพิราม\nพิราลัย\nพิริยะ\nพิรี้พิไร\nพิรุณ\nพิรุธ\nพิรุฬห์\nพิเรนทร์\nพิเราะ\nพิโรธ\nพิไร\nพิลังกาสา\nพิลาป\nพิลาส\nพิลิปดา\nพิลึก\nพิลึกกึกกือ\nพิลึกพิลั่น\nพิโลน\nพิไล\nพิศ\nพิศวง\nพิศวาส\nพิศาล\nพิศุทธ์\nพิศุทธิ์\nพิเศษ\nพิษ\nพิษฐาน\nพิษนาศน์\nพิสดาร\nพิสมร\nพิสมัย\nพิสัง\nพิสัช\nพิสัย\nพิสิฐ\nพิสุทธิ์\nพิสูจน์\nพิหค\nพิหาร\nพิฬาร\nพี\nพี่\nพี้\nพีชคณิต\nพีระมิด\nพึง\nพึ่ง\nพึ่บ\nพึ่บพั่บ\nพึม\nพึมพำ\nพืช\nพืด\nพื้น\nพุ\nพุก\nพุกาม\nพุง\nพุ่ง\nพุงดอ\nพุฒ\nพุฒิ\nพุด\nพุดตาน\nพุทธ\nพุทธะ\nพุทธังกูร\nพุทธางกูร\nพุทธันดร\nพุทธาภิเษก\nพุทธาวาส\nพุทธิ\nพุทโธ่\nพุทรา\nพุธ\nพุ่ม\nพุมเรียง\nพุ้ย\nพู\nพูพอน\nพู่\nพูด\nพูน\nพู้น\nพู่ระหง\nเพ\nเพ็ก\nเพกา\nเพคะ\nเพ็ง\nเพ่ง\nเพ็จ\nเพชฉลูกรรม\nเพชฌฆาต\nเพชร\nเพชรดา\nเพชรปาณี\nเพชรฤกษ์\nเพชรายุธ\nเพชรกลับ\nเพชรสังฆาต\nเพชรหลีก\nเพชรหึง\nเพ็ญ\nเพฑูริย์\nเพณี\nเพ็ดทูล\nเพดาน\nเพท\nเพทนา\nเพทาย\nเพทุบาย\nเพโทบาย\nเพ่นพ่าน\nเพนียด\nเพไนย\nเพ้ย\nเพรง\nเพรซีโอดิเมียม\nเพรา\nเพราะ\nเพริด\nเพริศ\nเพรียก\nเพรียง\nเพรียบ\nเพรี้ยม\nเพรียว\nเพรื่อ\nเพรือง\nเพล\nเพลง\nเพล็ด\nเพล้โพล้\nเพลา\nเพลาะ\nเพลิง\nเพลิดเพลิน\nเพลิน\nเพลีย\nเพลี้ย\nเพลี่ยง\nเพศ\nเพส\nเพสลาด\nเพ่อ\nเพ้อ\nเพ้อเจ้อ\nเพอิญ\nเพะ\nเพา\nเพาะ\nเพิก\nเพิง\nเพิ่ง\nเพิดเพ้ย\nเพิ่ม\nเพี้ย\nเพียง\nเพี้ยง\nเพียงออ\nเพี้ยน\nเพียบ\nเพียร\nเพื่อ\nเพื่อน\nแพ\nแพ้\nแพง\nแพ่ง\nแพงพวย\nแพทย์\nแพทยศาสตร์\nแพน\nแพ่น\nแพนก\nแพนงเชิง\nแพร\nแพร่\nแพรก\nแพร่ง\nแพรว\nแพร้ว\nแพลง\nแพลทินัม\nแพล็บ\nแพลม\nแพลเลเดียม\nแพละ\nแพละโลม\nแพว\nแพ้ว\nแพศย์\nแพศยา\nแพะ\nโพ\nโพก\nโพกพาย\nโพง\nโพงพาง\nโพชฌงค์\nโพซิตรอน\nโพด\nโพทะเล\nโพแทสเซียม\nโพธ\nโพธิ\nโพธิ์\nโพน\nโพ้น\nโพนทะนา\nโพบาย\nโพย\nโพยก๊วน\nโพยม\nโพรก\nโพรง\nโพรโทแอกทิเนียม\nโพรมีเทียม\nโพระดก\nโพล่\nโพลง\nโพล่ง\nโพล้ง\nโพลน\nโพล้เพล้\nโพละ\nโพสพ\nไพ\nไพ่\nไพจิตร\nไพชน\nไพชยนต์\nไพฑูรย์\nไพที\nไพบูลย์\nไพพรรณ\nไพร\nไพร่\nไพรจิตร\nไพรชน\nไพรชยนต์\nไพรฑูรย์\nไพรที\nไพรบูลย์\nไพรเราะ\nไพรัช\nไพรำ\nไพริน\nไพรินทร์\nไพรี\nไพเราะ\nไพโรจน์\nไพล\nไพล่\nไพศาขะ\nไพศาล\nไพเศษ\nไพสพ\nไพสิฐ\nไพหาร\nฟก\nฟ้ง\nฟรักโทส\nฟรี\nฟลูออรีน\nฟ่อ\nฟ้อ\nฟอก\nฟอง\nฟ่อง\nฟ้อง\nฟอด\nฟอน\nฟ่อน\nฟ้อน\nฟ้อแฟ้\nฟอร์มาลดีไฮด์\nฟอร์มาลิน\nฟอสฟอรัส\nฟอสเฟต\nฟัก\nฟักฟุ้น\nฟัง\nฟังก์ชัน\nฟัด\nฟัน\nฟั่น\nฟั้น\nฟ้า\nฟาก\nฟาง\nฟ่าง\nฟาด\nฟาทอม\nฟาน\nฟ่าม\nฟาย\nฟาร์ม\nฟาสซิสต์\nฟิด\nฟิต\nฟิบ\nฟิล์ม\nฟิวส์\nฟิสิกส์\nฟี่\nฟี้\nฟืดฟาด\nฟืน\nฟื้น\nฟืม\nฟุ\nฟุ้ง\nฟุต\nฟุน\nฟุบ\nฟุ่บ\nฟุ่มเฟือย\nฟุลสแก๊ป\nฟู\nฟู่\nฟูก\nฟูด\nฟูม\nเฟ็ด\nเฟ้น\nเฟลด์สปาร์\nเฟ้อ\nเฟอร์เมียม\nเฟอะ\nเฟอะฟะ\nเฟะ\nเฟะฟะ\nเฟิน\nเฟี้ยม\nเฟี้ยว\nเฟือ\nเฟื้อ\nเฟือง\nเฟื่อง\nเฟื้อง\nเฟือน\nเฟือย\nเฟื้อย\nแฟ่\nแฟง\nแฟชั่น\nแฟน\nแฟบ\nแฟ้ม\nแฟรนเซียม\nแฟลกซ์\nแฟลต\nแฟะ\nโฟกัส\nไฟ\nภควดี\nภควัต\nภควันต์\nภควัม\nภควา\nภควาน\nภคะ\nภคันทลา\nภคินี\nภณะ\nภณิดา\nภพ\nภมร\nภมริน\nภมรี\nภมุกา\nภยันตราย\nภยาคติ\nภระ\nภรณี\nภรต\nภรรดร\nภรรดา\nภรรยา\nภระมร\nภระมรี\nภราดร\nภราดรภาพ\nภราดา\nภริยา\nภฤศ\nภวะ\nภวตัณหา\nภวนะ\nภวังค์\nภวังคจิต\nภักดี\nภักตะ\nภักติ\nภักษ์\nภักษา\nภักษาหาร\nภัค\nภัคน์\nภังคะ\nภังคี\nภัจ\nภัณฑ์\nภัณฑาคาร\nภัณฑาคาริก\nภัณฑารักษ์\nภัณฑนะ\nภัณฑู\nภัต\nภัตตาคาร\nภัตตาหาร\nภัตร\nภัทระ\nภัทรกัป\nภัพ\nภัย\nภัสดา\nภัสตรา\nภัสมะ\nภัสสร\nภา\nภาค\nภาคย์\nภาคยานุวัติ\nภาคินี\nภาคิไนย\nภาคี\nภาคียะ\nภาชนะ\nภาชี\nภาณ\nภาณวาร\nภาณกะ\nภาณี\nภาณุ\nภาดร\nภาดา\nภาตระ\nภาตา\nภาตุ\nภาติกะ\nภาติยะ\nภาพ\nภาพย์\nภาม\nภาย\nภาร\nภาระ\nภารดี\nภารต\nภารตี\nภารยทรัพย์\nภารยา\nภารา\nภาวนา\nภาวะ\nภาษ\nภาษณ์\nภาษา\nภาษิต\nภาษี\nภาส\nภาสน์\nภาสวร\nภาสา\nภาสุระ\nภิกขา\nภิกขาจาร\nภิกขุ\nภิกขุนี\nภิกษา\nภิกษาจาร\nภิกษาหาร\nภิกษุ\nภิกษุณี\nภิงคาร\nภิญโญ\nภิตติ\nภินท์\nภินทนาการ\nภิยโย\nภิรมย์\nภิรมย์สุรางค์\nภิษัช\nภิสัก\nภีตะ\nภีมะ\nภีรุ\nภุกต์\nภุขัน\nภุช\nภุชงค์\nภุต\nภุมมะ\nภุมรัตน์\nภุมวาร\nภุมรา\nภุมริน\nภุมรี\nภุมเรศ\nภู\nภู่\nภูต\nภูติ\nภูม\nภูมิ\nภูมี\nภูริ\nภูรี\nภูวดล\nภูวนาถ\nภูวเนตร\nภูวไนย\nภูษา\nภูษิต\nเภกะ\nเภตรา\nเภท\nเภทุบาย\nเภรี\nเภสัช\nโภค\nโภคะ\nโภคิน\nโภคี\nโภไคย\nโภไคศวรรย์\nโภช\nโภชย์\nโภชก\nโภชนะ\nโภชนา\nโภชนาหาร\nโภชนียะ\nไภริน\nไภรี\nไภษัชคุรุ\nไภษัชย์\nมกร\nมกราคม\nมกุฎ\nมคธ\nมฆวัน\nมฆะ\nมฆา\nม่ง\nมงกุฎ\nมงโกรย\nมงคล\nมงคลวาร\nมณฑ์\nมณฑก\nมณฑนะ\nมณฑป\nมณฑล\nมณฑา\nมณฑารพ\nมณฑิระ\nมณเฑียร\nมณี\nมด\nมตะ\nมตกภัต\nมติ\nมทนะ\nมทะ\nมธุ\nมธุกร\nมธุการี\nมธุลีห์\nมธุระ\nมธุรพจน์\nมน\nมนินทรีย์\nม่น\nมนต์\nมนตร์\nมนตรี\nมนท์\nมนทิราลัย\nมนเทียร\nมนสิการ\nมนัส\nมนัสวี\nมนินทรีย์\nมนิมนา\nมนิลา\nมนุญ\nมนุษย์\nมนุษยชาติ\nมนุษยธรรม\nมนุษย์มนา\nมนุษยโลก\nมนุษยศาสตร์\nมนุษยสัมพันธ์\nมนุสาร\nมนู\nมนูสาร\nมโน\nมโนช\nมโนชญ์\nมโนราห์\nมโนสาเร่\nมโนห์รา\nมมังการ\nมยุรฉัตร\nมยุระ\nมยุรา\nมยุรี\nมยุเรศ\nมยูร\nมรกต\nมรคา\nมรฑป\nมรณ์\nมรณะ\nมรณกรรม\nมรณบัตร\nมรณภัย\nมรณภาพ\nมรดก\nมรรค\nมรรคา\nมรรตัย\nมรรยาท\nมรรษ\nมรสุม\nมริจ\nมริยาท\nมรีจิ\nมรุต\nมฤค\nมฤคย์\nมฤคศิระ\nมฤคศิรมาส\nมฤคเศียร\nมฤคินทร์\nมฤเคนทร์\nมฤดก\nมฤต\nมฤตยู\nมฤทุ\nมล\nมละ\nมลัก\nมลังเมลือง\nมล้าง\nมลาย\nมลายู\nมวก\nม่วง\nมวน\nม่วน\nม้วน\nม้วนต้วน\nมวย\nม้วย\nมวล\nมหกรรม\nมหรณพ\nมหรรณพ\nมหรสพ\nมหัจฉริยะ\nมหัต\nมหัทธนะ\nมหันต์\nมหันตโทษ\nมหัพภาค\nมหัศจรรย์\nมหา\nมหากฐิน\nมหากาฬ\nมหาขันธกะ\nมหาจักร\nมหาชน\nมหาชัย\nมหาชาติ\nมหาโชตรัต\nมหาดไทย\nมหาดเล็ก\nมหาตมะ\nมหาไถ่\nมหาเทพ\nมหาเทพี\nมหาเทวี\nมหาธาตุ\nมหานิกาย\nมหานิล\nมหาบพิตร\nมหาบัณฑิต\nมหาพน\nมหาพรหม\nมหาภารตะ\nมหาภิเนษกรมณ์\nมหาภูต\nมหาเมฆ\nมหายาน\nมหายุค\nมหาราช\nมหาฤกษ์\nมหาละลวย\nมหาละลาย\nมหาวงศ์\nมหาวรรค\nมหาวิทยาลัย\nมหาศักราช\nมหาศาล\nมหาสงกรานต์\nมหาสดมภ์\nมหาสดำ\nมหาสมุทร\nมหาสาวก\nมหาหงส์\nมหาหิงคุ์\nมหาอำนาจ\nมหาอุจ\nมหาอุด\nมหาอุปรากร\nมหาอุปราช\nมหิ\nมหิดล\nมหิธร\nมหิป\nมหิงส์\nมหิทธิ\nมหินท์\nมหิมา\nมหิศร\nมหิศวร\nมหิษ\nมหิษี\nมหึมา\nมเหยงค์\nมเหศ\nมเหศวร\nมเหศักดิ์\nมเหสักข์\nมเหสิ\nมเหสี\nมเหาฬาร\nมโหรสพ\nมโหระทึก\nมโหรี\nมโหฬาร\nมไหศวรรย์\nมอ\nมอง\nมองโกลอยด์\nมองโกเลีย\nมองคร่อ\nมอญ\nมอด\nม่อต้อ\nมอเตอร์\nมอเตอร์ไซค์\nมอน\nม่อน\nมอบ\nมอม\nมอมแมม\nม่อย\nมอร์ฟีน\nมอระกู่\nมอลโทส\nม่อลอกม่อแลก\nม่อห้อม\nม่อฮ่อม\nมะ\nมะกรูด\nมะกล่ำ\nมะกอก\nมะก่อง\nมะกะโรนี\nมะกา\nมะเกลือ\nมะเกี๋ยง\nมะข่วง\nมะขวิด\nมะขาม\nมะเขือ\nมะแข่น\nมะคังแดง\nมะค่า\nมะคำไก่\nมะคำดีควาย\nมะงั่ว\nมะงุมมะงาหรา\nมะซัก\nมะซาง\nมะดัน\nมะดีหวี\nมะดูก\nมะเดหวี\nมะเดื่อ\nมะต้อง\nมะตะบะ\nมะตาด\nมะตาหะรี\nมะตึ่ง\nมะตื๋น\nมะตูม\nมะแตก\nมะโต\nมะนาว\nมะปราง\nมะปริง\nมะฝ่อ\nมะพร้าว\nมะพลับ\nมะพูด\nมะแพน\nมะแพร้ว\nมะเฟือง\nมะแฟน\nมะไฟ\nมะม่วง\nมะม่าว\nมะมี่\nมะมื่น\nมะมุด\nมะเมอ\nมะเมีย\nมะเมื่อย\nมะแม\nมะยง\nมะยม\nมะระ\nมะริด\nมะรืน\nมะรุม\nมะรุมมะตุ้ม\nมะเร็ง\nมะเรื่อง\nมะโรง\nมะลอกมะแลก\nมะละกอ\nมะลิ\nมะลื่น\nมะลืมดำ\nมะลุลี\nมะแว้ง\nมะสัง\nมะเส็ง\nมะหวด\nมะหะหมัด\nมะหาด\nมะหิ่ง\nมะเหงก\nมะอึก\nมะฮอกกานี\nมัก\nมักกะโรนี\nมักกะลีผล\nมักกะสัน\nมักขะ\nมั่กขั้ก\nมักขิกา\nมัค\nมัคคะ\nมัคคุเทศก์\nมัคนายก\nมัฆวาน\nมั่ง\nมังกง\nมังกร\nมังกุ\nมังคละ\nมังค่า\nมังคุด\nมังตาน\nมังสวิรัติ\nมังสะ\nมังสี\nมัจจะ\nมัจจุ\nมัจฉริยะ\nมัจฉรี\nมัจฉะ\nมัจฉา\nมัชชะ\nมัชวิรัติ\nมัชชาระ\nมัชฌันติกสมัย\nมัชฌิม\nมัชฌิมา\nมัญจา\nมัญชิษฐา\nมัญชุ\nมัญชุสา\nมัญชูสา\nมัญเชฏฐะ\nมัฏฐะ\nมัณฑนศิลป์\nมัณฑนา\nมัด\nมัตตะ\nมัตตัญญู\nมัตตา\nมัตติกา\nมัตถกะ\nมัตถลุงค์\nมัตสยะ\nมัตสยา\nมัตสระ\nมัตสริน\nมัททวะ\nมัทนะ\nมัทยะ\nมัธยฐาน\nมัธยม\nมัธยันห์\nมัธยัสถ์\nมัน\nมั่น\nมันตา\nมันถะ\nมันทิระ\nมันทิราลัย\nมับ\nมั้ม\nมัมมี่\nมัย\nมัลละ\nมัลลิกา\nมัว\nมัวซัว\nมั่ว\nมัศยา\nมัสตุ\nมัสตาร์ด\nมัสมั่น\nมัสยิด\nมัสรู่\nมัสลิน\nมัสสุ\nมา\nม้า\nมาก\nมาคสิระ\nมาฆบูชา\nมาฆะ\nม้าง\nมางสะ\nมาณพ\nมาณวิกา\nมาด\nมาดา\nมาตงค์\nมาตร\nมาตรา\nมาตฤ\nมาตังคะ\nมาตา\nมาตามหัยกะ\nมาตามหัยกา\nมาตามหัยยิกา\nมาติกะ\nมาติกา\nมาตุ\nมาตุจฉา\nมาตุรงค์\nมาตุเรศ\nมาตุละ\nมาตุลา\nมาตุลานี\nมาทะ\nมาธยมิก\nมาธยมิกะ\nมาธุระ\nมาธุสร\nมาธูระ\nมาน\nม่าน\nม้าน\nมานพ\nมานะ\nมานัต\nมานัส\nมานิต\nมานี\nมานุษ\nมานุษยวิทยา\nมาโนชญ์\nมาบ\nมาภา\nม้าม\nม่าย\nมายา\nมาร\nมาราธิราช\nมารค\nมารดร\nมารดา\nมารยา\nมารยาท\nมารศรี\nมารษา\nมาริต\nมารุต\nมาลย์\nมาลัย\nมาลา\nมาลาตี\nมาลาเรีย\nมาลินี\nมาลี\nมาลุต\nมาศ\nมาส\nมาสก\nมาห์\nม่าห์\nมาหิส\nม่าเหมี่ยว\nมาฬก\nมิ\nมิค\nมิคสัญญี\nมิ่ง\nมิจฉา\nมิด\nมิตร\nมิติ\nมิเตอร์\nมิถยา\nมิถุน\nมิถุนายน\nมิทธะ\nมินตรา\nมินตา\nมินหม้อ\nมิ่ม\nมิ้ม\nมิไย\nมิรันตี\nมิลลิกรัม\nมิลลิบาร์\nมิลลิเมตร\nมิลลิลิตร\nมิลักขะ\nมิลักขู\nมิส\nมิสกรี\nมิสกวัน\nมิสซา\nมี\nมี่\nมีด\nมีเทน\nมีน\nมีนาคม\nมี่สั้ว\nมึง\nมึน\nมืด\nมืน\nมื่น\nมือ\nมื้อ\nมุ\nมุก\nมุกดา\nมุกดาหาร\nมุกุระ\nมุข\nมุขเด็จ\nมุขยประโยค\nมุโขโลกนะ\nมุคคะ\nมุง\nมุ่ง\nมุ้ง\nมุจฉา\nมุจนะ\nมุจลินท์\nมุญจนะ\nมุญชะ\nมุฐิ\nมุณฑกะ\nมุณฑะ\nมุด\nมุตกิด\nมุตฆาต\nมุตตะ\nมุตตา\nมุตติ\nมุตะ\nมุติ\nมุททา\nมุทธชะ\nมุทธา\nมุทธาภิเษก\nมุทรา\nมุทริกา\nมุทะลุ\nมุทา\nมุทิกา\nมุทิงค์\nมุทิตา\nมุทุ\nมุทุตา\nมุ่น\nมุนิ\nมุนินทร์\nมุนี\nมุบ\nมุบมิบ\nมุม\nมุ้ม\nมุ่ย\nมุรธา\nมุรธาภิเษก\nมุสละ\nมุสลิม\nมุสา\nมุสิก\nมุหงิด\nมุหน่าย\nมุหุต\nมุฮัมมัด\nมูก\nมูเซอ\nมูตร\nมู่ทู่\nมูน\nมูมมาม\nมูรติ\nมูรธา\nมูรธาภิเษก\nมูล\nมูละ\nมูลา\nมูลิกากร\nมู่ลี่\nมู่เล่\nมูสัง\nมูสิก\nมูสิกะ\nมูสิกทันต์\nเม\nเม็ก\nเมกะเฮิรตซ์\nเมขลา\nเมฆ\nเมฆา\nเมฆินทร์\nเมฆี\nเม็ง\nเม็ด\nเมตตา\nเมตไตรย\nเมตร\nเมตริก\nเมตริกตัน\nเมถุน\nเมท\nเมโท\nเมทนี\nเมทินี\nเมทนีดล\nเมทานอล\nเมทิลแอลกอฮอล์\nเมธ\nเมธา\nเมธาวี\nเมธี\nเมน\nเม่น\nเม้น\nเมนเดลีเวียม\nเมนทอล\nเม้ม\nเมรัย\nเมริเดียน\nเมรุ\nเมล์\nเมล็ด\nเมลือง\nเมษ\nเมษายน\nเมห์\nเมหนะ\nเมหะ\nเมะ\nเมา\nเม่า\nเม้า\nเมารี\nเมาลี\nเมาฬี\nเมาะ\nเมิง\nเมิน\nเมิล\nเมีย\nเมียง\nเมี่ยง\nเมี้ยน\nเมือ\nเมื้อ\nเมื่อ\nเมือก\nเมือง\nเมือบ\nเมื่อย\nแม่\nแม้\nแมก\nแมกนีเซียม\nแมง\nแมงกะพรุน\nแมงกานิน\nแมงกานีส\nแมงคา\nแมงคาเรือง\nแมงช้าง\nแมงดา\nแมงลัก\nแม่ตะงาว\nแมน\nแม่น\nแม้น\nแมลง\nแมลบ\nแมว\nแม้ว\nแมะ\nโม\nโม่\nโม้\nโมก\nโมกข์\nโมกษะ\nโมฆกรรม\nโมฆสัญญา\nโมฆะ\nโมฆียกรรม\nโมฆียะ\nโมง\nโม่ง\nโมงครุ่ม\nโมทนา\nโมโนแซ็กคาไรด์\nโมไนย\nโมเม\nโมเมนต์\nโมเย\nโมรา\nโมรี\nโมเรส\nโมลิบดีนัม\nโมลี\nโมเลกุล\nโมเสก\nโมเสส\nโม่ห์\nโมหะ\nโมหันธ์\nโมหาคติ\nโมโห\nไม่\nไม้\nไมกา\nไมครอน\nไมโครกรัม\nไมโครฟิล์ม\nไมโครโฟน\nไมโครมิเตอร์\nไมโครเมตร\nไมโครลิตร\nไมโครเวฟ\nไมตรี\nไมยราบ\nไมล์\nยก\nยกกระบัตร\nยกนะ\nยง\nยงโย่\nยชุรเวท\nยติ\nยติภังค์\nยถากรรม\nยถาภูตญาณ\nย่น\nยนต์\nยนตร์\nยม\nยมก\nยมโดย\nยมนา\nยมล\nยมะ\nยรรยง\nยล\nยวง\nยวด\nยวน\nยวบ\nย้วย\nยวรยาตร\nยศ\nยโส\nยอ\nย่อ\nยอก\nย็อกแย็ก\nยอง\nย่อง\nย้อง\nยอด\nยอน\nย้อน\nยอบ\nยอม\nย่อม\nย้อม\nย่อย\nย้อย\nย้อแย้\nยะ\nย่ะ\nยะยอบ\nยะยับ\nยัก\nยักข์\nยักขินี\nยักษ์\nยักษา\nยักษิณี\nยักษี\nยัง\nยั้ง\nยั่งยืน\nยัชโญปวีต\nยัญ\nยัญญะ\nยัด\nยัติภังค์\nยัน\nยั่น\nยันต์\nยันตร\nยันตร์\nยันตรกรรม\nยั่นตะนี\nยับ\nยั่ว\nยั้ว\nยั้วเยี้ย\nยัวรยาตร\nยัวะ\nยัษฏิ\nยา\nย่า\nยาก\nยาคุ\nยาคู\nยาง\nย่าง\nยางพารา\nยาจก\nยาจนา\nยาไฉน\nยาด\nยาดา\nยาตร\nยาตรา\nยาน\nย่าน\nย่านพาโหม\nยานมาศ\nยานุมาศ\nยานี\nยาม\nย่าม\nยามะ\nยามักการ\nยามา\nยาย\nย้าย\nยายี\nยาว\nย้าว\nยาวกาลิก\nยาวชีวิก\nยาสูบ\nย่าหยา\nยาหยี\nยำ\nย่ำ\nย้ำ\nยำเยีย\nยิก\nยิง\nยิ่ง\nยิฏฐะ\nยิน\nยิบ\nยิบหยี\nยิปซัม\nยิปซี\nยิ้ม\nยิมนาสติก\nยิหวา\nยี\nยี่\nยี้\nยี่ก่า\nยี่เก\nยี่เข่ง\nยี่โถ\nยีน\nยี่โป้\nยี่ภู่\nยีราฟ\nยี่สก\nยี่สง\nยี่สน\nยี่สาน\nยี่สุ่น\nยี่หระ\nยี่หร่า\nยี่ห้อ\nยี่หุบ\nยึกยัก\nยึกยือ\nยึด\nยืด\nยืน\nยื่น\nยืม\nยื้อ\nยุ\nยุกกระบัตร\nยุกดิ\nยุกติ\nยุกติธรรม\nยุกต์\nยุค\nยุคนธร\nยุคล\nยุคันต์\nยุคันธร\nยุคุนธร\nยุง\nยุ่ง\nยุ้ง\nยุด\nยุต\nยุติ\nยุทธ\nยุทธ์\nยุทธนา\nยุทโธปกรณ์\nยุบ\nยุ่บ\nยุ่บยั่บ\nยุบล\nยุพดี\nยุพเรศ\nยุพา\nยุพาน\nยุพาพาล\nยุพาพิน\nยุ่มย่าม\nยุ่ย\nยุ้ย\nยุรยาตร\nยูรยาตร\nยุวชน\nยุวดี\nยุวราช\nยุวา\nยุวาน\nยู\nยู่\nยูง\nยูโด\nยูถะ\nยูถิกา\nยูริก\nยูเรนัส\nยูเรเนียม\nยูโรเพียม\nเย\nเย้\nเยง\nเยซู\nเย็ด\nเย็น\nเย็นตาโฟ\nเย็นเตาโฟ\nเย็บ\nเย้ย\nเยอ\nเย่อ\nเยอรมัน\nเยอว\nเย่อหยิ่ง\nเยอะ\nเยอะแยะ\nเยา\nเย้า\nเยาว์\nเยาวชน\nเยาวมาลย์\nเยาวยอด\nเยาวราช\nเยาวเรศ\nเยาวลักษณ์\nเยาวพา\nเยาวพาณี\nเยาวพาน\nเยาะ\nเยิง\nเยิน\nเยิ่น\nเยิ่นเย้อ\nเยินยอ\nเยิบ\nเยิบยาบ\nเยิ้ม\nเยีย\nเยี่ยง\nเยี่ยงอย่าง\nเยียงผา\nเยียดยัด\nเยียน\nเยียบ\nเยี่ยม\nเยียรบับ\nเยียรยง\nเยียว\nเยี่ยว\nเยียวยา\nเยือ\nเยื่อ\nเยื้อ\nเยือก\nเยือง\nเยื่อง\nเยื้อง\nเยือน\nเยื้อน\nแย่\nแย้\nแยก\nแยง\nแย่ง\nแย้ง\nแยงแย่\nแยงแย้\nแยบ\nแย็บ\nแยม\nแย้ม\nแยแส\nแยะ\nโย\nโย้\nโยก\nโยกเยก\nโยคาพจร\nโยคาวจร\nโยคเกณฑ์\nโยคยะ\nโยคะ\nโยคิน\nโยคี\nโยง\nโย่ง\nโย่งเย่ง\nโยงโย่\nโยชน์\nโยชนา\nโยถิกะ\nโยทะกา\nโยธวาทิต\nโยธา\nโยธิน\nโยน\nโยนก\nโยนิโส\nโยนี\nโยม\nโยโส\nใย\nไย\nไย่\nไยดี\nไยไพ\nรก\nรง\nรงค์\nรงควัตถุ\nรงรอง\nรจนา\nรจเรข\nรจเลข\nรจิต\nรชตะ\nรชนิ\nรชนี\nรชะ\nรณรงค์\nรด\nรดี\nรตนะ\nรตะ\nรติ\nรถ\nรน\nร่น\nรบ\nรบาญ\nรพี\nรม\nร่ม\nรมณี\nรมณีย์\nรมณียสถาน\nรมย์\nรมเยศ\nรยางค์\nรวก\nรวง\nร่วง\nรวด\nรวน\nรวนเร\nร่วน\nรวบ\nรวม\nร่วม\nรวย\nรวิ\nรวิวาร\nรวี\nรศนา\nรส\nรสนา\nรสสุคนธ์\nรสายนเวท\nรสิก\nรหัท\nรหัส\nรโห\nรโหฐาน\nรอ\nร่อ\nรอก\nรอง\nร่อง\nร้อง\nรองเง็ง\nร่องแร่ง\nรอด\nรอน\nร่อน\nร้อน\nรอบ\nรอบคอบ\nรอม\nรอมชอม\nรอมร่อ\nรอย\nร่อย\nร้อย\nร่อแร่\nระ\nระกะ\nระกา\nระกำ\nระเกะระกะ\nระคน\nระคาง\nระคาย\nระแคะ\nระฆัง\nระงม\nระงับ\nระแง้\nระโงกหิน\nระชวย\nระดม\nระดะ\nระดับ\nระดา\nระด่าว\nระดู\nระเด่น\nระเดียง\nระแด\nระตู\nระทก\nระทด\nระทม\nระทวย\nระทา\nระทึก\nระแทะ\nระนาด\nระนาบ\nระนาม\nระนาว\nระเนน\nระเนระนาด\nระเนียด\nระแนง\nระแนะ\nระบบ\nระบม\nระบอบ\nระบัด\nระบับ\nระบาด\nระบาย\nระบำ\nระบิล\nระบือ\nระบุ\nระเบง\nระเบ็ง\nระเบิด\nระเบียง\nระเบียน\nระเบียบ\nระแบบ\nระมัดระวัง\nระมาด\nระเมียร\nระย่อ\nระย่อม\nระยะ\nระยั้ง\nระยับ\nระย้า\nระยาบ\nระยำ\nระยิบระยับ\nระโยง\nระโยงระยาง\nระรวย\nระรอง\nระร่อน\nระรัว\nระราน\nระร่าย\nระริก\nระรี่\nระรึง\nระรื่น\nระรื้น\nระเร้ง\nระเริง\nระเรียง\nระเรื่อย\nระแรง\nระลวง\nระลอก\nระลึก\nระวัง\nระวาง\nระวาย\nระวิง\nระแวง\nระแวดระวัง\nระไว\nระส่ำระสาย\nระหกระเหิน\nระหง\nระหวย\nระหว่าง\nระหองระแหง\nระหัด\nระหาย\nระเห็จ\nระเหย\nระเหระหน\nระเหหน\nระเหิด\nระเหินระหก\nระแหง\nระโหย\nระอา\nระอิดระอา\nระอุ\nรัก\nรักข์\nรักขิต\nรักตะ\nรักบี้\nรักเร่\nรักแร้\nรักษ์\nรักษา\nรัง\nรั้ง\nรังเกียจ\nรังแก\nรังค์\nรังควาน\nรังแค\nรังรอง\nรังวัด\nรังสิ\nรังสี\nรังสิมันตุ์\nรังสิมา\nรัจฉา\nรัช\nรัชชูปการ\nรัชมังคลาภิเษก\nรัชชุ\nรัชฎาภิเษก\nรัชดาภิเษก\nรัชนะ\nรัชนี\nรัญจวน\nรัฏฐาภิปาลโนบาย\nรัฐ\nรัฐประศาสโนบาย\nรัฐประศาสนศาสตร์\nรัด\nรัต\nรัตกัมพล\nรัตมณี\nรัตคน\nรัตจันทน์\nรัตตัญญู\nรัตติ\nรัตน์\nรัตนะ\nรัตนโกสินทร์\nรัตนโกสินทรศก\nรัตนชาติ\nรัตนตรัย\nรัตนบัลลังก์\nรัตนวราภรณ์\nรัตนสิงหาสน์\nรัตนา\nรัตนากร\nรัตนาภรณ์\nรัตนาวลี\nรัตมา\nรัถ\nรัถยา\nรัทเทอร์ฟอร์เดียม\nรัน\nรั้น\nรันทด\nรันทวย\nรับ\nรัมณียสถาน\nรัมภา\nรัมมี่\nรัมย์\nรัย\nรัว\nรั่ว\nรั้ว\nรัศมิมัต\nรัศมิมาน\nรัศมี\nรัษฎากร\nรัสเซีย\nรัสสะ\nรัสสระ\nรา\nร่า\nร้า\nราก\nรากษส\nรากสาด\nราคะ\nราคจริต\nราคา\nราคิน\nราคี\nราง\nร่าง\nร้าง\nรางจืด\nรางชาง\nรางวัล\nราช\nราชกิจจานุเบกษา\nราชนิกุล\nราชวโรงการ\nราชญี\nราชดัด\nราชพฤกษ์\nราชมาณพ\nราชมาษ\nราชมาส\nราชย์\nราชสีห์\nราชะ\nราชัน\nราชันย์\nราชัย\nราชา\nราชาธิปไตย\nราชาธิราช\nราชาภิเษก\nราชายตนะ\nราชาวดี\nราชี\nราชินิกุล\nราชินีกุล\nราชินี\nราชินูปถัมภ์\nราชูปถัมภ์\nราชูปโภค\nราเชน\nราเชนทร์\nราเชนทรยาน\nราโชวาท\nราไชศวรรย์\nราญ\nราญรอน\nราด\nราต\nราตร\nราตรี\nราน\nร่าน\nร้าน\nราบ\nราพณ์\nราพณาสูร\nราม\nรามเกียรติ์\nรามสูร\nรามัญ\nรามา\nราย\nร่าย\nร้าย\nราว\nร้าว\nราวี\nราศี\nราษฎร\nราษฎร์\nราษตรี\nราษราตรี\nราหุ\nราหู\nรำ\nร่ำ\nรำคาญ\nรำงับ\nรำจวน\nรำบาญ\nรำพัน\nรำพาย\nรำพึง\nรำเพย\nรำไพ\nรำมะนา\nรำมะนาด\nรำมะร่อ\nร่ำรวย\nร่ำร่ำ\nรำไร\nรำลึก\nรำหัด\nรำหัส\nริ\nริก\nริดสีดวง\nริน\nริ้น\nริบ\nริบบิ้น\nริบรี่\nริบหรี่\nริปุ\nริปู\nริม\nริ้ว\nริษยา\nรี\nรี่\nรี้พล\nรีด\nรีดักชัน\nรีต\nรีเนียม\nรีบ\nรีม\nรีรอ\nรี้ริก\nรึง\nรึ้ง\nรื่น\nรื้น\nรื้อ\nรุ\nรุก\nรุกข์\nรุกขชาติ\nรุกขเทวดา\nรุกขมูล\nรุกขา\nรุกรุย\nรุ่ง\nรุ้ง\nรุงรัง\nรุ่งริ่ง\nรุจ\nรุจา\nรุจนะ\nรุจิ\nรุจี\nรุจิระ\nรุจิรา\nรุด\nรุต\nรุทธ์\nรุทระ\nรุธิร\nรุธิระ\nรุเธียร\nรุน\nรุ่น\nรุบรู่\nรุม\nรุ่ม\nรุ่มร่าม\nรุย\nรุ่ย\nรุรุ\nรุหะ\nรู\nรู่\nรู้\nรูจี\nรูด\nรูทีเนียม\nรูบิเดียม\nรูป\nรูปิยะ\nรูปี\nรูเล็ตต์\nเร่\nเรข\nเรขา\nเรขาคณิต\nเร็ง\nเร่ง\nเร้ง\nเรณุ\nเรณู\nเรดอน\nเรดาร์\nเรเดียม\nเร้น\nเรรวน\nเรไร\nเร็ว\nเร่ว\nเรวดี\nเรอ\nเร่อ\nเรา\nเร่า\nเร้า\nเราะ\nเริง\nเริด\nเริม\nเริ่ม\nเริ้ม\nเริศร้าง\nเรี่ย\nเรี้ย\nเรียก\nเรียง\nเรียด\nเรียน\nเรียบ\nเรียม\nเรี่ยม\nเรียว\nเรี่ยว\nเรี้ยวรก\nเรือ\nเรื่อ\nเรื้อ\nเรือก\nเรือง\nเรื่อง\nเรื้อง\nเรืองรอง\nเรือด\nเรือน\nเรื้อน\nเรื่อย\nแร\nแร่\nแรก\nแร็กเกต\nแรง\nแร่ง\nแร้ง\nแรด\nแร้นแค้น\nแรม\nแร้ว\nแระ\nโร\nโร่\nโรค\nโรคา\nโรคาพาธ\nโรง\nโรจ\nโรจน์\nโรเดียม\nโรตี\nโรท\nโรธ\nโรม\nโรมัน\nโรเมอร์\nโรย\nโรเร\nโรหิณี\nโรหิต\nไร\nไร่\nไร้\nไรย์\nฤกษ์\nฤกษณะ\nฤคเวท\nฤชา\nฤชุ\nฤณ\nฤดี\nฤดียา\nฤดู\nฤต\nฤติยา\nฤตุ\nฤทธา\nฤทธิ์\nฤทัย\nฤษภ\nฤษยา\nฤษี\nฤๅ\nฤๅดี\nฤๅทัย\nฤๅษี\nฤๅสาย\nลก\nล่ก\nลฆุ\nลง\nล่ง\nลงกา\nล้งเล้ง\nลด\nลดา\nลดาวัลย์\nลน\nล้น\nลบ\nลบอง\nลพ\nลพุช\nลม\nล่ม\nล้ม\nลมาด\nลรรลุง\nลลนา\nลลิต\nลวก\nลวง\nล่วง\nล้วง\nลวณะ\nลวด\nล้วน\nลวนลาม\nลวนะ\nล่วม\nลวะ\nลวิตร\nลหุ\nลหุกาบัติ\nล่อ\nล้อ\nลอก\nล็อก\nล็อกเกต\nลอกแลก\nลอการิทึม\nลอง\nล่อง\nลองกอง\nลองจิจูด\nลองไน\nลอด\nลอตเตอรี่\nลอน\nล่อน\nลอบ\nลอม\nล้อม\nลอมชอม\nลอมพอก\nลอย\nล่อย\nล่อแล่\nลอว์เรนเซียม\nลออ\nละ\nล่ะ\nละคร\nละติจูด\nละบม\nละบอง\nละบือ\nละเบ็ง\nละโบม\nละม่อม\nละมั่ง\nละมาน\nละม้าย\nละมุ\nละมุด\nละมุน\nละเมอ\nละเมาะ\nละเมิด\nละเมียด\nละแมะ\nละโมก\nละโมบ\nละไม\nละลวย\nละลอก\nละล้า\nละล้าละลัง\nละลาน\nละลาบละล้วง\nละลาย\nละล้าว\nละล่ำละลัก\nละลิบ\nละลุม\nละเลง\nละเล้า\nละเลาะ\nละเลิง\nละเลียด\nละเลียบ\nละไล้\nละว้า\nละวาด\nละเวง\nละแวก\nละโว้\nละหมาด\nละห้อย\nละหาน\nละหาร\nละหุ่ง\nละเหย\nละเหี่ย\nละอง\nละออง\nละอาย\nละเอียด\nละแอน\nลัก\nลักขณะ\nลักขณา\nลักขะ\nลักขี\nลักจั่น\nลักปิดลักเปิด\nลักษณ์\nลักษณนาม\nลักษณะ\nลักษณาการ\nลักษมณ์\nลักษมาณา\nลักษมี\nลักษะ\nลัคคะ\nลัคน์\nลัคนา\nลัง\nลั่ง\nลังกา\nลังคี\nลังถึง\nลังลอง\nลังเล\nลังสาด\nลัชชา\nลัชชี\nลัญจ์\nลัญจกร\nลัญฉกร\nลัญฉน์\nลัฐิ\nลัฐิกา\nลัด\nลัดา\nลัทธ์\nลัทธิ\nลัน\nลั่น\nลันเต\nลันเตา\nลันไต\nลั่นทม\nลันโทม\nลับ\nลัพธ์\nลัพธิ\nลัภ\nลัภนะ\nลัภย์\nลัมพ์\nลัย\nลา\nล่า\nล้า\nลาก\nลาง\nล่าง\nล้าง\nลางลิง\nลางสาด\nลาช\nลาชะ\nลาชา\nลาญ\nลาด\nลาดเลา\nล้าต้า\nล่าเตียง\nลาน\nล่าน\nล้าน\nลาบ\nลาพอน\nลาภ\nลาม\nล่าม\nลามก\nลาย\nล้าย\nลายสือ\nลาลา\nลาว\nลาวัณย์\nลาวา\nลำ\nล่ำ\nล้ำ\nลำเข็ญ\nลำแข\nลำเค็ญ\nลำเจียก\nลำดวน\nลำดับ\nลำเนา\nลำบอง\nลำบาก\nลำปำ\nลำพวน\nลำพอง\nลำพัง\nลำพู\nลำเพ็ญ\nลำเพา\nลำแพน\nลำโพง\nลำไพ่\nลำภุขัน\nลำมะลอก\nลำยอง\nลำไย\nลำลอง\nล่ำลา\nลำลาบ\nลำลึก\nลำเลาะ\nลำเลิก\nลำเลียง\nลำเวียง\nลำเอียก\nลำเอียง\nลิ\nลิกขา\nลิกไนต์\nลิกู\nลิเก\nลิขนะ\nลิขสิทธิ์\nลิขิต\nลิง\nลิงค์\nลิด\nลิต\nลิตมัส\nลิตร\nลิเทียม\nลิ่น\nลิ้น\nลินจง\nลิ้นจี่\nลินลา\nลินสีด\nลิ่นฮื้อ\nลินิน\nลิบ\nลิปดา\nลิปสติก\nลิปิ\nลิฟต์\nลิเภา\nลิ่ม\nลิ้ม\nลิมป์\nลิมปนะ\nลิลิต\nลิว\nลิ่ว\nลิสง\nลี\nลี่\nลี้\nลีซอ\nลีบ\nลีลา\nลีลาศ\nลีฬหา\nลึก\nลึงค์\nลืด\nลื่น\nลื้น\nลืบ\nลืม\nลือ\nลื่อ\nลื้อ\nลุ\nลุก\nลุง\nลุ้ง\nลุ่น\nลุ้น\nลุพธ์\nลุ่ม\nลุมพี\nลุมพู\nลุย\nลุ่ย\nลุ้ย\nลู่\nลูก\nลูกระมาศ\nลูกเอ็น\nลูขะ\nลูทีเชียม\nลูบ\nเลก\nเล็ก\nเลข\nเลขา\nเลขาธิการ\nเลขานุการ\nเล็ง\nเล้ง\nเล่งฮื้อ\nเลเซอร์\nเลฑฑุ\nเลณฑุ\nเลณะ\nเล็ด\nเลน\nเล็น\nเล่น\nเลนส์\nเล็บ\nเลบง\nเลปกร\nเลปน์\nเลเป\nเลเพ\nเล็ม\nเล่ม\nเลย\nเลว\nเลวง\nเลวูโลส\nเลศ\nเลษฏุ\nเล่ห์\nเล่ห์กระเท่ห์\nเลหลัง\nเลหะ\nเลอ\nเล่อ\nเลอะ\nเลอะเทอะ\nเละ\nเละเทะ\nเลา\nเล่า\nเล้า\nเลากัย\nเล้าโลม\nเลาะ\nเลิก\nเลิ่กลั่ก\nเลิง\nเลิ้ง\nเลินเล่อ\nเลิศ\nเลีย\nเลียง\nเลี่ยง\nเลี้ยง\nเลียงผา\nเลียงฝ้าย\nเลียงมัน\nเลียน\nเลี่ยน\nเลียนไฟ\nเลียบ\nเลี่ยม\nเลียว\nเลี้ยว\nเลือก\nเลือง\nเลื่อง\nเลือด\nเลือน\nเลื่อน\nเลื่อม\nเลื่อย\nเลื้อย\nเลื่อยล้า\nแล\nแล่\nแล้\nแลก\nแล็กเกอร์\nแล็กโทส\nแลง\nแล่ง\nแล้ง\nแลน\nแล่น\nแลนทานัม\nแลบ\nแล้ว\nและ\nโล่\nโล้\nโลก\nโลกเชษฐ์\nโลกธรรม\nโลกธาตุ\nโลกนาถ\nโลกบาล\nโลกย์\nโลกัย\nโลกวัชชะ\nโลกวิทู\nโลกัตถจริยา\nโลกันตร์\nโลกา\nโลกาธิบดี\nโลกาธิปไตย\nโลกานุวัตร\nโลกาภิวัตน์\nโลกามิส\nโลกายัต\nโลกาวินาศ\nโลกิยะ\nโลกีย์\nโลกียวัตร\nโลกียวิสัย\nโลกียสุข\nโลกุตระ\nโลกุตรธรรม\nโลกุตรภูมิ\nโลง\nโล่ง\nโล้ง\nโล่งโจ้ง\nโล่งโต้ง\nโล้งโต้ง\nโลจนะ\nโลณะ\nโลด\nโล่ติ๊น\nโลโต\nโลท\nโลน\nโล้น\nโลภ\nโลม\nโลมเล้า\nโลมะ\nโลมา\nโลลุป\nโลเล\nโลโล\nโลโล้\nโลหะ\nโลหกุมภี\nโลหัช\nโลหิต\nไล่\nไล้\nไลย\nไลลา\nไล่เลี่ย\nฦๅ\nฦๅชา\nฦๅสาย\nวก\nวง\nวงก์\nวงกต\nวงศ์\nวงศกร\nวงศา\nวงษ์\nวจนะ\nวจี\nวชิระ\nวชิรปาณี\nวชิรหัตถ์\nวชิราวุธ\nวฏะ\nวฏาการ\nวณิช\nวณิชชา\nวณิชย์\nวณิชยา\nวณิพก\nวดี\nวทนะ\nวทัญญุตา\nวทัญญู\nวธุกา\nวธู\nวน\nวนศาสตร์\nวนสณฑ์\nวนสัณฑ์\nวนอุทยาน\nวนัส\nวนัสบดี\nวนา\nวนาดร\nวนาดอน\nวนานต์\nวนาลัย\nวนาลี\nวนาวาส\nวนาศรม\nวนาสณฑ์\nวนาสัณฑ์\nวนิดา\nวนิพก\nวเนจร\nวโนทยาน\nวยัคฆ์\nวยากรณ์\nวรดนู\nวรทาน\nวรมหาวิหาร\nวรงค์\nวรณะ\nวรรค\nวรรคย์\nวรรช\nวรรชย์\nวรรณะ\nวรรณกรรม\nวรรณคดี\nวรรณยุกต์\nวรรณยุต\nวรรณศิลป์\nวรรณนา\nวรรณพฤติ\nวรรณึก\nวรรธกะ\nวรรธนะ\nวรรษ\nวรรษา\nวรวิหาร\nวรัญญู\nวรางคณา\nวรางคนา\nวราห์\nวราหะ\nวรุณ\nวโรดม\nวฤก\nวลัช\nวลัญช์\nวลัญชน์\nวลัย\nวลาหก\nวลี\nวศค\nวศะ\nวศิน\nวสนะ\nวสภะ\nวสละ\nวสวัดดี\nวสวัตตี\nวสะ\nวสันต์\nวสันตดิลก\nวสันตฤดู\nวสันตวิษุวัต\nวสา\nวสี\nวสุ\nวสุธา\nวสุนธรา\nวสุมดี\nวหะ\nวอ\nวอก\nวอกแวก\nว่องไว\nวอด\nวอน\nว่อน\nว็อบ\nวอมแวม\nวอลเลย์บอล\nวอแว\nวะ\nวัก\nวักกะ\nวัคคีย์\nวัคคุ\nวัคซีน\nวัง\nวังก์\nวังชา\nวังเวง\nวังศะ\nวังสะ\nวัจจะ\nวัจกุฎี\nวัจฉละ\nวัจน์\nวัช\nวัชชะ\nวัชพืช\nวัชฌ์\nวัชระ\nวัชรปาณี\nวัชรยาน\nวัชรอาสน์\nวัชราสน์\nวัชรินทร์\nวัชรี\nวัชเรนทร์\nวัฏ\nวัฏฏะ\nวัฏจักร\nวัฏทุกข์\nวัฏสงสาร\nวัฏกะ\nวัฏฏิ\nวัฒกะ\nวัฒกี\nวัฒนธรรม\nวัฒนะ\nวัฒนา\nวัณ\nวัณโรค\nวัณฏ์\nวัณณะ\nวัณนา\nวัด\nวัต\nวัตต์\nวัตตา\nวัตถ์\nวัตถาภรณ์\nวัตถาลังการ\nวัตถุ\nวัตนะ\nวัตร\nวัตสดร\nวัตสะ\nวัติ\nวัทน์\nวัน\nวันต์\nวันทนา\nวันทนาการ\nวันทนีย์\nวันทยหัตถ์\nวันทยาวุธ\nวันทา\nวันทิ\nวับ\nวับวาบ\nวับวาม\nวับแวบ\nวับแวม\nวัปปะ\nวัมมิกะ\nวัย\nวัลก์\nวัลคุ\nวัลย์\nวัลลภ\nวัลลี\nวัว\nวัสสะ\nวัสโสทก\nวัสดุ\nวัสตร์\nวัสน์\nวัสนะ\nวัสสานะ\nวัสสานฤดู\nวา\nว่า\nว้า\nว้าเหว่\nวาก\nว้าก\nวากยสัมพันธ์\nวากยะ\nวาง\nว่าง\nว้าง\nวาจก\nวาจา\nวาจาไปยะ\nวาจาล\nวาชเปยะ\nวาณิช\nวาณิชกะ\nวาณิชย์\nวาณี\nวาด\nวาต\nวาตะ\nวาตภัย\nวาท\nวาทศาสตร์\nวาทศิลป์\nวาทกะ\nวาทนะ\nวาทย์\nวาทยกร\nวาทิต\nวาทิน\nวาที\nวาน\nวานซืน\nว่าน\nวานร\nวานรินทร์\nวาเนเดียม\nวาบ\nวาปี\nวาม\nวามน\nวามนาวตาร\nวามะ\nวาย\nว่าย\nว้าย\nวายะ\nวาโย\nวายามะ\nวายุ\nวายุกูล\nวาร\nวาระ\nวารสาร\nวารสารศาสตร์\nวาริ\nวารี\nวาริช\nวารีช\nวาริท\nวาริธร\nวารุณ\nวารุณี\nวาล\nวาลวีชนี\nวาล์ว\nวาลิกา\nวาลุกา\nวาว\nว่าว\nว้าว่อน\nว้าวุ่น\nวาสนะ\nวาสนา\nวาสพ\nวาสะ\nวาสิน\nวาสี\nวาสุกรี\nวาสุกี\nวาสุเทพ\nวาหนะ\nวาหะ\nวาหินี\nวาฬ\nวิกขัมภ์\nวิกขัมภนะ\nวิกเขป\nวิกรม\nวิกรัย\nวิกรานต์\nวิกฤต\nวิกฤติ\nวิกล\nวิกสิต\nวิกัต\nวิกัติ\nวิกัติการก\nวิกัป\nวิกัย\nวิการ\nวิกาล\nวิกาลโภชน์\nวิคหะ\nวิเคราะห์\nวิฆเนศ\nวิฆเนศวร\nวิฆาต\nวิง\nวิ่ง\nวิ่งเปี้ยว\nวิงวอน\nวิจฉิกะ\nวิจล\nวิจักขณ์\nวิจักษ์\nวิจักษณ์\nวิจัย\nวิจาร\nวิจารณ์\nวิจารณญาณ\nวิจิ\nวิจิกิจฉา\nวิจิต\nวิจิตร\nวิจิน\nวิจุณ\nวิจุรณ\nวิชชา\nวิชชุ\nวิชชุดา\nวิชชุตา\nวิชชุลดา\nวิชญะ\nวิชน\nวิชนี\nวิชย\nวิชัย\nวิชา\nวิชานนะ\nวิชิต\nวิเชียร\nวิญญัตติ\nวิญญาณ\nวิญญาณกทรัพย์\nวิญญู\nวิฑูรย์\nวิด\nวิตก\nวิตถาร\nวิตามิน\nวิถี\nวิทธะ\nวิทยฐานะ\nวิทยา\nวิทยาคม\nวิทยาคาร\nวิทยาลัย\nวิทยุ\nวิทยุต\nวิทวัส\nวิทัตถิ\nวิทัศน์\nวิทารณ์\nวิทิต\nวิทู\nวิทูร\nวิเทศ\nวิเทโศบาย\nวิธ\nวิธวา\nวิธาน\nวิธี\nวิธุระ\nวิธู\nวิธูปนะ\nวิ่น\nวินตกะ\nวินัย\nวินาที\nวินายก\nวินาศ\nวินิจ\nวินิจฉัย\nวินิต\nวินิบาต\nวินิปาติก\nวิเนต\nวิบัติ\nวิบาก\nวิบุล\nวิบุลย์\nวิบูล\nวิบูลย์\nวิปการ\nวิปฏิสาร\nวิปโยค\nวิประโยค\nวิปริต\nวิปลาส\nวิปวาส\nวิปักษ์\nวิปัสสก\nวิปัสสนา\nวิปัสสนายานิก\nวิพากษ์\nวิพิธทัศนา\nวิพุธ\nวิภว\nวิภวตัณหา\nวิภังค์\nวิภัช\nวิภัตติ\nวิภา\nวิภาค\nวิภาช\nวิภาดา\nวิภาวี\nวิภาษ\nวิภาส\nวิภู\nวิภูษณะ\nวิภูษา\nวิภูษิต\nวิมน\nวิมล\nวิมลัก\nวิมังสา\nวิมัติ\nวิมาน\nวิมุข\nวิมุต\nวิมุตติ\nวิเมลือง\nวิโมกข์\nวิโยค\nวิระ\nวิรงรอง\nวิรังรอง\nวิรัช\nวิรัต\nวิรัติ\nวิราคะ\nวิราม\nวิริยภาพ\nวิริยะ\nวิรุธ\nวิรุฬห์\nวิรุฬหก\nวิรูป\nวิรูปักษ์\nวิเรนทร์\nวิโรจ\nวิโรจน์\nวิโรฒ\nวิโรธ\nวิลันดา\nวิลัย\nวิลาด\nวิลาศ\nวิลาป\nวิลาวัณย์\nวิลาส\nวิลาสินี\nวิลิปดา\nวิลิศมาหรา\nวิเลป\nวิเลปนะ\nวิโลกนะ\nวิโลม\nวิไล\nวิไลวรรณ\nวิวรณ์\nวิวรรธน์\nวิวัฏ\nวิวัฒน์\nวิวัฒนาการ\nวิวัน\nวิวาท\nวิวาห์\nวิวาหมงคล\nวิวาหะ\nวิวิต\nวิวิธ\nวิเวก\nวิศรุต\nวิศว\nวิศวกร\nวิศวกรรม\nวิศวกรรมศาสตร์\nวิศัลย์\nวิศาขบูชา\nวิศาขา\nวิศาล\nวิศิษฏ์\nวิศุทธ์\nวิศุทธิ์\nวิเศษ\nวิเศษณ์\nวิษณุ\nวิษณุกรรม\nวิษธร\nวิษัย\nวิษาณ\nวิษุวัต\nวิสกี้\nวิสรรชนีย์\nวิสฤต\nวิสสุกรรม\nวิสัชนา\nวิสัญญี\nวิสัย\nวิสัยทัศน์\nวิสาขบูชา\nวิสาขะ\nวิสาขา\nวิสามัญ\nวิสามานยนาม\nวิสาร\nวิสารทะ\nวิสาล\nวิสาสะ\nวิสาหกิจ\nวิสิฐ\nวิสุงคามสีมา\nวิสุทธ์\nวิสุทธิ์\nวิสูตร\nวิเสท\nวิหค\nวิหลั่น\nวิหาร\nวิหิงสา\nวิเหสา\nวิฬาร\nวิฬาร์\nวี\nวีจิ\nวีชนี\nวีณา\nวี้ด\nวีรกรรม\nวีรชน\nวีรบุรุษ\nวีรสตรี\nวี่วัน\nวี่แวว\nวีสะ\nวุ้ง\nวุฐิ\nวุฒ\nวุฒิ\nวุด\nวุ่น\nวุ้น\nวุบ\nวุ้ย\nวุลแฟรม\nวู้\nวูดวาด\nวูบ\nวู่วาม\nเว้\nเวค\nเวคิน\nเวคี\nเวจ\nเวช\nเวชยันต์\nเวฐน์\nเวณิ\nเวณิก\nเวณุ\nเวตน์\nเวตร\nเวตาล\nเวท\nเวทคู\nเวทนา\nเวทย์\nเวทัลละ\nเวทางค์\nเวทางคศาสตร์\nเวทานต์\nเวทานตะ\nเวทิ\nเวที\nเวธะ\nเวน\nเว้น\nเวนไตย\nเวไนย\nเวมัต\nเว้ย\nเวยยากรณะ\nเวร\nเวรมณี\nเวรี\nเวโรจน์\nเวลา\nเวเลนซี\nเวศม์\nเวศย์\nเวศยา\nเวสน์\nเวสภู\nเวสม์\nเวสวัณ\nเวสสะ\nเวสสันดร\nเวสสุกรรม\nเวสสุวัณ\nเวสารัช\nเวสิยา\nเวหน\nเวหะ\nเวหา\nเวหาส\nเวฬุ\nเวฬุริยะ\nเว่อ\nเว้า\nเวิก\nเวิ้ง\nเวี่ย\nเวียง\nเวียด\nเวียดนาม\nเวียน\nเวียร\nเวี่ยว\nแว้\nแวง\nแว้ง\nแวด\nแว้ด\nแวน\nแว่น\nแวนดา\nแวบ\nแว็บ\nแวม\nแว็ม\nแวว\nแว่ว\nแวะ\nโว\nโว่\nโวการ\nโว่ง\nโวทาน\nโวย\nโว้ย\nโว้เว้\nโวหาร\nไว\nไว้\nไวกูณฐ์\nไวฑูรย์\nไวทย์\nไวน์\nไวพจน์\nไวยากรณ์\nไวยาวัจกร\nไวยาวัจมัย\nไวรัส\nไววรรณ\nไวษณพ\nไวโอลิน\nศก\nศกุน\nศกุนต์\nศกุนิ\nศกุนี\nศจี\nศตะ\nศตภิษัช\nศตวรรษ\nศตพรรษ\nศตกะ\nศนิ\nศพ\nศมนะ\nศมะ\nศยาม\nศยามล\nศร\nศรายุธ\nศราวรณ์\nศรรกรา\nศรวณะ\nศรวณีย์\nศรวิษฐา\nศรัณย์\nศรัณยู\nศรัท\nศรัทธา\nศรัย\nศราทธ์\nศราทธพรต\nศราพก\nศราวก\nศราวณะ\nศรี\nศรีตรัง\nศรุติ\nศฤคาล\nศฤงค์\nศฤงคาร\nศฤงคาริน\nศฤงคารี\nศลิษฏ์\nศลิษา\nศวะ\nศวัส\nศวา\nศวาน\nศศะ\nศศธร\nศศพินทุ์\nศศลักษณ์\nศศิ\nศศิน\nศศี\nศศิขัณฑ์\nศศิธร\nศศิมณฑล\nศศิวิมล\nศอ\nศอก\nศักดา\nศักดิ\nศักดิ์\nศักดินา\nศักติ\nศักย\nศักยภาพ\nศักย์\nศักยะ\nศักร\nศักรินทร์\nศักเรนทร์\nศักราช\nศังกร\nศัตรู\nศันสนะ\nศันสนีย์\nศัพท์\nศัยยา\nศัล\nศัลย์\nศัลยกรรม\nศัลยแพทย์\nศัลยศาสตร์\nศัสดร\nศัสตร\nศัสตรศาสตร์\nศัสตรา\nศัสตราวุธ\nศากตะ\nศากย\nศากยะ\nศากยพุทธ\nศากยมุนี\nศาฎก\nศาณ\nศานต์\nศานติ\nศาป\nศารท\nศารทูล\nศาริกา\nศาล\nศาลา\nศาศวัต\nศาสดา\nศาสตร์\nศาสตรา\nศาสตราจารย์\nศาสนา\nศาสนกิจ\nศาสนจักร\nศาสนธรรม\nศาสนบุคคล\nศาสนพิธี\nศาสนวัตถุ\nศาสนศาสตร์\nศาสนสถาน\nศาสนสมบัติ\nศาสนิกชน\nศาสนีย์\nศาสนูปถัมภก\nศาสน์\nศิกษก\nศิการ\nศิขร\nศิขริน\nศิขรี\nศิขัณฑ์\nศิคาล\nศิงขร\nศิงขริน\nศิตะ\nศิถี\nศิพิระ\nศิระ\nศิรประภา\nศิราภรณ์\nศิโรรัตน์\nศิโรเวฐน์\nศิรา\nศิรามพุช\nศิโรราบ\nศิลป\nศิลป์\nศิลปะ\nศิลปกร\nศิลปกรรม\nศิลปกิจ\nศิลปวัตถุ\nศิลปวิทยา\nศิลปศาสตร์\nศิลปศึกษา\nศิลปหัตถกรรม\nศิลปิน\nศิลปี\nศิลา\nศิวะ\nศิวโมกข์\nศิวลึงค์\nศิวเวท\nศิวาลัย\nศิศีระ\nศิษฎิ\nศิษฏ์\nศิษย์\nศิษยานุศิษย์\nศีขร\nศีต\nศีตกาล\nศีรษะ\nศีล\nศึก\nศึกษา\nศึกษาธิการ\nศึกษานิเทศก์\nศุกร์\nศุกรวรรณ\nศุกรวาร\nศุกระ\nศุกล\nศุกลปักษ์\nศุจิ\nศุทธะ\nศุทธิ\nศุนะ\nศุนิ\nศุภกร\nศุภเคราะห์\nศุภนิมิต\nศุภมัสดุ\nศุภมาตรา\nศุภมาส\nศุภอักษร\nศุภางค์\nศูกร\nศุลกากร\nศุลการักษ์\nศุลี\nศุษิร\nศูทร\nศูนย์\nศูนยวาท\nศูละ\nศูลิน\nเศรณี\nเศรษฐ\nเศรษฐ์\nเศรษฐกิจ\nเศรษฐศาสตร์\nเศรษฐี\nเศร้า\nเศลษ\nเศวต\nเศวตร\nเศวตัมพร\nเศษ\nเศาจ\nเศาร์\nเศารยะ\nเศิก\nเศียร\nโศก\nโศกา\nโศกาดูร\nโศกาลัย\nโศกี\nโศจิ\nโศธนะ\nโศภน\nโศภะ\nโศภา\nโศภิต\nโศภิน\nโศภิษฐ์\nโศภี\nโศรดา\nโศรตร\nโศลก\nไศล\nไศวะ\nษมา\nษัฏ\nษัฑ\nษัณ\nษัษ\nษัษฐะ\nษัษฐี\nโษฑศัน\nสก\nสกวาที\nสกฏะ\nสกทาคามิผล\nสกิทาคามิผล\nสกทาคามิมรรค\nสกิทาคามิมรรค\nสกทาคามี\nสกิทาคามี\nสกนธ์\nสกปรก\nสกรณีย์\nสกรรจ์\nสกรรมกริยา\nสกล\nสกลมหาสังฆปริณายก\nสกัด\nสกา\nสกาว\nสกี\nสกุณ\nสกุณา\nสกุณี\nสกุน\nสกุนต์\nสกุล\nสเกต\nสแกนเดียม\nสขะ\nสง\nส่ง\nสงกร\nสงกรานต์\nสงกา\nสงค์\nสงคร\nสงคราม\nสงเคราะห์\nสงฆ์\nสงบ\nสงวน\nส่งสการ\nสงสัย\nสงสาร\nสงสารวัฏ\nสงัด\nสง่า\nสฐะ\nสณฑ์\nสด\nสดมภ์\nสดับ\nสดับปกรณ์\nสดำ\nสดุดี\nสตะ\nสตน\nสตภิสชะ\nสตรอนเชียม\nสตริกนิน\nสตรี\nสตัฟฟ์\nสตัมภ์\nสตางค์\nสติ\nสติปัฏฐาน\nสตี\nสตู\nสตูป\nสเต๊ก\nสถบดี\nสถล\nสถวีระ\nสถาน\nสถานะ\nสถานี\nสถาบัน\nสถาปนา\nสถาปนิก\nสถาปัตยกรรม\nสถาปัตยกรรมศาสตร์\nสถาปัตยเรขา\nสถาปัตยเวท\nสถาพร\nสถาวร\nสถิต\nสถิตยศาสตร์\nสถิติ\nสถิร\nสถีรวาท\nสถุล\nสถูป\nสทิง\nสทึง\nสทุม\nสธนะ\nสาธุสะ\nสน\nส้น\nสนทนา\nสนทรรศ\nสนทรรศน์\nสนเทศ\nสนเท่ห์\nสนธยา\nสนธิ\nสนน\nสนม\nสนวน\nสนอง\nสนอบ\nสนอม\nสนะ\nสนัด\nสนั่น\nสนับ\nสนับทึบ\nสนับสนุน\nสนาน\nสนาม\nสนายุ\nสนิกะ\nสนิท\nสนิธ\nสนิม\nสนุก\nสนุกเกอร์\nสนุข\nสนุต\nสนุ่น\nสบ\nสบง\nสบถ\nสบัน\nสบาย\nสบู่\nสไบ\nสปริง\nสปอร์\nสปาเกตตี\nสเปกตรัม\nสเปกโทรสโกป\nสไปริลลัม\nสพาบ\nสภา\nสภาพ\nสภาวการณ์\nสภาวะ\nสม\nสมการ\nสมจารี\nสมดุล\nสมมูล\nส้ม\nสมญา\nสมณะ\nสมณบริขาร\nสมณศักดิ์\nสมณสารูป\nสมเด็จ\nสมถะ\nสมถยานิก\nสมถวิปัสสนา\nสมนาคุณ\nสมบัติ\nสมบุกสมบัน\nสมบูรณ์\nสมบูรณาญาสิทธิราชย์\nสมประดี\nสมปฤดี\nสมปฤๅดี\nส้มป่อย\nสมปัก\nสมผุส\nสมพง\nสมพงศ์\nสมพล\nสมพัตสร\nสมพาส\nสมเพช\nสมโพธน์\nสมโพธิ\nสมภพ\nสมภาร\nสมโภค\nสมโภช\nสมมต\nสมมติ\nสมมุติ\nสมมาตร\nส้มมือ\nสมโมท\nสมโยค\nสมร\nสมรด\nสมรรถ\nสมรรถนะ\nสมรรถภาพ\nสมรส\nสมฤดี\nสมฤติ\nสมวายะ\nสมเสร็จ\nสมอ\nสมอง\nสมะ\nสมัคร\nสมังคี\nสมัช\nสมัชชา\nสมัญญา\nสมัต\nสมัน\nสมันต์\nสมัย\nสมา\nสมาคม\nสมาจาร\nสมาชิก\nสมาทาน\nสมาธิ\nสมาน\nสมานฉันท์\nสมาบัติ\nสมาพันธรัฐ\nสมาส\nสม่ำเสมอ\nสมิง\nสมิต\nสมิติ\nสมิทธ์\nสมิทธิ\nสมี\nสมุก\nสมุจจัย\nสมุจเฉท\nสมุฏฐาน\nสมุด\nสมุทร\nสมุทรโคดม\nสมุทัย\nสมุน\nสมุนไพร\nสมุลแว้ง\nสมุห\nสมุห์\nสมุหกลาโหม\nสมุหเทศาภิบาล\nสมุหนาม\nสมุหนายก\nสโมธาน\nสโมสร\nสยด\nสยนะ\nสยบ\nสยมพร\nสยมภู\nสยอง\nสยอน\nสยัมวรา\nสยาม\nสยามานุสติ\nสยามินทร์\nสยาย\nสยิว\nสยิ้ว\nสยุมพร\nสยุมภู\nสร\nสรง\nสร่ง\nสรณะ\nสรณคมน์\nสรณาคมน์\nสรณตรัย\nสรตะ\nสรทะ\nสรนุก\nสรเนาะ\nสรไน\nสรเพชญ\nสรภะ\nสรภัญญะ\nสรภู\nสรม\nสรร\nสรรค์\nสรรพ\nสรรพคุณ\nสรรพนาม\nสรรพสามิต\nสรรพัชญ\nสรรพากร\nสรรพางค์\nสรรเพชญ\nสรรเพชุดา\nสรรเสริญ\nสรลอน\nสรเลข\nสรวง\nสรวม\nสรวล\nสรเสริญ\nสร้อย\nสระ\nสระกอ\nสระท้อน\nสระพรั่ง\nสระอาด\nสรั่ง\nสรัสวดี\nสร่าง\nสร้าง\nสราญ\nสรี้\nสรีระ\nสรีรกิจ\nสรีรธาตุ\nสรีรวิทยา\nสรีรศาสตร์\nสรีรังคาร\nสรีรางคาร\nสรุป\nสโรช\nสโรชะ\nสฤก\nสฤต\nสฤษฎิ\nสฤษฎี\nสฤษฏ์\nสฤษดิ์\nสลด\nสลบ\nสลวน\nสลวย\nสลอด\nสลอน\nสลอย\nสละ\nสลัก\nสลัด\nสลัดได\nสลับ\nสลัว\nสลา\nสลาก\nสลาง\nสล้าง\nสลาด\nสลาตัน\nสลาบ\nสลาย\nสลิด\nสลิล\nสลึก\nสลึง\nสลุต\nสลุบ\nสลุมพร\nสแลง\nสวการย์\nสวภาพ\nสวราชย์\nสวก\nส้วง\nสวด\nสวน\nสวนะ\nสวนาการ\nส่วน\nสวนิต\nสวบ\nสวม\nส้วม\nสวย\nส่วย\nส้วย\nสวยม\nสวรรค\nสวรรค์\nสวรรคต\nสวรรคาลัย\nสวรรยา\nสวระ\nสวะ\nสวัสดิ\nสวัสดิ์\nสวัสดิการ\nสวัสดิภาพ\nสวัสดิมงคล\nสวัสดี\nสวัสติ\nสวาตี\nสวัสติกะ\nสวา\nสวาปาม\nสวาคตะ\nสวาง\nสว่าง\nสวาด\nสวาดิ\nสวาท\nสว่าน\nสว้าน\nสวาบ\nสวามิ\nสวามี\nสวามินี\nสวาย\nสวาสดิ์\nสวาหะ\nสวิง\nสวิญญาณกทรัพย์\nสวิตช์\nสสาร\nสสุระ\nสสุรี\nสหกรณ์\nสหการ\nสหจร\nสหชาต\nสหชาติ\nสหธรรม\nสหธรรมิก\nสหประชาชาติ\nสหพันธ์\nสหพันธรัฐ\nสหภาพ\nสหศึกษา\nสหัช\nสหัมบดี\nสหัส\nสหัสสะ\nสหัสธารา\nสหัสนัยน์\nสหัสเนตร\nสหัสรังสี\nสหัสา\nสหาย\nสอ\nส่อ\nสอง\nส่อง\nส้อง\nสอด\nสอน\nส่อน\nสอบ\nสอพลอ\nส้อม\nสอย\nสะ\nสะกด\nสะกอ\nสะกาง\nสะการะ\nสะกิด\nสะกิดสะเกา\nสะเก็ด\nสะแก\nสะคร้อ\nสะคราญ\nสะค้าน\nสะเงาะสะแงะ\nสะดม\nสะดวก\nสะดิ้ง\nสะดึง\nสะดือ\nสะดุ้ง\nสะดุด\nสะเด็ด\nสะเดา\nสะเดาะ\nสะตอ\nสะตาหมัน\nสะตึ\nสะตือ\nสะตุ\nสะเต๊ะ\nสะโตก\nสะทก\nสะท้อน\nสะท้าน\nสะทึก\nสะเทิน\nสะเทิ้น\nสะเทือน\nสะเทื้อน\nสะบะ\nสะบัก\nสะบักสะบอม\nสะบัด\nสะบัดสะบิ้ง\nสะบั้น\nสะบันงา\nสะบ้า\nสะบู\nสะแบง\nสะเปะสะปะ\nสะพรั่ง\nสะพรึงกลัว\nสะพรึบ\nสะพรึ่บ\nสะพัก\nสะพัง\nสะพัด\nสะพั้น\nสะพาน\nสะพาย\nสะเพร่า\nสะโพก\nสะเภา\nสะใภ้\nสะโมง\nสะระตะ\nสะระแหน่\nสะลาง\nสะลาบ\nสะลึมสะลือ\nสะวี้ดสะว้าด\nสะสม\nสะสวย\nสะสาง\nสะเหล่อ\nสะอาง\nสะอาด\nสะอ้าน\nสะอิ้ง\nสะอิดสะเอียน\nสะอึก\nสะอื้น\nสะเอ้ง\nสะเอว\nสะเออะ\nสะโอดสะอง\nสะไอ\nสัก\nสักกะ\nสักยะ\nสักกัจจะ\nสักกายทิฐิ\nสักการ\nสักการะ\nสักขี\nสักวา\nสักหลาด\nสัค\nสัคคะ\nสั่ง\nสังกร\nสังกรณี\nสังกรประโยค\nสังกะตัง\nสังกะวัง\nสังกะวาด\nสังกะสี\nสังกัด\nสังกัปปะ\nสังกา\nสังการ\nสังกาศ\nสังกิเลส\nสังเกต\nสังข์\nสังขกร\nสังขตธรรม\nสังขตะ\nสังขยา\nสังขลิก\nสังขลิกา\nสังขาร\nสังขารา\nสังเขป\nสังค์\nสังคญาติ\nสังคม\nสังคหะ\nสังคัง\nสังคายนา\nสังคายนาย\nสังคีต\nสังคีติ\nสังเค็ด\nสังเคราะห์\nสังฆกรรม\nสังฆการี\nสังฆเถระ\nสังฆทาน\nสังฆนายก\nสังฆปาโมกข์\nสังฆภัต\nสังฆเภท\nสังฆมณฑล\nสังฆมนตรี\nสังฆราช\nสังฆสภา\nสังฆาณัติ\nสังฆาฏิ\nสังฆาทิเสส\nสังฆาธิการ\nสังฆานุสติ\nสังฆาวาส\nสังยุตนิกาย\nสังโยค\nสังโยชน์\nสังวร\nสังวัจฉระ\nสังวัธยาย\nสังวาล\nสังวาส\nสังเวคะ\nสังเวช\nสังเวชนียสถาน\nสังเวย\nสังเวียน\nสังสกฤต\nสังสการ\nสังสนทนา\nสั่งสนทนา\nสังสรรค์\nสังสารวัฏ\nสังสิทธิ\nสังสุทธ์\nสังสุทธิ\nสังหร\nสังหรณ์\nสังหาร\nสังหาริมทรัพย์\nสังหาริมะ\nสังหิต\nสัจ\nสัจกิริยา\nสัจจะ\nสัจญาณ\nสัจธรรม\nสัจนิยม\nสัจพจน์\nสัชฌะ\nสัชฌุ\nสัญจร\nสัญเจตนา\nสัญชาตญาณ\nสัญชาติ\nสัญฌา\nสัญญา\nสัญญาณ\nสัญญี\nสัญโญชน์\nสัญนิยม\nสัญประกาศ\nสัญลักษณ์\nสัฐิ\nสัณฐาน\nสัณฐิติ\nสัณฑ์\nสัณห์\nสัด\nสัดจอง\nสัต\nสัตตะ\nสัตตาหกรณียะ\nสัตตาหกาลิก\nสัตมวาร\nสัตสดก\nสัตตบงกช\nสัตตบรรณ\nสัตตบุษย์\nสัตตู\nสัตถันดร\nสัตถา\nสัตถิ\nสัตถุ\nสัตถุศาสนา\nสัตบรรณ\nสัตย์\nสัตยพรต\nสัตยวาที\nสัตยาเคราะห์\nสัตยาธิษฐาน\nสัตยาบัน\nสัตว์\nสัตวชาติ\nสัตวบาล\nสัตวแพทย์\nสัตววิทยา\nสัตวา\nสัทธรรม\nสัทธา\nสัทธาจริต\nสัทธาธิกะ\nสัทธินทรีย์\nสัทธิงวิหาริก\nสัทธิวิหาริก\nสัทวิทยา\nสัทศาสตร์\nสัทอักษร\nสัน\nสั่น\nสั้น\nสันดาน\nสันดาป\nสันโดษ\nสันต์\nสันตติ\nสันตะปาปา\nสันตะวา\nสันติ\nสันตุฏฐี\nสันถวไมตรี\nสันถวะ\nสันถัต\nสันถาร\nสันทนะ\nสันทะ\nสันทัด\nสันทัสนะ\nสันทาน\nสันทิฐิก\nสันทิส\nสันเทหะ\nสันธาน\nสันนิธิ\nสันนิบาต\nสันนิวาส\nสันนิษฐาน\nสันสกฤต\nสับ\nสับปลับ\nสับปลี้\nสับปะรด\nสัปคับ\nสัปดาห์\nสัปดาหะ\nสัปดน\nสัปตศก\nสัปทน\nสัปปะ\nสัปปิ\nสัปปุริส\nสัปปุรุษ\nสัประยุทธ์\nสัปหงก\nสัปเหร่อ\nสัพ\nสัพพะ\nสัพพัญญู\nสัพเพเหระ\nสัพยอก\nสัมบูรณ์\nสัมปชัญญะ\nสัมปทา\nสัมปทาน\nสัมปยุต\nสัมปโยค\nสัมประสิทธิ์\nสัมประหาร\nสัมปรายภพ\nสัมปรายิกภพ\nสัมปัตติ\nสัมผัปลาป\nสัมผัปลาปะ\nสัมผัส\nสัมพล\nสัมพหุลา\nสัมพัจฉรฉินท์\nสัมพัตสร\nสัมพัทธ์\nสัมพันธ์\nสัมพันธน์\nสัมพันธภาพ\nสัมพันธมิตร\nสัมพันธไมตรี\nสัมพาหะ\nสัมพุทธ\nสัมพุทธะ\nสัมโพธิ\nสัมภวะ\nสัมภเวสี\nสัมภัต\nสัมภัตตะ\nสัมภาระ\nสัมภาษณ์\nสัมโภคกาย\nสัมมนา\nสัมมัปธาน\nสัมมา\nสัมโมทนียกถา\nสัมฤทธิ\nสัมฤทธิ์\nสัมฤทธิศก\nสัยน์\nสัลเลข\nสัสดี\nสัสตทิฐิ\nสัสสะ\nสัสสุ\nสัสสู\nสา\nส่า\nสาก\nสากรรจ์\nสากล\nสากัจฉา\nสากัลย์\nสากิยะ\nสาเก\nสาขา\nสาคร\nสาคเรศ\nสาคู\nสาง\nส้าง\nสาชล\nสาฎก\nสาฏิก\nสาณี\nสาด\nสาไถย\nสาทร\nสาทิส\nสาทุ\nสาโท\nสาธก\nสาธยะ\nสาธยาย\nสาธารณะ\nสาธารณชน\nสาธารณประโยชน์\nสาธารณภัย\nสาธารณรัฐ\nสาธารณสถาน\nสาธารณสมบัติ\nสาธารณสุข\nสาธารณูปการ\nสาธารณูปโภค\nสาธารณ์\nสาธิต\nสาธุ\nสาน\nส่าน\nสานุ\nสานู\nสานุศิษย์\nสาบ\nสาบสูญ\nสาบาน\nสาป\nสาปไตย\nสาม\nสามชุก\nสามเณร\nสามเณรี\nสามนต์\nสามนตราช\nสามยทรัพย์\nสามล\nสามหาว\nสามะ\nสามัคคี\nสามัญ\nสามัตถิยะ\nสามานย์\nสามานยนาม\nสามารถ\nสามิต\nสามินี\nสามิภักดิ์\nสามี\nสามีจิกรรม\nสาย\nส่าย\nส้าย\nสายชู\nสายัณห์\nสายาห์\nสาร\nสารคดี\nสารธรรม\nสารนิเทศ\nสารบบ\nสารบรรณ\nสารบัญ\nสารบาญ\nสารบาญชี\nสารประโยชน์\nสารสนเทศ\nสารทุกข์\nสารถี\nสารท\nสารพัด\nสารพัน\nสารพางค์\nสารภาพ\nสารภี\nสารวัตร\nสาระ\nสาระแน\nสาระพา\nสาระยำ\nสาระวารี\nสาระสะมา\nสารัตถประโยชน์\nสารัตถศึกษา\nสารัตถะ\nสารัทธ์\nสารัมภ์\nสาราณียกร\nสาราณียธรรม\nสาราณียะ\nสารานุกรม\nสารีริกธาตุ\nสารูป\nสาโรช\nสาละ\nสาละวน\nสาลิ\nสาลิกา\nสาลินี\nสาลี\nสาลี่\nสาลู\nสาโลหิต\nสาว\nสาวก\nสาวิกา\nสาวิตร\nสาวิตรี\nสาสน\nสาสน์\nสาส์น\nสาสนา\nสาสม\nสาหร่าย\nสาหรี\nส่าหรี\nสาหัส\nสาเหตุ\nสาแหรก\nสำ\nสำส่อน\nส่ำ\nสำคัญ\nสำซ่าง\nสำแดง\nสำทับ\nสำนวน\nสำนอง\nสำนัก\nสำนาน\nสำนึก\nสำนึง\nสำเนา\nสำเนียง\nสำบัด\nสำปะลอ\nสำปะหลัง\nสำปั้น\nสำปันนี\nสำเภา\nสำมะงา\nสำมะโน\nสำมะลอ\nสำมะเลเทเมา\nสำมะหา\nสำรด\nสำรวจ\nสำรวม\nสำรวย\nสำรวล\nสำรอก\nสำรอง\nสำรับ\nสำราก\nสำราญ\nสำริด\nสำเร็จ\nสำเรา\nสำเริง\nสำโรง\nสำลัก\nสำลาน\nสำลี\nสำแลง\nสำหรวด\nสำหรับ\nสำหา\nสำเหนียก\nสำเหร่\nสำออย\nสำอาง\nสิ\nสิกข์\nสิข\nสิกขมานา\nสิกขา\nสิขร\nสิขรี\nสิขเรศ\nสิขา\nสิขานล\nสิขี\nสิคาล\nสิง\nสิ่ง\nสิงขร\nสิงค์\nสิงคลิ้ง\nสิงคลี\nสิงคาร\nสิงคาล\nสิงคี\nสิงโต\nสิงห์\nสิงหนาท\nสิงหบัญชร\nสิงหรา\nสิงหราช\nสิงหาคม\nสิงหาสน์\nสิงหล\nสิญจน์\nสิตะ\nสิตางศุ์\nสิถิล\nสิทธ์\nสิทธัตถะ\nสิทธา\nสิทธาจารย์\nสิทธารถ\nสิทธิ\nสิทธิ์\nสิทธิการิยะ\nสิธยะ\nสิน\nสิ้น\nสินเทา\nสินธพ\nสินธุ\nสินธุ์\nสินธุระ\nสินธู\nสินเธาว์\nสินาด\nสินิทธ์\nสินี\nสิเนรุ\nสิเนหก\nสิเนหะ\nสิเนหา\nสิเน่หา\nสิบ\nสิปปะ\nสิมพลี\nสิระ\nสิโรดม\nสิโรตม์\nสิริ\nสิรี\nสิลา\nสิว\nสิ่ว\nสิวะ\nสิวาลัย\nสิวิกา\nสี\nสี่\nสี้\nสีกา\nสีกุน\nสีข้าง\nสีด\nสีดอ\nสีดา\nสีตลรัศมี\nสีตโลทก\nสีโตทก\nสีทันดร\nสีมันต์\nสีมา\nสีละมัน\nสีวิกา\nสีสอ\nสีสะ\nสีสา\nสีสุก\nสีเสียด\nสีห์\nสีหนาท\nสีหบัญชร\nสีหราช\nสีหไสยา\nสีหไสยาสน์\nสีหะ\nสึก\nสึง\nสืบ\nสื่อ\nสุ\nสุก\nสุกข์\nสุกร\nสุกรม\nสุกำศพ\nสุกียากี้\nสุข\nสุขา\nสุขาภิบาล\nสุขารมณ์\nสุขาวดี\nสุขิน\nสุขี\nสุขุม\nสุขุมาล\nสุโข\nสุคต\nสุคติ\nสุคนธ\nสุคนธ์\nสุคนธชาติ\nสุคนธรส\nสุคันธ์\nสุคันธรส\nสุงกะ\nสุงกากร\nสุงสิง\nสุงสุมาร\nสุจริต\nสุจหนี่\nสุจิ\nสุจิต\nสุจิตร\nสุชน\nสุชัมบดี\nสุชา\nสุชาดา\nสุญ\nสุญญากาศ\nสุญตา\nสุญนิยม\nสุณ\nสุณิสา\nสุด\nสุดา\nสุต\nสุตตนิบาต\nสุตตะ\nสุตตันตปิฎก\nสุตตันตะ\nสุติ\nสุทธ\nสุทธ์\nสุทธาวาส\nสุทธิ\nสุทรรศน์\nสุทัศน์\nสุธา\nสุธาโภชน์\nสุธารส\nสุธาสินี\nสุธาสี\nสุธี\nสุนทร\nสุนทรี\nสุนทรียภาพ\nสุนทรียศาสตร์\nสุนทรียะ\nสุนัข\nสุนันท์\nสุโนก\nสุบดี\nสุบรรณ\nสุบิน\nสุปรีดิ์\nสุปรีย์\nสุปาณี\nสุพพัต\nสุพรรณ\nสุพรรณบัฏ\nสุพรรณภาชน์\nสุพรรณราช\nสุพรรณศรี\nสุพรรณถัน\nสุพรรณิการ์\nสุภร\nสุภัค\nสุภา\nสุภาพ\nสุภาษิต\nสุม\nสุ่ม\nสุมทุม\nสุมน\nสุมนะ\nสุมนัส\nสุมนา\nสุ้มเสียง\nสุมะ\nสุมาลี\nสุเมธ\nสุเมรุ\nสุรคต\nสุรเชษฐ์\nสุรบดี\nสุรภาพ\nสุรโลก\nสุรสีหนาท\nสุรเสียง\nสุรงค์\nสุรังค์\nสุรภี\nสุรัติ\nสุรัสวดี\nสุรา\nสุรางค์จำเรียง\nสุรางคนา\nสุรางคนางค์\nสุรารักษ์\nสุราลัย\nสุรินทร์\nสุรินทราหู\nสุริยะ\nสุริยกันต์\nสุริยกานต์\nสุริยการ\nสุริยกาล\nสุริยคติ\nสุริยคราส\nสุริยมณฑล\nสุริยวงศ์\nสุริยง\nสุริยา\nสุริเยนทร์\nสุริเยศ\nสุริโย\nสุริยน\nสุริยัน\nสุริยุปราคา\nสุรีย์\nสุรุ่ยสุร่าย\nสุลต่าน\nสุวคนธ์\nสุวภาพ\nสุวรรณ\nสุวรรณภูมิ\nสุวะ\nสุวาน\nสุวินัย\nสุวิมล\nสุษิระ\nสุสาน\nสุหนัต\nสุหร่ง\nสุหร่าย\nสุหฤท\nสุหัท\nสุเหร่า\nสู\nสู่\nสู้\nสูง\nสูจิ\nสูจิบัตร\nสูญ\nสูด\nสูต\nสูตร\nสูติ\nสูติกรรม\nสูตินรีเวช\nสูติบัตร\nสูติแพทย์\nสูติศาสตร์\nสูท\nสูทกรรม\nสูทศาสตร์\nสูบ\nสูปะ\nสูร\nสูรย์\nสูรยกานต์\nสูริ\nสูสี\nเส\nเสก\nเสกขบุคคล\nเสกขะ\nเสขบุคคล\nเสขะ\nเส็ง\nเส้ง\nเส็งเคร็ง\nเสงี่ยม\nเสฏฐี\nเสณี\nเสด\nเสด็จ\nเสตุ\nเสถียร\nเสทะ\nเสโท\nเสน\nเส้น\nเสนง\nเสน่ง\nเสน่ห์\nเสนหา\nเสน่หา\nเสนอ\nเสนะ\nเสนา\nเสนาธิการ\nเสนาบดี\nเสน่า\nเสนากุฎ\nเสนางค์\nเสนางคนิกร\nเสนานี\nเสนาสนะ\nเสนาะ\nเสนี\nเสนีย์\nเสนียะ\nเสนียด\nเสบย\nเสบียง\nเสพ\nเสพย์\nเสเพล\nเสภา\nเสม็ด\nเสมหะ\nเสมอ\nเสมา\nเสมียน\nเสมือน\nเสย\nเสร็จ\nเสริด\nเสริม\nเสรี\nเสลด\nเสลบรรพต\nเสลา\nเสลี่ยง\nเสลือกสลน\nเสโล\nเสวก\nเสวกามาตย์\nเสวนะ\nเสวนา\nเสวย\nเสวียน\nเสสรวง\nเสสรวล\nเสา\nเส้า\nเสาร์\nเสารภย์\nเสารี\nเสาวคนธ์\nเสาวธาร\nเสาวภา\nเสาวภาคย์\nเสาวภาพ\nเสาวรภย์\nเสาวรส\nเสาวลักษณ์\nเสาวณิต\nเสาวนะ\nเสาวนา\nเสาวนีย์\nเสาหฤท\nเสาะ\nเสาะแสะ\nเสิร์จ\nเสิร์ฟ\nเสีย\nเสียง\nเสี่ยง\nเสียด\nเสี้ยน\nเสียบ\nเสียม\nเสี่ยม\nเสี้ยม\nเสียว\nเสี่ยว\nเสี้ยว\nเสือ\nเสื่อ\nเสื้อ\nเสือก\nเสื่อม\nแส\nแส่\nแส้\nแสก\nแสง\nแสด\nแสดง\nแสตมป์\nแสน\nแสนย์\nแสนยากร\nแสนยานุภาพ\nแสบ\nแสม\nแสยก\nแสยง\nแสยะ\nแสรก\nแสร้ง\nแสลง\nแสล้ม\nแสวง\nแสะ\nโสก\nโสกโดก\nโสกันต์\nโสโครก\nโสณฑ์\nโสณิ\nโสณี\nโสด\nโสดก\nโสดม\nโสดา\nโสดาบัน\nโสดาปัตติผล\nโสดาปัตติมรรค\nโสต\nโสตทัศนวัสดุ\nโสตทัศนอุปกรณ์\nโสตทัศนูปกรณ์\nโสตินทรีย์\nโสตถิ\nโสทก\nโสทร\nโสธก\nโสธนะ\nโสน\nโสภณ\nโสภา\nโสภี\nโสภิณี\nโสเภณี\nโสม\nโสมนัส\nโสมม\nโสมย์\nโสร่ง\nโสรจ\nโสรวาร\nโสโร\nโสวรรณ\nโสหุ้ย\nโสฬส\nใส\nใส่\nไส\nไส้\nไสย\nไสยา\nไสยาสน์\nไสร้\nไสว\nหก\nหกคะเมน\nหง\nหงก\nหงส์\nหงสบาท\nหงสรถ\nหงอ\nหงอก\nหง่อง\nหงองแหงง\nหงอด\nหงอน\nหง่อม\nหงอย\nหง่อย\nหงัก\nหงับ\nหง่าง\nหงาย\nหง่าว\nหงำ\nหงิก\nหงิง\nหงิม\nหงึก\nหงุงหงิง\nหงุดหงิด\nหงุบ\nหงุ่ย\nหญ้า\nหญ้าฝรั่น\nหญ้ายายเภา\nหญิง\nหญิบ\nหด\nหตะ\nหทัย\nหน\nหนวก\nหน่วง\nหนวด\nหน่วย\nหน่วยกิต\nหนอ\nหน่อ\nหนอก\nหนอง\nหนอน\nหนอนตายหยาก\nหน่อย\nหน็อยแน่\nหนัก\nหนัง\nหนังสติ๊ก\nหนังสือ\nหนั่น\nหนับ\nหนา\nหน้า\nหน่าง\nหนาด\nหนาน\nหนาม\nหน่าย\nหนาว\nหนำ\nหนำเลี้ยบ\nหนี\nหนี้\nหนีบ\nหนึก\nหนึ่ง\nหนึบ\nหนืด\nหนุ\nหนุน\nหนุบ\nหนุ่ม\nหนุ่ย\nหนู\nห่ม\nหมก\nหมด\nหม่น\nหมวก\nหมวด\nหมวน\nหมอ\nหม่อ\nหม้อ\nหมอก\nหมอง\nหม่อง\nหมอน\nหม่อน\nหมอบ\nหม่อม\nหมอย\nหม้อห้อม\nหมัก\nหมักหมม\nหมัด\nหมัน\nหมั่น\nหมั้น\nหมับ\nหมา\nหม่า\nหมาก\nหมากฮอส\nหมาง\nหมาด\nหมามุ่ย\nหมามุ้ย\nหมาย\nหม้าย\nหมาร่า\nหม่ำ\nหม้ำ\nหมิ่น\nหมี\nหมี่\nหมึก\nหมืน\nหมื่น\nหมุด\nหมุน\nหมุบ\nหมุบหมับ\nหมุบหมิบ\nหมุ่ย\nหมุยขาว\nหมู\nหมู่\nหมูหริ่ง\nหยก\nหย่ง\nหยด\nหยวก\nหยวบ\nหยอก\nหยอกเอิน\nหย็อกหย็อย\nหยอง\nหย็อง\nหย่อง\nหย็องกรอด\nหย็องแหย็ง\nหยอด\nหยอน\nหย่อน\nหย่อม\nหย็อมแหย็ม\nหย็อย\nหย่อย\nหยัก\nหยักไย่\nหยักเหยา\nหยัง\nหยั่ง\nหยังหยัง\nหยัด\nหยัน\nหยับ\nหยั่วเมือง\nหย่า\nหยากเยื่อ\nหยากไย่\nหยาด\nหยาบ\nหยาม\nหยาว\nหย้าว\nหยำเป\nหยำเหยอะ\nหยำแหยะ\nหยิก\nหยิ่ง\nหยิบ\nหยิม\nหยี\nหยี่\nหยุกหยิก\nหยุด\nหยุ่น\nหยุบ\nหยุมหยิม\nหยูกยา\nหโยดม\nหรคุณ\nหรณะ\nหรดาล\nหรดี\nหรรษ์\nหรรษา\nหรอ\nหรอก\nหร็อมแหร็ม\nหรอย\nหระ\nหรับ\nหรา\nหริ\nหริ่ง\nหริณะ\nหริต\nหริตกี\nหรีตกี\nหรี่\nหรีด\nหรือ\nหรุบ\nหรุบรู่\nหรุบหรู่\nหรุ่ม\nหรู\nหรูหรา\nหฤทัย\nหฤทย์\nหฤษฎ์\nหฤษฎี\nหฤหรรษ์\nหฤโหด\nหลง\nหลงใหล\nหลงจู๊\nหลด\nหลน\nหล่น\nหลบ\nหล่ม\nหลวง\nหลวม\nหลอ\nหล่อ\nหลอก\nหลอด\nหลอน\nหล็อน\nหล่อน\nหลอม\nหละ\nหละหลวม\nหลัก\nหลัง\nหลั่ง\nหลัด\nหลั่น\nหลับ\nหลัว\nหลา\nหล้า\nหลาก\nหลาน\nหลาบ\nหลาม\nหลาย\nหลาว\nหลิ่ง\nหลิท\nหลิน\nหลิม\nหลิว\nหลิ่ว\nหลี\nหลีก\nหลีโก\nหลีบ\nหลีฮื้อ\nหลืบ\nหลุกหลิก\nหลุด\nหลุน\nหลุบ\nหลุม\nหลุมพอ\nหลุมพี\nหลู่\nหวง\nห่วง\nห้วง\nหวด\nหวน\nห้วน\nหวย\nห้วย\nหวอ\nหวอด\nหวะ\nหวัง\nหวัด\nหวั่น\nหวันยิหวา\nหวัว\nหวัวร่อ\nหวัวเราะ\nหวา\nหว่า\nหว้า\nหวาก\nหว่าง\nหวาด\nหวาน\nหว่าน\nหวาม\nหวาย\nหวำ\nหวิด\nหวิว\nหวี\nหวี่\nหวีด\nหวือ\nหวุดหวิด\nหวูด\nหอ\nห่อ\nห้อ\nหอก\nหอง\nห้อง\nหอน\nห่อน\nหอบ\nหอม\nห้อม\nหอย\nห้อย\nหะ\nหะยี\nหะหาย\nหัก\nหัจญ์\nหัจญี\nหัช\nหัฏฐะ\nหัด\nหัต\nหัตถ์\nหัตถกรรม\nหัตถการ\nหัตถกิจ\nหัตถบาส\nหัตถพันธ์\nหัตถาภรณ์\nหัตถศาสตร์\nหัตถศิลป์\nหัตถศึกษา\nหัตถาจารย์\nหัตถินี\nหัตถี\nหัน\nหั่น\nหั้น\nหันตรา\nหับ\nหัย\nหัว\nหัวร่อ\nหัวเราะ\nหัส\nหัสดิน\nหัสดี\nหัสต์\nหัสตะ\nหา\nห่า\nห้า\nหาก\nหาง\nห่าง\nห้าง\nหาญ\nหาด\nห่าน\nหาบ\nหาม\nห่าม\nห้าม\nหาย\nหายใจ\nหายนะ\nหาร\nหารือ\nหาว\nห้าว\nหาสะ\nหำ\nห้ำ\nหิ้ง\nหิงคุ\nหิงสา\nหิงห้อย\nหิ่งห้อย\nหิ่งหาย\nหิด\nหิต\nหิตานุหิตประโยชน์\nหิน\nหิมพาน\nหิมพานต์\nหิมวัต\nหิมวันต์\nหิมวา\nหิมะ\nหิมาลัย\nหิรัญ\nหิรัญญิการ์\nหิรัญบัฏ\nหิรัณย์\nหิรัณยรัศมี\nหิริ\nหิว\nหิ้ว\nหี\nหีด\nหีนยาน\nหีบ\nหึ\nหึง\nหึ่ง\nหึงสา\nหืด\nหืน\nหื่น\nหือ\nหื้อ\nหุง\nหุน\nหุ่น\nหุ้น\nหุนหัน\nหุบ\nหุ้ม\nหุยฮา\nหู\nหู่\nหูก\nหูด\nเห\nเห่\nเหง\nเหง่ง\nเหงา\nเหง้า\nเหงื่อ\nเหงือก\nเห็จ\nเห็ด\nเหติ\nเหตุ\nเห็น\nเหน่ง\nเหนงนายพราน\nเหน็ดเหนื่อย\nเหน็บ\nเหน่อ\nเห็นอ้ม\nเหนอะ\nเหนอะหนะ\nเหน้า\nเหนาะ\nเหนียง\nเหนี่ยง\nเหนี่ยน\nเหนียม\nเหนียว\nเหนี่ยว\nเหนือ\nเหนื่อย\nเห็บ\nเหม\nเหม่\nเหม็ง\nเหม่ง\nเหม็น\nเหมวดี\nเหม่อ\nเหมันต์\nเหมันตฤดู\nเหมา\nเหมายัน\nเหมาะ\nเหมียว\nเหมี่ยว\nเหมือง\nเหมือด\nเหมือน\nเหมื่อย\nเหย\nเหยง\nเหย่อย\nเหยา\nเหย่า\nเหย้า\nเหยาะ\nเหยาะแหยะ\nเหยิง\nเหยิบ\nเหยียด\nเหยียบ\nเหยี่ยว\nเหยื่อ\nเหยือก\nเหรอ\nเหรอะ\nเหรัญญิก\nเหรา\nเหราะ\nเหรียญ\nเหล่\nเหล็ก\nเหลน\nเหลว\nเหลอ\nเหลา\nเหล่า\nเหล้า\nเหลาะแหละ\nเหลิง\nเหลิงเจิ้ง\nเหลียน\nเหลี่ยม\nเหลียว\nเหลือ\nเหลือก\nเหลือง\nเหลือบ\nเหลือม\nเหลื่อม\nเหว\nเหว่\nเหวง\nเหวย\nเหวอะ\nเหวอะหวะ\nเหวี่ยง\nเห่อ\nเหอะ\nเหะ\nเหะหะ\nเหา\nเห่า\nเหาะ\nเหิน\nเหิม\nเหี้ย\nเหียง\nเหียน\nเหี้ยน\nเหี้ยม\nเหี่ยว\nเหื่อ\nเหือด\nแห\nแห่\nแห้\nแหก\nแหง\nแหง่\nแห่ง\nแห้ง\nแหงแก๋\nแหง่ง\nแหงน\nแหน\nแห้น\nแหนง\nแหนบ\nแหนม\nแหบ\nแหม\nแหม่\nแหม่ม\nแหมะ\nแหย\nแหย่\nแหยง\nแหย่ง\nแหยม\nแหย็ม\nแหยะ\nแหล่\nแหลก\nแหล่ง\nแหลน\nแหลม\nแหละ\nแหว\nแห้ว\nแหวก\nแหว่ง\nแหวด\nแหวน\nแหวะ\nแหะ\nโห่\nโหง\nโหด\nโหน\nโหนก\nโหน่ง\nโหม\nโหม่ง\nโหมด\nโหย\nโหยกเหยก\nโหยง\nโหย่ง\nโหร\nโหรง\nโหรงเหรง\nโหรดาจารย์\nโหระพา\nโหรา\nโหราจารย์\nโหราศาสตร์\nโหล\nโหล่\nโหลงโจ้ง\nโหว\nโหว่\nโหว้\nโหวกเหวก\nโหวง\nโหวด\nโหวต\nให้\nใหญ่\nใหม่\nไห\nไห่\nไห้\nไหน\nไหม\nไหม้\nไหรณย์\nไหล\nไหล่\nไหว\nไหว้\nไหหลำ\nอก\nอกตเวทิตา\nอกตเวที\nอกตัญญุตา\nอกตัญญู\nอกนิษฐ์\nอกรณีย์\nอกรรมกริยา\nอกัปปิยวัตถุ\nอกัปปิยะ\nอกุศล\nอคติ\nอคาธ\nอโฆษะ\nองก์\nองค์\nองคชาต\nองคมนตรี\nองครักษ์\nองคาพยพ\nองคุลี\nองศ์\nองศา\nองอาจ\nองุ่น\nอจลา\nอจินตา\nอจินไตย\nอจิระ\nอเจลก\nอเจละ\nอชะ\nอชิน\nอชินี\nอชิระ\nอฏวี\nอณิ\nอณู\nอโณทัย\nอด\nอดิถี\nอดิเทพ\nอดิเรก\nอดิศร\nอดิศวร\nอดิศัย\nอดีต\nอดุล\nอดุลย์\nอติ\nอติชาต\nอติมานะ\nอติราช\nอติเรก\nอติสาร\nอถรรพเวท\nอาถรรพเวท\nอทระ\nอทินนาทาน\nอธรรม\nอธิ\nอธิกมาส\nอธิกรณ์\nอธิกวาร\nอธิกสุรทิน\nอธิการ\nอธิคม\nอธิฏฐาน\nอธิบดี\nอธิบาย\nอธิป\nอธิปไตย\nอธิมาตร\nอธิมุตติ\nอธิโมกข์\nอธิราช\nอธิวาส\nอธิวาสนะ\nอธิศีล\nอธิษฐาน\nอธึก\nอ้น\nอนงค์\nอนงคณะ\nอนงคเลขา\nอนธการ\nอนนต์\nอนยะ\nอนรรฆ\nอนรรถ\nอนล\nอนวัช\nอนัญ\nอนัตตา\nอนันต์\nอนันตริยกรรม\nอนัม\nอนาคต\nอนาคามิผล\nอนาคามิมรรค\nอนาคามี\nอนาจาร\nอนาถ\nอนาถา\nอนาทร\nอนาธิปไตย\nอนามัย\nอนามิกา\nอนารยชน\nอนารยธรรม\nอนารยะ\nอนาลัย\nอนำ\nอนิจ\nอนิจจัง\nอนิจจา\nอนิฏฐารมณ์\nอนิยต\nอนิยม\nอนิล\nอนิวรรต\nอนิวรรตน์\nอนีกะ\nอนีจะ\nอนึก\nอนึ่ง\nอนุ\nอนุกร\nอนุกรม\nอนุกรรมการ\nอนุกระเบียด\nอนุกาชาด\nอนุการ\nอนุกูล\nอนุคามิก\nอนุเคราะห์\nอนุจร\nอนุช\nอนุชน\nอนุชา\nอนุชาต\nอนุชิต\nอนุญาต\nอนุญาโตตุลาการ\nอนุตร\nอนุเถระ\nอนุทิน\nอนุบท\nอนุบาล\nอนุประโยค\nอนุปริญญา\nอนุปสัมบัน\nอนุปัสนา\nอนุพงศ์\nอนุพัทธ์\nอนุพันธ์\nอนุโพธ\nอนุภรรยา\nอนุภริยา\nอนุภาค\nอนุภาษ\nอนุมัติ\nอนุมาตรา\nอนุมาน\nอนุมูล\nอนุโมทนา\nอนุโยค\nอนุรักษ์\nอนุรักษนิยม\nอนุราช\nอนุราธ\nอนุราธะ\nอนุราธา\nอนุรูป\nอนุโลม\nอนุวงศ์\nอนุวรรตน์\nอนุวัต\nอนุวัตน์\nอนุวัตร\nอนุวัติ\nอนุวาต\nอนุศาสก\nอนุศาสน์\nอนุศาสนาจารย์\nอนุศิษฏ์\nอนุสติ\nอนุสนธิ\nอนุสร\nอนุสรณ์\nอนุสัญญา\nอนุสัย\nอนุสาวรีย์\nอนุสาสนี\nอเนก\nอเนกคุณ\nอเนกรรถประโยค\nอเนจอนาถ\nอโนชา\nอโนดาต\nอบ\nอบเชย\nอบาย\nอปจายนธรรม\nอปจายนมัย\nอปมงคล\nอปยศ\nอประไมย\nอปรัณณชาติ\nอปรา\nอปราชัย\nอปราชิต\nอปริมาณ\nอปลักษณ์\nอปโลกน์\nอปวาท\nอเปหิ\nอพพะ\nอพยพ\nอภัพ\nอภัย\nอภิ\nอภิฆาต\nอภิชฌา\nอภิชน\nอภิชนาธิปไตย\nอภิชัย\nอภิชาต\nอภิชิต\nอภิญญา\nอภิญญาณ\nอภิธรรม\nอภิธาน\nอภิไธย\nอภินันท์\nอภินันทนาการ\nอภินัย\nอภินิหาร\nอภิเนษกรมณ์\nอภิบาล\nอภิปรัชญา\nอภิปราย\nอภิมหาอำนาจ\nอภิมานะ\nอภิมุข\nอภิรดี\nอภิรติ\nอภิรมย์\nอภิรักษ์\nอภิราม\nอภิรุต\nอภิรุม\nอภิรูป\nอภิลักขิต\nอภิลักขิตสมัย\nอภิเลปน์\nอภิวันท์\nอภิวาท\nอภิวาทน์\nอภิเษก\nอภิสมโพธิ\nอภิสมัย\nอภิสมาจาร\nอภิสัมโพธิ\nอภิสัมโพธิญาณ\nอภิสิต\nอภิสิทธิ์\nอภูตะ\nอม\nอมพะนำ\nอ้ม\nอมตธรรม\nอมตบท\nอมตะ\nอมนุษย์\nอมร\nอมรา\nอมราวดี\nอมรินทร์\nอมเรนทร์\nอมเรศ\nอมฤต\nอมัตร\nอมาตย์\nอมาวสี\nอมาวสุ\nอมาวาสี\nอมิตร\nอเมริกัน\nอย่า\nอยาก\nอย่าง\nอยุทธ์\nอยู่\nอร\nอรชร\nอรชุน\nอรดี\nอรติ\nอรทัย\nอรไท\nอรนุช\nอรพินท์\nอรพิม\nอรรค\nอรรฆ\nอรรฆย์\nอรรจน์\nอรรณพ\nอรรถ\nอรรถกถา\nอรรถกถาจารย์\nอรรถาธิบาย\nอรรธ\nอรสุม\nอรหะ\nอรหัง\nอรหัต\nอรหัตผล\nอรหัตมรรค\nอรหัน\nอรหันต์\nอรหันตฆาต\nอร่อย\nอรัญ\nอรัญญิก\nอรัญวาส\nอรัญวาสี\nอรัณย์\nอราดี\nอร่าม\nอริ\nอรินทร์\nอริน\nอริยกะ\nอริยทรัพย์\nอริยบุคคล\nอริยผล\nอริยมรรค\nอริยสั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nอำพล\nอำพะนำ\nอำพัน\nอำไพ\nอำเภอ\nอำมร\nอำมฤคโชค\nอำมฤต\nอำมหิต\nอำมาตย์\nอำมาตยาธิปไตย\nอำยวน\nอำรุง\nอำลา\nอำอวม\nอ้ำอึ้ง\nอิก\nอิง\nอิงค์\nอิงอร\nอิจฉา\nอิฉัน\nอิชยา\nอิฏฐารมณ์\nอิฐ\nอิฐผล\nอิด\nอิตถี\nอิตเทรียม\nอิตเทอร์เบียม\nอิติวุตตกะ\nอิทธิ\nอิน\nอินซูลิน\nอินเดีย\nอินเดียนแดง\nอินเดียม\nอินท์\nอินทขีล\nอินทนิล\nอินทผลัม\nอินทร์\nอินทรธนู\nอินทรวงศ์\nอินทรวิเชียร\nอินทรศักดิ์\nอินทราณี\nอินทราภิเษก\nอินทรายุธ\nอินทรี\nอินทรีย์\nอินทรียสังวร\nอินทีวร\nอินทุ\nอินฟราเรด\nอินัง\nอิ่ม\nอิมัลชัน\nอิริเดียม\nอิริยา\nอิริยาบถ\nอิรุพเพท\nอิเล็กตรอน\nอิเล็กทรอนิกส์\nอิเล็กโทน\nอิศร\nอิศวร\nอิษฏ์\nอิษฏี\nอิส\nอิสตรี\nอิสัตรี\nอิสรภาพ\nอิสระ\nอิสริยยศ\nอิสริยะ\nอิสริยาภรณ์\nอิสลาม\nอิสสา\nอิสิ\nอิสี\nอิหม่าม\nอิหลักอิเหลื่อ\nอี\nอี่\nอี้\nอี๊\nอี๋\nอี๋อ๋อ\nอีก\nอีก้อ\nอีก๋อย\nอีโก้ง\nอีจู้\nอี๊ด\nอีเต้อ\nอีโต้\nอีทุบ\nอีเทอร์\nอีนุงตุงนัง\nอีนูน\nอีโน\nอีแปะ\nอีโปง\nอีเพา\nอีมู\nอีรม\nอีลุ้ม\nอีลุ่ยฉุยแฉก\nอีเลิ้ง\nอีศ\nอีศวร\nอีส\nอีสาน\nอีสุกอีใส\nอีหรอบ\nอีหลักอีเหลื่อ\nอีหลี\nอีหลุกขลุกขลัก\nอีหลุกขลุกขลุ่ย\nอีเห็น\nอีเหน็บ\nอีเหนียว\nอีเหละเขละขละ\nอีเหละเขะขะ\nอีโหน่อีเหน่\nอีโหลกโขลกเขลก\nอีแอ่น\nอึ\nอึก\nอึ้ก\nอึ๊ก\nอึกทึก\nอึกอัก\nอึง\nอึ่ง\nอึ้ง\nอึด\nอึดตะปือ\nอึ้ดทึ่ด\nอึน\nอืด\nอื่น\nอื้น\nอือ\nอื้อ\nอื้อฮือ\nอุ\nอุก\nอุกกา\nอุกกาบาต\nอุกฤษฏ์\nอุกลาบาต\nอุค\nอุคระ\nอุคหนิมิต\nอุโฆษ\nอุ้ง\nอุจ\nอุจจาระ\nอุจฉุ\nอุจเฉท\nอุจเฉททิฐิ\nอุจาด\nอุชุ\nอุฏฐาการ\nอุณหภูมิ\nอุณหะ\nอุณหาหาร\nอุณหิส\nอุณา\nอุณาโลม\nอุด\nอุดเตา\nอุดม\nอุดมการณ์\nอุดมคติ\nอุดมศึกษา\nอุดร\nอุดหนุน\nอุตดม\nอุตตมะ\nอุตมภาพ\nอุตมางค์\nอุตดร\nอุตรกุรุทวีป\nอุตตรายัน\nอุตรนิกาย\nอุตรผลคุนี\nอุตตรผลคุนี\nอุตรภัทรบท\nอุตตรภัทรบท\nอุตตรภัททะ\nอุตราภิมุข\nอุตราวรรต\nอุตราวัฏ\nอุตราษาฒ\nอุตตราสาฬหะ\nอุตราสงค์\nอุตตานภาพ\nอุตพิด\nอุตรา\nอุตริ\nอุตริมนุสธรรม\nอุตลุด\nอุตส่าห์\nอุตสาหกรรม\nอุตสาหะ\nอุตุ\nอุตุนิยม\nอุตุนิยมวิทยา\nอุทก\nอุทกธาร\nอุทกธารา\nอุทกภัย\nอุทกวิทยา\nอุทกศาสตร์\nอุทธรณ์\nอุทธัจ\nอุทยาน\nอุทร\nอุทริยะ\nอุทลุม\nอุทัช\nอุทัย\nอุทาน\nอุทาร\nอุทาหรณ์\nอุทิศ\nอุทุมพร\nอุเทศ\nอุเทสิกเจดีย์\nอุธัจ\nอุ่น\nอุบ\nอุบล\nอุบะ\nอุบ๊ะ\nอุบัติ\nอุบาท\nอุบาทว์\nอุบาย\nอุบาสก\nอุบาสิกา\nอุเบกขา\nอุโบสถ\nอุปกรณ์\nอุปกรม\nอุปการ\nอุปการะ\nอุปการี\nอุปกิเลส\nอุปจาร\nอุปถัมภ์\nอุปถัมภก\nอุปทม\nอุปทูต\nอุปเทศ\nอุปเท่ห์\nอุปธิ\nอุปนัย\nอุปนิกขิต\nอุปนิษัท\nอุปนิสัย\nอุปบัติ\nอุปปาติกะ\nอุปพัทธ์\nอุปพันธ์\nอุปโภค\nอุปมา\nอุปมาน\nอุปไมย\nอุปยุวราช\nอุปรากร\nอุปราคา\nอุปราช\nอุปริ\nอุปริมปริยาย\nอุปโลกน์\nอุปเวท\nอุปสมบท\nอุปสมบัน\nอุปสัมบัน\nอุปสรรค\nอุปสัมปทา\nอุปฮาด\nอุปัชฌาย์\nอุปัชฌายวัตร\nอุปัชฌายะ\nอุปัฏฐาก\nอุปัฏฐานะ\nอุปัทวะ\nอุปัทวันตราย\nอุปาทาน\nอุปาหนา\nอุภัย\nอุ้ม\nอุมงค์\nอุโมงค์\nอุย\nอุ่ย\nอุ้ย\nอุ๊ย\nอุยยาน\nอุยยาม\nอุรณะ\nอุรพี\nอุระ\nอุรังอุตัง\nอุรัจฉัท\nอุรัจฉทะ\nอุรา\nอุรุ\nอุไร\nอุลกมณี\nอุลโลจ\nอุลามก\nอุลิด\nอุโลก\nอุแว้\nอุษณกร\nอุษณกาล\nอุษณรัศมี\nอุษณรุจี\nอุษณาการ\nอุษณีษ์\nอุษมะ\nอุษมัน\nอุษา\nอุษาโยค\nอุสภ\nอุสส่าห์\nอุสสาหะ\nอุสา\nอุสุ\nอุสุภ\nอุสุภราช\nอุสุม\nอุหรับ\nอุหลบ\nอุเหม่\nอุฬาร\nอู\nอู่\nอู้\nอูฐ\nอูด\nอูม\nอูย\nอูรุ\nอู๋อี๋\nเอ\nเอ้\nเอ๊\nเอก\nเอกเขนก\nเอกซเรย์\nเอกรรถประโยค\nเอกัคตา\nเอกังสพยากรณ์\nเอกังสวาที\nเอกา\nเอ้กา\nเอกาธิปไตย\nเอเคอร์\nเอง\nเอ็ง\nเอ๋ง\nเอ็ด\nเอ็ดตะโร\nเอดส์\nเอตทัคคะ\nเอ้เต\nเอทิล\nเอน\nเอ็น\nเอนไซม์\nเอ็นดู\nเอ็นอ่อน\nเอม\nเอ็มบริโอ\nเอย\nเอ่ย\nเอ๊ย\nเอ๋ย\nเอร็ดอร่อย\nเอราวัณ\nเอว\nเอ๊ว\nเอวัง\nเอฬกะ\nเอฬา\nเออ\nเอ่อ\nเออร์เบียม\nเอ้อระเหย\nเอ้อเร้อ\nเอ้อเฮอ\nเอ๊ะ\nเอะใจ\nเอะอะ\nเอะอะมะเทิ่ง\nเอา\nเอาทาร\nเอาทารย์\nเอารส\nเอาฬาร\nเอาะลาย\nเอิก\nเอิกเกริก\nเอิ้น\nเอิบ\nเอียง\nเอี้ยง\nเอียด\nเอี๊ยด\nเอียน\nเอี่ยน\nเอี่ยม\nเอี๊ยม\nเอี้ยมจุ๊น\nเอี้ยมเฟี้ยม\nเอี่ยว\nเอี้ยว\nเอื้อ\nเอื๊อก\nเอื้อง\nเอือด\nเอือน\nเอื้อน\nเอือม\nเอื้อม\nเอื่อย\nเอื้อย\nแอ\nแอ้\nแอ๋\nแอก\nแอกทิเนียม\nแอ่ง\nแอ้งแม้ง\nแอด\nแอ้ด\nแอ๊ด\nแอ่น\nแอนติเจน\nแอนติบอดี\nแอนติอิเล็กตรอน\nแอโนด\nแอบ\nแอม\nแอ้ม\nแอมแปร์\nแอมมิเตอร์\nแอมโมเนีย\nแอร่ม\nแอลกอฮอล์\nแอลฟา\nแอว\nแอ่ว\nแอ้วแซ่ว\nแอสทาทีน\nแอสไพริน\nแอสฟัลต์\nแอหนัง\nแออัด\nโอ\nโอ่\nโอ้\nโอ๋\nโอก\nโอ้ก\nโอ้กอ้าก\nโอ๊ก\nโอกาส\nโอฆชล\nโอฆสงสาร\nโอฆะ\nโอ่ง\nโองการ\nโองโขดง\nโอชะ\nโอชา\nโอโซน\nโอฐ\nโอด\nโอ๊ต\nโอตตัปปะ\nโอทนะ\nโอน\nโอบ\nโอปปาติกะ\nโอภา\nโอภาส\nโอม\nโอย\nโอ๊ย\nโอรส\nโอละพ่อ\nโอลิมปิก\nโอวาท\nโอษฐ์\nโอษฐชะ\nโอษฐภัย\nโอสถ\nโอห์ม\nโอหัง\nโอฬาร\nโอฬาริก\nโอฬารึก\nโอ้เอ้\nโอเอซิส\nโอ้โฮ\nไอ\nไอ้\nไอโซโทป\nไอน์สไตเนียม\nไอยรา\nไอยเรศ\nไอราพต\nไอราวัณ\nไอราวัต\nไอศกรีม\nไอศวรรย์\nไอศุริยสมบัติ\nไอศูรย์\nไอออน\nไอโอดีน\nฮกเกี้ยน\nฮด\nฮวงซุ้ย\nฮวน\nฮ้วนหมู\nฮวบ\nฮ่อ\nฮ้อ\nฮอกกี้\nฮอด\nฮ่อม\nฮ่อยจ๊อ\nฮอร์โมน\nฮอลแลนด์\nฮอลันดา\nฮะ\nฮะเบส\nฮะเรีย\nฮัก\nฮังเล\nฮัจญ์\nฮัจญะฮ์\nฮัจญี\nฮั่น\nฮั้ว\nฮา\nฮ้า\nฮ่างหลวง\nฮาจญ์\nฮาม\nฮาเร็ม\nฮาห์เนียม\nฮิจเราะห์\nฮินดู\nฮิปโปโปเตมัส\nฮิสทีเรีย\nฮีเลียม\nฮึ\nฮึก\nฮึด\nฮึดฮัด\nฮึ่ม\nฮึย\nฮึ่ย\nฮืดฮาด\nฮือ\nฮื่อ\nฮื้อ\nฮื้อฉี่\nฮุด\nฮุบ\nฮุยเลฮุย\nฮู้\nฮูก\nฮูม\nเฮ\nเฮฮา\nเฮกตาร์\nเฮกโตกรัม\nเฮกโตเมตร\nเฮกโตลิตร\nเฮง\nเฮ็ด\nเฮโมโกลบิน\nเฮย\nเฮ่ย\nเฮ้ย\nเฮโรอีน\nเฮลิคอปเตอร์\nเฮโล\nเฮละโล\nเฮ้ว\nเฮอ\nเฮ่อ\nเฮ้อ\nเฮอริเคน\nเฮิรตซ์\nเฮี้ยน\nเฮี้ยบ\nเฮี้ยว\nเฮือก\nเฮือน\nแฮ\nแฮ่\nแฮก\nแฮ่กึ๊น\nแฮนด์บอล\nแฮฟเนียม\nแฮม\nแฮะ\nโฮ\nโฮก\nโฮ่ง\nโฮ้ง\nโฮเต็ล\nโฮลเมียม\nโฮะ\nไฮ้\nไฮโกรมิเตอร์\nไฮดรา\nไฮโดร\nไฮโดรคาร์บอน\nไฮโดรเจน\nไฮโดรมิเตอร์\nไฮไฟ\nไฮโล\nไฮฮี\n"
+              .split(/[\r\n]+/)
+              .filter(function (w) {
+                return w.length > 1;
+              })
+      this.addWords(words, false)
+    }
+    if(finalize){
+      this.finalizeDict();
+    }
+  },
+
+  dictSeek: function (l, r, ch, strOffset, pos) {
+    var ans = null;
+    while (l <= r) {
+      var m = Math.floor((l + r) / 2),
+        dict_item = this.dict[m],
+        len = dict_item.length;
+      if (len <= strOffset) {
+        l = m + 1;
+      } else {
+        var ch_ = dict_item[strOffset];
+        if (ch_ < ch) {
+          l = m + 1;
+        } else if (ch_ > ch) {
+          r = m - 1;
+        } else {
+          ans = m;
+          if (pos == LEFT) {
+            r = m - 1;
+          } else {
+            l = m + 1;
+          }
+        }
+      }
+    }
+    return ans;
+  },
+
+  isFinal: function (acceptor) {
+    return this.dict[acceptor.l].length == acceptor.strOffset;
+  },
+
+  createAcceptor: function () {
+    return {
+      l: 0,
+      r: this.dict.length - 1,
+      strOffset: 0,
+      isFinal: false,
+      dict: this,
+      transit: function (ch) {
+        return this.dict.transit(this, ch);
+      },
+      isError: false,
+      tag: "DICT",
+      w: 1,
+      type: "DICT"
+    };
+  },
+
+  transit: function (acceptor, ch) {
+    var l = this.dictSeek(acceptor.l,
+      acceptor.r,
+      ch,
+      acceptor.strOffset,
+      LEFT);
+    if (l !== null) {
+      var r = this.dictSeek(l,
+        acceptor.r,
+        ch,
+        acceptor.strOffset,
+        RIGHT);
+      acceptor.l = l;
+      acceptor.r = r;
+      acceptor.strOffset++;
+      acceptor.isFinal = this.isFinal(acceptor);
+    } else {
+      acceptor.isError = true;
+    }
+    return acceptor;
+  },
+
+  sortuniq: function(a){
+    return a.sort().filter(function(item, pos, arr){
+      return !pos || item != arr[pos - 1];
+    })
+  },
+
+  flatten: function(a){
+    //[[1,2],[3]] -> [1,2,3]
+    return [].concat.apply([], a);
+  }
+};
+module.exports = WordcutDict;
+
+}).call(this,"/dist/tmp")
+},{"glob":16,"path":22}],3:[function(require,module,exports){
+var WordRule = {
+  createAcceptor: function(tag) {
+    if (tag["WORD_RULE"])
+      return null;
+
+    return {strOffset: 0,
+            isFinal: false,
+            transit: function(ch) {
+              var lch = ch.toLowerCase();
+              if (lch >= "a" && lch <= "z") {
+                this.isFinal = true;
+                this.strOffset++;
+              } else {
+                this.isError = true;
+              }
+              return this;
+            },
+            isError: false,
+            tag: "WORD_RULE",
+            type: "WORD_RULE",
+            w: 1};
+  }
+};
+
+var NumberRule = {
+  createAcceptor: function(tag) {
+    if (tag["NUMBER_RULE"])
+      return null;
+
+    return {strOffset: 0,
+            isFinal: false,
+            transit: function(ch) {
+              if (ch >= "0" && ch <= "9") {
+                this.isFinal = true;
+                this.strOffset++;
+              } else {
+                this.isError = true;
+              }
+              return this;
+            },
+            isError: false,
+            tag: "NUMBER_RULE",
+            type: "NUMBER_RULE",
+            w: 1};
+  }
+};
+
+var SpaceRule = {
+  tag: "SPACE_RULE",
+  createAcceptor: function(tag) {
+
+    if (tag["SPACE_RULE"])
+      return null;
+
+    return {strOffset: 0,
+            isFinal: false,
+            transit: function(ch) {
+              if (ch == " " || ch == "\t" || ch == "\r" || ch == "\n" ||
+                  ch == "\u00A0" || ch=="\u2003"//nbsp and emsp
+                 ) {
+                this.isFinal = true;
+                this.strOffset++;
+              } else {
+                this.isError = true;
+              }
+              return this;
+            },
+            isError: false,
+            tag: SpaceRule.tag,
+            w: 1,
+            type: "SPACE_RULE"};
+  }
+}
+
+var SingleSymbolRule = {
+  tag: "SINSYM",
+  createAcceptor: function(tag) {
+    return {strOffset: 0,
+            isFinal: false,
+            transit: function(ch) {
+              if (this.strOffset == 0 && ch.match(/^[\@\(\)\/\,\-\."`]$/)) {
+                this.isFinal = true;
+                this.strOffset++;
+              } else {
+                this.isError = true;
+              }
+              return this;
+            },
+            isError: false,
+            tag: "SINSYM",
+            w: 1,
+            type: "SINSYM"};
+  }
+}
+
+
+var LatinRules = [WordRule, SpaceRule, SingleSymbolRule, NumberRule];
+
+module.exports = LatinRules;
+
+},{}],4:[function(require,module,exports){
+var _ = require("underscore")
+  , WordcutCore = require("./wordcut_core");
+var PathInfoBuilder = {
+
+  /*
+    buildByPartAcceptors: function(path, acceptors, i) {
+    var 
+    var genInfos = partAcceptors.reduce(function(genInfos, acceptor) {
+      
+    }, []);
+    
+    return genInfos;
+  } 
+  */
+
+  buildByAcceptors: function(path, finalAcceptors, i) {
+    var self = this;
+    var infos = finalAcceptors.map(function(acceptor) {
+      var p = i - acceptor.strOffset + 1
+        , _info = path[p];            
+      
+      var info = {p: p, 
+                  mw: _info.mw + (acceptor.mw === undefined ? 0 : acceptor.mw),
+                  w: acceptor.w + _info.w,
+                  unk: (acceptor.unk ? acceptor.unk : 0) + _info.unk, 
+                  type: acceptor.type};
+
+      if (acceptor.type == "PART") {
+        for(var j = p + 1; j <= i; j++) {
+          path[j].merge = p;
+        }
+        info.merge = p;
+      }
+
+      return info;
+    });
+    return infos.filter(function(info) { return info; });
+  },
+  
+  fallback: function(path, leftBoundary, text, i) {
+    var _info = path[leftBoundary];
+    if (text[i].match(/[\u0E48-\u0E4E]/)) {
+      if (leftBoundary != 0) 
+        leftBoundary = path[leftBoundary].p;
+      return {p: leftBoundary,
+              mw: 0,
+              w: 1 + _info.w,
+              unk: 1 + _info.unk,
+              type: "UNK"};      
+/*    } else if(leftBoundary > 0 && path[leftBoundary].type !== "UNK") {
+      leftBoundary = path[leftBoundary].p;
+      return {p: leftBoundary,
+              w: 1 + _info.w,
+              unk: 1 + _info.unk,
+              type: "UNK"};            */
+    } else {      
+      return {p: leftBoundary,
+              mw: _info.mw,
+              w: 1 + _info.w,
+              unk: 1 + _info.unk,
+              type: "UNK"};
+    }
+  },
+  
+  build: function(path, finalAcceptors, i, leftBoundary, text) {
+    var basicPathInfos = this.buildByAcceptors(path, finalAcceptors, i);
+    if (basicPathInfos.length > 0) {
+      return basicPathInfos;
+    } else {
+      return [this.fallback(path, leftBoundary, text, i)];
+    }
+  }
+};
+
+module.exports = function() {
+  return _.clone(PathInfoBuilder);
+}
+
+},{"./wordcut_core":8,"underscore":25}],5:[function(require,module,exports){
+var _ = require("underscore");
+
+
+var PathSelector = {
+  selectPath: function(paths) {
+    var path = paths.reduce(function(selectedPath, path) {
+      if (selectedPath == null) {        
+        return path;
+      } else {
+        if (path.unk < selectedPath.unk) 
+          return path;        
+        if (path.unk == selectedPath.unk) {
+          if (path.mw < selectedPath.mw)
+            return path
+          if (path.mw == selectedPath.mw) {
+            if (path.w < selectedPath.w) 
+              return path;
+          }
+        }
+        return selectedPath;
+      }
+    }, null);
+    return path;
+  },
+  
+  createPath: function() {
+    return [{p:null, w:0, unk:0, type: "INIT", mw:0}];
+  }
+};
+
+module.exports = function() {
+  return _.clone(PathSelector);
+};
+
+},{"underscore":25}],6:[function(require,module,exports){
+function isMatch(pat, offset, ch) {
+  if (pat.length <= offset)
+    return false;
+  var _ch = pat[offset];
+  return _ch == ch ||
+         (_ch.match(/[กข]/) && ch.match(/[ก-ฮ]/)) ||
+         (_ch.match(/[มบ]/) && ch.match(/[ก-ฮ]/)) ||
+         (_ch.match(/\u0E49/) && ch.match(/[\u0E48-\u0E4B]/));
+}
+
+var Rule0 = {
+  pat: "เหก็ม",
+  createAcceptor: function(tag) {
+    return {strOffset: 0,
+            isFinal: false,
+            transit: function(ch) {
+              if (isMatch(Rule0.pat, this.strOffset,ch)) {                 
+                this.isFinal = (this.strOffset + 1 == Rule0.pat.length);                
+                this.strOffset++;
+              } else {              
+                this.isError = true;             
+              }
+              return this;
+            },
+            isError: false,
+            tag: "THAI_RULE",
+            type: "THAI_RULE", 
+            w: 1};                        
+  }
+};
+
+var PartRule = {
+  createAcceptor: function(tag) {
+    return {strOffset: 0,
+            patterns: [
+              "แก", "เก", "ก้", "กก์", "กา", "กี", "กิ", "กืก"  
+            ],
+            isFinal: false,
+            transit: function(ch) {
+              var offset = this.strOffset;
+              this.patterns = this.patterns.filter(function(pat) {
+                return isMatch(pat, offset, ch);
+              });
+              
+              if (this.patterns.length > 0) {
+                var len = 1 + offset;
+                this.isFinal = this.patterns.some(function(pat) {
+                  return pat.length == len; 
+                });
+                this.strOffset++;
+              } else {              
+                this.isError = true;             
+              }
+              return this;
+            },
+            isError: false,
+            tag: "PART",
+            type: "PART", 
+            unk: 1,
+            w: 1};                        
+  }
+};
+
+var ThaiRules = [Rule0, PartRule];
+
+module.exports = ThaiRules;
+
+},{}],7:[function(require,module,exports){
+var sys = require("sys")
+  , WordcutDict = require("./dict")
+  , WordcutCore = require("./wordcut_core")
+  , PathInfoBuilder = require("./path_info_builder")
+  , PathSelector = require("./path_selector")
+  , Acceptors = require("./acceptors")
+  , latinRules = require("./latin_rules")
+  , thaiRules = require("./thai_rules")
+  , _ = require("underscore");
+
+
+var Wordcut = Object.create(WordcutCore);
+Wordcut.defaultPathInfoBuilder = PathInfoBuilder;
+Wordcut.defaultPathSelector = PathSelector;
+Wordcut.defaultAcceptors = Acceptors;
+Wordcut.defaultLatinRules = latinRules;
+Wordcut.defaultThaiRules = thaiRules;
+Wordcut.defaultDict = WordcutDict;
+
+
+Wordcut.initNoDict = function(dict_path) {
+  var self = this;
+  self.pathInfoBuilder = new self.defaultPathInfoBuilder;
+  self.pathSelector = new self.defaultPathSelector;
+  self.acceptors = new self.defaultAcceptors;
+  self.defaultLatinRules.forEach(function(rule) {
+    self.acceptors.creators.push(rule);
+  });
+  self.defaultThaiRules.forEach(function(rule) {
+    self.acceptors.creators.push(rule);
+  });
+};
+
+Wordcut.init = function(dict_path, withDefault, additionalWords) {
+  withDefault = withDefault || false;
+  this.initNoDict();
+  var dict = _.clone(this.defaultDict);
+  dict.init(dict_path, withDefault, additionalWords);
+  this.acceptors.creators.push(dict);
+};
+
+module.exports = Wordcut;
+
+},{"./acceptors":1,"./dict":2,"./latin_rules":3,"./path_info_builder":4,"./path_selector":5,"./thai_rules":6,"./wordcut_core":8,"sys":28,"underscore":25}],8:[function(require,module,exports){
+var WordcutCore = {
+
+  buildPath: function(text) {
+    var self = this
+      , path = self.pathSelector.createPath()
+      , leftBoundary = 0;
+    self.acceptors.reset();
+    for (var i = 0; i < text.length; i++) {
+      var ch = text[i];
+      self.acceptors.transit(ch);
+
+      var possiblePathInfos = self
+        .pathInfoBuilder
+        .build(path,
+               self.acceptors.getFinalAcceptors(),
+               i,
+               leftBoundary,
+               text);
+      var selectedPath = self.pathSelector.selectPath(possiblePathInfos)
+
+      path.push(selectedPath);
+      if (selectedPath.type !== "UNK") {
+        leftBoundary = i;
+      }
+    }
+    return path;
+  },
+
+  pathToRanges: function(path) {
+    var e = path.length - 1
+     , ranges = [];
+
+    while (e > 0) {
+      var info = path[e]
+       , s = info.p;
+
+      if (info.merge !== undefined && ranges.length > 0) {
+        var r = ranges[ranges.length - 1];
+        r.s = info.merge;
+        s = r.s;
+      } else {
+        ranges.push({s:s, e:e});
+      }
+      e = s;
+    }
+    return ranges.reverse();
+  },
+
+  rangesToText: function(text, ranges, delimiter) {
+    return ranges.map(function(r) {
+      return text.substring(r.s, r.e);
+    }).join(delimiter);
+  },
+
+  cut: function(text, delimiter) {
+    var path = this.buildPath(text)
+      , ranges = this.pathToRanges(path);
+    return this
+      .rangesToText(text, ranges,
+                    (delimiter === undefined ? "|" : delimiter));
+  },
+
+  cutIntoRanges: function(text, noText) {
+    var path = this.buildPath(text)
+      , ranges = this.pathToRanges(path);
+
+    if (!noText) {
+      ranges.forEach(function(r) {
+        r.text = text.substring(r.s, r.e);
+      });
+    }
+    return ranges;
+  },
+
+  cutIntoArray: function(text) {
+    var path = this.buildPath(text)
+      , ranges = this.pathToRanges(path);
+    
+    return ranges.map(function(r) {
+      return text.substring(r.s, r.e)
+    });
+  }
+};
+
+module.exports = WordcutCore;
+
+},{}],9:[function(require,module,exports){
+// http://wiki.commonjs.org/wiki/Unit_Testing/1.0
+//
+// THIS IS NOT TESTED NOR LIKELY TO WORK OUTSIDE V8!
+//
+// Originally from narwhal.js (http://narwhaljs.org)
+// Copyright (c) 2009 Thomas Robinson <280north.com>
+//
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the 'Software'), to
+// deal in the Software without restriction, including without limitation the
+// rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
+// sell copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+//
+// The above copyright notice and this permission notice shall be included in
+// all copies or substantial portions of the Software.
+//
+// THE SOFTWARE IS PROVIDED 'AS IS', WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
+// ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
+// WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
+
+// when used in node, this will actually load the util module we depend on
+// versus loading the builtin util module as happens otherwise
+// this is a bug in node module loading as far as I am concerned
+var util = require('util/');
+
+var pSlice = Array.prototype.slice;
+var hasOwn = Object.prototype.hasOwnProperty;
+
+// 1. The assert module provides functions that throw
+// AssertionError's when particular conditions are not met. The
+// assert module must conform to the following interface.
+
+var assert = module.exports = ok;
+
+// 2. The AssertionError is defined in assert.
+// new assert.AssertionError({ message: message,
+//                             actual: actual,
+//                             expected: expected })
+
+assert.AssertionError = function AssertionError(options) {
+  this.name = 'AssertionError';
+  this.actual = options.actual;
+  this.expected = options.expected;
+  this.operator = options.operator;
+  if (options.message) {
+    this.message = options.message;
+    this.generatedMessage = false;
+  } else {
+    this.message = getMessage(this);
+    this.generatedMessage = true;
+  }
+  var stackStartFunction = options.stackStartFunction || fail;
+
+  if (Error.captureStackTrace) {
+    Error.captureStackTrace(this, stackStartFunction);
+  }
+  else {
+    // non v8 browsers so we can have a stacktrace
+    var err = new Error();
+    if (err.stack) {
+      var out = err.stack;
+
+      // try to strip useless frames
+      var fn_name = stackStartFunction.name;
+      var idx = out.indexOf('\n' + fn_name);
+      if (idx >= 0) {
+        // once we have located the function frame
+        // we need to strip out everything before it (and its line)
+        var next_line = out.indexOf('\n', idx + 1);
+        out = out.substring(next_line + 1);
+      }
+
+      this.stack = out;
+    }
+  }
+};
+
+// assert.AssertionError instanceof Error
+util.inherits(assert.AssertionError, Error);
+
+function replacer(key, value) {
+  if (util.isUndefined(value)) {
+    return '' + value;
+  }
+  if (util.isNumber(value) && !isFinite(value)) {
+    return value.toString();
+  }
+  if (util.isFunction(value) || util.isRegExp(value)) {
+    return value.toString();
+  }
+  return value;
+}
+
+function truncate(s, n) {
+  if (util.isString(s)) {
+    return s.length < n ? s : s.slice(0, n);
+  } else {
+    return s;
+  }
+}
+
+function getMessage(self) {
+  return truncate(JSON.stringify(self.actual, replacer), 128) + ' ' +
+         self.operator + ' ' +
+         truncate(JSON.stringify(self.expected, replacer), 128);
+}
+
+// At present only the three keys mentioned above are used and
+// understood by the spec. Implementations or sub modules can pass
+// other keys to the AssertionError's constructor - they will be
+// ignored.
+
+// 3. All of the following functions must throw an AssertionError
+// when a corresponding condition is not met, with a message that
+// may be undefined if not provided.  All assertion methods provide
+// both the actual and expected values to the assertion error for
+// display purposes.
+
+function fail(actual, expected, message, operator, stackStartFunction) {
+  throw new assert.AssertionError({
+    message: message,
+    actual: actual,
+    expected: expected,
+    operator: operator,
+    stackStartFunction: stackStartFunction
+  });
+}
+
+// EXTENSION! allows for well behaved errors defined elsewhere.
+assert.fail = fail;
+
+// 4. Pure assertion tests whether a value is truthy, as determined
+// by !!guard.
+// assert.ok(guard, message_opt);
+// This statement is equivalent to assert.equal(true, !!guard,
+// message_opt);. To test strictly for the value true, use
+// assert.strictEqual(true, guard, message_opt);.
+
+function ok(value, message) {
+  if (!value) fail(value, true, message, '==', assert.ok);
+}
+assert.ok = ok;
+
+// 5. The equality assertion tests shallow, coercive equality with
+// ==.
+// assert.equal(actual, expected, message_opt);
+
+assert.equal = function equal(actual, expected, message) {
+  if (actual != expected) fail(actual, expected, message, '==', assert.equal);
+};
+
+// 6. The non-equality assertion tests for whether two objects are not equal
+// with != assert.notEqual(actual, expected, message_opt);
+
+assert.notEqual = function notEqual(actual, expected, message) {
+  if (actual == expected) {
+    fail(actual, expected, message, '!=', assert.notEqual);
+  }
+};
+
+// 7. The equivalence assertion tests a deep equality relation.
+// assert.deepEqual(actual, expected, message_opt);
+
+assert.deepEqual = function deepEqual(actual, expected, message) {
+  if (!_deepEqual(actual, expected)) {
+    fail(actual, expected, message, 'deepEqual', assert.deepEqual);
+  }
+};
+
+function _deepEqual(actual, expected) {
+  // 7.1. All identical values are equivalent, as determined by ===.
+  if (actual === expected) {
+    return true;
+
+  } else if (util.isBuffer(actual) && util.isBuffer(expected)) {
+    if (actual.length != expected.length) return false;
+
+    for (var i = 0; i < actual.length; i++) {
+      if (actual[i] !== expected[i]) return false;
+    }
+
+    return true;
+
+  // 7.2. If the expected value is a Date object, the actual value is
+  // equivalent if it is also a Date object that refers to the same time.
+  } else if (util.isDate(actual) && util.isDate(expected)) {
+    return actual.getTime() === expected.getTime();
+
+  // 7.3 If the expected value is a RegExp object, the actual value is
+  // equivalent if it is also a RegExp object with the same source and
+  // properties (`global`, `multiline`, `lastIndex`, `ignoreCase`).
+  } else if (util.isRegExp(actual) && util.isRegExp(expected)) {
+    return actual.source === expected.source &&
+           actual.global === expected.global &&
+           actual.multiline === expected.multiline &&
+           actual.lastIndex === expected.lastIndex &&
+           actual.ignoreCase === expected.ignoreCase;
+
+  // 7.4. Other pairs that do not both pass typeof value == 'object',
+  // equivalence is determined by ==.
+  } else if (!util.isObject(actual) && !util.isObject(expected)) {
+    return actual == expected;
+
+  // 7.5 For all other Object pairs, including Array objects, equivalence is
+  // determined by having the same number of owned properties (as verified
+  // with Object.prototype.hasOwnProperty.call), the same set of keys
+  // (although not necessarily the same order), equivalent values for every
+  // corresponding key, and an identical 'prototype' property. Note: this
+  // accounts for both named and indexed properties on Arrays.
+  } else {
+    return objEquiv(actual, expected);
+  }
+}
+
+function isArguments(object) {
+  return Object.prototype.toString.call(object) == '[object Arguments]';
+}
+
+function objEquiv(a, b) {
+  if (util.isNullOrUndefined(a) || util.isNullOrUndefined(b))
+    return false;
+  // an identical 'prototype' property.
+  if (a.prototype !== b.prototype) return false;
+  // if one is a primitive, the other must be same
+  if (util.isPrimitive(a) || util.isPrimitive(b)) {
+    return a === b;
+  }
+  var aIsArgs = isArguments(a),
+      bIsArgs = isArguments(b);
+  if ((aIsArgs && !bIsArgs) || (!aIsArgs && bIsArgs))
+    return false;
+  if (aIsArgs) {
+    a = pSlice.call(a);
+    b = pSlice.call(b);
+    return _deepEqual(a, b);
+  }
+  var ka = objectKeys(a),
+      kb = objectKeys(b),
+      key, i;
+  // having the same number of owned properties (keys incorporates
+  // hasOwnProperty)
+  if (ka.length != kb.length)
+    return false;
+  //the same set of keys (although not necessarily the same order),
+  ka.sort();
+  kb.sort();
+  //~~~cheap key test
+  for (i = ka.length - 1; i >= 0; i--) {
+    if (ka[i] != kb[i])
+      return false;
+  }
+  //equivalent values for every corresponding key, and
+  //~~~possibly expensive deep test
+  for (i = ka.length - 1; i >= 0; i--) {
+    key = ka[i];
+    if (!_deepEqual(a[key], b[key])) return false;
+  }
+  return true;
+}
+
+// 8. The non-equivalence assertion tests for any deep inequality.
+// assert.notDeepEqual(actual, expected, message_opt);
+
+assert.notDeepEqual = function notDeepEqual(actual, expected, message) {
+  if (_deepEqual(actual, expected)) {
+    fail(actual, expected, message, 'notDeepEqual', assert.notDeepEqual);
+  }
+};
+
+// 9. The strict equality assertion tests strict equality, as determined by ===.
+// assert.strictEqual(actual, expected, message_opt);
+
+assert.strictEqual = function strictEqual(actual, expected, message) {
+  if (actual !== expected) {
+    fail(actual, expected, message, '===', assert.strictEqual);
+  }
+};
+
+// 10. The strict non-equality assertion tests for strict inequality, as
+// determined by !==.  assert.notStrictEqual(actual, expected, message_opt);
+
+assert.notStrictEqual = function notStrictEqual(actual, expected, message) {
+  if (actual === expected) {
+    fail(actual, expected, message, '!==', assert.notStrictEqual);
+  }
+};
+
+function expectedException(actual, expected) {
+  if (!actual || !expected) {
+    return false;
+  }
+
+  if (Object.prototype.toString.call(expected) == '[object RegExp]') {
+    return expected.test(actual);
+  } else if (actual instanceof expected) {
+    return true;
+  } else if (expected.call({}, actual) === true) {
+    return true;
+  }
+
+  return false;
+}
+
+function _throws(shouldThrow, block, expected, message) {
+  var actual;
+
+  if (util.isString(expected)) {
+    message = expected;
+    expected = null;
+  }
+
+  try {
+    block();
+  } catch (e) {
+    actual = e;
+  }
+
+  message = (expected && expected.name ? ' (' + expected.name + ').' : '.') +
+            (message ? ' ' + message : '.');
+
+  if (shouldThrow && !actual) {
+    fail(actual, expected, 'Missing expected exception' + message);
+  }
+
+  if (!shouldThrow && expectedException(actual, expected)) {
+    fail(actual, expected, 'Got unwanted exception' + message);
+  }
+
+  if ((shouldThrow && actual && expected &&
+      !expectedException(actual, expected)) || (!shouldThrow && actual)) {
+    throw actual;
+  }
+}
+
+// 11. Expected to throw an error:
+// assert.throws(block, Error_opt, message_opt);
+
+assert.throws = function(block, /*optional*/error, /*optional*/message) {
+  _throws.apply(this, [true].concat(pSlice.call(arguments)));
+};
+
+// EXTENSION! This is annoying to write outside this module.
+assert.doesNotThrow = function(block, /*optional*/message) {
+  _throws.apply(this, [false].concat(pSlice.call(arguments)));
+};
+
+assert.ifError = function(err) { if (err) {throw err;}};
+
+var objectKeys = Object.keys || function (obj) {
+  var keys = [];
+  for (var key in obj) {
+    if (hasOwn.call(obj, key)) keys.push(key);
+  }
+  return keys;
+};
+
+},{"util/":28}],10:[function(require,module,exports){
+'use strict';
+module.exports = balanced;
+function balanced(a, b, str) {
+  if (a instanceof RegExp) a = maybeMatch(a, str);
+  if (b instanceof RegExp) b = maybeMatch(b, str);
+
+  var r = range(a, b, str);
+
+  return r && {
+    start: r[0],
+    end: r[1],
+    pre: str.slice(0, r[0]),
+    body: str.slice(r[0] + a.length, r[1]),
+    post: str.slice(r[1] + b.length)
+  };
+}
+
+function maybeMatch(reg, str) {
+  var m = str.match(reg);
+  return m ? m[0] : null;
+}
+
+balanced.range = range;
+function range(a, b, str) {
+  var begs, beg, left, right, result;
+  var ai = str.indexOf(a);
+  var bi = str.indexOf(b, ai + 1);
+  var i = ai;
+
+  if (ai >= 0 && bi > 0) {
+    begs = [];
+    left = str.length;
+
+    while (i >= 0 && !result) {
+      if (i == ai) {
+        begs.push(i);
+        ai = str.indexOf(a, i + 1);
+      } else if (begs.length == 1) {
+        result = [ begs.pop(), bi ];
+      } else {
+        beg = begs.pop();
+        if (beg < left) {
+          left = beg;
+          right = bi;
+        }
+
+        bi = str.indexOf(b, i + 1);
+      }
+
+      i = ai < bi && ai >= 0 ? ai : bi;
+    }
+
+    if (begs.length) {
+      result = [ left, right ];
+    }
+  }
+
+  return result;
+}
+
+},{}],11:[function(require,module,exports){
+var concatMap = require('concat-map');
+var balanced = require('balanced-match');
+
+module.exports = expandTop;
+
+var escSlash = '\0SLASH'+Math.random()+'\0';
+var escOpen = '\0OPEN'+Math.random()+'\0';
+var escClose = '\0CLOSE'+Math.random()+'\0';
+var escComma = '\0COMMA'+Math.random()+'\0';
+var escPeriod = '\0PERIOD'+Math.random()+'\0';
+
+function numeric(str) {
+  return parseInt(str, 10) == str
+    ? parseInt(str, 10)
+    : str.charCodeAt(0);
+}
+
+function escapeBraces(str) {
+  return str.split('\\\\').join(escSlash)
+            .split('\\{').join(escOpen)
+            .split('\\}').join(escClose)
+            .split('\\,').join(escComma)
+            .split('\\.').join(escPeriod);
+}
+
+function unescapeBraces(str) {
+  return str.split(escSlash).join('\\')
+            .split(escOpen).join('{')
+            .split(escClose).join('}')
+            .split(escComma).join(',')
+            .split(escPeriod).join('.');
+}
+
+
+// Basically just str.split(","), but handling cases
+// where we have nested braced sections, which should be
+// treated as individual members, like {a,{b,c},d}
+function parseCommaParts(str) {
+  if (!str)
+    return [''];
+
+  var parts = [];
+  var m = balanced('{', '}', str);
+
+  if (!m)
+    return str.split(',');
+
+  var pre = m.pre;
+  var body = m.body;
+  var post = m.post;
+  var p = pre.split(',');
+
+  p[p.length-1] += '{' + body + '}';
+  var postParts = parseCommaParts(post);
+  if (post.length) {
+    p[p.length-1] += postParts.shift();
+    p.push.apply(p, postParts);
+  }
+
+  parts.push.apply(parts, p);
+
+  return parts;
+}
+
+function expandTop(str) {
+  if (!str)
+    return [];
+
+  // I don't know why Bash 4.3 does this, but it does.
+  // Anything starting with {} will have the first two bytes preserved
+  // but *only* at the top level, so {},a}b will not expand to anything,
+  // but a{},b}c will be expanded to [a}c,abc].
+  // One could argue that this is a bug in Bash, but since the goal of
+  // this module is to match Bash's rules, we escape a leading {}
+  if (str.substr(0, 2) === '{}') {
+    str = '\\{\\}' + str.substr(2);
+  }
+
+  return expand(escapeBraces(str), true).map(unescapeBraces);
+}
+
+function identity(e) {
+  return e;
+}
+
+function embrace(str) {
+  return '{' + str + '}';
+}
+function isPadded(el) {
+  return /^-?0\d/.test(el);
+}
+
+function lte(i, y) {
+  return i <= y;
+}
+function gte(i, y) {
+  return i >= y;
+}
+
+function expand(str, isTop) {
+  var expansions = [];
+
+  var m = balanced('{', '}', str);
+  if (!m || /\$$/.test(m.pre)) return [str];
+
+  var isNumericSequence = /^-?\d+\.\.-?\d+(?:\.\.-?\d+)?$/.test(m.body);
+  var isAlphaSequence = /^[a-zA-Z]\.\.[a-zA-Z](?:\.\.-?\d+)?$/.test(m.body);
+  var isSequence = isNumericSequence || isAlphaSequence;
+  var isOptions = m.body.indexOf(',') >= 0;
+  if (!isSequence && !isOptions) {
+    // {a},b}
+    if (m.post.match(/,.*\}/)) {
+      str = m.pre + '{' + m.body + escClose + m.post;
+      return expand(str);
+    }
+    return [str];
+  }
+
+  var n;
+  if (isSequence) {
+    n = m.body.split(/\.\./);
+  } else {
+    n = parseCommaParts(m.body);
+    if (n.length === 1) {
+      // x{{a,b}}y ==> x{a}y x{b}y
+      n = expand(n[0], false).map(embrace);
+      if (n.length === 1) {
+        var post = m.post.length
+          ? expand(m.post, false)
+          : [''];
+        return post.map(function(p) {
+          return m.pre + n[0] + p;
+        });
+      }
+    }
+  }
+
+  // at this point, n is the parts, and we know it's not a comma set
+  // with a single entry.
+
+  // no need to expand pre, since it is guaranteed to be free of brace-sets
+  var pre = m.pre;
+  var post = m.post.length
+    ? expand(m.post, false)
+    : [''];
+
+  var N;
+
+  if (isSequence) {
+    var x = numeric(n[0]);
+    var y = numeric(n[1]);
+    var width = Math.max(n[0].length, n[1].length)
+    var incr = n.length == 3
+      ? Math.abs(numeric(n[2]))
+      : 1;
+    var test = lte;
+    var reverse = y < x;
+    if (reverse) {
+      incr *= -1;
+      test = gte;
+    }
+    var pad = n.some(isPadded);
+
+    N = [];
+
+    for (var i = x; test(i, y); i += incr) {
+      var c;
+      if (isAlphaSequence) {
+        c = String.fromCharCode(i);
+        if (c === '\\')
+          c = '';
+      } else {
+        c = String(i);
+        if (pad) {
+          var need = width - c.length;
+          if (need > 0) {
+            var z = new Array(need + 1).join('0');
+            if (i < 0)
+              c = '-' + z + c.slice(1);
+            else
+              c = z + c;
+          }
+        }
+      }
+      N.push(c);
+    }
+  } else {
+    N = concatMap(n, function(el) { return expand(el, false) });
+  }
+
+  for (var j = 0; j < N.length; j++) {
+    for (var k = 0; k < post.length; k++) {
+      var expansion = pre + N[j] + post[k];
+      if (!isTop || isSequence || expansion)
+        expansions.push(expansion);
+    }
+  }
+
+  return expansions;
+}
+
+
+},{"balanced-match":10,"concat-map":13}],12:[function(require,module,exports){
+
+},{}],13:[function(require,module,exports){
+module.exports = function (xs, fn) {
+    var res = [];
+    for (var i = 0; i < xs.length; i++) {
+        var x = fn(xs[i], i);
+        if (isArray(x)) res.push.apply(res, x);
+        else res.push(x);
+    }
+    return res;
+};
+
+var isArray = Array.isArray || function (xs) {
+    return Object.prototype.toString.call(xs) === '[object Array]';
+};
+
+},{}],14:[function(require,module,exports){
+// Copyright Joyent, Inc. and other Node contributors.
+//
+// Permission is hereby granted, free of charge, to any person obtaining a
+// copy of this software and associated documentation files (the
+// "Software"), to deal in the Software without restriction, including
+// without limitation the rights to use, copy, modify, merge, publish,
+// distribute, sublicense, and/or sell copies of the Software, and to permit
+// persons to whom the Software is furnished to do so, subject to the
+// following conditions:
+//
+// The above copyright notice and this permission notice shall be included
+// in all copies or substantial portions of the Software.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
+// OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+// MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN
+// NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM,
+// DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR
+// OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE
+// USE OR OTHER DEALINGS IN THE SOFTWARE.
+
+function EventEmitter() {
+  this._events = this._events || {};
+  this._maxListeners = this._maxListeners || undefined;
+}
+module.exports = EventEmitter;
+
+// Backwards-compat with node 0.10.x
+EventEmitter.EventEmitter = EventEmitter;
+
+EventEmitter.prototype._events = undefined;
+EventEmitter.prototype._maxListeners = undefined;
+
+// By default EventEmitters will print a warning if more than 10 listeners are
+// added to it. This is a useful default which helps finding memory leaks.
+EventEmitter.defaultMaxListeners = 10;
+
+// Obviously not all Emitters should be limited to 10. This function allows
+// that to be increased. Set to zero for unlimited.
+EventEmitter.prototype.setMaxListeners = function(n) {
+  if (!isNumber(n) || n < 0 || isNaN(n))
+    throw TypeError('n must be a positive number');
+  this._maxListeners = n;
+  return this;
+};
+
+EventEmitter.prototype.emit = function(type) {
+  var er, handler, len, args, i, listeners;
+
+  if (!this._events)
+    this._events = {};
+
+  // If there is no 'error' event listener then throw.
+  if (type === 'error') {
+    if (!this._events.error ||
+        (isObject(this._events.error) && !this._events.error.length)) {
+      er = arguments[1];
+      if (er instanceof Error) {
+        throw er; // Unhandled 'error' event
+      }
+      throw TypeError('Uncaught, unspecified "error" event.');
+    }
+  }
+
+  handler = this._events[type];
+
+  if (isUndefined(handler))
+    return false;
+
+  if (isFunction(handler)) {
+    switch (arguments.length) {
+      // fast cases
+      case 1:
+        handler.call(this);
+        break;
+      case 2:
+        handler.call(this, arguments[1]);
+        break;
+      case 3:
+        handler.call(this, arguments[1], arguments[2]);
+        break;
+      // slower
+      default:
+        len = arguments.length;
+        args = new Array(len - 1);
+        for (i = 1; i < len; i++)
+          args[i - 1] = arguments[i];
+        handler.apply(this, args);
+    }
+  } else if (isObject(handler)) {
+    len = arguments.length;
+    args = new Array(len - 1);
+    for (i = 1; i < len; i++)
+      args[i - 1] = arguments[i];
+
+    listeners = handler.slice();
+    len = listeners.length;
+    for (i = 0; i < len; i++)
+      listeners[i].apply(this, args);
+  }
+
+  return true;
+};
+
+EventEmitter.prototype.addListener = function(type, listener) {
+  var m;
+
+  if (!isFunction(listener))
+    throw TypeError('listener must be a function');
+
+  if (!this._events)
+    this._events = {};
+
+  // To avoid recursion in the case that type === "newListener"! Before
+  // adding it to the listeners, first emit "newListener".
+  if (this._events.newListener)
+    this.emit('newListener', type,
+              isFunction(listener.listener) ?
+              listener.listener : listener);
+
+  if (!this._events[type])
+    // Optimize the case of one listener. Don't need the extra array object.
+    this._events[type] = listener;
+  else if (isObject(this._events[type]))
+    // If we've already got an array, just append.
+    this._events[type].push(listener);
+  else
+    // Adding the second element, need to change to array.
+    this._events[type] = [this._events[type], listener];
+
+  // Check for listener leak
+  if (isObject(this._events[type]) && !this._events[type].warned) {
+    var m;
+    if (!isUndefined(this._maxListeners)) {
+      m = this._maxListeners;
+    } else {
+      m = EventEmitter.defaultMaxListeners;
+    }
+
+    if (m && m > 0 && this._events[type].length > m) {
+      this._events[type].warned = true;
+      console.error('(node) warning: possible EventEmitter memory ' +
+                    'leak detected. %d listeners added. ' +
+                    'Use emitter.setMaxListeners() to increase limit.',
+                    this._events[type].length);
+      if (typeof console.trace === 'function') {
+        // not supported in IE 10
+        console.trace();
+      }
+    }
+  }
+
+  return this;
+};
+
+EventEmitter.prototype.on = EventEmitter.prototype.addListener;
+
+EventEmitter.prototype.once = function(type, listener) {
+  if (!isFunction(listener))
+    throw TypeError('listener must be a function');
+
+  var fired = false;
+
+  function g() {
+    this.removeListener(type, g);
+
+    if (!fired) {
+      fired = true;
+      listener.apply(this, arguments);
+    }
+  }
+
+  g.listener = listener;
+  this.on(type, g);
+
+  return this;
+};
+
+// emits a 'removeListener' event iff the listener was removed
+EventEmitter.prototype.removeListener = function(type, listener) {
+  var list, position, length, i;
+
+  if (!isFunction(listener))
+    throw TypeError('listener must be a function');
+
+  if (!this._events || !this._events[type])
+    return this;
+
+  list = this._events[type];
+  length = list.length;
+  position = -1;
+
+  if (list === listener ||
+      (isFunction(list.listener) && list.listener === listener)) {
+    delete this._events[type];
+    if (this._events.removeListener)
+      this.emit('removeListener', type, listener);
+
+  } else if (isObject(list)) {
+    for (i = length; i-- > 0;) {
+      if (list[i] === listener ||
+          (list[i].listener && list[i].listener === listener)) {
+        position = i;
+        break;
+      }
+    }
+
+    if (position < 0)
+      return this;
+
+    if (list.length === 1) {
+      list.length = 0;
+      delete this._events[type];
+    } else {
+      list.splice(position, 1);
+    }
+
+    if (this._events.removeListener)
+      this.emit('removeListener', type, listener);
+  }
+
+  return this;
+};
+
+EventEmitter.prototype.removeAllListeners = function(type) {
+  var key, listeners;
+
+  if (!this._events)
+    return this;
+
+  // not listening for removeListener, no need to emit
+  if (!this._events.removeListener) {
+    if (arguments.length === 0)
+      this._events = {};
+    else if (this._events[type])
+      delete this._events[type];
+    return this;
+  }
+
+  // emit removeListener for all listeners on all events
+  if (arguments.length === 0) {
+    for (key in this._events) {
+      if (key === 'removeListener') continue;
+      this.removeAllListeners(key);
+    }
+    this.removeAllListeners('removeListener');
+    this._events = {};
+    return this;
+  }
+
+  listeners = this._events[type];
+
+  if (isFunction(listeners)) {
+    this.removeListener(type, listeners);
+  } else {
+    // LIFO order
+    while (listeners.length)
+      this.removeListener(type, listeners[listeners.length - 1]);
+  }
+  delete this._events[type];
+
+  return this;
+};
+
+EventEmitter.prototype.listeners = function(type) {
+  var ret;
+  if (!this._events || !this._events[type])
+    ret = [];
+  else if (isFunction(this._events[type]))
+    ret = [this._events[type]];
+  else
+    ret = this._events[type].slice();
+  return ret;
+};
+
+EventEmitter.listenerCount = function(emitter, type) {
+  var ret;
+  if (!emitter._events || !emitter._events[type])
+    ret = 0;
+  else if (isFunction(emitter._events[type]))
+    ret = 1;
+  else
+    ret = emitter._events[type].length;
+  return ret;
+};
+
+function isFunction(arg) {
+  return typeof arg === 'function';
+}
+
+function isNumber(arg) {
+  return typeof arg === 'number';
+}
+
+function isObject(arg) {
+  return typeof arg === 'object' && arg !== null;
+}
+
+function isUndefined(arg) {
+  return arg === void 0;
+}
+
+},{}],15:[function(require,module,exports){
+(function (process){
+exports.alphasort = alphasort
+exports.alphasorti = alphasorti
+exports.setopts = setopts
+exports.ownProp = ownProp
+exports.makeAbs = makeAbs
+exports.finish = finish
+exports.mark = mark
+exports.isIgnored = isIgnored
+exports.childrenIgnored = childrenIgnored
+
+function ownProp (obj, field) {
+  return Object.prototype.hasOwnProperty.call(obj, field)
+}
+
+var path = require("path")
+var minimatch = require("minimatch")
+var isAbsolute = require("path-is-absolute")
+var Minimatch = minimatch.Minimatch
+
+function alphasorti (a, b) {
+  return a.toLowerCase().localeCompare(b.toLowerCase())
+}
+
+function alphasort (a, b) {
+  return a.localeCompare(b)
+}
+
+function setupIgnores (self, options) {
+  self.ignore = options.ignore || []
+
+  if (!Array.isArray(self.ignore))
+    self.ignore = [self.ignore]
+
+  if (self.ignore.length) {
+    self.ignore = self.ignore.map(ignoreMap)
+  }
+}
+
+function ignoreMap (pattern) {
+  var gmatcher = null
+  if (pattern.slice(-3) === '/**') {
+    var gpattern = pattern.replace(/(\/\*\*)+$/, '')
+    gmatcher = new Minimatch(gpattern)
+  }
+
+  return {
+    matcher: new Minimatch(pattern),
+    gmatcher: gmatcher
+  }
+}
+
+function setopts (self, pattern, options) {
+  if (!options)
+    options = {}
+
+  // base-matching: just use globstar for that.
+  if (options.matchBase && -1 === pattern.indexOf("/")) {
+    if (options.noglobstar) {
+      throw new Error("base matching requires globstar")
+    }
+    pattern = "**/" + pattern
+  }
+
+  self.silent = !!options.silent
+  self.pattern = pattern
+  self.strict = options.strict !== false
+  self.realpath = !!options.realpath
+  self.realpathCache = options.realpathCache || Object.create(null)
+  self.follow = !!options.follow
+  self.dot = !!options.dot
+  self.mark = !!options.mark
+  self.nodir = !!options.nodir
+  if (self.nodir)
+    self.mark = true
+  self.sync = !!options.sync
+  self.nounique = !!options.nounique
+  self.nonull = !!options.nonull
+  self.nosort = !!options.nosort
+  self.nocase = !!options.nocase
+  self.stat = !!options.stat
+  self.noprocess = !!options.noprocess
+
+  self.maxLength = options.maxLength || Infinity
+  self.cache = options.cache || Object.create(null)
+  self.statCache = options.statCache || Object.create(null)
+  self.symlinks = options.symlinks || Object.create(null)
+
+  setupIgnores(self, options)
+
+  self.changedCwd = false
+  var cwd = process.cwd()
+  if (!ownProp(options, "cwd"))
+    self.cwd = cwd
+  else {
+    self.cwd = options.cwd
+    self.changedCwd = path.resolve(options.cwd) !== cwd
+  }
+
+  self.root = options.root || path.resolve(self.cwd, "/")
+  self.root = path.resolve(self.root)
+  if (process.platform === "win32")
+    self.root = self.root.replace(/\\/g, "/")
+
+  self.nomount = !!options.nomount
+
+  // disable comments and negation unless the user explicitly
+  // passes in false as the option.
+  options.nonegate = options.nonegate === false ? false : true
+  options.nocomment = options.nocomment === false ? false : true
+  deprecationWarning(options)
+
+  self.minimatch = new Minimatch(pattern, options)
+  self.options = self.minimatch.options
+}
+
+// TODO(isaacs): remove entirely in v6
+// exported to reset in tests
+exports.deprecationWarned
+function deprecationWarning(options) {
+  if (!options.nonegate || !options.nocomment) {
+    if (process.noDeprecation !== true && !exports.deprecationWarned) {
+      var msg = 'glob WARNING: comments and negation will be disabled in v6'
+      if (process.throwDeprecation)
+        throw new Error(msg)
+      else if (process.traceDeprecation)
+        console.trace(msg)
+      else
+        console.error(msg)
+
+      exports.deprecationWarned = true
+    }
+  }
+}
+
+function finish (self) {
+  var nou = self.nounique
+  var all = nou ? [] : Object.create(null)
+
+  for (var i = 0, l = self.matches.length; i < l; i ++) {
+    var matches = self.matches[i]
+    if (!matches || Object.keys(matches).length === 0) {
+      if (self.nonull) {
+        // do like the shell, and spit out the literal glob
+        var literal = self.minimatch.globSet[i]
+        if (nou)
+          all.push(literal)
+        else
+          all[literal] = true
+      }
+    } else {
+      // had matches
+      var m = Object.keys(matches)
+      if (nou)
+        all.push.apply(all, m)
+      else
+        m.forEach(function (m) {
+          all[m] = true
+        })
+    }
+  }
+
+  if (!nou)
+    all = Object.keys(all)
+
+  if (!self.nosort)
+    all = all.sort(self.nocase ? alphasorti : alphasort)
+
+  // at *some* point we statted all of these
+  if (self.mark) {
+    for (var i = 0; i < all.length; i++) {
+      all[i] = self._mark(all[i])
+    }
+    if (self.nodir) {
+      all = all.filter(function (e) {
+        return !(/\/$/.test(e))
+      })
+    }
+  }
+
+  if (self.ignore.length)
+    all = all.filter(function(m) {
+      return !isIgnored(self, m)
+    })
+
+  self.found = all
+}
+
+function mark (self, p) {
+  var abs = makeAbs(self, p)
+  var c = self.cache[abs]
+  var m = p
+  if (c) {
+    var isDir = c === 'DIR' || Array.isArray(c)
+    var slash = p.slice(-1) === '/'
+
+    if (isDir && !slash)
+      m += '/'
+    else if (!isDir && slash)
+      m = m.slice(0, -1)
+
+    if (m !== p) {
+      var mabs = makeAbs(self, m)
+      self.statCache[mabs] = self.statCache[abs]
+      self.cache[mabs] = self.cache[abs]
+    }
+  }
+
+  return m
+}
+
+// lotta situps...
+function makeAbs (self, f) {
+  var abs = f
+  if (f.charAt(0) === '/') {
+    abs = path.join(self.root, f)
+  } else if (isAbsolute(f) || f === '') {
+    abs = f
+  } else if (self.changedCwd) {
+    abs = path.resolve(self.cwd, f)
+  } else {
+    abs = path.resolve(f)
+  }
+  return abs
+}
+
+
+// Return true, if pattern ends with globstar '**', for the accompanying parent directory.
+// Ex:- If node_modules/** is the pattern, add 'node_modules' to ignore list along with it's contents
+function isIgnored (self, path) {
+  if (!self.ignore.length)
+    return false
+
+  return self.ignore.some(function(item) {
+    return item.matcher.match(path) || !!(item.gmatcher && item.gmatcher.match(path))
+  })
+}
+
+function childrenIgnored (self, path) {
+  if (!self.ignore.length)
+    return false
+
+  return self.ignore.some(function(item) {
+    return !!(item.gmatcher && item.gmatcher.match(path))
+  })
+}
+
+}).call(this,require('_process'))
+},{"_process":24,"minimatch":20,"path":22,"path-is-absolute":23}],16:[function(require,module,exports){
+(function (process){
+// Approach:
+//
+// 1. Get the minimatch set
+// 2. For each pattern in the set, PROCESS(pattern, false)
+// 3. Store matches per-set, then uniq them
+//
+// PROCESS(pattern, inGlobStar)
+// Get the first [n] items from pattern that are all strings
+// Join these together.  This is PREFIX.
+//   If there is no more remaining, then stat(PREFIX) and
+//   add to matches if it succeeds.  END.
+//
+// If inGlobStar and PREFIX is symlink and points to dir
+//   set ENTRIES = []
+// else readdir(PREFIX) as ENTRIES
+//   If fail, END
+//
+// with ENTRIES
+//   If pattern[n] is GLOBSTAR
+//     // handle the case where the globstar match is empty
+//     // by pruning it out, and testing the resulting pattern
+//     PROCESS(pattern[0..n] + pattern[n+1 .. $], false)
+//     // handle other cases.
+//     for ENTRY in ENTRIES (not dotfiles)
+//       // attach globstar + tail onto the entry
+//       // Mark that this entry is a globstar match
+//       PROCESS(pattern[0..n] + ENTRY + pattern[n .. $], true)
+//
+//   else // not globstar
+//     for ENTRY in ENTRIES (not dotfiles, unless pattern[n] is dot)
+//       Test ENTRY against pattern[n]
+//       If fails, continue
+//       If passes, PROCESS(pattern[0..n] + item + pattern[n+1 .. $])
+//
+// Caveat:
+//   Cache all stats and readdirs results to minimize syscall.  Since all
+//   we ever care about is existence and directory-ness, we can just keep
+//   `true` for files, and [children,...] for directories, or `false` for
+//   things that don't exist.
+
+module.exports = glob
+
+var fs = require('fs')
+var minimatch = require('minimatch')
+var Minimatch = minimatch.Minimatch
+var inherits = require('inherits')
+var EE = require('events').EventEmitter
+var path = require('path')
+var assert = require('assert')
+var isAbsolute = require('path-is-absolute')
+var globSync = require('./sync.js')
+var common = require('./common.js')
+var alphasort = common.alphasort
+var alphasorti = common.alphasorti
+var setopts = common.setopts
+var ownProp = common.ownProp
+var inflight = require('inflight')
+var util = require('util')
+var childrenIgnored = common.childrenIgnored
+var isIgnored = common.isIgnored
+
+var once = require('once')
+
+function glob (pattern, options, cb) {
+  if (typeof options === 'function') cb = options, options = {}
+  if (!options) options = {}
+
+  if (options.sync) {
+    if (cb)
+      throw new TypeError('callback provided to sync glob')
+    return globSync(pattern, options)
+  }
+
+  return new Glob(pattern, options, cb)
+}
+
+glob.sync = globSync
+var GlobSync = glob.GlobSync = globSync.GlobSync
+
+// old api surface
+glob.glob = glob
+
+glob.hasMagic = function (pattern, options_) {
+  var options = util._extend({}, options_)
+  options.noprocess = true
+
+  var g = new Glob(pattern, options)
+  var set = g.minimatch.set
+  if (set.length > 1)
+    return true
+
+  for (var j = 0; j < set[0].length; j++) {
+    if (typeof set[0][j] !== 'string')
+      return true
+  }
+
+  return false
+}
+
+glob.Glob = Glob
+inherits(Glob, EE)
+function Glob (pattern, options, cb) {
+  if (typeof options === 'function') {
+    cb = options
+    options = null
+  }
+
+  if (options && options.sync) {
+    if (cb)
+      throw new TypeError('callback provided to sync glob')
+    return new GlobSync(pattern, options)
+  }
+
+  if (!(this instanceof Glob))
+    return new Glob(pattern, options, cb)
+
+  setopts(this, pattern, options)
+  this._didRealPath = false
+
+  // process each pattern in the minimatch set
+  var n = this.minimatch.set.length
+
+  // The matches are stored as {<filename>: true,...} so that
+  // duplicates are automagically pruned.
+  // Later, we do an Object.keys() on these.
+  // Keep them as a list so we can fill in when nonull is set.
+  this.matches = new Array(n)
+
+  if (typeof cb === 'function') {
+    cb = once(cb)
+    this.on('error', cb)
+    this.on('end', function (matches) {
+      cb(null, matches)
+    })
+  }
+
+  var self = this
+  var n = this.minimatch.set.length
+  this._processing = 0
+  this.matches = new Array(n)
+
+  this._emitQueue = []
+  this._processQueue = []
+  this.paused = false
+
+  if (this.noprocess)
+    return this
+
+  if (n === 0)
+    return done()
+
+  for (var i = 0; i < n; i ++) {
+    this._process(this.minimatch.set[i], i, false, done)
+  }
+
+  function done () {
+    --self._processing
+    if (self._processing <= 0)
+      self._finish()
+  }
+}
+
+Glob.prototype._finish = function () {
+  assert(this instanceof Glob)
+  if (this.aborted)
+    return
+
+  if (this.realpath && !this._didRealpath)
+    return this._realpath()
+
+  common.finish(this)
+  this.emit('end', this.found)
+}
+
+Glob.prototype._realpath = function () {
+  if (this._didRealpath)
+    return
+
+  this._didRealpath = true
+
+  var n = this.matches.length
+  if (n === 0)
+    return this._finish()
+
+  var self = this
+  for (var i = 0; i < this.matches.length; i++)
+    this._realpathSet(i, next)
+
+  function next () {
+    if (--n === 0)
+      self._finish()
+  }
+}
+
+Glob.prototype._realpathSet = function (index, cb) {
+  var matchset = this.matches[index]
+  if (!matchset)
+    return cb()
+
+  var found = Object.keys(matchset)
+  var self = this
+  var n = found.length
+
+  if (n === 0)
+    return cb()
+
+  var set = this.matches[index] = Object.create(null)
+  found.forEach(function (p, i) {
+    // If there's a problem with the stat, then it means that
+    // one or more of the links in the realpath couldn't be
+    // resolved.  just return the abs value in that case.
+    p = self._makeAbs(p)
+    fs.realpath(p, self.realpathCache, function (er, real) {
+      if (!er)
+        set[real] = true
+      else if (er.syscall === 'stat')
+        set[p] = true
+      else
+        self.emit('error', er) // srsly wtf right here
+
+      if (--n === 0) {
+        self.matches[index] = set
+        cb()
+      }
+    })
+  })
+}
+
+Glob.prototype._mark = function (p) {
+  return common.mark(this, p)
+}
+
+Glob.prototype._makeAbs = function (f) {
+  return common.makeAbs(this, f)
+}
+
+Glob.prototype.abort = function () {
+  this.aborted = true
+  this.emit('abort')
+}
+
+Glob.prototype.pause = function () {
+  if (!this.paused) {
+    this.paused = true
+    this.emit('pause')
+  }
+}
+
+Glob.prototype.resume = function () {
+  if (this.paused) {
+    this.emit('resume')
+    this.paused = false
+    if (this._emitQueue.length) {
+      var eq = this._emitQueue.slice(0)
+      this._emitQueue.length = 0
+      for (var i = 0; i < eq.length; i ++) {
+        var e = eq[i]
+        this._emitMatch(e[0], e[1])
+      }
+    }
+    if (this._processQueue.length) {
+      var pq = this._processQueue.slice(0)
+      this._processQueue.length = 0
+      for (var i = 0; i < pq.length; i ++) {
+        var p = pq[i]
+        this._processing--
+        this._process(p[0], p[1], p[2], p[3])
+      }
+    }
+  }
+}
+
+Glob.prototype._process = function (pattern, index, inGlobStar, cb) {
+  assert(this instanceof Glob)
+  assert(typeof cb === 'function')
+
+  if (this.aborted)
+    return
+
+  this._processing++
+  if (this.paused) {
+    this._processQueue.push([pattern, index, inGlobStar, cb])
+    return
+  }
+
+  //console.error('PROCESS %d', this._processing, pattern)
+
+  // Get the first [n] parts of pattern that are all strings.
+  var n = 0
+  while (typeof pattern[n] === 'string') {
+    n ++
+  }
+  // now n is the index of the first one that is *not* a string.
+
+  // see if there's anything else
+  var prefix
+  switch (n) {
+    // if not, then this is rather simple
+    case pattern.length:
+      this._processSimple(pattern.join('/'), index, cb)
+      return
+
+    case 0:
+      // pattern *starts* with some non-trivial item.
+      // going to readdir(cwd), but not include the prefix in matches.
+      prefix = null
+      break
+
+    default:
+      // pattern has some string bits in the front.
+      // whatever it starts with, whether that's 'absolute' like /foo/bar,
+      // or 'relative' like '../baz'
+      prefix = pattern.slice(0, n).join('/')
+      break
+  }
+
+  var remain = pattern.slice(n)
+
+  // get the list of entries.
+  var read
+  if (prefix === null)
+    read = '.'
+  else if (isAbsolute(prefix) || isAbsolute(pattern.join('/'))) {
+    if (!prefix || !isAbsolute(prefix))
+      prefix = '/' + prefix
+    read = prefix
+  } else
+    read = prefix
+
+  var abs = this._makeAbs(read)
+
+  //if ignored, skip _processing
+  if (childrenIgnored(this, read))
+    return cb()
+
+  var isGlobStar = remain[0] === minimatch.GLOBSTAR
+  if (isGlobStar)
+    this._processGlobStar(prefix, read, abs, remain, index, inGlobStar, cb)
+  else
+    this._processReaddir(prefix, read, abs, remain, index, inGlobStar, cb)
+}
+
+Glob.prototype._processReaddir = function (prefix, read, abs, remain, index, inGlobStar, cb) {
+  var self = this
+  this._readdir(abs, inGlobStar, function (er, entries) {
+    return self._processReaddir2(prefix, read, abs, remain, index, inGlobStar, entries, cb)
+  })
+}
+
+Glob.prototype._processReaddir2 = function (prefix, read, abs, remain, index, inGlobStar, entries, cb) {
+
+  // if the abs isn't a dir, then nothing can match!
+  if (!entries)
+    return cb()
+
+  // It will only match dot entries if it starts with a dot, or if
+  // dot is set.  Stuff like @(.foo|.bar) isn't allowed.
+  var pn = remain[0]
+  var negate = !!this.minimatch.negate
+  var rawGlob = pn._glob
+  var dotOk = this.dot || rawGlob.charAt(0) === '.'
+
+  var matchedEntries = []
+  for (var i = 0; i < entries.length; i++) {
+    var e = entries[i]
+    if (e.charAt(0) !== '.' || dotOk) {
+      var m
+      if (negate && !prefix) {
+        m = !e.match(pn)
+      } else {
+        m = e.match(pn)
+      }
+      if (m)
+        matchedEntries.push(e)
+    }
+  }
+
+  //console.error('prd2', prefix, entries, remain[0]._glob, matchedEntries)
+
+  var len = matchedEntries.length
+  // If there are no matched entries, then nothing matches.
+  if (len === 0)
+    return cb()
+
+  // if this is the last remaining pattern bit, then no need for
+  // an additional stat *unless* the user has specified mark or
+  // stat explicitly.  We know they exist, since readdir returned
+  // them.
+
+  if (remain.length === 1 && !this.mark && !this.stat) {
+    if (!this.matches[index])
+      this.matches[index] = Object.create(null)
+
+    for (var i = 0; i < len; i ++) {
+      var e = matchedEntries[i]
+      if (prefix) {
+        if (prefix !== '/')
+          e = prefix + '/' + e
+        else
+          e = prefix + e
+      }
+
+      if (e.charAt(0) === '/' && !this.nomount) {
+        e = path.join(this.root, e)
+      }
+      this._emitMatch(index, e)
+    }
+    // This was the last one, and no stats were needed
+    return cb()
+  }
+
+  // now test all matched entries as stand-ins for that part
+  // of the pattern.
+  remain.shift()
+  for (var i = 0; i < len; i ++) {
+    var e = matchedEntries[i]
+    var newPattern
+    if (prefix) {
+      if (prefix !== '/')
+        e = prefix + '/' + e
+      else
+        e = prefix + e
+    }
+    this._process([e].concat(remain), index, inGlobStar, cb)
+  }
+  cb()
+}
+
+Glob.prototype._emitMatch = function (index, e) {
+  if (this.aborted)
+    return
+
+  if (this.matches[index][e])
+    return
+
+  if (isIgnored(this, e))
+    return
+
+  if (this.paused) {
+    this._emitQueue.push([index, e])
+    return
+  }
+
+  var abs = this._makeAbs(e)
+
+  if (this.nodir) {
+    var c = this.cache[abs]
+    if (c === 'DIR' || Array.isArray(c))
+      return
+  }
+
+  if (this.mark)
+    e = this._mark(e)
+
+  this.matches[index][e] = true
+
+  var st = this.statCache[abs]
+  if (st)
+    this.emit('stat', e, st)
+
+  this.emit('match', e)
+}
+
+Glob.prototype._readdirInGlobStar = function (abs, cb) {
+  if (this.aborted)
+    return
+
+  // follow all symlinked directories forever
+  // just proceed as if this is a non-globstar situation
+  if (this.follow)
+    return this._readdir(abs, false, cb)
+
+  var lstatkey = 'lstat\0' + abs
+  var self = this
+  var lstatcb = inflight(lstatkey, lstatcb_)
+
+  if (lstatcb)
+    fs.lstat(abs, lstatcb)
+
+  function lstatcb_ (er, lstat) {
+    if (er)
+      return cb()
+
+    var isSym = lstat.isSymbolicLink()
+    self.symlinks[abs] = isSym
+
+    // If it's not a symlink or a dir, then it's definitely a regular file.
+    // don't bother doing a readdir in that case.
+    if (!isSym && !lstat.isDirectory()) {
+      self.cache[abs] = 'FILE'
+      cb()
+    } else
+      self._readdir(abs, false, cb)
+  }
+}
+
+Glob.prototype._readdir = function (abs, inGlobStar, cb) {
+  if (this.aborted)
+    return
+
+  cb = inflight('readdir\0'+abs+'\0'+inGlobStar, cb)
+  if (!cb)
+    return
+
+  //console.error('RD %j %j', +inGlobStar, abs)
+  if (inGlobStar && !ownProp(this.symlinks, abs))
+    return this._readdirInGlobStar(abs, cb)
+
+  if (ownProp(this.cache, abs)) {
+    var c = this.cache[abs]
+    if (!c || c === 'FILE')
+      return cb()
+
+    if (Array.isArray(c))
+      return cb(null, c)
+  }
+
+  var self = this
+  fs.readdir(abs, readdirCb(this, abs, cb))
+}
+
+function readdirCb (self, abs, cb) {
+  return function (er, entries) {
+    if (er)
+      self._readdirError(abs, er, cb)
+    else
+      self._readdirEntries(abs, entries, cb)
+  }
+}
+
+Glob.prototype._readdirEntries = function (abs, entries, cb) {
+  if (this.aborted)
+    return
+
+  // if we haven't asked to stat everything, then just
+  // assume that everything in there exists, so we can avoid
+  // having to stat it a second time.
+  if (!this.mark && !this.stat) {
+    for (var i = 0; i < entries.length; i ++) {
+      var e = entries[i]
+      if (abs === '/')
+        e = abs + e
+      else
+        e = abs + '/' + e
+      this.cache[e] = true
+    }
+  }
+
+  this.cache[abs] = entries
+  return cb(null, entries)
+}
+
+Glob.prototype._readdirError = function (f, er, cb) {
+  if (this.aborted)
+    return
+
+  // handle errors, and cache the information
+  switch (er.code) {
+    case 'ENOTSUP': // https://github.com/isaacs/node-glob/issues/205
+    case 'ENOTDIR': // totally normal. means it *does* exist.
+      this.cache[this._makeAbs(f)] = 'FILE'
+      break
+
+    case 'ENOENT': // not terribly unusual
+    case 'ELOOP':
+    case 'ENAMETOOLONG':
+    case 'UNKNOWN':
+      this.cache[this._makeAbs(f)] = false
+      break
+
+    default: // some unusual error.  Treat as failure.
+      this.cache[this._makeAbs(f)] = false
+      if (this.strict) {
+        this.emit('error', er)
+        // If the error is handled, then we abort
+        // if not, we threw out of here
+        this.abort()
+      }
+      if (!this.silent)
+        console.error('glob error', er)
+      break
+  }
+
+  return cb()
+}
+
+Glob.prototype._processGlobStar = function (prefix, read, abs, remain, index, inGlobStar, cb) {
+  var self = this
+  this._readdir(abs, inGlobStar, function (er, entries) {
+    self._processGlobStar2(prefix, read, abs, remain, index, inGlobStar, entries, cb)
+  })
+}
+
+
+Glob.prototype._processGlobStar2 = function (prefix, read, abs, remain, index, inGlobStar, entries, cb) {
+  //console.error('pgs2', prefix, remain[0], entries)
+
+  // no entries means not a dir, so it can never have matches
+  // foo.txt/** doesn't match foo.txt
+  if (!entries)
+    return cb()
+
+  // test without the globstar, and with every child both below
+  // and replacing the globstar.
+  var remainWithoutGlobStar = remain.slice(1)
+  var gspref = prefix ? [ prefix ] : []
+  var noGlobStar = gspref.concat(remainWithoutGlobStar)
+
+  // the noGlobStar pattern exits the inGlobStar state
+  this._process(noGlobStar, index, false, cb)
+
+  var isSym = this.symlinks[abs]
+  var len = entries.length
+
+  // If it's a symlink, and we're in a globstar, then stop
+  if (isSym && inGlobStar)
+    return cb()
+
+  for (var i = 0; i < len; i++) {
+    var e = entries[i]
+    if (e.charAt(0) === '.' && !this.dot)
+      continue
+
+    // these two cases enter the inGlobStar state
+    var instead = gspref.concat(entries[i], remainWithoutGlobStar)
+    this._process(instead, index, true, cb)
+
+    var below = gspref.concat(entries[i], remain)
+    this._process(below, index, true, cb)
+  }
+
+  cb()
+}
+
+Glob.prototype._processSimple = function (prefix, index, cb) {
+  // XXX review this.  Shouldn't it be doing the mounting etc
+  // before doing stat?  kinda weird?
+  var self = this
+  this._stat(prefix, function (er, exists) {
+    self._processSimple2(prefix, index, er, exists, cb)
+  })
+}
+Glob.prototype._processSimple2 = function (prefix, index, er, exists, cb) {
+
+  //console.error('ps2', prefix, exists)
+
+  if (!this.matches[index])
+    this.matches[index] = Object.create(null)
+
+  // If it doesn't exist, then just mark the lack of results
+  if (!exists)
+    return cb()
+
+  if (prefix && isAbsolute(prefix) && !this.nomount) {
+    var trail = /[\/\\]$/.test(prefix)
+    if (prefix.charAt(0) === '/') {
+      prefix = path.join(this.root, prefix)
+    } else {
+      prefix = path.resolve(this.root, prefix)
+      if (trail)
+        prefix += '/'
+    }
+  }
+
+  if (process.platform === 'win32')
+    prefix = prefix.replace(/\\/g, '/')
+
+  // Mark this as a match
+  this._emitMatch(index, prefix)
+  cb()
+}
+
+// Returns either 'DIR', 'FILE', or false
+Glob.prototype._stat = function (f, cb) {
+  var abs = this._makeAbs(f)
+  var needDir = f.slice(-1) === '/'
+
+  if (f.length > this.maxLength)
+    return cb()
+
+  if (!this.stat && ownProp(this.cache, abs)) {
+    var c = this.cache[abs]
+
+    if (Array.isArray(c))
+      c = 'DIR'
+
+    // It exists, but maybe not how we need it
+    if (!needDir || c === 'DIR')
+      return cb(null, c)
+
+    if (needDir && c === 'FILE')
+      return cb()
+
+    // otherwise we have to stat, because maybe c=true
+    // if we know it exists, but not what it is.
+  }
+
+  var exists
+  var stat = this.statCache[abs]
+  if (stat !== undefined) {
+    if (stat === false)
+      return cb(null, stat)
+    else {
+      var type = stat.isDirectory() ? 'DIR' : 'FILE'
+      if (needDir && type === 'FILE')
+        return cb()
+      else
+        return cb(null, type, stat)
+    }
+  }
+
+  var self = this
+  var statcb = inflight('stat\0' + abs, lstatcb_)
+  if (statcb)
+    fs.lstat(abs, statcb)
+
+  function lstatcb_ (er, lstat) {
+    if (lstat && lstat.isSymbolicLink()) {
+      // If it's a symlink, then treat it as the target, unless
+      // the target does not exist, then treat it as a file.
+      return fs.stat(abs, function (er, stat) {
+        if (er)
+          self._stat2(f, abs, null, lstat, cb)
+        else
+          self._stat2(f, abs, er, stat, cb)
+      })
+    } else {
+      self._stat2(f, abs, er, lstat, cb)
+    }
+  }
+}
+
+Glob.prototype._stat2 = function (f, abs, er, stat, cb) {
+  if (er) {
+    this.statCache[abs] = false
+    return cb()
+  }
+
+  var needDir = f.slice(-1) === '/'
+  this.statCache[abs] = stat
+
+  if (abs.slice(-1) === '/' && !stat.isDirectory())
+    return cb(null, false, stat)
+
+  var c = stat.isDirectory() ? 'DIR' : 'FILE'
+  this.cache[abs] = this.cache[abs] || c
+
+  if (needDir && c !== 'DIR')
+    return cb()
+
+  return cb(null, c, stat)
+}
+
+}).call(this,require('_process'))
+},{"./common.js":15,"./sync.js":17,"_process":24,"assert":9,"events":14,"fs":12,"inflight":18,"inherits":19,"minimatch":20,"once":21,"path":22,"path-is-absolute":23,"util":28}],17:[function(require,module,exports){
+(function (process){
+module.exports = globSync
+globSync.GlobSync = GlobSync
+
+var fs = require('fs')
+var minimatch = require('minimatch')
+var Minimatch = minimatch.Minimatch
+var Glob = require('./glob.js').Glob
+var util = require('util')
+var path = require('path')
+var assert = require('assert')
+var isAbsolute = require('path-is-absolute')
+var common = require('./common.js')
+var alphasort = common.alphasort
+var alphasorti = common.alphasorti
+var setopts = common.setopts
+var ownProp = common.ownProp
+var childrenIgnored = common.childrenIgnored
+
+function globSync (pattern, options) {
+  if (typeof options === 'function' || arguments.length === 3)
+    throw new TypeError('callback provided to sync glob\n'+
+                        'See: https://github.com/isaacs/node-glob/issues/167')
+
+  return new GlobSync(pattern, options).found
+}
+
+function GlobSync (pattern, options) {
+  if (!pattern)
+    throw new Error('must provide pattern')
+
+  if (typeof options === 'function' || arguments.length === 3)
+    throw new TypeError('callback provided to sync glob\n'+
+                        'See: https://github.com/isaacs/node-glob/issues/167')
+
+  if (!(this instanceof GlobSync))
+    return new GlobSync(pattern, options)
+
+  setopts(this, pattern, options)
+
+  if (this.noprocess)
+    return this
+
+  var n = this.minimatch.set.length
+  this.matches = new Array(n)
+  for (var i = 0; i < n; i ++) {
+    this._process(this.minimatch.set[i], i, false)
+  }
+  this._finish()
+}
+
+GlobSync.prototype._finish = function () {
+  assert(this instanceof GlobSync)
+  if (this.realpath) {
+    var self = this
+    this.matches.forEach(function (matchset, index) {
+      var set = self.matches[index] = Object.create(null)
+      for (var p in matchset) {
+        try {
+          p = self._makeAbs(p)
+          var real = fs.realpathSync(p, self.realpathCache)
+          set[real] = true
+        } catch (er) {
+          if (er.syscall === 'stat')
+            set[self._makeAbs(p)] = true
+          else
+            throw er
+        }
+      }
+    })
+  }
+  common.finish(this)
+}
+
+
+GlobSync.prototype._process = function (pattern, index, inGlobStar) {
+  assert(this instanceof GlobSync)
+
+  // Get the first [n] parts of pattern that are all strings.
+  var n = 0
+  while (typeof pattern[n] === 'string') {
+    n ++
+  }
+  // now n is the index of the first one that is *not* a string.
+
+  // See if there's anything else
+  var prefix
+  switch (n) {
+    // if not, then this is rather simple
+    case pattern.length:
+      this._processSimple(pattern.join('/'), index)
+      return
+
+    case 0:
+      // pattern *starts* with some non-trivial item.
+      // going to readdir(cwd), but not include the prefix in matches.
+      prefix = null
+      break
+
+    default:
+      // pattern has some string bits in the front.
+      // whatever it starts with, whether that's 'absolute' like /foo/bar,
+      // or 'relative' like '../baz'
+      prefix = pattern.slice(0, n).join('/')
+      break
+  }
+
+  var remain = pattern.slice(n)
+
+  // get the list of entries.
+  var read
+  if (prefix === null)
+    read = '.'
+  else if (isAbsolute(prefix) || isAbsolute(pattern.join('/'))) {
+    if (!prefix || !isAbsolute(prefix))
+      prefix = '/' + prefix
+    read = prefix
+  } else
+    read = prefix
+
+  var abs = this._makeAbs(read)
+
+  //if ignored, skip processing
+  if (childrenIgnored(this, read))
+    return
+
+  var isGlobStar = remain[0] === minimatch.GLOBSTAR
+  if (isGlobStar)
+    this._processGlobStar(prefix, read, abs, remain, index, inGlobStar)
+  else
+    this._processReaddir(prefix, read, abs, remain, index, inGlobStar)
+}
+
+
+GlobSync.prototype._processReaddir = function (prefix, read, abs, remain, index, inGlobStar) {
+  var entries = this._readdir(abs, inGlobStar)
+
+  // if the abs isn't a dir, then nothing can match!
+  if (!entries)
+    return
+
+  // It will only match dot entries if it starts with a dot, or if
+  // dot is set.  Stuff like @(.foo|.bar) isn't allowed.
+  var pn = remain[0]
+  var negate = !!this.minimatch.negate
+  var rawGlob = pn._glob
+  var dotOk = this.dot || rawGlob.charAt(0) === '.'
+
+  var matchedEntries = []
+  for (var i = 0; i < entries.length; i++) {
+    var e = entries[i]
+    if (e.charAt(0) !== '.' || dotOk) {
+      var m
+      if (negate && !prefix) {
+        m = !e.match(pn)
+      } else {
+        m = e.match(pn)
+      }
+      if (m)
+        matchedEntries.push(e)
+    }
+  }
+
+  var len = matchedEntries.length
+  // If there are no matched entries, then nothing matches.
+  if (len === 0)
+    return
+
+  // if this is the last remaining pattern bit, then no need for
+  // an additional stat *unless* the user has specified mark or
+  // stat explicitly.  We know they exist, since readdir returned
+  // them.
+
+  if (remain.length === 1 && !this.mark && !this.stat) {
+    if (!this.matches[index])
+      this.matches[index] = Object.create(null)
+
+    for (var i = 0; i < len; i ++) {
+      var e = matchedEntries[i]
+      if (prefix) {
+        if (prefix.slice(-1) !== '/')
+          e = prefix + '/' + e
+        else
+          e = prefix + e
+      }
+
+      if (e.charAt(0) === '/' && !this.nomount) {
+        e = path.join(this.root, e)
+      }
+      this.matches[index][e] = true
+    }
+    // This was the last one, and no stats were needed
+    return
+  }
+
+  // now test all matched entries as stand-ins for that part
+  // of the pattern.
+  remain.shift()
+  for (var i = 0; i < len; i ++) {
+    var e = matchedEntries[i]
+    var newPattern
+    if (prefix)
+      newPattern = [prefix, e]
+    else
+      newPattern = [e]
+    this._process(newPattern.concat(remain), index, inGlobStar)
+  }
+}
+
+
+GlobSync.prototype._emitMatch = function (index, e) {
+  var abs = this._makeAbs(e)
+  if (this.mark)
+    e = this._mark(e)
+
+  if (this.matches[index][e])
+    return
+
+  if (this.nodir) {
+    var c = this.cache[this._makeAbs(e)]
+    if (c === 'DIR' || Array.isArray(c))
+      return
+  }
+
+  this.matches[index][e] = true
+  if (this.stat)
+    this._stat(e)
+}
+
+
+GlobSync.prototype._readdirInGlobStar = function (abs) {
+  // follow all symlinked directories forever
+  // just proceed as if this is a non-globstar situation
+  if (this.follow)
+    return this._readdir(abs, false)
+
+  var entries
+  var lstat
+  var stat
+  try {
+    lstat = fs.lstatSync(abs)
+  } catch (er) {
+    // lstat failed, doesn't exist
+    return null
+  }
+
+  var isSym = lstat.isSymbolicLink()
+  this.symlinks[abs] = isSym
+
+  // If it's not a symlink or a dir, then it's definitely a regular file.
+  // don't bother doing a readdir in that case.
+  if (!isSym && !lstat.isDirectory())
+    this.cache[abs] = 'FILE'
+  else
+    entries = this._readdir(abs, false)
+
+  return entries
+}
+
+GlobSync.prototype._readdir = function (abs, inGlobStar) {
+  var entries
+
+  if (inGlobStar && !ownProp(this.symlinks, abs))
+    return this._readdirInGlobStar(abs)
+
+  if (ownProp(this.cache, abs)) {
+    var c = this.cache[abs]
+    if (!c || c === 'FILE')
+      return null
+
+    if (Array.isArray(c))
+      return c
+  }
+
+  try {
+    return this._readdirEntries(abs, fs.readdirSync(abs))
+  } catch (er) {
+    this._readdirError(abs, er)
+    return null
+  }
+}
+
+GlobSync.prototype._readdirEntries = function (abs, entries) {
+  // if we haven't asked to stat everything, then just
+  // assume that everything in there exists, so we can avoid
+  // having to stat it a second time.
+  if (!this.mark && !this.stat) {
+    for (var i = 0; i < entries.length; i ++) {
+      var e = entries[i]
+      if (abs === '/')
+        e = abs + e
+      else
+        e = abs + '/' + e
+      this.cache[e] = true
+    }
+  }
+
+  this.cache[abs] = entries
+
+  // mark and cache dir-ness
+  return entries
+}
+
+GlobSync.prototype._readdirError = function (f, er) {
+  // handle errors, and cache the information
+  switch (er.code) {
+    case 'ENOTSUP': // https://github.com/isaacs/node-glob/issues/205
+    case 'ENOTDIR': // totally normal. means it *does* exist.
+      this.cache[this._makeAbs(f)] = 'FILE'
+      break
+
+    case 'ENOENT': // not terribly unusual
+    case 'ELOOP':
+    case 'ENAMETOOLONG':
+    case 'UNKNOWN':
+      this.cache[this._makeAbs(f)] = false
+      break
+
+    default: // some unusual error.  Treat as failure.
+      this.cache[this._makeAbs(f)] = false
+      if (this.strict)
+        throw er
+      if (!this.silent)
+        console.error('glob error', er)
+      break
+  }
+}
+
+GlobSync.prototype._processGlobStar = function (prefix, read, abs, remain, index, inGlobStar) {
+
+  var entries = this._readdir(abs, inGlobStar)
+
+  // no entries means not a dir, so it can never have matches
+  // foo.txt/** doesn't match foo.txt
+  if (!entries)
+    return
+
+  // test without the globstar, and with every child both below
+  // and replacing the globstar.
+  var remainWithoutGlobStar = remain.slice(1)
+  var gspref = prefix ? [ prefix ] : []
+  var noGlobStar = gspref.concat(remainWithoutGlobStar)
+
+  // the noGlobStar pattern exits the inGlobStar state
+  this._process(noGlobStar, index, false)
+
+  var len = entries.length
+  var isSym = this.symlinks[abs]
+
+  // If it's a symlink, and we're in a globstar, then stop
+  if (isSym && inGlobStar)
+    return
+
+  for (var i = 0; i < len; i++) {
+    var e = entries[i]
+    if (e.charAt(0) === '.' && !this.dot)
+      continue
+
+    // these two cases enter the inGlobStar state
+    var instead = gspref.concat(entries[i], remainWithoutGlobStar)
+    this._process(instead, index, true)
+
+    var below = gspref.concat(entries[i], remain)
+    this._process(below, index, true)
+  }
+}
+
+GlobSync.prototype._processSimple = function (prefix, index) {
+  // XXX review this.  Shouldn't it be doing the mounting etc
+  // before doing stat?  kinda weird?
+  var exists = this._stat(prefix)
+
+  if (!this.matches[index])
+    this.matches[index] = Object.create(null)
+
+  // If it doesn't exist, then just mark the lack of results
+  if (!exists)
+    return
+
+  if (prefix && isAbsolute(prefix) && !this.nomount) {
+    var trail = /[\/\\]$/.test(prefix)
+    if (prefix.charAt(0) === '/') {
+      prefix = path.join(this.root, prefix)
+    } else {
+      prefix = path.resolve(this.root, prefix)
+      if (trail)
+        prefix += '/'
+    }
+  }
+
+  if (process.platform === 'win32')
+    prefix = prefix.replace(/\\/g, '/')
+
+  // Mark this as a match
+  this.matches[index][prefix] = true
+}
+
+// Returns either 'DIR', 'FILE', or false
+GlobSync.prototype._stat = function (f) {
+  var abs = this._makeAbs(f)
+  var needDir = f.slice(-1) === '/'
+
+  if (f.length > this.maxLength)
+    return false
+
+  if (!this.stat && ownProp(this.cache, abs)) {
+    var c = this.cache[abs]
+
+    if (Array.isArray(c))
+      c = 'DIR'
+
+    // It exists, but maybe not how we need it
+    if (!needDir || c === 'DIR')
+      return c
+
+    if (needDir && c === 'FILE')
+      return false
+
+    // otherwise we have to stat, because maybe c=true
+    // if we know it exists, but not what it is.
+  }
+
+  var exists
+  var stat = this.statCache[abs]
+  if (!stat) {
+    var lstat
+    try {
+      lstat = fs.lstatSync(abs)
+    } catch (er) {
+      return false
+    }
+
+    if (lstat.isSymbolicLink()) {
+      try {
+        stat = fs.statSync(abs)
+      } catch (er) {
+        stat = lstat
+      }
+    } else {
+      stat = lstat
+    }
+  }
+
+  this.statCache[abs] = stat
+
+  var c = stat.isDirectory() ? 'DIR' : 'FILE'
+  this.cache[abs] = this.cache[abs] || c
+
+  if (needDir && c !== 'DIR')
+    return false
+
+  return c
+}
+
+GlobSync.prototype._mark = function (p) {
+  return common.mark(this, p)
+}
+
+GlobSync.prototype._makeAbs = function (f) {
+  return common.makeAbs(this, f)
+}
+
+}).call(this,require('_process'))
+},{"./common.js":15,"./glob.js":16,"_process":24,"assert":9,"fs":12,"minimatch":20,"path":22,"path-is-absolute":23,"util":28}],18:[function(require,module,exports){
+(function (process){
+var wrappy = require('wrappy')
+var reqs = Object.create(null)
+var once = require('once')
+
+module.exports = wrappy(inflight)
+
+function inflight (key, cb) {
+  if (reqs[key]) {
+    reqs[key].push(cb)
+    return null
+  } else {
+    reqs[key] = [cb]
+    return makeres(key)
+  }
+}
+
+function makeres (key) {
+  return once(function RES () {
+    var cbs = reqs[key]
+    var len = cbs.length
+    var args = slice(arguments)
+
+    // XXX It's somewhat ambiguous whether a new callback added in this
+    // pass should be queued for later execution if something in the
+    // list of callbacks throws, or if it should just be discarded.
+    // However, it's such an edge case that it hardly matters, and either
+    // choice is likely as surprising as the other.
+    // As it happens, we do go ahead and schedule it for later execution.
+    try {
+      for (var i = 0; i < len; i++) {
+        cbs[i].apply(null, args)
+      }
+    } finally {
+      if (cbs.length > len) {
+        // added more in the interim.
+        // de-zalgo, just in case, but don't call again.
+        cbs.splice(0, len)
+        process.nextTick(function () {
+          RES.apply(null, args)
+        })
+      } else {
+        delete reqs[key]
+      }
+    }
+  })
+}
+
+function slice (args) {
+  var length = args.length
+  var array = []
+
+  for (var i = 0; i < length; i++) array[i] = args[i]
+  return array
+}
+
+}).call(this,require('_process'))
+},{"_process":24,"once":21,"wrappy":29}],19:[function(require,module,exports){
+if (typeof Object.create === 'function') {
+  // implementation from standard node.js 'util' module
+  module.exports = function inherits(ctor, superCtor) {
+    ctor.super_ = superCtor
+    ctor.prototype = Object.create(superCtor.prototype, {
+      constructor: {
+        value: ctor,
+        enumerable: false,
+        writable: true,
+        configurable: true
+      }
+    });
+  };
+} else {
+  // old school shim for old browsers
+  module.exports = function inherits(ctor, superCtor) {
+    ctor.super_ = superCtor
+    var TempCtor = function () {}
+    TempCtor.prototype = superCtor.prototype
+    ctor.prototype = new TempCtor()
+    ctor.prototype.constructor = ctor
+  }
+}
+
+},{}],20:[function(require,module,exports){
+module.exports = minimatch
+minimatch.Minimatch = Minimatch
+
+var path = { sep: '/' }
+try {
+  path = require('path')
+} catch (er) {}
+
+var GLOBSTAR = minimatch.GLOBSTAR = Minimatch.GLOBSTAR = {}
+var expand = require('brace-expansion')
+
+var plTypes = {
+  '!': { open: '(?:(?!(?:', close: '))[^/]*?)'},
+  '?': { open: '(?:', close: ')?' },
+  '+': { open: '(?:', close: ')+' },
+  '*': { open: '(?:', close: ')*' },
+  '@': { open: '(?:', close: ')' }
+}
+
+// any single thing other than /
+// don't need to escape / when using new RegExp()
+var qmark = '[^/]'
+
+// * => any number of characters
+var star = qmark + '*?'
+
+// ** when dots are allowed.  Anything goes, except .. and .
+// not (^ or / followed by one or two dots followed by $ or /),
+// followed by anything, any number of times.
+var twoStarDot = '(?:(?!(?:\\\/|^)(?:\\.{1,2})($|\\\/)).)*?'
+
+// not a ^ or / followed by a dot,
+// followed by anything, any number of times.
+var twoStarNoDot = '(?:(?!(?:\\\/|^)\\.).)*?'
+
+// characters that need to be escaped in RegExp.
+var reSpecials = charSet('().*{}+?[]^$\\!')
+
+// "abc" -> { a:true, b:true, c:true }
+function charSet (s) {
+  return s.split('').reduce(function (set, c) {
+    set[c] = true
+    return set
+  }, {})
+}
+
+// normalizes slashes.
+var slashSplit = /\/+/
+
+minimatch.filter = filter
+function filter (pattern, options) {
+  options = options || {}
+  return function (p, i, list) {
+    return minimatch(p, pattern, options)
+  }
+}
+
+function ext (a, b) {
+  a = a || {}
+  b = b || {}
+  var t = {}
+  Object.keys(b).forEach(function (k) {
+    t[k] = b[k]
+  })
+  Object.keys(a).forEach(function (k) {
+    t[k] = a[k]
+  })
+  return t
+}
+
+minimatch.defaults = function (def) {
+  if (!def || !Object.keys(def).length) return minimatch
+
+  var orig = minimatch
+
+  var m = function minimatch (p, pattern, options) {
+    return orig.minimatch(p, pattern, ext(def, options))
+  }
+
+  m.Minimatch = function Minimatch (pattern, options) {
+    return new orig.Minimatch(pattern, ext(def, options))
+  }
+
+  return m
+}
+
+Minimatch.defaults = function (def) {
+  if (!def || !Object.keys(def).length) return Minimatch
+  return minimatch.defaults(def).Minimatch
+}
+
+function minimatch (p, pattern, options) {
+  if (typeof pattern !== 'string') {
+    throw new TypeError('glob pattern string required')
+  }
+
+  if (!options) options = {}
+
+  // shortcut: comments match nothing.
+  if (!options.nocomment && pattern.charAt(0) === '#') {
+    return false
+  }
+
+  // "" only matches ""
+  if (pattern.trim() === '') return p === ''
+
+  return new Minimatch(pattern, options).match(p)
+}
+
+function Minimatch (pattern, options) {
+  if (!(this instanceof Minimatch)) {
+    return new Minimatch(pattern, options)
+  }
+
+  if (typeof pattern !== 'string') {
+    throw new TypeError('glob pattern string required')
+  }
+
+  if (!options) options = {}
+  pattern = pattern.trim()
+
+  // windows support: need to use /, not \
+  if (path.sep !== '/') {
+    pattern = pattern.split(path.sep).join('/')
+  }
+
+  this.options = options
+  this.set = []
+  this.pattern = pattern
+  this.regexp = null
+  this.negate = false
+  this.comment = false
+  this.empty = false
+
+  // make the set of regexps etc.
+  this.make()
+}
+
+Minimatch.prototype.debug = function () {}
+
+Minimatch.prototype.make = make
+function make () {
+  // don't do it more than once.
+  if (this._made) return
+
+  var pattern = this.pattern
+  var options = this.options
+
+  // empty patterns and comments match nothing.
+  if (!options.nocomment && pattern.charAt(0) === '#') {
+    this.comment = true
+    return
+  }
+  if (!pattern) {
+    this.empty = true
+    return
+  }
+
+  // step 1: figure out negation, etc.
+  this.parseNegate()
+
+  // step 2: expand braces
+  var set = this.globSet = this.braceExpand()
+
+  if (options.debug) this.debug = console.error
+
+  this.debug(this.pattern, set)
+
+  // step 3: now we have a set, so turn each one into a series of path-portion
+  // matching patterns.
+  // These will be regexps, except in the case of "**", which is
+  // set to the GLOBSTAR object for globstar behavior,
+  // and will not contain any / characters
+  set = this.globParts = set.map(function (s) {
+    return s.split(slashSplit)
+  })
+
+  this.debug(this.pattern, set)
+
+  // glob --> regexps
+  set = set.map(function (s, si, set) {
+    return s.map(this.parse, this)
+  }, this)
+
+  this.debug(this.pattern, set)
+
+  // filter out everything that didn't compile properly.
+  set = set.filter(function (s) {
+    return s.indexOf(false) === -1
+  })
+
+  this.debug(this.pattern, set)
+
+  this.set = set
+}
+
+Minimatch.prototype.parseNegate = parseNegate
+function parseNegate () {
+  var pattern = this.pattern
+  var negate = false
+  var options = this.options
+  var negateOffset = 0
+
+  if (options.nonegate) return
+
+  for (var i = 0, l = pattern.length
+    ; i < l && pattern.charAt(i) === '!'
+    ; i++) {
+    negate = !negate
+    negateOffset++
+  }
+
+  if (negateOffset) this.pattern = pattern.substr(negateOffset)
+  this.negate = negate
+}
+
+// Brace expansion:
+// a{b,c}d -> abd acd
+// a{b,}c -> abc ac
+// a{0..3}d -> a0d a1d a2d a3d
+// a{b,c{d,e}f}g -> abg acdfg acefg
+// a{b,c}d{e,f}g -> abdeg acdeg abdeg abdfg
+//
+// Invalid sets are not expanded.
+// a{2..}b -> a{2..}b
+// a{b}c -> a{b}c
+minimatch.braceExpand = function (pattern, options) {
+  return braceExpand(pattern, options)
+}
+
+Minimatch.prototype.braceExpand = braceExpand
+
+function braceExpand (pattern, options) {
+  if (!options) {
+    if (this instanceof Minimatch) {
+      options = this.options
+    } else {
+      options = {}
+    }
+  }
+
+  pattern = typeof pattern === 'undefined'
+    ? this.pattern : pattern
+
+  if (typeof pattern === 'undefined') {
+    throw new TypeError('undefined pattern')
+  }
+
+  if (options.nobrace ||
+    !pattern.match(/\{.*\}/)) {
+    // shortcut. no need to expand.
+    return [pattern]
+  }
+
+  return expand(pattern)
+}
+
+// parse a component of the expanded set.
+// At this point, no pattern may contain "/" in it
+// so we're going to return a 2d array, where each entry is the full
+// pattern, split on '/', and then turned into a regular expression.
+// A regexp is made at the end which joins each array with an
+// escaped /, and another full one which joins each regexp with |.
+//
+// Following the lead of Bash 4.1, note that "**" only has special meaning
+// when it is the *only* thing in a path portion.  Otherwise, any series
+// of * is equivalent to a single *.  Globstar behavior is enabled by
+// default, and can be disabled by setting options.noglobstar.
+Minimatch.prototype.parse = parse
+var SUBPARSE = {}
+function parse (pattern, isSub) {
+  if (pattern.length > 1024 * 64) {
+    throw new TypeError('pattern is too long')
+  }
+
+  var options = this.options
+
+  // shortcuts
+  if (!options.noglobstar && pattern === '**') return GLOBSTAR
+  if (pattern === '') return ''
+
+  var re = ''
+  var hasMagic = !!options.nocase
+  var escaping = false
+  // ? => one single character
+  var patternListStack = []
+  var negativeLists = []
+  var stateChar
+  var inClass = false
+  var reClassStart = -1
+  var classStart = -1
+  // . and .. never match anything that doesn't start with .,
+  // even when options.dot is set.
+  var patternStart = pattern.charAt(0) === '.' ? '' // anything
+  // not (start or / followed by . or .. followed by / or end)
+  : options.dot ? '(?!(?:^|\\\/)\\.{1,2}(?:$|\\\/))'
+  : '(?!\\.)'
+  var self = this
+
+  function clearStateChar () {
+    if (stateChar) {
+      // we had some state-tracking character
+      // that wasn't consumed by this pass.
+      switch (stateChar) {
+        case '*':
+          re += star
+          hasMagic = true
+        break
+        case '?':
+          re += qmark
+          hasMagic = true
+        break
+        default:
+          re += '\\' + stateChar
+        break
+      }
+      self.debug('clearStateChar %j %j', stateChar, re)
+      stateChar = false
+    }
+  }
+
+  for (var i = 0, len = pattern.length, c
+    ; (i < len) && (c = pattern.charAt(i))
+    ; i++) {
+    this.debug('%s\t%s %s %j', pattern, i, re, c)
+
+    // skip over any that are escaped.
+    if (escaping && reSpecials[c]) {
+      re += '\\' + c
+      escaping = false
+      continue
+    }
+
+    switch (c) {
+      case '/':
+        // completely not allowed, even escaped.
+        // Should already be path-split by now.
+        return false
+
+      case '\\':
+        clearStateChar()
+        escaping = true
+      continue
+
+      // the various stateChar values
+      // for the "extglob" stuff.
+      case '?':
+      case '*':
+      case '+':
+      case '@':
+      case '!':
+        this.debug('%s\t%s %s %j <-- stateChar', pattern, i, re, c)
+
+        // all of those are literals inside a class, except that
+        // the glob [!a] means [^a] in regexp
+        if (inClass) {
+          this.debug('  in class')
+          if (c === '!' && i === classStart + 1) c = '^'
+          re += c
+          continue
+        }
+
+        // if we already have a stateChar, then it means
+        // that there was something like ** or +? in there.
+        // Handle the stateChar, then proceed with this one.
+        self.debug('call clearStateChar %j', stateChar)
+        clearStateChar()
+        stateChar = c
+        // if extglob is disabled, then +(asdf|foo) isn't a thing.
+        // just clear the statechar *now*, rather than even diving into
+        // the patternList stuff.
+        if (options.noext) clearStateChar()
+      continue
+
+      case '(':
+        if (inClass) {
+          re += '('
+          continue
+        }
+
+        if (!stateChar) {
+          re += '\\('
+          continue
+        }
+
+        patternListStack.push({
+          type: stateChar,
+          start: i - 1,
+          reStart: re.length,
+          open: plTypes[stateChar].open,
+          close: plTypes[stateChar].close
+        })
+        // negation is (?:(?!js)[^/]*)
+        re += stateChar === '!' ? '(?:(?!(?:' : '(?:'
+        this.debug('plType %j %j', stateChar, re)
+        stateChar = false
+      continue
+
+      case ')':
+        if (inClass || !patternListStack.length) {
+          re += '\\)'
+          continue
+        }
+
+        clearStateChar()
+        hasMagic = true
+        var pl = patternListStack.pop()
+        // negation is (?:(?!js)[^/]*)
+        // The others are (?:<pattern>)<type>
+        re += pl.close
+        if (pl.type === '!') {
+          negativeLists.push(pl)
+        }
+        pl.reEnd = re.length
+      continue
+
+      case '|':
+        if (inClass || !patternListStack.length || escaping) {
+          re += '\\|'
+          escaping = false
+          continue
+        }
+
+        clearStateChar()
+        re += '|'
+      continue
+
+      // these are mostly the same in regexp and glob
+      case '[':
+        // swallow any state-tracking char before the [
+        clearStateChar()
+
+        if (inClass) {
+          re += '\\' + c
+          continue
+        }
+
+        inClass = true
+        classStart = i
+        reClassStart = re.length
+        re += c
+      continue
+
+      case ']':
+        //  a right bracket shall lose its special
+        //  meaning and represent itself in
+        //  a bracket expression if it occurs
+        //  first in the list.  -- POSIX.2 2.8.3.2
+        if (i === classStart + 1 || !inClass) {
+          re += '\\' + c
+          escaping = false
+          continue
+        }
+
+        // handle the case where we left a class open.
+        // "[z-a]" is valid, equivalent to "\[z-a\]"
+        if (inClass) {
+          // split where the last [ was, make sure we don't have
+          // an invalid re. if so, re-walk the contents of the
+          // would-be class to re-translate any characters that
+          // were passed through as-is
+          // TODO: It would probably be faster to determine this
+          // without a try/catch and a new RegExp, but it's tricky
+          // to do safely.  For now, this is safe and works.
+          var cs = pattern.substring(classStart + 1, i)
+          try {
+            RegExp('[' + cs + ']')
+          } catch (er) {
+            // not a valid class!
+            var sp = this.parse(cs, SUBPARSE)
+            re = re.substr(0, reClassStart) + '\\[' + sp[0] + '\\]'
+            hasMagic = hasMagic || sp[1]
+            inClass = false
+            continue
+          }
+        }
+
+        // finish up the class.
+        hasMagic = true
+        inClass = false
+        re += c
+      continue
+
+      default:
+        // swallow any state char that wasn't consumed
+        clearStateChar()
+
+        if (escaping) {
+          // no need
+          escaping = false
+        } else if (reSpecials[c]
+          && !(c === '^' && inClass)) {
+          re += '\\'
+        }
+
+        re += c
+
+    } // switch
+  } // for
+
+  // handle the case where we left a class open.
+  // "[abc" is valid, equivalent to "\[abc"
+  if (inClass) {
+    // split where the last [ was, and escape it
+    // this is a huge pita.  We now have to re-walk
+    // the contents of the would-be class to re-translate
+    // any characters that were passed through as-is
+    cs = pattern.substr(classStart + 1)
+    sp = this.parse(cs, SUBPARSE)
+    re = re.substr(0, reClassStart) + '\\[' + sp[0]
+    hasMagic = hasMagic || sp[1]
+  }
+
+  // handle the case where we had a +( thing at the *end*
+  // of the pattern.
+  // each pattern list stack adds 3 chars, and we need to go through
+  // and escape any | chars that were passed through as-is for the regexp.
+  // Go through and escape them, taking care not to double-escape any
+  // | chars that were already escaped.
+  for (pl = patternListStack.pop(); pl; pl = patternListStack.pop()) {
+    var tail = re.slice(pl.reStart + pl.open.length)
+    this.debug('setting tail', re, pl)
+    // maybe some even number of \, then maybe 1 \, followed by a |
+    tail = tail.replace(/((?:\\{2}){0,64})(\\?)\|/g, function (_, $1, $2) {
+      if (!$2) {
+        // the | isn't already escaped, so escape it.
+        $2 = '\\'
+      }
+
+      // need to escape all those slashes *again*, without escaping the
+      // one that we need for escaping the | character.  As it works out,
+      // escaping an even number of slashes can be done by simply repeating
+      // it exactly after itself.  That's why this trick works.
+      //
+      // I am sorry that you have to see this.
+      return $1 + $1 + $2 + '|'
+    })
+
+    this.debug('tail=%j\n   %s', tail, tail, pl, re)
+    var t = pl.type === '*' ? star
+      : pl.type === '?' ? qmark
+      : '\\' + pl.type
+
+    hasMagic = true
+    re = re.slice(0, pl.reStart) + t + '\\(' + tail
+  }
+
+  // handle trailing things that only matter at the very end.
+  clearStateChar()
+  if (escaping) {
+    // trailing \\
+    re += '\\\\'
+  }
+
+  // only need to apply the nodot start if the re starts with
+  // something that could conceivably capture a dot
+  var addPatternStart = false
+  switch (re.charAt(0)) {
+    case '.':
+    case '[':
+    case '(': addPatternStart = true
+  }
+
+  // Hack to work around lack of negative lookbehind in JS
+  // A pattern like: *.!(x).!(y|z) needs to ensure that a name
+  // like 'a.xyz.yz' doesn't match.  So, the first negative
+  // lookahead, has to look ALL the way ahead, to the end of
+  // the pattern.
+  for (var n = negativeLists.length - 1; n > -1; n--) {
+    var nl = negativeLists[n]
+
+    var nlBefore = re.slice(0, nl.reStart)
+    var nlFirst = re.slice(nl.reStart, nl.reEnd - 8)
+    var nlLast = re.slice(nl.reEnd - 8, nl.reEnd)
+    var nlAfter = re.slice(nl.reEnd)
+
+    nlLast += nlAfter
+
+    // Handle nested stuff like *(*.js|!(*.json)), where open parens
+    // mean that we should *not* include the ) in the bit that is considered
+    // "after" the negated section.
+    var openParensBefore = nlBefore.split('(').length - 1
+    var cleanAfter = nlAfter
+    for (i = 0; i < openParensBefore; i++) {
+      cleanAfter = cleanAfter.replace(/\)[+*?]?/, '')
+    }
+    nlAfter = cleanAfter
+
+    var dollar = ''
+    if (nlAfter === '' && isSub !== SUBPARSE) {
+      dollar = '$'
+    }
+    var newRe = nlBefore + nlFirst + nlAfter + dollar + nlLast
+    re = newRe
+  }
+
+  // if the re is not "" at this point, then we need to make sure
+  // it doesn't match against an empty path part.
+  // Otherwise a/* will match a/, which it should not.
+  if (re !== '' && hasMagic) {
+    re = '(?=.)' + re
+  }
+
+  if (addPatternStart) {
+    re = patternStart + re
+  }
+
+  // parsing just a piece of a larger pattern.
+  if (isSub === SUBPARSE) {
+    return [re, hasMagic]
+  }
+
+  // skip the regexp for non-magical patterns
+  // unescape anything in it, though, so that it'll be
+  // an exact match against a file etc.
+  if (!hasMagic) {
+    return globUnescape(pattern)
+  }
+
+  var flags = options.nocase ? 'i' : ''
+  try {
+    var regExp = new RegExp('^' + re + '$', flags)
+  } catch (er) {
+    // If it was an invalid regular expression, then it can't match
+    // anything.  This trick looks for a character after the end of
+    // the string, which is of course impossible, except in multi-line
+    // mode, but it's not a /m regex.
+    return new RegExp('$.')
+  }
+
+  regExp._glob = pattern
+  regExp._src = re
+
+  return regExp
+}
+
+minimatch.makeRe = function (pattern, options) {
+  return new Minimatch(pattern, options || {}).makeRe()
+}
+
+Minimatch.prototype.makeRe = makeRe
+function makeRe () {
+  if (this.regexp || this.regexp === false) return this.regexp
+
+  // at this point, this.set is a 2d array of partial
+  // pattern strings, or "**".
+  //
+  // It's better to use .match().  This function shouldn't
+  // be used, really, but it's pretty convenient sometimes,
+  // when you just want to work with a regex.
+  var set = this.set
+
+  if (!set.length) {
+    this.regexp = false
+    return this.regexp
+  }
+  var options = this.options
+
+  var twoStar = options.noglobstar ? star
+    : options.dot ? twoStarDot
+    : twoStarNoDot
+  var flags = options.nocase ? 'i' : ''
+
+  var re = set.map(function (pattern) {
+    return pattern.map(function (p) {
+      return (p === GLOBSTAR) ? twoStar
+      : (typeof p === 'string') ? regExpEscape(p)
+      : p._src
+    }).join('\\\/')
+  }).join('|')
+
+  // must match entire pattern
+  // ending in a * or ** will make it less strict.
+  re = '^(?:' + re + ')$'
+
+  // can match anything, as long as it's not this.
+  if (this.negate) re = '^(?!' + re + ').*$'
+
+  try {
+    this.regexp = new RegExp(re, flags)
+  } catch (ex) {
+    this.regexp = false
+  }
+  return this.regexp
+}
+
+minimatch.match = function (list, pattern, options) {
+  options = options || {}
+  var mm = new Minimatch(pattern, options)
+  list = list.filter(function (f) {
+    return mm.match(f)
+  })
+  if (mm.options.nonull && !list.length) {
+    list.push(pattern)
+  }
+  return list
+}
+
+Minimatch.prototype.match = match
+function match (f, partial) {
+  this.debug('match', f, this.pattern)
+  // short-circuit in the case of busted things.
+  // comments, etc.
+  if (this.comment) return false
+  if (this.empty) return f === ''
+
+  if (f === '/' && partial) return true
+
+  var options = this.options
+
+  // windows: need to use /, not \
+  if (path.sep !== '/') {
+    f = f.split(path.sep).join('/')
+  }
+
+  // treat the test path as a set of pathparts.
+  f = f.split(slashSplit)
+  this.debug(this.pattern, 'split', f)
+
+  // just ONE of the pattern sets in this.set needs to match
+  // in order for it to be valid.  If negating, then just one
+  // match means that we have failed.
+  // Either way, return on the first hit.
+
+  var set = this.set
+  this.debug(this.pattern, 'set', set)
+
+  // Find the basename of the path by looking for the last non-empty segment
+  var filename
+  var i
+  for (i = f.length - 1; i >= 0; i--) {
+    filename = f[i]
+    if (filename) break
+  }
+
+  for (i = 0; i < set.length; i++) {
+    var pattern = set[i]
+    var file = f
+    if (options.matchBase && pattern.length === 1) {
+      file = [filename]
+    }
+    var hit = this.matchOne(file, pattern, partial)
+    if (hit) {
+      if (options.flipNegate) return true
+      return !this.negate
+    }
+  }
+
+  // didn't get any hits.  this is success if it's a negative
+  // pattern, failure otherwise.
+  if (options.flipNegate) return false
+  return this.negate
+}
+
+// set partial to true to test if, for example,
+// "/a/b" matches the start of "/*/b/*/d"
+// Partial means, if you run out of file before you run
+// out of pattern, then that's fine, as long as all
+// the parts match.
+Minimatch.prototype.matchOne = function (file, pattern, partial) {
+  var options = this.options
+
+  this.debug('matchOne',
+    { 'this': this, file: file, pattern: pattern })
+
+  this.debug('matchOne', file.length, pattern.length)
+
+  for (var fi = 0,
+      pi = 0,
+      fl = file.length,
+      pl = pattern.length
+      ; (fi < fl) && (pi < pl)
+      ; fi++, pi++) {
+    this.debug('matchOne loop')
+    var p = pattern[pi]
+    var f = file[fi]
+
+    this.debug(pattern, p, f)
+
+    // should be impossible.
+    // some invalid regexp stuff in the set.
+    if (p === false) return false
+
+    if (p === GLOBSTAR) {
+      this.debug('GLOBSTAR', [pattern, p, f])
+
+      // "**"
+      // a/**/b/**/c would match the following:
+      // a/b/x/y/z/c
+      // a/x/y/z/b/c
+      // a/b/x/b/x/c
+      // a/b/c
+      // To do this, take the rest of the pattern after
+      // the **, and see if it would match the file remainder.
+      // If so, return success.
+      // If not, the ** "swallows" a segment, and try again.
+      // This is recursively awful.
+      //
+      // a/**/b/**/c matching a/b/x/y/z/c
+      // - a matches a
+      // - doublestar
+      //   - matchOne(b/x/y/z/c, b/**/c)
+      //     - b matches b
+      //     - doublestar
+      //       - matchOne(x/y/z/c, c) -> no
+      //       - matchOne(y/z/c, c) -> no
+      //       - matchOne(z/c, c) -> no
+      //       - matchOne(c, c) yes, hit
+      var fr = fi
+      var pr = pi + 1
+      if (pr === pl) {
+        this.debug('** at the end')
+        // a ** at the end will just swallow the rest.
+        // We have found a match.
+        // however, it will not swallow /.x, unless
+        // options.dot is set.
+        // . and .. are *never* matched by **, for explosively
+        // exponential reasons.
+        for (; fi < fl; fi++) {
+          if (file[fi] === '.' || file[fi] === '..' ||
+            (!options.dot && file[fi].charAt(0) === '.')) return false
+        }
+        return true
+      }
+
+      // ok, let's see if we can swallow whatever we can.
+      while (fr < fl) {
+        var swallowee = file[fr]
+
+        this.debug('\nglobstar while', file, fr, pattern, pr, swallowee)
+
+        // XXX remove this slice.  Just pass the start index.
+        if (this.matchOne(file.slice(fr), pattern.slice(pr), partial)) {
+          this.debug('globstar found match!', fr, fl, swallowee)
+          // found a match.
+          return true
+        } else {
+          // can't swallow "." or ".." ever.
+          // can only swallow ".foo" when explicitly asked.
+          if (swallowee === '.' || swallowee === '..' ||
+            (!options.dot && swallowee.charAt(0) === '.')) {
+            this.debug('dot detected!', file, fr, pattern, pr)
+            break
+          }
+
+          // ** swallows a segment, and continue.
+          this.debug('globstar swallow a segment, and continue')
+          fr++
+        }
+      }
+
+      // no match was found.
+      // However, in partial mode, we can't say this is necessarily over.
+      // If there's more *pattern* left, then
+      if (partial) {
+        // ran out of file
+        this.debug('\n>>> no match, partial?', file, fr, pattern, pr)
+        if (fr === fl) return true
+      }
+      return false
+    }
+
+    // something other than **
+    // non-magic patterns just have to match exactly
+    // patterns with magic have been turned into regexps.
+    var hit
+    if (typeof p === 'string') {
+      if (options.nocase) {
+        hit = f.toLowerCase() === p.toLowerCase()
+      } else {
+        hit = f === p
+      }
+      this.debug('string match', p, f, hit)
+    } else {
+      hit = f.match(p)
+      this.debug('pattern match', p, f, hit)
+    }
+
+    if (!hit) return false
+  }
+
+  // Note: ending in / means that we'll get a final ""
+  // at the end of the pattern.  This can only match a
+  // corresponding "" at the end of the file.
+  // If the file ends in /, then it can only match a
+  // a pattern that ends in /, unless the pattern just
+  // doesn't have any more for it. But, a/b/ should *not*
+  // match "a/b/*", even though "" matches against the
+  // [^/]*? pattern, except in partial mode, where it might
+  // simply not be reached yet.
+  // However, a/b/ should still satisfy a/*
+
+  // now either we fell off the end of the pattern, or we're done.
+  if (fi === fl && pi === pl) {
+    // ran out of pattern and filename at the same time.
+    // an exact hit!
+    return true
+  } else if (fi === fl) {
+    // ran out of file, but still had pattern left.
+    // this is ok if we're doing the match as part of
+    // a glob fs traversal.
+    return partial
+  } else if (pi === pl) {
+    // ran out of pattern, still have file left.
+    // this is only acceptable if we're on the very last
+    // empty segment of a file with a trailing slash.
+    // a/* should match a/b/
+    var emptyFileEnd = (fi === fl - 1) && (file[fi] === '')
+    return emptyFileEnd
+  }
+
+  // should be unreachable.
+  throw new Error('wtf?')
+}
+
+// replace stuff like \* with *
+function globUnescape (s) {
+  return s.replace(/\\(.)/g, '$1')
+}
+
+function regExpEscape (s) {
+  return s.replace(/[-[\]{}()*+?.,\\^$|#\s]/g, '\\$&')
+}
+
+},{"brace-expansion":11,"path":22}],21:[function(require,module,exports){
+var wrappy = require('wrappy')
+module.exports = wrappy(once)
+module.exports.strict = wrappy(onceStrict)
+
+once.proto = once(function () {
+  Object.defineProperty(Function.prototype, 'once', {
+    value: function () {
+      return once(this)
+    },
+    configurable: true
+  })
+
+  Object.defineProperty(Function.prototype, 'onceStrict', {
+    value: function () {
+      return onceStrict(this)
+    },
+    configurable: true
+  })
+})
+
+function once (fn) {
+  var f = function () {
+    if (f.called) return f.value
+    f.called = true
+    return f.value = fn.apply(this, arguments)
+  }
+  f.called = false
+  return f
+}
+
+function onceStrict (fn) {
+  var f = function () {
+    if (f.called)
+      throw new Error(f.onceError)
+    f.called = true
+    return f.value = fn.apply(this, arguments)
+  }
+  var name = fn.name || 'Function wrapped with `once`'
+  f.onceError = name + " shouldn't be called more than once"
+  f.called = false
+  return f
+}
+
+},{"wrappy":29}],22:[function(require,module,exports){
+(function (process){
+// Copyright Joyent, Inc. and other Node contributors.
+//
+// Permission is hereby granted, free of charge, to any person obtaining a
+// copy of this software and associated documentation files (the
+// "Software"), to deal in the Software without restriction, including
+// without limitation the rights to use, copy, modify, merge, publish,
+// distribute, sublicense, and/or sell copies of the Software, and to permit
+// persons to whom the Software is furnished to do so, subject to the
+// following conditions:
+//
+// The above copyright notice and this permission notice shall be included
+// in all copies or substantial portions of the Software.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
+// OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+// MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN
+// NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM,
+// DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR
+// OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE
+// USE OR OTHER DEALINGS IN THE SOFTWARE.
+
+// resolves . and .. elements in a path array with directory names there
+// must be no slashes, empty elements, or device names (c:\) in the array
+// (so also no leading and trailing slashes - it does not distinguish
+// relative and absolute paths)
+function normalizeArray(parts, allowAboveRoot) {
+  // if the path tries to go above the root, `up` ends up > 0
+  var up = 0;
+  for (var i = parts.length - 1; i >= 0; i--) {
+    var last = parts[i];
+    if (last === '.') {
+      parts.splice(i, 1);
+    } else if (last === '..') {
+      parts.splice(i, 1);
+      up++;
+    } else if (up) {
+      parts.splice(i, 1);
+      up--;
+    }
+  }
+
+  // if the path is allowed to go above the root, restore leading ..s
+  if (allowAboveRoot) {
+    for (; up--; up) {
+      parts.unshift('..');
+    }
+  }
+
+  return parts;
+}
+
+// Split a filename into [root, dir, basename, ext], unix version
+// 'root' is just a slash, or nothing.
+var splitPathRe =
+    /^(\/?|)([\s\S]*?)((?:\.{1,2}|[^\/]+?|)(\.[^.\/]*|))(?:[\/]*)$/;
+var splitPath = function(filename) {
+  return splitPathRe.exec(filename).slice(1);
+};
+
+// path.resolve([from ...], to)
+// posix version
+exports.resolve = function() {
+  var resolvedPath = '',
+      resolvedAbsolute = false;
+
+  for (var i = arguments.length - 1; i >= -1 && !resolvedAbsolute; i--) {
+    var path = (i >= 0) ? arguments[i] : process.cwd();
+
+    // Skip empty and invalid entries
+    if (typeof path !== 'string') {
+      throw new TypeError('Arguments to path.resolve must be strings');
+    } else if (!path) {
+      continue;
+    }
+
+    resolvedPath = path + '/' + resolvedPath;
+    resolvedAbsolute = path.charAt(0) === '/';
+  }
+
+  // At this point the path should be resolved to a full absolute path, but
+  // handle relative paths to be safe (might happen when process.cwd() fails)
+
+  // Normalize the path
+  resolvedPath = normalizeArray(filter(resolvedPath.split('/'), function(p) {
+    return !!p;
+  }), !resolvedAbsolute).join('/');
+
+  return ((resolvedAbsolute ? '/' : '') + resolvedPath) || '.';
+};
+
+// path.normalize(path)
+// posix version
+exports.normalize = function(path) {
+  var isAbsolute = exports.isAbsolute(path),
+      trailingSlash = substr(path, -1) === '/';
+
+  // Normalize the path
+  path = normalizeArray(filter(path.split('/'), function(p) {
+    return !!p;
+  }), !isAbsolute).join('/');
+
+  if (!path && !isAbsolute) {
+    path = '.';
+  }
+  if (path && trailingSlash) {
+    path += '/';
+  }
+
+  return (isAbsolute ? '/' : '') + path;
+};
+
+// posix version
+exports.isAbsolute = function(path) {
+  return path.charAt(0) === '/';
+};
+
+// posix version
+exports.join = function() {
+  var paths = Array.prototype.slice.call(arguments, 0);
+  return exports.normalize(filter(paths, function(p, index) {
+    if (typeof p !== 'string') {
+      throw new TypeError('Arguments to path.join must be strings');
+    }
+    return p;
+  }).join('/'));
+};
+
+
+// path.relative(from, to)
+// posix version
+exports.relative = function(from, to) {
+  from = exports.resolve(from).substr(1);
+  to = exports.resolve(to).substr(1);
+
+  function trim(arr) {
+    var start = 0;
+    for (; start < arr.length; start++) {
+      if (arr[start] !== '') break;
+    }
+
+    var end = arr.length - 1;
+    for (; end >= 0; end--) {
+      if (arr[end] !== '') break;
+    }
+
+    if (start > end) return [];
+    return arr.slice(start, end - start + 1);
+  }
+
+  var fromParts = trim(from.split('/'));
+  var toParts = trim(to.split('/'));
+
+  var length = Math.min(fromParts.length, toParts.length);
+  var samePartsLength = length;
+  for (var i = 0; i < length; i++) {
+    if (fromParts[i] !== toParts[i]) {
+      samePartsLength = i;
+      break;
+    }
+  }
+
+  var outputParts = [];
+  for (var i = samePartsLength; i < fromParts.length; i++) {
+    outputParts.push('..');
+  }
+
+  outputParts = outputParts.concat(toParts.slice(samePartsLength));
+
+  return outputParts.join('/');
+};
+
+exports.sep = '/';
+exports.delimiter = ':';
+
+exports.dirname = function(path) {
+  var result = splitPath(path),
+      root = result[0],
+      dir = result[1];
+
+  if (!root && !dir) {
+    // No dirname whatsoever
+    return '.';
+  }
+
+  if (dir) {
+    // It has a dirname, strip trailing slash
+    dir = dir.substr(0, dir.length - 1);
+  }
+
+  return root + dir;
+};
+
+
+exports.basename = function(path, ext) {
+  var f = splitPath(path)[2];
+  // TODO: make this comparison case-insensitive on windows?
+  if (ext && f.substr(-1 * ext.length) === ext) {
+    f = f.substr(0, f.length - ext.length);
+  }
+  return f;
+};
+
+
+exports.extname = function(path) {
+  return splitPath(path)[3];
+};
+
+function filter (xs, f) {
+    if (xs.filter) return xs.filter(f);
+    var res = [];
+    for (var i = 0; i < xs.length; i++) {
+        if (f(xs[i], i, xs)) res.push(xs[i]);
+    }
+    return res;
+}
+
+// String.prototype.substr - negative index don't work in IE8
+var substr = 'ab'.substr(-1) === 'b'
+    ? function (str, start, len) { return str.substr(start, len) }
+    : function (str, start, len) {
+        if (start < 0) start = str.length + start;
+        return str.substr(start, len);
+    }
+;
+
+}).call(this,require('_process'))
+},{"_process":24}],23:[function(require,module,exports){
+(function (process){
+'use strict';
+
+function posix(path) {
+	return path.charAt(0) === '/';
+}
+
+function win32(path) {
+	// https://github.com/nodejs/node/blob/b3fcc245fb25539909ef1d5eaa01dbf92e168633/lib/path.js#L56
+	var splitDeviceRe = /^([a-zA-Z]:|[\\\/]{2}[^\\\/]+[\\\/]+[^\\\/]+)?([\\\/])?([\s\S]*?)$/;
+	var result = splitDeviceRe.exec(path);
+	var device = result[1] || '';
+	var isUnc = Boolean(device && device.charAt(1) !== ':');
+
+	// UNC paths are always absolute
+	return Boolean(result[2] || isUnc);
+}
+
+module.exports = process.platform === 'win32' ? win32 : posix;
+module.exports.posix = posix;
+module.exports.win32 = win32;
+
+}).call(this,require('_process'))
+},{"_process":24}],24:[function(require,module,exports){
+// shim for using process in browser
+var process = module.exports = {};
+
+// cached from whatever global is present so that test runners that stub it
+// don't break things.  But we need to wrap it in a try catch in case it is
+// wrapped in strict mode code which doesn't define any globals.  It's inside a
+// function because try/catches deoptimize in certain engines.
+
+var cachedSetTimeout;
+var cachedClearTimeout;
+
+function defaultSetTimout() {
+    throw new Error('setTimeout has not been defined');
+}
+function defaultClearTimeout () {
+    throw new Error('clearTimeout has not been defined');
+}
+(function () {
+    try {
+        if (typeof setTimeout === 'function') {
+            cachedSetTimeout = setTimeout;
+        } else {
+            cachedSetTimeout = defaultSetTimout;
+        }
+    } catch (e) {
+        cachedSetTimeout = defaultSetTimout;
+    }
+    try {
+        if (typeof clearTimeout === 'function') {
+            cachedClearTimeout = clearTimeout;
+        } else {
+            cachedClearTimeout = defaultClearTimeout;
+        }
+    } catch (e) {
+        cachedClearTimeout = defaultClearTimeout;
+    }
+} ())
+function runTimeout(fun) {
+    if (cachedSetTimeout === setTimeout) {
+        //normal enviroments in sane situations
+        return setTimeout(fun, 0);
+    }
+    // if setTimeout wasn't available but was latter defined
+    if ((cachedSetTimeout === defaultSetTimout || !cachedSetTimeout) && setTimeout) {
+        cachedSetTimeout = setTimeout;
+        return setTimeout(fun, 0);
+    }
+    try {
+        // when when somebody has screwed with setTimeout but no I.E. maddness
+        return cachedSetTimeout(fun, 0);
+    } catch(e){
+        try {
+            // When we are in I.E. but the script has been evaled so I.E. doesn't trust the global object when called normally
+            return cachedSetTimeout.call(null, fun, 0);
+        } catch(e){
+            // same as above but when it's a version of I.E. that must have the global object for 'this', hopfully our context correct otherwise it will throw a global error
+            return cachedSetTimeout.call(this, fun, 0);
+        }
+    }
+
+
+}
+function runClearTimeout(marker) {
+    if (cachedClearTimeout === clearTimeout) {
+        //normal enviroments in sane situations
+        return clearTimeout(marker);
+    }
+    // if clearTimeout wasn't available but was latter defined
+    if ((cachedClearTimeout === defaultClearTimeout || !cachedClearTimeout) && clearTimeout) {
+        cachedClearTimeout = clearTimeout;
+        return clearTimeout(marker);
+    }
+    try {
+        // when when somebody has screwed with setTimeout but no I.E. maddness
+        return cachedClearTimeout(marker);
+    } catch (e){
+        try {
+            // When we are in I.E. but the script has been evaled so I.E. doesn't  trust the global object when called normally
+            return cachedClearTimeout.call(null, marker);
+        } catch (e){
+            // same as above but when it's a version of I.E. that must have the global object for 'this', hopfully our context correct otherwise it will throw a global error.
+            // Some versions of I.E. have different rules for clearTimeout vs setTimeout
+            return cachedClearTimeout.call(this, marker);
+        }
+    }
+
+
+
+}
+var queue = [];
+var draining = false;
+var currentQueue;
+var queueIndex = -1;
+
+function cleanUpNextTick() {
+    if (!draining || !currentQueue) {
+        return;
+    }
+    draining = false;
+    if (currentQueue.length) {
+        queue = currentQueue.concat(queue);
+    } else {
+        queueIndex = -1;
+    }
+    if (queue.length) {
+        drainQueue();
+    }
+}
+
+function drainQueue() {
+    if (draining) {
+        return;
+    }
+    var timeout = runTimeout(cleanUpNextTick);
+    draining = true;
+
+    var len = queue.length;
+    while(len) {
+        currentQueue = queue;
+        queue = [];
+        while (++queueIndex < len) {
+            if (currentQueue) {
+                currentQueue[queueIndex].run();
+            }
+        }
+        queueIndex = -1;
+        len = queue.length;
+    }
+    currentQueue = null;
+    draining = false;
+    runClearTimeout(timeout);
+}
+
+process.nextTick = function (fun) {
+    var args = new Array(arguments.length - 1);
+    if (arguments.length > 1) {
+        for (var i = 1; i < arguments.length; i++) {
+            args[i - 1] = arguments[i];
+        }
+    }
+    queue.push(new Item(fun, args));
+    if (queue.length === 1 && !draining) {
+        runTimeout(drainQueue);
+    }
+};
+
+// v8 likes predictible objects
+function Item(fun, array) {
+    this.fun = fun;
+    this.array = array;
+}
+Item.prototype.run = function () {
+    this.fun.apply(null, this.array);
+};
+process.title = 'browser';
+process.browser = true;
+process.env = {};
+process.argv = [];
+process.version = ''; // empty string to avoid regexp issues
+process.versions = {};
+
+function noop() {}
+
+process.on = noop;
+process.addListener = noop;
+process.once = noop;
+process.off = noop;
+process.removeListener = noop;
+process.removeAllListeners = noop;
+process.emit = noop;
+process.prependListener = noop;
+process.prependOnceListener = noop;
+
+process.listeners = function (name) { return [] }
+
+process.binding = function (name) {
+    throw new Error('process.binding is not supported');
+};
+
+process.cwd = function () { return '/' };
+process.chdir = function (dir) {
+    throw new Error('process.chdir is not supported');
+};
+process.umask = function() { return 0; };
+
+},{}],25:[function(require,module,exports){
+//     Underscore.js 1.8.3
+//     http://underscorejs.org
+//     (c) 2009-2015 Jeremy Ashkenas, DocumentCloud and Investigative Reporters & Editors
+//     Underscore may be freely distributed under the MIT license.
+
+(function() {
+
+  // Baseline setup
+  // --------------
+
+  // Establish the root object, `window` in the browser, or `exports` on the server.
+  var root = this;
+
+  // Save the previous value of the `_` variable.
+  var previousUnderscore = root._;
+
+  // Save bytes in the minified (but not gzipped) version:
+  var ArrayProto = Array.prototype, ObjProto = Object.prototype, FuncProto = Function.prototype;
+
+  // Create quick reference variables for speed access to core prototypes.
+  var
+    push             = ArrayProto.push,
+    slice            = ArrayProto.slice,
+    toString         = ObjProto.toString,
+    hasOwnProperty   = ObjProto.hasOwnProperty;
+
+  // All **ECMAScript 5** native function implementations that we hope to use
+  // are declared here.
+  var
+    nativeIsArray      = Array.isArray,
+    nativeKeys         = Object.keys,
+    nativeBind         = FuncProto.bind,
+    nativeCreate       = Object.create;
+
+  // Naked function reference for surrogate-prototype-swapping.
+  var Ctor = function(){};
+
+  // Create a safe reference to the Underscore object for use below.
+  var _ = function(obj) {
+    if (obj instanceof _) return obj;
+    if (!(this instanceof _)) return new _(obj);
+    this._wrapped = obj;
+  };
+
+  // Export the Underscore object for **Node.js**, with
+  // backwards-compatibility for the old `require()` API. If we're in
+  // the browser, add `_` as a global object.
+  if (typeof exports !== 'undefined') {
+    if (typeof module !== 'undefined' && module.exports) {
+      exports = module.exports = _;
+    }
+    exports._ = _;
+  } else {
+    root._ = _;
+  }
+
+  // Current version.
+  _.VERSION = '1.8.3';
+
+  // Internal function that returns an efficient (for current engines) version
+  // of the passed-in callback, to be repeatedly applied in other Underscore
+  // functions.
+  var optimizeCb = function(func, context, argCount) {
+    if (context === void 0) return func;
+    switch (argCount == null ? 3 : argCount) {
+      case 1: return function(value) {
+        return func.call(context, value);
+      };
+      case 2: return function(value, other) {
+        return func.call(context, value, other);
+      };
+      case 3: return function(value, index, collection) {
+        return func.call(context, value, index, collection);
+      };
+      case 4: return function(accumulator, value, index, collection) {
+        return func.call(context, accumulator, value, index, collection);
+      };
+    }
+    return function() {
+      return func.apply(context, arguments);
+    };
+  };
+
+  // A mostly-internal function to generate callbacks that can be applied
+  // to each element in a collection, returning the desired result — either
+  // identity, an arbitrary callback, a property matcher, or a property accessor.
+  var cb = function(value, context, argCount) {
+    if (value == null) return _.identity;
+    if (_.isFunction(value)) return optimizeCb(value, context, argCount);
+    if (_.isObject(value)) return _.matcher(value);
+    return _.property(value);
+  };
+  _.iteratee = function(value, context) {
+    return cb(value, context, Infinity);
+  };
+
+  // An internal function for creating assigner functions.
+  var createAssigner = function(keysFunc, undefinedOnly) {
+    return function(obj) {
+      var length = arguments.length;
+      if (length < 2 || obj == null) return obj;
+      for (var index = 1; index < length; index++) {
+        var source = arguments[index],
+            keys = keysFunc(source),
+            l = keys.length;
+        for (var i = 0; i < l; i++) {
+          var key = keys[i];
+          if (!undefinedOnly || obj[key] === void 0) obj[key] = source[key];
+        }
+      }
+      return obj;
+    };
+  };
+
+  // An internal function for creating a new object that inherits from another.
+  var baseCreate = function(prototype) {
+    if (!_.isObject(prototype)) return {};
+    if (nativeCreate) return nativeCreate(prototype);
+    Ctor.prototype = prototype;
+    var result = new Ctor;
+    Ctor.prototype = null;
+    return result;
+  };
+
+  var property = function(key) {
+    return function(obj) {
+      return obj == null ? void 0 : obj[key];
+    };
+  };
+
+  // Helper for collection methods to determine whether a collection
+  // should be iterated as an array or as an object
+  // Related: http://people.mozilla.org/~jorendorff/es6-draft.html#sec-tolength
+  // Avoids a very nasty iOS 8 JIT bug on ARM-64. #2094
+  var MAX_ARRAY_INDEX = Math.pow(2, 53) - 1;
+  var getLength = property('length');
+  var isArrayLike = function(collection) {
+    var length = getLength(collection);
+    return typeof length == 'number' && length >= 0 && length <= MAX_ARRAY_INDEX;
+  };
+
+  // Collection Functions
+  // --------------------
+
+  // The cornerstone, an `each` implementation, aka `forEach`.
+  // Handles raw objects in addition to array-likes. Treats all
+  // sparse array-likes as if they were dense.
+  _.each = _.forEach = function(obj, iteratee, context) {
+    iteratee = optimizeCb(iteratee, context);
+    var i, length;
+    if (isArrayLike(obj)) {
+      for (i = 0, length = obj.length; i < length; i++) {
+        iteratee(obj[i], i, obj);
+      }
+    } else {
+      var keys = _.keys(obj);
+      for (i = 0, length = keys.length; i < length; i++) {
+        iteratee(obj[keys[i]], keys[i], obj);
+      }
+    }
+    return obj;
+  };
+
+  // Return the results of applying the iteratee to each element.
+  _.map = _.collect = function(obj, iteratee, context) {
+    iteratee = cb(iteratee, context);
+    var keys = !isArrayLike(obj) && _.keys(obj),
+        length = (keys || obj).length,
+        results = Array(length);
+    for (var index = 0; index < length; index++) {
+      var currentKey = keys ? keys[index] : index;
+      results[index] = iteratee(obj[currentKey], currentKey, obj);
+    }
+    return results;
+  };
+
+  // Create a reducing function iterating left or right.
+  function createReduce(dir) {
+    // Optimized iterator function as using arguments.length
+    // in the main function will deoptimize the, see #1991.
+    function iterator(obj, iteratee, memo, keys, index, length) {
+      for (; index >= 0 && index < length; index += dir) {
+        var currentKey = keys ? keys[index] : index;
+        memo = iteratee(memo, obj[currentKey], currentKey, obj);
+      }
+      return memo;
+    }
+
+    return function(obj, iteratee, memo, context) {
+      iteratee = optimizeCb(iteratee, context, 4);
+      var keys = !isArrayLike(obj) && _.keys(obj),
+          length = (keys || obj).length,
+          index = dir > 0 ? 0 : length - 1;
+      // Determine the initial value if none is provided.
+      if (arguments.length < 3) {
+        memo = obj[keys ? keys[index] : index];
+        index += dir;
+      }
+      return iterator(obj, iteratee, memo, keys, index, length);
+    };
+  }
+
+  // **Reduce** builds up a single result from a list of values, aka `inject`,
+  // or `foldl`.
+  _.reduce = _.foldl = _.inject = createReduce(1);
+
+  // The right-associative version of reduce, also known as `foldr`.
+  _.reduceRight = _.foldr = createReduce(-1);
+
+  // Return the first value which passes a truth test. Aliased as `detect`.
+  _.find = _.detect = function(obj, predicate, context) {
+    var key;
+    if (isArrayLike(obj)) {
+      key = _.findIndex(obj, predicate, context);
+    } else {
+      key = _.findKey(obj, predicate, context);
+    }
+    if (key !== void 0 && key !== -1) return obj[key];
+  };
+
+  // Return all the elements that pass a truth test.
+  // Aliased as `select`.
+  _.filter = _.select = function(obj, predicate, context) {
+    var results = [];
+    predicate = cb(predicate, context);
+    _.each(obj, function(value, index, list) {
+      if (predicate(value, index, list)) results.push(value);
+    });
+    return results;
+  };
+
+  // Return all the elements for which a truth test fails.
+  _.reject = function(obj, predicate, context) {
+    return _.filter(obj, _.negate(cb(predicate)), context);
+  };
+
+  // Determine whether all of the elements match a truth test.
+  // Aliased as `all`.
+  _.every = _.all = function(obj, predicate, context) {
+    predicate = cb(predicate, context);
+    var keys = !isArrayLike(obj) && _.keys(obj),
+        length = (keys || obj).length;
+    for (var index = 0; index < length; index++) {
+      var currentKey = keys ? keys[index] : index;
+      if (!predicate(obj[currentKey], currentKey, obj)) return false;
+    }
+    return true;
+  };
+
+  // Determine if at least one element in the object matches a truth test.
+  // Aliased as `any`.
+  _.some = _.any = function(obj, predicate, context) {
+    predicate = cb(predicate, context);
+    var keys = !isArrayLike(obj) && _.keys(obj),
+        length = (keys || obj).length;
+    for (var index = 0; index < length; index++) {
+      var currentKey = keys ? keys[index] : index;
+      if (predicate(obj[currentKey], currentKey, obj)) return true;
+    }
+    return false;
+  };
+
+  // Determine if the array or object contains a given item (using `===`).
+  // Aliased as `includes` and `include`.
+  _.contains = _.includes = _.include = function(obj, item, fromIndex, guard) {
+    if (!isArrayLike(obj)) obj = _.values(obj);
+    if (typeof fromIndex != 'number' || guard) fromIndex = 0;
+    return _.indexOf(obj, item, fromIndex) >= 0;
+  };
+
+  // Invoke a method (with arguments) on every item in a collection.
+  _.invoke = function(obj, method) {
+    var args = slice.call(arguments, 2);
+    var isFunc = _.isFunction(method);
+    return _.map(obj, function(value) {
+      var func = isFunc ? method : value[method];
+      return func == null ? func : func.apply(value, args);
+    });
+  };
+
+  // Convenience version of a common use case of `map`: fetching a property.
+  _.pluck = function(obj, key) {
+    return _.map(obj, _.property(key));
+  };
+
+  // Convenience version of a common use case of `filter`: selecting only objects
+  // containing specific `key:value` pairs.
+  _.where = function(obj, attrs) {
+    return _.filter(obj, _.matcher(attrs));
+  };
+
+  // Convenience version of a common use case of `find`: getting the first object
+  // containing specific `key:value` pairs.
+  _.findWhere = function(obj, attrs) {
+    return _.find(obj, _.matcher(attrs));
+  };
+
+  // Return the maximum element (or element-based computation).
+  _.max = function(obj, iteratee, context) {
+    var result = -Infinity, lastComputed = -Infinity,
+        value, computed;
+    if (iteratee == null && obj != null) {
+      obj = isArrayLike(obj) ? obj : _.values(obj);
+      for (var i = 0, length = obj.length; i < length; i++) {
+        value = obj[i];
+        if (value > result) {
+          result = value;
+        }
+      }
+    } else {
+      iteratee = cb(iteratee, context);
+      _.each(obj, function(value, index, list) {
+        computed = iteratee(value, index, list);
+        if (computed > lastComputed || computed === -Infinity && result === -Infinity) {
+          result = value;
+          lastComputed = computed;
+        }
+      });
+    }
+    return result;
+  };
+
+  // Return the minimum element (or element-based computation).
+  _.min = function(obj, iteratee, context) {
+    var result = Infinity, lastComputed = Infinity,
+        value, computed;
+    if (iteratee == null && obj != null) {
+      obj = isArrayLike(obj) ? obj : _.values(obj);
+      for (var i = 0, length = obj.length; i < length; i++) {
+        value = obj[i];
+        if (value < result) {
+          result = value;
+        }
+      }
+    } else {
+      iteratee = cb(iteratee, context);
+      _.each(obj, function(value, index, list) {
+        computed = iteratee(value, index, list);
+        if (computed < lastComputed || computed === Infinity && result === Infinity) {
+          result = value;
+          lastComputed = computed;
+        }
+      });
+    }
+    return result;
+  };
+
+  // Shuffle a collection, using the modern version of the
+  // [Fisher-Yates shuffle](http://en.wikipedia.org/wiki/Fisher–Yates_shuffle).
+  _.shuffle = function(obj) {
+    var set = isArrayLike(obj) ? obj : _.values(obj);
+    var length = set.length;
+    var shuffled = Array(length);
+    for (var index = 0, rand; index < length; index++) {
+      rand = _.random(0, index);
+      if (rand !== index) shuffled[index] = shuffled[rand];
+      shuffled[rand] = set[index];
+    }
+    return shuffled;
+  };
+
+  // Sample **n** random values from a collection.
+  // If **n** is not specified, returns a single random element.
+  // The internal `guard` argument allows it to work with `map`.
+  _.sample = function(obj, n, guard) {
+    if (n == null || guard) {
+      if (!isArrayLike(obj)) obj = _.values(obj);
+      return obj[_.random(obj.length - 1)];
+    }
+    return _.shuffle(obj).slice(0, Math.max(0, n));
+  };
+
+  // Sort the object's values by a criterion produced by an iteratee.
+  _.sortBy = function(obj, iteratee, context) {
+    iteratee = cb(iteratee, context);
+    return _.pluck(_.map(obj, function(value, index, list) {
+      return {
+        value: value,
+        index: index,
+        criteria: iteratee(value, index, list)
+      };
+    }).sort(function(left, right) {
+      var a = left.criteria;
+      var b = right.criteria;
+      if (a !== b) {
+        if (a > b || a === void 0) return 1;
+        if (a < b || b === void 0) return -1;
+      }
+      return left.index - right.index;
+    }), 'value');
+  };
+
+  // An internal function used for aggregate "group by" operations.
+  var group = function(behavior) {
+    return function(obj, iteratee, context) {
+      var result = {};
+      iteratee = cb(iteratee, context);
+      _.each(obj, function(value, index) {
+        var key = iteratee(value, index, obj);
+        behavior(result, value, key);
+      });
+      return result;
+    };
+  };
+
+  // Groups the object's values by a criterion. Pass either a string attribute
+  // to group by, or a function that returns the criterion.
+  _.groupBy = group(function(result, value, key) {
+    if (_.has(result, key)) result[key].push(value); else result[key] = [value];
+  });
+
+  // Indexes the object's values by a criterion, similar to `groupBy`, but for
+  // when you know that your index values will be unique.
+  _.indexBy = group(function(result, value, key) {
+    result[key] = value;
+  });
+
+  // Counts instances of an object that group by a certain criterion. Pass
+  // either a string attribute to count by, or a function that returns the
+  // criterion.
+  _.countBy = group(function(result, value, key) {
+    if (_.has(result, key)) result[key]++; else result[key] = 1;
+  });
+
+  // Safely create a real, live array from anything iterable.
+  _.toArray = function(obj) {
+    if (!obj) return [];
+    if (_.isArray(obj)) return slice.call(obj);
+    if (isArrayLike(obj)) return _.map(obj, _.identity);
+    return _.values(obj);
+  };
+
+  // Return the number of elements in an object.
+  _.size = function(obj) {
+    if (obj == null) return 0;
+    return isArrayLike(obj) ? obj.length : _.keys(obj).length;
+  };
+
+  // Split a collection into two arrays: one whose elements all satisfy the given
+  // predicate, and one whose elements all do not satisfy the predicate.
+  _.partition = function(obj, predicate, context) {
+    predicate = cb(predicate, context);
+    var pass = [], fail = [];
+    _.each(obj, function(value, key, obj) {
+      (predicate(value, key, obj) ? pass : fail).push(value);
+    });
+    return [pass, fail];
+  };
+
+  // Array Functions
+  // ---------------
+
+  // Get the first element of an array. Passing **n** will return the first N
+  // values in the array. Aliased as `head` and `take`. The **guard** check
+  // allows it to work with `_.map`.
+  _.first = _.head = _.take = function(array, n, guard) {
+    if (array == null) return void 0;
+    if (n == null || guard) return array[0];
+    return _.initial(array, array.length - n);
+  };
+
+  // Returns everything but the last entry of the array. Especially useful on
+  // the arguments object. Passing **n** will return all the values in
+  // the array, excluding the last N.
+  _.initial = function(array, n, guard) {
+    return slice.call(array, 0, Math.max(0, array.length - (n == null || guard ? 1 : n)));
+  };
+
+  // Get the last element of an array. Passing **n** will return the last N
+  // values in the array.
+  _.last = function(array, n, guard) {
+    if (array == null) return void 0;
+    if (n == null || guard) return array[array.length - 1];
+    return _.rest(array, Math.max(0, array.length - n));
+  };
+
+  // Returns everything but the first entry of the array. Aliased as `tail` and `drop`.
+  // Especially useful on the arguments object. Passing an **n** will return
+  // the rest N values in the array.
+  _.rest = _.tail = _.drop = function(array, n, guard) {
+    return slice.call(array, n == null || guard ? 1 : n);
+  };
+
+  // Trim out all falsy values from an array.
+  _.compact = function(array) {
+    return _.filter(array, _.identity);
+  };
+
+  // Internal implementation of a recursive `flatten` function.
+  var flatten = function(input, shallow, strict, startIndex) {
+    var output = [], idx = 0;
+    for (var i = startIndex || 0, length = getLength(input); i < length; i++) {
+      var value = input[i];
+      if (isArrayLike(value) && (_.isArray(value) || _.isArguments(value))) {
+        //flatten current level of array or arguments object
+        if (!shallow) value = flatten(value, shallow, strict);
+        var j = 0, len = value.length;
+        output.length += len;
+        while (j < len) {
+          output[idx++] = value[j++];
+        }
+      } else if (!strict) {
+        output[idx++] = value;
+      }
+    }
+    return output;
+  };
+
+  // Flatten out an array, either recursively (by default), or just one level.
+  _.flatten = function(array, shallow) {
+    return flatten(array, shallow, false);
+  };
+
+  // Return a version of the array that does not contain the specified value(s).
+  _.without = function(array) {
+    return _.difference(array, slice.call(arguments, 1));
+  };
+
+  // Produce a duplicate-free version of the array. If the array has already
+  // been sorted, you have the option of using a faster algorithm.
+  // Aliased as `unique`.
+  _.uniq = _.unique = function(array, isSorted, iteratee, context) {
+    if (!_.isBoolean(isSorted)) {
+      context = iteratee;
+      iteratee = isSorted;
+      isSorted = false;
+    }
+    if (iteratee != null) iteratee = cb(iteratee, context);
+    var result = [];
+    var seen = [];
+    for (var i = 0, length = getLength(array); i < length; i++) {
+      var value = array[i],
+          computed = iteratee ? iteratee(value, i, array) : value;
+      if (isSorted) {
+        if (!i || seen !== computed) result.push(value);
+        seen = computed;
+      } else if (iteratee) {
+        if (!_.contains(seen, computed)) {
+          seen.push(computed);
+          result.push(value);
+        }
+      } else if (!_.contains(result, value)) {
+        result.push(value);
+      }
+    }
+    return result;
+  };
+
+  // Produce an array that contains the union: each distinct element from all of
+  // the passed-in arrays.
+  _.union = function() {
+    return _.uniq(flatten(arguments, true, true));
+  };
+
+  // Produce an array that contains every item shared between all the
+  // passed-in arrays.
+  _.intersection = function(array) {
+    var result = [];
+    var argsLength = arguments.length;
+    for (var i = 0, length = getLength(array); i < length; i++) {
+      var item = array[i];
+      if (_.contains(result, item)) continue;
+      for (var j = 1; j < argsLength; j++) {
+        if (!_.contains(arguments[j], item)) break;
+      }
+      if (j === argsLength) result.push(item);
+    }
+    return result;
+  };
+
+  // Take the difference between one array and a number of other arrays.
+  // Only the elements present in just the first array will remain.
+  _.difference = function(array) {
+    var rest = flatten(arguments, true, true, 1);
+    return _.filter(array, function(value){
+      return !_.contains(rest, value);
+    });
+  };
+
+  // Zip together multiple lists into a single array -- elements that share
+  // an index go together.
+  _.zip = function() {
+    return _.unzip(arguments);
+  };
+
+  // Complement of _.zip. Unzip accepts an array of arrays and groups
+  // each array's elements on shared indices
+  _.unzip = function(array) {
+    var length = array && _.max(array, getLength).length || 0;
+    var result = Array(length);
+
+    for (var index = 0; index < length; index++) {
+      result[index] = _.pluck(array, index);
+    }
+    return result;
+  };
+
+  // Converts lists into objects. Pass either a single array of `[key, value]`
+  // pairs, or two parallel arrays of the same length -- one of keys, and one of
+  // the corresponding values.
+  _.object = function(list, values) {
+    var result = {};
+    for (var i = 0, length = getLength(list); i < length; i++) {
+      if (values) {
+        result[list[i]] = values[i];
+      } else {
+        result[list[i][0]] = list[i][1];
+      }
+    }
+    return result;
+  };
+
+  // Generator function to create the findIndex and findLastIndex functions
+  function createPredicateIndexFinder(dir) {
+    return function(array, predicate, context) {
+      predicate = cb(predicate, context);
+      var length = getLength(array);
+      var index = dir > 0 ? 0 : length - 1;
+      for (; index >= 0 && index < length; index += dir) {
+        if (predicate(array[index], index, array)) return index;
+      }
+      return -1;
+    };
+  }
+
+  // Returns the first index on an array-like that passes a predicate test
+  _.findIndex = createPredicateIndexFinder(1);
+  _.findLastIndex = createPredicateIndexFinder(-1);
+
+  // Use a comparator function to figure out the smallest index at which
+  // an object should be inserted so as to maintain order. Uses binary search.
+  _.sortedIndex = function(array, obj, iteratee, context) {
+    iteratee = cb(iteratee, context, 1);
+    var value = iteratee(obj);
+    var low = 0, high = getLength(array);
+    while (low < high) {
+      var mid = Math.floor((low + high) / 2);
+      if (iteratee(array[mid]) < value) low = mid + 1; else high = mid;
+    }
+    return low;
+  };
+
+  // Generator function to create the indexOf and lastIndexOf functions
+  function createIndexFinder(dir, predicateFind, sortedIndex) {
+    return function(array, item, idx) {
+      var i = 0, length = getLength(array);
+      if (typeof idx == 'number') {
+        if (dir > 0) {
+            i = idx >= 0 ? idx : Math.max(idx + length, i);
+        } else {
+            length = idx >= 0 ? Math.min(idx + 1, length) : idx + length + 1;
+        }
+      } else if (sortedIndex && idx && length) {
+        idx = sortedIndex(array, item);
+        return array[idx] === item ? idx : -1;
+      }
+      if (item !== item) {
+        idx = predicateFind(slice.call(array, i, length), _.isNaN);
+        return idx >= 0 ? idx + i : -1;
+      }
+      for (idx = dir > 0 ? i : length - 1; idx >= 0 && idx < length; idx += dir) {
+        if (array[idx] === item) return idx;
+      }
+      return -1;
+    };
+  }
+
+  // Return the position of the first occurrence of an item in an array,
+  // or -1 if the item is not included in the array.
+  // If the array is large and already in sort order, pass `true`
+  // for **isSorted** to use binary search.
+  _.indexOf = createIndexFinder(1, _.findIndex, _.sortedIndex);
+  _.lastIndexOf = createIndexFinder(-1, _.findLastIndex);
+
+  // Generate an integer Array containing an arithmetic progression. A port of
+  // the native Python `range()` function. See
+  // [the Python documentation](http://docs.python.org/library/functions.html#range).
+  _.range = function(start, stop, step) {
+    if (stop == null) {
+      stop = start || 0;
+      start = 0;
+    }
+    step = step || 1;
+
+    var length = Math.max(Math.ceil((stop - start) / step), 0);
+    var range = Array(length);
+
+    for (var idx = 0; idx < length; idx++, start += step) {
+      range[idx] = start;
+    }
+
+    return range;
+  };
+
+  // Function (ahem) Functions
+  // ------------------
+
+  // Determines whether to execute a function as a constructor
+  // or a normal function with the provided arguments
+  var executeBound = function(sourceFunc, boundFunc, context, callingContext, args) {
+    if (!(callingContext instanceof boundFunc)) return sourceFunc.apply(context, args);
+    var self = baseCreate(sourceFunc.prototype);
+    var result = sourceFunc.apply(self, args);
+    if (_.isObject(result)) return result;
+    return self;
+  };
+
+  // Create a function bound to a given object (assigning `this`, and arguments,
+  // optionally). Delegates to **ECMAScript 5**'s native `Function.bind` if
+  // available.
+  _.bind = function(func, context) {
+    if (nativeBind && func.bind === nativeBind) return nativeBind.apply(func, slice.call(arguments, 1));
+    if (!_.isFunction(func)) throw new TypeError('Bind must be called on a function');
+    var args = slice.call(arguments, 2);
+    var bound = function() {
+      return executeBound(func, bound, context, this, args.concat(slice.call(arguments)));
+    };
+    return bound;
+  };
+
+  // Partially apply a function by creating a version that has had some of its
+  // arguments pre-filled, without changing its dynamic `this` context. _ acts
+  // as a placeholder, allowing any combination of arguments to be pre-filled.
+  _.partial = function(func) {
+    var boundArgs = slice.call(arguments, 1);
+    var bound = function() {
+      var position = 0, length = boundArgs.length;
+      var args = Array(length);
+      for (var i = 0; i < length; i++) {
+        args[i] = boundArgs[i] === _ ? arguments[position++] : boundArgs[i];
+      }
+      while (position < arguments.length) args.push(arguments[position++]);
+      return executeBound(func, bound, this, this, args);
+    };
+    return bound;
+  };
+
+  // Bind a number of an object's methods to that object. Remaining arguments
+  // are the method names to be bound. Useful for ensuring that all callbacks
+  // defined on an object belong to it.
+  _.bindAll = function(obj) {
+    var i, length = arguments.length, key;
+    if (length <= 1) throw new Error('bindAll must be passed function names');
+    for (i = 1; i < length; i++) {
+      key = arguments[i];
+      obj[key] = _.bind(obj[key], obj);
+    }
+    return obj;
+  };
+
+  // Memoize an expensive function by storing its results.
+  _.memoize = function(func, hasher) {
+    var memoize = function(key) {
+      var cache = memoize.cache;
+      var address = '' + (hasher ? hasher.apply(this, arguments) : key);
+      if (!_.has(cache, address)) cache[address] = func.apply(this, arguments);
+      return cache[address];
+    };
+    memoize.cache = {};
+    return memoize;
+  };
+
+  // Delays a function for the given number of milliseconds, and then calls
+  // it with the arguments supplied.
+  _.delay = function(func, wait) {
+    var args = slice.call(arguments, 2);
+    return setTimeout(function(){
+      return func.apply(null, args);
+    }, wait);
+  };
+
+  // Defers a function, scheduling it to run after the current call stack has
+  // cleared.
+  _.defer = _.partial(_.delay, _, 1);
+
+  // Returns a function, that, when invoked, will only be triggered at most once
+  // during a given window of time. Normally, the throttled function will run
+  // as much as it can, without ever going more than once per `wait` duration;
+  // but if you'd like to disable the execution on the leading edge, pass
+  // `{leading: false}`. To disable execution on the trailing edge, ditto.
+  _.throttle = function(func, wait, options) {
+    var context, args, result;
+    var timeout = null;
+    var previous = 0;
+    if (!options) options = {};
+    var later = function() {
+      previous = options.leading === false ? 0 : _.now();
+      timeout = null;
+      result = func.apply(context, args);
+      if (!timeout) context = args = null;
+    };
+    return function() {
+      var now = _.now();
+      if (!previous && options.leading === false) previous = now;
+      var remaining = wait - (now - previous);
+      context = this;
+      args = arguments;
+      if (remaining <= 0 || remaining > wait) {
+        if (timeout) {
+          clearTimeout(timeout);
+          timeout = null;
+        }
+        previous = now;
+        result = func.apply(context, args);
+        if (!timeout) context = args = null;
+      } else if (!timeout && options.trailing !== false) {
+        timeout = setTimeout(later, remaining);
+      }
+      return result;
+    };
+  };
+
+  // Returns a function, that, as long as it continues to be invoked, will not
+  // be triggered. The function will be called after it stops being called for
+  // N milliseconds. If `immediate` is passed, trigger the function on the
+  // leading edge, instead of the trailing.
+  _.debounce = function(func, wait, immediate) {
+    var timeout, args, context, timestamp, result;
+
+    var later = function() {
+      var last = _.now() - timestamp;
+
+      if (last < wait && last >= 0) {
+        timeout = setTimeout(later, wait - last);
+      } else {
+        timeout = null;
+        if (!immediate) {
+          result = func.apply(context, args);
+          if (!timeout) context = args = null;
+        }
+      }
+    };
+
+    return function() {
+      context = this;
+      args = arguments;
+      timestamp = _.now();
+      var callNow = immediate && !timeout;
+      if (!timeout) timeout = setTimeout(later, wait);
+      if (callNow) {
+        result = func.apply(context, args);
+        context = args = null;
+      }
+
+      return result;
+    };
+  };
+
+  // Returns the first function passed as an argument to the second,
+  // allowing you to adjust arguments, run code before and after, and
+  // conditionally execute the original function.
+  _.wrap = function(func, wrapper) {
+    return _.partial(wrapper, func);
+  };
+
+  // Returns a negated version of the passed-in predicate.
+  _.negate = function(predicate) {
+    return function() {
+      return !predicate.apply(this, arguments);
+    };
+  };
+
+  // Returns a function that is the composition of a list of functions, each
+  // consuming the return value of the function that follows.
+  _.compose = function() {
+    var args = arguments;
+    var start = args.length - 1;
+    return function() {
+      var i = start;
+      var result = args[start].apply(this, arguments);
+      while (i--) result = args[i].call(this, result);
+      return result;
+    };
+  };
+
+  // Returns a function that will only be executed on and after the Nth call.
+  _.after = function(times, func) {
+    return function() {
+      if (--times < 1) {
+        return func.apply(this, arguments);
+      }
+    };
+  };
+
+  // Returns a function that will only be executed up to (but not including) the Nth call.
+  _.before = function(times, func) {
+    var memo;
+    return function() {
+      if (--times > 0) {
+        memo = func.apply(this, arguments);
+      }
+      if (times <= 1) func = null;
+      return memo;
+    };
+  };
+
+  // Returns a function that will be executed at most one time, no matter how
+  // often you call it. Useful for lazy initialization.
+  _.once = _.partial(_.before, 2);
+
+  // Object Functions
+  // ----------------
+
+  // Keys in IE < 9 that won't be iterated by `for key in ...` and thus missed.
+  var hasEnumBug = !{toString: null}.propertyIsEnumerable('toString');
+  var nonEnumerableProps = ['valueOf', 'isPrototypeOf', 'toString',
+                      'propertyIsEnumerable', 'hasOwnProperty', 'toLocaleString'];
+
+  function collectNonEnumProps(obj, keys) {
+    var nonEnumIdx = nonEnumerableProps.length;
+    var constructor = obj.constructor;
+    var proto = (_.isFunction(constructor) && constructor.prototype) || ObjProto;
+
+    // Constructor is a special case.
+    var prop = 'constructor';
+    if (_.has(obj, prop) && !_.contains(keys, prop)) keys.push(prop);
+
+    while (nonEnumIdx--) {
+      prop = nonEnumerableProps[nonEnumIdx];
+      if (prop in obj && obj[prop] !== proto[prop] && !_.contains(keys, prop)) {
+        keys.push(prop);
+      }
+    }
+  }
+
+  // Retrieve the names of an object's own properties.
+  // Delegates to **ECMAScript 5**'s native `Object.keys`
+  _.keys = function(obj) {
+    if (!_.isObject(obj)) return [];
+    if (nativeKeys) return nativeKeys(obj);
+    var keys = [];
+    for (var key in obj) if (_.has(obj, key)) keys.push(key);
+    // Ahem, IE < 9.
+    if (hasEnumBug) collectNonEnumProps(obj, keys);
+    return keys;
+  };
+
+  // Retrieve all the property names of an object.
+  _.allKeys = function(obj) {
+    if (!_.isObject(obj)) return [];
+    var keys = [];
+    for (var key in obj) keys.push(key);
+    // Ahem, IE < 9.
+    if (hasEnumBug) collectNonEnumProps(obj, keys);
+    return keys;
+  };
+
+  // Retrieve the values of an object's properties.
+  _.values = function(obj) {
+    var keys = _.keys(obj);
+    var length = keys.length;
+    var values = Array(length);
+    for (var i = 0; i < length; i++) {
+      values[i] = obj[keys[i]];
+    }
+    return values;
+  };
+
+  // Returns the results of applying the iteratee to each element of the object
+  // In contrast to _.map it returns an object
+  _.mapObject = function(obj, iteratee, context) {
+    iteratee = cb(iteratee, context);
+    var keys =  _.keys(obj),
+          length = keys.length,
+          results = {},
+          currentKey;
+      for (var index = 0; index < length; index++) {
+        currentKey = keys[index];
+        results[currentKey] = iteratee(obj[currentKey], currentKey, obj);
+      }
+      return results;
+  };
+
+  // Convert an object into a list of `[key, value]` pairs.
+  _.pairs = function(obj) {
+    var keys = _.keys(obj);
+    var length = keys.length;
+    var pairs = Array(length);
+    for (var i = 0; i < length; i++) {
+      pairs[i] = [keys[i], obj[keys[i]]];
+    }
+    return pairs;
+  };
+
+  // Invert the keys and values of an object. The values must be serializable.
+  _.invert = function(obj) {
+    var result = {};
+    var keys = _.keys(obj);
+    for (var i = 0, length = keys.length; i < length; i++) {
+      result[obj[keys[i]]] = keys[i];
+    }
+    return result;
+  };
+
+  // Return a sorted list of the function names available on the object.
+  // Aliased as `methods`
+  _.functions = _.methods = function(obj) {
+    var names = [];
+    for (var key in obj) {
+      if (_.isFunction(obj[key])) names.push(key);
+    }
+    return names.sort();
+  };
+
+  // Extend a given object with all the properties in passed-in object(s).
+  _.extend = createAssigner(_.allKeys);
+
+  // Assigns a given object with all the own properties in the passed-in object(s)
+  // (https://developer.mozilla.org/docs/Web/JavaScript/Reference/Global_Objects/Object/assign)
+  _.extendOwn = _.assign = createAssigner(_.keys);
+
+  // Returns the first key on an object that passes a predicate test
+  _.findKey = function(obj, predicate, context) {
+    predicate = cb(predicate, context);
+    var keys = _.keys(obj), key;
+    for (var i = 0, length = keys.length; i < length; i++) {
+      key = keys[i];
+      if (predicate(obj[key], key, obj)) return key;
+    }
+  };
+
+  // Return a copy of the object only containing the whitelisted properties.
+  _.pick = function(object, oiteratee, context) {
+    var result = {}, obj = object, iteratee, keys;
+    if (obj == null) return result;
+    if (_.isFunction(oiteratee)) {
+      keys = _.allKeys(obj);
+      iteratee = optimizeCb(oiteratee, context);
+    } else {
+      keys = flatten(arguments, false, false, 1);
+      iteratee = function(value, key, obj) { return key in obj; };
+      obj = Object(obj);
+    }
+    for (var i = 0, length = keys.length; i < length; i++) {
+      var key = keys[i];
+      var value = obj[key];
+      if (iteratee(value, key, obj)) result[key] = value;
+    }
+    return result;
+  };
+
+   // Return a copy of the object without the blacklisted properties.
+  _.omit = function(obj, iteratee, context) {
+    if (_.isFunction(iteratee)) {
+      iteratee = _.negate(iteratee);
+    } else {
+      var keys = _.map(flatten(arguments, false, false, 1), String);
+      iteratee = function(value, key) {
+        return !_.contains(keys, key);
+      };
+    }
+    return _.pick(obj, iteratee, context);
+  };
+
+  // Fill in a given object with default properties.
+  _.defaults = createAssigner(_.allKeys, true);
+
+  // Creates an object that inherits from the given prototype object.
+  // If additional properties are provided then they will be added to the
+  // created object.
+  _.create = function(prototype, props) {
+    var result = baseCreate(prototype);
+    if (props) _.extendOwn(result, props);
+    return result;
+  };
+
+  // Create a (shallow-cloned) duplicate of an object.
+  _.clone = function(obj) {
+    if (!_.isObject(obj)) return obj;
+    return _.isArray(obj) ? obj.slice() : _.extend({}, obj);
+  };
+
+  // Invokes interceptor with the obj, and then returns obj.
+  // The primary purpose of this method is to "tap into" a method chain, in
+  // order to perform operations on intermediate results within the chain.
+  _.tap = function(obj, interceptor) {
+    interceptor(obj);
+    return obj;
+  };
+
+  // Returns whether an object has a given set of `key:value` pairs.
+  _.isMatch = function(object, attrs) {
+    var keys = _.keys(attrs), length = keys.length;
+    if (object == null) return !length;
+    var obj = Object(object);
+    for (var i = 0; i < length; i++) {
+      var key = keys[i];
+      if (attrs[key] !== obj[key] || !(key in obj)) return false;
+    }
+    return true;
+  };
+
+
+  // Internal recursive comparison function for `isEqual`.
+  var eq = function(a, b, aStack, bStack) {
+    // Identical objects are equal. `0 === -0`, but they aren't identical.
+    // See the [Harmony `egal` proposal](http://wiki.ecmascript.org/doku.php?id=harmony:egal).
+    if (a === b) return a !== 0 || 1 / a === 1 / b;
+    // A strict comparison is necessary because `null == undefined`.
+    if (a == null || b == null) return a === b;
+    // Unwrap any wrapped objects.
+    if (a instanceof _) a = a._wrapped;
+    if (b instanceof _) b = b._wrapped;
+    // Compare `[[Class]]` names.
+    var className = toString.call(a);
+    if (className !== toString.call(b)) return false;
+    switch (className) {
+      // Strings, numbers, regular expressions, dates, and booleans are compared by value.
+      case '[object RegExp]':
+      // RegExps are coerced to strings for comparison (Note: '' + /a/i === '/a/i')
+      case '[object String]':
+        // Primitives and their corresponding object wrappers are equivalent; thus, `"5"` is
+        // equivalent to `new String("5")`.
+        return '' + a === '' + b;
+      case '[object Number]':
+        // `NaN`s are equivalent, but non-reflexive.
+        // Object(NaN) is equivalent to NaN
+        if (+a !== +a) return +b !== +b;
+        // An `egal` comparison is performed for other numeric values.
+        return +a === 0 ? 1 / +a === 1 / b : +a === +b;
+      case '[object Date]':
+      case '[object Boolean]':
+        // Coerce dates and booleans to numeric primitive values. Dates are compared by their
+        // millisecond representations. Note that invalid dates with millisecond representations
+        // of `NaN` are not equivalent.
+        return +a === +b;
+    }
+
+    var areArrays = className === '[object Array]';
+    if (!areArrays) {
+      if (typeof a != 'object' || typeof b != 'object') return false;
+
+      // Objects with different constructors are not equivalent, but `Object`s or `Array`s
+      // from different frames are.
+      var aCtor = a.constructor, bCtor = b.constructor;
+      if (aCtor !== bCtor && !(_.isFunction(aCtor) && aCtor instanceof aCtor &&
+                               _.isFunction(bCtor) && bCtor instanceof bCtor)
+                          && ('constructor' in a && 'constructor' in b)) {
+        return false;
+      }
+    }
+    // Assume equality for cyclic structures. The algorithm for detecting cyclic
+    // structures is adapted from ES 5.1 section 15.12.3, abstract operation `JO`.
+
+    // Initializing stack of traversed objects.
+    // It's done here since we only need them for objects and arrays comparison.
+    aStack = aStack || [];
+    bStack = bStack || [];
+    var length = aStack.length;
+    while (length--) {
+      // Linear search. Performance is inversely proportional to the number of
+      // unique nested structures.
+      if (aStack[length] === a) return bStack[length] === b;
+    }
+
+    // Add the first object to the stack of traversed objects.
+    aStack.push(a);
+    bStack.push(b);
+
+    // Recursively compare objects and arrays.
+    if (areArrays) {
+      // Compare array lengths to determine if a deep comparison is necessary.
+      length = a.length;
+      if (length !== b.length) return false;
+      // Deep compare the contents, ignoring non-numeric properties.
+      while (length--) {
+        if (!eq(a[length], b[length], aStack, bStack)) return false;
+      }
+    } else {
+      // Deep compare objects.
+      var keys = _.keys(a), key;
+      length = keys.length;
+      // Ensure that both objects contain the same number of properties before comparing deep equality.
+      if (_.keys(b).length !== length) return false;
+      while (length--) {
+        // Deep compare each member
+        key = keys[length];
+        if (!(_.has(b, key) && eq(a[key], b[key], aStack, bStack))) return false;
+      }
+    }
+    // Remove the first object from the stack of traversed objects.
+    aStack.pop();
+    bStack.pop();
+    return true;
+  };
+
+  // Perform a deep comparison to check if two objects are equal.
+  _.isEqual = function(a, b) {
+    return eq(a, b);
+  };
+
+  // Is a given array, string, or object empty?
+  // An "empty" object has no enumerable own-properties.
+  _.isEmpty = function(obj) {
+    if (obj == null) return true;
+    if (isArrayLike(obj) && (_.isArray(obj) || _.isString(obj) || _.isArguments(obj))) return obj.length === 0;
+    return _.keys(obj).length === 0;
+  };
+
+  // Is a given value a DOM element?
+  _.isElement = function(obj) {
+    return !!(obj && obj.nodeType === 1);
+  };
+
+  // Is a given value an array?
+  // Delegates to ECMA5's native Array.isArray
+  _.isArray = nativeIsArray || function(obj) {
+    return toString.call(obj) === '[object Array]';
+  };
+
+  // Is a given variable an object?
+  _.isObject = function(obj) {
+    var type = typeof obj;
+    return type === 'function' || type === 'object' && !!obj;
+  };
+
+  // Add some isType methods: isArguments, isFunction, isString, isNumber, isDate, isRegExp, isError.
+  _.each(['Arguments', 'Function', 'String', 'Number', 'Date', 'RegExp', 'Error'], function(name) {
+    _['is' + name] = function(obj) {
+      return toString.call(obj) === '[object ' + name + ']';
+    };
+  });
+
+  // Define a fallback version of the method in browsers (ahem, IE < 9), where
+  // there isn't any inspectable "Arguments" type.
+  if (!_.isArguments(arguments)) {
+    _.isArguments = function(obj) {
+      return _.has(obj, 'callee');
+    };
+  }
+
+  // Optimize `isFunction` if appropriate. Work around some typeof bugs in old v8,
+  // IE 11 (#1621), and in Safari 8 (#1929).
+  if (typeof /./ != 'function' && typeof Int8Array != 'object') {
+    _.isFunction = function(obj) {
+      return typeof obj == 'function' || false;
+    };
+  }
+
+  // Is a given object a finite number?
+  _.isFinite = function(obj) {
+    return isFinite(obj) && !isNaN(parseFloat(obj));
+  };
+
+  // Is the given value `NaN`? (NaN is the only number which does not equal itself).
+  _.isNaN = function(obj) {
+    return _.isNumber(obj) && obj !== +obj;
+  };
+
+  // Is a given value a boolean?
+  _.isBoolean = function(obj) {
+    return obj === true || obj === false || toString.call(obj) === '[object Boolean]';
+  };
+
+  // Is a given value equal to null?
+  _.isNull = function(obj) {
+    return obj === null;
+  };
+
+  // Is a given variable undefined?
+  _.isUndefined = function(obj) {
+    return obj === void 0;
+  };
+
+  // Shortcut function for checking if an object has a given property directly
+  // on itself (in other words, not on a prototype).
+  _.has = function(obj, key) {
+    return obj != null && hasOwnProperty.call(obj, key);
+  };
+
+  // Utility Functions
+  // -----------------
+
+  // Run Underscore.js in *noConflict* mode, returning the `_` variable to its
+  // previous owner. Returns a reference to the Underscore object.
+  _.noConflict = function() {
+    root._ = previousUnderscore;
+    return this;
+  };
+
+  // Keep the identity function around for default iteratees.
+  _.identity = function(value) {
+    return value;
+  };
+
+  // Predicate-generating functions. Often useful outside of Underscore.
+  _.constant = function(value) {
+    return function() {
+      return value;
+    };
+  };
+
+  _.noop = function(){};
+
+  _.property = property;
+
+  // Generates a function for a given object that returns a given property.
+  _.propertyOf = function(obj) {
+    return obj == null ? function(){} : function(key) {
+      return obj[key];
+    };
+  };
+
+  // Returns a predicate for checking whether an object has a given set of
+  // `key:value` pairs.
+  _.matcher = _.matches = function(attrs) {
+    attrs = _.extendOwn({}, attrs);
+    return function(obj) {
+      return _.isMatch(obj, attrs);
+    };
+  };
+
+  // Run a function **n** times.
+  _.times = function(n, iteratee, context) {
+    var accum = Array(Math.max(0, n));
+    iteratee = optimizeCb(iteratee, context, 1);
+    for (var i = 0; i < n; i++) accum[i] = iteratee(i);
+    return accum;
+  };
+
+  // Return a random integer between min and max (inclusive).
+  _.random = function(min, max) {
+    if (max == null) {
+      max = min;
+      min = 0;
+    }
+    return min + Math.floor(Math.random() * (max - min + 1));
+  };
+
+  // A (possibly faster) way to get the current timestamp as an integer.
+  _.now = Date.now || function() {
+    return new Date().getTime();
+  };
+
+   // List of HTML entities for escaping.
+  var escapeMap = {
+    '&': '&amp;',
+    '<': '&lt;',
+    '>': '&gt;',
+    '"': '&quot;',
+    "'": '&#x27;',
+    '`': '&#x60;'
+  };
+  var unescapeMap = _.invert(escapeMap);
+
+  // Functions for escaping and unescaping strings to/from HTML interpolation.
+  var createEscaper = function(map) {
+    var escaper = function(match) {
+      return map[match];
+    };
+    // Regexes for identifying a key that needs to be escaped
+    var source = '(?:' + _.keys(map).join('|') + ')';
+    var testRegexp = RegExp(source);
+    var replaceRegexp = RegExp(source, 'g');
+    return function(string) {
+      string = string == null ? '' : '' + string;
+      return testRegexp.test(string) ? string.replace(replaceRegexp, escaper) : string;
+    };
+  };
+  _.escape = createEscaper(escapeMap);
+  _.unescape = createEscaper(unescapeMap);
+
+  // If the value of the named `property` is a function then invoke it with the
+  // `object` as context; otherwise, return it.
+  _.result = function(object, property, fallback) {
+    var value = object == null ? void 0 : object[property];
+    if (value === void 0) {
+      value = fallback;
+    }
+    return _.isFunction(value) ? value.call(object) : value;
+  };
+
+  // Generate a unique integer id (unique within the entire client session).
+  // Useful for temporary DOM ids.
+  var idCounter = 0;
+  _.uniqueId = function(prefix) {
+    var id = ++idCounter + '';
+    return prefix ? prefix + id : id;
+  };
+
+  // By default, Underscore uses ERB-style template delimiters, change the
+  // following template settings to use alternative delimiters.
+  _.templateSettings = {
+    evaluate    : /<%([\s\S]+?)%>/g,
+    interpolate : /<%=([\s\S]+?)%>/g,
+    escape      : /<%-([\s\S]+?)%>/g
+  };
+
+  // When customizing `templateSettings`, if you don't want to define an
+  // interpolation, evaluation or escaping regex, we need one that is
+  // guaranteed not to match.
+  var noMatch = /(.)^/;
+
+  // Certain characters need to be escaped so that they can be put into a
+  // string literal.
+  var escapes = {
+    "'":      "'",
+    '\\':     '\\',
+    '\r':     'r',
+    '\n':     'n',
+    '\u2028': 'u2028',
+    '\u2029': 'u2029'
+  };
+
+  var escaper = /\\|'|\r|\n|\u2028|\u2029/g;
+
+  var escapeChar = function(match) {
+    return '\\' + escapes[match];
+  };
+
+  // JavaScript micro-templating, similar to John Resig's implementation.
+  // Underscore templating handles arbitrary delimiters, preserves whitespace,
+  // and correctly escapes quotes within interpolated code.
+  // NB: `oldSettings` only exists for backwards compatibility.
+  _.template = function(text, settings, oldSettings) {
+    if (!settings && oldSettings) settings = oldSettings;
+    settings = _.defaults({}, settings, _.templateSettings);
+
+    // Combine delimiters into one regular expression via alternation.
+    var matcher = RegExp([
+      (settings.escape || noMatch).source,
+      (settings.interpolate || noMatch).source,
+      (settings.evaluate || noMatch).source
+    ].join('|') + '|$', 'g');
+
+    // Compile the template source, escaping string literals appropriately.
+    var index = 0;
+    var source = "__p+='";
+    text.replace(matcher, function(match, escape, interpolate, evaluate, offset) {
+      source += text.slice(index, offset).replace(escaper, escapeChar);
+      index = offset + match.length;
+
+      if (escape) {
+        source += "'+\n((__t=(" + escape + "))==null?'':_.escape(__t))+\n'";
+      } else if (interpolate) {
+        source += "'+\n((__t=(" + interpolate + "))==null?'':__t)+\n'";
+      } else if (evaluate) {
+        source += "';\n" + evaluate + "\n__p+='";
+      }
+
+      // Adobe VMs need the match returned to produce the correct offest.
+      return match;
+    });
+    source += "';\n";
+
+    // If a variable is not specified, place data values in local scope.
+    if (!settings.variable) source = 'with(obj||{}){\n' + source + '}\n';
+
+    source = "var __t,__p='',__j=Array.prototype.join," +
+      "print=function(){__p+=__j.call(arguments,'');};\n" +
+      source + 'return __p;\n';
+
+    try {
+      var render = new Function(settings.variable || 'obj', '_', source);
+    } catch (e) {
+      e.source = source;
+      throw e;
+    }
+
+    var template = function(data) {
+      return render.call(this, data, _);
+    };
+
+    // Provide the compiled source as a convenience for precompilation.
+    var argument = settings.variable || 'obj';
+    template.source = 'function(' + argument + '){\n' + source + '}';
+
+    return template;
+  };
+
+  // Add a "chain" function. Start chaining a wrapped Underscore object.
+  _.chain = function(obj) {
+    var instance = _(obj);
+    instance._chain = true;
+    return instance;
+  };
+
+  // OOP
+  // ---------------
+  // If Underscore is called as a function, it returns a wrapped object that
+  // can be used OO-style. This wrapper holds altered versions of all the
+  // underscore functions. Wrapped objects may be chained.
+
+  // Helper function to continue chaining intermediate results.
+  var result = function(instance, obj) {
+    return instance._chain ? _(obj).chain() : obj;
+  };
+
+  // Add your own custom functions to the Underscore object.
+  _.mixin = function(obj) {
+    _.each(_.functions(obj), function(name) {
+      var func = _[name] = obj[name];
+      _.prototype[name] = function() {
+        var args = [this._wrapped];
+        push.apply(args, arguments);
+        return result(this, func.apply(_, args));
+      };
+    });
+  };
+
+  // Add all of the Underscore functions to the wrapper object.
+  _.mixin(_);
+
+  // Add all mutator Array functions to the wrapper.
+  _.each(['pop', 'push', 'reverse', 'shift', 'sort', 'splice', 'unshift'], function(name) {
+    var method = ArrayProto[name];
+    _.prototype[name] = function() {
+      var obj = this._wrapped;
+      method.apply(obj, arguments);
+      if ((name === 'shift' || name === 'splice') && obj.length === 0) delete obj[0];
+      return result(this, obj);
+    };
+  });
+
+  // Add all accessor Array functions to the wrapper.
+  _.each(['concat', 'join', 'slice'], function(name) {
+    var method = ArrayProto[name];
+    _.prototype[name] = function() {
+      return result(this, method.apply(this._wrapped, arguments));
+    };
+  });
+
+  // Extracts the result from a wrapped and chained object.
+  _.prototype.value = function() {
+    return this._wrapped;
+  };
+
+  // Provide unwrapping proxy for some methods used in engine operations
+  // such as arithmetic and JSON stringification.
+  _.prototype.valueOf = _.prototype.toJSON = _.prototype.value;
+
+  _.prototype.toString = function() {
+    return '' + this._wrapped;
+  };
+
+  // AMD registration happens at the end for compatibility with AMD loaders
+  // that may not enforce next-turn semantics on modules. Even though general
+  // practice for AMD registration is to be anonymous, underscore registers
+  // as a named module because, like jQuery, it is a base library that is
+  // popular enough to be bundled in a third party lib, but not be part of
+  // an AMD load request. Those cases could generate an error when an
+  // anonymous define() is called outside of a loader request.
+  if (typeof define === 'function' && define.amd) {
+    define('underscore', [], function() {
+      return _;
+    });
+  }
+}.call(this));
+
+},{}],26:[function(require,module,exports){
+arguments[4][19][0].apply(exports,arguments)
+},{"dup":19}],27:[function(require,module,exports){
+module.exports = function isBuffer(arg) {
+  return arg && typeof arg === 'object'
+    && typeof arg.copy === 'function'
+    && typeof arg.fill === 'function'
+    && typeof arg.readUInt8 === 'function';
+}
+},{}],28:[function(require,module,exports){
+(function (process,global){
+// Copyright Joyent, Inc. and other Node contributors.
+//
+// Permission is hereby granted, free of charge, to any person obtaining a
+// copy of this software and associated documentation files (the
+// "Software"), to deal in the Software without restriction, including
+// without limitation the rights to use, copy, modify, merge, publish,
+// distribute, sublicense, and/or sell copies of the Software, and to permit
+// persons to whom the Software is furnished to do so, subject to the
+// following conditions:
+//
+// The above copyright notice and this permission notice shall be included
+// in all copies or substantial portions of the Software.
+//
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
+// OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+// MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN
+// NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM,
+// DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR
+// OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE
+// USE OR OTHER DEALINGS IN THE SOFTWARE.
+
+var formatRegExp = /%[sdj%]/g;
+exports.format = function(f) {
+  if (!isString(f)) {
+    var objects = [];
+    for (var i = 0; i < arguments.length; i++) {
+      objects.push(inspect(arguments[i]));
+    }
+    return objects.join(' ');
+  }
+
+  var i = 1;
+  var args = arguments;
+  var len = args.length;
+  var str = String(f).replace(formatRegExp, function(x) {
+    if (x === '%%') return '%';
+    if (i >= len) return x;
+    switch (x) {
+      case '%s': return String(args[i++]);
+      case '%d': return Number(args[i++]);
+      case '%j':
+        try {
+          return JSON.stringify(args[i++]);
+        } catch (_) {
+          return '[Circular]';
+        }
+      default:
+        return x;
+    }
+  });
+  for (var x = args[i]; i < len; x = args[++i]) {
+    if (isNull(x) || !isObject(x)) {
+      str += ' ' + x;
+    } else {
+      str += ' ' + inspect(x);
+    }
+  }
+  return str;
+};
+
+
+// Mark that a method should not be used.
+// Returns a modified function which warns once by default.
+// If --no-deprecation is set, then it is a no-op.
+exports.deprecate = function(fn, msg) {
+  // Allow for deprecating things in the process of starting up.
+  if (isUndefined(global.process)) {
+    return function() {
+      return exports.deprecate(fn, msg).apply(this, arguments);
+    };
+  }
+
+  if (process.noDeprecation === true) {
+    return fn;
+  }
+
+  var warned = false;
+  function deprecated() {
+    if (!warned) {
+      if (process.throwDeprecation) {
+        throw new Error(msg);
+      } else if (process.traceDeprecation) {
+        console.trace(msg);
+      } else {
+        console.error(msg);
+      }
+      warned = true;
+    }
+    return fn.apply(this, arguments);
+  }
+
+  return deprecated;
+};
+
+
+var debugs = {};
+var debugEnviron;
+exports.debuglog = function(set) {
+  if (isUndefined(debugEnviron))
+    debugEnviron = process.env.NODE_DEBUG || '';
+  set = set.toUpperCase();
+  if (!debugs[set]) {
+    if (new RegExp('\\b' + set + '\\b', 'i').test(debugEnviron)) {
+      var pid = process.pid;
+      debugs[set] = function() {
+        var msg = exports.format.apply(exports, arguments);
+        console.error('%s %d: %s', set, pid, msg);
+      };
+    } else {
+      debugs[set] = function() {};
+    }
+  }
+  return debugs[set];
+};
+
+
+/**
+ * Echos the value of a value. Trys to print the value out
+ * in the best way possible given the different types.
+ *
+ * @param {Object} obj The object to print out.
+ * @param {Object} opts Optional options object that alters the output.
+ */
+/* legacy: obj, showHidden, depth, colors*/
+function inspect(obj, opts) {
+  // default options
+  var ctx = {
+    seen: [],
+    stylize: stylizeNoColor
+  };
+  // legacy...
+  if (arguments.length >= 3) ctx.depth = arguments[2];
+  if (arguments.length >= 4) ctx.colors = arguments[3];
+  if (isBoolean(opts)) {
+    // legacy...
+    ctx.showHidden = opts;
+  } else if (opts) {
+    // got an "options" object
+    exports._extend(ctx, opts);
+  }
+  // set default options
+  if (isUndefined(ctx.showHidden)) ctx.showHidden = false;
+  if (isUndefined(ctx.depth)) ctx.depth = 2;
+  if (isUndefined(ctx.colors)) ctx.colors = false;
+  if (isUndefined(ctx.customInspect)) ctx.customInspect = true;
+  if (ctx.colors) ctx.stylize = stylizeWithColor;
+  return formatValue(ctx, obj, ctx.depth);
+}
+exports.inspect = inspect;
+
+
+// http://en.wikipedia.org/wiki/ANSI_escape_code#graphics
+inspect.colors = {
+  'bold' : [1, 22],
+  'italic' : [3, 23],
+  'underline' : [4, 24],
+  'inverse' : [7, 27],
+  'white' : [37, 39],
+  'grey' : [90, 39],
+  'black' : [30, 39],
+  'blue' : [34, 39],
+  'cyan' : [36, 39],
+  'green' : [32, 39],
+  'magenta' : [35, 39],
+  'red' : [31, 39],
+  'yellow' : [33, 39]
+};
+
+// Don't use 'blue' not visible on cmd.exe
+inspect.styles = {
+  'special': 'cyan',
+  'number': 'yellow',
+  'boolean': 'yellow',
+  'undefined': 'grey',
+  'null': 'bold',
+  'string': 'green',
+  'date': 'magenta',
+  // "name": intentionally not styling
+  'regexp': 'red'
+};
+
+
+function stylizeWithColor(str, styleType) {
+  var style = inspect.styles[styleType];
+
+  if (style) {
+    return '\u001b[' + inspect.colors[style][0] + 'm' + str +
+           '\u001b[' + inspect.colors[style][1] + 'm';
+  } else {
+    return str;
+  }
+}
+
+
+function stylizeNoColor(str, styleType) {
+  return str;
+}
+
+
+function arrayToHash(array) {
+  var hash = {};
+
+  array.forEach(function(val, idx) {
+    hash[val] = true;
+  });
+
+  return hash;
+}
+
+
+function formatValue(ctx, value, recurseTimes) {
+  // Provide a hook for user-specified inspect functions.
+  // Check that value is an object with an inspect function on it
+  if (ctx.customInspect &&
+      value &&
+      isFunction(value.inspect) &&
+      // Filter out the util module, it's inspect function is special
+      value.inspect !== exports.inspect &&
+      // Also filter out any prototype objects using the circular check.
+      !(value.constructor && value.constructor.prototype === value)) {
+    var ret = value.inspect(recurseTimes, ctx);
+    if (!isString(ret)) {
+      ret = formatValue(ctx, ret, recurseTimes);
+    }
+    return ret;
+  }
+
+  // Primitive types cannot have properties
+  var primitive = formatPrimitive(ctx, value);
+  if (primitive) {
+    return primitive;
+  }
+
+  // Look up the keys of the object.
+  var keys = Object.keys(value);
+  var visibleKeys = arrayToHash(keys);
+
+  if (ctx.showHidden) {
+    keys = Object.getOwnPropertyNames(value);
+  }
+
+  // IE doesn't make error fields non-enumerable
+  // http://msdn.microsoft.com/en-us/library/ie/dww52sbt(v=vs.94).aspx
+  if (isError(value)
+      && (keys.indexOf('message') >= 0 || keys.indexOf('description') >= 0)) {
+    return formatError(value);
+  }
+
+  // Some type of object without properties can be shortcutted.
+  if (keys.length === 0) {
+    if (isFunction(value)) {
+      var name = value.name ? ': ' + value.name : '';
+      return ctx.stylize('[Function' + name + ']', 'special');
+    }
+    if (isRegExp(value)) {
+      return ctx.stylize(RegExp.prototype.toString.call(value), 'regexp');
+    }
+    if (isDate(value)) {
+      return ctx.stylize(Date.prototype.toString.call(value), 'date');
+    }
+    if (isError(value)) {
+      return formatError(value);
+    }
+  }
+
+  var base = '', array = false, braces = ['{', '}'];
+
+  // Make Array say that they are Array
+  if (isArray(value)) {
+    array = true;
+    braces = ['[', ']'];
+  }
+
+  // Make functions say that they are functions
+  if (isFunction(value)) {
+    var n = value.name ? ': ' + value.name : '';
+    base = ' [Function' + n + ']';
+  }
+
+  // Make RegExps say that they are RegExps
+  if (isRegExp(value)) {
+    base = ' ' + RegExp.prototype.toString.call(value);
+  }
+
+  // Make dates with properties first say the date
+  if (isDate(value)) {
+    base = ' ' + Date.prototype.toUTCString.call(value);
+  }
+
+  // Make error with message first say the error
+  if (isError(value)) {
+    base = ' ' + formatError(value);
+  }
+
+  if (keys.length === 0 && (!array || value.length == 0)) {
+    return braces[0] + base + braces[1];
+  }
+
+  if (recurseTimes < 0) {
+    if (isRegExp(value)) {
+      return ctx.stylize(RegExp.prototype.toString.call(value), 'regexp');
+    } else {
+      return ctx.stylize('[Object]', 'special');
+    }
+  }
+
+  ctx.seen.push(value);
+
+  var output;
+  if (array) {
+    output = formatArray(ctx, value, recurseTimes, visibleKeys, keys);
+  } else {
+    output = keys.map(function(key) {
+      return formatProperty(ctx, value, recurseTimes, visibleKeys, key, array);
+    });
+  }
+
+  ctx.seen.pop();
+
+  return reduceToSingleString(output, base, braces);
+}
+
+
+function formatPrimitive(ctx, value) {
+  if (isUndefined(value))
+    return ctx.stylize('undefined', 'undefined');
+  if (isString(value)) {
+    var simple = '\'' + JSON.stringify(value).replace(/^"|"$/g, '')
+                                             .replace(/'/g, "\\'")
+                                             .replace(/\\"/g, '"') + '\'';
+    return ctx.stylize(simple, 'string');
+  }
+  if (isNumber(value))
+    return ctx.stylize('' + value, 'number');
+  if (isBoolean(value))
+    return ctx.stylize('' + value, 'boolean');
+  // For some reason typeof null is "object", so special case here.
+  if (isNull(value))
+    return ctx.stylize('null', 'null');
+}
+
+
+function formatError(value) {
+  return '[' + Error.prototype.toString.call(value) + ']';
+}
+
+
+function formatArray(ctx, value, recurseTimes, visibleKeys, keys) {
+  var output = [];
+  for (var i = 0, l = value.length; i < l; ++i) {
+    if (hasOwnProperty(value, String(i))) {
+      output.push(formatProperty(ctx, value, recurseTimes, visibleKeys,
+          String(i), true));
+    } else {
+      output.push('');
+    }
+  }
+  keys.forEach(function(key) {
+    if (!key.match(/^\d+$/)) {
+      output.push(formatProperty(ctx, value, recurseTimes, visibleKeys,
+          key, true));
+    }
+  });
+  return output;
+}
+
+
+function formatProperty(ctx, value, recurseTimes, visibleKeys, key, array) {
+  var name, str, desc;
+  desc = Object.getOwnPropertyDescriptor(value, key) || { value: value[key] };
+  if (desc.get) {
+    if (desc.set) {
+      str = ctx.stylize('[Getter/Setter]', 'special');
+    } else {
+      str = ctx.stylize('[Getter]', 'special');
+    }
+  } else {
+    if (desc.set) {
+      str = ctx.stylize('[Setter]', 'special');
+    }
+  }
+  if (!hasOwnProperty(visibleKeys, key)) {
+    name = '[' + key + ']';
+  }
+  if (!str) {
+    if (ctx.seen.indexOf(desc.value) < 0) {
+      if (isNull(recurseTimes)) {
+        str = formatValue(ctx, desc.value, null);
+      } else {
+        str = formatValue(ctx, desc.value, recurseTimes - 1);
+      }
+      if (str.indexOf('\n') > -1) {
+        if (array) {
+          str = str.split('\n').map(function(line) {
+            return '  ' + line;
+          }).join('\n').substr(2);
+        } else {
+          str = '\n' + str.split('\n').map(function(line) {
+            return '   ' + line;
+          }).join('\n');
+        }
+      }
+    } else {
+      str = ctx.stylize('[Circular]', 'special');
+    }
+  }
+  if (isUndefined(name)) {
+    if (array && key.match(/^\d+$/)) {
+      return str;
+    }
+    name = JSON.stringify('' + key);
+    if (name.match(/^"([a-zA-Z_][a-zA-Z_0-9]*)"$/)) {
+      name = name.substr(1, name.length - 2);
+      name = ctx.stylize(name, 'name');
+    } else {
+      name = name.replace(/'/g, "\\'")
+                 .replace(/\\"/g, '"')
+                 .replace(/(^"|"$)/g, "'");
+      name = ctx.stylize(name, 'string');
+    }
+  }
+
+  return name + ': ' + str;
+}
+
+
+function reduceToSingleString(output, base, braces) {
+  var numLinesEst = 0;
+  var length = output.reduce(function(prev, cur) {
+    numLinesEst++;
+    if (cur.indexOf('\n') >= 0) numLinesEst++;
+    return prev + cur.replace(/\u001b\[\d\d?m/g, '').length + 1;
+  }, 0);
+
+  if (length > 60) {
+    return braces[0] +
+           (base === '' ? '' : base + '\n ') +
+           ' ' +
+           output.join(',\n  ') +
+           ' ' +
+           braces[1];
+  }
+
+  return braces[0] + base + ' ' + output.join(', ') + ' ' + braces[1];
+}
+
+
+// NOTE: These type checking functions intentionally don't use `instanceof`
+// because it is fragile and can be easily faked with `Object.create()`.
+function isArray(ar) {
+  return Array.isArray(ar);
+}
+exports.isArray = isArray;
+
+function isBoolean(arg) {
+  return typeof arg === 'boolean';
+}
+exports.isBoolean = isBoolean;
+
+function isNull(arg) {
+  return arg === null;
+}
+exports.isNull = isNull;
+
+function isNullOrUndefined(arg) {
+  return arg == null;
+}
+exports.isNullOrUndefined = isNullOrUndefined;
+
+function isNumber(arg) {
+  return typeof arg === 'number';
+}
+exports.isNumber = isNumber;
+
+function isString(arg) {
+  return typeof arg === 'string';
+}
+exports.isString = isString;
+
+function isSymbol(arg) {
+  return typeof arg === 'symbol';
+}
+exports.isSymbol = isSymbol;
+
+function isUndefined(arg) {
+  return arg === void 0;
+}
+exports.isUndefined = isUndefined;
+
+function isRegExp(re) {
+  return isObject(re) && objectToString(re) === '[object RegExp]';
+}
+exports.isRegExp = isRegExp;
+
+function isObject(arg) {
+  return typeof arg === 'object' && arg !== null;
+}
+exports.isObject = isObject;
+
+function isDate(d) {
+  return isObject(d) && objectToString(d) === '[object Date]';
+}
+exports.isDate = isDate;
+
+function isError(e) {
+  return isObject(e) &&
+      (objectToString(e) === '[object Error]' || e instanceof Error);
+}
+exports.isError = isError;
+
+function isFunction(arg) {
+  return typeof arg === 'function';
+}
+exports.isFunction = isFunction;
+
+function isPrimitive(arg) {
+  return arg === null ||
+         typeof arg === 'boolean' ||
+         typeof arg === 'number' ||
+         typeof arg === 'string' ||
+         typeof arg === 'symbol' ||  // ES6 symbol
+         typeof arg === 'undefined';
+}
+exports.isPrimitive = isPrimitive;
+
+exports.isBuffer = require('./support/isBuffer');
+
+function objectToString(o) {
+  return Object.prototype.toString.call(o);
+}
+
+
+function pad(n) {
+  return n < 10 ? '0' + n.toString(10) : n.toString(10);
+}
+
+
+var months = ['Jan', 'Feb', 'Mar', 'Apr', 'May', 'Jun', 'Jul', 'Aug', 'Sep',
+              'Oct', 'Nov', 'Dec'];
+
+// 26 Feb 16:19:34
+function timestamp() {
+  var d = new Date();
+  var time = [pad(d.getHours()),
+              pad(d.getMinutes()),
+              pad(d.getSeconds())].join(':');
+  return [d.getDate(), months[d.getMonth()], time].join(' ');
+}
+
+
+// log is just a thin wrapper to console.log that prepends a timestamp
+exports.log = function() {
+  console.log('%s - %s', timestamp(), exports.format.apply(exports, arguments));
+};
+
+
+/**
+ * Inherit the prototype methods from one constructor into another.
+ *
+ * The Function.prototype.inherits from lang.js rewritten as a standalone
+ * function (not on Function.prototype). NOTE: If this file is to be loaded
+ * during bootstrapping this function needs to be rewritten using some native
+ * functions as prototype setup using normal JavaScript does not work as
+ * expected during bootstrapping (see mirror.js in r114903).
+ *
+ * @param {function} ctor Constructor function which needs to inherit the
+ *     prototype.
+ * @param {function} superCtor Constructor function to inherit prototype from.
+ */
+exports.inherits = require('inherits');
+
+exports._extend = function(origin, add) {
+  // Don't do anything if add isn't an object
+  if (!add || !isObject(add)) return origin;
+
+  var keys = Object.keys(add);
+  var i = keys.length;
+  while (i--) {
+    origin[keys[i]] = add[keys[i]];
+  }
+  return origin;
+};
+
+function hasOwnProperty(obj, prop) {
+  return Object.prototype.hasOwnProperty.call(obj, prop);
+}
+
+}).call(this,require('_process'),typeof global !== "undefined" ? global : typeof self !== "undefined" ? self : typeof window !== "undefined" ? window : {})
+},{"./support/isBuffer":27,"_process":24,"inherits":26}],29:[function(require,module,exports){
+// Returns a wrapper function that returns a wrapped callback
+// The wrapper function should do some stuff, and return a
+// presumably different callback function.
+// This makes sure that own properties are retained, so that
+// decorations and such are not lost along the way.
+module.exports = wrappy
+function wrappy (fn, cb) {
+  if (fn && cb) return wrappy(fn)(cb)
+
+  if (typeof fn !== 'function')
+    throw new TypeError('need wrapper function')
+
+  Object.keys(fn).forEach(function (k) {
+    wrapper[k] = fn[k]
+  })
+
+  return wrapper
+
+  function wrapper() {
+    var args = new Array(arguments.length)
+    for (var i = 0; i < args.length; i++) {
+      args[i] = arguments[i]
+    }
+    var ret = fn.apply(this, args)
+    var cb = args[args.length-1]
+    if (typeof ret === 'function' && ret !== cb) {
+      Object.keys(cb).forEach(function (k) {
+        ret[k] = cb[k]
+      })
+    }
+    return ret
+  }
+}
+
+},{}]},{},[7])(7)
+});
\ No newline at end of file
diff --git a/ja/assets/javascripts/workers/search.b8dbb3d2.min.js b/ja/assets/javascripts/workers/search.b8dbb3d2.min.js
new file mode 100644
index 000000000..c8a1ec8d8
--- /dev/null
+++ b/ja/assets/javascripts/workers/search.b8dbb3d2.min.js
@@ -0,0 +1,42 @@
+"use strict";(()=>{var xe=Object.create;var U=Object.defineProperty,ve=Object.defineProperties,Se=Object.getOwnPropertyDescriptor,Te=Object.getOwnPropertyDescriptors,Qe=Object.getOwnPropertyNames,Y=Object.getOwnPropertySymbols,Ee=Object.getPrototypeOf,X=Object.prototype.hasOwnProperty,be=Object.prototype.propertyIsEnumerable;var Z=Math.pow,J=(t,e,r)=>e in t?U(t,e,{enumerable:!0,configurable:!0,writable:!0,value:r}):t[e]=r,A=(t,e)=>{for(var r in e||(e={}))X.call(e,r)&&J(t,r,e[r]);if(Y)for(var r of Y(e))be.call(e,r)&&J(t,r,e[r]);return t},G=(t,e)=>ve(t,Te(e));var Le=(t,e)=>()=>(e||t((e={exports:{}}).exports,e),e.exports);var we=(t,e,r,n)=>{if(e&&typeof e=="object"||typeof e=="function")for(let i of Qe(e))!X.call(t,i)&&i!==r&&U(t,i,{get:()=>e[i],enumerable:!(n=Se(e,i))||n.enumerable});return t};var Pe=(t,e,r)=>(r=t!=null?xe(Ee(t)):{},we(e||!t||!t.__esModule?U(r,"default",{value:t,enumerable:!0}):r,t));var B=(t,e,r)=>new Promise((n,i)=>{var s=u=>{try{a(r.next(u))}catch(c){i(c)}},o=u=>{try{a(r.throw(u))}catch(c){i(c)}},a=u=>u.done?n(u.value):Promise.resolve(u.value).then(s,o);a((r=r.apply(t,e)).next())});var te=Le((K,ee)=>{/**
+ * lunr - http://lunrjs.com - A bit like Solr, but much smaller and not as bright - 2.3.9
+ * Copyright (C) 2020 Oliver Nightingale
+ * @license MIT
+ */(function(){var t=function(e){var r=new t.Builder;return r.pipeline.add(t.trimmer,t.stopWordFilter,t.stemmer),r.searchPipeline.add(t.stemmer),e.call(r,r),r.build()};t.version="2.3.9";/*!
+ * lunr.utils
+ * Copyright (C) 2020 Oliver Nightingale
+ */t.utils={},t.utils.warn=function(e){return function(r){e.console&&console.warn&&console.warn(r)}}(this),t.utils.asString=function(e){return e==null?"":e.toString()},t.utils.clone=function(e){if(e==null)return e;for(var r=Object.create(null),n=Object.keys(e),i=0;i<n.length;i++){var s=n[i],o=e[s];if(Array.isArray(o)){r[s]=o.slice();continue}if(typeof o=="string"||typeof o=="number"||typeof o=="boolean"){r[s]=o;continue}throw new TypeError("clone is not deep and does not support nested objects")}return r},t.FieldRef=function(e,r,n){this.docRef=e,this.fieldName=r,this._stringValue=n},t.FieldRef.joiner="/",t.FieldRef.fromString=function(e){var r=e.indexOf(t.FieldRef.joiner);if(r===-1)throw"malformed field ref string";var n=e.slice(0,r),i=e.slice(r+1);return new t.FieldRef(i,n,e)},t.FieldRef.prototype.toString=function(){return this._stringValue==null&&(this._stringValue=this.fieldName+t.FieldRef.joiner+this.docRef),this._stringValue};/*!
+ * lunr.Set
+ * Copyright (C) 2020 Oliver Nightingale
+ */t.Set=function(e){if(this.elements=Object.create(null),e){this.length=e.length;for(var r=0;r<this.length;r++)this.elements[e[r]]=!0}else this.length=0},t.Set.complete={intersect:function(e){return e},union:function(){return this},contains:function(){return!0}},t.Set.empty={intersect:function(){return this},union:function(e){return e},contains:function(){return!1}},t.Set.prototype.contains=function(e){return!!this.elements[e]},t.Set.prototype.intersect=function(e){var r,n,i,s=[];if(e===t.Set.complete)return this;if(e===t.Set.empty)return e;this.length<e.length?(r=this,n=e):(r=e,n=this),i=Object.keys(r.elements);for(var o=0;o<i.length;o++){var a=i[o];a in n.elements&&s.push(a)}return new t.Set(s)},t.Set.prototype.union=function(e){return e===t.Set.complete?t.Set.complete:e===t.Set.empty?this:new t.Set(Object.keys(this.elements).concat(Object.keys(e.elements)))},t.idf=function(e,r){var n=0;for(var i in e)i!="_index"&&(n+=Object.keys(e[i]).length);var s=(r-n+.5)/(n+.5);return Math.log(1+Math.abs(s))},t.Token=function(e,r){this.str=e||"",this.metadata=r||{}},t.Token.prototype.toString=function(){return this.str},t.Token.prototype.update=function(e){return this.str=e(this.str,this.metadata),this},t.Token.prototype.clone=function(e){return e=e||function(r){return r},new t.Token(e(this.str,this.metadata),this.metadata)};/*!
+ * lunr.tokenizer
+ * Copyright (C) 2020 Oliver Nightingale
+ */t.tokenizer=function(e,r){if(e==null||e==null)return[];if(Array.isArray(e))return e.map(function(g){return new t.Token(t.utils.asString(g).toLowerCase(),t.utils.clone(r))});for(var n=e.toString().toLowerCase(),i=n.length,s=[],o=0,a=0;o<=i;o++){var u=n.charAt(o),c=o-a;if(u.match(t.tokenizer.separator)||o==i){if(c>0){var f=t.utils.clone(r)||{};f.position=[a,c],f.index=s.length,s.push(new t.Token(n.slice(a,o),f))}a=o+1}}return s},t.tokenizer.separator=/[\s\-]+/;/*!
+ * lunr.Pipeline
+ * Copyright (C) 2020 Oliver Nightingale
+ */t.Pipeline=function(){this._stack=[]},t.Pipeline.registeredFunctions=Object.create(null),t.Pipeline.registerFunction=function(e,r){r in this.registeredFunctions&&t.utils.warn("Overwriting existing registered function: "+r),e.label=r,t.Pipeline.registeredFunctions[e.label]=e},t.Pipeline.warnIfFunctionNotRegistered=function(e){var r=e.label&&e.label in this.registeredFunctions;r||t.utils.warn(`Function is not registered with pipeline. This may cause problems when serialising the index.
+`,e)},t.Pipeline.load=function(e){var r=new t.Pipeline;return e.forEach(function(n){var i=t.Pipeline.registeredFunctions[n];if(i)r.add(i);else throw new Error("Cannot load unregistered function: "+n)}),r},t.Pipeline.prototype.add=function(){var e=Array.prototype.slice.call(arguments);e.forEach(function(r){t.Pipeline.warnIfFunctionNotRegistered(r),this._stack.push(r)},this)},t.Pipeline.prototype.after=function(e,r){t.Pipeline.warnIfFunctionNotRegistered(r);var n=this._stack.indexOf(e);if(n==-1)throw new Error("Cannot find existingFn");n=n+1,this._stack.splice(n,0,r)},t.Pipeline.prototype.before=function(e,r){t.Pipeline.warnIfFunctionNotRegistered(r);var n=this._stack.indexOf(e);if(n==-1)throw new Error("Cannot find existingFn");this._stack.splice(n,0,r)},t.Pipeline.prototype.remove=function(e){var r=this._stack.indexOf(e);r!=-1&&this._stack.splice(r,1)},t.Pipeline.prototype.run=function(e){for(var r=this._stack.length,n=0;n<r;n++){for(var i=this._stack[n],s=[],o=0;o<e.length;o++){var a=i(e[o],o,e);if(!(a==null||a===""))if(Array.isArray(a))for(var u=0;u<a.length;u++)s.push(a[u]);else s.push(a)}e=s}return e},t.Pipeline.prototype.runString=function(e,r){var n=new t.Token(e,r);return this.run([n]).map(function(i){return i.toString()})},t.Pipeline.prototype.reset=function(){this._stack=[]},t.Pipeline.prototype.toJSON=function(){return this._stack.map(function(e){return t.Pipeline.warnIfFunctionNotRegistered(e),e.label})};/*!
+ * lunr.Vector
+ * Copyright (C) 2020 Oliver Nightingale
+ */t.Vector=function(e){this._magnitude=0,this.elements=e||[]},t.Vector.prototype.positionForIndex=function(e){if(this.elements.length==0)return 0;for(var r=0,n=this.elements.length/2,i=n-r,s=Math.floor(i/2),o=this.elements[s*2];i>1&&(o<e&&(r=s),o>e&&(n=s),o!=e);)i=n-r,s=r+Math.floor(i/2),o=this.elements[s*2];if(o==e||o>e)return s*2;if(o<e)return(s+1)*2},t.Vector.prototype.insert=function(e,r){this.upsert(e,r,function(){throw"duplicate index"})},t.Vector.prototype.upsert=function(e,r,n){this._magnitude=0;var i=this.positionForIndex(e);this.elements[i]==e?this.elements[i+1]=n(this.elements[i+1],r):this.elements.splice(i,0,e,r)},t.Vector.prototype.magnitude=function(){if(this._magnitude)return this._magnitude;for(var e=0,r=this.elements.length,n=1;n<r;n+=2){var i=this.elements[n];e+=i*i}return this._magnitude=Math.sqrt(e)},t.Vector.prototype.dot=function(e){for(var r=0,n=this.elements,i=e.elements,s=n.length,o=i.length,a=0,u=0,c=0,f=0;c<s&&f<o;)a=n[c],u=i[f],a<u?c+=2:a>u?f+=2:a==u&&(r+=n[c+1]*i[f+1],c+=2,f+=2);return r},t.Vector.prototype.similarity=function(e){return this.dot(e)/this.magnitude()||0},t.Vector.prototype.toArray=function(){for(var e=new Array(this.elements.length/2),r=1,n=0;r<this.elements.length;r+=2,n++)e[n]=this.elements[r];return e},t.Vector.prototype.toJSON=function(){return this.elements};/*!
+ * lunr.stemmer
+ * Copyright (C) 2020 Oliver Nightingale
+ * Includes code from - http://tartarus.org/~martin/PorterStemmer/js.txt
+ */t.stemmer=function(){var e={ational:"ate",tional:"tion",enci:"ence",anci:"ance",izer:"ize",bli:"ble",alli:"al",entli:"ent",eli:"e",ousli:"ous",ization:"ize",ation:"ate",ator:"ate",alism:"al",iveness:"ive",fulness:"ful",ousness:"ous",aliti:"al",iviti:"ive",biliti:"ble",logi:"log"},r={icate:"ic",ative:"",alize:"al",iciti:"ic",ical:"ic",ful:"",ness:""},n="[^aeiou]",i="[aeiouy]",s=n+"[^aeiouy]*",o=i+"[aeiou]*",a="^("+s+")?"+o+s,u="^("+s+")?"+o+s+"("+o+")?$",c="^("+s+")?"+o+s+o+s,f="^("+s+")?"+i,g=new RegExp(a),l=new RegExp(c),m=new RegExp(u),x=new RegExp(f),v=/^(.+?)(ss|i)es$/,d=/^(.+?)([^s])s$/,y=/^(.+?)eed$/,b=/^(.+?)(ed|ing)$/,E=/.$/,w=/(at|bl|iz)$/,R=new RegExp("([^aeiouylsz])\\1$"),j=new RegExp("^"+s+i+"[^aeiouwxy]$"),_=/^(.+?[^aeiou])y$/,D=/^(.+?)(ational|tional|enci|anci|izer|bli|alli|entli|eli|ousli|ization|ation|ator|alism|iveness|fulness|ousness|aliti|iviti|biliti|logi)$/,N=/^(.+?)(icate|ative|alize|iciti|ical|ful|ness)$/,C=/^(.+?)(al|ance|ence|er|ic|able|ible|ant|ement|ment|ent|ou|ism|ate|iti|ous|ive|ize)$/,V=/^(.+?)(s|t)(ion)$/,P=/^(.+?)e$/,z=/ll$/,$=new RegExp("^"+s+i+"[^aeiouwxy]$"),M=function(h){var S,k,L,p,T,O,F;if(h.length<3)return h;if(L=h.substr(0,1),L=="y"&&(h=L.toUpperCase()+h.substr(1)),p=v,T=d,p.test(h)?h=h.replace(p,"$1$2"):T.test(h)&&(h=h.replace(T,"$1$2")),p=y,T=b,p.test(h)){var Q=p.exec(h);p=g,p.test(Q[1])&&(p=E,h=h.replace(p,""))}else if(T.test(h)){var Q=T.exec(h);S=Q[1],T=x,T.test(S)&&(h=S,T=w,O=R,F=j,T.test(h)?h=h+"e":O.test(h)?(p=E,h=h.replace(p,"")):F.test(h)&&(h=h+"e"))}if(p=_,p.test(h)){var Q=p.exec(h);S=Q[1],h=S+"i"}if(p=D,p.test(h)){var Q=p.exec(h);S=Q[1],k=Q[2],p=g,p.test(S)&&(h=S+e[k])}if(p=N,p.test(h)){var Q=p.exec(h);S=Q[1],k=Q[2],p=g,p.test(S)&&(h=S+r[k])}if(p=C,T=V,p.test(h)){var Q=p.exec(h);S=Q[1],p=l,p.test(S)&&(h=S)}else if(T.test(h)){var Q=T.exec(h);S=Q[1]+Q[2],T=l,T.test(S)&&(h=S)}if(p=P,p.test(h)){var Q=p.exec(h);S=Q[1],p=l,T=m,O=$,(p.test(S)||T.test(S)&&!O.test(S))&&(h=S)}return p=z,T=l,p.test(h)&&T.test(h)&&(p=E,h=h.replace(p,"")),L=="y"&&(h=L.toLowerCase()+h.substr(1)),h};return function(I){return I.update(M)}}(),t.Pipeline.registerFunction(t.stemmer,"stemmer");/*!
+ * lunr.stopWordFilter
+ * Copyright (C) 2020 Oliver Nightingale
+ */t.generateStopWordFilter=function(e){var r=e.reduce(function(n,i){return n[i]=i,n},{});return function(n){if(n&&r[n.toString()]!==n.toString())return n}},t.stopWordFilter=t.generateStopWordFilter(["a","able","about","across","after","all","almost","also","am","among","an","and","any","are","as","at","be","because","been","but","by","can","cannot","could","dear","did","do","does","either","else","ever","every","for","from","get","got","had","has","have","he","her","hers","him","his","how","however","i","if","in","into","is","it","its","just","least","let","like","likely","may","me","might","most","must","my","neither","no","nor","not","of","off","often","on","only","or","other","our","own","rather","said","say","says","she","should","since","so","some","than","that","the","their","them","then","there","these","they","this","tis","to","too","twas","us","wants","was","we","were","what","when","where","which","while","who","whom","why","will","with","would","yet","you","your"]),t.Pipeline.registerFunction(t.stopWordFilter,"stopWordFilter");/*!
+ * lunr.trimmer
+ * Copyright (C) 2020 Oliver Nightingale
+ */t.trimmer=function(e){return e.update(function(r){return r.replace(/^\W+/,"").replace(/\W+$/,"")})},t.Pipeline.registerFunction(t.trimmer,"trimmer");/*!
+ * lunr.TokenSet
+ * Copyright (C) 2020 Oliver Nightingale
+ */t.TokenSet=function(){this.final=!1,this.edges={},this.id=t.TokenSet._nextId,t.TokenSet._nextId+=1},t.TokenSet._nextId=1,t.TokenSet.fromArray=function(e){for(var r=new t.TokenSet.Builder,n=0,i=e.length;n<i;n++)r.insert(e[n]);return r.finish(),r.root},t.TokenSet.fromClause=function(e){return"editDistance"in e?t.TokenSet.fromFuzzyString(e.term,e.editDistance):t.TokenSet.fromString(e.term)},t.TokenSet.fromFuzzyString=function(e,r){for(var n=new t.TokenSet,i=[{node:n,editsRemaining:r,str:e}];i.length;){var s=i.pop();if(s.str.length>0){var o=s.str.charAt(0),a;o in s.node.edges?a=s.node.edges[o]:(a=new t.TokenSet,s.node.edges[o]=a),s.str.length==1&&(a.final=!0),i.push({node:a,editsRemaining:s.editsRemaining,str:s.str.slice(1)})}if(s.editsRemaining!=0){if("*"in s.node.edges)var u=s.node.edges["*"];else{var u=new t.TokenSet;s.node.edges["*"]=u}if(s.str.length==0&&(u.final=!0),i.push({node:u,editsRemaining:s.editsRemaining-1,str:s.str}),s.str.length>1&&i.push({node:s.node,editsRemaining:s.editsRemaining-1,str:s.str.slice(1)}),s.str.length==1&&(s.node.final=!0),s.str.length>=1){if("*"in s.node.edges)var c=s.node.edges["*"];else{var c=new t.TokenSet;s.node.edges["*"]=c}s.str.length==1&&(c.final=!0),i.push({node:c,editsRemaining:s.editsRemaining-1,str:s.str.slice(1)})}if(s.str.length>1){var f=s.str.charAt(0),g=s.str.charAt(1),l;g in s.node.edges?l=s.node.edges[g]:(l=new t.TokenSet,s.node.edges[g]=l),s.str.length==1&&(l.final=!0),i.push({node:l,editsRemaining:s.editsRemaining-1,str:f+s.str.slice(2)})}}}return n},t.TokenSet.fromString=function(e){for(var r=new t.TokenSet,n=r,i=0,s=e.length;i<s;i++){var o=e[i],a=i==s-1;if(o=="*")r.edges[o]=r,r.final=a;else{var u=new t.TokenSet;u.final=a,r.edges[o]=u,r=u}}return n},t.TokenSet.prototype.toArray=function(){for(var e=[],r=[{prefix:"",node:this}];r.length;){var n=r.pop(),i=Object.keys(n.node.edges),s=i.length;n.node.final&&(n.prefix.charAt(0),e.push(n.prefix));for(var o=0;o<s;o++){var a=i[o];r.push({prefix:n.prefix.concat(a),node:n.node.edges[a]})}}return e},t.TokenSet.prototype.toString=function(){if(this._str)return this._str;for(var e=this.final?"1":"0",r=Object.keys(this.edges).sort(),n=r.length,i=0;i<n;i++){var s=r[i],o=this.edges[s];e=e+s+o.id}return e},t.TokenSet.prototype.intersect=function(e){for(var r=new t.TokenSet,n=void 0,i=[{qNode:e,output:r,node:this}];i.length;){n=i.pop();for(var s=Object.keys(n.qNode.edges),o=s.length,a=Object.keys(n.node.edges),u=a.length,c=0;c<o;c++)for(var f=s[c],g=0;g<u;g++){var l=a[g];if(l==f||f=="*"){var m=n.node.edges[l],x=n.qNode.edges[f],v=m.final&&x.final,d=void 0;l in n.output.edges?(d=n.output.edges[l],d.final=d.final||v):(d=new t.TokenSet,d.final=v,n.output.edges[l]=d),i.push({qNode:x,output:d,node:m})}}}return r},t.TokenSet.Builder=function(){this.previousWord="",this.root=new t.TokenSet,this.uncheckedNodes=[],this.minimizedNodes={}},t.TokenSet.Builder.prototype.insert=function(e){var r,n=0;if(e<this.previousWord)throw new Error("Out of order word insertion");for(var i=0;i<e.length&&i<this.previousWord.length&&e[i]==this.previousWord[i];i++)n++;this.minimize(n),this.uncheckedNodes.length==0?r=this.root:r=this.uncheckedNodes[this.uncheckedNodes.length-1].child;for(var i=n;i<e.length;i++){var s=new t.TokenSet,o=e[i];r.edges[o]=s,this.uncheckedNodes.push({parent:r,char:o,child:s}),r=s}r.final=!0,this.previousWord=e},t.TokenSet.Builder.prototype.finish=function(){this.minimize(0)},t.TokenSet.Builder.prototype.minimize=function(e){for(var r=this.uncheckedNodes.length-1;r>=e;r--){var n=this.uncheckedNodes[r],i=n.child.toString();i in this.minimizedNodes?n.parent.edges[n.char]=this.minimizedNodes[i]:(n.child._str=i,this.minimizedNodes[i]=n.child),this.uncheckedNodes.pop()}};/*!
+ * lunr.Index
+ * Copyright (C) 2020 Oliver Nightingale
+ */t.Index=function(e){this.invertedIndex=e.invertedIndex,this.fieldVectors=e.fieldVectors,this.tokenSet=e.tokenSet,this.fields=e.fields,this.pipeline=e.pipeline},t.Index.prototype.search=function(e){return this.query(function(r){var n=new t.QueryParser(e,r);n.parse()})},t.Index.prototype.query=function(e){for(var r=new t.Query(this.fields),n=Object.create(null),i=Object.create(null),s=Object.create(null),o=Object.create(null),a=Object.create(null),u=0;u<this.fields.length;u++)i[this.fields[u]]=new t.Vector;e.call(r,r);for(var u=0;u<r.clauses.length;u++){var c=r.clauses[u],f=null,g=t.Set.empty;c.usePipeline?f=this.pipeline.runString(c.term,{fields:c.fields}):f=[c.term];for(var l=0;l<f.length;l++){var m=f[l];c.term=m;var x=t.TokenSet.fromClause(c),v=this.tokenSet.intersect(x).toArray();if(v.length===0&&c.presence===t.Query.presence.REQUIRED){for(var d=0;d<c.fields.length;d++){var y=c.fields[d];o[y]=t.Set.empty}break}for(var b=0;b<v.length;b++)for(var E=v[b],w=this.invertedIndex[E],R=w._index,d=0;d<c.fields.length;d++){var y=c.fields[d],j=w[y],_=Object.keys(j),D=E+"/"+y,N=new t.Set(_);if(c.presence==t.Query.presence.REQUIRED&&(g=g.union(N),o[y]===void 0&&(o[y]=t.Set.complete)),c.presence==t.Query.presence.PROHIBITED){a[y]===void 0&&(a[y]=t.Set.empty),a[y]=a[y].union(N);continue}if(i[y].upsert(R,c.boost,function(ye,me){return ye+me}),!s[D]){for(var C=0;C<_.length;C++){var V=_[C],P=new t.FieldRef(V,y),z=j[V],$;($=n[P])===void 0?n[P]=new t.MatchData(E,y,z):$.add(E,y,z)}s[D]=!0}}}if(c.presence===t.Query.presence.REQUIRED)for(var d=0;d<c.fields.length;d++){var y=c.fields[d];o[y]=o[y].intersect(g)}}for(var M=t.Set.complete,I=t.Set.empty,u=0;u<this.fields.length;u++){var y=this.fields[u];o[y]&&(M=M.intersect(o[y])),a[y]&&(I=I.union(a[y]))}var h=Object.keys(n),S=[],k=Object.create(null);if(r.isNegated()){h=Object.keys(this.fieldVectors);for(var u=0;u<h.length;u++){var P=h[u],L=t.FieldRef.fromString(P);n[P]=new t.MatchData}}for(var u=0;u<h.length;u++){var L=t.FieldRef.fromString(h[u]),p=L.docRef;if(M.contains(p)&&!I.contains(p)){var T=this.fieldVectors[L],O=i[L.fieldName].similarity(T),F;if((F=k[p])!==void 0)F.score+=O,F.matchData.combine(n[L]);else{var Q={ref:p,score:O,matchData:n[L]};k[p]=Q,S.push(Q)}}}return S.sort(function(pe,ge){return ge.score-pe.score})},t.Index.prototype.toJSON=function(){var e=Object.keys(this.invertedIndex).sort().map(function(n){return[n,this.invertedIndex[n]]},this),r=Object.keys(this.fieldVectors).map(function(n){return[n,this.fieldVectors[n].toJSON()]},this);return{version:t.version,fields:this.fields,fieldVectors:r,invertedIndex:e,pipeline:this.pipeline.toJSON()}},t.Index.load=function(e){var r={},n={},i=e.fieldVectors,s=Object.create(null),o=e.invertedIndex,a=new t.TokenSet.Builder,u=t.Pipeline.load(e.pipeline);e.version!=t.version&&t.utils.warn("Version mismatch when loading serialised index. Current version of lunr '"+t.version+"' does not match serialized index '"+e.version+"'");for(var c=0;c<i.length;c++){var f=i[c],g=f[0],l=f[1];n[g]=new t.Vector(l)}for(var c=0;c<o.length;c++){var f=o[c],m=f[0],x=f[1];a.insert(m),s[m]=x}return a.finish(),r.fields=e.fields,r.fieldVectors=n,r.invertedIndex=s,r.tokenSet=a.root,r.pipeline=u,new t.Index(r)};/*!
+ * lunr.Builder
+ * Copyright (C) 2020 Oliver Nightingale
+ */t.Builder=function(){this._ref="id",this._fields=Object.create(null),this._documents=Object.create(null),this.invertedIndex=Object.create(null),this.fieldTermFrequencies={},this.fieldLengths={},this.tokenizer=t.tokenizer,this.pipeline=new t.Pipeline,this.searchPipeline=new t.Pipeline,this.documentCount=0,this._b=.75,this._k1=1.2,this.termIndex=0,this.metadataWhitelist=[]},t.Builder.prototype.ref=function(e){this._ref=e},t.Builder.prototype.field=function(e,r){if(/\//.test(e))throw new RangeError("Field '"+e+"' contains illegal character '/'");this._fields[e]=r||{}},t.Builder.prototype.b=function(e){e<0?this._b=0:e>1?this._b=1:this._b=e},t.Builder.prototype.k1=function(e){this._k1=e},t.Builder.prototype.add=function(e,r){var n=e[this._ref],i=Object.keys(this._fields);this._documents[n]=r||{},this.documentCount+=1;for(var s=0;s<i.length;s++){var o=i[s],a=this._fields[o].extractor,u=a?a(e):e[o],c=this.tokenizer(u,{fields:[o]}),f=this.pipeline.run(c),g=new t.FieldRef(n,o),l=Object.create(null);this.fieldTermFrequencies[g]=l,this.fieldLengths[g]=0,this.fieldLengths[g]+=f.length;for(var m=0;m<f.length;m++){var x=f[m];if(l[x]==null&&(l[x]=0),l[x]+=1,this.invertedIndex[x]==null){var v=Object.create(null);v._index=this.termIndex,this.termIndex+=1;for(var d=0;d<i.length;d++)v[i[d]]=Object.create(null);this.invertedIndex[x]=v}this.invertedIndex[x][o][n]==null&&(this.invertedIndex[x][o][n]=Object.create(null));for(var y=0;y<this.metadataWhitelist.length;y++){var b=this.metadataWhitelist[y],E=x.metadata[b];this.invertedIndex[x][o][n][b]==null&&(this.invertedIndex[x][o][n][b]=[]),this.invertedIndex[x][o][n][b].push(E)}}}},t.Builder.prototype.calculateAverageFieldLengths=function(){for(var e=Object.keys(this.fieldLengths),r=e.length,n={},i={},s=0;s<r;s++){var o=t.FieldRef.fromString(e[s]),a=o.fieldName;i[a]||(i[a]=0),i[a]+=1,n[a]||(n[a]=0),n[a]+=this.fieldLengths[o]}for(var u=Object.keys(this._fields),s=0;s<u.length;s++){var c=u[s];n[c]=n[c]/i[c]}this.averageFieldLength=n},t.Builder.prototype.createFieldVectors=function(){for(var e={},r=Object.keys(this.fieldTermFrequencies),n=r.length,i=Object.create(null),s=0;s<n;s++){for(var o=t.FieldRef.fromString(r[s]),a=o.fieldName,u=this.fieldLengths[o],c=new t.Vector,f=this.fieldTermFrequencies[o],g=Object.keys(f),l=g.length,m=this._fields[a].boost||1,x=this._documents[o.docRef].boost||1,v=0;v<l;v++){var d=g[v],y=f[d],b=this.invertedIndex[d]._index,E,w,R;i[d]===void 0?(E=t.idf(this.invertedIndex[d],this.documentCount),i[d]=E):E=i[d],w=E*((this._k1+1)*y)/(this._k1*(1-this._b+this._b*(u/this.averageFieldLength[a]))+y),w*=m,w*=x,R=Math.round(w*1e3)/1e3,c.insert(b,R)}e[o]=c}this.fieldVectors=e},t.Builder.prototype.createTokenSet=function(){this.tokenSet=t.TokenSet.fromArray(Object.keys(this.invertedIndex).sort())},t.Builder.prototype.build=function(){return this.calculateAverageFieldLengths(),this.createFieldVectors(),this.createTokenSet(),new t.Index({invertedIndex:this.invertedIndex,fieldVectors:this.fieldVectors,tokenSet:this.tokenSet,fields:Object.keys(this._fields),pipeline:this.searchPipeline})},t.Builder.prototype.use=function(e){var r=Array.prototype.slice.call(arguments,1);r.unshift(this),e.apply(this,r)},t.MatchData=function(e,r,n){for(var i=Object.create(null),s=Object.keys(n||{}),o=0;o<s.length;o++){var a=s[o];i[a]=n[a].slice()}this.metadata=Object.create(null),e!==void 0&&(this.metadata[e]=Object.create(null),this.metadata[e][r]=i)},t.MatchData.prototype.combine=function(e){for(var r=Object.keys(e.metadata),n=0;n<r.length;n++){var i=r[n],s=Object.keys(e.metadata[i]);this.metadata[i]==null&&(this.metadata[i]=Object.create(null));for(var o=0;o<s.length;o++){var a=s[o],u=Object.keys(e.metadata[i][a]);this.metadata[i][a]==null&&(this.metadata[i][a]=Object.create(null));for(var c=0;c<u.length;c++){var 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+
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+{
+  "version": 3,
+  "sources": ["node_modules/lunr/lunr.js", "src/templates/assets/javascripts/integrations/search/worker/main/index.ts", "src/templates/assets/javascripts/browser/element/_/index.ts", "src/templates/assets/javascripts/polyfills/index.ts", "src/templates/assets/javascripts/integrations/search/config/index.ts", "src/templates/assets/javascripts/integrations/search/internal/_/index.ts", "src/templates/assets/javascripts/integrations/search/internal/extract/index.ts", "src/templates/assets/javascripts/integrations/search/internal/highlight/index.ts", "src/templates/assets/javascripts/integrations/search/internal/tokenize/index.ts", "src/templates/assets/javascripts/integrations/search/query/transform/index.ts", "src/templates/assets/javascripts/integrations/search/query/_/index.ts", "src/templates/assets/javascripts/integrations/search/query/segment/index.ts", "src/templates/assets/javascripts/integrations/search/_/index.ts"],
+  "sourcesContent": ["/**\n * lunr - http://lunrjs.com - A bit like Solr, but much smaller and not as bright - 2.3.9\n * Copyright (C) 2020 Oliver Nightingale\n * @license MIT\n */\n\n;(function(){\n\n/**\n * A convenience function for configuring and constructing\n * a new lunr Index.\n *\n * A lunr.Builder instance is created and the pipeline setup\n * with a trimmer, stop word filter and stemmer.\n *\n * This builder object is yielded to the configuration function\n * that is passed as a parameter, allowing the list of fields\n * and other builder parameters to be customised.\n *\n * All documents _must_ be added within the passed config function.\n *\n * @example\n * var idx = lunr(function () {\n *   this.field('title')\n *   this.field('body')\n *   this.ref('id')\n *\n *   documents.forEach(function (doc) {\n *     this.add(doc)\n *   }, this)\n * })\n *\n * @see {@link lunr.Builder}\n * @see {@link lunr.Pipeline}\n * @see {@link lunr.trimmer}\n * @see {@link lunr.stopWordFilter}\n * @see {@link lunr.stemmer}\n * @namespace {function} lunr\n */\nvar lunr = function (config) {\n  var builder = new lunr.Builder\n\n  builder.pipeline.add(\n    lunr.trimmer,\n    lunr.stopWordFilter,\n    lunr.stemmer\n  )\n\n  builder.searchPipeline.add(\n    lunr.stemmer\n  )\n\n  config.call(builder, builder)\n  return builder.build()\n}\n\nlunr.version = \"2.3.9\"\n/*!\n * lunr.utils\n * Copyright (C) 2020 Oliver Nightingale\n */\n\n/**\n * A namespace containing utils for the rest of the lunr library\n * @namespace lunr.utils\n */\nlunr.utils = {}\n\n/**\n * Print a warning message to the console.\n *\n * @param {String} message The message to be printed.\n * @memberOf lunr.utils\n * @function\n */\nlunr.utils.warn = (function (global) {\n  /* eslint-disable no-console */\n  return function (message) {\n    if (global.console && console.warn) {\n      console.warn(message)\n    }\n  }\n  /* eslint-enable no-console */\n})(this)\n\n/**\n * Convert an object to a string.\n *\n * In the case of `null` and `undefined` the function returns\n * the empty string, in all other cases the result of calling\n * `toString` on the passed object is returned.\n *\n * @param {Any} obj The object to convert to a string.\n * @return {String} string representation of the passed object.\n * @memberOf lunr.utils\n */\nlunr.utils.asString = function (obj) {\n  if (obj === void 0 || obj === null) {\n    return \"\"\n  } else {\n    return obj.toString()\n  }\n}\n\n/**\n * Clones an object.\n *\n * Will create a copy of an existing object such that any mutations\n * on the copy cannot affect the original.\n *\n * Only shallow objects are supported, passing a nested object to this\n * function will cause a TypeError.\n *\n * Objects with primitives, and arrays of primitives are supported.\n *\n * @param {Object} obj The object to clone.\n * @return {Object} a clone of the passed object.\n * @throws {TypeError} when a nested object is passed.\n * @memberOf Utils\n */\nlunr.utils.clone = function (obj) {\n  if (obj === null || obj === undefined) {\n    return obj\n  }\n\n  var clone = Object.create(null),\n      keys = Object.keys(obj)\n\n  for (var i = 0; i < keys.length; i++) {\n    var key = keys[i],\n        val = obj[key]\n\n    if (Array.isArray(val)) {\n      clone[key] = val.slice()\n      continue\n    }\n\n    if (typeof val === 'string' ||\n        typeof val === 'number' ||\n        typeof val === 'boolean') {\n      clone[key] = val\n      continue\n    }\n\n    throw new TypeError(\"clone is not deep and does not support nested objects\")\n  }\n\n  return clone\n}\nlunr.FieldRef = function (docRef, fieldName, stringValue) {\n  this.docRef = docRef\n  this.fieldName = fieldName\n  this._stringValue = stringValue\n}\n\nlunr.FieldRef.joiner = \"/\"\n\nlunr.FieldRef.fromString = function (s) {\n  var n = s.indexOf(lunr.FieldRef.joiner)\n\n  if (n === -1) {\n    throw \"malformed field ref string\"\n  }\n\n  var fieldRef = s.slice(0, n),\n      docRef = s.slice(n + 1)\n\n  return new lunr.FieldRef (docRef, fieldRef, s)\n}\n\nlunr.FieldRef.prototype.toString = function () {\n  if (this._stringValue == undefined) {\n    this._stringValue = this.fieldName + lunr.FieldRef.joiner + this.docRef\n  }\n\n  return this._stringValue\n}\n/*!\n * lunr.Set\n * Copyright (C) 2020 Oliver Nightingale\n */\n\n/**\n * A lunr set.\n *\n * @constructor\n */\nlunr.Set = function (elements) {\n  this.elements = Object.create(null)\n\n  if (elements) {\n    this.length = elements.length\n\n    for (var i = 0; i < this.length; i++) {\n      this.elements[elements[i]] = true\n    }\n  } else {\n    this.length = 0\n  }\n}\n\n/**\n * A complete set that contains all elements.\n *\n * @static\n * @readonly\n * @type {lunr.Set}\n */\nlunr.Set.complete = {\n  intersect: function (other) {\n    return other\n  },\n\n  union: function () {\n    return this\n  },\n\n  contains: function () {\n    return true\n  }\n}\n\n/**\n * An empty set that contains no elements.\n *\n * @static\n * @readonly\n * @type {lunr.Set}\n */\nlunr.Set.empty = {\n  intersect: function () {\n    return this\n  },\n\n  union: function (other) {\n    return other\n  },\n\n  contains: function () {\n    return false\n  }\n}\n\n/**\n * Returns true if this set contains the specified object.\n *\n * @param {object} object - Object whose presence in this set is to be tested.\n * @returns {boolean} - True if this set contains the specified object.\n */\nlunr.Set.prototype.contains = function (object) {\n  return !!this.elements[object]\n}\n\n/**\n * Returns a new set containing only the elements that are present in both\n * this set and the specified set.\n *\n * @param {lunr.Set} other - set to intersect with this set.\n * @returns {lunr.Set} a new set that is the intersection of this and the specified set.\n */\n\nlunr.Set.prototype.intersect = function (other) {\n  var a, b, elements, intersection = []\n\n  if (other === lunr.Set.complete) {\n    return this\n  }\n\n  if (other === lunr.Set.empty) {\n    return other\n  }\n\n  if (this.length < other.length) {\n    a = this\n    b = other\n  } else {\n    a = other\n    b = this\n  }\n\n  elements = Object.keys(a.elements)\n\n  for (var i = 0; i < elements.length; i++) {\n    var element = elements[i]\n    if (element in b.elements) {\n      intersection.push(element)\n    }\n  }\n\n  return new lunr.Set (intersection)\n}\n\n/**\n * Returns a new set combining the elements of this and the specified set.\n *\n * @param {lunr.Set} other - set to union with this set.\n * @return {lunr.Set} a new set that is the union of this and the specified set.\n */\n\nlunr.Set.prototype.union = function (other) {\n  if (other === lunr.Set.complete) {\n    return lunr.Set.complete\n  }\n\n  if (other === lunr.Set.empty) {\n    return this\n  }\n\n  return new lunr.Set(Object.keys(this.elements).concat(Object.keys(other.elements)))\n}\n/**\n * A function to calculate the inverse document frequency for\n * a posting. This is shared between the builder and the index\n *\n * @private\n * @param {object} posting - The posting for a given term\n * @param {number} documentCount - The total number of documents.\n */\nlunr.idf = function (posting, documentCount) {\n  var documentsWithTerm = 0\n\n  for (var fieldName in posting) {\n    if (fieldName == '_index') continue // Ignore the term index, its not a field\n    documentsWithTerm += Object.keys(posting[fieldName]).length\n  }\n\n  var x = (documentCount - documentsWithTerm + 0.5) / (documentsWithTerm + 0.5)\n\n  return Math.log(1 + Math.abs(x))\n}\n\n/**\n * A token wraps a string representation of a token\n * as it is passed through the text processing pipeline.\n *\n * @constructor\n * @param {string} [str=''] - The string token being wrapped.\n * @param {object} [metadata={}] - Metadata associated with this token.\n */\nlunr.Token = function (str, metadata) {\n  this.str = str || \"\"\n  this.metadata = metadata || {}\n}\n\n/**\n * Returns the token string that is being wrapped by this object.\n *\n * @returns {string}\n */\nlunr.Token.prototype.toString = function () {\n  return this.str\n}\n\n/**\n * A token update function is used when updating or optionally\n * when cloning a token.\n *\n * @callback lunr.Token~updateFunction\n * @param {string} str - The string representation of the token.\n * @param {Object} metadata - All metadata associated with this token.\n */\n\n/**\n * Applies the given function to the wrapped string token.\n *\n * @example\n * token.update(function (str, metadata) {\n *   return str.toUpperCase()\n * })\n *\n * @param {lunr.Token~updateFunction} fn - A function to apply to the token string.\n * @returns {lunr.Token}\n */\nlunr.Token.prototype.update = function (fn) {\n  this.str = fn(this.str, this.metadata)\n  return this\n}\n\n/**\n * Creates a clone of this token. Optionally a function can be\n * applied to the cloned token.\n *\n * @param {lunr.Token~updateFunction} [fn] - An optional function to apply to the cloned token.\n * @returns {lunr.Token}\n */\nlunr.Token.prototype.clone = function (fn) {\n  fn = fn || function (s) { return s }\n  return new lunr.Token (fn(this.str, this.metadata), this.metadata)\n}\n/*!\n * lunr.tokenizer\n * Copyright (C) 2020 Oliver Nightingale\n */\n\n/**\n * A function for splitting a string into tokens ready to be inserted into\n * the search index. Uses `lunr.tokenizer.separator` to split strings, change\n * the value of this property to change how strings are split into tokens.\n *\n * This tokenizer will convert its parameter to a string by calling `toString` and\n * then will split this string on the character in `lunr.tokenizer.separator`.\n * Arrays will have their elements converted to strings and wrapped in a lunr.Token.\n *\n * Optional metadata can be passed to the tokenizer, this metadata will be cloned and\n * added as metadata to every token that is created from the object to be tokenized.\n *\n * @static\n * @param {?(string|object|object[])} obj - The object to convert into tokens\n * @param {?object} metadata - Optional metadata to associate with every token\n * @returns {lunr.Token[]}\n * @see {@link lunr.Pipeline}\n */\nlunr.tokenizer = function (obj, metadata) {\n  if (obj == null || obj == undefined) {\n    return []\n  }\n\n  if (Array.isArray(obj)) {\n    return obj.map(function (t) {\n      return new lunr.Token(\n        lunr.utils.asString(t).toLowerCase(),\n        lunr.utils.clone(metadata)\n      )\n    })\n  }\n\n  var str = obj.toString().toLowerCase(),\n      len = str.length,\n      tokens = []\n\n  for (var sliceEnd = 0, sliceStart = 0; sliceEnd <= len; sliceEnd++) {\n    var char = str.charAt(sliceEnd),\n        sliceLength = sliceEnd - sliceStart\n\n    if ((char.match(lunr.tokenizer.separator) || sliceEnd == len)) {\n\n      if (sliceLength > 0) {\n        var tokenMetadata = lunr.utils.clone(metadata) || {}\n        tokenMetadata[\"position\"] = [sliceStart, sliceLength]\n        tokenMetadata[\"index\"] = tokens.length\n\n        tokens.push(\n          new lunr.Token (\n            str.slice(sliceStart, sliceEnd),\n            tokenMetadata\n          )\n        )\n      }\n\n      sliceStart = sliceEnd + 1\n    }\n\n  }\n\n  return tokens\n}\n\n/**\n * The separator used to split a string into tokens. Override this property to change the behaviour of\n * `lunr.tokenizer` behaviour when tokenizing strings. By default this splits on whitespace and hyphens.\n *\n * @static\n * @see lunr.tokenizer\n */\nlunr.tokenizer.separator = /[\\s\\-]+/\n/*!\n * lunr.Pipeline\n * Copyright (C) 2020 Oliver Nightingale\n */\n\n/**\n * lunr.Pipelines maintain an ordered list of functions to be applied to all\n * tokens in documents entering the search index and queries being ran against\n * the index.\n *\n * An instance of lunr.Index created with the lunr shortcut will contain a\n * pipeline with a stop word filter and an English language stemmer. Extra\n * functions can be added before or after either of these functions or these\n * default functions can be removed.\n *\n * When run the pipeline will call each function in turn, passing a token, the\n * index of that token in the original list of all tokens and finally a list of\n * all the original tokens.\n *\n * The output of functions in the pipeline will be passed to the next function\n * in the pipeline. To exclude a token from entering the index the function\n * should return undefined, the rest of the pipeline will not be called with\n * this token.\n *\n * For serialisation of pipelines to work, all functions used in an instance of\n * a pipeline should be registered with lunr.Pipeline. Registered functions can\n * then be loaded. If trying to load a serialised pipeline that uses functions\n * that are not registered an error will be thrown.\n *\n * If not planning on serialising the pipeline then registering pipeline functions\n * is not necessary.\n *\n * @constructor\n */\nlunr.Pipeline = function () {\n  this._stack = []\n}\n\nlunr.Pipeline.registeredFunctions = Object.create(null)\n\n/**\n * A pipeline function maps lunr.Token to lunr.Token. A lunr.Token contains the token\n * string as well as all known metadata. A pipeline function can mutate the token string\n * or mutate (or add) metadata for a given token.\n *\n * A pipeline function can indicate that the passed token should be discarded by returning\n * null, undefined or an empty string. This token will not be passed to any downstream pipeline\n * functions and will not be added to the index.\n *\n * Multiple tokens can be returned by returning an array of tokens. Each token will be passed\n * to any downstream pipeline functions and all will returned tokens will be added to the index.\n *\n * Any number of pipeline functions may be chained together using a lunr.Pipeline.\n *\n * @interface lunr.PipelineFunction\n * @param {lunr.Token} token - A token from the document being processed.\n * @param {number} i - The index of this token in the complete list of tokens for this document/field.\n * @param {lunr.Token[]} tokens - All tokens for this document/field.\n * @returns {(?lunr.Token|lunr.Token[])}\n */\n\n/**\n * Register a function with the pipeline.\n *\n * Functions that are used in the pipeline should be registered if the pipeline\n * needs to be serialised, or a serialised pipeline needs to be loaded.\n *\n * Registering a function does not add it to a pipeline, functions must still be\n * added to instances of the pipeline for them to be used when running a pipeline.\n *\n * @param {lunr.PipelineFunction} fn - The function to check for.\n * @param {String} label - The label to register this function with\n */\nlunr.Pipeline.registerFunction = function (fn, label) {\n  if (label in this.registeredFunctions) {\n    lunr.utils.warn('Overwriting existing registered function: ' + label)\n  }\n\n  fn.label = label\n  lunr.Pipeline.registeredFunctions[fn.label] = fn\n}\n\n/**\n * Warns if the function is not registered as a Pipeline function.\n *\n * @param {lunr.PipelineFunction} fn - The function to check for.\n * @private\n */\nlunr.Pipeline.warnIfFunctionNotRegistered = function (fn) {\n  var isRegistered = fn.label && (fn.label in this.registeredFunctions)\n\n  if (!isRegistered) {\n    lunr.utils.warn('Function is not registered with pipeline. This may cause problems when serialising the index.\\n', fn)\n  }\n}\n\n/**\n * Loads a previously serialised pipeline.\n *\n * All functions to be loaded must already be registered with lunr.Pipeline.\n * If any function from the serialised data has not been registered then an\n * error will be thrown.\n *\n * @param {Object} serialised - The serialised pipeline to load.\n * @returns {lunr.Pipeline}\n */\nlunr.Pipeline.load = function (serialised) {\n  var pipeline = new lunr.Pipeline\n\n  serialised.forEach(function (fnName) {\n    var fn = lunr.Pipeline.registeredFunctions[fnName]\n\n    if (fn) {\n      pipeline.add(fn)\n    } else {\n      throw new Error('Cannot load unregistered function: ' + fnName)\n    }\n  })\n\n  return pipeline\n}\n\n/**\n * Adds new functions to the end of the pipeline.\n *\n * Logs a warning if the function has not been registered.\n *\n * @param {lunr.PipelineFunction[]} functions - Any number of functions to add to the pipeline.\n */\nlunr.Pipeline.prototype.add = function () {\n  var fns = Array.prototype.slice.call(arguments)\n\n  fns.forEach(function (fn) {\n    lunr.Pipeline.warnIfFunctionNotRegistered(fn)\n    this._stack.push(fn)\n  }, this)\n}\n\n/**\n * Adds a single function after a function that already exists in the\n * pipeline.\n *\n * Logs a warning if the function has not been registered.\n *\n * @param {lunr.PipelineFunction} existingFn - A function that already exists in the pipeline.\n * @param {lunr.PipelineFunction} newFn - The new function to add to the pipeline.\n */\nlunr.Pipeline.prototype.after = function (existingFn, newFn) {\n  lunr.Pipeline.warnIfFunctionNotRegistered(newFn)\n\n  var pos = this._stack.indexOf(existingFn)\n  if (pos == -1) {\n    throw new Error('Cannot find existingFn')\n  }\n\n  pos = pos + 1\n  this._stack.splice(pos, 0, newFn)\n}\n\n/**\n * Adds a single function before a function that already exists in the\n * pipeline.\n *\n * Logs a warning if the function has not been registered.\n *\n * @param {lunr.PipelineFunction} existingFn - A function that already exists in the pipeline.\n * @param {lunr.PipelineFunction} newFn - The new function to add to the pipeline.\n */\nlunr.Pipeline.prototype.before = function (existingFn, newFn) {\n  lunr.Pipeline.warnIfFunctionNotRegistered(newFn)\n\n  var pos = this._stack.indexOf(existingFn)\n  if (pos == -1) {\n    throw new Error('Cannot find existingFn')\n  }\n\n  this._stack.splice(pos, 0, newFn)\n}\n\n/**\n * Removes a function from the pipeline.\n *\n * @param {lunr.PipelineFunction} fn The function to remove from the pipeline.\n */\nlunr.Pipeline.prototype.remove = function (fn) {\n  var pos = this._stack.indexOf(fn)\n  if (pos == -1) {\n    return\n  }\n\n  this._stack.splice(pos, 1)\n}\n\n/**\n * Runs the current list of functions that make up the pipeline against the\n * passed tokens.\n *\n * @param {Array} tokens The tokens to run through the pipeline.\n * @returns {Array}\n */\nlunr.Pipeline.prototype.run = function (tokens) {\n  var stackLength = this._stack.length\n\n  for (var i = 0; i < stackLength; i++) {\n    var fn = this._stack[i]\n    var memo = []\n\n    for (var j = 0; j < tokens.length; j++) {\n      var result = fn(tokens[j], j, tokens)\n\n      if (result === null || result === void 0 || result === '') continue\n\n      if (Array.isArray(result)) {\n        for (var k = 0; k < result.length; k++) {\n          memo.push(result[k])\n        }\n      } else {\n        memo.push(result)\n      }\n    }\n\n    tokens = memo\n  }\n\n  return tokens\n}\n\n/**\n * Convenience method for passing a string through a pipeline and getting\n * strings out. This method takes care of wrapping the passed string in a\n * token and mapping the resulting tokens back to strings.\n *\n * @param {string} str - The string to pass through the pipeline.\n * @param {?object} metadata - Optional metadata to associate with the token\n * passed to the pipeline.\n * @returns {string[]}\n */\nlunr.Pipeline.prototype.runString = function (str, metadata) {\n  var token = new lunr.Token (str, metadata)\n\n  return this.run([token]).map(function (t) {\n    return t.toString()\n  })\n}\n\n/**\n * Resets the pipeline by removing any existing processors.\n *\n */\nlunr.Pipeline.prototype.reset = function () {\n  this._stack = []\n}\n\n/**\n * Returns a representation of the pipeline ready for serialisation.\n *\n * Logs a warning if the function has not been registered.\n *\n * @returns {Array}\n */\nlunr.Pipeline.prototype.toJSON = function () {\n  return this._stack.map(function (fn) {\n    lunr.Pipeline.warnIfFunctionNotRegistered(fn)\n\n    return fn.label\n  })\n}\n/*!\n * lunr.Vector\n * Copyright (C) 2020 Oliver Nightingale\n */\n\n/**\n * A vector is used to construct the vector space of documents and queries. These\n * vectors support operations to determine the similarity between two documents or\n * a document and a query.\n *\n * Normally no parameters are required for initializing a vector, but in the case of\n * loading a previously dumped vector the raw elements can be provided to the constructor.\n *\n * For performance reasons vectors are implemented with a flat array, where an elements\n * index is immediately followed by its value. E.g. [index, value, index, value]. This\n * allows the underlying array to be as sparse as possible and still offer decent\n * performance when being used for vector calculations.\n *\n * @constructor\n * @param {Number[]} [elements] - The flat list of element index and element value pairs.\n */\nlunr.Vector = function (elements) {\n  this._magnitude = 0\n  this.elements = elements || []\n}\n\n\n/**\n * Calculates the position within the vector to insert a given index.\n *\n * This is used internally by insert and upsert. If there are duplicate indexes then\n * the position is returned as if the value for that index were to be updated, but it\n * is the callers responsibility to check whether there is a duplicate at that index\n *\n * @param {Number} insertIdx - The index at which the element should be inserted.\n * @returns {Number}\n */\nlunr.Vector.prototype.positionForIndex = function (index) {\n  // For an empty vector the tuple can be inserted at the beginning\n  if (this.elements.length == 0) {\n    return 0\n  }\n\n  var start = 0,\n      end = this.elements.length / 2,\n      sliceLength = end - start,\n      pivotPoint = Math.floor(sliceLength / 2),\n      pivotIndex = this.elements[pivotPoint * 2]\n\n  while (sliceLength > 1) {\n    if (pivotIndex < index) {\n      start = pivotPoint\n    }\n\n    if (pivotIndex > index) {\n      end = pivotPoint\n    }\n\n    if (pivotIndex == index) {\n      break\n    }\n\n    sliceLength = end - start\n    pivotPoint = start + Math.floor(sliceLength / 2)\n    pivotIndex = this.elements[pivotPoint * 2]\n  }\n\n  if (pivotIndex == index) {\n    return pivotPoint * 2\n  }\n\n  if (pivotIndex > index) {\n    return pivotPoint * 2\n  }\n\n  if (pivotIndex < index) {\n    return (pivotPoint + 1) * 2\n  }\n}\n\n/**\n * Inserts an element at an index within the vector.\n *\n * Does not allow duplicates, will throw an error if there is already an entry\n * for this index.\n *\n * @param {Number} insertIdx - The index at which the element should be inserted.\n * @param {Number} val - The value to be inserted into the vector.\n */\nlunr.Vector.prototype.insert = function (insertIdx, val) {\n  this.upsert(insertIdx, val, function () {\n    throw \"duplicate index\"\n  })\n}\n\n/**\n * Inserts or updates an existing index within the vector.\n *\n * @param {Number} insertIdx - The index at which the element should be inserted.\n * @param {Number} val - The value to be inserted into the vector.\n * @param {function} fn - A function that is called for updates, the existing value and the\n * requested value are passed as arguments\n */\nlunr.Vector.prototype.upsert = function (insertIdx, val, fn) {\n  this._magnitude = 0\n  var position = this.positionForIndex(insertIdx)\n\n  if (this.elements[position] == insertIdx) {\n    this.elements[position + 1] = fn(this.elements[position + 1], val)\n  } else {\n    this.elements.splice(position, 0, insertIdx, val)\n  }\n}\n\n/**\n * Calculates the magnitude of this vector.\n *\n * @returns {Number}\n */\nlunr.Vector.prototype.magnitude = function () {\n  if (this._magnitude) return this._magnitude\n\n  var sumOfSquares = 0,\n      elementsLength = this.elements.length\n\n  for (var i = 1; i < elementsLength; i += 2) {\n    var val = this.elements[i]\n    sumOfSquares += val * val\n  }\n\n  return this._magnitude = Math.sqrt(sumOfSquares)\n}\n\n/**\n * Calculates the dot product of this vector and another vector.\n *\n * @param {lunr.Vector} otherVector - The vector to compute the dot product with.\n * @returns {Number}\n */\nlunr.Vector.prototype.dot = function (otherVector) {\n  var dotProduct = 0,\n      a = this.elements, b = otherVector.elements,\n      aLen = a.length, bLen = b.length,\n      aVal = 0, bVal = 0,\n      i = 0, j = 0\n\n  while (i < aLen && j < bLen) {\n    aVal = a[i], bVal = b[j]\n    if (aVal < bVal) {\n      i += 2\n    } else if (aVal > bVal) {\n      j += 2\n    } else if (aVal == bVal) {\n      dotProduct += a[i + 1] * b[j + 1]\n      i += 2\n      j += 2\n    }\n  }\n\n  return dotProduct\n}\n\n/**\n * Calculates the similarity between this vector and another vector.\n *\n * @param {lunr.Vector} otherVector - The other vector to calculate the\n * similarity with.\n * @returns {Number}\n */\nlunr.Vector.prototype.similarity = function (otherVector) {\n  return this.dot(otherVector) / this.magnitude() || 0\n}\n\n/**\n * Converts the vector to an array of the elements within the vector.\n *\n * @returns {Number[]}\n */\nlunr.Vector.prototype.toArray = function () {\n  var output = new Array (this.elements.length / 2)\n\n  for (var i = 1, j = 0; i < this.elements.length; i += 2, j++) {\n    output[j] = this.elements[i]\n  }\n\n  return output\n}\n\n/**\n * A JSON serializable representation of the vector.\n *\n * @returns {Number[]}\n */\nlunr.Vector.prototype.toJSON = function () {\n  return this.elements\n}\n/* eslint-disable */\n/*!\n * lunr.stemmer\n * Copyright (C) 2020 Oliver Nightingale\n * Includes code from - http://tartarus.org/~martin/PorterStemmer/js.txt\n */\n\n/**\n * lunr.stemmer is an english language stemmer, this is a JavaScript\n * implementation of the PorterStemmer taken from http://tartarus.org/~martin\n *\n * @static\n * @implements {lunr.PipelineFunction}\n * @param {lunr.Token} token - The string to stem\n * @returns {lunr.Token}\n * @see {@link lunr.Pipeline}\n * @function\n */\nlunr.stemmer = (function(){\n  var step2list = {\n      \"ational\" : \"ate\",\n      \"tional\" : \"tion\",\n      \"enci\" : \"ence\",\n      \"anci\" : \"ance\",\n      \"izer\" : \"ize\",\n      \"bli\" : \"ble\",\n      \"alli\" : \"al\",\n      \"entli\" : \"ent\",\n      \"eli\" : \"e\",\n      \"ousli\" : \"ous\",\n      \"ization\" : \"ize\",\n      \"ation\" : \"ate\",\n      \"ator\" : \"ate\",\n      \"alism\" : \"al\",\n      \"iveness\" : \"ive\",\n      \"fulness\" : \"ful\",\n      \"ousness\" : \"ous\",\n      \"aliti\" : \"al\",\n      \"iviti\" : \"ive\",\n      \"biliti\" : \"ble\",\n      \"logi\" : \"log\"\n    },\n\n    step3list = {\n      \"icate\" : \"ic\",\n      \"ative\" : \"\",\n      \"alize\" : \"al\",\n      \"iciti\" : \"ic\",\n      \"ical\" : \"ic\",\n      \"ful\" : \"\",\n      \"ness\" : \"\"\n    },\n\n    c = \"[^aeiou]\",          // consonant\n    v = \"[aeiouy]\",          // vowel\n    C = c + \"[^aeiouy]*\",    // consonant sequence\n    V = v + \"[aeiou]*\",      // vowel sequence\n\n    mgr0 = \"^(\" + C + \")?\" + V + C,               // [C]VC... is m>0\n    meq1 = \"^(\" + C + \")?\" + V + C + \"(\" + V + \")?$\",  // [C]VC[V] is m=1\n    mgr1 = \"^(\" + C + \")?\" + V + C + V + C,       // [C]VCVC... is m>1\n    s_v = \"^(\" + C + \")?\" + v;                   // vowel in stem\n\n  var re_mgr0 = new RegExp(mgr0);\n  var re_mgr1 = new RegExp(mgr1);\n  var re_meq1 = new RegExp(meq1);\n  var re_s_v = new RegExp(s_v);\n\n  var re_1a = /^(.+?)(ss|i)es$/;\n  var re2_1a = /^(.+?)([^s])s$/;\n  var re_1b = /^(.+?)eed$/;\n  var re2_1b = /^(.+?)(ed|ing)$/;\n  var re_1b_2 = /.$/;\n  var re2_1b_2 = /(at|bl|iz)$/;\n  var re3_1b_2 = new RegExp(\"([^aeiouylsz])\\\\1$\");\n  var re4_1b_2 = new RegExp(\"^\" + C + v + \"[^aeiouwxy]$\");\n\n  var re_1c = /^(.+?[^aeiou])y$/;\n  var re_2 = /^(.+?)(ational|tional|enci|anci|izer|bli|alli|entli|eli|ousli|ization|ation|ator|alism|iveness|fulness|ousness|aliti|iviti|biliti|logi)$/;\n\n  var re_3 = /^(.+?)(icate|ative|alize|iciti|ical|ful|ness)$/;\n\n  var re_4 = /^(.+?)(al|ance|ence|er|ic|able|ible|ant|ement|ment|ent|ou|ism|ate|iti|ous|ive|ize)$/;\n  var re2_4 = /^(.+?)(s|t)(ion)$/;\n\n  var re_5 = /^(.+?)e$/;\n  var re_5_1 = /ll$/;\n  var re3_5 = new RegExp(\"^\" + C + v + \"[^aeiouwxy]$\");\n\n  var porterStemmer = function porterStemmer(w) {\n    var stem,\n      suffix,\n      firstch,\n      re,\n      re2,\n      re3,\n      re4;\n\n    if (w.length < 3) { return w; }\n\n    firstch = w.substr(0,1);\n    if (firstch == \"y\") {\n      w = firstch.toUpperCase() + w.substr(1);\n    }\n\n    // Step 1a\n    re = re_1a\n    re2 = re2_1a;\n\n    if (re.test(w)) { w = w.replace(re,\"$1$2\"); }\n    else if (re2.test(w)) { w = w.replace(re2,\"$1$2\"); }\n\n    // Step 1b\n    re = re_1b;\n    re2 = re2_1b;\n    if (re.test(w)) {\n      var fp = re.exec(w);\n      re = re_mgr0;\n      if (re.test(fp[1])) {\n        re = re_1b_2;\n        w = w.replace(re,\"\");\n      }\n    } else if (re2.test(w)) {\n      var fp = re2.exec(w);\n      stem = fp[1];\n      re2 = re_s_v;\n      if (re2.test(stem)) {\n        w = stem;\n        re2 = re2_1b_2;\n        re3 = re3_1b_2;\n        re4 = re4_1b_2;\n        if (re2.test(w)) { w = w + \"e\"; }\n        else if (re3.test(w)) { re = re_1b_2; w = w.replace(re,\"\"); }\n        else if (re4.test(w)) { w = w + \"e\"; }\n      }\n    }\n\n    // Step 1c - replace suffix y or Y by i if preceded by a non-vowel which is not the first letter of the word (so cry -> cri, by -> by, say -> say)\n    re = re_1c;\n    if (re.test(w)) {\n      var fp = re.exec(w);\n      stem = fp[1];\n      w = stem + \"i\";\n    }\n\n    // Step 2\n    re = re_2;\n    if (re.test(w)) {\n      var fp = re.exec(w);\n      stem = fp[1];\n      suffix = fp[2];\n      re = re_mgr0;\n      if (re.test(stem)) {\n        w = stem + step2list[suffix];\n      }\n    }\n\n    // Step 3\n    re = re_3;\n    if (re.test(w)) {\n      var fp = re.exec(w);\n      stem = fp[1];\n      suffix = fp[2];\n      re = re_mgr0;\n      if (re.test(stem)) {\n        w = stem + step3list[suffix];\n      }\n    }\n\n    // Step 4\n    re = re_4;\n    re2 = re2_4;\n    if (re.test(w)) {\n      var fp = re.exec(w);\n      stem = fp[1];\n      re = re_mgr1;\n      if (re.test(stem)) {\n        w = stem;\n      }\n    } else if (re2.test(w)) {\n      var fp = re2.exec(w);\n      stem = fp[1] + fp[2];\n      re2 = re_mgr1;\n      if (re2.test(stem)) {\n        w = stem;\n      }\n    }\n\n    // Step 5\n    re = re_5;\n    if (re.test(w)) {\n      var fp = re.exec(w);\n      stem = fp[1];\n      re = re_mgr1;\n      re2 = re_meq1;\n      re3 = re3_5;\n      if (re.test(stem) || (re2.test(stem) && !(re3.test(stem)))) {\n        w = stem;\n      }\n    }\n\n    re = re_5_1;\n    re2 = re_mgr1;\n    if (re.test(w) && re2.test(w)) {\n      re = re_1b_2;\n      w = w.replace(re,\"\");\n    }\n\n    // and turn initial Y back to y\n\n    if (firstch == \"y\") {\n      w = firstch.toLowerCase() + w.substr(1);\n    }\n\n    return w;\n  };\n\n  return function (token) {\n    return token.update(porterStemmer);\n  }\n})();\n\nlunr.Pipeline.registerFunction(lunr.stemmer, 'stemmer')\n/*!\n * lunr.stopWordFilter\n * Copyright (C) 2020 Oliver Nightingale\n */\n\n/**\n * lunr.generateStopWordFilter builds a stopWordFilter function from the provided\n * list of stop words.\n *\n * The built in lunr.stopWordFilter is built using this generator and can be used\n * to generate custom stopWordFilters for applications or non English languages.\n *\n * @function\n * @param {Array} token The token to pass through the filter\n * @returns {lunr.PipelineFunction}\n * @see lunr.Pipeline\n * @see lunr.stopWordFilter\n */\nlunr.generateStopWordFilter = function (stopWords) {\n  var words = stopWords.reduce(function (memo, stopWord) {\n    memo[stopWord] = stopWord\n    return memo\n  }, {})\n\n  return function (token) {\n    if (token && words[token.toString()] !== token.toString()) return token\n  }\n}\n\n/**\n * lunr.stopWordFilter is an English language stop word list filter, any words\n * contained in the list will not be passed through the filter.\n *\n * This is intended to be used in the Pipeline. If the token does not pass the\n * filter then undefined will be returned.\n *\n * @function\n * @implements {lunr.PipelineFunction}\n * @params {lunr.Token} token - A token to check for being a stop word.\n * @returns {lunr.Token}\n * @see {@link lunr.Pipeline}\n */\nlunr.stopWordFilter = lunr.generateStopWordFilter([\n  'a',\n  'able',\n  'about',\n  'across',\n  'after',\n  'all',\n  'almost',\n  'also',\n  'am',\n  'among',\n  'an',\n  'and',\n  'any',\n  'are',\n  'as',\n  'at',\n  'be',\n  'because',\n  'been',\n  'but',\n  'by',\n  'can',\n  'cannot',\n  'could',\n  'dear',\n  'did',\n  'do',\n  'does',\n  'either',\n  'else',\n  'ever',\n  'every',\n  'for',\n  'from',\n  'get',\n  'got',\n  'had',\n  'has',\n  'have',\n  'he',\n  'her',\n  'hers',\n  'him',\n  'his',\n  'how',\n  'however',\n  'i',\n  'if',\n  'in',\n  'into',\n  'is',\n  'it',\n  'its',\n  'just',\n  'least',\n  'let',\n  'like',\n  'likely',\n  'may',\n  'me',\n  'might',\n  'most',\n  'must',\n  'my',\n  'neither',\n  'no',\n  'nor',\n  'not',\n  'of',\n  'off',\n  'often',\n  'on',\n  'only',\n  'or',\n  'other',\n  'our',\n  'own',\n  'rather',\n  'said',\n  'say',\n  'says',\n  'she',\n  'should',\n  'since',\n  'so',\n  'some',\n  'than',\n  'that',\n  'the',\n  'their',\n  'them',\n  'then',\n  'there',\n  'these',\n  'they',\n  'this',\n  'tis',\n  'to',\n  'too',\n  'twas',\n  'us',\n  'wants',\n  'was',\n  'we',\n  'were',\n  'what',\n  'when',\n  'where',\n  'which',\n  'while',\n  'who',\n  'whom',\n  'why',\n  'will',\n  'with',\n  'would',\n  'yet',\n  'you',\n  'your'\n])\n\nlunr.Pipeline.registerFunction(lunr.stopWordFilter, 'stopWordFilter')\n/*!\n * lunr.trimmer\n * Copyright (C) 2020 Oliver Nightingale\n */\n\n/**\n * lunr.trimmer is a pipeline function for trimming non word\n * characters from the beginning and end of tokens before they\n * enter the index.\n *\n * This implementation may not work correctly for non latin\n * characters and should either be removed or adapted for use\n * with languages with non-latin characters.\n *\n * @static\n * @implements {lunr.PipelineFunction}\n * @param {lunr.Token} token The token to pass through the filter\n * @returns {lunr.Token}\n * @see lunr.Pipeline\n */\nlunr.trimmer = function (token) {\n  return token.update(function (s) {\n    return s.replace(/^\\W+/, '').replace(/\\W+$/, '')\n  })\n}\n\nlunr.Pipeline.registerFunction(lunr.trimmer, 'trimmer')\n/*!\n * lunr.TokenSet\n * Copyright (C) 2020 Oliver Nightingale\n */\n\n/**\n * A token set is used to store the unique list of all tokens\n * within an index. Token sets are also used to represent an\n * incoming query to the index, this query token set and index\n * token set are then intersected to find which tokens to look\n * up in the inverted index.\n *\n * A token set can hold multiple tokens, as in the case of the\n * index token set, or it can hold a single token as in the\n * case of a simple query token set.\n *\n * Additionally token sets are used to perform wildcard matching.\n * Leading, contained and trailing wildcards are supported, and\n * from this edit distance matching can also be provided.\n *\n * Token sets are implemented as a minimal finite state automata,\n * where both common prefixes and suffixes are shared between tokens.\n * This helps to reduce the space used for storing the token set.\n *\n * @constructor\n */\nlunr.TokenSet = function () {\n  this.final = false\n  this.edges = {}\n  this.id = lunr.TokenSet._nextId\n  lunr.TokenSet._nextId += 1\n}\n\n/**\n * Keeps track of the next, auto increment, identifier to assign\n * to a new tokenSet.\n *\n * TokenSets require a unique identifier to be correctly minimised.\n *\n * @private\n */\nlunr.TokenSet._nextId = 1\n\n/**\n * Creates a TokenSet instance from the given sorted array of words.\n *\n * @param {String[]} arr - A sorted array of strings to create the set from.\n * @returns {lunr.TokenSet}\n * @throws Will throw an error if the input array is not sorted.\n */\nlunr.TokenSet.fromArray = function (arr) {\n  var builder = new lunr.TokenSet.Builder\n\n  for (var i = 0, len = arr.length; i < len; i++) {\n    builder.insert(arr[i])\n  }\n\n  builder.finish()\n  return builder.root\n}\n\n/**\n * Creates a token set from a query clause.\n *\n * @private\n * @param {Object} clause - A single clause from lunr.Query.\n * @param {string} clause.term - The query clause term.\n * @param {number} [clause.editDistance] - The optional edit distance for the term.\n * @returns {lunr.TokenSet}\n */\nlunr.TokenSet.fromClause = function (clause) {\n  if ('editDistance' in clause) {\n    return lunr.TokenSet.fromFuzzyString(clause.term, clause.editDistance)\n  } else {\n    return lunr.TokenSet.fromString(clause.term)\n  }\n}\n\n/**\n * Creates a token set representing a single string with a specified\n * edit distance.\n *\n * Insertions, deletions, substitutions and transpositions are each\n * treated as an edit distance of 1.\n *\n * Increasing the allowed edit distance will have a dramatic impact\n * on the performance of both creating and intersecting these TokenSets.\n * It is advised to keep the edit distance less than 3.\n *\n * @param {string} str - The string to create the token set from.\n * @param {number} editDistance - The allowed edit distance to match.\n * @returns {lunr.Vector}\n */\nlunr.TokenSet.fromFuzzyString = function (str, editDistance) {\n  var root = new lunr.TokenSet\n\n  var stack = [{\n    node: root,\n    editsRemaining: editDistance,\n    str: str\n  }]\n\n  while (stack.length) {\n    var frame = stack.pop()\n\n    // no edit\n    if (frame.str.length > 0) {\n      var char = frame.str.charAt(0),\n          noEditNode\n\n      if (char in frame.node.edges) {\n        noEditNode = frame.node.edges[char]\n      } else {\n        noEditNode = new lunr.TokenSet\n        frame.node.edges[char] = noEditNode\n      }\n\n      if (frame.str.length == 1) {\n        noEditNode.final = true\n      }\n\n      stack.push({\n        node: noEditNode,\n        editsRemaining: frame.editsRemaining,\n        str: frame.str.slice(1)\n      })\n    }\n\n    if (frame.editsRemaining == 0) {\n      continue\n    }\n\n    // insertion\n    if (\"*\" in frame.node.edges) {\n      var insertionNode = frame.node.edges[\"*\"]\n    } else {\n      var insertionNode = new lunr.TokenSet\n      frame.node.edges[\"*\"] = insertionNode\n    }\n\n    if (frame.str.length == 0) {\n      insertionNode.final = true\n    }\n\n    stack.push({\n      node: insertionNode,\n      editsRemaining: frame.editsRemaining - 1,\n      str: frame.str\n    })\n\n    // deletion\n    // can only do a deletion if we have enough edits remaining\n    // and if there are characters left to delete in the string\n    if (frame.str.length > 1) {\n      stack.push({\n        node: frame.node,\n        editsRemaining: frame.editsRemaining - 1,\n        str: frame.str.slice(1)\n      })\n    }\n\n    // deletion\n    // just removing the last character from the str\n    if (frame.str.length == 1) {\n      frame.node.final = true\n    }\n\n    // substitution\n    // can only do a substitution if we have enough edits remaining\n    // and if there are characters left to substitute\n    if (frame.str.length >= 1) {\n      if (\"*\" in frame.node.edges) {\n        var substitutionNode = frame.node.edges[\"*\"]\n      } else {\n        var substitutionNode = new lunr.TokenSet\n        frame.node.edges[\"*\"] = substitutionNode\n      }\n\n      if (frame.str.length == 1) {\n        substitutionNode.final = true\n      }\n\n      stack.push({\n        node: substitutionNode,\n        editsRemaining: frame.editsRemaining - 1,\n        str: frame.str.slice(1)\n      })\n    }\n\n    // transposition\n    // can only do a transposition if there are edits remaining\n    // and there are enough characters to transpose\n    if (frame.str.length > 1) {\n      var charA = frame.str.charAt(0),\n          charB = frame.str.charAt(1),\n          transposeNode\n\n      if (charB in frame.node.edges) {\n        transposeNode = frame.node.edges[charB]\n      } else {\n        transposeNode = new lunr.TokenSet\n        frame.node.edges[charB] = transposeNode\n      }\n\n      if (frame.str.length == 1) {\n        transposeNode.final = true\n      }\n\n      stack.push({\n        node: transposeNode,\n        editsRemaining: frame.editsRemaining - 1,\n        str: charA + frame.str.slice(2)\n      })\n    }\n  }\n\n  return root\n}\n\n/**\n * Creates a TokenSet from a string.\n *\n * The string may contain one or more wildcard characters (*)\n * that will allow wildcard matching when intersecting with\n * another TokenSet.\n *\n * @param {string} str - The string to create a TokenSet from.\n * @returns {lunr.TokenSet}\n */\nlunr.TokenSet.fromString = function (str) {\n  var node = new lunr.TokenSet,\n      root = node\n\n  /*\n   * Iterates through all characters within the passed string\n   * appending a node for each character.\n   *\n   * When a wildcard character is found then a self\n   * referencing edge is introduced to continually match\n   * any number of any characters.\n   */\n  for (var i = 0, len = str.length; i < len; i++) {\n    var char = str[i],\n        final = (i == len - 1)\n\n    if (char == \"*\") {\n      node.edges[char] = node\n      node.final = final\n\n    } else {\n      var next = new lunr.TokenSet\n      next.final = final\n\n      node.edges[char] = next\n      node = next\n    }\n  }\n\n  return root\n}\n\n/**\n * Converts this TokenSet into an array of strings\n * contained within the TokenSet.\n *\n * This is not intended to be used on a TokenSet that\n * contains wildcards, in these cases the results are\n * undefined and are likely to cause an infinite loop.\n *\n * @returns {string[]}\n */\nlunr.TokenSet.prototype.toArray = function () {\n  var words = []\n\n  var stack = [{\n    prefix: \"\",\n    node: this\n  }]\n\n  while (stack.length) {\n    var frame = stack.pop(),\n        edges = Object.keys(frame.node.edges),\n        len = edges.length\n\n    if (frame.node.final) {\n      /* In Safari, at this point the prefix is sometimes corrupted, see:\n       * https://github.com/olivernn/lunr.js/issues/279 Calling any\n       * String.prototype method forces Safari to \"cast\" this string to what\n       * it's supposed to be, fixing the bug. */\n      frame.prefix.charAt(0)\n      words.push(frame.prefix)\n    }\n\n    for (var i = 0; i < len; i++) {\n      var edge = edges[i]\n\n      stack.push({\n        prefix: frame.prefix.concat(edge),\n        node: frame.node.edges[edge]\n      })\n    }\n  }\n\n  return words\n}\n\n/**\n * Generates a string representation of a TokenSet.\n *\n * This is intended to allow TokenSets to be used as keys\n * in objects, largely to aid the construction and minimisation\n * of a TokenSet. As such it is not designed to be a human\n * friendly representation of the TokenSet.\n *\n * @returns {string}\n */\nlunr.TokenSet.prototype.toString = function () {\n  // NOTE: Using Object.keys here as this.edges is very likely\n  // to enter 'hash-mode' with many keys being added\n  //\n  // avoiding a for-in loop here as it leads to the function\n  // being de-optimised (at least in V8). From some simple\n  // benchmarks the performance is comparable, but allowing\n  // V8 to optimize may mean easy performance wins in the future.\n\n  if (this._str) {\n    return this._str\n  }\n\n  var str = this.final ? '1' : '0',\n      labels = Object.keys(this.edges).sort(),\n      len = labels.length\n\n  for (var i = 0; i < len; i++) {\n    var label = labels[i],\n        node = this.edges[label]\n\n    str = str + label + node.id\n  }\n\n  return str\n}\n\n/**\n * Returns a new TokenSet that is the intersection of\n * this TokenSet and the passed TokenSet.\n *\n * This intersection will take into account any wildcards\n * contained within the TokenSet.\n *\n * @param {lunr.TokenSet} b - An other TokenSet to intersect with.\n * @returns {lunr.TokenSet}\n */\nlunr.TokenSet.prototype.intersect = function (b) {\n  var output = new lunr.TokenSet,\n      frame = undefined\n\n  var stack = [{\n    qNode: b,\n    output: output,\n    node: this\n  }]\n\n  while (stack.length) {\n    frame = stack.pop()\n\n    // NOTE: As with the #toString method, we are using\n    // Object.keys and a for loop instead of a for-in loop\n    // as both of these objects enter 'hash' mode, causing\n    // the function to be de-optimised in V8\n    var qEdges = Object.keys(frame.qNode.edges),\n        qLen = qEdges.length,\n        nEdges = Object.keys(frame.node.edges),\n        nLen = nEdges.length\n\n    for (var q = 0; q < qLen; q++) {\n      var qEdge = qEdges[q]\n\n      for (var n = 0; n < nLen; n++) {\n        var nEdge = nEdges[n]\n\n        if (nEdge == qEdge || qEdge == '*') {\n          var node = frame.node.edges[nEdge],\n              qNode = frame.qNode.edges[qEdge],\n              final = node.final && qNode.final,\n              next = undefined\n\n          if (nEdge in frame.output.edges) {\n            // an edge already exists for this character\n            // no need to create a new node, just set the finality\n            // bit unless this node is already final\n            next = frame.output.edges[nEdge]\n            next.final = next.final || final\n\n          } else {\n            // no edge exists yet, must create one\n            // set the finality bit and insert it\n            // into the output\n            next = new lunr.TokenSet\n            next.final = final\n            frame.output.edges[nEdge] = next\n          }\n\n          stack.push({\n            qNode: qNode,\n            output: next,\n            node: node\n          })\n        }\n      }\n    }\n  }\n\n  return output\n}\nlunr.TokenSet.Builder = function () {\n  this.previousWord = \"\"\n  this.root = new lunr.TokenSet\n  this.uncheckedNodes = []\n  this.minimizedNodes = {}\n}\n\nlunr.TokenSet.Builder.prototype.insert = function (word) {\n  var node,\n      commonPrefix = 0\n\n  if (word < this.previousWord) {\n    throw new Error (\"Out of order word insertion\")\n  }\n\n  for (var i = 0; i < word.length && i < this.previousWord.length; i++) {\n    if (word[i] != this.previousWord[i]) break\n    commonPrefix++\n  }\n\n  this.minimize(commonPrefix)\n\n  if (this.uncheckedNodes.length == 0) {\n    node = this.root\n  } else {\n    node = this.uncheckedNodes[this.uncheckedNodes.length - 1].child\n  }\n\n  for (var i = commonPrefix; i < word.length; i++) {\n    var nextNode = new lunr.TokenSet,\n        char = word[i]\n\n    node.edges[char] = nextNode\n\n    this.uncheckedNodes.push({\n      parent: node,\n      char: char,\n      child: nextNode\n    })\n\n    node = nextNode\n  }\n\n  node.final = true\n  this.previousWord = word\n}\n\nlunr.TokenSet.Builder.prototype.finish = function () {\n  this.minimize(0)\n}\n\nlunr.TokenSet.Builder.prototype.minimize = function (downTo) {\n  for (var i = this.uncheckedNodes.length - 1; i >= downTo; i--) {\n    var node = this.uncheckedNodes[i],\n        childKey = node.child.toString()\n\n    if (childKey in this.minimizedNodes) {\n      node.parent.edges[node.char] = this.minimizedNodes[childKey]\n    } else {\n      // Cache the key for this node since\n      // we know it can't change anymore\n      node.child._str = childKey\n\n      this.minimizedNodes[childKey] = node.child\n    }\n\n    this.uncheckedNodes.pop()\n  }\n}\n/*!\n * lunr.Index\n * Copyright (C) 2020 Oliver Nightingale\n */\n\n/**\n * An index contains the built index of all documents and provides a query interface\n * to the index.\n *\n * Usually instances of lunr.Index will not be created using this constructor, instead\n * lunr.Builder should be used to construct new indexes, or lunr.Index.load should be\n * used to load previously built and serialized indexes.\n *\n * @constructor\n * @param {Object} attrs - The attributes of the built search index.\n * @param {Object} attrs.invertedIndex - An index of term/field to document reference.\n * @param {Object<string, lunr.Vector>} attrs.fieldVectors - Field vectors\n * @param {lunr.TokenSet} attrs.tokenSet - An set of all corpus tokens.\n * @param {string[]} attrs.fields - The names of indexed document fields.\n * @param {lunr.Pipeline} attrs.pipeline - The pipeline to use for search terms.\n */\nlunr.Index = function (attrs) {\n  this.invertedIndex = attrs.invertedIndex\n  this.fieldVectors = attrs.fieldVectors\n  this.tokenSet = attrs.tokenSet\n  this.fields = attrs.fields\n  this.pipeline = attrs.pipeline\n}\n\n/**\n * A result contains details of a document matching a search query.\n * @typedef {Object} lunr.Index~Result\n * @property {string} ref - The reference of the document this result represents.\n * @property {number} score - A number between 0 and 1 representing how similar this document is to the query.\n * @property {lunr.MatchData} matchData - Contains metadata about this match including which term(s) caused the match.\n */\n\n/**\n * Although lunr provides the ability to create queries using lunr.Query, it also provides a simple\n * query language which itself is parsed into an instance of lunr.Query.\n *\n * For programmatically building queries it is advised to directly use lunr.Query, the query language\n * is best used for human entered text rather than program generated text.\n *\n * At its simplest queries can just be a single term, e.g. `hello`, multiple terms are also supported\n * and will be combined with OR, e.g `hello world` will match documents that contain either 'hello'\n * or 'world', though those that contain both will rank higher in the results.\n *\n * Wildcards can be included in terms to match one or more unspecified characters, these wildcards can\n * be inserted anywhere within the term, and more than one wildcard can exist in a single term. Adding\n * wildcards will increase the number of documents that will be found but can also have a negative\n * impact on query performance, especially with wildcards at the beginning of a term.\n *\n * Terms can be restricted to specific fields, e.g. `title:hello`, only documents with the term\n * hello in the title field will match this query. Using a field not present in the index will lead\n * to an error being thrown.\n *\n * Modifiers can also be added to terms, lunr supports edit distance and boost modifiers on terms. A term\n * boost will make documents matching that term score higher, e.g. `foo^5`. Edit distance is also supported\n * to provide fuzzy matching, e.g. 'hello~2' will match documents with hello with an edit distance of 2.\n * Avoid large values for edit distance to improve query performance.\n *\n * Each term also supports a presence modifier. By default a term's presence in document is optional, however\n * this can be changed to either required or prohibited. For a term's presence to be required in a document the\n * term should be prefixed with a '+', e.g. `+foo bar` is a search for documents that must contain 'foo' and\n * optionally contain 'bar'. Conversely a leading '-' sets the terms presence to prohibited, i.e. it must not\n * appear in a document, e.g. `-foo bar` is a search for documents that do not contain 'foo' but may contain 'bar'.\n *\n * To escape special characters the backslash character '\\' can be used, this allows searches to include\n * characters that would normally be considered modifiers, e.g. `foo\\~2` will search for a term \"foo~2\" instead\n * of attempting to apply a boost of 2 to the search term \"foo\".\n *\n * @typedef {string} lunr.Index~QueryString\n * @example <caption>Simple single term query</caption>\n * hello\n * @example <caption>Multiple term query</caption>\n * hello world\n * @example <caption>term scoped to a field</caption>\n * title:hello\n * @example <caption>term with a boost of 10</caption>\n * hello^10\n * @example <caption>term with an edit distance of 2</caption>\n * hello~2\n * @example <caption>terms with presence modifiers</caption>\n * -foo +bar baz\n */\n\n/**\n * Performs a search against the index using lunr query syntax.\n *\n * Results will be returned sorted by their score, the most relevant results\n * will be returned first.  For details on how the score is calculated, please see\n * the {@link https://lunrjs.com/guides/searching.html#scoring|guide}.\n *\n * For more programmatic querying use lunr.Index#query.\n *\n * @param {lunr.Index~QueryString} queryString - A string containing a lunr query.\n * @throws {lunr.QueryParseError} If the passed query string cannot be parsed.\n * @returns {lunr.Index~Result[]}\n */\nlunr.Index.prototype.search = function (queryString) {\n  return this.query(function (query) {\n    var parser = new lunr.QueryParser(queryString, query)\n    parser.parse()\n  })\n}\n\n/**\n * A query builder callback provides a query object to be used to express\n * the query to perform on the index.\n *\n * @callback lunr.Index~queryBuilder\n * @param {lunr.Query} query - The query object to build up.\n * @this lunr.Query\n */\n\n/**\n * Performs a query against the index using the yielded lunr.Query object.\n *\n * If performing programmatic queries against the index, this method is preferred\n * over lunr.Index#search so as to avoid the additional query parsing overhead.\n *\n * A query object is yielded to the supplied function which should be used to\n * express the query to be run against the index.\n *\n * Note that although this function takes a callback parameter it is _not_ an\n * asynchronous operation, the callback is just yielded a query object to be\n * customized.\n *\n * @param {lunr.Index~queryBuilder} fn - A function that is used to build the query.\n * @returns {lunr.Index~Result[]}\n */\nlunr.Index.prototype.query = function (fn) {\n  // for each query clause\n  // * process terms\n  // * expand terms from token set\n  // * find matching documents and metadata\n  // * get document vectors\n  // * score documents\n\n  var query = new lunr.Query(this.fields),\n      matchingFields = Object.create(null),\n      queryVectors = Object.create(null),\n      termFieldCache = Object.create(null),\n      requiredMatches = Object.create(null),\n      prohibitedMatches = Object.create(null)\n\n  /*\n   * To support field level boosts a query vector is created per\n   * field. An empty vector is eagerly created to support negated\n   * queries.\n   */\n  for (var i = 0; i < this.fields.length; i++) {\n    queryVectors[this.fields[i]] = new lunr.Vector\n  }\n\n  fn.call(query, query)\n\n  for (var i = 0; i < query.clauses.length; i++) {\n    /*\n     * Unless the pipeline has been disabled for this term, which is\n     * the case for terms with wildcards, we need to pass the clause\n     * term through the search pipeline. A pipeline returns an array\n     * of processed terms. Pipeline functions may expand the passed\n     * term, which means we may end up performing multiple index lookups\n     * for a single query term.\n     */\n    var clause = query.clauses[i],\n        terms = null,\n        clauseMatches = lunr.Set.empty\n\n    if (clause.usePipeline) {\n      terms = this.pipeline.runString(clause.term, {\n        fields: clause.fields\n      })\n    } else {\n      terms = [clause.term]\n    }\n\n    for (var m = 0; m < terms.length; m++) {\n      var term = terms[m]\n\n      /*\n       * Each term returned from the pipeline needs to use the same query\n       * clause object, e.g. the same boost and or edit distance. The\n       * simplest way to do this is to re-use the clause object but mutate\n       * its term property.\n       */\n      clause.term = term\n\n      /*\n       * From the term in the clause we create a token set which will then\n       * be used to intersect the indexes token set to get a list of terms\n       * to lookup in the inverted index\n       */\n      var termTokenSet = lunr.TokenSet.fromClause(clause),\n          expandedTerms = this.tokenSet.intersect(termTokenSet).toArray()\n\n      /*\n       * If a term marked as required does not exist in the tokenSet it is\n       * impossible for the search to return any matches. We set all the field\n       * scoped required matches set to empty and stop examining any further\n       * clauses.\n       */\n      if (expandedTerms.length === 0 && clause.presence === lunr.Query.presence.REQUIRED) {\n        for (var k = 0; k < clause.fields.length; k++) {\n          var field = clause.fields[k]\n          requiredMatches[field] = lunr.Set.empty\n        }\n\n        break\n      }\n\n      for (var j = 0; j < expandedTerms.length; j++) {\n        /*\n         * For each term get the posting and termIndex, this is required for\n         * building the query vector.\n         */\n        var expandedTerm = expandedTerms[j],\n            posting = this.invertedIndex[expandedTerm],\n            termIndex = posting._index\n\n        for (var k = 0; k < clause.fields.length; k++) {\n          /*\n           * For each field that this query term is scoped by (by default\n           * all fields are in scope) we need to get all the document refs\n           * that have this term in that field.\n           *\n           * The posting is the entry in the invertedIndex for the matching\n           * term from above.\n           */\n          var field = clause.fields[k],\n              fieldPosting = posting[field],\n              matchingDocumentRefs = Object.keys(fieldPosting),\n              termField = expandedTerm + \"/\" + field,\n              matchingDocumentsSet = new lunr.Set(matchingDocumentRefs)\n\n          /*\n           * if the presence of this term is required ensure that the matching\n           * documents are added to the set of required matches for this clause.\n           *\n           */\n          if (clause.presence == lunr.Query.presence.REQUIRED) {\n            clauseMatches = clauseMatches.union(matchingDocumentsSet)\n\n            if (requiredMatches[field] === undefined) {\n              requiredMatches[field] = lunr.Set.complete\n            }\n          }\n\n          /*\n           * if the presence of this term is prohibited ensure that the matching\n           * documents are added to the set of prohibited matches for this field,\n           * creating that set if it does not yet exist.\n           */\n          if (clause.presence == lunr.Query.presence.PROHIBITED) {\n            if (prohibitedMatches[field] === undefined) {\n              prohibitedMatches[field] = lunr.Set.empty\n            }\n\n            prohibitedMatches[field] = prohibitedMatches[field].union(matchingDocumentsSet)\n\n            /*\n             * Prohibited matches should not be part of the query vector used for\n             * similarity scoring and no metadata should be extracted so we continue\n             * to the next field\n             */\n            continue\n          }\n\n          /*\n           * The query field vector is populated using the termIndex found for\n           * the term and a unit value with the appropriate boost applied.\n           * Using upsert because there could already be an entry in the vector\n           * for the term we are working with. In that case we just add the scores\n           * together.\n           */\n          queryVectors[field].upsert(termIndex, clause.boost, function (a, b) { return a + b })\n\n          /**\n           * If we've already seen this term, field combo then we've already collected\n           * the matching documents and metadata, no need to go through all that again\n           */\n          if (termFieldCache[termField]) {\n            continue\n          }\n\n          for (var l = 0; l < matchingDocumentRefs.length; l++) {\n            /*\n             * All metadata for this term/field/document triple\n             * are then extracted and collected into an instance\n             * of lunr.MatchData ready to be returned in the query\n             * results\n             */\n            var matchingDocumentRef = matchingDocumentRefs[l],\n                matchingFieldRef = new lunr.FieldRef (matchingDocumentRef, field),\n                metadata = fieldPosting[matchingDocumentRef],\n                fieldMatch\n\n            if ((fieldMatch = matchingFields[matchingFieldRef]) === undefined) {\n              matchingFields[matchingFieldRef] = new lunr.MatchData (expandedTerm, field, metadata)\n            } else {\n              fieldMatch.add(expandedTerm, field, metadata)\n            }\n\n          }\n\n          termFieldCache[termField] = true\n        }\n      }\n    }\n\n    /**\n     * If the presence was required we need to update the requiredMatches field sets.\n     * We do this after all fields for the term have collected their matches because\n     * the clause terms presence is required in _any_ of the fields not _all_ of the\n     * fields.\n     */\n    if (clause.presence === lunr.Query.presence.REQUIRED) {\n      for (var k = 0; k < clause.fields.length; k++) {\n        var field = clause.fields[k]\n        requiredMatches[field] = requiredMatches[field].intersect(clauseMatches)\n      }\n    }\n  }\n\n  /**\n   * Need to combine the field scoped required and prohibited\n   * matching documents into a global set of required and prohibited\n   * matches\n   */\n  var allRequiredMatches = lunr.Set.complete,\n      allProhibitedMatches = lunr.Set.empty\n\n  for (var i = 0; i < this.fields.length; i++) {\n    var field = this.fields[i]\n\n    if (requiredMatches[field]) {\n      allRequiredMatches = allRequiredMatches.intersect(requiredMatches[field])\n    }\n\n    if (prohibitedMatches[field]) {\n      allProhibitedMatches = allProhibitedMatches.union(prohibitedMatches[field])\n    }\n  }\n\n  var matchingFieldRefs = Object.keys(matchingFields),\n      results = [],\n      matches = Object.create(null)\n\n  /*\n   * If the query is negated (contains only prohibited terms)\n   * we need to get _all_ fieldRefs currently existing in the\n   * index. This is only done when we know that the query is\n   * entirely prohibited terms to avoid any cost of getting all\n   * fieldRefs unnecessarily.\n   *\n   * Additionally, blank MatchData must be created to correctly\n   * populate the results.\n   */\n  if (query.isNegated()) {\n    matchingFieldRefs = Object.keys(this.fieldVectors)\n\n    for (var i = 0; i < matchingFieldRefs.length; i++) {\n      var matchingFieldRef = matchingFieldRefs[i]\n      var fieldRef = lunr.FieldRef.fromString(matchingFieldRef)\n      matchingFields[matchingFieldRef] = new lunr.MatchData\n    }\n  }\n\n  for (var i = 0; i < matchingFieldRefs.length; i++) {\n    /*\n     * Currently we have document fields that match the query, but we\n     * need to return documents. The matchData and scores are combined\n     * from multiple fields belonging to the same document.\n     *\n     * Scores are calculated by field, using the query vectors created\n     * above, and combined into a final document score using addition.\n     */\n    var fieldRef = lunr.FieldRef.fromString(matchingFieldRefs[i]),\n        docRef = fieldRef.docRef\n\n    if (!allRequiredMatches.contains(docRef)) {\n      continue\n    }\n\n    if (allProhibitedMatches.contains(docRef)) {\n      continue\n    }\n\n    var fieldVector = this.fieldVectors[fieldRef],\n        score = queryVectors[fieldRef.fieldName].similarity(fieldVector),\n        docMatch\n\n    if ((docMatch = matches[docRef]) !== undefined) {\n      docMatch.score += score\n      docMatch.matchData.combine(matchingFields[fieldRef])\n    } else {\n      var match = {\n        ref: docRef,\n        score: score,\n        matchData: matchingFields[fieldRef]\n      }\n      matches[docRef] = match\n      results.push(match)\n    }\n  }\n\n  /*\n   * Sort the results objects by score, highest first.\n   */\n  return results.sort(function (a, b) {\n    return b.score - a.score\n  })\n}\n\n/**\n * Prepares the index for JSON serialization.\n *\n * The schema for this JSON blob will be described in a\n * separate JSON schema file.\n *\n * @returns {Object}\n */\nlunr.Index.prototype.toJSON = function () {\n  var invertedIndex = Object.keys(this.invertedIndex)\n    .sort()\n    .map(function (term) {\n      return [term, this.invertedIndex[term]]\n    }, this)\n\n  var fieldVectors = Object.keys(this.fieldVectors)\n    .map(function (ref) {\n      return [ref, this.fieldVectors[ref].toJSON()]\n    }, this)\n\n  return {\n    version: lunr.version,\n    fields: this.fields,\n    fieldVectors: fieldVectors,\n    invertedIndex: invertedIndex,\n    pipeline: this.pipeline.toJSON()\n  }\n}\n\n/**\n * Loads a previously serialized lunr.Index\n *\n * @param {Object} serializedIndex - A previously serialized lunr.Index\n * @returns {lunr.Index}\n */\nlunr.Index.load = function (serializedIndex) {\n  var attrs = {},\n      fieldVectors = {},\n      serializedVectors = serializedIndex.fieldVectors,\n      invertedIndex = Object.create(null),\n      serializedInvertedIndex = serializedIndex.invertedIndex,\n      tokenSetBuilder = new lunr.TokenSet.Builder,\n      pipeline = lunr.Pipeline.load(serializedIndex.pipeline)\n\n  if (serializedIndex.version != lunr.version) {\n    lunr.utils.warn(\"Version mismatch when loading serialised index. Current version of lunr '\" + lunr.version + \"' does not match serialized index '\" + serializedIndex.version + \"'\")\n  }\n\n  for (var i = 0; i < serializedVectors.length; i++) {\n    var tuple = serializedVectors[i],\n        ref = tuple[0],\n        elements = tuple[1]\n\n    fieldVectors[ref] = new lunr.Vector(elements)\n  }\n\n  for (var i = 0; i < serializedInvertedIndex.length; i++) {\n    var tuple = serializedInvertedIndex[i],\n        term = tuple[0],\n        posting = tuple[1]\n\n    tokenSetBuilder.insert(term)\n    invertedIndex[term] = posting\n  }\n\n  tokenSetBuilder.finish()\n\n  attrs.fields = serializedIndex.fields\n\n  attrs.fieldVectors = fieldVectors\n  attrs.invertedIndex = invertedIndex\n  attrs.tokenSet = tokenSetBuilder.root\n  attrs.pipeline = pipeline\n\n  return new lunr.Index(attrs)\n}\n/*!\n * lunr.Builder\n * Copyright (C) 2020 Oliver Nightingale\n */\n\n/**\n * lunr.Builder performs indexing on a set of documents and\n * returns instances of lunr.Index ready for querying.\n *\n * All configuration of the index is done via the builder, the\n * fields to index, the document reference, the text processing\n * pipeline and document scoring parameters are all set on the\n * builder before indexing.\n *\n * @constructor\n * @property {string} _ref - Internal reference to the document reference field.\n * @property {string[]} _fields - Internal reference to the document fields to index.\n * @property {object} invertedIndex - The inverted index maps terms to document fields.\n * @property {object} documentTermFrequencies - Keeps track of document term frequencies.\n * @property {object} documentLengths - Keeps track of the length of documents added to the index.\n * @property {lunr.tokenizer} tokenizer - Function for splitting strings into tokens for indexing.\n * @property {lunr.Pipeline} pipeline - The pipeline performs text processing on tokens before indexing.\n * @property {lunr.Pipeline} searchPipeline - A pipeline for processing search terms before querying the index.\n * @property {number} documentCount - Keeps track of the total number of documents indexed.\n * @property {number} _b - A parameter to control field length normalization, setting this to 0 disabled normalization, 1 fully normalizes field lengths, the default value is 0.75.\n * @property {number} _k1 - A parameter to control how quickly an increase in term frequency results in term frequency saturation, the default value is 1.2.\n * @property {number} termIndex - A counter incremented for each unique term, used to identify a terms position in the vector space.\n * @property {array} metadataWhitelist - A list of metadata keys that have been whitelisted for entry in the index.\n */\nlunr.Builder = function () {\n  this._ref = \"id\"\n  this._fields = Object.create(null)\n  this._documents = Object.create(null)\n  this.invertedIndex = Object.create(null)\n  this.fieldTermFrequencies = {}\n  this.fieldLengths = {}\n  this.tokenizer = lunr.tokenizer\n  this.pipeline = new lunr.Pipeline\n  this.searchPipeline = new lunr.Pipeline\n  this.documentCount = 0\n  this._b = 0.75\n  this._k1 = 1.2\n  this.termIndex = 0\n  this.metadataWhitelist = []\n}\n\n/**\n * Sets the document field used as the document reference. Every document must have this field.\n * The type of this field in the document should be a string, if it is not a string it will be\n * coerced into a string by calling toString.\n *\n * The default ref is 'id'.\n *\n * The ref should _not_ be changed during indexing, it should be set before any documents are\n * added to the index. Changing it during indexing can lead to inconsistent results.\n *\n * @param {string} ref - The name of the reference field in the document.\n */\nlunr.Builder.prototype.ref = function (ref) {\n  this._ref = ref\n}\n\n/**\n * A function that is used to extract a field from a document.\n *\n * Lunr expects a field to be at the top level of a document, if however the field\n * is deeply nested within a document an extractor function can be used to extract\n * the right field for indexing.\n *\n * @callback fieldExtractor\n * @param {object} doc - The document being added to the index.\n * @returns {?(string|object|object[])} obj - The object that will be indexed for this field.\n * @example <caption>Extracting a nested field</caption>\n * function (doc) { return doc.nested.field }\n */\n\n/**\n * Adds a field to the list of document fields that will be indexed. Every document being\n * indexed should have this field. Null values for this field in indexed documents will\n * not cause errors but will limit the chance of that document being retrieved by searches.\n *\n * All fields should be added before adding documents to the index. Adding fields after\n * a document has been indexed will have no effect on already indexed documents.\n *\n * Fields can be boosted at build time. This allows terms within that field to have more\n * importance when ranking search results. Use a field boost to specify that matches within\n * one field are more important than other fields.\n *\n * @param {string} fieldName - The name of a field to index in all documents.\n * @param {object} attributes - Optional attributes associated with this field.\n * @param {number} [attributes.boost=1] - Boost applied to all terms within this field.\n * @param {fieldExtractor} [attributes.extractor] - Function to extract a field from a document.\n * @throws {RangeError} fieldName cannot contain unsupported characters '/'\n */\nlunr.Builder.prototype.field = function (fieldName, attributes) {\n  if (/\\//.test(fieldName)) {\n    throw new RangeError (\"Field '\" + fieldName + \"' contains illegal character '/'\")\n  }\n\n  this._fields[fieldName] = attributes || {}\n}\n\n/**\n * A parameter to tune the amount of field length normalisation that is applied when\n * calculating relevance scores. A value of 0 will completely disable any normalisation\n * and a value of 1 will fully normalise field lengths. The default is 0.75. Values of b\n * will be clamped to the range 0 - 1.\n *\n * @param {number} number - The value to set for this tuning parameter.\n */\nlunr.Builder.prototype.b = function (number) {\n  if (number < 0) {\n    this._b = 0\n  } else if (number > 1) {\n    this._b = 1\n  } else {\n    this._b = number\n  }\n}\n\n/**\n * A parameter that controls the speed at which a rise in term frequency results in term\n * frequency saturation. The default value is 1.2. Setting this to a higher value will give\n * slower saturation levels, a lower value will result in quicker saturation.\n *\n * @param {number} number - The value to set for this tuning parameter.\n */\nlunr.Builder.prototype.k1 = function (number) {\n  this._k1 = number\n}\n\n/**\n * Adds a document to the index.\n *\n * Before adding fields to the index the index should have been fully setup, with the document\n * ref and all fields to index already having been specified.\n *\n * The document must have a field name as specified by the ref (by default this is 'id') and\n * it should have all fields defined for indexing, though null or undefined values will not\n * cause errors.\n *\n * Entire documents can be boosted at build time. Applying a boost to a document indicates that\n * this document should rank higher in search results than other documents.\n *\n * @param {object} doc - The document to add to the index.\n * @param {object} attributes - Optional attributes associated with this document.\n * @param {number} [attributes.boost=1] - Boost applied to all terms within this document.\n */\nlunr.Builder.prototype.add = function (doc, attributes) {\n  var docRef = doc[this._ref],\n      fields = Object.keys(this._fields)\n\n  this._documents[docRef] = attributes || {}\n  this.documentCount += 1\n\n  for (var i = 0; i < fields.length; i++) {\n    var fieldName = fields[i],\n        extractor = this._fields[fieldName].extractor,\n        field = extractor ? extractor(doc) : doc[fieldName],\n        tokens = this.tokenizer(field, {\n          fields: [fieldName]\n        }),\n        terms = this.pipeline.run(tokens),\n        fieldRef = new lunr.FieldRef (docRef, fieldName),\n        fieldTerms = Object.create(null)\n\n    this.fieldTermFrequencies[fieldRef] = fieldTerms\n    this.fieldLengths[fieldRef] = 0\n\n    // store the length of this field for this document\n    this.fieldLengths[fieldRef] += terms.length\n\n    // calculate term frequencies for this field\n    for (var j = 0; j < terms.length; j++) {\n      var term = terms[j]\n\n      if (fieldTerms[term] == undefined) {\n        fieldTerms[term] = 0\n      }\n\n      fieldTerms[term] += 1\n\n      // add to inverted index\n      // create an initial posting if one doesn't exist\n      if (this.invertedIndex[term] == undefined) {\n        var posting = Object.create(null)\n        posting[\"_index\"] = this.termIndex\n        this.termIndex += 1\n\n        for (var k = 0; k < fields.length; k++) {\n          posting[fields[k]] = Object.create(null)\n        }\n\n        this.invertedIndex[term] = posting\n      }\n\n      // add an entry for this term/fieldName/docRef to the invertedIndex\n      if (this.invertedIndex[term][fieldName][docRef] == undefined) {\n        this.invertedIndex[term][fieldName][docRef] = Object.create(null)\n      }\n\n      // store all whitelisted metadata about this token in the\n      // inverted index\n      for (var l = 0; l < this.metadataWhitelist.length; l++) {\n        var metadataKey = this.metadataWhitelist[l],\n            metadata = term.metadata[metadataKey]\n\n        if (this.invertedIndex[term][fieldName][docRef][metadataKey] == undefined) {\n          this.invertedIndex[term][fieldName][docRef][metadataKey] = []\n        }\n\n        this.invertedIndex[term][fieldName][docRef][metadataKey].push(metadata)\n      }\n    }\n\n  }\n}\n\n/**\n * Calculates the average document length for this index\n *\n * @private\n */\nlunr.Builder.prototype.calculateAverageFieldLengths = function () {\n\n  var fieldRefs = Object.keys(this.fieldLengths),\n      numberOfFields = fieldRefs.length,\n      accumulator = {},\n      documentsWithField = {}\n\n  for (var i = 0; i < numberOfFields; i++) {\n    var fieldRef = lunr.FieldRef.fromString(fieldRefs[i]),\n        field = fieldRef.fieldName\n\n    documentsWithField[field] || (documentsWithField[field] = 0)\n    documentsWithField[field] += 1\n\n    accumulator[field] || (accumulator[field] = 0)\n    accumulator[field] += this.fieldLengths[fieldRef]\n  }\n\n  var fields = Object.keys(this._fields)\n\n  for (var i = 0; i < fields.length; i++) {\n    var fieldName = fields[i]\n    accumulator[fieldName] = accumulator[fieldName] / documentsWithField[fieldName]\n  }\n\n  this.averageFieldLength = accumulator\n}\n\n/**\n * Builds a vector space model of every document using lunr.Vector\n *\n * @private\n */\nlunr.Builder.prototype.createFieldVectors = function () {\n  var fieldVectors = {},\n      fieldRefs = Object.keys(this.fieldTermFrequencies),\n      fieldRefsLength = fieldRefs.length,\n      termIdfCache = Object.create(null)\n\n  for (var i = 0; i < fieldRefsLength; i++) {\n    var fieldRef = lunr.FieldRef.fromString(fieldRefs[i]),\n        fieldName = fieldRef.fieldName,\n        fieldLength = this.fieldLengths[fieldRef],\n        fieldVector = new lunr.Vector,\n        termFrequencies = this.fieldTermFrequencies[fieldRef],\n        terms = Object.keys(termFrequencies),\n        termsLength = terms.length\n\n\n    var fieldBoost = this._fields[fieldName].boost || 1,\n        docBoost = this._documents[fieldRef.docRef].boost || 1\n\n    for (var j = 0; j < termsLength; j++) {\n      var term = terms[j],\n          tf = termFrequencies[term],\n          termIndex = this.invertedIndex[term]._index,\n          idf, score, scoreWithPrecision\n\n      if (termIdfCache[term] === undefined) {\n        idf = lunr.idf(this.invertedIndex[term], this.documentCount)\n        termIdfCache[term] = idf\n      } else {\n        idf = termIdfCache[term]\n      }\n\n      score = idf * ((this._k1 + 1) * tf) / (this._k1 * (1 - this._b + this._b * (fieldLength / this.averageFieldLength[fieldName])) + tf)\n      score *= fieldBoost\n      score *= docBoost\n      scoreWithPrecision = Math.round(score * 1000) / 1000\n      // Converts 1.23456789 to 1.234.\n      // Reducing the precision so that the vectors take up less\n      // space when serialised. Doing it now so that they behave\n      // the same before and after serialisation. Also, this is\n      // the fastest approach to reducing a number's precision in\n      // JavaScript.\n\n      fieldVector.insert(termIndex, scoreWithPrecision)\n    }\n\n    fieldVectors[fieldRef] = fieldVector\n  }\n\n  this.fieldVectors = fieldVectors\n}\n\n/**\n * Creates a token set of all tokens in the index using lunr.TokenSet\n *\n * @private\n */\nlunr.Builder.prototype.createTokenSet = function () {\n  this.tokenSet = lunr.TokenSet.fromArray(\n    Object.keys(this.invertedIndex).sort()\n  )\n}\n\n/**\n * Builds the index, creating an instance of lunr.Index.\n *\n * This completes the indexing process and should only be called\n * once all documents have been added to the index.\n *\n * @returns {lunr.Index}\n */\nlunr.Builder.prototype.build = function () {\n  this.calculateAverageFieldLengths()\n  this.createFieldVectors()\n  this.createTokenSet()\n\n  return new lunr.Index({\n    invertedIndex: this.invertedIndex,\n    fieldVectors: this.fieldVectors,\n    tokenSet: this.tokenSet,\n    fields: Object.keys(this._fields),\n    pipeline: this.searchPipeline\n  })\n}\n\n/**\n * Applies a plugin to the index builder.\n *\n * A plugin is a function that is called with the index builder as its context.\n * Plugins can be used to customise or extend the behaviour of the index\n * in some way. A plugin is just a function, that encapsulated the custom\n * behaviour that should be applied when building the index.\n *\n * The plugin function will be called with the index builder as its argument, additional\n * arguments can also be passed when calling use. The function will be called\n * with the index builder as its context.\n *\n * @param {Function} plugin The plugin to apply.\n */\nlunr.Builder.prototype.use = function (fn) {\n  var args = Array.prototype.slice.call(arguments, 1)\n  args.unshift(this)\n  fn.apply(this, args)\n}\n/**\n * Contains and collects metadata about a matching document.\n * A single instance of lunr.MatchData is returned as part of every\n * lunr.Index~Result.\n *\n * @constructor\n * @param {string} term - The term this match data is associated with\n * @param {string} field - The field in which the term was found\n * @param {object} metadata - The metadata recorded about this term in this field\n * @property {object} metadata - A cloned collection of metadata associated with this document.\n * @see {@link lunr.Index~Result}\n */\nlunr.MatchData = function (term, field, metadata) {\n  var clonedMetadata = Object.create(null),\n      metadataKeys = Object.keys(metadata || {})\n\n  // Cloning the metadata to prevent the original\n  // being mutated during match data combination.\n  // Metadata is kept in an array within the inverted\n  // index so cloning the data can be done with\n  // Array#slice\n  for (var i = 0; i < metadataKeys.length; i++) {\n    var key = metadataKeys[i]\n    clonedMetadata[key] = metadata[key].slice()\n  }\n\n  this.metadata = Object.create(null)\n\n  if (term !== undefined) {\n    this.metadata[term] = Object.create(null)\n    this.metadata[term][field] = clonedMetadata\n  }\n}\n\n/**\n * An instance of lunr.MatchData will be created for every term that matches a\n * document. However only one instance is required in a lunr.Index~Result. This\n * method combines metadata from another instance of lunr.MatchData with this\n * objects metadata.\n *\n * @param {lunr.MatchData} otherMatchData - Another instance of match data to merge with this one.\n * @see {@link lunr.Index~Result}\n */\nlunr.MatchData.prototype.combine = function (otherMatchData) {\n  var terms = Object.keys(otherMatchData.metadata)\n\n  for (var i = 0; i < terms.length; i++) {\n    var term = terms[i],\n        fields = Object.keys(otherMatchData.metadata[term])\n\n    if (this.metadata[term] == undefined) {\n      this.metadata[term] = Object.create(null)\n    }\n\n    for (var j = 0; j < fields.length; j++) {\n      var field = fields[j],\n          keys = Object.keys(otherMatchData.metadata[term][field])\n\n      if (this.metadata[term][field] == undefined) {\n        this.metadata[term][field] = Object.create(null)\n      }\n\n      for (var k = 0; k < keys.length; k++) {\n        var key = keys[k]\n\n        if (this.metadata[term][field][key] == undefined) {\n          this.metadata[term][field][key] = otherMatchData.metadata[term][field][key]\n        } else {\n          this.metadata[term][field][key] = this.metadata[term][field][key].concat(otherMatchData.metadata[term][field][key])\n        }\n\n      }\n    }\n  }\n}\n\n/**\n * Add metadata for a term/field pair to this instance of match data.\n *\n * @param {string} term - The term this match data is associated with\n * @param {string} field - The field in which the term was found\n * @param {object} metadata - The metadata recorded about this term in this field\n */\nlunr.MatchData.prototype.add = function (term, field, metadata) {\n  if (!(term in this.metadata)) {\n    this.metadata[term] = Object.create(null)\n    this.metadata[term][field] = metadata\n    return\n  }\n\n  if (!(field in this.metadata[term])) {\n    this.metadata[term][field] = metadata\n    return\n  }\n\n  var metadataKeys = Object.keys(metadata)\n\n  for (var i = 0; i < metadataKeys.length; i++) {\n    var key = metadataKeys[i]\n\n    if (key in this.metadata[term][field]) {\n      this.metadata[term][field][key] = this.metadata[term][field][key].concat(metadata[key])\n    } else {\n      this.metadata[term][field][key] = metadata[key]\n    }\n  }\n}\n/**\n * A lunr.Query provides a programmatic way of defining queries to be performed\n * against a {@link lunr.Index}.\n *\n * Prefer constructing a lunr.Query using the {@link lunr.Index#query} method\n * so the query object is pre-initialized with the right index fields.\n *\n * @constructor\n * @property {lunr.Query~Clause[]} clauses - An array of query clauses.\n * @property {string[]} allFields - An array of all available fields in a lunr.Index.\n */\nlunr.Query = function (allFields) {\n  this.clauses = []\n  this.allFields = allFields\n}\n\n/**\n * Constants for indicating what kind of automatic wildcard insertion will be used when constructing a query clause.\n *\n * This allows wildcards to be added to the beginning and end of a term without having to manually do any string\n * concatenation.\n *\n * The wildcard constants can be bitwise combined to select both leading and trailing wildcards.\n *\n * @constant\n * @default\n * @property {number} wildcard.NONE - The term will have no wildcards inserted, this is the default behaviour\n * @property {number} wildcard.LEADING - Prepend the term with a wildcard, unless a leading wildcard already exists\n * @property {number} wildcard.TRAILING - Append a wildcard to the term, unless a trailing wildcard already exists\n * @see lunr.Query~Clause\n * @see lunr.Query#clause\n * @see lunr.Query#term\n * @example <caption>query term with trailing wildcard</caption>\n * query.term('foo', { wildcard: lunr.Query.wildcard.TRAILING })\n * @example <caption>query term with leading and trailing wildcard</caption>\n * query.term('foo', {\n *   wildcard: lunr.Query.wildcard.LEADING | lunr.Query.wildcard.TRAILING\n * })\n */\n\nlunr.Query.wildcard = new String (\"*\")\nlunr.Query.wildcard.NONE = 0\nlunr.Query.wildcard.LEADING = 1\nlunr.Query.wildcard.TRAILING = 2\n\n/**\n * Constants for indicating what kind of presence a term must have in matching documents.\n *\n * @constant\n * @enum {number}\n * @see lunr.Query~Clause\n * @see lunr.Query#clause\n * @see lunr.Query#term\n * @example <caption>query term with required presence</caption>\n * query.term('foo', { presence: lunr.Query.presence.REQUIRED })\n */\nlunr.Query.presence = {\n  /**\n   * Term's presence in a document is optional, this is the default value.\n   */\n  OPTIONAL: 1,\n\n  /**\n   * Term's presence in a document is required, documents that do not contain\n   * this term will not be returned.\n   */\n  REQUIRED: 2,\n\n  /**\n   * Term's presence in a document is prohibited, documents that do contain\n   * this term will not be returned.\n   */\n  PROHIBITED: 3\n}\n\n/**\n * A single clause in a {@link lunr.Query} contains a term and details on how to\n * match that term against a {@link lunr.Index}.\n *\n * @typedef {Object} lunr.Query~Clause\n * @property {string[]} fields - The fields in an index this clause should be matched against.\n * @property {number} [boost=1] - Any boost that should be applied when matching this clause.\n * @property {number} [editDistance] - Whether the term should have fuzzy matching applied, and how fuzzy the match should be.\n * @property {boolean} [usePipeline] - Whether the term should be passed through the search pipeline.\n * @property {number} [wildcard=lunr.Query.wildcard.NONE] - Whether the term should have wildcards appended or prepended.\n * @property {number} [presence=lunr.Query.presence.OPTIONAL] - The terms presence in any matching documents.\n */\n\n/**\n * Adds a {@link lunr.Query~Clause} to this query.\n *\n * Unless the clause contains the fields to be matched all fields will be matched. In addition\n * a default boost of 1 is applied to the clause.\n *\n * @param {lunr.Query~Clause} clause - The clause to add to this query.\n * @see lunr.Query~Clause\n * @returns {lunr.Query}\n */\nlunr.Query.prototype.clause = function (clause) {\n  if (!('fields' in clause)) {\n    clause.fields = this.allFields\n  }\n\n  if (!('boost' in clause)) {\n    clause.boost = 1\n  }\n\n  if (!('usePipeline' in clause)) {\n    clause.usePipeline = true\n  }\n\n  if (!('wildcard' in clause)) {\n    clause.wildcard = lunr.Query.wildcard.NONE\n  }\n\n  if ((clause.wildcard & lunr.Query.wildcard.LEADING) && (clause.term.charAt(0) != lunr.Query.wildcard)) {\n    clause.term = \"*\" + clause.term\n  }\n\n  if ((clause.wildcard & lunr.Query.wildcard.TRAILING) && (clause.term.slice(-1) != lunr.Query.wildcard)) {\n    clause.term = \"\" + clause.term + \"*\"\n  }\n\n  if (!('presence' in clause)) {\n    clause.presence = lunr.Query.presence.OPTIONAL\n  }\n\n  this.clauses.push(clause)\n\n  return this\n}\n\n/**\n * A negated query is one in which every clause has a presence of\n * prohibited. These queries require some special processing to return\n * the expected results.\n *\n * @returns boolean\n */\nlunr.Query.prototype.isNegated = function () {\n  for (var i = 0; i < this.clauses.length; i++) {\n    if (this.clauses[i].presence != lunr.Query.presence.PROHIBITED) {\n      return false\n    }\n  }\n\n  return true\n}\n\n/**\n * Adds a term to the current query, under the covers this will create a {@link lunr.Query~Clause}\n * to the list of clauses that make up this query.\n *\n * The term is used as is, i.e. no tokenization will be performed by this method. Instead conversion\n * to a token or token-like string should be done before calling this method.\n *\n * The term will be converted to a string by calling `toString`. Multiple terms can be passed as an\n * array, each term in the array will share the same options.\n *\n * @param {object|object[]} term - The term(s) to add to the query.\n * @param {object} [options] - Any additional properties to add to the query clause.\n * @returns {lunr.Query}\n * @see lunr.Query#clause\n * @see lunr.Query~Clause\n * @example <caption>adding a single term to a query</caption>\n * query.term(\"foo\")\n * @example <caption>adding a single term to a query and specifying search fields, term boost and automatic trailing wildcard</caption>\n * query.term(\"foo\", {\n *   fields: [\"title\"],\n *   boost: 10,\n *   wildcard: lunr.Query.wildcard.TRAILING\n * })\n * @example <caption>using lunr.tokenizer to convert a string to tokens before using them as terms</caption>\n * query.term(lunr.tokenizer(\"foo bar\"))\n */\nlunr.Query.prototype.term = function (term, options) {\n  if (Array.isArray(term)) {\n    term.forEach(function (t) { this.term(t, lunr.utils.clone(options)) }, this)\n    return this\n  }\n\n  var clause = options || {}\n  clause.term = term.toString()\n\n  this.clause(clause)\n\n  return this\n}\nlunr.QueryParseError = function (message, start, end) {\n  this.name = \"QueryParseError\"\n  this.message = message\n  this.start = start\n  this.end = end\n}\n\nlunr.QueryParseError.prototype = new Error\nlunr.QueryLexer = function (str) {\n  this.lexemes = []\n  this.str = str\n  this.length = str.length\n  this.pos = 0\n  this.start = 0\n  this.escapeCharPositions = []\n}\n\nlunr.QueryLexer.prototype.run = function () {\n  var state = lunr.QueryLexer.lexText\n\n  while (state) {\n    state = state(this)\n  }\n}\n\nlunr.QueryLexer.prototype.sliceString = function () {\n  var subSlices = [],\n      sliceStart = this.start,\n      sliceEnd = this.pos\n\n  for (var i = 0; i < this.escapeCharPositions.length; i++) {\n    sliceEnd = this.escapeCharPositions[i]\n    subSlices.push(this.str.slice(sliceStart, sliceEnd))\n    sliceStart = sliceEnd + 1\n  }\n\n  subSlices.push(this.str.slice(sliceStart, this.pos))\n  this.escapeCharPositions.length = 0\n\n  return subSlices.join('')\n}\n\nlunr.QueryLexer.prototype.emit = function (type) {\n  this.lexemes.push({\n    type: type,\n    str: this.sliceString(),\n    start: this.start,\n    end: this.pos\n  })\n\n  this.start = this.pos\n}\n\nlunr.QueryLexer.prototype.escapeCharacter = function () {\n  this.escapeCharPositions.push(this.pos - 1)\n  this.pos += 1\n}\n\nlunr.QueryLexer.prototype.next = function () {\n  if (this.pos >= this.length) {\n    return lunr.QueryLexer.EOS\n  }\n\n  var char = this.str.charAt(this.pos)\n  this.pos += 1\n  return char\n}\n\nlunr.QueryLexer.prototype.width = function () {\n  return this.pos - this.start\n}\n\nlunr.QueryLexer.prototype.ignore = function () {\n  if (this.start == this.pos) {\n    this.pos += 1\n  }\n\n  this.start = this.pos\n}\n\nlunr.QueryLexer.prototype.backup = function () {\n  this.pos -= 1\n}\n\nlunr.QueryLexer.prototype.acceptDigitRun = function () {\n  var char, charCode\n\n  do {\n    char = this.next()\n    charCode = char.charCodeAt(0)\n  } while (charCode > 47 && charCode < 58)\n\n  if (char != lunr.QueryLexer.EOS) {\n    this.backup()\n  }\n}\n\nlunr.QueryLexer.prototype.more = function () {\n  return this.pos < this.length\n}\n\nlunr.QueryLexer.EOS = 'EOS'\nlunr.QueryLexer.FIELD = 'FIELD'\nlunr.QueryLexer.TERM = 'TERM'\nlunr.QueryLexer.EDIT_DISTANCE = 'EDIT_DISTANCE'\nlunr.QueryLexer.BOOST = 'BOOST'\nlunr.QueryLexer.PRESENCE = 'PRESENCE'\n\nlunr.QueryLexer.lexField = function (lexer) {\n  lexer.backup()\n  lexer.emit(lunr.QueryLexer.FIELD)\n  lexer.ignore()\n  return lunr.QueryLexer.lexText\n}\n\nlunr.QueryLexer.lexTerm = function (lexer) {\n  if (lexer.width() > 1) {\n    lexer.backup()\n    lexer.emit(lunr.QueryLexer.TERM)\n  }\n\n  lexer.ignore()\n\n  if (lexer.more()) {\n    return lunr.QueryLexer.lexText\n  }\n}\n\nlunr.QueryLexer.lexEditDistance = function (lexer) {\n  lexer.ignore()\n  lexer.acceptDigitRun()\n  lexer.emit(lunr.QueryLexer.EDIT_DISTANCE)\n  return lunr.QueryLexer.lexText\n}\n\nlunr.QueryLexer.lexBoost = function (lexer) {\n  lexer.ignore()\n  lexer.acceptDigitRun()\n  lexer.emit(lunr.QueryLexer.BOOST)\n  return lunr.QueryLexer.lexText\n}\n\nlunr.QueryLexer.lexEOS = function (lexer) {\n  if (lexer.width() > 0) {\n    lexer.emit(lunr.QueryLexer.TERM)\n  }\n}\n\n// This matches the separator used when tokenising fields\n// within a document. These should match otherwise it is\n// not possible to search for some tokens within a document.\n//\n// It is possible for the user to change the separator on the\n// tokenizer so it _might_ clash with any other of the special\n// characters already used within the search string, e.g. :.\n//\n// This means that it is possible to change the separator in\n// such a way that makes some words unsearchable using a search\n// string.\nlunr.QueryLexer.termSeparator = lunr.tokenizer.separator\n\nlunr.QueryLexer.lexText = function (lexer) {\n  while (true) {\n    var char = lexer.next()\n\n    if (char == lunr.QueryLexer.EOS) {\n      return lunr.QueryLexer.lexEOS\n    }\n\n    // Escape character is '\\'\n    if (char.charCodeAt(0) == 92) {\n      lexer.escapeCharacter()\n      continue\n    }\n\n    if (char == \":\") {\n      return lunr.QueryLexer.lexField\n    }\n\n    if (char == \"~\") {\n      lexer.backup()\n      if (lexer.width() > 0) {\n        lexer.emit(lunr.QueryLexer.TERM)\n      }\n      return lunr.QueryLexer.lexEditDistance\n    }\n\n    if (char == \"^\") {\n      lexer.backup()\n      if (lexer.width() > 0) {\n        lexer.emit(lunr.QueryLexer.TERM)\n      }\n      return lunr.QueryLexer.lexBoost\n    }\n\n    // \"+\" indicates term presence is required\n    // checking for length to ensure that only\n    // leading \"+\" are considered\n    if (char == \"+\" && lexer.width() === 1) {\n      lexer.emit(lunr.QueryLexer.PRESENCE)\n      return lunr.QueryLexer.lexText\n    }\n\n    // \"-\" indicates term presence is prohibited\n    // checking for length to ensure that only\n    // leading \"-\" are considered\n    if (char == \"-\" && lexer.width() === 1) {\n      lexer.emit(lunr.QueryLexer.PRESENCE)\n      return lunr.QueryLexer.lexText\n    }\n\n    if (char.match(lunr.QueryLexer.termSeparator)) {\n      return lunr.QueryLexer.lexTerm\n    }\n  }\n}\n\nlunr.QueryParser = function (str, query) {\n  this.lexer = new lunr.QueryLexer (str)\n  this.query = query\n  this.currentClause = {}\n  this.lexemeIdx = 0\n}\n\nlunr.QueryParser.prototype.parse = function () {\n  this.lexer.run()\n  this.lexemes = this.lexer.lexemes\n\n  var state = lunr.QueryParser.parseClause\n\n  while (state) {\n    state = state(this)\n  }\n\n  return this.query\n}\n\nlunr.QueryParser.prototype.peekLexeme = function () {\n  return this.lexemes[this.lexemeIdx]\n}\n\nlunr.QueryParser.prototype.consumeLexeme = function () {\n  var lexeme = this.peekLexeme()\n  this.lexemeIdx += 1\n  return lexeme\n}\n\nlunr.QueryParser.prototype.nextClause = function () {\n  var completedClause = this.currentClause\n  this.query.clause(completedClause)\n  this.currentClause = {}\n}\n\nlunr.QueryParser.parseClause = function (parser) {\n  var lexeme = parser.peekLexeme()\n\n  if (lexeme == undefined) {\n    return\n  }\n\n  switch (lexeme.type) {\n    case lunr.QueryLexer.PRESENCE:\n      return lunr.QueryParser.parsePresence\n    case lunr.QueryLexer.FIELD:\n      return lunr.QueryParser.parseField\n    case lunr.QueryLexer.TERM:\n      return lunr.QueryParser.parseTerm\n    default:\n      var errorMessage = \"expected either a field or a term, found \" + lexeme.type\n\n      if (lexeme.str.length >= 1) {\n        errorMessage += \" with value '\" + lexeme.str + \"'\"\n      }\n\n      throw new lunr.QueryParseError (errorMessage, lexeme.start, lexeme.end)\n  }\n}\n\nlunr.QueryParser.parsePresence = function (parser) {\n  var lexeme = parser.consumeLexeme()\n\n  if (lexeme == undefined) {\n    return\n  }\n\n  switch (lexeme.str) {\n    case \"-\":\n      parser.currentClause.presence = lunr.Query.presence.PROHIBITED\n      break\n    case \"+\":\n      parser.currentClause.presence = lunr.Query.presence.REQUIRED\n      break\n    default:\n      var errorMessage = \"unrecognised presence operator'\" + lexeme.str + \"'\"\n      throw new lunr.QueryParseError (errorMessage, lexeme.start, lexeme.end)\n  }\n\n  var nextLexeme = parser.peekLexeme()\n\n  if (nextLexeme == undefined) {\n    var errorMessage = \"expecting term or field, found nothing\"\n    throw new lunr.QueryParseError (errorMessage, lexeme.start, lexeme.end)\n  }\n\n  switch (nextLexeme.type) {\n    case lunr.QueryLexer.FIELD:\n      return lunr.QueryParser.parseField\n    case lunr.QueryLexer.TERM:\n      return lunr.QueryParser.parseTerm\n    default:\n      var errorMessage = \"expecting term or field, found '\" + nextLexeme.type + \"'\"\n      throw new lunr.QueryParseError (errorMessage, nextLexeme.start, nextLexeme.end)\n  }\n}\n\nlunr.QueryParser.parseField = function (parser) {\n  var lexeme = parser.consumeLexeme()\n\n  if (lexeme == undefined) {\n    return\n  }\n\n  if (parser.query.allFields.indexOf(lexeme.str) == -1) {\n    var possibleFields = parser.query.allFields.map(function (f) { return \"'\" + f + \"'\" }).join(', '),\n        errorMessage = \"unrecognised field '\" + lexeme.str + \"', possible fields: \" + possibleFields\n\n    throw new lunr.QueryParseError (errorMessage, lexeme.start, lexeme.end)\n  }\n\n  parser.currentClause.fields = [lexeme.str]\n\n  var nextLexeme = parser.peekLexeme()\n\n  if (nextLexeme == undefined) {\n    var errorMessage = \"expecting term, found nothing\"\n    throw new lunr.QueryParseError (errorMessage, lexeme.start, lexeme.end)\n  }\n\n  switch (nextLexeme.type) {\n    case lunr.QueryLexer.TERM:\n      return lunr.QueryParser.parseTerm\n    default:\n      var errorMessage = \"expecting term, found '\" + nextLexeme.type + \"'\"\n      throw new lunr.QueryParseError (errorMessage, nextLexeme.start, nextLexeme.end)\n  }\n}\n\nlunr.QueryParser.parseTerm = function (parser) {\n  var lexeme = parser.consumeLexeme()\n\n  if (lexeme == undefined) {\n    return\n  }\n\n  parser.currentClause.term = lexeme.str.toLowerCase()\n\n  if (lexeme.str.indexOf(\"*\") != -1) {\n    parser.currentClause.usePipeline = false\n  }\n\n  var nextLexeme = parser.peekLexeme()\n\n  if (nextLexeme == undefined) {\n    parser.nextClause()\n    return\n  }\n\n  switch (nextLexeme.type) {\n    case lunr.QueryLexer.TERM:\n      parser.nextClause()\n      return lunr.QueryParser.parseTerm\n    case lunr.QueryLexer.FIELD:\n      parser.nextClause()\n      return lunr.QueryParser.parseField\n    case lunr.QueryLexer.EDIT_DISTANCE:\n      return lunr.QueryParser.parseEditDistance\n    case lunr.QueryLexer.BOOST:\n      return lunr.QueryParser.parseBoost\n    case lunr.QueryLexer.PRESENCE:\n      parser.nextClause()\n      return lunr.QueryParser.parsePresence\n    default:\n      var errorMessage = \"Unexpected lexeme type '\" + nextLexeme.type + \"'\"\n      throw new lunr.QueryParseError (errorMessage, nextLexeme.start, nextLexeme.end)\n  }\n}\n\nlunr.QueryParser.parseEditDistance = function (parser) {\n  var lexeme = parser.consumeLexeme()\n\n  if (lexeme == undefined) {\n    return\n  }\n\n  var editDistance = parseInt(lexeme.str, 10)\n\n  if (isNaN(editDistance)) {\n    var errorMessage = \"edit distance must be numeric\"\n    throw new lunr.QueryParseError (errorMessage, lexeme.start, lexeme.end)\n  }\n\n  parser.currentClause.editDistance = editDistance\n\n  var nextLexeme = parser.peekLexeme()\n\n  if (nextLexeme == undefined) {\n    parser.nextClause()\n    return\n  }\n\n  switch (nextLexeme.type) {\n    case lunr.QueryLexer.TERM:\n      parser.nextClause()\n      return lunr.QueryParser.parseTerm\n    case lunr.QueryLexer.FIELD:\n      parser.nextClause()\n      return lunr.QueryParser.parseField\n    case lunr.QueryLexer.EDIT_DISTANCE:\n      return lunr.QueryParser.parseEditDistance\n    case lunr.QueryLexer.BOOST:\n      return lunr.QueryParser.parseBoost\n    case lunr.QueryLexer.PRESENCE:\n      parser.nextClause()\n      return lunr.QueryParser.parsePresence\n    default:\n      var errorMessage = \"Unexpected lexeme type '\" + nextLexeme.type + \"'\"\n      throw new lunr.QueryParseError (errorMessage, nextLexeme.start, nextLexeme.end)\n  }\n}\n\nlunr.QueryParser.parseBoost = function (parser) {\n  var lexeme = parser.consumeLexeme()\n\n  if (lexeme == undefined) {\n    return\n  }\n\n  var boost = parseInt(lexeme.str, 10)\n\n  if (isNaN(boost)) {\n    var errorMessage = \"boost must be numeric\"\n    throw new lunr.QueryParseError (errorMessage, lexeme.start, lexeme.end)\n  }\n\n  parser.currentClause.boost = boost\n\n  var nextLexeme = parser.peekLexeme()\n\n  if (nextLexeme == undefined) {\n    parser.nextClause()\n    return\n  }\n\n  switch (nextLexeme.type) {\n    case lunr.QueryLexer.TERM:\n      parser.nextClause()\n      return lunr.QueryParser.parseTerm\n    case lunr.QueryLexer.FIELD:\n      parser.nextClause()\n      return lunr.QueryParser.parseField\n    case lunr.QueryLexer.EDIT_DISTANCE:\n      return lunr.QueryParser.parseEditDistance\n    case lunr.QueryLexer.BOOST:\n      return lunr.QueryParser.parseBoost\n    case lunr.QueryLexer.PRESENCE:\n      parser.nextClause()\n      return lunr.QueryParser.parsePresence\n    default:\n      var errorMessage = \"Unexpected lexeme type '\" + nextLexeme.type + \"'\"\n      throw new lunr.QueryParseError (errorMessage, nextLexeme.start, nextLexeme.end)\n  }\n}\n\n  /**\n   * export the module via AMD, CommonJS or as a browser global\n   * Export code from https://github.com/umdjs/umd/blob/master/returnExports.js\n   */\n  ;(function (root, factory) {\n    if (typeof define === 'function' && define.amd) {\n      // AMD. Register as an anonymous module.\n      define(factory)\n    } else if (typeof exports === 'object') {\n      /**\n       * Node. Does not work with strict CommonJS, but\n       * only CommonJS-like enviroments that support module.exports,\n       * like Node.\n       */\n      module.exports = factory()\n    } else {\n      // Browser globals (root is window)\n      root.lunr = factory()\n    }\n  }(this, function () {\n    /**\n     * Just return a value to define the module export.\n     * This example returns an object, but the module\n     * can return a function as the exported value.\n     */\n    return lunr\n  }))\n})();\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A RTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport lunr from \"lunr\"\n\nimport { getElement } from \"~/browser/element/_\"\nimport \"~/polyfills\"\n\nimport { Search } from \"../../_\"\nimport { SearchConfig } from \"../../config\"\nimport {\n  SearchMessage,\n  SearchMessageType\n} from \"../message\"\n\n/* ----------------------------------------------------------------------------\n * Types\n * ------------------------------------------------------------------------- */\n\n/**\n * Add support for `iframe-worker` shim\n *\n * While `importScripts` is synchronous when executed inside of a web worker,\n * it's not possible to provide a synchronous shim implementation. The cool\n * thing is that awaiting a non-Promise will convert it into a Promise, so\n * extending the type definition to return a `Promise` shouldn't break anything.\n *\n * @see https://bit.ly/2PjDnXi - GitHub comment\n *\n * @param urls - Scripts to load\n *\n * @returns Promise resolving with no result\n */\ndeclare global {\n  function importScripts(...urls: string[]): Promise<void> | void\n}\n\n/* ----------------------------------------------------------------------------\n * Data\n * ------------------------------------------------------------------------- */\n\n/**\n * Search index\n */\nlet index: Search\n\n/* ----------------------------------------------------------------------------\n * Helper functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Fetch (= import) multi-language support through `lunr-languages`\n *\n * This function automatically imports the stemmers necessary to process the\n * languages which are defined as part of the search configuration.\n *\n * If the worker runs inside of an `iframe` (when using `iframe-worker` as\n * a shim), the base URL for the stemmers to be loaded must be determined by\n * searching for the first `script` element with a `src` attribute, which will\n * contain the contents of this script.\n *\n * @param config - Search configuration\n *\n * @returns Promise resolving with no result\n */\nasync function setupSearchLanguages(\n  config: SearchConfig\n): Promise<void> {\n  let base = \"../lunr\"\n\n  /* Detect `iframe-worker` and fix base URL */\n  if (typeof parent !== \"undefined\" && \"IFrameWorker\" in parent) {\n    const worker = getElement<HTMLScriptElement>(\"script[src]\")!\n    const [path] = worker.src.split(\"/worker\")\n\n    /* Prefix base with path */\n    base = base.replace(\"..\", path)\n  }\n\n  /* Add scripts for languages */\n  const scripts = []\n  for (const lang of config.lang) {\n    switch (lang) {\n\n      /* Add segmenter for Japanese */\n      case \"ja\":\n        scripts.push(`${base}/tinyseg.js`)\n        break\n\n      /* Add segmenter for Hindi and Thai */\n      case \"hi\":\n      case \"th\":\n        scripts.push(`${base}/wordcut.js`)\n        break\n    }\n\n    /* Add language support */\n    if (lang !== \"en\")\n      scripts.push(`${base}/min/lunr.${lang}.min.js`)\n  }\n\n  /* Add multi-language support */\n  if (config.lang.length > 1)\n    scripts.push(`${base}/min/lunr.multi.min.js`)\n\n  /* Load scripts synchronously */\n  if (scripts.length)\n    await importScripts(\n      `${base}/min/lunr.stemmer.support.min.js`,\n      ...scripts\n    )\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Message handler\n *\n * @param message - Source message\n *\n * @returns Target message\n */\nexport async function handler(\n  message: SearchMessage\n): Promise<SearchMessage> {\n  switch (message.type) {\n\n    /* Search setup message */\n    case SearchMessageType.SETUP:\n      await setupSearchLanguages(message.data.config)\n      index = new Search(message.data)\n      return {\n        type: SearchMessageType.READY\n      }\n\n    /* Search query message */\n    case SearchMessageType.QUERY:\n      const query = message.data\n      try {\n        return {\n          type: SearchMessageType.RESULT,\n          data: index.search(query)\n        }\n\n      /* Return empty result in case of error */\n      } catch (err) {\n        console.warn(`Invalid query: ${query} \u2013 see https://bit.ly/2s3ChXG`)\n        console.warn(err)\n        return {\n          type: SearchMessageType.RESULT,\n          data: { items: [] }\n        }\n      }\n\n    /* All other messages */\n    default:\n      throw new TypeError(\"Invalid message type\")\n  }\n}\n\n/* ----------------------------------------------------------------------------\n * Worker\n * ------------------------------------------------------------------------- */\n\n/* Expose Lunr.js in global scope, or stemmers won't work */\nself.lunr = lunr\n\n/* Handle messages */\naddEventListener(\"message\", async ev => {\n  postMessage(await handler(ev.data))\n})\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Retrieve all elements matching the query selector\n *\n * @template T - Element type\n *\n * @param selector - Query selector\n * @param node - Node of reference\n *\n * @returns Elements\n */\nexport function getElements<T extends keyof HTMLElementTagNameMap>(\n  selector: T, node?: ParentNode\n): HTMLElementTagNameMap[T][]\n\nexport function getElements<T extends HTMLElement>(\n  selector: string, node?: ParentNode\n): T[]\n\nexport function getElements<T extends HTMLElement>(\n  selector: string, node: ParentNode = document\n): T[] {\n  return Array.from(node.querySelectorAll<T>(selector))\n}\n\n/**\n * Retrieve an element matching a query selector or throw a reference error\n *\n * Note that this function assumes that the element is present. If unsure if an\n * element is existent, use the `getOptionalElement` function instead.\n *\n * @template T - Element type\n *\n * @param selector - Query selector\n * @param node - Node of reference\n *\n * @returns Element\n */\nexport function getElement<T extends keyof HTMLElementTagNameMap>(\n  selector: T, node?: ParentNode\n): HTMLElementTagNameMap[T]\n\nexport function getElement<T extends HTMLElement>(\n  selector: string, node?: ParentNode\n): T\n\nexport function getElement<T extends HTMLElement>(\n  selector: string, node: ParentNode = document\n): T {\n  const el = getOptionalElement<T>(selector, node)\n  if (typeof el === \"undefined\")\n    throw new ReferenceError(\n      `Missing element: expected \"${selector}\" to be present`\n    )\n\n  /* Return element */\n  return el\n}\n\n/* ------------------------------------------------------------------------- */\n\n/**\n * Retrieve an optional element matching the query selector\n *\n * @template T - Element type\n *\n * @param selector - Query selector\n * @param node - Node of reference\n *\n * @returns Element or nothing\n */\nexport function getOptionalElement<T extends keyof HTMLElementTagNameMap>(\n  selector: T, node?: ParentNode\n): HTMLElementTagNameMap[T] | undefined\n\nexport function getOptionalElement<T extends HTMLElement>(\n  selector: string, node?: ParentNode\n): T | undefined\n\nexport function getOptionalElement<T extends HTMLElement>(\n  selector: string, node: ParentNode = document\n): T | undefined {\n  return node.querySelector<T>(selector) || undefined\n}\n\n/**\n * Retrieve the currently active element\n *\n * @returns Element or nothing\n */\nexport function getActiveElement(): HTMLElement | undefined {\n  return (\n    document.activeElement?.shadowRoot?.activeElement as HTMLElement ??\n    document.activeElement as HTMLElement ??\n    undefined\n  )\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\n/* ----------------------------------------------------------------------------\n * Polyfills\n * ------------------------------------------------------------------------- */\n\n/* Polyfill `Object.entries` */\nif (!Object.entries)\n  Object.entries = function (obj: object) {\n    const data: [string, string][] = []\n    for (const key of Object.keys(obj))\n      // @ts-expect-error - ignore property access warning\n      data.push([key, obj[key]])\n\n    /* Return entries */\n    return data\n  }\n\n/* Polyfill `Object.values` */\nif (!Object.values)\n  Object.values = function (obj: object) {\n    const data: string[] = []\n    for (const key of Object.keys(obj))\n      // @ts-expect-error - ignore property access warning\n      data.push(obj[key])\n\n    /* Return values */\n    return data\n  }\n\n/* ------------------------------------------------------------------------- */\n\n/* Polyfills for `Element` */\nif (typeof Element !== \"undefined\") {\n\n  /* Polyfill `Element.scrollTo` */\n  if (!Element.prototype.scrollTo)\n    Element.prototype.scrollTo = function (\n      x?: ScrollToOptions | number, y?: number\n    ): void {\n      if (typeof x === \"object\") {\n        this.scrollLeft = x.left!\n        this.scrollTop = x.top!\n      } else {\n        this.scrollLeft = x!\n        this.scrollTop = y!\n      }\n    }\n\n  /* Polyfill `Element.replaceWith` */\n  if (!Element.prototype.replaceWith)\n    Element.prototype.replaceWith = function (\n      ...nodes: Array<string | Node>\n    ): void {\n      const parent = this.parentNode\n      if (parent) {\n        if (nodes.length === 0)\n          parent.removeChild(this)\n\n        /* Replace children and create text nodes */\n        for (let i = nodes.length - 1; i >= 0; i--) {\n          let node = nodes[i]\n          if (typeof node === \"string\")\n            node = document.createTextNode(node)\n          else if (node.parentNode)\n            node.parentNode.removeChild(node)\n\n          /* Replace child or insert before previous sibling */\n          if (!i)\n            parent.replaceChild(node, this)\n          else\n            parent.insertBefore(this.previousSibling!, node)\n        }\n      }\n    }\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\n/* ----------------------------------------------------------------------------\n * Types\n * ------------------------------------------------------------------------- */\n\n/**\n * Search configuration\n */\nexport interface SearchConfig {\n  lang: string[]                       /* Search languages */\n  separator: string                    /* Search separator */\n  pipeline: SearchPipelineFn[]         /* Search pipeline */\n}\n\n/**\n * Search document\n */\nexport interface SearchDocument {\n  location: string                     /* Document location */\n  title: string                        /* Document title */\n  text: string                         /* Document text */\n  tags?: string[]                      /* Document tags */\n  boost?: number                       /* Document boost */\n  parent?: SearchDocument              /* Document parent */\n}\n\n/**\n * Search options\n */\nexport interface SearchOptions {\n  suggest: boolean                     /* Search suggestions */\n}\n\n/* ------------------------------------------------------------------------- */\n\n/**\n * Search index\n */\nexport interface SearchIndex {\n  config: SearchConfig                 /* Search configuration */\n  docs: SearchDocument[]               /* Search documents */\n  options: SearchOptions               /* Search options */\n}\n\n/* ----------------------------------------------------------------------------\n * Helper types\n * ------------------------------------------------------------------------- */\n\n/**\n * Search pipeline function\n */\ntype SearchPipelineFn =\n  | \"trimmer\"                          /* Trimmer */\n  | \"stopWordFilter\"                   /* Stop word filter */\n  | \"stemmer\"                          /* Stemmer */\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Create a search document map\n *\n * This function creates a mapping of URLs (including anchors) to the actual\n * articles and sections. It relies on the invariant that the search index is\n * ordered with the main article appearing before all sections with anchors.\n * If this is not the case, the logic music be changed.\n *\n * @param docs - Search documents\n *\n * @returns Search document map\n */\nexport function setupSearchDocumentMap(\n  docs: SearchDocument[]\n): Map<string, SearchDocument> {\n  const map = new Map<string, SearchDocument>()\n  for (const doc of docs) {\n    const [path] = doc.location.split(\"#\")\n\n    /* Add document article */\n    const article = map.get(path)\n    if (typeof article === \"undefined\") {\n      map.set(path, doc)\n\n      /* Add document section */\n    } else {\n      map.set(doc.location, doc)\n      doc.parent = article\n    }\n  }\n\n  /* Return search document map */\n  return map\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\n/* ----------------------------------------------------------------------------\n * Helper types\n * ------------------------------------------------------------------------- */\n\n/**\n * Visitor function\n *\n * @param start - Start offset\n * @param end - End offset\n */\ntype VisitorFn = (\n  start: number, end: number\n) => void\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Split a string using the given separator\n *\n * @param input - Input value\n * @param separator - Separator\n * @param fn - Visitor function\n */\nexport function split(\n  input: string, separator: RegExp, fn: VisitorFn\n): void {\n  separator = new RegExp(separator, \"g\")\n\n  /* Split string using separator */\n  let match: RegExpExecArray | null\n  let index = 0\n  do {\n    match = separator.exec(input)\n\n    /* Emit non-empty range */\n    const until = match?.index ?? input.length\n    if (index < until)\n      fn(index, until)\n\n    /* Update last index */\n    if (match) {\n      const [term] = match\n      index = match.index + term.length\n\n      /* Support zero-length lookaheads */\n      if (term.length === 0)\n        separator.lastIndex = match.index + 1\n    }\n  } while (match)\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\n/* ----------------------------------------------------------------------------\n * Types\n * ------------------------------------------------------------------------- */\n\n/**\n * Extraction type\n *\n * This type defines the possible values that are encoded into the first two\n * bits of a section that is part of the blocks of a tokenization table. There\n * are three types of interest: HTML opening and closing tags, as well as the\n * actual text content we need to extract for indexing.\n */\nexport const enum Extract {\n  TAG_OPEN  = 0,                       /* HTML opening tag */\n  TEXT      = 1,                       /* Text content */\n  TAG_CLOSE = 2                        /* HTML closing tag */\n}\n\n/* ----------------------------------------------------------------------------\n * Helper types\n * ------------------------------------------------------------------------- */\n\n/**\n * Visitor function\n *\n * @param block - Block index\n * @param type - Extraction type\n * @param start - Start offset\n * @param end - End offset\n */\ntype VisitorFn = (\n  block: number, type: Extract, start: number, end: number\n) => void\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Split a string into markup and text sections\n *\n * This function scans a string and divides it up into sections of markup and\n * text. For each section, it invokes the given visitor function with the block\n * index, extraction type, as well as start and end offsets. Using a visitor\n * function (= streaming data) is ideal for minimizing pressure on the GC.\n *\n * @param input - Input value\n * @param fn - Visitor function\n */\nexport function extract(\n  input: string, fn: VisitorFn\n): void {\n\n  let block = 0                        /* Current block */\n  let start = 0                        /* Current start offset */\n  let end = 0                          /* Current end offset */\n\n  /* Split string into sections */\n  for (let stack = 0; end < input.length; end++) {\n\n    /* Opening tag after non-empty section */\n    if (input.charAt(end) === \"<\" && end > start) {\n      fn(block, Extract.TEXT, start, start = end)\n\n    /* Closing tag */\n    } else if (input.charAt(end) === \">\") {\n      if (input.charAt(start + 1) === \"/\") {\n        if (--stack === 0)\n          fn(block++, Extract.TAG_CLOSE, start, end + 1)\n\n      /* Tag is not self-closing */\n      } else if (input.charAt(end - 1) !== \"/\") {\n        if (stack++ === 0)\n          fn(block, Extract.TAG_OPEN, start, end + 1)\n      }\n\n      /* New section */\n      start = end + 1\n    }\n  }\n\n  /* Add trailing section */\n  if (end > start)\n    fn(block, Extract.TEXT, start, end)\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\n/* ----------------------------------------------------------------------------\n * Types\n * ------------------------------------------------------------------------- */\n\n/**\n * Position table\n */\nexport type PositionTable = number[][]\n\n/**\n * Position\n */\nexport type Position = number\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Highlight all occurrences in a string\n *\n * This function receives a field's value (e.g. like `title` or `text`), it's\n * position table that was generated during indexing, and the positions found\n * when executing the query. It then highlights all occurrences, and returns\n * their concatenation. In case of multiple blocks, two are returned.\n *\n * @param input - Input value\n * @param table - Table for indexing\n * @param positions - Occurrences\n * @param full - Full results\n *\n * @returns Highlighted string value\n */\nexport function highlight(\n  input: string, table: PositionTable, positions: Position[], full = false\n): string {\n  return highlightAll([input], table, positions, full).pop()!\n}\n\n/**\n * Highlight all occurrences in a set of strings\n *\n * @param inputs - Input values\n * @param table - Table for indexing\n * @param positions - Occurrences\n * @param full - Full results\n *\n * @returns Highlighted string values\n */\nexport function highlightAll(\n  inputs: string[], table: PositionTable, positions: Position[], full = false\n): string[] {\n\n  /* Map blocks to input values */\n  const mapping = [0]\n  for (let t = 1; t < table.length; t++) {\n    const prev = table[t - 1]\n    const next = table[t]\n\n    /* Check if table points to new block */\n    const p = prev[prev.length - 1] >>> 2 & 0x3FF\n    const q = next[0]               >>> 12\n\n    /* Add block to mapping */\n    mapping.push(+(p > q) + mapping[mapping.length - 1])\n  }\n\n  /* Highlight strings one after another */\n  return inputs.map((input, i) => {\n    let cursor = 0\n\n    /* Map occurrences to blocks */\n    const blocks = new Map<number, number[]>()\n    for (const p of positions.sort((a, b) => a - b)) {\n      const index = p & 0xFFFFF\n      const block = p >>> 20\n      if (mapping[block] !== i)\n        continue\n\n      /* Ensure presence of block group */\n      let group = blocks.get(block)\n      if (typeof group === \"undefined\")\n        blocks.set(block, group = [])\n\n      /* Add index to group */\n      group.push(index)\n    }\n\n    /* Just return string, if no occurrences */\n    if (blocks.size === 0)\n      return input\n\n    /* Compute slices */\n    const slices: string[] = []\n    for (const [block, indexes] of blocks) {\n      const t = table[block]\n\n      /* Extract positions and length */\n      const start  = t[0]            >>> 12\n      const end    = t[t.length - 1] >>> 12\n      const length = t[t.length - 1] >>> 2 & 0x3FF\n\n      /* Add prefix, if full results are desired */\n      if (full && start > cursor)\n        slices.push(input.slice(cursor, start))\n\n      /* Extract and highlight slice */\n      let slice = input.slice(start, end + length)\n      for (const j of indexes.sort((a, b) => b - a)) {\n\n        /* Retrieve offset and length of match */\n        const p = (t[j] >>> 12) - start\n        const q = (t[j] >>> 2 & 0x3FF) + p\n\n        /* Wrap occurrence */\n        slice = [\n          slice.slice(0, p),\n          \"<mark>\",\n          slice.slice(p, q),\n          \"</mark>\",\n          slice.slice(q)\n        ].join(\"\")\n      }\n\n      /* Update cursor */\n      cursor = end + length\n\n      /* Append slice and abort if we have two */\n      if (slices.push(slice) === 2)\n        break\n    }\n\n    /* Add suffix, if full results are desired */\n    if (full && cursor < input.length)\n      slices.push(input.slice(cursor))\n\n    /* Return highlighted slices */\n    return slices.join(\"\")\n  })\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport { split } from \"../_\"\nimport {\n  Extract,\n  extract\n} from \"../extract\"\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Split a string or set of strings into tokens\n *\n * This tokenizer supersedes the default tokenizer that is provided by Lunr.js,\n * as it is aware of HTML tags and allows for multi-character splitting.\n *\n * It takes the given inputs, splits each of them into markup and text sections,\n * tokenizes and segments (if necessary) each of them, and then indexes them in\n * a table by using a compact bit representation. Bitwise techniques are used\n * to write and read from the table during indexing and querying.\n *\n * @see https://bit.ly/3W3Xw4J - Search: better, faster, smaller\n *\n * @param input - Input value(s)\n *\n * @returns Tokens\n */\nexport function tokenize(\n  input?: string | string[]\n): lunr.Token[] {\n  const tokens: lunr.Token[] = []\n  if (typeof input === \"undefined\")\n    return tokens\n\n  /* Tokenize strings one after another */\n  const inputs = Array.isArray(input) ? input : [input]\n  for (let i = 0; i < inputs.length; i++) {\n    const table = lunr.tokenizer.table\n    const total = table.length\n\n    /* Split string into sections and tokenize content blocks */\n    extract(inputs[i], (block, type, start, end) => {\n      table[block += total] ||= []\n      switch (type) {\n\n        /* Handle markup */\n        case Extract.TAG_OPEN:\n        case Extract.TAG_CLOSE:\n          table[block].push(\n            start       << 12 |\n            end - start <<  2 |\n            type\n          )\n          break\n\n        /* Handle text content */\n        case Extract.TEXT:\n          const section = inputs[i].slice(start, end)\n          split(section, lunr.tokenizer.separator, (index, until) => {\n\n            /**\n             * Apply segmenter after tokenization. Note that the segmenter will\n             * also split words at word boundaries, which is not what we want,\n             * so we need to check if we can somehow mitigate this behavior.\n             */\n            if (typeof lunr.segmenter !== \"undefined\") {\n              const subsection = section.slice(index, until)\n              if (/^[MHIK]$/.test(lunr.segmenter.ctype_(subsection))) {\n                const segments = lunr.segmenter.segment(subsection)\n                for (let s = 0, l = 0; s < segments.length; s++) {\n\n                  /* Add block to section */\n                  table[block] ||= []\n                  table[block].push(\n                    start + index + l  << 12 |\n                    segments[s].length <<  2 |\n                    type\n                  )\n\n                  /* Add token with position */\n                  tokens.push(new lunr.Token(\n                    segments[s].toLowerCase(), {\n                      position: block << 20 | table[block].length - 1\n                    }\n                  ))\n\n                  /* Keep track of length */\n                  l += segments[s].length\n                }\n                return\n              }\n            }\n\n            /* Add block to section */\n            table[block].push(\n              start + index << 12 |\n              until - index <<  2 |\n              type\n            )\n\n            /* Add token with position */\n            tokens.push(new lunr.Token(\n              section.slice(index, until).toLowerCase(), {\n                position: block << 20 | table[block].length - 1\n              }\n            ))\n          })\n      }\n    })\n  }\n\n  /* Return tokens */\n  return tokens\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\n/* ----------------------------------------------------------------------------\n * Helper types\n * ------------------------------------------------------------------------- */\n\n/**\n * Visitor function\n *\n * @param value - String value\n *\n * @returns String term(s)\n */\ntype VisitorFn = (\n  value: string\n) => string | string[]\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Default transformation function\n *\n * 1. Trim excess whitespace from left and right.\n *\n * 2. Search for parts in quotation marks and prepend a `+` modifier to denote\n *    that the resulting document must contain all parts, converting the query\n *    to an `AND` query (as opposed to the default `OR` behavior). While users\n *    may expect parts enclosed in quotation marks to map to span queries, i.e.\n *    for which order is important, Lunr.js doesn't support them, so the best\n *    we can do is to convert the parts to an `AND` query.\n *\n * 3. Replace control characters which are not located at the beginning of the\n *    query or preceded by white space, or are not followed by a non-whitespace\n *    character or are at the end of the query string. Furthermore, filter\n *    unmatched quotation marks.\n *\n * 4. Split the query string at whitespace, then pass each part to the visitor\n *    function for tokenization, and append a wildcard to every resulting term\n *    that is not explicitly marked with a `+`, `-`, `~` or `^` modifier, since\n *    it ensures consistent and stable ranking when multiple terms are entered.\n *    Also, if a fuzzy or boost modifier are given, but no numeric value has\n *    been entered, default to 1 to not induce a query error.\n *\n * @param query - Query value\n * @param fn - Visitor function\n *\n * @returns Transformed query value\n */\nexport function transform(\n  query: string, fn: VisitorFn = term => term\n): string {\n  return query\n\n    /* => 1 */\n    .trim()\n\n    /* => 2 */\n    .split(/\"([^\"]+)\"/g)\n      .map((parts, index) => index & 1\n        ? parts.replace(/^\\b|^(?![^\\x00-\\x7F]|$)|\\s+/g, \" +\")\n        : parts\n      )\n      .join(\"\")\n\n    /* => 3 */\n    .replace(/\"|(?:^|\\s+)[*+\\-:^~]+(?=\\s+|$)/g, \"\")\n\n    /* => 4 */\n    .split(/\\s+/g)\n      .reduce((prev, term) => {\n        const next = fn(term)\n        return [...prev, ...Array.isArray(next) ? next : [next]]\n      }, [] as string[])\n      .map(term => /([~^]$)/.test(term) ? `${term}1` : term)\n      .map(term => /(^[+-]|[~^]\\d+$)/.test(term) ? term : `${term}*`)\n      .join(\" \")\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport { split } from \"../../internal\"\nimport { transform } from \"../transform\"\n\n/* ----------------------------------------------------------------------------\n * Types\n * ------------------------------------------------------------------------- */\n\n/**\n * Search query clause\n */\nexport interface SearchQueryClause {\n  presence: lunr.Query.presence        /* Clause presence */\n  term: string                         /* Clause term */\n}\n\n/* ------------------------------------------------------------------------- */\n\n/**\n * Search query terms\n */\nexport type SearchQueryTerms = Record<string, boolean>\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Transform search query\n *\n * This function lexes the given search query and applies the transformation\n * function to each term, preserving markup like `+` and `-` modifiers.\n *\n * @param query - Search query\n *\n * @returns Search query\n */\nexport function transformSearchQuery(\n  query: string\n): string {\n\n  /* Split query terms with tokenizer */\n  return transform(query, part => {\n    const terms: string[] = []\n\n    /* Initialize lexer and analyze part */\n    const lexer = new lunr.QueryLexer(part)\n    lexer.run()\n\n    /* Extract and tokenize term from lexeme */\n    for (const { type, str: term, start, end } of lexer.lexemes)\n      switch (type) {\n\n        /* Hack: remove colon - see https://bit.ly/3wD3T3I */\n        case \"FIELD\":\n          if (![\"title\", \"text\", \"tags\"].includes(term))\n            part = [\n              part.slice(0, end),\n              \" \",\n              part.slice(end + 1)\n            ].join(\"\")\n          break\n\n        /* Tokenize term */\n        case \"TERM\":\n          split(term, lunr.tokenizer.separator, (...range) => {\n            terms.push([\n              part.slice(0, start),\n              term.slice(...range),\n              part.slice(end)\n            ].join(\"\"))\n          })\n      }\n\n    /* Return terms */\n    return terms\n  })\n}\n\n/* ------------------------------------------------------------------------- */\n\n/**\n * Parse a search query for analysis\n *\n * Lunr.js itself has a bug where it doesn't detect or remove wildcards for\n * query clauses, so we must do this here.\n *\n * @see https://bit.ly/3DpTGtz - GitHub issue\n *\n * @param value - Query value\n *\n * @returns Search query clauses\n */\nexport function parseSearchQuery(\n  value: string\n): SearchQueryClause[] {\n  const query  = new lunr.Query([\"title\", \"text\", \"tags\"])\n  const parser = new lunr.QueryParser(value, query)\n\n  /* Parse Search query */\n  parser.parse()\n  for (const clause of query.clauses) {\n    clause.usePipeline = true\n\n    /* Handle leading wildcard */\n    if (clause.term.startsWith(\"*\")) {\n      clause.wildcard = lunr.Query.wildcard.LEADING\n      clause.term = clause.term.slice(1)\n    }\n\n    /* Handle trailing wildcard */\n    if (clause.term.endsWith(\"*\")) {\n      clause.wildcard = lunr.Query.wildcard.TRAILING\n      clause.term = clause.term.slice(0, -1)\n    }\n  }\n\n  /* Return query clauses */\n  return query.clauses\n}\n\n/**\n * Analyze the search query clauses in regard to the search terms found\n *\n * @param query - Search query clauses\n * @param terms - Search terms\n *\n * @returns Search query terms\n */\nexport function getSearchQueryTerms(\n  query: SearchQueryClause[], terms: string[]\n): SearchQueryTerms {\n  const clauses = new Set<SearchQueryClause>(query)\n\n  /* Match query clauses against terms */\n  const result: SearchQueryTerms = {}\n  for (let t = 0; t < terms.length; t++)\n    for (const clause of clauses)\n      if (terms[t].startsWith(clause.term)) {\n        result[clause.term] = true\n        clauses.delete(clause)\n      }\n\n  /* Annotate unmatched non-stopword query clauses */\n  for (const clause of clauses)\n    if (lunr.stopWordFilter?.(clause.term))\n      result[clause.term] = false\n\n  /* Return query terms */\n  return result\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Segment a search query using the inverted index\n *\n * This function implements a clever approach to text segmentation for Asian\n * languages, as it used the information already available in the search index.\n * The idea is to greedily segment the search query based on the tokens that are\n * already part of the index, as described in the linked issue.\n *\n * @see https://bit.ly/3lwjrk7 - GitHub issue\n *\n * @param query - Query value\n * @param index - Inverted index\n *\n * @returns Segmented query value\n */\nexport function segment(\n  query: string, index: object\n): Iterable<string> {\n  const segments = new Set<string>()\n\n  /* Segment search query */\n  const wordcuts = new Uint16Array(query.length)\n  for (let i = 0; i < query.length; i++)\n    for (let j = i + 1; j < query.length; j++) {\n      const value = query.slice(i, j)\n      if (value in index)\n        wordcuts[i] = j - i\n    }\n\n  /* Compute longest matches with minimum overlap */\n  const stack = [0]\n  for (let s = stack.length; s > 0;) {\n    const p = stack[--s]\n    for (let q = 1; q < wordcuts[p]; q++)\n      if (wordcuts[p + q] > wordcuts[p] - q) {\n        segments.add(query.slice(p, p + q))\n        stack[s++] = p + q\n      }\n\n    /* Continue at end of query string */\n    const q = p + wordcuts[p]\n    if (wordcuts[q] && q < query.length - 1)\n      stack[s++] = q\n\n    /* Add current segment */\n    segments.add(query.slice(p, q))\n  }\n\n  // @todo fix this case in the code block above, this is a hotfix\n  if (segments.has(\"\"))\n    return new Set([query])\n\n  /* Return segmented query value */\n  return segments\n}\n", "/*\n * Copyright (c) 2016-2024 Martin Donath <martin.donath@squidfunk.com>\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to\n * deal in the Software without restriction, including without limitation the\n * rights to use, copy, modify, merge, publish, distribute, sublicense, and/or\n * sell copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS\n * IN THE SOFTWARE.\n */\n\nimport {\n  SearchDocument,\n  SearchIndex,\n  SearchOptions,\n  setupSearchDocumentMap\n} from \"../config\"\nimport {\n  Position,\n  PositionTable,\n  highlight,\n  highlightAll,\n  tokenize\n} from \"../internal\"\nimport {\n  SearchQueryTerms,\n  getSearchQueryTerms,\n  parseSearchQuery,\n  segment,\n  transformSearchQuery\n} from \"../query\"\n\n/* ----------------------------------------------------------------------------\n * Types\n * ------------------------------------------------------------------------- */\n\n/**\n * Search item\n */\nexport interface SearchItem\n  extends SearchDocument\n{\n  score: number                        /* Score (relevance) */\n  terms: SearchQueryTerms              /* Search query terms */\n}\n\n/**\n * Search result\n */\nexport interface SearchResult {\n  items: SearchItem[][]                /* Search items */\n  suggest?: string[]                   /* Search suggestions */\n}\n\n/* ----------------------------------------------------------------------------\n * Functions\n * ------------------------------------------------------------------------- */\n\n/**\n * Create field extractor factory\n *\n * @param table - Position table map\n *\n * @returns Extractor factory\n */\nfunction extractor(table: Map<string, PositionTable>) {\n  return (name: keyof SearchDocument) => {\n    return (doc: SearchDocument) => {\n      if (typeof doc[name] === \"undefined\")\n        return undefined\n\n      /* Compute identifier and initialize table */\n      const id = [doc.location, name].join(\":\")\n      table.set(id, lunr.tokenizer.table = [])\n\n      /* Return field value */\n      return doc[name]\n    }\n  }\n}\n\n/**\n * Compute the difference of two lists of strings\n *\n * @param a - 1st list of strings\n * @param b - 2nd list of strings\n *\n * @returns Difference\n */\nfunction difference(a: string[], b: string[]): string[] {\n  const [x, y] = [new Set(a), new Set(b)]\n  return [\n    ...new Set([...x].filter(value => !y.has(value)))\n  ]\n}\n\n/* ----------------------------------------------------------------------------\n * Class\n * ------------------------------------------------------------------------- */\n\n/**\n * Search index\n */\nexport class Search {\n\n  /**\n   * Search document map\n   */\n  protected map: Map<string, SearchDocument>\n\n  /**\n   * Search options\n   */\n  protected options: SearchOptions\n\n  /**\n   * The underlying Lunr.js search index\n   */\n  protected index: lunr.Index\n\n  /**\n   * Internal position table map\n   */\n  protected table: Map<string, PositionTable>\n\n  /**\n   * Create the search integration\n   *\n   * @param data - Search index\n   */\n  public constructor({ config, docs, options }: SearchIndex) {\n    const field = extractor(this.table = new Map())\n\n    /* Set up document map and options */\n    this.map = setupSearchDocumentMap(docs)\n    this.options = options\n\n    /* Set up document index */\n    this.index = lunr(function () {\n      this.metadataWhitelist = [\"position\"]\n      this.b(0)\n\n      /* Set up (multi-)language support */\n      if (config.lang.length === 1 && config.lang[0] !== \"en\") {\n        // @ts-expect-error - namespace indexing not supported\n        this.use(lunr[config.lang[0]])\n      } else if (config.lang.length > 1) {\n        this.use(lunr.multiLanguage(...config.lang))\n      }\n\n      /* Set up custom tokenizer (must be after language setup) */\n      this.tokenizer = tokenize as typeof lunr.tokenizer\n      lunr.tokenizer.separator = new RegExp(config.separator)\n\n      /* Set up custom segmenter, if loaded */\n      lunr.segmenter = \"TinySegmenter\" in lunr\n        ? new lunr.TinySegmenter()\n        : undefined\n\n      /* Compute functions to be removed from the pipeline */\n      const fns = difference([\n        \"trimmer\", \"stopWordFilter\", \"stemmer\"\n      ], config.pipeline)\n\n      /* Remove functions from the pipeline for registered languages */\n      for (const lang of config.lang.map(language => (\n        // @ts-expect-error - namespace indexing not supported\n        language === \"en\" ? lunr : lunr[language]\n      )))\n        for (const fn of fns) {\n          this.pipeline.remove(lang[fn])\n          this.searchPipeline.remove(lang[fn])\n        }\n\n      /* Set up index reference */\n      this.ref(\"location\")\n\n      /* Set up index fields */\n      this.field(\"title\", { boost: 1e3, extractor: field(\"title\") })\n      this.field(\"text\",  { boost: 1e0, extractor: field(\"text\") })\n      this.field(\"tags\",  { boost: 1e6, extractor: field(\"tags\") })\n\n      /* Add documents to index */\n      for (const doc of docs)\n        this.add(doc, { boost: doc.boost })\n    })\n  }\n\n  /**\n   * Search for matching documents\n   *\n   * @param query - Search query\n   *\n   * @returns Search result\n   */\n  public search(query: string): SearchResult {\n\n    // Experimental Chinese segmentation\n    query = query.replace(/\\p{sc=Han}+/gu, value => {\n      return [...segment(value, this.index.invertedIndex)]\n        .join(\"* \")\n    })\n\n    // @todo: move segmenter (above) into transformSearchQuery\n    query = transformSearchQuery(query)\n    if (!query)\n      return { items: [] }\n\n    /* Parse query to extract clauses for analysis */\n    const clauses = parseSearchQuery(query)\n      .filter(clause => (\n        clause.presence !== lunr.Query.presence.PROHIBITED\n      ))\n\n    /* Perform search and post-process results */\n    const groups = this.index.search(query)\n\n      /* Apply post-query boosts based on title and search query terms */\n      .reduce<SearchItem[]>((item, { ref, score, matchData }) => {\n        let doc = this.map.get(ref)\n        if (typeof doc !== \"undefined\") {\n\n          /* Shallow copy document */\n          doc = { ...doc }\n          if (doc.tags)\n            doc.tags = [...doc.tags]\n\n          /* Compute and analyze search query terms */\n          const terms = getSearchQueryTerms(\n            clauses,\n            Object.keys(matchData.metadata)\n          )\n\n          /* Highlight matches in fields */\n          for (const field of this.index.fields) {\n            if (typeof doc[field] === \"undefined\")\n              continue\n\n            /* Collect positions from matches */\n            const positions: Position[] = []\n            for (const match of Object.values(matchData.metadata))\n              if (typeof match[field] !== \"undefined\")\n                positions.push(...match[field].position)\n\n            /* Skip highlighting, if no positions were collected */\n            if (!positions.length)\n              continue\n\n            /* Load table and determine highlighting method */\n            const table = this.table.get([doc.location, field].join(\":\"))!\n            const fn = Array.isArray(doc[field])\n              ? highlightAll\n              : highlight\n\n            // @ts-expect-error - stop moaning, TypeScript!\n            doc[field] = fn(doc[field], table, positions, field !== \"text\")\n          }\n\n          /* Highlight title and text and apply post-query boosts */\n          const boost = +!doc.parent +\n            Object.values(terms)\n              .filter(t => t).length /\n            Object.keys(terms).length\n\n          /* Append item */\n          item.push({\n            ...doc,\n            score: score * (1 + boost ** 2),\n            terms\n          })\n        }\n        return item\n      }, [])\n\n      /* Sort search results again after applying boosts */\n      .sort((a, b) => b.score - a.score)\n\n      /* Group search results by article */\n      .reduce((items, result) => {\n        const doc = this.map.get(result.location)\n        if (typeof doc !== \"undefined\") {\n          const ref = doc.parent\n            ? doc.parent.location\n            : doc.location\n          items.set(ref, [...items.get(ref) || [], result])\n        }\n        return items\n      }, new Map<string, SearchItem[]>())\n\n    /* Ensure that every item set has an article */\n    for (const [ref, items] of groups)\n      if (!items.find(item => item.location === ref)) {\n        const doc = this.map.get(ref)!\n        items.push({ ...doc, score: 0, terms: {} })\n      }\n\n    /* Generate search suggestions, if desired */\n    let suggest: string[] | undefined\n    if (this.options.suggest) {\n      const titles = this.index.query(builder => {\n        for (const clause of clauses)\n          builder.term(clause.term, {\n            fields: [\"title\"],\n            presence: lunr.Query.presence.REQUIRED,\n            wildcard: lunr.Query.wildcard.TRAILING\n          })\n      })\n\n      /* Retrieve suggestions for best match */\n      suggest = titles.length\n        ? Object.keys(titles[0].matchData.metadata)\n        : []\n    }\n\n    /* Return search result */\n    return {\n      items: [...groups.values()],\n      ...typeof suggest !== \"undefined\" && { suggest }\n    }\n  }\n}\n"],
+  "mappings": 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index 000000000..d75ff6a07
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diff --git a/ja/assets/stylesheets/palette.06af60db.min.css b/ja/assets/stylesheets/palette.06af60db.min.css
new file mode 100644
index 000000000..c91504772
--- /dev/null
+++ b/ja/assets/stylesheets/palette.06af60db.min.css
@@ -0,0 +1,2 @@
+@media 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+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_introduction/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
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+      
+        
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+      
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+        
+          
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+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
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+            
+              
+            
+              
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+  
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+  
+  
+    <li class="md-nav__item">
+      <a href="../installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
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+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
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+      
+      <a href="./" class="md-nav__link md-nav__link--active">
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+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
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+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 内容の微調整
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; 内容の作成
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#3-docker" class="md-nav__link">
+    <span class="md-ellipsis">
+      3. &nbsp; Dockerデプロイメント
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
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+        </nav>
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+  
+  <span class="md-ellipsis">
+    参考文献
+  </span>
+  
+
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+            
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+                  <div class="md-sidebar__inner">
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+  
+  
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+  
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+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 内容の微調整
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; 内容の作成
+    </span>
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+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#3-docker" class="md-nav__link">
+    <span class="md-ellipsis">
+      3. &nbsp; Dockerデプロイメント
+    </span>
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+</li>
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+  
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+      title="編集"
+      class="md-content__button md-icon"
+    >
+      
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
+    </a>
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+  
+
+
+<!-- Page content -->
+<h1 id="162">16.2 &nbsp; コントリビューション<a class="headerlink" href="#162" title="Permanent link">&para;</a></h1>
+<p>著者の能力に限りがあるため、本書にはいくつかの省略や誤りが避けられません。ご理解をお願いします。誤字、リンク切れ、内容の欠落、文章の曖昧さ、説明の不明確さ、または不合理な文章構造を発見された場合は、読者により良質な学習リソースを提供するため、修正にご協力ください。</p>
+<p>すべての<a href="https://github.com/krahets/hello-algo/graphs/contributors">コントリビューター</a>のGitHub IDは、本書のリポジトリ、ウェブ、PDFバージョンのホームページに表示され、オープンソースコミュニティへの無私の貢献に感謝いたします。</p>
+<div class="admonition success">
+<p class="admonition-title">オープンソースの魅力</p>
+<p>紙の本の2つの印刷版の間隔はしばしば長く、内容の更新が非常に不便です。</p>
+<p>しかし、このオープンソースの本では、内容の更新サイクルは数日、さらには数時間に短縮されます。</p>
+</div>
+<h3 id="1">1. &nbsp; 内容の微調整<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<p>下の図に示すように、各ページの右上角に「編集アイコン」があります。以下の手順に従ってテキストやコードを修正できます。</p>
+<ol>
+<li>「編集アイコン」をクリックします。「このリポジトリをフォークしますか」と促された場合は、同意してください。</li>
+<li>Markdownソースファイルの内容を修正し、内容の正確性を確認し、フォーマットの一貫性を保つようにしてください。</li>
+<li>ページの下部で修正説明を記入し、「Propose file change」ボタンをクリックします。ページがリダイレクトされた後、「Create pull request」ボタンをクリックしてプルリクエストを開始します。</li>
+</ol>
+<p><a class="glightbox" href="../contribution.assets/edit_markdown.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="ページ編集ボタン" class="animation-figure" src="../contribution.assets/edit_markdown.png" /></a></p>
+<p align="center"> 図 16-3 &nbsp; ページ編集ボタン </p>
+
+<p>図は直接修正できないため、新しい<a href="https://github.com/krahets/hello-algo/issues">Issue</a>を作成するか、問題を説明するコメントが必要です。できるだけ早く図を再描画して置き換えます。</p>
+<h3 id="2">2. &nbsp; 内容の作成<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
+<p>このオープンソースプロジェクトへの参加に興味がある場合、コードを他のプログラミング言語に翻訳したり、記事の内容を拡張したりすることを含めて、以下のプルリクエストワークフローを実装する必要があります。</p>
+<ol>
+<li>GitHubにログインし、本書の<a href="https://github.com/krahets/hello-algo">コードリポジトリ</a>を個人アカウントにフォークします。</li>
+<li>フォークしたリポジトリのウェブページに移動し、<code>git clone</code>コマンドを使用してリポジトリをローカルマシンにクローンします。</li>
+<li>ローカルで内容を作成し、完全なテストを実行してコードの正確性を検証します。</li>
+<li>ローカルで行った変更をコミットし、リモートリポジトリにプッシュします。</li>
+<li>リポジトリのウェブページを更新し、「Create pull request」ボタンをクリックしてプルリクエストを開始します。</li>
+</ol>
+<h3 id="3-docker">3. &nbsp; Dockerデプロイメント<a class="headerlink" href="#3-docker" title="Permanent link">&para;</a></h3>
+<p><code>hello-algo</code>ルートディレクトリで、以下のDockerスクリプトを実行して<code>http://localhost:8000</code>でプロジェクトにアクセスします：</p>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a>docker-compose<span class="w"> </span>up<span class="w"> </span>-d
+</code></pre></div>
+<p>以下のコマンドを使用してデプロイメントを削除します：</p>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a>docker-compose<span class="w"> </span>down
+</code></pre></div>
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+    第 2 章 &nbsp; 計算量解析
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+    2.1 &nbsp; アルゴリズム効率評価
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+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="./" class="md-nav__link md-nav__link--active">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link md-nav__link--active" for="__nav_18" id="__nav_18_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_19" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_reference/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9 3v15h3V3H9m3 2 4 13 3-1-4-13-3 1M5 5v13h3V5H5M3 19v2h18v-2H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    参考文献
+  </span>
+  
+
+            </a>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_19_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_19">
+            <span class="md-nav__icon md-icon"></span>
+            参考文献
+          </label>
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+        </nav>
+      
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m13.13 22.19-1.63-3.83c1.57-.58 3.04-1.36 4.4-2.27l-2.77 6.1M5.64 12.5l-3.83-1.63 6.1-2.77C7 9.46 6.22 10.93 5.64 12.5M19.22 4c.28 0 .53 0 .74.05.17 1.39-.02 4.25-3.3 7.53-1.7 1.71-3.73 3.02-6.01 3.89l-2.15-2.1c.92-2.31 2.23-4.34 3.92-6.03C15.18 4.58 17.64 4 19.22 4m0-2c-1.98 0-4.98.69-8.22 3.93-2.19 2.19-3.5 4.6-4.35 6.71-.28.75-.09 1.57.46 2.13l2.13 2.12c.38.38.89.61 1.42.61.23 0 .47-.06.7-.15A19.1 19.1 0 0 0 18.07 13c5.66-5.66 3.54-10.61 3.54-10.61S20.7 2 19.22 2m-4.68 7.46c-.78-.78-.78-2.05 0-2.83s2.05-.78 2.83 0c.77.78.78 2.05 0 2.83-.78.78-2.05.78-2.83 0m-5.66 7.07-1.41-1.41 1.41 1.41M6.24 22l3.64-3.64c-.34-.09-.67-.24-.97-.45L4.83 22h1.41M2 22h1.41l4.77-4.76-1.42-1.41L2 20.59V22m0-2.83 4.09-4.08c-.21-.3-.36-.62-.45-.97L2 17.76v1.41Z"/></svg>
+  
+  <span class="md-ellipsis">
+    はじめに
+  </span>
+  
+
+            </a>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_1_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_1">
+            <span class="md-nav__icon md-icon"></span>
+            はじめに
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
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+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_2" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_preface/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M21 4H3a2 2 0 0 0-2 2v13a2 2 0 0 0 2 2h18a2 2 0 0 0 2-2V6a2 2 0 0 0-2-2M3 19V6h8v13H3m18 0h-8V6h8v13m-7-9.5h6V11h-6V9.5m0 2.5h6v1.5h-6V12m0 2.5h6V16h-6v-1.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 0 章 &nbsp; 前書き
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_2" id="__nav_2_label" tabindex="0">
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_2_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_2">
+            <span class="md-nav__icon md-icon"></span>
+            第 0 章 &nbsp; 前書き
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/about_the_book/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.1 &nbsp; この本について
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/suggestions/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.2 &nbsp; 本書の使い方
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_introduction/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
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+            
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+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1611-ide" class="md-nav__link">
+    <span class="md-ellipsis">
+      16.1.1 &nbsp; IDEのインストール
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1612" class="md-nav__link">
+    <span class="md-ellipsis">
+      16.1.2 &nbsp; 言語環境のインストール
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="16.1.2   言語環境のインストール">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1-python" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; Python環境
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2-cc" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; C/C++環境
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#3-java" class="md-nav__link">
+    <span class="md-ellipsis">
+      3. &nbsp; Java環境
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#4-c" class="md-nav__link">
+    <span class="md-ellipsis">
+      4. &nbsp; C#環境
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#5-go" class="md-nav__link">
+    <span class="md-ellipsis">
+      5. &nbsp; Go環境
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#6-swift" class="md-nav__link">
+    <span class="md-ellipsis">
+      6. &nbsp; Swift環境
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#7-javascript" class="md-nav__link">
+    <span class="md-ellipsis">
+      7. &nbsp; JavaScript環境
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#8-typescript" class="md-nav__link">
+    <span class="md-ellipsis">
+      8. &nbsp; TypeScript環境
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#9-dart" class="md-nav__link">
+    <span class="md-ellipsis">
+      9. &nbsp; Dart環境
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#10-rust" class="md-nav__link">
+    <span class="md-ellipsis">
+      10. &nbsp; Rust環境
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
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+    
+      
+        
+          
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_19" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_reference/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9 3v15h3V3H9m3 2 4 13 3-1-4-13-3 1M5 5v13h3V5H5M3 19v2h18v-2H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    参考文献
+  </span>
+  
+
+            </a>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_19_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_19">
+            <span class="md-nav__icon md-icon"></span>
+            参考文献
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+  </ul>
+</nav>
+                  </div>
+                </div>
+              </div>
+            
+            
+              
+              <div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
+                <div class="md-sidebar__scrollwrap">
+                  <div class="md-sidebar__inner">
+                    
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1611-ide" class="md-nav__link">
+    <span class="md-ellipsis">
+      16.1.1 &nbsp; IDEのインストール
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1612" class="md-nav__link">
+    <span class="md-ellipsis">
+      16.1.2 &nbsp; 言語環境のインストール
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="16.1.2   言語環境のインストール">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1-python" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; Python環境
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2-cc" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; C/C++環境
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#3-java" class="md-nav__link">
+    <span class="md-ellipsis">
+      3. &nbsp; Java環境
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#4-c" class="md-nav__link">
+    <span class="md-ellipsis">
+      4. &nbsp; C#環境
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#5-go" class="md-nav__link">
+    <span class="md-ellipsis">
+      5. &nbsp; Go環境
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#6-swift" class="md-nav__link">
+    <span class="md-ellipsis">
+      6. &nbsp; Swift環境
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#7-javascript" class="md-nav__link">
+    <span class="md-ellipsis">
+      7. &nbsp; JavaScript環境
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#8-typescript" class="md-nav__link">
+    <span class="md-ellipsis">
+      8. &nbsp; TypeScript環境
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#9-dart" class="md-nav__link">
+    <span class="md-ellipsis">
+      9. &nbsp; Dart環境
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#10-rust" class="md-nav__link">
+    <span class="md-ellipsis">
+      10. &nbsp; Rust環境
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+                  </div>
+                </div>
+              </div>
+            
+          
+          
+            <div class="md-content" data-md-component="content">
+              <article class="md-content__inner md-typeset">
+                
+                  <!-- Tags -->
+
+
+<!-- Actions -->
+<!-- Actions -->
+
+
+  <!-- Edit button -->
+  
+    <a
+      href="https://github.com/krahets/hello-algo/tree/main/ja/docs/chapter_appendix/installation.md"
+      title="編集"
+      class="md-content__button md-icon"
+    >
+      
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
+    </a>
+  
+
+  <!-- View button -->
+  
+
+
+<!-- Page content -->
+<h1 id="161">16.1 &nbsp; インストール<a class="headerlink" href="#161" title="Permanent link">&para;</a></h1>
+<h2 id="1611-ide">16.1.1 &nbsp; IDEのインストール<a class="headerlink" href="#1611-ide" title="Permanent link">&para;</a></h2>
+<p>ローカルの統合開発環境（IDE）として、オープンソースで軽量なVS Codeを使用することをお勧めします。<a href="https://code.visualstudio.com/">VS Code公式ウェブサイト</a>にアクセスし、お使いのオペレーティングシステムに適したVS Codeのバージョンを選択してダウンロードし、インストールしてください。</p>
+<p><a class="glightbox" href="../installation.assets/vscode_installation.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="公式ウェブサイトからVS Codeをダウンロード" class="animation-figure" src="../installation.assets/vscode_installation.png" /></a></p>
+<p align="center"> 図 16-1 &nbsp; 公式ウェブサイトからVS Codeをダウンロード </p>
+
+<p>VS Codeには強力な拡張機能エコシステムがあり、ほとんどのプログラミング言語の実行とデバッグをサポートしています。例えば、「Python Extension Pack」をインストールした後、Pythonコードをデバッグできます。インストール手順を下の図に示します。</p>
+<p><a class="glightbox" href="../installation.assets/vscode_extension_installation.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="VS Code拡張機能パックのインストール" class="animation-figure" src="../installation.assets/vscode_extension_installation.png" /></a></p>
+<p align="center"> 図 16-2 &nbsp; VS Code拡張機能パックのインストール </p>
+
+<h2 id="1612">16.1.2 &nbsp; 言語環境のインストール<a class="headerlink" href="#1612" title="Permanent link">&para;</a></h2>
+<h3 id="1-python">1. &nbsp; Python環境<a class="headerlink" href="#1-python" title="Permanent link">&para;</a></h3>
+<ol>
+<li><a href="https://docs.conda.io/en/latest/miniconda.html">Miniconda3</a>をダウンロードしてインストールします。Python 3.10以降が必要です。</li>
+<li>VS Code拡張機能マーケットプレイスで<code>python</code>を検索し、Python Extension Packをインストールします。</li>
+<li>（オプション）コマンドラインで<code>pip install black</code>を入力して、コードフォーマッティングツールをインストールします。</li>
+</ol>
+<h3 id="2-cc">2. &nbsp; C/C++環境<a class="headerlink" href="#2-cc" title="Permanent link">&para;</a></h3>
+<ol>
+<li>Windowsシステムでは<a href="https://sourceforge.net/projects/mingw-w64/files/">MinGW</a>をインストールする必要があります（<a href="https://blog.csdn.net/qq_33698226/article/details/129031241">設定チュートリアル</a>）。MacOSにはClangが付属しているため、インストールは不要です。</li>
+<li>VS Code拡張機能マーケットプレイスで<code>c++</code>を検索し、C/C++ Extension Packをインストールします。</li>
+<li>（オプション）設定ページを開き、<code>Clang_format_fallback Style</code>コードフォーマッティングオプションを検索し、<code>{ BasedOnStyle: Microsoft, BreakBeforeBraces: Attach }</code>に設定します。</li>
+</ol>
+<h3 id="3-java">3. &nbsp; Java環境<a class="headerlink" href="#3-java" title="Permanent link">&para;</a></h3>
+<ol>
+<li><a href="https://jdk.java.net/18/">OpenJDK</a>をダウンロードしてインストールします（バージョンはJDK 9より新しい必要があります）。</li>
+<li>VS Code拡張機能マーケットプレイスで<code>java</code>を検索し、Extension Pack for Javaをインストールします。</li>
+</ol>
+<h3 id="4-c">4. &nbsp; C#環境<a class="headerlink" href="#4-c" title="Permanent link">&para;</a></h3>
+<ol>
+<li><a href="https://dotnet.microsoft.com/en-us/download">.Net 8.0</a>をダウンロードしてインストールします。</li>
+<li>VS Code拡張機能マーケットプレイスで<code>C# Dev Kit</code>を検索し、C# Dev Kitをインストールします（<a href="https://code.visualstudio.com/docs/csharp/get-started">設定チュートリアル</a>）。</li>
+<li>Visual Studioを使用することもできます（<a href="https://learn.microsoft.com/zh-cn/visualstudio/install/install-visual-studio?view=vs-2022">インストールチュートリアル</a>）。</li>
+</ol>
+<h3 id="5-go">5. &nbsp; Go環境<a class="headerlink" href="#5-go" title="Permanent link">&para;</a></h3>
+<ol>
+<li><a href="https://go.dev/dl/">go</a>をダウンロードしてインストールします。</li>
+<li>VS Code拡張機能マーケットプレイスで<code>go</code>を検索し、Goをインストールします。</li>
+<li><code>Ctrl + Shift + P</code>を押してコマンドバーを呼び出し、goと入力し、<code>Go: Install/Update Tools</code>を選択し、すべてを選択してインストールします。</li>
+</ol>
+<h3 id="6-swift">6. &nbsp; Swift環境<a class="headerlink" href="#6-swift" title="Permanent link">&para;</a></h3>
+<ol>
+<li><a href="https://www.swift.org/download/">Swift</a>をダウンロードしてインストールします。</li>
+<li>VS Code拡張機能マーケットプレイスで<code>swift</code>を検索し、<a href="https://marketplace.visualstudio.com/items?itemName=sswg.swift-lang">Swift for Visual Studio Code</a>をインストールします。</li>
+</ol>
+<h3 id="7-javascript">7. &nbsp; JavaScript環境<a class="headerlink" href="#7-javascript" title="Permanent link">&para;</a></h3>
+<ol>
+<li><a href="https://nodejs.org/en/">Node.js</a>をダウンロードしてインストールします。</li>
+<li>（オプション）VS Code拡張機能マーケットプレイスで<code>Prettier</code>を検索し、コードフォーマッティングツールをインストールします。</li>
+</ol>
+<h3 id="8-typescript">8. &nbsp; TypeScript環境<a class="headerlink" href="#8-typescript" title="Permanent link">&para;</a></h3>
+<ol>
+<li>JavaScript環境と同じインストール手順に従います。</li>
+<li><a href="https://github.com/privatenumber/tsx?tab=readme-ov-file#global-installation">TypeScript Execute (tsx)</a>をインストールします。</li>
+<li>VS Code拡張機能マーケットプレイスで<code>typescript</code>を検索し、<a href="https://marketplace.visualstudio.com/items?itemName=yoavbls.pretty-ts-errors">Pretty TypeScript Errors</a>をインストールします。</li>
+</ol>
+<h3 id="9-dart">9. &nbsp; Dart環境<a class="headerlink" href="#9-dart" title="Permanent link">&para;</a></h3>
+<ol>
+<li><a href="https://dart.dev/get-dart">Dart</a>をダウンロードしてインストールします。</li>
+<li>VS Code拡張機能マーケットプレイスで<code>dart</code>を検索し、<a href="https://marketplace.visualstudio.com/items?itemName=Dart-Code.dart-code">Dart</a>をインストールします。</li>
+</ol>
+<h3 id="10-rust">10. &nbsp; Rust環境<a class="headerlink" href="#10-rust" title="Permanent link">&para;</a></h3>
+<ol>
+<li><a href="https://www.rust-lang.org/tools/install">Rust</a>をダウンロードしてインストールします。</li>
+<li>VS Code拡張機能マーケットプレイスで<code>rust</code>を検索し、<a href="https://marketplace.visualstudio.com/items?itemName=rust-lang.rust-analyzer">rust-analyzer</a>をインストールします。</li>
+</ol>
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new file mode 100644
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+  
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+  
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+      <a href="../../chapter_preface/about_the_book/" class="md-nav__link">
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+      <a href="../../chapter_preface/summary/" class="md-nav__link">
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+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
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+  
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+    1.1 &nbsp; アルゴリズムはどこにでもある
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+  
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+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
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+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
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+    </li>
+  
+
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+              
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+  
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+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
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+    </li>
+  
+
+              
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+          
+        
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+        
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+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
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+  
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+            第 2 章 &nbsp; 計算量解析
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+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
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+    2.1 &nbsp; アルゴリズム効率評価
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+  
+
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+
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+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
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+    2.2 &nbsp; 反復と再帰
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+  
+
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+    </li>
+  
+
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+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
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+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
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+
+              
+            
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+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
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+  
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+    第 3 章 &nbsp; データ構造
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+            第 3 章 &nbsp; データ構造
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+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
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+    3.1 &nbsp; データ構造の分類
+  </span>
+  
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+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
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+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
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+
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+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
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+  </span>
+  
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+    </li>
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+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
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+  </span>
+  
+
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+    </li>
+  
+
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+  
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+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
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+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
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+  
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+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
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+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
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+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
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+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
+      </a>
+      
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
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+          
+        
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+    
+    
+    
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+      
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+            <a href="../../chapter_reference/" class="md-nav__link ">
+              
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9 3v15h3V3H9m3 2 4 13 3-1-4-13-3 1M5 5v13h3V5H5M3 19v2h18v-2H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    参考文献
+  </span>
+  
+
+            </a>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_19_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_19">
+            <span class="md-nav__icon md-icon"></span>
+            参考文献
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+      
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+  
+
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+  </ul>
+</nav>
+                  </div>
+                </div>
+              </div>
+            
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+              
+              <div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
+                <div class="md-sidebar__scrollwrap">
+                  <div class="md-sidebar__inner">
+                    
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
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+  
+  
+</nav>
+                  </div>
+                </div>
+              </div>
+            
+          
+          
+            <div class="md-content" data-md-component="content">
+              <article class="md-content__inner md-typeset">
+                
+                  <!-- Tags -->
+
+
+<!-- Actions -->
+<!-- Actions -->
+
+
+  <!-- Edit button -->
+  
+    <a
+      href="https://github.com/krahets/hello-algo/tree/main/ja/docs/chapter_appendix/terminology.md"
+      title="編集"
+      class="md-content__button md-icon"
+    >
+      
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
+    </a>
+  
+
+  <!-- View button -->
+  
+
+
+<!-- Page content -->
+<h1 id="163">16.3 &nbsp; 用語集<a class="headerlink" href="#163" title="Permanent link">&para;</a></h1>
+<p>下の表は本書に登場する重要な用語をリストアップしており、以下の点に注意する価値があります。</p>
+<ul>
+<li>英語文献を読みやすくするため、用語の英語名を覚えることをお勧めします。</li>
+<li>一部の用語は簡体字中国語と繁体字中国語で異なる名前を持ちます。</li>
+</ul>
+<p align="center"> 表 16-1 &nbsp; データ構造とアルゴリズムの重要用語 </p>
+
+<div class="center-table">
+<table>
+<thead>
+<tr>
+<th>English</th>
+<th>日本語</th>
+<th>简体中文</th>
+<th>繁体中文</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td>algorithm</td>
+<td>アルゴリズム</td>
+<td>算法</td>
+<td>演算法</td>
+</tr>
+<tr>
+<td>data structure</td>
+<td>データ構造</td>
+<td>数据结构</td>
+<td>資料結構</td>
+</tr>
+<tr>
+<td>code</td>
+<td>コード</td>
+<td>代码</td>
+<td>程式碼</td>
+</tr>
+<tr>
+<td>file</td>
+<td>ファイル</td>
+<td>文件</td>
+<td>檔案</td>
+</tr>
+<tr>
+<td>function</td>
+<td>関数</td>
+<td>函数</td>
+<td>函式</td>
+</tr>
+<tr>
+<td>method</td>
+<td>メソッド</td>
+<td>方法</td>
+<td>方法</td>
+</tr>
+<tr>
+<td>variable</td>
+<td>変数</td>
+<td>变量</td>
+<td>變數</td>
+</tr>
+<tr>
+<td>asymptotic complexity analysis</td>
+<td>漸近計算量解析</td>
+<td>渐近复杂度分析</td>
+<td>漸近複雜度分析</td>
+</tr>
+<tr>
+<td>time complexity</td>
+<td>時間計算量</td>
+<td>时间复杂度</td>
+<td>時間複雜度</td>
+</tr>
+<tr>
+<td>space complexity</td>
+<td>空間計算量</td>
+<td>空间复杂度</td>
+<td>空間複雜度</td>
+</tr>
+<tr>
+<td>loop</td>
+<td>ループ</td>
+<td>循环</td>
+<td>迴圈</td>
+</tr>
+<tr>
+<td>iteration</td>
+<td>反復</td>
+<td>迭代</td>
+<td>迭代</td>
+</tr>
+<tr>
+<td>recursion</td>
+<td>再帰</td>
+<td>递归</td>
+<td>遞迴</td>
+</tr>
+<tr>
+<td>tail recursion</td>
+<td>末尾再帰</td>
+<td>尾递归</td>
+<td>尾遞迴</td>
+</tr>
+<tr>
+<td>recursion tree</td>
+<td>再帰木</td>
+<td>递归树</td>
+<td>遞迴樹</td>
+</tr>
+<tr>
+<td>big-<span class="arithmatex">\(O\)</span> notation</td>
+<td>ビッグO記法</td>
+<td>大 <span class="arithmatex">\(O\)</span> 记号</td>
+<td>大 <span class="arithmatex">\(O\)</span> 記號</td>
+</tr>
+<tr>
+<td>asymptotic upper bound</td>
+<td>漸近上界</td>
+<td>渐近上界</td>
+<td>漸近上界</td>
+</tr>
+<tr>
+<td>sign-magnitude</td>
+<td>符号と絶対値</td>
+<td>原码</td>
+<td>原碼</td>
+</tr>
+<tr>
+<td>1's complement</td>
+<td>1の補数</td>
+<td>反码</td>
+<td>一補數</td>
+</tr>
+<tr>
+<td>2's complement</td>
+<td>2の補数</td>
+<td>补码</td>
+<td>二補數</td>
+</tr>
+<tr>
+<td>array</td>
+<td>配列</td>
+<td>数组</td>
+<td>陣列</td>
+</tr>
+<tr>
+<td>index</td>
+<td>インデックス</td>
+<td>索引</td>
+<td>索引</td>
+</tr>
+<tr>
+<td>linked list</td>
+<td>連結リスト</td>
+<td>链表</td>
+<td>鏈結串列</td>
+</tr>
+<tr>
+<td>linked list node, list node</td>
+<td>連結リストノード</td>
+<td>链表节点</td>
+<td>鏈結串列節點</td>
+</tr>
+<tr>
+<td>head node</td>
+<td>先頭ノード</td>
+<td>头节点</td>
+<td>頭節點</td>
+</tr>
+<tr>
+<td>tail node</td>
+<td>末尾ノード</td>
+<td>尾节点</td>
+<td>尾節點</td>
+</tr>
+<tr>
+<td>list</td>
+<td>リスト</td>
+<td>列表</td>
+<td>串列</td>
+</tr>
+<tr>
+<td>dynamic array</td>
+<td>動的配列</td>
+<td>动态数组</td>
+<td>動態陣列</td>
+</tr>
+<tr>
+<td>hard disk</td>
+<td>ハードディスク</td>
+<td>硬盘</td>
+<td>硬碟</td>
+</tr>
+<tr>
+<td>random-access memory (RAM)</td>
+<td>メモリ</td>
+<td>内存</td>
+<td>記憶體</td>
+</tr>
+<tr>
+<td>cache memory</td>
+<td>キャッシュメモリ</td>
+<td>缓存</td>
+<td>快取</td>
+</tr>
+<tr>
+<td>cache miss</td>
+<td>キャッシュミス</td>
+<td>缓存未命中</td>
+<td>快取未命中</td>
+</tr>
+<tr>
+<td>cache hit rate</td>
+<td>キャッシュヒット率</td>
+<td>缓存命中率</td>
+<td>快取命中率</td>
+</tr>
+<tr>
+<td>stack</td>
+<td>スタック</td>
+<td>栈</td>
+<td>堆疊</td>
+</tr>
+<tr>
+<td>top of the stack</td>
+<td>スタックトップ</td>
+<td>栈顶</td>
+<td>堆疊頂</td>
+</tr>
+<tr>
+<td>bottom of the stack</td>
+<td>スタックボトム</td>
+<td>栈底</td>
+<td>堆疊底</td>
+</tr>
+<tr>
+<td>queue</td>
+<td>キュー</td>
+<td>队列</td>
+<td>佇列</td>
+</tr>
+<tr>
+<td>double-ended queue</td>
+<td>両端キュー</td>
+<td>双向队列</td>
+<td>雙向佇列</td>
+</tr>
+<tr>
+<td>front of the queue</td>
+<td>キューの先頭</td>
+<td>队首</td>
+<td>佇列首</td>
+</tr>
+<tr>
+<td>rear of the queue</td>
+<td>キューの末尾</td>
+<td>队尾</td>
+<td>佇列尾</td>
+</tr>
+<tr>
+<td>hash table</td>
+<td>ハッシュテーブル</td>
+<td>哈希表</td>
+<td>雜湊表</td>
+</tr>
+<tr>
+<td>hash set</td>
+<td>ハッシュセット</td>
+<td>哈希集合</td>
+<td>雜湊集合</td>
+</tr>
+<tr>
+<td>bucket</td>
+<td>バケット</td>
+<td>桶</td>
+<td>桶</td>
+</tr>
+<tr>
+<td>hash function</td>
+<td>ハッシュ関数</td>
+<td>哈希函数</td>
+<td>雜湊函式</td>
+</tr>
+<tr>
+<td>hash collision</td>
+<td>ハッシュ衝突</td>
+<td>哈希冲突</td>
+<td>雜湊衝突</td>
+</tr>
+<tr>
+<td>load factor</td>
+<td>負荷率</td>
+<td>负载因子</td>
+<td>負載因子</td>
+</tr>
+<tr>
+<td>separate chaining</td>
+<td>チェイン法</td>
+<td>链式地址</td>
+<td>鏈結位址</td>
+</tr>
+<tr>
+<td>open addressing</td>
+<td>オープンアドレス法</td>
+<td>开放寻址</td>
+<td>開放定址</td>
+</tr>
+<tr>
+<td>linear probing</td>
+<td>線形プローブ法</td>
+<td>线性探测</td>
+<td>線性探查</td>
+</tr>
+<tr>
+<td>lazy deletion</td>
+<td>遅延削除</td>
+<td>懒删除</td>
+<td>懶刪除</td>
+</tr>
+<tr>
+<td>binary tree</td>
+<td>二分木</td>
+<td>二叉树</td>
+<td>二元樹</td>
+</tr>
+<tr>
+<td>tree node</td>
+<td>木のノード</td>
+<td>树节点</td>
+<td>樹節點</td>
+</tr>
+<tr>
+<td>left-child node</td>
+<td>左の子ノード</td>
+<td>左子节点</td>
+<td>左子節點</td>
+</tr>
+<tr>
+<td>right-child node</td>
+<td>右の子ノード</td>
+<td>右子节点</td>
+<td>右子節點</td>
+</tr>
+<tr>
+<td>parent node</td>
+<td>親ノード</td>
+<td>父节点</td>
+<td>父節點</td>
+</tr>
+<tr>
+<td>left subtree</td>
+<td>左の部分木</td>
+<td>左子树</td>
+<td>左子樹</td>
+</tr>
+<tr>
+<td>right subtree</td>
+<td>右の部分木</td>
+<td>右子树</td>
+<td>右子樹</td>
+</tr>
+<tr>
+<td>root node</td>
+<td>ルートノード</td>
+<td>根节点</td>
+<td>根節點</td>
+</tr>
+<tr>
+<td>leaf node</td>
+<td>葉ノード</td>
+<td>叶节点</td>
+<td>葉節點</td>
+</tr>
+<tr>
+<td>edge</td>
+<td>エッジ</td>
+<td>边</td>
+<td>邊</td>
+</tr>
+<tr>
+<td>level</td>
+<td>レベル</td>
+<td>层</td>
+<td>層</td>
+</tr>
+<tr>
+<td>degree</td>
+<td>次数</td>
+<td>度</td>
+<td>度</td>
+</tr>
+<tr>
+<td>height</td>
+<td>高さ</td>
+<td>高度</td>
+<td>高度</td>
+</tr>
+<tr>
+<td>depth</td>
+<td>深さ</td>
+<td>深度</td>
+<td>深度</td>
+</tr>
+<tr>
+<td>perfect binary tree</td>
+<td>完全二分木</td>
+<td>完美二叉树</td>
+<td>完美二元樹</td>
+</tr>
+<tr>
+<td>complete binary tree</td>
+<td>完全二分木</td>
+<td>完全二叉树</td>
+<td>完全二元樹</td>
+</tr>
+<tr>
+<td>full binary tree</td>
+<td>満二分木</td>
+<td>完满二叉树</td>
+<td>完滿二元樹</td>
+</tr>
+<tr>
+<td>balanced binary tree</td>
+<td>平衡二分木</td>
+<td>平衡二叉树</td>
+<td>平衡二元樹</td>
+</tr>
+<tr>
+<td>binary search tree</td>
+<td>二分探索木</td>
+<td>二叉搜索树</td>
+<td>二元搜尋樹</td>
+</tr>
+<tr>
+<td>AVL tree</td>
+<td>AVL木</td>
+<td>AVL 树</td>
+<td>AVL 樹</td>
+</tr>
+<tr>
+<td>red-black tree</td>
+<td>赤黒木</td>
+<td>红黑树</td>
+<td>紅黑樹</td>
+</tr>
+<tr>
+<td>level-order traversal</td>
+<td>レベル順走査</td>
+<td>层序遍历</td>
+<td>層序走訪</td>
+</tr>
+<tr>
+<td>breadth-first traversal</td>
+<td>幅優先走査</td>
+<td>广度优先遍历</td>
+<td>廣度優先走訪</td>
+</tr>
+<tr>
+<td>depth-first traversal</td>
+<td>深さ優先走査</td>
+<td>深度优先遍历</td>
+<td>深度優先走訪</td>
+</tr>
+<tr>
+<td>binary search tree</td>
+<td>二分探索木</td>
+<td>二叉搜索树</td>
+<td>二元搜尋樹</td>
+</tr>
+<tr>
+<td>balanced binary search tree</td>
+<td>平衡二分探索木</td>
+<td>平衡二叉搜索树</td>
+<td>平衡二元搜尋樹</td>
+</tr>
+<tr>
+<td>balance factor</td>
+<td>平衡因子</td>
+<td>平衡因子</td>
+<td>平衡因子</td>
+</tr>
+<tr>
+<td>heap</td>
+<td>ヒープ</td>
+<td>堆</td>
+<td>堆積</td>
+</tr>
+<tr>
+<td>max heap</td>
+<td>最大ヒープ</td>
+<td>大顶堆</td>
+<td>大頂堆積</td>
+</tr>
+<tr>
+<td>min heap</td>
+<td>最小ヒープ</td>
+<td>小顶堆</td>
+<td>小頂堆積</td>
+</tr>
+<tr>
+<td>priority queue</td>
+<td>優先度キュー</td>
+<td>优先队列</td>
+<td>優先佇列</td>
+</tr>
+<tr>
+<td>heapify</td>
+<td>ヒープ化</td>
+<td>堆化</td>
+<td>堆積化</td>
+</tr>
+<tr>
+<td>top-<span class="arithmatex">\(k\)</span> problem</td>
+<td>Top-<span class="arithmatex">\(k\)</span> 問題</td>
+<td>Top-<span class="arithmatex">\(k\)</span> 问题</td>
+<td>Top-<span class="arithmatex">\(k\)</span> 問題</td>
+</tr>
+<tr>
+<td>graph</td>
+<td>グラフ</td>
+<td>图</td>
+<td>圖</td>
+</tr>
+<tr>
+<td>vertex</td>
+<td>頂点</td>
+<td>顶点</td>
+<td>頂點</td>
+</tr>
+<tr>
+<td>undirected graph</td>
+<td>無向グラフ</td>
+<td>无向图</td>
+<td>無向圖</td>
+</tr>
+<tr>
+<td>directed graph</td>
+<td>有向グラフ</td>
+<td>有向图</td>
+<td>有向圖</td>
+</tr>
+<tr>
+<td>connected graph</td>
+<td>連結グラフ</td>
+<td>连通图</td>
+<td>連通圖</td>
+</tr>
+<tr>
+<td>disconnected graph</td>
+<td>非連結グラフ</td>
+<td>非连通图</td>
+<td>非連通圖</td>
+</tr>
+<tr>
+<td>weighted graph</td>
+<td>重み付きグラフ</td>
+<td>有权图</td>
+<td>有權圖</td>
+</tr>
+<tr>
+<td>adjacency</td>
+<td>隣接</td>
+<td>邻接</td>
+<td>鄰接</td>
+</tr>
+<tr>
+<td>path</td>
+<td>パス</td>
+<td>路径</td>
+<td>路徑</td>
+</tr>
+<tr>
+<td>in-degree</td>
+<td>入次数</td>
+<td>入度</td>
+<td>入度</td>
+</tr>
+<tr>
+<td>out-degree</td>
+<td>出次数</td>
+<td>出度</td>
+<td>出度</td>
+</tr>
+<tr>
+<td>adjacency matrix</td>
+<td>隣接行列</td>
+<td>邻接矩阵</td>
+<td>鄰接矩陣</td>
+</tr>
+<tr>
+<td>adjacency list</td>
+<td>隣接リスト</td>
+<td>邻接表</td>
+<td>鄰接表</td>
+</tr>
+<tr>
+<td>breadth-first search</td>
+<td>幅優先探索</td>
+<td>广度优先搜索</td>
+<td>廣度優先搜尋</td>
+</tr>
+<tr>
+<td>depth-first search</td>
+<td>深さ優先探索</td>
+<td>深度优先搜索</td>
+<td>深度優先搜尋</td>
+</tr>
+<tr>
+<td>binary search</td>
+<td>二分探索</td>
+<td>二分查找</td>
+<td>二分搜尋</td>
+</tr>
+<tr>
+<td>searching algorithm</td>
+<td>探索アルゴリズム</td>
+<td>搜索算法</td>
+<td>搜尋演算法</td>
+</tr>
+<tr>
+<td>sorting algorithm</td>
+<td>ソートアルゴリズム</td>
+<td>排序算法</td>
+<td>排序演算法</td>
+</tr>
+<tr>
+<td>selection sort</td>
+<td>選択ソート</td>
+<td>选择排序</td>
+<td>選擇排序</td>
+</tr>
+<tr>
+<td>bubble sort</td>
+<td>バブルソート</td>
+<td>冒泡排序</td>
+<td>泡沫排序</td>
+</tr>
+<tr>
+<td>insertion sort</td>
+<td>挿入ソート</td>
+<td>插入排序</td>
+<td>插入排序</td>
+</tr>
+<tr>
+<td>quick sort</td>
+<td>クイックソート</td>
+<td>快速排序</td>
+<td>快速排序</td>
+</tr>
+<tr>
+<td>merge sort</td>
+<td>マージソート</td>
+<td>归并排序</td>
+<td>合併排序</td>
+</tr>
+<tr>
+<td>heap sort</td>
+<td>ヒープソート</td>
+<td>堆排序</td>
+<td>堆積排序</td>
+</tr>
+<tr>
+<td>bucket sort</td>
+<td>バケットソート</td>
+<td>桶排序</td>
+<td>桶排序</td>
+</tr>
+<tr>
+<td>counting sort</td>
+<td>計数ソート</td>
+<td>计数排序</td>
+<td>計數排序</td>
+</tr>
+<tr>
+<td>radix sort</td>
+<td>基数ソート</td>
+<td>基数排序</td>
+<td>基數排序</td>
+</tr>
+<tr>
+<td>divide and conquer</td>
+<td>分割統治法</td>
+<td>分治</td>
+<td>分治</td>
+</tr>
+<tr>
+<td>hanota problem</td>
+<td>ハノイの塔問題</td>
+<td>汉诺塔问题</td>
+<td>河內塔問題</td>
+</tr>
+<tr>
+<td>backtracking algorithm</td>
+<td>バックトラッキング</td>
+<td>回溯算法</td>
+<td>回溯演算法</td>
+</tr>
+<tr>
+<td>constraint</td>
+<td>制約</td>
+<td>约束</td>
+<td>約束</td>
+</tr>
+<tr>
+<td>solution</td>
+<td>解</td>
+<td>解</td>
+<td>解</td>
+</tr>
+<tr>
+<td>state</td>
+<td>状態</td>
+<td>状态</td>
+<td>狀態</td>
+</tr>
+<tr>
+<td>pruning</td>
+<td>枝刈り</td>
+<td>剪枝</td>
+<td>剪枝</td>
+</tr>
+<tr>
+<td>permutations problem</td>
+<td>順列問題</td>
+<td>全排列问题</td>
+<td>全排列問題</td>
+</tr>
+<tr>
+<td>subset-sum problem</td>
+<td>部分集合和問題</td>
+<td>子集和问题</td>
+<td>子集合問題</td>
+</tr>
+<tr>
+<td><span class="arithmatex">\(n\)</span>-queens problem</td>
+<td><span class="arithmatex">\(n\)</span> クイーン問題</td>
+<td><span class="arithmatex">\(n\)</span> 皇后问题</td>
+<td><span class="arithmatex">\(n\)</span> 皇后問題</td>
+</tr>
+<tr>
+<td>dynamic programming</td>
+<td>動的プログラミング</td>
+<td>动态规划</td>
+<td>動態規劃</td>
+</tr>
+<tr>
+<td>initial state</td>
+<td>初期状態</td>
+<td>初始状态</td>
+<td>初始狀態</td>
+</tr>
+<tr>
+<td>state-transition equation</td>
+<td>状態遷移方程式</td>
+<td>状态转移方程</td>
+<td>狀態轉移方程</td>
+</tr>
+<tr>
+<td>knapsack problem</td>
+<td>ナップサック問題</td>
+<td>背包问题</td>
+<td>背包問題</td>
+</tr>
+<tr>
+<td>edit distance problem</td>
+<td>編集距離問題</td>
+<td>编辑距离问题</td>
+<td>編輯距離問題</td>
+</tr>
+<tr>
+<td>greedy algorithm</td>
+<td>貪欲アルゴリズム</td>
+<td>贪心算法</td>
+<td>貪婪演算法</td>
+</tr>
+</tbody>
+</table>
+</div>
+
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+      <a href="../../chapter_preface/summary/" class="md-nav__link">
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+  
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+    第 1 章 &nbsp; アルゴリズムとの出会い
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+  
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+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
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+    1.3 &nbsp; まとめ
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+        
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+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
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+            第 2 章 &nbsp; 計算量解析
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+    2.1 &nbsp; アルゴリズム効率評価
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+    2.2 &nbsp; 反復と再帰
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+  
+
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+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
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+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
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+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
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+    </li>
+  
+
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+  
+  
+  
+  
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+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
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+  
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+    第 3 章 &nbsp; データ構造
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#411" class="md-nav__link">
+    <span class="md-ellipsis">
+      4.1.1 &nbsp; 配列の一般的な操作
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="4.1.1   配列の一般的な操作">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 配列の初期化
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; 要素へのアクセス
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#3" class="md-nav__link">
+    <span class="md-ellipsis">
+      3. &nbsp; 要素の挿入
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#4" class="md-nav__link">
+    <span class="md-ellipsis">
+      4. &nbsp; 要素の削除
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#5" class="md-nav__link">
+    <span class="md-ellipsis">
+      5. &nbsp; 配列の走査
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#6" class="md-nav__link">
+    <span class="md-ellipsis">
+      6. &nbsp; 要素の検索
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#7" class="md-nav__link">
+    <span class="md-ellipsis">
+      7. &nbsp; 配列の拡張
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#412" class="md-nav__link">
+    <span class="md-ellipsis">
+      4.1.2 &nbsp; 配列の利点と制限
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#413" class="md-nav__link">
+    <span class="md-ellipsis">
+      4.1.3 &nbsp; 配列の典型的な応用
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_19" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_reference/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9 3v15h3V3H9m3 2 4 13 3-1-4-13-3 1M5 5v13h3V5H5M3 19v2h18v-2H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    参考文献
+  </span>
+  
+
+            </a>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_19_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_19">
+            <span class="md-nav__icon md-icon"></span>
+            参考文献
+          </label>
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+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#411" class="md-nav__link">
+    <span class="md-ellipsis">
+      4.1.1 &nbsp; 配列の一般的な操作
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="4.1.1   配列の一般的な操作">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 配列の初期化
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; 要素へのアクセス
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#3" class="md-nav__link">
+    <span class="md-ellipsis">
+      3. &nbsp; 要素の挿入
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#4" class="md-nav__link">
+    <span class="md-ellipsis">
+      4. &nbsp; 要素の削除
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#5" class="md-nav__link">
+    <span class="md-ellipsis">
+      5. &nbsp; 配列の走査
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#6" class="md-nav__link">
+    <span class="md-ellipsis">
+      6. &nbsp; 要素の検索
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#7" class="md-nav__link">
+    <span class="md-ellipsis">
+      7. &nbsp; 配列の拡張
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#412" class="md-nav__link">
+    <span class="md-ellipsis">
+      4.1.2 &nbsp; 配列の利点と制限
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#413" class="md-nav__link">
+    <span class="md-ellipsis">
+      4.1.3 &nbsp; 配列の典型的な応用
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+                  </div>
+                </div>
+              </div>
+            
+          
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+      href="https://github.com/krahets/hello-algo/tree/main/ja/docs/chapter_array_and_linkedlist/array.md"
+      title="編集"
+      class="md-content__button md-icon"
+    >
+      
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
+    </a>
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+<!-- Page content -->
+<h1 id="41">4.1 &nbsp; 配列<a class="headerlink" href="#41" title="Permanent link">&para;</a></h1>
+<p><u>配列</u>は線形データ構造で、同じような項目が並んでいるようなもので、コンピュータのメモリ内の連続した空間に一緒に格納されます。これは整理された格納を維持するシーケンスのようなものです。この並びの各項目には、<u>インデックス</u>として知られる独自の「位置」があります。以下の図を参照して、配列の動作を観察し、これらの重要な用語を理解してください。</p>
+<p><a class="glightbox" href="../array.assets/array_definition.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="配列の定義と格納方法" class="animation-figure" src="../array.assets/array_definition.png" /></a></p>
+<p align="center"> 図 4-1 &nbsp; 配列の定義と格納方法 </p>
+
+<h2 id="411">4.1.1 &nbsp; 配列の一般的な操作<a class="headerlink" href="#411" title="Permanent link">&para;</a></h2>
+<h3 id="1">1. &nbsp; 配列の初期化<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<p>配列は必要に応じて2つの方法で初期化できます：初期値なしまたは指定された初期値付きです。初期値が指定されていない場合、ほとんどのプログラミング言語は配列要素を<span class="arithmatex">\(0\)</span>に設定します：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="c1"># 配列を初期化</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="n">arr</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="mi">5</span>  <span class="c1"># [ 0, 0, 0, 0, 0 ]</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">4</span><span class="p">]</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 配列を初期化 */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="c1">// スタックに格納</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="kt">int</span><span class="w"> </span><span class="n">arr</span><span class="p">[</span><span class="mi">5</span><span class="p">];</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="kt">int</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="mi">5</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="w"> </span><span class="p">};</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="c1">// ヒープに格納（手動でのメモリ解放が必要）</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="kt">int</span><span class="o">*</span><span class="w"> </span><span class="n">arr1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="mi">5</span><span class="p">];</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="kt">int</span><span class="o">*</span><span class="w"> </span><span class="n">nums1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="mi">5</span><span class="p">]</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="w"> </span><span class="p">};</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 配列を初期化 */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="mi">5</span><span class="o">]</span><span class="p">;</span><span class="w"> </span><span class="c1">// { 0, 0, 0, 0, 0 }</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="w"> </span><span class="p">};</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 配列を初期化 */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="mi">5</span><span class="p">];</span><span class="w"> </span><span class="c1">// [ 0, 0, 0, 0, 0 ]</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">];</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 配列を初期化 */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">var</span><span class="w"> </span><span class="nx">arr</span><span class="w"> </span><span class="p">[</span><span class="mi">5</span><span class="p">]</span><span class="kt">int</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="c1">// Goでは、長さを指定（[5]int）すると配列を示し、指定しない（[]int）とスライスを示します。</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="c1">// Goの配列はコンパイル時に固定長を持つよう設計されているため、長さの指定には定数のみ使用できます。</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="c1">// extend()メソッドの実装の便宜上、ここではSliceを配列として扱います。</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="nx">nums</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">{</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 配列を初期化 */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">let</span><span class="w"> </span><span class="nv">arr</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="mi">5</span><span class="p">)</span><span class="w"> </span><span class="c1">// [0, 0, 0, 0, 0]</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="kd">let</span><span class="w"> </span><span class="nv">nums</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">]</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 配列を初期化 */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">var</span><span class="w"> </span><span class="nx">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="mf">5</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="kd">var</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="mf">3</span><span class="p">,</span><span class="w"> </span><span class="mf">2</span><span class="p">,</span><span class="w"> </span><span class="mf">5</span><span class="p">,</span><span class="w"> </span><span class="mf">4</span><span class="p">];</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 配列を初期化 */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">let</span><span class="w"> </span><span class="nx">arr</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="mf">5</span><span class="p">).</span><span class="nx">fill</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="kd">let</span><span class="w"> </span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="mf">3</span><span class="p">,</span><span class="w"> </span><span class="mf">2</span><span class="p">,</span><span class="w"> </span><span class="mf">5</span><span class="p">,</span><span class="w"> </span><span class="mf">4</span><span class="p">];</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 配列を初期化 */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="m">5</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// [0, 0, 0, 0, 0]</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="m">3</span><span class="p">,</span><span class="w"> </span><span class="m">2</span><span class="p">,</span><span class="w"> </span><span class="m">5</span><span class="p">,</span><span class="w"> </span><span class="m">4</span><span class="p">];</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 配列を初期化 */</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="kd">let</span><span class="w"> </span><span class="n">arr</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="kt">i32</span><span class="p">;</span><span class="w"> </span><span class="mi">5</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="mi">5</span><span class="p">];</span><span class="w"> </span><span class="c1">// [0, 0, 0, 0, 0]</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="kd">let</span><span class="w"> </span><span class="n">slice</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="p">[</span><span class="kt">i32</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">&amp;</span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="mi">5</span><span class="p">];</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="c1">// Rustでは、長さを指定（[i32; 5]）すると配列を示し、指定しない（&amp;[i32]）とスライスを示します。</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="c1">// Rustの配列はコンパイル時に固定長を持つよう設計されているため、長さの指定には定数のみ使用できます。</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="c1">// 一般的にRustでは動的配列としてVectorが使用されます。</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="c1">// extend()メソッドの実装の便宜上、ここではベクターを配列として扱います。</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="kd">let</span><span class="w"> </span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">];</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 配列を初期化 */</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">arr</span><span class="p">[</span><span class="mi">5</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">};</span><span class="w"> </span><span class="c1">// { 0, 0, 0, 0, 0 }</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="kt">int</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="mi">5</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="w"> </span><span class="p">};</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.zig</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">// 配列を初期化</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="kr">var</span><span class="w"> </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="n">_</span><span class="p">]</span><span class="kt">i32</span><span class="p">{</span><span class="mi">0</span><span class="p">}</span><span class="w"> </span><span class="o">**</span><span class="w"> </span><span class="mi">5</span><span class="p">;</span><span class="w"> </span><span class="c1">// { 0, 0, 0, 0, 0 }</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="kr">var</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="n">_</span><span class="p">]</span><span class="kt">i32</span><span class="p">{</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="w"> </span><span class="p">};</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h3 id="2">2. &nbsp; 要素へのアクセス<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
+<p>配列内の要素は連続したメモリ空間に格納されるため、各要素のメモリアドレスを計算することが簡単になります。以下の図に示されている公式は、配列のメモリアドレス（特に、最初の要素のアドレス）と要素のインデックスを利用して、要素のメモリアドレスを決定するのに役立ちます。この計算により、目的の要素への直接アクセスが合理化されます。</p>
+<p><a class="glightbox" href="../array.assets/array_memory_location_calculation.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="配列要素のメモリアドレス計算" class="animation-figure" src="../array.assets/array_memory_location_calculation.png" /></a></p>
+<p align="center"> 図 4-2 &nbsp; 配列要素のメモリアドレス計算 </p>
+
+<p>上の図で観察されるように、配列のインデックスは慣例的に<span class="arithmatex">\(0\)</span>から始まります。これは直感に反するように見えるかもしれません。数を数えるのは通常<span class="arithmatex">\(1\)</span>から始まるためですが、アドレス計算公式内では、**インデックスは本質的にメモリアドレスからのオフセット**です。最初の要素のアドレスでは、このオフセットは<span class="arithmatex">\(0\)</span>で、そのインデックスが<span class="arithmatex">\(0\)</span>であることを検証しています。</p>
+<p>配列内の要素へのアクセスは非常に効率的で、<span class="arithmatex">\(O(1)\)</span>時間で任意の要素にランダムアクセスできます。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:14"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><input id="__tabbed_2_14" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label><label for="__tabbed_2_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.py</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">random_access</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;要素へのランダムアクセス&quot;&quot;&quot;</span>
+<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>    <span class="c1"># 区間 [0, len(nums)-1] から数値をランダムに選択</span>
+<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a>    <span class="n">random_index</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">randint</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a>    <span class="c1"># ランダムな要素を取得して返す</span>
+<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a>    <span class="n">random_num</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">random_index</span><span class="p">]</span>
+<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a>    <span class="k">return</span> <span class="n">random_num</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 要素への乱数アクセス */</span>
+<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">randomAccess</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">    </span><span class="c1">// [0, size)の範囲で乱数を選択</span>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">randomIndex</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rand</span><span class="p">()</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">size</span><span class="p">;</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w">    </span><span class="c1">// 乱数要素を取得して返却</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">randomNum</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">randomIndex</span><span class="p">];</span>
+<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">randomNum</span><span class="p">;</span>
+<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 要素へのランダムアクセス */</span>
+<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">randomAccess</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="c1">// 区間 [0, nums.length) からランダムに数を選択</span>
+<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">randomIndex</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ThreadLocalRandom</span><span class="p">.</span><span class="na">current</span><span class="p">().</span><span class="na">nextInt</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="p">);</span>
+<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">    </span><span class="c1">// ランダム要素を取得して返す</span>
+<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">randomNum</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">randomIndex</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">randomNum</span><span class="p">;</span>
+<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">array</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">RandomAccess</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">randomAccess</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">randomAccess</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">randomAccess</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">randomAccess</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">randomAccess</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">random_access</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">randomAccess</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">randomAccess</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">random_access</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.zig</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">randomAccess</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h3 id="3">3. &nbsp; 要素の挿入<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
+<p>配列要素はメモリ内で密に詰まっており、それらの間に追加データを収容するための空間はありません。以下の図に示すように、配列の中央に要素を挿入するには、後続のすべての要素を1つずつ後ろにシフトして、新しい要素のための空間を作る必要があります。</p>
+<p><a class="glightbox" href="../array.assets/array_insert_element.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="配列要素挿入の例" class="animation-figure" src="../array.assets/array_insert_element.png" /></a></p>
+<p align="center"> 図 4-3 &nbsp; 配列要素挿入の例 </p>
+
+<p>配列の長さが固定されているため、要素を挿入すると必然的に配列の最後の要素が失われることに注意することが重要です。この問題を解決する方法は「リスト」の章で探求されます。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="3:14"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><input id="__tabbed_3_14" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label><label for="__tabbed_3_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.py</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">num</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">index</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;インデックス index に要素 num を挿入&quot;&quot;&quot;</span>
+<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a>    <span class="c1"># インデックス index より後のすべての要素を1つ後ろに移動</span>
+<a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">index</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a>        <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a>    <span class="c1"># num を index の位置の要素に代入</span>
+<a id="__codelineno-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a>    <span class="n">nums</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">=</span> <span class="n">num</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.cpp</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="cm">/* `index`に要素numを挿入 */</span>
+<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a><span class="w">    </span><span class="c1">// `index`より後のすべての要素を1つ後ろに移動</span>
+<a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a><span class="w">    </span><span class="c1">// indexの位置にnumを代入</span>
+<a id="__codelineno-28-8" name="__codelineno-28-8" href="#__codelineno-28-8"></a><span class="w">    </span><span class="n">nums</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-28-9" name="__codelineno-28-9" href="#__codelineno-28-9"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.java</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="cm">/* `index` に要素 num を挿入 */</span>
+<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w">    </span><span class="c1">// `index` より後のすべての要素を1つ後ろに移動</span>
+<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="w">    </span><span class="c1">// index の要素に num を代入</span>
+<a id="__codelineno-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a><span class="w">    </span><span class="n">nums</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-29-9" name="__codelineno-29-9" href="#__codelineno-29-9"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.cs</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">array</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Insert</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.go</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">insert</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.swift</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="bp">insert</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.js</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">insert</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.ts</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">insert</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.dart</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">insert</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.rs</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">insert</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.c</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">insert</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.kt</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">insert</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.rb</span><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">insert</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.zig</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">insert</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h3 id="4">4. &nbsp; 要素の削除<a class="headerlink" href="#4" title="Permanent link">&para;</a></h3>
+<p>同様に、以下の図に示すように、インデックス<span class="arithmatex">\(i\)</span>の要素を削除するには、インデックス<span class="arithmatex">\(i\)</span>に続くすべての要素を1つずつ前に移動する必要があります。</p>
+<p><a class="glightbox" href="../array.assets/array_remove_element.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="配列要素削除の例" class="animation-figure" src="../array.assets/array_remove_element.png" /></a></p>
+<p align="center"> 図 4-4 &nbsp; 配列要素削除の例 </p>
+
+<p>削除後、元の最後の要素は「意味がない」ものになるため、特定の修正は必要ないことに注意してください。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="4:14"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><input id="__tabbed_4_6" name="__tabbed_4" type="radio" /><input id="__tabbed_4_7" name="__tabbed_4" type="radio" /><input id="__tabbed_4_8" name="__tabbed_4" type="radio" /><input id="__tabbed_4_9" name="__tabbed_4" type="radio" /><input id="__tabbed_4_10" name="__tabbed_4" type="radio" /><input id="__tabbed_4_11" name="__tabbed_4" type="radio" /><input id="__tabbed_4_12" name="__tabbed_4" type="radio" /><input id="__tabbed_4_13" name="__tabbed_4" type="radio" /><input id="__tabbed_4_14" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">Python</label><label for="__tabbed_4_2">C++</label><label for="__tabbed_4_3">Java</label><label for="__tabbed_4_4">C#</label><label for="__tabbed_4_5">Go</label><label for="__tabbed_4_6">Swift</label><label for="__tabbed_4_7">JS</label><label for="__tabbed_4_8">TS</label><label for="__tabbed_4_9">Dart</label><label for="__tabbed_4_10">Rust</label><label for="__tabbed_4_11">C</label><label for="__tabbed_4_12">Kotlin</label><label for="__tabbed_4_13">Ruby</label><label for="__tabbed_4_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.py</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">index</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-41-2" name="__codelineno-41-2" href="#__codelineno-41-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;インデックス index の要素を削除&quot;&quot;&quot;</span>
+<a id="__codelineno-41-3" name="__codelineno-41-3" href="#__codelineno-41-3"></a>    <span class="c1"># インデックス index より後のすべての要素を1つ前に移動</span>
+<a id="__codelineno-41-4" name="__codelineno-41-4" href="#__codelineno-41-4"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">index</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-41-5" name="__codelineno-41-5" href="#__codelineno-41-5"></a>        <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.cpp</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="cm">/* `index`の要素を削除 */</span>
+<a id="__codelineno-42-2" name="__codelineno-42-2" href="#__codelineno-42-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></a><span class="w">    </span><span class="c1">// `index`より後のすべての要素を1つ前に移動</span>
+<a id="__codelineno-42-4" name="__codelineno-42-4" href="#__codelineno-42-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-5" name="__codelineno-42-5" href="#__codelineno-42-5"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-42-6" name="__codelineno-42-6" href="#__codelineno-42-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-42-7" name="__codelineno-42-7" href="#__codelineno-42-7"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.java</span><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="cm">/* `index` の要素を削除 */</span>
+<a id="__codelineno-43-2" name="__codelineno-43-2" href="#__codelineno-43-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-3" name="__codelineno-43-3" href="#__codelineno-43-3"></a><span class="w">    </span><span class="c1">// `index` より後のすべての要素を1つ前に移動</span>
+<a id="__codelineno-43-4" name="__codelineno-43-4" href="#__codelineno-43-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-5" name="__codelineno-43-5" href="#__codelineno-43-5"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-43-6" name="__codelineno-43-6" href="#__codelineno-43-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-43-7" name="__codelineno-43-7" href="#__codelineno-43-7"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.cs</span><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">array</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Remove</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.go</span><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">remove</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.swift</span><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">remove</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.js</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">remove</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.ts</span><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">remove</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.dart</span><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">remove</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.rs</span><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">remove</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.c</span><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">removeItem</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.kt</span><pre><span></span><code><a id="__codelineno-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">remove</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.rb</span><pre><span></span><code><a id="__codelineno-53-1" name="__codelineno-53-1" href="#__codelineno-53-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">remove</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.zig</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">remove</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>要約すると、配列の挿入と削除操作には以下の欠点があります：</p>
+<ul>
+<li><strong>高い時間計算量</strong>：配列の挿入と削除の両方の平均時間計算量は<span class="arithmatex">\(O(n)\)</span>で、ここで<span class="arithmatex">\(n\)</span>は配列の長さです。</li>
+<li><strong>要素の損失</strong>：配列の長さが固定されているため、挿入時に配列の容量を超える要素は失われます。</li>
+<li><strong>メモリの無駄</strong>：より長い配列を初期化して前部分のみを利用すると、挿入時に「意味のない」末尾要素が生じ、メモリ空間の無駄につながります。</li>
+</ul>
+<h3 id="5">5. &nbsp; 配列の走査<a class="headerlink" href="#5" title="Permanent link">&para;</a></h3>
+<p>ほとんどのプログラミング言語では、インデックスを使用するか、各要素を直接反復することで配列を走査できます：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="5:14"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><input id="__tabbed_5_7" name="__tabbed_5" type="radio" /><input id="__tabbed_5_8" name="__tabbed_5" type="radio" /><input id="__tabbed_5_9" name="__tabbed_5" type="radio" /><input id="__tabbed_5_10" name="__tabbed_5" type="radio" /><input id="__tabbed_5_11" name="__tabbed_5" type="radio" /><input id="__tabbed_5_12" name="__tabbed_5" type="radio" /><input id="__tabbed_5_13" name="__tabbed_5" type="radio" /><input id="__tabbed_5_14" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">Python</label><label for="__tabbed_5_2">C++</label><label for="__tabbed_5_3">Java</label><label for="__tabbed_5_4">C#</label><label for="__tabbed_5_5">Go</label><label for="__tabbed_5_6">Swift</label><label for="__tabbed_5_7">JS</label><label for="__tabbed_5_8">TS</label><label for="__tabbed_5_9">Dart</label><label for="__tabbed_5_10">Rust</label><label for="__tabbed_5_11">C</label><label for="__tabbed_5_12">Kotlin</label><label for="__tabbed_5_13">Ruby</label><label for="__tabbed_5_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.py</span><pre><span></span><code><a id="__codelineno-55-1" name="__codelineno-55-1" href="#__codelineno-55-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">traverse</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]):</span>
+<a id="__codelineno-55-2" name="__codelineno-55-2" href="#__codelineno-55-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;配列の走査&quot;&quot;&quot;</span>
+<a id="__codelineno-55-3" name="__codelineno-55-3" href="#__codelineno-55-3"></a>    <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-55-4" name="__codelineno-55-4" href="#__codelineno-55-4"></a>    <span class="c1"># インデックスによる配列の走査</span>
+<a id="__codelineno-55-5" name="__codelineno-55-5" href="#__codelineno-55-5"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)):</span>
+<a id="__codelineno-55-6" name="__codelineno-55-6" href="#__codelineno-55-6"></a>        <span class="n">count</span> <span class="o">+=</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+<a id="__codelineno-55-7" name="__codelineno-55-7" href="#__codelineno-55-7"></a>    <span class="c1"># 配列要素の走査</span>
+<a id="__codelineno-55-8" name="__codelineno-55-8" href="#__codelineno-55-8"></a>    <span class="k">for</span> <span class="n">num</span> <span class="ow">in</span> <span class="n">nums</span><span class="p">:</span>
+<a id="__codelineno-55-9" name="__codelineno-55-9" href="#__codelineno-55-9"></a>        <span class="n">count</span> <span class="o">+=</span> <span class="n">num</span>
+<a id="__codelineno-55-10" name="__codelineno-55-10" href="#__codelineno-55-10"></a>    <span class="c1"># データのインデックスと要素の両方を走査</span>
+<a id="__codelineno-55-11" name="__codelineno-55-11" href="#__codelineno-55-11"></a>    <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">num</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">nums</span><span class="p">):</span>
+<a id="__codelineno-55-12" name="__codelineno-55-12" href="#__codelineno-55-12"></a>        <span class="n">count</span> <span class="o">+=</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+<a id="__codelineno-55-13" name="__codelineno-55-13" href="#__codelineno-55-13"></a>        <span class="n">count</span> <span class="o">+=</span> <span class="n">num</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.cpp</span><pre><span></span><code><a id="__codelineno-56-1" name="__codelineno-56-1" href="#__codelineno-56-1"></a><span class="cm">/* 配列の走査 */</span>
+<a id="__codelineno-56-2" name="__codelineno-56-2" href="#__codelineno-56-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">traverse</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-56-3" name="__codelineno-56-3" href="#__codelineno-56-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-56-4" name="__codelineno-56-4" href="#__codelineno-56-4"></a><span class="w">    </span><span class="c1">// インデックスによる配列の走査</span>
+<a id="__codelineno-56-5" name="__codelineno-56-5" href="#__codelineno-56-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-56-6" name="__codelineno-56-6" href="#__codelineno-56-6"></a><span class="w">        </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-56-7" name="__codelineno-56-7" href="#__codelineno-56-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-56-8" name="__codelineno-56-8" href="#__codelineno-56-8"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.java</span><pre><span></span><code><a id="__codelineno-57-1" name="__codelineno-57-1" href="#__codelineno-57-1"></a><span class="cm">/* 配列を走査 */</span>
+<a id="__codelineno-57-2" name="__codelineno-57-2" href="#__codelineno-57-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">traverse</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-3" name="__codelineno-57-3" href="#__codelineno-57-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-57-4" name="__codelineno-57-4" href="#__codelineno-57-4"></a><span class="w">    </span><span class="c1">// インデックスによる配列の走査</span>
+<a id="__codelineno-57-5" name="__codelineno-57-5" href="#__codelineno-57-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-6" name="__codelineno-57-6" href="#__codelineno-57-6"></a><span class="w">        </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-57-7" name="__codelineno-57-7" href="#__codelineno-57-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-57-8" name="__codelineno-57-8" href="#__codelineno-57-8"></a><span class="w">    </span><span class="c1">// 配列要素の走査</span>
+<a id="__codelineno-57-9" name="__codelineno-57-9" href="#__codelineno-57-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-10" name="__codelineno-57-10" href="#__codelineno-57-10"></a><span class="w">        </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-57-11" name="__codelineno-57-11" href="#__codelineno-57-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-57-12" name="__codelineno-57-12" href="#__codelineno-57-12"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.cs</span><pre><span></span><code><a id="__codelineno-58-1" name="__codelineno-58-1" href="#__codelineno-58-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">array</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Traverse</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.go</span><pre><span></span><code><a id="__codelineno-59-1" name="__codelineno-59-1" href="#__codelineno-59-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">traverse</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.swift</span><pre><span></span><code><a id="__codelineno-60-1" name="__codelineno-60-1" href="#__codelineno-60-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">traverse</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.js</span><pre><span></span><code><a id="__codelineno-61-1" name="__codelineno-61-1" href="#__codelineno-61-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">traverse</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.ts</span><pre><span></span><code><a id="__codelineno-62-1" name="__codelineno-62-1" href="#__codelineno-62-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">traverse</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.dart</span><pre><span></span><code><a id="__codelineno-63-1" name="__codelineno-63-1" href="#__codelineno-63-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">traverse</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.rs</span><pre><span></span><code><a id="__codelineno-64-1" name="__codelineno-64-1" href="#__codelineno-64-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">traverse</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.c</span><pre><span></span><code><a id="__codelineno-65-1" name="__codelineno-65-1" href="#__codelineno-65-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">traverse</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.kt</span><pre><span></span><code><a id="__codelineno-66-1" name="__codelineno-66-1" href="#__codelineno-66-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">traverse</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.rb</span><pre><span></span><code><a id="__codelineno-67-1" name="__codelineno-67-1" href="#__codelineno-67-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">traverse</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.zig</span><pre><span></span><code><a id="__codelineno-68-1" name="__codelineno-68-1" href="#__codelineno-68-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">traverse</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h3 id="6">6. &nbsp; 要素の検索<a class="headerlink" href="#6" title="Permanent link">&para;</a></h3>
+<p>配列内の特定の要素を見つけることは、配列を反復し、各要素をチェックして目的の値と一致するかどうかを決定することを含みます。</p>
+<p>配列は線形データ構造であるため、この操作は一般的に「線形探索」と呼ばれます。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="6:14"><input checked="checked" id="__tabbed_6_1" name="__tabbed_6" type="radio" /><input id="__tabbed_6_2" name="__tabbed_6" type="radio" /><input id="__tabbed_6_3" name="__tabbed_6" type="radio" /><input id="__tabbed_6_4" name="__tabbed_6" type="radio" /><input id="__tabbed_6_5" name="__tabbed_6" type="radio" /><input id="__tabbed_6_6" name="__tabbed_6" type="radio" /><input id="__tabbed_6_7" name="__tabbed_6" type="radio" /><input id="__tabbed_6_8" name="__tabbed_6" type="radio" /><input id="__tabbed_6_9" name="__tabbed_6" type="radio" /><input id="__tabbed_6_10" name="__tabbed_6" type="radio" /><input id="__tabbed_6_11" name="__tabbed_6" type="radio" /><input id="__tabbed_6_12" name="__tabbed_6" type="radio" /><input id="__tabbed_6_13" name="__tabbed_6" type="radio" /><input id="__tabbed_6_14" name="__tabbed_6" type="radio" /><div class="tabbed-labels"><label for="__tabbed_6_1">Python</label><label for="__tabbed_6_2">C++</label><label for="__tabbed_6_3">Java</label><label for="__tabbed_6_4">C#</label><label for="__tabbed_6_5">Go</label><label for="__tabbed_6_6">Swift</label><label for="__tabbed_6_7">JS</label><label for="__tabbed_6_8">TS</label><label for="__tabbed_6_9">Dart</label><label for="__tabbed_6_10">Rust</label><label for="__tabbed_6_11">C</label><label for="__tabbed_6_12">Kotlin</label><label for="__tabbed_6_13">Ruby</label><label for="__tabbed_6_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.py</span><pre><span></span><code><a id="__codelineno-69-1" name="__codelineno-69-1" href="#__codelineno-69-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">find</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">target</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-69-2" name="__codelineno-69-2" href="#__codelineno-69-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;配列内の指定された要素を検索&quot;&quot;&quot;</span>
+<a id="__codelineno-69-3" name="__codelineno-69-3" href="#__codelineno-69-3"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)):</span>
+<a id="__codelineno-69-4" name="__codelineno-69-4" href="#__codelineno-69-4"></a>        <span class="k">if</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">==</span> <span class="n">target</span><span class="p">:</span>
+<a id="__codelineno-69-5" name="__codelineno-69-5" href="#__codelineno-69-5"></a>            <span class="k">return</span> <span class="n">i</span>
+<a id="__codelineno-69-6" name="__codelineno-69-6" href="#__codelineno-69-6"></a>    <span class="k">return</span> <span class="o">-</span><span class="mi">1</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.cpp</span><pre><span></span><code><a id="__codelineno-70-1" name="__codelineno-70-1" href="#__codelineno-70-1"></a><span class="cm">/* 配列内の指定要素を検索 */</span>
+<a id="__codelineno-70-2" name="__codelineno-70-2" href="#__codelineno-70-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">find</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-70-3" name="__codelineno-70-3" href="#__codelineno-70-3"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-70-4" name="__codelineno-70-4" href="#__codelineno-70-4"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">target</span><span class="p">)</span>
+<a id="__codelineno-70-5" name="__codelineno-70-5" href="#__codelineno-70-5"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-70-6" name="__codelineno-70-6" href="#__codelineno-70-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-70-7" name="__codelineno-70-7" href="#__codelineno-70-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
+<a id="__codelineno-70-8" name="__codelineno-70-8" href="#__codelineno-70-8"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.java</span><pre><span></span><code><a id="__codelineno-71-1" name="__codelineno-71-1" href="#__codelineno-71-1"></a><span class="cm">/* 配列内で指定された要素を検索 */</span>
+<a id="__codelineno-71-2" name="__codelineno-71-2" href="#__codelineno-71-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">find</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-71-3" name="__codelineno-71-3" href="#__codelineno-71-3"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-71-4" name="__codelineno-71-4" href="#__codelineno-71-4"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">target</span><span class="p">)</span>
+<a id="__codelineno-71-5" name="__codelineno-71-5" href="#__codelineno-71-5"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-71-6" name="__codelineno-71-6" href="#__codelineno-71-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-71-7" name="__codelineno-71-7" href="#__codelineno-71-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-71-8" name="__codelineno-71-8" href="#__codelineno-71-8"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.cs</span><pre><span></span><code><a id="__codelineno-72-1" name="__codelineno-72-1" href="#__codelineno-72-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">array</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Find</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.go</span><pre><span></span><code><a id="__codelineno-73-1" name="__codelineno-73-1" href="#__codelineno-73-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">find</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.swift</span><pre><span></span><code><a id="__codelineno-74-1" name="__codelineno-74-1" href="#__codelineno-74-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="bp">find</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.js</span><pre><span></span><code><a id="__codelineno-75-1" name="__codelineno-75-1" href="#__codelineno-75-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">find</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.ts</span><pre><span></span><code><a id="__codelineno-76-1" name="__codelineno-76-1" href="#__codelineno-76-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">find</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.dart</span><pre><span></span><code><a id="__codelineno-77-1" name="__codelineno-77-1" href="#__codelineno-77-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">find</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.rs</span><pre><span></span><code><a id="__codelineno-78-1" name="__codelineno-78-1" href="#__codelineno-78-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">find</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.c</span><pre><span></span><code><a id="__codelineno-79-1" name="__codelineno-79-1" href="#__codelineno-79-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">find</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.kt</span><pre><span></span><code><a id="__codelineno-80-1" name="__codelineno-80-1" href="#__codelineno-80-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">find</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.rb</span><pre><span></span><code><a id="__codelineno-81-1" name="__codelineno-81-1" href="#__codelineno-81-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">find</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.zig</span><pre><span></span><code><a id="__codelineno-82-1" name="__codelineno-82-1" href="#__codelineno-82-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">find</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h3 id="7">7. &nbsp; 配列の拡張<a class="headerlink" href="#7" title="Permanent link">&para;</a></h3>
+<p>複雑なシステム環境では、安全な容量拡張のために配列の後にメモリ空間の可用性を確保することが困難になります。その結果、ほとんどのプログラミング言語では、**配列の長さは不変**です。</p>
+<p>配列を拡張するには、より大きな配列を作成し、元の配列から要素をコピーする必要があります。この操作の時間計算量は<span class="arithmatex">\(O(n)\)</span>で、大きな配列では時間がかかる可能性があります。コードは以下の通りです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="7:14"><input checked="checked" id="__tabbed_7_1" name="__tabbed_7" type="radio" /><input id="__tabbed_7_2" name="__tabbed_7" type="radio" /><input id="__tabbed_7_3" name="__tabbed_7" type="radio" /><input id="__tabbed_7_4" name="__tabbed_7" type="radio" /><input id="__tabbed_7_5" name="__tabbed_7" type="radio" /><input id="__tabbed_7_6" name="__tabbed_7" type="radio" /><input id="__tabbed_7_7" name="__tabbed_7" type="radio" /><input id="__tabbed_7_8" name="__tabbed_7" type="radio" /><input id="__tabbed_7_9" name="__tabbed_7" type="radio" /><input id="__tabbed_7_10" name="__tabbed_7" type="radio" /><input id="__tabbed_7_11" name="__tabbed_7" type="radio" /><input id="__tabbed_7_12" name="__tabbed_7" type="radio" /><input id="__tabbed_7_13" name="__tabbed_7" type="radio" /><input id="__tabbed_7_14" name="__tabbed_7" type="radio" /><div class="tabbed-labels"><label for="__tabbed_7_1">Python</label><label for="__tabbed_7_2">C++</label><label for="__tabbed_7_3">Java</label><label for="__tabbed_7_4">C#</label><label for="__tabbed_7_5">Go</label><label for="__tabbed_7_6">Swift</label><label for="__tabbed_7_7">JS</label><label for="__tabbed_7_8">TS</label><label for="__tabbed_7_9">Dart</label><label for="__tabbed_7_10">Rust</label><label for="__tabbed_7_11">C</label><label for="__tabbed_7_12">Kotlin</label><label for="__tabbed_7_13">Ruby</label><label for="__tabbed_7_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.py</span><pre><span></span><code><a id="__codelineno-83-1" name="__codelineno-83-1" href="#__codelineno-83-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">extend</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">enlarge</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
+<a id="__codelineno-83-2" name="__codelineno-83-2" href="#__codelineno-83-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;配列の長さを拡張&quot;&quot;&quot;</span>
+<a id="__codelineno-83-3" name="__codelineno-83-3" href="#__codelineno-83-3"></a>    <span class="c1"># 拡張された長さの配列を初期化</span>
+<a id="__codelineno-83-4" name="__codelineno-83-4" href="#__codelineno-83-4"></a>    <span class="n">res</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span> <span class="o">+</span> <span class="n">enlarge</span><span class="p">)</span>
+<a id="__codelineno-83-5" name="__codelineno-83-5" href="#__codelineno-83-5"></a>    <span class="c1"># 元の配列のすべての要素を新しい配列にコピー</span>
+<a id="__codelineno-83-6" name="__codelineno-83-6" href="#__codelineno-83-6"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)):</span>
+<a id="__codelineno-83-7" name="__codelineno-83-7" href="#__codelineno-83-7"></a>        <span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+<a id="__codelineno-83-8" name="__codelineno-83-8" href="#__codelineno-83-8"></a>    <span class="c1"># 拡張後の新しい配列を返す</span>
+<a id="__codelineno-83-9" name="__codelineno-83-9" href="#__codelineno-83-9"></a>    <span class="k">return</span> <span class="n">res</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.cpp</span><pre><span></span><code><a id="__codelineno-84-1" name="__codelineno-84-1" href="#__codelineno-84-1"></a><span class="cm">/* 配列長の拡張 */</span>
+<a id="__codelineno-84-2" name="__codelineno-84-2" href="#__codelineno-84-2"></a><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="nf">extend</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">enlarge</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-84-3" name="__codelineno-84-3" href="#__codelineno-84-3"></a><span class="w">    </span><span class="c1">// 拡張された長さの配列を初期化</span>
+<a id="__codelineno-84-4" name="__codelineno-84-4" href="#__codelineno-84-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">size</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">enlarge</span><span class="p">];</span>
+<a id="__codelineno-84-5" name="__codelineno-84-5" href="#__codelineno-84-5"></a><span class="w">    </span><span class="c1">// 元の配列の全要素を新しい配列にコピー</span>
+<a id="__codelineno-84-6" name="__codelineno-84-6" href="#__codelineno-84-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-84-7" name="__codelineno-84-7" href="#__codelineno-84-7"></a><span class="w">        </span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-84-8" name="__codelineno-84-8" href="#__codelineno-84-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-84-9" name="__codelineno-84-9" href="#__codelineno-84-9"></a><span class="w">    </span><span class="c1">// メモリを解放</span>
+<a id="__codelineno-84-10" name="__codelineno-84-10" href="#__codelineno-84-10"></a><span class="w">    </span><span class="k">delete</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">;</span>
+<a id="__codelineno-84-11" name="__codelineno-84-11" href="#__codelineno-84-11"></a><span class="w">    </span><span class="c1">// 拡張後の新しい配列を返却</span>
+<a id="__codelineno-84-12" name="__codelineno-84-12" href="#__codelineno-84-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-84-13" name="__codelineno-84-13" href="#__codelineno-84-13"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.java</span><pre><span></span><code><a id="__codelineno-85-1" name="__codelineno-85-1" href="#__codelineno-85-1"></a><span class="cm">/* 配列長の拡張 */</span>
+<a id="__codelineno-85-2" name="__codelineno-85-2" href="#__codelineno-85-2"></a><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="nf">extend</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">enlarge</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-85-3" name="__codelineno-85-3" href="#__codelineno-85-3"></a><span class="w">    </span><span class="c1">// 拡張された長さの配列を初期化</span>
+<a id="__codelineno-85-4" name="__codelineno-85-4" href="#__codelineno-85-4"></a><span class="w">    </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">enlarge</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-85-5" name="__codelineno-85-5" href="#__codelineno-85-5"></a><span class="w">    </span><span class="c1">// 元の配列のすべての要素を新しい配列にコピー</span>
+<a id="__codelineno-85-6" name="__codelineno-85-6" href="#__codelineno-85-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-85-7" name="__codelineno-85-7" href="#__codelineno-85-7"></a><span class="w">        </span><span class="n">res</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-85-8" name="__codelineno-85-8" href="#__codelineno-85-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-85-9" name="__codelineno-85-9" href="#__codelineno-85-9"></a><span class="w">    </span><span class="c1">// 拡張後の新しい配列を返す</span>
+<a id="__codelineno-85-10" name="__codelineno-85-10" href="#__codelineno-85-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-85-11" name="__codelineno-85-11" href="#__codelineno-85-11"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.cs</span><pre><span></span><code><a id="__codelineno-86-1" name="__codelineno-86-1" href="#__codelineno-86-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">array</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Extend</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.go</span><pre><span></span><code><a id="__codelineno-87-1" name="__codelineno-87-1" href="#__codelineno-87-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">extend</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.swift</span><pre><span></span><code><a id="__codelineno-88-1" name="__codelineno-88-1" href="#__codelineno-88-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="bp">extend</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.js</span><pre><span></span><code><a id="__codelineno-89-1" name="__codelineno-89-1" href="#__codelineno-89-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">extend</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.ts</span><pre><span></span><code><a id="__codelineno-90-1" name="__codelineno-90-1" href="#__codelineno-90-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">extend</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.dart</span><pre><span></span><code><a id="__codelineno-91-1" name="__codelineno-91-1" href="#__codelineno-91-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">extend</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.rs</span><pre><span></span><code><a id="__codelineno-92-1" name="__codelineno-92-1" href="#__codelineno-92-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">extend</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.c</span><pre><span></span><code><a id="__codelineno-93-1" name="__codelineno-93-1" href="#__codelineno-93-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">extend</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.kt</span><pre><span></span><code><a id="__codelineno-94-1" name="__codelineno-94-1" href="#__codelineno-94-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">extend</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.rb</span><pre><span></span><code><a id="__codelineno-95-1" name="__codelineno-95-1" href="#__codelineno-95-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="kp">extend</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array.zig</span><pre><span></span><code><a id="__codelineno-96-1" name="__codelineno-96-1" href="#__codelineno-96-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">extend</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h2 id="412">4.1.2 &nbsp; 配列の利点と制限<a class="headerlink" href="#412" title="Permanent link">&para;</a></h2>
+<p>配列は連続したメモリ空間に格納され、同じ型の要素で構成されます。このアプローチは、システムがデータ構造操作の効率を最適化するために活用できる実質的な事前情報を提供します。</p>
+<ul>
+<li><strong>高い空間効率</strong>：配列はデータのための連続したメモリブロックを割り当て、追加の構造的オーバーヘッドの必要性を排除します。</li>
+<li><strong>ランダムアクセスのサポート</strong>：配列は任意の要素への<span class="arithmatex">\(O(1)\)</span>時間アクセスを可能にします。</li>
+<li><strong>キャッシュ局所性</strong>：配列要素にアクセスするとき、コンピュータはそれらを読み込むだけでなく、周囲のデータもキャッシュし、高速キャッシュを利用して後続の操作速度を向上させます。</li>
+</ul>
+<p>しかし、連続空間格納は諸刃の剣で、以下の制限があります：</p>
+<ul>
+<li><strong>挿入と削除の効率が低い</strong>：配列に多くの要素が蓄積されると、要素の挿入や削除には大量の要素をシフトする必要があります。</li>
+<li><strong>固定長</strong>：配列の長さは初期化後に固定されます。配列を拡張するには、すべてのデータを新しい配列にコピーする必要があり、大きなコストがかかります。</li>
+<li><strong>空間の無駄</strong>：割り当てられた配列サイズが必要以上に大きい場合、余分な空間が無駄になります。</li>
+</ul>
+<h2 id="413">4.1.3 &nbsp; 配列の典型的な応用<a class="headerlink" href="#413" title="Permanent link">&para;</a></h2>
+<p>配列は基本的で広く使用されるデータ構造です。様々なアルゴリズムで頻繁に応用され、複雑なデータ構造の実装に役立ちます。</p>
+<ul>
+<li><strong>ランダムアクセス</strong>：配列はランダムサンプリングが必要なときのデータ格納に理想的です。インデックスに基づいてランダムシーケンスを生成することで、効率的にランダムサンプリングを実現できます。</li>
+<li><strong>ソートと検索</strong>：配列はソートと検索アルゴリズムで最も一般的に使用されるデータ構造です。クイックソート、マージソート、二分探索などの技術は主に配列で動作します。</li>
+<li><strong>ルックアップテーブル</strong>：配列は迅速な要素や関係の取得のための効率的なルックアップテーブルとして機能します。例えば、文字をASCIIコードにマッピングすることは、ASCIIコード値をインデックスとして使用し、対応する要素を配列に格納することで簡単になります。</li>
+<li><strong>機械学習</strong>：ニューラルネットワークの領域では、配列はベクトル、行列、テンソルを含む重要な線形代数演算の実行において重要な役割を果たします。配列はニューラルネットワークプログラミングにおいて主要かつ最も広範囲に使用されるデータ構造として機能します。</li>
+<li><strong>データ構造の実装</strong>：配列は、スタック、キュー、ハッシュ表、ヒープ、グラフなど、様々なデータ構造を実装するための構成要素として機能します。例えば、グラフの隣接行列表現は本質的に二次元配列です。</li>
+</ul>
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m13.13 22.19-1.63-3.83c1.57-.58 3.04-1.36 4.4-2.27l-2.77 6.1M5.64 12.5l-3.83-1.63 6.1-2.77C7 9.46 6.22 10.93 5.64 12.5M19.22 4c.28 0 .53 0 .74.05.17 1.39-.02 4.25-3.3 7.53-1.7 1.71-3.73 3.02-6.01 3.89l-2.15-2.1c.92-2.31 2.23-4.34 3.92-6.03C15.18 4.58 17.64 4 19.22 4m0-2c-1.98 0-4.98.69-8.22 3.93-2.19 2.19-3.5 4.6-4.35 6.71-.28.75-.09 1.57.46 2.13l2.13 2.12c.38.38.89.61 1.42.61.23 0 .47-.06.7-.15A19.1 19.1 0 0 0 18.07 13c5.66-5.66 3.54-10.61 3.54-10.61S20.7 2 19.22 2m-4.68 7.46c-.78-.78-.78-2.05 0-2.83s2.05-.78 2.83 0c.77.78.78 2.05 0 2.83-.78.78-2.05.78-2.83 0m-5.66 7.07-1.41-1.41 1.41 1.41M6.24 22l3.64-3.64c-.34-.09-.67-.24-.97-.45L4.83 22h1.41M2 22h1.41l4.77-4.76-1.42-1.41L2 20.59V22m0-2.83 4.09-4.08c-.21-.3-.36-.62-.45-.97L2 17.76v1.41Z"/></svg>
+  
+  <span class="md-ellipsis">
+    はじめに
+  </span>
+  
+
+            </a>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_1_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_1">
+            <span class="md-nav__icon md-icon"></span>
+            はじめに
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_2" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_preface/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M21 4H3a2 2 0 0 0-2 2v13a2 2 0 0 0 2 2h18a2 2 0 0 0 2-2V6a2 2 0 0 0-2-2M3 19V6h8v13H3m18 0h-8V6h8v13m-7-9.5h6V11h-6V9.5m0 2.5h6v1.5h-6V12m0 2.5h6V16h-6v-1.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 0 章 &nbsp; 前書き
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_2" id="__nav_2_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_2_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_2">
+            <span class="md-nav__icon md-icon"></span>
+            第 0 章 &nbsp; 前書き
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_preface/about_the_book/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.1 &nbsp; この本について
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_preface/suggestions/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.2 &nbsp; 本書の使い方
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_preface/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_introduction/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="./" class="md-nav__link md-nav__link--active">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link md-nav__link--active" for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
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+<p class="admonition-title">Abstract</p>
+<p>データ構造の世界は頑丈なレンガの壁に似ています。</p>
+<p>配列では、レンガがぴったりと整列し、それぞれが次のものと継ぎ目なく隣り合って、統一された形成を作っている姿を想像してください。一方、連結リストでは、これらのレンガが自由に散らばり、それらの間を優雅に編み込む蔦に抱かれています。</p>
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diff --git a/ja/chapter_array_and_linkedlist/linked_list.assets/linkedlist_insert_node.png b/ja/chapter_array_and_linkedlist/linked_list.assets/linkedlist_insert_node.png
new file mode 100644
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+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_introduction/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#421" class="md-nav__link">
+    <span class="md-ellipsis">
+      4.2.1 &nbsp; 連結リストの一般的な操作
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="4.2.1   連結リストの一般的な操作">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 連結リストの初期化
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; ノードの挿入
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#3" class="md-nav__link">
+    <span class="md-ellipsis">
+      3. &nbsp; ノードの削除
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#4" class="md-nav__link">
+    <span class="md-ellipsis">
+      4. &nbsp; ノードへのアクセス
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#5" class="md-nav__link">
+    <span class="md-ellipsis">
+      5. &nbsp; ノードの検索
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#422-vs" class="md-nav__link">
+    <span class="md-ellipsis">
+      4.2.2 &nbsp; 配列 vs. 連結リスト
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#423" class="md-nav__link">
+    <span class="md-ellipsis">
+      4.2.3 &nbsp; 連結リストの一般的な種類
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#424" class="md-nav__link">
+    <span class="md-ellipsis">
+      4.2.4 &nbsp; 連結リストの典型的な応用
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
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+    </li>
+  
+
+              
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+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
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+    14.7 &nbsp; まとめ
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+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
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+  </span>
+  
+
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+
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+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
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+    16.2 &nbsp; 一緒に創作に参加
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+  
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+
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+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
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+    16.3 &nbsp; 用語集
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+  
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+                  <div class="md-sidebar__inner">
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+  
+  
+  
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+  
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+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
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+      
+        <li class="md-nav__item">
+  <a href="#421" class="md-nav__link">
+    <span class="md-ellipsis">
+      4.2.1 &nbsp; 連結リストの一般的な操作
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="4.2.1   連結リストの一般的な操作">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 連結リストの初期化
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; ノードの挿入
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#3" class="md-nav__link">
+    <span class="md-ellipsis">
+      3. &nbsp; ノードの削除
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#4" class="md-nav__link">
+    <span class="md-ellipsis">
+      4. &nbsp; ノードへのアクセス
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#5" class="md-nav__link">
+    <span class="md-ellipsis">
+      5. &nbsp; ノードの検索
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#422-vs" class="md-nav__link">
+    <span class="md-ellipsis">
+      4.2.2 &nbsp; 配列 vs. 連結リスト
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#423" class="md-nav__link">
+    <span class="md-ellipsis">
+      4.2.3 &nbsp; 連結リストの一般的な種類
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#424" class="md-nav__link">
+    <span class="md-ellipsis">
+      4.2.4 &nbsp; 連結リストの典型的な応用
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+                  </div>
+                </div>
+              </div>
+            
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+              <article class="md-content__inner md-typeset">
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+      title="編集"
+      class="md-content__button md-icon"
+    >
+      
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
+    </a>
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+
+  <!-- View button -->
+  
+
+
+<!-- Page content -->
+<h1 id="42">4.2 &nbsp; 連結リスト<a class="headerlink" href="#42" title="Permanent link">&para;</a></h1>
+<p>メモリ空間は、すべてのプログラム間で共有されるリソースです。複雑なシステム環境では、使用可能なメモリがメモリ空間全体に分散している可能性があります。配列に割り当てられるメモリは連続している必要があることを理解していますが、非常に大きな配列の場合、十分な大きさの連続メモリ空間を見つけるのは困難な場合があります。ここで、連結リストの柔軟な利点が明らかになります。</p>
+<p><u>連結リスト</u>は線形データ構造であり、各要素はノードオブジェクトで、ノードは「参照」を通じて相互接続されています。これらの参照は後続ノードのメモリアドレスを保持し、1つのノードから次のノードへのナビゲーションを可能にします。</p>
+<p>連結リストの設計では、ノードを連続するメモリアドレスを必要とせずに、メモリ位置全体に分散配置することができます。</p>
+<p><a class="glightbox" href="../linked_list.assets/linkedlist_definition.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="連結リストの定義と格納方法" class="animation-figure" src="../linked_list.assets/linkedlist_definition.png" /></a></p>
+<p align="center"> 図 4-5 &nbsp; 連結リストの定義と格納方法 </p>
+
+<p>上図に示すように、連結リストの基本的な構成要素は<u>ノード</u>オブジェクトです。各ノードは2つの主要なコンポーネントで構成されています：ノードの「値」と次のノードへの「参照」です。</p>
+<ul>
+<li>連結リストの最初のノードは「ヘッドノード」、最後のノードは「テールノード」です。</li>
+<li>テールノードは「null」を指し、Javaでは<code>null</code>、C++では<code>nullptr</code>、Pythonでは<code>None</code>として指定されます。</li>
+<li>C、C++、Go、Rustなどのポインタをサポートする言語では、この「参照」は通常「ポインタ」として実装されます。</li>
+</ul>
+<p>以下のコードが示すように、連結リストの<code>ListNode</code>は値を保持するだけでなく、追加の参照（またはポインタ）も維持する必要があります。したがって、<strong>連結リストは同じ量のデータを格納する場合、配列よりも多くのメモリ空間を占有します</strong>。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">ListNode</span><span class="p">:</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;連結リストノードクラス&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">val</span>               <span class="c1"># ノード値</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">next</span><span class="p">:</span> <span class="n">ListNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span> <span class="c1"># 次のノードへの参照</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 連結リストノード構造体 */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="k">struct</span><span class="w"> </span><span class="nc">ListNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w">         </span><span class="c1">// ノード値</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">next</span><span class="p">;</span><span class="w">  </span><span class="c1">// 次のノードへのポインタ</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="n">ListNode</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">x</span><span class="p">)</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">x</span><span class="p">),</span><span class="w"> </span><span class="n">next</span><span class="p">(</span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{}</span><span class="w">  </span><span class="c1">// コンストラクタ</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="p">};</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 連結リストノードクラス */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kd">class</span> <span class="nc">ListNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w">        </span><span class="c1">// ノード値</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="n">next</span><span class="p">;</span><span class="w">  </span><span class="c1">// 次のノードへの参照</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="n">ListNode</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">x</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">x</span><span class="p">;</span><span class="w"> </span><span class="p">}</span><span class="w">  </span><span class="c1">// コンストラクタ</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 連結リストノードクラス */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="k">class</span><span class="w"> </span><span class="nf">ListNode</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">x</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w">  </span><span class="c1">// コンストラクタ</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">x</span><span class="p">;</span><span class="w">         </span><span class="c1">// ノード値</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="n">ListNode</span><span class="o">?</span><span class="w"> </span><span class="n">next</span><span class="p">;</span><span class="w">      </span><span class="c1">// 次のノードへの参照</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 連結リストノード構造体 */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">type</span><span class="w"> </span><span class="nx">ListNode</span><span class="w"> </span><span class="kd">struct</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="nx">Val</span><span class="w">  </span><span class="kt">int</span><span class="w">       </span><span class="c1">// ノード値</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="nx">Next</span><span class="w"> </span><span class="o">*</span><span class="nx">ListNode</span><span class="w"> </span><span class="c1">// 次のノードへのポインタ</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="p">}</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="c1">// NewListNode コンストラクタ、新しい連結リストを作成</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="kd">func</span><span class="w"> </span><span class="nx">NewListNode</span><span class="p">(</span><span class="nx">val</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="nx">ListNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">ListNode</span><span class="p">{</span>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w">        </span><span class="nx">Val</span><span class="p">:</span><span class="w">  </span><span class="nx">val</span><span class="p">,</span>
+<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w">        </span><span class="nx">Next</span><span class="p">:</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span>
+<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 連結リストノードクラス */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">ListNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">val</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="c1">// ノード値</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">next</span><span class="p">:</span><span class="w"> </span><span class="n">ListNode</span><span class="p">?</span><span class="w"> </span><span class="c1">// 次のノードへの参照</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">    </span><span class="kd">init</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// コンストラクタ</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w">        </span><span class="n">val</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">x</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 連結リストノードクラス */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">ListNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">(</span><span class="nx">val</span><span class="p">,</span><span class="w"> </span><span class="nx">next</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="nx">val</span><span class="p">);</span><span class="w">       </span><span class="c1">// ノード値</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="nx">next</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="nx">next</span><span class="p">);</span><span class="w"> </span><span class="c1">// 次のノードへの参照</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 連結リストノードクラス */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">ListNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w">    </span><span class="nx">val</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">;</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">    </span><span class="nx">next</span><span class="o">:</span><span class="w"> </span><span class="kt">ListNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">(</span><span class="nx">val?</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="nx">next?</span><span class="o">:</span><span class="w"> </span><span class="kt">ListNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">0</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">val</span><span class="p">;</span><span class="w">        </span><span class="c1">// ノード値</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">next</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">null</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">next</span><span class="p">;</span><span class="w">  </span><span class="c1">// 次のノードへの参照</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 連結リストノードクラス */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">ListNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w"> </span><span class="c1">// ノード値</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="n">ListNode</span><span class="o">?</span><span class="w"> </span><span class="n">next</span><span class="p">;</span><span class="w"> </span><span class="c1">// 次のノードへの参照</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">  </span><span class="n">ListNode</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="p">[</span><span class="k">this</span><span class="p">.</span><span class="n">next</span><span class="p">]);</span><span class="w"> </span><span class="c1">// コンストラクタ</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="k">use</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">rc</span><span class="p">::</span><span class="n">Rc</span><span class="p">;</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">use</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">cell</span><span class="p">::</span><span class="n">RefCell</span><span class="p">;</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="cm">/* 連結リストノードクラス */</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="cp">#[derive(Debug)]</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="k">struct</span><span class="w"> </span><span class="nc">ListNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">    </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="c1">// ノード値</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">    </span><span class="n">next</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">ListNode</span><span class="o">&gt;&gt;&gt;</span><span class="p">,</span><span class="w"> </span><span class="c1">// 次のノードへのポインタ</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 連結リストノード構造体 */</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="k">typedef</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="nc">ListNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w">               </span><span class="c1">// ノード値</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">    </span><span class="k">struct</span><span class="w"> </span><span class="nc">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">next</span><span class="p">;</span><span class="w"> </span><span class="c1">// 次のノードへのポインタ</span>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="p">}</span><span class="w"> </span><span class="n">ListNode</span><span class="p">;</span>
+<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="nf">newListNode</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w">    </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="w"> </span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">ListNode</span><span class="p">));</span>
+<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w">    </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="w">    </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
+<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">// 連結リストノードクラス</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="kr">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="kr">comptime</span><span class="w"> </span><span class="n">T</span><span class="o">:</span><span class="w"> </span><span class="kt">type</span><span class="p">)</span><span class="w"> </span><span class="kt">type</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w">        </span><span class="kr">const</span><span class="w"> </span><span class="n">Self</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">@This</span><span class="p">();</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w">        </span><span class="n">val</span><span class="o">:</span><span class="w"> </span><span class="n">T</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="c1">// ノード値</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w">        </span><span class="n">next</span><span class="o">:</span><span class="w"> </span><span class="o">?*</span><span class="n">Self</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="c1">// 次のノードへのポインタ</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w">        </span><span class="c1">// コンストラクタ</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="w">        </span><span class="kr">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="n">init</span><span class="p">(</span><span class="n">self</span><span class="o">:</span><span class="w"> </span><span class="o">*</span><span class="n">Self</span><span class="p">,</span><span class="w"> </span><span class="n">x</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-12-11" name="__codelineno-12-11" href="#__codelineno-12-11"></a><span class="w">            </span><span class="n">self</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">x</span><span class="p">;</span>
+<a id="__codelineno-12-12" name="__codelineno-12-12" href="#__codelineno-12-12"></a><span class="w">            </span><span class="n">self</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-12-13" name="__codelineno-12-13" href="#__codelineno-12-13"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-12-14" name="__codelineno-12-14" href="#__codelineno-12-14"></a><span class="w">    </span><span class="p">};</span>
+<a id="__codelineno-12-15" name="__codelineno-12-15" href="#__codelineno-12-15"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h2 id="421">4.2.1 &nbsp; 連結リストの一般的な操作<a class="headerlink" href="#421" title="Permanent link">&para;</a></h2>
+<h3 id="1">1. &nbsp; 連結リストの初期化<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<p>連結リストの構築は2段階のプロセスです：まず各ノードオブジェクトを初期化し、次にノード間の参照リンクを形成します。初期化後、ヘッドノードから<code>next</code>参照をたどってすべてのノードを順次巡回できます。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:13"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.py</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="c1"># 連結リストを初期化: 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="c1"># 各ノードを初期化</span>
+<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="n">n0</span> <span class="o">=</span> <span class="n">ListNode</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a><span class="n">n1</span> <span class="o">=</span> <span class="n">ListNode</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
+<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a><span class="n">n2</span> <span class="o">=</span> <span class="n">ListNode</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a><span class="n">n3</span> <span class="o">=</span> <span class="n">ListNode</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
+<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a><span class="n">n4</span> <span class="o">=</span> <span class="n">ListNode</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
+<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a><span class="c1"># ノード間の参照を構築</span>
+<a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a><span class="n">n0</span><span class="o">.</span><span class="n">next</span> <span class="o">=</span> <span class="n">n1</span>
+<a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a><span class="n">n1</span><span class="o">.</span><span class="n">next</span> <span class="o">=</span> <span class="n">n2</span>
+<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a><span class="n">n2</span><span class="o">.</span><span class="n">next</span> <span class="o">=</span> <span class="n">n3</span>
+<a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a><span class="n">n3</span><span class="o">.</span><span class="n">next</span> <span class="o">=</span> <span class="n">n4</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 連結リストを初期化: 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */</span>
+<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="c1">// 各ノードを初期化</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="n">ListNode</span><span class="o">*</span><span class="w"> </span><span class="n">n0</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="n">ListNode</span><span class="o">*</span><span class="w"> </span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="n">ListNode</span><span class="o">*</span><span class="w"> </span><span class="n">n2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="n">ListNode</span><span class="o">*</span><span class="w"> </span><span class="n">n3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
+<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="n">ListNode</span><span class="o">*</span><span class="w"> </span><span class="n">n4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
+<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="c1">// ノード間の参照を構築</span>
+<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="n">n0</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n1</span><span class="p">;</span>
+<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="n">n1</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span><span class="p">;</span>
+<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="n">n2</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n3</span><span class="p">;</span>
+<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="n">n3</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n4</span><span class="p">;</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 連結リストを初期化: 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */</span>
+<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="c1">// 各ノードを初期化</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">n0</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
+<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">n2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">n3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
+<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">n4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
+<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="c1">// ノード間の参照を構築</span>
+<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="n">n0</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n1</span><span class="p">;</span>
+<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="n">n1</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span><span class="p">;</span>
+<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="n">n2</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n3</span><span class="p">;</span>
+<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="n">n3</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n4</span><span class="p">;</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 連結リストを初期化: 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="c1">// 各ノードを初期化</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">n0</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">n2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">n3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">n4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="c1">// ノード間の参照を構築</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="n">n0</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n1</span><span class="p">;</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="n">n1</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span><span class="p">;</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="n">n2</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n3</span><span class="p">;</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="n">n3</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n4</span><span class="p">;</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* 連結リストを初期化: 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="c1">// 各ノードを初期化</span>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="nx">n0</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">NewListNode</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="nx">n1</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">NewListNode</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
+<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="nx">n2</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">NewListNode</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="nx">n3</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">NewListNode</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
+<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="nx">n4</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">NewListNode</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
+<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="c1">// ノード間の参照を構築</span>
+<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="nx">n0</span><span class="p">.</span><span class="nx">Next</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">n1</span>
+<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="nx">n1</span><span class="p">.</span><span class="nx">Next</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">n2</span>
+<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="nx">n2</span><span class="p">.</span><span class="nx">Next</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">n3</span>
+<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="nx">n3</span><span class="p">.</span><span class="nx">Next</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">n4</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* 連結リストを初期化: 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */</span>
+<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="c1">// 各ノードを初期化</span>
+<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="kd">let</span><span class="w"> </span><span class="nv">n0</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="kd">let</span><span class="w"> </span><span class="nv">n1</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="mi">3</span><span class="p">)</span>
+<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="kd">let</span><span class="w"> </span><span class="nv">n2</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="kd">let</span><span class="w"> </span><span class="nv">n3</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="mi">5</span><span class="p">)</span>
+<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="kd">let</span><span class="w"> </span><span class="nv">n4</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="mi">4</span><span class="p">)</span>
+<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="c1">// ノード間の参照を構築</span>
+<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="n">n0</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">n1</span>
+<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a><span class="n">n1</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">n2</span>
+<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="n">n2</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">n3</span>
+<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a><span class="n">n3</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">n4</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* 連結リストを初期化: 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */</span>
+<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="c1">// 各ノードを初期化</span>
+<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="kd">const</span><span class="w"> </span><span class="nx">n0</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">ListNode</span><span class="p">(</span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="kd">const</span><span class="w"> </span><span class="nx">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">ListNode</span><span class="p">(</span><span class="mf">3</span><span class="p">);</span>
+<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="kd">const</span><span class="w"> </span><span class="nx">n2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">ListNode</span><span class="p">(</span><span class="mf">2</span><span class="p">);</span>
+<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="kd">const</span><span class="w"> </span><span class="nx">n3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">ListNode</span><span class="p">(</span><span class="mf">5</span><span class="p">);</span>
+<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="kd">const</span><span class="w"> </span><span class="nx">n4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">ListNode</span><span class="p">(</span><span class="mf">4</span><span class="p">);</span>
+<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a><span class="c1">// ノード間の参照を構築</span>
+<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a><span class="nx">n0</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n1</span><span class="p">;</span>
+<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a><span class="nx">n1</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n2</span><span class="p">;</span>
+<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="nx">n2</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n3</span><span class="p">;</span>
+<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a><span class="nx">n3</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n4</span><span class="p">;</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* 連結リストを初期化: 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="c1">// 各ノードを初期化</span>
+<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="kd">const</span><span class="w"> </span><span class="nx">n0</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">ListNode</span><span class="p">(</span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="kd">const</span><span class="w"> </span><span class="nx">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">ListNode</span><span class="p">(</span><span class="mf">3</span><span class="p">);</span>
+<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="kd">const</span><span class="w"> </span><span class="nx">n2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">ListNode</span><span class="p">(</span><span class="mf">2</span><span class="p">);</span>
+<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="kd">const</span><span class="w"> </span><span class="nx">n3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">ListNode</span><span class="p">(</span><span class="mf">5</span><span class="p">);</span>
+<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="kd">const</span><span class="w"> </span><span class="nx">n4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">ListNode</span><span class="p">(</span><span class="mf">4</span><span class="p">);</span>
+<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="c1">// ノード間の参照を構築</span>
+<a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a><span class="nx">n0</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n1</span><span class="p">;</span>
+<a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a><span class="nx">n1</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n2</span><span class="p">;</span>
+<a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a><span class="nx">n2</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n3</span><span class="p">;</span>
+<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a><span class="nx">n3</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n4</span><span class="p">;</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* 連結リストを初期化: 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */</span>
+<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="c1">// 各ノードを初期化</span>
+<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">n0</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="m">1</span><span class="p">);</span>
+<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="m">3</span><span class="p">);</span>
+<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">n2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="m">2</span><span class="p">);</span>
+<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">n3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="m">5</span><span class="p">);</span>
+<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">n4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="m">4</span><span class="p">);</span>
+<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="c1">// ノード間の参照を構築</span>
+<a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a><span class="n">n0</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n1</span><span class="p">;</span>
+<a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a><span class="n">n1</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span><span class="p">;</span>
+<a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a><span class="n">n2</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n3</span><span class="p">;</span>
+<a id="__codelineno-21-12" name="__codelineno-21-12" href="#__codelineno-21-12"></a><span class="n">n3</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n4</span><span class="p">;</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="cm">/* 連結リストを初期化: 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */</span>
+<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="c1">// 各ノードを初期化</span>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="kd">let</span><span class="w"> </span><span class="n">n0</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Rc</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="n">RefCell</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">next</span><span class="p">:</span><span class="w"> </span><span class="nb">None</span><span class="w"> </span><span class="p">}));</span>
+<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="kd">let</span><span class="w"> </span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Rc</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="n">RefCell</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="n">next</span><span class="p">:</span><span class="w"> </span><span class="nb">None</span><span class="w"> </span><span class="p">}));</span>
+<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="kd">let</span><span class="w"> </span><span class="n">n2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Rc</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="n">RefCell</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="n">next</span><span class="p">:</span><span class="w"> </span><span class="nb">None</span><span class="w"> </span><span class="p">}));</span>
+<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="kd">let</span><span class="w"> </span><span class="n">n3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Rc</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="n">RefCell</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="n">next</span><span class="p">:</span><span class="w"> </span><span class="nb">None</span><span class="w"> </span><span class="p">}));</span>
+<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="kd">let</span><span class="w"> </span><span class="n">n4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Rc</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="n">RefCell</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="mi">4</span><span class="p">,</span><span class="w"> </span><span class="n">next</span><span class="p">:</span><span class="w"> </span><span class="nb">None</span><span class="w"> </span><span class="p">}));</span>
+<a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a>
+<a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a><span class="c1">// ノード間の参照を構築</span>
+<a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a><span class="n">n0</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">n1</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
+<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a><span class="n">n1</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">n2</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
+<a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="n">n2</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">n3</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
+<a id="__codelineno-22-13" name="__codelineno-22-13" href="#__codelineno-22-13"></a><span class="n">n3</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">n4</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="cm">/* 連結リストを初期化: 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */</span>
+<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="c1">// 各ノードを初期化</span>
+<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="n">ListNode</span><span class="o">*</span><span class="w"> </span><span class="n">n0</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newListNode</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="n">ListNode</span><span class="o">*</span><span class="w"> </span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newListNode</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
+<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="n">ListNode</span><span class="o">*</span><span class="w"> </span><span class="n">n2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newListNode</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="n">ListNode</span><span class="o">*</span><span class="w"> </span><span class="n">n3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newListNode</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
+<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="n">ListNode</span><span class="o">*</span><span class="w"> </span><span class="n">n4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newListNode</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
+<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="c1">// ノード間の参照を構築</span>
+<a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></a><span class="n">n0</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n1</span><span class="p">;</span>
+<a id="__codelineno-23-10" name="__codelineno-23-10" href="#__codelineno-23-10"></a><span class="n">n1</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span><span class="p">;</span>
+<a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a><span class="n">n2</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n3</span><span class="p">;</span>
+<a id="__codelineno-23-12" name="__codelineno-23-12" href="#__codelineno-23-12"></a><span class="n">n3</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n4</span><span class="p">;</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.zig</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="c1">// 連結リストを初期化</span>
+<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="c1">// 各ノードを初期化</span>
+<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="kr">var</span><span class="w"> </span><span class="n">n0</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">inc</span><span class="p">.</span><span class="n">ListNode</span><span class="p">(</span><span class="kt">i32</span><span class="p">){.</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">};</span>
+<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="kr">var</span><span class="w"> </span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">inc</span><span class="p">.</span><span class="n">ListNode</span><span class="p">(</span><span class="kt">i32</span><span class="p">){.</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">3</span><span class="p">};</span>
+<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="kr">var</span><span class="w"> </span><span class="n">n2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">inc</span><span class="p">.</span><span class="n">ListNode</span><span class="p">(</span><span class="kt">i32</span><span class="p">){.</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">};</span>
+<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="kr">var</span><span class="w"> </span><span class="n">n3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">inc</span><span class="p">.</span><span class="n">ListNode</span><span class="p">(</span><span class="kt">i32</span><span class="p">){.</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">5</span><span class="p">};</span>
+<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="kr">var</span><span class="w"> </span><span class="n">n4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">inc</span><span class="p">.</span><span class="n">ListNode</span><span class="p">(</span><span class="kt">i32</span><span class="p">){.</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">4</span><span class="p">};</span>
+<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="c1">// ノード間の参照を構築</span>
+<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="n">n0</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">&amp;</span><span class="n">n1</span><span class="p">;</span>
+<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a><span class="n">n1</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">&amp;</span><span class="n">n2</span><span class="p">;</span>
+<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="n">n2</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">&amp;</span><span class="n">n3</span><span class="p">;</span>
+<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a><span class="n">n3</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">&amp;</span><span class="n">n4</span><span class="p">;</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>配列全体は1つの変数です。例えば、配列<code>nums</code>には<code>nums[0]</code>、<code>nums[1]</code>などの要素が含まれますが、連結リストは複数の異なるノードオブジェクトで構成されています。<strong>通常、連結リストはそのヘッドノードで参照されます</strong>。例えば、前のコードスニペットの連結リストは<code>n0</code>として参照されます。</p>
+<h3 id="2">2. &nbsp; ノードの挿入<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
+<p>連結リストにノードを挿入するのは非常に簡単です。下図に示すように、隣接する2つのノード<code>n0</code>と<code>n1</code>の間に新しいノード<code>P</code>を挿入することを目指すとします。<strong>これは2つのノード参照（ポインタ）を変更するだけで実現でき</strong>、時間計算量は<span class="arithmatex">\(O(1)\)</span>です。</p>
+<p>比較すると、配列に要素を挿入する時間計算量は<span class="arithmatex">\(O(n)\)</span>であり、大量のデータを扱う場合には効率が悪くなります。</p>
+<p><a class="glightbox" href="../linked_list.assets/linkedlist_insert_node.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="連結リストノード挿入の例" class="animation-figure" src="../linked_list.assets/linkedlist_insert_node.png" /></a></p>
+<p align="center"> 図 4-6 &nbsp; 連結リストノード挿入の例 </p>
+
+<div class="tabbed-set tabbed-alternate" data-tabs="3:14"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><input id="__tabbed_3_14" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label><label for="__tabbed_3_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.py</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="n">n0</span><span class="p">:</span> <span class="n">ListNode</span><span class="p">,</span> <span class="n">P</span><span class="p">:</span> <span class="n">ListNode</span><span class="p">):</span>
+<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;連結リストのノード n0 の後にノード P を挿入&quot;&quot;&quot;</span>
+<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a>    <span class="n">n1</span> <span class="o">=</span> <span class="n">n0</span><span class="o">.</span><span class="n">next</span>
+<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a>    <span class="n">P</span><span class="o">.</span><span class="n">next</span> <span class="o">=</span> <span class="n">n1</span>
+<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a>    <span class="n">n0</span><span class="o">.</span><span class="n">next</span> <span class="o">=</span> <span class="n">P</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.cpp</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="cm">/* 連結リストのノードn0の後にノードPを挿入 */</span>
+<a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">n0</span><span class="p">,</span><span class="w"> </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">P</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n0</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a><span class="w">    </span><span class="n">P</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n1</span><span class="p">;</span>
+<a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a><span class="w">    </span><span class="n">n0</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">P</span><span class="p">;</span>
+<a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.java</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="cm">/* 連結リストでノード n0 の後にノード P を挿入 */</span>
+<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="n">n0</span><span class="p">,</span><span class="w"> </span><span class="n">ListNode</span><span class="w"> </span><span class="n">P</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n0</span><span class="p">.</span><span class="na">next</span><span class="p">;</span>
+<a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a><span class="w">    </span><span class="n">P</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n1</span><span class="p">;</span>
+<a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a><span class="w">    </span><span class="n">n0</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">P</span><span class="p">;</span>
+<a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.cs</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">linked_list</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Insert</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.go</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">insertNode</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.swift</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="bp">insert</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.js</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">insert</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.ts</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">insert</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.dart</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">insert</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.rs</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">insert</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.c</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">insert</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.kt</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">insert</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.rb</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">insert</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.zig</span><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">insert</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h3 id="3">3. &nbsp; ノードの削除<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
+<p>下図に示すように、連結リストからノードを削除することも非常に簡単で、<strong>1つのノードの参照（ポインタ）を変更するだけです</strong>。</p>
+<p>重要な点は、ノード<code>P</code>が削除された後も<code>n1</code>を指し続けていることですが、連結リストの巡回中にはアクセスできなくなることです。これは事実上、<code>P</code>が連結リストの一部ではなくなったことを意味します。</p>
+<p><a class="glightbox" href="../linked_list.assets/linkedlist_remove_node.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="連結リストノードの削除" class="animation-figure" src="../linked_list.assets/linkedlist_remove_node.png" /></a></p>
+<p align="center"> 図 4-7 &nbsp; 連結リストノードの削除 </p>
+
+<div class="tabbed-set tabbed-alternate" data-tabs="4:14"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><input id="__tabbed_4_6" name="__tabbed_4" type="radio" /><input id="__tabbed_4_7" name="__tabbed_4" type="radio" /><input id="__tabbed_4_8" name="__tabbed_4" type="radio" /><input id="__tabbed_4_9" name="__tabbed_4" type="radio" /><input id="__tabbed_4_10" name="__tabbed_4" type="radio" /><input id="__tabbed_4_11" name="__tabbed_4" type="radio" /><input id="__tabbed_4_12" name="__tabbed_4" type="radio" /><input id="__tabbed_4_13" name="__tabbed_4" type="radio" /><input id="__tabbed_4_14" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">Python</label><label for="__tabbed_4_2">C++</label><label for="__tabbed_4_3">Java</label><label for="__tabbed_4_4">C#</label><label for="__tabbed_4_5">Go</label><label for="__tabbed_4_6">Swift</label><label for="__tabbed_4_7">JS</label><label for="__tabbed_4_8">TS</label><label for="__tabbed_4_9">Dart</label><label for="__tabbed_4_10">Rust</label><label for="__tabbed_4_11">C</label><label for="__tabbed_4_12">Kotlin</label><label for="__tabbed_4_13">Ruby</label><label for="__tabbed_4_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.py</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="n">n0</span><span class="p">:</span> <span class="n">ListNode</span><span class="p">):</span>
+<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;連結リストのノード n0 の後の最初のノードを削除&quot;&quot;&quot;</span>
+<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a>    <span class="k">if</span> <span class="ow">not</span> <span class="n">n0</span><span class="o">.</span><span class="n">next</span><span class="p">:</span>
+<a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a>        <span class="k">return</span>
+<a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a>    <span class="c1"># n0 -&gt; P -&gt; n1</span>
+<a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a>    <span class="n">P</span> <span class="o">=</span> <span class="n">n0</span><span class="o">.</span><span class="n">next</span>
+<a id="__codelineno-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></a>    <span class="n">n1</span> <span class="o">=</span> <span class="n">P</span><span class="o">.</span><span class="n">next</span>
+<a id="__codelineno-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a>    <span class="n">n0</span><span class="o">.</span><span class="n">next</span> <span class="o">=</span> <span class="n">n1</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.cpp</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="cm">/* 連結リストのノードn0の後の最初のノードを削除 */</span>
+<a id="__codelineno-41-2" name="__codelineno-41-2" href="#__codelineno-41-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">n0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-41-3" name="__codelineno-41-3" href="#__codelineno-41-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n0</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span>
+<a id="__codelineno-41-4" name="__codelineno-41-4" href="#__codelineno-41-4"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-41-5" name="__codelineno-41-5" href="#__codelineno-41-5"></a><span class="w">    </span><span class="c1">// n0 -&gt; P -&gt; n1</span>
+<a id="__codelineno-41-6" name="__codelineno-41-6" href="#__codelineno-41-6"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">P</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n0</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-41-7" name="__codelineno-41-7" href="#__codelineno-41-7"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">P</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-41-8" name="__codelineno-41-8" href="#__codelineno-41-8"></a><span class="w">    </span><span class="n">n0</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n1</span><span class="p">;</span>
+<a id="__codelineno-41-9" name="__codelineno-41-9" href="#__codelineno-41-9"></a><span class="w">    </span><span class="c1">// メモリを解放</span>
+<a id="__codelineno-41-10" name="__codelineno-41-10" href="#__codelineno-41-10"></a><span class="w">    </span><span class="k">delete</span><span class="w"> </span><span class="n">P</span><span class="p">;</span>
+<a id="__codelineno-41-11" name="__codelineno-41-11" href="#__codelineno-41-11"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.java</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="cm">/* 連結リストでノード n0 の後の最初のノードを削除 */</span>
+<a id="__codelineno-42-2" name="__codelineno-42-2" href="#__codelineno-42-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="n">n0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n0</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
+<a id="__codelineno-42-4" name="__codelineno-42-4" href="#__codelineno-42-4"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-42-5" name="__codelineno-42-5" href="#__codelineno-42-5"></a><span class="w">    </span><span class="c1">// n0 -&gt; P -&gt; n1</span>
+<a id="__codelineno-42-6" name="__codelineno-42-6" href="#__codelineno-42-6"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="n">P</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n0</span><span class="p">.</span><span class="na">next</span><span class="p">;</span>
+<a id="__codelineno-42-7" name="__codelineno-42-7" href="#__codelineno-42-7"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">P</span><span class="p">.</span><span class="na">next</span><span class="p">;</span>
+<a id="__codelineno-42-8" name="__codelineno-42-8" href="#__codelineno-42-8"></a><span class="w">    </span><span class="n">n0</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n1</span><span class="p">;</span>
+<a id="__codelineno-42-9" name="__codelineno-42-9" href="#__codelineno-42-9"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.cs</span><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">linked_list</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Remove</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.go</span><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">removeItem</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.swift</span><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">remove</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.js</span><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">remove</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.ts</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">remove</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.dart</span><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">remove</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.rs</span><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">remove</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.c</span><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">removeItem</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.kt</span><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">remove</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.rb</span><pre><span></span><code><a id="__codelineno-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">remove</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.zig</span><pre><span></span><code><a id="__codelineno-53-1" name="__codelineno-53-1" href="#__codelineno-53-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">remove</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h3 id="4">4. &nbsp; ノードへのアクセス<a class="headerlink" href="#4" title="Permanent link">&para;</a></h3>
+<p><strong>連結リストでのノードへのアクセスは効率が悪いです</strong>。前述したように、配列の任意の要素には<span class="arithmatex">\(O(1)\)</span>時間でアクセスできます。対照的に、連結リストでは、プログラムはヘッドノードから開始して目的のノードが見つかるまで順次ノードを巡回する必要があります。つまり、連結リストの<span class="arithmatex">\(i\)</span>番目のノードにアクセスするには、プログラムは<span class="arithmatex">\(i - 1\)</span>個のノードを反復処理する必要があり、時間計算量は<span class="arithmatex">\(O(n)\)</span>になります。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="5:14"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><input id="__tabbed_5_7" name="__tabbed_5" type="radio" /><input id="__tabbed_5_8" name="__tabbed_5" type="radio" /><input id="__tabbed_5_9" name="__tabbed_5" type="radio" /><input id="__tabbed_5_10" name="__tabbed_5" type="radio" /><input id="__tabbed_5_11" name="__tabbed_5" type="radio" /><input id="__tabbed_5_12" name="__tabbed_5" type="radio" /><input id="__tabbed_5_13" name="__tabbed_5" type="radio" /><input id="__tabbed_5_14" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">Python</label><label for="__tabbed_5_2">C++</label><label for="__tabbed_5_3">Java</label><label for="__tabbed_5_4">C#</label><label for="__tabbed_5_5">Go</label><label for="__tabbed_5_6">Swift</label><label for="__tabbed_5_7">JS</label><label for="__tabbed_5_8">TS</label><label for="__tabbed_5_9">Dart</label><label for="__tabbed_5_10">Rust</label><label for="__tabbed_5_11">C</label><label for="__tabbed_5_12">Kotlin</label><label for="__tabbed_5_13">Ruby</label><label for="__tabbed_5_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.py</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">access</span><span class="p">(</span><span class="n">head</span><span class="p">:</span> <span class="n">ListNode</span><span class="p">,</span> <span class="n">index</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">ListNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-54-2" name="__codelineno-54-2" href="#__codelineno-54-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;連結リストのインデックス index のノードにアクセス&quot;&quot;&quot;</span>
+<a id="__codelineno-54-3" name="__codelineno-54-3" href="#__codelineno-54-3"></a>    <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">index</span><span class="p">):</span>
+<a id="__codelineno-54-4" name="__codelineno-54-4" href="#__codelineno-54-4"></a>        <span class="k">if</span> <span class="ow">not</span> <span class="n">head</span><span class="p">:</span>
+<a id="__codelineno-54-5" name="__codelineno-54-5" href="#__codelineno-54-5"></a>            <span class="k">return</span> <span class="kc">None</span>
+<a id="__codelineno-54-6" name="__codelineno-54-6" href="#__codelineno-54-6"></a>        <span class="n">head</span> <span class="o">=</span> <span class="n">head</span><span class="o">.</span><span class="n">next</span>
+<a id="__codelineno-54-7" name="__codelineno-54-7" href="#__codelineno-54-7"></a>    <span class="k">return</span> <span class="n">head</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.cpp</span><pre><span></span><code><a id="__codelineno-55-1" name="__codelineno-55-1" href="#__codelineno-55-1"></a><span class="cm">/* 連結リストの`index`番目のノードにアクセス */</span>
+<a id="__codelineno-55-2" name="__codelineno-55-2" href="#__codelineno-55-2"></a><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="nf">access</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">head</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-55-3" name="__codelineno-55-3" href="#__codelineno-55-3"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-55-4" name="__codelineno-55-4" href="#__codelineno-55-4"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">head</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span>
+<a id="__codelineno-55-5" name="__codelineno-55-5" href="#__codelineno-55-5"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="k">nullptr</span><span class="p">;</span>
+<a id="__codelineno-55-6" name="__codelineno-55-6" href="#__codelineno-55-6"></a><span class="w">        </span><span class="n">head</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">head</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-55-7" name="__codelineno-55-7" href="#__codelineno-55-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-55-8" name="__codelineno-55-8" href="#__codelineno-55-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">head</span><span class="p">;</span>
+<a id="__codelineno-55-9" name="__codelineno-55-9" href="#__codelineno-55-9"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.java</span><pre><span></span><code><a id="__codelineno-56-1" name="__codelineno-56-1" href="#__codelineno-56-1"></a><span class="cm">/* 連結リストの `index` のノードにアクセス */</span>
+<a id="__codelineno-56-2" name="__codelineno-56-2" href="#__codelineno-56-2"></a><span class="n">ListNode</span><span class="w"> </span><span class="nf">access</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="n">head</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-56-3" name="__codelineno-56-3" href="#__codelineno-56-3"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-56-4" name="__codelineno-56-4" href="#__codelineno-56-4"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">head</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
+<a id="__codelineno-56-5" name="__codelineno-56-5" href="#__codelineno-56-5"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-56-6" name="__codelineno-56-6" href="#__codelineno-56-6"></a><span class="w">        </span><span class="n">head</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">head</span><span class="p">.</span><span class="na">next</span><span class="p">;</span>
+<a id="__codelineno-56-7" name="__codelineno-56-7" href="#__codelineno-56-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-56-8" name="__codelineno-56-8" href="#__codelineno-56-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">head</span><span class="p">;</span>
+<a id="__codelineno-56-9" name="__codelineno-56-9" href="#__codelineno-56-9"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.cs</span><pre><span></span><code><a id="__codelineno-57-1" name="__codelineno-57-1" href="#__codelineno-57-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">linked_list</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Access</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.go</span><pre><span></span><code><a id="__codelineno-58-1" name="__codelineno-58-1" href="#__codelineno-58-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">access</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.swift</span><pre><span></span><code><a id="__codelineno-59-1" name="__codelineno-59-1" href="#__codelineno-59-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">access</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.js</span><pre><span></span><code><a id="__codelineno-60-1" name="__codelineno-60-1" href="#__codelineno-60-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">access</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.ts</span><pre><span></span><code><a id="__codelineno-61-1" name="__codelineno-61-1" href="#__codelineno-61-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">access</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.dart</span><pre><span></span><code><a id="__codelineno-62-1" name="__codelineno-62-1" href="#__codelineno-62-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">access</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.rs</span><pre><span></span><code><a id="__codelineno-63-1" name="__codelineno-63-1" href="#__codelineno-63-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">access</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.c</span><pre><span></span><code><a id="__codelineno-64-1" name="__codelineno-64-1" href="#__codelineno-64-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">access</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.kt</span><pre><span></span><code><a id="__codelineno-65-1" name="__codelineno-65-1" href="#__codelineno-65-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">access</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.rb</span><pre><span></span><code><a id="__codelineno-66-1" name="__codelineno-66-1" href="#__codelineno-66-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">access</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.zig</span><pre><span></span><code><a id="__codelineno-67-1" name="__codelineno-67-1" href="#__codelineno-67-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">access</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h3 id="5">5. &nbsp; ノードの検索<a class="headerlink" href="#5" title="Permanent link">&para;</a></h3>
+<p>連結リストを巡回して、値が<code>target</code>に一致するノードを見つけ、連結リスト内でのそのノードのインデックスを出力します。この手順も線形検索の例です。対応するコードは以下のとおりです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="6:14"><input checked="checked" id="__tabbed_6_1" name="__tabbed_6" type="radio" /><input id="__tabbed_6_2" name="__tabbed_6" type="radio" /><input id="__tabbed_6_3" name="__tabbed_6" type="radio" /><input id="__tabbed_6_4" name="__tabbed_6" type="radio" /><input id="__tabbed_6_5" name="__tabbed_6" type="radio" /><input id="__tabbed_6_6" name="__tabbed_6" type="radio" /><input id="__tabbed_6_7" name="__tabbed_6" type="radio" /><input id="__tabbed_6_8" name="__tabbed_6" type="radio" /><input id="__tabbed_6_9" name="__tabbed_6" type="radio" /><input id="__tabbed_6_10" name="__tabbed_6" type="radio" /><input id="__tabbed_6_11" name="__tabbed_6" type="radio" /><input id="__tabbed_6_12" name="__tabbed_6" type="radio" /><input id="__tabbed_6_13" name="__tabbed_6" type="radio" /><input id="__tabbed_6_14" name="__tabbed_6" type="radio" /><div class="tabbed-labels"><label for="__tabbed_6_1">Python</label><label for="__tabbed_6_2">C++</label><label for="__tabbed_6_3">Java</label><label for="__tabbed_6_4">C#</label><label for="__tabbed_6_5">Go</label><label for="__tabbed_6_6">Swift</label><label for="__tabbed_6_7">JS</label><label for="__tabbed_6_8">TS</label><label for="__tabbed_6_9">Dart</label><label for="__tabbed_6_10">Rust</label><label for="__tabbed_6_11">C</label><label for="__tabbed_6_12">Kotlin</label><label for="__tabbed_6_13">Ruby</label><label for="__tabbed_6_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.py</span><pre><span></span><code><a id="__codelineno-68-1" name="__codelineno-68-1" href="#__codelineno-68-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">find</span><span class="p">(</span><span class="n">head</span><span class="p">:</span> <span class="n">ListNode</span><span class="p">,</span> <span class="n">target</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-68-2" name="__codelineno-68-2" href="#__codelineno-68-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;連結リストで値 target を持つ最初のノードを検索&quot;&quot;&quot;</span>
+<a id="__codelineno-68-3" name="__codelineno-68-3" href="#__codelineno-68-3"></a>    <span class="n">index</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-68-4" name="__codelineno-68-4" href="#__codelineno-68-4"></a>    <span class="k">while</span> <span class="n">head</span><span class="p">:</span>
+<a id="__codelineno-68-5" name="__codelineno-68-5" href="#__codelineno-68-5"></a>        <span class="k">if</span> <span class="n">head</span><span class="o">.</span><span class="n">val</span> <span class="o">==</span> <span class="n">target</span><span class="p">:</span>
+<a id="__codelineno-68-6" name="__codelineno-68-6" href="#__codelineno-68-6"></a>            <span class="k">return</span> <span class="n">index</span>
+<a id="__codelineno-68-7" name="__codelineno-68-7" href="#__codelineno-68-7"></a>        <span class="n">head</span> <span class="o">=</span> <span class="n">head</span><span class="o">.</span><span class="n">next</span>
+<a id="__codelineno-68-8" name="__codelineno-68-8" href="#__codelineno-68-8"></a>        <span class="n">index</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-68-9" name="__codelineno-68-9" href="#__codelineno-68-9"></a>    <span class="k">return</span> <span class="o">-</span><span class="mi">1</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.cpp</span><pre><span></span><code><a id="__codelineno-69-1" name="__codelineno-69-1" href="#__codelineno-69-1"></a><span class="cm">/* 連結リストで値がtargetの最初のノードを検索 */</span>
+<a id="__codelineno-69-2" name="__codelineno-69-2" href="#__codelineno-69-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">find</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">head</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-69-3" name="__codelineno-69-3" href="#__codelineno-69-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-69-4" name="__codelineno-69-4" href="#__codelineno-69-4"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">head</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-69-5" name="__codelineno-69-5" href="#__codelineno-69-5"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">head</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">target</span><span class="p">)</span>
+<a id="__codelineno-69-6" name="__codelineno-69-6" href="#__codelineno-69-6"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">index</span><span class="p">;</span>
+<a id="__codelineno-69-7" name="__codelineno-69-7" href="#__codelineno-69-7"></a><span class="w">        </span><span class="n">head</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">head</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-69-8" name="__codelineno-69-8" href="#__codelineno-69-8"></a><span class="w">        </span><span class="n">index</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-69-9" name="__codelineno-69-9" href="#__codelineno-69-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-69-10" name="__codelineno-69-10" href="#__codelineno-69-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
+<a id="__codelineno-69-11" name="__codelineno-69-11" href="#__codelineno-69-11"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.java</span><pre><span></span><code><a id="__codelineno-70-1" name="__codelineno-70-1" href="#__codelineno-70-1"></a><span class="cm">/* 連結リストで値 target を持つ最初のノードを検索 */</span>
+<a id="__codelineno-70-2" name="__codelineno-70-2" href="#__codelineno-70-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">find</span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="n">head</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-70-3" name="__codelineno-70-3" href="#__codelineno-70-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-70-4" name="__codelineno-70-4" href="#__codelineno-70-4"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">head</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-70-5" name="__codelineno-70-5" href="#__codelineno-70-5"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">head</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">target</span><span class="p">)</span>
+<a id="__codelineno-70-6" name="__codelineno-70-6" href="#__codelineno-70-6"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">index</span><span class="p">;</span>
+<a id="__codelineno-70-7" name="__codelineno-70-7" href="#__codelineno-70-7"></a><span class="w">        </span><span class="n">head</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">head</span><span class="p">.</span><span class="na">next</span><span class="p">;</span>
+<a id="__codelineno-70-8" name="__codelineno-70-8" href="#__codelineno-70-8"></a><span class="w">        </span><span class="n">index</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-70-9" name="__codelineno-70-9" href="#__codelineno-70-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-70-10" name="__codelineno-70-10" href="#__codelineno-70-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-70-11" name="__codelineno-70-11" href="#__codelineno-70-11"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.cs</span><pre><span></span><code><a id="__codelineno-71-1" name="__codelineno-71-1" href="#__codelineno-71-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">linked_list</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Find</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.go</span><pre><span></span><code><a id="__codelineno-72-1" name="__codelineno-72-1" href="#__codelineno-72-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">findNode</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.swift</span><pre><span></span><code><a id="__codelineno-73-1" name="__codelineno-73-1" href="#__codelineno-73-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="bp">find</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.js</span><pre><span></span><code><a id="__codelineno-74-1" name="__codelineno-74-1" href="#__codelineno-74-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">find</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.ts</span><pre><span></span><code><a id="__codelineno-75-1" name="__codelineno-75-1" href="#__codelineno-75-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">find</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.dart</span><pre><span></span><code><a id="__codelineno-76-1" name="__codelineno-76-1" href="#__codelineno-76-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">find</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.rs</span><pre><span></span><code><a id="__codelineno-77-1" name="__codelineno-77-1" href="#__codelineno-77-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">find</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.c</span><pre><span></span><code><a id="__codelineno-78-1" name="__codelineno-78-1" href="#__codelineno-78-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">find</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.kt</span><pre><span></span><code><a id="__codelineno-79-1" name="__codelineno-79-1" href="#__codelineno-79-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">find</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.rb</span><pre><span></span><code><a id="__codelineno-80-1" name="__codelineno-80-1" href="#__codelineno-80-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">find</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linked_list.zig</span><pre><span></span><code><a id="__codelineno-81-1" name="__codelineno-81-1" href="#__codelineno-81-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">find</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h2 id="422-vs">4.2.2 &nbsp; 配列 vs. 連結リスト<a class="headerlink" href="#422-vs" title="Permanent link">&para;</a></h2>
+<p>下表は配列と連結リストの特性をまとめ、様々な操作における効率も比較しています。それぞれが対照的な格納戦略を使用するため、それぞれの特性と操作効率は明確に対比されています。</p>
+<p align="center"> 表 4-1 &nbsp; 配列と連結リストの効率比較 </p>
+
+<div class="center-table">
+<table>
+<thead>
+<tr>
+<th></th>
+<th>配列</th>
+<th>連結リスト</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td>格納方式</td>
+<td>連続メモリ空間</td>
+<td>分散メモリ空間</td>
+</tr>
+<tr>
+<td>容量拡張</td>
+<td>固定長</td>
+<td>柔軟な拡張</td>
+</tr>
+<tr>
+<td>メモリ効率</td>
+<td>要素あたりのメモリ少、潜在的な空間の無駄</td>
+<td>要素あたりのメモリ多</td>
+</tr>
+<tr>
+<td>要素へのアクセス</td>
+<td><span class="arithmatex">\(O(1)\)</span></td>
+<td><span class="arithmatex">\(O(n)\)</span></td>
+</tr>
+<tr>
+<td>要素の追加</td>
+<td><span class="arithmatex">\(O(n)\)</span></td>
+<td><span class="arithmatex">\(O(1)\)</span></td>
+</tr>
+<tr>
+<td>要素の削除</td>
+<td><span class="arithmatex">\(O(n)\)</span></td>
+<td><span class="arithmatex">\(O(1)\)</span></td>
+</tr>
+</tbody>
+</table>
+</div>
+<h2 id="423">4.2.3 &nbsp; 連結リストの一般的な種類<a class="headerlink" href="#423" title="Permanent link">&para;</a></h2>
+<p>下図に示すように、連結リストには3つの一般的な種類があります。</p>
+<ul>
+<li><strong>単方向連結リスト</strong>：これは前述した標準的な連結リストです。単方向連結リストのノードには値と次のノードへの参照が含まれます。最初のノードはヘッドノードと呼ばれ、null（<code>None</code>）を指す最後のノードはテールノードです。</li>
+<li><strong>循環連結リスト</strong>：これは単方向連結リストのテールノードがヘッドノードを指してループを作ることで形成されます。循環連結リストでは、任意のノードがヘッドノードとして機能できます。</li>
+<li><strong>双方向連結リスト</strong>：単方向連結リストとは対照的に、双方向連結リストは2つの方向で参照を維持します。各ノードには後続者（次のノード）と前任者（前のノード）の両方への参照（ポインタ）が含まれます。双方向連結リストはどちらの方向にも巡回できるより多くの柔軟性を提供しますが、より多くのメモリ空間も消費します。</li>
+</ul>
+<div class="tabbed-set tabbed-alternate" data-tabs="7:13"><input checked="checked" id="__tabbed_7_1" name="__tabbed_7" type="radio" /><input id="__tabbed_7_2" name="__tabbed_7" type="radio" /><input id="__tabbed_7_3" name="__tabbed_7" type="radio" /><input id="__tabbed_7_4" name="__tabbed_7" type="radio" /><input id="__tabbed_7_5" name="__tabbed_7" type="radio" /><input id="__tabbed_7_6" name="__tabbed_7" type="radio" /><input id="__tabbed_7_7" name="__tabbed_7" type="radio" /><input id="__tabbed_7_8" name="__tabbed_7" type="radio" /><input id="__tabbed_7_9" name="__tabbed_7" type="radio" /><input id="__tabbed_7_10" name="__tabbed_7" type="radio" /><input id="__tabbed_7_11" name="__tabbed_7" type="radio" /><input id="__tabbed_7_12" name="__tabbed_7" type="radio" /><input id="__tabbed_7_13" name="__tabbed_7" type="radio" /><div class="tabbed-labels"><label for="__tabbed_7_1">Python</label><label for="__tabbed_7_2">C++</label><label for="__tabbed_7_3">Java</label><label for="__tabbed_7_4">C#</label><label for="__tabbed_7_5">Go</label><label for="__tabbed_7_6">Swift</label><label for="__tabbed_7_7">JS</label><label for="__tabbed_7_8">TS</label><label for="__tabbed_7_9">Dart</label><label for="__tabbed_7_10">Rust</label><label for="__tabbed_7_11">C</label><label for="__tabbed_7_12">Kotlin</label><label for="__tabbed_7_13">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-82-1" name="__codelineno-82-1" href="#__codelineno-82-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">ListNode</span><span class="p">:</span>
+<a id="__codelineno-82-2" name="__codelineno-82-2" href="#__codelineno-82-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;双方向連結リストノードクラス&quot;&quot;&quot;</span>
+<a id="__codelineno-82-3" name="__codelineno-82-3" href="#__codelineno-82-3"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-82-4" name="__codelineno-82-4" href="#__codelineno-82-4"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">val</span>                <span class="c1"># ノード値</span>
+<a id="__codelineno-82-5" name="__codelineno-82-5" href="#__codelineno-82-5"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">next</span><span class="p">:</span> <span class="n">ListNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span>  <span class="c1"># 後続ノードへの参照</span>
+<a id="__codelineno-82-6" name="__codelineno-82-6" href="#__codelineno-82-6"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">prev</span><span class="p">:</span> <span class="n">ListNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span>  <span class="c1"># 前任ノードへの参照</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-83-1" name="__codelineno-83-1" href="#__codelineno-83-1"></a><span class="cm">/* 双方向連結リストノード構造体 */</span>
+<a id="__codelineno-83-2" name="__codelineno-83-2" href="#__codelineno-83-2"></a><span class="k">struct</span><span class="w"> </span><span class="nc">ListNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-83-3" name="__codelineno-83-3" href="#__codelineno-83-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w">         </span><span class="c1">// ノード値</span>
+<a id="__codelineno-83-4" name="__codelineno-83-4" href="#__codelineno-83-4"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">next</span><span class="p">;</span><span class="w">  </span><span class="c1">// 後続ノードへのポインタ</span>
+<a id="__codelineno-83-5" name="__codelineno-83-5" href="#__codelineno-83-5"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">prev</span><span class="p">;</span><span class="w">  </span><span class="c1">// 前任ノードへのポインタ</span>
+<a id="__codelineno-83-6" name="__codelineno-83-6" href="#__codelineno-83-6"></a><span class="w">    </span><span class="n">ListNode</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">x</span><span class="p">)</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">x</span><span class="p">),</span><span class="w"> </span><span class="n">next</span><span class="p">(</span><span class="k">nullptr</span><span class="p">),</span><span class="w"> </span><span class="n">prev</span><span class="p">(</span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{}</span><span class="w">  </span><span class="c1">// コンストラクタ</span>
+<a id="__codelineno-83-7" name="__codelineno-83-7" href="#__codelineno-83-7"></a><span class="p">};</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-84-1" name="__codelineno-84-1" href="#__codelineno-84-1"></a><span class="cm">/* 双方向連結リストノードクラス */</span>
+<a id="__codelineno-84-2" name="__codelineno-84-2" href="#__codelineno-84-2"></a><span class="kd">class</span> <span class="nc">ListNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-84-3" name="__codelineno-84-3" href="#__codelineno-84-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w">        </span><span class="c1">// ノード値</span>
+<a id="__codelineno-84-4" name="__codelineno-84-4" href="#__codelineno-84-4"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="n">next</span><span class="p">;</span><span class="w">  </span><span class="c1">// 次のノードへの参照</span>
+<a id="__codelineno-84-5" name="__codelineno-84-5" href="#__codelineno-84-5"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="n">prev</span><span class="p">;</span><span class="w">  </span><span class="c1">// 前任ノードへの参照</span>
+<a id="__codelineno-84-6" name="__codelineno-84-6" href="#__codelineno-84-6"></a><span class="w">    </span><span class="n">ListNode</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">x</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">x</span><span class="p">;</span><span class="w"> </span><span class="p">}</span><span class="w">  </span><span class="c1">// コンストラクタ</span>
+<a id="__codelineno-84-7" name="__codelineno-84-7" href="#__codelineno-84-7"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-85-1" name="__codelineno-85-1" href="#__codelineno-85-1"></a><span class="cm">/* 双方向連結リストノードクラス */</span>
+<a id="__codelineno-85-2" name="__codelineno-85-2" href="#__codelineno-85-2"></a><span class="k">class</span><span class="w"> </span><span class="nf">ListNode</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">x</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w">  </span><span class="c1">// コンストラクタ</span>
+<a id="__codelineno-85-3" name="__codelineno-85-3" href="#__codelineno-85-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">x</span><span class="p">;</span><span class="w">    </span><span class="c1">// ノード値</span>
+<a id="__codelineno-85-4" name="__codelineno-85-4" href="#__codelineno-85-4"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="n">next</span><span class="p">;</span><span class="w">  </span><span class="c1">// 次のノードへの参照</span>
+<a id="__codelineno-85-5" name="__codelineno-85-5" href="#__codelineno-85-5"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="n">prev</span><span class="p">;</span><span class="w">  </span><span class="c1">// 前任ノードへの参照</span>
+<a id="__codelineno-85-6" name="__codelineno-85-6" href="#__codelineno-85-6"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-86-1" name="__codelineno-86-1" href="#__codelineno-86-1"></a><span class="cm">/* 双方向連結リストノード構造体 */</span>
+<a id="__codelineno-86-2" name="__codelineno-86-2" href="#__codelineno-86-2"></a><span class="kd">type</span><span class="w"> </span><span class="nx">DoublyListNode</span><span class="w"> </span><span class="kd">struct</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-86-3" name="__codelineno-86-3" href="#__codelineno-86-3"></a><span class="w">    </span><span class="nx">Val</span><span class="w">  </span><span class="kt">int</span><span class="w">             </span><span class="c1">// ノード値</span>
+<a id="__codelineno-86-4" name="__codelineno-86-4" href="#__codelineno-86-4"></a><span class="w">    </span><span class="nx">Next</span><span class="w"> </span><span class="o">*</span><span class="nx">DoublyListNode</span><span class="w"> </span><span class="c1">// 後続ノードへのポインタ</span>
+<a id="__codelineno-86-5" name="__codelineno-86-5" href="#__codelineno-86-5"></a><span class="w">    </span><span class="nx">Prev</span><span class="w"> </span><span class="o">*</span><span class="nx">DoublyListNode</span><span class="w"> </span><span class="c1">// 前任ノードへのポインタ</span>
+<a id="__codelineno-86-6" name="__codelineno-86-6" href="#__codelineno-86-6"></a><span class="p">}</span>
+<a id="__codelineno-86-7" name="__codelineno-86-7" href="#__codelineno-86-7"></a>
+<a id="__codelineno-86-8" name="__codelineno-86-8" href="#__codelineno-86-8"></a><span class="c1">// NewDoublyListNode 初期化</span>
+<a id="__codelineno-86-9" name="__codelineno-86-9" href="#__codelineno-86-9"></a><span class="kd">func</span><span class="w"> </span><span class="nx">NewDoublyListNode</span><span class="p">(</span><span class="nx">val</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="nx">DoublyListNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-86-10" name="__codelineno-86-10" href="#__codelineno-86-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">DoublyListNode</span><span class="p">{</span>
+<a id="__codelineno-86-11" name="__codelineno-86-11" href="#__codelineno-86-11"></a><span class="w">        </span><span class="nx">Val</span><span class="p">:</span><span class="w">  </span><span class="nx">val</span><span class="p">,</span>
+<a id="__codelineno-86-12" name="__codelineno-86-12" href="#__codelineno-86-12"></a><span class="w">        </span><span class="nx">Next</span><span class="p">:</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span>
+<a id="__codelineno-86-13" name="__codelineno-86-13" href="#__codelineno-86-13"></a><span class="w">        </span><span class="nx">Prev</span><span class="p">:</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span>
+<a id="__codelineno-86-14" name="__codelineno-86-14" href="#__codelineno-86-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-86-15" name="__codelineno-86-15" href="#__codelineno-86-15"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-87-1" name="__codelineno-87-1" href="#__codelineno-87-1"></a><span class="cm">/* 双方向連結リストノードクラス */</span>
+<a id="__codelineno-87-2" name="__codelineno-87-2" href="#__codelineno-87-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">ListNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-87-3" name="__codelineno-87-3" href="#__codelineno-87-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">val</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="c1">// ノード値</span>
+<a id="__codelineno-87-4" name="__codelineno-87-4" href="#__codelineno-87-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">next</span><span class="p">:</span><span class="w"> </span><span class="n">ListNode</span><span class="p">?</span><span class="w"> </span><span class="c1">// 次のノードへの参照</span>
+<a id="__codelineno-87-5" name="__codelineno-87-5" href="#__codelineno-87-5"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">prev</span><span class="p">:</span><span class="w"> </span><span class="n">ListNode</span><span class="p">?</span><span class="w"> </span><span class="c1">// 前任ノードへの参照</span>
+<a id="__codelineno-87-6" name="__codelineno-87-6" href="#__codelineno-87-6"></a>
+<a id="__codelineno-87-7" name="__codelineno-87-7" href="#__codelineno-87-7"></a><span class="w">    </span><span class="kd">init</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// コンストラクタ</span>
+<a id="__codelineno-87-8" name="__codelineno-87-8" href="#__codelineno-87-8"></a><span class="w">        </span><span class="n">val</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">x</span>
+<a id="__codelineno-87-9" name="__codelineno-87-9" href="#__codelineno-87-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-87-10" name="__codelineno-87-10" href="#__codelineno-87-10"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-88-1" name="__codelineno-88-1" href="#__codelineno-88-1"></a><span class="cm">/* 双方向連結リストノードクラス */</span>
+<a id="__codelineno-88-2" name="__codelineno-88-2" href="#__codelineno-88-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">ListNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-88-3" name="__codelineno-88-3" href="#__codelineno-88-3"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">(</span><span class="nx">val</span><span class="p">,</span><span class="w"> </span><span class="nx">next</span><span class="p">,</span><span class="w"> </span><span class="nx">prev</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-88-4" name="__codelineno-88-4" href="#__codelineno-88-4"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">val</span><span class="w">  </span><span class="o">===</span><span class="w">  </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="nx">val</span><span class="p">;</span><span class="w">        </span><span class="c1">// ノード値</span>
+<a id="__codelineno-88-5" name="__codelineno-88-5" href="#__codelineno-88-5"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">next</span><span class="w">  </span><span class="o">===</span><span class="w">  </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="nx">next</span><span class="p">;</span><span class="w">  </span><span class="c1">// 後続ノードへの参照</span>
+<a id="__codelineno-88-6" name="__codelineno-88-6" href="#__codelineno-88-6"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">prev</span><span class="w">  </span><span class="o">===</span><span class="w">  </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="nx">prev</span><span class="p">;</span><span class="w">  </span><span class="c1">// 前任ノードへの参照</span>
+<a id="__codelineno-88-7" name="__codelineno-88-7" href="#__codelineno-88-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-88-8" name="__codelineno-88-8" href="#__codelineno-88-8"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-89-1" name="__codelineno-89-1" href="#__codelineno-89-1"></a><span class="cm">/* 双方向連結リストノードクラス */</span>
+<a id="__codelineno-89-2" name="__codelineno-89-2" href="#__codelineno-89-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">ListNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-89-3" name="__codelineno-89-3" href="#__codelineno-89-3"></a><span class="w">    </span><span class="nx">val</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">;</span>
+<a id="__codelineno-89-4" name="__codelineno-89-4" href="#__codelineno-89-4"></a><span class="w">    </span><span class="nx">next</span><span class="o">:</span><span class="w"> </span><span class="kt">ListNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-89-5" name="__codelineno-89-5" href="#__codelineno-89-5"></a><span class="w">    </span><span class="nx">prev</span><span class="o">:</span><span class="w"> </span><span class="kt">ListNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-89-6" name="__codelineno-89-6" href="#__codelineno-89-6"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">(</span><span class="nx">val?</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="nx">next?</span><span class="o">:</span><span class="w"> </span><span class="kt">ListNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="nx">prev?</span><span class="o">:</span><span class="w"> </span><span class="kt">ListNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-89-7" name="__codelineno-89-7" href="#__codelineno-89-7"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">val</span><span class="w">  </span><span class="o">===</span><span class="w">  </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">0</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">val</span><span class="p">;</span><span class="w">        </span><span class="c1">// ノード値</span>
+<a id="__codelineno-89-8" name="__codelineno-89-8" href="#__codelineno-89-8"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">next</span><span class="w">  </span><span class="o">===</span><span class="w">  </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">null</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">next</span><span class="p">;</span><span class="w">  </span><span class="c1">// 後続ノードへの参照</span>
+<a id="__codelineno-89-9" name="__codelineno-89-9" href="#__codelineno-89-9"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">prev</span><span class="w">  </span><span class="o">===</span><span class="w">  </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">null</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">prev</span><span class="p">;</span><span class="w">  </span><span class="c1">// 前任ノードへの参照</span>
+<a id="__codelineno-89-10" name="__codelineno-89-10" href="#__codelineno-89-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-89-11" name="__codelineno-89-11" href="#__codelineno-89-11"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-90-1" name="__codelineno-90-1" href="#__codelineno-90-1"></a><span class="cm">/* 双方向連結リストノードクラス */</span>
+<a id="__codelineno-90-2" name="__codelineno-90-2" href="#__codelineno-90-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">ListNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-90-3" name="__codelineno-90-3" href="#__codelineno-90-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w">        </span><span class="c1">// ノード値</span>
+<a id="__codelineno-90-4" name="__codelineno-90-4" href="#__codelineno-90-4"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="n">next</span><span class="p">;</span><span class="w">  </span><span class="c1">// 次のノードへの参照</span>
+<a id="__codelineno-90-5" name="__codelineno-90-5" href="#__codelineno-90-5"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="n">prev</span><span class="p">;</span><span class="w">  </span><span class="c1">// 前任ノードへの参照</span>
+<a id="__codelineno-90-6" name="__codelineno-90-6" href="#__codelineno-90-6"></a><span class="w">    </span><span class="n">ListNode</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="p">[</span><span class="k">this</span><span class="p">.</span><span class="n">next</span><span class="p">,</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">prev</span><span class="p">]);</span><span class="w">  </span><span class="c1">// コンストラクタ</span>
+<a id="__codelineno-90-7" name="__codelineno-90-7" href="#__codelineno-90-7"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-91-1" name="__codelineno-91-1" href="#__codelineno-91-1"></a><span class="k">use</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">rc</span><span class="p">::</span><span class="n">Rc</span><span class="p">;</span>
+<a id="__codelineno-91-2" name="__codelineno-91-2" href="#__codelineno-91-2"></a><span class="k">use</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">cell</span><span class="p">::</span><span class="n">RefCell</span><span class="p">;</span>
+<a id="__codelineno-91-3" name="__codelineno-91-3" href="#__codelineno-91-3"></a>
+<a id="__codelineno-91-4" name="__codelineno-91-4" href="#__codelineno-91-4"></a><span class="cm">/* 双方向連結リストノード型 */</span>
+<a id="__codelineno-91-5" name="__codelineno-91-5" href="#__codelineno-91-5"></a><span class="cp">#[derive(Debug)]</span>
+<a id="__codelineno-91-6" name="__codelineno-91-6" href="#__codelineno-91-6"></a><span class="k">struct</span><span class="w"> </span><span class="nc">ListNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-91-7" name="__codelineno-91-7" href="#__codelineno-91-7"></a><span class="w">    </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="c1">// ノード値</span>
+<a id="__codelineno-91-8" name="__codelineno-91-8" href="#__codelineno-91-8"></a><span class="w">    </span><span class="n">next</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">ListNode</span><span class="o">&gt;&gt;&gt;</span><span class="p">,</span><span class="w"> </span><span class="c1">// 後続ノードへのポインタ</span>
+<a id="__codelineno-91-9" name="__codelineno-91-9" href="#__codelineno-91-9"></a><span class="w">    </span><span class="n">prev</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">ListNode</span><span class="o">&gt;&gt;&gt;</span><span class="p">,</span><span class="w"> </span><span class="c1">// 前任ノードへのポインタ</span>
+<a id="__codelineno-91-10" name="__codelineno-91-10" href="#__codelineno-91-10"></a><span class="p">}</span>
+<a id="__codelineno-91-11" name="__codelineno-91-11" href="#__codelineno-91-11"></a>
+<a id="__codelineno-91-12" name="__codelineno-91-12" href="#__codelineno-91-12"></a><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-91-13" name="__codelineno-91-13" href="#__codelineno-91-13"></a><span class="k">impl</span><span class="w"> </span><span class="n">ListNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-91-14" name="__codelineno-91-14" href="#__codelineno-91-14"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">new</span><span class="p">(</span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nc">Self</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-91-15" name="__codelineno-91-15" href="#__codelineno-91-15"></a><span class="w">        </span><span class="n">ListNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-91-16" name="__codelineno-91-16" href="#__codelineno-91-16"></a><span class="w">            </span><span class="n">val</span><span class="p">,</span>
+<a id="__codelineno-91-17" name="__codelineno-91-17" href="#__codelineno-91-17"></a><span class="w">            </span><span class="n">next</span><span class="p">:</span><span class="w"> </span><span class="nb">None</span><span class="p">,</span>
+<a id="__codelineno-91-18" name="__codelineno-91-18" href="#__codelineno-91-18"></a><span class="w">            </span><span class="n">prev</span><span class="p">:</span><span class="w"> </span><span class="nb">None</span><span class="p">,</span>
+<a id="__codelineno-91-19" name="__codelineno-91-19" href="#__codelineno-91-19"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-91-20" name="__codelineno-91-20" href="#__codelineno-91-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-91-21" name="__codelineno-91-21" href="#__codelineno-91-21"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-92-1" name="__codelineno-92-1" href="#__codelineno-92-1"></a><span class="cm">/* 双方向連結リストノード構造体 */</span>
+<a id="__codelineno-92-2" name="__codelineno-92-2" href="#__codelineno-92-2"></a><span class="k">typedef</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="nc">ListNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-92-3" name="__codelineno-92-3" href="#__codelineno-92-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w">               </span><span class="c1">// ノード値</span>
+<a id="__codelineno-92-4" name="__codelineno-92-4" href="#__codelineno-92-4"></a><span class="w">    </span><span class="k">struct</span><span class="w"> </span><span class="nc">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">next</span><span class="p">;</span><span class="w"> </span><span class="c1">// 後続ノードへのポインタ</span>
+<a id="__codelineno-92-5" name="__codelineno-92-5" href="#__codelineno-92-5"></a><span class="w">    </span><span class="k">struct</span><span class="w"> </span><span class="nc">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">prev</span><span class="p">;</span><span class="w"> </span><span class="c1">// 前任ノードへのポインタ</span>
+<a id="__codelineno-92-6" name="__codelineno-92-6" href="#__codelineno-92-6"></a><span class="p">}</span><span class="w"> </span><span class="n">ListNode</span><span class="p">;</span>
+<a id="__codelineno-92-7" name="__codelineno-92-7" href="#__codelineno-92-7"></a>
+<a id="__codelineno-92-8" name="__codelineno-92-8" href="#__codelineno-92-8"></a><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-92-9" name="__codelineno-92-9" href="#__codelineno-92-9"></a><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="nf">newListNode</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-92-10" name="__codelineno-92-10" href="#__codelineno-92-10"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="p">,</span><span class="w"> </span><span class="o">*</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-92-11" name="__codelineno-92-11" href="#__codelineno-92-11"></a><span class="w">    </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="w"> </span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">ListNode</span><span class="p">));</span>
+<a id="__codelineno-92-12" name="__codelineno-92-12" href="#__codelineno-92-12"></a><span class="w">    </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-92-13" name="__codelineno-92-13" href="#__codelineno-92-13"></a><span class="w">    </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
+<a id="__codelineno-92-14" name="__codelineno-92-14" href="#__codelineno-92-14"></a><span class="w">    </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
+<a id="__codelineno-92-15" name="__codelineno-92-15" href="#__codelineno-92-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-92-16" name="__codelineno-92-16" href="#__codelineno-92-16"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-93-1" name="__codelineno-93-1" href="#__codelineno-93-1"></a>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-94-1" name="__codelineno-94-1" href="#__codelineno-94-1"></a><span class="c1">// 双方向連結リストノードクラス</span>
+<a id="__codelineno-94-2" name="__codelineno-94-2" href="#__codelineno-94-2"></a><span class="kr">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="kr">comptime</span><span class="w"> </span><span class="n">T</span><span class="o">:</span><span class="w"> </span><span class="kt">type</span><span class="p">)</span><span class="w"> </span><span class="kt">type</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-94-3" name="__codelineno-94-3" href="#__codelineno-94-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-94-4" name="__codelineno-94-4" href="#__codelineno-94-4"></a><span class="w">        </span><span class="kr">const</span><span class="w"> </span><span class="n">Self</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">@This</span><span class="p">();</span>
+<a id="__codelineno-94-5" name="__codelineno-94-5" href="#__codelineno-94-5"></a>
+<a id="__codelineno-94-6" name="__codelineno-94-6" href="#__codelineno-94-6"></a><span class="w">        </span><span class="n">val</span><span class="o">:</span><span class="w"> </span><span class="n">T</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="c1">// ノード値</span>
+<a id="__codelineno-94-7" name="__codelineno-94-7" href="#__codelineno-94-7"></a><span class="w">        </span><span class="n">next</span><span class="o">:</span><span class="w"> </span><span class="o">?*</span><span class="n">Self</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="c1">// 後続ノードへのポインタ</span>
+<a id="__codelineno-94-8" name="__codelineno-94-8" href="#__codelineno-94-8"></a><span class="w">        </span><span class="n">prev</span><span class="o">:</span><span class="w"> </span><span class="o">?*</span><span class="n">Self</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="c1">// 前任ノードへのポインタ</span>
+<a id="__codelineno-94-9" name="__codelineno-94-9" href="#__codelineno-94-9"></a>
+<a id="__codelineno-94-10" name="__codelineno-94-10" href="#__codelineno-94-10"></a><span class="w">        </span><span class="c1">// コンストラクタ</span>
+<a id="__codelineno-94-11" name="__codelineno-94-11" href="#__codelineno-94-11"></a><span class="w">        </span><span class="kr">pub</span><span class="w"> </span><span class="k">fn</span><span class="w"> </span><span class="n">init</span><span class="p">(</span><span class="n">self</span><span class="o">:</span><span class="w"> </span><span class="o">*</span><span class="n">Self</span><span class="p">,</span><span class="w"> </span><span class="n">x</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-94-12" name="__codelineno-94-12" href="#__codelineno-94-12"></a><span class="w">            </span><span class="n">self</span><span class="p">.</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">x</span><span class="p">;</span>
+<a id="__codelineno-94-13" name="__codelineno-94-13" href="#__codelineno-94-13"></a><span class="w">            </span><span class="n">self</span><span class="p">.</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-94-14" name="__codelineno-94-14" href="#__codelineno-94-14"></a><span class="w">            </span><span class="n">self</span><span class="p">.</span><span class="n">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-94-15" name="__codelineno-94-15" href="#__codelineno-94-15"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-94-16" name="__codelineno-94-16" href="#__codelineno-94-16"></a><span class="w">    </span><span class="p">};</span>
+<a id="__codelineno-94-17" name="__codelineno-94-17" href="#__codelineno-94-17"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p><a class="glightbox" href="../linked_list.assets/linkedlist_common_types.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="連結リストの一般的な種類" class="animation-figure" src="../linked_list.assets/linkedlist_common_types.png" /></a></p>
+<p align="center"> 図 4-8 &nbsp; 連結リストの一般的な種類 </p>
+
+<h2 id="424">4.2.4 &nbsp; 連結リストの典型的な応用<a class="headerlink" href="#424" title="Permanent link">&para;</a></h2>
+<p>単方向連結リストは、スタック、キュー、ハッシュ表、グラフの実装によく使用されます。</p>
+<ul>
+<li><strong>スタックとキュー</strong>：単方向連結リストで、挿入と削除が同じ端で行われる場合、スタック（後入先出）のように動作します。逆に、挿入が一方の端で、削除がもう一方の端で行われる場合、キュー（先入先出）のように機能します。</li>
+<li><strong>ハッシュ表</strong>：連結リストは、ハッシュ衝突を解決する人気の方法である連鎖法で使用されます。ここでは、すべての衝突した要素が連結リストにグループ化されます。</li>
+<li><strong>グラフ</strong>：グラフ表現の標準的な方法である隣接リストは、各グラフ頂点を連結リストに関連付けます。このリストには、対応する頂点に接続された頂点を表す要素が含まれます。</li>
+</ul>
+<p>双方向連結リストは、前後の要素への高速アクセスが必要なシナリオに最適です。</p>
+<ul>
+<li><strong>高度なデータ構造</strong>：赤黒木やB木などの構造では、ノードの親へのアクセスが重要です。これは各ノードに親ノードへの参照を組み込むことで実現され、双方向連結リストに似ています。</li>
+<li><strong>ブラウザ履歴</strong>：Webブラウザでは、双方向連結リストにより、ユーザーが前進または後退ボタンをクリックしたときの訪問ページの履歴ナビゲーションが容易になります。</li>
+<li><strong>LRUアルゴリズム</strong>：双方向連結リストは、最近最少使用（LRU）キャッシュ削除アルゴリズムに適しており、最近最少使用データの迅速な識別と、高速なノード追加・削除を可能にします。</li>
+</ul>
+<p>循環連結リストは、オペレーティングシステムでのリソーススケジューリングなど、周期的な操作が必要なアプリケーションに最適です。</p>
+<ul>
+<li><strong>ラウンドロビンスケジューリングアルゴリズム</strong>：オペレーティングシステムでは、ラウンドロビンスケジューリングアルゴリズムは一般的なCPUスケジューリング方法であり、プロセスのグループを循環する必要があります。各プロセスにはタイムスライスが割り当てられ、期限切れになるとCPUは次のプロセスに回転します。この循環操作は循環連結リストを使用して効率的に実現でき、すべてのプロセス間で公平かつ時分割システムを可能にします。</li>
+<li><strong>データバッファ</strong>：循環連結リストは、オーディオやビデオプレーヤーなどのデータバッファでも使用され、データストリームが複数のバッファブロックに分割され、シームレスな再生のために循環方式で配置されます。</li>
+</ul>
+
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+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#431" class="md-nav__link">
+    <span class="md-ellipsis">
+      4.3.1 &nbsp; リストの一般的な操作
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="4.3.1   リストの一般的な操作">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; リストの初期化
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; 要素へのアクセス
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#3" class="md-nav__link">
+    <span class="md-ellipsis">
+      3. &nbsp; 要素の挿入と削除
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#4" class="md-nav__link">
+    <span class="md-ellipsis">
+      4. &nbsp; リストの反復
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#5" class="md-nav__link">
+    <span class="md-ellipsis">
+      5. &nbsp; リストの連結
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#6" class="md-nav__link">
+    <span class="md-ellipsis">
+      6. &nbsp; リストのソート
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#432" class="md-nav__link">
+    <span class="md-ellipsis">
+      4.3.2 &nbsp; リストの実装
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
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+  
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+  
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+    </li>
+  
+
+              
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+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
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+      </a>
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+  
+
+              
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+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
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+
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+  
+
+              
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+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
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+  
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+
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+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
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+  <span class="md-ellipsis">
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+  <a href="#431" class="md-nav__link">
+    <span class="md-ellipsis">
+      4.3.1 &nbsp; リストの一般的な操作
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="4.3.1   リストの一般的な操作">
+      <ul class="md-nav__list">
+        
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+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; リストの初期化
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; 要素へのアクセス
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#3" class="md-nav__link">
+    <span class="md-ellipsis">
+      3. &nbsp; 要素の挿入と削除
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#4" class="md-nav__link">
+    <span class="md-ellipsis">
+      4. &nbsp; リストの反復
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#5" class="md-nav__link">
+    <span class="md-ellipsis">
+      5. &nbsp; リストの連結
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#6" class="md-nav__link">
+    <span class="md-ellipsis">
+      6. &nbsp; リストのソート
+    </span>
+  </a>
+  
+</li>
+        
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+    </nav>
+  
+</li>
+      
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+  <a href="#432" class="md-nav__link">
+    <span class="md-ellipsis">
+      4.3.2 &nbsp; リストの実装
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+                  </div>
+                </div>
+              </div>
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+      
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
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+<!-- Page content -->
+<h1 id="43">4.3 &nbsp; リスト<a class="headerlink" href="#43" title="Permanent link">&para;</a></h1>
+<p><u>リスト</u>は、要素へのアクセス、変更、追加、削除、走査などの操作をサポートする、順序付けられた要素のコレクションを表す抽象的なデータ構造の概念であり、ユーザーが容量制限を考慮する必要がありません。リストは連結リストまたは配列に基づいて実装できます。</p>
+<ul>
+<li>連結リストは本質的にリストとして機能し、要素の追加、削除、検索、変更の操作をサポートし、サイズを動的に調整する柔軟性があります。</li>
+<li>配列もこれらの操作をサポートしますが、長さが不変であるため、長さ制限のあるリストと考えることができます。</li>
+</ul>
+<p>配列を使用してリストを実装する場合、<strong>長さの不変性によりリストの実用性が低下します</strong>。これは、事前に格納するデータ量を予測することが困難な場合が多く、適切なリスト長を選択することが困難であるためです。長さが小さすぎると要件を満たさない可能性があり、大きすぎるとメモリ空間を無駄にする可能性があります。</p>
+<p>この問題を解決するために、<u>動的配列</u>を使用してリストを実装できます。これは配列の利点を継承し、プログラム実行中に動的に拡張できます。</p>
+<p>実際、<strong>多くのプログラミング言語の標準ライブラリは動的配列を使用してリストを実装しています</strong>。例えば、Pythonの<code>list</code>、Javaの<code>ArrayList</code>、C++の<code>vector</code>、C#の<code>List</code>などです。以下の議論では、「リスト」と「動的配列」を同義の概念として扱います。</p>
+<h2 id="431">4.3.1 &nbsp; リストの一般的な操作<a class="headerlink" href="#431" title="Permanent link">&para;</a></h2>
+<h3 id="1">1. &nbsp; リストの初期化<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<p>通常、「初期値なし」と「初期値あり」の2つの初期化方法を使用します。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="c1"># リストを初期化</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="c1"># 初期値なし</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="n">nums1</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="p">[]</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="c1"># 初期値あり</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">4</span><span class="p">]</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* リストを初期化 */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="c1">// 注意: C++では、vectorがここで説明されているnumsに相当します</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="c1">// 初期値なし</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums1</span><span class="p">;</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="c1">// 初期値あり</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="w"> </span><span class="p">};</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* リストを初期化 */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="c1">// 初期値なし</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="c1">// 初期値あり（要素型はint[]のラッパークラスInteger[]である必要があります）</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="n">Integer</span><span class="o">[]</span><span class="w"> </span><span class="n">numbers</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Integer</span><span class="o">[]</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="w"> </span><span class="p">};</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">(</span><span class="n">Arrays</span><span class="p">.</span><span class="na">asList</span><span class="p">(</span><span class="n">numbers</span><span class="p">));</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* リストを初期化 */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="c1">// 初期値なし</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="c1">// 初期値あり</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">numbers</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">];</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[..</span><span class="w"> </span><span class="n">numbers</span><span class="p">];</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list_test.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* リストを初期化 */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="c1">// 初期値なし</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="nx">nums1</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">{}</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="c1">// 初期値あり</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="nx">nums</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">{</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* リストを初期化 */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="c1">// 初期値なし</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="kd">let</span><span class="w"> </span><span class="nv">nums1</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[]</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="c1">// 初期値あり</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="kd">var</span><span class="w"> </span><span class="nv">nums</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">]</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* リストを初期化 */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="c1">// 初期値なし</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="kd">const</span><span class="w"> </span><span class="nx">nums1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="c1">// 初期値あり</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="kd">const</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="mf">3</span><span class="p">,</span><span class="w"> </span><span class="mf">2</span><span class="p">,</span><span class="w"> </span><span class="mf">5</span><span class="p">,</span><span class="w"> </span><span class="mf">4</span><span class="p">];</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* リストを初期化 */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="c1">// 初期値なし</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="kd">const</span><span class="w"> </span><span class="nx">nums1</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="c1">// 初期値あり</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="kd">const</span><span class="w"> </span><span class="nx">nums</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="mf">3</span><span class="p">,</span><span class="w"> </span><span class="mf">2</span><span class="p">,</span><span class="w"> </span><span class="mf">5</span><span class="p">,</span><span class="w"> </span><span class="mf">4</span><span class="p">];</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* リストを初期化 */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="c1">// 初期値なし</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="c1">// 初期値あり</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="m">3</span><span class="p">,</span><span class="w"> </span><span class="m">2</span><span class="p">,</span><span class="w"> </span><span class="m">5</span><span class="p">,</span><span class="w"> </span><span class="m">4</span><span class="p">];</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* リストを初期化 */</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="c1">// 初期値なし</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="kd">let</span><span class="w"> </span><span class="n">nums1</span><span class="p">:</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Vec</span><span class="p">::</span><span class="n">new</span><span class="p">();</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="c1">// 初期値あり</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="kd">let</span><span class="w"> </span><span class="n">nums</span><span class="p">:</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">];</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="c1">// Cは組み込みの動的配列を提供していません</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.zig</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">// リストを初期化</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="kr">var</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span><span class="p">.</span><span class="n">ArrayList</span><span class="p">(</span><span class="kt">i32</span><span class="p">).</span><span class="n">init</span><span class="p">(</span><span class="n">std</span><span class="p">.</span><span class="n">heap</span><span class="p">.</span><span class="n">page_allocator</span><span class="p">);</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="k">defer</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">deinit</span><span class="p">();</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="k">try</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">appendSlice</span><span class="p">(</span><span class="o">&amp;</span><span class="p">[</span><span class="n">_</span><span class="p">]</span><span class="kt">i32</span><span class="p">{</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="w"> </span><span class="p">});</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h3 id="2">2. &nbsp; 要素へのアクセス<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
+<p>リストは本質的に配列であるため、<span class="arithmatex">\(O(1)\)</span>時間で要素にアクセスし更新することができ、非常に効率的です。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:13"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.py</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="c1"># 要素にアクセス</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="n">num</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>  <span class="c1"># インデックス1の要素にアクセス</span>
+<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>
+<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a><span class="c1"># 要素を更新</span>
+<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a><span class="n">nums</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span>    <span class="c1"># インデックス1の要素を0に更新</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 要素にアクセス */</span>
+<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="mi">1</span><span class="p">];</span><span class="w">  </span><span class="c1">// インデックス1の要素にアクセス</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="cm">/* 要素を更新 */</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="n">nums</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">  </span><span class="c1">// インデックス1の要素を0に更新</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 要素にアクセス */</span>
+<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span><span class="w">  </span><span class="c1">// インデックス1の要素にアクセス</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a>
+<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="cm">/* 要素を更新 */</span>
+<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="n">nums</span><span class="p">.</span><span class="na">set</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span><span class="w">  </span><span class="c1">// インデックス1の要素を0に更新</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 要素にアクセス */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="mi">1</span><span class="p">];</span><span class="w">  </span><span class="c1">// インデックス1の要素にアクセス</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="cm">/* 要素を更新 */</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="n">nums</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">  </span><span class="c1">// インデックス1の要素を0に更新</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list_test.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* 要素にアクセス */</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="nx">num</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="w">  </span><span class="c1">// インデックス1の要素にアクセス</span>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a>
+<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="cm">/* 要素を更新 */</span>
+<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="nx">nums</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span><span class="w">     </span><span class="c1">// インデックス1の要素を0に更新</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* 要素にアクセス */</span>
+<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="kd">let</span><span class="w"> </span><span class="nv">num</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="c1">// インデックス1の要素にアクセス</span>
+<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a>
+<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="cm">/* 要素を更新 */</span>
+<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="n">nums</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="c1">// インデックス1の要素を0に更新</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* 要素にアクセス */</span>
+<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="kd">const</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="mf">1</span><span class="p">];</span><span class="w">  </span><span class="c1">// インデックス1の要素にアクセス</span>
+<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a>
+<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="cm">/* 要素を更新 */</span>
+<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="nx">nums</span><span class="p">[</span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w">  </span><span class="c1">// インデックス1の要素を0に更新</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* 要素にアクセス */</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="kd">const</span><span class="w"> </span><span class="nx">num</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="mf">1</span><span class="p">];</span><span class="w">  </span><span class="c1">// インデックス1の要素にアクセス</span>
+<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a>
+<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="cm">/* 要素を更新 */</span>
+<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="nx">nums</span><span class="p">[</span><span class="mf">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w">  </span><span class="c1">// インデックス1の要素を0に更新</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* 要素にアクセス */</span>
+<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="kt">int</span><span class="w"> </span><span class="kt">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="m">1</span><span class="p">];</span><span class="w">  </span><span class="c1">// インデックス1の要素にアクセス</span>
+<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a>
+<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="cm">/* 要素を更新 */</span>
+<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="n">nums</span><span class="p">[</span><span class="m">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w">  </span><span class="c1">// インデックス1の要素を0に更新</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="cm">/* 要素にアクセス */</span>
+<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="kd">let</span><span class="w"> </span><span class="n">num</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="mi">1</span><span class="p">];</span><span class="w">  </span><span class="c1">// インデックス1の要素にアクセス</span>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="cm">/* 要素を更新 */</span>
+<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="n">nums</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">             </span><span class="c1">// インデックス1の要素を0に更新</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="c1">// Cは組み込みの動的配列を提供していません</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.zig</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="c1">// 要素にアクセス</span>
+<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="kr">var</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">items</span><span class="p">[</span><span class="mi">1</span><span class="p">];</span><span class="w"> </span><span class="c1">// インデックス1の要素にアクセス</span>
+<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a>
+<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="c1">// 要素を更新</span>
+<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="n">nums</span><span class="p">.</span><span class="n">items</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// インデックス1の要素を0に更新</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h3 id="3">3. &nbsp; 要素の挿入と削除<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
+<p>配列と比較して、リストは要素の追加と削除においてより柔軟性を提供します。リストの末尾への要素追加は<span class="arithmatex">\(O(1)\)</span>操作ですが、リストの他の場所での要素の挿入と削除の効率は配列と同じままで、時間計算量は<span class="arithmatex">\(O(n)\)</span>です。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="3:13"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.py</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="c1"># リストをクリア</span>
+<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a><span class="n">nums</span><span class="o">.</span><span class="n">clear</span><span class="p">()</span>
+<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a>
+<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a><span class="c1"># 末尾に要素を追加</span>
+<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="n">nums</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a><span class="n">nums</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
+<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a><span class="n">nums</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a><span class="n">nums</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
+<a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a><span class="n">nums</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
+<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a>
+<a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a><span class="c1"># 中間に要素を挿入</span>
+<a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a><span class="n">nums</span><span class="o">.</span><span class="n">insert</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">6</span><span class="p">)</span>  <span class="c1"># インデックス3に数値6を挿入</span>
+<a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a>
+<a id="__codelineno-26-14" name="__codelineno-26-14" href="#__codelineno-26-14"></a><span class="c1"># 要素を削除</span>
+<a id="__codelineno-26-15" name="__codelineno-26-15" href="#__codelineno-26-15"></a><span class="n">nums</span><span class="o">.</span><span class="n">pop</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>        <span class="c1"># インデックス3の要素を削除</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.cpp</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="cm">/* リストをクリア */</span>
+<a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a><span class="n">nums</span><span class="p">.</span><span class="n">clear</span><span class="p">();</span>
+<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a>
+<a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a><span class="cm">/* 末尾に要素を追加 */</span>
+<a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a><span class="n">nums</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a><span class="n">nums</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
+<a id="__codelineno-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a><span class="n">nums</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-27-8" name="__codelineno-27-8" href="#__codelineno-27-8"></a><span class="n">nums</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
+<a id="__codelineno-27-9" name="__codelineno-27-9" href="#__codelineno-27-9"></a><span class="n">nums</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
+<a id="__codelineno-27-10" name="__codelineno-27-10" href="#__codelineno-27-10"></a>
+<a id="__codelineno-27-11" name="__codelineno-27-11" href="#__codelineno-27-11"></a><span class="cm">/* 中間に要素を挿入 */</span>
+<a id="__codelineno-27-12" name="__codelineno-27-12" href="#__codelineno-27-12"></a><span class="n">nums</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="n">nums</span><span class="p">.</span><span class="n">begin</span><span class="p">()</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">6</span><span class="p">);</span><span class="w">  </span><span class="c1">// インデックス3に数値6を挿入</span>
+<a id="__codelineno-27-13" name="__codelineno-27-13" href="#__codelineno-27-13"></a>
+<a id="__codelineno-27-14" name="__codelineno-27-14" href="#__codelineno-27-14"></a><span class="cm">/* 要素を削除 */</span>
+<a id="__codelineno-27-15" name="__codelineno-27-15" href="#__codelineno-27-15"></a><span class="n">nums</span><span class="p">.</span><span class="n">erase</span><span class="p">(</span><span class="n">nums</span><span class="p">.</span><span class="n">begin</span><span class="p">()</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">3</span><span class="p">);</span><span class="w">      </span><span class="c1">// インデックス3の要素を削除</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.java</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="cm">/* リストをクリア */</span>
+<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="n">nums</span><span class="p">.</span><span class="na">clear</span><span class="p">();</span>
+<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a>
+<a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a><span class="cm">/* 末尾に要素を追加 */</span>
+<a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a><span class="n">nums</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a><span class="n">nums</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
+<a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a><span class="n">nums</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-28-8" name="__codelineno-28-8" href="#__codelineno-28-8"></a><span class="n">nums</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
+<a id="__codelineno-28-9" name="__codelineno-28-9" href="#__codelineno-28-9"></a><span class="n">nums</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
+<a id="__codelineno-28-10" name="__codelineno-28-10" href="#__codelineno-28-10"></a>
+<a id="__codelineno-28-11" name="__codelineno-28-11" href="#__codelineno-28-11"></a><span class="cm">/* 中間に要素を挿入 */</span>
+<a id="__codelineno-28-12" name="__codelineno-28-12" href="#__codelineno-28-12"></a><span class="n">nums</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">6</span><span class="p">);</span><span class="w">  </span><span class="c1">// インデックス3に数値6を挿入</span>
+<a id="__codelineno-28-13" name="__codelineno-28-13" href="#__codelineno-28-13"></a>
+<a id="__codelineno-28-14" name="__codelineno-28-14" href="#__codelineno-28-14"></a><span class="cm">/* 要素を削除 */</span>
+<a id="__codelineno-28-15" name="__codelineno-28-15" href="#__codelineno-28-15"></a><span class="n">nums</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span><span class="w">  </span><span class="c1">// インデックス3の要素を削除</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.cs</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="cm">/* リストをクリア */</span>
+<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="n">nums</span><span class="p">.</span><span class="n">Clear</span><span class="p">();</span>
+<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a>
+<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="cm">/* 末尾に要素を追加 */</span>
+<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a><span class="n">nums</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a><span class="n">nums</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
+<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="n">nums</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a><span class="n">nums</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
+<a id="__codelineno-29-9" name="__codelineno-29-9" href="#__codelineno-29-9"></a><span class="n">nums</span><span class="p">.</span><span class="n">Add</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
+<a id="__codelineno-29-10" name="__codelineno-29-10" href="#__codelineno-29-10"></a>
+<a id="__codelineno-29-11" name="__codelineno-29-11" href="#__codelineno-29-11"></a><span class="cm">/* 中間に要素を挿入 */</span>
+<a id="__codelineno-29-12" name="__codelineno-29-12" href="#__codelineno-29-12"></a><span class="n">nums</span><span class="p">.</span><span class="n">Insert</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">6</span><span class="p">);</span>
+<a id="__codelineno-29-13" name="__codelineno-29-13" href="#__codelineno-29-13"></a>
+<a id="__codelineno-29-14" name="__codelineno-29-14" href="#__codelineno-29-14"></a><span class="cm">/* 要素を削除 */</span>
+<a id="__codelineno-29-15" name="__codelineno-29-15" href="#__codelineno-29-15"></a><span class="n">nums</span><span class="p">.</span><span class="n">RemoveAt</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list_test.go</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* リストをクリア */</span>
+<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="nx">nums</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kc">nil</span>
+<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a>
+<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="cm">/* 末尾に要素を追加 */</span>
+<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a><span class="nx">nums</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="nx">nums</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">)</span>
+<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a><span class="nx">nums</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a><span class="nx">nums</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">)</span>
+<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a><span class="nx">nums</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">)</span>
+<a id="__codelineno-30-10" name="__codelineno-30-10" href="#__codelineno-30-10"></a>
+<a id="__codelineno-30-11" name="__codelineno-30-11" href="#__codelineno-30-11"></a><span class="cm">/* 中間に要素を挿入 */</span>
+<a id="__codelineno-30-12" name="__codelineno-30-12" href="#__codelineno-30-12"></a><span class="nx">nums</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">nums</span><span class="p">[:</span><span class="mi">3</span><span class="p">],</span><span class="w"> </span><span class="nb">append</span><span class="p">([]</span><span class="kt">int</span><span class="p">{</span><span class="mi">6</span><span class="p">},</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="mi">3</span><span class="p">:]</span><span class="o">...</span><span class="p">)</span><span class="o">...</span><span class="p">)</span><span class="w"> </span><span class="c1">// インデックス3に数値6を挿入</span>
+<a id="__codelineno-30-13" name="__codelineno-30-13" href="#__codelineno-30-13"></a>
+<a id="__codelineno-30-14" name="__codelineno-30-14" href="#__codelineno-30-14"></a><span class="cm">/* 要素を削除 */</span>
+<a id="__codelineno-30-15" name="__codelineno-30-15" href="#__codelineno-30-15"></a><span class="nx">nums</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">nums</span><span class="p">[:</span><span class="mi">3</span><span class="p">],</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="mi">4</span><span class="p">:]</span><span class="o">...</span><span class="p">)</span><span class="w"> </span><span class="c1">// インデックス3の要素を削除</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.swift</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="cm">/* リストをクリア */</span>
+<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a><span class="n">nums</span><span class="p">.</span><span class="bp">removeAll</span><span class="p">()</span>
+<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a>
+<a id="__codelineno-31-4" name="__codelineno-31-4" href="#__codelineno-31-4"></a><span class="cm">/* 末尾に要素を追加 */</span>
+<a id="__codelineno-31-5" name="__codelineno-31-5" href="#__codelineno-31-5"></a><span class="n">nums</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-31-6" name="__codelineno-31-6" href="#__codelineno-31-6"></a><span class="n">nums</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
+<a id="__codelineno-31-7" name="__codelineno-31-7" href="#__codelineno-31-7"></a><span class="n">nums</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-31-8" name="__codelineno-31-8" href="#__codelineno-31-8"></a><span class="n">nums</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
+<a id="__codelineno-31-9" name="__codelineno-31-9" href="#__codelineno-31-9"></a><span class="n">nums</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
+<a id="__codelineno-31-10" name="__codelineno-31-10" href="#__codelineno-31-10"></a>
+<a id="__codelineno-31-11" name="__codelineno-31-11" href="#__codelineno-31-11"></a><span class="cm">/* 中間に要素を挿入 */</span>
+<a id="__codelineno-31-12" name="__codelineno-31-12" href="#__codelineno-31-12"></a><span class="n">nums</span><span class="p">.</span><span class="bp">insert</span><span class="p">(</span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="n">at</span><span class="p">:</span><span class="w"> </span><span class="mi">3</span><span class="p">)</span><span class="w"> </span><span class="c1">// インデックス3に数値6を挿入</span>
+<a id="__codelineno-31-13" name="__codelineno-31-13" href="#__codelineno-31-13"></a>
+<a id="__codelineno-31-14" name="__codelineno-31-14" href="#__codelineno-31-14"></a><span class="cm">/* 要素を削除 */</span>
+<a id="__codelineno-31-15" name="__codelineno-31-15" href="#__codelineno-31-15"></a><span class="n">nums</span><span class="p">.</span><span class="n">remove</span><span class="p">(</span><span class="n">at</span><span class="p">:</span><span class="w"> </span><span class="mi">3</span><span class="p">)</span><span class="w"> </span><span class="c1">// インデックス3の要素を削除</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.js</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="cm">/* リストをクリア */</span>
+<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a>
+<a id="__codelineno-32-4" name="__codelineno-32-4" href="#__codelineno-32-4"></a><span class="cm">/* 末尾に要素を追加 */</span>
+<a id="__codelineno-32-5" name="__codelineno-32-5" href="#__codelineno-32-5"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-32-6" name="__codelineno-32-6" href="#__codelineno-32-6"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">3</span><span class="p">);</span>
+<a id="__codelineno-32-7" name="__codelineno-32-7" href="#__codelineno-32-7"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">2</span><span class="p">);</span>
+<a id="__codelineno-32-8" name="__codelineno-32-8" href="#__codelineno-32-8"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">5</span><span class="p">);</span>
+<a id="__codelineno-32-9" name="__codelineno-32-9" href="#__codelineno-32-9"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">4</span><span class="p">);</span>
+<a id="__codelineno-32-10" name="__codelineno-32-10" href="#__codelineno-32-10"></a>
+<a id="__codelineno-32-11" name="__codelineno-32-11" href="#__codelineno-32-11"></a><span class="cm">/* 中間に要素を挿入 */</span>
+<a id="__codelineno-32-12" name="__codelineno-32-12" href="#__codelineno-32-12"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">splice</span><span class="p">(</span><span class="mf">3</span><span class="p">,</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="mf">6</span><span class="p">);</span>
+<a id="__codelineno-32-13" name="__codelineno-32-13" href="#__codelineno-32-13"></a>
+<a id="__codelineno-32-14" name="__codelineno-32-14" href="#__codelineno-32-14"></a><span class="cm">/* 要素を削除 */</span>
+<a id="__codelineno-32-15" name="__codelineno-32-15" href="#__codelineno-32-15"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">splice</span><span class="p">(</span><span class="mf">3</span><span class="p">,</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.ts</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="cm">/* リストをクリア */</span>
+<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a>
+<a id="__codelineno-33-4" name="__codelineno-33-4" href="#__codelineno-33-4"></a><span class="cm">/* 末尾に要素を追加 */</span>
+<a id="__codelineno-33-5" name="__codelineno-33-5" href="#__codelineno-33-5"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-33-6" name="__codelineno-33-6" href="#__codelineno-33-6"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">3</span><span class="p">);</span>
+<a id="__codelineno-33-7" name="__codelineno-33-7" href="#__codelineno-33-7"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">2</span><span class="p">);</span>
+<a id="__codelineno-33-8" name="__codelineno-33-8" href="#__codelineno-33-8"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">5</span><span class="p">);</span>
+<a id="__codelineno-33-9" name="__codelineno-33-9" href="#__codelineno-33-9"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">4</span><span class="p">);</span>
+<a id="__codelineno-33-10" name="__codelineno-33-10" href="#__codelineno-33-10"></a>
+<a id="__codelineno-33-11" name="__codelineno-33-11" href="#__codelineno-33-11"></a><span class="cm">/* 中間に要素を挿入 */</span>
+<a id="__codelineno-33-12" name="__codelineno-33-12" href="#__codelineno-33-12"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">splice</span><span class="p">(</span><span class="mf">3</span><span class="p">,</span><span class="w"> </span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="mf">6</span><span class="p">);</span>
+<a id="__codelineno-33-13" name="__codelineno-33-13" href="#__codelineno-33-13"></a>
+<a id="__codelineno-33-14" name="__codelineno-33-14" href="#__codelineno-33-14"></a><span class="cm">/* 要素を削除 */</span>
+<a id="__codelineno-33-15" name="__codelineno-33-15" href="#__codelineno-33-15"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">splice</span><span class="p">(</span><span class="mf">3</span><span class="p">,</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.dart</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="cm">/* リストをクリア */</span>
+<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a><span class="n">nums</span><span class="p">.</span><span class="n">clear</span><span class="p">();</span>
+<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a>
+<a id="__codelineno-34-4" name="__codelineno-34-4" href="#__codelineno-34-4"></a><span class="cm">/* 末尾に要素を追加 */</span>
+<a id="__codelineno-34-5" name="__codelineno-34-5" href="#__codelineno-34-5"></a><span class="n">nums</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="m">1</span><span class="p">);</span>
+<a id="__codelineno-34-6" name="__codelineno-34-6" href="#__codelineno-34-6"></a><span class="n">nums</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="m">3</span><span class="p">);</span>
+<a id="__codelineno-34-7" name="__codelineno-34-7" href="#__codelineno-34-7"></a><span class="n">nums</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="m">2</span><span class="p">);</span>
+<a id="__codelineno-34-8" name="__codelineno-34-8" href="#__codelineno-34-8"></a><span class="n">nums</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="m">5</span><span class="p">);</span>
+<a id="__codelineno-34-9" name="__codelineno-34-9" href="#__codelineno-34-9"></a><span class="n">nums</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="m">4</span><span class="p">);</span>
+<a id="__codelineno-34-10" name="__codelineno-34-10" href="#__codelineno-34-10"></a>
+<a id="__codelineno-34-11" name="__codelineno-34-11" href="#__codelineno-34-11"></a><span class="cm">/* 中間に要素を挿入 */</span>
+<a id="__codelineno-34-12" name="__codelineno-34-12" href="#__codelineno-34-12"></a><span class="n">nums</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="m">3</span><span class="p">,</span><span class="w"> </span><span class="m">6</span><span class="p">);</span><span class="w"> </span><span class="c1">// インデックス3に数値6を挿入</span>
+<a id="__codelineno-34-13" name="__codelineno-34-13" href="#__codelineno-34-13"></a>
+<a id="__codelineno-34-14" name="__codelineno-34-14" href="#__codelineno-34-14"></a><span class="cm">/* 要素を削除 */</span>
+<a id="__codelineno-34-15" name="__codelineno-34-15" href="#__codelineno-34-15"></a><span class="n">nums</span><span class="p">.</span><span class="n">removeAt</span><span class="p">(</span><span class="m">3</span><span class="p">);</span><span class="w"> </span><span class="c1">// インデックス3の要素を削除</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.rs</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="cm">/* リストをクリア */</span>
+<a id="__codelineno-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></a><span class="n">nums</span><span class="p">.</span><span class="n">clear</span><span class="p">();</span>
+<a id="__codelineno-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a>
+<a id="__codelineno-35-4" name="__codelineno-35-4" href="#__codelineno-35-4"></a><span class="cm">/* 末尾に要素を追加 */</span>
+<a id="__codelineno-35-5" name="__codelineno-35-5" href="#__codelineno-35-5"></a><span class="n">nums</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-35-6" name="__codelineno-35-6" href="#__codelineno-35-6"></a><span class="n">nums</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
+<a id="__codelineno-35-7" name="__codelineno-35-7" href="#__codelineno-35-7"></a><span class="n">nums</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-35-8" name="__codelineno-35-8" href="#__codelineno-35-8"></a><span class="n">nums</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
+<a id="__codelineno-35-9" name="__codelineno-35-9" href="#__codelineno-35-9"></a><span class="n">nums</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
+<a id="__codelineno-35-10" name="__codelineno-35-10" href="#__codelineno-35-10"></a>
+<a id="__codelineno-35-11" name="__codelineno-35-11" href="#__codelineno-35-11"></a><span class="cm">/* 中間に要素を挿入 */</span>
+<a id="__codelineno-35-12" name="__codelineno-35-12" href="#__codelineno-35-12"></a><span class="n">nums</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">6</span><span class="p">);</span><span class="w">  </span><span class="c1">// インデックス3に数値6を挿入</span>
+<a id="__codelineno-35-13" name="__codelineno-35-13" href="#__codelineno-35-13"></a>
+<a id="__codelineno-35-14" name="__codelineno-35-14" href="#__codelineno-35-14"></a><span class="cm">/* 要素を削除 */</span>
+<a id="__codelineno-35-15" name="__codelineno-35-15" href="#__codelineno-35-15"></a><span class="n">nums</span><span class="p">.</span><span class="n">remove</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span><span class="w">    </span><span class="c1">// インデックス3の要素を削除</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.c</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="c1">// Cは組み込みの動的配列を提供していません</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.kt</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.zig</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="c1">// リストをクリア</span>
+<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a><span class="n">nums</span><span class="p">.</span><span class="n">clearRetainingCapacity</span><span class="p">();</span>
+<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a>
+<a id="__codelineno-38-4" name="__codelineno-38-4" href="#__codelineno-38-4"></a><span class="c1">// 末尾に要素を追加</span>
+<a id="__codelineno-38-5" name="__codelineno-38-5" href="#__codelineno-38-5"></a><span class="k">try</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-38-6" name="__codelineno-38-6" href="#__codelineno-38-6"></a><span class="k">try</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
+<a id="__codelineno-38-7" name="__codelineno-38-7" href="#__codelineno-38-7"></a><span class="k">try</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-38-8" name="__codelineno-38-8" href="#__codelineno-38-8"></a><span class="k">try</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
+<a id="__codelineno-38-9" name="__codelineno-38-9" href="#__codelineno-38-9"></a><span class="k">try</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
+<a id="__codelineno-38-10" name="__codelineno-38-10" href="#__codelineno-38-10"></a>
+<a id="__codelineno-38-11" name="__codelineno-38-11" href="#__codelineno-38-11"></a><span class="c1">// 中間に要素を挿入</span>
+<a id="__codelineno-38-12" name="__codelineno-38-12" href="#__codelineno-38-12"></a><span class="k">try</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">6</span><span class="p">);</span><span class="w"> </span><span class="c1">// インデックス3に数値6を挿入</span>
+<a id="__codelineno-38-13" name="__codelineno-38-13" href="#__codelineno-38-13"></a>
+<a id="__codelineno-38-14" name="__codelineno-38-14" href="#__codelineno-38-14"></a><span class="c1">// 要素を削除</span>
+<a id="__codelineno-38-15" name="__codelineno-38-15" href="#__codelineno-38-15"></a><span class="n">_</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">orderedRemove</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span><span class="w"> </span><span class="c1">// インデックス3の要素を削除</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h3 id="4">4. &nbsp; リストの反復<a class="headerlink" href="#4" title="Permanent link">&para;</a></h3>
+<p>配列と同様に、リストはインデックスを使用して反復することも、各要素を直接反復することもできます。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="4:13"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><input id="__tabbed_4_6" name="__tabbed_4" type="radio" /><input id="__tabbed_4_7" name="__tabbed_4" type="radio" /><input id="__tabbed_4_8" name="__tabbed_4" type="radio" /><input id="__tabbed_4_9" name="__tabbed_4" type="radio" /><input id="__tabbed_4_10" name="__tabbed_4" type="radio" /><input id="__tabbed_4_11" name="__tabbed_4" type="radio" /><input id="__tabbed_4_12" name="__tabbed_4" type="radio" /><input id="__tabbed_4_13" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">Python</label><label for="__tabbed_4_2">C++</label><label for="__tabbed_4_3">Java</label><label for="__tabbed_4_4">C#</label><label for="__tabbed_4_5">Go</label><label for="__tabbed_4_6">Swift</label><label for="__tabbed_4_7">JS</label><label for="__tabbed_4_8">TS</label><label for="__tabbed_4_9">Dart</label><label for="__tabbed_4_10">Rust</label><label for="__tabbed_4_11">C</label><label for="__tabbed_4_12">Kotlin</label><label for="__tabbed_4_13">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.py</span><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="c1"># インデックスでリストを反復</span>
+<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a><span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-39-3" name="__codelineno-39-3" href="#__codelineno-39-3"></a><span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)):</span>
+<a id="__codelineno-39-4" name="__codelineno-39-4" href="#__codelineno-39-4"></a>    <span class="n">count</span> <span class="o">+=</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+<a id="__codelineno-39-5" name="__codelineno-39-5" href="#__codelineno-39-5"></a>
+<a id="__codelineno-39-6" name="__codelineno-39-6" href="#__codelineno-39-6"></a><span class="c1"># リスト要素を直接反復</span>
+<a id="__codelineno-39-7" name="__codelineno-39-7" href="#__codelineno-39-7"></a><span class="k">for</span> <span class="n">num</span> <span class="ow">in</span> <span class="n">nums</span><span class="p">:</span>
+<a id="__codelineno-39-8" name="__codelineno-39-8" href="#__codelineno-39-8"></a>    <span class="n">count</span> <span class="o">+=</span> <span class="n">num</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.cpp</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="cm">/* インデックスでリストを反復 */</span>
+<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a><span class="w">    </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a><span class="p">}</span>
+<a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a>
+<a id="__codelineno-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></a><span class="cm">/* リスト要素を直接反復 */</span>
+<a id="__codelineno-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-40-9" name="__codelineno-40-9" href="#__codelineno-40-9"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-40-10" name="__codelineno-40-10" href="#__codelineno-40-10"></a><span class="w">    </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-40-11" name="__codelineno-40-11" href="#__codelineno-40-11"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.java</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="cm">/* インデックスでリストを反復 */</span>
+<a id="__codelineno-41-2" name="__codelineno-41-2" href="#__codelineno-41-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-41-3" name="__codelineno-41-3" href="#__codelineno-41-3"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-41-4" name="__codelineno-41-4" href="#__codelineno-41-4"></a><span class="w">    </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-41-5" name="__codelineno-41-5" href="#__codelineno-41-5"></a><span class="p">}</span>
+<a id="__codelineno-41-6" name="__codelineno-41-6" href="#__codelineno-41-6"></a>
+<a id="__codelineno-41-7" name="__codelineno-41-7" href="#__codelineno-41-7"></a><span class="cm">/* リスト要素を直接反復 */</span>
+<a id="__codelineno-41-8" name="__codelineno-41-8" href="#__codelineno-41-8"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-41-9" name="__codelineno-41-9" href="#__codelineno-41-9"></a><span class="w">    </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-41-10" name="__codelineno-41-10" href="#__codelineno-41-10"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.cs</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="cm">/* インデックスでリストを反復 */</span>
+<a id="__codelineno-42-2" name="__codelineno-42-2" href="#__codelineno-42-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">Count</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-4" name="__codelineno-42-4" href="#__codelineno-42-4"></a><span class="w">    </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-42-5" name="__codelineno-42-5" href="#__codelineno-42-5"></a><span class="p">}</span>
+<a id="__codelineno-42-6" name="__codelineno-42-6" href="#__codelineno-42-6"></a>
+<a id="__codelineno-42-7" name="__codelineno-42-7" href="#__codelineno-42-7"></a><span class="cm">/* リスト要素を直接反復 */</span>
+<a id="__codelineno-42-8" name="__codelineno-42-8" href="#__codelineno-42-8"></a><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-42-9" name="__codelineno-42-9" href="#__codelineno-42-9"></a><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-10" name="__codelineno-42-10" href="#__codelineno-42-10"></a><span class="w">    </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-42-11" name="__codelineno-42-11" href="#__codelineno-42-11"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list_test.go</span><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="cm">/* インデックスでリストを反復 */</span>
+<a id="__codelineno-43-2" name="__codelineno-43-2" href="#__codelineno-43-2"></a><span class="nx">count</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-43-3" name="__codelineno-43-3" href="#__codelineno-43-3"></a><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">nums</span><span class="p">);</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-4" name="__codelineno-43-4" href="#__codelineno-43-4"></a><span class="w">    </span><span class="nx">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">]</span>
+<a id="__codelineno-43-5" name="__codelineno-43-5" href="#__codelineno-43-5"></a><span class="p">}</span>
+<a id="__codelineno-43-6" name="__codelineno-43-6" href="#__codelineno-43-6"></a>
+<a id="__codelineno-43-7" name="__codelineno-43-7" href="#__codelineno-43-7"></a><span class="cm">/* リスト要素を直接反復 */</span>
+<a id="__codelineno-43-8" name="__codelineno-43-8" href="#__codelineno-43-8"></a><span class="nx">count</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-43-9" name="__codelineno-43-9" href="#__codelineno-43-9"></a><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-10" name="__codelineno-43-10" href="#__codelineno-43-10"></a><span class="w">    </span><span class="nx">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">num</span>
+<a id="__codelineno-43-11" name="__codelineno-43-11" href="#__codelineno-43-11"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.swift</span><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="cm">/* インデックスでリストを反復 */</span>
+<a id="__codelineno-44-2" name="__codelineno-44-2" href="#__codelineno-44-2"></a><span class="kd">var</span><span class="w"> </span><span class="nv">count</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-44-3" name="__codelineno-44-3" href="#__codelineno-44-3"></a><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="bp">indices</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-4" name="__codelineno-44-4" href="#__codelineno-44-4"></a><span class="w">    </span><span class="bp">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+<a id="__codelineno-44-5" name="__codelineno-44-5" href="#__codelineno-44-5"></a><span class="p">}</span>
+<a id="__codelineno-44-6" name="__codelineno-44-6" href="#__codelineno-44-6"></a>
+<a id="__codelineno-44-7" name="__codelineno-44-7" href="#__codelineno-44-7"></a><span class="cm">/* リスト要素を直接反復 */</span>
+<a id="__codelineno-44-8" name="__codelineno-44-8" href="#__codelineno-44-8"></a><span class="bp">count</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-44-9" name="__codelineno-44-9" href="#__codelineno-44-9"></a><span class="k">for</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-10" name="__codelineno-44-10" href="#__codelineno-44-10"></a><span class="w">    </span><span class="bp">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">num</span>
+<a id="__codelineno-44-11" name="__codelineno-44-11" href="#__codelineno-44-11"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.js</span><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="cm">/* インデックスでリストを反復 */</span>
+<a id="__codelineno-45-2" name="__codelineno-45-2" href="#__codelineno-45-2"></a><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-45-3" name="__codelineno-45-3" href="#__codelineno-45-3"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-4" name="__codelineno-45-4" href="#__codelineno-45-4"></a><span class="w">    </span><span class="nx">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">];</span>
+<a id="__codelineno-45-5" name="__codelineno-45-5" href="#__codelineno-45-5"></a><span class="p">}</span>
+<a id="__codelineno-45-6" name="__codelineno-45-6" href="#__codelineno-45-6"></a>
+<a id="__codelineno-45-7" name="__codelineno-45-7" href="#__codelineno-45-7"></a><span class="cm">/* リスト要素を直接反復 */</span>
+<a id="__codelineno-45-8" name="__codelineno-45-8" href="#__codelineno-45-8"></a><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-45-9" name="__codelineno-45-9" href="#__codelineno-45-9"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-10" name="__codelineno-45-10" href="#__codelineno-45-10"></a><span class="w">    </span><span class="nx">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">num</span><span class="p">;</span>
+<a id="__codelineno-45-11" name="__codelineno-45-11" href="#__codelineno-45-11"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.ts</span><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="cm">/* インデックスでリストを反復 */</span>
+<a id="__codelineno-46-2" name="__codelineno-46-2" href="#__codelineno-46-2"></a><span class="kd">let</span><span class="w"> </span><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-46-3" name="__codelineno-46-3" href="#__codelineno-46-3"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">nums</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-4" name="__codelineno-46-4" href="#__codelineno-46-4"></a><span class="w">    </span><span class="nx">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">nums</span><span class="p">[</span><span class="nx">i</span><span class="p">];</span>
+<a id="__codelineno-46-5" name="__codelineno-46-5" href="#__codelineno-46-5"></a><span class="p">}</span>
+<a id="__codelineno-46-6" name="__codelineno-46-6" href="#__codelineno-46-6"></a>
+<a id="__codelineno-46-7" name="__codelineno-46-7" href="#__codelineno-46-7"></a><span class="cm">/* リスト要素を直接反復 */</span>
+<a id="__codelineno-46-8" name="__codelineno-46-8" href="#__codelineno-46-8"></a><span class="nx">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-46-9" name="__codelineno-46-9" href="#__codelineno-46-9"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">num</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-10" name="__codelineno-46-10" href="#__codelineno-46-10"></a><span class="w">    </span><span class="nx">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="nx">num</span><span class="p">;</span>
+<a id="__codelineno-46-11" name="__codelineno-46-11" href="#__codelineno-46-11"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.dart</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="cm">/* インデックスでリストを反復 */</span>
+<a id="__codelineno-47-2" name="__codelineno-47-2" href="#__codelineno-47-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-47-3" name="__codelineno-47-3" href="#__codelineno-47-3"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-4" name="__codelineno-47-4" href="#__codelineno-47-4"></a><span class="w">    </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-47-5" name="__codelineno-47-5" href="#__codelineno-47-5"></a><span class="p">}</span>
+<a id="__codelineno-47-6" name="__codelineno-47-6" href="#__codelineno-47-6"></a>
+<a id="__codelineno-47-7" name="__codelineno-47-7" href="#__codelineno-47-7"></a><span class="cm">/* リスト要素を直接反復 */</span>
+<a id="__codelineno-47-8" name="__codelineno-47-8" href="#__codelineno-47-8"></a><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-47-9" name="__codelineno-47-9" href="#__codelineno-47-9"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">var</span><span class="w"> </span><span class="kt">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-10" name="__codelineno-47-10" href="#__codelineno-47-10"></a><span class="w">    </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="kt">num</span><span class="p">;</span>
+<a id="__codelineno-47-11" name="__codelineno-47-11" href="#__codelineno-47-11"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.rs</span><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="c1">// インデックスでリストを反復</span>
+<a id="__codelineno-48-2" name="__codelineno-48-2" href="#__codelineno-48-2"></a><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">_count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-48-3" name="__codelineno-48-3" href="#__codelineno-48-3"></a><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">nums</span><span class="p">.</span><span class="n">len</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-4" name="__codelineno-48-4" href="#__codelineno-48-4"></a><span class="w">    </span><span class="n">_count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-48-5" name="__codelineno-48-5" href="#__codelineno-48-5"></a><span class="p">}</span>
+<a id="__codelineno-48-6" name="__codelineno-48-6" href="#__codelineno-48-6"></a>
+<a id="__codelineno-48-7" name="__codelineno-48-7" href="#__codelineno-48-7"></a><span class="c1">// リスト要素を直接反復</span>
+<a id="__codelineno-48-8" name="__codelineno-48-8" href="#__codelineno-48-8"></a><span class="n">_count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-48-9" name="__codelineno-48-9" href="#__codelineno-48-9"></a><span class="k">for</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-10" name="__codelineno-48-10" href="#__codelineno-48-10"></a><span class="w">    </span><span class="n">_count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-48-11" name="__codelineno-48-11" href="#__codelineno-48-11"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.c</span><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="c1">// Cは組み込みの動的配列を提供していません</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.kt</span><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.zig</span><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="c1">// インデックスでリストを反復</span>
+<a id="__codelineno-51-2" name="__codelineno-51-2" href="#__codelineno-51-2"></a><span class="kr">var</span><span class="w"> </span><span class="n">count</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-51-3" name="__codelineno-51-3" href="#__codelineno-51-3"></a><span class="kr">var</span><span class="w"> </span><span class="n">i</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-51-4" name="__codelineno-51-4" href="#__codelineno-51-4"></a><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">items</span><span class="p">.</span><span class="n">len</span><span class="p">)</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-51-5" name="__codelineno-51-5" href="#__codelineno-51-5"></a><span class="w">    </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-51-6" name="__codelineno-51-6" href="#__codelineno-51-6"></a><span class="p">}</span>
+<a id="__codelineno-51-7" name="__codelineno-51-7" href="#__codelineno-51-7"></a>
+<a id="__codelineno-51-8" name="__codelineno-51-8" href="#__codelineno-51-8"></a><span class="c1">// リスト要素を直接反復</span>
+<a id="__codelineno-51-9" name="__codelineno-51-9" href="#__codelineno-51-9"></a><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-51-10" name="__codelineno-51-10" href="#__codelineno-51-10"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">.</span><span class="n">items</span><span class="p">)</span><span class="w"> </span><span class="o">|</span><span class="n">num</span><span class="o">|</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-51-11" name="__codelineno-51-11" href="#__codelineno-51-11"></a><span class="w">    </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-51-12" name="__codelineno-51-12" href="#__codelineno-51-12"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h3 id="5">5. &nbsp; リストの連結<a class="headerlink" href="#5" title="Permanent link">&para;</a></h3>
+<p>新しいリスト<code>nums1</code>が与えられたとき、それを元のリストの末尾に追加できます。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="5:13"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><input id="__tabbed_5_7" name="__tabbed_5" type="radio" /><input id="__tabbed_5_8" name="__tabbed_5" type="radio" /><input id="__tabbed_5_9" name="__tabbed_5" type="radio" /><input id="__tabbed_5_10" name="__tabbed_5" type="radio" /><input id="__tabbed_5_11" name="__tabbed_5" type="radio" /><input id="__tabbed_5_12" name="__tabbed_5" type="radio" /><input id="__tabbed_5_13" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">Python</label><label for="__tabbed_5_2">C++</label><label for="__tabbed_5_3">Java</label><label for="__tabbed_5_4">C#</label><label for="__tabbed_5_5">Go</label><label for="__tabbed_5_6">Swift</label><label for="__tabbed_5_7">JS</label><label for="__tabbed_5_8">TS</label><label for="__tabbed_5_9">Dart</label><label for="__tabbed_5_10">Rust</label><label for="__tabbed_5_11">C</label><label for="__tabbed_5_12">Kotlin</label><label for="__tabbed_5_13">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.py</span><pre><span></span><code><a id="__codelineno-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="c1"># 2つのリストを連結</span>
+<a id="__codelineno-52-2" name="__codelineno-52-2" href="#__codelineno-52-2"></a><span class="n">nums1</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="mi">6</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">9</span><span class="p">]</span>
+<a id="__codelineno-52-3" name="__codelineno-52-3" href="#__codelineno-52-3"></a><span class="n">nums</span> <span class="o">+=</span> <span class="n">nums1</span>  <span class="c1"># nums1をnumsの末尾に連結</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.cpp</span><pre><span></span><code><a id="__codelineno-53-1" name="__codelineno-53-1" href="#__codelineno-53-1"></a><span class="cm">/* 2つのリストを連結 */</span>
+<a id="__codelineno-53-2" name="__codelineno-53-2" href="#__codelineno-53-2"></a><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">10</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="w"> </span><span class="p">};</span>
+<a id="__codelineno-53-3" name="__codelineno-53-3" href="#__codelineno-53-3"></a><span class="c1">// nums1をnumsの末尾に連結</span>
+<a id="__codelineno-53-4" name="__codelineno-53-4" href="#__codelineno-53-4"></a><span class="n">nums</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="n">nums</span><span class="p">.</span><span class="n">end</span><span class="p">(),</span><span class="w"> </span><span class="n">nums1</span><span class="p">.</span><span class="n">begin</span><span class="p">(),</span><span class="w"> </span><span class="n">nums1</span><span class="p">.</span><span class="n">end</span><span class="p">());</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.java</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="cm">/* 2つのリストを連結 */</span>
+<a id="__codelineno-54-2" name="__codelineno-54-2" href="#__codelineno-54-2"></a><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">(</span><span class="n">Arrays</span><span class="p">.</span><span class="na">asList</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">Integer</span><span class="o">[]</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">10</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="w"> </span><span class="p">}));</span>
+<a id="__codelineno-54-3" name="__codelineno-54-3" href="#__codelineno-54-3"></a><span class="n">nums</span><span class="p">.</span><span class="na">addAll</span><span class="p">(</span><span class="n">nums1</span><span class="p">);</span><span class="w">  </span><span class="c1">// nums1をnumsの末尾に連結</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.cs</span><pre><span></span><code><a id="__codelineno-55-1" name="__codelineno-55-1" href="#__codelineno-55-1"></a><span class="cm">/* 2つのリストを連結 */</span>
+<a id="__codelineno-55-2" name="__codelineno-55-2" href="#__codelineno-55-2"></a><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">10</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="p">];</span>
+<a id="__codelineno-55-3" name="__codelineno-55-3" href="#__codelineno-55-3"></a><span class="n">nums</span><span class="p">.</span><span class="n">AddRange</span><span class="p">(</span><span class="n">nums1</span><span class="p">);</span><span class="w">  </span><span class="c1">// nums1をnumsの末尾に連結</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list_test.go</span><pre><span></span><code><a id="__codelineno-56-1" name="__codelineno-56-1" href="#__codelineno-56-1"></a><span class="cm">/* 2つのリストを連結 */</span>
+<a id="__codelineno-56-2" name="__codelineno-56-2" href="#__codelineno-56-2"></a><span class="nx">nums1</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span><span class="p">{</span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">10</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="p">}</span>
+<a id="__codelineno-56-3" name="__codelineno-56-3" href="#__codelineno-56-3"></a><span class="nx">nums</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">nums</span><span class="p">,</span><span class="w"> </span><span class="nx">nums1</span><span class="o">...</span><span class="p">)</span><span class="w">  </span><span class="c1">// nums1をnumsの末尾に連結</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.swift</span><pre><span></span><code><a id="__codelineno-57-1" name="__codelineno-57-1" href="#__codelineno-57-1"></a><span class="cm">/* 2つのリストを連結 */</span>
+<a id="__codelineno-57-2" name="__codelineno-57-2" href="#__codelineno-57-2"></a><span class="kd">let</span><span class="w"> </span><span class="nv">nums1</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[</span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">10</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="p">]</span>
+<a id="__codelineno-57-3" name="__codelineno-57-3" href="#__codelineno-57-3"></a><span class="n">nums</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="n">contentsOf</span><span class="p">:</span><span class="w"> </span><span class="n">nums1</span><span class="p">)</span><span class="w"> </span><span class="c1">// nums1をnumsの末尾に連結</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.js</span><pre><span></span><code><a id="__codelineno-58-1" name="__codelineno-58-1" href="#__codelineno-58-1"></a><span class="cm">/* 2つのリストを連結 */</span>
+<a id="__codelineno-58-2" name="__codelineno-58-2" href="#__codelineno-58-2"></a><span class="kd">const</span><span class="w"> </span><span class="nx">nums1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mf">6</span><span class="p">,</span><span class="w"> </span><span class="mf">8</span><span class="p">,</span><span class="w"> </span><span class="mf">7</span><span class="p">,</span><span class="w"> </span><span class="mf">10</span><span class="p">,</span><span class="w"> </span><span class="mf">9</span><span class="p">];</span>
+<a id="__codelineno-58-3" name="__codelineno-58-3" href="#__codelineno-58-3"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">push</span><span class="p">(...</span><span class="nx">nums1</span><span class="p">);</span><span class="w">  </span><span class="c1">// nums1をnumsの末尾に連結</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.ts</span><pre><span></span><code><a id="__codelineno-59-1" name="__codelineno-59-1" href="#__codelineno-59-1"></a><span class="cm">/* 2つのリストを連結 */</span>
+<a id="__codelineno-59-2" name="__codelineno-59-2" href="#__codelineno-59-2"></a><span class="kd">const</span><span class="w"> </span><span class="nx">nums1</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mf">6</span><span class="p">,</span><span class="w"> </span><span class="mf">8</span><span class="p">,</span><span class="w"> </span><span class="mf">7</span><span class="p">,</span><span class="w"> </span><span class="mf">10</span><span class="p">,</span><span class="w"> </span><span class="mf">9</span><span class="p">];</span>
+<a id="__codelineno-59-3" name="__codelineno-59-3" href="#__codelineno-59-3"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">push</span><span class="p">(...</span><span class="nx">nums1</span><span class="p">);</span><span class="w">  </span><span class="c1">// nums1をnumsの末尾に連結</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.dart</span><pre><span></span><code><a id="__codelineno-60-1" name="__codelineno-60-1" href="#__codelineno-60-1"></a><span class="cm">/* 2つのリストを連結 */</span>
+<a id="__codelineno-60-2" name="__codelineno-60-2" href="#__codelineno-60-2"></a><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="m">6</span><span class="p">,</span><span class="w"> </span><span class="m">8</span><span class="p">,</span><span class="w"> </span><span class="m">7</span><span class="p">,</span><span class="w"> </span><span class="m">10</span><span class="p">,</span><span class="w"> </span><span class="m">9</span><span class="p">];</span>
+<a id="__codelineno-60-3" name="__codelineno-60-3" href="#__codelineno-60-3"></a><span class="n">nums</span><span class="p">.</span><span class="n">addAll</span><span class="p">(</span><span class="n">nums1</span><span class="p">);</span><span class="w">  </span><span class="c1">// nums1をnumsの末尾に連結</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.rs</span><pre><span></span><code><a id="__codelineno-61-1" name="__codelineno-61-1" href="#__codelineno-61-1"></a><span class="cm">/* 2つのリストを連結 */</span>
+<a id="__codelineno-61-2" name="__codelineno-61-2" href="#__codelineno-61-2"></a><span class="kd">let</span><span class="w"> </span><span class="n">nums1</span><span class="p">:</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">10</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="p">];</span>
+<a id="__codelineno-61-3" name="__codelineno-61-3" href="#__codelineno-61-3"></a><span class="n">nums</span><span class="p">.</span><span class="n">extend</span><span class="p">(</span><span class="n">nums1</span><span class="p">);</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.c</span><pre><span></span><code><a id="__codelineno-62-1" name="__codelineno-62-1" href="#__codelineno-62-1"></a><span class="c1">// Cは組み込みの動的配列を提供していません</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.kt</span><pre><span></span><code><a id="__codelineno-63-1" name="__codelineno-63-1" href="#__codelineno-63-1"></a>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.zig</span><pre><span></span><code><a id="__codelineno-64-1" name="__codelineno-64-1" href="#__codelineno-64-1"></a><span class="c1">// 2つのリストを連結</span>
+<a id="__codelineno-64-2" name="__codelineno-64-2" href="#__codelineno-64-2"></a><span class="kr">var</span><span class="w"> </span><span class="n">nums1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">std</span><span class="p">.</span><span class="n">ArrayList</span><span class="p">(</span><span class="kt">i32</span><span class="p">).</span><span class="n">init</span><span class="p">(</span><span class="n">std</span><span class="p">.</span><span class="n">heap</span><span class="p">.</span><span class="n">page_allocator</span><span class="p">);</span>
+<a id="__codelineno-64-3" name="__codelineno-64-3" href="#__codelineno-64-3"></a><span class="k">defer</span><span class="w"> </span><span class="n">nums1</span><span class="p">.</span><span class="n">deinit</span><span class="p">();</span>
+<a id="__codelineno-64-4" name="__codelineno-64-4" href="#__codelineno-64-4"></a><span class="k">try</span><span class="w"> </span><span class="n">nums1</span><span class="p">.</span><span class="n">appendSlice</span><span class="p">(</span><span class="o">&amp;</span><span class="p">[</span><span class="n">_</span><span class="p">]</span><span class="kt">i32</span><span class="p">{</span><span class="w"> </span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">10</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="w"> </span><span class="p">});</span>
+<a id="__codelineno-64-5" name="__codelineno-64-5" href="#__codelineno-64-5"></a><span class="k">try</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">insertSlice</span><span class="p">(</span><span class="n">nums</span><span class="p">.</span><span class="n">items</span><span class="p">.</span><span class="n">len</span><span class="p">,</span><span class="w"> </span><span class="n">nums1</span><span class="p">.</span><span class="n">items</span><span class="p">);</span><span class="w"> </span><span class="c1">// nums1をnumsの末尾に連結</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h3 id="6">6. &nbsp; リストのソート<a class="headerlink" href="#6" title="Permanent link">&para;</a></h3>
+<p>リストがソートされると、「二分探索」や「双ポインタ」アルゴリズムなど、配列関連のアルゴリズム問題でよく使用されるアルゴリズムを使用できます。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="6:13"><input checked="checked" id="__tabbed_6_1" name="__tabbed_6" type="radio" /><input id="__tabbed_6_2" name="__tabbed_6" type="radio" /><input id="__tabbed_6_3" name="__tabbed_6" type="radio" /><input id="__tabbed_6_4" name="__tabbed_6" type="radio" /><input id="__tabbed_6_5" name="__tabbed_6" type="radio" /><input id="__tabbed_6_6" name="__tabbed_6" type="radio" /><input id="__tabbed_6_7" name="__tabbed_6" type="radio" /><input id="__tabbed_6_8" name="__tabbed_6" type="radio" /><input id="__tabbed_6_9" name="__tabbed_6" type="radio" /><input id="__tabbed_6_10" name="__tabbed_6" type="radio" /><input id="__tabbed_6_11" name="__tabbed_6" type="radio" /><input id="__tabbed_6_12" name="__tabbed_6" type="radio" /><input id="__tabbed_6_13" name="__tabbed_6" type="radio" /><div class="tabbed-labels"><label for="__tabbed_6_1">Python</label><label for="__tabbed_6_2">C++</label><label for="__tabbed_6_3">Java</label><label for="__tabbed_6_4">C#</label><label for="__tabbed_6_5">Go</label><label for="__tabbed_6_6">Swift</label><label for="__tabbed_6_7">JS</label><label for="__tabbed_6_8">TS</label><label for="__tabbed_6_9">Dart</label><label for="__tabbed_6_10">Rust</label><label for="__tabbed_6_11">C</label><label for="__tabbed_6_12">Kotlin</label><label for="__tabbed_6_13">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.py</span><pre><span></span><code><a id="__codelineno-65-1" name="__codelineno-65-1" href="#__codelineno-65-1"></a><span class="c1"># リストをソート</span>
+<a id="__codelineno-65-2" name="__codelineno-65-2" href="#__codelineno-65-2"></a><span class="n">nums</span><span class="o">.</span><span class="n">sort</span><span class="p">()</span>  <span class="c1"># ソート後、リスト要素は昇順になります</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.cpp</span><pre><span></span><code><a id="__codelineno-66-1" name="__codelineno-66-1" href="#__codelineno-66-1"></a><span class="cm">/* リストをソート */</span>
+<a id="__codelineno-66-2" name="__codelineno-66-2" href="#__codelineno-66-2"></a><span class="n">sort</span><span class="p">(</span><span class="n">nums</span><span class="p">.</span><span class="n">begin</span><span class="p">(),</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">end</span><span class="p">());</span><span class="w">  </span><span class="c1">// ソート後、リスト要素は昇順になります</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.java</span><pre><span></span><code><a id="__codelineno-67-1" name="__codelineno-67-1" href="#__codelineno-67-1"></a><span class="cm">/* リストをソート */</span>
+<a id="__codelineno-67-2" name="__codelineno-67-2" href="#__codelineno-67-2"></a><span class="n">Collections</span><span class="p">.</span><span class="na">sort</span><span class="p">(</span><span class="n">nums</span><span class="p">);</span><span class="w">  </span><span class="c1">// ソート後、リスト要素は昇順になります</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.cs</span><pre><span></span><code><a id="__codelineno-68-1" name="__codelineno-68-1" href="#__codelineno-68-1"></a><span class="cm">/* リストをソート */</span>
+<a id="__codelineno-68-2" name="__codelineno-68-2" href="#__codelineno-68-2"></a><span class="n">nums</span><span class="p">.</span><span class="n">Sort</span><span class="p">();</span><span class="w"> </span><span class="c1">// ソート後、リスト要素は昇順になります</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list_test.go</span><pre><span></span><code><a id="__codelineno-69-1" name="__codelineno-69-1" href="#__codelineno-69-1"></a><span class="cm">/* リストをソート */</span>
+<a id="__codelineno-69-2" name="__codelineno-69-2" href="#__codelineno-69-2"></a><span class="nx">sort</span><span class="p">.</span><span class="nx">Ints</span><span class="p">(</span><span class="nx">nums</span><span class="p">)</span><span class="w">  </span><span class="c1">// ソート後、リスト要素は昇順になります</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.swift</span><pre><span></span><code><a id="__codelineno-70-1" name="__codelineno-70-1" href="#__codelineno-70-1"></a><span class="cm">/* リストをソート */</span>
+<a id="__codelineno-70-2" name="__codelineno-70-2" href="#__codelineno-70-2"></a><span class="n">nums</span><span class="p">.</span><span class="bp">sort</span><span class="p">()</span><span class="w"> </span><span class="c1">// ソート後、リスト要素は昇順になります</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.js</span><pre><span></span><code><a id="__codelineno-71-1" name="__codelineno-71-1" href="#__codelineno-71-1"></a><span class="cm">/* リストをソート */</span>
+<a id="__codelineno-71-2" name="__codelineno-71-2" href="#__codelineno-71-2"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">sort</span><span class="p">((</span><span class="nx">a</span><span class="p">,</span><span class="w"> </span><span class="nx">b</span><span class="p">)</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">b</span><span class="p">);</span><span class="w">  </span><span class="c1">// ソート後、リスト要素は昇順になります</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.ts</span><pre><span></span><code><a id="__codelineno-72-1" name="__codelineno-72-1" href="#__codelineno-72-1"></a><span class="cm">/* リストをソート */</span>
+<a id="__codelineno-72-2" name="__codelineno-72-2" href="#__codelineno-72-2"></a><span class="nx">nums</span><span class="p">.</span><span class="nx">sort</span><span class="p">((</span><span class="nx">a</span><span class="p">,</span><span class="w"> </span><span class="nx">b</span><span class="p">)</span><span class="w"> </span><span class="p">=&gt;</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="nx">b</span><span class="p">);</span><span class="w">  </span><span class="c1">// ソート後、リスト要素は昇順になります</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.dart</span><pre><span></span><code><a id="__codelineno-73-1" name="__codelineno-73-1" href="#__codelineno-73-1"></a><span class="cm">/* リストをソート */</span>
+<a id="__codelineno-73-2" name="__codelineno-73-2" href="#__codelineno-73-2"></a><span class="n">nums</span><span class="p">.</span><span class="n">sort</span><span class="p">();</span><span class="w"> </span><span class="c1">// ソート後、リスト要素は昇順になります</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.rs</span><pre><span></span><code><a id="__codelineno-74-1" name="__codelineno-74-1" href="#__codelineno-74-1"></a><span class="cm">/* リストをソート */</span>
+<a id="__codelineno-74-2" name="__codelineno-74-2" href="#__codelineno-74-2"></a><span class="n">nums</span><span class="p">.</span><span class="n">sort</span><span class="p">();</span><span class="w"> </span><span class="c1">// ソート後、リスト要素は昇順になります</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.c</span><pre><span></span><code><a id="__codelineno-75-1" name="__codelineno-75-1" href="#__codelineno-75-1"></a><span class="c1">// Cは組み込みの動的配列を提供していません</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.kt</span><pre><span></span><code><a id="__codelineno-76-1" name="__codelineno-76-1" href="#__codelineno-76-1"></a>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">list.zig</span><pre><span></span><code><a id="__codelineno-77-1" name="__codelineno-77-1" href="#__codelineno-77-1"></a><span class="c1">// リストをソート</span>
+<a id="__codelineno-77-2" name="__codelineno-77-2" href="#__codelineno-77-2"></a><span class="n">std</span><span class="p">.</span><span class="n">sort</span><span class="p">.</span><span class="n">sort</span><span class="p">(</span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">items</span><span class="p">,</span><span class="w"> </span><span class="p">{},</span><span class="w"> </span><span class="kr">comptime</span><span class="w"> </span><span class="n">std</span><span class="p">.</span><span class="n">sort</span><span class="p">.</span><span class="n">asc</span><span class="p">(</span><span class="kt">i32</span><span class="p">));</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h2 id="432">4.3.2 &nbsp; リストの実装<a class="headerlink" href="#432" title="Permanent link">&para;</a></h2>
+<p>多くのプログラミング言語には、Java、C++、Pythonなどを含む組み込みリストが付属しています。それらの実装は、初期容量や拡張係数などの様々なパラメータを慎重に考慮した設定で、複雑になりがちです。興味のある読者は、さらなる学習のためにソースコードを調べることができます。</p>
+<p>リストがどのように動作するかの理解を深めるために、3つの重要な設計側面に焦点を当てて、簡略化されたリストの実装を試みます：</p>
+<ul>
+<li><strong>初期容量</strong>：配列に合理的な初期容量を選択します。この例では、初期容量として10を選択します。</li>
+<li><strong>サイズ記録</strong>：リスト内の現在の要素数を記録する変数<code>size</code>を宣言し、要素の挿入と削除でリアルタイムに更新します。この変数により、リストの末尾を特定し、拡張が必要かどうかを判断できます。</li>
+<li><strong>拡張メカニズム</strong>：要素挿入時にリストが満杯に達した場合、拡張プロセスが必要です。これには拡張係数に基づいてより大きな配列を作成し、現在の配列からすべての要素を新しい配列に転送することが含まれます。この例では、拡張のたびに配列サイズを2倍にすることを規定します。</li>
+</ul>
+<div class="tabbed-set tabbed-alternate" data-tabs="7:14"><input checked="checked" id="__tabbed_7_1" name="__tabbed_7" type="radio" /><input id="__tabbed_7_2" name="__tabbed_7" type="radio" /><input id="__tabbed_7_3" name="__tabbed_7" type="radio" /><input id="__tabbed_7_4" name="__tabbed_7" type="radio" /><input id="__tabbed_7_5" name="__tabbed_7" type="radio" /><input id="__tabbed_7_6" name="__tabbed_7" type="radio" /><input id="__tabbed_7_7" name="__tabbed_7" type="radio" /><input id="__tabbed_7_8" name="__tabbed_7" type="radio" /><input id="__tabbed_7_9" name="__tabbed_7" type="radio" /><input id="__tabbed_7_10" name="__tabbed_7" type="radio" /><input id="__tabbed_7_11" name="__tabbed_7" type="radio" /><input id="__tabbed_7_12" name="__tabbed_7" type="radio" /><input id="__tabbed_7_13" name="__tabbed_7" type="radio" /><input id="__tabbed_7_14" name="__tabbed_7" type="radio" /><div class="tabbed-labels"><label for="__tabbed_7_1">Python</label><label for="__tabbed_7_2">C++</label><label for="__tabbed_7_3">Java</label><label for="__tabbed_7_4">C#</label><label for="__tabbed_7_5">Go</label><label for="__tabbed_7_6">Swift</label><label for="__tabbed_7_7">JS</label><label for="__tabbed_7_8">TS</label><label for="__tabbed_7_9">Dart</label><label for="__tabbed_7_10">Rust</label><label for="__tabbed_7_11">C</label><label for="__tabbed_7_12">Kotlin</label><label for="__tabbed_7_13">Ruby</label><label for="__tabbed_7_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_list.py</span><pre><span></span><code><a id="__codelineno-78-1" name="__codelineno-78-1" href="#__codelineno-78-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">MyList</span><span class="p">:</span>
+<a id="__codelineno-78-2" name="__codelineno-78-2" href="#__codelineno-78-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;リストクラス&quot;&quot;&quot;</span>
+<a id="__codelineno-78-3" name="__codelineno-78-3" href="#__codelineno-78-3"></a>
+<a id="__codelineno-78-4" name="__codelineno-78-4" href="#__codelineno-78-4"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<a id="__codelineno-78-5" name="__codelineno-78-5" href="#__codelineno-78-5"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;コンストラクタ&quot;&quot;&quot;</span>
+<a id="__codelineno-78-6" name="__codelineno-78-6" href="#__codelineno-78-6"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_capacity</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">10</span>  <span class="c1"># リストの容量</span>
+<a id="__codelineno-78-7" name="__codelineno-78-7" href="#__codelineno-78-7"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_arr</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">_capacity</span>  <span class="c1"># 配列（リスト要素を格納）</span>
+<a id="__codelineno-78-8" name="__codelineno-78-8" href="#__codelineno-78-8"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">0</span>  <span class="c1"># リストの長さ（現在の要素数）</span>
+<a id="__codelineno-78-9" name="__codelineno-78-9" href="#__codelineno-78-9"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_extend_ratio</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">2</span>  <span class="c1"># 各リスト拡張の倍数</span>
+<a id="__codelineno-78-10" name="__codelineno-78-10" href="#__codelineno-78-10"></a>
+<a id="__codelineno-78-11" name="__codelineno-78-11" href="#__codelineno-78-11"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">size</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-78-12" name="__codelineno-78-12" href="#__codelineno-78-12"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;リストの長さ（現在の要素数）を取得&quot;&quot;&quot;</span>
+<a id="__codelineno-78-13" name="__codelineno-78-13" href="#__codelineno-78-13"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span>
+<a id="__codelineno-78-14" name="__codelineno-78-14" href="#__codelineno-78-14"></a>
+<a id="__codelineno-78-15" name="__codelineno-78-15" href="#__codelineno-78-15"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">capacity</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-78-16" name="__codelineno-78-16" href="#__codelineno-78-16"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;リストの容量を取得&quot;&quot;&quot;</span>
+<a id="__codelineno-78-17" name="__codelineno-78-17" href="#__codelineno-78-17"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_capacity</span>
+<a id="__codelineno-78-18" name="__codelineno-78-18" href="#__codelineno-78-18"></a>
+<a id="__codelineno-78-19" name="__codelineno-78-19" href="#__codelineno-78-19"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">get</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">index</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-78-20" name="__codelineno-78-20" href="#__codelineno-78-20"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;要素にアクセス&quot;&quot;&quot;</span>
+<a id="__codelineno-78-21" name="__codelineno-78-21" href="#__codelineno-78-21"></a>        <span class="c1"># インデックスが範囲外の場合、以下のように例外をスロー</span>
+<a id="__codelineno-78-22" name="__codelineno-78-22" href="#__codelineno-78-22"></a>        <span class="k">if</span> <span class="n">index</span> <span class="o">&lt;</span> <span class="mi">0</span> <span class="ow">or</span> <span class="n">index</span> <span class="o">&gt;=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span><span class="p">:</span>
+<a id="__codelineno-78-23" name="__codelineno-78-23" href="#__codelineno-78-23"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;Index out of bounds&quot;</span><span class="p">)</span>
+<a id="__codelineno-78-24" name="__codelineno-78-24" href="#__codelineno-78-24"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_arr</span><span class="p">[</span><span class="n">index</span><span class="p">]</span>
+<a id="__codelineno-78-25" name="__codelineno-78-25" href="#__codelineno-78-25"></a>
+<a id="__codelineno-78-26" name="__codelineno-78-26" href="#__codelineno-78-26"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">set</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">num</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">index</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-78-27" name="__codelineno-78-27" href="#__codelineno-78-27"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;要素を更新&quot;&quot;&quot;</span>
+<a id="__codelineno-78-28" name="__codelineno-78-28" href="#__codelineno-78-28"></a>        <span class="k">if</span> <span class="n">index</span> <span class="o">&lt;</span> <span class="mi">0</span> <span class="ow">or</span> <span class="n">index</span> <span class="o">&gt;=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span><span class="p">:</span>
+<a id="__codelineno-78-29" name="__codelineno-78-29" href="#__codelineno-78-29"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;Index out of bounds&quot;</span><span class="p">)</span>
+<a id="__codelineno-78-30" name="__codelineno-78-30" href="#__codelineno-78-30"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_arr</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">=</span> <span class="n">num</span>
+<a id="__codelineno-78-31" name="__codelineno-78-31" href="#__codelineno-78-31"></a>
+<a id="__codelineno-78-32" name="__codelineno-78-32" href="#__codelineno-78-32"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">add</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">num</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-78-33" name="__codelineno-78-33" href="#__codelineno-78-33"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;末尾に要素を追加&quot;&quot;&quot;</span>
+<a id="__codelineno-78-34" name="__codelineno-78-34" href="#__codelineno-78-34"></a>        <span class="c1"># 要素数が容量を超える場合、拡張メカニズムをトリガー</span>
+<a id="__codelineno-78-35" name="__codelineno-78-35" href="#__codelineno-78-35"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span> <span class="o">==</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span><span class="p">():</span>
+<a id="__codelineno-78-36" name="__codelineno-78-36" href="#__codelineno-78-36"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">extend_capacity</span><span class="p">()</span>
+<a id="__codelineno-78-37" name="__codelineno-78-37" href="#__codelineno-78-37"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_arr</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">_size</span><span class="p">]</span> <span class="o">=</span> <span class="n">num</span>
+<a id="__codelineno-78-38" name="__codelineno-78-38" href="#__codelineno-78-38"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-78-39" name="__codelineno-78-39" href="#__codelineno-78-39"></a>
+<a id="__codelineno-78-40" name="__codelineno-78-40" href="#__codelineno-78-40"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">num</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">index</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-78-41" name="__codelineno-78-41" href="#__codelineno-78-41"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;中間に要素を挿入&quot;&quot;&quot;</span>
+<a id="__codelineno-78-42" name="__codelineno-78-42" href="#__codelineno-78-42"></a>        <span class="k">if</span> <span class="n">index</span> <span class="o">&lt;</span> <span class="mi">0</span> <span class="ow">or</span> <span class="n">index</span> <span class="o">&gt;=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span><span class="p">:</span>
+<a id="__codelineno-78-43" name="__codelineno-78-43" href="#__codelineno-78-43"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;Index out of bounds&quot;</span><span class="p">)</span>
+<a id="__codelineno-78-44" name="__codelineno-78-44" href="#__codelineno-78-44"></a>        <span class="c1"># 要素数が容量を超える場合、拡張メカニズムをトリガー</span>
+<a id="__codelineno-78-45" name="__codelineno-78-45" href="#__codelineno-78-45"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">==</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span><span class="p">():</span>
+<a id="__codelineno-78-46" name="__codelineno-78-46" href="#__codelineno-78-46"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">extend_capacity</span><span class="p">()</span>
+<a id="__codelineno-78-47" name="__codelineno-78-47" href="#__codelineno-78-47"></a>        <span class="c1"># インデックス index より後のすべての要素を1つ後ろに移動</span>
+<a id="__codelineno-78-48" name="__codelineno-78-48" href="#__codelineno-78-48"></a>        <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">index</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-78-49" name="__codelineno-78-49" href="#__codelineno-78-49"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">_arr</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_arr</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
+<a id="__codelineno-78-50" name="__codelineno-78-50" href="#__codelineno-78-50"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_arr</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">=</span> <span class="n">num</span>
+<a id="__codelineno-78-51" name="__codelineno-78-51" href="#__codelineno-78-51"></a>        <span class="c1"># 要素数を更新</span>
+<a id="__codelineno-78-52" name="__codelineno-78-52" href="#__codelineno-78-52"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-78-53" name="__codelineno-78-53" href="#__codelineno-78-53"></a>
+<a id="__codelineno-78-54" name="__codelineno-78-54" href="#__codelineno-78-54"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">index</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-78-55" name="__codelineno-78-55" href="#__codelineno-78-55"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;要素を削除&quot;&quot;&quot;</span>
+<a id="__codelineno-78-56" name="__codelineno-78-56" href="#__codelineno-78-56"></a>        <span class="k">if</span> <span class="n">index</span> <span class="o">&lt;</span> <span class="mi">0</span> <span class="ow">or</span> <span class="n">index</span> <span class="o">&gt;=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span><span class="p">:</span>
+<a id="__codelineno-78-57" name="__codelineno-78-57" href="#__codelineno-78-57"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;Index out of bounds&quot;</span><span class="p">)</span>
+<a id="__codelineno-78-58" name="__codelineno-78-58" href="#__codelineno-78-58"></a>        <span class="n">num</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_arr</span><span class="p">[</span><span class="n">index</span><span class="p">]</span>
+<a id="__codelineno-78-59" name="__codelineno-78-59" href="#__codelineno-78-59"></a>        <span class="c1"># インデックス index より後のすべての要素を1つ前に移動</span>
+<a id="__codelineno-78-60" name="__codelineno-78-60" href="#__codelineno-78-60"></a>        <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">index</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">-</span> <span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-78-61" name="__codelineno-78-61" href="#__codelineno-78-61"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">_arr</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_arr</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-78-62" name="__codelineno-78-62" href="#__codelineno-78-62"></a>        <span class="c1"># 要素数を更新</span>
+<a id="__codelineno-78-63" name="__codelineno-78-63" href="#__codelineno-78-63"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">-=</span> <span class="mi">1</span>
+<a id="__codelineno-78-64" name="__codelineno-78-64" href="#__codelineno-78-64"></a>        <span class="c1"># 削除された要素を返す</span>
+<a id="__codelineno-78-65" name="__codelineno-78-65" href="#__codelineno-78-65"></a>        <span class="k">return</span> <span class="n">num</span>
+<a id="__codelineno-78-66" name="__codelineno-78-66" href="#__codelineno-78-66"></a>
+<a id="__codelineno-78-67" name="__codelineno-78-67" href="#__codelineno-78-67"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">extend_capacity</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<a id="__codelineno-78-68" name="__codelineno-78-68" href="#__codelineno-78-68"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;リストを拡張&quot;&quot;&quot;</span>
+<a id="__codelineno-78-69" name="__codelineno-78-69" href="#__codelineno-78-69"></a>        <span class="c1"># 元の配列の _extend_ratio 倍の長さの新しい配列を作成し、元の配列を新しい配列にコピー</span>
+<a id="__codelineno-78-70" name="__codelineno-78-70" href="#__codelineno-78-70"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_arr</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_arr</span> <span class="o">+</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span><span class="p">()</span> <span class="o">*</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_extend_ratio</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-78-71" name="__codelineno-78-71" href="#__codelineno-78-71"></a>        <span class="c1"># リストの容量を更新</span>
+<a id="__codelineno-78-72" name="__codelineno-78-72" href="#__codelineno-78-72"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_capacity</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_arr</span><span class="p">)</span>
+<a id="__codelineno-78-73" name="__codelineno-78-73" href="#__codelineno-78-73"></a>
+<a id="__codelineno-78-74" name="__codelineno-78-74" href="#__codelineno-78-74"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">to_array</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
+<a id="__codelineno-78-75" name="__codelineno-78-75" href="#__codelineno-78-75"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;有効な長さのリストを返す&quot;&quot;&quot;</span>
+<a id="__codelineno-78-76" name="__codelineno-78-76" href="#__codelineno-78-76"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_arr</span><span class="p">[:</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span><span class="p">]</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_list.cpp</span><pre><span></span><code><a id="__codelineno-79-1" name="__codelineno-79-1" href="#__codelineno-79-1"></a><span class="cm">/* リストクラス */</span>
+<a id="__codelineno-79-2" name="__codelineno-79-2" href="#__codelineno-79-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">MyList</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-79-3" name="__codelineno-79-3" href="#__codelineno-79-3"></a><span class="w">  </span><span class="k">private</span><span class="o">:</span>
+<a id="__codelineno-79-4" name="__codelineno-79-4" href="#__codelineno-79-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">arr</span><span class="p">;</span><span class="w">             </span><span class="c1">// 配列（リスト要素を格納）</span>
+<a id="__codelineno-79-5" name="__codelineno-79-5" href="#__codelineno-79-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">arrCapacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">10</span><span class="p">;</span><span class="w"> </span><span class="c1">// リストの容量</span>
+<a id="__codelineno-79-6" name="__codelineno-79-6" href="#__codelineno-79-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">arrSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">      </span><span class="c1">// リストの長さ（現在の要素数）</span>
+<a id="__codelineno-79-7" name="__codelineno-79-7" href="#__codelineno-79-7"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">extendRatio</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w">   </span><span class="c1">// リスト拡張時の倍率</span>
+<a id="__codelineno-79-8" name="__codelineno-79-8" href="#__codelineno-79-8"></a>
+<a id="__codelineno-79-9" name="__codelineno-79-9" href="#__codelineno-79-9"></a><span class="w">  </span><span class="k">public</span><span class="o">:</span>
+<a id="__codelineno-79-10" name="__codelineno-79-10" href="#__codelineno-79-10"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-79-11" name="__codelineno-79-11" href="#__codelineno-79-11"></a><span class="w">    </span><span class="n">MyList</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-79-12" name="__codelineno-79-12" href="#__codelineno-79-12"></a><span class="w">        </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">arrCapacity</span><span class="p">];</span>
+<a id="__codelineno-79-13" name="__codelineno-79-13" href="#__codelineno-79-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-79-14" name="__codelineno-79-14" href="#__codelineno-79-14"></a>
+<a id="__codelineno-79-15" name="__codelineno-79-15" href="#__codelineno-79-15"></a><span class="w">    </span><span class="cm">/* デストラクタ */</span>
+<a id="__codelineno-79-16" name="__codelineno-79-16" href="#__codelineno-79-16"></a><span class="w">    </span><span class="o">~</span><span class="n">MyList</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-79-17" name="__codelineno-79-17" href="#__codelineno-79-17"></a><span class="w">        </span><span class="k">delete</span><span class="p">[]</span><span class="w"> </span><span class="n">arr</span><span class="p">;</span>
+<a id="__codelineno-79-18" name="__codelineno-79-18" href="#__codelineno-79-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-79-19" name="__codelineno-79-19" href="#__codelineno-79-19"></a>
+<a id="__codelineno-79-20" name="__codelineno-79-20" href="#__codelineno-79-20"></a><span class="w">    </span><span class="cm">/* リストの長さを取得（現在の要素数）*/</span>
+<a id="__codelineno-79-21" name="__codelineno-79-21" href="#__codelineno-79-21"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-79-22" name="__codelineno-79-22" href="#__codelineno-79-22"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">arrSize</span><span class="p">;</span>
+<a id="__codelineno-79-23" name="__codelineno-79-23" href="#__codelineno-79-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-79-24" name="__codelineno-79-24" href="#__codelineno-79-24"></a>
+<a id="__codelineno-79-25" name="__codelineno-79-25" href="#__codelineno-79-25"></a><span class="w">    </span><span class="cm">/* リストの容量を取得 */</span>
+<a id="__codelineno-79-26" name="__codelineno-79-26" href="#__codelineno-79-26"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-79-27" name="__codelineno-79-27" href="#__codelineno-79-27"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">arrCapacity</span><span class="p">;</span>
+<a id="__codelineno-79-28" name="__codelineno-79-28" href="#__codelineno-79-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-79-29" name="__codelineno-79-29" href="#__codelineno-79-29"></a>
+<a id="__codelineno-79-30" name="__codelineno-79-30" href="#__codelineno-79-30"></a><span class="w">    </span><span class="cm">/* 要素にアクセス */</span>
+<a id="__codelineno-79-31" name="__codelineno-79-31" href="#__codelineno-79-31"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">get</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-79-32" name="__codelineno-79-32" href="#__codelineno-79-32"></a><span class="w">        </span><span class="c1">// インデックスが範囲外の場合、例外をスロー（以下同様）</span>
+<a id="__codelineno-79-33" name="__codelineno-79-33" href="#__codelineno-79-33"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">())</span>
+<a id="__codelineno-79-34" name="__codelineno-79-34" href="#__codelineno-79-34"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;Index out of bounds&quot;</span><span class="p">);</span>
+<a id="__codelineno-79-35" name="__codelineno-79-35" href="#__codelineno-79-35"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">arr</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
+<a id="__codelineno-79-36" name="__codelineno-79-36" href="#__codelineno-79-36"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-79-37" name="__codelineno-79-37" href="#__codelineno-79-37"></a>
+<a id="__codelineno-79-38" name="__codelineno-79-38" href="#__codelineno-79-38"></a><span class="w">    </span><span class="cm">/* 要素を更新 */</span>
+<a id="__codelineno-79-39" name="__codelineno-79-39" href="#__codelineno-79-39"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">set</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-79-40" name="__codelineno-79-40" href="#__codelineno-79-40"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">())</span>
+<a id="__codelineno-79-41" name="__codelineno-79-41" href="#__codelineno-79-41"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;Index out of bounds&quot;</span><span class="p">);</span>
+<a id="__codelineno-79-42" name="__codelineno-79-42" href="#__codelineno-79-42"></a><span class="w">        </span><span class="n">arr</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-79-43" name="__codelineno-79-43" href="#__codelineno-79-43"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-79-44" name="__codelineno-79-44" href="#__codelineno-79-44"></a>
+<a id="__codelineno-79-45" name="__codelineno-79-45" href="#__codelineno-79-45"></a><span class="w">    </span><span class="cm">/* 末尾に要素を追加 */</span>
+<a id="__codelineno-79-46" name="__codelineno-79-46" href="#__codelineno-79-46"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">add</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-79-47" name="__codelineno-79-47" href="#__codelineno-79-47"></a><span class="w">        </span><span class="c1">// 要素数が容量を超えた場合、拡張メカニズムをトリガー</span>
+<a id="__codelineno-79-48" name="__codelineno-79-48" href="#__codelineno-79-48"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">capacity</span><span class="p">())</span>
+<a id="__codelineno-79-49" name="__codelineno-79-49" href="#__codelineno-79-49"></a><span class="w">            </span><span class="n">extendCapacity</span><span class="p">();</span>
+<a id="__codelineno-79-50" name="__codelineno-79-50" href="#__codelineno-79-50"></a><span class="w">        </span><span class="n">arr</span><span class="p">[</span><span class="n">size</span><span class="p">()]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-79-51" name="__codelineno-79-51" href="#__codelineno-79-51"></a><span class="w">        </span><span class="c1">// 要素数を更新</span>
+<a id="__codelineno-79-52" name="__codelineno-79-52" href="#__codelineno-79-52"></a><span class="w">        </span><span class="n">arrSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-79-53" name="__codelineno-79-53" href="#__codelineno-79-53"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-79-54" name="__codelineno-79-54" href="#__codelineno-79-54"></a>
+<a id="__codelineno-79-55" name="__codelineno-79-55" href="#__codelineno-79-55"></a><span class="w">    </span><span class="cm">/* 中間に要素を挿入 */</span>
+<a id="__codelineno-79-56" name="__codelineno-79-56" href="#__codelineno-79-56"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">insert</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-79-57" name="__codelineno-79-57" href="#__codelineno-79-57"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">())</span>
+<a id="__codelineno-79-58" name="__codelineno-79-58" href="#__codelineno-79-58"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;Index out of bounds&quot;</span><span class="p">);</span>
+<a id="__codelineno-79-59" name="__codelineno-79-59" href="#__codelineno-79-59"></a><span class="w">        </span><span class="c1">// 要素数が容量を超えた場合、拡張メカニズムをトリガー</span>
+<a id="__codelineno-79-60" name="__codelineno-79-60" href="#__codelineno-79-60"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">capacity</span><span class="p">())</span>
+<a id="__codelineno-79-61" name="__codelineno-79-61" href="#__codelineno-79-61"></a><span class="w">            </span><span class="n">extendCapacity</span><span class="p">();</span>
+<a id="__codelineno-79-62" name="__codelineno-79-62" href="#__codelineno-79-62"></a><span class="w">        </span><span class="c1">// `index`より後のすべての要素を1つ後ろに移動</span>
+<a id="__codelineno-79-63" name="__codelineno-79-63" href="#__codelineno-79-63"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-79-64" name="__codelineno-79-64" href="#__codelineno-79-64"></a><span class="w">            </span><span class="n">arr</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-79-65" name="__codelineno-79-65" href="#__codelineno-79-65"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-79-66" name="__codelineno-79-66" href="#__codelineno-79-66"></a><span class="w">        </span><span class="n">arr</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-79-67" name="__codelineno-79-67" href="#__codelineno-79-67"></a><span class="w">        </span><span class="c1">// 要素数を更新</span>
+<a id="__codelineno-79-68" name="__codelineno-79-68" href="#__codelineno-79-68"></a><span class="w">        </span><span class="n">arrSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-79-69" name="__codelineno-79-69" href="#__codelineno-79-69"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-79-70" name="__codelineno-79-70" href="#__codelineno-79-70"></a>
+<a id="__codelineno-79-71" name="__codelineno-79-71" href="#__codelineno-79-71"></a><span class="w">    </span><span class="cm">/* 要素を削除 */</span>
+<a id="__codelineno-79-72" name="__codelineno-79-72" href="#__codelineno-79-72"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-79-73" name="__codelineno-79-73" href="#__codelineno-79-73"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">())</span>
+<a id="__codelineno-79-74" name="__codelineno-79-74" href="#__codelineno-79-74"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;Index out of bounds&quot;</span><span class="p">);</span>
+<a id="__codelineno-79-75" name="__codelineno-79-75" href="#__codelineno-79-75"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
+<a id="__codelineno-79-76" name="__codelineno-79-76" href="#__codelineno-79-76"></a><span class="w">        </span><span class="c1">// `index`より後のすべての要素を1つ前に移動</span>
+<a id="__codelineno-79-77" name="__codelineno-79-77" href="#__codelineno-79-77"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-79-78" name="__codelineno-79-78" href="#__codelineno-79-78"></a><span class="w">            </span><span class="n">arr</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-79-79" name="__codelineno-79-79" href="#__codelineno-79-79"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-79-80" name="__codelineno-79-80" href="#__codelineno-79-80"></a><span class="w">        </span><span class="c1">// 要素数を更新</span>
+<a id="__codelineno-79-81" name="__codelineno-79-81" href="#__codelineno-79-81"></a><span class="w">        </span><span class="n">arrSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-79-82" name="__codelineno-79-82" href="#__codelineno-79-82"></a><span class="w">        </span><span class="c1">// 削除された要素を返却</span>
+<a id="__codelineno-79-83" name="__codelineno-79-83" href="#__codelineno-79-83"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-79-84" name="__codelineno-79-84" href="#__codelineno-79-84"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-79-85" name="__codelineno-79-85" href="#__codelineno-79-85"></a>
+<a id="__codelineno-79-86" name="__codelineno-79-86" href="#__codelineno-79-86"></a><span class="w">    </span><span class="cm">/* リストを拡張 */</span>
+<a id="__codelineno-79-87" name="__codelineno-79-87" href="#__codelineno-79-87"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">extendCapacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-79-88" name="__codelineno-79-88" href="#__codelineno-79-88"></a><span class="w">        </span><span class="c1">// 元の配列のextendRatio倍の長さで新しい配列を作成</span>
+<a id="__codelineno-79-89" name="__codelineno-79-89" href="#__codelineno-79-89"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">newCapacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">capacity</span><span class="p">()</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">extendRatio</span><span class="p">;</span>
+<a id="__codelineno-79-90" name="__codelineno-79-90" href="#__codelineno-79-90"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="p">;</span>
+<a id="__codelineno-79-91" name="__codelineno-79-91" href="#__codelineno-79-91"></a><span class="w">        </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">newCapacity</span><span class="p">];</span>
+<a id="__codelineno-79-92" name="__codelineno-79-92" href="#__codelineno-79-92"></a><span class="w">        </span><span class="c1">// 元の配列のすべての要素を新しい配列にコピー</span>
+<a id="__codelineno-79-93" name="__codelineno-79-93" href="#__codelineno-79-93"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-79-94" name="__codelineno-79-94" href="#__codelineno-79-94"></a><span class="w">            </span><span class="n">arr</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-79-95" name="__codelineno-79-95" href="#__codelineno-79-95"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-79-96" name="__codelineno-79-96" href="#__codelineno-79-96"></a><span class="w">        </span><span class="c1">// メモリを解放</span>
+<a id="__codelineno-79-97" name="__codelineno-79-97" href="#__codelineno-79-97"></a><span class="w">        </span><span class="k">delete</span><span class="p">[]</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
+<a id="__codelineno-79-98" name="__codelineno-79-98" href="#__codelineno-79-98"></a><span class="w">        </span><span class="n">arrCapacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newCapacity</span><span class="p">;</span>
+<a id="__codelineno-79-99" name="__codelineno-79-99" href="#__codelineno-79-99"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-79-100" name="__codelineno-79-100" href="#__codelineno-79-100"></a>
+<a id="__codelineno-79-101" name="__codelineno-79-101" href="#__codelineno-79-101"></a><span class="w">    </span><span class="cm">/* リストをVectorに変換して印刷用に使用 */</span>
+<a id="__codelineno-79-102" name="__codelineno-79-102" href="#__codelineno-79-102"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">toVector</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-79-103" name="__codelineno-79-103" href="#__codelineno-79-103"></a><span class="w">        </span><span class="c1">// 有効な長さ範囲内の要素のみを変換</span>
+<a id="__codelineno-79-104" name="__codelineno-79-104" href="#__codelineno-79-104"></a><span class="w">        </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">vec</span><span class="p">(</span><span class="n">size</span><span class="p">());</span>
+<a id="__codelineno-79-105" name="__codelineno-79-105" href="#__codelineno-79-105"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-79-106" name="__codelineno-79-106" href="#__codelineno-79-106"></a><span class="w">            </span><span class="n">vec</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-79-107" name="__codelineno-79-107" href="#__codelineno-79-107"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-79-108" name="__codelineno-79-108" href="#__codelineno-79-108"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">vec</span><span class="p">;</span>
+<a id="__codelineno-79-109" name="__codelineno-79-109" href="#__codelineno-79-109"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-79-110" name="__codelineno-79-110" href="#__codelineno-79-110"></a><span class="p">};</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_list.java</span><pre><span></span><code><a id="__codelineno-80-1" name="__codelineno-80-1" href="#__codelineno-80-1"></a><span class="cm">/* リストクラス */</span>
+<a id="__codelineno-80-2" name="__codelineno-80-2" href="#__codelineno-80-2"></a><span class="kd">class</span> <span class="nc">MyList</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-80-3" name="__codelineno-80-3" href="#__codelineno-80-3"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">arr</span><span class="p">;</span><span class="w"> </span><span class="c1">// 配列（リスト要素を格納）</span>
+<a id="__codelineno-80-4" name="__codelineno-80-4" href="#__codelineno-80-4"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">10</span><span class="p">;</span><span class="w"> </span><span class="c1">// リスト容量</span>
+<a id="__codelineno-80-5" name="__codelineno-80-5" href="#__codelineno-80-5"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// リスト長（現在の要素数）</span>
+<a id="__codelineno-80-6" name="__codelineno-80-6" href="#__codelineno-80-6"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">extendRatio</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// リストの各拡張倍率</span>
+<a id="__codelineno-80-7" name="__codelineno-80-7" href="#__codelineno-80-7"></a>
+<a id="__codelineno-80-8" name="__codelineno-80-8" href="#__codelineno-80-8"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-80-9" name="__codelineno-80-9" href="#__codelineno-80-9"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="nf">MyList</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-80-10" name="__codelineno-80-10" href="#__codelineno-80-10"></a><span class="w">        </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">capacity</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-80-11" name="__codelineno-80-11" href="#__codelineno-80-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-80-12" name="__codelineno-80-12" href="#__codelineno-80-12"></a>
+<a id="__codelineno-80-13" name="__codelineno-80-13" href="#__codelineno-80-13"></a><span class="w">    </span><span class="cm">/* リスト長を取得（現在の要素数） */</span>
+<a id="__codelineno-80-14" name="__codelineno-80-14" href="#__codelineno-80-14"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-80-15" name="__codelineno-80-15" href="#__codelineno-80-15"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">size</span><span class="p">;</span>
+<a id="__codelineno-80-16" name="__codelineno-80-16" href="#__codelineno-80-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-80-17" name="__codelineno-80-17" href="#__codelineno-80-17"></a>
+<a id="__codelineno-80-18" name="__codelineno-80-18" href="#__codelineno-80-18"></a><span class="w">    </span><span class="cm">/* リスト容量を取得 */</span>
+<a id="__codelineno-80-19" name="__codelineno-80-19" href="#__codelineno-80-19"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">capacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-80-20" name="__codelineno-80-20" href="#__codelineno-80-20"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span>
+<a id="__codelineno-80-21" name="__codelineno-80-21" href="#__codelineno-80-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-80-22" name="__codelineno-80-22" href="#__codelineno-80-22"></a>
+<a id="__codelineno-80-23" name="__codelineno-80-23" href="#__codelineno-80-23"></a><span class="w">    </span><span class="cm">/* 要素へのアクセス */</span>
+<a id="__codelineno-80-24" name="__codelineno-80-24" href="#__codelineno-80-24"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">get</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-80-25" name="__codelineno-80-25" href="#__codelineno-80-25"></a><span class="w">        </span><span class="c1">// インデックスが範囲外の場合、以下のように例外をスロー</span>
+<a id="__codelineno-80-26" name="__codelineno-80-26" href="#__codelineno-80-26"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">)</span>
+<a id="__codelineno-80-27" name="__codelineno-80-27" href="#__codelineno-80-27"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">(</span><span class="s">&quot;インデックスが範囲外です&quot;</span><span class="p">);</span>
+<a id="__codelineno-80-28" name="__codelineno-80-28" href="#__codelineno-80-28"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">arr</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-80-29" name="__codelineno-80-29" href="#__codelineno-80-29"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-80-30" name="__codelineno-80-30" href="#__codelineno-80-30"></a>
+<a id="__codelineno-80-31" name="__codelineno-80-31" href="#__codelineno-80-31"></a><span class="w">    </span><span class="cm">/* 要素の更新 */</span>
+<a id="__codelineno-80-32" name="__codelineno-80-32" href="#__codelineno-80-32"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">set</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-80-33" name="__codelineno-80-33" href="#__codelineno-80-33"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">)</span>
+<a id="__codelineno-80-34" name="__codelineno-80-34" href="#__codelineno-80-34"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">(</span><span class="s">&quot;インデックスが範囲外です&quot;</span><span class="p">);</span>
+<a id="__codelineno-80-35" name="__codelineno-80-35" href="#__codelineno-80-35"></a><span class="w">        </span><span class="n">arr</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-80-36" name="__codelineno-80-36" href="#__codelineno-80-36"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-80-37" name="__codelineno-80-37" href="#__codelineno-80-37"></a>
+<a id="__codelineno-80-38" name="__codelineno-80-38" href="#__codelineno-80-38"></a><span class="w">    </span><span class="cm">/* 末尾に要素を追加 */</span>
+<a id="__codelineno-80-39" name="__codelineno-80-39" href="#__codelineno-80-39"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">add</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-80-40" name="__codelineno-80-40" href="#__codelineno-80-40"></a><span class="w">        </span><span class="c1">// 要素数が容量を超える場合、拡張メカニズムを実行</span>
+<a id="__codelineno-80-41" name="__codelineno-80-41" href="#__codelineno-80-41"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">size</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">capacity</span><span class="p">())</span>
+<a id="__codelineno-80-42" name="__codelineno-80-42" href="#__codelineno-80-42"></a><span class="w">            </span><span class="n">extendCapacity</span><span class="p">();</span>
+<a id="__codelineno-80-43" name="__codelineno-80-43" href="#__codelineno-80-43"></a><span class="w">        </span><span class="n">arr</span><span class="o">[</span><span class="n">size</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-80-44" name="__codelineno-80-44" href="#__codelineno-80-44"></a><span class="w">        </span><span class="c1">// 要素数を更新</span>
+<a id="__codelineno-80-45" name="__codelineno-80-45" href="#__codelineno-80-45"></a><span class="w">        </span><span class="n">size</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-80-46" name="__codelineno-80-46" href="#__codelineno-80-46"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-80-47" name="__codelineno-80-47" href="#__codelineno-80-47"></a>
+<a id="__codelineno-80-48" name="__codelineno-80-48" href="#__codelineno-80-48"></a><span class="w">    </span><span class="cm">/* 中間に要素を挿入 */</span>
+<a id="__codelineno-80-49" name="__codelineno-80-49" href="#__codelineno-80-49"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-80-50" name="__codelineno-80-50" href="#__codelineno-80-50"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">)</span>
+<a id="__codelineno-80-51" name="__codelineno-80-51" href="#__codelineno-80-51"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">(</span><span class="s">&quot;インデックスが範囲外です&quot;</span><span class="p">);</span>
+<a id="__codelineno-80-52" name="__codelineno-80-52" href="#__codelineno-80-52"></a><span class="w">        </span><span class="c1">// 要素数が容量を超える場合、拡張メカニズムを実行</span>
+<a id="__codelineno-80-53" name="__codelineno-80-53" href="#__codelineno-80-53"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">size</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">capacity</span><span class="p">())</span>
+<a id="__codelineno-80-54" name="__codelineno-80-54" href="#__codelineno-80-54"></a><span class="w">            </span><span class="n">extendCapacity</span><span class="p">();</span>
+<a id="__codelineno-80-55" name="__codelineno-80-55" href="#__codelineno-80-55"></a><span class="w">        </span><span class="c1">// `index` より後のすべての要素を1つ後ろに移動</span>
+<a id="__codelineno-80-56" name="__codelineno-80-56" href="#__codelineno-80-56"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-80-57" name="__codelineno-80-57" href="#__codelineno-80-57"></a><span class="w">            </span><span class="n">arr</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-80-58" name="__codelineno-80-58" href="#__codelineno-80-58"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-80-59" name="__codelineno-80-59" href="#__codelineno-80-59"></a><span class="w">        </span><span class="n">arr</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-80-60" name="__codelineno-80-60" href="#__codelineno-80-60"></a><span class="w">        </span><span class="c1">// 要素数を更新</span>
+<a id="__codelineno-80-61" name="__codelineno-80-61" href="#__codelineno-80-61"></a><span class="w">        </span><span class="n">size</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-80-62" name="__codelineno-80-62" href="#__codelineno-80-62"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-80-63" name="__codelineno-80-63" href="#__codelineno-80-63"></a>
+<a id="__codelineno-80-64" name="__codelineno-80-64" href="#__codelineno-80-64"></a><span class="w">    </span><span class="cm">/* 要素の削除 */</span>
+<a id="__codelineno-80-65" name="__codelineno-80-65" href="#__codelineno-80-65"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-80-66" name="__codelineno-80-66" href="#__codelineno-80-66"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">)</span>
+<a id="__codelineno-80-67" name="__codelineno-80-67" href="#__codelineno-80-67"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">(</span><span class="s">&quot;インデックスが範囲外です&quot;</span><span class="p">);</span>
+<a id="__codelineno-80-68" name="__codelineno-80-68" href="#__codelineno-80-68"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-80-69" name="__codelineno-80-69" href="#__codelineno-80-69"></a><span class="w">        </span><span class="c1">// `index` より後のすべての要素を1つ前に移動</span>
+<a id="__codelineno-80-70" name="__codelineno-80-70" href="#__codelineno-80-70"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-80-71" name="__codelineno-80-71" href="#__codelineno-80-71"></a><span class="w">            </span><span class="n">arr</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-80-72" name="__codelineno-80-72" href="#__codelineno-80-72"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-80-73" name="__codelineno-80-73" href="#__codelineno-80-73"></a><span class="w">        </span><span class="c1">// 要素数を更新</span>
+<a id="__codelineno-80-74" name="__codelineno-80-74" href="#__codelineno-80-74"></a><span class="w">        </span><span class="n">size</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-80-75" name="__codelineno-80-75" href="#__codelineno-80-75"></a><span class="w">        </span><span class="c1">// 削除された要素を返す</span>
+<a id="__codelineno-80-76" name="__codelineno-80-76" href="#__codelineno-80-76"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-80-77" name="__codelineno-80-77" href="#__codelineno-80-77"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-80-78" name="__codelineno-80-78" href="#__codelineno-80-78"></a>
+<a id="__codelineno-80-79" name="__codelineno-80-79" href="#__codelineno-80-79"></a><span class="w">    </span><span class="cm">/* リストを拡張 */</span>
+<a id="__codelineno-80-80" name="__codelineno-80-80" href="#__codelineno-80-80"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">extendCapacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-80-81" name="__codelineno-80-81" href="#__codelineno-80-81"></a><span class="w">        </span><span class="c1">// 元の配列の長さを extendRatio 倍した新しい配列を作成し、元の配列を新しい配列にコピー</span>
+<a id="__codelineno-80-82" name="__codelineno-80-82" href="#__codelineno-80-82"></a><span class="w">        </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Arrays</span><span class="p">.</span><span class="na">copyOf</span><span class="p">(</span><span class="n">arr</span><span class="p">,</span><span class="w"> </span><span class="n">capacity</span><span class="p">()</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">extendRatio</span><span class="p">);</span>
+<a id="__codelineno-80-83" name="__codelineno-80-83" href="#__codelineno-80-83"></a><span class="w">        </span><span class="c1">// リスト容量を更新</span>
+<a id="__codelineno-80-84" name="__codelineno-80-84" href="#__codelineno-80-84"></a><span class="w">        </span><span class="n">capacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="p">.</span><span class="na">length</span><span class="p">;</span>
+<a id="__codelineno-80-85" name="__codelineno-80-85" href="#__codelineno-80-85"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-80-86" name="__codelineno-80-86" href="#__codelineno-80-86"></a>
+<a id="__codelineno-80-87" name="__codelineno-80-87" href="#__codelineno-80-87"></a><span class="w">    </span><span class="cm">/* リストを配列に変換 */</span>
+<a id="__codelineno-80-88" name="__codelineno-80-88" href="#__codelineno-80-88"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="nf">toArray</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-80-89" name="__codelineno-80-89" href="#__codelineno-80-89"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">size</span><span class="p">();</span>
+<a id="__codelineno-80-90" name="__codelineno-80-90" href="#__codelineno-80-90"></a><span class="w">        </span><span class="c1">// 有効な長さ範囲内の要素のみを変換</span>
+<a id="__codelineno-80-91" name="__codelineno-80-91" href="#__codelineno-80-91"></a><span class="w">        </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">size</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-80-92" name="__codelineno-80-92" href="#__codelineno-80-92"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-80-93" name="__codelineno-80-93" href="#__codelineno-80-93"></a><span class="w">            </span><span class="n">arr</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">get</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-80-94" name="__codelineno-80-94" href="#__codelineno-80-94"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-80-95" name="__codelineno-80-95" href="#__codelineno-80-95"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">arr</span><span class="p">;</span>
+<a id="__codelineno-80-96" name="__codelineno-80-96" href="#__codelineno-80-96"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-80-97" name="__codelineno-80-97" href="#__codelineno-80-97"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_list.cs</span><pre><span></span><code><a id="__codelineno-81-1" name="__codelineno-81-1" href="#__codelineno-81-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">MyList</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_list.go</span><pre><span></span><code><a id="__codelineno-82-1" name="__codelineno-82-1" href="#__codelineno-82-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">myList</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_list.swift</span><pre><span></span><code><a id="__codelineno-83-1" name="__codelineno-83-1" href="#__codelineno-83-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">MyList</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_list.js</span><pre><span></span><code><a id="__codelineno-84-1" name="__codelineno-84-1" href="#__codelineno-84-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">MyList</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_list.ts</span><pre><span></span><code><a id="__codelineno-85-1" name="__codelineno-85-1" href="#__codelineno-85-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">MyList</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_list.dart</span><pre><span></span><code><a id="__codelineno-86-1" name="__codelineno-86-1" href="#__codelineno-86-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MyList</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_list.rs</span><pre><span></span><code><a id="__codelineno-87-1" name="__codelineno-87-1" href="#__codelineno-87-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MyList</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_list.c</span><pre><span></span><code><a id="__codelineno-88-1" name="__codelineno-88-1" href="#__codelineno-88-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MyList</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_list.kt</span><pre><span></span><code><a id="__codelineno-89-1" name="__codelineno-89-1" href="#__codelineno-89-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">MyList</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_list.rb</span><pre><span></span><code><a id="__codelineno-90-1" name="__codelineno-90-1" href="#__codelineno-90-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">MyList</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_list.zig</span><pre><span></span><code><a id="__codelineno-91-1" name="__codelineno-91-1" href="#__codelineno-91-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MyList</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
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diff --git a/ja/chapter_array_and_linkedlist/ram_and_cache.assets/storage_pyramid.png b/ja/chapter_array_and_linkedlist/ram_and_cache.assets/storage_pyramid.png
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+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
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+        
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+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
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+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
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+            
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+  
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+  
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+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#441" class="md-nav__link">
+    <span class="md-ellipsis">
+      4.4.1 &nbsp; コンピュータ記憶装置
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#442" class="md-nav__link">
+    <span class="md-ellipsis">
+      4.4.2 &nbsp; データ構造のメモリ効率
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#443" class="md-nav__link">
+    <span class="md-ellipsis">
+      4.4.3 &nbsp; データ構造のキャッシュ効率
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
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+            
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+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_19" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_reference/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9 3v15h3V3H9m3 2 4 13 3-1-4-13-3 1M5 5v13h3V5H5M3 19v2h18v-2H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    参考文献
+  </span>
+  
+
+            </a>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_19_label" aria-expanded="false">
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+            参考文献
+          </label>
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+        </nav>
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+      4.4.1 &nbsp; コンピュータ記憶装置
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+      
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+      4.4.2 &nbsp; データ構造のメモリ効率
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+      4.4.3 &nbsp; データ構造のキャッシュ効率
+    </span>
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+</li>
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+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
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+<h1 id="44">4.4 &nbsp; メモリとキャッシュ *<a class="headerlink" href="#44" title="Permanent link">&para;</a></h1>
+<p>この章の最初の2つのセクションでは、「連続格納」と「分散格納」をそれぞれ表現する2つの基本的なデータ構造である配列と連結リストを探究しました。</p>
+<p>実際、<strong>物理構造はプログラムがメモリとキャッシュをどの程度効率的に利用するかを大きく決定し</strong>、これがアルゴリズムの全体的なパフォーマンスに影響を与えます。</p>
+<h2 id="441">4.4.1 &nbsp; コンピュータ記憶装置<a class="headerlink" href="#441" title="Permanent link">&para;</a></h2>
+<p>コンピュータには3種類の記憶装置があります：<u>ハードディスク</u>、<u>ランダムアクセスメモリ（RAM）</u>、および<u>キャッシュメモリ</u>です。以下の表は、コンピュータシステムにおけるそれぞれの役割とパフォーマンス特性を示しています。</p>
+<p align="center"> 表 4-2 &nbsp; コンピュータ記憶装置 </p>
+
+<div class="center-table">
+<table>
+<thead>
+<tr>
+<th></th>
+<th>ハードディスク</th>
+<th>メモリ</th>
+<th>キャッシュ</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td>用途</td>
+<td>OS、プログラム、ファイルなどのデータの長期保存</td>
+<td>現在実行中のプログラムと処理中のデータの一時保存</td>
+<td>頻繁にアクセスされるデータと命令を保存し、CPUのメモリへのアクセス数を削減</td>
+</tr>
+<tr>
+<td>揮発性</td>
+<td>電源オフ後もデータは失われない</td>
+<td>電源オフ後にデータは失われる</td>
+<td>電源オフ後にデータは失われる</td>
+</tr>
+<tr>
+<td>容量</td>
+<td>より大きい、TBレベル</td>
+<td>より小さい、GBレベル</td>
+<td>非常に小さい、MBレベル</td>
+</tr>
+<tr>
+<td>速度</td>
+<td>より遅い、数百から数千MB/s</td>
+<td>より高速、数十GB/s</td>
+<td>非常に高速、数十から数百GB/s</td>
+</tr>
+<tr>
+<td>価格（USD）</td>
+<td>より安価、数セント/GB</td>
+<td>より高価、数ドル/GB</td>
+<td>非常に高価、CPUと一緒に価格設定</td>
+</tr>
+</tbody>
+</table>
+</div>
+<p>コンピュータ記憶システムは、下図に示すようにピラミッドとして視覚化できます。ピラミッドの上部にある記憶装置ほど高速で、容量が小さく、より高価です。このマルチレベル設計は偶然ではなく、コンピュータ科学者とエンジニアによる慎重な検討の結果です。</p>
+<ul>
+<li><strong>ハードディスクをメモリに置き換えるのは困難です</strong>。第一に、メモリ内のデータは電源オフ後に失われるため、長期データ保存には適していません。第二に、メモリはハードディスクよりも大幅に高価で、消費者市場での広範囲な使用の実現可能性を制限しています。</li>
+<li><strong>キャッシュは大容量と高速のトレードオフに直面しています</strong>。L1、L2、L3キャッシュの容量が増加するにつれて、その物理サイズが大きくなり、CPUコアからの距離が増加します。これによりデータ転送時間が長くなり、アクセス遅延が高くなります。現在の技術では、マルチレベルキャッシュ構造が容量、速度、コストの間の最適なバランスを提供します。</li>
+</ul>
+<p><a class="glightbox" href="../ram_and_cache.assets/storage_pyramid.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="コンピュータ記憶システム" class="animation-figure" src="../ram_and_cache.assets/storage_pyramid.png" /></a></p>
+<p align="center"> 図 4-9 &nbsp; コンピュータ記憶システム </p>
+
+<div class="admonition tip">
+<p class="admonition-title">Tip</p>
+<p>コンピュータの記憶階層は、速度、容量、コストの間の慎重なバランスを反映しています。このタイプのトレードオフは様々な業界で一般的であり、利益と制限の間の最適なバランスを見つけることが重要です。</p>
+</div>
+<p>全体的に、<strong>ハードディスクは大量のデータの長期保存を提供し、メモリはプログラム実行中に処理されるデータの一時保存として機能し、キャッシュは頻繁にアクセスされるデータと命令を保存して実行効率を向上させます</strong>。それらは一緒になってコンピュータシステムの効率的な動作を保証します。</p>
+<p>下図に示すように、プログラム実行中、データはハードディスクからメモリに読み込まれ、CPU計算が行われます。CPUの拡張として機能するキャッシュは、**メモリからインテリジェントにデータを先読み**し、CPUのより高速なデータアクセスを可能にします。これによりプログラム実行効率が大幅に向上し、低速なメモリへの依存が減少します。</p>
+<p><a class="glightbox" href="../ram_and_cache.assets/computer_storage_devices.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="ハードディスク、メモリ、キャッシュ間のデータフロー" class="animation-figure" src="../ram_and_cache.assets/computer_storage_devices.png" /></a></p>
+<p align="center"> 図 4-10 &nbsp; ハードディスク、メモリ、キャッシュ間のデータフロー </p>
+
+<h2 id="442">4.4.2 &nbsp; データ構造のメモリ効率<a class="headerlink" href="#442" title="Permanent link">&para;</a></h2>
+<p>メモリ空間利用の観点から、配列と連結リストにはそれぞれ利点と制限があります。</p>
+<p>一方で、**メモリは限られており、複数のプログラム間で共有できない**ため、データ構造での空間使用の最適化は重要です。配列は要素が密接にパックされており、連結リストのように参照（ポインタ）のための追加メモリを必要としないため、空間効率的です。しかし、配列は連続したメモリブロックを事前に割り当てる必要があり、割り当てられた空間が実際の必要量を超える場合、無駄につながる可能性があります。配列の拡張も追加の時間と空間のオーバーヘッドを伴います。対照的に、連結リストは各ノードに対してメモリを動的に割り当て・解放し、ポインタのための追加メモリのコストでより大きな柔軟性を提供します。</p>
+<p>一方で、プログラム実行中、<strong>繰り返されるメモリの割り当てと解放はメモリの断片化を増加させ</strong>、メモリ利用効率を低下させます。配列は連続記憶方式により、メモリ断片化を引き起こす可能性が比較的低いです。対照的に、連結リストは要素を非連続の場所に保存し、頻繁な挿入と削除はメモリ断片化を悪化させる可能性があります。</p>
+<h2 id="443">4.4.3 &nbsp; データ構造のキャッシュ効率<a class="headerlink" href="#443" title="Permanent link">&para;</a></h2>
+<p>キャッシュはメモリよりも空間容量がはるかに小さいですが、はるかに高速で、プログラム実行速度において重要な役割を果たします。限られた容量のため、キャッシュは頻繁にアクセスされるデータのサブセットのみを保存できます。CPUがキャッシュに存在しないデータにアクセスしようとすると、<u>キャッシュミス</u>が発生し、CPUは低速なメモリから必要なデータを取得する必要があり、パフォーマンスに影響を与える可能性があります。</p>
+<p>明らかに、<strong>キャッシュミスが少ないほど、CPUのデータ読み書き効率が高く</strong>、プログラムパフォーマンスが向上します。CPUがキャッシュからデータを正常に取得する割合は<u>キャッシュヒット率</u>と呼ばれ、キャッシュ効率を測定するためによく使用される指標です。</p>
+<p>より高い効率を達成するために、キャッシュは以下のデータロードメカニズムを採用します。</p>
+<ul>
+<li><strong>キャッシュライン</strong>：キャッシュは個々のバイトではなく、キャッシュラインと呼ばれる単位でデータを保存・ロードして動作します。このアプローチは、一度により大きなデータブロックを転送することで効率を向上させます。</li>
+<li><strong>先読みメカニズム</strong>：プロセッサはデータアクセスパターン（例：連続または固定ストライドアクセス）を予測し、これらのパターンに基づいてデータをキャッシュに先読みして、キャッシュヒット率を向上させます。</li>
+<li><strong>空間的局所性</strong>：特定のデータがアクセスされると、近くのデータもまもなくアクセスされる可能性があります。これを活用するために、キャッシュは要求されたデータと一緒に隣接するデータをロードし、ヒット率を向上させます。</li>
+<li><strong>時間的局所性</strong>：データがアクセスされた場合、近い将来に再びアクセスされる可能性があります。キャッシュはこの原理を使用して、最近アクセスされたデータを保持してヒット率を向上させます。</li>
+</ul>
+<p>実際、<strong>配列と連結リストは異なるキャッシュ利用効率を持ち</strong>、これは主に以下の側面に反映されます。</p>
+<ul>
+<li><strong>占有空間</strong>：連結リスト要素は配列要素よりも多くの空間を占有するため、キャッシュに保持される有効データが少なくなります。</li>
+<li><strong>キャッシュライン</strong>：連結リストデータはメモリ全体に散在し、キャッシュは「行単位でロード」されるため、ロードされる無効データの割合が高くなります。</li>
+<li><strong>先読みメカニズム</strong>：配列のデータアクセスパターンは連結リストよりも「予測可能」で、つまりシステムがこれからロードされるデータを推測しやすいです。</li>
+<li><strong>空間的局所性</strong>：配列は連続したメモリ空間に保存されるため、ロードされているデータの近くのデータがまもなくアクセスされる可能性が高くなります。</li>
+</ul>
+<p>全体的に、<strong>配列はより高いキャッシュヒット率を持ち、一般的に連結リストよりも操作効率が高いです</strong>。これにより、配列に基づくデータ構造はアルゴリズム問題の解決において人気があります。</p>
+<p>**高いキャッシュ効率が配列が常に連結リストより優れているという意味ではない**ことに注意すべきです。データ構造の選択は特定のアプリケーション要件に依存すべきです。例えば、配列と連結リストの両方が「スタック」データ構造を実装できますが（次章で詳細説明）、それらは異なるシナリオに適しています。</p>
+<ul>
+<li>アルゴリズム問題では、より高い操作効率とランダムアクセス機能を提供するため、配列に基づくスタックを選択する傾向があります。唯一のコストは配列に対して一定量のメモリ空間を事前に割り当てる必要があることです。</li>
+<li>データ量が非常に大きく、高度に動的で、スタックの予想サイズを推定するのが困難な場合、連結リストに基づくスタックがより良い選択です。連結リストは大量のデータをメモリの異なる部分に分散でき、配列拡張の追加オーバーヘッドを回避できます。</li>
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+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 重要な復習
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#2-q-a" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; Q &amp; A
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
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+<h1 id="45">4.5 &nbsp; まとめ<a class="headerlink" href="#45" title="Permanent link">&para;</a></h1>
+<h3 id="1">1. &nbsp; 重要な復習<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<ul>
+<li>配列と連結リストは2つの基本的なデータ構造であり、コンピュータメモリにおける2つの格納方法を表しています：連続空間格納と非連続空間格納です。それらの特性は互いに補完し合います。</li>
+<li>配列はランダムアクセスをサポートし、使用するメモリが少ない一方で、要素の挿入と削除は非効率的で、初期化後の長さが固定されています。</li>
+<li>連結リストは参照（ポインタ）の変更によって効率的なノードの挿入と削除を実装し、長さを柔軟に調整できますが、ノードアクセス効率が低く、より多くのメモリを消費します。</li>
+<li>連結リストの一般的な種類には、単方向連結リスト、循環連結リスト、双方向連結リストがあり、それぞれに独自の応用シナリオがあります。</li>
+<li>リストは要素の順序付けられたコレクションで、追加、削除、変更をサポートし、通常は動的配列に基づいて実装され、配列の利点を保持しながら柔軟な長さ調整を可能にします。</li>
+<li>リストの出現により配列の実用性が大幅に向上しましたが、一部のメモリ空間の無駄につながる可能性があります。</li>
+<li>プログラム実行中、データは主にメモリに格納されます。配列はより高いメモリ空間効率を提供し、連結リストはメモリ使用においてより柔軟です。</li>
+<li>キャッシュは、キャッシュライン、先読み、空間的局所性、時間的局所性などのメカニズムを通じてCPUに高速データアクセスを提供し、プログラム実行効率を大幅に向上させます。</li>
+<li>より高いキャッシュヒット率により、配列は一般的に連結リストよりも効率的です。データ構造を選択する際は、特定のニーズとシナリオに基づいて適切な選択をすべきです。</li>
+</ul>
+<h3 id="2-q-a">2. &nbsp; Q &amp; A<a class="headerlink" href="#2-q-a" title="Permanent link">&para;</a></h3>
+<p><strong>Q</strong>：配列をスタックに格納するかヒープに格納するかは、時間と空間効率に影響しますか？</p>
+<p>スタックとヒープの両方に格納される配列は連続したメモリ空間に格納され、データ操作効率は本質的に同じです。しかし、スタックとヒープには独自の特性があり、以下の違いが生じます。</p>
+<ol>
+<li>割り当てと解放効率：スタックはより小さなメモリブロックで、コンパイラによって自動的に割り当てられます。ヒープメモリは比較的大きく、コードで動的に割り当てることができ、断片化しやすいです。したがって、ヒープでの割り当てと解放操作は一般的にスタックよりも遅くなります。</li>
+<li>サイズ制限：スタックメモリは比較的小さく、ヒープサイズは一般的に利用可能なメモリによって制限されます。したがって、ヒープは大きな配列の格納により適しています。</li>
+<li>柔軟性：スタック上の配列のサイズはコンパイル時に決定される必要がありますが、ヒープ上の配列のサイズは実行時に動的に決定できます。</li>
+</ol>
+<p><strong>Q</strong>：なぜ配列は同じ型の要素を必要とし、連結リストは同じ型の要素を強調しないのですか？</p>
+<p>連結リストは参照（ポインタ）によって接続されたノードで構成され、各ノードはint、double、string、objectなど、異なる型のデータを格納できます。</p>
+<p>対照的に、配列要素は同じ型である必要があり、これにより対応する要素位置にアクセスするためのオフセットを計算できます。例えば、intとlong型の両方を含む配列で、単一要素がそれぞれ4バイトと8バイトを占有する場合、配列に2つの異なる長さの要素が含まれているため、以下の式を使用してオフセットを計算できません。</p>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="c1"># 要素メモリアドレス = 配列メモリアドレス + 要素長 * 要素インデックス</span>
+</code></pre></div>
+<p><strong>Q</strong>：ノードを削除した後、<code>P.next</code>を<code>None</code>に設定する必要がありますか？</p>
+<p><code>P.next</code>を変更しなくても問題ありません。連結リストの観点から、ヘッドノードからテールノードまでの巡回で<code>P</code>に遭遇することはもうありません。これは、ノード<code>P</code>がリストから効果的に削除されたことを意味し、<code>P</code>が指す場所はもはやリストに影響しません。</p>
+<p>ガベージコレクションの観点から、Java、Python、Goなどの自動ガベージコレクションメカニズムを持つ言語では、ノード<code>P</code>が収集されるかどうかは、それを指す参照がまだあるかどうかに依存し、<code>P.next</code>の値には依存しません。CやC++などの言語では、ノードのメモリを手動で解放する必要があります。</p>
+<p><strong>Q</strong>：連結リストでは、挿入と削除操作の時間計算量は<code>O(1)</code>です。しかし、挿入や削除前の要素検索には<code>O(n)</code>時間がかかるので、なぜ時間計算量は<code>O(n)</code>ではないのですか？</p>
+<p>要素を最初に検索してから削除する場合、時間計算量は確かに<code>O(n)</code>です。しかし、連結リストの挿入と削除における<code>O(1)</code>の利点は他のアプリケーションで実現できます。例えば、連結リストを使用した両端キューの実装では、常にヘッドとテールノードを指すポインタを維持し、各挿入と削除操作を<code>O(1)</code>にします。</p>
+<p><strong>Q</strong>：「連結リストの定義と格納方法」の図で、薄青色の格納ノードは単一のメモリアドレスを占有しますか、それともノード値と半分を共有しますか？</p>
+<p>図は単なる定性的な表現であり、定量的分析は特定の状況に依存します。</p>
+<ul>
+<li>異なる型のノード値は異なる量の空間を占有します。例えば、int、long、double、オブジェクトインスタンスです。</li>
+<li>ポインタ変数によって占有されるメモリ空間は、使用されるオペレーティングシステムとコンパイル環境に依存し、通常8バイトまたは4バイトです。</li>
+</ul>
+<p><strong>Q</strong>：リストの末尾への要素追加は常に<code>O(1)</code>ですか？</p>
+<p>要素を追加することでリスト長を超える場合、リストは最初に拡張される必要があります。システムは新しいメモリブロックを要求し、元のリストのすべての要素を移動するため、この場合の時間計算量は<code>O(n)</code>になります。</p>
+<p><strong>Q</strong>：「リストの出現により配列の実用性が大幅に向上しましたが、一部のメモリ空間の無駄につながる可能性があります」という文は、容量、長さ、拡張係数などの追加変数によって占有されるメモリを指していますか？</p>
+<p>ここでの空間の無駄は主に2つの側面を指します：一方で、リストは初期長で設定されますが、常に必要とは限りません。他方で、頻繁な拡張を防ぐため、拡張は通常<span class="arithmatex">\(\times 1.5\)</span>などの係数で乗算されます。これにより多くの空きスロットが生まれ、通常は完全に埋めることができません。</p>
+<p><strong>Q</strong>：Pythonで<code>n = [1, 2, 3]</code>を初期化した後、これら3つの要素のアドレスは連続していますが、<code>m = [2, 1, 3]</code>を初期化すると、各要素の<code>id</code>は連続していないが<code>n</code>のものと同一です。これらの要素のアドレスが連続していない場合、<code>m</code>はまだ配列ですか？</p>
+<p>リスト要素を連結リストノード<code>n = [n1, n2, n3, n4, n5]</code>に置き換える場合、これら5つのノードオブジェクトも通常メモリ全体に分散しています。しかし、リストインデックスが与えられれば、<code>O(1)</code>時間でノードのメモリアドレスにアクセスでき、対応するノードにアクセスできます。これは、配列がノード自体ではなく、ノードへの参照を格納するためです。</p>
+<p>多くの言語とは異なり、Pythonでは数値もオブジェクトとしてラップされ、リストは数値自体ではなく、これらの数値への参照を格納します。したがって、2つの配列の同じ数値が同じ<code>id</code>を持ち、これらの数値のメモリアドレスは連続である必要がないことがわかります。</p>
+<p><strong>Q</strong>：C++ STLの<code>std::list</code>はすでに双方向連結リストを実装していますが、一部のアルゴリズム書籍では直接使用していないようです。何か制限がありますか？</p>
+<p>一方で、アルゴリズムを実装する際は配列を使用することを好み、必要な場合のみ連結リストを使用します。主に2つの理由があります。</p>
+<ul>
+<li>空間オーバーヘッド：各要素に2つの追加ポインタ（前の要素用と次の要素用）が必要なため、<code>std::list</code>は通常<code>std::vector</code>よりも多くの空間を占有します。</li>
+<li>キャッシュ非友好的：データが連続して格納されていないため、<code>std::list</code>はキャッシュ利用率が低くなります。一般的に、<code>std::vector</code>の方がパフォーマンスが優れています。</li>
+</ul>
+<p>他方で、連結リストは主に二分木とグラフに必要です。スタックとキューは、連結リストではなく、プログラミング言語の<code>stack</code>と<code>queue</code>クラスを使用して実装されることが多いです。</p>
+<p><strong>Q</strong>：リスト<code>res = [0] * self.size()</code>を初期化すると、<code>res</code>の各要素は同じアドレスを参照しますか？</p>
+<p>いいえ。しかし、この問題は二次元配列で発生します。例えば、二次元リスト<code>res = [[0]] * self.size()</code>を初期化すると、同じリスト<code>[0]</code>を複数回参照することになります。</p>
+<p><strong>Q</strong>：ノードを削除する際、その後続ノードへの参照を断つ必要がありますか？</p>
+<p>データ構造とアルゴリズム（問題解決）の観点から、プログラムのロジックが正しい限り、リンクを断たなくても問題ありません。標準ライブラリの観点から、リンクを断つ方が安全で論理的に明確です。リンクを断たず、削除されたノードが適切にリサイクルされない場合、後続ノードのメモリのリサイクルに影響を与える可能性があります。</p>
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+  
+  <span class="md-ellipsis">
+    0.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_introduction/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1311" class="md-nav__link">
+    <span class="md-ellipsis">
+      13.1.1 &nbsp; 試行と後退
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1312" class="md-nav__link">
+    <span class="md-ellipsis">
+      13.1.2 &nbsp; 剪定
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1313" class="md-nav__link">
+    <span class="md-ellipsis">
+      13.1.3 &nbsp; フレームワークコード
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1314" class="md-nav__link">
+    <span class="md-ellipsis">
+      13.1.4 &nbsp; よく使われる用語
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1315" class="md-nav__link">
+    <span class="md-ellipsis">
+      13.1.5 &nbsp; 長所と限界
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1316" class="md-nav__link">
+    <span class="md-ellipsis">
+      13.1.6 &nbsp; バックトラッキングの典型的な例題
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
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+  
+
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+    </li>
+  
+
+              
+            
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+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
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+  
+
+              
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+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
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+
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+
+              
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+  
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+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
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+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
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+    </li>
+  
+
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+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
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+        
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+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
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+
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+      目次
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+      
+        <li class="md-nav__item">
+  <a href="#1311" class="md-nav__link">
+    <span class="md-ellipsis">
+      13.1.1 &nbsp; 試行と後退
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1312" class="md-nav__link">
+    <span class="md-ellipsis">
+      13.1.2 &nbsp; 剪定
+    </span>
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+  
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+      
+        <li class="md-nav__item">
+  <a href="#1313" class="md-nav__link">
+    <span class="md-ellipsis">
+      13.1.3 &nbsp; フレームワークコード
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1314" class="md-nav__link">
+    <span class="md-ellipsis">
+      13.1.4 &nbsp; よく使われる用語
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1315" class="md-nav__link">
+    <span class="md-ellipsis">
+      13.1.5 &nbsp; 長所と限界
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1316" class="md-nav__link">
+    <span class="md-ellipsis">
+      13.1.6 &nbsp; バックトラッキングの典型的な例題
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
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+      
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
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+<h1 id="131">13.1 &nbsp; バックトラッキングアルゴリズム<a class="headerlink" href="#131" title="Permanent link">&para;</a></h1>
+<p><u>バックトラッキングアルゴリズム</u>は全数探索によって問題を解決する方法です。その核心概念は、初期状態から開始してすべての可能な解を総当たりで探索することです。アルゴリズムは正しいものを記録し、解が見つかるか、すべての可能な解が試されたが解が見つからないまで続けます。</p>
+<p>バックトラッキングは通常「深さ優先探索」を使用して解空間を走査します。「二分木」の章で、前順、中順、後順走査はすべて深さ優先探索であることを述べました。次に、前順走査を使用してバックトラッキング問題を解決し、アルゴリズムの動作を段階的に理解していきます。</p>
+<div class="admonition question">
+<p class="admonition-title">例1</p>
+<p>二分木が与えられた場合、値が <span class="arithmatex">\(7\)</span> のすべてのノードを検索して記録し、リストで返してください。</p>
+</div>
+<p>この問題を解決するために、この木を前順で走査し、現在のノードの値が <span class="arithmatex">\(7\)</span> かどうかを確認します。そうであれば、ノードの値を結果リスト <code>res</code> に追加します。プロセスは以下の図に示されています：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:14"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><input id="__tabbed_1_14" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label><label for="__tabbed_1_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_i_compact.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">pre_order</span><span class="p">(</span><span class="n">root</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">):</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;前順走査：例一&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="k">if</span> <span class="n">root</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>        <span class="k">return</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="k">if</span> <span class="n">root</span><span class="o">.</span><span class="n">val</span> <span class="o">==</span> <span class="mi">7</span><span class="p">:</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>        <span class="c1"># 解を記録</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>        <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>    <span class="n">pre_order</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">left</span><span class="p">)</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>    <span class="n">pre_order</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_i_compact.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 前順走査：例１ */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">        </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">root</span><span class="p">);</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">);</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_i_compact.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 前順走査：例１ */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">        </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">root</span><span class="p">);</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">left</span><span class="p">);</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">right</span><span class="p">);</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_i_compact.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">preorder_traversal_i_compact</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">PreOrder</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_i_compact.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">preOrderI</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_i_compact.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">preOrder</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_i_compact.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">preOrder</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_i_compact.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">preOrder</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_i_compact.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">preOrder</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_i_compact.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">pre_order</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_i_compact.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">preOrder</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_i_compact.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">preOrder</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_i_compact.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">pre_order</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_i_compact.zig</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">preOrder</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p><a class="glightbox" href="../backtracking_algorithm.assets/preorder_find_nodes.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="前順走査でのノード検索" class="animation-figure" src="../backtracking_algorithm.assets/preorder_find_nodes.png" /></a></p>
+<p align="center"> 図 13-1 &nbsp; 前順走査でのノード検索 </p>
+
+<h2 id="1311">13.1.1 &nbsp; 試行と後退<a class="headerlink" href="#1311" title="Permanent link">&para;</a></h2>
+<p><strong>解空間を探索する際に「試行」と「後退」戦略を使用するため、バックトラッキングアルゴリズムと呼ばれます</strong>。探索中、満足のいく解を得るためにもはや進めない状態に遭遇するたびに、前の選択を取り消して前の状態に戻り、次の試行のために他の可能な選択を選択できるようにします。</p>
+<p>例1では、各ノードの訪問が「試行」を開始します。そして葉ノードを通過するか、<code>return</code> 文で親ノードに戻ることが「後退」を示唆します。</p>
+<p><strong>後退は単に関数の戻り値ではないことに注意してください</strong>。例1の問題を少し拡張して、それが何を意味するかを説明します。</p>
+<div class="admonition question">
+<p class="admonition-title">例2</p>
+<p>二分木で、値が <span class="arithmatex">\(7\)</span> のすべてのノードを検索し、すべてのマッチングノードについて、<strong>ルートノードからそのノードまでのパスを返してください</strong>。</p>
+</div>
+<p>例1のコードに基づいて、訪問したノードパスを記録するために <code>path</code> というリストを使用する必要があります。値が <span class="arithmatex">\(7\)</span> のノードに到達すると、<code>path</code> をコピーして結果リスト <code>res</code> に追加します。走査後、<code>res</code> にはすべての解が保持されます。コードは以下の通りです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:14"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><input id="__tabbed_2_14" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label><label for="__tabbed_2_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_ii_compact.py</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">pre_order</span><span class="p">(</span><span class="n">root</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">):</span>
+<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;前順走査：例二&quot;&quot;&quot;</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a>    <span class="k">if</span> <span class="n">root</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a>        <span class="k">return</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a>    <span class="c1"># 試行</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a>    <span class="n">path</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
+<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a>    <span class="k">if</span> <span class="n">root</span><span class="o">.</span><span class="n">val</span> <span class="o">==</span> <span class="mi">7</span><span class="p">:</span>
+<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a>        <span class="c1"># 解を記録</span>
+<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a>        <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">path</span><span class="p">))</span>
+<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a>    <span class="n">pre_order</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">left</span><span class="p">)</span>
+<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a>    <span class="n">pre_order</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>
+<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a>    <span class="c1"># 撤回</span>
+<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a>    <span class="n">path</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_ii_compact.cpp</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 前順走査：例２ */</span>
+<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">    </span><span class="c1">// 試行</span>
+<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">    </span><span class="n">path</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">root</span><span class="p">);</span>
+<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w">        </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">path</span><span class="p">);</span>
+<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">);</span>
+<a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="w">    </span><span class="c1">// 回退</span>
+<a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="w">    </span><span class="n">path</span><span class="p">.</span><span class="n">pop_back</span><span class="p">();</span>
+<a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_ii_compact.java</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 前順走査：例２ */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">    </span><span class="c1">// 試行</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">    </span><span class="n">path</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">root</span><span class="p">);</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w">        </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">(</span><span class="n">path</span><span class="p">));</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">left</span><span class="p">);</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">right</span><span class="p">);</span>
+<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="w">    </span><span class="c1">// 回退</span>
+<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="w">    </span><span class="n">path</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">path</span><span class="p">.</span><span class="na">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_ii_compact.cs</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">preorder_traversal_ii_compact</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">PreOrder</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_ii_compact.go</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">preOrderII</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_ii_compact.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">preOrder</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_ii_compact.js</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">preOrder</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_ii_compact.ts</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">preOrder</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_ii_compact.dart</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">preOrder</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_ii_compact.rs</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">pre_order</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_ii_compact.c</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">preOrder</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_ii_compact.kt</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">preOrder</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_ii_compact.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">pre_order</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_ii_compact.zig</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">preOrder</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>各「試行」で、現在のノードを <code>path</code> に追加することでパスを記録します。「後退」が必要なときはいつでも、<code>path</code> からノードをポップして**この失敗した試行前の状態を復元します**。</p>
+<p>以下の図に示すプロセスを観察することで、<strong>試行は「前進」のようで、後退は「元に戻す」のようです</strong>。後者のペアは、対応するものに対する逆操作と見なすことができます。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="3:11"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">&lt;1&gt;</label><label for="__tabbed_3_2">&lt;2&gt;</label><label for="__tabbed_3_3">&lt;3&gt;</label><label for="__tabbed_3_4">&lt;4&gt;</label><label for="__tabbed_3_5">&lt;5&gt;</label><label for="__tabbed_3_6">&lt;6&gt;</label><label for="__tabbed_3_7">&lt;7&gt;</label><label for="__tabbed_3_8">&lt;8&gt;</label><label for="__tabbed_3_9">&lt;9&gt;</label><label for="__tabbed_3_10">&lt;10&gt;</label><label for="__tabbed_3_11">&lt;11&gt;</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<p><a class="glightbox" href="../backtracking_algorithm.assets/preorder_find_paths_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="試行と後退" class="animation-figure" src="../backtracking_algorithm.assets/preorder_find_paths_step1.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../backtracking_algorithm.assets/preorder_find_paths_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="preorder_find_paths_step2" class="animation-figure" src="../backtracking_algorithm.assets/preorder_find_paths_step2.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../backtracking_algorithm.assets/preorder_find_paths_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="preorder_find_paths_step3" class="animation-figure" src="../backtracking_algorithm.assets/preorder_find_paths_step3.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../backtracking_algorithm.assets/preorder_find_paths_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="preorder_find_paths_step4" class="animation-figure" src="../backtracking_algorithm.assets/preorder_find_paths_step4.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../backtracking_algorithm.assets/preorder_find_paths_step5.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="preorder_find_paths_step5" class="animation-figure" src="../backtracking_algorithm.assets/preorder_find_paths_step5.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../backtracking_algorithm.assets/preorder_find_paths_step6.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="preorder_find_paths_step6" class="animation-figure" src="../backtracking_algorithm.assets/preorder_find_paths_step6.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../backtracking_algorithm.assets/preorder_find_paths_step7.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="preorder_find_paths_step7" class="animation-figure" src="../backtracking_algorithm.assets/preorder_find_paths_step7.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../backtracking_algorithm.assets/preorder_find_paths_step8.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="preorder_find_paths_step8" class="animation-figure" src="../backtracking_algorithm.assets/preorder_find_paths_step8.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../backtracking_algorithm.assets/preorder_find_paths_step9.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="preorder_find_paths_step9" class="animation-figure" src="../backtracking_algorithm.assets/preorder_find_paths_step9.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../backtracking_algorithm.assets/preorder_find_paths_step10.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="preorder_find_paths_step10" class="animation-figure" src="../backtracking_algorithm.assets/preorder_find_paths_step10.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../backtracking_algorithm.assets/preorder_find_paths_step11.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="preorder_find_paths_step11" class="animation-figure" src="../backtracking_algorithm.assets/preorder_find_paths_step11.png" /></a></p>
+</div>
+</div>
+</div>
+<p align="center"> 図 13-2 &nbsp; 試行と後退 </p>
+
+<h2 id="1312">13.1.2 &nbsp; 剪定<a class="headerlink" href="#1312" title="Permanent link">&para;</a></h2>
+<p>複雑なバックトラッキング問題は通常1つ以上の制約を含み、<strong>これらは「剪定」によく使用されます</strong>。</p>
+<div class="admonition question">
+<p class="admonition-title">例3</p>
+<p>二分木で、値が <span class="arithmatex">\(7\)</span> のすべてのノードを検索し、ルートからこれらのノードまでのパスを返してください。<strong>ただし、パスには値が <span class="arithmatex">\(3\)</span> のノードを含まないという制限があります</strong>。</p>
+</div>
+<p>上記の制約を満たすために、<strong>剪定操作を追加する必要があります</strong>：検索プロセス中に、値が <span class="arithmatex">\(3\)</span> のノードに遭遇した場合、そのパスを通じてさらに検索することを即座に中止します。コードは以下の通りです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="4:14"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><input id="__tabbed_4_6" name="__tabbed_4" type="radio" /><input id="__tabbed_4_7" name="__tabbed_4" type="radio" /><input id="__tabbed_4_8" name="__tabbed_4" type="radio" /><input id="__tabbed_4_9" name="__tabbed_4" type="radio" /><input id="__tabbed_4_10" name="__tabbed_4" type="radio" /><input id="__tabbed_4_11" name="__tabbed_4" type="radio" /><input id="__tabbed_4_12" name="__tabbed_4" type="radio" /><input id="__tabbed_4_13" name="__tabbed_4" type="radio" /><input id="__tabbed_4_14" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">Python</label><label for="__tabbed_4_2">C++</label><label for="__tabbed_4_3">Java</label><label for="__tabbed_4_4">C#</label><label for="__tabbed_4_5">Go</label><label for="__tabbed_4_6">Swift</label><label for="__tabbed_4_7">JS</label><label for="__tabbed_4_8">TS</label><label for="__tabbed_4_9">Dart</label><label for="__tabbed_4_10">Rust</label><label for="__tabbed_4_11">C</label><label for="__tabbed_4_12">Kotlin</label><label for="__tabbed_4_13">Ruby</label><label for="__tabbed_4_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_iii_compact.py</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">pre_order</span><span class="p">(</span><span class="n">root</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">):</span>
+<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;前順走査：例三&quot;&quot;&quot;</span>
+<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a>    <span class="c1"># 枝刈り</span>
+<a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a>    <span class="k">if</span> <span class="n">root</span> <span class="ow">is</span> <span class="kc">None</span> <span class="ow">or</span> <span class="n">root</span><span class="o">.</span><span class="n">val</span> <span class="o">==</span> <span class="mi">3</span><span class="p">:</span>
+<a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a>        <span class="k">return</span>
+<a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a>    <span class="c1"># 試行</span>
+<a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a>    <span class="n">path</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
+<a id="__codelineno-28-8" name="__codelineno-28-8" href="#__codelineno-28-8"></a>    <span class="k">if</span> <span class="n">root</span><span class="o">.</span><span class="n">val</span> <span class="o">==</span> <span class="mi">7</span><span class="p">:</span>
+<a id="__codelineno-28-9" name="__codelineno-28-9" href="#__codelineno-28-9"></a>        <span class="c1"># 解を記録</span>
+<a id="__codelineno-28-10" name="__codelineno-28-10" href="#__codelineno-28-10"></a>        <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">path</span><span class="p">))</span>
+<a id="__codelineno-28-11" name="__codelineno-28-11" href="#__codelineno-28-11"></a>    <span class="n">pre_order</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">left</span><span class="p">)</span>
+<a id="__codelineno-28-12" name="__codelineno-28-12" href="#__codelineno-28-12"></a>    <span class="n">pre_order</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>
+<a id="__codelineno-28-13" name="__codelineno-28-13" href="#__codelineno-28-13"></a>    <span class="c1"># 撤回</span>
+<a id="__codelineno-28-14" name="__codelineno-28-14" href="#__codelineno-28-14"></a>    <span class="n">path</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_iii_compact.cpp</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="cm">/* 前順走査：例３ */</span>
+<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w">    </span><span class="c1">// 剪定</span>
+<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">root</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">3</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="w">    </span><span class="c1">// 試行</span>
+<a id="__codelineno-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a><span class="w">    </span><span class="n">path</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">root</span><span class="p">);</span>
+<a id="__codelineno-29-9" name="__codelineno-29-9" href="#__codelineno-29-9"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-10" name="__codelineno-29-10" href="#__codelineno-29-10"></a><span class="w">        </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-29-11" name="__codelineno-29-11" href="#__codelineno-29-11"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">path</span><span class="p">);</span>
+<a id="__codelineno-29-12" name="__codelineno-29-12" href="#__codelineno-29-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-13" name="__codelineno-29-13" href="#__codelineno-29-13"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">);</span>
+<a id="__codelineno-29-14" name="__codelineno-29-14" href="#__codelineno-29-14"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-29-15" name="__codelineno-29-15" href="#__codelineno-29-15"></a><span class="w">    </span><span class="c1">// 回退</span>
+<a id="__codelineno-29-16" name="__codelineno-29-16" href="#__codelineno-29-16"></a><span class="w">    </span><span class="n">path</span><span class="p">.</span><span class="n">pop_back</span><span class="p">();</span>
+<a id="__codelineno-29-17" name="__codelineno-29-17" href="#__codelineno-29-17"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_iii_compact.java</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* 前順走査：例３ */</span>
+<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w">    </span><span class="c1">// 剪定</span>
+<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">root</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">3</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a><span class="w">    </span><span class="c1">// 試行</span>
+<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a><span class="w">    </span><span class="n">path</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">root</span><span class="p">);</span>
+<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-10" name="__codelineno-30-10" href="#__codelineno-30-10"></a><span class="w">        </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-30-11" name="__codelineno-30-11" href="#__codelineno-30-11"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">(</span><span class="n">path</span><span class="p">));</span>
+<a id="__codelineno-30-12" name="__codelineno-30-12" href="#__codelineno-30-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-13" name="__codelineno-30-13" href="#__codelineno-30-13"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">left</span><span class="p">);</span>
+<a id="__codelineno-30-14" name="__codelineno-30-14" href="#__codelineno-30-14"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">right</span><span class="p">);</span>
+<a id="__codelineno-30-15" name="__codelineno-30-15" href="#__codelineno-30-15"></a><span class="w">    </span><span class="c1">// 回退</span>
+<a id="__codelineno-30-16" name="__codelineno-30-16" href="#__codelineno-30-16"></a><span class="w">    </span><span class="n">path</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">path</span><span class="p">.</span><span class="na">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-30-17" name="__codelineno-30-17" href="#__codelineno-30-17"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_iii_compact.cs</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">preorder_traversal_iii_compact</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">PreOrder</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_iii_compact.go</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">preOrderIII</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_iii_compact.swift</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">preOrder</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_iii_compact.js</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">preOrder</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_iii_compact.ts</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">preOrder</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_iii_compact.dart</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">preOrder</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_iii_compact.rs</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">pre_order</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_iii_compact.c</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">preOrder</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_iii_compact.kt</span><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">preOrder</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_iii_compact.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">pre_order</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_iii_compact.zig</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">preOrder</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>「剪定」は非常に生き生きとした名詞です。以下の図に示すように、検索プロセスで、<strong>制約を満たさない検索分岐を「切り取り」ます</strong>。さらなる不要な試行を避け、検索効率を向上させます。</p>
+<p><a class="glightbox" href="../backtracking_algorithm.assets/preorder_find_constrained_paths.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="制約に基づく剪定" class="animation-figure" src="../backtracking_algorithm.assets/preorder_find_constrained_paths.png" /></a></p>
+<p align="center"> 図 13-3 &nbsp; 制約に基づく剪定 </p>
+
+<h2 id="1313">13.1.3 &nbsp; フレームワークコード<a class="headerlink" href="#1313" title="Permanent link">&para;</a></h2>
+<p>今度は、バックトラッキングから「試行、後退、剪定」の主要なフレームワークを抽出して、コードの汎用性を向上させてみましょう。</p>
+<p>以下のフレームワークコードでは、<code>state</code> は問題の現在の状態を表し、<code>choices</code> は現在の状態で利用可能な選択肢を表します：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="5:14"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><input id="__tabbed_5_7" name="__tabbed_5" type="radio" /><input id="__tabbed_5_8" name="__tabbed_5" type="radio" /><input id="__tabbed_5_9" name="__tabbed_5" type="radio" /><input id="__tabbed_5_10" name="__tabbed_5" type="radio" /><input id="__tabbed_5_11" name="__tabbed_5" type="radio" /><input id="__tabbed_5_12" name="__tabbed_5" type="radio" /><input id="__tabbed_5_13" name="__tabbed_5" type="radio" /><input id="__tabbed_5_14" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">Python</label><label for="__tabbed_5_2">C++</label><label for="__tabbed_5_3">Java</label><label for="__tabbed_5_4">C#</label><label for="__tabbed_5_5">Go</label><label for="__tabbed_5_6">Swift</label><label for="__tabbed_5_7">JS</label><label for="__tabbed_5_8">TS</label><label for="__tabbed_5_9">Dart</label><label for="__tabbed_5_10">Rust</label><label for="__tabbed_5_11">C</label><label for="__tabbed_5_12">Kotlin</label><label for="__tabbed_5_13">Ruby</label><label for="__tabbed_5_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="n">State</span><span class="p">,</span> <span class="n">choices</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">choice</span><span class="p">],</span> <span class="n">res</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">state</span><span class="p">]):</span>
+<a id="__codelineno-42-2" name="__codelineno-42-2" href="#__codelineno-42-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;バックトラッキングアルゴリズムフレームワーク&quot;&quot;&quot;</span>
+<a id="__codelineno-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></a>    <span class="c1"># 解かどうかを確認</span>
+<a id="__codelineno-42-4" name="__codelineno-42-4" href="#__codelineno-42-4"></a>    <span class="k">if</span> <span class="n">is_solution</span><span class="p">(</span><span class="n">state</span><span class="p">):</span>
+<a id="__codelineno-42-5" name="__codelineno-42-5" href="#__codelineno-42-5"></a>        <span class="c1"># 解を記録</span>
+<a id="__codelineno-42-6" name="__codelineno-42-6" href="#__codelineno-42-6"></a>        <span class="n">record_solution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-42-7" name="__codelineno-42-7" href="#__codelineno-42-7"></a>        <span class="c1"># 検索を停止</span>
+<a id="__codelineno-42-8" name="__codelineno-42-8" href="#__codelineno-42-8"></a>        <span class="k">return</span>
+<a id="__codelineno-42-9" name="__codelineno-42-9" href="#__codelineno-42-9"></a>    <span class="c1"># すべての選択肢を反復</span>
+<a id="__codelineno-42-10" name="__codelineno-42-10" href="#__codelineno-42-10"></a>    <span class="k">for</span> <span class="n">choice</span> <span class="ow">in</span> <span class="n">choices</span><span class="p">:</span>
+<a id="__codelineno-42-11" name="__codelineno-42-11" href="#__codelineno-42-11"></a>        <span class="c1"># 剪定：選択肢が有効かどうかを確認</span>
+<a id="__codelineno-42-12" name="__codelineno-42-12" href="#__codelineno-42-12"></a>        <span class="k">if</span> <span class="n">is_valid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">choice</span><span class="p">):</span>
+<a id="__codelineno-42-13" name="__codelineno-42-13" href="#__codelineno-42-13"></a>            <span class="c1"># 試行：選択を行い、状態を更新</span>
+<a id="__codelineno-42-14" name="__codelineno-42-14" href="#__codelineno-42-14"></a>            <span class="n">make_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">choice</span><span class="p">)</span>
+<a id="__codelineno-42-15" name="__codelineno-42-15" href="#__codelineno-42-15"></a>            <span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">choices</span><span class="p">,</span> <span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-42-16" name="__codelineno-42-16" href="#__codelineno-42-16"></a>            <span class="c1"># 後退：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-42-17" name="__codelineno-42-17" href="#__codelineno-42-17"></a>            <span class="n">undo_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">choice</span><span class="p">)</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="cm">/* バックトラッキングアルゴリズムフレームワーク */</span>
+<a id="__codelineno-43-2" name="__codelineno-43-2" href="#__codelineno-43-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">State</span><span class="w"> </span><span class="o">*</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">Choice</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">State</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-3" name="__codelineno-43-3" href="#__codelineno-43-3"></a><span class="w">    </span><span class="c1">// 解かどうかを確認</span>
+<a id="__codelineno-43-4" name="__codelineno-43-4" href="#__codelineno-43-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-5" name="__codelineno-43-5" href="#__codelineno-43-5"></a><span class="w">        </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-43-6" name="__codelineno-43-6" href="#__codelineno-43-6"></a><span class="w">        </span><span class="n">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-43-7" name="__codelineno-43-7" href="#__codelineno-43-7"></a><span class="w">        </span><span class="c1">// 検索を停止</span>
+<a id="__codelineno-43-8" name="__codelineno-43-8" href="#__codelineno-43-8"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-43-9" name="__codelineno-43-9" href="#__codelineno-43-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-43-10" name="__codelineno-43-10" href="#__codelineno-43-10"></a><span class="w">    </span><span class="c1">// すべての選択肢を反復</span>
+<a id="__codelineno-43-11" name="__codelineno-43-11" href="#__codelineno-43-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Choice</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-12" name="__codelineno-43-12" href="#__codelineno-43-12"></a><span class="w">        </span><span class="c1">// 剪定：選択肢が有効かどうかを確認</span>
+<a id="__codelineno-43-13" name="__codelineno-43-13" href="#__codelineno-43-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-14" name="__codelineno-43-14" href="#__codelineno-43-14"></a><span class="w">            </span><span class="c1">// 試行：選択を行い、状態を更新</span>
+<a id="__codelineno-43-15" name="__codelineno-43-15" href="#__codelineno-43-15"></a><span class="w">            </span><span class="n">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
+<a id="__codelineno-43-16" name="__codelineno-43-16" href="#__codelineno-43-16"></a><span class="w">            </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-43-17" name="__codelineno-43-17" href="#__codelineno-43-17"></a><span class="w">            </span><span class="c1">// 後退：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-43-18" name="__codelineno-43-18" href="#__codelineno-43-18"></a><span class="w">            </span><span class="n">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
+<a id="__codelineno-43-19" name="__codelineno-43-19" href="#__codelineno-43-19"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-43-20" name="__codelineno-43-20" href="#__codelineno-43-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-43-21" name="__codelineno-43-21" href="#__codelineno-43-21"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="cm">/* バックトラッキングアルゴリズムフレームワーク */</span>
+<a id="__codelineno-44-2" name="__codelineno-44-2" href="#__codelineno-44-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">State</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Choice</span><span class="o">&gt;</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">State</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-3" name="__codelineno-44-3" href="#__codelineno-44-3"></a><span class="w">    </span><span class="c1">// 解かどうかを確認</span>
+<a id="__codelineno-44-4" name="__codelineno-44-4" href="#__codelineno-44-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-5" name="__codelineno-44-5" href="#__codelineno-44-5"></a><span class="w">        </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-44-6" name="__codelineno-44-6" href="#__codelineno-44-6"></a><span class="w">        </span><span class="n">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-44-7" name="__codelineno-44-7" href="#__codelineno-44-7"></a><span class="w">        </span><span class="c1">// 検索を停止</span>
+<a id="__codelineno-44-8" name="__codelineno-44-8" href="#__codelineno-44-8"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-44-9" name="__codelineno-44-9" href="#__codelineno-44-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-44-10" name="__codelineno-44-10" href="#__codelineno-44-10"></a><span class="w">    </span><span class="c1">// すべての選択肢を反復</span>
+<a id="__codelineno-44-11" name="__codelineno-44-11" href="#__codelineno-44-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Choice</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-12" name="__codelineno-44-12" href="#__codelineno-44-12"></a><span class="w">        </span><span class="c1">// 剪定：選択肢が有効かどうかを確認</span>
+<a id="__codelineno-44-13" name="__codelineno-44-13" href="#__codelineno-44-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-14" name="__codelineno-44-14" href="#__codelineno-44-14"></a><span class="w">            </span><span class="c1">// 試行：選択を行い、状態を更新</span>
+<a id="__codelineno-44-15" name="__codelineno-44-15" href="#__codelineno-44-15"></a><span class="w">            </span><span class="n">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
+<a id="__codelineno-44-16" name="__codelineno-44-16" href="#__codelineno-44-16"></a><span class="w">            </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-44-17" name="__codelineno-44-17" href="#__codelineno-44-17"></a><span class="w">            </span><span class="c1">// 後退：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-44-18" name="__codelineno-44-18" href="#__codelineno-44-18"></a><span class="w">            </span><span class="n">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
+<a id="__codelineno-44-19" name="__codelineno-44-19" href="#__codelineno-44-19"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-44-20" name="__codelineno-44-20" href="#__codelineno-44-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-44-21" name="__codelineno-44-21" href="#__codelineno-44-21"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="cm">/* バックトラッキングアルゴリズムフレームワーク */</span>
+<a id="__codelineno-45-2" name="__codelineno-45-2" href="#__codelineno-45-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">Backtrack</span><span class="p">(</span><span class="n">State</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Choice</span><span class="o">&gt;</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">State</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-3" name="__codelineno-45-3" href="#__codelineno-45-3"></a><span class="w">    </span><span class="c1">// 解かどうかを確認</span>
+<a id="__codelineno-45-4" name="__codelineno-45-4" href="#__codelineno-45-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">IsSolution</span><span class="p">(</span><span class="n">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-5" name="__codelineno-45-5" href="#__codelineno-45-5"></a><span class="w">        </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-45-6" name="__codelineno-45-6" href="#__codelineno-45-6"></a><span class="w">        </span><span class="n">RecordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-45-7" name="__codelineno-45-7" href="#__codelineno-45-7"></a><span class="w">        </span><span class="c1">// 検索を停止</span>
+<a id="__codelineno-45-8" name="__codelineno-45-8" href="#__codelineno-45-8"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-45-9" name="__codelineno-45-9" href="#__codelineno-45-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-45-10" name="__codelineno-45-10" href="#__codelineno-45-10"></a><span class="w">    </span><span class="c1">// すべての選択肢を反復</span>
+<a id="__codelineno-45-11" name="__codelineno-45-11" href="#__codelineno-45-11"></a><span class="w">    </span><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="n">Choice</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-12" name="__codelineno-45-12" href="#__codelineno-45-12"></a><span class="w">        </span><span class="c1">// 剪定：選択肢が有効かどうかを確認</span>
+<a id="__codelineno-45-13" name="__codelineno-45-13" href="#__codelineno-45-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">IsValid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-14" name="__codelineno-45-14" href="#__codelineno-45-14"></a><span class="w">            </span><span class="c1">// 試行：選択を行い、状態を更新</span>
+<a id="__codelineno-45-15" name="__codelineno-45-15" href="#__codelineno-45-15"></a><span class="w">            </span><span class="n">MakeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
+<a id="__codelineno-45-16" name="__codelineno-45-16" href="#__codelineno-45-16"></a><span class="w">            </span><span class="n">Backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-45-17" name="__codelineno-45-17" href="#__codelineno-45-17"></a><span class="w">            </span><span class="c1">// 後退：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-45-18" name="__codelineno-45-18" href="#__codelineno-45-18"></a><span class="w">            </span><span class="n">UndoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
+<a id="__codelineno-45-19" name="__codelineno-45-19" href="#__codelineno-45-19"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-45-20" name="__codelineno-45-20" href="#__codelineno-45-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-45-21" name="__codelineno-45-21" href="#__codelineno-45-21"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="cm">/* バックトラッキングアルゴリズムフレームワーク */</span>
+<a id="__codelineno-46-2" name="__codelineno-46-2" href="#__codelineno-46-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="w"> </span><span class="o">*</span><span class="nx">State</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="w"> </span><span class="p">[]</span><span class="nx">Choice</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="w"> </span><span class="o">*</span><span class="p">[]</span><span class="nx">State</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-3" name="__codelineno-46-3" href="#__codelineno-46-3"></a><span class="w">    </span><span class="c1">// 解かどうかを確認</span>
+<a id="__codelineno-46-4" name="__codelineno-46-4" href="#__codelineno-46-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">isSolution</span><span class="p">(</span><span class="nx">state</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-5" name="__codelineno-46-5" href="#__codelineno-46-5"></a><span class="w">        </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-46-6" name="__codelineno-46-6" href="#__codelineno-46-6"></a><span class="w">        </span><span class="nx">recordSolution</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span>
+<a id="__codelineno-46-7" name="__codelineno-46-7" href="#__codelineno-46-7"></a><span class="w">        </span><span class="c1">// 検索を停止</span>
+<a id="__codelineno-46-8" name="__codelineno-46-8" href="#__codelineno-46-8"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-46-9" name="__codelineno-46-9" href="#__codelineno-46-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-46-10" name="__codelineno-46-10" href="#__codelineno-46-10"></a><span class="w">    </span><span class="c1">// すべての選択肢を反復</span>
+<a id="__codelineno-46-11" name="__codelineno-46-11" href="#__codelineno-46-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">choices</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-12" name="__codelineno-46-12" href="#__codelineno-46-12"></a><span class="w">        </span><span class="c1">// 剪定：選択肢が有効かどうかを確認</span>
+<a id="__codelineno-46-13" name="__codelineno-46-13" href="#__codelineno-46-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="nx">isValid</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-14" name="__codelineno-46-14" href="#__codelineno-46-14"></a><span class="w">            </span><span class="c1">// 試行：選択を行い、状態を更新</span>
+<a id="__codelineno-46-15" name="__codelineno-46-15" href="#__codelineno-46-15"></a><span class="w">            </span><span class="nx">makeChoice</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">)</span>
+<a id="__codelineno-46-16" name="__codelineno-46-16" href="#__codelineno-46-16"></a><span class="w">            </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span>
+<a id="__codelineno-46-17" name="__codelineno-46-17" href="#__codelineno-46-17"></a><span class="w">            </span><span class="c1">// 後退：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-46-18" name="__codelineno-46-18" href="#__codelineno-46-18"></a><span class="w">            </span><span class="nx">undoChoice</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">)</span>
+<a id="__codelineno-46-19" name="__codelineno-46-19" href="#__codelineno-46-19"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-46-20" name="__codelineno-46-20" href="#__codelineno-46-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-46-21" name="__codelineno-46-21" href="#__codelineno-46-21"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="cm">/* バックトラッキングアルゴリズムフレームワーク */</span>
+<a id="__codelineno-47-2" name="__codelineno-47-2" href="#__codelineno-47-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="n">State</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="n">Choice</span><span class="p">],</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="kr">inout</span><span class="w"> </span><span class="p">[</span><span class="n">State</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-3" name="__codelineno-47-3" href="#__codelineno-47-3"></a><span class="w">    </span><span class="c1">// 解かどうかを確認</span>
+<a id="__codelineno-47-4" name="__codelineno-47-4" href="#__codelineno-47-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">state</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-5" name="__codelineno-47-5" href="#__codelineno-47-5"></a><span class="w">        </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-47-6" name="__codelineno-47-6" href="#__codelineno-47-6"></a><span class="w">        </span><span class="n">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-47-7" name="__codelineno-47-7" href="#__codelineno-47-7"></a><span class="w">        </span><span class="c1">// 検索を停止</span>
+<a id="__codelineno-47-8" name="__codelineno-47-8" href="#__codelineno-47-8"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-47-9" name="__codelineno-47-9" href="#__codelineno-47-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-47-10" name="__codelineno-47-10" href="#__codelineno-47-10"></a><span class="w">    </span><span class="c1">// すべての選択肢を反復</span>
+<a id="__codelineno-47-11" name="__codelineno-47-11" href="#__codelineno-47-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-12" name="__codelineno-47-12" href="#__codelineno-47-12"></a><span class="w">        </span><span class="c1">// 剪定：選択肢が有効かどうかを確認</span>
+<a id="__codelineno-47-13" name="__codelineno-47-13" href="#__codelineno-47-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">:</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-14" name="__codelineno-47-14" href="#__codelineno-47-14"></a><span class="w">            </span><span class="c1">// 試行：選択を行い、状態を更新</span>
+<a id="__codelineno-47-15" name="__codelineno-47-15" href="#__codelineno-47-15"></a><span class="w">            </span><span class="n">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">:</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span>
+<a id="__codelineno-47-16" name="__codelineno-47-16" href="#__codelineno-47-16"></a><span class="w">            </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-47-17" name="__codelineno-47-17" href="#__codelineno-47-17"></a><span class="w">            </span><span class="c1">// 後退：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-47-18" name="__codelineno-47-18" href="#__codelineno-47-18"></a><span class="w">            </span><span class="n">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="p">&amp;</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">:</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span>
+<a id="__codelineno-47-19" name="__codelineno-47-19" href="#__codelineno-47-19"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-47-20" name="__codelineno-47-20" href="#__codelineno-47-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-47-21" name="__codelineno-47-21" href="#__codelineno-47-21"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="cm">/* バックトラッキングアルゴリズムフレームワーク */</span>
+<a id="__codelineno-48-2" name="__codelineno-48-2" href="#__codelineno-48-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-3" name="__codelineno-48-3" href="#__codelineno-48-3"></a><span class="w">    </span><span class="c1">// 解かどうかを確認</span>
+<a id="__codelineno-48-4" name="__codelineno-48-4" href="#__codelineno-48-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">isSolution</span><span class="p">(</span><span class="nx">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-5" name="__codelineno-48-5" href="#__codelineno-48-5"></a><span class="w">        </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-48-6" name="__codelineno-48-6" href="#__codelineno-48-6"></a><span class="w">        </span><span class="nx">recordSolution</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-48-7" name="__codelineno-48-7" href="#__codelineno-48-7"></a><span class="w">        </span><span class="c1">// 検索を停止</span>
+<a id="__codelineno-48-8" name="__codelineno-48-8" href="#__codelineno-48-8"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-48-9" name="__codelineno-48-9" href="#__codelineno-48-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-48-10" name="__codelineno-48-10" href="#__codelineno-48-10"></a><span class="w">    </span><span class="c1">// すべての選択肢を反復</span>
+<a id="__codelineno-48-11" name="__codelineno-48-11" href="#__codelineno-48-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">choice</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-12" name="__codelineno-48-12" href="#__codelineno-48-12"></a><span class="w">        </span><span class="c1">// 剪定：選択肢が有効かどうかを確認</span>
+<a id="__codelineno-48-13" name="__codelineno-48-13" href="#__codelineno-48-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">isValid</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-14" name="__codelineno-48-14" href="#__codelineno-48-14"></a><span class="w">            </span><span class="c1">// 試行：選択を行い、状態を更新</span>
+<a id="__codelineno-48-15" name="__codelineno-48-15" href="#__codelineno-48-15"></a><span class="w">            </span><span class="nx">makeChoice</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">);</span>
+<a id="__codelineno-48-16" name="__codelineno-48-16" href="#__codelineno-48-16"></a><span class="w">            </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-48-17" name="__codelineno-48-17" href="#__codelineno-48-17"></a><span class="w">            </span><span class="c1">// 後退：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-48-18" name="__codelineno-48-18" href="#__codelineno-48-18"></a><span class="w">            </span><span class="nx">undoChoice</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">);</span>
+<a id="__codelineno-48-19" name="__codelineno-48-19" href="#__codelineno-48-19"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-48-20" name="__codelineno-48-20" href="#__codelineno-48-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-48-21" name="__codelineno-48-21" href="#__codelineno-48-21"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="cm">/* バックトラッキングアルゴリズムフレームワーク */</span>
+<a id="__codelineno-49-2" name="__codelineno-49-2" href="#__codelineno-49-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="o">:</span><span class="w"> </span><span class="kt">State</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="o">:</span><span class="w"> </span><span class="kt">Choice</span><span class="p">[],</span><span class="w"> </span><span class="nx">res</span><span class="o">:</span><span class="w"> </span><span class="kt">State</span><span class="p">[])</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-49-3" name="__codelineno-49-3" href="#__codelineno-49-3"></a><span class="w">    </span><span class="c1">// 解かどうかを確認</span>
+<a id="__codelineno-49-4" name="__codelineno-49-4" href="#__codelineno-49-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">isSolution</span><span class="p">(</span><span class="nx">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-49-5" name="__codelineno-49-5" href="#__codelineno-49-5"></a><span class="w">        </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-49-6" name="__codelineno-49-6" href="#__codelineno-49-6"></a><span class="w">        </span><span class="nx">recordSolution</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-49-7" name="__codelineno-49-7" href="#__codelineno-49-7"></a><span class="w">        </span><span class="c1">// 検索を停止</span>
+<a id="__codelineno-49-8" name="__codelineno-49-8" href="#__codelineno-49-8"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-49-9" name="__codelineno-49-9" href="#__codelineno-49-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-49-10" name="__codelineno-49-10" href="#__codelineno-49-10"></a><span class="w">    </span><span class="c1">// すべての選択肢を反復</span>
+<a id="__codelineno-49-11" name="__codelineno-49-11" href="#__codelineno-49-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">choice</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-49-12" name="__codelineno-49-12" href="#__codelineno-49-12"></a><span class="w">        </span><span class="c1">// 剪定：選択肢が有効かどうかを確認</span>
+<a id="__codelineno-49-13" name="__codelineno-49-13" href="#__codelineno-49-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">isValid</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-49-14" name="__codelineno-49-14" href="#__codelineno-49-14"></a><span class="w">            </span><span class="c1">// 試行：選択を行い、状態を更新</span>
+<a id="__codelineno-49-15" name="__codelineno-49-15" href="#__codelineno-49-15"></a><span class="w">            </span><span class="nx">makeChoice</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">);</span>
+<a id="__codelineno-49-16" name="__codelineno-49-16" href="#__codelineno-49-16"></a><span class="w">            </span><span class="nx">backtrack</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choices</span><span class="p">,</span><span class="w"> </span><span class="nx">res</span><span class="p">);</span>
+<a id="__codelineno-49-17" name="__codelineno-49-17" href="#__codelineno-49-17"></a><span class="w">            </span><span class="c1">// 後退：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-49-18" name="__codelineno-49-18" href="#__codelineno-49-18"></a><span class="w">            </span><span class="nx">undoChoice</span><span class="p">(</span><span class="nx">state</span><span class="p">,</span><span class="w"> </span><span class="nx">choice</span><span class="p">);</span>
+<a id="__codelineno-49-19" name="__codelineno-49-19" href="#__codelineno-49-19"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-49-20" name="__codelineno-49-20" href="#__codelineno-49-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-49-21" name="__codelineno-49-21" href="#__codelineno-49-21"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="cm">/* バックトラッキングアルゴリズムフレームワーク */</span>
+<a id="__codelineno-50-2" name="__codelineno-50-2" href="#__codelineno-50-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">backtrack</span><span class="p">(</span><span class="n">State</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Choice</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">State</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-50-3" name="__codelineno-50-3" href="#__codelineno-50-3"></a><span class="w">  </span><span class="c1">// 解かどうかを確認</span>
+<a id="__codelineno-50-4" name="__codelineno-50-4" href="#__codelineno-50-4"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-50-5" name="__codelineno-50-5" href="#__codelineno-50-5"></a><span class="w">    </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-50-6" name="__codelineno-50-6" href="#__codelineno-50-6"></a><span class="w">    </span><span class="n">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-50-7" name="__codelineno-50-7" href="#__codelineno-50-7"></a><span class="w">    </span><span class="c1">// 検索を停止</span>
+<a id="__codelineno-50-8" name="__codelineno-50-8" href="#__codelineno-50-8"></a><span class="w">    </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-50-9" name="__codelineno-50-9" href="#__codelineno-50-9"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-50-10" name="__codelineno-50-10" href="#__codelineno-50-10"></a><span class="w">  </span><span class="c1">// すべての選択肢を反復</span>
+<a id="__codelineno-50-11" name="__codelineno-50-11" href="#__codelineno-50-11"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Choice</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-50-12" name="__codelineno-50-12" href="#__codelineno-50-12"></a><span class="w">    </span><span class="c1">// 剪定：選択肢が有効かどうかを確認</span>
+<a id="__codelineno-50-13" name="__codelineno-50-13" href="#__codelineno-50-13"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-50-14" name="__codelineno-50-14" href="#__codelineno-50-14"></a><span class="w">      </span><span class="c1">// 試行：選択を行い、状態を更新</span>
+<a id="__codelineno-50-15" name="__codelineno-50-15" href="#__codelineno-50-15"></a><span class="w">      </span><span class="n">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
+<a id="__codelineno-50-16" name="__codelineno-50-16" href="#__codelineno-50-16"></a><span class="w">      </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-50-17" name="__codelineno-50-17" href="#__codelineno-50-17"></a><span class="w">      </span><span class="c1">// 後退：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-50-18" name="__codelineno-50-18" href="#__codelineno-50-18"></a><span class="w">      </span><span class="n">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
+<a id="__codelineno-50-19" name="__codelineno-50-19" href="#__codelineno-50-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-50-20" name="__codelineno-50-20" href="#__codelineno-50-20"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-50-21" name="__codelineno-50-21" href="#__codelineno-50-21"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="cm">/* バックトラッキングアルゴリズムフレームワーク */</span>
+<a id="__codelineno-51-2" name="__codelineno-51-2" href="#__codelineno-51-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="n">State</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nb">Vec</span><span class="o">&lt;</span><span class="n">Choice</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="kp">&amp;</span><span class="nc">mut</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="n">State</span><span class="o">&gt;</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-51-3" name="__codelineno-51-3" href="#__codelineno-51-3"></a><span class="w">    </span><span class="c1">// 解かどうかを確認</span>
+<a id="__codelineno-51-4" name="__codelineno-51-4" href="#__codelineno-51-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">is_solution</span><span class="p">(</span><span class="n">state</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-51-5" name="__codelineno-51-5" href="#__codelineno-51-5"></a><span class="w">        </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-51-6" name="__codelineno-51-6" href="#__codelineno-51-6"></a><span class="w">        </span><span class="n">record_solution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-51-7" name="__codelineno-51-7" href="#__codelineno-51-7"></a><span class="w">        </span><span class="c1">// 検索を停止</span>
+<a id="__codelineno-51-8" name="__codelineno-51-8" href="#__codelineno-51-8"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-51-9" name="__codelineno-51-9" href="#__codelineno-51-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-51-10" name="__codelineno-51-10" href="#__codelineno-51-10"></a><span class="w">    </span><span class="c1">// すべての選択肢を反復</span>
+<a id="__codelineno-51-11" name="__codelineno-51-11" href="#__codelineno-51-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-51-12" name="__codelineno-51-12" href="#__codelineno-51-12"></a><span class="w">        </span><span class="c1">// 剪定：選択肢が有効かどうかを確認</span>
+<a id="__codelineno-51-13" name="__codelineno-51-13" href="#__codelineno-51-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">is_valid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-51-14" name="__codelineno-51-14" href="#__codelineno-51-14"></a><span class="w">            </span><span class="c1">// 試行：選択を行い、状態を更新</span>
+<a id="__codelineno-51-15" name="__codelineno-51-15" href="#__codelineno-51-15"></a><span class="w">            </span><span class="n">make_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
+<a id="__codelineno-51-16" name="__codelineno-51-16" href="#__codelineno-51-16"></a><span class="w">            </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-51-17" name="__codelineno-51-17" href="#__codelineno-51-17"></a><span class="w">            </span><span class="c1">// 後退：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-51-18" name="__codelineno-51-18" href="#__codelineno-51-18"></a><span class="w">            </span><span class="n">undo_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
+<a id="__codelineno-51-19" name="__codelineno-51-19" href="#__codelineno-51-19"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-51-20" name="__codelineno-51-20" href="#__codelineno-51-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-51-21" name="__codelineno-51-21" href="#__codelineno-51-21"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="cm">/* バックトラッキングアルゴリズムフレームワーク */</span>
+<a id="__codelineno-52-2" name="__codelineno-52-2" href="#__codelineno-52-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">State</span><span class="w"> </span><span class="o">*</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">Choice</span><span class="w"> </span><span class="o">*</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">numChoices</span><span class="p">,</span><span class="w"> </span><span class="n">State</span><span class="w"> </span><span class="o">*</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">numRes</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-52-3" name="__codelineno-52-3" href="#__codelineno-52-3"></a><span class="w">    </span><span class="c1">// 解かどうかを確認</span>
+<a id="__codelineno-52-4" name="__codelineno-52-4" href="#__codelineno-52-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-52-5" name="__codelineno-52-5" href="#__codelineno-52-5"></a><span class="w">        </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-52-6" name="__codelineno-52-6" href="#__codelineno-52-6"></a><span class="w">        </span><span class="n">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">numRes</span><span class="p">);</span>
+<a id="__codelineno-52-7" name="__codelineno-52-7" href="#__codelineno-52-7"></a><span class="w">        </span><span class="c1">// 検索を停止</span>
+<a id="__codelineno-52-8" name="__codelineno-52-8" href="#__codelineno-52-8"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-52-9" name="__codelineno-52-9" href="#__codelineno-52-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-52-10" name="__codelineno-52-10" href="#__codelineno-52-10"></a><span class="w">    </span><span class="c1">// すべての選択肢を反復</span>
+<a id="__codelineno-52-11" name="__codelineno-52-11" href="#__codelineno-52-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">numChoices</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-52-12" name="__codelineno-52-12" href="#__codelineno-52-12"></a><span class="w">        </span><span class="c1">// 剪定：選択肢が有効かどうかを確認</span>
+<a id="__codelineno-52-13" name="__codelineno-52-13" href="#__codelineno-52-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-52-14" name="__codelineno-52-14" href="#__codelineno-52-14"></a><span class="w">            </span><span class="c1">// 試行：選択を行い、状態を更新</span>
+<a id="__codelineno-52-15" name="__codelineno-52-15" href="#__codelineno-52-15"></a><span class="w">            </span><span class="n">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
+<a id="__codelineno-52-16" name="__codelineno-52-16" href="#__codelineno-52-16"></a><span class="w">            </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">numChoices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">numRes</span><span class="p">);</span>
+<a id="__codelineno-52-17" name="__codelineno-52-17" href="#__codelineno-52-17"></a><span class="w">            </span><span class="c1">// 後退：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-52-18" name="__codelineno-52-18" href="#__codelineno-52-18"></a><span class="w">            </span><span class="n">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
+<a id="__codelineno-52-19" name="__codelineno-52-19" href="#__codelineno-52-19"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-52-20" name="__codelineno-52-20" href="#__codelineno-52-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-52-21" name="__codelineno-52-21" href="#__codelineno-52-21"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-53-1" name="__codelineno-53-1" href="#__codelineno-53-1"></a><span class="cm">/* バックトラッキングアルゴリズムフレームワーク */</span>
+<a id="__codelineno-53-2" name="__codelineno-53-2" href="#__codelineno-53-2"></a><span class="kd">fun</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">:</span><span class="w"> </span><span class="n">State?,</span><span class="w"> </span><span class="n">choices</span><span class="p">:</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Choice?&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">:</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">State?&gt;</span><span class="o">?</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-53-3" name="__codelineno-53-3" href="#__codelineno-53-3"></a><span class="w">    </span><span class="c1">// 解かどうかを確認</span>
+<a id="__codelineno-53-4" name="__codelineno-53-4" href="#__codelineno-53-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-53-5" name="__codelineno-53-5" href="#__codelineno-53-5"></a><span class="w">        </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-53-6" name="__codelineno-53-6" href="#__codelineno-53-6"></a><span class="w">        </span><span class="n">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-53-7" name="__codelineno-53-7" href="#__codelineno-53-7"></a><span class="w">        </span><span class="c1">// 検索を停止</span>
+<a id="__codelineno-53-8" name="__codelineno-53-8" href="#__codelineno-53-8"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-53-9" name="__codelineno-53-9" href="#__codelineno-53-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-53-10" name="__codelineno-53-10" href="#__codelineno-53-10"></a><span class="w">    </span><span class="c1">// すべての選択肢を反復</span>
+<a id="__codelineno-53-11" name="__codelineno-53-11" href="#__codelineno-53-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">choice</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-53-12" name="__codelineno-53-12" href="#__codelineno-53-12"></a><span class="w">        </span><span class="c1">// 剪定：選択肢が有効かどうかを確認</span>
+<a id="__codelineno-53-13" name="__codelineno-53-13" href="#__codelineno-53-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-53-14" name="__codelineno-53-14" href="#__codelineno-53-14"></a><span class="w">            </span><span class="c1">// 試行：選択を行い、状態を更新</span>
+<a id="__codelineno-53-15" name="__codelineno-53-15" href="#__codelineno-53-15"></a><span class="w">            </span><span class="n">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span>
+<a id="__codelineno-53-16" name="__codelineno-53-16" href="#__codelineno-53-16"></a><span class="w">            </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-53-17" name="__codelineno-53-17" href="#__codelineno-53-17"></a><span class="w">            </span><span class="c1">// 後退：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-53-18" name="__codelineno-53-18" href="#__codelineno-53-18"></a><span class="w">            </span><span class="n">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span>
+<a id="__codelineno-53-19" name="__codelineno-53-19" href="#__codelineno-53-19"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-53-20" name="__codelineno-53-20" href="#__codelineno-53-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-53-21" name="__codelineno-53-21" href="#__codelineno-53-21"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="c1">### バックトラッキングアルゴリズムフレームワーク ###</span>
+<a id="__codelineno-54-2" name="__codelineno-54-2" href="#__codelineno-54-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-54-3" name="__codelineno-54-3" href="#__codelineno-54-3"></a><span class="w">    </span><span class="c1"># 解かどうかを確認</span>
+<a id="__codelineno-54-4" name="__codelineno-54-4" href="#__codelineno-54-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">is_solution?</span><span class="p">(</span><span class="n">state</span><span class="p">)</span>
+<a id="__codelineno-54-5" name="__codelineno-54-5" href="#__codelineno-54-5"></a><span class="w">        </span><span class="c1"># 解を記録</span>
+<a id="__codelineno-54-6" name="__codelineno-54-6" href="#__codelineno-54-6"></a><span class="w">        </span><span class="n">record_solution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-54-7" name="__codelineno-54-7" href="#__codelineno-54-7"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-54-8" name="__codelineno-54-8" href="#__codelineno-54-8"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-54-9" name="__codelineno-54-9" href="#__codelineno-54-9"></a>
+<a id="__codelineno-54-10" name="__codelineno-54-10" href="#__codelineno-54-10"></a><span class="w">    </span><span class="c1"># すべての選択肢を反復</span>
+<a id="__codelineno-54-11" name="__codelineno-54-11" href="#__codelineno-54-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">choices</span>
+<a id="__codelineno-54-12" name="__codelineno-54-12" href="#__codelineno-54-12"></a><span class="w">        </span><span class="c1"># 剪定：選択肢が有効かどうかを確認</span>
+<a id="__codelineno-54-13" name="__codelineno-54-13" href="#__codelineno-54-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="n">is_valid?</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span>
+<a id="__codelineno-54-14" name="__codelineno-54-14" href="#__codelineno-54-14"></a><span class="w">            </span><span class="c1"># 試行：選択を行い、状態を更新</span>
+<a id="__codelineno-54-15" name="__codelineno-54-15" href="#__codelineno-54-15"></a><span class="w">            </span><span class="n">make_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span>
+<a id="__codelineno-54-16" name="__codelineno-54-16" href="#__codelineno-54-16"></a><span class="w">            </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-54-17" name="__codelineno-54-17" href="#__codelineno-54-17"></a><span class="w">            </span><span class="c1"># 後退：選択を取り消し、前の状態に戻す</span>
+<a id="__codelineno-54-18" name="__codelineno-54-18" href="#__codelineno-54-18"></a><span class="w">            </span><span class="n">undo_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span>
+<a id="__codelineno-54-19" name="__codelineno-54-19" href="#__codelineno-54-19"></a><span class="w">        </span><span class="k">end</span>
+<a id="__codelineno-54-20" name="__codelineno-54-20" href="#__codelineno-54-20"></a><span class="w">    </span><span class="k">end</span>
+<a id="__codelineno-54-21" name="__codelineno-54-21" href="#__codelineno-54-21"></a><span class="k">end</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-55-1" name="__codelineno-55-1" href="#__codelineno-55-1"></a>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>次に、フレームワークコードに基づいて例題 3 を解きます。状態 <code>state</code> はノードの走査経路を表し、選択肢 <code>choices</code> は現在ノードの左子ノードと右子ノード、結果 <code>res</code> は経路リストです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="6:14"><input checked="checked" id="__tabbed_6_1" name="__tabbed_6" type="radio" /><input id="__tabbed_6_2" name="__tabbed_6" type="radio" /><input id="__tabbed_6_3" name="__tabbed_6" type="radio" /><input id="__tabbed_6_4" name="__tabbed_6" type="radio" /><input id="__tabbed_6_5" name="__tabbed_6" type="radio" /><input id="__tabbed_6_6" name="__tabbed_6" type="radio" /><input id="__tabbed_6_7" name="__tabbed_6" type="radio" /><input id="__tabbed_6_8" name="__tabbed_6" type="radio" /><input id="__tabbed_6_9" name="__tabbed_6" type="radio" /><input id="__tabbed_6_10" name="__tabbed_6" type="radio" /><input id="__tabbed_6_11" name="__tabbed_6" type="radio" /><input id="__tabbed_6_12" name="__tabbed_6" type="radio" /><input id="__tabbed_6_13" name="__tabbed_6" type="radio" /><input id="__tabbed_6_14" name="__tabbed_6" type="radio" /><div class="tabbed-labels"><label for="__tabbed_6_1">Python</label><label for="__tabbed_6_2">C++</label><label for="__tabbed_6_3">Java</label><label for="__tabbed_6_4">C#</label><label for="__tabbed_6_5">Go</label><label for="__tabbed_6_6">Swift</label><label for="__tabbed_6_7">JS</label><label for="__tabbed_6_8">TS</label><label for="__tabbed_6_9">Dart</label><label for="__tabbed_6_10">Rust</label><label for="__tabbed_6_11">C</label><label for="__tabbed_6_12">Kotlin</label><label for="__tabbed_6_13">Ruby</label><label for="__tabbed_6_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_iii_template.py</span><pre><span></span><code><a id="__codelineno-56-1" name="__codelineno-56-1" href="#__codelineno-56-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">is_solution</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="nb">bool</span><span class="p">:</span>
+<a id="__codelineno-56-2" name="__codelineno-56-2" href="#__codelineno-56-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;現在の状態が解かどうかを判定&quot;&quot;&quot;</span>
+<a id="__codelineno-56-3" name="__codelineno-56-3" href="#__codelineno-56-3"></a>    <span class="k">return</span> <span class="n">state</span> <span class="ow">and</span> <span class="n">state</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span><span class="o">.</span><span class="n">val</span> <span class="o">==</span> <span class="mi">7</span>
+<a id="__codelineno-56-4" name="__codelineno-56-4" href="#__codelineno-56-4"></a>
+<a id="__codelineno-56-5" name="__codelineno-56-5" href="#__codelineno-56-5"></a><span class="k">def</span><span class="w"> </span><span class="nf">record_solution</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span> <span class="n">res</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">]]):</span>
+<a id="__codelineno-56-6" name="__codelineno-56-6" href="#__codelineno-56-6"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;解を記録&quot;&quot;&quot;</span>
+<a id="__codelineno-56-7" name="__codelineno-56-7" href="#__codelineno-56-7"></a>    <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">state</span><span class="p">))</span>
+<a id="__codelineno-56-8" name="__codelineno-56-8" href="#__codelineno-56-8"></a>
+<a id="__codelineno-56-9" name="__codelineno-56-9" href="#__codelineno-56-9"></a><span class="k">def</span><span class="w"> </span><span class="nf">is_valid</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span> <span class="n">choice</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">bool</span><span class="p">:</span>
+<a id="__codelineno-56-10" name="__codelineno-56-10" href="#__codelineno-56-10"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;現在の状態下で選択が合法かどうかを判定&quot;&quot;&quot;</span>
+<a id="__codelineno-56-11" name="__codelineno-56-11" href="#__codelineno-56-11"></a>    <span class="k">return</span> <span class="n">choice</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span> <span class="ow">and</span> <span class="n">choice</span><span class="o">.</span><span class="n">val</span> <span class="o">!=</span> <span class="mi">3</span>
+<a id="__codelineno-56-12" name="__codelineno-56-12" href="#__codelineno-56-12"></a>
+<a id="__codelineno-56-13" name="__codelineno-56-13" href="#__codelineno-56-13"></a><span class="k">def</span><span class="w"> </span><span class="nf">make_choice</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span> <span class="n">choice</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">):</span>
+<a id="__codelineno-56-14" name="__codelineno-56-14" href="#__codelineno-56-14"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;状態を更新&quot;&quot;&quot;</span>
+<a id="__codelineno-56-15" name="__codelineno-56-15" href="#__codelineno-56-15"></a>    <span class="n">state</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">choice</span><span class="p">)</span>
+<a id="__codelineno-56-16" name="__codelineno-56-16" href="#__codelineno-56-16"></a>
+<a id="__codelineno-56-17" name="__codelineno-56-17" href="#__codelineno-56-17"></a><span class="k">def</span><span class="w"> </span><span class="nf">undo_choice</span><span class="p">(</span><span class="n">state</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span> <span class="n">choice</span><span class="p">:</span> <span class="n">TreeNode</span><span class="p">):</span>
+<a id="__codelineno-56-18" name="__codelineno-56-18" href="#__codelineno-56-18"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;状態を復元&quot;&quot;&quot;</span>
+<a id="__codelineno-56-19" name="__codelineno-56-19" href="#__codelineno-56-19"></a>    <span class="n">state</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
+<a id="__codelineno-56-20" name="__codelineno-56-20" href="#__codelineno-56-20"></a>
+<a id="__codelineno-56-21" name="__codelineno-56-21" href="#__codelineno-56-21"></a><span class="k">def</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span>
+<a id="__codelineno-56-22" name="__codelineno-56-22" href="#__codelineno-56-22"></a>    <span class="n">state</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span> <span class="n">choices</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">],</span> <span class="n">res</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">]]</span>
+<a id="__codelineno-56-23" name="__codelineno-56-23" href="#__codelineno-56-23"></a><span class="p">):</span>
+<a id="__codelineno-56-24" name="__codelineno-56-24" href="#__codelineno-56-24"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;バックトラッキングアルゴリズム：例三&quot;&quot;&quot;</span>
+<a id="__codelineno-56-25" name="__codelineno-56-25" href="#__codelineno-56-25"></a>    <span class="c1"># 解かどうかをチェック</span>
+<a id="__codelineno-56-26" name="__codelineno-56-26" href="#__codelineno-56-26"></a>    <span class="k">if</span> <span class="n">is_solution</span><span class="p">(</span><span class="n">state</span><span class="p">):</span>
+<a id="__codelineno-56-27" name="__codelineno-56-27" href="#__codelineno-56-27"></a>        <span class="c1"># 解を記録</span>
+<a id="__codelineno-56-28" name="__codelineno-56-28" href="#__codelineno-56-28"></a>        <span class="n">record_solution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-56-29" name="__codelineno-56-29" href="#__codelineno-56-29"></a>    <span class="c1"># すべての選択肢を走査</span>
+<a id="__codelineno-56-30" name="__codelineno-56-30" href="#__codelineno-56-30"></a>    <span class="k">for</span> <span class="n">choice</span> <span class="ow">in</span> <span class="n">choices</span><span class="p">:</span>
+<a id="__codelineno-56-31" name="__codelineno-56-31" href="#__codelineno-56-31"></a>        <span class="c1"># 枝刈り：選択が合法かどうかをチェック</span>
+<a id="__codelineno-56-32" name="__codelineno-56-32" href="#__codelineno-56-32"></a>        <span class="k">if</span> <span class="n">is_valid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">choice</span><span class="p">):</span>
+<a id="__codelineno-56-33" name="__codelineno-56-33" href="#__codelineno-56-33"></a>            <span class="c1"># 試行：選択を行い、状態を更新</span>
+<a id="__codelineno-56-34" name="__codelineno-56-34" href="#__codelineno-56-34"></a>            <span class="n">make_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">choice</span><span class="p">)</span>
+<a id="__codelineno-56-35" name="__codelineno-56-35" href="#__codelineno-56-35"></a>            <span class="c1"># 次の選択ラウンドに進む</span>
+<a id="__codelineno-56-36" name="__codelineno-56-36" href="#__codelineno-56-36"></a>            <span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="p">[</span><span class="n">choice</span><span class="o">.</span><span class="n">left</span><span class="p">,</span> <span class="n">choice</span><span class="o">.</span><span class="n">right</span><span class="p">],</span> <span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-56-37" name="__codelineno-56-37" href="#__codelineno-56-37"></a>            <span class="c1"># 撤回：選択を取り消し、前の状態に復元</span>
+<a id="__codelineno-56-38" name="__codelineno-56-38" href="#__codelineno-56-38"></a>            <span class="n">undo_choice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">choice</span><span class="p">)</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_iii_template.cpp</span><pre><span></span><code><a id="__codelineno-57-1" name="__codelineno-57-1" href="#__codelineno-57-1"></a><span class="cm">/* 現在の状態が解かどうかを判定 */</span>
+<a id="__codelineno-57-2" name="__codelineno-57-2" href="#__codelineno-57-2"></a><span class="kt">bool</span><span class="w"> </span><span class="nf">isSolution</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">state</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-3" name="__codelineno-57-3" href="#__codelineno-57-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">!</span><span class="n">state</span><span class="p">.</span><span class="n">empty</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="n">back</span><span class="p">()</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="p">;</span>
+<a id="__codelineno-57-4" name="__codelineno-57-4" href="#__codelineno-57-4"></a><span class="p">}</span>
+<a id="__codelineno-57-5" name="__codelineno-57-5" href="#__codelineno-57-5"></a>
+<a id="__codelineno-57-6" name="__codelineno-57-6" href="#__codelineno-57-6"></a><span class="cm">/* 解を記録 */</span>
+<a id="__codelineno-57-7" name="__codelineno-57-7" href="#__codelineno-57-7"></a><span class="kt">void</span><span class="w"> </span><span class="nf">recordSolution</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*&gt;&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-8" name="__codelineno-57-8" href="#__codelineno-57-8"></a><span class="w">    </span><span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">state</span><span class="p">);</span>
+<a id="__codelineno-57-9" name="__codelineno-57-9" href="#__codelineno-57-9"></a><span class="p">}</span>
+<a id="__codelineno-57-10" name="__codelineno-57-10" href="#__codelineno-57-10"></a>
+<a id="__codelineno-57-11" name="__codelineno-57-11" href="#__codelineno-57-11"></a><span class="cm">/* 現在の状態下で選択が合法かどうかを判定 */</span>
+<a id="__codelineno-57-12" name="__codelineno-57-12" href="#__codelineno-57-12"></a><span class="kt">bool</span><span class="w"> </span><span class="nf">isValid</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-13" name="__codelineno-57-13" href="#__codelineno-57-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">choice</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span>
+<a id="__codelineno-57-14" name="__codelineno-57-14" href="#__codelineno-57-14"></a><span class="p">}</span>
+<a id="__codelineno-57-15" name="__codelineno-57-15" href="#__codelineno-57-15"></a>
+<a id="__codelineno-57-16" name="__codelineno-57-16" href="#__codelineno-57-16"></a><span class="cm">/* 状態を更新 */</span>
+<a id="__codelineno-57-17" name="__codelineno-57-17" href="#__codelineno-57-17"></a><span class="kt">void</span><span class="w"> </span><span class="nf">makeChoice</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-18" name="__codelineno-57-18" href="#__codelineno-57-18"></a><span class="w">    </span><span class="n">state</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">choice</span><span class="p">);</span>
+<a id="__codelineno-57-19" name="__codelineno-57-19" href="#__codelineno-57-19"></a><span class="p">}</span>
+<a id="__codelineno-57-20" name="__codelineno-57-20" href="#__codelineno-57-20"></a>
+<a id="__codelineno-57-21" name="__codelineno-57-21" href="#__codelineno-57-21"></a><span class="cm">/* 状態を復元 */</span>
+<a id="__codelineno-57-22" name="__codelineno-57-22" href="#__codelineno-57-22"></a><span class="kt">void</span><span class="w"> </span><span class="nf">undoChoice</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-23" name="__codelineno-57-23" href="#__codelineno-57-23"></a><span class="w">    </span><span class="n">state</span><span class="p">.</span><span class="n">pop_back</span><span class="p">();</span>
+<a id="__codelineno-57-24" name="__codelineno-57-24" href="#__codelineno-57-24"></a><span class="p">}</span>
+<a id="__codelineno-57-25" name="__codelineno-57-25" href="#__codelineno-57-25"></a>
+<a id="__codelineno-57-26" name="__codelineno-57-26" href="#__codelineno-57-26"></a><span class="cm">/* バックトラッキングアルゴリズム：例３ */</span>
+<a id="__codelineno-57-27" name="__codelineno-57-27" href="#__codelineno-57-27"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*&gt;&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-28" name="__codelineno-57-28" href="#__codelineno-57-28"></a><span class="w">    </span><span class="c1">// 解かどうかをチェック</span>
+<a id="__codelineno-57-29" name="__codelineno-57-29" href="#__codelineno-57-29"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-30" name="__codelineno-57-30" href="#__codelineno-57-30"></a><span class="w">        </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-57-31" name="__codelineno-57-31" href="#__codelineno-57-31"></a><span class="w">        </span><span class="n">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-57-32" name="__codelineno-57-32" href="#__codelineno-57-32"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-57-33" name="__codelineno-57-33" href="#__codelineno-57-33"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-57-34" name="__codelineno-57-34" href="#__codelineno-57-34"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">choice</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-35" name="__codelineno-57-35" href="#__codelineno-57-35"></a><span class="w">        </span><span class="c1">// 剪定：選択が合法かどうかをチェック</span>
+<a id="__codelineno-57-36" name="__codelineno-57-36" href="#__codelineno-57-36"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-37" name="__codelineno-57-37" href="#__codelineno-57-37"></a><span class="w">            </span><span class="c1">// 試行：選択を行い、状態を更新</span>
+<a id="__codelineno-57-38" name="__codelineno-57-38" href="#__codelineno-57-38"></a><span class="w">            </span><span class="n">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
+<a id="__codelineno-57-39" name="__codelineno-57-39" href="#__codelineno-57-39"></a><span class="w">            </span><span class="c1">// 次のラウンドの選択に進む</span>
+<a id="__codelineno-57-40" name="__codelineno-57-40" href="#__codelineno-57-40"></a><span class="w">            </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="n">nextChoices</span><span class="p">{</span><span class="n">choice</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">};</span>
+<a id="__codelineno-57-41" name="__codelineno-57-41" href="#__codelineno-57-41"></a><span class="w">            </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">nextChoices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-57-42" name="__codelineno-57-42" href="#__codelineno-57-42"></a><span class="w">            </span><span class="c1">// 回退：選択を取り消し、前の状態に復元</span>
+<a id="__codelineno-57-43" name="__codelineno-57-43" href="#__codelineno-57-43"></a><span class="w">            </span><span class="n">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
+<a id="__codelineno-57-44" name="__codelineno-57-44" href="#__codelineno-57-44"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-57-45" name="__codelineno-57-45" href="#__codelineno-57-45"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-57-46" name="__codelineno-57-46" href="#__codelineno-57-46"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_iii_template.java</span><pre><span></span><code><a id="__codelineno-58-1" name="__codelineno-58-1" href="#__codelineno-58-1"></a><span class="cm">/* 現在の状態が解かどうかを判定 */</span>
+<a id="__codelineno-58-2" name="__codelineno-58-2" href="#__codelineno-58-2"></a><span class="kt">boolean</span><span class="w"> </span><span class="nf">isSolution</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-3" name="__codelineno-58-3" href="#__codelineno-58-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">!</span><span class="n">state</span><span class="p">.</span><span class="na">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">state</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="na">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">).</span><span class="na">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">7</span><span class="p">;</span>
+<a id="__codelineno-58-4" name="__codelineno-58-4" href="#__codelineno-58-4"></a><span class="p">}</span>
+<a id="__codelineno-58-5" name="__codelineno-58-5" href="#__codelineno-58-5"></a>
+<a id="__codelineno-58-6" name="__codelineno-58-6" href="#__codelineno-58-6"></a><span class="cm">/* 解を記録 */</span>
+<a id="__codelineno-58-7" name="__codelineno-58-7" href="#__codelineno-58-7"></a><span class="kt">void</span><span class="w"> </span><span class="nf">recordSolution</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-8" name="__codelineno-58-8" href="#__codelineno-58-8"></a><span class="w">    </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">(</span><span class="n">state</span><span class="p">));</span>
+<a id="__codelineno-58-9" name="__codelineno-58-9" href="#__codelineno-58-9"></a><span class="p">}</span>
+<a id="__codelineno-58-10" name="__codelineno-58-10" href="#__codelineno-58-10"></a>
+<a id="__codelineno-58-11" name="__codelineno-58-11" href="#__codelineno-58-11"></a><span class="cm">/* 現在の状態下で選択が合法かどうかを判定 */</span>
+<a id="__codelineno-58-12" name="__codelineno-58-12" href="#__codelineno-58-12"></a><span class="kt">boolean</span><span class="w"> </span><span class="nf">isValid</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-13" name="__codelineno-58-13" href="#__codelineno-58-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span>
+<a id="__codelineno-58-14" name="__codelineno-58-14" href="#__codelineno-58-14"></a><span class="p">}</span>
+<a id="__codelineno-58-15" name="__codelineno-58-15" href="#__codelineno-58-15"></a>
+<a id="__codelineno-58-16" name="__codelineno-58-16" href="#__codelineno-58-16"></a><span class="cm">/* 状態を更新 */</span>
+<a id="__codelineno-58-17" name="__codelineno-58-17" href="#__codelineno-58-17"></a><span class="kt">void</span><span class="w"> </span><span class="nf">makeChoice</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-18" name="__codelineno-58-18" href="#__codelineno-58-18"></a><span class="w">    </span><span class="n">state</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">choice</span><span class="p">);</span>
+<a id="__codelineno-58-19" name="__codelineno-58-19" href="#__codelineno-58-19"></a><span class="p">}</span>
+<a id="__codelineno-58-20" name="__codelineno-58-20" href="#__codelineno-58-20"></a>
+<a id="__codelineno-58-21" name="__codelineno-58-21" href="#__codelineno-58-21"></a><span class="cm">/* 状態を復元 */</span>
+<a id="__codelineno-58-22" name="__codelineno-58-22" href="#__codelineno-58-22"></a><span class="kt">void</span><span class="w"> </span><span class="nf">undoChoice</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-23" name="__codelineno-58-23" href="#__codelineno-58-23"></a><span class="w">    </span><span class="n">state</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="na">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-58-24" name="__codelineno-58-24" href="#__codelineno-58-24"></a><span class="p">}</span>
+<a id="__codelineno-58-25" name="__codelineno-58-25" href="#__codelineno-58-25"></a>
+<a id="__codelineno-58-26" name="__codelineno-58-26" href="#__codelineno-58-26"></a><span class="cm">/* バックトラッキングアルゴリズム：例３ */</span>
+<a id="__codelineno-58-27" name="__codelineno-58-27" href="#__codelineno-58-27"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-28" name="__codelineno-58-28" href="#__codelineno-58-28"></a><span class="w">    </span><span class="c1">// 解かどうかをチェック</span>
+<a id="__codelineno-58-29" name="__codelineno-58-29" href="#__codelineno-58-29"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isSolution</span><span class="p">(</span><span class="n">state</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-30" name="__codelineno-58-30" href="#__codelineno-58-30"></a><span class="w">        </span><span class="c1">// 解を記録</span>
+<a id="__codelineno-58-31" name="__codelineno-58-31" href="#__codelineno-58-31"></a><span class="w">        </span><span class="n">recordSolution</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-58-32" name="__codelineno-58-32" href="#__codelineno-58-32"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-58-33" name="__codelineno-58-33" href="#__codelineno-58-33"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-58-34" name="__codelineno-58-34" href="#__codelineno-58-34"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-35" name="__codelineno-58-35" href="#__codelineno-58-35"></a><span class="w">        </span><span class="c1">// 剪定：選択が合法かどうかをチェック</span>
+<a id="__codelineno-58-36" name="__codelineno-58-36" href="#__codelineno-58-36"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isValid</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-37" name="__codelineno-58-37" href="#__codelineno-58-37"></a><span class="w">            </span><span class="c1">// 試行：選択を行い、状態を更新</span>
+<a id="__codelineno-58-38" name="__codelineno-58-38" href="#__codelineno-58-38"></a><span class="w">            </span><span class="n">makeChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
+<a id="__codelineno-58-39" name="__codelineno-58-39" href="#__codelineno-58-39"></a><span class="w">            </span><span class="c1">// 次のラウンドの選択に進む</span>
+<a id="__codelineno-58-40" name="__codelineno-58-40" href="#__codelineno-58-40"></a><span class="w">            </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">Arrays</span><span class="p">.</span><span class="na">asList</span><span class="p">(</span><span class="n">choice</span><span class="p">.</span><span class="na">left</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">.</span><span class="na">right</span><span class="p">),</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-58-41" name="__codelineno-58-41" href="#__codelineno-58-41"></a><span class="w">            </span><span class="c1">// 回退：選択を取り消し、前の状態に復元</span>
+<a id="__codelineno-58-42" name="__codelineno-58-42" href="#__codelineno-58-42"></a><span class="w">            </span><span class="n">undoChoice</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choice</span><span class="p">);</span>
+<a id="__codelineno-58-43" name="__codelineno-58-43" href="#__codelineno-58-43"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-58-44" name="__codelineno-58-44" href="#__codelineno-58-44"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-58-45" name="__codelineno-58-45" href="#__codelineno-58-45"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_iii_template.cs</span><pre><span></span><code><a id="__codelineno-59-1" name="__codelineno-59-1" href="#__codelineno-59-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">preorder_traversal_iii_template</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">IsSolution</span><span class="p">}</span>
+<a id="__codelineno-59-2" name="__codelineno-59-2" href="#__codelineno-59-2"></a>
+<a id="__codelineno-59-3" name="__codelineno-59-3" href="#__codelineno-59-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">preorder_traversal_iii_template</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">RecordSolution</span><span class="p">}</span>
+<a id="__codelineno-59-4" name="__codelineno-59-4" href="#__codelineno-59-4"></a>
+<a id="__codelineno-59-5" name="__codelineno-59-5" href="#__codelineno-59-5"></a><span class="na">[class]</span><span class="p">{</span><span class="n">preorder_traversal_iii_template</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">IsValid</span><span class="p">}</span>
+<a id="__codelineno-59-6" name="__codelineno-59-6" href="#__codelineno-59-6"></a>
+<a id="__codelineno-59-7" name="__codelineno-59-7" href="#__codelineno-59-7"></a><span class="na">[class]</span><span class="p">{</span><span class="n">preorder_traversal_iii_template</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">MakeChoice</span><span class="p">}</span>
+<a id="__codelineno-59-8" name="__codelineno-59-8" href="#__codelineno-59-8"></a>
+<a id="__codelineno-59-9" name="__codelineno-59-9" href="#__codelineno-59-9"></a><span class="na">[class]</span><span class="p">{</span><span class="n">preorder_traversal_iii_template</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">UndoChoice</span><span class="p">}</span>
+<a id="__codelineno-59-10" name="__codelineno-59-10" href="#__codelineno-59-10"></a>
+<a id="__codelineno-59-11" name="__codelineno-59-11" href="#__codelineno-59-11"></a><span class="na">[class]</span><span class="p">{</span><span class="n">preorder_traversal_iii_template</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Backtrack</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_iii_template.go</span><pre><span></span><code><a id="__codelineno-60-1" name="__codelineno-60-1" href="#__codelineno-60-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">isSolution</span><span class="p">}</span>
+<a id="__codelineno-60-2" name="__codelineno-60-2" href="#__codelineno-60-2"></a>
+<a id="__codelineno-60-3" name="__codelineno-60-3" href="#__codelineno-60-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">recordSolution</span><span class="p">}</span>
+<a id="__codelineno-60-4" name="__codelineno-60-4" href="#__codelineno-60-4"></a>
+<a id="__codelineno-60-5" name="__codelineno-60-5" href="#__codelineno-60-5"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">isValid</span><span class="p">}</span>
+<a id="__codelineno-60-6" name="__codelineno-60-6" href="#__codelineno-60-6"></a>
+<a id="__codelineno-60-7" name="__codelineno-60-7" href="#__codelineno-60-7"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">makeChoice</span><span class="p">}</span>
+<a id="__codelineno-60-8" name="__codelineno-60-8" href="#__codelineno-60-8"></a>
+<a id="__codelineno-60-9" name="__codelineno-60-9" href="#__codelineno-60-9"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">undoChoice</span><span class="p">}</span>
+<a id="__codelineno-60-10" name="__codelineno-60-10" href="#__codelineno-60-10"></a>
+<a id="__codelineno-60-11" name="__codelineno-60-11" href="#__codelineno-60-11"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">backtrackIII</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_iii_template.swift</span><pre><span></span><code><a id="__codelineno-61-1" name="__codelineno-61-1" href="#__codelineno-61-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">isSolution</span><span class="p">}</span>
+<a id="__codelineno-61-2" name="__codelineno-61-2" href="#__codelineno-61-2"></a>
+<a id="__codelineno-61-3" name="__codelineno-61-3" href="#__codelineno-61-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">recordSolution</span><span class="p">}</span>
+<a id="__codelineno-61-4" name="__codelineno-61-4" href="#__codelineno-61-4"></a>
+<a id="__codelineno-61-5" name="__codelineno-61-5" href="#__codelineno-61-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">isValid</span><span class="p">}</span>
+<a id="__codelineno-61-6" name="__codelineno-61-6" href="#__codelineno-61-6"></a>
+<a id="__codelineno-61-7" name="__codelineno-61-7" href="#__codelineno-61-7"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">makeChoice</span><span class="p">}</span>
+<a id="__codelineno-61-8" name="__codelineno-61-8" href="#__codelineno-61-8"></a>
+<a id="__codelineno-61-9" name="__codelineno-61-9" href="#__codelineno-61-9"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">undoChoice</span><span class="p">}</span>
+<a id="__codelineno-61-10" name="__codelineno-61-10" href="#__codelineno-61-10"></a>
+<a id="__codelineno-61-11" name="__codelineno-61-11" href="#__codelineno-61-11"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_iii_template.js</span><pre><span></span><code><a id="__codelineno-62-1" name="__codelineno-62-1" href="#__codelineno-62-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">isSolution</span><span class="p">}</span>
+<a id="__codelineno-62-2" name="__codelineno-62-2" href="#__codelineno-62-2"></a>
+<a id="__codelineno-62-3" name="__codelineno-62-3" href="#__codelineno-62-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">recordSolution</span><span class="p">}</span>
+<a id="__codelineno-62-4" name="__codelineno-62-4" href="#__codelineno-62-4"></a>
+<a id="__codelineno-62-5" name="__codelineno-62-5" href="#__codelineno-62-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">isValid</span><span class="p">}</span>
+<a id="__codelineno-62-6" name="__codelineno-62-6" href="#__codelineno-62-6"></a>
+<a id="__codelineno-62-7" name="__codelineno-62-7" href="#__codelineno-62-7"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">makeChoice</span><span class="p">}</span>
+<a id="__codelineno-62-8" name="__codelineno-62-8" href="#__codelineno-62-8"></a>
+<a id="__codelineno-62-9" name="__codelineno-62-9" href="#__codelineno-62-9"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">undoChoice</span><span class="p">}</span>
+<a id="__codelineno-62-10" name="__codelineno-62-10" href="#__codelineno-62-10"></a>
+<a id="__codelineno-62-11" name="__codelineno-62-11" href="#__codelineno-62-11"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">backtrack</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_iii_template.ts</span><pre><span></span><code><a id="__codelineno-63-1" name="__codelineno-63-1" href="#__codelineno-63-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">isSolution</span><span class="p">}</span>
+<a id="__codelineno-63-2" name="__codelineno-63-2" href="#__codelineno-63-2"></a>
+<a id="__codelineno-63-3" name="__codelineno-63-3" href="#__codelineno-63-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">recordSolution</span><span class="p">}</span>
+<a id="__codelineno-63-4" name="__codelineno-63-4" href="#__codelineno-63-4"></a>
+<a id="__codelineno-63-5" name="__codelineno-63-5" href="#__codelineno-63-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">isValid</span><span class="p">}</span>
+<a id="__codelineno-63-6" name="__codelineno-63-6" href="#__codelineno-63-6"></a>
+<a id="__codelineno-63-7" name="__codelineno-63-7" href="#__codelineno-63-7"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">makeChoice</span><span class="p">}</span>
+<a id="__codelineno-63-8" name="__codelineno-63-8" href="#__codelineno-63-8"></a>
+<a id="__codelineno-63-9" name="__codelineno-63-9" href="#__codelineno-63-9"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">undoChoice</span><span class="p">}</span>
+<a id="__codelineno-63-10" name="__codelineno-63-10" href="#__codelineno-63-10"></a>
+<a id="__codelineno-63-11" name="__codelineno-63-11" href="#__codelineno-63-11"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">backtrack</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_iii_template.dart</span><pre><span></span><code><a id="__codelineno-64-1" name="__codelineno-64-1" href="#__codelineno-64-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">isSolution</span><span class="p">}</span>
+<a id="__codelineno-64-2" name="__codelineno-64-2" href="#__codelineno-64-2"></a>
+<a id="__codelineno-64-3" name="__codelineno-64-3" href="#__codelineno-64-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">recordSolution</span><span class="p">}</span>
+<a id="__codelineno-64-4" name="__codelineno-64-4" href="#__codelineno-64-4"></a>
+<a id="__codelineno-64-5" name="__codelineno-64-5" href="#__codelineno-64-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">isValid</span><span class="p">}</span>
+<a id="__codelineno-64-6" name="__codelineno-64-6" href="#__codelineno-64-6"></a>
+<a id="__codelineno-64-7" name="__codelineno-64-7" href="#__codelineno-64-7"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">makeChoice</span><span class="p">}</span>
+<a id="__codelineno-64-8" name="__codelineno-64-8" href="#__codelineno-64-8"></a>
+<a id="__codelineno-64-9" name="__codelineno-64-9" href="#__codelineno-64-9"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">undoChoice</span><span class="p">}</span>
+<a id="__codelineno-64-10" name="__codelineno-64-10" href="#__codelineno-64-10"></a>
+<a id="__codelineno-64-11" name="__codelineno-64-11" href="#__codelineno-64-11"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_iii_template.rs</span><pre><span></span><code><a id="__codelineno-65-1" name="__codelineno-65-1" href="#__codelineno-65-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">is_solution</span><span class="p">}</span>
+<a id="__codelineno-65-2" name="__codelineno-65-2" href="#__codelineno-65-2"></a>
+<a id="__codelineno-65-3" name="__codelineno-65-3" href="#__codelineno-65-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">record_solution</span><span class="p">}</span>
+<a id="__codelineno-65-4" name="__codelineno-65-4" href="#__codelineno-65-4"></a>
+<a id="__codelineno-65-5" name="__codelineno-65-5" href="#__codelineno-65-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">is_valid</span><span class="p">}</span>
+<a id="__codelineno-65-6" name="__codelineno-65-6" href="#__codelineno-65-6"></a>
+<a id="__codelineno-65-7" name="__codelineno-65-7" href="#__codelineno-65-7"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">make_choice</span><span class="p">}</span>
+<a id="__codelineno-65-8" name="__codelineno-65-8" href="#__codelineno-65-8"></a>
+<a id="__codelineno-65-9" name="__codelineno-65-9" href="#__codelineno-65-9"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">undo_choice</span><span class="p">}</span>
+<a id="__codelineno-65-10" name="__codelineno-65-10" href="#__codelineno-65-10"></a>
+<a id="__codelineno-65-11" name="__codelineno-65-11" href="#__codelineno-65-11"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_iii_template.c</span><pre><span></span><code><a id="__codelineno-66-1" name="__codelineno-66-1" href="#__codelineno-66-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">isSolution</span><span class="p">}</span>
+<a id="__codelineno-66-2" name="__codelineno-66-2" href="#__codelineno-66-2"></a>
+<a id="__codelineno-66-3" name="__codelineno-66-3" href="#__codelineno-66-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">recordSolution</span><span class="p">}</span>
+<a id="__codelineno-66-4" name="__codelineno-66-4" href="#__codelineno-66-4"></a>
+<a id="__codelineno-66-5" name="__codelineno-66-5" href="#__codelineno-66-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">isValid</span><span class="p">}</span>
+<a id="__codelineno-66-6" name="__codelineno-66-6" href="#__codelineno-66-6"></a>
+<a id="__codelineno-66-7" name="__codelineno-66-7" href="#__codelineno-66-7"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">makeChoice</span><span class="p">}</span>
+<a id="__codelineno-66-8" name="__codelineno-66-8" href="#__codelineno-66-8"></a>
+<a id="__codelineno-66-9" name="__codelineno-66-9" href="#__codelineno-66-9"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">undoChoice</span><span class="p">}</span>
+<a id="__codelineno-66-10" name="__codelineno-66-10" href="#__codelineno-66-10"></a>
+<a id="__codelineno-66-11" name="__codelineno-66-11" href="#__codelineno-66-11"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_iii_template.kt</span><pre><span></span><code><a id="__codelineno-67-1" name="__codelineno-67-1" href="#__codelineno-67-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">isSolution</span><span class="p">}</span>
+<a id="__codelineno-67-2" name="__codelineno-67-2" href="#__codelineno-67-2"></a>
+<a id="__codelineno-67-3" name="__codelineno-67-3" href="#__codelineno-67-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">recordSolution</span><span class="p">}</span>
+<a id="__codelineno-67-4" name="__codelineno-67-4" href="#__codelineno-67-4"></a>
+<a id="__codelineno-67-5" name="__codelineno-67-5" href="#__codelineno-67-5"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">isValid</span><span class="p">}</span>
+<a id="__codelineno-67-6" name="__codelineno-67-6" href="#__codelineno-67-6"></a>
+<a id="__codelineno-67-7" name="__codelineno-67-7" href="#__codelineno-67-7"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">makeChoice</span><span class="p">}</span>
+<a id="__codelineno-67-8" name="__codelineno-67-8" href="#__codelineno-67-8"></a>
+<a id="__codelineno-67-9" name="__codelineno-67-9" href="#__codelineno-67-9"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">undoChoice</span><span class="p">}</span>
+<a id="__codelineno-67-10" name="__codelineno-67-10" href="#__codelineno-67-10"></a>
+<a id="__codelineno-67-11" name="__codelineno-67-11" href="#__codelineno-67-11"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">backtrack</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_iii_template.rb</span><pre><span></span><code><a id="__codelineno-68-1" name="__codelineno-68-1" href="#__codelineno-68-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">is_solution</span><span class="p">}</span>
+<a id="__codelineno-68-2" name="__codelineno-68-2" href="#__codelineno-68-2"></a>
+<a id="__codelineno-68-3" name="__codelineno-68-3" href="#__codelineno-68-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">record_solution</span><span class="p">}</span>
+<a id="__codelineno-68-4" name="__codelineno-68-4" href="#__codelineno-68-4"></a>
+<a id="__codelineno-68-5" name="__codelineno-68-5" href="#__codelineno-68-5"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">is_valid</span><span class="p">}</span>
+<a id="__codelineno-68-6" name="__codelineno-68-6" href="#__codelineno-68-6"></a>
+<a id="__codelineno-68-7" name="__codelineno-68-7" href="#__codelineno-68-7"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">make_choice</span><span class="p">}</span>
+<a id="__codelineno-68-8" name="__codelineno-68-8" href="#__codelineno-68-8"></a>
+<a id="__codelineno-68-9" name="__codelineno-68-9" href="#__codelineno-68-9"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">undo_choice</span><span class="p">}</span>
+<a id="__codelineno-68-10" name="__codelineno-68-10" href="#__codelineno-68-10"></a>
+<a id="__codelineno-68-11" name="__codelineno-68-11" href="#__codelineno-68-11"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">backtrack</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">preorder_traversal_iii_template.zig</span><pre><span></span><code><a id="__codelineno-69-1" name="__codelineno-69-1" href="#__codelineno-69-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">isSolution</span><span class="p">}</span>
+<a id="__codelineno-69-2" name="__codelineno-69-2" href="#__codelineno-69-2"></a>
+<a id="__codelineno-69-3" name="__codelineno-69-3" href="#__codelineno-69-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">recordSolution</span><span class="p">}</span>
+<a id="__codelineno-69-4" name="__codelineno-69-4" href="#__codelineno-69-4"></a>
+<a id="__codelineno-69-5" name="__codelineno-69-5" href="#__codelineno-69-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">isValid</span><span class="p">}</span>
+<a id="__codelineno-69-6" name="__codelineno-69-6" href="#__codelineno-69-6"></a>
+<a id="__codelineno-69-7" name="__codelineno-69-7" href="#__codelineno-69-7"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">makeChoice</span><span class="p">}</span>
+<a id="__codelineno-69-8" name="__codelineno-69-8" href="#__codelineno-69-8"></a>
+<a id="__codelineno-69-9" name="__codelineno-69-9" href="#__codelineno-69-9"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">undoChoice</span><span class="p">}</span>
+<a id="__codelineno-69-10" name="__codelineno-69-10" href="#__codelineno-69-10"></a>
+<a id="__codelineno-69-11" name="__codelineno-69-11" href="#__codelineno-69-11"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>問題文の意味に従い、値が <span class="arithmatex">\(7\)</span> のノードを見つけた後も探索を続ける必要があります。<strong>したがって、解を記録した後の <code>return</code> 文を削除する必要があります</strong>。次の図は、<code>return</code> 文を保持する場合と削除する場合の探索過程の比較です。</p>
+<p><a class="glightbox" href="../backtracking_algorithm.assets/backtrack_remove_return_or_not.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="returnを保持する場合と削除する場合の探索過程の比較" class="animation-figure" src="../backtracking_algorithm.assets/backtrack_remove_return_or_not.png" /></a></p>
+<p align="center"> 図 13-4 &nbsp; returnを保持する場合と削除する場合の探索過程の比較 </p>
+
+<p>前順走査に基づくコード実装と比べると、バックトラッキングアルゴリズムのフレームワークに基づく実装はやや冗長に見えますが、汎用性はより高いです。実際、<strong>多くのバックトラッキング問題はこのフレームワークの下で解くことができます</strong>。具体的な問題に応じて <code>state</code> と <code>choices</code> を定義し、フレームワーク内の各メソッドを実装すればよいのです。</p>
+<h2 id="1314">13.1.4 &nbsp; よく使われる用語<a class="headerlink" href="#1314" title="Permanent link">&para;</a></h2>
+<p>アルゴリズム問題をより明確に分析するために、バックトラッキングアルゴリズムでよく使われる用語の意味をまとめ、例題 3 の対応例を以下の表に示します。</p>
+<p align="center"> 表 13-1 &nbsp; バックトラッキングアルゴリズムでよく使われる用語 </p>
+
+<div class="center-table">
+<table>
+<thead>
+<tr>
+<th>名称</th>
+<th>定義</th>
+<th>例題 3</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td>解（solution）</td>
+<td>解は問題の特定条件を満たす答えであり、1 つまたは複数存在する可能性がある</td>
+<td>根ノードからノード <span class="arithmatex">\(7\)</span> までの制約条件を満たすすべての経路</td>
+</tr>
+<tr>
+<td>制約条件（constraint）</td>
+<td>制約条件は、解の実現可能性を制限する条件であり、通常は枝刈りに使用される</td>
+<td>経路にノード <span class="arithmatex">\(3\)</span> を含まない</td>
+</tr>
+<tr>
+<td>状態（state）</td>
+<td>状態は、ある時点での問題の状況を表し、これまでに行った選択を含む</td>
+<td>現在訪問したノード経路、すなわち <code>path</code> ノードリスト</td>
+</tr>
+<tr>
+<td>試行（attempt）</td>
+<td>試行は、利用可能な選択肢に基づいて解空間を探索する過程であり、選択を行い、状態を更新し、解かどうかを確認する</td>
+<td>左（右）子ノードを再帰的に訪問し、ノードを <code>path</code> に追加し、ノードの値が <span class="arithmatex">\(7\)</span> かを確認する</td>
+</tr>
+<tr>
+<td>バックトラック（backtracking）</td>
+<td>制約条件を満たさない状態に遭遇した場合、以前の選択を取り消して前の状態に戻ること</td>
+<td>葉ノードを越えたとき、探索終了、値が <span class="arithmatex">\(3\)</span> のノードに遭遇したとき探索を終了し、関数が戻る</td>
+</tr>
+<tr>
+<td>枝刈り（pruning）</td>
+<td>問題の特性や制約条件に基づき、無意味な探索経路を避ける方法であり、探索効率を向上させる</td>
+<td>値が <span class="arithmatex">\(3\)</span> のノードに遭遇した場合、それ以上探索しない</td>
+</tr>
+</tbody>
+</table>
+</div>
+<div class="admonition tip">
+<p class="admonition-title">Tip</p>
+<p>問題、解、状態などの概念は一般的なものであり、分割統治、バックトラッキング、動的計画法、貪欲法などのアルゴリズムにも関係します。</p>
+</div>
+<h2 id="1315">13.1.5 &nbsp; 長所と限界<a class="headerlink" href="#1315" title="Permanent link">&para;</a></h2>
+<p>バックトラッキングアルゴリズムは本質的に深さ優先探索（DFS）アルゴリズムの一種であり、条件を満たす解を見つけるまであらゆる可能な解を試みます。この方法の利点は、すべての可能な解を見つけられる点であり、適切な枝刈りを行えば効率が高いことです。</p>
+<p>しかし、大規模または複雑な問題を扱う場合、<strong>バックトラッキングアルゴリズムの実行効率は許容できないほど低下する可能性があります</strong>。</p>
+<ul>
+<li><strong>時間</strong>：バックトラッキングアルゴリズムは通常、状態空間のすべての可能性を探索する必要があり、時間計算量は指数オーダーまたは階乗オーダーに達する可能性があります。</li>
+<li><strong>空間</strong>：再帰呼び出し中に現在の状態（例：経路、枝刈り用の補助変数など）を保存する必要があり、深さが大きい場合、空間の使用量が増加します。</li>
+</ul>
+<p>それでもなお、<strong>バックトラッキングアルゴリズムは特定の探索問題や制約満足問題の最良の解法であることが多いです</strong>。これらの問題では、どの選択が有効な解を生成するかを予測できないため、すべての可能な選択を試す必要があります。このような場合、**効率の最適化が鍵**となります。一般的な最適化手法は次の 2 つです。</p>
+<ul>
+<li><strong>枝刈り</strong>：解を生成しないことが確実な経路を避けることで、時間と空間を節約します。</li>
+<li><strong>ヒューリスティック探索</strong>：探索中に戦略や評価値を導入し、有効な解を生成する可能性が高い経路を優先的に探索します。</li>
+</ul>
+<h2 id="1316">13.1.6 &nbsp; バックトラッキングの典型的な例題<a class="headerlink" href="#1316" title="Permanent link">&para;</a></h2>
+<p>バックトラッキングアルゴリズムは、多くの探索問題、制約満足問題、組合せ最適化問題を解くのに使用できます。</p>
+<p><strong>探索問題</strong>：この種の問題の目標は、特定の条件を満たす解を見つけることです。</p>
+<ul>
+<li>全順列問題：与えられた集合のすべての可能な順列を求める。</li>
+<li>部分和問題：与えられた集合と目標和に対して、和が目標値になるすべての部分集合を求める。</li>
+<li>ハノイの塔：3 本の柱と異なるサイズの円盤があり、すべての円盤を 1 本の柱から別の柱に移す。1 回に 1 枚しか動かせず、大きな円盤を小さい円盤の上に置くことはできない。</li>
+</ul>
+<p><strong>制約満足問題</strong>：この種の問題の目標は、すべての制約条件を満たす解を見つけることです。</p>
+<ul>
+<li><span class="arithmatex">\(n\)</span> クイーン問題：<span class="arithmatex">\(n imes n\)</span> のチェス盤に <span class="arithmatex">\(n\)</span> 個のクイーンを配置し、互いに攻撃しないようにする。</li>
+<li>数独：<span class="arithmatex">\(9 imes 9\)</span> のグリッドに数字 <span class="arithmatex">\(1\)</span> ~ <span class="arithmatex">\(9\)</span> を入力し、各行、列、<span class="arithmatex">\(3 imes 3\)</span> のサブグリッドに重複がないようにする。</li>
+<li>グラフ彩色問題：与えられた無向グラフに対し、隣接頂点が異なる色になるように最小限の色で彩色する。</li>
+</ul>
+<p><strong>組合せ最適化問題</strong>：この種の問題の目標は、組合せ空間内で特定の条件を満たす最適解を見つけることです。</p>
+<ul>
+<li>0-1 ナップサック問題：与えられた物品群とバックパックがあり、各物品には価値と重さが設定されている。バックパックの容量制限内で、総価値を最大化する物品の選択を求める。</li>
+<li>旅行セールスマン問題：グラフ上で、1 つの点から出発し、すべての他の点を 1 回ずつ訪問して出発点に戻る最短経路を求める。</li>
+<li>最大クリーク問題：与えられた無向グラフの中で、任意の 2 頂点間に辺が存在する最大の完全部分グラフを見つける。</li>
+</ul>
+<p>注意すべきは、多くの組合せ最適化問題に対して、バックトラッキングが最適解法ではないということです。</p>
+<ul>
+<li>0-1 ナップサック問題は、時間効率を高めるために動的計画法がよく使用されます。</li>
+<li>旅行セールスマン問題は有名な NP-Hard 問題であり、遺伝的アルゴリズムやアントコロニーアルゴリズムなどの手法がよく使われます。</li>
+<li>最大クリーク問題はグラフ理論の古典的な問題であり、貪欲法などのヒューリスティックアルゴリズムで解くことができます。</li>
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+            d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
+    </svg>
+    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+</div>
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+        </aside>
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+  <nav class="md-header__inner md-grid" aria-label="ヘッダー">
+    <a href=".." title="Hello アルゴリズム" class="md-header__button md-logo" aria-label="Hello アルゴリズム" data-md-component="logo">
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+  <img src="../assets/images/logo.svg" alt="logo">
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+            Hello アルゴリズム
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+        <div class="md-header__topic" data-md-component="header-topic">
+          <span class="md-ellipsis">
+            
+              第 13 章 &nbsp; バックトラッキング
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+      </label>
+    
+  
+    
+    
+    
+    <input class="md-option" data-md-color-media="" data-md-color-scheme="slate" data-md-color-primary="black" data-md-color-accent="teal"  aria-label="ライトモード"  type="radio" name="__palette" id="__palette_1">
+    
+      <label class="md-header__button md-icon" title="ライトモード" for="__palette_0" hidden>
+        <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07 19.07 3.5m-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13.51 1.67m-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87.4 1.31M19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35-2.53-2.2m4.33-2.7 1.15-2.77 2.2 2.54-3.35.23m1.15-4.96-1.14-2.78 3.34.24-2.2 2.54M9.63 18.93l2.77 1.15-2.53 2.19-.24-3.34Z"/></svg>
+      </label>
+    
+  
+</form>
+      
+    
+    
+      <script>var media,input,key,value,palette=__md_get("__palette");if(palette&&palette.color){"(prefers-color-scheme)"===palette.color.media&&(media=matchMedia("(prefers-color-scheme: light)"),input=document.querySelector(media.matches?"[data-md-color-media='(prefers-color-scheme: light)']":"[data-md-color-media='(prefers-color-scheme: dark)']"),palette.color.media=input.getAttribute("data-md-color-media"),palette.color.scheme=input.getAttribute("data-md-color-scheme"),palette.color.primary=input.getAttribute("data-md-color-primary"),palette.color.accent=input.getAttribute("data-md-color-accent"));for([key,value]of Object.entries(palette.color))document.body.setAttribute("data-md-color-"+key,value)}</script>
+    
+    
+      <div class="md-header__option">
+  <div class="md-select">
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+    <button class="md-header__button md-icon" aria-label="言語切り替え">
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+    </button>
+    <div class="md-select__inner">
+      <ul class="md-select__list">
+        
+          <li class="md-select__item">
+            <a href="/chapter_backtracking/" hreflang="zh" class="md-select__link">
+              简体中文
+            </a>
+          </li>
+        
+          <li class="md-select__item">
+            <a href="/zh-hant/chapter_backtracking/" hreflang="zh-Hant" class="md-select__link">
+              繁體中文
+            </a>
+          </li>
+        
+          <li class="md-select__item">
+            <a href="/en/chapter_backtracking/" hreflang="en" class="md-select__link">
+              English
+            </a>
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+        
+          <li class="md-select__item">
+            <a href="/ja/chapter_backtracking/" hreflang="ja" class="md-select__link">
+              日本語
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+    
+    
+      <label class="md-header__button md-icon" for="__search">
+        
+        <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.516 6.516 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5Z"/></svg>
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+      <div class="md-search" data-md-component="search" role="dialog">
+  <label class="md-search__overlay" for="__search"></label>
+  <div class="md-search__inner" role="search">
+    <form class="md-search__form" name="search">
+      <input type="text" class="md-search__input" name="query" aria-label="検索" placeholder="検索" autocapitalize="off" autocorrect="off" autocomplete="off" spellcheck="false" data-md-component="search-query" required>
+      <label class="md-search__icon md-icon" for="__search">
+        
+        <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.516 6.516 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5Z"/></svg>
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+            
+            <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 16.08c-.76 0-1.44.3-1.96.77L8.91 12.7c.05-.23.09-.46.09-.7 0-.24-.04-.47-.09-.7l7.05-4.11c.54.5 1.25.81 2.04.81a3 3 0 0 0 3-3 3 3 0 0 0-3-3 3 3 0 0 0-3 3c0 .24.04.47.09.7L8.04 9.81C7.5 9.31 6.79 9 6 9a3 3 0 0 0-3 3 3 3 0 0 0 3 3c.79 0 1.5-.31 2.04-.81l7.12 4.15c-.05.21-.08.43-.08.66 0 1.61 1.31 2.91 2.92 2.91 1.61 0 2.92-1.3 2.92-2.91A2.92 2.92 0 0 0 18 16.08Z"/></svg>
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+        </button>
+      </nav>
+      
+        <div class="md-search__suggest" data-md-component="search-suggest"></div>
+      
+    </form>
+    <div class="md-search__output">
+      <div class="md-search__scrollwrap" data-md-scrollfix>
+        <div class="md-search-result" data-md-component="search-result">
+          <div class="md-search-result__meta">
+            検索を初期化
+          </div>
+          <ol class="md-search-result__list" role="presentation"></ol>
+        </div>
+      </div>
+    </div>
+  </div>
+</div>
+    
+    
+      <div class="md-header__source">
+        <a href="https://github.com/krahets/hello-algo" title="リポジトリへ" class="md-source" data-md-component="source">
+  <div class="md-source__icon md-icon">
+    
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 496 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"/></svg>
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+  <div class="md-source__repository">
+    krahets/hello-algo
+  </div>
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+      <main class="md-main" data-md-component="main">
+        <div class="md-main__inner md-grid">
+          
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+              
+              <div class="md-sidebar md-sidebar--primary" data-md-component="sidebar" data-md-type="navigation" >
+                <div class="md-sidebar__scrollwrap">
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+    <a href=".." title="Hello アルゴリズム" class="md-nav__button md-logo" aria-label="Hello アルゴリズム" data-md-component="logo">
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+  </div>
+  <div class="md-source__repository">
+    krahets/hello-algo
+  </div>
+</a>
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+      
+      
+  
+  
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+    
+    
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+        
+          
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_1" >
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+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_hello_algo/" class="md-nav__link ">
+              
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m13.13 22.19-1.63-3.83c1.57-.58 3.04-1.36 4.4-2.27l-2.77 6.1M5.64 12.5l-3.83-1.63 6.1-2.77C7 9.46 6.22 10.93 5.64 12.5M19.22 4c.28 0 .53 0 .74.05.17 1.39-.02 4.25-3.3 7.53-1.7 1.71-3.73 3.02-6.01 3.89l-2.15-2.1c.92-2.31 2.23-4.34 3.92-6.03C15.18 4.58 17.64 4 19.22 4m0-2c-1.98 0-4.98.69-8.22 3.93-2.19 2.19-3.5 4.6-4.35 6.71-.28.75-.09 1.57.46 2.13l2.13 2.12c.38.38.89.61 1.42.61.23 0 .47-.06.7-.15A19.1 19.1 0 0 0 18.07 13c5.66-5.66 3.54-10.61 3.54-10.61S20.7 2 19.22 2m-4.68 7.46c-.78-.78-.78-2.05 0-2.83s2.05-.78 2.83 0c.77.78.78 2.05 0 2.83-.78.78-2.05.78-2.83 0m-5.66 7.07-1.41-1.41 1.41 1.41M6.24 22l3.64-3.64c-.34-.09-.67-.24-.97-.45L4.83 22h1.41M2 22h1.41l4.77-4.76-1.42-1.41L2 20.59V22m0-2.83 4.09-4.08c-.21-.3-.36-.62-.45-.97L2 17.76v1.41Z"/></svg>
+  
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+    はじめに
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+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_2" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_preface/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M21 4H3a2 2 0 0 0-2 2v13a2 2 0 0 0 2 2h18a2 2 0 0 0 2-2V6a2 2 0 0 0-2-2M3 19V6h8v13H3m18 0h-8V6h8v13m-7-9.5h6V11h-6V9.5m0 2.5h6v1.5h-6V12m0 2.5h6V16h-6v-1.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 0 章 &nbsp; 前書き
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_2" id="__nav_2_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_2_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_2">
+            <span class="md-nav__icon md-icon"></span>
+            第 0 章 &nbsp; 前書き
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_preface/about_the_book/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.1 &nbsp; この本について
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_preface/suggestions/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.2 &nbsp; 本書の使い方
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_preface/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_introduction/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="./" class="md-nav__link md-nav__link--active">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link md-nav__link--active" for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
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+<h1 id="13">第 13 章 &nbsp; バックトラッキング<a class="headerlink" href="#13" title="Permanent link">&para;</a></h1>
+<p><a class="glightbox" href="../assets/covers/chapter_backtracking.jpg" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="バックトラッキング" class="cover-image" src="../assets/covers/chapter_backtracking.jpg" /></a></p>
+<div class="admonition abstract">
+<p class="admonition-title">Abstract</p>
+<p>迷路の探検家のように、私たちは前進する道で障害に遭遇することがあります。</p>
+<p>バックトラッキングの力は、私たちに新しく始めること、試し続けること、そして最終的に光への出口を見つけることを可能にします。</p>
+</div>
+<h2 id="_1">章の内容<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h2>
+<ul>
+<li><a href="backtracking_algorithm/">13.1 &nbsp; バックトラッキングアルゴリズム</a></li>
+<li><a href="permutations_problem/">13.2 &nbsp; 順列問題</a></li>
+<li><a href="subset_sum_problem/">13.3 &nbsp; 部分集合和問題</a></li>
+<li><a href="n_queens_problem/">13.4 &nbsp; Nクイーン問題</a></li>
+<li><a href="summary/">13.5 &nbsp; まとめ</a></li>
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+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 行ごとの配置戦略
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; 列と対角線の剪定
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#3" class="md-nav__link">
+    <span class="md-ellipsis">
+      3. &nbsp; コード実装
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+            第 16 章 &nbsp; 付録
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+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 行ごとの配置戦略
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; 列と対角線の剪定
+    </span>
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+<h1 id="134-n">13.4 &nbsp; Nクイーン問題<a class="headerlink" href="#134-n" title="Permanent link">&para;</a></h1>
+<div class="admonition question">
+<p class="admonition-title">Question</p>
+<p>チェスのルールによると、クイーンは同じ行、列、または対角線上の駒を攻撃できます。<span class="arithmatex">\(n\)</span> 個のクイーンと <span class="arithmatex">\(n \times n\)</span> のチェスボードが与えられた場合、2つのクイーンが互いに攻撃できない配置を見つけてください。</p>
+</div>
+<p>以下の図に示すように、<span class="arithmatex">\(n = 4\)</span> の場合、2つの解があります。バックトラッキングアルゴリズムの観点から、<span class="arithmatex">\(n \times n\)</span> のチェスボードには <span class="arithmatex">\(n^2\)</span> 個のマスがあり、すべての可能な選択肢 <code>choices</code> を示しています。チェスボードの状態 <code>state</code> は、各クイーンが配置されるにつれて継続的に変化します。</p>
+<p><a class="glightbox" href="../n_queens_problem.assets/solution_4_queens.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="4クイーン問題の解" class="animation-figure" src="../n_queens_problem.assets/solution_4_queens.png" /></a></p>
+<p align="center"> 図 13-15 &nbsp; 4クイーン問題の解 </p>
+
+<p>以下の図は、この問題の3つの制約を示しています：<strong>複数のクイーンは同じ行、列、または対角線を占有できません</strong>。対角線は主対角線 <code>\</code> と副対角線 <code>/</code> に分かれることに注意することが重要です。</p>
+<p><a class="glightbox" href="../n_queens_problem.assets/n_queens_constraints.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Nクイーン問題の制約" class="animation-figure" src="../n_queens_problem.assets/n_queens_constraints.png" /></a></p>
+<p align="center"> 図 13-16 &nbsp; Nクイーン問題の制約 </p>
+
+<h3 id="1">1. &nbsp; 行ごとの配置戦略<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<p>クイーンの数がチェスボードの行数と等しく、どちらも <span class="arithmatex">\(n\)</span> であるため、**チェスボードの各行には1つのクイーンのみが配置できることが**容易に結論付けられます。</p>
+<p>これは、行ごとの配置戦略を採用できることを意味します：最初の行から開始して、最後の行に到達するまで行ごとに1つのクイーンを配置します。</p>
+<p>以下の図は、4クイーン問題の行ごとの配置プロセスを示しています。スペースの制限により、図は最初の行の1つの検索分岐のみを展開し、列と対角線の制約を満たさない配置を剪定します。</p>
+<p><a class="glightbox" href="../n_queens_problem.assets/n_queens_placing.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="行ごとの配置戦略" class="animation-figure" src="../n_queens_problem.assets/n_queens_placing.png" /></a></p>
+<p align="center"> 図 13-17 &nbsp; 行ごとの配置戦略 </p>
+
+<p>本質的に、<strong>行ごとの配置戦略は剪定関数として機能し</strong>、同じ行に複数のクイーンを配置するすべての検索分岐を除去します。</p>
+<h3 id="2">2. &nbsp; 列と対角線の剪定<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
+<p>列の制約を満たすために、長さ <span class="arithmatex">\(n\)</span> のブール配列 <code>cols</code> を使用して、各列にクイーンが占有されているかどうかを追跡できます。各配置決定の前に、<code>cols</code> を使用してすでにクイーンがある列を剪定し、バックトラッキング中に動的に更新されます。</p>
+<div class="admonition tip">
+<p class="admonition-title">Tip</p>
+<p>行列の原点は左上隅にあり、行インデックスは上から下に増加し、列インデックスは左から右に増加することに注意してください。</p>
+</div>
+<p>対角線の制約はどうでしょうか？チェスボード上の特定のセルの行と列のインデックスを <span class="arithmatex">\((row, col)\)</span> とします。特定の主対角線を選択することで、その対角線上のすべてのセルで差 <span class="arithmatex">\(row - col\)</span> が同じであることに気付きます。<strong>つまり、<span class="arithmatex">\(row - col\)</span> は主対角線上で定数値です</strong>。</p>
+<p>言い換えると、2つのセルが <span class="arithmatex">\(row_1 - col_1 = row_2 - col_2\)</span> を満たす場合、それらは確実に同じ主対角線上にあります。このパターンを使用して、以下の図に示す配列 <code>diags1</code> を利用して、クイーンが主対角線上にあるかどうかを追跡できます。</p>
+<p>同様に、<strong><span class="arithmatex">\(row + col\)</span> の和は副対角線上のすべてのセルで定数値です</strong>。配列 <code>diags2</code> を使用して副対角線の制約も処理できます。</p>
+<p><a class="glightbox" href="../n_queens_problem.assets/n_queens_cols_diagonals.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="列と対角線の制約の処理" class="animation-figure" src="../n_queens_problem.assets/n_queens_cols_diagonals.png" /></a></p>
+<p align="center"> 図 13-18 &nbsp; 列と対角線の制約の処理 </p>
+
+<h3 id="3">3. &nbsp; コード実装<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
+<p><span class="arithmatex">\(n\)</span> 次元の正方行列では、<span class="arithmatex">\(row - col\)</span> の範囲は <span class="arithmatex">\([-n + 1, n - 1]\)</span> で、<span class="arithmatex">\(row + col\)</span> の範囲は <span class="arithmatex">\([0, 2n - 2]\)</span> であることに注意してください。したがって、主対角線と副対角線の数はどちらも <span class="arithmatex">\(2n - 1\)</span> で、配列 <code>diags1</code> と <code>diags2</code> の長さは <span class="arithmatex">\(2n - 1\)</span> です。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:14"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><input id="__tabbed_1_14" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label><label for="__tabbed_1_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">n_queens.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a>    <span class="n">row</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="n">state</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">str</span><span class="p">]],</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="n">res</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">str</span><span class="p">]]],</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="n">cols</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">bool</span><span class="p">],</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>    <span class="n">diags1</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">bool</span><span class="p">],</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>    <span class="n">diags2</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">bool</span><span class="p">],</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a><span class="p">):</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;バックトラッキングアルゴリズム：n クイーン&quot;&quot;&quot;</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>    <span class="c1"># すべての行が配置されたら、解を記録</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>    <span class="k">if</span> <span class="n">row</span> <span class="o">==</span> <span class="n">n</span><span class="p">:</span>
+<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>        <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">([</span><span class="nb">list</span><span class="p">(</span><span class="n">row</span><span class="p">)</span> <span class="k">for</span> <span class="n">row</span> <span class="ow">in</span> <span class="n">state</span><span class="p">])</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>        <span class="k">return</span>
+<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>    <span class="c1"># すべての列を走査</span>
+<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>    <span class="k">for</span> <span class="n">col</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
+<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>        <span class="c1"># セルに対応する主対角線と副対角線を計算</span>
+<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a>        <span class="n">diag1</span> <span class="o">=</span> <span class="n">row</span> <span class="o">-</span> <span class="n">col</span> <span class="o">+</span> <span class="n">n</span> <span class="o">-</span> <span class="mi">1</span>
+<a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a>        <span class="n">diag2</span> <span class="o">=</span> <span class="n">row</span> <span class="o">+</span> <span class="n">col</span>
+<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a>        <span class="c1"># 枝刈り：セルの列、主対角線、副対角線にクイーンを配置しない</span>
+<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a>        <span class="k">if</span> <span class="ow">not</span> <span class="n">cols</span><span class="p">[</span><span class="n">col</span><span class="p">]</span> <span class="ow">and</span> <span class="ow">not</span> <span class="n">diags1</span><span class="p">[</span><span class="n">diag1</span><span class="p">]</span> <span class="ow">and</span> <span class="ow">not</span> <span class="n">diags2</span><span class="p">[</span><span class="n">diag2</span><span class="p">]:</span>
+<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a>            <span class="c1"># 試行：セルにクイーンを配置</span>
+<a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a>            <span class="n">state</span><span class="p">[</span><span class="n">row</span><span class="p">][</span><span class="n">col</span><span class="p">]</span> <span class="o">=</span> <span class="s2">&quot;Q&quot;</span>
+<a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a>            <span class="n">cols</span><span class="p">[</span><span class="n">col</span><span class="p">]</span> <span class="o">=</span> <span class="n">diags1</span><span class="p">[</span><span class="n">diag1</span><span class="p">]</span> <span class="o">=</span> <span class="n">diags2</span><span class="p">[</span><span class="n">diag2</span><span class="p">]</span> <span class="o">=</span> <span class="kc">True</span>
+<a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a>            <span class="c1"># 次の行を配置</span>
+<a id="__codelineno-0-26" name="__codelineno-0-26" href="#__codelineno-0-26"></a>            <span class="n">backtrack</span><span class="p">(</span><span class="n">row</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="n">state</span><span class="p">,</span> <span class="n">res</span><span class="p">,</span> <span class="n">cols</span><span class="p">,</span> <span class="n">diags1</span><span class="p">,</span> <span class="n">diags2</span><span class="p">)</span>
+<a id="__codelineno-0-27" name="__codelineno-0-27" href="#__codelineno-0-27"></a>            <span class="c1"># 撤回：セルを空のスポットに復元</span>
+<a id="__codelineno-0-28" name="__codelineno-0-28" href="#__codelineno-0-28"></a>            <span class="n">state</span><span class="p">[</span><span class="n">row</span><span class="p">][</span><span class="n">col</span><span class="p">]</span> <span class="o">=</span> <span class="s2">&quot;#&quot;</span>
+<a id="__codelineno-0-29" name="__codelineno-0-29" href="#__codelineno-0-29"></a>            <span class="n">cols</span><span class="p">[</span><span class="n">col</span><span class="p">]</span> <span class="o">=</span> <span class="n">diags1</span><span class="p">[</span><span class="n">diag1</span><span class="p">]</span> <span class="o">=</span> <span class="n">diags2</span><span class="p">[</span><span class="n">diag2</span><span class="p">]</span> <span class="o">=</span> <span class="kc">False</span>
+<a id="__codelineno-0-30" name="__codelineno-0-30" href="#__codelineno-0-30"></a>
+<a id="__codelineno-0-31" name="__codelineno-0-31" href="#__codelineno-0-31"></a><span class="k">def</span><span class="w"> </span><span class="nf">n_queens</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">str</span><span class="p">]]]:</span>
+<a id="__codelineno-0-32" name="__codelineno-0-32" href="#__codelineno-0-32"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;n クイーンを解く&quot;&quot;&quot;</span>
+<a id="__codelineno-0-33" name="__codelineno-0-33" href="#__codelineno-0-33"></a>    <span class="c1"># n*n サイズのチェスボードを初期化、&#39;Q&#39; はクイーンを表し、&#39;#&#39; は空のスポットを表す</span>
+<a id="__codelineno-0-34" name="__codelineno-0-34" href="#__codelineno-0-34"></a>    <span class="n">state</span> <span class="o">=</span> <span class="p">[[</span><span class="s2">&quot;#&quot;</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">)]</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">)]</span>
+<a id="__codelineno-0-35" name="__codelineno-0-35" href="#__codelineno-0-35"></a>    <span class="n">cols</span> <span class="o">=</span> <span class="p">[</span><span class="kc">False</span><span class="p">]</span> <span class="o">*</span> <span class="n">n</span>  <span class="c1"># クイーンがある列を記録</span>
+<a id="__codelineno-0-36" name="__codelineno-0-36" href="#__codelineno-0-36"></a>    <span class="n">diags1</span> <span class="o">=</span> <span class="p">[</span><span class="kc">False</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>  <span class="c1"># クイーンがある主対角線を記録</span>
+<a id="__codelineno-0-37" name="__codelineno-0-37" href="#__codelineno-0-37"></a>    <span class="n">diags2</span> <span class="o">=</span> <span class="p">[</span><span class="kc">False</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>  <span class="c1"># クイーンがある副対角線を記録</span>
+<a id="__codelineno-0-38" name="__codelineno-0-38" href="#__codelineno-0-38"></a>    <span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>
+<a id="__codelineno-0-39" name="__codelineno-0-39" href="#__codelineno-0-39"></a>    <span class="n">backtrack</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="n">state</span><span class="p">,</span> <span class="n">res</span><span class="p">,</span> <span class="n">cols</span><span class="p">,</span> <span class="n">diags1</span><span class="p">,</span> <span class="n">diags2</span><span class="p">)</span>
+<a id="__codelineno-0-40" name="__codelineno-0-40" href="#__codelineno-0-40"></a>
+<a id="__codelineno-0-41" name="__codelineno-0-41" href="#__codelineno-0-41"></a>    <span class="k">return</span> <span class="n">res</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">n_queens.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* バックトラッキングアルゴリズム：n クイーン */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">row</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="n">string</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="n">string</span><span class="o">&gt;&gt;&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">bool</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">cols</span><span class="p">,</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">               </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">bool</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">diags1</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">bool</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">diags2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="c1">// すべての行が配置されたら、解を記録</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">row</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">state</span><span class="p">);</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">    </span><span class="c1">// すべての列を走査</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">col</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">col</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">col</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">        </span><span class="c1">// セルに対応する主対角線と副対角線を計算</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">diag1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">row</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">col</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">diag2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">row</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">col</span><span class="p">;</span>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">        </span><span class="c1">// 剪定：セルの列、主対角線、副対角線にクイーンを配置することを許可しない</span>
+<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">cols</span><span class="p">[</span><span class="n">col</span><span class="p">]</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="o">!</span><span class="n">diags1</span><span class="p">[</span><span class="n">diag1</span><span class="p">]</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="o">!</span><span class="n">diags2</span><span class="p">[</span><span class="n">diag2</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">            </span><span class="c1">// 試行：セルにクイーンを配置</span>
+<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w">            </span><span class="n">state</span><span class="p">[</span><span class="n">row</span><span class="p">][</span><span class="n">col</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;Q&quot;</span><span class="p">;</span>
+<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w">            </span><span class="n">cols</span><span class="p">[</span><span class="n">col</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">diags1</span><span class="p">[</span><span class="n">diag1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">diags2</span><span class="p">[</span><span class="n">diag2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">true</span><span class="p">;</span>
+<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="w">            </span><span class="c1">// 次の行を配置</span>
+<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="w">            </span><span class="n">backtrack</span><span class="p">(</span><span class="n">row</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">cols</span><span class="p">,</span><span class="w"> </span><span class="n">diags1</span><span class="p">,</span><span class="w"> </span><span class="n">diags2</span><span class="p">);</span>
+<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="w">            </span><span class="c1">// 回退：セルを空のスポットに復元</span>
+<a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a><span class="w">            </span><span class="n">state</span><span class="p">[</span><span class="n">row</span><span class="p">][</span><span class="n">col</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;#&quot;</span><span class="p">;</span>
+<a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a><span class="w">            </span><span class="n">cols</span><span class="p">[</span><span class="n">col</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">diags1</span><span class="p">[</span><span class="n">diag1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">diags2</span><span class="p">[</span><span class="n">diag2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">false</span><span class="p">;</span>
+<a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-26" name="__codelineno-1-26" href="#__codelineno-1-26"></a><span class="p">}</span>
+<a id="__codelineno-1-27" name="__codelineno-1-27" href="#__codelineno-1-27"></a>
+<a id="__codelineno-1-28" name="__codelineno-1-28" href="#__codelineno-1-28"></a><span class="cm">/* n クイーンを解く */</span>
+<a id="__codelineno-1-29" name="__codelineno-1-29" href="#__codelineno-1-29"></a><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="n">string</span><span class="o">&gt;&gt;&gt;</span><span class="w"> </span><span class="n">nQueens</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-30" name="__codelineno-1-30" href="#__codelineno-1-30"></a><span class="w">    </span><span class="c1">// n*n サイズのチェスボードを初期化、&#39;Q&#39; はクイーンを表し、&#39;#&#39; は空のスポットを表す</span>
+<a id="__codelineno-1-31" name="__codelineno-1-31" href="#__codelineno-1-31"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="n">string</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">string</span><span class="o">&gt;</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;#&quot;</span><span class="p">));</span>
+<a id="__codelineno-1-32" name="__codelineno-1-32" href="#__codelineno-1-32"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">bool</span><span class="o">&gt;</span><span class="w"> </span><span class="n">cols</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="nb">false</span><span class="p">);</span><span class="w">           </span><span class="c1">// クイーンのある列を記録</span>
+<a id="__codelineno-1-33" name="__codelineno-1-33" href="#__codelineno-1-33"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">bool</span><span class="o">&gt;</span><span class="w"> </span><span class="n">diags1</span><span class="p">(</span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="nb">false</span><span class="p">);</span><span class="w"> </span><span class="c1">// クイーンのある主対角線を記録</span>
+<a id="__codelineno-1-34" name="__codelineno-1-34" href="#__codelineno-1-34"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">bool</span><span class="o">&gt;</span><span class="w"> </span><span class="n">diags2</span><span class="p">(</span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="nb">false</span><span class="p">);</span><span class="w"> </span><span class="c1">// クイーンのある副対角線を記録</span>
+<a id="__codelineno-1-35" name="__codelineno-1-35" href="#__codelineno-1-35"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="n">string</span><span class="o">&gt;&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-1-36" name="__codelineno-1-36" href="#__codelineno-1-36"></a>
+<a id="__codelineno-1-37" name="__codelineno-1-37" href="#__codelineno-1-37"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">cols</span><span class="p">,</span><span class="w"> </span><span class="n">diags1</span><span class="p">,</span><span class="w"> </span><span class="n">diags2</span><span class="p">);</span>
+<a id="__codelineno-1-38" name="__codelineno-1-38" href="#__codelineno-1-38"></a>
+<a id="__codelineno-1-39" name="__codelineno-1-39" href="#__codelineno-1-39"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-1-40" name="__codelineno-1-40" href="#__codelineno-1-40"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">n_queens.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* バックトラッキングアルゴリズム：n クイーン */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">row</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">String</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">String</span><span class="o">&gt;&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">,</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">        </span><span class="kt">boolean</span><span class="o">[]</span><span class="w"> </span><span class="n">cols</span><span class="p">,</span><span class="w"> </span><span class="kt">boolean</span><span class="o">[]</span><span class="w"> </span><span class="n">diags1</span><span class="p">,</span><span class="w"> </span><span class="kt">boolean</span><span class="o">[]</span><span class="w"> </span><span class="n">diags2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="c1">// すべての行が配置されたら、解を記録</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">row</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">String</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">copyState</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">String</span><span class="o">&gt;</span><span class="w"> </span><span class="n">sRow</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">state</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">            </span><span class="n">copyState</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">(</span><span class="n">sRow</span><span class="p">));</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">copyState</span><span class="p">);</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">    </span><span class="c1">// すべての列を走査</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">col</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">col</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">col</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">        </span><span class="c1">// セルに対応する主対角線と副対角線を計算</span>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">diag1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">row</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">col</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">diag2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">row</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">col</span><span class="p">;</span>
+<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w">        </span><span class="c1">// 剪定：セルの列、主対角線、副対角線にクイーンを配置することを許可しない</span>
+<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">cols</span><span class="o">[</span><span class="n">col</span><span class="o">]</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="o">!</span><span class="n">diags1</span><span class="o">[</span><span class="n">diag1</span><span class="o">]</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="o">!</span><span class="n">diags2</span><span class="o">[</span><span class="n">diag2</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="w">            </span><span class="c1">// 試行：セルにクイーンを配置</span>
+<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="w">            </span><span class="n">state</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">row</span><span class="p">).</span><span class="na">set</span><span class="p">(</span><span class="n">col</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;Q&quot;</span><span class="p">);</span>
+<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a><span class="w">            </span><span class="n">cols</span><span class="o">[</span><span class="n">col</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">diags1</span><span class="o">[</span><span class="n">diag1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">diags2</span><span class="o">[</span><span class="n">diag2</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span><span class="p">;</span>
+<a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a><span class="w">            </span><span class="c1">// 次の行を配置</span>
+<a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a><span class="w">            </span><span class="n">backtrack</span><span class="p">(</span><span class="n">row</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">cols</span><span class="p">,</span><span class="w"> </span><span class="n">diags1</span><span class="p">,</span><span class="w"> </span><span class="n">diags2</span><span class="p">);</span>
+<a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a><span class="w">            </span><span class="c1">// 回退：セルを空のスポットに復元</span>
+<a id="__codelineno-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></a><span class="w">            </span><span class="n">state</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">row</span><span class="p">).</span><span class="na">set</span><span class="p">(</span><span class="n">col</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;#&quot;</span><span class="p">);</span>
+<a id="__codelineno-2-27" name="__codelineno-2-27" href="#__codelineno-2-27"></a><span class="w">            </span><span class="n">cols</span><span class="o">[</span><span class="n">col</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">diags1</span><span class="o">[</span><span class="n">diag1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">diags2</span><span class="o">[</span><span class="n">diag2</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">false</span><span class="p">;</span>
+<a id="__codelineno-2-28" name="__codelineno-2-28" href="#__codelineno-2-28"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-2-29" name="__codelineno-2-29" href="#__codelineno-2-29"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-30" name="__codelineno-2-30" href="#__codelineno-2-30"></a><span class="p">}</span>
+<a id="__codelineno-2-31" name="__codelineno-2-31" href="#__codelineno-2-31"></a>
+<a id="__codelineno-2-32" name="__codelineno-2-32" href="#__codelineno-2-32"></a><span class="cm">/* n クイーンを解く */</span>
+<a id="__codelineno-2-33" name="__codelineno-2-33" href="#__codelineno-2-33"></a><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">String</span><span class="o">&gt;&gt;&gt;</span><span class="w"> </span><span class="nf">nQueens</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-34" name="__codelineno-2-34" href="#__codelineno-2-34"></a><span class="w">    </span><span class="c1">// n*n サイズのチェスボードを初期化、&#39;Q&#39; はクイーンを表し、&#39;#&#39; は空のスポットを表す</span>
+<a id="__codelineno-2-35" name="__codelineno-2-35" href="#__codelineno-2-35"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">String</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-2-36" name="__codelineno-2-36" href="#__codelineno-2-36"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-37" name="__codelineno-2-37" href="#__codelineno-2-37"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="n">String</span><span class="o">&gt;</span><span class="w"> </span><span class="n">row</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-2-38" name="__codelineno-2-38" href="#__codelineno-2-38"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-39" name="__codelineno-2-39" href="#__codelineno-2-39"></a><span class="w">            </span><span class="n">row</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="s">&quot;#&quot;</span><span class="p">);</span>
+<a id="__codelineno-2-40" name="__codelineno-2-40" href="#__codelineno-2-40"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-2-41" name="__codelineno-2-41" href="#__codelineno-2-41"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">row</span><span class="p">);</span>
+<a id="__codelineno-2-42" name="__codelineno-2-42" href="#__codelineno-2-42"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-43" name="__codelineno-2-43" href="#__codelineno-2-43"></a><span class="w">    </span><span class="kt">boolean</span><span class="o">[]</span><span class="w"> </span><span class="n">cols</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">boolean</span><span class="o">[</span><span class="n">n</span><span class="o">]</span><span class="p">;</span><span class="w"> </span><span class="c1">// クイーンのある列を記録</span>
+<a id="__codelineno-2-44" name="__codelineno-2-44" href="#__codelineno-2-44"></a><span class="w">    </span><span class="kt">boolean</span><span class="o">[]</span><span class="w"> </span><span class="n">diags1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">boolean</span><span class="o">[</span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span><span class="w"> </span><span class="c1">// クイーンのある主対角線を記録</span>
+<a id="__codelineno-2-45" name="__codelineno-2-45" href="#__codelineno-2-45"></a><span class="w">    </span><span class="kt">boolean</span><span class="o">[]</span><span class="w"> </span><span class="n">diags2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">boolean</span><span class="o">[</span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span><span class="w"> </span><span class="c1">// クイーンのある副対角線を記録</span>
+<a id="__codelineno-2-46" name="__codelineno-2-46" href="#__codelineno-2-46"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">String</span><span class="o">&gt;&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-2-47" name="__codelineno-2-47" href="#__codelineno-2-47"></a>
+<a id="__codelineno-2-48" name="__codelineno-2-48" href="#__codelineno-2-48"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">cols</span><span class="p">,</span><span class="w"> </span><span class="n">diags1</span><span class="p">,</span><span class="w"> </span><span class="n">diags2</span><span class="p">);</span>
+<a id="__codelineno-2-49" name="__codelineno-2-49" href="#__codelineno-2-49"></a>
+<a id="__codelineno-2-50" name="__codelineno-2-50" href="#__codelineno-2-50"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-2-51" name="__codelineno-2-51" href="#__codelineno-2-51"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">n_queens.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">n_queens</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Backtrack</span><span class="p">}</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">n_queens</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">NQueens</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">n_queens.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">backtrack</span><span class="p">}</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">nQueens</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">n_queens.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">nQueens</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">n_queens.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">backtrack</span><span class="p">}</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">nQueens</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">n_queens.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">backtrack</span><span class="p">}</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">nQueens</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">n_queens.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">nQueens</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">n_queens.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">n_queens</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">n_queens.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">nQueens</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">n_queens.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">nQueens</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">n_queens.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">n_queens</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">n_queens.zig</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a>
+<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">nQueens</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p><span class="arithmatex">\(n\)</span> 個のクイーンを行ごとに配置し、列の制約を考慮して、最初の行から最後の行まで、<span class="arithmatex">\(n\)</span>、<span class="arithmatex">\(n-1\)</span>、<span class="arithmatex">\(\dots\)</span>、<span class="arithmatex">\(2\)</span>、<span class="arithmatex">\(1\)</span> の選択肢があり、<span class="arithmatex">\(O(n!)\)</span> 時間を使用します。解を記録する際、行列 <code>state</code> をコピーして <code>res</code> に追加する必要があり、コピー操作は <span class="arithmatex">\(O(n^2)\)</span> 時間を使用します。したがって、<strong>全体の時間計算量は <span class="arithmatex">\(O(n! \cdot n^2)\)</span> です</strong>。実際には、対角線制約に基づく剪定により検索空間を大幅に削減できるため、多くの場合、検索効率は上記の時間計算量よりも優れています。</p>
+<p>配列 <code>state</code> は <span class="arithmatex">\(O(n^2)\)</span> 空間を使用し、配列 <code>cols</code>、<code>diags1</code>、<code>diags2</code> はそれぞれ <span class="arithmatex">\(O(n)\)</span> 空間を使用します。最大再帰深度は <span class="arithmatex">\(n\)</span> で、<span class="arithmatex">\(O(n)\)</span> のスタックフレーム空間を使用します。したがって、<strong>空間計算量は <span class="arithmatex">\(O(n^2)\)</span> です</strong>。</p>
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diff --git a/ja/chapter_backtracking/permutations_problem.assets/permutations_ii_pruning_summary.png b/ja/chapter_backtracking/permutations_problem.assets/permutations_ii_pruning_summary.png
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+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1321" class="md-nav__link">
+    <span class="md-ellipsis">
+      13.2.1 &nbsp; 重複要素がない場合
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="13.2.1   重複要素がない場合">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 重複選択の剪定
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; コード実装
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1322" class="md-nav__link">
+    <span class="md-ellipsis">
+      13.2.2 &nbsp; 重複要素を考慮する場合
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="13.2.2   重複要素を考慮する場合">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1_1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 等値要素の剪定
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2_1" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; コード実装
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#3-2" class="md-nav__link">
+    <span class="md-ellipsis">
+      3. &nbsp; 2つの剪定方法の比較
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
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+  
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+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
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+    </li>
+  
+
+              
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+        </nav>
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+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
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+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
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+
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+              
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+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
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+  
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+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1321" class="md-nav__link">
+    <span class="md-ellipsis">
+      13.2.1 &nbsp; 重複要素がない場合
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="13.2.1   重複要素がない場合">
+      <ul class="md-nav__list">
+        
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+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 重複選択の剪定
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; コード実装
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1322" class="md-nav__link">
+    <span class="md-ellipsis">
+      13.2.2 &nbsp; 重複要素を考慮する場合
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="13.2.2   重複要素を考慮する場合">
+      <ul class="md-nav__list">
+        
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+  <a href="#1_1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 等値要素の剪定
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2_1" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; コード実装
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#3-2" class="md-nav__link">
+    <span class="md-ellipsis">
+      3. &nbsp; 2つの剪定方法の比較
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
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+</li>
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+      
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
+    </a>
+  
+
+  <!-- View button -->
+  
+
+
+<!-- Page content -->
+<h1 id="132">13.2 &nbsp; 順列問題<a class="headerlink" href="#132" title="Permanent link">&para;</a></h1>
+<p>順列問題は、バックトラッキングアルゴリズムの典型的な応用です。これは、配列や文字列などの与えられた集合から要素のすべての可能な配置（順列）を見つけることを含みます。</p>
+<p>以下の表は、入力配列とその対応する順列を含むいくつかの例を示しています。</p>
+<p align="center"> 表 13-2 &nbsp; 順列の例 </p>
+
+<div class="center-table">
+<table>
+<thead>
+<tr>
+<th style="text-align: left;">入力配列</th>
+<th style="text-align: left;">順列</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td style="text-align: left;"><span class="arithmatex">\([1]\)</span></td>
+<td style="text-align: left;"><span class="arithmatex">\([1]\)</span></td>
+</tr>
+<tr>
+<td style="text-align: left;"><span class="arithmatex">\([1, 2]\)</span></td>
+<td style="text-align: left;"><span class="arithmatex">\([1, 2], [2, 1]\)</span></td>
+</tr>
+<tr>
+<td style="text-align: left;"><span class="arithmatex">\([1, 2, 3]\)</span></td>
+<td style="text-align: left;"><span class="arithmatex">\([1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]\)</span></td>
+</tr>
+</tbody>
+</table>
+</div>
+<h2 id="1321">13.2.1 &nbsp; 重複要素がない場合<a class="headerlink" href="#1321" title="Permanent link">&para;</a></h2>
+<div class="admonition question">
+<p class="admonition-title">Question</p>
+<p>重複要素のない整数配列が与えられた場合、すべての可能な順列を返してください。</p>
+</div>
+<p>バックトラッキングの観点から、<strong>順列を生成するプロセスを一連の選択として見ることができます。</strong> 入力配列が <span class="arithmatex">\([1, 2, 3]\)</span> だとします。最初に <span class="arithmatex">\(1\)</span> を選択し、次に <span class="arithmatex">\(3\)</span>、最後に <span class="arithmatex">\(2\)</span> を選択すると、順列 <span class="arithmatex">\([1, 3, 2]\)</span> が得られます。「バックトラッキング」は前の選択を取り消して、代替オプションを探索することを意味します。</p>
+<p>コーディングの観点から、候補集合 <code>choices</code> は入力配列のすべての要素で構成され、<code>state</code> はこれまでに選択された要素を保持します。各要素は一度だけ選択できるため、<strong><code>state</code> のすべての要素は一意である必要があります</strong>。</p>
+<p>以下の図に示すように、検索プロセスを再帰木に展開できます。各ノードは現在の <code>state</code> を表します。ルートノードから開始して、3回の選択の後、葉ノードに到達します—それぞれが順列に対応します。</p>
+<p><a class="glightbox" href="../permutations_problem.assets/permutations_i.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="順列の再帰木" class="animation-figure" src="../permutations_problem.assets/permutations_i.png" /></a></p>
+<p align="center"> 図 13-5 &nbsp; 順列の再帰木 </p>
+
+<h3 id="1">1. &nbsp; 重複選択の剪定<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<p>各要素が一度だけ選択されることを保証するために、ブール配列 <code>selected</code> を導入します。ここで <code>selected[i]</code> は <code>choices[i]</code> が選択されたかどうかを示します。次に、この配列に基づいて剪定ステップを実行します：</p>
+<ul>
+<li><code>choice[i]</code> を選択した後、<code>selected[i]</code> を <span class="arithmatex">\(\text{True}\)</span> に設定して選択されたとマークします。</li>
+<li><code>choices</code> を反復処理する際、選択されたとマークされたすべての要素をスキップします（つまり、それらの分岐を剪定します）。</li>
+</ul>
+<p>以下の図に示すように、最初のラウンドで1を選択し、2番目のラウンドで3を選択し、最後のラウンドで2を選択するとします。2番目のラウンドで要素1の分岐と、3番目のラウンドで要素1と3の分岐を剪定する必要があります。</p>
+<p><a class="glightbox" href="../permutations_problem.assets/permutations_i_pruning.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="順列の剪定例" class="animation-figure" src="../permutations_problem.assets/permutations_i_pruning.png" /></a></p>
+<p align="center"> 図 13-6 &nbsp; 順列の剪定例 </p>
+
+<p>図から、この剪定プロセスが検索空間を <span class="arithmatex">\(O(n^n)\)</span> から <span class="arithmatex">\(O(n!)\)</span> に削減することがわかります。</p>
+<h3 id="2">2. &nbsp; コード実装<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
+<p>この理解により、フレームワークコードの「空欄を埋める」ことができます。全体のコードを簡潔に保つため、フレームワークの各部分を個別に実装せず、代わりに <code>backtrack()</code> 関数ですべてを展開します：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:14"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><input id="__tabbed_1_14" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label><label for="__tabbed_1_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">permutations_i.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a>    <span class="n">state</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">choices</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">selected</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">bool</span><span class="p">],</span> <span class="n">res</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]]</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="p">):</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;バックトラッキングアルゴリズム：順列 I&quot;&quot;&quot;</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="c1"># 状態の長さが要素数と等しいとき、解を記録</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">state</span><span class="p">)</span> <span class="o">==</span> <span class="nb">len</span><span class="p">(</span><span class="n">choices</span><span class="p">):</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>        <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">state</span><span class="p">))</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>        <span class="k">return</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>    <span class="c1"># すべての選択肢を走査</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>    <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">choice</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">choices</span><span class="p">):</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>        <span class="c1"># 枝刈り：要素の重複選択を許可しない</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>        <span class="k">if</span> <span class="ow">not</span> <span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]:</span>
+<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>            <span class="c1"># 試行：選択を行い、状態を更新</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>            <span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="kc">True</span>
+<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>            <span class="n">state</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">choice</span><span class="p">)</span>
+<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>            <span class="c1"># 次の選択ラウンドに進む</span>
+<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>            <span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">choices</span><span class="p">,</span> <span class="n">selected</span><span class="p">,</span> <span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a>            <span class="c1"># 撤回：選択を取り消し、前の状態に復元</span>
+<a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a>            <span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="kc">False</span>
+<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a>            <span class="n">state</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
+<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a>
+<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a><span class="k">def</span><span class="w"> </span><span class="nf">permutations_i</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]]:</span>
+<a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;順列 I&quot;&quot;&quot;</span>
+<a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a>    <span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>
+<a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a>    <span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="o">=</span><span class="p">[],</span> <span class="n">choices</span><span class="o">=</span><span class="n">nums</span><span class="p">,</span> <span class="n">selected</span><span class="o">=</span><span class="p">[</span><span class="kc">False</span><span class="p">]</span> <span class="o">*</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">),</span> <span class="n">res</span><span class="o">=</span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-0-26" name="__codelineno-0-26" href="#__codelineno-0-26"></a>    <span class="k">return</span> <span class="n">res</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">permutations_i.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* バックトラッキングアルゴリズム：順列 I */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">bool</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">selected</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// 状態の長さが要素数と等しくなったら、解を記録</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="n">size</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">state</span><span class="p">);</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">        </span><span class="c1">// 剪定：要素の重複選択を許可しない</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">            </span><span class="c1">// 試行：選択を行い、状態を更新</span>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">            </span><span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">true</span><span class="p">;</span>
+<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">            </span><span class="n">state</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">choice</span><span class="p">);</span>
+<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">            </span><span class="c1">// 次のラウンドの選択に進む</span>
+<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w">            </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">selected</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w">            </span><span class="c1">// 回退：選択を取り消し、前の状態に復元</span>
+<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="w">            </span><span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">false</span><span class="p">;</span>
+<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="w">            </span><span class="n">state</span><span class="p">.</span><span class="n">pop_back</span><span class="p">();</span>
+<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a><span class="p">}</span>
+<a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a>
+<a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a><span class="cm">/* 順列 I */</span>
+<a id="__codelineno-1-26" name="__codelineno-1-26" href="#__codelineno-1-26"></a><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">permutationsI</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-27" name="__codelineno-1-27" href="#__codelineno-1-27"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">;</span>
+<a id="__codelineno-1-28" name="__codelineno-1-28" href="#__codelineno-1-28"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">bool</span><span class="o">&gt;</span><span class="w"> </span><span class="n">selected</span><span class="p">(</span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">(),</span><span class="w"> </span><span class="nb">false</span><span class="p">);</span>
+<a id="__codelineno-1-29" name="__codelineno-1-29" href="#__codelineno-1-29"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-1-30" name="__codelineno-1-30" href="#__codelineno-1-30"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">selected</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-1-31" name="__codelineno-1-31" href="#__codelineno-1-31"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-1-32" name="__codelineno-1-32" href="#__codelineno-1-32"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">permutations_i.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* バックトラッキングアルゴリズム：順列 I */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="kt">boolean</span><span class="o">[]</span><span class="w"> </span><span class="n">selected</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// 状態の長さが要素数と等しくなったら、解を記録</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="na">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="na">length</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="p">(</span><span class="n">state</span><span class="p">));</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="na">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">        </span><span class="c1">// 剪定：要素の重複選択を許可しない</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">selected</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">            </span><span class="c1">// 試行：選択を行い、状態を更新</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">            </span><span class="n">selected</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span><span class="p">;</span>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">            </span><span class="n">state</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">choice</span><span class="p">);</span>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">            </span><span class="c1">// 次のラウンドの選択に進む</span>
+<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w">            </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">selected</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w">            </span><span class="c1">// 回退：選択を取り消し、前の状態に復元</span>
+<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w">            </span><span class="n">selected</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">false</span><span class="p">;</span>
+<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="w">            </span><span class="n">state</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="na">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a><span class="p">}</span>
+<a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a>
+<a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a><span class="cm">/* 順列 I */</span>
+<a id="__codelineno-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></a><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="nf">permutationsI</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-27" name="__codelineno-2-27" href="#__codelineno-2-27"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-2-28" name="__codelineno-2-28" href="#__codelineno-2-28"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="p">(),</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">boolean</span><span class="o">[</span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-2-29" name="__codelineno-2-29" href="#__codelineno-2-29"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-2-30" name="__codelineno-2-30" href="#__codelineno-2-30"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">permutations_i.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">permutations_i</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Backtrack</span><span class="p">}</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">permutations_i</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">PermutationsI</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">permutations_i.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">backtrackI</span><span class="p">}</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">permutationsI</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">permutations_i.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">permutationsI</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">permutations_i.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">backtrack</span><span class="p">}</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">permutationsI</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">permutations_i.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">backtrack</span><span class="p">}</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">permutationsI</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">permutations_i.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">permutationsI</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">permutations_i.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">permutations_i</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">permutations_i.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">permutationsI</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">permutations_i.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">permutationsI</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">permutations_i.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">permutations_i</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">permutations_i.zig</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a>
+<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">permutationsI</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h2 id="1322">13.2.2 &nbsp; 重複要素を考慮する場合<a class="headerlink" href="#1322" title="Permanent link">&para;</a></h2>
+<div class="admonition question">
+<p class="admonition-title">Question</p>
+<p>**重複要素を含む可能性のある**整数配列が与えられた場合、すべての一意の順列を返してください。</p>
+</div>
+<p>入力配列が <span class="arithmatex">\([1, 1, 2]\)</span> だとします。2つの同一要素 <span class="arithmatex">\(1\)</span> を区別するために、2番目を <span class="arithmatex">\(\hat{1}\)</span> とラベル付けします。</p>
+<p>以下の図に示すように、この方法で生成される順列の半分は重複です：</p>
+<p><a class="glightbox" href="../permutations_problem.assets/permutations_ii.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="重複順列" class="animation-figure" src="../permutations_problem.assets/permutations_ii.png" /></a></p>
+<p align="center"> 図 13-7 &nbsp; 重複順列 </p>
+
+<p>では、これらの重複順列をどのように除去できるでしょうか？一つの直接的なアプローチは、すべての順列を生成した後にハッシュセットを使用して重複を除去することです。しかし、これはあまり優雅ではありません。<strong>重複を生成する分岐は本来不要であり、事前に剪定されるべきだからです</strong>、これによりアルゴリズムの効率が向上します。</p>
+<h3 id="1_1">1. &nbsp; 等値要素の剪定<a class="headerlink" href="#1_1" title="Permanent link">&para;</a></h3>
+<p>以下の図を見ると、最初のラウンドで <span class="arithmatex">\(1\)</span> または <span class="arithmatex">\(\hat{1}\)</span> を選択すると同じ順列につながるため、<span class="arithmatex">\(\hat{1}\)</span> を剪定します。</p>
+<p>同様に、最初のラウンドで <span class="arithmatex">\(2\)</span> を選択した後、2番目のラウンドで <span class="arithmatex">\(1\)</span> または <span class="arithmatex">\(\hat{1}\)</span> を選択しても重複分岐につながるため、その時も <span class="arithmatex">\(\hat{1}\)</span> を剪定します。</p>
+<p>本質的に、<strong>私たちの目標は、複数の同一要素が選択の各ラウンドで一度だけ選択されることを保証することです。</strong></p>
+<p><a class="glightbox" href="../permutations_problem.assets/permutations_ii_pruning.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="重複順列の剪定" class="animation-figure" src="../permutations_problem.assets/permutations_ii_pruning.png" /></a></p>
+<p align="center"> 図 13-8 &nbsp; 重複順列の剪定 </p>
+
+<h3 id="2_1">2. &nbsp; コード実装<a class="headerlink" href="#2_1" title="Permanent link">&para;</a></h3>
+<p>前の問題のコードに基づいて、各ラウンドでハッシュセット <code>duplicated</code> を導入します。このセットは、すでに試行した要素を追跡し、重複を剪定できるようにします：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:14"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><input id="__tabbed_2_14" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label><label for="__tabbed_2_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">permutations_ii.py</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span>
+<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a>    <span class="n">state</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">choices</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">selected</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">bool</span><span class="p">],</span> <span class="n">res</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]]</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="p">):</span>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;バックトラッキングアルゴリズム：順列 II&quot;&quot;&quot;</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a>    <span class="c1"># 状態の長さが要素数と等しいとき、解を記録</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a>    <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">state</span><span class="p">)</span> <span class="o">==</span> <span class="nb">len</span><span class="p">(</span><span class="n">choices</span><span class="p">):</span>
+<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a>        <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">state</span><span class="p">))</span>
+<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a>        <span class="k">return</span>
+<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a>    <span class="c1"># すべての選択肢を走査</span>
+<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a>    <span class="n">duplicated</span> <span class="o">=</span> <span class="nb">set</span><span class="p">[</span><span class="nb">int</span><span class="p">]()</span>
+<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a>    <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">choice</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">choices</span><span class="p">):</span>
+<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a>        <span class="c1"># 枝刈り：要素の重複選択を許可せず、等しい要素の重複選択も許可しない</span>
+<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a>        <span class="k">if</span> <span class="ow">not</span> <span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="ow">and</span> <span class="n">choice</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">duplicated</span><span class="p">:</span>
+<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a>            <span class="c1"># 試行：選択を行い、状態を更新</span>
+<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a>            <span class="n">duplicated</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">choice</span><span class="p">)</span>  <span class="c1"># 選択された要素値を記録</span>
+<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a>            <span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="kc">True</span>
+<a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a>            <span class="n">state</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">choice</span><span class="p">)</span>
+<a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a>            <span class="c1"># 次の選択ラウンドに進む</span>
+<a id="__codelineno-14-19" name="__codelineno-14-19" href="#__codelineno-14-19"></a>            <span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">choices</span><span class="p">,</span> <span class="n">selected</span><span class="p">,</span> <span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-14-20" name="__codelineno-14-20" href="#__codelineno-14-20"></a>            <span class="c1"># 撤回：選択を取り消し、前の状態に復元</span>
+<a id="__codelineno-14-21" name="__codelineno-14-21" href="#__codelineno-14-21"></a>            <span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="kc">False</span>
+<a id="__codelineno-14-22" name="__codelineno-14-22" href="#__codelineno-14-22"></a>            <span class="n">state</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
+<a id="__codelineno-14-23" name="__codelineno-14-23" href="#__codelineno-14-23"></a>
+<a id="__codelineno-14-24" name="__codelineno-14-24" href="#__codelineno-14-24"></a><span class="k">def</span><span class="w"> </span><span class="nf">permutations_ii</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]]:</span>
+<a id="__codelineno-14-25" name="__codelineno-14-25" href="#__codelineno-14-25"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;順列 II&quot;&quot;&quot;</span>
+<a id="__codelineno-14-26" name="__codelineno-14-26" href="#__codelineno-14-26"></a>    <span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>
+<a id="__codelineno-14-27" name="__codelineno-14-27" href="#__codelineno-14-27"></a>    <span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="o">=</span><span class="p">[],</span> <span class="n">choices</span><span class="o">=</span><span class="n">nums</span><span class="p">,</span> <span class="n">selected</span><span class="o">=</span><span class="p">[</span><span class="kc">False</span><span class="p">]</span> <span class="o">*</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">),</span> <span class="n">res</span><span class="o">=</span><span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-14-28" name="__codelineno-14-28" href="#__codelineno-14-28"></a>    <span class="k">return</span> <span class="n">res</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">permutations_ii.cpp</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* バックトラッキングアルゴリズム：順列 II */</span>
+<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">bool</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">selected</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="c1">// 状態の長さが要素数と等しくなったら、解を記録</span>
+<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="n">size</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">state</span><span class="p">);</span>
+<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w">    </span><span class="n">unordered_set</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">duplicated</span><span class="p">;</span>
+<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="w">        </span><span class="c1">// 剪定：要素の重複選択を許可せず、等しい要素の重複選択も許可しない</span>
+<a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">duplicated</span><span class="p">.</span><span class="n">find</span><span class="p">(</span><span class="n">choice</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">duplicated</span><span class="p">.</span><span class="n">end</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="w">            </span><span class="c1">// 試行：選択を行い、状態を更新</span>
+<a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="w">            </span><span class="n">duplicated</span><span class="p">.</span><span class="n">emplace</span><span class="p">(</span><span class="n">choice</span><span class="p">);</span><span class="w"> </span><span class="c1">// 選択された要素値を記録</span>
+<a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a><span class="w">            </span><span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">true</span><span class="p">;</span>
+<a id="__codelineno-15-17" name="__codelineno-15-17" href="#__codelineno-15-17"></a><span class="w">            </span><span class="n">state</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">choice</span><span class="p">);</span>
+<a id="__codelineno-15-18" name="__codelineno-15-18" href="#__codelineno-15-18"></a><span class="w">            </span><span class="c1">// 次のラウンドの選択に進む</span>
+<a id="__codelineno-15-19" name="__codelineno-15-19" href="#__codelineno-15-19"></a><span class="w">            </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">selected</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-15-20" name="__codelineno-15-20" href="#__codelineno-15-20"></a><span class="w">            </span><span class="c1">// 回退：選択を取り消し、前の状態に復元</span>
+<a id="__codelineno-15-21" name="__codelineno-15-21" href="#__codelineno-15-21"></a><span class="w">            </span><span class="n">selected</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">false</span><span class="p">;</span>
+<a id="__codelineno-15-22" name="__codelineno-15-22" href="#__codelineno-15-22"></a><span class="w">            </span><span class="n">state</span><span class="p">.</span><span class="n">pop_back</span><span class="p">();</span>
+<a id="__codelineno-15-23" name="__codelineno-15-23" href="#__codelineno-15-23"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-15-24" name="__codelineno-15-24" href="#__codelineno-15-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-25" name="__codelineno-15-25" href="#__codelineno-15-25"></a><span class="p">}</span>
+<a id="__codelineno-15-26" name="__codelineno-15-26" href="#__codelineno-15-26"></a>
+<a id="__codelineno-15-27" name="__codelineno-15-27" href="#__codelineno-15-27"></a><span class="cm">/* 順列 II */</span>
+<a id="__codelineno-15-28" name="__codelineno-15-28" href="#__codelineno-15-28"></a><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">permutationsII</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-29" name="__codelineno-15-29" href="#__codelineno-15-29"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">;</span>
+<a id="__codelineno-15-30" name="__codelineno-15-30" href="#__codelineno-15-30"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">bool</span><span class="o">&gt;</span><span class="w"> </span><span class="n">selected</span><span class="p">(</span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">(),</span><span class="w"> </span><span class="nb">false</span><span class="p">);</span>
+<a id="__codelineno-15-31" name="__codelineno-15-31" href="#__codelineno-15-31"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-15-32" name="__codelineno-15-32" href="#__codelineno-15-32"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">selected</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-15-33" name="__codelineno-15-33" href="#__codelineno-15-33"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-15-34" name="__codelineno-15-34" href="#__codelineno-15-34"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">permutations_ii.java</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* バックトラッキングアルゴリズム：順列 II */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="kt">boolean</span><span class="o">[]</span><span class="w"> </span><span class="n">selected</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="c1">// 状態の長さが要素数と等しくなったら、解を記録</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="na">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="na">length</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="p">(</span><span class="n">state</span><span class="p">));</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w">    </span><span class="n">Set</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">duplicated</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">HashSet</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="p">();</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="na">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="w">        </span><span class="c1">// 剪定：要素の重複選択を許可せず、等しい要素の重複選択も許可しない</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">selected</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="o">!</span><span class="n">duplicated</span><span class="p">.</span><span class="na">contains</span><span class="p">(</span><span class="n">choice</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="w">            </span><span class="c1">// 試行：選択を行い、状態を更新</span>
+<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="w">            </span><span class="n">duplicated</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">choice</span><span class="p">);</span><span class="w"> </span><span class="c1">// 選択された要素値を記録</span>
+<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a><span class="w">            </span><span class="n">selected</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span><span class="p">;</span>
+<a id="__codelineno-16-17" name="__codelineno-16-17" href="#__codelineno-16-17"></a><span class="w">            </span><span class="n">state</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">choice</span><span class="p">);</span>
+<a id="__codelineno-16-18" name="__codelineno-16-18" href="#__codelineno-16-18"></a><span class="w">            </span><span class="c1">// 次のラウンドの選択に進む</span>
+<a id="__codelineno-16-19" name="__codelineno-16-19" href="#__codelineno-16-19"></a><span class="w">            </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">selected</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-16-20" name="__codelineno-16-20" href="#__codelineno-16-20"></a><span class="w">            </span><span class="c1">// 回退：選択を取り消し、前の状態に復元</span>
+<a id="__codelineno-16-21" name="__codelineno-16-21" href="#__codelineno-16-21"></a><span class="w">            </span><span class="n">selected</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">false</span><span class="p">;</span>
+<a id="__codelineno-16-22" name="__codelineno-16-22" href="#__codelineno-16-22"></a><span class="w">            </span><span class="n">state</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="na">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-16-23" name="__codelineno-16-23" href="#__codelineno-16-23"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-16-24" name="__codelineno-16-24" href="#__codelineno-16-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-25" name="__codelineno-16-25" href="#__codelineno-16-25"></a><span class="p">}</span>
+<a id="__codelineno-16-26" name="__codelineno-16-26" href="#__codelineno-16-26"></a>
+<a id="__codelineno-16-27" name="__codelineno-16-27" href="#__codelineno-16-27"></a><span class="cm">/* 順列 II */</span>
+<a id="__codelineno-16-28" name="__codelineno-16-28" href="#__codelineno-16-28"></a><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="nf">permutationsII</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-29" name="__codelineno-16-29" href="#__codelineno-16-29"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-16-30" name="__codelineno-16-30" href="#__codelineno-16-30"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="p">(),</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">boolean</span><span class="o">[</span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-16-31" name="__codelineno-16-31" href="#__codelineno-16-31"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-16-32" name="__codelineno-16-32" href="#__codelineno-16-32"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">permutations_ii.cs</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">permutations_ii</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Backtrack</span><span class="p">}</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">permutations_ii</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">PermutationsII</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">permutations_ii.go</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">backtrackII</span><span class="p">}</span>
+<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a>
+<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">permutationsII</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">permutations_ii.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a>
+<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">permutationsII</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">permutations_ii.js</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">backtrack</span><span class="p">}</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a>
+<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">permutationsII</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">permutations_ii.ts</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">backtrack</span><span class="p">}</span>
+<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a>
+<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">permutationsII</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">permutations_ii.dart</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">permutationsII</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">permutations_ii.rs</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a>
+<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">permutations_ii</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">permutations_ii.c</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a>
+<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">permutationsII</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">permutations_ii.kt</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a>
+<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">permutationsII</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">permutations_ii.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a>
+<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">permutations_ii</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">permutations_ii.zig</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a>
+<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">permutationsII</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>すべての要素が異なると仮定すると、<span class="arithmatex">\(n\)</span> 個の要素の順列は <span class="arithmatex">\(n!\)</span> （階乗）個あります。各結果を記録するには長さ <span class="arithmatex">\(n\)</span> のリストをコピーする必要があり、これには <span class="arithmatex">\(O(n)\)</span> 時間がかかります。<strong>したがって、総時間計算量は <span class="arithmatex">\(O(n!n)\)</span> です。</strong></p>
+<p>最大再帰深度は <span class="arithmatex">\(n\)</span> で、<span class="arithmatex">\(O(n)\)</span> のスタック空間を使用します。<code>selected</code> 配列も <span class="arithmatex">\(O(n)\)</span> 空間が必要です。一度に最大 <span class="arithmatex">\(n\)</span> 個の個別の <code>duplicated</code> セットが存在する可能性があるため、それらは集合的に <span class="arithmatex">\(O(n^2)\)</span> 空間を占有します。<strong>したがって、空間計算量は <span class="arithmatex">\(O(n^2)\)</span> です。</strong></p>
+<h3 id="3-2">3. &nbsp; 2つの剪定方法の比較<a class="headerlink" href="#3-2" title="Permanent link">&para;</a></h3>
+<p><code>selected</code> と <code>duplicated</code> はどちらも剪定メカニズムとして機能しますが、異なる問題をターゲットにしています：</p>
+<ul>
+<li><strong>重複選択の剪定</strong>（<code>selected</code> 経由）：検索全体に単一の <code>selected</code> 配列があり、現在の状態にすでにある要素を示します。これにより、同じ要素が <code>state</code> に複数回現れることを防ぎます。</li>
+<li><strong>等値要素の剪定</strong>（<code>duplicated</code> 経由）：<code>backtrack</code> 関数の各呼び出しは独自の <code>duplicated</code> セットを使用し、その特定の反復（<code>for</code> ループ）ですでに選択された要素を記録します。これにより、等しい要素が選択の各ラウンドで一度だけ選択されることを保証します。</li>
+</ul>
+<p>以下の図は、これら2つの剪定戦略の範囲を示しています。木の各ノードは選択を表します。ルートから任意の葉への経路は、1つの完全な順列に対応します。</p>
+<p><a class="glightbox" href="../permutations_problem.assets/permutations_ii_pruning_summary.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="2つの剪定条件の範囲" class="animation-figure" src="../permutations_problem.assets/permutations_ii_pruning_summary.png" /></a></p>
+<p align="center"> 図 13-9 &nbsp; 2つの剪定条件の範囲 </p>
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+  
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+  
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+      <a href="../../chapter_preface/about_the_book/" class="md-nav__link">
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+      <a href="../../chapter_preface/summary/" class="md-nav__link">
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+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
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+  
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+    1.1 &nbsp; アルゴリズムはどこにでもある
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+  
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+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
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+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
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+    </li>
+  
+
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+              
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+  
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+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
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+    </li>
+  
+
+              
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+          
+        
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+        
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+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
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+  
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+            第 2 章 &nbsp; 計算量解析
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+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
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+    2.1 &nbsp; アルゴリズム効率評価
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+  
+
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+
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+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
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+    2.2 &nbsp; 反復と再帰
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+  
+
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+    </li>
+  
+
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+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
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+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
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+
+              
+            
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+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
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+  
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+    第 3 章 &nbsp; データ構造
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+            第 3 章 &nbsp; データ構造
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+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
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+    3.1 &nbsp; データ構造の分類
+  </span>
+  
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+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
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+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
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+
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+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
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+  </span>
+  
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+    </li>
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+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
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+  </span>
+  
+
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+    </li>
+  
+
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+  
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+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
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+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
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+  
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+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1331" class="md-nav__link">
+    <span class="md-ellipsis">
+      13.3.1 &nbsp; 重複要素がない場合
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="13.3.1   重複要素がない場合">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 順列解法の参考
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; 重複部分集合の剪定
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#3" class="md-nav__link">
+    <span class="md-ellipsis">
+      3. &nbsp; コード実装
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1332" class="md-nav__link">
+    <span class="md-ellipsis">
+      13.3.2 &nbsp; 重複要素がある場合を考慮
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="13.3.2   重複要素がある場合を考慮">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1_1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 等値要素の剪定
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2_1" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; コード実装
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
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+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
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+  
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+    
+      
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+          
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
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+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_19" >
+        
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+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_reference/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9 3v15h3V3H9m3 2 4 13 3-1-4-13-3 1M5 5v13h3V5H5M3 19v2h18v-2H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    参考文献
+  </span>
+  
+
+            </a>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_19_label" aria-expanded="false">
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+            <span class="md-nav__icon md-icon"></span>
+            参考文献
+          </label>
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+            
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+        </nav>
+      
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+</nav>
+                  </div>
+                </div>
+              </div>
+            
+            
+              
+              <div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
+                <div class="md-sidebar__scrollwrap">
+                  <div class="md-sidebar__inner">
+                    
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1331" class="md-nav__link">
+    <span class="md-ellipsis">
+      13.3.1 &nbsp; 重複要素がない場合
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="13.3.1   重複要素がない場合">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 順列解法の参考
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; 重複部分集合の剪定
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#3" class="md-nav__link">
+    <span class="md-ellipsis">
+      3. &nbsp; コード実装
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1332" class="md-nav__link">
+    <span class="md-ellipsis">
+      13.3.2 &nbsp; 重複要素がある場合を考慮
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="13.3.2   重複要素がある場合を考慮">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1_1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 等値要素の剪定
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2_1" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; コード実装
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+                  </div>
+                </div>
+              </div>
+            
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+          
+            <div class="md-content" data-md-component="content">
+              <article class="md-content__inner md-typeset">
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+<h1 id="133">13.3 &nbsp; 部分集合和問題<a class="headerlink" href="#133" title="Permanent link">&para;</a></h1>
+<h2 id="1331">13.3.1 &nbsp; 重複要素がない場合<a class="headerlink" href="#1331" title="Permanent link">&para;</a></h2>
+<div class="admonition question">
+<p class="admonition-title">Question</p>
+<p>正の整数の配列 <code>nums</code> とターゲット正整数 <code>target</code> が与えられた場合、組み合わせ内の要素の和が <code>target</code> に等しくなるようなすべての可能な組み合わせを見つけてください。与えられた配列には重複要素がなく、各要素は複数回選択できます。これらの組み合わせを重複する組み合わせを含まないリストとして返してください。</p>
+</div>
+<p>例えば、入力集合 <span class="arithmatex">\(\{3, 4, 5\}\)</span> とターゲット整数 <span class="arithmatex">\(9\)</span> の場合、解は <span class="arithmatex">\(\{3, 3, 3\}, \{4, 5\}\)</span> です。以下の2点に注意してください。</p>
+<ul>
+<li>入力集合の要素は無制限に選択できます。</li>
+<li>部分集合は要素の順序を区別しません。例えば <span class="arithmatex">\(\{4, 5\}\)</span> と <span class="arithmatex">\(\{5, 4\}\)</span> は同じ部分集合です。</li>
+</ul>
+<h3 id="1">1. &nbsp; 順列解法の参考<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<p>順列問題と同様に、部分集合の生成を一連の選択として想像でき、選択プロセス中に「要素和」をリアルタイムで更新できます。要素和が <code>target</code> に等しくなったとき、部分集合を結果リストに記録します。</p>
+<p>順列問題とは異なり、<strong>この問題では要素は無制限に選択できるため</strong>、要素が選択されたかどうかを記録するための <code>selected</code> ブール配列を使用する必要がありません。順列コードに軽微な修正を加えて、最初に問題を解決できます：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:14"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><input id="__tabbed_1_14" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label><label for="__tabbed_1_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">subset_sum_i_naive.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a>    <span class="n">state</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="n">target</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="n">total</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="n">choices</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="n">res</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]],</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="p">):</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;バックトラッキングアルゴリズム：部分集合の和 I&quot;&quot;&quot;</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>    <span class="c1"># 部分集合の和が target と等しいとき、解を記録</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>    <span class="k">if</span> <span class="n">total</span> <span class="o">==</span> <span class="n">target</span><span class="p">:</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>        <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">state</span><span class="p">))</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>        <span class="k">return</span>
+<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>    <span class="c1"># すべての選択肢を走査</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">choices</span><span class="p">)):</span>
+<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>        <span class="c1"># 枝刈り：部分集合の和が target を超える場合、その選択をスキップ</span>
+<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>        <span class="k">if</span> <span class="n">total</span> <span class="o">+</span> <span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">target</span><span class="p">:</span>
+<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>            <span class="k">continue</span>
+<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a>        <span class="c1"># 試行：選択を行い、要素と total を更新</span>
+<a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a>        <span class="n">state</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
+<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a>        <span class="c1"># 次の選択ラウンドに進む</span>
+<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a>        <span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">target</span><span class="p">,</span> <span class="n">total</span> <span class="o">+</span> <span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">choices</span><span class="p">,</span> <span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a>        <span class="c1"># 撤回：選択を取り消し、前の状態に復元</span>
+<a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a>        <span class="n">state</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
+<a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a>
+<a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a><span class="k">def</span><span class="w"> </span><span class="nf">subset_sum_i_naive</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">target</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]]:</span>
+<a id="__codelineno-0-26" name="__codelineno-0-26" href="#__codelineno-0-26"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;部分集合の和 I を解く（重複する部分集合を含む）&quot;&quot;&quot;</span>
+<a id="__codelineno-0-27" name="__codelineno-0-27" href="#__codelineno-0-27"></a>    <span class="n">state</span> <span class="o">=</span> <span class="p">[]</span>  <span class="c1"># 状態（部分集合）</span>
+<a id="__codelineno-0-28" name="__codelineno-0-28" href="#__codelineno-0-28"></a>    <span class="n">total</span> <span class="o">=</span> <span class="mi">0</span>  <span class="c1"># 部分集合の和</span>
+<a id="__codelineno-0-29" name="__codelineno-0-29" href="#__codelineno-0-29"></a>    <span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>  <span class="c1"># 結果リスト（部分集合リスト）</span>
+<a id="__codelineno-0-30" name="__codelineno-0-30" href="#__codelineno-0-30"></a>    <span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">target</span><span class="p">,</span> <span class="n">total</span><span class="p">,</span> <span class="n">nums</span><span class="p">,</span> <span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-0-31" name="__codelineno-0-31" href="#__codelineno-0-31"></a>    <span class="k">return</span> <span class="n">res</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">subset_sum_i_naive.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* バックトラッキングアルゴリズム：部分集合和 I */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">total</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// 部分集合の和がtargetと等しいとき、解を記録</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">total</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">state</span><span class="p">);</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">        </span><span class="c1">// 剪定：部分集合の和がtargetを超えた場合、その選択をスキップ</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">total</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">            </span><span class="k">continue</span><span class="p">;</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">        </span><span class="c1">// 試行：選択を行い、要素とtotalを更新</span>
+<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
+<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">        </span><span class="c1">// 次のラウンドの選択に進む</span>
+<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w">        </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">total</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w">        </span><span class="c1">// 回退：選択を取り消し、前の状態に復元</span>
+<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="n">pop_back</span><span class="p">();</span>
+<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="p">}</span>
+<a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a>
+<a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a><span class="cm">/* 部分集合和 I を解く（重複する部分集合を含む） */</span>
+<a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">subsetSumINaive</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">;</span><span class="w">       </span><span class="c1">// 状態（部分集合）</span>
+<a id="__codelineno-1-26" name="__codelineno-1-26" href="#__codelineno-1-26"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">total</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">           </span><span class="c1">// 部分集合の和</span>
+<a id="__codelineno-1-27" name="__codelineno-1-27" href="#__codelineno-1-27"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">;</span><span class="w"> </span><span class="c1">// 結果リスト（部分集合リスト）</span>
+<a id="__codelineno-1-28" name="__codelineno-1-28" href="#__codelineno-1-28"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">total</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-1-29" name="__codelineno-1-29" href="#__codelineno-1-29"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-1-30" name="__codelineno-1-30" href="#__codelineno-1-30"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">subset_sum_i_naive.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* バックトラッキングアルゴリズム：部分集合和 I */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">total</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// 部分集合の和がtargetと等しいとき、解を記録</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">total</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">(</span><span class="n">state</span><span class="p">));</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="na">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">        </span><span class="c1">// 剪定：部分集合の和がtargetを超えた場合、その選択をスキップ</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">total</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">            </span><span class="k">continue</span><span class="p">;</span>
+<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">        </span><span class="c1">// 試行：選択を行い、要素とtotalを更新</span>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">);</span>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">        </span><span class="c1">// 次のラウンドの選択に進む</span>
+<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w">        </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">total</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w">        </span><span class="c1">// 回退：選択を取り消し、前の状態に復元</span>
+<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="na">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="p">}</span>
+<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a>
+<a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a><span class="cm">/* 部分集合和 I を解く（重複する部分集合を含む） */</span>
+<a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="nf">subsetSumINaive</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span><span class="w"> </span><span class="c1">// 状態（部分集合）</span>
+<a id="__codelineno-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">total</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 部分集合の和</span>
+<a id="__codelineno-2-27" name="__codelineno-2-27" href="#__codelineno-2-27"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span><span class="w"> </span><span class="c1">// 結果リスト（部分集合リスト）</span>
+<a id="__codelineno-2-28" name="__codelineno-2-28" href="#__codelineno-2-28"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">total</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-2-29" name="__codelineno-2-29" href="#__codelineno-2-29"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-2-30" name="__codelineno-2-30" href="#__codelineno-2-30"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">subset_sum_i_naive.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">subset_sum_i_naive</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Backtrack</span><span class="p">}</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">subset_sum_i_naive</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">SubsetSumINaive</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">subset_sum_i_naive.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">backtrackSubsetSumINaive</span><span class="p">}</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">subsetSumINaive</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">subset_sum_i_naive.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">subsetSumINaive</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">subset_sum_i_naive.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">backtrack</span><span class="p">}</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">subsetSumINaive</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">subset_sum_i_naive.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">backtrack</span><span class="p">}</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">subsetSumINaive</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">subset_sum_i_naive.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">subsetSumINaive</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">subset_sum_i_naive.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">subset_sum_i_naive</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">subset_sum_i_naive.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">subsetSumINaive</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">subset_sum_i_naive.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">subsetSumINaive</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">subset_sum_i_naive.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">subset_sum_i_naive</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">subset_sum_i_naive.zig</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a>
+<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">subsetSumINaive</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>配列 <span class="arithmatex">\([3, 4, 5]\)</span> とターゲット要素 <span class="arithmatex">\(9\)</span> を上記のコードに入力すると、結果 <span class="arithmatex">\([3, 3, 3], [4, 5], [5, 4]\)</span> が得られます。<strong>和が <span class="arithmatex">\(9\)</span> のすべての部分集合を正常に見つけましたが、重複する部分集合 <span class="arithmatex">\([4, 5]\)</span> と <span class="arithmatex">\([5, 4]\)</span> が含まれています</strong>。</p>
+<p>これは、検索プロセスが選択の順序を区別するためですが、部分集合は選択順序を区別しません。以下の図に示すように、<span class="arithmatex">\(5\)</span> の前に <span class="arithmatex">\(4\)</span> を選択することと <span class="arithmatex">\(4\)</span> の前に <span class="arithmatex">\(5\)</span> を選択することは異なる分岐ですが、同じ部分集合に対応します。</p>
+<p><a class="glightbox" href="../subset_sum_problem.assets/subset_sum_i_naive.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="部分集合の検索と境界外の剪定" class="animation-figure" src="../subset_sum_problem.assets/subset_sum_i_naive.png" /></a></p>
+<p align="center"> 図 13-10 &nbsp; 部分集合の検索と境界外の剪定 </p>
+
+<p>重複する部分集合を除去するために、<strong>直接的なアイデアは結果リストを重複除去することです</strong>。しかし、この方法は2つの理由で非常に非効率的です。</p>
+<ul>
+<li>配列要素が多い場合、特に <code>target</code> が大きい場合、検索プロセスで大量の重複する部分集合が生成されます。</li>
+<li>部分集合（配列）の差異を比較することは非常に時間がかかり、まず配列をソートし、次に配列の各要素の差異を比較する必要があります。</li>
+</ul>
+<h3 id="2">2. &nbsp; 重複部分集合の剪定<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
+<p><strong>剪定を通じて検索プロセス中に重複除去を検討します</strong>。以下の図を観察すると、異なる順序で配列要素を選択するときに重複する部分集合が生成されます。例えば、以下の状況です。</p>
+<ol>
+<li>最初のラウンドで <span class="arithmatex">\(3\)</span> を選択し、2番目のラウンドで <span class="arithmatex">\(4\)</span> を選択すると、これら2つの要素を含むすべての部分集合が生成され、<span class="arithmatex">\([3, 4, \dots]\)</span> と表記されます。</li>
+<li>後で、最初のラウンドで <span class="arithmatex">\(4\)</span> が選択されたとき、<strong>2番目のラウンドは <span class="arithmatex">\(3\)</span> をスキップすべきです</strong>。この選択によって生成される部分集合 <span class="arithmatex">\([4, 3, \dots]\)</span> はステップ <code>1.</code> の部分集合と完全に重複するからです。</li>
+</ol>
+<p>検索プロセスでは、各層の選択が左から右に一つずつ試行されるため、右側の分岐ほどより多く剪定されます。</p>
+<ol>
+<li>最初の2ラウンドで <span class="arithmatex">\(3\)</span> と <span class="arithmatex">\(5\)</span> を選択し、部分集合 <span class="arithmatex">\([3, 5, \dots]\)</span> を生成します。</li>
+<li>最初の2ラウンドで <span class="arithmatex">\(4\)</span> と <span class="arithmatex">\(5\)</span> を選択し、部分集合 <span class="arithmatex">\([4, 5, \dots]\)</span> を生成します。</li>
+<li>最初のラウンドで <span class="arithmatex">\(5\)</span> が選択された場合、<strong>2番目のラウンドは <span class="arithmatex">\(3\)</span> と <span class="arithmatex">\(4\)</span> をスキップすべきです</strong>。部分集合 <span class="arithmatex">\([5, 3, \dots]\)</span> と <span class="arithmatex">\([5, 4, \dots]\)</span> はステップ <code>1.</code> と <code>2.</code> で記述された部分集合と完全に重複するからです。</li>
+</ol>
+<p><a class="glightbox" href="../subset_sum_problem.assets/subset_sum_i_pruning.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="異なる選択順序による重複部分集合" class="animation-figure" src="../subset_sum_problem.assets/subset_sum_i_pruning.png" /></a></p>
+<p align="center"> 図 13-11 &nbsp; 異なる選択順序による重複部分集合 </p>
+
+<p>要約すると、入力配列 <span class="arithmatex">\([x_1, x_2, \dots, x_n]\)</span> が与えられた場合、検索プロセスでの選択シーケンスは <span class="arithmatex">\([x_{i_1}, x_{i_2}, \dots, x_{i_m}]\)</span> であるべきで、<span class="arithmatex">\(i_1 \leq i_2 \leq \dots \leq i_m\)</span> を満たす必要があります。<strong>この条件を満たさない選択シーケンスは重複を引き起こし、剪定されるべきです</strong>。</p>
+<h3 id="3">3. &nbsp; コード実装<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
+<p>この剪定を実装するために、変数 <code>start</code> を初期化し、これは走査の開始点を示します。<strong>選択 <span class="arithmatex">\(x_{i}\)</span> を行った後、次のラウンドをインデックス <span class="arithmatex">\(i\)</span> から開始するように設定します</strong>。これにより、選択シーケンスが <span class="arithmatex">\(i_1 \leq i_2 \leq \dots \leq i_m\)</span> を満たすことが保証され、部分集合の一意性が保証されます。</p>
+<p>さらに、コードに以下の2つの最適化を行いました。</p>
+<ul>
+<li>検索を開始する前に、配列 <code>nums</code> をソートします。すべての選択の走査で、<strong>部分集合和が <code>target</code> を超えたときにループを直接終了します</strong>。後続の要素はより大きく、それらの部分集合和は確実に <code>target</code> を超えるからです。</li>
+<li>要素和変数 <code>total</code> を除去し、<strong><code>target</code> に対して減算を実行して要素和をカウントします</strong>。<code>target</code> が <span class="arithmatex">\(0\)</span> に等しくなったとき、解を記録します。</li>
+</ul>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:14"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><input id="__tabbed_2_14" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label><label for="__tabbed_2_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">subset_sum_i.py</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span>
+<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a>    <span class="n">state</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">target</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">choices</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">start</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">res</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]]</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="p">):</span>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;バックトラッキングアルゴリズム：部分集合の和 I&quot;&quot;&quot;</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a>    <span class="c1"># 部分集合の和が target と等しいとき、解を記録</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a>    <span class="k">if</span> <span class="n">target</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
+<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a>        <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">state</span><span class="p">))</span>
+<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a>        <span class="k">return</span>
+<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a>    <span class="c1"># すべての選択肢を走査</span>
+<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a>    <span class="c1"># 枝刈り二：start から走査を開始して重複する部分集合の生成を避ける</span>
+<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">start</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">choices</span><span class="p">)):</span>
+<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a>        <span class="c1"># 枝刈り一：部分集合の和が target を超える場合、直ちにループを終了</span>
+<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a>        <span class="c1"># これは配列がソートされており、後の要素がより大きいため、部分集合の和は必ず target を超えるため</span>
+<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a>        <span class="k">if</span> <span class="n">target</span> <span class="o">-</span> <span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">&lt;</span> <span class="mi">0</span><span class="p">:</span>
+<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a>            <span class="k">break</span>
+<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a>        <span class="c1"># 試行：選択を行い、target、start を更新</span>
+<a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a>        <span class="n">state</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
+<a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a>        <span class="c1"># 次の選択ラウンドに進む</span>
+<a id="__codelineno-14-19" name="__codelineno-14-19" href="#__codelineno-14-19"></a>        <span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">target</span> <span class="o">-</span> <span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">choices</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-14-20" name="__codelineno-14-20" href="#__codelineno-14-20"></a>        <span class="c1"># 撤回：選択を取り消し、前の状態に復元</span>
+<a id="__codelineno-14-21" name="__codelineno-14-21" href="#__codelineno-14-21"></a>        <span class="n">state</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
+<a id="__codelineno-14-22" name="__codelineno-14-22" href="#__codelineno-14-22"></a>
+<a id="__codelineno-14-23" name="__codelineno-14-23" href="#__codelineno-14-23"></a><span class="k">def</span><span class="w"> </span><span class="nf">subset_sum_i</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">target</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]]:</span>
+<a id="__codelineno-14-24" name="__codelineno-14-24" href="#__codelineno-14-24"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;部分集合の和 I を解く&quot;&quot;&quot;</span>
+<a id="__codelineno-14-25" name="__codelineno-14-25" href="#__codelineno-14-25"></a>    <span class="n">state</span> <span class="o">=</span> <span class="p">[]</span>  <span class="c1"># 状態（部分集合）</span>
+<a id="__codelineno-14-26" name="__codelineno-14-26" href="#__codelineno-14-26"></a>    <span class="n">nums</span><span class="o">.</span><span class="n">sort</span><span class="p">()</span>  <span class="c1"># nums をソート</span>
+<a id="__codelineno-14-27" name="__codelineno-14-27" href="#__codelineno-14-27"></a>    <span class="n">start</span> <span class="o">=</span> <span class="mi">0</span>  <span class="c1"># 走査の開始点</span>
+<a id="__codelineno-14-28" name="__codelineno-14-28" href="#__codelineno-14-28"></a>    <span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>  <span class="c1"># 結果リスト（部分集合リスト）</span>
+<a id="__codelineno-14-29" name="__codelineno-14-29" href="#__codelineno-14-29"></a>    <span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">target</span><span class="p">,</span> <span class="n">nums</span><span class="p">,</span> <span class="n">start</span><span class="p">,</span> <span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-14-30" name="__codelineno-14-30" href="#__codelineno-14-30"></a>    <span class="k">return</span> <span class="n">res</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">subset_sum_i.cpp</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* バックトラッキングアルゴリズム：部分集合和 I */</span>
+<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">start</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="c1">// 部分集合の和がtargetと等しいとき、解を記録</span>
+<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">target</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">state</span><span class="p">);</span>
+<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w">    </span><span class="c1">// 剪定二：startから走査を開始し、重複する部分集合の生成を回避</span>
+<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">start</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="w">        </span><span class="c1">// 剪定一：部分集合の和がtargetを超えた場合、即座にループを終了</span>
+<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="w">        </span><span class="c1">// 配列がソートされているため、後の要素はさらに大きく、部分集合の和は必ずtargetを超える</span>
+<a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a><span class="w">        </span><span class="c1">// 試行：選択を行い、target、startを更新</span>
+<a id="__codelineno-15-17" name="__codelineno-15-17" href="#__codelineno-15-17"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
+<a id="__codelineno-15-18" name="__codelineno-15-18" href="#__codelineno-15-18"></a><span class="w">        </span><span class="c1">// 次のラウンドの選択に進む</span>
+<a id="__codelineno-15-19" name="__codelineno-15-19" href="#__codelineno-15-19"></a><span class="w">        </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-15-20" name="__codelineno-15-20" href="#__codelineno-15-20"></a><span class="w">        </span><span class="c1">// 回退：選択を取り消し、前の状態に復元</span>
+<a id="__codelineno-15-21" name="__codelineno-15-21" href="#__codelineno-15-21"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="n">pop_back</span><span class="p">();</span>
+<a id="__codelineno-15-22" name="__codelineno-15-22" href="#__codelineno-15-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-23" name="__codelineno-15-23" href="#__codelineno-15-23"></a><span class="p">}</span>
+<a id="__codelineno-15-24" name="__codelineno-15-24" href="#__codelineno-15-24"></a>
+<a id="__codelineno-15-25" name="__codelineno-15-25" href="#__codelineno-15-25"></a><span class="cm">/* 部分集合和 I を解く */</span>
+<a id="__codelineno-15-26" name="__codelineno-15-26" href="#__codelineno-15-26"></a><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">subsetSumI</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-27" name="__codelineno-15-27" href="#__codelineno-15-27"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">;</span><span class="w">              </span><span class="c1">// 状態（部分集合）</span>
+<a id="__codelineno-15-28" name="__codelineno-15-28" href="#__codelineno-15-28"></a><span class="w">    </span><span class="n">sort</span><span class="p">(</span><span class="n">nums</span><span class="p">.</span><span class="n">begin</span><span class="p">(),</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">end</span><span class="p">());</span><span class="w"> </span><span class="c1">// nums をソート</span>
+<a id="__codelineno-15-29" name="__codelineno-15-29" href="#__codelineno-15-29"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">start</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">                  </span><span class="c1">// 走査の開始点</span>
+<a id="__codelineno-15-30" name="__codelineno-15-30" href="#__codelineno-15-30"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">;</span><span class="w">        </span><span class="c1">// 結果リスト（部分集合リスト）</span>
+<a id="__codelineno-15-31" name="__codelineno-15-31" href="#__codelineno-15-31"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">start</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-15-32" name="__codelineno-15-32" href="#__codelineno-15-32"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-15-33" name="__codelineno-15-33" href="#__codelineno-15-33"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">subset_sum_i.java</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* バックトラッキングアルゴリズム：部分集合和 I */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">start</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="c1">// 部分集合の和がtargetと等しいとき、解を記録</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">target</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">(</span><span class="n">state</span><span class="p">));</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w">    </span><span class="c1">// 剪定二：startから走査を開始し、重複する部分集合の生成を回避</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">start</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="na">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="w">        </span><span class="c1">// 剪定一：部分集合の和がtargetを超えた場合、即座にループを終了</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="w">        </span><span class="c1">// 配列がソートされているため、後の要素はさらに大きく、部分集合の和は必ずtargetを超える</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a><span class="w">        </span><span class="c1">// 試行：選択を行い、target、startを更新</span>
+<a id="__codelineno-16-17" name="__codelineno-16-17" href="#__codelineno-16-17"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">);</span>
+<a id="__codelineno-16-18" name="__codelineno-16-18" href="#__codelineno-16-18"></a><span class="w">        </span><span class="c1">// 次のラウンドの選択に進む</span>
+<a id="__codelineno-16-19" name="__codelineno-16-19" href="#__codelineno-16-19"></a><span class="w">        </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-16-20" name="__codelineno-16-20" href="#__codelineno-16-20"></a><span class="w">        </span><span class="c1">// 回退：選択を取り消し、前の状態に復元</span>
+<a id="__codelineno-16-21" name="__codelineno-16-21" href="#__codelineno-16-21"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="na">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-16-22" name="__codelineno-16-22" href="#__codelineno-16-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-23" name="__codelineno-16-23" href="#__codelineno-16-23"></a><span class="p">}</span>
+<a id="__codelineno-16-24" name="__codelineno-16-24" href="#__codelineno-16-24"></a>
+<a id="__codelineno-16-25" name="__codelineno-16-25" href="#__codelineno-16-25"></a><span class="cm">/* 部分集合和 I を解く */</span>
+<a id="__codelineno-16-26" name="__codelineno-16-26" href="#__codelineno-16-26"></a><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="nf">subsetSumI</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-27" name="__codelineno-16-27" href="#__codelineno-16-27"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span><span class="w"> </span><span class="c1">// 状態（部分集合）</span>
+<a id="__codelineno-16-28" name="__codelineno-16-28" href="#__codelineno-16-28"></a><span class="w">    </span><span class="n">Arrays</span><span class="p">.</span><span class="na">sort</span><span class="p">(</span><span class="n">nums</span><span class="p">);</span><span class="w"> </span><span class="c1">// nums をソート</span>
+<a id="__codelineno-16-29" name="__codelineno-16-29" href="#__codelineno-16-29"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">start</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 走査の開始点</span>
+<a id="__codelineno-16-30" name="__codelineno-16-30" href="#__codelineno-16-30"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span><span class="w"> </span><span class="c1">// 結果リスト（部分集合リスト）</span>
+<a id="__codelineno-16-31" name="__codelineno-16-31" href="#__codelineno-16-31"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">start</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-16-32" name="__codelineno-16-32" href="#__codelineno-16-32"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-16-33" name="__codelineno-16-33" href="#__codelineno-16-33"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">subset_sum_i.cs</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">subset_sum_i</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Backtrack</span><span class="p">}</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">subset_sum_i</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">SubsetSumI</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">subset_sum_i.go</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">backtrackSubsetSumI</span><span class="p">}</span>
+<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a>
+<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">subsetSumI</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">subset_sum_i.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a>
+<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">subsetSumI</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">subset_sum_i.js</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">backtrack</span><span class="p">}</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a>
+<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">subsetSumI</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">subset_sum_i.ts</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">backtrack</span><span class="p">}</span>
+<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a>
+<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">subsetSumI</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">subset_sum_i.dart</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">subsetSumI</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">subset_sum_i.rs</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a>
+<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">subset_sum_i</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">subset_sum_i.c</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a>
+<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">subsetSumI</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">subset_sum_i.kt</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a>
+<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">subsetSumI</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">subset_sum_i.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a>
+<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">subset_sum_i</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">subset_sum_i.zig</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a>
+<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">subsetSumI</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>以下の図は、配列 <span class="arithmatex">\([3, 4, 5]\)</span> とターゲット要素 <span class="arithmatex">\(9\)</span> を上記のコードに入力した後の全体的なバックトラッキングプロセスを示しています。</p>
+<p><a class="glightbox" href="../subset_sum_problem.assets/subset_sum_i.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="部分集合和 I のバックトラッキングプロセス" class="animation-figure" src="../subset_sum_problem.assets/subset_sum_i.png" /></a></p>
+<p align="center"> 図 13-12 &nbsp; 部分集合和 I のバックトラッキングプロセス </p>
+
+<h2 id="1332">13.3.2 &nbsp; 重複要素がある場合を考慮<a class="headerlink" href="#1332" title="Permanent link">&para;</a></h2>
+<div class="admonition question">
+<p class="admonition-title">Question</p>
+<p>正の整数の配列 <code>nums</code> とターゲット正整数 <code>target</code> が与えられた場合、組み合わせ内の要素の和が <code>target</code> に等しくなるようなすべての可能な組み合わせを見つけてください。<strong>与えられた配列には重複要素が含まれる可能性があり、各要素は一度だけ選択できます</strong>。これらの組み合わせを重複する組み合わせを含まないリストとして返してください。</p>
+</div>
+<p>前の問題と比較して、<strong>この問題の入力配列には重複要素が含まれる可能性があり</strong>、新しい問題が導入されます。例えば、配列 <span class="arithmatex">\([4, \hat{4}, 5]\)</span> とターゲット要素 <span class="arithmatex">\(9\)</span> が与えられた場合、既存のコードの出力結果は <span class="arithmatex">\([4, 5], [\hat{4}, 5]\)</span> となり、重複する部分集合が生成されます。</p>
+<p><strong>この重複の理由は、特定のラウンドで等しい要素が複数回選択されることです</strong>。以下の図では、最初のラウンドに3つの選択肢があり、そのうち2つが <span class="arithmatex">\(4\)</span> であり、2つの重複する検索分岐を生成し、重複する部分集合を出力します。同様に、2番目のラウンドの2つの <span class="arithmatex">\(4\)</span> も重複する部分集合を生成します。</p>
+<p><a class="glightbox" href="../subset_sum_problem.assets/subset_sum_ii_repeat.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="等しい要素による重複部分集合" class="animation-figure" src="../subset_sum_problem.assets/subset_sum_ii_repeat.png" /></a></p>
+<p align="center"> 図 13-13 &nbsp; 等しい要素による重複部分集合 </p>
+
+<h3 id="1_1">1. &nbsp; 等値要素の剪定<a class="headerlink" href="#1_1" title="Permanent link">&para;</a></h3>
+<p>この問題を解決するために、<strong>等しい要素がラウンドごとに一度だけ選択されるように制限する必要があります</strong>。実装は非常に巧妙です：配列がソートされているため、等しい要素は隣接しています。これは、特定のラウンドの選択で、現在の要素がその左側の要素と等しい場合、それはすでに選択されていることを意味するため、現在の要素を直接スキップします。</p>
+<p>同時に、<strong>この問題では各配列要素は一度だけ選択できると規定されています</strong>。幸い、変数 <code>start</code> を使用してこの制約も満たすことができます：選択 <span class="arithmatex">\(x_{i}\)</span> を行った後、次のラウンドをインデックス <span class="arithmatex">\(i + 1\)</span> から前方に開始するように設定します。これにより、重複する部分集合が除去されるだけでなく、要素の重複選択も回避されます。</p>
+<h3 id="2_1">2. &nbsp; コード実装<a class="headerlink" href="#2_1" title="Permanent link">&para;</a></h3>
+<div class="tabbed-set tabbed-alternate" data-tabs="3:14"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><input id="__tabbed_3_14" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label><label for="__tabbed_3_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">subset_sum_ii.py</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span>
+<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a>    <span class="n">state</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">target</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">choices</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">start</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">res</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]]</span>
+<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a><span class="p">):</span>
+<a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;バックトラッキングアルゴリズム：部分集合の和 II&quot;&quot;&quot;</span>
+<a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a>    <span class="c1"># 部分集合の和が target と等しいとき、解を記録</span>
+<a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a>    <span class="k">if</span> <span class="n">target</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
+<a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a>        <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="n">state</span><span class="p">))</span>
+<a id="__codelineno-28-8" name="__codelineno-28-8" href="#__codelineno-28-8"></a>        <span class="k">return</span>
+<a id="__codelineno-28-9" name="__codelineno-28-9" href="#__codelineno-28-9"></a>    <span class="c1"># すべての選択肢を走査</span>
+<a id="__codelineno-28-10" name="__codelineno-28-10" href="#__codelineno-28-10"></a>    <span class="c1"># 枝刈り二：start から走査を開始して重複する部分集合の生成を避ける</span>
+<a id="__codelineno-28-11" name="__codelineno-28-11" href="#__codelineno-28-11"></a>    <span class="c1"># 枝刈り三：start から走査を開始して同じ要素の重複選択を避ける</span>
+<a id="__codelineno-28-12" name="__codelineno-28-12" href="#__codelineno-28-12"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">start</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">choices</span><span class="p">)):</span>
+<a id="__codelineno-28-13" name="__codelineno-28-13" href="#__codelineno-28-13"></a>        <span class="c1"># 枝刈り一：部分集合の和が target を超える場合、直ちにループを終了</span>
+<a id="__codelineno-28-14" name="__codelineno-28-14" href="#__codelineno-28-14"></a>        <span class="c1"># これは配列がソートされており、後の要素がより大きいため、部分集合の和は必ず target を超えるため</span>
+<a id="__codelineno-28-15" name="__codelineno-28-15" href="#__codelineno-28-15"></a>        <span class="k">if</span> <span class="n">target</span> <span class="o">-</span> <span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">&lt;</span> <span class="mi">0</span><span class="p">:</span>
+<a id="__codelineno-28-16" name="__codelineno-28-16" href="#__codelineno-28-16"></a>            <span class="k">break</span>
+<a id="__codelineno-28-17" name="__codelineno-28-17" href="#__codelineno-28-17"></a>        <span class="c1"># 枝刈り四：要素が左の要素と等しい場合、検索分岐が重複していることを示すため、スキップ</span>
+<a id="__codelineno-28-18" name="__codelineno-28-18" href="#__codelineno-28-18"></a>        <span class="k">if</span> <span class="n">i</span> <span class="o">&gt;</span> <span class="n">start</span> <span class="ow">and</span> <span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">==</span> <span class="n">choices</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]:</span>
+<a id="__codelineno-28-19" name="__codelineno-28-19" href="#__codelineno-28-19"></a>            <span class="k">continue</span>
+<a id="__codelineno-28-20" name="__codelineno-28-20" href="#__codelineno-28-20"></a>        <span class="c1"># 試行：選択を行い、target、start を更新</span>
+<a id="__codelineno-28-21" name="__codelineno-28-21" href="#__codelineno-28-21"></a>        <span class="n">state</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
+<a id="__codelineno-28-22" name="__codelineno-28-22" href="#__codelineno-28-22"></a>        <span class="c1"># 次の選択ラウンドに進む</span>
+<a id="__codelineno-28-23" name="__codelineno-28-23" href="#__codelineno-28-23"></a>        <span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">target</span> <span class="o">-</span> <span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">choices</span><span class="p">,</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-28-24" name="__codelineno-28-24" href="#__codelineno-28-24"></a>        <span class="c1"># 撤回：選択を取り消し、前の状態に復元</span>
+<a id="__codelineno-28-25" name="__codelineno-28-25" href="#__codelineno-28-25"></a>        <span class="n">state</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
+<a id="__codelineno-28-26" name="__codelineno-28-26" href="#__codelineno-28-26"></a>
+<a id="__codelineno-28-27" name="__codelineno-28-27" href="#__codelineno-28-27"></a><span class="k">def</span><span class="w"> </span><span class="nf">subset_sum_ii</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">target</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]]:</span>
+<a id="__codelineno-28-28" name="__codelineno-28-28" href="#__codelineno-28-28"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;部分集合の和 II を解く&quot;&quot;&quot;</span>
+<a id="__codelineno-28-29" name="__codelineno-28-29" href="#__codelineno-28-29"></a>    <span class="n">state</span> <span class="o">=</span> <span class="p">[]</span>  <span class="c1"># 状態（部分集合）</span>
+<a id="__codelineno-28-30" name="__codelineno-28-30" href="#__codelineno-28-30"></a>    <span class="n">nums</span><span class="o">.</span><span class="n">sort</span><span class="p">()</span>  <span class="c1"># nums をソート</span>
+<a id="__codelineno-28-31" name="__codelineno-28-31" href="#__codelineno-28-31"></a>    <span class="n">start</span> <span class="o">=</span> <span class="mi">0</span>  <span class="c1"># 走査の開始点</span>
+<a id="__codelineno-28-32" name="__codelineno-28-32" href="#__codelineno-28-32"></a>    <span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>  <span class="c1"># 結果リスト（部分集合リスト）</span>
+<a id="__codelineno-28-33" name="__codelineno-28-33" href="#__codelineno-28-33"></a>    <span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span> <span class="n">target</span><span class="p">,</span> <span class="n">nums</span><span class="p">,</span> <span class="n">start</span><span class="p">,</span> <span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-28-34" name="__codelineno-28-34" href="#__codelineno-28-34"></a>    <span class="k">return</span> <span class="n">res</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">subset_sum_ii.cpp</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="cm">/* バックトラッキングアルゴリズム：部分集合和 II */</span>
+<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">start</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w">    </span><span class="c1">// 部分集合の和がtargetと等しいとき、解を記録</span>
+<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">target</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">state</span><span class="p">);</span>
+<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-29-9" name="__codelineno-29-9" href="#__codelineno-29-9"></a><span class="w">    </span><span class="c1">// 剪定二：startから走査を開始し、重複する部分集合の生成を回避</span>
+<a id="__codelineno-29-10" name="__codelineno-29-10" href="#__codelineno-29-10"></a><span class="w">    </span><span class="c1">// 剪定三：startから走査を開始し、同じ要素の繰り返し選択を回避</span>
+<a id="__codelineno-29-11" name="__codelineno-29-11" href="#__codelineno-29-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">start</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-12" name="__codelineno-29-12" href="#__codelineno-29-12"></a><span class="w">        </span><span class="c1">// 剪定一：部分集合の和がtargetを超えた場合、即座にループを終了</span>
+<a id="__codelineno-29-13" name="__codelineno-29-13" href="#__codelineno-29-13"></a><span class="w">        </span><span class="c1">// 配列がソートされているため、後の要素はさらに大きく、部分集合の和は必ずtargetを超える</span>
+<a id="__codelineno-29-14" name="__codelineno-29-14" href="#__codelineno-29-14"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-15" name="__codelineno-29-15" href="#__codelineno-29-15"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-29-16" name="__codelineno-29-16" href="#__codelineno-29-16"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-29-17" name="__codelineno-29-17" href="#__codelineno-29-17"></a><span class="w">        </span><span class="c1">// 剪定四：要素が左の要素と等しい場合、検索ブランチの重複を示すのでスキップ</span>
+<a id="__codelineno-29-18" name="__codelineno-29-18" href="#__codelineno-29-18"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">start</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-19" name="__codelineno-29-19" href="#__codelineno-29-19"></a><span class="w">            </span><span class="k">continue</span><span class="p">;</span>
+<a id="__codelineno-29-20" name="__codelineno-29-20" href="#__codelineno-29-20"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-29-21" name="__codelineno-29-21" href="#__codelineno-29-21"></a><span class="w">        </span><span class="c1">// 試行：選択を行い、target、startを更新</span>
+<a id="__codelineno-29-22" name="__codelineno-29-22" href="#__codelineno-29-22"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
+<a id="__codelineno-29-23" name="__codelineno-29-23" href="#__codelineno-29-23"></a><span class="w">        </span><span class="c1">// 次のラウンドの選択に進む</span>
+<a id="__codelineno-29-24" name="__codelineno-29-24" href="#__codelineno-29-24"></a><span class="w">        </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">choices</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-29-25" name="__codelineno-29-25" href="#__codelineno-29-25"></a><span class="w">        </span><span class="c1">// 回退：選択を取り消し、前の状態に復元</span>
+<a id="__codelineno-29-26" name="__codelineno-29-26" href="#__codelineno-29-26"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="n">pop_back</span><span class="p">();</span>
+<a id="__codelineno-29-27" name="__codelineno-29-27" href="#__codelineno-29-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-28" name="__codelineno-29-28" href="#__codelineno-29-28"></a><span class="p">}</span>
+<a id="__codelineno-29-29" name="__codelineno-29-29" href="#__codelineno-29-29"></a>
+<a id="__codelineno-29-30" name="__codelineno-29-30" href="#__codelineno-29-30"></a><span class="cm">/* 部分集合和 II を解く */</span>
+<a id="__codelineno-29-31" name="__codelineno-29-31" href="#__codelineno-29-31"></a><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">subsetSumII</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-32" name="__codelineno-29-32" href="#__codelineno-29-32"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">;</span><span class="w">              </span><span class="c1">// 状態（部分集合）</span>
+<a id="__codelineno-29-33" name="__codelineno-29-33" href="#__codelineno-29-33"></a><span class="w">    </span><span class="n">sort</span><span class="p">(</span><span class="n">nums</span><span class="p">.</span><span class="n">begin</span><span class="p">(),</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">end</span><span class="p">());</span><span class="w"> </span><span class="c1">// nums をソート</span>
+<a id="__codelineno-29-34" name="__codelineno-29-34" href="#__codelineno-29-34"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">start</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">                  </span><span class="c1">// 走査の開始点</span>
+<a id="__codelineno-29-35" name="__codelineno-29-35" href="#__codelineno-29-35"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">;</span><span class="w">        </span><span class="c1">// 結果リスト（部分集合リスト）</span>
+<a id="__codelineno-29-36" name="__codelineno-29-36" href="#__codelineno-29-36"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">start</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-29-37" name="__codelineno-29-37" href="#__codelineno-29-37"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-29-38" name="__codelineno-29-38" href="#__codelineno-29-38"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">subset_sum_ii.java</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* バックトラッキングアルゴリズム：部分集合和 II */</span>
+<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">start</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w">    </span><span class="c1">// 部分集合の和がtargetと等しいとき、解を記録</span>
+<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">target</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">(</span><span class="n">state</span><span class="p">));</span>
+<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a><span class="w">    </span><span class="c1">// 剪定二：startから走査を開始し、重複する部分集合の生成を回避</span>
+<a id="__codelineno-30-10" name="__codelineno-30-10" href="#__codelineno-30-10"></a><span class="w">    </span><span class="c1">// 剪定三：startから走査を開始し、同じ要素の繰り返し選択を回避</span>
+<a id="__codelineno-30-11" name="__codelineno-30-11" href="#__codelineno-30-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">start</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">choices</span><span class="p">.</span><span class="na">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-12" name="__codelineno-30-12" href="#__codelineno-30-12"></a><span class="w">        </span><span class="c1">// 剪定一：部分集合の和がtargetを超えた場合、即座にループを終了</span>
+<a id="__codelineno-30-13" name="__codelineno-30-13" href="#__codelineno-30-13"></a><span class="w">        </span><span class="c1">// 配列がソートされているため、後の要素はさらに大きく、部分集合の和は必ずtargetを超える</span>
+<a id="__codelineno-30-14" name="__codelineno-30-14" href="#__codelineno-30-14"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-15" name="__codelineno-30-15" href="#__codelineno-30-15"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-30-16" name="__codelineno-30-16" href="#__codelineno-30-16"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-30-17" name="__codelineno-30-17" href="#__codelineno-30-17"></a><span class="w">        </span><span class="c1">// 剪定四：要素が左の要素と等しい場合、検索ブランチの重複を示すのでスキップ</span>
+<a id="__codelineno-30-18" name="__codelineno-30-18" href="#__codelineno-30-18"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">start</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-19" name="__codelineno-30-19" href="#__codelineno-30-19"></a><span class="w">            </span><span class="k">continue</span><span class="p">;</span>
+<a id="__codelineno-30-20" name="__codelineno-30-20" href="#__codelineno-30-20"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-30-21" name="__codelineno-30-21" href="#__codelineno-30-21"></a><span class="w">        </span><span class="c1">// 試行：選択を行い、target、startを更新</span>
+<a id="__codelineno-30-22" name="__codelineno-30-22" href="#__codelineno-30-22"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">);</span>
+<a id="__codelineno-30-23" name="__codelineno-30-23" href="#__codelineno-30-23"></a><span class="w">        </span><span class="c1">// 次のラウンドの選択に進む</span>
+<a id="__codelineno-30-24" name="__codelineno-30-24" href="#__codelineno-30-24"></a><span class="w">        </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">choices</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-30-25" name="__codelineno-30-25" href="#__codelineno-30-25"></a><span class="w">        </span><span class="c1">// 回退：選択を取り消し、前の状態に復元</span>
+<a id="__codelineno-30-26" name="__codelineno-30-26" href="#__codelineno-30-26"></a><span class="w">        </span><span class="n">state</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">state</span><span class="p">.</span><span class="na">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-30-27" name="__codelineno-30-27" href="#__codelineno-30-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-28" name="__codelineno-30-28" href="#__codelineno-30-28"></a><span class="p">}</span>
+<a id="__codelineno-30-29" name="__codelineno-30-29" href="#__codelineno-30-29"></a>
+<a id="__codelineno-30-30" name="__codelineno-30-30" href="#__codelineno-30-30"></a><span class="cm">/* 部分集合和 II を解く */</span>
+<a id="__codelineno-30-31" name="__codelineno-30-31" href="#__codelineno-30-31"></a><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="nf">subsetSumII</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-32" name="__codelineno-30-32" href="#__codelineno-30-32"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span><span class="w"> </span><span class="c1">// 状態（部分集合）</span>
+<a id="__codelineno-30-33" name="__codelineno-30-33" href="#__codelineno-30-33"></a><span class="w">    </span><span class="n">Arrays</span><span class="p">.</span><span class="na">sort</span><span class="p">(</span><span class="n">nums</span><span class="p">);</span><span class="w"> </span><span class="c1">// nums をソート</span>
+<a id="__codelineno-30-34" name="__codelineno-30-34" href="#__codelineno-30-34"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">start</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 走査の開始点</span>
+<a id="__codelineno-30-35" name="__codelineno-30-35" href="#__codelineno-30-35"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span><span class="w"> </span><span class="c1">// 結果リスト（部分集合リスト）</span>
+<a id="__codelineno-30-36" name="__codelineno-30-36" href="#__codelineno-30-36"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">start</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-30-37" name="__codelineno-30-37" href="#__codelineno-30-37"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-30-38" name="__codelineno-30-38" href="#__codelineno-30-38"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">subset_sum_ii.cs</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">subset_sum_ii</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Backtrack</span><span class="p">}</span>
+<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a>
+<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">subset_sum_ii</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">SubsetSumII</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">subset_sum_ii.go</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">backtrackSubsetSumII</span><span class="p">}</span>
+<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a>
+<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">subsetSumII</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">subset_sum_ii.swift</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a>
+<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">subsetSumII</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">subset_sum_ii.js</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">backtrack</span><span class="p">}</span>
+<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a>
+<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">subsetSumII</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">subset_sum_ii.ts</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">backtrack</span><span class="p">}</span>
+<a id="__codelineno-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></a>
+<a id="__codelineno-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">subsetSumII</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">subset_sum_ii.dart</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a>
+<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">subsetSumII</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">subset_sum_ii.rs</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a>
+<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">subset_sum_ii</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">subset_sum_ii.c</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a>
+<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">subsetSumII</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">subset_sum_ii.kt</span><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a>
+<a id="__codelineno-39-3" name="__codelineno-39-3" href="#__codelineno-39-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">subsetSumII</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">subset_sum_ii.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a>
+<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">subset_sum_ii</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">subset_sum_ii.zig</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-41-2" name="__codelineno-41-2" href="#__codelineno-41-2"></a>
+<a id="__codelineno-41-3" name="__codelineno-41-3" href="#__codelineno-41-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">subsetSumII</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>以下の図は、配列 <span class="arithmatex">\([4, 4, 5]\)</span> とターゲット要素 <span class="arithmatex">\(9\)</span> のバックトラッキングプロセスを示し、4種類の剪定操作が含まれています。図とコードのコメントを組み合わせて、検索プロセス全体と各種類の剪定操作の動作を理解してください。</p>
+<p><a class="glightbox" href="../subset_sum_problem.assets/subset_sum_ii.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="部分集合和 II のバックトラッキングプロセス" class="animation-figure" src="../subset_sum_problem.assets/subset_sum_ii.png" /></a></p>
+<p align="center"> 図 13-14 &nbsp; 部分集合和 II のバックトラッキングプロセス </p>
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+    0.2 &nbsp; 本書の使い方
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_introduction/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 重要な復習
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#2-q-a" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; Q &amp; A
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
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+<h1 id="135">13.5 &nbsp; まとめ<a class="headerlink" href="#135" title="Permanent link">&para;</a></h1>
+<h3 id="1">1. &nbsp; 重要な復習<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<ul>
+<li>バックトラッキングアルゴリズムの本質は全数探索です。解空間の深さ優先走査を実行することで条件を満たす解を求めます。検索中に満足のいく解が見つかった場合、それを記録し、すべての解が見つかるか走査が完了するまで続けます。</li>
+<li>バックトラッキングアルゴリズムの検索プロセスには試行と後退が含まれます。深さ優先探索を使用して様々な選択を探索し、選択が制約を満たさない場合、前の選択を取り消します。そして前の状態に戻って他のオプションを試し続けます。試行と後退は反対方向の操作です。</li>
+<li>バックトラッキング問題には通常複数の制約が含まれます。これらの制約は剪定操作を実行するために使用できます。剪定は不要な検索分岐を事前に終了し、検索効率を大幅に向上させることができます。</li>
+<li>バックトラッキングアルゴリズムは主に検索問題と制約満足問題を解決するために使用されます。組み合わせ最適化問題はバックトラッキングを使用して解決できますが、多くの場合、より効率的または効果的な解決方法が利用可能です。</li>
+<li>順列問題は、与えられた集合の要素のすべての可能な順列を検索することを目的とします。各要素が選択されたかどうかを記録するために配列を使用し、同じ要素の重複選択を避けます。これにより、各要素が一度だけ選択されることが保証されます。</li>
+<li>順列問題では、集合に重複要素が含まれている場合、最終結果に重複順列が含まれます。同一要素が各ラウンドで一度だけ選択できるように制限する必要があり、これは通常ハッシュセットを使用して実装されます。</li>
+<li>部分集合和問題は、与えられた集合でターゲット値に合計する全ての部分集合を見つけることを目的とします。集合は要素の順序を区別しませんが、検索プロセスでは重複する部分集合が生成される可能性があります。これは、アルゴリズムが異なる要素順序を独特のパスとして探索するために発生します。バックトラッキングの前に、データをソートし、各ラウンドの走査の開始点を示す変数を設定します。これにより、重複する部分集合を生成する検索分岐を剪定できます。</li>
+<li>部分集合和問題では、配列内の等しい要素は重複集合を生成する可能性があります。配列がすでにソートされているという前提条件を使用して、隣接する要素が等しいかどうかを判定することで剪定を行います。これにより、等しい要素がラウンドごとに一度だけ選択されることが保証されます。</li>
+<li><span class="arithmatex">\(n\)</span> クイーン問題は、2つのクイーンが互いに攻撃できないように <span class="arithmatex">\(n \times n\)</span> のチェスボードに <span class="arithmatex">\(n\)</span> 個のクイーンを配置する方案を見つけることを目的とします。問題の制約には行制約、列制約、および主対角線と副対角線の制約が含まれます。行制約を満たすために、行ごとに1つのクイーンを配置する戦略を採用し、各行に1つのクイーンが配置されることを保証します。</li>
+<li>列制約と対角線制約の処理は似ています。列制約については、各列にクイーンがあるかどうかを記録する配列を使用し、選択されたセルが合法かどうかを示します。対角線制約については、2つの配列を使用して主対角線と副対角線にそれぞれクイーンの存在を記録します。課題は、同じ主対角線または副対角線上のセルの行と列のインデックス間の関係を決定することです。</li>
+</ul>
+<h3 id="2-q-a">2. &nbsp; Q &amp; A<a class="headerlink" href="#2-q-a" title="Permanent link">&para;</a></h3>
+<p><strong>Q</strong>: バックトラッキングと再帰の関係をどのように理解すればよいですか？</p>
+<p>全体的に、バックトラッキングは「アルゴリズム戦略」であり、再帰はより「ツール」です。</p>
+<ul>
+<li>バックトラッキングアルゴリズムは通常再帰に基づいています。しかし、バックトラッキングは再帰の応用シナリオの一つであり、特に検索問題においてです。</li>
+<li>再帰の構造は「部分問題分解」の問題解決パラダイムを反映します。分割統治、バックトラッキング、動的プログラミング（メモ化再帰）を含む問題の解決でよく使用されます。</li>
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+    第 2 章 &nbsp; 計算量解析
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_19" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_reference/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9 3v15h3V3H9m3 2 4 13 3-1-4-13-3 1M5 5v13h3V5H5M3 19v2h18v-2H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    参考文献
+  </span>
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+<h1 id="2">第 2 章 &nbsp; 複雑度解析<a class="headerlink" href="#2" title="Permanent link">&para;</a></h1>
+<p><a class="glightbox" href="../assets/covers/chapter_complexity_analysis.jpg" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Complexity analysis" class="cover-image" src="../assets/covers/chapter_complexity_analysis.jpg" /></a></p>
+<div class="admonition abstract">
+<p class="admonition-title">Abstract</p>
+<p>複雑度解析は、アルゴリズムの広大な宇宙における時空のナビゲーターのようなものです。</p>
+<p>時間と空間の次元をより深く探求し、より優雅な解決策を求めるためのガイドとなります。</p>
+</div>
+<h2 id="_1">章の内容<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h2>
+<ul>
+<li><a href="performance_evaluation/">2.1 &nbsp; アルゴリズム効率評価</a></li>
+<li><a href="iteration_and_recursion/">2.2 &nbsp; 反復と再帰</a></li>
+<li><a href="time_complexity/">2.3 &nbsp; 時間計算量</a></li>
+<li><a href="space_complexity/">2.4 &nbsp; 空間計算量</a></li>
+<li><a href="summary/">2.5 &nbsp; まとめ</a></li>
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+  
+  <span class="md-ellipsis">
+    0.2 &nbsp; 本書の使い方
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_introduction/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#221" class="md-nav__link">
+    <span class="md-ellipsis">
+      2.2.1 &nbsp; 反復
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="2.2.1   反復">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1-for" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; forループ
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2-while" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; whileループ
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#3" class="md-nav__link">
+    <span class="md-ellipsis">
+      3. &nbsp; ネストしたループ
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#222" class="md-nav__link">
+    <span class="md-ellipsis">
+      2.2.2 &nbsp; 再帰
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="2.2.2   再帰">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 呼び出しスタック
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; 末尾再帰
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#3_1" class="md-nav__link">
+    <span class="md-ellipsis">
+      3. &nbsp; 再帰木
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#223" class="md-nav__link">
+    <span class="md-ellipsis">
+      2.2.3 &nbsp; 比較
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
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+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
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+        <li class="md-nav__item">
+  <a href="#221" class="md-nav__link">
+    <span class="md-ellipsis">
+      2.2.1 &nbsp; 反復
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="2.2.1   反復">
+      <ul class="md-nav__list">
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+  <a href="#1-for" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; forループ
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2-while" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; whileループ
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#3" class="md-nav__link">
+    <span class="md-ellipsis">
+      3. &nbsp; ネストしたループ
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#222" class="md-nav__link">
+    <span class="md-ellipsis">
+      2.2.2 &nbsp; 再帰
+    </span>
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+  
+    <nav class="md-nav" aria-label="2.2.2   再帰">
+      <ul class="md-nav__list">
+        
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+    <span class="md-ellipsis">
+      1. &nbsp; 呼び出しスタック
+    </span>
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+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; 末尾再帰
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#3_1" class="md-nav__link">
+    <span class="md-ellipsis">
+      3. &nbsp; 再帰木
+    </span>
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+  
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+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
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+      2.2.3 &nbsp; 比較
+    </span>
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+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
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+<h1 id="22">2.2 &nbsp; 反復と再帰<a class="headerlink" href="#22" title="Permanent link">&para;</a></h1>
+<p>アルゴリズムにおいて、タスクの繰り返し実行は非常に一般的であり、複雑度の分析と密接に関係しています。したがって、時間計算量と空間計算量の概念を詳しく学ぶ前に、まずプログラミングで繰り返しタスクを実装する方法を探究しましょう。これには、2つの基本的なプログラミング制御構造である反復と再帰の理解が含まれます。</p>
+<h2 id="221">2.2.1 &nbsp; 反復<a class="headerlink" href="#221" title="Permanent link">&para;</a></h2>
+<p><u>反復</u>は、タスクを繰り返し実行するための制御構造です。反復では、プログラムは特定の条件が満たされている限りコードブロックを繰り返し実行し、この条件が満たされなくなるまで続けます。</p>
+<h3 id="1-for">1. &nbsp; forループ<a class="headerlink" href="#1-for" title="Permanent link">&para;</a></h3>
+<p><code>for</code>ループは反復の最も一般的な形式の1つであり、<strong>反復回数が事前に分かっている場合に特に適しています</strong>。</p>
+<p>以下の関数は<code>for</code>ループを使用して<span class="arithmatex">\(1 + 2 + \dots + n\)</span>の合計を実行し、合計を変数<code>res</code>に格納します。Pythonでは、<code>range(a, b)</code>は<code>a</code>を含み<code>b</code>を除く区間を作成することに注意してください。つまり、<span class="arithmatex">\(a\)</span>から<span class="arithmatex">\(b−1\)</span>までの範囲で反復します。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:14"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><input id="__tabbed_1_14" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label><label for="__tabbed_1_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">for_loop</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;forループ&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="n">res</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="c1"># 1, 2, ..., n-1, n の合計をループ</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>        <span class="n">res</span> <span class="o">+=</span> <span class="n">i</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>    <span class="k">return</span> <span class="n">res</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* for ループ */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">forLoop</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="c1">// 1, 2, ..., n-1, n の合計をループ計算</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="o">++</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* for ループ */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">forLoop</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="c1">// 1, 2, ..., n-1, n の合計をループ計算</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">iteration</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">ForLoop</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">forLoop</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">forLoop</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">forLoop</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">forLoop</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">forLoop</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">for_loop</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">forLoop</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">forLoop</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">for_loop</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.zig</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">forLoop</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>以下の図はこの合計関数を表しています。</p>
+<p><a class="glightbox" href="../iteration_and_recursion.assets/iteration.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Flowchart of the sum function" class="animation-figure" src="../iteration_and_recursion.assets/iteration.png" /></a></p>
+<p align="center"> 図 2-1 &nbsp; Flowchart of the sum function </p>
+
+<p>この合計関数での操作数は入力データのサイズ<span class="arithmatex">\(n\)</span>に比例する、つまり線形関係があります。<strong>この「線形関係」こそが時間計算量が記述するものです</strong>。このトピックについては次のセクションで詳しく説明します。</p>
+<h3 id="2-while">2. &nbsp; whileループ<a class="headerlink" href="#2-while" title="Permanent link">&para;</a></h3>
+<p><code>for</code>ループと同様に、<code>while</code>ループは反復を実装するためのもう1つのアプローチです。<code>while</code>ループでは、プログラムは各反復の開始時に条件をチェックし、条件が真の場合は実行を継続し、そうでなければループを終了します。</p>
+<p>以下では<code>while</code>ループを使用して合計<span class="arithmatex">\(1 + 2 + \dots + n\)</span>を実装します。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:14"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><input id="__tabbed_2_14" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label><label for="__tabbed_2_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.py</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">while_loop</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;whileループ&quot;&quot;&quot;</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a>    <span class="n">res</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a>    <span class="n">i</span> <span class="o">=</span> <span class="mi">1</span>  <span class="c1"># 条件変数を初期化</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a>    <span class="c1"># 1, 2, ..., n-1, n の合計をループ</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a>    <span class="k">while</span> <span class="n">i</span> <span class="o">&lt;=</span> <span class="n">n</span><span class="p">:</span>
+<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a>        <span class="n">res</span> <span class="o">+=</span> <span class="n">i</span>
+<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a>        <span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>  <span class="c1"># 条件変数を更新</span>
+<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a>    <span class="k">return</span> <span class="n">res</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.cpp</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* while ループ */</span>
+<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">whileLoop</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 条件変数を初期化</span>
+<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">    </span><span class="c1">// 1, 2, ..., n-1, n の合計をループ計算</span>
+<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">        </span><span class="n">i</span><span class="o">++</span><span class="p">;</span><span class="w"> </span><span class="c1">// 条件変数を更新</span>
+<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.java</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* while ループ */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">whileLoop</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 条件変数を初期化</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">    </span><span class="c1">// 1, 2, ..., n-1, n の合計をループ計算</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">        </span><span class="n">i</span><span class="o">++</span><span class="p">;</span><span class="w"> </span><span class="c1">// 条件変数を更新</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.cs</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">iteration</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">WhileLoop</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.go</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">whileLoop</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">whileLoop</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.js</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">whileLoop</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.ts</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">whileLoop</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.dart</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">whileLoop</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.rs</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">while_loop</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.c</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">whileLoop</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.kt</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">whileLoop</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">while_loop</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.zig</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">whileLoop</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p><strong><code>while</code>ループは<code>for</code>ループよりも柔軟性を提供します</strong>。特に、条件変数のカスタム初期化と各ステップでの変更が可能です。</p>
+<p>例えば、以下のコードでは、条件変数<span class="arithmatex">\(i\)</span>が各ラウンドで2回更新されますが、これは<code>for</code>ループでは実装が不便です。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="3:14"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><input id="__tabbed_3_14" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label><label for="__tabbed_3_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.py</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">while_loop_ii</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;whileループ（2つの更新）&quot;&quot;&quot;</span>
+<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a>    <span class="n">res</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a>    <span class="n">i</span> <span class="o">=</span> <span class="mi">1</span>  <span class="c1"># 条件変数を初期化</span>
+<a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a>    <span class="c1"># 1, 4, 10, ... の合計をループ</span>
+<a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a>    <span class="k">while</span> <span class="n">i</span> <span class="o">&lt;=</span> <span class="n">n</span><span class="p">:</span>
+<a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a>        <span class="n">res</span> <span class="o">+=</span> <span class="n">i</span>
+<a id="__codelineno-28-8" name="__codelineno-28-8" href="#__codelineno-28-8"></a>        <span class="c1"># 条件変数を更新</span>
+<a id="__codelineno-28-9" name="__codelineno-28-9" href="#__codelineno-28-9"></a>        <span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-28-10" name="__codelineno-28-10" href="#__codelineno-28-10"></a>        <span class="n">i</span> <span class="o">*=</span> <span class="mi">2</span>
+<a id="__codelineno-28-11" name="__codelineno-28-11" href="#__codelineno-28-11"></a>    <span class="k">return</span> <span class="n">res</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.cpp</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="cm">/* while ループ（2つの更新） */</span>
+<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">whileLoopII</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 条件変数を初期化</span>
+<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a><span class="w">    </span><span class="c1">// 1, 4, 10, ... の合計をループ計算</span>
+<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a><span class="w">        </span><span class="c1">// 条件変数を更新</span>
+<a id="__codelineno-29-9" name="__codelineno-29-9" href="#__codelineno-29-9"></a><span class="w">        </span><span class="n">i</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-29-10" name="__codelineno-29-10" href="#__codelineno-29-10"></a><span class="w">        </span><span class="n">i</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-29-11" name="__codelineno-29-11" href="#__codelineno-29-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-12" name="__codelineno-29-12" href="#__codelineno-29-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-29-13" name="__codelineno-29-13" href="#__codelineno-29-13"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.java</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* while ループ（2つの更新） */</span>
+<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">whileLoopII</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 条件変数を初期化</span>
+<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a><span class="w">    </span><span class="c1">// 1, 4, 10, ... の合計をループ計算</span>
+<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a><span class="w">        </span><span class="c1">// 条件変数を更新</span>
+<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a><span class="w">        </span><span class="n">i</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-30-10" name="__codelineno-30-10" href="#__codelineno-30-10"></a><span class="w">        </span><span class="n">i</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-30-11" name="__codelineno-30-11" href="#__codelineno-30-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-12" name="__codelineno-30-12" href="#__codelineno-30-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-30-13" name="__codelineno-30-13" href="#__codelineno-30-13"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.cs</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">iteration</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">WhileLoopII</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.go</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">whileLoopII</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.swift</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">whileLoopII</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.js</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">whileLoopII</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.ts</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">whileLoopII</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.dart</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">whileLoopII</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.rs</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">while_loop_ii</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.c</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">whileLoopII</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.kt</span><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">whileLoopII</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">while_loop_ii</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.zig</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">whileLoopII</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>全体的に、<strong><code>for</code>ループはより簡潔で、<code>while</code>ループはより柔軟です</strong>。どちらも反復構造を実装できます。どちらを使用するかは、問題の具体的な要件に基づいて決定する必要があります。</p>
+<h3 id="3">3. &nbsp; ネストしたループ<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
+<p>1つのループ構造を別のループ構造内にネストできます。以下は<code>for</code>ループを使用した例です：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="4:14"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><input id="__tabbed_4_6" name="__tabbed_4" type="radio" /><input id="__tabbed_4_7" name="__tabbed_4" type="radio" /><input id="__tabbed_4_8" name="__tabbed_4" type="radio" /><input id="__tabbed_4_9" name="__tabbed_4" type="radio" /><input id="__tabbed_4_10" name="__tabbed_4" type="radio" /><input id="__tabbed_4_11" name="__tabbed_4" type="radio" /><input id="__tabbed_4_12" name="__tabbed_4" type="radio" /><input id="__tabbed_4_13" name="__tabbed_4" type="radio" /><input id="__tabbed_4_14" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">Python</label><label for="__tabbed_4_2">C++</label><label for="__tabbed_4_3">Java</label><label for="__tabbed_4_4">C#</label><label for="__tabbed_4_5">Go</label><label for="__tabbed_4_6">Swift</label><label for="__tabbed_4_7">JS</label><label for="__tabbed_4_8">TS</label><label for="__tabbed_4_9">Dart</label><label for="__tabbed_4_10">Rust</label><label for="__tabbed_4_11">C</label><label for="__tabbed_4_12">Kotlin</label><label for="__tabbed_4_13">Ruby</label><label for="__tabbed_4_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.py</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">nested_for_loop</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">str</span><span class="p">:</span>
+<a id="__codelineno-42-2" name="__codelineno-42-2" href="#__codelineno-42-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;二重forループ&quot;&quot;&quot;</span>
+<a id="__codelineno-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></a>    <span class="n">res</span> <span class="o">=</span> <span class="s2">&quot;&quot;</span>
+<a id="__codelineno-42-4" name="__codelineno-42-4" href="#__codelineno-42-4"></a>    <span class="c1"># i = 1, 2, ..., n-1, n をループ</span>
+<a id="__codelineno-42-5" name="__codelineno-42-5" href="#__codelineno-42-5"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-42-6" name="__codelineno-42-6" href="#__codelineno-42-6"></a>        <span class="c1"># j = 1, 2, ..., n-1, n をループ</span>
+<a id="__codelineno-42-7" name="__codelineno-42-7" href="#__codelineno-42-7"></a>        <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-42-8" name="__codelineno-42-8" href="#__codelineno-42-8"></a>            <span class="n">res</span> <span class="o">+=</span> <span class="sa">f</span><span class="s2">&quot;(</span><span class="si">{</span><span class="n">i</span><span class="si">}</span><span class="s2">, </span><span class="si">{</span><span class="n">j</span><span class="si">}</span><span class="s2">), &quot;</span>
+<a id="__codelineno-42-9" name="__codelineno-42-9" href="#__codelineno-42-9"></a>    <span class="k">return</span> <span class="n">res</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.cpp</span><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="cm">/* 2重 for ループ */</span>
+<a id="__codelineno-43-2" name="__codelineno-43-2" href="#__codelineno-43-2"></a><span class="n">string</span><span class="w"> </span><span class="nf">nestedForLoop</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-3" name="__codelineno-43-3" href="#__codelineno-43-3"></a><span class="w">    </span><span class="n">ostringstream</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-43-4" name="__codelineno-43-4" href="#__codelineno-43-4"></a><span class="w">    </span><span class="c1">// ループ i = 1, 2, ..., n-1, n</span>
+<a id="__codelineno-43-5" name="__codelineno-43-5" href="#__codelineno-43-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="o">++</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-6" name="__codelineno-43-6" href="#__codelineno-43-6"></a><span class="w">        </span><span class="c1">// ループ j = 1, 2, ..., n-1, n</span>
+<a id="__codelineno-43-7" name="__codelineno-43-7" href="#__codelineno-43-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="o">++</span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-8" name="__codelineno-43-8" href="#__codelineno-43-8"></a><span class="w">            </span><span class="n">res</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;(&quot;</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;, &quot;</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;), &quot;</span><span class="p">;</span>
+<a id="__codelineno-43-9" name="__codelineno-43-9" href="#__codelineno-43-9"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-43-10" name="__codelineno-43-10" href="#__codelineno-43-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-43-11" name="__codelineno-43-11" href="#__codelineno-43-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">str</span><span class="p">();</span>
+<a id="__codelineno-43-12" name="__codelineno-43-12" href="#__codelineno-43-12"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.java</span><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="cm">/* 2重 for ループ */</span>
+<a id="__codelineno-44-2" name="__codelineno-44-2" href="#__codelineno-44-2"></a><span class="n">String</span><span class="w"> </span><span class="nf">nestedForLoop</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-3" name="__codelineno-44-3" href="#__codelineno-44-3"></a><span class="w">    </span><span class="n">StringBuilder</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">StringBuilder</span><span class="p">();</span>
+<a id="__codelineno-44-4" name="__codelineno-44-4" href="#__codelineno-44-4"></a><span class="w">    </span><span class="c1">// ループ i = 1, 2, ..., n-1, n</span>
+<a id="__codelineno-44-5" name="__codelineno-44-5" href="#__codelineno-44-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-6" name="__codelineno-44-6" href="#__codelineno-44-6"></a><span class="w">        </span><span class="c1">// ループ j = 1, 2, ..., n-1, n</span>
+<a id="__codelineno-44-7" name="__codelineno-44-7" href="#__codelineno-44-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-8" name="__codelineno-44-8" href="#__codelineno-44-8"></a><span class="w">            </span><span class="n">res</span><span class="p">.</span><span class="na">append</span><span class="p">(</span><span class="s">&quot;(&quot;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s">&quot;, &quot;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s">&quot;), &quot;</span><span class="p">);</span>
+<a id="__codelineno-44-9" name="__codelineno-44-9" href="#__codelineno-44-9"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-44-10" name="__codelineno-44-10" href="#__codelineno-44-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-44-11" name="__codelineno-44-11" href="#__codelineno-44-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="na">toString</span><span class="p">();</span>
+<a id="__codelineno-44-12" name="__codelineno-44-12" href="#__codelineno-44-12"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.cs</span><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">iteration</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">NestedForLoop</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.go</span><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">nestedForLoop</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.swift</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">nestedForLoop</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.js</span><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">nestedForLoop</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.ts</span><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">nestedForLoop</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.dart</span><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">nestedForLoop</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.rs</span><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">nested_for_loop</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.c</span><pre><span></span><code><a id="__codelineno-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">nestedForLoop</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.kt</span><pre><span></span><code><a id="__codelineno-53-1" name="__codelineno-53-1" href="#__codelineno-53-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">nestedForLoop</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.rb</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">nested_for_loop</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">iteration.zig</span><pre><span></span><code><a id="__codelineno-55-1" name="__codelineno-55-1" href="#__codelineno-55-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">nestedForLoop</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>以下の図はこのネストしたループを表しています。</p>
+<p><a class="glightbox" href="../iteration_and_recursion.assets/nested_iteration.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Flowchart of the nested loop" class="animation-figure" src="../iteration_and_recursion.assets/nested_iteration.png" /></a></p>
+<p align="center"> 図 2-2 &nbsp; Flowchart of the nested loop </p>
+
+<p>このような場合、関数の操作数は<span class="arithmatex">\(n^2\)</span>に比例します。つまり、アルゴリズムの実行時間と入力データのサイズ<span class="arithmatex">\(n\)</span>には「二次関係」があります。</p>
+<p>さらにネストしたループを追加することで複雑度を高めることができ、各レベルのネストは事実上「次元を増加」させ、時間計算量を「三次」、「四次」などに引き上げます。</p>
+<h2 id="222">2.2.2 &nbsp; 再帰<a class="headerlink" href="#222" title="Permanent link">&para;</a></h2>
+<p><u>再帰</u>は、関数が自分自身を呼び出すことで問題を解決するアルゴリズム戦略です。主に2つのフェーズが含まれます：</p>
+<ol>
+<li><strong>呼び出し</strong>: プログラムが自分自身を繰り返し呼び出し、しばしばより小さいまたはより単純な引数で、「終了条件」に向かって進みます。</li>
+<li><strong>返却</strong>: 「終了条件」がトリガーされると、プログラムは最も深い再帰関数から返り始め、各レイヤーの結果を集約します。</li>
+</ol>
+<p>実装の観点から、再帰コードは主に3つの要素を含みます。</p>
+<ol>
+<li><strong>終了条件</strong>: 「呼び出し」から「返却」にいつ切り替えるかを決定します。</li>
+<li><strong>再帰呼び出し</strong>: 「呼び出し」に対応し、関数が自分自身を呼び出し、通常はより小さいまたはより単純化されたパラメータで行います。</li>
+<li><strong>結果の返却</strong>: 「返却」に対応し、現在の再帰レベルの結果が前のレイヤーに返されます。</li>
+</ol>
+<p>以下のコードを観察してください。単純に関数<code>recur(n)</code>を呼び出すだけで<span class="arithmatex">\(1 + 2 + \dots + n\)</span>の合計を計算できます：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="5:14"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><input id="__tabbed_5_7" name="__tabbed_5" type="radio" /><input id="__tabbed_5_8" name="__tabbed_5" type="radio" /><input id="__tabbed_5_9" name="__tabbed_5" type="radio" /><input id="__tabbed_5_10" name="__tabbed_5" type="radio" /><input id="__tabbed_5_11" name="__tabbed_5" type="radio" /><input id="__tabbed_5_12" name="__tabbed_5" type="radio" /><input id="__tabbed_5_13" name="__tabbed_5" type="radio" /><input id="__tabbed_5_14" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">Python</label><label for="__tabbed_5_2">C++</label><label for="__tabbed_5_3">Java</label><label for="__tabbed_5_4">C#</label><label for="__tabbed_5_5">Go</label><label for="__tabbed_5_6">Swift</label><label for="__tabbed_5_7">JS</label><label for="__tabbed_5_8">TS</label><label for="__tabbed_5_9">Dart</label><label for="__tabbed_5_10">Rust</label><label for="__tabbed_5_11">C</label><label for="__tabbed_5_12">Kotlin</label><label for="__tabbed_5_13">Ruby</label><label for="__tabbed_5_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.py</span><pre><span></span><code><a id="__codelineno-56-1" name="__codelineno-56-1" href="#__codelineno-56-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-56-2" name="__codelineno-56-2" href="#__codelineno-56-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;再帰&quot;&quot;&quot;</span>
+<a id="__codelineno-56-3" name="__codelineno-56-3" href="#__codelineno-56-3"></a>    <span class="c1"># 終了条件</span>
+<a id="__codelineno-56-4" name="__codelineno-56-4" href="#__codelineno-56-4"></a>    <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
+<a id="__codelineno-56-5" name="__codelineno-56-5" href="#__codelineno-56-5"></a>        <span class="k">return</span> <span class="mi">1</span>
+<a id="__codelineno-56-6" name="__codelineno-56-6" href="#__codelineno-56-6"></a>    <span class="c1"># 再帰：再帰呼び出し</span>
+<a id="__codelineno-56-7" name="__codelineno-56-7" href="#__codelineno-56-7"></a>    <span class="n">res</span> <span class="o">=</span> <span class="n">recur</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-56-8" name="__codelineno-56-8" href="#__codelineno-56-8"></a>    <span class="c1"># 復帰：結果を返す</span>
+<a id="__codelineno-56-9" name="__codelineno-56-9" href="#__codelineno-56-9"></a>    <span class="k">return</span> <span class="n">n</span> <span class="o">+</span> <span class="n">res</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.cpp</span><pre><span></span><code><a id="__codelineno-57-1" name="__codelineno-57-1" href="#__codelineno-57-1"></a><span class="cm">/* 再帰 */</span>
+<a id="__codelineno-57-2" name="__codelineno-57-2" href="#__codelineno-57-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">recur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-3" name="__codelineno-57-3" href="#__codelineno-57-3"></a><span class="w">    </span><span class="c1">// 終了条件</span>
+<a id="__codelineno-57-4" name="__codelineno-57-4" href="#__codelineno-57-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-57-5" name="__codelineno-57-5" href="#__codelineno-57-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-57-6" name="__codelineno-57-6" href="#__codelineno-57-6"></a><span class="w">    </span><span class="c1">// 再帰：再帰呼び出し</span>
+<a id="__codelineno-57-7" name="__codelineno-57-7" href="#__codelineno-57-7"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-57-8" name="__codelineno-57-8" href="#__codelineno-57-8"></a><span class="w">    </span><span class="c1">// 戻り値：結果を返す</span>
+<a id="__codelineno-57-9" name="__codelineno-57-9" href="#__codelineno-57-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-57-10" name="__codelineno-57-10" href="#__codelineno-57-10"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.java</span><pre><span></span><code><a id="__codelineno-58-1" name="__codelineno-58-1" href="#__codelineno-58-1"></a><span class="cm">/* 再帰 */</span>
+<a id="__codelineno-58-2" name="__codelineno-58-2" href="#__codelineno-58-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">recur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-3" name="__codelineno-58-3" href="#__codelineno-58-3"></a><span class="w">    </span><span class="c1">// 終了条件</span>
+<a id="__codelineno-58-4" name="__codelineno-58-4" href="#__codelineno-58-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-58-5" name="__codelineno-58-5" href="#__codelineno-58-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-58-6" name="__codelineno-58-6" href="#__codelineno-58-6"></a><span class="w">    </span><span class="c1">// 再帰：再帰呼び出し</span>
+<a id="__codelineno-58-7" name="__codelineno-58-7" href="#__codelineno-58-7"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-58-8" name="__codelineno-58-8" href="#__codelineno-58-8"></a><span class="w">    </span><span class="c1">// 戻り値：結果を返す</span>
+<a id="__codelineno-58-9" name="__codelineno-58-9" href="#__codelineno-58-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-58-10" name="__codelineno-58-10" href="#__codelineno-58-10"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.cs</span><pre><span></span><code><a id="__codelineno-59-1" name="__codelineno-59-1" href="#__codelineno-59-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">recursion</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Recur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.go</span><pre><span></span><code><a id="__codelineno-60-1" name="__codelineno-60-1" href="#__codelineno-60-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">recur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.swift</span><pre><span></span><code><a id="__codelineno-61-1" name="__codelineno-61-1" href="#__codelineno-61-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">recur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.js</span><pre><span></span><code><a id="__codelineno-62-1" name="__codelineno-62-1" href="#__codelineno-62-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">recur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.ts</span><pre><span></span><code><a id="__codelineno-63-1" name="__codelineno-63-1" href="#__codelineno-63-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">recur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.dart</span><pre><span></span><code><a id="__codelineno-64-1" name="__codelineno-64-1" href="#__codelineno-64-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">recur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.rs</span><pre><span></span><code><a id="__codelineno-65-1" name="__codelineno-65-1" href="#__codelineno-65-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">recur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.c</span><pre><span></span><code><a id="__codelineno-66-1" name="__codelineno-66-1" href="#__codelineno-66-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">recur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.kt</span><pre><span></span><code><a id="__codelineno-67-1" name="__codelineno-67-1" href="#__codelineno-67-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">recur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.rb</span><pre><span></span><code><a id="__codelineno-68-1" name="__codelineno-68-1" href="#__codelineno-68-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">recur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.zig</span><pre><span></span><code><a id="__codelineno-69-1" name="__codelineno-69-1" href="#__codelineno-69-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">recur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>以下の図はこの関数の再帰プロセスを示しています。</p>
+<p><a class="glightbox" href="../iteration_and_recursion.assets/recursion_sum.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Recursive process of the sum function" class="animation-figure" src="../iteration_and_recursion.assets/recursion_sum.png" /></a></p>
+<p align="center"> 図 2-3 &nbsp; Recursive process of the sum function </p>
+
+<p>反復と再帰は計算の観点から同じ結果を達成できますが、<strong>それらは思考と問題解決の全く異なるパラダイムを表します</strong>。</p>
+<ul>
+<li><strong>反復</strong>: 「ボトムアップ」で問題を解決します。最も基本的なステップから始まり、タスクが完了するまでこれらのステップを繰り返し追加または累積します。</li>
+<li><strong>再帰</strong>: 「トップダウン」で問題を解決します。元の問題をより小さなサブ問題に分解し、各サブ問題は元の問題と同じ形式を持ちます。これらのサブ問題は、解が分かっているベースケースで停止するまで、さらに小さなサブ問題に分解されます。</li>
+</ul>
+<p>先ほどの合計関数の例を取ってみましょう。<span class="arithmatex">\(f(n) = 1 + 2 + \dots + n\)</span>として定義されます。</p>
+<ul>
+<li><strong>反復</strong>: このアプローチでは、ループ内で合計プロセスをシミュレートします。<span class="arithmatex">\(1\)</span>から始まり<span class="arithmatex">\(n\)</span>まで横断し、各反復で合計操作を実行して最終的に<span class="arithmatex">\(f(n)\)</span>を計算します。</li>
+<li><strong>再帰</strong>: ここでは、問題はサブ問題に分解されます：<span class="arithmatex">\(f(n) = n + f(n-1)\)</span>。この分解は、ベースケースの<span class="arithmatex">\(f(1) = 1\)</span>に到達するまで再帰的に続き、そこで再帰が終了します。</li>
+</ul>
+<h3 id="1">1. &nbsp; 呼び出しスタック<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<p>再帰関数が自分自身を呼び出すたびに、システムは新しく開始された関数にメモリを割り当てて、ローカル変数、戻りアドレス、その他の関連情報を格納します。これは2つの主要な結果をもたらします。</p>
+<ul>
+<li>関数のコンテキストデータは「スタックフレーム空間」と呼ばれるメモリ領域に格納され、関数が返された後にのみ解放されます。したがって、<strong>再帰は一般的に反復よりも多くのメモリ空間を消費します</strong>。</li>
+<li>再帰呼び出しは追加のオーバーヘッドを導入します。<strong>したがって、再帰は通常ループよりも時間効率が劣ります。</strong></li>
+</ul>
+<p>以下の図に示されているように、終了条件がトリガーされる前に<span class="arithmatex">\(n\)</span>個の未返却の再帰関数があり、<strong>再帰の深さが<span class="arithmatex">\(n\)</span>であることを示しています</strong>。</p>
+<p><a class="glightbox" href="../iteration_and_recursion.assets/recursion_sum_depth.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Recursion call depth" class="animation-figure" src="../iteration_and_recursion.assets/recursion_sum_depth.png" /></a></p>
+<p align="center"> 図 2-4 &nbsp; Recursion call depth </p>
+
+<p>実際には、プログラミング言語で許可される再帰の深さは通常制限されており、過度に深い再帰はスタックオーバーフローエラーを引き起こす可能性があります。</p>
+<h3 id="2">2. &nbsp; 末尾再帰<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
+<p>興味深いことに、<strong>関数が返す直前の最後のステップとして再帰呼び出しを実行する場合</strong>、コンパイラまたはインタープリターによって反復と同じ空間効率になるように最適化できます。このシナリオは<u>末尾再帰</u>として知られています。</p>
+<ul>
+<li><strong>通常の再帰</strong>: 標準的な再帰では、関数が前のレベルに戻ったとき、さらにコードを実行し続けるため、システムは前の呼び出しのコンテキストを保存する必要があります。</li>
+<li><strong>末尾再帰</strong>: ここでは、再帰呼び出しは関数が返す前の最終操作です。これは、前のレベルに戻った際に、さらなるアクションが必要ないことを意味するため、システムは前のレベルのコンテキストを保存する必要がありません。</li>
+</ul>
+<p>例えば、<span class="arithmatex">\(1 + 2 + \dots + n\)</span>の計算では、結果変数<code>res</code>を関数のパラメータにすることで、末尾再帰を実現できます：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="6:14"><input checked="checked" id="__tabbed_6_1" name="__tabbed_6" type="radio" /><input id="__tabbed_6_2" name="__tabbed_6" type="radio" /><input id="__tabbed_6_3" name="__tabbed_6" type="radio" /><input id="__tabbed_6_4" name="__tabbed_6" type="radio" /><input id="__tabbed_6_5" name="__tabbed_6" type="radio" /><input id="__tabbed_6_6" name="__tabbed_6" type="radio" /><input id="__tabbed_6_7" name="__tabbed_6" type="radio" /><input id="__tabbed_6_8" name="__tabbed_6" type="radio" /><input id="__tabbed_6_9" name="__tabbed_6" type="radio" /><input id="__tabbed_6_10" name="__tabbed_6" type="radio" /><input id="__tabbed_6_11" name="__tabbed_6" type="radio" /><input id="__tabbed_6_12" name="__tabbed_6" type="radio" /><input id="__tabbed_6_13" name="__tabbed_6" type="radio" /><input id="__tabbed_6_14" name="__tabbed_6" type="radio" /><div class="tabbed-labels"><label for="__tabbed_6_1">Python</label><label for="__tabbed_6_2">C++</label><label for="__tabbed_6_3">Java</label><label for="__tabbed_6_4">C#</label><label for="__tabbed_6_5">Go</label><label for="__tabbed_6_6">Swift</label><label for="__tabbed_6_7">JS</label><label for="__tabbed_6_8">TS</label><label for="__tabbed_6_9">Dart</label><label for="__tabbed_6_10">Rust</label><label for="__tabbed_6_11">C</label><label for="__tabbed_6_12">Kotlin</label><label for="__tabbed_6_13">Ruby</label><label for="__tabbed_6_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.py</span><pre><span></span><code><a id="__codelineno-70-1" name="__codelineno-70-1" href="#__codelineno-70-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">tail_recur</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">res</span><span class="p">):</span>
+<a id="__codelineno-70-2" name="__codelineno-70-2" href="#__codelineno-70-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;末尾再帰&quot;&quot;&quot;</span>
+<a id="__codelineno-70-3" name="__codelineno-70-3" href="#__codelineno-70-3"></a>    <span class="c1"># 終了条件</span>
+<a id="__codelineno-70-4" name="__codelineno-70-4" href="#__codelineno-70-4"></a>    <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
+<a id="__codelineno-70-5" name="__codelineno-70-5" href="#__codelineno-70-5"></a>        <span class="k">return</span> <span class="n">res</span>
+<a id="__codelineno-70-6" name="__codelineno-70-6" href="#__codelineno-70-6"></a>    <span class="c1"># 末尾再帰呼び出し</span>
+<a id="__codelineno-70-7" name="__codelineno-70-7" href="#__codelineno-70-7"></a>    <span class="k">return</span> <span class="n">tail_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">res</span> <span class="o">+</span> <span class="n">n</span><span class="p">)</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.cpp</span><pre><span></span><code><a id="__codelineno-71-1" name="__codelineno-71-1" href="#__codelineno-71-1"></a><span class="cm">/* 末尾再帰 */</span>
+<a id="__codelineno-71-2" name="__codelineno-71-2" href="#__codelineno-71-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">tailRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-71-3" name="__codelineno-71-3" href="#__codelineno-71-3"></a><span class="w">    </span><span class="c1">// 終了条件</span>
+<a id="__codelineno-71-4" name="__codelineno-71-4" href="#__codelineno-71-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-71-5" name="__codelineno-71-5" href="#__codelineno-71-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-71-6" name="__codelineno-71-6" href="#__codelineno-71-6"></a><span class="w">    </span><span class="c1">// 末尾再帰呼び出し</span>
+<a id="__codelineno-71-7" name="__codelineno-71-7" href="#__codelineno-71-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">tailRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="p">);</span>
+<a id="__codelineno-71-8" name="__codelineno-71-8" href="#__codelineno-71-8"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.java</span><pre><span></span><code><a id="__codelineno-72-1" name="__codelineno-72-1" href="#__codelineno-72-1"></a><span class="cm">/* 末尾再帰 */</span>
+<a id="__codelineno-72-2" name="__codelineno-72-2" href="#__codelineno-72-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">tailRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-72-3" name="__codelineno-72-3" href="#__codelineno-72-3"></a><span class="w">    </span><span class="c1">// 終了条件</span>
+<a id="__codelineno-72-4" name="__codelineno-72-4" href="#__codelineno-72-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-72-5" name="__codelineno-72-5" href="#__codelineno-72-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-72-6" name="__codelineno-72-6" href="#__codelineno-72-6"></a><span class="w">    </span><span class="c1">// 末尾再帰呼び出し</span>
+<a id="__codelineno-72-7" name="__codelineno-72-7" href="#__codelineno-72-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">tailRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="p">);</span>
+<a id="__codelineno-72-8" name="__codelineno-72-8" href="#__codelineno-72-8"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.cs</span><pre><span></span><code><a id="__codelineno-73-1" name="__codelineno-73-1" href="#__codelineno-73-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">recursion</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">TailRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.go</span><pre><span></span><code><a id="__codelineno-74-1" name="__codelineno-74-1" href="#__codelineno-74-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">tailRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.swift</span><pre><span></span><code><a id="__codelineno-75-1" name="__codelineno-75-1" href="#__codelineno-75-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">tailRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.js</span><pre><span></span><code><a id="__codelineno-76-1" name="__codelineno-76-1" href="#__codelineno-76-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">tailRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.ts</span><pre><span></span><code><a id="__codelineno-77-1" name="__codelineno-77-1" href="#__codelineno-77-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">tailRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.dart</span><pre><span></span><code><a id="__codelineno-78-1" name="__codelineno-78-1" href="#__codelineno-78-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">tailRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.rs</span><pre><span></span><code><a id="__codelineno-79-1" name="__codelineno-79-1" href="#__codelineno-79-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">tail_recur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.c</span><pre><span></span><code><a id="__codelineno-80-1" name="__codelineno-80-1" href="#__codelineno-80-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">tailRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.kt</span><pre><span></span><code><a id="__codelineno-81-1" name="__codelineno-81-1" href="#__codelineno-81-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">tailRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.rb</span><pre><span></span><code><a id="__codelineno-82-1" name="__codelineno-82-1" href="#__codelineno-82-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">tail_recur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.zig</span><pre><span></span><code><a id="__codelineno-83-1" name="__codelineno-83-1" href="#__codelineno-83-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">tailRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>末尾再帰の実行プロセスは以下の図に示されています。通常の再帰と末尾再帰を比較すると、合計操作のポイントが異なります。</p>
+<ul>
+<li><strong>通常の再帰</strong>: 合計操作は「返却」フェーズで発生し、各レイヤーが返った後にもう一度合計が必要です。</li>
+<li><strong>末尾再帰</strong>: 合計操作は「呼び出し」フェーズで発生し、「返却」フェーズは各レイヤーを通じて返すだけです。</li>
+</ul>
+<p><a class="glightbox" href="../iteration_and_recursion.assets/tail_recursion_sum.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Tail recursion process" class="animation-figure" src="../iteration_and_recursion.assets/tail_recursion_sum.png" /></a></p>
+<p align="center"> 図 2-5 &nbsp; Tail recursion process </p>
+
+<div class="admonition tip">
+<p class="admonition-title">Tip</p>
+<p>多くのコンパイラやインタープリターは末尾再帰最適化をサポートしていないことに注意してください。例えば、Pythonはデフォルトで末尾再帰最適化をサポートしていないため、関数が末尾再帰の形式であっても、スタックオーバーフローの問題に遭遇する可能性があります。</p>
+</div>
+<h3 id="3_1">3. &nbsp; 再帰木<a class="headerlink" href="#3_1" title="Permanent link">&para;</a></h3>
+<p>「分割統治」に関連するアルゴリズムを扱う際、再帰は反復よりもしばしばより直感的なアプローチとより読みやすいコードを提供します。「フィボナッチ数列」を例に取ってみましょう。</p>
+<div class="admonition question">
+<p class="admonition-title">Question</p>
+<p>フィボナッチ数列<span class="arithmatex">\(0, 1, 1, 2, 3, 5, 8, 13, \dots\)</span>が与えられた場合、数列の<span class="arithmatex">\(n\)</span>番目の数を求めなさい。</p>
+</div>
+<p>フィボナッチ数列の<span class="arithmatex">\(n\)</span>番目の数を<span class="arithmatex">\(f(n)\)</span>とすると、2つの結論を簡単に導き出せます：</p>
+<ul>
+<li>数列の最初の2つの数は<span class="arithmatex">\(f(1) = 0\)</span>と<span class="arithmatex">\(f(2) = 1\)</span>です。</li>
+<li>数列の各数は前の2つの数の合計です。つまり、<span class="arithmatex">\(f(n) = f(n - 1) + f(n - 2)\)</span>です。</li>
+</ul>
+<p>再帰関係を使用し、最初の2つの数を終了条件として考慮すると、再帰コードを書けます。<code>fib(n)</code>を呼び出すとフィボナッチ数列の<span class="arithmatex">\(n\)</span>番目の数が得られます：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="7:14"><input checked="checked" id="__tabbed_7_1" name="__tabbed_7" type="radio" /><input id="__tabbed_7_2" name="__tabbed_7" type="radio" /><input id="__tabbed_7_3" name="__tabbed_7" type="radio" /><input id="__tabbed_7_4" name="__tabbed_7" type="radio" /><input id="__tabbed_7_5" name="__tabbed_7" type="radio" /><input id="__tabbed_7_6" name="__tabbed_7" type="radio" /><input id="__tabbed_7_7" name="__tabbed_7" type="radio" /><input id="__tabbed_7_8" name="__tabbed_7" type="radio" /><input id="__tabbed_7_9" name="__tabbed_7" type="radio" /><input id="__tabbed_7_10" name="__tabbed_7" type="radio" /><input id="__tabbed_7_11" name="__tabbed_7" type="radio" /><input id="__tabbed_7_12" name="__tabbed_7" type="radio" /><input id="__tabbed_7_13" name="__tabbed_7" type="radio" /><input id="__tabbed_7_14" name="__tabbed_7" type="radio" /><div class="tabbed-labels"><label for="__tabbed_7_1">Python</label><label for="__tabbed_7_2">C++</label><label for="__tabbed_7_3">Java</label><label for="__tabbed_7_4">C#</label><label for="__tabbed_7_5">Go</label><label for="__tabbed_7_6">Swift</label><label for="__tabbed_7_7">JS</label><label for="__tabbed_7_8">TS</label><label for="__tabbed_7_9">Dart</label><label for="__tabbed_7_10">Rust</label><label for="__tabbed_7_11">C</label><label for="__tabbed_7_12">Kotlin</label><label for="__tabbed_7_13">Ruby</label><label for="__tabbed_7_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.py</span><pre><span></span><code><a id="__codelineno-84-1" name="__codelineno-84-1" href="#__codelineno-84-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">fib</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-84-2" name="__codelineno-84-2" href="#__codelineno-84-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;フィボナッチ数列：再帰&quot;&quot;&quot;</span>
+<a id="__codelineno-84-3" name="__codelineno-84-3" href="#__codelineno-84-3"></a>    <span class="c1"># 終了条件 f(1) = 0, f(2) = 1</span>
+<a id="__codelineno-84-4" name="__codelineno-84-4" href="#__codelineno-84-4"></a>    <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">1</span> <span class="ow">or</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">2</span><span class="p">:</span>
+<a id="__codelineno-84-5" name="__codelineno-84-5" href="#__codelineno-84-5"></a>        <span class="k">return</span> <span class="n">n</span> <span class="o">-</span> <span class="mi">1</span>
+<a id="__codelineno-84-6" name="__codelineno-84-6" href="#__codelineno-84-6"></a>    <span class="c1"># 再帰呼び出し f(n) = f(n-1) + f(n-2)</span>
+<a id="__codelineno-84-7" name="__codelineno-84-7" href="#__codelineno-84-7"></a>    <span class="n">res</span> <span class="o">=</span> <span class="n">fib</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">+</span> <span class="n">fib</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-84-8" name="__codelineno-84-8" href="#__codelineno-84-8"></a>    <span class="c1"># 結果 f(n) を返す</span>
+<a id="__codelineno-84-9" name="__codelineno-84-9" href="#__codelineno-84-9"></a>    <span class="k">return</span> <span class="n">res</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.cpp</span><pre><span></span><code><a id="__codelineno-85-1" name="__codelineno-85-1" href="#__codelineno-85-1"></a><span class="cm">/* フィボナッチ数列：再帰 */</span>
+<a id="__codelineno-85-2" name="__codelineno-85-2" href="#__codelineno-85-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">fib</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-85-3" name="__codelineno-85-3" href="#__codelineno-85-3"></a><span class="w">    </span><span class="c1">// 終了条件 f(1) = 0, f(2) = 1</span>
+<a id="__codelineno-85-4" name="__codelineno-85-4" href="#__codelineno-85-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-85-5" name="__codelineno-85-5" href="#__codelineno-85-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-85-6" name="__codelineno-85-6" href="#__codelineno-85-6"></a><span class="w">    </span><span class="c1">// 再帰呼び出し f(n) = f(n-1) + f(n-2)</span>
+<a id="__codelineno-85-7" name="__codelineno-85-7" href="#__codelineno-85-7"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">fib</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">fib</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-85-8" name="__codelineno-85-8" href="#__codelineno-85-8"></a><span class="w">    </span><span class="c1">// 結果 f(n) を返す</span>
+<a id="__codelineno-85-9" name="__codelineno-85-9" href="#__codelineno-85-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-85-10" name="__codelineno-85-10" href="#__codelineno-85-10"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.java</span><pre><span></span><code><a id="__codelineno-86-1" name="__codelineno-86-1" href="#__codelineno-86-1"></a><span class="cm">/* フィボナッチ数列：再帰 */</span>
+<a id="__codelineno-86-2" name="__codelineno-86-2" href="#__codelineno-86-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">fib</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-86-3" name="__codelineno-86-3" href="#__codelineno-86-3"></a><span class="w">    </span><span class="c1">// 終了条件 f(1) = 0, f(2) = 1</span>
+<a id="__codelineno-86-4" name="__codelineno-86-4" href="#__codelineno-86-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-86-5" name="__codelineno-86-5" href="#__codelineno-86-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-86-6" name="__codelineno-86-6" href="#__codelineno-86-6"></a><span class="w">    </span><span class="c1">// 再帰呼び出し f(n) = f(n-1) + f(n-2)</span>
+<a id="__codelineno-86-7" name="__codelineno-86-7" href="#__codelineno-86-7"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">fib</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">fib</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-86-8" name="__codelineno-86-8" href="#__codelineno-86-8"></a><span class="w">    </span><span class="c1">// 結果 f(n) を返す</span>
+<a id="__codelineno-86-9" name="__codelineno-86-9" href="#__codelineno-86-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-86-10" name="__codelineno-86-10" href="#__codelineno-86-10"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.cs</span><pre><span></span><code><a id="__codelineno-87-1" name="__codelineno-87-1" href="#__codelineno-87-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">recursion</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Fib</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.go</span><pre><span></span><code><a id="__codelineno-88-1" name="__codelineno-88-1" href="#__codelineno-88-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">fib</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.swift</span><pre><span></span><code><a id="__codelineno-89-1" name="__codelineno-89-1" href="#__codelineno-89-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">fib</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.js</span><pre><span></span><code><a id="__codelineno-90-1" name="__codelineno-90-1" href="#__codelineno-90-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">fib</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.ts</span><pre><span></span><code><a id="__codelineno-91-1" name="__codelineno-91-1" href="#__codelineno-91-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">fib</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.dart</span><pre><span></span><code><a id="__codelineno-92-1" name="__codelineno-92-1" href="#__codelineno-92-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">fib</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.rs</span><pre><span></span><code><a id="__codelineno-93-1" name="__codelineno-93-1" href="#__codelineno-93-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">fib</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.c</span><pre><span></span><code><a id="__codelineno-94-1" name="__codelineno-94-1" href="#__codelineno-94-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">fib</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.kt</span><pre><span></span><code><a id="__codelineno-95-1" name="__codelineno-95-1" href="#__codelineno-95-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">fib</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.rb</span><pre><span></span><code><a id="__codelineno-96-1" name="__codelineno-96-1" href="#__codelineno-96-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">fib</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.zig</span><pre><span></span><code><a id="__codelineno-97-1" name="__codelineno-97-1" href="#__codelineno-97-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">fib</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>上記のコードを観察すると、それ自体の中で2つの関数を再帰的に呼び出していることがわかります。<strong>つまり、1回の呼び出しで2つの分岐呼び出しが生成されます</strong>。以下の図に示されているように、この継続的な再帰呼び出しは最終的に深さ<span class="arithmatex">\(n\)</span>の<u>再帰木</u>を作成します。</p>
+<p><a class="glightbox" href="../iteration_and_recursion.assets/recursion_tree.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Fibonacci sequence recursion tree" class="animation-figure" src="../iteration_and_recursion.assets/recursion_tree.png" /></a></p>
+<p align="center"> 図 2-6 &nbsp; Fibonacci sequence recursion tree </p>
+
+<p>基本的に、再帰は「問題をより小さなサブ問題に分解する」パラダイムを体現しています。この分割統治戦略は重要です。</p>
+<ul>
+<li>アルゴリズムの観点から、探索、ソート、バックトラッキング、分割統治、動的プログラミングなどの多くの重要な戦略は、直接的または間接的にこの思考方法を使用しています。</li>
+<li>データ構造の観点から、再帰は連結リスト、木、グラフを扱うのに自然に適しており、これらは分割統治アプローチを使用した分析に適しているためです。</li>
+</ul>
+<h2 id="223">2.2.3 &nbsp; 比較<a class="headerlink" href="#223" title="Permanent link">&para;</a></h2>
+<p>上記の内容をまとめると、以下の表は実装、性能、適用性の観点から反復と再帰の違いを示しています。</p>
+<p align="center"> 表: 反復と再帰の特性の比較 </p>
+
+<div class="center-table">
+<table>
+<thead>
+<tr>
+<th></th>
+<th>反復</th>
+<th>再帰</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td>アプローチ</td>
+<td>ループ構造</td>
+<td>関数が自分自身を呼び出す</td>
+</tr>
+<tr>
+<td>時間効率</td>
+<td>一般的により高い効率、関数呼び出しのオーバーヘッドなし</td>
+<td>各関数呼び出しがオーバーヘッドを生成</td>
+</tr>
+<tr>
+<td>メモリ使用量</td>
+<td>通常は固定サイズのメモリ空間を使用</td>
+<td>累積的な関数呼び出しが大量のスタックフレーム空間を使用する可能性</td>
+</tr>
+<tr>
+<td>適用可能な問題</td>
+<td>単純なループタスクに適している、直感的で読みやすいコード</td>
+<td>問題の分解に適している（木、グラフ、分割統治、バックトラッキングなど）、簡潔で明確なコード構造</td>
+</tr>
+</tbody>
+</table>
+</div>
+<div class="admonition tip">
+<p class="admonition-title">Tip</p>
+<p>以下の内容が理解しにくい場合は、「スタック」の章を読んだ後に再び訪れることを検討してください。</p>
+</div>
+<p>それでは、反復と再帰の本質的な関連は何でしょうか？上記の再帰関数を例に取ると、合計操作は再帰の「返却」フェーズで発生します。これは、最初に呼び出された関数が最後に合計操作を完了することを意味し、<strong>スタックの「後入れ先出し」原理を反映しています</strong>。</p>
+<p>「呼び出しスタック」や「スタックフレーム空間」などの再帰用語は、再帰とスタックの密接な関係を示しています。</p>
+<ol>
+<li><strong>呼び出し</strong>: 関数が呼び出されると、システムは「呼び出しスタック」上にその関数用の新しいスタックフレームを割り当て、ローカル変数、パラメータ、戻りアドレス、その他のデータを格納します。</li>
+<li><strong>返却</strong>: 関数が実行を完了して返ると、対応するスタックフレームが「呼び出しスタック」から削除され、前の関数の実行環境が復元されます。</li>
+</ol>
+<p>したがって、<strong>明示的なスタックを使用して呼び出しスタックの動作をシミュレートできます</strong>。これにより再帰を反復形式に変換できます：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="8:14"><input checked="checked" id="__tabbed_8_1" name="__tabbed_8" type="radio" /><input id="__tabbed_8_2" name="__tabbed_8" type="radio" /><input id="__tabbed_8_3" name="__tabbed_8" type="radio" /><input id="__tabbed_8_4" name="__tabbed_8" type="radio" /><input id="__tabbed_8_5" name="__tabbed_8" type="radio" /><input id="__tabbed_8_6" name="__tabbed_8" type="radio" /><input id="__tabbed_8_7" name="__tabbed_8" type="radio" /><input id="__tabbed_8_8" name="__tabbed_8" type="radio" /><input id="__tabbed_8_9" name="__tabbed_8" type="radio" /><input id="__tabbed_8_10" name="__tabbed_8" type="radio" /><input id="__tabbed_8_11" name="__tabbed_8" type="radio" /><input id="__tabbed_8_12" name="__tabbed_8" type="radio" /><input id="__tabbed_8_13" name="__tabbed_8" type="radio" /><input id="__tabbed_8_14" name="__tabbed_8" type="radio" /><div class="tabbed-labels"><label for="__tabbed_8_1">Python</label><label for="__tabbed_8_2">C++</label><label for="__tabbed_8_3">Java</label><label for="__tabbed_8_4">C#</label><label for="__tabbed_8_5">Go</label><label for="__tabbed_8_6">Swift</label><label for="__tabbed_8_7">JS</label><label for="__tabbed_8_8">TS</label><label for="__tabbed_8_9">Dart</label><label for="__tabbed_8_10">Rust</label><label for="__tabbed_8_11">C</label><label for="__tabbed_8_12">Kotlin</label><label for="__tabbed_8_13">Ruby</label><label for="__tabbed_8_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.py</span><pre><span></span><code><a id="__codelineno-98-1" name="__codelineno-98-1" href="#__codelineno-98-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">for_loop_recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-98-2" name="__codelineno-98-2" href="#__codelineno-98-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;反復で再帰をシミュレート&quot;&quot;&quot;</span>
+<a id="__codelineno-98-3" name="__codelineno-98-3" href="#__codelineno-98-3"></a>    <span class="c1"># 明示的なスタックを使用してシステムコールスタックをシミュレート</span>
+<a id="__codelineno-98-4" name="__codelineno-98-4" href="#__codelineno-98-4"></a>    <span class="n">stack</span> <span class="o">=</span> <span class="p">[]</span>
+<a id="__codelineno-98-5" name="__codelineno-98-5" href="#__codelineno-98-5"></a>    <span class="n">res</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-98-6" name="__codelineno-98-6" href="#__codelineno-98-6"></a>    <span class="c1"># 再帰：再帰呼び出し</span>
+<a id="__codelineno-98-7" name="__codelineno-98-7" href="#__codelineno-98-7"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-98-8" name="__codelineno-98-8" href="#__codelineno-98-8"></a>        <span class="c1"># 「スタックへのプッシュ」で「再帰」をシミュレート</span>
+<a id="__codelineno-98-9" name="__codelineno-98-9" href="#__codelineno-98-9"></a>        <span class="n">stack</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
+<a id="__codelineno-98-10" name="__codelineno-98-10" href="#__codelineno-98-10"></a>    <span class="c1"># 復帰：結果を返す</span>
+<a id="__codelineno-98-11" name="__codelineno-98-11" href="#__codelineno-98-11"></a>    <span class="k">while</span> <span class="n">stack</span><span class="p">:</span>
+<a id="__codelineno-98-12" name="__codelineno-98-12" href="#__codelineno-98-12"></a>        <span class="c1"># 「スタックからのポップ」で「復帰」をシミュレート</span>
+<a id="__codelineno-98-13" name="__codelineno-98-13" href="#__codelineno-98-13"></a>        <span class="n">res</span> <span class="o">+=</span> <span class="n">stack</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
+<a id="__codelineno-98-14" name="__codelineno-98-14" href="#__codelineno-98-14"></a>    <span class="c1"># res = 1+2+3+...+n</span>
+<a id="__codelineno-98-15" name="__codelineno-98-15" href="#__codelineno-98-15"></a>    <span class="k">return</span> <span class="n">res</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.cpp</span><pre><span></span><code><a id="__codelineno-99-1" name="__codelineno-99-1" href="#__codelineno-99-1"></a><span class="cm">/* 反復で再帰をシミュレート */</span>
+<a id="__codelineno-99-2" name="__codelineno-99-2" href="#__codelineno-99-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">forLoopRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-99-3" name="__codelineno-99-3" href="#__codelineno-99-3"></a><span class="w">    </span><span class="c1">// 明示的なスタックを使用してシステムコールスタックをシミュレート</span>
+<a id="__codelineno-99-4" name="__codelineno-99-4" href="#__codelineno-99-4"></a><span class="w">    </span><span class="n">stack</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">stack</span><span class="p">;</span>
+<a id="__codelineno-99-5" name="__codelineno-99-5" href="#__codelineno-99-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-99-6" name="__codelineno-99-6" href="#__codelineno-99-6"></a><span class="w">    </span><span class="c1">// 再帰：再帰呼び出し</span>
+<a id="__codelineno-99-7" name="__codelineno-99-7" href="#__codelineno-99-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-99-8" name="__codelineno-99-8" href="#__codelineno-99-8"></a><span class="w">        </span><span class="c1">// 「スタックへのプッシュ」で「再帰」をシミュレート</span>
+<a id="__codelineno-99-9" name="__codelineno-99-9" href="#__codelineno-99-9"></a><span class="w">        </span><span class="n">stack</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-99-10" name="__codelineno-99-10" href="#__codelineno-99-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-99-11" name="__codelineno-99-11" href="#__codelineno-99-11"></a><span class="w">    </span><span class="c1">// 戻り値：結果を返す</span>
+<a id="__codelineno-99-12" name="__codelineno-99-12" href="#__codelineno-99-12"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">stack</span><span class="p">.</span><span class="n">empty</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-99-13" name="__codelineno-99-13" href="#__codelineno-99-13"></a><span class="w">        </span><span class="c1">// 「スタックからのポップ」で「戻り値」をシミュレート</span>
+<a id="__codelineno-99-14" name="__codelineno-99-14" href="#__codelineno-99-14"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="n">top</span><span class="p">();</span>
+<a id="__codelineno-99-15" name="__codelineno-99-15" href="#__codelineno-99-15"></a><span class="w">        </span><span class="n">stack</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span>
+<a id="__codelineno-99-16" name="__codelineno-99-16" href="#__codelineno-99-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-99-17" name="__codelineno-99-17" href="#__codelineno-99-17"></a><span class="w">    </span><span class="c1">// res = 1+2+3+...+n</span>
+<a id="__codelineno-99-18" name="__codelineno-99-18" href="#__codelineno-99-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-99-19" name="__codelineno-99-19" href="#__codelineno-99-19"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.java</span><pre><span></span><code><a id="__codelineno-100-1" name="__codelineno-100-1" href="#__codelineno-100-1"></a><span class="cm">/* 反復で再帰をシミュレート */</span>
+<a id="__codelineno-100-2" name="__codelineno-100-2" href="#__codelineno-100-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">forLoopRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-100-3" name="__codelineno-100-3" href="#__codelineno-100-3"></a><span class="w">    </span><span class="c1">// 明示的なスタックを使用してシステムコールスタックをシミュレート</span>
+<a id="__codelineno-100-4" name="__codelineno-100-4" href="#__codelineno-100-4"></a><span class="w">    </span><span class="n">Stack</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">stack</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Stack</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-100-5" name="__codelineno-100-5" href="#__codelineno-100-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-100-6" name="__codelineno-100-6" href="#__codelineno-100-6"></a><span class="w">    </span><span class="c1">// 再帰：再帰呼び出し</span>
+<a id="__codelineno-100-7" name="__codelineno-100-7" href="#__codelineno-100-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-100-8" name="__codelineno-100-8" href="#__codelineno-100-8"></a><span class="w">        </span><span class="c1">// 「スタックへのプッシュ」で「再帰」をシミュレート</span>
+<a id="__codelineno-100-9" name="__codelineno-100-9" href="#__codelineno-100-9"></a><span class="w">        </span><span class="n">stack</span><span class="p">.</span><span class="na">push</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-100-10" name="__codelineno-100-10" href="#__codelineno-100-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-100-11" name="__codelineno-100-11" href="#__codelineno-100-11"></a><span class="w">    </span><span class="c1">// 戻り値：結果を返す</span>
+<a id="__codelineno-100-12" name="__codelineno-100-12" href="#__codelineno-100-12"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">stack</span><span class="p">.</span><span class="na">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-100-13" name="__codelineno-100-13" href="#__codelineno-100-13"></a><span class="w">        </span><span class="c1">// 「スタックからのポップ」で「戻り値」をシミュレート</span>
+<a id="__codelineno-100-14" name="__codelineno-100-14" href="#__codelineno-100-14"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="na">pop</span><span class="p">();</span>
+<a id="__codelineno-100-15" name="__codelineno-100-15" href="#__codelineno-100-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-100-16" name="__codelineno-100-16" href="#__codelineno-100-16"></a><span class="w">    </span><span class="c1">// res = 1+2+3+...+n</span>
+<a id="__codelineno-100-17" name="__codelineno-100-17" href="#__codelineno-100-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-100-18" name="__codelineno-100-18" href="#__codelineno-100-18"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.cs</span><pre><span></span><code><a id="__codelineno-101-1" name="__codelineno-101-1" href="#__codelineno-101-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">recursion</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">ForLoopRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.go</span><pre><span></span><code><a id="__codelineno-102-1" name="__codelineno-102-1" href="#__codelineno-102-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">forLoopRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.swift</span><pre><span></span><code><a id="__codelineno-103-1" name="__codelineno-103-1" href="#__codelineno-103-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">forLoopRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.js</span><pre><span></span><code><a id="__codelineno-104-1" name="__codelineno-104-1" href="#__codelineno-104-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">forLoopRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.ts</span><pre><span></span><code><a id="__codelineno-105-1" name="__codelineno-105-1" href="#__codelineno-105-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">forLoopRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.dart</span><pre><span></span><code><a id="__codelineno-106-1" name="__codelineno-106-1" href="#__codelineno-106-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">forLoopRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.rs</span><pre><span></span><code><a id="__codelineno-107-1" name="__codelineno-107-1" href="#__codelineno-107-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">for_loop_recur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.c</span><pre><span></span><code><a id="__codelineno-108-1" name="__codelineno-108-1" href="#__codelineno-108-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">forLoopRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.kt</span><pre><span></span><code><a id="__codelineno-109-1" name="__codelineno-109-1" href="#__codelineno-109-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">forLoopRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.rb</span><pre><span></span><code><a id="__codelineno-110-1" name="__codelineno-110-1" href="#__codelineno-110-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">for_loop_recur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">recursion.zig</span><pre><span></span><code><a id="__codelineno-111-1" name="__codelineno-111-1" href="#__codelineno-111-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">forLoopRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>上記のコードを観察すると、再帰が反復に変換されたとき、コードはより複雑になります。反復と再帰はしばしば相互に変換できますが、2つの理由でそうすることが常に推奨されるわけではありません：</p>
+<ul>
+<li>変換されたコードは理解がより困難になり、読みにくくなる可能性があります。</li>
+<li>一部の複雑な問題では、システムの呼び出しスタックの動作をシミュレートすることは非常に困難です。</li>
+</ul>
+<p>結論として、<strong>反復または再帰を選択するかは問題の具体的な性質によります</strong>。プログラミングの実践では、両方の長所と短所を比較検討し、手元の状況に最も適したアプローチを選択することが重要です。</p>
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+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#211" class="md-nav__link">
+    <span class="md-ellipsis">
+      2.1.1 &nbsp; 実際のテスト
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#212" class="md-nav__link">
+    <span class="md-ellipsis">
+      2.1.2 &nbsp; 理論的推定
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
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+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
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+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_19" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_reference/" class="md-nav__link ">
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+<h1 id="21">2.1 &nbsp; アルゴリズムの効率評価<a class="headerlink" href="#21" title="Permanent link">&para;</a></h1>
+<p>アルゴリズム設計において、私たちは順序に従って以下の2つの目標を追求します。</p>
+<ol>
+<li><strong>問題の解決策を見つける</strong>: アルゴリズムは、指定された入力範囲内で確実に正しい解を見つけることができるべきです。</li>
+<li><strong>最適解を求める</strong>: 同じ問題に対して複数の解決策が存在する場合があり、私たちは可能な限り最も効率的なアルゴリズムを見つけることを目指します。</li>
+</ol>
+<p>つまり、問題を解決できることを前提として、アルゴリズムの効率がアルゴリズムを評価する主要な基準となっており、これには以下の2つの次元が含まれます。</p>
+<ul>
+<li><strong>時間効率</strong>: アルゴリズムが実行される速度。</li>
+<li><strong>空間効率</strong>: アルゴリズムが占有するメモリ空間のサイズ。</li>
+</ul>
+<p>要するに、<strong>私たちの目標は、高速でメモリ効率の良いデータ構造とアルゴリズムを設計することです</strong>。アルゴリズムの効率を効果的に評価することは重要です。なぜなら、そうすることで初めて様々なアルゴリズムを比較し、アルゴリズムの設計と最適化プロセスを導くことができるからです。</p>
+<p>効率評価には主に2つの方法があります：実際のテストと理論的推定です。</p>
+<h2 id="211">2.1.1 &nbsp; 実際のテスト<a class="headerlink" href="#211" title="Permanent link">&para;</a></h2>
+<p>アルゴリズム<code>A</code>と<code>B</code>があり、どちらも同じ問題を解決でき、それらの効率を比較する必要があるとします。最も直接的な方法は、コンピュータを使用してこれら2つのアルゴリズムを実行し、実行時間とメモリ使用量を監視・記録することです。この評価方法は実際の状況を反映しますが、大きな制限があります。</p>
+<p>一方で、<strong>テスト環境からの干渉を排除することは困難です</strong>。ハードウェア構成はアルゴリズムの性能に影響を与える可能性があります。例えば、並列度の高いアルゴリズムはマルチコアCPUでの実行により適していますし、集約的なメモリ操作を含むアルゴリズムは高性能メモリでより良い性能を発揮します。アルゴリズムのテスト結果は、異なるマシン間で変わる可能性があります。これは、平均効率を計算するために複数のマシンでテストすることが実用的でないことを意味します。</p>
+<p>一方で、<strong>完全なテストを実施することは非常にリソース集約的です</strong>。アルゴリズムの効率は入力データサイズによって変わります。例えば、データ量が少ない場合はアルゴリズム<code>A</code>が<code>B</code>より速く実行される可能性がありますが、データ量が多い場合はテスト結果が逆になる可能性があります。したがって、説得力のある結論を導くためには、幅広い入力データサイズをテストする必要があり、これには過度な計算リソースが必要になります。</p>
+<h2 id="212">2.1.2 &nbsp; 理論的推定<a class="headerlink" href="#212" title="Permanent link">&para;</a></h2>
+<p>実際のテストの大きな制限により、計算のみでアルゴリズムの効率を評価することを検討できます。この推定方法は<u>漸近的複雑度解析</u>、または単に<u>複雑度解析</u>として知られています。</p>
+<p>複雑度解析は、アルゴリズムの実行に必要な時間と空間リソースと入力データのサイズとの関係を反映します。<strong>これは、入力データのサイズが増加するにつれて、アルゴリズムに必要な時間と空間の増加傾向を記述します</strong>。この定義は複雑に聞こえるかもしれませんが、より良く理解するために3つの重要なポイントに分解できます。</p>
+<ul>
+<li>「時間と空間リソース」は、それぞれ<u>時間計算量</u>と<u>空間計算量</u>に対応します。</li>
+<li>「入力データのサイズが増加するにつれて」は、複雑度がアルゴリズムの効率と入力データ量との関係を反映することを意味します。</li>
+<li>「時間と空間の増加傾向」は、複雑度解析が実行時間や占有空間の具体的な値ではなく、時間や空間が増加する「率」に焦点を当てることを示します。</li>
+</ul>
+<p><strong>複雑度解析は実際のテスト方法の欠点を克服します</strong>。これは以下の側面で反映されます：</p>
+<ul>
+<li>実際にコードを実行する必要がないため、より環境に優しく、エネルギー効率が良いです。</li>
+<li>テスト環境に依存せず、すべての動作プラットフォームに適用できます。</li>
+<li>異なるデータ量でのアルゴリズムの効率を反映でき、特に大量データでのアルゴリズムの性能を示します。</li>
+</ul>
+<div class="admonition tip">
+<p class="admonition-title">Tip</p>
+<p>複雑度の概念についてまだ混乱している場合でも、心配しないでください。以降の章で詳しく取り上げます。</p>
+</div>
+<p>複雑度解析は、アルゴリズムの効率を評価する「ものさし」を提供し、実行に必要な時間と空間リソースを測定し、異なるアルゴリズムの効率を比較することを可能にします。</p>
+<p>複雑度は数学的概念であり、初心者には抽象的で困難かもしれません。この観点から、複雑度解析は最初に紹介するのに最も適したトピックではないかもしれません。しかし、特定のデータ構造やアルゴリズムの特性について議論するとき、その速度と空間使用量を分析することを避けるのは困難です。</p>
+<p>要約すると、データ構造とアルゴリズムに深く入る前に複雑度解析の基本的な理解を身につけることをお勧めします。<strong>これにより、簡単なアルゴリズムで複雑度解析を実行できるようになります</strong>。</p>
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+  </div>
+  <div class="md-source__repository">
+    krahets/hello-algo
+  </div>
+</a>
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+  
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+    
+      
+      
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+  
+  <span class="md-ellipsis">
+    はじめに
+  </span>
+  
+
+            </a>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_1_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_1">
+            <span class="md-nav__icon md-icon"></span>
+            はじめに
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
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+  
+  
+  
+  
+    
+    
+      
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+        
+      
+        
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+        
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+    
+    
+    
+    
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+      
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+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_preface/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M21 4H3a2 2 0 0 0-2 2v13a2 2 0 0 0 2 2h18a2 2 0 0 0 2-2V6a2 2 0 0 0-2-2M3 19V6h8v13H3m18 0h-8V6h8v13m-7-9.5h6V11h-6V9.5m0 2.5h6v1.5h-6V12m0 2.5h6V16h-6v-1.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 0 章 &nbsp; 前書き
+  </span>
+  
+
+            </a>
+            
+              
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+          <label class="md-nav__title" for="__nav_2">
+            <span class="md-nav__icon md-icon"></span>
+            第 0 章 &nbsp; 前書き
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
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+            
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/about_the_book/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.1 &nbsp; この本について
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/suggestions/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.2 &nbsp; 本書の使い方
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
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+          </ul>
+        </nav>
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+    </li>
+  
+
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+      
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+  
+  
+  
+  
+    
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+      
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+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_introduction/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
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+  
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+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#241" class="md-nav__link">
+    <span class="md-ellipsis">
+      2.4.1 &nbsp; アルゴリズムに関連する空間
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#242" class="md-nav__link">
+    <span class="md-ellipsis">
+      2.4.2 &nbsp; 計算方法
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#243" class="md-nav__link">
+    <span class="md-ellipsis">
+      2.4.3 &nbsp; 一般的な種類
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="2.4.3   一般的な種類">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1-o1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 定数オーダー
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2-on" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; 線形オーダー
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#3-on2" class="md-nav__link">
+    <span class="md-ellipsis">
+      3. &nbsp; 二次オーダー
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#4-o2n" class="md-nav__link">
+    <span class="md-ellipsis">
+      4. &nbsp; 指数オーダー
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#5-olog-n" class="md-nav__link">
+    <span class="md-ellipsis">
+      5. &nbsp; 対数オーダー
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#244" class="md-nav__link">
+    <span class="md-ellipsis">
+      2.4.4 &nbsp; 時間と空間のバランス
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
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+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
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+            
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+  
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+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
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+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
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+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
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+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
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+  
+
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+      
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+          
+        
+      
+    
+    
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+      
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+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_19" >
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+          
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+            <a href="../../chapter_reference/" class="md-nav__link ">
+              
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9 3v15h3V3H9m3 2 4 13 3-1-4-13-3 1M5 5v13h3V5H5M3 19v2h18v-2H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    参考文献
+  </span>
+  
+
+            </a>
+            
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+        
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+            参考文献
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+</nav>
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+              </div>
+            
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+              
+              <div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
+                <div class="md-sidebar__scrollwrap">
+                  <div class="md-sidebar__inner">
+                    
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#241" class="md-nav__link">
+    <span class="md-ellipsis">
+      2.4.1 &nbsp; アルゴリズムに関連する空間
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#242" class="md-nav__link">
+    <span class="md-ellipsis">
+      2.4.2 &nbsp; 計算方法
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#243" class="md-nav__link">
+    <span class="md-ellipsis">
+      2.4.3 &nbsp; 一般的な種類
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="2.4.3   一般的な種類">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1-o1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 定数オーダー
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2-on" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; 線形オーダー
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#3-on2" class="md-nav__link">
+    <span class="md-ellipsis">
+      3. &nbsp; 二次オーダー
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#4-o2n" class="md-nav__link">
+    <span class="md-ellipsis">
+      4. &nbsp; 指数オーダー
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#5-olog-n" class="md-nav__link">
+    <span class="md-ellipsis">
+      5. &nbsp; 対数オーダー
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#244" class="md-nav__link">
+    <span class="md-ellipsis">
+      2.4.4 &nbsp; 時間と空間のバランス
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+                  </div>
+                </div>
+              </div>
+            
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+          
+            <div class="md-content" data-md-component="content">
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+      class="md-content__button md-icon"
+    >
+      
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
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+<h1 id="24">2.4 &nbsp; 空間計算量<a class="headerlink" href="#24" title="Permanent link">&para;</a></h1>
+<p><u>空間計算量</u>は、データ量が増加するにつれてアルゴリズムが占有するメモリ空間の増加傾向を測定するために使用されます。この概念は時間計算量と非常に似ていますが、「実行時間」が「占有メモリ空間」に置き換えられています。</p>
+<h2 id="241">2.4.1 &nbsp; アルゴリズムに関連する空間<a class="headerlink" href="#241" title="Permanent link">&para;</a></h2>
+<p>アルゴリズムが実行中に使用するメモリ空間には、主に以下の種類があります。</p>
+<ul>
+<li><strong>入力空間</strong>: アルゴリズムの入力データを格納するために使用されます。</li>
+<li><strong>一時空間</strong>: アルゴリズムの実行中に変数、オブジェクト、関数コンテキスト、その他のデータを格納するために使用されます。</li>
+<li><strong>出力空間</strong>: アルゴリズムの出力データを格納するために使用されます。</li>
+</ul>
+<p>一般的に、空間計算量の統計範囲には「一時空間」と「出力空間」の両方が含まれます。</p>
+<p>一時空間はさらに3つの部分に分けることができます。</p>
+<ul>
+<li><strong>一時データ</strong>: アルゴリズムの実行中に様々な定数、変数、オブジェクトなどを保存するために使用されます。</li>
+<li><strong>スタックフレーム空間</strong>: 呼び出された関数のコンテキストデータを保存するために使用されます。システムは関数が呼び出されるたびにスタックの頂上にスタックフレームを作成し、関数が返された後にスタックフレーム空間を解放します。</li>
+<li><strong>命令空間</strong>: コンパイル済みプログラム命令を格納するために使用され、実際の統計では通常無視できます。</li>
+</ul>
+<p>プログラムの空間計算量を分析する際、<strong>通常は一時データ、スタックフレーム空間、出力データをカウントします</strong>。以下の図に示されています。</p>
+<p><a class="glightbox" href="../space_complexity.assets/space_types.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Space types used in algorithms" class="animation-figure" src="../space_complexity.assets/space_types.png" /></a></p>
+<p align="center"> 図 2-15 &nbsp; Space types used in algorithms </p>
+
+<p>関連するコードは以下の通りです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">Node</span><span class="p">:</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;クラス&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">x</span>               <span class="c1"># ノード値</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">next</span><span class="p">:</span> <span class="n">Node</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span>   <span class="c1"># 次のノードへの参照</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="k">def</span><span class="w"> </span><span class="nf">function</span><span class="p">()</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;関数&quot;&quot;&quot;</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>    <span class="c1"># 特定の操作を実行...</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>    <span class="k">return</span> <span class="mi">0</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a><span class="k">def</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>    <span class="c1"># 入力データ</span>
+<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>    <span class="n">A</span> <span class="o">=</span> <span class="mi">0</span>                   <span class="c1"># 一時データ（定数、通常大文字）</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>    <span class="n">b</span> <span class="o">=</span> <span class="mi">0</span>                   <span class="c1"># 一時データ（変数）</span>
+<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>    <span class="n">node</span> <span class="o">=</span> <span class="n">Node</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>          <span class="c1"># 一時データ（オブジェクト）</span>
+<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>    <span class="n">c</span> <span class="o">=</span> <span class="n">function</span><span class="p">()</span>          <span class="c1"># スタックフレーム空間（関数呼び出し）</span>
+<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>    <span class="k">return</span> <span class="n">A</span> <span class="o">+</span> <span class="n">b</span> <span class="o">+</span> <span class="n">c</span>        <span class="c1"># 出力データ</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 構造体 */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="k">struct</span><span class="w"> </span><span class="nc">Node</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="n">Node</span><span class="w"> </span><span class="o">*</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="n">Node</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">x</span><span class="p">)</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">x</span><span class="p">),</span><span class="w"> </span><span class="n">next</span><span class="p">(</span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{}</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="p">};</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="cm">/* 関数 */</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="kt">int</span><span class="w"> </span><span class="nf">func</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">    </span><span class="c1">// 特定の操作を実行...</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="p">}</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="kt">int</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w">          </span><span class="c1">// 入力データ</span>
+<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">    </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">            </span><span class="c1">// 一時データ（定数）</span>
+<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">                  </span><span class="c1">// 一時データ（変数）</span>
+<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w">    </span><span class="n">Node</span><span class="o">*</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Node</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span><span class="w">   </span><span class="c1">// 一時データ（オブジェクト）</span>
+<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">func</span><span class="p">();</span><span class="w">             </span><span class="c1">// スタックフレーム空間（関数呼び出し）</span>
+<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">c</span><span class="p">;</span><span class="w">           </span><span class="c1">// 出力データ</span>
+<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* クラス */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kd">class</span> <span class="nc">Node</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="n">Node</span><span class="w"> </span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="n">Node</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">x</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">x</span><span class="p">;</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="p">}</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="cm">/* 関数 */</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="kt">int</span><span class="w"> </span><span class="nf">function</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">    </span><span class="c1">// 特定の操作を実行...</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="p">}</span>
+<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="kt">int</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w">          </span><span class="c1">// 入力データ</span>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">    </span><span class="kd">final</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">            </span><span class="c1">// 一時データ（定数）</span>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">                  </span><span class="c1">// 一時データ（変数）</span>
+<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w">    </span><span class="n">Node</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Node</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span><span class="w">    </span><span class="c1">// 一時データ（オブジェクト）</span>
+<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">function</span><span class="p">();</span><span class="w">         </span><span class="c1">// スタックフレーム空間（関数呼び出し）</span>
+<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">c</span><span class="p">;</span><span class="w">           </span><span class="c1">// 出力データ</span>
+<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* クラス */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">Node</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="n">Node</span><span class="w"> </span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">    </span><span class="n">Node</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">x</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">x</span><span class="p">;</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="p">}</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="cm">/* 関数 */</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Function</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="w">    </span><span class="c1">// 特定の操作を実行...</span>
+<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="p">}</span>
+<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a>
+<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w">  </span><span class="c1">// 入力データ</span>
+<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w">    </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">    </span><span class="c1">// 一時データ（定数）</span>
+<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">          </span><span class="c1">// 一時データ（変数）</span>
+<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w">    </span><span class="n">Node</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// 一時データ（オブジェクト）</span>
+<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Function</span><span class="p">();</span><span class="w"> </span><span class="c1">// スタックフレーム空間（関数呼び出し）</span>
+<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">c</span><span class="p">;</span><span class="w">   </span><span class="c1">// 出力データ</span>
+<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 構造体 */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">type</span><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="kd">struct</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="nx">val</span><span class="w">  </span><span class="kt">int</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="nx">next</span><span class="w"> </span><span class="o">*</span><span class="nx">node</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="p">}</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="cm">/* ノード構造体を作成 */</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="kd">func</span><span class="w"> </span><span class="nx">newNode</span><span class="p">(</span><span class="nx">val</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="nx">node</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">node</span><span class="p">{</span><span class="nx">val</span><span class="p">:</span><span class="w"> </span><span class="nx">val</span><span class="p">}</span>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="p">}</span>
+<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a>
+<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="cm">/* 関数 */</span>
+<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="kd">func</span><span class="w"> </span><span class="nx">function</span><span class="p">()</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w">    </span><span class="c1">// 特定の操作を実行...</span>
+<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="p">}</span>
+<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a>
+<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="kd">func</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 入力データ</span>
+<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span><span class="w">             </span><span class="c1">// 一時データ（定数）</span>
+<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="w">    </span><span class="nx">b</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="w">                  </span><span class="c1">// 一時データ（変数）</span>
+<a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a><span class="w">    </span><span class="nx">newNode</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span><span class="w">              </span><span class="c1">// 一時データ（オブジェクト）</span>
+<a id="__codelineno-4-22" name="__codelineno-4-22" href="#__codelineno-4-22"></a><span class="w">    </span><span class="nx">c</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">function</span><span class="p">()</span><span class="w">         </span><span class="c1">// スタックフレーム空間（関数呼び出し）</span>
+<a id="__codelineno-4-23" name="__codelineno-4-23" href="#__codelineno-4-23"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">c</span><span class="w">        </span><span class="c1">// 出力データ</span>
+<a id="__codelineno-4-24" name="__codelineno-4-24" href="#__codelineno-4-24"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* クラス */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">Node</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">val</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">next</span><span class="p">:</span><span class="w"> </span><span class="n">Node</span><span class="p">?</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">    </span><span class="kd">init</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w">        </span><span class="n">val</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">x</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="p">}</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a>
+<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="cm">/* 関数 */</span>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="kd">func</span><span class="w"> </span><span class="nf">function</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="w">    </span><span class="c1">// 特定の操作を実行...</span>
+<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="p">}</span>
+<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a>
+<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="kd">func</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 入力データ</span>
+<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span><span class="w">                   </span><span class="c1">// 一時データ（定数）</span>
+<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">b</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span><span class="w">                   </span><span class="c1">// 一時データ（変数）</span>
+<a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">node</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">Node</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w">       </span><span class="c1">// 一時データ（オブジェクト）</span>
+<a id="__codelineno-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">c</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">function</span><span class="p">()</span><span class="w">          </span><span class="c1">// スタックフレーム空間（関数呼び出し）</span>
+<a id="__codelineno-5-22" name="__codelineno-5-22" href="#__codelineno-5-22"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">c</span><span class="w">            </span><span class="c1">// 出力データ</span>
+<a id="__codelineno-5-23" name="__codelineno-5-23" href="#__codelineno-5-23"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* クラス */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">Node</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w">    </span><span class="nx">val</span><span class="p">;</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">    </span><span class="nx">next</span><span class="p">;</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">(</span><span class="nx">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="nx">val</span><span class="p">;</span><span class="w"> </span><span class="c1">// ノード値</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span><span class="w">                       </span><span class="c1">// 次のノードへの参照</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="p">}</span>
+<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a>
+<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="cm">/* 関数 */</span>
+<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="kd">function</span><span class="w"> </span><span class="nx">constFunc</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="w">    </span><span class="c1">// 特定の操作を実行</span>
+<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="p">}</span>
+<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a>
+<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w">         </span><span class="c1">// 入力データ</span>
+<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w">                </span><span class="c1">// 一時データ（定数）</span>
+<a id="__codelineno-6-19" name="__codelineno-6-19" href="#__codelineno-6-19"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w">                  </span><span class="c1">// 一時データ（変数）</span>
+<a id="__codelineno-6-20" name="__codelineno-6-20" href="#__codelineno-6-20"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">Node</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span><span class="w">   </span><span class="c1">// 一時データ（オブジェクト）</span>
+<a id="__codelineno-6-21" name="__codelineno-6-21" href="#__codelineno-6-21"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">constFunc</span><span class="p">();</span><span class="w">      </span><span class="c1">// スタックフレーム空間（関数呼び出し）</span>
+<a id="__codelineno-6-22" name="__codelineno-6-22" href="#__codelineno-6-22"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">c</span><span class="p">;</span><span class="w">           </span><span class="c1">// 出力データ</span>
+<a id="__codelineno-6-23" name="__codelineno-6-23" href="#__codelineno-6-23"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* クラス */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">Node</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w">    </span><span class="nx">val</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">;</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">    </span><span class="nx">next</span><span class="o">:</span><span class="w"> </span><span class="kt">Node</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">(</span><span class="nx">val?</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">0</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">val</span><span class="p">;</span><span class="w"> </span><span class="c1">// ノード値</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span><span class="w">                       </span><span class="c1">// 次のノードへの参照</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="p">}</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a>
+<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="cm">/* 関数 */</span>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="kd">function</span><span class="w"> </span><span class="nx">constFunc</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="w">    </span><span class="c1">// 特定の操作を実行</span>
+<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="p">}</span>
+<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a>
+<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 入力データ</span>
+<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w">                        </span><span class="c1">// 一時データ（定数）</span>
+<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w">                          </span><span class="c1">// 一時データ（変数）</span>
+<a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">Node</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span><span class="w">           </span><span class="c1">// 一時データ（オブジェクト）</span>
+<a id="__codelineno-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">constFunc</span><span class="p">();</span><span class="w">              </span><span class="c1">// スタックフレーム空間（関数呼び出し）</span>
+<a id="__codelineno-7-22" name="__codelineno-7-22" href="#__codelineno-7-22"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">c</span><span class="p">;</span><span class="w">                   </span><span class="c1">// 出力データ</span>
+<a id="__codelineno-7-23" name="__codelineno-7-23" href="#__codelineno-7-23"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* クラス */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">Node</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="n">Node</span><span class="w"> </span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">  </span><span class="n">Node</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="p">[</span><span class="k">this</span><span class="p">.</span><span class="n">next</span><span class="p">]);</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="p">}</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="cm">/* 関数 */</span>
+<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="kt">int</span><span class="w"> </span><span class="n">function</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="w">  </span><span class="c1">// 特定の操作を実行...</span>
+<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="p">}</span>
+<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a>
+<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="kt">int</span><span class="w"> </span><span class="n">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w">  </span><span class="c1">// 入力データ</span>
+<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="w">  </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w">      </span><span class="c1">// 一時データ（定数）</span>
+<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w">            </span><span class="c1">// 一時データ（変数）</span>
+<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a><span class="w">  </span><span class="n">Node</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Node</span><span class="p">(</span><span class="m">0</span><span class="p">);</span><span class="w">  </span><span class="c1">// 一時データ（オブジェクト）</span>
+<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">function</span><span class="p">();</span><span class="w">   </span><span class="c1">// スタックフレーム空間（関数呼び出し）</span>
+<a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">c</span><span class="p">;</span><span class="w">     </span><span class="c1">// 出力データ</span>
+<a id="__codelineno-8-20" name="__codelineno-8-20" href="#__codelineno-8-20"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="k">use</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">rc</span><span class="p">::</span><span class="n">Rc</span><span class="p">;</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">use</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">cell</span><span class="p">::</span><span class="n">RefCell</span><span class="p">;</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="cm">/* 構造体 */</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="k">struct</span><span class="w"> </span><span class="nc">Node</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">    </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">    </span><span class="n">next</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">Node</span><span class="o">&gt;&gt;&gt;</span><span class="p">,</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="p">}</span>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="k">impl</span><span class="w"> </span><span class="n">Node</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">new</span><span class="p">(</span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nc">Self</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w">        </span><span class="bp">Self</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="nc">val</span><span class="p">,</span><span class="w"> </span><span class="n">next</span><span class="p">:</span><span class="w"> </span><span class="nb">None</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="p">}</span>
+<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a>
+<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="cm">/* 関数 */</span>
+<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="k">fn</span><span class="w"> </span><span class="nf">function</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="w">    </span><span class="c1">// 特定の操作を実行...</span>
+<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="p">}</span>
+<a id="__codelineno-9-22" name="__codelineno-9-22" href="#__codelineno-9-22"></a>
+<a id="__codelineno-9-23" name="__codelineno-9-23" href="#__codelineno-9-23"></a><span class="k">fn</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span><span class="w">   </span><span class="c1">// 入力データ</span>
+<a id="__codelineno-9-24" name="__codelineno-9-24" href="#__codelineno-9-24"></a><span class="w">    </span><span class="k">const</span><span class="w"> </span><span class="n">a</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">           </span><span class="c1">// 一時データ（定数）</span>
+<a id="__codelineno-9-25" name="__codelineno-9-25" href="#__codelineno-9-25"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">              </span><span class="c1">// 一時データ（変数）</span>
+<a id="__codelineno-9-26" name="__codelineno-9-26" href="#__codelineno-9-26"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Node</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span><span class="w">    </span><span class="c1">// 一時データ（オブジェクト）</span>
+<a id="__codelineno-9-27" name="__codelineno-9-27" href="#__codelineno-9-27"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">function</span><span class="p">();</span><span class="w">         </span><span class="c1">// スタックフレーム空間（関数呼び出し）</span>
+<a id="__codelineno-9-28" name="__codelineno-9-28" href="#__codelineno-9-28"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">c</span><span class="p">;</span><span class="w">           </span><span class="c1">// 出力データ</span>
+<a id="__codelineno-9-29" name="__codelineno-9-29" href="#__codelineno-9-29"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 関数 */</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">func</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="c1">// 特定の操作を実行...</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="p">}</span>
+<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="kt">int</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w">  </span><span class="c1">// 入力データ</span>
+<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w">    </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">    </span><span class="c1">// 一時データ（定数）</span>
+<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">          </span><span class="c1">// 一時データ（変数）</span>
+<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">func</span><span class="p">();</span><span class="w">     </span><span class="c1">// スタックフレーム空間（関数呼び出し）</span>
+<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">c</span><span class="p">;</span><span class="w">   </span><span class="c1">// 出力データ</span>
+<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h2 id="242">2.4.2 &nbsp; 計算方法<a class="headerlink" href="#242" title="Permanent link">&para;</a></h2>
+<p>空間計算量を計算する方法は時間計算量とほぼ同様で、統計対象を「操作数」から「使用空間のサイズ」に変更するだけです。</p>
+<p>しかし、時間計算量とは異なり、<strong>通常は最悪ケース空間計算量のみに焦点を当てます</strong>。これは、メモリ空間がハード要件であり、すべての入力データの下で十分なメモリ空間が確保されていることを保証する必要があるためです。</p>
+<p>以下のコードを考えてみましょう。最悪ケース空間計算量の「最悪ケース」という用語には2つの意味があります。</p>
+<ol>
+<li><strong>最悪の入力データに基づく</strong>: <span class="arithmatex">\(n &lt; 10\)</span>の場合、空間計算量は<span class="arithmatex">\(O(1)\)</span>ですが、<span class="arithmatex">\(n &gt; 10\)</span>の場合、初期化された配列<code>nums</code>が<span class="arithmatex">\(O(n)\)</span>の空間を占有するため、最悪ケース空間計算量は<span class="arithmatex">\(O(n)\)</span>です。</li>
+<li><strong>アルゴリズムの実行中に使用されるピークメモリに基づく</strong>: 例えば、最後の行を実行する前、プログラムは<span class="arithmatex">\(O(1)\)</span>の空間を占有します。配列<code>nums</code>を初期化する際、プログラムは<span class="arithmatex">\(O(n)\)</span>の空間を占有するため、最悪ケース空間計算量は<span class="arithmatex">\(O(n)\)</span>です。</li>
+</ol>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:13"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a>    <span class="n">a</span> <span class="o">=</span> <span class="mi">0</span>               <span class="c1"># O(1)</span>
+<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>    <span class="n">b</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="mi">10000</span>     <span class="c1"># O(1)</span>
+<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a>    <span class="k">if</span> <span class="n">n</span> <span class="o">&gt;</span> <span class="mi">10</span><span class="p">:</span>
+<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a>        <span class="n">nums</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">n</span>  <span class="c1"># O(n)</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">               </span><span class="c1">// O(1)</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">b</span><span class="p">(</span><span class="mi">10000</span><span class="p">);</span><span class="w">    </span><span class="c1">// O(1)</span>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">10</span><span class="p">)</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w">        </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">(</span><span class="n">n</span><span class="p">);</span><span class="w"> </span><span class="c1">// O(n)</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">                   </span><span class="c1">// O(1)</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="mi">10000</span><span class="o">]</span><span class="p">;</span><span class="w">    </span><span class="c1">// O(1)</span>
+<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">10</span><span class="p">)</span>
+<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">        </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">n</span><span class="o">]</span><span class="p">;</span><span class="w"> </span><span class="c1">// O(n)</span>
+<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="k">void</span><span class="w"> </span><span class="nf">Algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">                   </span><span class="c1">// O(1)</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="mi">10000</span><span class="p">];</span><span class="w">    </span><span class="c1">// O(1)</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">10</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">        </span><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">n</span><span class="p">];</span><span class="w"> </span><span class="c1">// O(n)</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="kd">func</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="w">                      </span><span class="c1">// O(1)</span>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="w">    </span><span class="nx">b</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="mi">10000</span><span class="p">)</span><span class="w">     </span><span class="c1">// O(1)</span>
+<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span>
+<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="mi">10</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="w">        </span><span class="nx">nums</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">([]</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="nx">n</span><span class="p">)</span><span class="w">  </span><span class="c1">// O(n)</span>
+<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="w">    </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="nx">a</span><span class="p">,</span><span class="w"> </span><span class="nx">b</span><span class="p">,</span><span class="w"> </span><span class="nx">nums</span><span class="p">)</span>
+<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="kd">func</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="c1">// O(1)</span>
+<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nv">b</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="mi">10000</span><span class="p">)</span><span class="w"> </span><span class="c1">// O(1)</span>
+<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">10</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="nv">nums</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="c1">// O(n)</span>
+<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w">                   </span><span class="c1">// O(1)</span>
+<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="mf">10000</span><span class="p">);</span><span class="w">    </span><span class="c1">// O(1)</span>
+<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mf">10</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">n</span><span class="p">);</span><span class="w"> </span><span class="c1">// O(n)</span>
+<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w">                   </span><span class="c1">// O(1)</span>
+<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="w">    </span><span class="kd">const</span><span class="w"> </span><span class="nx">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="mf">10000</span><span class="p">);</span><span class="w">    </span><span class="c1">// O(1)</span>
+<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mf">10</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="w">        </span><span class="kd">const</span><span class="w"> </span><span class="nx">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="nx">n</span><span class="p">);</span><span class="w"> </span><span class="c1">// O(n)</span>
+<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="kt">void</span><span class="w"> </span><span class="n">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w">                            </span><span class="c1">// O(1)</span>
+<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="w">  </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="m">10000</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">);</span><span class="w">  </span><span class="c1">// O(1)</span>
+<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="m">10</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// O(n)</span>
+<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="k">fn</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">                           </span><span class="c1">// O(1)</span>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="mi">10000</span><span class="p">];</span><span class="w">                  </span><span class="c1">// O(1)</span>
+<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">10</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="w">        </span><span class="kd">let</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="kt">usize</span><span class="p">];</span><span class="w">  </span><span class="c1">// O(n)</span>
+<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">               </span><span class="c1">// O(1)</span>
+<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">b</span><span class="p">[</span><span class="mi">10000</span><span class="p">];</span><span class="w">            </span><span class="c1">// O(1)</span>
+<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">10</span><span class="p">)</span>
+<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">n</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="mi">0</span><span class="p">};</span><span class="w">   </span><span class="c1">// O(n)</span>
+<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p><strong>再帰関数では、スタックフレーム空間を考慮に入れる必要があります</strong>。以下のコードを考えてみましょう：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="3:13"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">function</span><span class="p">()</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a>    <span class="c1"># 特定の操作を実行</span>
+<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a>    <span class="k">return</span> <span class="mi">0</span>
+<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a>
+<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="k">def</span><span class="w"> </span><span class="nf">loop</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;ループ O(1)&quot;&quot;&quot;</span>
+<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a>    <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
+<a id="__codelineno-26-8" name="__codelineno-26-8" href="#__codelineno-26-8"></a>        <span class="n">function</span><span class="p">()</span>
+<a id="__codelineno-26-9" name="__codelineno-26-9" href="#__codelineno-26-9"></a>
+<a id="__codelineno-26-10" name="__codelineno-26-10" href="#__codelineno-26-10"></a><span class="k">def</span><span class="w"> </span><span class="nf">recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-26-11" name="__codelineno-26-11" href="#__codelineno-26-11"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;再帰 O(n)&quot;&quot;&quot;</span>
+<a id="__codelineno-26-12" name="__codelineno-26-12" href="#__codelineno-26-12"></a>    <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
+<a id="__codelineno-26-13" name="__codelineno-26-13" href="#__codelineno-26-13"></a>        <span class="k">return</span>
+<a id="__codelineno-26-14" name="__codelineno-26-14" href="#__codelineno-26-14"></a>    <span class="k">return</span> <span class="n">recur</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="kt">int</span><span class="w"> </span><span class="nf">func</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a><span class="w">    </span><span class="c1">// 特定の操作を実行</span>
+<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a><span class="p">}</span>
+<a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a><span class="cm">/* サイクル O(1) */</span>
+<a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a><span class="kt">void</span><span class="w"> </span><span class="nf">loop</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-27-8" name="__codelineno-27-8" href="#__codelineno-27-8"></a><span class="w">        </span><span class="n">func</span><span class="p">();</span>
+<a id="__codelineno-27-9" name="__codelineno-27-9" href="#__codelineno-27-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-27-10" name="__codelineno-27-10" href="#__codelineno-27-10"></a><span class="p">}</span>
+<a id="__codelineno-27-11" name="__codelineno-27-11" href="#__codelineno-27-11"></a><span class="cm">/* 再帰 O(n) */</span>
+<a id="__codelineno-27-12" name="__codelineno-27-12" href="#__codelineno-27-12"></a><span class="kt">void</span><span class="w"> </span><span class="nf">recur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-27-13" name="__codelineno-27-13" href="#__codelineno-27-13"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-27-14" name="__codelineno-27-14" href="#__codelineno-27-14"></a><span class="w">    </span><span class="n">recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-27-15" name="__codelineno-27-15" href="#__codelineno-27-15"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="kt">int</span><span class="w"> </span><span class="nf">function</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="w">    </span><span class="c1">// 特定の操作を実行</span>
+<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a><span class="p">}</span>
+<a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a><span class="cm">/* サイクル O(1) */</span>
+<a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a><span class="kt">void</span><span class="w"> </span><span class="nf">loop</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-8" name="__codelineno-28-8" href="#__codelineno-28-8"></a><span class="w">        </span><span class="n">function</span><span class="p">();</span>
+<a id="__codelineno-28-9" name="__codelineno-28-9" href="#__codelineno-28-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-10" name="__codelineno-28-10" href="#__codelineno-28-10"></a><span class="p">}</span>
+<a id="__codelineno-28-11" name="__codelineno-28-11" href="#__codelineno-28-11"></a><span class="cm">/* 再帰 O(n) */</span>
+<a id="__codelineno-28-12" name="__codelineno-28-12" href="#__codelineno-28-12"></a><span class="kt">void</span><span class="w"> </span><span class="nf">recur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-13" name="__codelineno-28-13" href="#__codelineno-28-13"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-28-14" name="__codelineno-28-14" href="#__codelineno-28-14"></a><span class="w">    </span><span class="n">recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-28-15" name="__codelineno-28-15" href="#__codelineno-28-15"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Function</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="w">    </span><span class="c1">// 特定の操作を実行</span>
+<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="p">}</span>
+<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a><span class="cm">/* サイクル O(1) */</span>
+<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a><span class="k">void</span><span class="w"> </span><span class="nf">Loop</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a><span class="w">        </span><span class="n">Function</span><span class="p">();</span>
+<a id="__codelineno-29-9" name="__codelineno-29-9" href="#__codelineno-29-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-10" name="__codelineno-29-10" href="#__codelineno-29-10"></a><span class="p">}</span>
+<a id="__codelineno-29-11" name="__codelineno-29-11" href="#__codelineno-29-11"></a><span class="cm">/* 再帰 O(n) */</span>
+<a id="__codelineno-29-12" name="__codelineno-29-12" href="#__codelineno-29-12"></a><span class="kt">int</span><span class="w"> </span><span class="nf">Recur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-13" name="__codelineno-29-13" href="#__codelineno-29-13"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-29-14" name="__codelineno-29-14" href="#__codelineno-29-14"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nf">Recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-29-15" name="__codelineno-29-15" href="#__codelineno-29-15"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="kd">func</span><span class="w"> </span><span class="nx">function</span><span class="p">()</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="w">    </span><span class="c1">// 特定の操作を実行</span>
+<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="p">}</span>
+<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a>
+<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="cm">/* サイクル O(1) */</span>
+<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a><span class="kd">func</span><span class="w"> </span><span class="nx">loop</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a><span class="w">        </span><span class="nx">function</span><span class="p">()</span>
+<a id="__codelineno-30-10" name="__codelineno-30-10" href="#__codelineno-30-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-11" name="__codelineno-30-11" href="#__codelineno-30-11"></a><span class="p">}</span>
+<a id="__codelineno-30-12" name="__codelineno-30-12" href="#__codelineno-30-12"></a>
+<a id="__codelineno-30-13" name="__codelineno-30-13" href="#__codelineno-30-13"></a><span class="cm">/* 再帰 O(n) */</span>
+<a id="__codelineno-30-14" name="__codelineno-30-14" href="#__codelineno-30-14"></a><span class="kd">func</span><span class="w"> </span><span class="nx">recur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-15" name="__codelineno-30-15" href="#__codelineno-30-15"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-16" name="__codelineno-30-16" href="#__codelineno-30-16"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-30-17" name="__codelineno-30-17" href="#__codelineno-30-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-18" name="__codelineno-30-18" href="#__codelineno-30-18"></a><span class="w">    </span><span class="nx">recur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-30-19" name="__codelineno-30-19" href="#__codelineno-30-19"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="p">@</span><span class="n">discardableResult</span>
+<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">function</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="w">    </span><span class="c1">// 特定の操作を実行</span>
+<a id="__codelineno-31-4" name="__codelineno-31-4" href="#__codelineno-31-4"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-31-5" name="__codelineno-31-5" href="#__codelineno-31-5"></a><span class="p">}</span>
+<a id="__codelineno-31-6" name="__codelineno-31-6" href="#__codelineno-31-6"></a>
+<a id="__codelineno-31-7" name="__codelineno-31-7" href="#__codelineno-31-7"></a><span class="cm">/* サイクル O(1) */</span>
+<a id="__codelineno-31-8" name="__codelineno-31-8" href="#__codelineno-31-8"></a><span class="kd">func</span><span class="w"> </span><span class="nf">loop</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-9" name="__codelineno-31-9" href="#__codelineno-31-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-10" name="__codelineno-31-10" href="#__codelineno-31-10"></a><span class="w">        </span><span class="n">function</span><span class="p">()</span>
+<a id="__codelineno-31-11" name="__codelineno-31-11" href="#__codelineno-31-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-12" name="__codelineno-31-12" href="#__codelineno-31-12"></a><span class="p">}</span>
+<a id="__codelineno-31-13" name="__codelineno-31-13" href="#__codelineno-31-13"></a>
+<a id="__codelineno-31-14" name="__codelineno-31-14" href="#__codelineno-31-14"></a><span class="cm">/* 再帰 O(n) */</span>
+<a id="__codelineno-31-15" name="__codelineno-31-15" href="#__codelineno-31-15"></a><span class="kd">func</span><span class="w"> </span><span class="nf">recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-16" name="__codelineno-31-16" href="#__codelineno-31-16"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-17" name="__codelineno-31-17" href="#__codelineno-31-17"></a><span class="w">        </span><span class="k">return</span>
+<a id="__codelineno-31-18" name="__codelineno-31-18" href="#__codelineno-31-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-19" name="__codelineno-31-19" href="#__codelineno-31-19"></a><span class="w">    </span><span class="n">recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-31-20" name="__codelineno-31-20" href="#__codelineno-31-20"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="kd">function</span><span class="w"> </span><span class="nx">constFunc</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a><span class="w">    </span><span class="c1">// 特定の操作を実行</span>
+<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-32-4" name="__codelineno-32-4" href="#__codelineno-32-4"></a><span class="p">}</span>
+<a id="__codelineno-32-5" name="__codelineno-32-5" href="#__codelineno-32-5"></a><span class="cm">/* サイクル O(1) */</span>
+<a id="__codelineno-32-6" name="__codelineno-32-6" href="#__codelineno-32-6"></a><span class="kd">function</span><span class="w"> </span><span class="nx">loop</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-7" name="__codelineno-32-7" href="#__codelineno-32-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-8" name="__codelineno-32-8" href="#__codelineno-32-8"></a><span class="w">        </span><span class="nx">constFunc</span><span class="p">();</span>
+<a id="__codelineno-32-9" name="__codelineno-32-9" href="#__codelineno-32-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-10" name="__codelineno-32-10" href="#__codelineno-32-10"></a><span class="p">}</span>
+<a id="__codelineno-32-11" name="__codelineno-32-11" href="#__codelineno-32-11"></a><span class="cm">/* 再帰 O(n) */</span>
+<a id="__codelineno-32-12" name="__codelineno-32-12" href="#__codelineno-32-12"></a><span class="kd">function</span><span class="w"> </span><span class="nx">recur</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-13" name="__codelineno-32-13" href="#__codelineno-32-13"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-32-14" name="__codelineno-32-14" href="#__codelineno-32-14"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">recur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-32-15" name="__codelineno-32-15" href="#__codelineno-32-15"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="kd">function</span><span class="w"> </span><span class="nx">constFunc</span><span class="p">()</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a><span class="w">    </span><span class="c1">// 特定の操作を実行</span>
+<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+<a id="__codelineno-33-4" name="__codelineno-33-4" href="#__codelineno-33-4"></a><span class="p">}</span>
+<a id="__codelineno-33-5" name="__codelineno-33-5" href="#__codelineno-33-5"></a><span class="cm">/* サイクル O(1) */</span>
+<a id="__codelineno-33-6" name="__codelineno-33-6" href="#__codelineno-33-6"></a><span class="kd">function</span><span class="w"> </span><span class="nx">loop</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-7" name="__codelineno-33-7" href="#__codelineno-33-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-8" name="__codelineno-33-8" href="#__codelineno-33-8"></a><span class="w">        </span><span class="nx">constFunc</span><span class="p">();</span>
+<a id="__codelineno-33-9" name="__codelineno-33-9" href="#__codelineno-33-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-10" name="__codelineno-33-10" href="#__codelineno-33-10"></a><span class="p">}</span>
+<a id="__codelineno-33-11" name="__codelineno-33-11" href="#__codelineno-33-11"></a><span class="cm">/* 再帰 O(n) */</span>
+<a id="__codelineno-33-12" name="__codelineno-33-12" href="#__codelineno-33-12"></a><span class="kd">function</span><span class="w"> </span><span class="nx">recur</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-33-13" name="__codelineno-33-13" href="#__codelineno-33-13"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-33-14" name="__codelineno-33-14" href="#__codelineno-33-14"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">recur</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-33-15" name="__codelineno-33-15" href="#__codelineno-33-15"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="kt">int</span><span class="w"> </span><span class="n">function</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a><span class="w">  </span><span class="c1">// 特定の操作を実行</span>
+<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><span class="w">  </span><span class="k">return</span><span class="w"> </span><span class="m">0</span><span class="p">;</span>
+<a id="__codelineno-34-4" name="__codelineno-34-4" href="#__codelineno-34-4"></a><span class="p">}</span>
+<a id="__codelineno-34-5" name="__codelineno-34-5" href="#__codelineno-34-5"></a><span class="cm">/* サイクル O(1) */</span>
+<a id="__codelineno-34-6" name="__codelineno-34-6" href="#__codelineno-34-6"></a><span class="kt">void</span><span class="w"> </span><span class="n">loop</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-7" name="__codelineno-34-7" href="#__codelineno-34-7"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-8" name="__codelineno-34-8" href="#__codelineno-34-8"></a><span class="w">    </span><span class="n">function</span><span class="p">();</span>
+<a id="__codelineno-34-9" name="__codelineno-34-9" href="#__codelineno-34-9"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-34-10" name="__codelineno-34-10" href="#__codelineno-34-10"></a><span class="p">}</span>
+<a id="__codelineno-34-11" name="__codelineno-34-11" href="#__codelineno-34-11"></a><span class="cm">/* 再帰 O(n) */</span>
+<a id="__codelineno-34-12" name="__codelineno-34-12" href="#__codelineno-34-12"></a><span class="kt">void</span><span class="w"> </span><span class="n">recur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-13" name="__codelineno-34-13" href="#__codelineno-34-13"></a><span class="w">  </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="m">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-34-14" name="__codelineno-34-14" href="#__codelineno-34-14"></a><span class="w">  </span><span class="n">recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="m">1</span><span class="p">);</span>
+<a id="__codelineno-34-15" name="__codelineno-34-15" href="#__codelineno-34-15"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="k">fn</span><span class="w"> </span><span class="nf">function</span><span class="p">()</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></a><span class="w">    </span><span class="c1">// 特定の操作を実行</span>
+<a id="__codelineno-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-35-4" name="__codelineno-35-4" href="#__codelineno-35-4"></a><span class="p">}</span>
+<a id="__codelineno-35-5" name="__codelineno-35-5" href="#__codelineno-35-5"></a><span class="cm">/* サイクル O(1) */</span>
+<a id="__codelineno-35-6" name="__codelineno-35-6" href="#__codelineno-35-6"></a><span class="k">fn</span><span class="w"> </span><span class="nf">loop</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-7" name="__codelineno-35-7" href="#__codelineno-35-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-8" name="__codelineno-35-8" href="#__codelineno-35-8"></a><span class="w">        </span><span class="n">function</span><span class="p">();</span>
+<a id="__codelineno-35-9" name="__codelineno-35-9" href="#__codelineno-35-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-10" name="__codelineno-35-10" href="#__codelineno-35-10"></a><span class="p">}</span>
+<a id="__codelineno-35-11" name="__codelineno-35-11" href="#__codelineno-35-11"></a><span class="cm">/* 再帰 O(n) */</span>
+<a id="__codelineno-35-12" name="__codelineno-35-12" href="#__codelineno-35-12"></a><span class="n">void</span><span class="w"> </span><span class="n">recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-13" name="__codelineno-35-13" href="#__codelineno-35-13"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-14" name="__codelineno-35-14" href="#__codelineno-35-14"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-35-15" name="__codelineno-35-15" href="#__codelineno-35-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-16" name="__codelineno-35-16" href="#__codelineno-35-16"></a><span class="w">    </span><span class="n">recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-35-17" name="__codelineno-35-17" href="#__codelineno-35-17"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="kt">int</span><span class="w"> </span><span class="nf">func</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a><span class="w">    </span><span class="c1">// 特定の操作を実行</span>
+<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-36-4" name="__codelineno-36-4" href="#__codelineno-36-4"></a><span class="p">}</span>
+<a id="__codelineno-36-5" name="__codelineno-36-5" href="#__codelineno-36-5"></a><span class="cm">/* サイクル O(1) */</span>
+<a id="__codelineno-36-6" name="__codelineno-36-6" href="#__codelineno-36-6"></a><span class="kt">void</span><span class="w"> </span><span class="nf">loop</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-7" name="__codelineno-36-7" href="#__codelineno-36-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-8" name="__codelineno-36-8" href="#__codelineno-36-8"></a><span class="w">        </span><span class="n">func</span><span class="p">();</span>
+<a id="__codelineno-36-9" name="__codelineno-36-9" href="#__codelineno-36-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-36-10" name="__codelineno-36-10" href="#__codelineno-36-10"></a><span class="p">}</span>
+<a id="__codelineno-36-11" name="__codelineno-36-11" href="#__codelineno-36-11"></a><span class="cm">/* 再帰 O(n) */</span>
+<a id="__codelineno-36-12" name="__codelineno-36-12" href="#__codelineno-36-12"></a><span class="kt">void</span><span class="w"> </span><span class="nf">recur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-13" name="__codelineno-36-13" href="#__codelineno-36-13"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-36-14" name="__codelineno-36-14" href="#__codelineno-36-14"></a><span class="w">    </span><span class="n">recur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-36-15" name="__codelineno-36-15" href="#__codelineno-36-15"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p><code>loop()</code>関数と<code>recur()</code>関数の時間計算量は両方とも<span class="arithmatex">\(O(n)\)</span>ですが、それらの空間計算量は異なります。</p>
+<ul>
+<li><code>loop()</code>関数はループ内で<code>function()</code>を<span class="arithmatex">\(n\)</span>回呼び出し、各反復の<code>function()</code>は返ってそのスタックフレーム空間を解放するため、空間計算量は<span class="arithmatex">\(O(1)\)</span>のままです。</li>
+<li>再帰関数<code>recur()</code>は実行中に<span class="arithmatex">\(n\)</span>個の未返却の<code>recur()</code>インスタンスが同時に存在するため、<span class="arithmatex">\(O(n)\)</span>のスタックフレーム空間を占有します。</li>
+</ul>
+<h2 id="243">2.4.3 &nbsp; 一般的な種類<a class="headerlink" href="#243" title="Permanent link">&para;</a></h2>
+<p>入力データのサイズを<span class="arithmatex">\(n\)</span>とすると、下図は一般的な空間計算量の種類を示しています（低いものから高いものへと並べられています）。</p>
+<div class="arithmatex">\[
+\begin{aligned}
+&amp; O(1) &lt; O(\log n) &lt; O(n) &lt; O(n^2) &lt; O(2^n) \newline
+&amp; \text{定数} &lt; \text{対数} &lt; \text{線形} &lt; \text{二次} &lt; \text{指数}
+\end{aligned}
+\]</div>
+<p><a class="glightbox" href="../space_complexity.assets/space_complexity_common_types.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Common types of space complexity" class="animation-figure" src="../space_complexity.assets/space_complexity_common_types.png" /></a></p>
+<p align="center"> 図 2-16 &nbsp; Common types of space complexity </p>
+
+<h3 id="1-o1">1. &nbsp; 定数オーダー <span class="arithmatex">\(O(1)\)</span><a class="headerlink" href="#1-o1" title="Permanent link">&para;</a></h3>
+<p>定数オーダーは、入力データサイズ<span class="arithmatex">\(n\)</span>とは無関係な定数、変数、オブジェクトで一般的です。</p>
+<p>ループで変数を初期化したり関数を呼び出したりするために占有されるメモリは、次のサイクルに入る際に解放され、空間上で累積されないため、空間計算量は<span class="arithmatex">\(O(1)\)</span>のままです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="4:14"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><input id="__tabbed_4_6" name="__tabbed_4" type="radio" /><input id="__tabbed_4_7" name="__tabbed_4" type="radio" /><input id="__tabbed_4_8" name="__tabbed_4" type="radio" /><input id="__tabbed_4_9" name="__tabbed_4" type="radio" /><input id="__tabbed_4_10" name="__tabbed_4" type="radio" /><input id="__tabbed_4_11" name="__tabbed_4" type="radio" /><input id="__tabbed_4_12" name="__tabbed_4" type="radio" /><input id="__tabbed_4_13" name="__tabbed_4" type="radio" /><input id="__tabbed_4_14" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">Python</label><label for="__tabbed_4_2">C++</label><label for="__tabbed_4_3">Java</label><label for="__tabbed_4_4">C#</label><label for="__tabbed_4_5">Go</label><label for="__tabbed_4_6">Swift</label><label for="__tabbed_4_7">JS</label><label for="__tabbed_4_8">TS</label><label for="__tabbed_4_9">Dart</label><label for="__tabbed_4_10">Rust</label><label for="__tabbed_4_11">C</label><label for="__tabbed_4_12">Kotlin</label><label for="__tabbed_4_13">Ruby</label><label for="__tabbed_4_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.py</span><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">function</span><span class="p">()</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;関数&quot;&quot;&quot;</span>
+<a id="__codelineno-39-3" name="__codelineno-39-3" href="#__codelineno-39-3"></a>    <span class="c1"># 何らかの操作を実行</span>
+<a id="__codelineno-39-4" name="__codelineno-39-4" href="#__codelineno-39-4"></a>    <span class="k">return</span> <span class="mi">0</span>
+<a id="__codelineno-39-5" name="__codelineno-39-5" href="#__codelineno-39-5"></a>
+<a id="__codelineno-39-6" name="__codelineno-39-6" href="#__codelineno-39-6"></a><span class="k">def</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-39-7" name="__codelineno-39-7" href="#__codelineno-39-7"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;定数複雑度&quot;&quot;&quot;</span>
+<a id="__codelineno-39-8" name="__codelineno-39-8" href="#__codelineno-39-8"></a>    <span class="c1"># 定数、変数、オブジェクトは O(1) のスペースを占有</span>
+<a id="__codelineno-39-9" name="__codelineno-39-9" href="#__codelineno-39-9"></a>    <span class="n">a</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-39-10" name="__codelineno-39-10" href="#__codelineno-39-10"></a>    <span class="n">nums</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="mi">10000</span>
+<a id="__codelineno-39-11" name="__codelineno-39-11" href="#__codelineno-39-11"></a>    <span class="n">node</span> <span class="o">=</span> <span class="n">ListNode</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-39-12" name="__codelineno-39-12" href="#__codelineno-39-12"></a>    <span class="c1"># ループ内の変数は O(1) のスペースを占有</span>
+<a id="__codelineno-39-13" name="__codelineno-39-13" href="#__codelineno-39-13"></a>    <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
+<a id="__codelineno-39-14" name="__codelineno-39-14" href="#__codelineno-39-14"></a>        <span class="n">c</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-39-15" name="__codelineno-39-15" href="#__codelineno-39-15"></a>    <span class="c1"># ループ内の関数は O(1) のスペースを占有</span>
+<a id="__codelineno-39-16" name="__codelineno-39-16" href="#__codelineno-39-16"></a>    <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
+<a id="__codelineno-39-17" name="__codelineno-39-17" href="#__codelineno-39-17"></a>        <span class="n">function</span><span class="p">()</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.cpp</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="cm">/* 関数 */</span>
+<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">func</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="w">    </span><span class="c1">// 何らかの操作を実行</span>
+<a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a><span class="p">}</span>
+<a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a>
+<a id="__codelineno-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></a><span class="cm">/* 定数計算量 */</span>
+<a id="__codelineno-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a><span class="kt">void</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-40-9" name="__codelineno-40-9" href="#__codelineno-40-9"></a><span class="w">    </span><span class="c1">// 定数、変数、オブジェクトは O(1) 空間を占める</span>
+<a id="__codelineno-40-10" name="__codelineno-40-10" href="#__codelineno-40-10"></a><span class="w">    </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-40-11" name="__codelineno-40-11" href="#__codelineno-40-11"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-40-12" name="__codelineno-40-12" href="#__codelineno-40-12"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">(</span><span class="mi">10000</span><span class="p">);</span>
+<a id="__codelineno-40-13" name="__codelineno-40-13" href="#__codelineno-40-13"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="n">node</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-40-14" name="__codelineno-40-14" href="#__codelineno-40-14"></a><span class="w">    </span><span class="c1">// ループ内の変数は O(1) 空間を占める</span>
+<a id="__codelineno-40-15" name="__codelineno-40-15" href="#__codelineno-40-15"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-40-16" name="__codelineno-40-16" href="#__codelineno-40-16"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-40-17" name="__codelineno-40-17" href="#__codelineno-40-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-40-18" name="__codelineno-40-18" href="#__codelineno-40-18"></a><span class="w">    </span><span class="c1">// ループ内の関数は O(1) 空間を占める</span>
+<a id="__codelineno-40-19" name="__codelineno-40-19" href="#__codelineno-40-19"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-40-20" name="__codelineno-40-20" href="#__codelineno-40-20"></a><span class="w">        </span><span class="n">func</span><span class="p">();</span>
+<a id="__codelineno-40-21" name="__codelineno-40-21" href="#__codelineno-40-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-40-22" name="__codelineno-40-22" href="#__codelineno-40-22"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.java</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="cm">/* 関数 */</span>
+<a id="__codelineno-41-2" name="__codelineno-41-2" href="#__codelineno-41-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">function</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-41-3" name="__codelineno-41-3" href="#__codelineno-41-3"></a><span class="w">    </span><span class="c1">// 何らかの操作を実行</span>
+<a id="__codelineno-41-4" name="__codelineno-41-4" href="#__codelineno-41-4"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-41-5" name="__codelineno-41-5" href="#__codelineno-41-5"></a><span class="p">}</span>
+<a id="__codelineno-41-6" name="__codelineno-41-6" href="#__codelineno-41-6"></a>
+<a id="__codelineno-41-7" name="__codelineno-41-7" href="#__codelineno-41-7"></a><span class="cm">/* 定数計算量 */</span>
+<a id="__codelineno-41-8" name="__codelineno-41-8" href="#__codelineno-41-8"></a><span class="kt">void</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-41-9" name="__codelineno-41-9" href="#__codelineno-41-9"></a><span class="w">    </span><span class="c1">// 定数、変数、オブジェクトは O(1) 空間を占める</span>
+<a id="__codelineno-41-10" name="__codelineno-41-10" href="#__codelineno-41-10"></a><span class="w">    </span><span class="kd">final</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-41-11" name="__codelineno-41-11" href="#__codelineno-41-11"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-41-12" name="__codelineno-41-12" href="#__codelineno-41-12"></a><span class="w">    </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="mi">10000</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-41-13" name="__codelineno-41-13" href="#__codelineno-41-13"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-41-14" name="__codelineno-41-14" href="#__codelineno-41-14"></a><span class="w">    </span><span class="c1">// ループ内の変数は O(1) 空間を占める</span>
+<a id="__codelineno-41-15" name="__codelineno-41-15" href="#__codelineno-41-15"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-41-16" name="__codelineno-41-16" href="#__codelineno-41-16"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-41-17" name="__codelineno-41-17" href="#__codelineno-41-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-41-18" name="__codelineno-41-18" href="#__codelineno-41-18"></a><span class="w">    </span><span class="c1">// ループ内の関数は O(1) 空間を占める</span>
+<a id="__codelineno-41-19" name="__codelineno-41-19" href="#__codelineno-41-19"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-41-20" name="__codelineno-41-20" href="#__codelineno-41-20"></a><span class="w">        </span><span class="n">function</span><span class="p">();</span>
+<a id="__codelineno-41-21" name="__codelineno-41-21" href="#__codelineno-41-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-41-22" name="__codelineno-41-22" href="#__codelineno-41-22"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.cs</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">space_complexity</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Function</span><span class="p">}</span>
+<a id="__codelineno-42-2" name="__codelineno-42-2" href="#__codelineno-42-2"></a>
+<a id="__codelineno-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">space_complexity</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Constant</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.go</span><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">function</span><span class="p">}</span>
+<a id="__codelineno-43-2" name="__codelineno-43-2" href="#__codelineno-43-2"></a>
+<a id="__codelineno-43-3" name="__codelineno-43-3" href="#__codelineno-43-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">spaceConstant</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.swift</span><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">function</span><span class="p">}</span>
+<a id="__codelineno-44-2" name="__codelineno-44-2" href="#__codelineno-44-2"></a>
+<a id="__codelineno-44-3" name="__codelineno-44-3" href="#__codelineno-44-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">constant</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.js</span><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">constFunc</span><span class="p">}</span>
+<a id="__codelineno-45-2" name="__codelineno-45-2" href="#__codelineno-45-2"></a>
+<a id="__codelineno-45-3" name="__codelineno-45-3" href="#__codelineno-45-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">constant</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.ts</span><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">constFunc</span><span class="p">}</span>
+<a id="__codelineno-46-2" name="__codelineno-46-2" href="#__codelineno-46-2"></a>
+<a id="__codelineno-46-3" name="__codelineno-46-3" href="#__codelineno-46-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">constant</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.dart</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">function</span><span class="p">}</span>
+<a id="__codelineno-47-2" name="__codelineno-47-2" href="#__codelineno-47-2"></a>
+<a id="__codelineno-47-3" name="__codelineno-47-3" href="#__codelineno-47-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">constant</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.rs</span><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">function</span><span class="p">}</span>
+<a id="__codelineno-48-2" name="__codelineno-48-2" href="#__codelineno-48-2"></a>
+<a id="__codelineno-48-3" name="__codelineno-48-3" href="#__codelineno-48-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">constant</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.c</span><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">func</span><span class="p">}</span>
+<a id="__codelineno-49-2" name="__codelineno-49-2" href="#__codelineno-49-2"></a>
+<a id="__codelineno-49-3" name="__codelineno-49-3" href="#__codelineno-49-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">constant</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.kt</span><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">function</span><span class="p">}</span>
+<a id="__codelineno-50-2" name="__codelineno-50-2" href="#__codelineno-50-2"></a>
+<a id="__codelineno-50-3" name="__codelineno-50-3" href="#__codelineno-50-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">constant</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.rb</span><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">function</span><span class="p">}</span>
+<a id="__codelineno-51-2" name="__codelineno-51-2" href="#__codelineno-51-2"></a>
+<a id="__codelineno-51-3" name="__codelineno-51-3" href="#__codelineno-51-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">constant</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.zig</span><pre><span></span><code><a id="__codelineno-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">function</span><span class="p">}</span>
+<a id="__codelineno-52-2" name="__codelineno-52-2" href="#__codelineno-52-2"></a>
+<a id="__codelineno-52-3" name="__codelineno-52-3" href="#__codelineno-52-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">constant</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h3 id="2-on">2. &nbsp; 線形オーダー <span class="arithmatex">\(O(n)\)</span><a class="headerlink" href="#2-on" title="Permanent link">&para;</a></h3>
+<p>線形オーダーは配列、連結リスト、スタック、キューなどで一般的で、要素数は<span class="arithmatex">\(n\)</span>に比例します：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="5:14"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><input id="__tabbed_5_7" name="__tabbed_5" type="radio" /><input id="__tabbed_5_8" name="__tabbed_5" type="radio" /><input id="__tabbed_5_9" name="__tabbed_5" type="radio" /><input id="__tabbed_5_10" name="__tabbed_5" type="radio" /><input id="__tabbed_5_11" name="__tabbed_5" type="radio" /><input id="__tabbed_5_12" name="__tabbed_5" type="radio" /><input id="__tabbed_5_13" name="__tabbed_5" type="radio" /><input id="__tabbed_5_14" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">Python</label><label for="__tabbed_5_2">C++</label><label for="__tabbed_5_3">Java</label><label for="__tabbed_5_4">C#</label><label for="__tabbed_5_5">Go</label><label for="__tabbed_5_6">Swift</label><label for="__tabbed_5_7">JS</label><label for="__tabbed_5_8">TS</label><label for="__tabbed_5_9">Dart</label><label for="__tabbed_5_10">Rust</label><label for="__tabbed_5_11">C</label><label for="__tabbed_5_12">Kotlin</label><label for="__tabbed_5_13">Ruby</label><label for="__tabbed_5_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.py</span><pre><span></span><code><a id="__codelineno-53-1" name="__codelineno-53-1" href="#__codelineno-53-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-53-2" name="__codelineno-53-2" href="#__codelineno-53-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;線形複雑度&quot;&quot;&quot;</span>
+<a id="__codelineno-53-3" name="__codelineno-53-3" href="#__codelineno-53-3"></a>    <span class="c1"># 長さ n のリストは O(n) のスペースを占有</span>
+<a id="__codelineno-53-4" name="__codelineno-53-4" href="#__codelineno-53-4"></a>    <span class="n">nums</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">n</span>
+<a id="__codelineno-53-5" name="__codelineno-53-5" href="#__codelineno-53-5"></a>    <span class="c1"># 長さ n のハッシュマップは O(n) のスペースを占有</span>
+<a id="__codelineno-53-6" name="__codelineno-53-6" href="#__codelineno-53-6"></a>    <span class="n">hmap</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">[</span><span class="nb">int</span><span class="p">,</span> <span class="nb">str</span><span class="p">]()</span>
+<a id="__codelineno-53-7" name="__codelineno-53-7" href="#__codelineno-53-7"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
+<a id="__codelineno-53-8" name="__codelineno-53-8" href="#__codelineno-53-8"></a>        <span class="n">hmap</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="nb">str</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.cpp</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="cm">/* 線形計算量 */</span>
+<a id="__codelineno-54-2" name="__codelineno-54-2" href="#__codelineno-54-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-54-3" name="__codelineno-54-3" href="#__codelineno-54-3"></a><span class="w">    </span><span class="c1">// 長さ n の配列は O(n) 空間を占める</span>
+<a id="__codelineno-54-4" name="__codelineno-54-4" href="#__codelineno-54-4"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">(</span><span class="n">n</span><span class="p">);</span>
+<a id="__codelineno-54-5" name="__codelineno-54-5" href="#__codelineno-54-5"></a><span class="w">    </span><span class="c1">// 長さ n のリストは O(n) 空間を占める</span>
+<a id="__codelineno-54-6" name="__codelineno-54-6" href="#__codelineno-54-6"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">ListNode</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nodes</span><span class="p">;</span>
+<a id="__codelineno-54-7" name="__codelineno-54-7" href="#__codelineno-54-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-54-8" name="__codelineno-54-8" href="#__codelineno-54-8"></a><span class="w">        </span><span class="n">nodes</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">ListNode</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
+<a id="__codelineno-54-9" name="__codelineno-54-9" href="#__codelineno-54-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-54-10" name="__codelineno-54-10" href="#__codelineno-54-10"></a><span class="w">    </span><span class="c1">// 長さ n のハッシュテーブルは O(n) 空間を占める</span>
+<a id="__codelineno-54-11" name="__codelineno-54-11" href="#__codelineno-54-11"></a><span class="w">    </span><span class="n">unordered_map</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="n">string</span><span class="o">&gt;</span><span class="w"> </span><span class="n">map</span><span class="p">;</span>
+<a id="__codelineno-54-12" name="__codelineno-54-12" href="#__codelineno-54-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-54-13" name="__codelineno-54-13" href="#__codelineno-54-13"></a><span class="w">        </span><span class="n">map</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">to_string</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-54-14" name="__codelineno-54-14" href="#__codelineno-54-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-54-15" name="__codelineno-54-15" href="#__codelineno-54-15"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.java</span><pre><span></span><code><a id="__codelineno-55-1" name="__codelineno-55-1" href="#__codelineno-55-1"></a><span class="cm">/* 線形計算量 */</span>
+<a id="__codelineno-55-2" name="__codelineno-55-2" href="#__codelineno-55-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-55-3" name="__codelineno-55-3" href="#__codelineno-55-3"></a><span class="w">    </span><span class="c1">// 長さ n の配列は O(n) 空間を占める</span>
+<a id="__codelineno-55-4" name="__codelineno-55-4" href="#__codelineno-55-4"></a><span class="w">    </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">n</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-55-5" name="__codelineno-55-5" href="#__codelineno-55-5"></a><span class="w">    </span><span class="c1">// 長さ n のリストは O(n) 空間を占める</span>
+<a id="__codelineno-55-6" name="__codelineno-55-6" href="#__codelineno-55-6"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">ListNode</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nodes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-55-7" name="__codelineno-55-7" href="#__codelineno-55-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-55-8" name="__codelineno-55-8" href="#__codelineno-55-8"></a><span class="w">        </span><span class="n">nodes</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
+<a id="__codelineno-55-9" name="__codelineno-55-9" href="#__codelineno-55-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-55-10" name="__codelineno-55-10" href="#__codelineno-55-10"></a><span class="w">    </span><span class="c1">// 長さ n のハッシュテーブルは O(n) 空間を占める</span>
+<a id="__codelineno-55-11" name="__codelineno-55-11" href="#__codelineno-55-11"></a><span class="w">    </span><span class="n">Map</span><span class="o">&lt;</span><span class="n">Integer</span><span class="p">,</span><span class="w"> </span><span class="n">String</span><span class="o">&gt;</span><span class="w"> </span><span class="n">map</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">HashMap</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-55-12" name="__codelineno-55-12" href="#__codelineno-55-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-55-13" name="__codelineno-55-13" href="#__codelineno-55-13"></a><span class="w">        </span><span class="n">map</span><span class="p">.</span><span class="na">put</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">String</span><span class="p">.</span><span class="na">valueOf</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
+<a id="__codelineno-55-14" name="__codelineno-55-14" href="#__codelineno-55-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-55-15" name="__codelineno-55-15" href="#__codelineno-55-15"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.cs</span><pre><span></span><code><a id="__codelineno-56-1" name="__codelineno-56-1" href="#__codelineno-56-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">space_complexity</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Linear</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.go</span><pre><span></span><code><a id="__codelineno-57-1" name="__codelineno-57-1" href="#__codelineno-57-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">spaceLinear</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.swift</span><pre><span></span><code><a id="__codelineno-58-1" name="__codelineno-58-1" href="#__codelineno-58-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">linear</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.js</span><pre><span></span><code><a id="__codelineno-59-1" name="__codelineno-59-1" href="#__codelineno-59-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">linear</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.ts</span><pre><span></span><code><a id="__codelineno-60-1" name="__codelineno-60-1" href="#__codelineno-60-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">linear</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.dart</span><pre><span></span><code><a id="__codelineno-61-1" name="__codelineno-61-1" href="#__codelineno-61-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">linear</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.rs</span><pre><span></span><code><a id="__codelineno-62-1" name="__codelineno-62-1" href="#__codelineno-62-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">linear</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.c</span><pre><span></span><code><a id="__codelineno-63-1" name="__codelineno-63-1" href="#__codelineno-63-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">HashTable</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<a id="__codelineno-63-2" name="__codelineno-63-2" href="#__codelineno-63-2"></a>
+<a id="__codelineno-63-3" name="__codelineno-63-3" href="#__codelineno-63-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">linear</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.kt</span><pre><span></span><code><a id="__codelineno-64-1" name="__codelineno-64-1" href="#__codelineno-64-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">linear</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.rb</span><pre><span></span><code><a id="__codelineno-65-1" name="__codelineno-65-1" href="#__codelineno-65-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">linear</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.zig</span><pre><span></span><code><a id="__codelineno-66-1" name="__codelineno-66-1" href="#__codelineno-66-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">linear</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>下図に示されているように、この関数の再帰深度は<span class="arithmatex">\(n\)</span>で、<span class="arithmatex">\(n\)</span>個の未返却の<code>linear_recur()</code>関数インスタンスがあり、<span class="arithmatex">\(O(n)\)</span>サイズのスタックフレーム空間を使用します：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="6:14"><input checked="checked" id="__tabbed_6_1" name="__tabbed_6" type="radio" /><input id="__tabbed_6_2" name="__tabbed_6" type="radio" /><input id="__tabbed_6_3" name="__tabbed_6" type="radio" /><input id="__tabbed_6_4" name="__tabbed_6" type="radio" /><input id="__tabbed_6_5" name="__tabbed_6" type="radio" /><input id="__tabbed_6_6" name="__tabbed_6" type="radio" /><input id="__tabbed_6_7" name="__tabbed_6" type="radio" /><input id="__tabbed_6_8" name="__tabbed_6" type="radio" /><input id="__tabbed_6_9" name="__tabbed_6" type="radio" /><input id="__tabbed_6_10" name="__tabbed_6" type="radio" /><input id="__tabbed_6_11" name="__tabbed_6" type="radio" /><input id="__tabbed_6_12" name="__tabbed_6" type="radio" /><input id="__tabbed_6_13" name="__tabbed_6" type="radio" /><input id="__tabbed_6_14" name="__tabbed_6" type="radio" /><div class="tabbed-labels"><label for="__tabbed_6_1">Python</label><label for="__tabbed_6_2">C++</label><label for="__tabbed_6_3">Java</label><label for="__tabbed_6_4">C#</label><label for="__tabbed_6_5">Go</label><label for="__tabbed_6_6">Swift</label><label for="__tabbed_6_7">JS</label><label for="__tabbed_6_8">TS</label><label for="__tabbed_6_9">Dart</label><label for="__tabbed_6_10">Rust</label><label for="__tabbed_6_11">C</label><label for="__tabbed_6_12">Kotlin</label><label for="__tabbed_6_13">Ruby</label><label for="__tabbed_6_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.py</span><pre><span></span><code><a id="__codelineno-67-1" name="__codelineno-67-1" href="#__codelineno-67-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">linear_recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-67-2" name="__codelineno-67-2" href="#__codelineno-67-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;線形複雑度（再帰実装）&quot;&quot;&quot;</span>
+<a id="__codelineno-67-3" name="__codelineno-67-3" href="#__codelineno-67-3"></a>    <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;再帰 n =&quot;</span><span class="p">,</span> <span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-67-4" name="__codelineno-67-4" href="#__codelineno-67-4"></a>    <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
+<a id="__codelineno-67-5" name="__codelineno-67-5" href="#__codelineno-67-5"></a>        <span class="k">return</span>
+<a id="__codelineno-67-6" name="__codelineno-67-6" href="#__codelineno-67-6"></a>    <span class="n">linear_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.cpp</span><pre><span></span><code><a id="__codelineno-68-1" name="__codelineno-68-1" href="#__codelineno-68-1"></a><span class="cm">/* 線形計算量（再帰実装） */</span>
+<a id="__codelineno-68-2" name="__codelineno-68-2" href="#__codelineno-68-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">linearRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-68-3" name="__codelineno-68-3" href="#__codelineno-68-3"></a><span class="w">    </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;再帰 n = &quot;</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
+<a id="__codelineno-68-4" name="__codelineno-68-4" href="#__codelineno-68-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-68-5" name="__codelineno-68-5" href="#__codelineno-68-5"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-68-6" name="__codelineno-68-6" href="#__codelineno-68-6"></a><span class="w">    </span><span class="n">linearRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-68-7" name="__codelineno-68-7" href="#__codelineno-68-7"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.java</span><pre><span></span><code><a id="__codelineno-69-1" name="__codelineno-69-1" href="#__codelineno-69-1"></a><span class="cm">/* 線形計算量（再帰実装） */</span>
+<a id="__codelineno-69-2" name="__codelineno-69-2" href="#__codelineno-69-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">linearRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-69-3" name="__codelineno-69-3" href="#__codelineno-69-3"></a><span class="w">    </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="s">&quot;再帰 n = &quot;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="p">);</span>
+<a id="__codelineno-69-4" name="__codelineno-69-4" href="#__codelineno-69-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-69-5" name="__codelineno-69-5" href="#__codelineno-69-5"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-69-6" name="__codelineno-69-6" href="#__codelineno-69-6"></a><span class="w">    </span><span class="n">linearRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-69-7" name="__codelineno-69-7" href="#__codelineno-69-7"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.cs</span><pre><span></span><code><a id="__codelineno-70-1" name="__codelineno-70-1" href="#__codelineno-70-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">space_complexity</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">LinearRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.go</span><pre><span></span><code><a id="__codelineno-71-1" name="__codelineno-71-1" href="#__codelineno-71-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">spaceLinearRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.swift</span><pre><span></span><code><a id="__codelineno-72-1" name="__codelineno-72-1" href="#__codelineno-72-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">linearRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.js</span><pre><span></span><code><a id="__codelineno-73-1" name="__codelineno-73-1" href="#__codelineno-73-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">linearRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.ts</span><pre><span></span><code><a id="__codelineno-74-1" name="__codelineno-74-1" href="#__codelineno-74-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">linearRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.dart</span><pre><span></span><code><a id="__codelineno-75-1" name="__codelineno-75-1" href="#__codelineno-75-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">linearRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.rs</span><pre><span></span><code><a id="__codelineno-76-1" name="__codelineno-76-1" href="#__codelineno-76-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">linear_recur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.c</span><pre><span></span><code><a id="__codelineno-77-1" name="__codelineno-77-1" href="#__codelineno-77-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">linearRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.kt</span><pre><span></span><code><a id="__codelineno-78-1" name="__codelineno-78-1" href="#__codelineno-78-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">linearRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.rb</span><pre><span></span><code><a id="__codelineno-79-1" name="__codelineno-79-1" href="#__codelineno-79-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">linear_recur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.zig</span><pre><span></span><code><a id="__codelineno-80-1" name="__codelineno-80-1" href="#__codelineno-80-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">linearRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p><a class="glightbox" href="../space_complexity.assets/space_complexity_recursive_linear.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Recursive function generating linear order space complexity" class="animation-figure" src="../space_complexity.assets/space_complexity_recursive_linear.png" /></a></p>
+<p align="center"> 図 2-17 &nbsp; Recursive function generating linear order space complexity </p>
+
+<h3 id="3-on2">3. &nbsp; 二次オーダー <span class="arithmatex">\(O(n^2)\)</span><a class="headerlink" href="#3-on2" title="Permanent link">&para;</a></h3>
+<p>二次オーダーは行列やグラフで一般的で、要素数は<span class="arithmatex">\(n\)</span>の二乗に比例します：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="7:14"><input checked="checked" id="__tabbed_7_1" name="__tabbed_7" type="radio" /><input id="__tabbed_7_2" name="__tabbed_7" type="radio" /><input id="__tabbed_7_3" name="__tabbed_7" type="radio" /><input id="__tabbed_7_4" name="__tabbed_7" type="radio" /><input id="__tabbed_7_5" name="__tabbed_7" type="radio" /><input id="__tabbed_7_6" name="__tabbed_7" type="radio" /><input id="__tabbed_7_7" name="__tabbed_7" type="radio" /><input id="__tabbed_7_8" name="__tabbed_7" type="radio" /><input id="__tabbed_7_9" name="__tabbed_7" type="radio" /><input id="__tabbed_7_10" name="__tabbed_7" type="radio" /><input id="__tabbed_7_11" name="__tabbed_7" type="radio" /><input id="__tabbed_7_12" name="__tabbed_7" type="radio" /><input id="__tabbed_7_13" name="__tabbed_7" type="radio" /><input id="__tabbed_7_14" name="__tabbed_7" type="radio" /><div class="tabbed-labels"><label for="__tabbed_7_1">Python</label><label for="__tabbed_7_2">C++</label><label for="__tabbed_7_3">Java</label><label for="__tabbed_7_4">C#</label><label for="__tabbed_7_5">Go</label><label for="__tabbed_7_6">Swift</label><label for="__tabbed_7_7">JS</label><label for="__tabbed_7_8">TS</label><label for="__tabbed_7_9">Dart</label><label for="__tabbed_7_10">Rust</label><label for="__tabbed_7_11">C</label><label for="__tabbed_7_12">Kotlin</label><label for="__tabbed_7_13">Ruby</label><label for="__tabbed_7_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.py</span><pre><span></span><code><a id="__codelineno-81-1" name="__codelineno-81-1" href="#__codelineno-81-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-81-2" name="__codelineno-81-2" href="#__codelineno-81-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;平方複雑度&quot;&quot;&quot;</span>
+<a id="__codelineno-81-3" name="__codelineno-81-3" href="#__codelineno-81-3"></a>    <span class="c1"># 二次元リストは O(n^2) のスペースを占有</span>
+<a id="__codelineno-81-4" name="__codelineno-81-4" href="#__codelineno-81-4"></a>    <span class="n">num_matrix</span> <span class="o">=</span> <span class="p">[[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">n</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">)]</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.cpp</span><pre><span></span><code><a id="__codelineno-82-1" name="__codelineno-82-1" href="#__codelineno-82-1"></a><span class="cm">/* 二次計算量 */</span>
+<a id="__codelineno-82-2" name="__codelineno-82-2" href="#__codelineno-82-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-82-3" name="__codelineno-82-3" href="#__codelineno-82-3"></a><span class="w">    </span><span class="c1">// 二次元リストは O(n^2) 空間を占める</span>
+<a id="__codelineno-82-4" name="__codelineno-82-4" href="#__codelineno-82-4"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">numMatrix</span><span class="p">;</span>
+<a id="__codelineno-82-5" name="__codelineno-82-5" href="#__codelineno-82-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-82-6" name="__codelineno-82-6" href="#__codelineno-82-6"></a><span class="w">        </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
+<a id="__codelineno-82-7" name="__codelineno-82-7" href="#__codelineno-82-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-82-8" name="__codelineno-82-8" href="#__codelineno-82-8"></a><span class="w">            </span><span class="n">tmp</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-82-9" name="__codelineno-82-9" href="#__codelineno-82-9"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-82-10" name="__codelineno-82-10" href="#__codelineno-82-10"></a><span class="w">        </span><span class="n">numMatrix</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">tmp</span><span class="p">);</span>
+<a id="__codelineno-82-11" name="__codelineno-82-11" href="#__codelineno-82-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-82-12" name="__codelineno-82-12" href="#__codelineno-82-12"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.java</span><pre><span></span><code><a id="__codelineno-83-1" name="__codelineno-83-1" href="#__codelineno-83-1"></a><span class="cm">/* 二次計算量 */</span>
+<a id="__codelineno-83-2" name="__codelineno-83-2" href="#__codelineno-83-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-83-3" name="__codelineno-83-3" href="#__codelineno-83-3"></a><span class="w">    </span><span class="c1">// 行列は O(n^2) 空間を占める</span>
+<a id="__codelineno-83-4" name="__codelineno-83-4" href="#__codelineno-83-4"></a><span class="w">    </span><span class="kt">int</span><span class="o">[][]</span><span class="w"> </span><span class="n">numMatrix</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="n">n</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-83-5" name="__codelineno-83-5" href="#__codelineno-83-5"></a><span class="w">    </span><span class="c1">// 二次元リストは O(n^2) 空間を占める</span>
+<a id="__codelineno-83-6" name="__codelineno-83-6" href="#__codelineno-83-6"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">numList</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-83-7" name="__codelineno-83-7" href="#__codelineno-83-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-83-8" name="__codelineno-83-8" href="#__codelineno-83-8"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-83-9" name="__codelineno-83-9" href="#__codelineno-83-9"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-83-10" name="__codelineno-83-10" href="#__codelineno-83-10"></a><span class="w">            </span><span class="n">tmp</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-83-11" name="__codelineno-83-11" href="#__codelineno-83-11"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-83-12" name="__codelineno-83-12" href="#__codelineno-83-12"></a><span class="w">        </span><span class="n">numList</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">tmp</span><span class="p">);</span>
+<a id="__codelineno-83-13" name="__codelineno-83-13" href="#__codelineno-83-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-83-14" name="__codelineno-83-14" href="#__codelineno-83-14"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.cs</span><pre><span></span><code><a id="__codelineno-84-1" name="__codelineno-84-1" href="#__codelineno-84-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">space_complexity</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Quadratic</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.go</span><pre><span></span><code><a id="__codelineno-85-1" name="__codelineno-85-1" href="#__codelineno-85-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">spaceQuadratic</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.swift</span><pre><span></span><code><a id="__codelineno-86-1" name="__codelineno-86-1" href="#__codelineno-86-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">quadratic</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.js</span><pre><span></span><code><a id="__codelineno-87-1" name="__codelineno-87-1" href="#__codelineno-87-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">quadratic</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.ts</span><pre><span></span><code><a id="__codelineno-88-1" name="__codelineno-88-1" href="#__codelineno-88-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">quadratic</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.dart</span><pre><span></span><code><a id="__codelineno-89-1" name="__codelineno-89-1" href="#__codelineno-89-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">quadratic</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.rs</span><pre><span></span><code><a id="__codelineno-90-1" name="__codelineno-90-1" href="#__codelineno-90-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">quadratic</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.c</span><pre><span></span><code><a id="__codelineno-91-1" name="__codelineno-91-1" href="#__codelineno-91-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">quadratic</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.kt</span><pre><span></span><code><a id="__codelineno-92-1" name="__codelineno-92-1" href="#__codelineno-92-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">quadratic</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.rb</span><pre><span></span><code><a id="__codelineno-93-1" name="__codelineno-93-1" href="#__codelineno-93-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">quadratic</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.zig</span><pre><span></span><code><a id="__codelineno-94-1" name="__codelineno-94-1" href="#__codelineno-94-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">quadratic</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>下図に示されているように、この関数の再帰深度は<span class="arithmatex">\(n\)</span>で、各再帰呼び出しで長さ<span class="arithmatex">\(n\)</span>、<span class="arithmatex">\(n-1\)</span>、<span class="arithmatex">\(\dots\)</span>、<span class="arithmatex">\(2\)</span>、<span class="arithmatex">\(1\)</span>の配列が初期化され、平均<span class="arithmatex">\(n/2\)</span>となり、全体として<span class="arithmatex">\(O(n^2)\)</span>の空間を占有します：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="8:14"><input checked="checked" id="__tabbed_8_1" name="__tabbed_8" type="radio" /><input id="__tabbed_8_2" name="__tabbed_8" type="radio" /><input id="__tabbed_8_3" name="__tabbed_8" type="radio" /><input id="__tabbed_8_4" name="__tabbed_8" type="radio" /><input id="__tabbed_8_5" name="__tabbed_8" type="radio" /><input id="__tabbed_8_6" name="__tabbed_8" type="radio" /><input id="__tabbed_8_7" name="__tabbed_8" type="radio" /><input id="__tabbed_8_8" name="__tabbed_8" type="radio" /><input id="__tabbed_8_9" name="__tabbed_8" type="radio" /><input id="__tabbed_8_10" name="__tabbed_8" type="radio" /><input id="__tabbed_8_11" name="__tabbed_8" type="radio" /><input id="__tabbed_8_12" name="__tabbed_8" type="radio" /><input id="__tabbed_8_13" name="__tabbed_8" type="radio" /><input id="__tabbed_8_14" name="__tabbed_8" type="radio" /><div class="tabbed-labels"><label for="__tabbed_8_1">Python</label><label for="__tabbed_8_2">C++</label><label for="__tabbed_8_3">Java</label><label for="__tabbed_8_4">C#</label><label for="__tabbed_8_5">Go</label><label for="__tabbed_8_6">Swift</label><label for="__tabbed_8_7">JS</label><label for="__tabbed_8_8">TS</label><label for="__tabbed_8_9">Dart</label><label for="__tabbed_8_10">Rust</label><label for="__tabbed_8_11">C</label><label for="__tabbed_8_12">Kotlin</label><label for="__tabbed_8_13">Ruby</label><label for="__tabbed_8_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.py</span><pre><span></span><code><a id="__codelineno-95-1" name="__codelineno-95-1" href="#__codelineno-95-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">quadratic_recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-95-2" name="__codelineno-95-2" href="#__codelineno-95-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;平方複雑度（再帰実装）&quot;&quot;&quot;</span>
+<a id="__codelineno-95-3" name="__codelineno-95-3" href="#__codelineno-95-3"></a>    <span class="k">if</span> <span class="n">n</span> <span class="o">&lt;=</span> <span class="mi">0</span><span class="p">:</span>
+<a id="__codelineno-95-4" name="__codelineno-95-4" href="#__codelineno-95-4"></a>        <span class="k">return</span> <span class="mi">0</span>
+<a id="__codelineno-95-5" name="__codelineno-95-5" href="#__codelineno-95-5"></a>    <span class="n">nums</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">n</span>
+<a id="__codelineno-95-6" name="__codelineno-95-6" href="#__codelineno-95-6"></a>    <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;再帰 n = </span><span class="si">{</span><span class="n">n</span><span class="si">}</span><span class="s2"> の中で配列の長さ = </span><span class="si">{</span><span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span><span class="si">}</span><span class="s2">&quot;</span><span class="p">)</span>
+<a id="__codelineno-95-7" name="__codelineno-95-7" href="#__codelineno-95-7"></a>    <span class="k">return</span> <span class="n">quadratic_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.cpp</span><pre><span></span><code><a id="__codelineno-96-1" name="__codelineno-96-1" href="#__codelineno-96-1"></a><span class="cm">/* 二次計算量（再帰実装） */</span>
+<a id="__codelineno-96-2" name="__codelineno-96-2" href="#__codelineno-96-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">quadraticRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-96-3" name="__codelineno-96-3" href="#__codelineno-96-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-96-4" name="__codelineno-96-4" href="#__codelineno-96-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-96-5" name="__codelineno-96-5" href="#__codelineno-96-5"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">(</span><span class="n">n</span><span class="p">);</span>
+<a id="__codelineno-96-6" name="__codelineno-96-6" href="#__codelineno-96-6"></a><span class="w">    </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;再帰 n = &quot;</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;, nums の長さ = &quot;</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
+<a id="__codelineno-96-7" name="__codelineno-96-7" href="#__codelineno-96-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">quadraticRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-96-8" name="__codelineno-96-8" href="#__codelineno-96-8"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.java</span><pre><span></span><code><a id="__codelineno-97-1" name="__codelineno-97-1" href="#__codelineno-97-1"></a><span class="cm">/* 二次計算量（再帰実装） */</span>
+<a id="__codelineno-97-2" name="__codelineno-97-2" href="#__codelineno-97-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">quadraticRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-97-3" name="__codelineno-97-3" href="#__codelineno-97-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-97-4" name="__codelineno-97-4" href="#__codelineno-97-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-97-5" name="__codelineno-97-5" href="#__codelineno-97-5"></a><span class="w">    </span><span class="c1">// 配列 nums の長さ = n, n-1, ..., 2, 1</span>
+<a id="__codelineno-97-6" name="__codelineno-97-6" href="#__codelineno-97-6"></a><span class="w">    </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">n</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-97-7" name="__codelineno-97-7" href="#__codelineno-97-7"></a><span class="w">    </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="s">&quot;再帰 n = &quot;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s">&quot; の nums の長さ = &quot;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="p">);</span>
+<a id="__codelineno-97-8" name="__codelineno-97-8" href="#__codelineno-97-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">quadraticRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-97-9" name="__codelineno-97-9" href="#__codelineno-97-9"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.cs</span><pre><span></span><code><a id="__codelineno-98-1" name="__codelineno-98-1" href="#__codelineno-98-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">space_complexity</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">QuadraticRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.go</span><pre><span></span><code><a id="__codelineno-99-1" name="__codelineno-99-1" href="#__codelineno-99-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">spaceQuadraticRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.swift</span><pre><span></span><code><a id="__codelineno-100-1" name="__codelineno-100-1" href="#__codelineno-100-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">quadraticRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.js</span><pre><span></span><code><a id="__codelineno-101-1" name="__codelineno-101-1" href="#__codelineno-101-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">quadraticRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.ts</span><pre><span></span><code><a id="__codelineno-102-1" name="__codelineno-102-1" href="#__codelineno-102-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">quadraticRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.dart</span><pre><span></span><code><a id="__codelineno-103-1" name="__codelineno-103-1" href="#__codelineno-103-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">quadraticRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.rs</span><pre><span></span><code><a id="__codelineno-104-1" name="__codelineno-104-1" href="#__codelineno-104-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">quadratic_recur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.c</span><pre><span></span><code><a id="__codelineno-105-1" name="__codelineno-105-1" href="#__codelineno-105-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">quadraticRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.kt</span><pre><span></span><code><a id="__codelineno-106-1" name="__codelineno-106-1" href="#__codelineno-106-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">quadraticRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.rb</span><pre><span></span><code><a id="__codelineno-107-1" name="__codelineno-107-1" href="#__codelineno-107-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">quadratic_recur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.zig</span><pre><span></span><code><a id="__codelineno-108-1" name="__codelineno-108-1" href="#__codelineno-108-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">quadraticRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p><a class="glightbox" href="../space_complexity.assets/space_complexity_recursive_quadratic.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Recursive function generating quadratic order space complexity" class="animation-figure" src="../space_complexity.assets/space_complexity_recursive_quadratic.png" /></a></p>
+<p align="center"> 図 2-18 &nbsp; Recursive function generating quadratic order space complexity </p>
+
+<h3 id="4-o2n">4. &nbsp; 指数オーダー <span class="arithmatex">\(O(2^n)\)</span><a class="headerlink" href="#4-o2n" title="Permanent link">&para;</a></h3>
+<p>指数オーダーは二分木で一般的です。下図を観察すると、<span class="arithmatex">\(n\)</span>レベルの「完全二分木」は<span class="arithmatex">\(2^n - 1\)</span>個のノードを持ち、<span class="arithmatex">\(O(2^n)\)</span>の空間を占有します：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="9:14"><input checked="checked" id="__tabbed_9_1" name="__tabbed_9" type="radio" /><input id="__tabbed_9_2" name="__tabbed_9" type="radio" /><input id="__tabbed_9_3" name="__tabbed_9" type="radio" /><input id="__tabbed_9_4" name="__tabbed_9" type="radio" /><input id="__tabbed_9_5" name="__tabbed_9" type="radio" /><input id="__tabbed_9_6" name="__tabbed_9" type="radio" /><input id="__tabbed_9_7" name="__tabbed_9" type="radio" /><input id="__tabbed_9_8" name="__tabbed_9" type="radio" /><input id="__tabbed_9_9" name="__tabbed_9" type="radio" /><input id="__tabbed_9_10" name="__tabbed_9" type="radio" /><input id="__tabbed_9_11" name="__tabbed_9" type="radio" /><input id="__tabbed_9_12" name="__tabbed_9" type="radio" /><input id="__tabbed_9_13" name="__tabbed_9" type="radio" /><input id="__tabbed_9_14" name="__tabbed_9" type="radio" /><div class="tabbed-labels"><label for="__tabbed_9_1">Python</label><label for="__tabbed_9_2">C++</label><label for="__tabbed_9_3">Java</label><label for="__tabbed_9_4">C#</label><label for="__tabbed_9_5">Go</label><label for="__tabbed_9_6">Swift</label><label for="__tabbed_9_7">JS</label><label for="__tabbed_9_8">TS</label><label for="__tabbed_9_9">Dart</label><label for="__tabbed_9_10">Rust</label><label for="__tabbed_9_11">C</label><label for="__tabbed_9_12">Kotlin</label><label for="__tabbed_9_13">Ruby</label><label for="__tabbed_9_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.py</span><pre><span></span><code><a id="__codelineno-109-1" name="__codelineno-109-1" href="#__codelineno-109-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">build_tree</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-109-2" name="__codelineno-109-2" href="#__codelineno-109-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;指数複雑度（完全二分木の構築）&quot;&quot;&quot;</span>
+<a id="__codelineno-109-3" name="__codelineno-109-3" href="#__codelineno-109-3"></a>    <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
+<a id="__codelineno-109-4" name="__codelineno-109-4" href="#__codelineno-109-4"></a>        <span class="k">return</span> <span class="kc">None</span>
+<a id="__codelineno-109-5" name="__codelineno-109-5" href="#__codelineno-109-5"></a>    <span class="n">root</span> <span class="o">=</span> <span class="n">TreeNode</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-109-6" name="__codelineno-109-6" href="#__codelineno-109-6"></a>    <span class="n">root</span><span class="o">.</span><span class="n">left</span> <span class="o">=</span> <span class="n">build_tree</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-109-7" name="__codelineno-109-7" href="#__codelineno-109-7"></a>    <span class="n">root</span><span class="o">.</span><span class="n">right</span> <span class="o">=</span> <span class="n">build_tree</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-109-8" name="__codelineno-109-8" href="#__codelineno-109-8"></a>    <span class="k">return</span> <span class="n">root</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.cpp</span><pre><span></span><code><a id="__codelineno-110-1" name="__codelineno-110-1" href="#__codelineno-110-1"></a><span class="cm">/* 指数計算量（完全二分木の構築） */</span>
+<a id="__codelineno-110-2" name="__codelineno-110-2" href="#__codelineno-110-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">buildTree</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-110-3" name="__codelineno-110-3" href="#__codelineno-110-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-110-4" name="__codelineno-110-4" href="#__codelineno-110-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">nullptr</span><span class="p">;</span>
+<a id="__codelineno-110-5" name="__codelineno-110-5" href="#__codelineno-110-5"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-110-6" name="__codelineno-110-6" href="#__codelineno-110-6"></a><span class="w">    </span><span class="n">root</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buildTree</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-110-7" name="__codelineno-110-7" href="#__codelineno-110-7"></a><span class="w">    </span><span class="n">root</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buildTree</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-110-8" name="__codelineno-110-8" href="#__codelineno-110-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
+<a id="__codelineno-110-9" name="__codelineno-110-9" href="#__codelineno-110-9"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.java</span><pre><span></span><code><a id="__codelineno-111-1" name="__codelineno-111-1" href="#__codelineno-111-1"></a><span class="cm">/* 指数計算量（完全二分木の構築） */</span>
+<a id="__codelineno-111-2" name="__codelineno-111-2" href="#__codelineno-111-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="nf">buildTree</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-111-3" name="__codelineno-111-3" href="#__codelineno-111-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-111-4" name="__codelineno-111-4" href="#__codelineno-111-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-111-5" name="__codelineno-111-5" href="#__codelineno-111-5"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-111-6" name="__codelineno-111-6" href="#__codelineno-111-6"></a><span class="w">    </span><span class="n">root</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buildTree</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-111-7" name="__codelineno-111-7" href="#__codelineno-111-7"></a><span class="w">    </span><span class="n">root</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buildTree</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-111-8" name="__codelineno-111-8" href="#__codelineno-111-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
+<a id="__codelineno-111-9" name="__codelineno-111-9" href="#__codelineno-111-9"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.cs</span><pre><span></span><code><a id="__codelineno-112-1" name="__codelineno-112-1" href="#__codelineno-112-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">space_complexity</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">BuildTree</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.go</span><pre><span></span><code><a id="__codelineno-113-1" name="__codelineno-113-1" href="#__codelineno-113-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">buildTree</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.swift</span><pre><span></span><code><a id="__codelineno-114-1" name="__codelineno-114-1" href="#__codelineno-114-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">buildTree</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.js</span><pre><span></span><code><a id="__codelineno-115-1" name="__codelineno-115-1" href="#__codelineno-115-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">buildTree</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.ts</span><pre><span></span><code><a id="__codelineno-116-1" name="__codelineno-116-1" href="#__codelineno-116-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">buildTree</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.dart</span><pre><span></span><code><a id="__codelineno-117-1" name="__codelineno-117-1" href="#__codelineno-117-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">buildTree</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.rs</span><pre><span></span><code><a id="__codelineno-118-1" name="__codelineno-118-1" href="#__codelineno-118-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">build_tree</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.c</span><pre><span></span><code><a id="__codelineno-119-1" name="__codelineno-119-1" href="#__codelineno-119-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">buildTree</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.kt</span><pre><span></span><code><a id="__codelineno-120-1" name="__codelineno-120-1" href="#__codelineno-120-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">buildTree</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.rb</span><pre><span></span><code><a id="__codelineno-121-1" name="__codelineno-121-1" href="#__codelineno-121-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">build_tree</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">space_complexity.zig</span><pre><span></span><code><a id="__codelineno-122-1" name="__codelineno-122-1" href="#__codelineno-122-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">buildTree</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p><a class="glightbox" href="../space_complexity.assets/space_complexity_exponential.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Full binary tree generating exponential order space complexity" class="animation-figure" src="../space_complexity.assets/space_complexity_exponential.png" /></a></p>
+<p align="center"> 図 2-19 &nbsp; Full binary tree generating exponential order space complexity </p>
+
+<h3 id="5-olog-n">5. &nbsp; 対数オーダー <span class="arithmatex">\(O(\log n)\)</span><a class="headerlink" href="#5-olog-n" title="Permanent link">&para;</a></h3>
+<p>対数オーダーは分割統治アルゴリズムで一般的です。例えば、マージソートでは、長さ<span class="arithmatex">\(n\)</span>の配列が各ラウンドで再帰的に半分に分割され、高さ<span class="arithmatex">\(\log n\)</span>の再帰木を形成し、<span class="arithmatex">\(O(\log n)\)</span>のスタックフレーム空間を使用します。</p>
+<p>別の例は、数値を文字列に変換することです。正の整数<span class="arithmatex">\(n\)</span>が与えられた場合、その桁数は<span class="arithmatex">\(\log_{10} n + 1\)</span>で、文字列の長さに対応するため、空間計算量は<span class="arithmatex">\(O(\log_{10} n + 1) = O(\log n)\)</span>です。</p>
+<h2 id="244">2.4.4 &nbsp; 時間と空間のバランス<a class="headerlink" href="#244" title="Permanent link">&para;</a></h2>
+<p>理想的には、時間計算量と空間計算量の両方が最適であることを目指します。しかし、実際には両方を同時に最適化することはしばしば困難です。</p>
+<p><strong>時間計算量を下げることは通常、空間計算量の増加を代償とし、その逆も同様です</strong>。アルゴリズムの速度を向上させるためにメモリ空間を犠牲にするアプローチは「時空トレードオフ」として知られ、その逆は「空時トレードオフ」として知られています。</p>
+<p>選択は、どちらの側面をより重視するかに依存します。ほとんどの場合、時間は空間よりも貴重であるため、「時空トレードオフ」がより一般的な戦略です。もちろん、大量のデータを扱う際は空間計算量を制御することも非常に重要です。</p>
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+  
+  <span class="md-ellipsis">
+    はじめに
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+            はじめに
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M21 4H3a2 2 0 0 0-2 2v13a2 2 0 0 0 2 2h18a2 2 0 0 0 2-2V6a2 2 0 0 0-2-2M3 19V6h8v13H3m18 0h-8V6h8v13m-7-9.5h6V11h-6V9.5m0 2.5h6v1.5h-6V12m0 2.5h6V16h-6v-1.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 0 章 &nbsp; 前書き
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+            第 0 章 &nbsp; 前書き
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+            
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+  
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+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/about_the_book/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.1 &nbsp; この本について
+  </span>
+  
+
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+
+              
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+  
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+    <li class="md-nav__item">
+      <a href="../../chapter_preface/suggestions/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    0.2 &nbsp; 本書の使い方
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.3 &nbsp; まとめ
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+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_introduction/" class="md-nav__link ">
+              
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
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+            第 1 章 &nbsp; アルゴリズムとの出会い
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+      <a href="../../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
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+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
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+  
+
+              
+            
+              
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+  
+  
+  
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+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
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+    </li>
+  
+
+              
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+        </nav>
+      
+    </li>
+  
+
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+      
+      
+  
+  
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+  
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+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
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+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
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+            
+              
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+              
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+  
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+  
+    <li class="md-nav__item">
+      <a href="../performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
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+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
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+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
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+    2.5 &nbsp; まとめ
+  </span>
+  
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+      
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+
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+  
+  
+  
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+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 重要なレビュー
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#2-q-a" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; Q &amp; A
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+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
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+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
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+            
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
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+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
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+  
+
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+      
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+          
+        
+      
+    
+    
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+    
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+      
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+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_19" >
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+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_reference/" class="md-nav__link ">
+              
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9 3v15h3V3H9m3 2 4 13 3-1-4-13-3 1M5 5v13h3V5H5M3 19v2h18v-2H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    参考文献
+  </span>
+  
+
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+            
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+              <div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
+                <div class="md-sidebar__scrollwrap">
+                  <div class="md-sidebar__inner">
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+  
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+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 重要なレビュー
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#2-q-a" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; Q &amp; A
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+  
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+                </div>
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+<h1 id="25">2.5 &nbsp; まとめ<a class="headerlink" href="#25" title="Permanent link">&para;</a></h1>
+<h3 id="1">1. &nbsp; 重要なレビュー<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<p><strong>アルゴリズム効率評価</strong></p>
+<ul>
+<li>時間効率と空間効率は、アルゴリズムの優劣を評価する2つの主要な基準です。</li>
+<li>実際のテストによってアルゴリズムの効率を評価できますが、テスト環境の影響を排除することは困難で、大量の計算リソースを消費します。</li>
+<li>複雑度分析は実際のテストの欠点を克服できます。その結果はすべての動作プラットフォームに適用でき、異なるデータスケールでのアルゴリズムの効率を明らかにできます。</li>
+</ul>
+<p><strong>時間計算量</strong></p>
+<ul>
+<li>時間計算量は、データ量の増加に伴うアルゴリズムの実行時間の傾向を測定し、アルゴリズムの効率を効果的に評価します。しかし、入力データ量が少ない場合や時間計算量が同じ場合など、特定のケースでは失敗することがあり、アルゴリズムの効率を正確に比較することが困難になります。</li>
+<li>最悪ケース時間計算量はビッグ<span class="arithmatex">\(O\)</span>記法を使用して表記され、漸近上限を表し、<span class="arithmatex">\(n\)</span>が無限大に近づくにつれての操作数<span class="arithmatex">\(T(n)\)</span>の増加レベルを反映します。</li>
+<li>時間計算量の計算には2つのステップが含まれます：まず操作数をカウントし、次に漸近上限を決定します。</li>
+<li>一般的な時間計算量は、低いものから高いものへと並べると、<span class="arithmatex">\(O(1)\)</span>、<span class="arithmatex">\(O(\log n)\)</span>、<span class="arithmatex">\(O(n)\)</span>、<span class="arithmatex">\(O(n \log n)\)</span>、<span class="arithmatex">\(O(n^2)\)</span>、<span class="arithmatex">\(O(2^n)\)</span>、<span class="arithmatex">\(O(n!)\)</span>などが含まれます。</li>
+<li>一部のアルゴリズムの時間計算量は固定されておらず、入力データの分布に依存します。時間計算量は最悪、最良、平均のケースに分けられます。最良ケースは、入力データが最良ケースを達成するために厳格な条件を満たす必要があるため、ほとんど使用されません。</li>
+<li>平均時間計算量は、ランダムデータ入力下でのアルゴリズムの効率を反映し、実際のアプリケーションでのアルゴリズムの性能に密接に類似しています。平均時間計算量の計算には、入力データの分布とその後の数学的期待値を考慮する必要があります。</li>
+</ul>
+<p><strong>空間計算量</strong></p>
+<ul>
+<li>空間計算量は、時間計算量と同様に、データ量の増加に伴うアルゴリズムが占有するメモリ空間の傾向を測定します。</li>
+<li>アルゴリズムの実行中に使用される関連メモリ空間は、入力空間、一時空間、出力空間に分けることができます。一般的に、入力空間は空間計算量の計算に含まれません。一時空間は一時データ、スタックフレーム空間、命令空間に分けることができ、スタックフレーム空間は通常、再帰関数でのみ空間計算量に影響します。</li>
+<li>通常は最悪ケース空間計算量のみに焦点を当てます。これは、最悪の入力データと操作の最悪の瞬間でのアルゴリズムの空間計算量を計算することを意味します。</li>
+<li>一般的な空間計算量は、低いものから高いものへと並べると、<span class="arithmatex">\(O(1)\)</span>、<span class="arithmatex">\(O(\log n)\)</span>、<span class="arithmatex">\(O(n)\)</span>、<span class="arithmatex">\(O(n^2)\)</span>、<span class="arithmatex">\(O(2^n)\)</span>などが含まれます。</li>
+</ul>
+<h3 id="2-q-a">2. &nbsp; Q &amp; A<a class="headerlink" href="#2-q-a" title="Permanent link">&para;</a></h3>
+<p><strong>Q</strong>: 末尾再帰の空間計算量は<span class="arithmatex">\(O(1)\)</span>ですか？</p>
+<p>理論的には、末尾再帰関数の空間計算量は<span class="arithmatex">\(O(1)\)</span>に最適化できます。しかし、ほとんどのプログラミング言語（Java、Python、C++、Go、C#など）は末尾再帰の自動最適化をサポートしていないため、一般的に空間計算量は<span class="arithmatex">\(O(n)\)</span>と考えられています。</p>
+<p><strong>Q</strong>: 「関数」と「メソッド」という用語の違いは何ですか？</p>
+<p><u>関数</u>は独立して実行でき、すべてのパラメータが明示的に渡されます。<u>メソッド</u>はオブジェクトに関連付けられ、それを呼び出すオブジェクトに暗黙的に渡され、クラスのインスタンス内に含まれるデータを操作できます。</p>
+<p>一般的なプログラミング言語からの例をいくつか示します：</p>
+<ul>
+<li>Cは手続き型プログラミング言語で、オブジェクト指向の概念がないため、関数のみがあります。しかし、構造体（struct）を作成することでオブジェクト指向プログラミングをシミュレートでき、これらの構造体に関連付けられた関数は他のプログラミング言語のメソッドと同等です。</li>
+<li>JavaとC#はオブジェクト指向プログラミング言語で、コードブロック（メソッド）は通常クラスの一部です。静的メソッドはクラスにバインドされ、特定のインスタンス変数にアクセスできないため、関数のように動作します。</li>
+<li>C++とPythonは手続き型プログラミング（関数）とオブジェクト指向プログラミング（メソッド）の両方をサポートしています。</li>
+</ul>
+<p><strong>Q</strong>: 「空間計算量の一般的な種類」の図は、占有空間の絶対サイズを反映していますか？</p>
+<p>いいえ、図は空間計算量を示しており、これは増加傾向を反映するものであり、占有空間の絶対サイズではありません。</p>
+<p><span class="arithmatex">\(n = 8\)</span>を取ると、各曲線の値がその関数に対応していないことに気づくかもしれません。これは、各曲線に定数項が含まれているためで、値の範囲を視覚的に快適な範囲に圧縮することを意図しています。</p>
+<p>実際には、通常は各メソッドの「定数項」複雑度を知らないため、複雑度のみに基づいて<span class="arithmatex">\(n = 8\)</span>の最良ソリューションを選択することは一般的に不可能です。しかし、<span class="arithmatex">\(n = 8^5\)</span>の場合、増加傾向が支配的になるため、選択がはるかに容易になります。</p>
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+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_1" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hello_algo/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m13.13 22.19-1.63-3.83c1.57-.58 3.04-1.36 4.4-2.27l-2.77 6.1M5.64 12.5l-3.83-1.63 6.1-2.77C7 9.46 6.22 10.93 5.64 12.5M19.22 4c.28 0 .53 0 .74.05.17 1.39-.02 4.25-3.3 7.53-1.7 1.71-3.73 3.02-6.01 3.89l-2.15-2.1c.92-2.31 2.23-4.34 3.92-6.03C15.18 4.58 17.64 4 19.22 4m0-2c-1.98 0-4.98.69-8.22 3.93-2.19 2.19-3.5 4.6-4.35 6.71-.28.75-.09 1.57.46 2.13l2.13 2.12c.38.38.89.61 1.42.61.23 0 .47-.06.7-.15A19.1 19.1 0 0 0 18.07 13c5.66-5.66 3.54-10.61 3.54-10.61S20.7 2 19.22 2m-4.68 7.46c-.78-.78-.78-2.05 0-2.83s2.05-.78 2.83 0c.77.78.78 2.05 0 2.83-.78.78-2.05.78-2.83 0m-5.66 7.07-1.41-1.41 1.41 1.41M6.24 22l3.64-3.64c-.34-.09-.67-.24-.97-.45L4.83 22h1.41M2 22h1.41l4.77-4.76-1.42-1.41L2 20.59V22m0-2.83 4.09-4.08c-.21-.3-.36-.62-.45-.97L2 17.76v1.41Z"/></svg>
+  
+  <span class="md-ellipsis">
+    はじめに
+  </span>
+  
+
+            </a>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_1_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_1">
+            <span class="md-nav__icon md-icon"></span>
+            はじめに
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
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+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_2" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_preface/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M21 4H3a2 2 0 0 0-2 2v13a2 2 0 0 0 2 2h18a2 2 0 0 0 2-2V6a2 2 0 0 0-2-2M3 19V6h8v13H3m18 0h-8V6h8v13m-7-9.5h6V11h-6V9.5m0 2.5h6v1.5h-6V12m0 2.5h6V16h-6v-1.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 0 章 &nbsp; 前書き
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_2" id="__nav_2_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_2_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_2">
+            <span class="md-nav__icon md-icon"></span>
+            第 0 章 &nbsp; 前書き
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/about_the_book/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.1 &nbsp; この本について
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/suggestions/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.2 &nbsp; 本書の使い方
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_introduction/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#231" class="md-nav__link">
+    <span class="md-ellipsis">
+      2.3.1 &nbsp; 時間増加傾向の評価
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#232" class="md-nav__link">
+    <span class="md-ellipsis">
+      2.3.2 &nbsp; 漸近上限
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#233" class="md-nav__link">
+    <span class="md-ellipsis">
+      2.3.3 &nbsp; 計算方法
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="2.3.3   計算方法">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1-1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; ステップ1: 操作数のカウント
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2-2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; ステップ2: 漸近上限の決定
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#234" class="md-nav__link">
+    <span class="md-ellipsis">
+      2.3.4 &nbsp; 一般的な時間計算量の種類
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="2.3.4   一般的な時間計算量の種類">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1-o1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 定数オーダー
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2-on" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; 線形オーダー
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#3-on2" class="md-nav__link">
+    <span class="md-ellipsis">
+      3. &nbsp; 二次オーダー
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#4-o2n" class="md-nav__link">
+    <span class="md-ellipsis">
+      4. &nbsp; 指数オーダー
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#5-olog-n" class="md-nav__link">
+    <span class="md-ellipsis">
+      5. &nbsp; 対数オーダー
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#6-on-log-n" class="md-nav__link">
+    <span class="md-ellipsis">
+      6. &nbsp; 線形対数オーダー
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#7-on" class="md-nav__link">
+    <span class="md-ellipsis">
+      7. &nbsp; 階乗オーダー
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#235" class="md-nav__link">
+    <span class="md-ellipsis">
+      2.3.5 &nbsp; 最悪、最良、平均時間計算量
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
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+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
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+      
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+          
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
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+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_19" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_reference/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9 3v15h3V3H9m3 2 4 13 3-1-4-13-3 1M5 5v13h3V5H5M3 19v2h18v-2H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    参考文献
+  </span>
+  
+
+            </a>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_19_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_19">
+            <span class="md-nav__icon md-icon"></span>
+            参考文献
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+  </ul>
+</nav>
+                  </div>
+                </div>
+              </div>
+            
+            
+              
+              <div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
+                <div class="md-sidebar__scrollwrap">
+                  <div class="md-sidebar__inner">
+                    
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#231" class="md-nav__link">
+    <span class="md-ellipsis">
+      2.3.1 &nbsp; 時間増加傾向の評価
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#232" class="md-nav__link">
+    <span class="md-ellipsis">
+      2.3.2 &nbsp; 漸近上限
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#233" class="md-nav__link">
+    <span class="md-ellipsis">
+      2.3.3 &nbsp; 計算方法
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="2.3.3   計算方法">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1-1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; ステップ1: 操作数のカウント
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2-2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; ステップ2: 漸近上限の決定
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#234" class="md-nav__link">
+    <span class="md-ellipsis">
+      2.3.4 &nbsp; 一般的な時間計算量の種類
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="2.3.4   一般的な時間計算量の種類">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1-o1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 定数オーダー
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2-on" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; 線形オーダー
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#3-on2" class="md-nav__link">
+    <span class="md-ellipsis">
+      3. &nbsp; 二次オーダー
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#4-o2n" class="md-nav__link">
+    <span class="md-ellipsis">
+      4. &nbsp; 指数オーダー
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#5-olog-n" class="md-nav__link">
+    <span class="md-ellipsis">
+      5. &nbsp; 対数オーダー
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#6-on-log-n" class="md-nav__link">
+    <span class="md-ellipsis">
+      6. &nbsp; 線形対数オーダー
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#7-on" class="md-nav__link">
+    <span class="md-ellipsis">
+      7. &nbsp; 階乗オーダー
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#235" class="md-nav__link">
+    <span class="md-ellipsis">
+      2.3.5 &nbsp; 最悪、最良、平均時間計算量
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+                  </div>
+                </div>
+              </div>
+            
+          
+          
+            <div class="md-content" data-md-component="content">
+              <article class="md-content__inner md-typeset">
+                
+                  <!-- Tags -->
+
+
+<!-- Actions -->
+<!-- Actions -->
+
+
+  <!-- Edit button -->
+  
+    <a
+      href="https://github.com/krahets/hello-algo/tree/main/ja/docs/chapter_computational_complexity/time_complexity.md"
+      title="編集"
+      class="md-content__button md-icon"
+    >
+      
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
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+<h1 id="23">2.3 &nbsp; 時間計算量<a class="headerlink" href="#23" title="Permanent link">&para;</a></h1>
+<p>実行時間は、アルゴリズムの効率を直感的に評価できます。アルゴリズムの実行時間を正確に推定するにはどうすればよいでしょうか？</p>
+<ol>
+<li><strong>実行プラットフォームの決定</strong>: これには、ハードウェア構成、プログラミング言語、システム環境などが含まれ、これらすべてがコードの実行効率に影響する可能性があります。</li>
+<li><strong>様々な計算操作の実行時間の評価</strong>: 例えば、加算操作<code>+</code>は1 ns、乗算操作<code>*</code>は10 ns、印刷操作<code>print()</code>は5 nsなどかかる可能性があります。</li>
+<li><strong>コード内のすべての計算操作をカウント</strong>: これらすべての操作の実行時間を合計すると、総実行時間が得られます。</li>
+</ol>
+<p>例えば、入力サイズが<span class="arithmatex">\(n\)</span>の以下のコードを考えてみましょう：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="c1"># 特定の操作プラットフォーム下で</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="n">a</span> <span class="o">=</span> <span class="mi">2</span>      <span class="c1"># 1 ns</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="n">a</span> <span class="o">=</span> <span class="n">a</span> <span class="o">+</span> <span class="mi">1</span>  <span class="c1"># 1 ns</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="n">a</span> <span class="o">=</span> <span class="n">a</span> <span class="o">*</span> <span class="mi">2</span>  <span class="c1"># 10 ns</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="c1"># n回ループ</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>    <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>  <span class="c1"># 1 ns</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>        <span class="nb">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>        <span class="c1"># 5 ns</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="c1">// 特定の操作プラットフォーム下で</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w">  </span><span class="c1">// 1 ns</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// 1 ns</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w">  </span><span class="c1">// 10 ns</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="c1">// n回ループ</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w">  </span><span class="c1">// 1 ns, 毎回i++が実行される</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">        </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span><span class="w">         </span><span class="c1">// 5 ns</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="c1">// 特定の操作プラットフォーム下で</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w">  </span><span class="c1">// 1 ns</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// 1 ns</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w">  </span><span class="c1">// 10 ns</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="c1">// n回ループ</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w">  </span><span class="c1">// 1 ns, 毎回i++が実行される</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">        </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span><span class="w">     </span><span class="c1">// 5 ns</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="c1">// 特定の操作プラットフォーム下で</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">Algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w">  </span><span class="c1">// 1 ns</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// 1 ns</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w">  </span><span class="c1">// 10 ns</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">    </span><span class="c1">// n回ループ</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w">  </span><span class="c1">// 1 ns, 毎回i++が実行される</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w">        </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span><span class="w">      </span><span class="c1">// 5 ns</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="c1">// 特定の操作プラットフォーム下で</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">2</span><span class="w">     </span><span class="c1">// 1 ns</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w">  </span><span class="c1">// 1 ns</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="w">  </span><span class="c1">// 10 ns</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w">    </span><span class="c1">// n回ループ</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span><span class="w">  </span><span class="c1">// 1 ns</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w">        </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="nx">a</span><span class="p">)</span><span class="w">        </span><span class="c1">// 5 ns</span>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="c1">// 特定の操作プラットフォーム下で</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="c1">// 1 ns</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1">// 1 ns</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="c1">// 10 ns</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">    </span><span class="c1">// n回ループ</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 1 ns</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w">        </span><span class="bp">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="c1">// 5 ns</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="c1">// 特定の操作プラットフォーム下で</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 1 ns</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 1 ns</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 10 ns</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">    </span><span class="c1">// n回ループ</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w">    </span><span class="k">for</span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 1 ns, 毎回i++が実行される</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w">        </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// 5 ns</span>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="c1">// 特定の操作プラットフォーム下で</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nx">a</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 1 ns</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 1 ns</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 10 ns</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">    </span><span class="c1">// n回ループ</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w">    </span><span class="k">for</span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 1 ns, 毎回i++が実行される</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w">        </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// 5 ns</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="c1">// 特定の操作プラットフォーム下で</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 1 ns</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 1 ns</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">  </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="m">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 10 ns</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w">  </span><span class="c1">// n回ループ</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 1 ns, 毎回i++が実行される</span>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="w">    </span><span class="n">print</span><span class="p">(</span><span class="m">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// 5 ns</span>
+<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="c1">// 特定の操作プラットフォーム下で</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w">      </span><span class="c1">// 1 ns</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">          </span><span class="c1">// 1 ns</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w">          </span><span class="c1">// 10 ns</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">    </span><span class="c1">// n回ループ</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span><span class="w">     </span><span class="c1">// 毎回i++で1 ns</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w">        </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;{}&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span><span class="w">  </span><span class="c1">// 5 ns</span>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="c1">// 特定の操作プラットフォーム下で</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w">  </span><span class="c1">// 1 ns</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// 1 ns</span>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w">  </span><span class="c1">// 10 ns</span>
+<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w">    </span><span class="c1">// n回ループ</span>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w">   </span><span class="c1">// 1 ns, 毎回i++が実行される</span>
+<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="w">        </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;%d&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span><span class="w">            </span><span class="c1">// 5 ns</span>
+<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">// 特定の操作プラットフォーム下で</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">algorithm</span><span class="p">(</span><span class="n">n</span><span class="o">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="w">    </span><span class="kr">var</span><span class="w"> </span><span class="n">a</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 1 ns</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 1 ns</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 10 ns</span>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="w">    </span><span class="c1">// n回ループ</span>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="p">..</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="o">|</span><span class="n">_</span><span class="o">|</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 1 ns</span>
+<a id="__codelineno-12-8" name="__codelineno-12-8" href="#__codelineno-12-8"></a><span class="w">        </span><span class="n">std</span><span class="p">.</span><span class="n">debug</span><span class="p">.</span><span class="n">print</span><span class="p">(</span><span class="s">&quot;{}</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">,</span><span class="w"> </span><span class="p">.{</span><span class="mi">0</span><span class="p">});</span><span class="w"> </span><span class="c1">// 5 ns</span>
+<a id="__codelineno-12-9" name="__codelineno-12-9" href="#__codelineno-12-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-12-10" name="__codelineno-12-10" href="#__codelineno-12-10"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>上記の方法を使用すると、アルゴリズムの実行時間は<span class="arithmatex">\((6n + 12)\)</span> nsとして計算できます：</p>
+<div class="arithmatex">\[
+1 + 1 + 10 + (1 + 5) \times n = 6n + 12
+\]</div>
+<p>しかし、実際には、<strong>アルゴリズムの実行時間をカウントすることは実用的でも合理的でもありません</strong>。第一に、推定時間を実行プラットフォームに結び付けたくありません。アルゴリズムは様々なプラットフォームで実行される必要があるからです。第二に、各種操作の実行時間を知ることは困難であり、推定プロセスを難しくします。</p>
+<h2 id="231">2.3.1 &nbsp; 時間増加傾向の評価<a class="headerlink" href="#231" title="Permanent link">&para;</a></h2>
+<p>時間計算量分析は、アルゴリズムの実行時間をカウントするのではなく、**データ量が増加するにつれての実行時間の増加傾向**を分析します。</p>
+<p>この「時間増加傾向」の概念を例で理解しましょう。入力データサイズを<span class="arithmatex">\(n\)</span>とし、3つのアルゴリズム<code>A</code>、<code>B</code>、<code>C</code>を考えてみます：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:13"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="c1"># アルゴリズムAの時間計算量：定数オーダー</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="k">def</span><span class="w"> </span><span class="nf">algorithm_A</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>    <span class="nb">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a><span class="c1"># アルゴリズムBの時間計算量：線形オーダー</span>
+<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a><span class="k">def</span><span class="w"> </span><span class="nf">algorithm_B</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a>    <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
+<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a>        <span class="nb">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a><span class="c1"># アルゴリズムCの時間計算量：定数オーダー</span>
+<a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a><span class="k">def</span><span class="w"> </span><span class="nf">algorithm_C</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a>    <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1000000</span><span class="p">):</span>
+<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a>        <span class="nb">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="c1">// アルゴリズムAの時間計算量：定数オーダー</span>
+<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm_A</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">    </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="p">}</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="c1">// アルゴリズムBの時間計算量：線形オーダー</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm_B</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w">        </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
+<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="p">}</span>
+<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="c1">// アルゴリズムCの時間計算量：定数オーダー</span>
+<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm_C</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">1000000</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="w">        </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
+<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="c1">// アルゴリズムAの時間計算量：定数オーダー</span>
+<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm_A</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="p">}</span>
+<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="c1">// アルゴリズムBの時間計算量：線形オーダー</span>
+<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm_B</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">        </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="p">}</span>
+<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="c1">// アルゴリズムCの時間計算量：定数オーダー</span>
+<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm_C</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">1000000</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="w">        </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="c1">// アルゴリズムAの時間計算量：定数オーダー</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="k">void</span><span class="w"> </span><span class="nf">AlgorithmA</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="p">}</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="c1">// アルゴリズムBの時間計算量：線形オーダー</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="k">void</span><span class="w"> </span><span class="nf">AlgorithmB</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">        </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="p">}</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="c1">// アルゴリズムCの時間計算量：定数オーダー</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="k">void</span><span class="w"> </span><span class="nf">AlgorithmC</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">1000000</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="w">        </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="c1">// アルゴリズムAの時間計算量：定数オーダー</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="kd">func</span><span class="w"> </span><span class="nx">algorithm_A</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="w">    </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="p">}</span>
+<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="c1">// アルゴリズムBの時間計算量：線形オーダー</span>
+<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="kd">func</span><span class="w"> </span><span class="nx">algorithm_B</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="w">        </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="p">}</span>
+<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="c1">// アルゴリズムCの時間計算量：定数オーダー</span>
+<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="kd">func</span><span class="w"> </span><span class="nx">algorithm_C</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="mi">1000000</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-14" name="__codelineno-17-14" href="#__codelineno-17-14"></a><span class="w">        </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-17-15" name="__codelineno-17-15" href="#__codelineno-17-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-17-16" name="__codelineno-17-16" href="#__codelineno-17-16"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="c1">// アルゴリズムAの時間計算量：定数オーダー</span>
+<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="kd">func</span><span class="w"> </span><span class="nf">algorithmA</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="w">    </span><span class="bp">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="p">}</span>
+<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a>
+<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="c1">// アルゴリズムBの時間計算量：線形オーダー</span>
+<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="kd">func</span><span class="w"> </span><span class="nf">algorithmB</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="w">        </span><span class="bp">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="p">}</span>
+<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a>
+<a id="__codelineno-18-13" name="__codelineno-18-13" href="#__codelineno-18-13"></a><span class="c1">// アルゴリズムCの時間計算量：定数オーダー</span>
+<a id="__codelineno-18-14" name="__codelineno-18-14" href="#__codelineno-18-14"></a><span class="kd">func</span><span class="w"> </span><span class="nf">algorithmC</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-15" name="__codelineno-18-15" href="#__codelineno-18-15"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="mi">1_000_000</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-16" name="__codelineno-18-16" href="#__codelineno-18-16"></a><span class="w">        </span><span class="bp">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-18-17" name="__codelineno-18-17" href="#__codelineno-18-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-18-18" name="__codelineno-18-18" href="#__codelineno-18-18"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="c1">// アルゴリズムAの時間計算量：定数オーダー</span>
+<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm_A</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="w">    </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="p">}</span>
+<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="c1">// アルゴリズムBの時間計算量：線形オーダー</span>
+<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm_B</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a><span class="w">        </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a><span class="p">}</span>
+<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="c1">// アルゴリズムCの時間計算量：定数オーダー</span>
+<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm_C</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">1000000</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-14" name="__codelineno-19-14" href="#__codelineno-19-14"></a><span class="w">        </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-19-15" name="__codelineno-19-15" href="#__codelineno-19-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-19-16" name="__codelineno-19-16" href="#__codelineno-19-16"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="c1">// アルゴリズムAの時間計算量：定数オーダー</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm_A</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="w">    </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="p">}</span>
+<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="c1">// アルゴリズムBの時間計算量：線形オーダー</span>
+<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm_B</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="w">        </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a><span class="p">}</span>
+<a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a><span class="c1">// アルゴリズムCの時間計算量：定数オーダー</span>
+<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm_C</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-13" name="__codelineno-20-13" href="#__codelineno-20-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">1000000</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-14" name="__codelineno-20-14" href="#__codelineno-20-14"></a><span class="w">        </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-20-15" name="__codelineno-20-15" href="#__codelineno-20-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-20-16" name="__codelineno-20-16" href="#__codelineno-20-16"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="c1">// アルゴリズムAの時間計算量：定数オーダー</span>
+<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="kt">void</span><span class="w"> </span><span class="n">algorithmA</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="w">  </span><span class="n">print</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
+<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="p">}</span>
+<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="c1">// アルゴリズムBの時間計算量：線形オーダー</span>
+<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a><span class="kt">void</span><span class="w"> </span><span class="n">algorithmB</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="w">    </span><span class="n">print</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
+<a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a><span class="p">}</span>
+<a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a><span class="c1">// アルゴリズムCの時間計算量：定数オーダー</span>
+<a id="__codelineno-21-12" name="__codelineno-21-12" href="#__codelineno-21-12"></a><span class="kt">void</span><span class="w"> </span><span class="n">algorithmC</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-13" name="__codelineno-21-13" href="#__codelineno-21-13"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">1000000</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-14" name="__codelineno-21-14" href="#__codelineno-21-14"></a><span class="w">    </span><span class="n">print</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
+<a id="__codelineno-21-15" name="__codelineno-21-15" href="#__codelineno-21-15"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-21-16" name="__codelineno-21-16" href="#__codelineno-21-16"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="c1">// アルゴリズムAの時間計算量：定数オーダー</span>
+<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="k">fn</span><span class="w"> </span><span class="nf">algorithm_A</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="w">    </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;{}&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="p">}</span>
+<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="c1">// アルゴリズムBの時間計算量：線形オーダー</span>
+<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="k">fn</span><span class="w"> </span><span class="nf">algorithm_B</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a><span class="w">        </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;{}&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a><span class="p">}</span>
+<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a><span class="c1">// アルゴリズムCの時間計算量：定数オーダー</span>
+<a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="k">fn</span><span class="w"> </span><span class="nf">algorithm_C</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-13" name="__codelineno-22-13" href="#__codelineno-22-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="mi">1000000</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-14" name="__codelineno-22-14" href="#__codelineno-22-14"></a><span class="w">        </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;{}&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-22-15" name="__codelineno-22-15" href="#__codelineno-22-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-22-16" name="__codelineno-22-16" href="#__codelineno-22-16"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="c1">// アルゴリズムAの時間計算量：定数オーダー</span>
+<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm_A</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="w">    </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;%d&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="p">}</span>
+<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="c1">// アルゴリズムBの時間計算量：線形オーダー</span>
+<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm_B</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="w">        </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;%d&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-10" name="__codelineno-23-10" href="#__codelineno-23-10"></a><span class="p">}</span>
+<a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a><span class="c1">// アルゴリズムCの時間計算量：定数オーダー</span>
+<a id="__codelineno-23-12" name="__codelineno-23-12" href="#__codelineno-23-12"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm_C</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-13" name="__codelineno-23-13" href="#__codelineno-23-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">1000000</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-23-14" name="__codelineno-23-14" href="#__codelineno-23-14"></a><span class="w">        </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;%d&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-23-15" name="__codelineno-23-15" href="#__codelineno-23-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-23-16" name="__codelineno-23-16" href="#__codelineno-23-16"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="c1">// アルゴリズムAの時間計算量：定数オーダー</span>
+<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="k">fn</span><span class="w"> </span><span class="n">algorithm_A</span><span class="p">(</span><span class="n">n</span><span class="o">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="w">    </span><span class="n">_</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span>
+<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="w">    </span><span class="n">std</span><span class="p">.</span><span class="n">debug</span><span class="p">.</span><span class="n">print</span><span class="p">(</span><span class="s">&quot;{}</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">,</span><span class="w"> </span><span class="p">.{</span><span class="mi">0</span><span class="p">});</span>
+<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="p">}</span>
+<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="c1">// アルゴリズムBの時間計算量：線形オーダー</span>
+<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="k">fn</span><span class="w"> </span><span class="n">algorithm_B</span><span class="p">(</span><span class="n">n</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="p">..</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="o">|</span><span class="n">_</span><span class="o">|</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="w">        </span><span class="n">std</span><span class="p">.</span><span class="n">debug</span><span class="p">.</span><span class="n">print</span><span class="p">(</span><span class="s">&quot;{}</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">,</span><span class="w"> </span><span class="p">.{</span><span class="mi">0</span><span class="p">});</span>
+<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="p">}</span>
+<a id="__codelineno-25-12" name="__codelineno-25-12" href="#__codelineno-25-12"></a><span class="c1">// アルゴリズムCの時間計算量：定数オーダー</span>
+<a id="__codelineno-25-13" name="__codelineno-25-13" href="#__codelineno-25-13"></a><span class="k">fn</span><span class="w"> </span><span class="n">algorithm_C</span><span class="p">(</span><span class="n">n</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-25-14" name="__codelineno-25-14" href="#__codelineno-25-14"></a><span class="w">    </span><span class="n">_</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span>
+<a id="__codelineno-25-15" name="__codelineno-25-15" href="#__codelineno-25-15"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="p">..</span><span class="mi">1000000</span><span class="p">)</span><span class="w"> </span><span class="o">|</span><span class="n">_</span><span class="o">|</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-25-16" name="__codelineno-25-16" href="#__codelineno-25-16"></a><span class="w">        </span><span class="n">std</span><span class="p">.</span><span class="n">debug</span><span class="p">.</span><span class="n">print</span><span class="p">(</span><span class="s">&quot;{}</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">,</span><span class="w"> </span><span class="p">.{</span><span class="mi">0</span><span class="p">});</span>
+<a id="__codelineno-25-17" name="__codelineno-25-17" href="#__codelineno-25-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-25-18" name="__codelineno-25-18" href="#__codelineno-25-18"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>下図はこれら3つのアルゴリズムの時間計算量を示しています。</p>
+<ul>
+<li>アルゴリズム<code>A</code>には1つの印刷操作のみがあり、その実行時間は<span class="arithmatex">\(n\)</span>とともに増加しません。その時間計算量は「定数オーダー」と考えられます。</li>
+<li>アルゴリズム<code>B</code>には<span class="arithmatex">\(n\)</span>回ループする印刷操作があり、その実行時間は<span class="arithmatex">\(n\)</span>と線形に増加します。その時間計算量は「線形オーダー」です。</li>
+<li>アルゴリズム<code>C</code>には1,000,000回ループする印刷操作があります。時間はかかりますが、入力データサイズ<span class="arithmatex">\(n\)</span>とは無関係です。したがって、<code>C</code>の時間計算量は<code>A</code>と同じ「定数オーダー」です。</li>
+</ul>
+<p><a class="glightbox" href="../time_complexity.assets/time_complexity_simple_example.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Time growth trend of algorithms a, b, and c" class="animation-figure" src="../time_complexity.assets/time_complexity_simple_example.png" /></a></p>
+<p align="center"> 図 2-7 &nbsp; Time growth trend of algorithms a, b, and c </p>
+
+<p>アルゴリズムの実行時間を直接カウントすることと比較して、時間計算量分析の特徴は何でしょうか？</p>
+<ul>
+<li><strong>時間計算量はアルゴリズムの効率を効果的に評価します</strong>。例えば、アルゴリズム<code>B</code>は線形に増加する実行時間を持ち、<span class="arithmatex">\(n &gt; 1\)</span>の時はアルゴリズム<code>A</code>より遅く、<span class="arithmatex">\(n &gt; 1,000,000\)</span>の時は<code>C</code>より遅くなります。実際、入力データサイズ<span class="arithmatex">\(n\)</span>が十分に大きい限り、「定数オーダー」複雑度アルゴリズムは常に「線形オーダー」よりも優れており、時間増加傾向の本質を示しています。</li>
+<li><strong>時間計算量分析はより直感的です</strong>。明らかに、実行プラットフォームと計算操作の種類は実行時間増加の傾向とは無関係です。したがって、時間計算量分析では、すべての計算操作の実行時間を同じ「単位時間」として扱うことができ、「計算操作実行時間カウント」を「計算操作カウント」に単純化できます。これにより推定の複雑さが大幅に軽減されます。</li>
+<li><strong>時間計算量には制限があります</strong>。例えば、アルゴリズム<code>A</code>と<code>C</code>は同じ時間計算量を持ちますが、実際の実行時間は大きく異なる場合があります。同様に、アルゴリズム<code>B</code>は<code>C</code>よりも高い時間計算量を持ちますが、入力データサイズ<span class="arithmatex">\(n\)</span>が小さい場合は明らかに優れています。これらの場合、時間計算量のみに基づいてアルゴリズムの効率を判断することは困難です。しかし、これらの問題にもかかわらず、複雑度分析はアルゴリズムの効率を評価するための最も効果的で一般的に使用される方法です。</li>
+</ul>
+<h2 id="232">2.3.2 &nbsp; 漸近上限<a class="headerlink" href="#232" title="Permanent link">&para;</a></h2>
+<p>入力サイズが<span class="arithmatex">\(n\)</span>の関数を考えてみましょう：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="3:13"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a>    <span class="n">a</span> <span class="o">=</span> <span class="mi">1</span>      <span class="c1"># +1</span>
+<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a>    <span class="n">a</span> <span class="o">=</span> <span class="n">a</span> <span class="o">+</span> <span class="mi">1</span>  <span class="c1"># +1</span>
+<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a>    <span class="n">a</span> <span class="o">=</span> <span class="n">a</span> <span class="o">*</span> <span class="mi">2</span>  <span class="c1"># +1</span>
+<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a>    <span class="c1"># n回ループ</span>
+<a id="__codelineno-26-6" name="__codelineno-26-6" href="#__codelineno-26-6"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>  <span class="c1"># +1</span>
+<a id="__codelineno-26-7" name="__codelineno-26-7" href="#__codelineno-26-7"></a>        <span class="nb">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>        <span class="c1"># +1</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// +1</span>
+<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// +1</span>
+<a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w">  </span><span class="c1">// +1</span>
+<a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a><span class="w">    </span><span class="c1">// n回ループ</span>
+<a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// +1 (毎回i++が実行される)</span>
+<a id="__codelineno-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a><span class="w">        </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span><span class="w">    </span><span class="c1">// +1</span>
+<a id="__codelineno-27-8" name="__codelineno-27-8" href="#__codelineno-27-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-27-9" name="__codelineno-27-9" href="#__codelineno-27-9"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// +1</span>
+<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// +1</span>
+<a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w">  </span><span class="c1">// +1</span>
+<a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a><span class="w">    </span><span class="c1">// n回ループ</span>
+<a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// +1 (毎回i++が実行される)</span>
+<a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a><span class="w">        </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span><span class="w">    </span><span class="c1">// +1</span>
+<a id="__codelineno-28-8" name="__codelineno-28-8" href="#__codelineno-28-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-9" name="__codelineno-28-9" href="#__codelineno-28-9"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="k">void</span><span class="w"> </span><span class="nf">Algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// +1</span>
+<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// +1</span>
+<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w">  </span><span class="c1">// +1</span>
+<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a><span class="w">    </span><span class="c1">// n回ループ</span>
+<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w">   </span><span class="c1">// +1 (毎回i++が実行される)</span>
+<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="w">        </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span><span class="w">   </span><span class="c1">// +1</span>
+<a id="__codelineno-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-9" name="__codelineno-29-9" href="#__codelineno-29-9"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="kd">func</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="w">      </span><span class="c1">// +1</span>
+<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w">   </span><span class="c1">// +1</span>
+<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="w">   </span><span class="c1">// +1</span>
+<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a><span class="w">    </span><span class="c1">// n回ループ</span>
+<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span><span class="w">   </span><span class="c1">// +1</span>
+<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a><span class="w">        </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="nx">a</span><span class="p">)</span><span class="w">         </span><span class="c1">// +1</span>
+<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="kd">func</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1">// +1</span>
+<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1">// +1</span>
+<a id="__codelineno-31-4" name="__codelineno-31-4" href="#__codelineno-31-4"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="c1">// +1</span>
+<a id="__codelineno-31-5" name="__codelineno-31-5" href="#__codelineno-31-5"></a><span class="w">    </span><span class="c1">// n回ループ</span>
+<a id="__codelineno-31-6" name="__codelineno-31-6" href="#__codelineno-31-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// +1</span>
+<a id="__codelineno-31-7" name="__codelineno-31-7" href="#__codelineno-31-7"></a><span class="w">        </span><span class="bp">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="c1">// +1</span>
+<a id="__codelineno-31-8" name="__codelineno-31-8" href="#__codelineno-31-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-31-9" name="__codelineno-31-9" href="#__codelineno-31-9"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
+<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
+<a id="__codelineno-32-4" name="__codelineno-32-4" href="#__codelineno-32-4"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
+<a id="__codelineno-32-5" name="__codelineno-32-5" href="#__codelineno-32-5"></a><span class="w">    </span><span class="c1">// n回ループ</span>
+<a id="__codelineno-32-6" name="__codelineno-32-6" href="#__codelineno-32-6"></a><span class="w">    </span><span class="k">for</span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">){</span><span class="w"> </span><span class="c1">// +1 (毎回i++が実行される)</span>
+<a id="__codelineno-32-7" name="__codelineno-32-7" href="#__codelineno-32-7"></a><span class="w">        </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// +1</span>
+<a id="__codelineno-32-8" name="__codelineno-32-8" href="#__codelineno-32-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-32-9" name="__codelineno-32-9" href="#__codelineno-32-9"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="p">{</span>
+<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nx">a</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
+<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
+<a id="__codelineno-33-4" name="__codelineno-33-4" href="#__codelineno-33-4"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mf">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
+<a id="__codelineno-33-5" name="__codelineno-33-5" href="#__codelineno-33-5"></a><span class="w">    </span><span class="c1">// n回ループ</span>
+<a id="__codelineno-33-6" name="__codelineno-33-6" href="#__codelineno-33-6"></a><span class="w">    </span><span class="k">for</span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">){</span><span class="w"> </span><span class="c1">// +1 (毎回i++が実行される)</span>
+<a id="__codelineno-33-7" name="__codelineno-33-7" href="#__codelineno-33-7"></a><span class="w">        </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// +1</span>
+<a id="__codelineno-33-8" name="__codelineno-33-8" href="#__codelineno-33-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-33-9" name="__codelineno-33-9" href="#__codelineno-33-9"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="kt">void</span><span class="w"> </span><span class="n">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
+<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><span class="w">  </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
+<a id="__codelineno-34-4" name="__codelineno-34-4" href="#__codelineno-34-4"></a><span class="w">  </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="m">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
+<a id="__codelineno-34-5" name="__codelineno-34-5" href="#__codelineno-34-5"></a><span class="w">  </span><span class="c1">// n回ループ</span>
+<a id="__codelineno-34-6" name="__codelineno-34-6" href="#__codelineno-34-6"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// +1 (毎回i++が実行される)</span>
+<a id="__codelineno-34-7" name="__codelineno-34-7" href="#__codelineno-34-7"></a><span class="w">    </span><span class="n">print</span><span class="p">(</span><span class="m">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// +1</span>
+<a id="__codelineno-34-8" name="__codelineno-34-8" href="#__codelineno-34-8"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-34-9" name="__codelineno-34-9" href="#__codelineno-34-9"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="k">fn</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">   </span><span class="c1">// +1</span>
+<a id="__codelineno-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">      </span><span class="c1">// +1</span>
+<a id="__codelineno-35-4" name="__codelineno-35-4" href="#__codelineno-35-4"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w">      </span><span class="c1">// +1</span>
+<a id="__codelineno-35-5" name="__codelineno-35-5" href="#__codelineno-35-5"></a>
+<a id="__codelineno-35-6" name="__codelineno-35-6" href="#__codelineno-35-6"></a><span class="w">    </span><span class="c1">// n回ループ</span>
+<a id="__codelineno-35-7" name="__codelineno-35-7" href="#__codelineno-35-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="n">n</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// +1 (毎回i++が実行される)</span>
+<a id="__codelineno-35-8" name="__codelineno-35-8" href="#__codelineno-35-8"></a><span class="w">        </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;{}&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// +1</span>
+<a id="__codelineno-35-9" name="__codelineno-35-9" href="#__codelineno-35-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-35-10" name="__codelineno-35-10" href="#__codelineno-35-10"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// +1</span>
+<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// +1</span>
+<a id="__codelineno-36-4" name="__codelineno-36-4" href="#__codelineno-36-4"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w">  </span><span class="c1">// +1</span>
+<a id="__codelineno-36-5" name="__codelineno-36-5" href="#__codelineno-36-5"></a><span class="w">    </span><span class="c1">// n回ループ</span>
+<a id="__codelineno-36-6" name="__codelineno-36-6" href="#__codelineno-36-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w">   </span><span class="c1">// +1 (毎回i++が実行される)</span>
+<a id="__codelineno-36-7" name="__codelineno-36-7" href="#__codelineno-36-7"></a><span class="w">        </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;%d&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span><span class="w">            </span><span class="c1">// +1</span>
+<a id="__codelineno-36-8" name="__codelineno-36-8" href="#__codelineno-36-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-36-9" name="__codelineno-36-9" href="#__codelineno-36-9"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="k">fn</span><span class="w"> </span><span class="n">algorithm</span><span class="p">(</span><span class="n">n</span><span class="o">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a><span class="w">    </span><span class="kr">var</span><span class="w"> </span><span class="n">a</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
+<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
+<a id="__codelineno-38-4" name="__codelineno-38-4" href="#__codelineno-38-4"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// +1</span>
+<a id="__codelineno-38-5" name="__codelineno-38-5" href="#__codelineno-38-5"></a><span class="w">    </span><span class="c1">// n回ループ</span>
+<a id="__codelineno-38-6" name="__codelineno-38-6" href="#__codelineno-38-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="mi">0</span><span class="p">..</span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="o">|</span><span class="n">_</span><span class="o">|</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// +1 (毎回i++が実行される)</span>
+<a id="__codelineno-38-7" name="__codelineno-38-7" href="#__codelineno-38-7"></a><span class="w">        </span><span class="n">std</span><span class="p">.</span><span class="n">debug</span><span class="p">.</span><span class="n">print</span><span class="p">(</span><span class="s">&quot;{}</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">,</span><span class="w"> </span><span class="p">.{</span><span class="mi">0</span><span class="p">});</span><span class="w"> </span><span class="c1">// +1</span>
+<a id="__codelineno-38-8" name="__codelineno-38-8" href="#__codelineno-38-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-38-9" name="__codelineno-38-9" href="#__codelineno-38-9"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>アルゴリズムの操作数を入力サイズ<span class="arithmatex">\(n\)</span>の関数として表す関数を<span class="arithmatex">\(T(n)\)</span>とすると、以下の例を考えてみましょう：</p>
+<div class="arithmatex">\[
+T(n) = 3 + 2n
+\]</div>
+<p><span class="arithmatex">\(T(n)\)</span>は線形関数であるため、その増加傾向は線形であり、したがって、その時間計算量は線形オーダーで、<span class="arithmatex">\(O(n)\)</span>と表記されます。この数学記法は<u>ビッグO記法</u>として知られ、関数<span class="arithmatex">\(T(n)\)</span>の<u>漸近上限</u>を表します。</p>
+<p>本質的に、時間計算量分析は「操作数<span class="arithmatex">\(T(n)\)</span>」の漸近上限を見つけることです。それには正確な数学的定義があります。</p>
+<div class="admonition note">
+<p class="admonition-title">漸近上限</p>
+<p>すべての<span class="arithmatex">\(n &gt; n_0\)</span>に対して<span class="arithmatex">\(T(n) \leq c \cdot f(n)\)</span>となるような正の実数<span class="arithmatex">\(c\)</span>と<span class="arithmatex">\(n_0\)</span>が存在する場合、<span class="arithmatex">\(f(n)\)</span>は<span class="arithmatex">\(T(n)\)</span>の漸近上限とみなされ、<span class="arithmatex">\(T(n) = O(f(n))\)</span>と表記されます。</p>
+</div>
+<p>下図に示されているように、漸近上限の計算では、<span class="arithmatex">\(n\)</span>が無限大に近づくにつれて、<span class="arithmatex">\(T(n)\)</span>と<span class="arithmatex">\(f(n)\)</span>が同じ増加オーダーを持ち、定数因子<span class="arithmatex">\(c\)</span>のみが異なるような関数<span class="arithmatex">\(f(n)\)</span>を見つけることが含まれます。</p>
+<p><a class="glightbox" href="../time_complexity.assets/asymptotic_upper_bound.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Asymptotic upper bound of a function" class="animation-figure" src="../time_complexity.assets/asymptotic_upper_bound.png" /></a></p>
+<p align="center"> 図 2-8 &nbsp; Asymptotic upper bound of a function </p>
+
+<h2 id="233">2.3.3 &nbsp; 計算方法<a class="headerlink" href="#233" title="Permanent link">&para;</a></h2>
+<p>漸近上限の概念は数学的に濃密に見えるかもしれませんが、今すぐ完全に理解する必要はありません。まず計算方法を理解し、時間をかけて練習し理解しましょう。</p>
+<p><span class="arithmatex">\(f(n)\)</span>が決まれば、時間計算量<span class="arithmatex">\(O(f(n))\)</span>が得られます。しかし、漸近上限<span class="arithmatex">\(f(n)\)</span>をどのように決定するのでしょうか？このプロセスには一般的に2つのステップが含まれます：操作数のカウントと漸近上限の決定です。</p>
+<h3 id="1-1">1. &nbsp; ステップ1: 操作数のカウント<a class="headerlink" href="#1-1" title="Permanent link">&para;</a></h3>
+<p>このステップでは、コードを行ごとに確認します。しかし、<span class="arithmatex">\(c \cdot f(n)\)</span>の定数<span class="arithmatex">\(c\)</span>の存在により、<strong><span class="arithmatex">\(T(n)\)</span>のすべての係数と定数項は無視できます</strong>。この原理により、操作をカウントする際の簡略化技法が可能になります。</p>
+<ol>
+<li><strong><span class="arithmatex">\(T(n)\)</span>の定数項を無視します</strong>。これらは<span class="arithmatex">\(n\)</span>とは無関係であるため、時間計算量に影響しません。</li>
+<li><strong>すべての係数を省略します</strong>。例えば、<span class="arithmatex">\(2n\)</span>、<span class="arithmatex">\(5n + 1\)</span>回などのループは、<span class="arithmatex">\(n\)</span>の前の係数が時間計算量に影響しないため、<span class="arithmatex">\(n\)</span>回に簡略化できます。</li>
+<li><strong>ネストしたループには乗算を使用します</strong>。総操作数は各ループの操作数の積であり、ポイント1と2の簡略化技法を各ループレベルに適用します。</li>
+</ol>
+<p>関数が与えられた場合、これらの技法を使用して操作をカウントできます：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="4:13"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><input id="__tabbed_4_6" name="__tabbed_4" type="radio" /><input id="__tabbed_4_7" name="__tabbed_4" type="radio" /><input id="__tabbed_4_8" name="__tabbed_4" type="radio" /><input id="__tabbed_4_9" name="__tabbed_4" type="radio" /><input id="__tabbed_4_10" name="__tabbed_4" type="radio" /><input id="__tabbed_4_11" name="__tabbed_4" type="radio" /><input id="__tabbed_4_12" name="__tabbed_4" type="radio" /><input id="__tabbed_4_13" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">Python</label><label for="__tabbed_4_2">C++</label><label for="__tabbed_4_3">Java</label><label for="__tabbed_4_4">C#</label><label for="__tabbed_4_5">Go</label><label for="__tabbed_4_6">Swift</label><label for="__tabbed_4_7">JS</label><label for="__tabbed_4_8">TS</label><label for="__tabbed_4_9">Dart</label><label for="__tabbed_4_10">Rust</label><label for="__tabbed_4_11">C</label><label for="__tabbed_4_12">Kotlin</label><label for="__tabbed_4_13">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a>    <span class="n">a</span> <span class="o">=</span> <span class="mi">1</span>      <span class="c1"># +0 (技法1)</span>
+<a id="__codelineno-39-3" name="__codelineno-39-3" href="#__codelineno-39-3"></a>    <span class="n">a</span> <span class="o">=</span> <span class="n">a</span> <span class="o">+</span> <span class="n">n</span>  <span class="c1"># +0 (技法1)</span>
+<a id="__codelineno-39-4" name="__codelineno-39-4" href="#__codelineno-39-4"></a>    <span class="c1"># +n (技法2)</span>
+<a id="__codelineno-39-5" name="__codelineno-39-5" href="#__codelineno-39-5"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">5</span> <span class="o">*</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-39-6" name="__codelineno-39-6" href="#__codelineno-39-6"></a>        <span class="nb">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-39-7" name="__codelineno-39-7" href="#__codelineno-39-7"></a>    <span class="c1"># +n*n (技法3)</span>
+<a id="__codelineno-39-8" name="__codelineno-39-8" href="#__codelineno-39-8"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">n</span><span class="p">):</span>
+<a id="__codelineno-39-9" name="__codelineno-39-9" href="#__codelineno-39-9"></a>        <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-39-10" name="__codelineno-39-10" href="#__codelineno-39-10"></a>            <span class="nb">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// +0 (技法1)</span>
+<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w">  </span><span class="c1">// +0 (技法1)</span>
+<a id="__codelineno-40-4" name="__codelineno-40-4" href="#__codelineno-40-4"></a><span class="w">    </span><span class="c1">// +n (技法2)</span>
+<a id="__codelineno-40-5" name="__codelineno-40-5" href="#__codelineno-40-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-40-6" name="__codelineno-40-6" href="#__codelineno-40-6"></a><span class="w">        </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
+<a id="__codelineno-40-7" name="__codelineno-40-7" href="#__codelineno-40-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-40-8" name="__codelineno-40-8" href="#__codelineno-40-8"></a><span class="w">    </span><span class="c1">// +n*n (技法3)</span>
+<a id="__codelineno-40-9" name="__codelineno-40-9" href="#__codelineno-40-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-40-10" name="__codelineno-40-10" href="#__codelineno-40-10"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-40-11" name="__codelineno-40-11" href="#__codelineno-40-11"></a><span class="w">            </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
+<a id="__codelineno-40-12" name="__codelineno-40-12" href="#__codelineno-40-12"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-40-13" name="__codelineno-40-13" href="#__codelineno-40-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-40-14" name="__codelineno-40-14" href="#__codelineno-40-14"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-41-2" name="__codelineno-41-2" href="#__codelineno-41-2"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// +0 (技法1)</span>
+<a id="__codelineno-41-3" name="__codelineno-41-3" href="#__codelineno-41-3"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w">  </span><span class="c1">// +0 (技法1)</span>
+<a id="__codelineno-41-4" name="__codelineno-41-4" href="#__codelineno-41-4"></a><span class="w">    </span><span class="c1">// +n (技法2)</span>
+<a id="__codelineno-41-5" name="__codelineno-41-5" href="#__codelineno-41-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-41-6" name="__codelineno-41-6" href="#__codelineno-41-6"></a><span class="w">        </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-41-7" name="__codelineno-41-7" href="#__codelineno-41-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-41-8" name="__codelineno-41-8" href="#__codelineno-41-8"></a><span class="w">    </span><span class="c1">// +n*n (技法3)</span>
+<a id="__codelineno-41-9" name="__codelineno-41-9" href="#__codelineno-41-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-41-10" name="__codelineno-41-10" href="#__codelineno-41-10"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-41-11" name="__codelineno-41-11" href="#__codelineno-41-11"></a><span class="w">            </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-41-12" name="__codelineno-41-12" href="#__codelineno-41-12"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-41-13" name="__codelineno-41-13" href="#__codelineno-41-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-41-14" name="__codelineno-41-14" href="#__codelineno-41-14"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="k">void</span><span class="w"> </span><span class="nf">Algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-2" name="__codelineno-42-2" href="#__codelineno-42-2"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// +0 (技法1)</span>
+<a id="__codelineno-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w">  </span><span class="c1">// +0 (技法1)</span>
+<a id="__codelineno-42-4" name="__codelineno-42-4" href="#__codelineno-42-4"></a><span class="w">    </span><span class="c1">// +n (技法2)</span>
+<a id="__codelineno-42-5" name="__codelineno-42-5" href="#__codelineno-42-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-6" name="__codelineno-42-6" href="#__codelineno-42-6"></a><span class="w">        </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-42-7" name="__codelineno-42-7" href="#__codelineno-42-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-42-8" name="__codelineno-42-8" href="#__codelineno-42-8"></a><span class="w">    </span><span class="c1">// +n*n (技法3)</span>
+<a id="__codelineno-42-9" name="__codelineno-42-9" href="#__codelineno-42-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-10" name="__codelineno-42-10" href="#__codelineno-42-10"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-42-11" name="__codelineno-42-11" href="#__codelineno-42-11"></a><span class="w">            </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-42-12" name="__codelineno-42-12" href="#__codelineno-42-12"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-42-13" name="__codelineno-42-13" href="#__codelineno-42-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-42-14" name="__codelineno-42-14" href="#__codelineno-42-14"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="kd">func</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-2" name="__codelineno-43-2" href="#__codelineno-43-2"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">1</span><span class="w">     </span><span class="c1">// +0 (技法1)</span>
+<a id="__codelineno-43-3" name="__codelineno-43-3" href="#__codelineno-43-3"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">n</span><span class="w">  </span><span class="c1">// +0 (技法1)</span>
+<a id="__codelineno-43-4" name="__codelineno-43-4" href="#__codelineno-43-4"></a><span class="w">    </span><span class="c1">// +n (技法2)</span>
+<a id="__codelineno-43-5" name="__codelineno-43-5" href="#__codelineno-43-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="mi">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-6" name="__codelineno-43-6" href="#__codelineno-43-6"></a><span class="w">        </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-43-7" name="__codelineno-43-7" href="#__codelineno-43-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-43-8" name="__codelineno-43-8" href="#__codelineno-43-8"></a><span class="w">    </span><span class="c1">// +n*n (技法3)</span>
+<a id="__codelineno-43-9" name="__codelineno-43-9" href="#__codelineno-43-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-10" name="__codelineno-43-10" href="#__codelineno-43-10"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="p">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-11" name="__codelineno-43-11" href="#__codelineno-43-11"></a><span class="w">            </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-43-12" name="__codelineno-43-12" href="#__codelineno-43-12"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-43-13" name="__codelineno-43-13" href="#__codelineno-43-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-43-14" name="__codelineno-43-14" href="#__codelineno-43-14"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="kd">func</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-2" name="__codelineno-44-2" href="#__codelineno-44-2"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="c1">// +0 (技法1)</span>
+<a id="__codelineno-44-3" name="__codelineno-44-3" href="#__codelineno-44-3"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="c1">// +0 (技法1)</span>
+<a id="__codelineno-44-4" name="__codelineno-44-4" href="#__codelineno-44-4"></a><span class="w">    </span><span class="c1">// +n (技法2)</span>
+<a id="__codelineno-44-5" name="__codelineno-44-5" href="#__codelineno-44-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="p">(</span><span class="mi">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-6" name="__codelineno-44-6" href="#__codelineno-44-6"></a><span class="w">        </span><span class="bp">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-44-7" name="__codelineno-44-7" href="#__codelineno-44-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-44-8" name="__codelineno-44-8" href="#__codelineno-44-8"></a><span class="w">    </span><span class="c1">// +n*n (技法3)</span>
+<a id="__codelineno-44-9" name="__codelineno-44-9" href="#__codelineno-44-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="p">(</span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-10" name="__codelineno-44-10" href="#__codelineno-44-10"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="kc">_</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="p">..</span><span class="o">&lt;</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-11" name="__codelineno-44-11" href="#__codelineno-44-11"></a><span class="w">            </span><span class="bp">print</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-44-12" name="__codelineno-44-12" href="#__codelineno-44-12"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-44-13" name="__codelineno-44-13" href="#__codelineno-44-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-44-14" name="__codelineno-44-14" href="#__codelineno-44-14"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-2" name="__codelineno-45-2" href="#__codelineno-45-2"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// +0 (技法1)</span>
+<a id="__codelineno-45-3" name="__codelineno-45-3" href="#__codelineno-45-3"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w">  </span><span class="c1">// +0 (技法1)</span>
+<a id="__codelineno-45-4" name="__codelineno-45-4" href="#__codelineno-45-4"></a><span class="w">    </span><span class="c1">// +n (技法2)</span>
+<a id="__codelineno-45-5" name="__codelineno-45-5" href="#__codelineno-45-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-6" name="__codelineno-45-6" href="#__codelineno-45-6"></a><span class="w">        </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-45-7" name="__codelineno-45-7" href="#__codelineno-45-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-45-8" name="__codelineno-45-8" href="#__codelineno-45-8"></a><span class="w">    </span><span class="c1">// +n*n (技法3)</span>
+<a id="__codelineno-45-9" name="__codelineno-45-9" href="#__codelineno-45-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-10" name="__codelineno-45-10" href="#__codelineno-45-10"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-45-11" name="__codelineno-45-11" href="#__codelineno-45-11"></a><span class="w">            </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-45-12" name="__codelineno-45-12" href="#__codelineno-45-12"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-45-13" name="__codelineno-45-13" href="#__codelineno-45-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-45-14" name="__codelineno-45-14" href="#__codelineno-45-14"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="kd">function</span><span class="w"> </span><span class="nx">algorithm</span><span class="p">(</span><span class="nx">n</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">)</span><span class="o">:</span><span class="w"> </span><span class="ow">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-2" name="__codelineno-46-2" href="#__codelineno-46-2"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// +0 (技法1)</span>
+<a id="__codelineno-46-3" name="__codelineno-46-3" href="#__codelineno-46-3"></a><span class="w">    </span><span class="nx">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w">  </span><span class="c1">// +0 (技法1)</span>
+<a id="__codelineno-46-4" name="__codelineno-46-4" href="#__codelineno-46-4"></a><span class="w">    </span><span class="c1">// +n (技法2)</span>
+<a id="__codelineno-46-5" name="__codelineno-46-5" href="#__codelineno-46-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-6" name="__codelineno-46-6" href="#__codelineno-46-6"></a><span class="w">        </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-46-7" name="__codelineno-46-7" href="#__codelineno-46-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-46-8" name="__codelineno-46-8" href="#__codelineno-46-8"></a><span class="w">    </span><span class="c1">// +n*n (技法3)</span>
+<a id="__codelineno-46-9" name="__codelineno-46-9" href="#__codelineno-46-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mf">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="nx">n</span><span class="p">;</span><span class="w"> </span><span class="nx">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-10" name="__codelineno-46-10" href="#__codelineno-46-10"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">let</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="nx">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mf">1</span><span class="p">;</span><span class="w"> </span><span class="nx">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-46-11" name="__codelineno-46-11" href="#__codelineno-46-11"></a><span class="w">            </span><span class="nx">console</span><span class="p">.</span><span class="nx">log</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-46-12" name="__codelineno-46-12" href="#__codelineno-46-12"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-46-13" name="__codelineno-46-13" href="#__codelineno-46-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-46-14" name="__codelineno-46-14" href="#__codelineno-46-14"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="kt">void</span><span class="w"> </span><span class="n">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-2" name="__codelineno-47-2" href="#__codelineno-47-2"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// +0 (技法1)</span>
+<a id="__codelineno-47-3" name="__codelineno-47-3" href="#__codelineno-47-3"></a><span class="w">  </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="c1">// +0 (技法1)</span>
+<a id="__codelineno-47-4" name="__codelineno-47-4" href="#__codelineno-47-4"></a><span class="w">  </span><span class="c1">// +n (技法2)</span>
+<a id="__codelineno-47-5" name="__codelineno-47-5" href="#__codelineno-47-5"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-6" name="__codelineno-47-6" href="#__codelineno-47-6"></a><span class="w">    </span><span class="n">print</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
+<a id="__codelineno-47-7" name="__codelineno-47-7" href="#__codelineno-47-7"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-47-8" name="__codelineno-47-8" href="#__codelineno-47-8"></a><span class="w">  </span><span class="c1">// +n*n (技法3)</span>
+<a id="__codelineno-47-9" name="__codelineno-47-9" href="#__codelineno-47-9"></a><span class="w">  </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="m">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-10" name="__codelineno-47-10" href="#__codelineno-47-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="m">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-47-11" name="__codelineno-47-11" href="#__codelineno-47-11"></a><span class="w">      </span><span class="n">print</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
+<a id="__codelineno-47-12" name="__codelineno-47-12" href="#__codelineno-47-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-47-13" name="__codelineno-47-13" href="#__codelineno-47-13"></a><span class="w">  </span><span class="p">}</span>
+<a id="__codelineno-47-14" name="__codelineno-47-14" href="#__codelineno-47-14"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="k">fn</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="n">n</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-2" name="__codelineno-48-2" href="#__codelineno-48-2"></a><span class="w">    </span><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">     </span><span class="c1">// +0 (技法1)</span>
+<a id="__codelineno-48-3" name="__codelineno-48-3" href="#__codelineno-48-3"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w">        </span><span class="c1">// +0 (技法1)</span>
+<a id="__codelineno-48-4" name="__codelineno-48-4" href="#__codelineno-48-4"></a>
+<a id="__codelineno-48-5" name="__codelineno-48-5" href="#__codelineno-48-5"></a><span class="w">    </span><span class="c1">// +n (技法2)</span>
+<a id="__codelineno-48-6" name="__codelineno-48-6" href="#__codelineno-48-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="p">(</span><span class="mi">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-7" name="__codelineno-48-7" href="#__codelineno-48-7"></a><span class="w">        </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;{}&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-48-8" name="__codelineno-48-8" href="#__codelineno-48-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-48-9" name="__codelineno-48-9" href="#__codelineno-48-9"></a>
+<a id="__codelineno-48-10" name="__codelineno-48-10" href="#__codelineno-48-10"></a><span class="w">    </span><span class="c1">// +n*n (技法3)</span>
+<a id="__codelineno-48-11" name="__codelineno-48-11" href="#__codelineno-48-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="p">(</span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-12" name="__codelineno-48-12" href="#__codelineno-48-12"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="mi">0</span><span class="o">..</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-48-13" name="__codelineno-48-13" href="#__codelineno-48-13"></a><span class="w">            </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;{}&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-48-14" name="__codelineno-48-14" href="#__codelineno-48-14"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-48-15" name="__codelineno-48-15" href="#__codelineno-48-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-48-16" name="__codelineno-48-16" href="#__codelineno-48-16"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="kt">void</span><span class="w"> </span><span class="nf">algorithm</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-49-2" name="__codelineno-49-2" href="#__codelineno-49-2"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">  </span><span class="c1">// +0 (技法1)</span>
+<a id="__codelineno-49-3" name="__codelineno-49-3" href="#__codelineno-49-3"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w">  </span><span class="c1">// +0 (技法1)</span>
+<a id="__codelineno-49-4" name="__codelineno-49-4" href="#__codelineno-49-4"></a><span class="w">    </span><span class="c1">// +n (技法2)</span>
+<a id="__codelineno-49-5" name="__codelineno-49-5" href="#__codelineno-49-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-49-6" name="__codelineno-49-6" href="#__codelineno-49-6"></a><span class="w">        </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;%d&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-49-7" name="__codelineno-49-7" href="#__codelineno-49-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-49-8" name="__codelineno-49-8" href="#__codelineno-49-8"></a><span class="w">    </span><span class="c1">// +n*n (技法3)</span>
+<a id="__codelineno-49-9" name="__codelineno-49-9" href="#__codelineno-49-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-49-10" name="__codelineno-49-10" href="#__codelineno-49-10"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-49-11" name="__codelineno-49-11" href="#__codelineno-49-11"></a><span class="w">            </span><span class="n">printf</span><span class="p">(</span><span class="s">&quot;%d&quot;</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-49-12" name="__codelineno-49-12" href="#__codelineno-49-12"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-49-13" name="__codelineno-49-13" href="#__codelineno-49-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-49-14" name="__codelineno-49-14" href="#__codelineno-49-14"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="k">fn</span><span class="w"> </span><span class="n">algorithm</span><span class="p">(</span><span class="n">n</span><span class="o">:</span><span class="w"> </span><span class="kt">usize</span><span class="p">)</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-51-2" name="__codelineno-51-2" href="#__codelineno-51-2"></a><span class="w">    </span><span class="kr">var</span><span class="w"> </span><span class="n">a</span><span class="o">:</span><span class="w"> </span><span class="kt">i32</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">     </span><span class="c1">// +0 (技法1)</span>
+<a id="__codelineno-51-3" name="__codelineno-51-3" href="#__codelineno-51-3"></a><span class="w">    </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nb">@as</span><span class="p">(</span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="nb">@intCast</span><span class="p">(</span><span class="n">n</span><span class="p">));</span><span class="w">        </span><span class="c1">// +0 (技法1)</span>
+<a id="__codelineno-51-4" name="__codelineno-51-4" href="#__codelineno-51-4"></a>
+<a id="__codelineno-51-5" name="__codelineno-51-5" href="#__codelineno-51-5"></a><span class="w">    </span><span class="c1">// +n (技法2)</span>
+<a id="__codelineno-51-6" name="__codelineno-51-6" href="#__codelineno-51-6"></a><span class="w">    </span><span class="k">for</span><span class="p">(</span><span class="mi">0</span><span class="p">..(</span><span class="mi">5</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">))</span><span class="w"> </span><span class="o">|</span><span class="n">_</span><span class="o">|</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-51-7" name="__codelineno-51-7" href="#__codelineno-51-7"></a><span class="w">        </span><span class="n">std</span><span class="p">.</span><span class="n">debug</span><span class="p">.</span><span class="n">print</span><span class="p">(</span><span class="s">&quot;{}</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">,</span><span class="w"> </span><span class="p">.{</span><span class="mi">0</span><span class="p">});</span>
+<a id="__codelineno-51-8" name="__codelineno-51-8" href="#__codelineno-51-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-51-9" name="__codelineno-51-9" href="#__codelineno-51-9"></a>
+<a id="__codelineno-51-10" name="__codelineno-51-10" href="#__codelineno-51-10"></a><span class="w">    </span><span class="c1">// +n*n (技法3)</span>
+<a id="__codelineno-51-11" name="__codelineno-51-11" href="#__codelineno-51-11"></a><span class="w">    </span><span class="k">for</span><span class="p">(</span><span class="mi">0</span><span class="p">..(</span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">n</span><span class="p">))</span><span class="w"> </span><span class="o">|</span><span class="n">_</span><span class="o">|</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-51-12" name="__codelineno-51-12" href="#__codelineno-51-12"></a><span class="w">        </span><span class="k">for</span><span class="p">(</span><span class="mi">0</span><span class="p">..(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">))</span><span class="w"> </span><span class="o">|</span><span class="n">_</span><span class="o">|</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-51-13" name="__codelineno-51-13" href="#__codelineno-51-13"></a><span class="w">            </span><span class="n">std</span><span class="p">.</span><span class="n">debug</span><span class="p">.</span><span class="n">print</span><span class="p">(</span><span class="s">&quot;{}</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">,</span><span class="w"> </span><span class="p">.{</span><span class="mi">0</span><span class="p">});</span>
+<a id="__codelineno-51-14" name="__codelineno-51-14" href="#__codelineno-51-14"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-51-15" name="__codelineno-51-15" href="#__codelineno-51-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-51-16" name="__codelineno-51-16" href="#__codelineno-51-16"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>以下の式は、簡略化前後のカウント結果を示しており、どちらも<span class="arithmatex">\(O(n^2)\)</span>の時間計算量に導きます：</p>
+<div class="arithmatex">\[
+\begin{aligned}
+T(n) &amp; = 2n(n + 1) + (5n + 1) + 2 &amp; \text{完全カウント (-.-|||)} \newline
+&amp; = 2n^2 + 7n + 3 \newline
+T(n) &amp; = n^2 + n &amp; \text{簡略化カウント (o.O)}
+\end{aligned}
+\]</div>
+<h3 id="2-2">2. &nbsp; ステップ2: 漸近上限の決定<a class="headerlink" href="#2-2" title="Permanent link">&para;</a></h3>
+<p><strong>時間計算量は<span class="arithmatex">\(T(n)\)</span>の最高次項によって決定されます</strong>。これは、<span class="arithmatex">\(n\)</span>が無限大に近づくにつれて、最高次項が支配的になり、他の項の影響は無視できるようになるためです。</p>
+<p>以下の表は、異なる操作カウントとそれに対応する時間計算量の例を示しています。係数が増加オーダーを変更できないことを強調するために、誇張された値が使用されています。<span class="arithmatex">\(n\)</span>が非常に大きくなると、これらの定数は重要でなくなります。</p>
+<p align="center"> 表: 異なる操作カウントに対する時間計算量 </p>
+
+<div class="center-table">
+<table>
+<thead>
+<tr>
+<th>操作カウント <span class="arithmatex">\(T(n)\)</span></th>
+<th>時間計算量 <span class="arithmatex">\(O(f(n))\)</span></th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td><span class="arithmatex">\(100000\)</span></td>
+<td><span class="arithmatex">\(O(1)\)</span></td>
+</tr>
+<tr>
+<td><span class="arithmatex">\(3n + 2\)</span></td>
+<td><span class="arithmatex">\(O(n)\)</span></td>
+</tr>
+<tr>
+<td><span class="arithmatex">\(2n^2 + 3n + 2\)</span></td>
+<td><span class="arithmatex">\(O(n^2)\)</span></td>
+</tr>
+<tr>
+<td><span class="arithmatex">\(n^3 + 10000n^2\)</span></td>
+<td><span class="arithmatex">\(O(n^3)\)</span></td>
+</tr>
+<tr>
+<td><span class="arithmatex">\(2^n + 10000n^{10000}\)</span></td>
+<td><span class="arithmatex">\(O(2^n)\)</span></td>
+</tr>
+</tbody>
+</table>
+</div>
+<h2 id="234">2.3.4 &nbsp; 一般的な時間計算量の種類<a class="headerlink" href="#234" title="Permanent link">&para;</a></h2>
+<p>入力データサイズを<span class="arithmatex">\(n\)</span>としましょう。一般的な時間計算量の種類を下図に示し、低いものから高いものへと並べています：</p>
+<div class="arithmatex">\[
+\begin{aligned}
+&amp; O(1) &lt; O(\log n) &lt; O(n) &lt; O(n \log n) &lt; O(n^2) &lt; O(2^n) &lt; O(n!) \newline
+&amp; \text{定数} &lt; \text{対数} &lt; \text{線形} &lt; \text{線形対数} &lt; \text{二次} &lt; \text{指数} &lt; \text{階乗}
+\end{aligned}
+\]</div>
+<p><a class="glightbox" href="../time_complexity.assets/time_complexity_common_types.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Common types of time complexity" class="animation-figure" src="../time_complexity.assets/time_complexity_common_types.png" /></a></p>
+<p align="center"> 図 2-9 &nbsp; Common types of time complexity </p>
+
+<h3 id="1-o1">1. &nbsp; 定数オーダー <span class="arithmatex">\(O(1)\)</span><a class="headerlink" href="#1-o1" title="Permanent link">&para;</a></h3>
+<p>定数オーダーは、操作数が入力データサイズ<span class="arithmatex">\(n\)</span>とは無関係であることを意味します。以下の関数では、操作数<code>size</code>が大きい場合でも、<span class="arithmatex">\(n\)</span>とは無関係であるため、時間計算量は<span class="arithmatex">\(O(1)\)</span>のままです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="5:14"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><input id="__tabbed_5_7" name="__tabbed_5" type="radio" /><input id="__tabbed_5_8" name="__tabbed_5" type="radio" /><input id="__tabbed_5_9" name="__tabbed_5" type="radio" /><input id="__tabbed_5_10" name="__tabbed_5" type="radio" /><input id="__tabbed_5_11" name="__tabbed_5" type="radio" /><input id="__tabbed_5_12" name="__tabbed_5" type="radio" /><input id="__tabbed_5_13" name="__tabbed_5" type="radio" /><input id="__tabbed_5_14" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">Python</label><label for="__tabbed_5_2">C++</label><label for="__tabbed_5_3">Java</label><label for="__tabbed_5_4">C#</label><label for="__tabbed_5_5">Go</label><label for="__tabbed_5_6">Swift</label><label for="__tabbed_5_7">JS</label><label for="__tabbed_5_8">TS</label><label for="__tabbed_5_9">Dart</label><label for="__tabbed_5_10">Rust</label><label for="__tabbed_5_11">C</label><label for="__tabbed_5_12">Kotlin</label><label for="__tabbed_5_13">Ruby</label><label for="__tabbed_5_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-52-2" name="__codelineno-52-2" href="#__codelineno-52-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;定数複雑度&quot;&quot;&quot;</span>
+<a id="__codelineno-52-3" name="__codelineno-52-3" href="#__codelineno-52-3"></a>    <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-52-4" name="__codelineno-52-4" href="#__codelineno-52-4"></a>    <span class="n">size</span> <span class="o">=</span> <span class="mi">100000</span>
+<a id="__codelineno-52-5" name="__codelineno-52-5" href="#__codelineno-52-5"></a>    <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">size</span><span class="p">):</span>
+<a id="__codelineno-52-6" name="__codelineno-52-6" href="#__codelineno-52-6"></a>        <span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-52-7" name="__codelineno-52-7" href="#__codelineno-52-7"></a>    <span class="k">return</span> <span class="n">count</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-53-1" name="__codelineno-53-1" href="#__codelineno-53-1"></a><span class="cm">/* 定数計算量 */</span>
+<a id="__codelineno-53-2" name="__codelineno-53-2" href="#__codelineno-53-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-53-3" name="__codelineno-53-3" href="#__codelineno-53-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-53-4" name="__codelineno-53-4" href="#__codelineno-53-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">100000</span><span class="p">;</span>
+<a id="__codelineno-53-5" name="__codelineno-53-5" href="#__codelineno-53-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span>
+<a id="__codelineno-53-6" name="__codelineno-53-6" href="#__codelineno-53-6"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-53-7" name="__codelineno-53-7" href="#__codelineno-53-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-53-8" name="__codelineno-53-8" href="#__codelineno-53-8"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="cm">/* 定数計算量 */</span>
+<a id="__codelineno-54-2" name="__codelineno-54-2" href="#__codelineno-54-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">constant</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-54-3" name="__codelineno-54-3" href="#__codelineno-54-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-54-4" name="__codelineno-54-4" href="#__codelineno-54-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">100000</span><span class="p">;</span>
+<a id="__codelineno-54-5" name="__codelineno-54-5" href="#__codelineno-54-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span>
+<a id="__codelineno-54-6" name="__codelineno-54-6" href="#__codelineno-54-6"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-54-7" name="__codelineno-54-7" href="#__codelineno-54-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-54-8" name="__codelineno-54-8" href="#__codelineno-54-8"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-55-1" name="__codelineno-55-1" href="#__codelineno-55-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">time_complexity</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Constant</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-56-1" name="__codelineno-56-1" href="#__codelineno-56-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">constant</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-57-1" name="__codelineno-57-1" href="#__codelineno-57-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">constant</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-58-1" name="__codelineno-58-1" href="#__codelineno-58-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">constant</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-59-1" name="__codelineno-59-1" href="#__codelineno-59-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">constant</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-60-1" name="__codelineno-60-1" href="#__codelineno-60-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">constant</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-61-1" name="__codelineno-61-1" href="#__codelineno-61-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">constant</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-62-1" name="__codelineno-62-1" href="#__codelineno-62-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">constant</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.kt</span><pre><span></span><code><a id="__codelineno-63-1" name="__codelineno-63-1" href="#__codelineno-63-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">constant</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.rb</span><pre><span></span><code><a id="__codelineno-64-1" name="__codelineno-64-1" href="#__codelineno-64-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">constant</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.zig</span><pre><span></span><code><a id="__codelineno-65-1" name="__codelineno-65-1" href="#__codelineno-65-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">constant</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h3 id="2-on">2. &nbsp; 線形オーダー <span class="arithmatex">\(O(n)\)</span><a class="headerlink" href="#2-on" title="Permanent link">&para;</a></h3>
+<p>線形オーダーは、操作数が入力データサイズ<span class="arithmatex">\(n\)</span>と線形に増加することを示します。線形オーダーは一般的に単一ループ構造で現れます：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="6:14"><input checked="checked" id="__tabbed_6_1" name="__tabbed_6" type="radio" /><input id="__tabbed_6_2" name="__tabbed_6" type="radio" /><input id="__tabbed_6_3" name="__tabbed_6" type="radio" /><input id="__tabbed_6_4" name="__tabbed_6" type="radio" /><input id="__tabbed_6_5" name="__tabbed_6" type="radio" /><input id="__tabbed_6_6" name="__tabbed_6" type="radio" /><input id="__tabbed_6_7" name="__tabbed_6" type="radio" /><input id="__tabbed_6_8" name="__tabbed_6" type="radio" /><input id="__tabbed_6_9" name="__tabbed_6" type="radio" /><input id="__tabbed_6_10" name="__tabbed_6" type="radio" /><input id="__tabbed_6_11" name="__tabbed_6" type="radio" /><input id="__tabbed_6_12" name="__tabbed_6" type="radio" /><input id="__tabbed_6_13" name="__tabbed_6" type="radio" /><input id="__tabbed_6_14" name="__tabbed_6" type="radio" /><div class="tabbed-labels"><label for="__tabbed_6_1">Python</label><label for="__tabbed_6_2">C++</label><label for="__tabbed_6_3">Java</label><label for="__tabbed_6_4">C#</label><label for="__tabbed_6_5">Go</label><label for="__tabbed_6_6">Swift</label><label for="__tabbed_6_7">JS</label><label for="__tabbed_6_8">TS</label><label for="__tabbed_6_9">Dart</label><label for="__tabbed_6_10">Rust</label><label for="__tabbed_6_11">C</label><label for="__tabbed_6_12">Kotlin</label><label for="__tabbed_6_13">Ruby</label><label for="__tabbed_6_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-66-1" name="__codelineno-66-1" href="#__codelineno-66-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-66-2" name="__codelineno-66-2" href="#__codelineno-66-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;線形複雑度&quot;&quot;&quot;</span>
+<a id="__codelineno-66-3" name="__codelineno-66-3" href="#__codelineno-66-3"></a>    <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-66-4" name="__codelineno-66-4" href="#__codelineno-66-4"></a>    <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
+<a id="__codelineno-66-5" name="__codelineno-66-5" href="#__codelineno-66-5"></a>        <span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-66-6" name="__codelineno-66-6" href="#__codelineno-66-6"></a>    <span class="k">return</span> <span class="n">count</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-67-1" name="__codelineno-67-1" href="#__codelineno-67-1"></a><span class="cm">/* 線形計算量 */</span>
+<a id="__codelineno-67-2" name="__codelineno-67-2" href="#__codelineno-67-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-67-3" name="__codelineno-67-3" href="#__codelineno-67-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-67-4" name="__codelineno-67-4" href="#__codelineno-67-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span>
+<a id="__codelineno-67-5" name="__codelineno-67-5" href="#__codelineno-67-5"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-67-6" name="__codelineno-67-6" href="#__codelineno-67-6"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-67-7" name="__codelineno-67-7" href="#__codelineno-67-7"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-68-1" name="__codelineno-68-1" href="#__codelineno-68-1"></a><span class="cm">/* 線形計算量 */</span>
+<a id="__codelineno-68-2" name="__codelineno-68-2" href="#__codelineno-68-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">linear</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-68-3" name="__codelineno-68-3" href="#__codelineno-68-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-68-4" name="__codelineno-68-4" href="#__codelineno-68-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span>
+<a id="__codelineno-68-5" name="__codelineno-68-5" href="#__codelineno-68-5"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-68-6" name="__codelineno-68-6" href="#__codelineno-68-6"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-68-7" name="__codelineno-68-7" href="#__codelineno-68-7"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-69-1" name="__codelineno-69-1" href="#__codelineno-69-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">time_complexity</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Linear</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-70-1" name="__codelineno-70-1" href="#__codelineno-70-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">linear</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-71-1" name="__codelineno-71-1" href="#__codelineno-71-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">linear</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-72-1" name="__codelineno-72-1" href="#__codelineno-72-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">linear</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-73-1" name="__codelineno-73-1" href="#__codelineno-73-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">linear</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-74-1" name="__codelineno-74-1" href="#__codelineno-74-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">linear</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-75-1" name="__codelineno-75-1" href="#__codelineno-75-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">linear</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-76-1" name="__codelineno-76-1" href="#__codelineno-76-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">linear</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.kt</span><pre><span></span><code><a id="__codelineno-77-1" name="__codelineno-77-1" href="#__codelineno-77-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">linear</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.rb</span><pre><span></span><code><a id="__codelineno-78-1" name="__codelineno-78-1" href="#__codelineno-78-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">linear</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.zig</span><pre><span></span><code><a id="__codelineno-79-1" name="__codelineno-79-1" href="#__codelineno-79-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">linear</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>配列の走査や連結リストの走査などの操作は時間計算量が<span class="arithmatex">\(O(n)\)</span>で、<span class="arithmatex">\(n\)</span>は配列またはリストの長さです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="7:14"><input checked="checked" id="__tabbed_7_1" name="__tabbed_7" type="radio" /><input id="__tabbed_7_2" name="__tabbed_7" type="radio" /><input id="__tabbed_7_3" name="__tabbed_7" type="radio" /><input id="__tabbed_7_4" name="__tabbed_7" type="radio" /><input id="__tabbed_7_5" name="__tabbed_7" type="radio" /><input id="__tabbed_7_6" name="__tabbed_7" type="radio" /><input id="__tabbed_7_7" name="__tabbed_7" type="radio" /><input id="__tabbed_7_8" name="__tabbed_7" type="radio" /><input id="__tabbed_7_9" name="__tabbed_7" type="radio" /><input id="__tabbed_7_10" name="__tabbed_7" type="radio" /><input id="__tabbed_7_11" name="__tabbed_7" type="radio" /><input id="__tabbed_7_12" name="__tabbed_7" type="radio" /><input id="__tabbed_7_13" name="__tabbed_7" type="radio" /><input id="__tabbed_7_14" name="__tabbed_7" type="radio" /><div class="tabbed-labels"><label for="__tabbed_7_1">Python</label><label for="__tabbed_7_2">C++</label><label for="__tabbed_7_3">Java</label><label for="__tabbed_7_4">C#</label><label for="__tabbed_7_5">Go</label><label for="__tabbed_7_6">Swift</label><label for="__tabbed_7_7">JS</label><label for="__tabbed_7_8">TS</label><label for="__tabbed_7_9">Dart</label><label for="__tabbed_7_10">Rust</label><label for="__tabbed_7_11">C</label><label for="__tabbed_7_12">Kotlin</label><label for="__tabbed_7_13">Ruby</label><label for="__tabbed_7_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-80-1" name="__codelineno-80-1" href="#__codelineno-80-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">array_traversal</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-80-2" name="__codelineno-80-2" href="#__codelineno-80-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;線形複雑度（配列の走査）&quot;&quot;&quot;</span>
+<a id="__codelineno-80-3" name="__codelineno-80-3" href="#__codelineno-80-3"></a>    <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-80-4" name="__codelineno-80-4" href="#__codelineno-80-4"></a>    <span class="c1"># ループ回数は配列の長さに比例する</span>
+<a id="__codelineno-80-5" name="__codelineno-80-5" href="#__codelineno-80-5"></a>    <span class="k">for</span> <span class="n">num</span> <span class="ow">in</span> <span class="n">nums</span><span class="p">:</span>
+<a id="__codelineno-80-6" name="__codelineno-80-6" href="#__codelineno-80-6"></a>        <span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-80-7" name="__codelineno-80-7" href="#__codelineno-80-7"></a>    <span class="k">return</span> <span class="n">count</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-81-1" name="__codelineno-81-1" href="#__codelineno-81-1"></a><span class="cm">/* 線形計算量（配列の走査） */</span>
+<a id="__codelineno-81-2" name="__codelineno-81-2" href="#__codelineno-81-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">arrayTraversal</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-81-3" name="__codelineno-81-3" href="#__codelineno-81-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-81-4" name="__codelineno-81-4" href="#__codelineno-81-4"></a><span class="w">    </span><span class="c1">// ループ回数は配列の長さに比例</span>
+<a id="__codelineno-81-5" name="__codelineno-81-5" href="#__codelineno-81-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-81-6" name="__codelineno-81-6" href="#__codelineno-81-6"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-81-7" name="__codelineno-81-7" href="#__codelineno-81-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-81-8" name="__codelineno-81-8" href="#__codelineno-81-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-81-9" name="__codelineno-81-9" href="#__codelineno-81-9"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-82-1" name="__codelineno-82-1" href="#__codelineno-82-1"></a><span class="cm">/* 線形計算量（配列の走査） */</span>
+<a id="__codelineno-82-2" name="__codelineno-82-2" href="#__codelineno-82-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">arrayTraversal</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-82-3" name="__codelineno-82-3" href="#__codelineno-82-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-82-4" name="__codelineno-82-4" href="#__codelineno-82-4"></a><span class="w">    </span><span class="c1">// ループ回数は配列の長さに比例</span>
+<a id="__codelineno-82-5" name="__codelineno-82-5" href="#__codelineno-82-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-82-6" name="__codelineno-82-6" href="#__codelineno-82-6"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-82-7" name="__codelineno-82-7" href="#__codelineno-82-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-82-8" name="__codelineno-82-8" href="#__codelineno-82-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-82-9" name="__codelineno-82-9" href="#__codelineno-82-9"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-83-1" name="__codelineno-83-1" href="#__codelineno-83-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">time_complexity</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">ArrayTraversal</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-84-1" name="__codelineno-84-1" href="#__codelineno-84-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">arrayTraversal</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-85-1" name="__codelineno-85-1" href="#__codelineno-85-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">arrayTraversal</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-86-1" name="__codelineno-86-1" href="#__codelineno-86-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">arrayTraversal</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-87-1" name="__codelineno-87-1" href="#__codelineno-87-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">arrayTraversal</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-88-1" name="__codelineno-88-1" href="#__codelineno-88-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">arrayTraversal</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-89-1" name="__codelineno-89-1" href="#__codelineno-89-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">array_traversal</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-90-1" name="__codelineno-90-1" href="#__codelineno-90-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">arrayTraversal</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.kt</span><pre><span></span><code><a id="__codelineno-91-1" name="__codelineno-91-1" href="#__codelineno-91-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">arrayTraversal</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.rb</span><pre><span></span><code><a id="__codelineno-92-1" name="__codelineno-92-1" href="#__codelineno-92-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">array_traversal</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.zig</span><pre><span></span><code><a id="__codelineno-93-1" name="__codelineno-93-1" href="#__codelineno-93-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">arrayTraversal</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p><strong>入力データサイズ<span class="arithmatex">\(n\)</span>は入力データの種類に基づいて決定する必要があります</strong>。例えば、最初の例では、<span class="arithmatex">\(n\)</span>は入力データサイズを表し、2番目の例では、配列の長さ<span class="arithmatex">\(n\)</span>がデータサイズです。</p>
+<h3 id="3-on2">3. &nbsp; 二次オーダー <span class="arithmatex">\(O(n^2)\)</span><a class="headerlink" href="#3-on2" title="Permanent link">&para;</a></h3>
+<p>二次オーダーは、操作数が入力データサイズ<span class="arithmatex">\(n\)</span>の二乗に比例して増加することを意味します。二次オーダーは通常ネストしたループで現れ、外側と内側のループの両方が時間計算量<span class="arithmatex">\(O(n)\)</span>を持ち、全体の複雑度は<span class="arithmatex">\(O(n^2)\)</span>になります：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="8:14"><input checked="checked" id="__tabbed_8_1" name="__tabbed_8" type="radio" /><input id="__tabbed_8_2" name="__tabbed_8" type="radio" /><input id="__tabbed_8_3" name="__tabbed_8" type="radio" /><input id="__tabbed_8_4" name="__tabbed_8" type="radio" /><input id="__tabbed_8_5" name="__tabbed_8" type="radio" /><input id="__tabbed_8_6" name="__tabbed_8" type="radio" /><input id="__tabbed_8_7" name="__tabbed_8" type="radio" /><input id="__tabbed_8_8" name="__tabbed_8" type="radio" /><input id="__tabbed_8_9" name="__tabbed_8" type="radio" /><input id="__tabbed_8_10" name="__tabbed_8" type="radio" /><input id="__tabbed_8_11" name="__tabbed_8" type="radio" /><input id="__tabbed_8_12" name="__tabbed_8" type="radio" /><input id="__tabbed_8_13" name="__tabbed_8" type="radio" /><input id="__tabbed_8_14" name="__tabbed_8" type="radio" /><div class="tabbed-labels"><label for="__tabbed_8_1">Python</label><label for="__tabbed_8_2">C++</label><label for="__tabbed_8_3">Java</label><label for="__tabbed_8_4">C#</label><label for="__tabbed_8_5">Go</label><label for="__tabbed_8_6">Swift</label><label for="__tabbed_8_7">JS</label><label for="__tabbed_8_8">TS</label><label for="__tabbed_8_9">Dart</label><label for="__tabbed_8_10">Rust</label><label for="__tabbed_8_11">C</label><label for="__tabbed_8_12">Kotlin</label><label for="__tabbed_8_13">Ruby</label><label for="__tabbed_8_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-94-1" name="__codelineno-94-1" href="#__codelineno-94-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-94-2" name="__codelineno-94-2" href="#__codelineno-94-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;二次複雑度&quot;&quot;&quot;</span>
+<a id="__codelineno-94-3" name="__codelineno-94-3" href="#__codelineno-94-3"></a>    <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-94-4" name="__codelineno-94-4" href="#__codelineno-94-4"></a>    <span class="c1"># ループ回数はデータサイズnの二乗に比例する</span>
+<a id="__codelineno-94-5" name="__codelineno-94-5" href="#__codelineno-94-5"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
+<a id="__codelineno-94-6" name="__codelineno-94-6" href="#__codelineno-94-6"></a>        <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
+<a id="__codelineno-94-7" name="__codelineno-94-7" href="#__codelineno-94-7"></a>            <span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-94-8" name="__codelineno-94-8" href="#__codelineno-94-8"></a>    <span class="k">return</span> <span class="n">count</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-95-1" name="__codelineno-95-1" href="#__codelineno-95-1"></a><span class="cm">/* 二次計算量 */</span>
+<a id="__codelineno-95-2" name="__codelineno-95-2" href="#__codelineno-95-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-95-3" name="__codelineno-95-3" href="#__codelineno-95-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-95-4" name="__codelineno-95-4" href="#__codelineno-95-4"></a><span class="w">    </span><span class="c1">// ループ回数はデータサイズ n の二乗に比例</span>
+<a id="__codelineno-95-5" name="__codelineno-95-5" href="#__codelineno-95-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-95-6" name="__codelineno-95-6" href="#__codelineno-95-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-95-7" name="__codelineno-95-7" href="#__codelineno-95-7"></a><span class="w">            </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-95-8" name="__codelineno-95-8" href="#__codelineno-95-8"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-95-9" name="__codelineno-95-9" href="#__codelineno-95-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-95-10" name="__codelineno-95-10" href="#__codelineno-95-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-95-11" name="__codelineno-95-11" href="#__codelineno-95-11"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-96-1" name="__codelineno-96-1" href="#__codelineno-96-1"></a><span class="cm">/* 二次計算量 */</span>
+<a id="__codelineno-96-2" name="__codelineno-96-2" href="#__codelineno-96-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">quadratic</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-96-3" name="__codelineno-96-3" href="#__codelineno-96-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-96-4" name="__codelineno-96-4" href="#__codelineno-96-4"></a><span class="w">    </span><span class="c1">// ループ回数はデータサイズ n の二乗に比例</span>
+<a id="__codelineno-96-5" name="__codelineno-96-5" href="#__codelineno-96-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-96-6" name="__codelineno-96-6" href="#__codelineno-96-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-96-7" name="__codelineno-96-7" href="#__codelineno-96-7"></a><span class="w">            </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-96-8" name="__codelineno-96-8" href="#__codelineno-96-8"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-96-9" name="__codelineno-96-9" href="#__codelineno-96-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-96-10" name="__codelineno-96-10" href="#__codelineno-96-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-96-11" name="__codelineno-96-11" href="#__codelineno-96-11"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-97-1" name="__codelineno-97-1" href="#__codelineno-97-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">time_complexity</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Quadratic</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-98-1" name="__codelineno-98-1" href="#__codelineno-98-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">quadratic</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-99-1" name="__codelineno-99-1" href="#__codelineno-99-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">quadratic</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-100-1" name="__codelineno-100-1" href="#__codelineno-100-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">quadratic</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-101-1" name="__codelineno-101-1" href="#__codelineno-101-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">quadratic</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-102-1" name="__codelineno-102-1" href="#__codelineno-102-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">quadratic</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-103-1" name="__codelineno-103-1" href="#__codelineno-103-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">quadratic</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-104-1" name="__codelineno-104-1" href="#__codelineno-104-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">quadratic</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.kt</span><pre><span></span><code><a id="__codelineno-105-1" name="__codelineno-105-1" href="#__codelineno-105-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">quadratic</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.rb</span><pre><span></span><code><a id="__codelineno-106-1" name="__codelineno-106-1" href="#__codelineno-106-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">quadratic</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.zig</span><pre><span></span><code><a id="__codelineno-107-1" name="__codelineno-107-1" href="#__codelineno-107-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">quadratic</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>下図は定数オーダー、線形オーダー、二次オーダーの時間計算量を比較しています。</p>
+<p><a class="glightbox" href="../time_complexity.assets/time_complexity_constant_linear_quadratic.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Constant, linear, and quadratic order time complexities" class="animation-figure" src="../time_complexity.assets/time_complexity_constant_linear_quadratic.png" /></a></p>
+<p align="center"> 図 2-10 &nbsp; Constant, linear, and quadratic order time complexities </p>
+
+<p>例えば、バブルソートでは、外側のループが<span class="arithmatex">\(n - 1\)</span>回実行され、内側のループが<span class="arithmatex">\(n-1\)</span>、<span class="arithmatex">\(n-2\)</span>、...、<span class="arithmatex">\(2\)</span>、<span class="arithmatex">\(1\)</span>回実行され、平均<span class="arithmatex">\(n / 2\)</span>回となり、時間計算量は<span class="arithmatex">\(O((n - 1) n / 2) = O(n^2)\)</span>になります：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="9:14"><input checked="checked" id="__tabbed_9_1" name="__tabbed_9" type="radio" /><input id="__tabbed_9_2" name="__tabbed_9" type="radio" /><input id="__tabbed_9_3" name="__tabbed_9" type="radio" /><input id="__tabbed_9_4" name="__tabbed_9" type="radio" /><input id="__tabbed_9_5" name="__tabbed_9" type="radio" /><input id="__tabbed_9_6" name="__tabbed_9" type="radio" /><input id="__tabbed_9_7" name="__tabbed_9" type="radio" /><input id="__tabbed_9_8" name="__tabbed_9" type="radio" /><input id="__tabbed_9_9" name="__tabbed_9" type="radio" /><input id="__tabbed_9_10" name="__tabbed_9" type="radio" /><input id="__tabbed_9_11" name="__tabbed_9" type="radio" /><input id="__tabbed_9_12" name="__tabbed_9" type="radio" /><input id="__tabbed_9_13" name="__tabbed_9" type="radio" /><input id="__tabbed_9_14" name="__tabbed_9" type="radio" /><div class="tabbed-labels"><label for="__tabbed_9_1">Python</label><label for="__tabbed_9_2">C++</label><label for="__tabbed_9_3">Java</label><label for="__tabbed_9_4">C#</label><label for="__tabbed_9_5">Go</label><label for="__tabbed_9_6">Swift</label><label for="__tabbed_9_7">JS</label><label for="__tabbed_9_8">TS</label><label for="__tabbed_9_9">Dart</label><label for="__tabbed_9_10">Rust</label><label for="__tabbed_9_11">C</label><label for="__tabbed_9_12">Kotlin</label><label for="__tabbed_9_13">Ruby</label><label for="__tabbed_9_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-108-1" name="__codelineno-108-1" href="#__codelineno-108-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">bubble_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-108-2" name="__codelineno-108-2" href="#__codelineno-108-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;二次複雑度（バブルソート）&quot;&quot;&quot;</span>
+<a id="__codelineno-108-3" name="__codelineno-108-3" href="#__codelineno-108-3"></a>    <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>  <span class="c1"># カウンタ</span>
+<a id="__codelineno-108-4" name="__codelineno-108-4" href="#__codelineno-108-4"></a>    <span class="c1"># 外側のループ: 未ソート範囲は [0, i]</span>
+<a id="__codelineno-108-5" name="__codelineno-108-5" href="#__codelineno-108-5"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-108-6" name="__codelineno-108-6" href="#__codelineno-108-6"></a>        <span class="c1"># 内側のループ: 未ソート範囲 [0, i] の最大要素を右端にスワップ</span>
+<a id="__codelineno-108-7" name="__codelineno-108-7" href="#__codelineno-108-7"></a>        <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">i</span><span class="p">):</span>
+<a id="__codelineno-108-8" name="__codelineno-108-8" href="#__codelineno-108-8"></a>            <span class="k">if</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]:</span>
+<a id="__codelineno-108-9" name="__codelineno-108-9" href="#__codelineno-108-9"></a>                <span class="c1"># nums[j] と nums[j + 1] をスワップ</span>
+<a id="__codelineno-108-10" name="__codelineno-108-10" href="#__codelineno-108-10"></a>                <span class="n">tmp</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
+<a id="__codelineno-108-11" name="__codelineno-108-11" href="#__codelineno-108-11"></a>                <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-108-12" name="__codelineno-108-12" href="#__codelineno-108-12"></a>                <span class="n">nums</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">tmp</span>
+<a id="__codelineno-108-13" name="__codelineno-108-13" href="#__codelineno-108-13"></a>                <span class="n">count</span> <span class="o">+=</span> <span class="mi">3</span>  <span class="c1"># 要素のスワップは3つの個別操作を含む</span>
+<a id="__codelineno-108-14" name="__codelineno-108-14" href="#__codelineno-108-14"></a>    <span class="k">return</span> <span class="n">count</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-109-1" name="__codelineno-109-1" href="#__codelineno-109-1"></a><span class="cm">/* 二次計算量（バブルソート） */</span>
+<a id="__codelineno-109-2" name="__codelineno-109-2" href="#__codelineno-109-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">bubbleSort</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-109-3" name="__codelineno-109-3" href="#__codelineno-109-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// カウンター</span>
+<a id="__codelineno-109-4" name="__codelineno-109-4" href="#__codelineno-109-4"></a><span class="w">    </span><span class="c1">// 外側ループ：未ソート範囲は [0, i]</span>
+<a id="__codelineno-109-5" name="__codelineno-109-5" href="#__codelineno-109-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-109-6" name="__codelineno-109-6" href="#__codelineno-109-6"></a><span class="w">        </span><span class="c1">// 内側ループ：未ソート範囲 [0, i] の最大要素を範囲の右端にスワップ</span>
+<a id="__codelineno-109-7" name="__codelineno-109-7" href="#__codelineno-109-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-109-8" name="__codelineno-109-8" href="#__codelineno-109-8"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-109-9" name="__codelineno-109-9" href="#__codelineno-109-9"></a><span class="w">                </span><span class="c1">// nums[j] と nums[j + 1] をスワップ</span>
+<a id="__codelineno-109-10" name="__codelineno-109-10" href="#__codelineno-109-10"></a><span class="w">                </span><span class="kt">int</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-109-11" name="__codelineno-109-11" href="#__codelineno-109-11"></a><span class="w">                </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-109-12" name="__codelineno-109-12" href="#__codelineno-109-12"></a><span class="w">                </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
+<a id="__codelineno-109-13" name="__codelineno-109-13" href="#__codelineno-109-13"></a><span class="w">                </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="c1">// 要素のスワップには3つの個別操作が含まれる</span>
+<a id="__codelineno-109-14" name="__codelineno-109-14" href="#__codelineno-109-14"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-109-15" name="__codelineno-109-15" href="#__codelineno-109-15"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-109-16" name="__codelineno-109-16" href="#__codelineno-109-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-109-17" name="__codelineno-109-17" href="#__codelineno-109-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-109-18" name="__codelineno-109-18" href="#__codelineno-109-18"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-110-1" name="__codelineno-110-1" href="#__codelineno-110-1"></a><span class="cm">/* 二次計算量（バブルソート） */</span>
+<a id="__codelineno-110-2" name="__codelineno-110-2" href="#__codelineno-110-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">bubbleSort</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-110-3" name="__codelineno-110-3" href="#__codelineno-110-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// カウンター</span>
+<a id="__codelineno-110-4" name="__codelineno-110-4" href="#__codelineno-110-4"></a><span class="w">    </span><span class="c1">// 外側ループ：未ソート範囲は [0, i]</span>
+<a id="__codelineno-110-5" name="__codelineno-110-5" href="#__codelineno-110-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-110-6" name="__codelineno-110-6" href="#__codelineno-110-6"></a><span class="w">        </span><span class="c1">// 内側ループ：未ソート範囲 [0, i] の最大要素を範囲の右端にスワップ</span>
+<a id="__codelineno-110-7" name="__codelineno-110-7" href="#__codelineno-110-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-110-8" name="__codelineno-110-8" href="#__codelineno-110-8"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-110-9" name="__codelineno-110-9" href="#__codelineno-110-9"></a><span class="w">                </span><span class="c1">// nums[j] と nums[j + 1] をスワップ</span>
+<a id="__codelineno-110-10" name="__codelineno-110-10" href="#__codelineno-110-10"></a><span class="w">                </span><span class="kt">int</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-110-11" name="__codelineno-110-11" href="#__codelineno-110-11"></a><span class="w">                </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-110-12" name="__codelineno-110-12" href="#__codelineno-110-12"></a><span class="w">                </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
+<a id="__codelineno-110-13" name="__codelineno-110-13" href="#__codelineno-110-13"></a><span class="w">                </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="c1">// 要素のスワップには3つの個別操作が含まれる</span>
+<a id="__codelineno-110-14" name="__codelineno-110-14" href="#__codelineno-110-14"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-110-15" name="__codelineno-110-15" href="#__codelineno-110-15"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-110-16" name="__codelineno-110-16" href="#__codelineno-110-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-110-17" name="__codelineno-110-17" href="#__codelineno-110-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-110-18" name="__codelineno-110-18" href="#__codelineno-110-18"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-111-1" name="__codelineno-111-1" href="#__codelineno-111-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">time_complexity</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">BubbleSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-112-1" name="__codelineno-112-1" href="#__codelineno-112-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">bubbleSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-113-1" name="__codelineno-113-1" href="#__codelineno-113-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">bubbleSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-114-1" name="__codelineno-114-1" href="#__codelineno-114-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">bubbleSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-115-1" name="__codelineno-115-1" href="#__codelineno-115-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">bubbleSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-116-1" name="__codelineno-116-1" href="#__codelineno-116-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">bubbleSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-117-1" name="__codelineno-117-1" href="#__codelineno-117-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">bubble_sort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-118-1" name="__codelineno-118-1" href="#__codelineno-118-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">bubbleSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.kt</span><pre><span></span><code><a id="__codelineno-119-1" name="__codelineno-119-1" href="#__codelineno-119-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">bubbleSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.rb</span><pre><span></span><code><a id="__codelineno-120-1" name="__codelineno-120-1" href="#__codelineno-120-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">bubble_sort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.zig</span><pre><span></span><code><a id="__codelineno-121-1" name="__codelineno-121-1" href="#__codelineno-121-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">bubbleSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h3 id="4-o2n">4. &nbsp; 指数オーダー <span class="arithmatex">\(O(2^n)\)</span><a class="headerlink" href="#4-o2n" title="Permanent link">&para;</a></h3>
+<p>生物学的「細胞分裂」は指数オーダー増加の典型例です：1つの細胞から始まり、1回の分裂後に2つ、2回の分裂後に4つとなり、<span class="arithmatex">\(n\)</span>回の分裂後に<span class="arithmatex">\(2^n\)</span>個の細胞になります。</p>
+<p>下図とコードは細胞分裂プロセスをシミュレートし、時間計算量は<span class="arithmatex">\(O(2^n)\)</span>です：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="10:14"><input checked="checked" id="__tabbed_10_1" name="__tabbed_10" type="radio" /><input id="__tabbed_10_2" name="__tabbed_10" type="radio" /><input id="__tabbed_10_3" name="__tabbed_10" type="radio" /><input id="__tabbed_10_4" name="__tabbed_10" type="radio" /><input id="__tabbed_10_5" name="__tabbed_10" type="radio" /><input id="__tabbed_10_6" name="__tabbed_10" type="radio" /><input id="__tabbed_10_7" name="__tabbed_10" type="radio" /><input id="__tabbed_10_8" name="__tabbed_10" type="radio" /><input id="__tabbed_10_9" name="__tabbed_10" type="radio" /><input id="__tabbed_10_10" name="__tabbed_10" type="radio" /><input id="__tabbed_10_11" name="__tabbed_10" type="radio" /><input id="__tabbed_10_12" name="__tabbed_10" type="radio" /><input id="__tabbed_10_13" name="__tabbed_10" type="radio" /><input id="__tabbed_10_14" name="__tabbed_10" type="radio" /><div class="tabbed-labels"><label for="__tabbed_10_1">Python</label><label for="__tabbed_10_2">C++</label><label for="__tabbed_10_3">Java</label><label for="__tabbed_10_4">C#</label><label for="__tabbed_10_5">Go</label><label for="__tabbed_10_6">Swift</label><label for="__tabbed_10_7">JS</label><label for="__tabbed_10_8">TS</label><label for="__tabbed_10_9">Dart</label><label for="__tabbed_10_10">Rust</label><label for="__tabbed_10_11">C</label><label for="__tabbed_10_12">Kotlin</label><label for="__tabbed_10_13">Ruby</label><label for="__tabbed_10_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-122-1" name="__codelineno-122-1" href="#__codelineno-122-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">exponential</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-122-2" name="__codelineno-122-2" href="#__codelineno-122-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;指数複雑度（ループ実装）&quot;&quot;&quot;</span>
+<a id="__codelineno-122-3" name="__codelineno-122-3" href="#__codelineno-122-3"></a>    <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-122-4" name="__codelineno-122-4" href="#__codelineno-122-4"></a>    <span class="n">base</span> <span class="o">=</span> <span class="mi">1</span>
+<a id="__codelineno-122-5" name="__codelineno-122-5" href="#__codelineno-122-5"></a>    <span class="c1"># セルは毎回2つに分裂し、1, 2, 4, 8, ..., 2^(n-1) の数列を形成する</span>
+<a id="__codelineno-122-6" name="__codelineno-122-6" href="#__codelineno-122-6"></a>    <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
+<a id="__codelineno-122-7" name="__codelineno-122-7" href="#__codelineno-122-7"></a>        <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">base</span><span class="p">):</span>
+<a id="__codelineno-122-8" name="__codelineno-122-8" href="#__codelineno-122-8"></a>            <span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-122-9" name="__codelineno-122-9" href="#__codelineno-122-9"></a>        <span class="n">base</span> <span class="o">*=</span> <span class="mi">2</span>
+<a id="__codelineno-122-10" name="__codelineno-122-10" href="#__codelineno-122-10"></a>    <span class="c1"># count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
+<a id="__codelineno-122-11" name="__codelineno-122-11" href="#__codelineno-122-11"></a>    <span class="k">return</span> <span class="n">count</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-123-1" name="__codelineno-123-1" href="#__codelineno-123-1"></a><span class="cm">/* 指数計算量（ループ実装） */</span>
+<a id="__codelineno-123-2" name="__codelineno-123-2" href="#__codelineno-123-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">exponential</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-123-3" name="__codelineno-123-3" href="#__codelineno-123-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-123-4" name="__codelineno-123-4" href="#__codelineno-123-4"></a><span class="w">    </span><span class="c1">// セルは毎ラウンド2つに分裂し、数列 1, 2, 4, 8, ..., 2^(n-1) を形成</span>
+<a id="__codelineno-123-5" name="__codelineno-123-5" href="#__codelineno-123-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-123-6" name="__codelineno-123-6" href="#__codelineno-123-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">base</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-123-7" name="__codelineno-123-7" href="#__codelineno-123-7"></a><span class="w">            </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-123-8" name="__codelineno-123-8" href="#__codelineno-123-8"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-123-9" name="__codelineno-123-9" href="#__codelineno-123-9"></a><span class="w">        </span><span class="n">base</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-123-10" name="__codelineno-123-10" href="#__codelineno-123-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-123-11" name="__codelineno-123-11" href="#__codelineno-123-11"></a><span class="w">    </span><span class="c1">// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
+<a id="__codelineno-123-12" name="__codelineno-123-12" href="#__codelineno-123-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-123-13" name="__codelineno-123-13" href="#__codelineno-123-13"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-124-1" name="__codelineno-124-1" href="#__codelineno-124-1"></a><span class="cm">/* 指数計算量（ループ実装） */</span>
+<a id="__codelineno-124-2" name="__codelineno-124-2" href="#__codelineno-124-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">exponential</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-124-3" name="__codelineno-124-3" href="#__codelineno-124-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-124-4" name="__codelineno-124-4" href="#__codelineno-124-4"></a><span class="w">    </span><span class="c1">// セルは毎ラウンド2つに分裂し、数列 1, 2, 4, 8, ..., 2^(n-1) を形成</span>
+<a id="__codelineno-124-5" name="__codelineno-124-5" href="#__codelineno-124-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-124-6" name="__codelineno-124-6" href="#__codelineno-124-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">base</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-124-7" name="__codelineno-124-7" href="#__codelineno-124-7"></a><span class="w">            </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-124-8" name="__codelineno-124-8" href="#__codelineno-124-8"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-124-9" name="__codelineno-124-9" href="#__codelineno-124-9"></a><span class="w">        </span><span class="n">base</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-124-10" name="__codelineno-124-10" href="#__codelineno-124-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-124-11" name="__codelineno-124-11" href="#__codelineno-124-11"></a><span class="w">    </span><span class="c1">// count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1</span>
+<a id="__codelineno-124-12" name="__codelineno-124-12" href="#__codelineno-124-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-124-13" name="__codelineno-124-13" href="#__codelineno-124-13"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-125-1" name="__codelineno-125-1" href="#__codelineno-125-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">time_complexity</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Exponential</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-126-1" name="__codelineno-126-1" href="#__codelineno-126-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">exponential</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-127-1" name="__codelineno-127-1" href="#__codelineno-127-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">exponential</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-128-1" name="__codelineno-128-1" href="#__codelineno-128-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">exponential</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-129-1" name="__codelineno-129-1" href="#__codelineno-129-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">exponential</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-130-1" name="__codelineno-130-1" href="#__codelineno-130-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">exponential</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-131-1" name="__codelineno-131-1" href="#__codelineno-131-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">exponential</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-132-1" name="__codelineno-132-1" href="#__codelineno-132-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">exponential</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.kt</span><pre><span></span><code><a id="__codelineno-133-1" name="__codelineno-133-1" href="#__codelineno-133-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">exponential</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.rb</span><pre><span></span><code><a id="__codelineno-134-1" name="__codelineno-134-1" href="#__codelineno-134-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">exponential</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.zig</span><pre><span></span><code><a id="__codelineno-135-1" name="__codelineno-135-1" href="#__codelineno-135-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">exponential</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p><a class="glightbox" href="../time_complexity.assets/time_complexity_exponential.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Exponential order time complexity" class="animation-figure" src="../time_complexity.assets/time_complexity_exponential.png" /></a></p>
+<p align="center"> 図 2-11 &nbsp; Exponential order time complexity </p>
+
+<p>実際には、指数オーダーは再帰関数でよく現れます。例えば、以下のコードでは、再帰的に2つの半分に分割し、<span class="arithmatex">\(n\)</span>回の分割後に停止します：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="11:14"><input checked="checked" id="__tabbed_11_1" name="__tabbed_11" type="radio" /><input id="__tabbed_11_2" name="__tabbed_11" type="radio" /><input id="__tabbed_11_3" name="__tabbed_11" type="radio" /><input id="__tabbed_11_4" name="__tabbed_11" type="radio" /><input id="__tabbed_11_5" name="__tabbed_11" type="radio" /><input id="__tabbed_11_6" name="__tabbed_11" type="radio" /><input id="__tabbed_11_7" name="__tabbed_11" type="radio" /><input id="__tabbed_11_8" name="__tabbed_11" type="radio" /><input id="__tabbed_11_9" name="__tabbed_11" type="radio" /><input id="__tabbed_11_10" name="__tabbed_11" type="radio" /><input id="__tabbed_11_11" name="__tabbed_11" type="radio" /><input id="__tabbed_11_12" name="__tabbed_11" type="radio" /><input id="__tabbed_11_13" name="__tabbed_11" type="radio" /><input id="__tabbed_11_14" name="__tabbed_11" type="radio" /><div class="tabbed-labels"><label for="__tabbed_11_1">Python</label><label for="__tabbed_11_2">C++</label><label for="__tabbed_11_3">Java</label><label for="__tabbed_11_4">C#</label><label for="__tabbed_11_5">Go</label><label for="__tabbed_11_6">Swift</label><label for="__tabbed_11_7">JS</label><label for="__tabbed_11_8">TS</label><label for="__tabbed_11_9">Dart</label><label for="__tabbed_11_10">Rust</label><label for="__tabbed_11_11">C</label><label for="__tabbed_11_12">Kotlin</label><label for="__tabbed_11_13">Ruby</label><label for="__tabbed_11_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-136-1" name="__codelineno-136-1" href="#__codelineno-136-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">exp_recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-136-2" name="__codelineno-136-2" href="#__codelineno-136-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;指数複雑度（再帰実装）&quot;&quot;&quot;</span>
+<a id="__codelineno-136-3" name="__codelineno-136-3" href="#__codelineno-136-3"></a>    <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
+<a id="__codelineno-136-4" name="__codelineno-136-4" href="#__codelineno-136-4"></a>        <span class="k">return</span> <span class="mi">1</span>
+<a id="__codelineno-136-5" name="__codelineno-136-5" href="#__codelineno-136-5"></a>    <span class="k">return</span> <span class="n">exp_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">+</span> <span class="n">exp_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-137-1" name="__codelineno-137-1" href="#__codelineno-137-1"></a><span class="cm">/* 指数計算量（再帰実装） */</span>
+<a id="__codelineno-137-2" name="__codelineno-137-2" href="#__codelineno-137-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">expRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-137-3" name="__codelineno-137-3" href="#__codelineno-137-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-137-4" name="__codelineno-137-4" href="#__codelineno-137-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-137-5" name="__codelineno-137-5" href="#__codelineno-137-5"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-137-6" name="__codelineno-137-6" href="#__codelineno-137-6"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-138-1" name="__codelineno-138-1" href="#__codelineno-138-1"></a><span class="cm">/* 指数計算量（再帰実装） */</span>
+<a id="__codelineno-138-2" name="__codelineno-138-2" href="#__codelineno-138-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">expRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-138-3" name="__codelineno-138-3" href="#__codelineno-138-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-138-4" name="__codelineno-138-4" href="#__codelineno-138-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-138-5" name="__codelineno-138-5" href="#__codelineno-138-5"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">expRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-138-6" name="__codelineno-138-6" href="#__codelineno-138-6"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-139-1" name="__codelineno-139-1" href="#__codelineno-139-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">time_complexity</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">ExpRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-140-1" name="__codelineno-140-1" href="#__codelineno-140-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">expRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-141-1" name="__codelineno-141-1" href="#__codelineno-141-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">expRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-142-1" name="__codelineno-142-1" href="#__codelineno-142-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">expRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-143-1" name="__codelineno-143-1" href="#__codelineno-143-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">expRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-144-1" name="__codelineno-144-1" href="#__codelineno-144-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">expRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-145-1" name="__codelineno-145-1" href="#__codelineno-145-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">exp_recur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-146-1" name="__codelineno-146-1" href="#__codelineno-146-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">expRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.kt</span><pre><span></span><code><a id="__codelineno-147-1" name="__codelineno-147-1" href="#__codelineno-147-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">expRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.rb</span><pre><span></span><code><a id="__codelineno-148-1" name="__codelineno-148-1" href="#__codelineno-148-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">exp_recur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.zig</span><pre><span></span><code><a id="__codelineno-149-1" name="__codelineno-149-1" href="#__codelineno-149-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">expRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>指数オーダーの増加は極めて急速で、全数探索法（ブルートフォース、バックトラッキングなど）でよく見られます。大規模問題では、指数オーダーは受け入れられず、しばしば動的プログラミングや貪欲アルゴリズムが解決策として必要になります。</p>
+<h3 id="5-olog-n">5. &nbsp; 対数オーダー <span class="arithmatex">\(O(\log n)\)</span><a class="headerlink" href="#5-olog-n" title="Permanent link">&para;</a></h3>
+<p>指数オーダーとは対照的に、対数オーダーは「各ラウンドでサイズが半分になる」状況を反映します。入力データサイズが<span class="arithmatex">\(n\)</span>の場合、各ラウンドでサイズが半分になるため、反復回数は<span class="arithmatex">\(\log_2 n\)</span>で、これは<span class="arithmatex">\(2^n\)</span>の逆関数です。</p>
+<p>下図とコードは「各ラウンドで半分にする」プロセスをシミュレートし、時間計算量は<span class="arithmatex">\(O(\log_2 n)\)</span>で、一般的に<span class="arithmatex">\(O(\log n)\)</span>と省略されます：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="12:14"><input checked="checked" id="__tabbed_12_1" name="__tabbed_12" type="radio" /><input id="__tabbed_12_2" name="__tabbed_12" type="radio" /><input id="__tabbed_12_3" name="__tabbed_12" type="radio" /><input id="__tabbed_12_4" name="__tabbed_12" type="radio" /><input id="__tabbed_12_5" name="__tabbed_12" type="radio" /><input id="__tabbed_12_6" name="__tabbed_12" type="radio" /><input id="__tabbed_12_7" name="__tabbed_12" type="radio" /><input id="__tabbed_12_8" name="__tabbed_12" type="radio" /><input id="__tabbed_12_9" name="__tabbed_12" type="radio" /><input id="__tabbed_12_10" name="__tabbed_12" type="radio" /><input id="__tabbed_12_11" name="__tabbed_12" type="radio" /><input id="__tabbed_12_12" name="__tabbed_12" type="radio" /><input id="__tabbed_12_13" name="__tabbed_12" type="radio" /><input id="__tabbed_12_14" name="__tabbed_12" type="radio" /><div class="tabbed-labels"><label for="__tabbed_12_1">Python</label><label for="__tabbed_12_2">C++</label><label for="__tabbed_12_3">Java</label><label for="__tabbed_12_4">C#</label><label for="__tabbed_12_5">Go</label><label for="__tabbed_12_6">Swift</label><label for="__tabbed_12_7">JS</label><label for="__tabbed_12_8">TS</label><label for="__tabbed_12_9">Dart</label><label for="__tabbed_12_10">Rust</label><label for="__tabbed_12_11">C</label><label for="__tabbed_12_12">Kotlin</label><label for="__tabbed_12_13">Ruby</label><label for="__tabbed_12_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-150-1" name="__codelineno-150-1" href="#__codelineno-150-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">logarithmic</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-150-2" name="__codelineno-150-2" href="#__codelineno-150-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;対数複雑度（ループ実装）&quot;&quot;&quot;</span>
+<a id="__codelineno-150-3" name="__codelineno-150-3" href="#__codelineno-150-3"></a>    <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-150-4" name="__codelineno-150-4" href="#__codelineno-150-4"></a>    <span class="k">while</span> <span class="n">n</span> <span class="o">&gt;</span> <span class="mi">1</span><span class="p">:</span>
+<a id="__codelineno-150-5" name="__codelineno-150-5" href="#__codelineno-150-5"></a>        <span class="n">n</span> <span class="o">=</span> <span class="n">n</span> <span class="o">/</span> <span class="mi">2</span>
+<a id="__codelineno-150-6" name="__codelineno-150-6" href="#__codelineno-150-6"></a>        <span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-150-7" name="__codelineno-150-7" href="#__codelineno-150-7"></a>    <span class="k">return</span> <span class="n">count</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-151-1" name="__codelineno-151-1" href="#__codelineno-151-1"></a><span class="cm">/* 対数計算量（ループ実装） */</span>
+<a id="__codelineno-151-2" name="__codelineno-151-2" href="#__codelineno-151-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">logarithmic</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-151-3" name="__codelineno-151-3" href="#__codelineno-151-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-151-4" name="__codelineno-151-4" href="#__codelineno-151-4"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-151-5" name="__codelineno-151-5" href="#__codelineno-151-5"></a><span class="w">        </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-151-6" name="__codelineno-151-6" href="#__codelineno-151-6"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-151-7" name="__codelineno-151-7" href="#__codelineno-151-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-151-8" name="__codelineno-151-8" href="#__codelineno-151-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-151-9" name="__codelineno-151-9" href="#__codelineno-151-9"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-152-1" name="__codelineno-152-1" href="#__codelineno-152-1"></a><span class="cm">/* 対数計算量（ループ実装） */</span>
+<a id="__codelineno-152-2" name="__codelineno-152-2" href="#__codelineno-152-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">logarithmic</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-152-3" name="__codelineno-152-3" href="#__codelineno-152-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-152-4" name="__codelineno-152-4" href="#__codelineno-152-4"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-152-5" name="__codelineno-152-5" href="#__codelineno-152-5"></a><span class="w">        </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-152-6" name="__codelineno-152-6" href="#__codelineno-152-6"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-152-7" name="__codelineno-152-7" href="#__codelineno-152-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-152-8" name="__codelineno-152-8" href="#__codelineno-152-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-152-9" name="__codelineno-152-9" href="#__codelineno-152-9"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-153-1" name="__codelineno-153-1" href="#__codelineno-153-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">time_complexity</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Logarithmic</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-154-1" name="__codelineno-154-1" href="#__codelineno-154-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">logarithmic</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-155-1" name="__codelineno-155-1" href="#__codelineno-155-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">logarithmic</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-156-1" name="__codelineno-156-1" href="#__codelineno-156-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">logarithmic</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-157-1" name="__codelineno-157-1" href="#__codelineno-157-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">logarithmic</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-158-1" name="__codelineno-158-1" href="#__codelineno-158-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">logarithmic</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-159-1" name="__codelineno-159-1" href="#__codelineno-159-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">logarithmic</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-160-1" name="__codelineno-160-1" href="#__codelineno-160-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">logarithmic</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.kt</span><pre><span></span><code><a id="__codelineno-161-1" name="__codelineno-161-1" href="#__codelineno-161-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">logarithmic</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.rb</span><pre><span></span><code><a id="__codelineno-162-1" name="__codelineno-162-1" href="#__codelineno-162-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">logarithmic</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.zig</span><pre><span></span><code><a id="__codelineno-163-1" name="__codelineno-163-1" href="#__codelineno-163-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">logarithmic</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p><a class="glightbox" href="../time_complexity.assets/time_complexity_logarithmic.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Logarithmic order time complexity" class="animation-figure" src="../time_complexity.assets/time_complexity_logarithmic.png" /></a></p>
+<p align="center"> 図 2-12 &nbsp; Logarithmic order time complexity </p>
+
+<p>指数オーダーと同様に、対数オーダーも再帰関数で頻繁に現れます。以下のコードは高さ<span class="arithmatex">\(\log_2 n\)</span>の再帰木を形成します：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="13:14"><input checked="checked" id="__tabbed_13_1" name="__tabbed_13" type="radio" /><input id="__tabbed_13_2" name="__tabbed_13" type="radio" /><input id="__tabbed_13_3" name="__tabbed_13" type="radio" /><input id="__tabbed_13_4" name="__tabbed_13" type="radio" /><input id="__tabbed_13_5" name="__tabbed_13" type="radio" /><input id="__tabbed_13_6" name="__tabbed_13" type="radio" /><input id="__tabbed_13_7" name="__tabbed_13" type="radio" /><input id="__tabbed_13_8" name="__tabbed_13" type="radio" /><input id="__tabbed_13_9" name="__tabbed_13" type="radio" /><input id="__tabbed_13_10" name="__tabbed_13" type="radio" /><input id="__tabbed_13_11" name="__tabbed_13" type="radio" /><input id="__tabbed_13_12" name="__tabbed_13" type="radio" /><input id="__tabbed_13_13" name="__tabbed_13" type="radio" /><input id="__tabbed_13_14" name="__tabbed_13" type="radio" /><div class="tabbed-labels"><label for="__tabbed_13_1">Python</label><label for="__tabbed_13_2">C++</label><label for="__tabbed_13_3">Java</label><label for="__tabbed_13_4">C#</label><label for="__tabbed_13_5">Go</label><label for="__tabbed_13_6">Swift</label><label for="__tabbed_13_7">JS</label><label for="__tabbed_13_8">TS</label><label for="__tabbed_13_9">Dart</label><label for="__tabbed_13_10">Rust</label><label for="__tabbed_13_11">C</label><label for="__tabbed_13_12">Kotlin</label><label for="__tabbed_13_13">Ruby</label><label for="__tabbed_13_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-164-1" name="__codelineno-164-1" href="#__codelineno-164-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">log_recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-164-2" name="__codelineno-164-2" href="#__codelineno-164-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;対数複雑度（再帰実装）&quot;&quot;&quot;</span>
+<a id="__codelineno-164-3" name="__codelineno-164-3" href="#__codelineno-164-3"></a>    <span class="k">if</span> <span class="n">n</span> <span class="o">&lt;=</span> <span class="mi">1</span><span class="p">:</span>
+<a id="__codelineno-164-4" name="__codelineno-164-4" href="#__codelineno-164-4"></a>        <span class="k">return</span> <span class="mi">0</span>
+<a id="__codelineno-164-5" name="__codelineno-164-5" href="#__codelineno-164-5"></a>    <span class="k">return</span> <span class="n">log_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-165-1" name="__codelineno-165-1" href="#__codelineno-165-1"></a><span class="cm">/* 対数計算量（再帰実装） */</span>
+<a id="__codelineno-165-2" name="__codelineno-165-2" href="#__codelineno-165-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">logRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-165-3" name="__codelineno-165-3" href="#__codelineno-165-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-165-4" name="__codelineno-165-4" href="#__codelineno-165-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-165-5" name="__codelineno-165-5" href="#__codelineno-165-5"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">logRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-165-6" name="__codelineno-165-6" href="#__codelineno-165-6"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-166-1" name="__codelineno-166-1" href="#__codelineno-166-1"></a><span class="cm">/* 対数計算量（再帰実装） */</span>
+<a id="__codelineno-166-2" name="__codelineno-166-2" href="#__codelineno-166-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">logRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-166-3" name="__codelineno-166-3" href="#__codelineno-166-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-166-4" name="__codelineno-166-4" href="#__codelineno-166-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-166-5" name="__codelineno-166-5" href="#__codelineno-166-5"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">logRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-166-6" name="__codelineno-166-6" href="#__codelineno-166-6"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-167-1" name="__codelineno-167-1" href="#__codelineno-167-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">time_complexity</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">LogRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-168-1" name="__codelineno-168-1" href="#__codelineno-168-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">logRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-169-1" name="__codelineno-169-1" href="#__codelineno-169-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">logRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-170-1" name="__codelineno-170-1" href="#__codelineno-170-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">logRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-171-1" name="__codelineno-171-1" href="#__codelineno-171-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">logRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-172-1" name="__codelineno-172-1" href="#__codelineno-172-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">logRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-173-1" name="__codelineno-173-1" href="#__codelineno-173-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">log_recur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-174-1" name="__codelineno-174-1" href="#__codelineno-174-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">logRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.kt</span><pre><span></span><code><a id="__codelineno-175-1" name="__codelineno-175-1" href="#__codelineno-175-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">logRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.rb</span><pre><span></span><code><a id="__codelineno-176-1" name="__codelineno-176-1" href="#__codelineno-176-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">log_recur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.zig</span><pre><span></span><code><a id="__codelineno-177-1" name="__codelineno-177-1" href="#__codelineno-177-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">logRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>対数オーダーは分割統治戦略に基づくアルゴリズムの典型で、「多くに分割」と「複雑な問題を単純化」するアプローチを体現しています。増加が遅く、定数オーダーの次に最も理想的な時間計算量です。</p>
+<div class="admonition tip">
+<p class="admonition-title"><span class="arithmatex">\(O(\log n)\)</span>の底は何ですか？</p>
+<p>技術的には、「<span class="arithmatex">\(m\)</span>に分割」は時間計算量<span class="arithmatex">\(O(\log_m n)\)</span>に対応します。対数の底変更公式を使用すると、異なる対数複雑度を等価にできます：</p>
+<div class="arithmatex">\[
+O(\log_m n) = O(\log_k n / \log_k m) = O(\log_k n)
+\]</div>
+<p>これは、底<span class="arithmatex">\(m\)</span>を複雑度に影響を与えることなく変更できることを意味します。したがって、しばしば底<span class="arithmatex">\(m\)</span>を省略し、単に対数オーダーを<span class="arithmatex">\(O(\log n)\)</span>と表記します。</p>
+</div>
+<h3 id="6-on-log-n">6. &nbsp; 線形対数オーダー <span class="arithmatex">\(O(n \log n)\)</span><a class="headerlink" href="#6-on-log-n" title="Permanent link">&para;</a></h3>
+<p>線形対数オーダーはネストしたループでよく現れ、2つのループの複雑度がそれぞれ<span class="arithmatex">\(O(\log n)\)</span>と<span class="arithmatex">\(O(n)\)</span>です。関連するコードは以下の通りです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="14:14"><input checked="checked" id="__tabbed_14_1" name="__tabbed_14" type="radio" /><input id="__tabbed_14_2" name="__tabbed_14" type="radio" /><input id="__tabbed_14_3" name="__tabbed_14" type="radio" /><input id="__tabbed_14_4" name="__tabbed_14" type="radio" /><input id="__tabbed_14_5" name="__tabbed_14" type="radio" /><input id="__tabbed_14_6" name="__tabbed_14" type="radio" /><input id="__tabbed_14_7" name="__tabbed_14" type="radio" /><input id="__tabbed_14_8" name="__tabbed_14" type="radio" /><input id="__tabbed_14_9" name="__tabbed_14" type="radio" /><input id="__tabbed_14_10" name="__tabbed_14" type="radio" /><input id="__tabbed_14_11" name="__tabbed_14" type="radio" /><input id="__tabbed_14_12" name="__tabbed_14" type="radio" /><input id="__tabbed_14_13" name="__tabbed_14" type="radio" /><input id="__tabbed_14_14" name="__tabbed_14" type="radio" /><div class="tabbed-labels"><label for="__tabbed_14_1">Python</label><label for="__tabbed_14_2">C++</label><label for="__tabbed_14_3">Java</label><label for="__tabbed_14_4">C#</label><label for="__tabbed_14_5">Go</label><label for="__tabbed_14_6">Swift</label><label for="__tabbed_14_7">JS</label><label for="__tabbed_14_8">TS</label><label for="__tabbed_14_9">Dart</label><label for="__tabbed_14_10">Rust</label><label for="__tabbed_14_11">C</label><label for="__tabbed_14_12">Kotlin</label><label for="__tabbed_14_13">Ruby</label><label for="__tabbed_14_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-178-1" name="__codelineno-178-1" href="#__codelineno-178-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">linear_log_recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-178-2" name="__codelineno-178-2" href="#__codelineno-178-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;線形対数複雑度&quot;&quot;&quot;</span>
+<a id="__codelineno-178-3" name="__codelineno-178-3" href="#__codelineno-178-3"></a>    <span class="k">if</span> <span class="n">n</span> <span class="o">&lt;=</span> <span class="mi">1</span><span class="p">:</span>
+<a id="__codelineno-178-4" name="__codelineno-178-4" href="#__codelineno-178-4"></a>        <span class="k">return</span> <span class="mi">1</span>
+<a id="__codelineno-178-5" name="__codelineno-178-5" href="#__codelineno-178-5"></a>    <span class="n">count</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">linear_log_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">//</span> <span class="mi">2</span><span class="p">)</span> <span class="o">+</span> <span class="n">linear_log_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">//</span> <span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-178-6" name="__codelineno-178-6" href="#__codelineno-178-6"></a>    <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
+<a id="__codelineno-178-7" name="__codelineno-178-7" href="#__codelineno-178-7"></a>        <span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-178-8" name="__codelineno-178-8" href="#__codelineno-178-8"></a>    <span class="k">return</span> <span class="n">count</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-179-1" name="__codelineno-179-1" href="#__codelineno-179-1"></a><span class="cm">/* 線形対数計算量 */</span>
+<a id="__codelineno-179-2" name="__codelineno-179-2" href="#__codelineno-179-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">linearLogRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-179-3" name="__codelineno-179-3" href="#__codelineno-179-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-179-4" name="__codelineno-179-4" href="#__codelineno-179-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-179-5" name="__codelineno-179-5" href="#__codelineno-179-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-179-6" name="__codelineno-179-6" href="#__codelineno-179-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-179-7" name="__codelineno-179-7" href="#__codelineno-179-7"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-179-8" name="__codelineno-179-8" href="#__codelineno-179-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-179-9" name="__codelineno-179-9" href="#__codelineno-179-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-179-10" name="__codelineno-179-10" href="#__codelineno-179-10"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-180-1" name="__codelineno-180-1" href="#__codelineno-180-1"></a><span class="cm">/* 線形対数計算量 */</span>
+<a id="__codelineno-180-2" name="__codelineno-180-2" href="#__codelineno-180-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">linearLogRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-180-3" name="__codelineno-180-3" href="#__codelineno-180-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-180-4" name="__codelineno-180-4" href="#__codelineno-180-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-180-5" name="__codelineno-180-5" href="#__codelineno-180-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">linearLogRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-180-6" name="__codelineno-180-6" href="#__codelineno-180-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-180-7" name="__codelineno-180-7" href="#__codelineno-180-7"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-180-8" name="__codelineno-180-8" href="#__codelineno-180-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-180-9" name="__codelineno-180-9" href="#__codelineno-180-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-180-10" name="__codelineno-180-10" href="#__codelineno-180-10"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-181-1" name="__codelineno-181-1" href="#__codelineno-181-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">time_complexity</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">LinearLogRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-182-1" name="__codelineno-182-1" href="#__codelineno-182-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">linearLogRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-183-1" name="__codelineno-183-1" href="#__codelineno-183-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">linearLogRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-184-1" name="__codelineno-184-1" href="#__codelineno-184-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">linearLogRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-185-1" name="__codelineno-185-1" href="#__codelineno-185-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">linearLogRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-186-1" name="__codelineno-186-1" href="#__codelineno-186-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">linearLogRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-187-1" name="__codelineno-187-1" href="#__codelineno-187-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">linear_log_recur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-188-1" name="__codelineno-188-1" href="#__codelineno-188-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">linearLogRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.kt</span><pre><span></span><code><a id="__codelineno-189-1" name="__codelineno-189-1" href="#__codelineno-189-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">linearLogRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.rb</span><pre><span></span><code><a id="__codelineno-190-1" name="__codelineno-190-1" href="#__codelineno-190-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">linear_log_recur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.zig</span><pre><span></span><code><a id="__codelineno-191-1" name="__codelineno-191-1" href="#__codelineno-191-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">linearLogRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>下図は線形対数オーダーがどのように生成されるかを示しています。二分木の各レベルには<span class="arithmatex">\(n\)</span>個の操作があり、木には<span class="arithmatex">\(\log_2 n + 1\)</span>レベルがあり、時間計算量は<span class="arithmatex">\(O(n \log n)\)</span>になります。</p>
+<p><a class="glightbox" href="../time_complexity.assets/time_complexity_logarithmic_linear.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Linear-logarithmic order time complexity" class="animation-figure" src="../time_complexity.assets/time_complexity_logarithmic_linear.png" /></a></p>
+<p align="center"> 図 2-13 &nbsp; Linear-logarithmic order time complexity </p>
+
+<p>主流のソートアルゴリズムは通常<span class="arithmatex">\(O(n \log n)\)</span>の時間計算量を持ち、クイックソート、マージソート、ヒープソートなどがあります。</p>
+<h3 id="7-on">7. &nbsp; 階乗オーダー <span class="arithmatex">\(O(n!)\)</span><a class="headerlink" href="#7-on" title="Permanent link">&para;</a></h3>
+<p>階乗オーダーは「全順列」の数学問題に対応します。<span class="arithmatex">\(n\)</span>個の異なる要素が与えられた場合、可能な順列の総数は：</p>
+<div class="arithmatex">\[
+n! = n \times (n - 1) \times (n - 2) \times \dots \times 2 \times 1
+\]</div>
+<p>階乗は通常再帰を使用して実装されます。以下のコードと図に示されているように、第1レベルは<span class="arithmatex">\(n\)</span>個の分岐に分割され、第2レベルは<span class="arithmatex">\(n - 1\)</span>個の分岐に分割され、第<span class="arithmatex">\(n\)</span>レベル後に停止します：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="15:14"><input checked="checked" id="__tabbed_15_1" name="__tabbed_15" type="radio" /><input id="__tabbed_15_2" name="__tabbed_15" type="radio" /><input id="__tabbed_15_3" name="__tabbed_15" type="radio" /><input id="__tabbed_15_4" name="__tabbed_15" type="radio" /><input id="__tabbed_15_5" name="__tabbed_15" type="radio" /><input id="__tabbed_15_6" name="__tabbed_15" type="radio" /><input id="__tabbed_15_7" name="__tabbed_15" type="radio" /><input id="__tabbed_15_8" name="__tabbed_15" type="radio" /><input id="__tabbed_15_9" name="__tabbed_15" type="radio" /><input id="__tabbed_15_10" name="__tabbed_15" type="radio" /><input id="__tabbed_15_11" name="__tabbed_15" type="radio" /><input id="__tabbed_15_12" name="__tabbed_15" type="radio" /><input id="__tabbed_15_13" name="__tabbed_15" type="radio" /><input id="__tabbed_15_14" name="__tabbed_15" type="radio" /><div class="tabbed-labels"><label for="__tabbed_15_1">Python</label><label for="__tabbed_15_2">C++</label><label for="__tabbed_15_3">Java</label><label for="__tabbed_15_4">C#</label><label for="__tabbed_15_5">Go</label><label for="__tabbed_15_6">Swift</label><label for="__tabbed_15_7">JS</label><label for="__tabbed_15_8">TS</label><label for="__tabbed_15_9">Dart</label><label for="__tabbed_15_10">Rust</label><label for="__tabbed_15_11">C</label><label for="__tabbed_15_12">Kotlin</label><label for="__tabbed_15_13">Ruby</label><label for="__tabbed_15_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.py</span><pre><span></span><code><a id="__codelineno-192-1" name="__codelineno-192-1" href="#__codelineno-192-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">factorial_recur</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-192-2" name="__codelineno-192-2" href="#__codelineno-192-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;階乗複雑度（再帰実装）&quot;&quot;&quot;</span>
+<a id="__codelineno-192-3" name="__codelineno-192-3" href="#__codelineno-192-3"></a>    <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
+<a id="__codelineno-192-4" name="__codelineno-192-4" href="#__codelineno-192-4"></a>        <span class="k">return</span> <span class="mi">1</span>
+<a id="__codelineno-192-5" name="__codelineno-192-5" href="#__codelineno-192-5"></a>    <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-192-6" name="__codelineno-192-6" href="#__codelineno-192-6"></a>    <span class="c1"># 1つからnに分岐</span>
+<a id="__codelineno-192-7" name="__codelineno-192-7" href="#__codelineno-192-7"></a>    <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
+<a id="__codelineno-192-8" name="__codelineno-192-8" href="#__codelineno-192-8"></a>        <span class="n">count</span> <span class="o">+=</span> <span class="n">factorial_recur</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-192-9" name="__codelineno-192-9" href="#__codelineno-192-9"></a>    <span class="k">return</span> <span class="n">count</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-193-1" name="__codelineno-193-1" href="#__codelineno-193-1"></a><span class="cm">/* 階乗計算量（再帰実装） */</span>
+<a id="__codelineno-193-2" name="__codelineno-193-2" href="#__codelineno-193-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">factorialRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-193-3" name="__codelineno-193-3" href="#__codelineno-193-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-193-4" name="__codelineno-193-4" href="#__codelineno-193-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-193-5" name="__codelineno-193-5" href="#__codelineno-193-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-193-6" name="__codelineno-193-6" href="#__codelineno-193-6"></a><span class="w">    </span><span class="c1">// 1から n に分裂</span>
+<a id="__codelineno-193-7" name="__codelineno-193-7" href="#__codelineno-193-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-193-8" name="__codelineno-193-8" href="#__codelineno-193-8"></a><span class="w">        </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">factorialRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-193-9" name="__codelineno-193-9" href="#__codelineno-193-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-193-10" name="__codelineno-193-10" href="#__codelineno-193-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-193-11" name="__codelineno-193-11" href="#__codelineno-193-11"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.java</span><pre><span></span><code><a id="__codelineno-194-1" name="__codelineno-194-1" href="#__codelineno-194-1"></a><span class="cm">/* 階乗計算量（再帰実装） */</span>
+<a id="__codelineno-194-2" name="__codelineno-194-2" href="#__codelineno-194-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">factorialRecur</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-194-3" name="__codelineno-194-3" href="#__codelineno-194-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-194-4" name="__codelineno-194-4" href="#__codelineno-194-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-194-5" name="__codelineno-194-5" href="#__codelineno-194-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-194-6" name="__codelineno-194-6" href="#__codelineno-194-6"></a><span class="w">    </span><span class="c1">// 1から n に分裂</span>
+<a id="__codelineno-194-7" name="__codelineno-194-7" href="#__codelineno-194-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-194-8" name="__codelineno-194-8" href="#__codelineno-194-8"></a><span class="w">        </span><span class="n">count</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">factorialRecur</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-194-9" name="__codelineno-194-9" href="#__codelineno-194-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-194-10" name="__codelineno-194-10" href="#__codelineno-194-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-194-11" name="__codelineno-194-11" href="#__codelineno-194-11"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.cs</span><pre><span></span><code><a id="__codelineno-195-1" name="__codelineno-195-1" href="#__codelineno-195-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">time_complexity</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">FactorialRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.go</span><pre><span></span><code><a id="__codelineno-196-1" name="__codelineno-196-1" href="#__codelineno-196-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">factorialRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.swift</span><pre><span></span><code><a id="__codelineno-197-1" name="__codelineno-197-1" href="#__codelineno-197-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">factorialRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.js</span><pre><span></span><code><a id="__codelineno-198-1" name="__codelineno-198-1" href="#__codelineno-198-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">factorialRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.ts</span><pre><span></span><code><a id="__codelineno-199-1" name="__codelineno-199-1" href="#__codelineno-199-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">factorialRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.dart</span><pre><span></span><code><a id="__codelineno-200-1" name="__codelineno-200-1" href="#__codelineno-200-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">factorialRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.rs</span><pre><span></span><code><a id="__codelineno-201-1" name="__codelineno-201-1" href="#__codelineno-201-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">factorial_recur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.c</span><pre><span></span><code><a id="__codelineno-202-1" name="__codelineno-202-1" href="#__codelineno-202-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">factorialRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.kt</span><pre><span></span><code><a id="__codelineno-203-1" name="__codelineno-203-1" href="#__codelineno-203-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">factorialRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.rb</span><pre><span></span><code><a id="__codelineno-204-1" name="__codelineno-204-1" href="#__codelineno-204-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">factorial_recur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">time_complexity.zig</span><pre><span></span><code><a id="__codelineno-205-1" name="__codelineno-205-1" href="#__codelineno-205-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">factorialRecur</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p><a class="glightbox" href="../time_complexity.assets/time_complexity_factorial.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Factorial order time complexity" class="animation-figure" src="../time_complexity.assets/time_complexity_factorial.png" /></a></p>
+<p align="center"> 図 2-14 &nbsp; Factorial order time complexity </p>
+
+<p>階乗オーダーは指数オーダーよりもさらに速く増加することに注意してください。より大きな<span class="arithmatex">\(n\)</span>値では受け入れられません。</p>
+<h2 id="235">2.3.5 &nbsp; 最悪、最良、平均時間計算量<a class="headerlink" href="#235" title="Permanent link">&para;</a></h2>
+<p><strong>アルゴリズムの時間効率は固定されていないことが多く、入力データの分布に依存します</strong>。長さ<span class="arithmatex">\(n\)</span>の配列<code>nums</code>があり、<span class="arithmatex">\(1\)</span>から<span class="arithmatex">\(n\)</span>までの数で構成され、それぞれが一度だけ現れますが、ランダムにシャッフルされた順序であるとします。タスクは要素<span class="arithmatex">\(1\)</span>のインデックスを返すことです。以下の結論を導けます：</p>
+<ul>
+<li><code>nums = [?, ?, ..., 1]</code>の場合、つまり最後の要素が<span class="arithmatex">\(1\)</span>の場合、配列の完全な走査が必要で、<strong>最悪ケース時間計算量<span class="arithmatex">\(O(n)\)</span>を達成します</strong>。</li>
+<li><code>nums = [1, ?, ?, ...]</code>の場合、つまり最初の要素が<span class="arithmatex">\(1\)</span>の場合、配列の長さに関係なく、さらなる走査は不要で、<strong>最良ケース時間計算量<span class="arithmatex">\(\Omega(1)\)</span>を達成します</strong>。</li>
+</ul>
+<p>「最悪ケース時間計算量」は漸近上限に対応し、大きな<span class="arithmatex">\(O\)</span>記法で表されます。対応して、「最良ケース時間計算量」は漸近下限に対応し、<span class="arithmatex">\(\Omega\)</span>で表されます：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="16:14"><input checked="checked" id="__tabbed_16_1" name="__tabbed_16" type="radio" /><input id="__tabbed_16_2" name="__tabbed_16" type="radio" /><input id="__tabbed_16_3" name="__tabbed_16" type="radio" /><input id="__tabbed_16_4" name="__tabbed_16" type="radio" /><input id="__tabbed_16_5" name="__tabbed_16" type="radio" /><input id="__tabbed_16_6" name="__tabbed_16" type="radio" /><input id="__tabbed_16_7" name="__tabbed_16" type="radio" /><input id="__tabbed_16_8" name="__tabbed_16" type="radio" /><input id="__tabbed_16_9" name="__tabbed_16" type="radio" /><input id="__tabbed_16_10" name="__tabbed_16" type="radio" /><input id="__tabbed_16_11" name="__tabbed_16" type="radio" /><input id="__tabbed_16_12" name="__tabbed_16" type="radio" /><input id="__tabbed_16_13" name="__tabbed_16" type="radio" /><input id="__tabbed_16_14" name="__tabbed_16" type="radio" /><div class="tabbed-labels"><label for="__tabbed_16_1">Python</label><label for="__tabbed_16_2">C++</label><label for="__tabbed_16_3">Java</label><label for="__tabbed_16_4">C#</label><label for="__tabbed_16_5">Go</label><label for="__tabbed_16_6">Swift</label><label for="__tabbed_16_7">JS</label><label for="__tabbed_16_8">TS</label><label for="__tabbed_16_9">Dart</label><label for="__tabbed_16_10">Rust</label><label for="__tabbed_16_11">C</label><label for="__tabbed_16_12">Kotlin</label><label for="__tabbed_16_13">Ruby</label><label for="__tabbed_16_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">worst_best_time_complexity.py</span><pre><span></span><code><a id="__codelineno-206-1" name="__codelineno-206-1" href="#__codelineno-206-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">random_numbers</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
+<a id="__codelineno-206-2" name="__codelineno-206-2" href="#__codelineno-206-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;要素 1, 2, ..., n を含む配列を生成、順序はシャッフル&quot;&quot;&quot;</span>
+<a id="__codelineno-206-3" name="__codelineno-206-3" href="#__codelineno-206-3"></a>    <span class="c1"># 配列 nums = 1, 2, 3, ..., n を生成</span>
+<a id="__codelineno-206-4" name="__codelineno-206-4" href="#__codelineno-206-4"></a>    <span class="n">nums</span> <span class="o">=</span> <span class="p">[</span><span class="n">i</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)]</span>
+<a id="__codelineno-206-5" name="__codelineno-206-5" href="#__codelineno-206-5"></a>    <span class="c1"># 配列要素をランダムにシャッフル</span>
+<a id="__codelineno-206-6" name="__codelineno-206-6" href="#__codelineno-206-6"></a>    <span class="n">random</span><span class="o">.</span><span class="n">shuffle</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
+<a id="__codelineno-206-7" name="__codelineno-206-7" href="#__codelineno-206-7"></a>    <span class="k">return</span> <span class="n">nums</span>
+<a id="__codelineno-206-8" name="__codelineno-206-8" href="#__codelineno-206-8"></a>
+<a id="__codelineno-206-9" name="__codelineno-206-9" href="#__codelineno-206-9"></a><span class="k">def</span><span class="w"> </span><span class="nf">find_one</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-206-10" name="__codelineno-206-10" href="#__codelineno-206-10"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;配列 nums で数値 1 のインデックスを検索&quot;&quot;&quot;</span>
+<a id="__codelineno-206-11" name="__codelineno-206-11" href="#__codelineno-206-11"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)):</span>
+<a id="__codelineno-206-12" name="__codelineno-206-12" href="#__codelineno-206-12"></a>        <span class="c1"># 要素 1 が配列の最初にある場合、最良時間計算量 O(1) を達成</span>
+<a id="__codelineno-206-13" name="__codelineno-206-13" href="#__codelineno-206-13"></a>        <span class="c1"># 要素 1 が配列の最後にある場合、最悪時間計算量 O(n) を達成</span>
+<a id="__codelineno-206-14" name="__codelineno-206-14" href="#__codelineno-206-14"></a>        <span class="k">if</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
+<a id="__codelineno-206-15" name="__codelineno-206-15" href="#__codelineno-206-15"></a>            <span class="k">return</span> <span class="n">i</span>
+<a id="__codelineno-206-16" name="__codelineno-206-16" href="#__codelineno-206-16"></a>    <span class="k">return</span> <span class="o">-</span><span class="mi">1</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">worst_best_time_complexity.cpp</span><pre><span></span><code><a id="__codelineno-207-1" name="__codelineno-207-1" href="#__codelineno-207-1"></a><span class="cm">/* 要素 {1, 2, ..., n} をランダムにシャッフルした配列を生成 */</span>
+<a id="__codelineno-207-2" name="__codelineno-207-2" href="#__codelineno-207-2"></a><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">randomNumbers</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-207-3" name="__codelineno-207-3" href="#__codelineno-207-3"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">(</span><span class="n">n</span><span class="p">);</span>
+<a id="__codelineno-207-4" name="__codelineno-207-4" href="#__codelineno-207-4"></a><span class="w">    </span><span class="c1">// 配列 nums = { 1, 2, 3, ..., n } を生成</span>
+<a id="__codelineno-207-5" name="__codelineno-207-5" href="#__codelineno-207-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-207-6" name="__codelineno-207-6" href="#__codelineno-207-6"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-207-7" name="__codelineno-207-7" href="#__codelineno-207-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-207-8" name="__codelineno-207-8" href="#__codelineno-207-8"></a><span class="w">    </span><span class="c1">// システム時刻を使用してランダムシードを生成</span>
+<a id="__codelineno-207-9" name="__codelineno-207-9" href="#__codelineno-207-9"></a><span class="w">    </span><span class="kt">unsigned</span><span class="w"> </span><span class="n">seed</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">chrono</span><span class="o">::</span><span class="n">system_clock</span><span class="o">::</span><span class="n">now</span><span class="p">().</span><span class="n">time_since_epoch</span><span class="p">().</span><span class="n">count</span><span class="p">();</span>
+<a id="__codelineno-207-10" name="__codelineno-207-10" href="#__codelineno-207-10"></a><span class="w">    </span><span class="c1">// 配列要素をランダムにシャッフル</span>
+<a id="__codelineno-207-11" name="__codelineno-207-11" href="#__codelineno-207-11"></a><span class="w">    </span><span class="n">shuffle</span><span class="p">(</span><span class="n">nums</span><span class="p">.</span><span class="n">begin</span><span class="p">(),</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">end</span><span class="p">(),</span><span class="w"> </span><span class="n">default_random_engine</span><span class="p">(</span><span class="n">seed</span><span class="p">));</span>
+<a id="__codelineno-207-12" name="__codelineno-207-12" href="#__codelineno-207-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="p">;</span>
+<a id="__codelineno-207-13" name="__codelineno-207-13" href="#__codelineno-207-13"></a><span class="p">}</span>
+<a id="__codelineno-207-14" name="__codelineno-207-14" href="#__codelineno-207-14"></a>
+<a id="__codelineno-207-15" name="__codelineno-207-15" href="#__codelineno-207-15"></a><span class="cm">/* 配列 nums で数値1のインデックスを見つける */</span>
+<a id="__codelineno-207-16" name="__codelineno-207-16" href="#__codelineno-207-16"></a><span class="kt">int</span><span class="w"> </span><span class="n">findOne</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-207-17" name="__codelineno-207-17" href="#__codelineno-207-17"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-207-18" name="__codelineno-207-18" href="#__codelineno-207-18"></a><span class="w">        </span><span class="c1">// 要素1が配列の先頭にある場合、最良時間計算量 O(1) を達成</span>
+<a id="__codelineno-207-19" name="__codelineno-207-19" href="#__codelineno-207-19"></a><span class="w">        </span><span class="c1">// 要素1が配列の末尾にある場合、最悪時間計算量 O(n) を達成</span>
+<a id="__codelineno-207-20" name="__codelineno-207-20" href="#__codelineno-207-20"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-207-21" name="__codelineno-207-21" href="#__codelineno-207-21"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-207-22" name="__codelineno-207-22" href="#__codelineno-207-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-207-23" name="__codelineno-207-23" href="#__codelineno-207-23"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
+<a id="__codelineno-207-24" name="__codelineno-207-24" href="#__codelineno-207-24"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">worst_best_time_complexity.java</span><pre><span></span><code><a id="__codelineno-208-1" name="__codelineno-208-1" href="#__codelineno-208-1"></a><span class="cm">/* 要素 {1, 2, ..., n} をランダムにシャッフルした配列を生成 */</span>
+<a id="__codelineno-208-2" name="__codelineno-208-2" href="#__codelineno-208-2"></a><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="nf">randomNumbers</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-208-3" name="__codelineno-208-3" href="#__codelineno-208-3"></a><span class="w">    </span><span class="n">Integer</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Integer</span><span class="o">[</span><span class="n">n</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-208-4" name="__codelineno-208-4" href="#__codelineno-208-4"></a><span class="w">    </span><span class="c1">// 配列 nums = { 1, 2, 3, ..., n } を生成</span>
+<a id="__codelineno-208-5" name="__codelineno-208-5" href="#__codelineno-208-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-208-6" name="__codelineno-208-6" href="#__codelineno-208-6"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-208-7" name="__codelineno-208-7" href="#__codelineno-208-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-208-8" name="__codelineno-208-8" href="#__codelineno-208-8"></a><span class="w">    </span><span class="c1">// 配列要素をランダムにシャッフル</span>
+<a id="__codelineno-208-9" name="__codelineno-208-9" href="#__codelineno-208-9"></a><span class="w">    </span><span class="n">Collections</span><span class="p">.</span><span class="na">shuffle</span><span class="p">(</span><span class="n">Arrays</span><span class="p">.</span><span class="na">asList</span><span class="p">(</span><span class="n">nums</span><span class="p">));</span>
+<a id="__codelineno-208-10" name="__codelineno-208-10" href="#__codelineno-208-10"></a><span class="w">    </span><span class="c1">// Integer[] -&gt; int[]</span>
+<a id="__codelineno-208-11" name="__codelineno-208-11" href="#__codelineno-208-11"></a><span class="w">    </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">n</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-208-12" name="__codelineno-208-12" href="#__codelineno-208-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-208-13" name="__codelineno-208-13" href="#__codelineno-208-13"></a><span class="w">        </span><span class="n">res</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-208-14" name="__codelineno-208-14" href="#__codelineno-208-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-208-15" name="__codelineno-208-15" href="#__codelineno-208-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-208-16" name="__codelineno-208-16" href="#__codelineno-208-16"></a><span class="p">}</span>
+<a id="__codelineno-208-17" name="__codelineno-208-17" href="#__codelineno-208-17"></a>
+<a id="__codelineno-208-18" name="__codelineno-208-18" href="#__codelineno-208-18"></a><span class="cm">/* 配列 nums で数値1のインデックスを見つける */</span>
+<a id="__codelineno-208-19" name="__codelineno-208-19" href="#__codelineno-208-19"></a><span class="kt">int</span><span class="w"> </span><span class="nf">findOne</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-208-20" name="__codelineno-208-20" href="#__codelineno-208-20"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-208-21" name="__codelineno-208-21" href="#__codelineno-208-21"></a><span class="w">        </span><span class="c1">// 要素1が配列の先頭にある場合、最良時間計算量 O(1) を達成</span>
+<a id="__codelineno-208-22" name="__codelineno-208-22" href="#__codelineno-208-22"></a><span class="w">        </span><span class="c1">// 要素1が配列の末尾にある場合、最悪時間計算量 O(n) を達成</span>
+<a id="__codelineno-208-23" name="__codelineno-208-23" href="#__codelineno-208-23"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-208-24" name="__codelineno-208-24" href="#__codelineno-208-24"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-208-25" name="__codelineno-208-25" href="#__codelineno-208-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-208-26" name="__codelineno-208-26" href="#__codelineno-208-26"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-208-27" name="__codelineno-208-27" href="#__codelineno-208-27"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">worst_best_time_complexity.cs</span><pre><span></span><code><a id="__codelineno-209-1" name="__codelineno-209-1" href="#__codelineno-209-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">worst_best_time_complexity</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">RandomNumbers</span><span class="p">}</span>
+<a id="__codelineno-209-2" name="__codelineno-209-2" href="#__codelineno-209-2"></a>
+<a id="__codelineno-209-3" name="__codelineno-209-3" href="#__codelineno-209-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">worst_best_time_complexity</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">FindOne</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">worst_best_time_complexity.go</span><pre><span></span><code><a id="__codelineno-210-1" name="__codelineno-210-1" href="#__codelineno-210-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">randomNumbers</span><span class="p">}</span>
+<a id="__codelineno-210-2" name="__codelineno-210-2" href="#__codelineno-210-2"></a>
+<a id="__codelineno-210-3" name="__codelineno-210-3" href="#__codelineno-210-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">findOne</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">worst_best_time_complexity.swift</span><pre><span></span><code><a id="__codelineno-211-1" name="__codelineno-211-1" href="#__codelineno-211-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">randomNumbers</span><span class="p">}</span>
+<a id="__codelineno-211-2" name="__codelineno-211-2" href="#__codelineno-211-2"></a>
+<a id="__codelineno-211-3" name="__codelineno-211-3" href="#__codelineno-211-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">findOne</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">worst_best_time_complexity.js</span><pre><span></span><code><a id="__codelineno-212-1" name="__codelineno-212-1" href="#__codelineno-212-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">randomNumbers</span><span class="p">}</span>
+<a id="__codelineno-212-2" name="__codelineno-212-2" href="#__codelineno-212-2"></a>
+<a id="__codelineno-212-3" name="__codelineno-212-3" href="#__codelineno-212-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">findOne</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">worst_best_time_complexity.ts</span><pre><span></span><code><a id="__codelineno-213-1" name="__codelineno-213-1" href="#__codelineno-213-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">randomNumbers</span><span class="p">}</span>
+<a id="__codelineno-213-2" name="__codelineno-213-2" href="#__codelineno-213-2"></a>
+<a id="__codelineno-213-3" name="__codelineno-213-3" href="#__codelineno-213-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">findOne</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">worst_best_time_complexity.dart</span><pre><span></span><code><a id="__codelineno-214-1" name="__codelineno-214-1" href="#__codelineno-214-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">randomNumbers</span><span class="p">}</span>
+<a id="__codelineno-214-2" name="__codelineno-214-2" href="#__codelineno-214-2"></a>
+<a id="__codelineno-214-3" name="__codelineno-214-3" href="#__codelineno-214-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">findOne</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">worst_best_time_complexity.rs</span><pre><span></span><code><a id="__codelineno-215-1" name="__codelineno-215-1" href="#__codelineno-215-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">random_numbers</span><span class="p">}</span>
+<a id="__codelineno-215-2" name="__codelineno-215-2" href="#__codelineno-215-2"></a>
+<a id="__codelineno-215-3" name="__codelineno-215-3" href="#__codelineno-215-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">find_one</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">worst_best_time_complexity.c</span><pre><span></span><code><a id="__codelineno-216-1" name="__codelineno-216-1" href="#__codelineno-216-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">randomNumbers</span><span class="p">}</span>
+<a id="__codelineno-216-2" name="__codelineno-216-2" href="#__codelineno-216-2"></a>
+<a id="__codelineno-216-3" name="__codelineno-216-3" href="#__codelineno-216-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">findOne</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">worst_best_time_complexity.kt</span><pre><span></span><code><a id="__codelineno-217-1" name="__codelineno-217-1" href="#__codelineno-217-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">randomNumbers</span><span class="p">}</span>
+<a id="__codelineno-217-2" name="__codelineno-217-2" href="#__codelineno-217-2"></a>
+<a id="__codelineno-217-3" name="__codelineno-217-3" href="#__codelineno-217-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">findOne</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">worst_best_time_complexity.rb</span><pre><span></span><code><a id="__codelineno-218-1" name="__codelineno-218-1" href="#__codelineno-218-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">random_numbers</span><span class="p">}</span>
+<a id="__codelineno-218-2" name="__codelineno-218-2" href="#__codelineno-218-2"></a>
+<a id="__codelineno-218-3" name="__codelineno-218-3" href="#__codelineno-218-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">find_one</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">worst_best_time_complexity.zig</span><pre><span></span><code><a id="__codelineno-219-1" name="__codelineno-219-1" href="#__codelineno-219-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">randomNumbers</span><span class="p">}</span>
+<a id="__codelineno-219-2" name="__codelineno-219-2" href="#__codelineno-219-2"></a>
+<a id="__codelineno-219-3" name="__codelineno-219-3" href="#__codelineno-219-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">findOne</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>最良ケース時間計算量は実際にはほとんど使用されないことに注意してください。通常は非常に低い確率でのみ達成可能で、誤解を招く可能性があるからです。<strong>最悪ケース時間計算量はより実用的で、効率の安全値を提供し</strong>、アルゴリズムを自信を持って使用できるようにします。</p>
+<p>上記の例から、最悪ケースと最良ケースの時間計算量は両方とも「特殊なデータ分布」下でのみ発生し、発生確率が小さく、アルゴリズムの実行効率を正確に反映しない可能性があることが明らかです。対照的に、<strong>平均時間計算量はランダム入力データ下でのアルゴリズムの効率を反映でき</strong>、<span class="arithmatex">\(\Theta\)</span>記法で表されます。</p>
+<p>一部のアルゴリズムでは、ランダムデータ分布下での平均ケースを簡単に推定できます。例えば、前述の例では、入力配列がシャッフルされているため、要素<span class="arithmatex">\(1\)</span>が任意のインデックスに現れる確率は等しいです。したがって、アルゴリズムの平均ループ数は配列長さの半分<span class="arithmatex">\(n / 2\)</span>で、平均時間計算量は<span class="arithmatex">\(\Theta(n / 2) = \Theta(n)\)</span>です。</p>
+<p>しかし、より複雑なアルゴリズムの平均時間計算量を計算することは非常に困難です。データ分布下での全体的な数学的期待値を分析することが困難だからです。そのような場合、通常はアルゴリズムの効率を判断する基準として最悪ケース時間計算量を使用します。</p>
+<div class="admonition question">
+<p class="admonition-title"><span class="arithmatex">\(\Theta\)</span>記号はなぜほとんど見られないのですか？</p>
+<p>おそらく<span class="arithmatex">\(O\)</span>記法がより一般的に話されるため、平均時間計算量を表すためによく使用されます。しかし、厳密に言えば、この実践は正確ではありません。この本や他の資料で「平均時間計算量<span class="arithmatex">\(O(n)\)</span>」のような表現に遭遇した場合は、直接<span class="arithmatex">\(\Theta(n)\)</span>として理解してください。</p>
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+      <a href="../../chapter_preface/suggestions/" class="md-nav__link">
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+    0.2 &nbsp; 本書の使い方
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+      <a href="../../chapter_preface/summary/" class="md-nav__link">
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+    0.3 &nbsp; まとめ
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+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
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+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
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+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
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+  
+
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+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
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+    1.3 &nbsp; まとめ
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+          
+        
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+        
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+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
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+            第 2 章 &nbsp; 計算量解析
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+    2.1 &nbsp; アルゴリズム効率評価
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+  
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+    2.2 &nbsp; 反復と再帰
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+  
+
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+
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+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
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+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
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+
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+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
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+  
+  
+  
+  
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+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
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+    第 3 章 &nbsp; データ構造
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+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
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+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
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+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
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+          </ul>
+        </nav>
+      
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+  
+
+    
+      
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+      
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+          
+        
+      
+    
+    
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+    
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+      
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+            <a href="../../chapter_reference/" class="md-nav__link ">
+              
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9 3v15h3V3H9m3 2 4 13 3-1-4-13-3 1M5 5v13h3V5H5M3 19v2h18v-2H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    参考文献
+  </span>
+  
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+            
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+<h1 id="32">3.2 &nbsp; 基本データ型<a class="headerlink" href="#32" title="Permanent link">&para;</a></h1>
+<p>コンピュータ内のデータについて考える際、テキスト、画像、動画、音声、3Dモデルなど、様々な形式が思い浮かびます。これらの組織的な形式は異なりますが、すべて様々な基本データ型から構成されています。</p>
+<p>**基本データ型とは、CPUが直接操作できるもの**であり、アルゴリズムで直接使用されます。主に以下が含まれます。</p>
+<ul>
+<li>整数型：<code>byte</code>、<code>short</code>、<code>int</code>、<code>long</code></li>
+<li>浮動小数点型：<code>float</code>、<code>double</code>、小数を表現するために使用</li>
+<li>文字型：<code>char</code>、様々な言語の文字、句読点、さらには絵文字を表現するために使用</li>
+<li>ブール型：<code>bool</code>、「はい」または「いいえ」の判断を表現するために使用</li>
+</ul>
+<p><strong>基本データ型は、コンピュータ内で二進形式で格納されます</strong>。1つの二進桁は1ビットです。ほとんどの現代的なオペレーティングシステムでは、1バイトは8ビットで構成されています。</p>
+<p>基本データ型の値の範囲は、それらが占める空間のサイズに依存します。以下では、Javaを例に説明します。</p>
+<ul>
+<li>整数型<code>byte</code>は1バイト = 8ビットを占め、<span class="arithmatex">\(2^8\)</span>個の数値を表現できます。</li>
+<li>整数型<code>int</code>は4バイト = 32ビットを占め、<span class="arithmatex">\(2^{32}\)</span>個の数値を表現できます。</li>
+</ul>
+<p>以下の表は、Javaにおける様々な基本データ型が占める空間、値の範囲、デフォルト値を示しています。この表を暗記する必要はありませんが、一般的な理解を持ち、必要時に参照することをお勧めします。</p>
+<p align="center"> 表 3-1 &nbsp; 基本データ型が占める空間と値の範囲 </p>
+
+<div class="center-table">
+<table>
+<thead>
+<tr>
+<th>型</th>
+<th>シンボル</th>
+<th>占有空間</th>
+<th>最小値</th>
+<th>最大値</th>
+<th>デフォルト値</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td>整数</td>
+<td><code>byte</code></td>
+<td>1バイト</td>
+<td><span class="arithmatex">\(-2^7\)</span> (<span class="arithmatex">\(-128\)</span>)</td>
+<td><span class="arithmatex">\(2^7 - 1\)</span> (<span class="arithmatex">\(127\)</span>)</td>
+<td>0</td>
+</tr>
+<tr>
+<td></td>
+<td><code>short</code></td>
+<td>2バイト</td>
+<td><span class="arithmatex">\(-2^{15}\)</span></td>
+<td><span class="arithmatex">\(2^{15} - 1\)</span></td>
+<td>0</td>
+</tr>
+<tr>
+<td></td>
+<td><code>int</code></td>
+<td>4バイト</td>
+<td><span class="arithmatex">\(-2^{31}\)</span></td>
+<td><span class="arithmatex">\(2^{31} - 1\)</span></td>
+<td>0</td>
+</tr>
+<tr>
+<td></td>
+<td><code>long</code></td>
+<td>8バイト</td>
+<td><span class="arithmatex">\(-2^{63}\)</span></td>
+<td><span class="arithmatex">\(2^{63} - 1\)</span></td>
+<td>0</td>
+</tr>
+<tr>
+<td>浮動小数点</td>
+<td><code>float</code></td>
+<td>4バイト</td>
+<td><span class="arithmatex">\(1.175 \times 10^{-38}\)</span></td>
+<td><span class="arithmatex">\(3.403 \times 10^{38}\)</span></td>
+<td><span class="arithmatex">\(0.0\text{f}\)</span></td>
+</tr>
+<tr>
+<td></td>
+<td><code>double</code></td>
+<td>8バイト</td>
+<td><span class="arithmatex">\(2.225 \times 10^{-308}\)</span></td>
+<td><span class="arithmatex">\(1.798 \times 10^{308}\)</span></td>
+<td>0.0</td>
+</tr>
+<tr>
+<td>文字</td>
+<td><code>char</code></td>
+<td>2バイト</td>
+<td>0</td>
+<td><span class="arithmatex">\(2^{16} - 1\)</span></td>
+<td>0</td>
+</tr>
+<tr>
+<td>ブール</td>
+<td><code>bool</code></td>
+<td>1バイト</td>
+<td><span class="arithmatex">\(\text{false}\)</span></td>
+<td><span class="arithmatex">\(\text{true}\)</span></td>
+<td><span class="arithmatex">\(\text{false}\)</span></td>
+</tr>
+</tbody>
+</table>
+</div>
+<p>上記の表はJavaの基本データ型に特有であることにご注意ください。すべてのプログラミング言語には独自のデータ型定義があり、占有空間、値の範囲、デフォルト値が異なる場合があります。</p>
+<ul>
+<li>Pythonでは、整数型<code>int</code>は任意のサイズになることができ、利用可能なメモリによってのみ制限されます。浮動小数点<code>float</code>は倍精度64ビットです。<code>char</code>型は存在せず、単一文字は実際には長さ1の文字列<code>str</code>です。</li>
+<li>CおよびC++では基本データ型のサイズが指定されておらず、実装とプラットフォームによって異なります。上記の表はLP64<a href="https://en.cppreference.com/w/cpp/language/types#Properties">データモデル</a>に従っており、LinuxやmacOSを含むUnix 64ビットオペレーティングシステムで使用されています。</li>
+<li>CおよびC++における<code>char</code>のサイズは1バイトですが、ほとんどのプログラミング言語では、特定の文字エンコーディング方法に依存し、詳細は「文字エンコーディング」の章で説明されています。</li>
+<li>ブール値の表現には1ビット（0または1）のみが必要ですが、通常はメモリ内に1バイトとして格納されます。これは、現代のコンピュータCPUが通常1バイトを最小のアドレス可能なメモリ単位として使用するためです。</li>
+</ul>
+<p>では、基本データ型とデータ構造の関係は何でしょうか？データ構造とは、コンピュータ内でデータを組織化し格納する方法であることを知っています。ここでの焦点は「データ」ではなく「構造」です。</p>
+<p>「数値の列」を表現したい場合、自然に配列の使用を考えます。これは、配列の線形構造が数値の隣接性と順序性を表現できるためですが、格納される内容が整数<code>int</code>、小数<code>float</code>、文字<code>char</code>のいずれであっても、「データ構造」とは無関係です。</p>
+<p>言い換えると、<strong>基本データ型はデータの「内容型」を提供し、データ構造はデータの「組織化方法」を提供します</strong>。例えば、以下のコードでは、同じデータ構造（配列）を使用して、<code>int</code>、<code>float</code>、<code>char</code>、<code>bool</code>などの異なる基本データ型を格納し表現しています。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="c1"># 様々な基本データ型を使用して配列を初期化</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="n">numbers</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="mi">5</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="n">decimals</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">float</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="mf">0.0</span><span class="p">]</span> <span class="o">*</span> <span class="mi">5</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="c1"># Pythonの文字は実際には長さ1の文字列</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a><span class="n">characters</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">str</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="s1">&#39;0&#39;</span><span class="p">]</span> <span class="o">*</span> <span class="mi">5</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a><span class="n">bools</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">bool</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="kc">False</span><span class="p">]</span> <span class="o">*</span> <span class="mi">5</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="c1"># Pythonのリストは様々な基本データ型とオブジェクト参照を自由に格納可能</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="n">data</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="s1">&#39;a&#39;</span><span class="p">,</span> <span class="kc">False</span><span class="p">,</span> <span class="n">ListNode</span><span class="p">(</span><span class="mi">0</span><span class="p">)]</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="c1">// 様々な基本データ型を使用して配列を初期化</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">numbers</span><span class="p">[</span><span class="mi">5</span><span class="p">];</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="kt">float</span><span class="w"> </span><span class="n">decimals</span><span class="p">[</span><span class="mi">5</span><span class="p">];</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="kt">char</span><span class="w"> </span><span class="n">characters</span><span class="p">[</span><span class="mi">5</span><span class="p">];</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="kt">bool</span><span class="w"> </span><span class="n">bools</span><span class="p">[</span><span class="mi">5</span><span class="p">];</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="c1">// 様々な基本データ型を使用して配列を初期化</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">numbers</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="mi">5</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="kt">float</span><span class="o">[]</span><span class="w"> </span><span class="n">decimals</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">float</span><span class="o">[</span><span class="mi">5</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="kt">char</span><span class="o">[]</span><span class="w"> </span><span class="n">characters</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">char</span><span class="o">[</span><span class="mi">5</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="kt">boolean</span><span class="o">[]</span><span class="w"> </span><span class="n">bools</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">boolean</span><span class="o">[</span><span class="mi">5</span><span class="o">]</span><span class="p">;</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="c1">// 様々な基本データ型を使用して配列を初期化</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kt">int</span><span class="p">[]</span><span class="w"> </span><span class="n">numbers</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="mi">5</span><span class="p">];</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="kt">float</span><span class="p">[]</span><span class="w"> </span><span class="n">decimals</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">float</span><span class="p">[</span><span class="mi">5</span><span class="p">];</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="kt">char</span><span class="p">[]</span><span class="w"> </span><span class="n">characters</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">char</span><span class="p">[</span><span class="mi">5</span><span class="p">];</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="kt">bool</span><span class="p">[]</span><span class="w"> </span><span class="n">bools</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">bool</span><span class="p">[</span><span class="mi">5</span><span class="p">];</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="c1">// 様々な基本データ型を使用して配列を初期化</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">var</span><span class="w"> </span><span class="nx">numbers</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[</span><span class="mi">5</span><span class="p">]</span><span class="kt">int</span><span class="p">{}</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="kd">var</span><span class="w"> </span><span class="nx">decimals</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[</span><span class="mi">5</span><span class="p">]</span><span class="kt">float64</span><span class="p">{}</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="kd">var</span><span class="w"> </span><span class="nx">characters</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[</span><span class="mi">5</span><span class="p">]</span><span class="kt">byte</span><span class="p">{}</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="kd">var</span><span class="w"> </span><span class="nx">bools</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[</span><span class="mi">5</span><span class="p">]</span><span class="kt">bool</span><span class="p">{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="c1">// 様々な基本データ型を使用して配列を初期化</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">let</span><span class="w"> </span><span class="nv">numbers</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="mi">5</span><span class="p">)</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="kd">let</span><span class="w"> </span><span class="nv">decimals</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="mf">0.0</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="mi">5</span><span class="p">)</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="kd">let</span><span class="w"> </span><span class="nv">characters</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Character</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="s">&quot;a&quot;</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="mi">5</span><span class="p">)</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="kd">let</span><span class="w"> </span><span class="nv">bools</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">Array</span><span class="p">(</span><span class="n">repeating</span><span class="p">:</span><span class="w"> </span><span class="kc">false</span><span class="p">,</span><span class="w"> </span><span class="bp">count</span><span class="p">:</span><span class="w"> </span><span class="mi">5</span><span class="p">)</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="c1">// JavaScriptの配列は様々な基本データ型とオブジェクトを自由に格納可能</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">const</span><span class="w"> </span><span class="nx">array</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mf">0</span><span class="p">,</span><span class="w"> </span><span class="mf">0.0</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;a&#39;</span><span class="p">,</span><span class="w"> </span><span class="kc">false</span><span class="p">];</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="c1">// 様々な基本データ型を使用して配列を初期化</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">const</span><span class="w"> </span><span class="nx">numbers</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="kd">const</span><span class="w"> </span><span class="nx">characters</span><span class="o">:</span><span class="w"> </span><span class="kt">string</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="kd">const</span><span class="w"> </span><span class="nx">bools</span><span class="o">:</span><span class="w"> </span><span class="kt">boolean</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="c1">// 様々な基本データ型を使用して配列を初期化</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">numbers</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="m">5</span><span class="p">,</span><span class="w"> </span><span class="m">0</span><span class="p">);</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="n">List</span><span class="o">&lt;</span><span class="kt">double</span><span class="o">&gt;</span><span class="w"> </span><span class="n">decimals</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="m">5</span><span class="p">,</span><span class="w"> </span><span class="m">0.0</span><span class="p">);</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="n">List</span><span class="o">&lt;</span><span class="kt">String</span><span class="o">&gt;</span><span class="w"> </span><span class="n">characters</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="m">5</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;a&#39;</span><span class="p">);</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="n">List</span><span class="o">&lt;</span><span class="kt">bool</span><span class="o">&gt;</span><span class="w"> </span><span class="n">bools</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">List</span><span class="p">.</span><span class="n">filled</span><span class="p">(</span><span class="m">5</span><span class="p">,</span><span class="w"> </span><span class="kc">false</span><span class="p">);</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="c1">// 様々な基本データ型を使用して配列を初期化</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="kd">let</span><span class="w"> </span><span class="n">numbers</span><span class="p">:</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="mi">5</span><span class="p">];</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="kd">let</span><span class="w"> </span><span class="n">decimals</span><span class="p">:</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">f32</span><span class="o">&gt;</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="mf">0.0</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">];</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="kd">let</span><span class="w"> </span><span class="n">characters</span><span class="p">:</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">char</span><span class="o">&gt;</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="sc">&#39;0&#39;</span><span class="p">;</span><span class="w"> </span><span class="mi">5</span><span class="p">];</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="kd">let</span><span class="w"> </span><span class="n">bools</span><span class="p">:</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">bool</span><span class="o">&gt;</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="fm">vec!</span><span class="p">[</span><span class="kc">false</span><span class="p">;</span><span class="w"> </span><span class="mi">5</span><span class="p">];</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="c1">// 様々な基本データ型を使用して配列を初期化</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">numbers</span><span class="p">[</span><span class="mi">10</span><span class="p">];</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="kt">float</span><span class="w"> </span><span class="n">decimals</span><span class="p">[</span><span class="mi">10</span><span class="p">];</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="kt">char</span><span class="w"> </span><span class="n">characters</span><span class="p">[</span><span class="mi">10</span><span class="p">];</span>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="kt">bool</span><span class="w"> </span><span class="n">bools</span><span class="p">[</span><span class="mi">10</span><span class="p">];</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">// 様々な基本データ型を使用して配列を初期化</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a><span class="kr">var</span><span class="w"> </span><span class="n">numbers</span><span class="o">:</span><span class="w"> </span><span class="p">[</span><span class="mi">5</span><span class="p">]</span><span class="kt">i32</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">undefined</span><span class="p">;</span>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="kr">var</span><span class="w"> </span><span class="n">decimals</span><span class="o">:</span><span class="w"> </span><span class="p">[</span><span class="mi">5</span><span class="p">]</span><span class="kt">f32</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">undefined</span><span class="p">;</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a><span class="kr">var</span><span class="w"> </span><span class="n">characters</span><span class="o">:</span><span class="w"> </span><span class="p">[</span><span class="mi">5</span><span class="p">]</span><span class="kt">u8</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">undefined</span><span class="p">;</span>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="kr">var</span><span class="w"> </span><span class="n">bools</span><span class="o">:</span><span class="w"> </span><span class="p">[</span><span class="mi">5</span><span class="p">]</span><span class="kt">bool</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">undefined</span><span class="p">;</span>
+</code></pre></div>
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+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#341-ascii" class="md-nav__link">
+    <span class="md-ellipsis">
+      3.4.1 &nbsp; ASCII文字セット
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#342-gbk" class="md-nav__link">
+    <span class="md-ellipsis">
+      3.4.2 &nbsp; GBK文字セット
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#343-unicode" class="md-nav__link">
+    <span class="md-ellipsis">
+      3.4.3 &nbsp; Unicode文字セット
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#344-utf-8" class="md-nav__link">
+    <span class="md-ellipsis">
+      3.4.4 &nbsp; UTF-8エンコーディング
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#345" class="md-nav__link">
+    <span class="md-ellipsis">
+      3.4.5 &nbsp; プログラミング言語における文字エンコーディング
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
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+    
+    
+    
+    
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+      
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+  
+  <span class="md-ellipsis">
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+            
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+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
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+    </li>
+  
+
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+            
+              
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+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
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+  
+
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+  
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+</nav>
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+            
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+              <div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
+                <div class="md-sidebar__scrollwrap">
+                  <div class="md-sidebar__inner">
+                    
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+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
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+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#341-ascii" class="md-nav__link">
+    <span class="md-ellipsis">
+      3.4.1 &nbsp; ASCII文字セット
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#342-gbk" class="md-nav__link">
+    <span class="md-ellipsis">
+      3.4.2 &nbsp; GBK文字セット
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#343-unicode" class="md-nav__link">
+    <span class="md-ellipsis">
+      3.4.3 &nbsp; Unicode文字セット
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#344-utf-8" class="md-nav__link">
+    <span class="md-ellipsis">
+      3.4.4 &nbsp; UTF-8エンコーディング
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#345" class="md-nav__link">
+    <span class="md-ellipsis">
+      3.4.5 &nbsp; プログラミング言語における文字エンコーディング
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+                  </div>
+                </div>
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+      
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
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+<!-- Page content -->
+<h1 id="34">3.4 &nbsp; 文字エンコーディング *<a class="headerlink" href="#34" title="Permanent link">&para;</a></h1>
+<p>コンピュータシステムでは、すべてのデータが二進形式で格納され、<code>char</code>も例外ではありません。文字を表現するために、各文字と二進数の一対一のマッピングを定義する「文字セット」を開発する必要があります。文字セットがあれば、コンピュータは表を参照して二進数を文字に変換できます。</p>
+<h2 id="341-ascii">3.4.1 &nbsp; ASCII文字セット<a class="headerlink" href="#341-ascii" title="Permanent link">&para;</a></h2>
+<p><u>ASCIIコード</u>は最も初期の文字セットの一つで、正式にはAmerican Standard Code for Information Interchangeとして知られています。7つの二進桁（1バイトの下位7ビット）を使用して文字を表現し、最大128種類の異なる文字を表現できます。以下の図に示すように、ASCIIには英語の大文字と小文字、0〜9の数字、様々な句読点、特定の制御文字（改行やタブなど）が含まれています。</p>
+<p><a class="glightbox" href="../character_encoding.assets/ascii_table.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="ASCIIコード" class="animation-figure" src="../character_encoding.assets/ascii_table.png" /></a></p>
+<p align="center"> 図 3-6 &nbsp; ASCIIコード </p>
+
+<p>しかし、<strong>ASCIIは英語の文字のみを表現できます</strong>。コンピュータのグローバル化に伴い、より多くの言語を表現するために<u>EASCII</u>と呼ばれる文字セットが開発されました。ASCIIの7ビット構造から8ビットに拡張し、256文字の表現を可能にしました。</p>
+<p>世界的に、様々な地域固有のEASCII文字セットが導入されました。これらのセットの最初の128文字はASCIIと一致していますが、残りの128文字は異なる言語の要件に対応するために異なって定義されています。</p>
+<h2 id="342-gbk">3.4.2 &nbsp; GBK文字セット<a class="headerlink" href="#342-gbk" title="Permanent link">&para;</a></h2>
+<p>後に、**EASCIIでも多くの言語の文字要件を満たすことができない**ことが判明しました。例えば、中国語には約10万の漢字があり、そのうち数千が定期的に使用されています。1980年、中国標準化委員会は6763の中国語文字を含む<u>GB2312</u>文字セットを発表し、中国語のコンピュータ処理ニーズを本質的に満たしました。</p>
+<p>しかし、GB2312は一部の稀少文字や繁体字を処理できませんでした。<u>GBK</u>文字セットはGB2312を拡張し、21886の中国語文字を含んでいます。GBKエンコーディングスキームでは、ASCII文字は1バイトで表現され、中国語文字は2バイトを使用します。</p>
+<h2 id="343-unicode">3.4.3 &nbsp; Unicode文字セット<a class="headerlink" href="#343-unicode" title="Permanent link">&para;</a></h2>
+<p>コンピュータ技術の急速な発展と多数の文字セットおよびエンコーディング標準により、数多くの問題が発生しました。一方では、これらの文字セットは一般的に特定の言語の文字のみを定義し、多言語環境では適切に機能できませんでした。他方では、同じ言語に対する複数の文字セット標準の存在により、異なるエンコーディング標準を使用するコンピュータ間で情報交換を行う際に文字化けが発生しました。</p>
+<p>当時の研究者たちは考えました：<strong>世界のすべての言語と記号を含む包括的な文字セットが開発されれば、言語横断環境と文字化けに関連する問題を解決できるのではないでしょうか？</strong> このアイデアにインスパイアされて、広範囲な文字セットであるUnicodeが誕生しました。</p>
+<p><u>Unicode</u>は中国語で「统一码」（統一コード）と呼ばれ、理論的に100万文字以上を収容できます。世界中のすべての文字を単一のセットに組み込み、様々な言語の処理と表示のための汎用文字セットを提供し、異なるエンコーディング標準による文字化けの問題を減らすことを目指しています。</p>
+<p>1991年のリリース以来、Unicodeは新しい言語と文字を含むよう継続的に拡張されています。2022年9月現在、Unicodeには149,186文字が含まれており、様々な言語の文字、記号、さらには絵文字も含まれています。広大なUnicode文字セットでは、一般的に使用される文字は2バイトを占有し、一部の稀少な文字は3バイトまたは4バイトを占有する場合があります。</p>
+<p>Unicodeは各文字に数値（「コードポイント」と呼ばれる）を割り当てる汎用文字セットですが、<strong>これらの文字コードポイントがコンピュータシステムにどのように格納されるべきかは指定していません</strong>。疑問が生じるかもしれません：システムはテキスト内の異なる長さのUnicodeコードポイントをどのように解釈するのでしょうか？例えば、2バイトのコードが与えられた場合、システムはそれが単一の2バイト文字を表すのか、2つの1バイト文字を表すのかをどのように判断するのでしょうか？</p>
+<p><strong>この問題に対する簡単な解決策は、すべての文字を等長エンコーディングとして格納することです</strong>。以下の図に示すように、「Hello」の各文字は1バイトを占有し、「算法」（アルゴリズム）の各文字は2バイトを占有します。上位ビットをゼロで埋めることで、「Hello 算法」のすべての文字を2バイトとしてエンコードできます。この方法により、システムは2バイトごとに文字を解釈し、フレーズの内容を復元できます。</p>
+<p><a class="glightbox" href="../character_encoding.assets/unicode_hello_algo.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Unicodeエンコーディング例" class="animation-figure" src="../character_encoding.assets/unicode_hello_algo.png" /></a></p>
+<p align="center"> 図 3-7 &nbsp; Unicodeエンコーディング例 </p>
+
+<p>しかし、ASCIIが示したように、英語のエンコーディングには1バイトのみが必要です。上記のアプローチを使用すると、英語テキストが占有する空間がASCIIエンコーディングと比較して2倍になり、メモリ空間の無駄になります。したがって、より効率的なUnicodeエンコーディング方法が必要です。</p>
+<h2 id="344-utf-8">3.4.4 &nbsp; UTF-8エンコーディング<a class="headerlink" href="#344-utf-8" title="Permanent link">&para;</a></h2>
+<p>現在、UTF-8は国際的に最も広く使用されているUnicodeエンコーディング方法になっています。**これは可変長エンコーディング**で、文字の複雑さに応じて1〜4バイトを使用して文字を表現します。ASCII文字は1バイトのみが必要で、ラテン文字とギリシャ文字は2バイト、一般的に使用される中国語文字は3バイト、その他の稀少な文字は4バイトが必要です。</p>
+<p>UTF-8のエンコーディング規則は複雑ではなく、2つのケースに分けることができます：</p>
+<ul>
+<li>1バイト文字の場合、最上位ビットを<span class="arithmatex">\(0\)</span>に設定し、残りの7ビットをUnicodeコードポイントに設定します。注目すべきは、ASCII文字がUnicodeセットの最初の128コードポイントを占有することです。これは**UTF-8エンコーディングがASCIIと後方互換性がある**ことを意味します。これは、UTF-8を使用して古いASCIIテキストを解析できることを意味します。</li>
+<li>長さ<span class="arithmatex">\(n\)</span>バイトの文字（<span class="arithmatex">\(n &gt; 1\)</span>）の場合、最初のバイトの最上位<span class="arithmatex">\(n\)</span>ビットを<span class="arithmatex">\(1\)</span>に設定し、<span class="arithmatex">\((n + 1)^{\text{th}}\)</span>ビットを<span class="arithmatex">\(0\)</span>に設定します。2番目のバイトから、各バイトの最上位2ビットを<span class="arithmatex">\(10\)</span>に設定します。残りのビットはUnicodeコードポイントを埋めるために使用されます。</li>
+</ul>
+<p>以下の図は「Hello算法」のUTF-8エンコーディングを示しています。最上位<span class="arithmatex">\(n\)</span>ビットが<span class="arithmatex">\(1\)</span>に設定されているため、システムは最上位ビットで<span class="arithmatex">\(1\)</span>に設定されたビット数を数えることで文字の長さを<span class="arithmatex">\(n\)</span>として決定できることが観察できます。</p>
+<p>しかし、なぜ残りのバイトの最上位2ビットを<span class="arithmatex">\(10\)</span>に設定するのでしょうか？実際、この<span class="arithmatex">\(10\)</span>は一種のチェックサムとして機能します。システムが間違ったバイトからテキストの解析を開始した場合、バイトの先頭の<span class="arithmatex">\(10\)</span>によりシステムは異常を迅速に検出できます。</p>
+<p><span class="arithmatex">\(10\)</span>をチェックサムとして使用する理由は、UTF-8エンコーディング規則の下では、文字の最上位2ビットが<span class="arithmatex">\(10\)</span>になることは不可能だからです。これは矛盾により証明できます：文字の最上位2ビットが<span class="arithmatex">\(10\)</span>の場合、文字の長さが<span class="arithmatex">\(1\)</span>であることを示し、これはASCIIに対応します。しかし、ASCII文字の最上位ビットは<span class="arithmatex">\(0\)</span>であるべきで、これは仮定と矛盾します。</p>
+<p><a class="glightbox" href="../character_encoding.assets/utf-8_hello_algo.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="UTF-8エンコーディング例" class="animation-figure" src="../character_encoding.assets/utf-8_hello_algo.png" /></a></p>
+<p align="center"> 図 3-8 &nbsp; UTF-8エンコーディング例 </p>
+
+<p>UTF-8以外にも、他の一般的なエンコーディング方法には以下があります：</p>
+<ul>
+<li><strong>UTF-16エンコーディング</strong>：2または4バイトを使用して文字を表現します。すべてのASCII文字と一般的に使用される非英語文字は2バイトで表現され、少数の文字は4バイトが必要です。2バイト文字の場合、UTF-16エンコーディングはUnicodeコードポイントと等しくなります。</li>
+<li><strong>UTF-32エンコーディング</strong>：すべての文字が4バイトを使用します。これは、UTF-32がUTF-8やUTF-16よりも多くの空間を占有することを意味し、特にASCII文字の割合が高いテキストでは顕著です。</li>
+</ul>
+<p>ストレージ空間の観点から、UTF-8を使用して英語文字を表現することは1バイトのみが必要なため非常に効率的です。UTF-16を使用して一部の非英語文字（中国語など）をエンコードすることは、2バイトのみが必要なためより効率的になる場合があります。一方、UTF-8では3バイトが必要になる場合があります。</p>
+<p>互換性の観点から、UTF-8は最も汎用性があり、多くのツールとライブラリがUTF-8を優先的にサポートしています。</p>
+<h2 id="345">3.4.5 &nbsp; プログラミング言語における文字エンコーディング<a class="headerlink" href="#345" title="Permanent link">&para;</a></h2>
+<p>歴史的に、多くのプログラミング言語はプログラム実行中の文字列処理にUTF-16やUTF-32などの固定長エンコーディングを利用していました。これにより文字列を配列として処理でき、いくつかの利点があります：</p>
+<ul>
+<li><strong>ランダムアクセス</strong>：UTF-16でエンコードされた文字列は簡単にランダムアクセスできます。可変長エンコーディングであるUTF-8の場合、<span class="arithmatex">\(i^{th}\)</span>文字の位置を特定するには文字列の開始から<span class="arithmatex">\(i^{th}\)</span>位置まで走査する必要があり、<span class="arithmatex">\(O(n)\)</span>時間がかかります。</li>
+<li><strong>文字数カウント</strong>：ランダムアクセスと同様に、UTF-16でエンコードされた文字列の文字数をカウントすることは<span class="arithmatex">\(O(1)\)</span>操作です。しかし、UTF-8でエンコードされた文字列の文字数をカウントするには文字列全体を走査する必要があります。</li>
+<li><strong>文字列操作</strong>：分割、連結、挿入、削除などの多くの文字列操作は、UTF-16でエンコードされた文字列で簡単です。これらの操作は一般的に、UTF-8エンコーディングの有効性を確保するためにUTF-8でエンコードされた文字列で追加の計算が必要です。</li>
+</ul>
+<p>プログラミング言語における文字エンコーディングスキームの設計は、様々な要因を含む興味深いトピックです：</p>
+<ul>
+<li>Javaの<code>String</code>型はUTF-16エンコーディングを使用し、各文字が2バイトを占有します。これは、16ビットがすべての可能な文字を表現するのに十分であるという初期の信念に基づいており、後に間違いであることが証明されました。Unicode標準が16ビットを超えて拡張されると、Javaの文字は「サロゲートペア」として知られる16ビット値のペアで表現される場合があります。</li>
+<li>JavaScriptとTypeScriptは、Javaと同様の理由でUTF-16エンコーディングを使用します。JavaScriptが1995年にNetscapeによって最初に導入されたとき、Unicodeはまだ初期段階にあり、16ビットエンコーディングはすべてのUnicode文字を表現するのに十分でした。</li>
+<li>C#はUTF-16エンコーディングを使用し、これは主にMicrosoftによって設計された.NETプラットフォーム、および多くのMicrosoft技術（Windowsオペレーティングシステムを含む）がUTF-16エンコーディングを広範囲に使用しているためです。</li>
+</ul>
+<p>文字数の過小評価により、これらの言語は16ビットを超えるUnicode文字を表現するために「サロゲートペア」を使用する必要がありました。このアプローチには欠点があります：サロゲートペアを含む文字列は2バイトまたは4バイトを占有する文字を持つ場合があり、固定長エンコーディングの利点を失います。さらに、サロゲートペアの処理はプログラミングに複雑さとデバッグの困難さを追加します。</p>
+<p>これらの課題に対処するため、一部の言語は代替エンコーディング戦略を採用しています：</p>
+<ul>
+<li>Pythonの<code>str</code>型は、文字のストレージ長が文字列内の最大のUnicodeコードポイントに依存する柔軟な表現でUnicodeエンコーディングを使用します。すべての文字がASCIIの場合、各文字は1バイトを占有し、基本多言語面（BMP）内の文字は2バイト、BMPを超える文字は4バイトを占有します。</li>
+<li>Goの<code>string</code>型は内部的にUTF-8エンコーディングを使用します。Goは個別のUnicodeコードポイントを表現するための<code>rune</code>型も提供します。</li>
+<li>Rustの<code>str</code>と<code>String</code>型は内部的にUTF-8エンコーディングを使用します。Rustは個別のUnicodeコードポイント用の<code>char</code>型も提供します。</li>
+</ul>
+<p>上記の議論は、プログラミング言語での文字列の格納方法に関するものであり、**ファイルでの文字列の格納方法やネットワーク上での送信方法とは異なる**ことに注意することが重要です。ファイルストレージやネットワーク送信では、文字列は通常、最適な互換性と空間効率のためにUTF-8形式でエンコードされます。</p>
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+  </div>
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+  
+  <span class="md-ellipsis">
+    はじめに
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+  
+
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+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_1_label" aria-expanded="false">
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+            <span class="md-nav__icon md-icon"></span>
+            はじめに
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
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+              
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+    </li>
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+        
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+            <a href="../../chapter_preface/" class="md-nav__link ">
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M21 4H3a2 2 0 0 0-2 2v13a2 2 0 0 0 2 2h18a2 2 0 0 0 2-2V6a2 2 0 0 0-2-2M3 19V6h8v13H3m18 0h-8V6h8v13m-7-9.5h6V11h-6V9.5m0 2.5h6v1.5h-6V12m0 2.5h6V16h-6v-1.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 0 章 &nbsp; 前書き
+  </span>
+  
+
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+            
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+          <label class="md-nav__title" for="__nav_2">
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+            第 0 章 &nbsp; 前書き
+          </label>
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+            
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+  
+  
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+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/about_the_book/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.1 &nbsp; この本について
+  </span>
+  
+
+      </a>
+    </li>
+  
+
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+  
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+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/suggestions/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    0.2 &nbsp; 本書の使い方
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.3 &nbsp; まとめ
+  </span>
+  
+
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+        
+      
+        
+      
+        
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+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
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+        
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+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_introduction/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
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+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
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+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
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+            
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+      <a href="../../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
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+        
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+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
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+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_computational_complexity/" class="md-nav__link ">
+              
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
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+            
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+  
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+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
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+    </li>
+  
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+              
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+        </nav>
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+  
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+  
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+    
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+      
+        
+          
+        
+      
+        
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+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
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+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
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+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
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+            
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+    <li class="md-nav__item md-nav__item--active">
+      
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+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#311" class="md-nav__link">
+    <span class="md-ellipsis">
+      3.1.1 &nbsp; 論理構造：線形と非線形
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#312" class="md-nav__link">
+    <span class="md-ellipsis">
+      3.1.2 &nbsp; 物理構造：連続と分散
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
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+
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+  
+    <li class="md-nav__item">
+      <a href="../basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
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+    </li>
+  
+
+              
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+        </nav>
+      
+    </li>
+  
+
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+  
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+          
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+        
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+    
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+    
+    <li class="md-nav__item md-nav__item--nested">
+      
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+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
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+            
+              
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+  
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+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
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+      
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+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
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+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
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+        
+          
+          
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+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
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+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
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+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
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+    </li>
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+
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+  
+  
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+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
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+          </ul>
+        </nav>
+      
+    </li>
+  
+
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+          
+        
+      
+        
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+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
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+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
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+  
+
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+    </li>
+  
+
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+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
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+    </li>
+  
+
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+  
+  
+  
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+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
+                
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+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
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+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
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+
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+              
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+        </nav>
+      
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+              
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+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
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+            第 16 章 &nbsp; 付録
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+            
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+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
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+    </li>
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+
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+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
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+    </li>
+  
+
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+              
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+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
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+  
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+      
+        <li class="md-nav__item">
+  <a href="#311" class="md-nav__link">
+    <span class="md-ellipsis">
+      3.1.1 &nbsp; 論理構造：線形と非線形
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#312" class="md-nav__link">
+    <span class="md-ellipsis">
+      3.1.2 &nbsp; 物理構造：連続と分散
+    </span>
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+</li>
+      
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+  
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+      title="編集"
+      class="md-content__button md-icon"
+    >
+      
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
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+  
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+
+<!-- Page content -->
+<h1 id="31">3.1 &nbsp; データ構造の分類<a class="headerlink" href="#31" title="Permanent link">&para;</a></h1>
+<p>一般的なデータ構造には、配列、連結リスト、スタック、キュー、ハッシュ表、木、ヒープ、グラフがあります。これらは「論理構造」と「物理構造」に分類できます。</p>
+<h2 id="311">3.1.1 &nbsp; 論理構造：線形と非線形<a class="headerlink" href="#311" title="Permanent link">&para;</a></h2>
+<p><strong>論理構造はデータ要素間の論理的関係を明らかにします</strong>。配列と連結リストでは、データは特定の順序で配置され、データ間の線形関係を示しています。一方、木では、データは上から下へ階層的に配置され、「祖先」と「子孫」間の派生関係を示しています。そして、グラフはノードとエッジから構成され、複雑なネットワーク関係を反映しています。</p>
+<p>下図に示されているように、論理構造は「線形」と「非線形」の2つの主要カテゴリに分けることができます。線形構造はより直感的で、データが論理関係において線形に配置されていることを示しています。非線形構造は、逆に非線形に配置されています。</p>
+<ul>
+<li><strong>線形データ構造</strong>：配列、連結リスト、スタック、キュー、ハッシュ表。要素が一対一の順次関係を持ちます。</li>
+<li><strong>非線形データ構造</strong>：木、ヒープ、グラフ、ハッシュ表。</li>
+</ul>
+<p>非線形データ構造は、さらに木構造とネットワーク構造に分けることができます。</p>
+<ul>
+<li><strong>木構造</strong>：木、ヒープ、ハッシュ表。要素が一対多の関係を持ちます。</li>
+<li><strong>ネットワーク構造</strong>：グラフ。要素が多対多の関係を持ちます。</li>
+</ul>
+<p><a class="glightbox" href="../classification_of_data_structure.assets/classification_logic_structure.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Linear and non-linear data structures" class="animation-figure" src="../classification_of_data_structure.assets/classification_logic_structure.png" /></a></p>
+<p align="center"> 図 3-1 &nbsp; Linear and non-linear data structures </p>
+
+<h2 id="312">3.1.2 &nbsp; 物理構造：連続と分散<a class="headerlink" href="#312" title="Permanent link">&para;</a></h2>
+<p><strong>アルゴリズムの実行中、処理されるデータはメモリに格納されます</strong>。下図はコンピュータのメモリスティックを示しており、各黒い正方形は物理メモリ空間です。メモリを巨大なExcelスプレッドシートと考えることができ、各セルは一定量のデータを格納できます。</p>
+<p><strong>システムはメモリアドレスによって目標位置のデータにアクセスします</strong>。下図に示されているように、コンピュータは特定のルールに従って表の各セルに一意の識別子を割り当て、各メモリ空間が一意のメモリアドレスを持つことを保証します。これらのアドレスにより、プログラムはメモリに格納されたデータにアクセスできます。</p>
+<p><a class="glightbox" href="../classification_of_data_structure.assets/computer_memory_location.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Memory stick, memory spaces, memory addresses" class="animation-figure" src="../classification_of_data_structure.assets/computer_memory_location.png" /></a></p>
+<p align="center"> 図 3-2 &nbsp; Memory stick, memory spaces, memory addresses </p>
+
+<div class="admonition tip">
+<p class="admonition-title">Tip</p>
+<p>メモリをExcelスプレッドシートに比較することは簡略化された類推であることに注意してください。メモリの実際の動作メカニズムはより複雑で、アドレス空間、メモリ管理、キャッシュメカニズム、仮想メモリ、物理メモリなどの概念が関係しています。</p>
+</div>
+<p>メモリはすべてのプログラムの共有リソースです。あるメモリブロックが1つのプログラムによって占有されると、他のプログラムが同時に使用することはできません。<strong>したがって、メモリリソースはデータ構造とアルゴリズムの設計における重要な考慮事項です</strong>。例えば、アルゴリズムのピークメモリ使用量は、システムの残り空きメモリを超えてはいけません。連続したメモリブロックが不足している場合は、非連続メモリブロックに格納できるデータ構造を選択する必要があります。</p>
+<p>下図に示されているように、<strong>物理構造はコンピュータメモリにおけるデータの格納方法を反映し</strong>、連続空間格納（配列）と非連続空間格納（連結リスト）に分けることができます。2つのタイプの物理構造は、時間効率と空間効率の観点で補完的な特性を示します。</p>
+<p><a class="glightbox" href="../classification_of_data_structure.assets/classification_phisical_structure.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Contiguous space storage and dispersed space storage" class="animation-figure" src="../classification_of_data_structure.assets/classification_phisical_structure.png" /></a></p>
+<p align="center"> 図 3-3 &nbsp; Contiguous space storage and dispersed space storage </p>
+
+<p><strong>すべてのデータ構造は配列、連結リスト、またはその組み合わせに基づいて実装されていることに注意してください</strong>。例えば、スタックとキューは配列または連結リストのどちらでも実装できます。ハッシュ表の実装には配列と連結リストの両方が関係する場合があります。</p>
+<ul>
+<li><strong>配列ベースの実装</strong>：スタック、キュー、ハッシュ表、木、ヒープ、グラフ、行列、テンソル（次元<span class="arithmatex">\(\geq 3\)</span>の配列）。</li>
+<li><strong>連結リストベースの実装</strong>：スタック、キュー、ハッシュ表、木、ヒープ、グラフなど。</li>
+</ul>
+<p>配列に基づいて実装されたデータ構造は「静的データ構造」とも呼ばれ、初期化後に長さを変更できないことを意味します。逆に、連結リストに基づいたものは「動的データ構造」と呼ばれ、プログラム実行中にサイズを調整できます。</p>
+<div class="admonition tip">
+<p class="admonition-title">Tip</p>
+<p>物理構造を理解するのが困難な場合は、次の章「配列と連結リスト」を読んでから、この節に戻ることをお勧めします。</p>
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m13.13 22.19-1.63-3.83c1.57-.58 3.04-1.36 4.4-2.27l-2.77 6.1M5.64 12.5l-3.83-1.63 6.1-2.77C7 9.46 6.22 10.93 5.64 12.5M19.22 4c.28 0 .53 0 .74.05.17 1.39-.02 4.25-3.3 7.53-1.7 1.71-3.73 3.02-6.01 3.89l-2.15-2.1c.92-2.31 2.23-4.34 3.92-6.03C15.18 4.58 17.64 4 19.22 4m0-2c-1.98 0-4.98.69-8.22 3.93-2.19 2.19-3.5 4.6-4.35 6.71-.28.75-.09 1.57.46 2.13l2.13 2.12c.38.38.89.61 1.42.61.23 0 .47-.06.7-.15A19.1 19.1 0 0 0 18.07 13c5.66-5.66 3.54-10.61 3.54-10.61S20.7 2 19.22 2m-4.68 7.46c-.78-.78-.78-2.05 0-2.83s2.05-.78 2.83 0c.77.78.78 2.05 0 2.83-.78.78-2.05.78-2.83 0m-5.66 7.07-1.41-1.41 1.41 1.41M6.24 22l3.64-3.64c-.34-.09-.67-.24-.97-.45L4.83 22h1.41M2 22h1.41l4.77-4.76-1.42-1.41L2 20.59V22m0-2.83 4.09-4.08c-.21-.3-.36-.62-.45-.97L2 17.76v1.41Z"/></svg>
+  
+  <span class="md-ellipsis">
+    はじめに
+  </span>
+  
+
+            </a>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_1_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_1">
+            <span class="md-nav__icon md-icon"></span>
+            はじめに
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_2" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_preface/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M21 4H3a2 2 0 0 0-2 2v13a2 2 0 0 0 2 2h18a2 2 0 0 0 2-2V6a2 2 0 0 0-2-2M3 19V6h8v13H3m18 0h-8V6h8v13m-7-9.5h6V11h-6V9.5m0 2.5h6v1.5h-6V12m0 2.5h6V16h-6v-1.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 0 章 &nbsp; 前書き
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_2" id="__nav_2_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_2_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_2">
+            <span class="md-nav__icon md-icon"></span>
+            第 0 章 &nbsp; 前書き
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_preface/about_the_book/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.1 &nbsp; この本について
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_preface/suggestions/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.2 &nbsp; 本書の使い方
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_preface/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_introduction/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="./" class="md-nav__link md-nav__link--active">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link md-nav__link--active" for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
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+  
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+      <a href="../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
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+<p><a class="glightbox" href="../assets/covers/chapter_data_structure.jpg" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Data structures" class="cover-image" src="../assets/covers/chapter_data_structure.jpg" /></a></p>
+<div class="admonition abstract">
+<p class="admonition-title">Abstract</p>
+<p>データ構造は堅牢で多様なフレームワークとして機能します。</p>
+<p>データの整然とした組織化のための設計図を提供し、その上でアルゴリズムが生き生きと動き出します。</p>
+</div>
+<h2 id="_1">章の内容<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h2>
+<ul>
+<li><a href="classification_of_data_structure/">3.1 &nbsp; データ構造の分類</a></li>
+<li><a href="basic_data_types/">3.2 &nbsp; 基本データ型</a></li>
+<li><a href="number_encoding/">3.3 &nbsp; 数値エンコーディング *</a></li>
+<li><a href="character_encoding/">3.4 &nbsp; 文字エンコーディング *</a></li>
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#331" class="md-nav__link">
+    <span class="md-ellipsis">
+      3.3.1 &nbsp; 整数エンコーディング
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#332" class="md-nav__link">
+    <span class="md-ellipsis">
+      3.3.2 &nbsp; 浮動小数点数エンコーディング
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_19" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_reference/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9 3v15h3V3H9m3 2 4 13 3-1-4-13-3 1M5 5v13h3V5H5M3 19v2h18v-2H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    参考文献
+  </span>
+  
+
+            </a>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_19_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_19">
+            <span class="md-nav__icon md-icon"></span>
+            参考文献
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
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+            
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+        </nav>
+      
+    </li>
+  
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+    
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+</nav>
+                  </div>
+                </div>
+              </div>
+            
+            
+              
+              <div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
+                <div class="md-sidebar__scrollwrap">
+                  <div class="md-sidebar__inner">
+                    
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#331" class="md-nav__link">
+    <span class="md-ellipsis">
+      3.3.1 &nbsp; 整数エンコーディング
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#332" class="md-nav__link">
+    <span class="md-ellipsis">
+      3.3.2 &nbsp; 浮動小数点数エンコーディング
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+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
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+<h1 id="33">3.3 &nbsp; 数値エンコーディング *<a class="headerlink" href="#33" title="Permanent link">&para;</a></h1>
+<div class="admonition tip">
+<p class="admonition-title">Tip</p>
+<p>本書では、アスタリスク「*」が付いた章は任意読書です。時間が不足している場合や難しいと感じる場合は、最初はこれらをスキップして、必須の章を完了した後に戻ることができます。</p>
+</div>
+<h2 id="331">3.3.1 &nbsp; 整数エンコーディング<a class="headerlink" href="#331" title="Permanent link">&para;</a></h2>
+<p>前の節の表で、すべての整数型は正の数よりも1つ多い負の数を表現できることを観察しました。例えば、<code>byte</code>の範囲は<span class="arithmatex">\([-128, 127]\)</span>です。この現象は直感に反するように見え、その根本的な理由には符号絶対値、1の補数、2の補数エンコーディングの知識が関与しています。</p>
+<p>まず重要なことは、**数値はコンピュータ内で2の補数形式で格納される**ということです。なぜそうなのかを分析する前に、これら3つのエンコーディング方法を定義しましょう：</p>
+<ul>
+<li><strong>符号絶対値</strong>：数値の二進表現の最上位ビットを符号ビットとし、<span class="arithmatex">\(0\)</span>は正の数、<span class="arithmatex">\(1\)</span>は負の数を表します。残りのビットは数値の値を表します。</li>
+<li><strong>1の補数</strong>：正の数の1の補数は符号絶対値と同じです。負の数の場合、符号ビット以外のすべてのビットを反転して得られます。</li>
+<li><strong>2の補数</strong>：正の数の2の補数は符号絶対値と同じです。負の数の場合、その1の補数に<span class="arithmatex">\(1\)</span>を加えて得られます。</li>
+</ul>
+<p>以下の図は、符号絶対値、1の補数、2の補数間の変換を示しています：</p>
+<p><a class="glightbox" href="../number_encoding.assets/1s_2s_complement.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="符号絶対値、1の補数、2の補数間の変換" class="animation-figure" src="../number_encoding.assets/1s_2s_complement.png" /></a></p>
+<p align="center"> 図 3-4 &nbsp; 符号絶対値、1の補数、2の補数間の変換 </p>
+
+<p><u>符号絶対値</u>は最も直感的ですが、制限があります。一つには、<strong>符号絶対値の負の数は計算で直接使用できません</strong>。例えば、符号絶対値で<span class="arithmatex">\(1 + (-2)\)</span>を計算すると<span class="arithmatex">\(-3\)</span>になり、これは正しくありません。</p>
+<div class="arithmatex">\[
+\begin{aligned}
+&amp; 1 + (-2) \newline
+&amp; \rightarrow 0000 \; 0001 + 1000 \; 0010 \newline
+&amp; = 1000 \; 0011 \newline
+&amp; \rightarrow -3
+\end{aligned}
+\]</div>
+<p>この問題に対処するため、コンピュータは<u>1の補数</u>を導入しました。1の補数に変換して<span class="arithmatex">\(1 + (-2)\)</span>を計算し、結果を符号絶対値に戻すと、正しい結果<span class="arithmatex">\(-1\)</span>が得られます。</p>
+<div class="arithmatex">\[
+\begin{aligned}
+&amp; 1 + (-2) \newline
+&amp; \rightarrow 0000 \; 0001 \; \text{(符号絶対値)} + 1000 \; 0010 \; \text{(符号絶対値)} \newline
+&amp; = 0000 \; 0001 \; \text{(1の補数)} + 1111 \; 1101 \; \text{(1の補数)} \newline
+&amp; = 1111 \; 1110 \; \text{(1の補数)} \newline
+&amp; = 1000 \; 0001 \; \text{(符号絶対値)} \newline
+&amp; \rightarrow -1
+\end{aligned}
+\]</div>
+<p>また、<strong>符号絶対値では0に2つの表現があります</strong>：<span class="arithmatex">\(+0\)</span>と<span class="arithmatex">\(-0\)</span>です。これは0に対して2つの異なる二進エンコーディングがあることを意味し、曖昧さを引き起こす可能性があります。例えば、条件チェックで正と負の0を区別しないと、正しくない結果になる可能性があります。この曖昧さに対処するには追加のチェックが必要で、計算効率が低下する可能性があります。</p>
+<div class="arithmatex">\[
+\begin{aligned}
++0 &amp; \rightarrow 0000 \; 0000 \newline
+-0 &amp; \rightarrow 1000 \; 0000
+\end{aligned}
+\]</div>
+<p>符号絶対値と同様に、1の補数も正と負の0の曖昧さに悩まされます。そのため、コンピュータはさらに<u>2の補数</u>を導入しました。符号絶対値、1の補数、2の補数における負の0の変換過程を観察してみましょう：</p>
+<div class="arithmatex">\[
+\begin{aligned}
+-0 \rightarrow \; &amp; 1000 \; 0000 \; \text{(符号絶対値)} \newline
+= \; &amp; 1111 \; 1111 \; \text{(1の補数)} \newline
+= 1 \; &amp; 0000 \; 0000 \; \text{(2の補数)} \newline
+\end{aligned}
+\]</div>
+<p>負の0の1の補数に<span class="arithmatex">\(1\)</span>を加えると桁上がりが発生しますが、<code>byte</code>の長さは8ビットのみのため、9番目のビットへの桁上がり<span class="arithmatex">\(1\)</span>は破棄されます。したがって、**負の0の2の補数は<span class="arithmatex">\(0000 \; 0000\)</span>**で、正の0と同じになり、曖昧さが解決されます。</p>
+<p>最後の謎は、<code>byte</code>の<span class="arithmatex">\([-128, 127]\)</span>の範囲で、追加の負の数<span class="arithmatex">\(-128\)</span>があることです。<span class="arithmatex">\([-127, +127]\)</span>の区間では、すべての整数に対応する符号絶対値、1の補数、2の補数があり、相互変換が可能であることを観察します。</p>
+<p>しかし、<strong>2の補数<span class="arithmatex">\(1000 \; 0000\)</span>は対応する符号絶対値を持たない例外です</strong>。変換方法によると、その符号絶対値は<span class="arithmatex">\(0000 \; 0000\)</span>で、0を示します。これは矛盾を示しています。なぜなら、その2の補数は自分自身を表すべきだからです。コンピュータは、この特別な2の補数<span class="arithmatex">\(1000 \; 0000\)</span>を<span class="arithmatex">\(-128\)</span>を表すものとして指定しています。実際、2の補数での<span class="arithmatex">\((-1) + (-127)\)</span>の計算結果は<span class="arithmatex">\(-128\)</span>になります。</p>
+<div class="arithmatex">\[
+\begin{aligned}
+&amp; (-127) + (-1) \newline
+&amp; \rightarrow 1111 \; 1111 \; \text{(符号絶対値)} + 1000 \; 0001 \; \text{(符号絶対値)} \newline
+&amp; = 1000 \; 0000 \; \text{(1の補数)} + 1111 \; 1110 \; \text{(1の補数)} \newline
+&amp; = 1000 \; 0001 \; \text{(2の補数)} + 1111 \; 1111 \; \text{(2の補数)} \newline
+&amp; = 1000 \; 0000 \; \text{(2の補数)} \newline
+&amp; \rightarrow -128
+\end{aligned}
+\]</div>
+<p>お気づきかもしれませんが、これらの計算はすべて加算であり、重要な事実を示唆しています：<strong>コンピュータの内部ハードウェア回路は主に加算演算を中心に設計されています</strong>。これは、加算が乗算、除算、減算などの他の演算と比較してハードウェアで実装しやすく、並列化が容易で高速計算が可能だからです。</p>
+<p>これはコンピュータが加算のみを実行できることを意味するものではありません。<strong>加算と基本的な論理演算を組み合わせることで、コンピュータは様々な他の数学演算を実行できます</strong>。例えば、減算<span class="arithmatex">\(a - b\)</span>は<span class="arithmatex">\(a + (-b)\)</span>に変換でき、乗算と除算は複数の加算または減算に変換できます。</p>
+<p>コンピュータで2の補数を使用する理由をまとめることができます：2の補数表現により、コンピュータは同じ回路と演算を使用して正と負の数の加算を処理でき、減算用の特別なハードウェア回路の必要性を排除し、正と負の0の曖昧さを回避できます。これによりハードウェア設計が大幅に簡素化され、計算効率が向上します。</p>
+<p>2の補数の設計は非常に巧妙で、スペースの制約により、ここで停止します。興味のある読者はさらに探求することを奨励します。</p>
+<h2 id="332">3.3.2 &nbsp; 浮動小数点数エンコーディング<a class="headerlink" href="#332" title="Permanent link">&para;</a></h2>
+<p>興味深いことに気づいたかもしれません：同じ4バイトの長さにもかかわらず、なぜ<code>float</code>は<code>int</code>と比較してはるかに大きい値の範囲を持つのでしょうか？これは直感に反するように見えます。<code>float</code>は分数を表現する必要があるため、範囲が縮小すると予想されるからです。</p>
+<p>実際、<strong>これは浮動小数点数（<code>float</code>）で使用される異なる表現方法によるものです</strong>。32ビットの二進数を次のように考えてみましょう：</p>
+<div class="arithmatex">\[
+b_{31} b_{30} b_{29} \ldots b_2 b_1 b_0
+\]</div>
+<p>IEEE 754標準によると、32ビットの<code>float</code>は次の3つの部分で構成されます：</p>
+<ul>
+<li>符号ビット<span class="arithmatex">\(\mathrm{S}\)</span>：1ビットを占有し、<span class="arithmatex">\(b_{31}\)</span>に対応します。</li>
+<li>指数ビット<span class="arithmatex">\(\mathrm{E}\)</span>：8ビットを占有し、<span class="arithmatex">\(b_{30} b_{29} \ldots b_{23}\)</span>に対応します。</li>
+<li>仮数ビット<span class="arithmatex">\(\mathrm{N}\)</span>：23ビットを占有し、<span class="arithmatex">\(b_{22} b_{21} \ldots b_0\)</span>に対応します。</li>
+</ul>
+<p>二進<code>float</code>数の値は次のように計算されます：</p>
+<div class="arithmatex">\[
+\text{val} = (-1)^{b_{31}} \times 2^{\left(b_{30} b_{29} \ldots b_{23}\right)_2 - 127} \times \left(1 . b_{22} b_{21} \ldots b_0\right)_2
+\]</div>
+<p>十進公式に変換すると、次のようになります：</p>
+<div class="arithmatex">\[
+\text{val} = (-1)^{\mathrm{S}} \times 2^{\mathrm{E} - 127} \times (1 + \mathrm{N})
+\]</div>
+<p>各成分の範囲は：</p>
+<div class="arithmatex">\[
+\begin{aligned}
+\mathrm{S} \in &amp; \{ 0, 1\}, \quad \mathrm{E} \in \{ 1, 2, \dots, 254 \} \newline
+(1 + \mathrm{N}) = &amp; (1 + \sum_{i=1}^{23} b_{23-i} \times 2^{-i}) \subset [1, 2 - 2^{-23}]
+\end{aligned}
+\]</div>
+<p><a class="glightbox" href="../number_encoding.assets/ieee_754_float.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="IEEE 754標準での浮動小数点数の計算例" class="animation-figure" src="../number_encoding.assets/ieee_754_float.png" /></a></p>
+<p align="center"> 図 3-5 &nbsp; IEEE 754標準での浮動小数点数の計算例 </p>
+
+<p>上の図を観察すると、例のデータ<span class="arithmatex">\(\mathrm{S} = 0\)</span>、<span class="arithmatex">\(\mathrm{E} = 124\)</span>、<span class="arithmatex">\(\mathrm{N} = 2^{-2} + 2^{-3} = 0.375\)</span>が与えられた場合：</p>
+<div class="arithmatex">\[
+\text{val} = (-1)^0 \times 2^{124 - 127} \times (1 + 0.375) = 0.171875
+\]</div>
+<p>これで最初の質問に答えることができます：<strong><code>float</code>の表現には指数ビットが含まれているため、<code>int</code>よりもはるかに大きい範囲を持ちます</strong>。上記の計算に基づくと、<code>float</code>で表現可能な最大正の数は約<span class="arithmatex">\(2^{254 - 127} \times (2 - 2^{-23}) \approx 3.4 \times 10^{38}\)</span>で、最小負の数は符号ビットを切り替えることで得られます。</p>
+<p><strong>しかし、<code>float</code>の拡張された範囲のトレードオフは精度の犠牲です</strong>。整数型<code>int</code>は32ビットすべてを数値表現に使用し、値は均等に分布していますが、指数ビットのため、<code>float</code>の値が大きいほど、隣接する数値間の差が大きくなります。</p>
+<p>以下の表に示すように、指数ビット<span class="arithmatex">\(\mathrm{E} = 0\)</span>と<span class="arithmatex">\(\mathrm{E} = 255\)</span>は特別な意味を持ち、<strong>0、無限大、<span class="arithmatex">\(\mathrm{NaN}\)</span>などを表現するために使用されます</strong>。</p>
+<p align="center"> 表 3-2 &nbsp; 指数ビットの意味 </p>
+
+<div class="center-table">
+<table>
+<thead>
+<tr>
+<th>指数ビットE</th>
+<th>仮数ビット<span class="arithmatex">\(\mathrm{N} = 0\)</span></th>
+<th>仮数ビット<span class="arithmatex">\(\mathrm{N} \ne 0\)</span></th>
+<th>計算公式</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td><span class="arithmatex">\(0\)</span></td>
+<td><span class="arithmatex">\(\pm 0\)</span></td>
+<td>非正規化数</td>
+<td><span class="arithmatex">\((-1)^{\mathrm{S}} \times 2^{-126} \times (0.\mathrm{N})\)</span></td>
+</tr>
+<tr>
+<td><span class="arithmatex">\(1, 2, \dots, 254\)</span></td>
+<td>正規化数</td>
+<td>正規化数</td>
+<td><span class="arithmatex">\((-1)^{\mathrm{S}} \times 2^{(\mathrm{E} -127)} \times (1.\mathrm{N})\)</span></td>
+</tr>
+<tr>
+<td><span class="arithmatex">\(255\)</span></td>
+<td><span class="arithmatex">\(\pm \infty\)</span></td>
+<td><span class="arithmatex">\(\mathrm{NaN}\)</span></td>
+<td></td>
+</tr>
+</tbody>
+</table>
+</div>
+<p>非正規化数は浮動小数点数の精度を大幅に向上させることは注目に値します。最小の正の正規化数は<span class="arithmatex">\(2^{-126}\)</span>で、最小の正の非正規化数は<span class="arithmatex">\(2^{-126} \times 2^{-23}\)</span>です。</p>
+<p>倍精度<code>double</code>も<code>float</code>と同様の表現方法を使用しますが、簡潔さのためここでは詳述しません。</p>
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+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 重要なポイント
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#2-q-a" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; Q &amp; A
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
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+<h1 id="35">3.5 &nbsp; まとめ<a class="headerlink" href="#35" title="Permanent link">&para;</a></h1>
+<h3 id="1">1. &nbsp; 重要なポイント<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<ul>
+<li>データ構造は論理構造と物理構造の2つの観点から分類できます。論理構造はデータ間の論理的関係を記述し、物理構造はデータがメモリにどのように格納されるかを記述します。</li>
+<li>よく使用される論理構造には、線形構造、木、ネットワークがあります。通常、論理構造に基づいてデータ構造を線形（配列、連結リスト、スタック、キュー）と非線形（木、グラフ、ヒープ）に分けます。ハッシュ表の実装は線形と非線形の両方のデータ構造を含む場合があります。</li>
+<li>プログラムが実行中の際、データはメモリに格納されます。各メモリ空間には対応するアドレスがあり、プログラムはこれらのアドレスを通じてデータにアクセスします。</li>
+<li>物理構造は連続空間格納（配列）と離散空間格納（連結リスト）に分けることができます。すべてのデータ構造は配列、連結リスト、またはその両方の組み合わせを使用して実装されます。</li>
+<li>コンピュータの基本データ型には、整数（<code>byte</code>、<code>short</code>、<code>int</code>、<code>long</code>）、浮動小数点数（<code>float</code>、<code>double</code>）、文字（<code>char</code>）、ブール値（<code>bool</code>）が含まれます。データ型の値の範囲は、そのサイズと表現に依存します。</li>
+<li>符号絶対値、1の補数、2の補数は、コンピュータで整数をエンコードする3つの方法であり、相互に変換することができます。符号絶対値の最上位ビットは符号ビットで、残りのビットは数値の値を表します。</li>
+<li>整数はコンピュータで2の補数によってエンコードされます。この表現の利点には、(i)コンピュータが正と負の整数の加算を統一できる、(ii)減算用の特別なハードウェア回路を設計する必要がない、(iii)正と負の0の曖昧さがない、があります。</li>
+<li>浮動小数点数のエンコーディングは、1つの符号ビット、8つの指数ビット、23の仮数ビットで構成されます。指数ビットのため、浮動小数点数の範囲は整数よりもはるかに大きくなりますが、精度を犠牲にします。</li>
+<li>ASCIIは最初期の英語文字セットで、1バイトの長さで計127文字です。GBKは人気のある中国語文字セットで、2万文字以上の中国語文字を含みます。Unicodeは世界の様々な言語の文字を含む完全な文字セット標準を提供することを目的とし、文字エンコーディング方法の不一致による文字化け問題を解決します。</li>
+<li>UTF-8は最も人気があり一般的なUnicodeエンコーディング方法です。これは可変長エンコーディング方法で、優れた拡張性と空間効率を持ちます。UTF-16とUTF-32は固定長エンコーディング方法です。中国語文字をエンコードする際、UTF-16はUTF-8よりも少ない空間を使用します。JavaやC#などのプログラミング言語はデフォルトでUTF-16エンコーディングを使用します。</li>
+</ul>
+<h3 id="2-q-a">2. &nbsp; Q &amp; A<a class="headerlink" href="#2-q-a" title="Permanent link">&para;</a></h3>
+<p><strong>Q</strong>: なぜハッシュ表は線形と非線形の両方のデータ構造を含むのですか？</p>
+<p>ハッシュ表の基礎構造は配列です。ハッシュ衝突を解決するために、「チェイン法」を使用する場合があります（後の節「ハッシュ衝突」で説明）：配列の各バケットは連結リストを指し、その長さが特定の閾値より大きくなると木（通常は赤黒木）に変換される可能性があります。
+格納の観点から、ハッシュ表の基礎構造は配列で、各バケットには値、連結リスト、または木が含まれる場合があります。したがって、ハッシュ表は線形データ構造（配列、連結リスト）と非線形データ構造（木）の両方を含む場合があります。</p>
+<p><strong>Q</strong>: <code>char</code>型の長さは1バイトですか？</p>
+<p><code>char</code>型の長さは、プログラミング言語のエンコーディング方法によって決まります。例えば、Java、JavaScript、TypeScript、C#はすべてUTF-16エンコーディング（Unicodeコードポイントを保存するため）を使用するため、<code>char</code>型の長さは2バイトです。</p>
+<p><strong>Q</strong>: 配列ベースのデータ構造を「静的データ構造」と呼ぶことに曖昧さはありませんか？スタックもプッシュやポップなどの「動的」操作を実行できます。</p>
+<p>スタックは動的なデータ操作を実装できますが、データ構造は依然として「静的」です（長さが固定）。配列ベースのデータ構造は動的に要素を追加または削除できますが、その容量は固定されています。スタックサイズが事前に割り当てられたサイズを超える場合、古い配列は新しく作成されたより大きな配列にコピーされます。</p>
+<p><strong>Q</strong>: スタック（キュー）を構築する際、そのサイズが指定されていないのに、なぜ「静的データ構造」なのですか？</p>
+<p>高級プログラミング言語では、スタック（キュー）の初期容量を手動で指定する必要はありません。このタスクはクラス内で自動的に完了されます。例えば、Javaの<code>ArrayList</code>の初期容量は通常10です。さらに、拡張操作も自動的に完了されます。詳細については、後続の「リスト」の章を参照してください。</p>
+<p><strong>Q</strong>: 符号絶対値を2の補数に変換する方法は「最初に否定してから1を加える」ですので、2の補数を符号絶対値に変換することはその逆操作「最初に1を減算してから否定する」であるべきです。
+しかし、2の補数も「最初に否定してから1を加える」を通じて符号絶対値に変換できます。なぜですか？</p>
+<p><strong>A</strong>: これは、符号絶対値と2の補数間の相互変換が「補数」の計算と等価だからです。まず補数を定義します：<span class="arithmatex">\(a + b = c\)</span>と仮定すると、<span class="arithmatex">\(a\)</span>は<span class="arithmatex">\(b\)</span>の<span class="arithmatex">\(c\)</span>に対する補数と言い、逆に<span class="arithmatex">\(b\)</span>は<span class="arithmatex">\(a\)</span>の<span class="arithmatex">\(c\)</span>に対する補数と言います。</p>
+<p>長さ<span class="arithmatex">\(n = 4\)</span>の二進数<span class="arithmatex">\(0010\)</span>が与えられた場合、この数が符号絶対値（符号ビットを無視）の場合、その2の補数は「最初に否定してから1を加える」ことで得られます：</p>
+<div class="arithmatex">\[
+0010 \rightarrow 1101 \rightarrow 1110
+\]</div>
+<p>符号絶対値と2の補数の和が<span class="arithmatex">\(0010 + 1110 = 10000\)</span>であることを観察します。つまり、2の補数<span class="arithmatex">\(1110\)</span>は符号絶対値<span class="arithmatex">\(0010\)</span>の<span class="arithmatex">\(10000\)</span>に対する「補数」です。<strong>これは、上記の「最初に否定してから1を加える」が<span class="arithmatex">\(10000\)</span>に対する補数の計算と等価であることを意味します</strong>。</p>
+<p>では、<span class="arithmatex">\(1110\)</span>の<span class="arithmatex">\(10000\)</span>に対する「補数」は何でしょうか？「最初に否定してから1を加える」ことで計算できます：</p>
+<div class="arithmatex">\[
+1110 \rightarrow 0001 \rightarrow 0010
+\]</div>
+<p>言い換えると、符号絶対値と2の補数は互いに<span class="arithmatex">\(10000\)</span>に対する「補数」であるため、「符号絶対値から2の補数」と「2の補数から符号絶対値」は同じ操作（最初に否定してから1を加える）で実装できます。</p>
+<p>もちろん、「最初に否定してから1を加える」の逆操作を使用して2の補数<span class="arithmatex">\(1110\)</span>の符号絶対値を求めることもできます。つまり、「最初に1を減算してから否定する」：</p>
+<div class="arithmatex">\[
+1110 \rightarrow 1101 \rightarrow 0010
+\]</div>
+<p>要約すると、「最初に否定してから1を加える」と「最初に1を減算してから否定する」は両方とも<span class="arithmatex">\(10000\)</span>に対する補数を計算しており、等価です。</p>
+<p>本質的に、「否定」操作は実際には<span class="arithmatex">\(1111\)</span>に対する補数を求めることです（<code>符号絶対値 + 1の補数 = 1111</code>が常に成り立つため）。そして1の補数に1を加えることは<span class="arithmatex">\(10000\)</span>に対する2の補数と等しくなります。</p>
+<p>上記では<span class="arithmatex">\(n = 4\)</span>を例に取りましたが、任意の桁数の任意の二進数に一般化できます。</p>
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m13.13 22.19-1.63-3.83c1.57-.58 3.04-1.36 4.4-2.27l-2.77 6.1M5.64 12.5l-3.83-1.63 6.1-2.77C7 9.46 6.22 10.93 5.64 12.5M19.22 4c.28 0 .53 0 .74.05.17 1.39-.02 4.25-3.3 7.53-1.7 1.71-3.73 3.02-6.01 3.89l-2.15-2.1c.92-2.31 2.23-4.34 3.92-6.03C15.18 4.58 17.64 4 19.22 4m0-2c-1.98 0-4.98.69-8.22 3.93-2.19 2.19-3.5 4.6-4.35 6.71-.28.75-.09 1.57.46 2.13l2.13 2.12c.38.38.89.61 1.42.61.23 0 .47-.06.7-.15A19.1 19.1 0 0 0 18.07 13c5.66-5.66 3.54-10.61 3.54-10.61S20.7 2 19.22 2m-4.68 7.46c-.78-.78-.78-2.05 0-2.83s2.05-.78 2.83 0c.77.78.78 2.05 0 2.83-.78.78-2.05.78-2.83 0m-5.66 7.07-1.41-1.41 1.41 1.41M6.24 22l3.64-3.64c-.34-.09-.67-.24-.97-.45L4.83 22h1.41M2 22h1.41l4.77-4.76-1.42-1.41L2 20.59V22m0-2.83 4.09-4.08c-.21-.3-.36-.62-.45-.97L2 17.76v1.41Z"/></svg>
+  
+  <span class="md-ellipsis">
+    はじめに
+  </span>
+  
+
+            </a>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_1_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_1">
+            <span class="md-nav__icon md-icon"></span>
+            はじめに
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
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+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_2" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_preface/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M21 4H3a2 2 0 0 0-2 2v13a2 2 0 0 0 2 2h18a2 2 0 0 0 2-2V6a2 2 0 0 0-2-2M3 19V6h8v13H3m18 0h-8V6h8v13m-7-9.5h6V11h-6V9.5m0 2.5h6v1.5h-6V12m0 2.5h6V16h-6v-1.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 0 章 &nbsp; 前書き
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_2" id="__nav_2_label" tabindex="0">
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_2_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_2">
+            <span class="md-nav__icon md-icon"></span>
+            第 0 章 &nbsp; 前書き
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/about_the_book/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.1 &nbsp; この本について
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/suggestions/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.2 &nbsp; 本書の使い方
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_introduction/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 分割統治に基づく二分探索の実装
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
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+<h1 id="122">12.2 &nbsp; 分割統治検索戦略<a class="headerlink" href="#122" title="Permanent link">&para;</a></h1>
+<p>私たちは検索アルゴリズムが主に2つのカテゴリに分類されることを学びました。</p>
+<ul>
+<li><strong>総当たり検索</strong>：データ構造を走査することで実装され、時間計算量は <span class="arithmatex">\(O(n)\)</span> です。</li>
+<li><strong>適応検索</strong>：独特なデータ組織形式や事前情報を利用し、時間計算量は <span class="arithmatex">\(O(\log n)\)</span> または <span class="arithmatex">\(O(1)\)</span> に達することができます。</li>
+</ul>
+<p>実際、<strong>時間計算量が <span class="arithmatex">\(O(\log n)\)</span> の検索アルゴリズムは通常分割統治戦略に基づいています</strong>。例えば、二分探索や木などです。</p>
+<ul>
+<li>二分探索の各ステップは、問題（配列内でターゲット要素を検索する）をより小さな問題（配列の半分でターゲット要素を検索する）に分割し、配列が空になるかターゲット要素が見つかるまで続けます。</li>
+<li>木は分割統治のアイデアを表現し、二分探索木、AVL木、ヒープなどのデータ構造では、様々な操作の時間計算量は <span class="arithmatex">\(O(\log n)\)</span> です。</li>
+</ul>
+<p>二分探索の分割統治戦略は以下の通りです。</p>
+<ul>
+<li><strong>問題を分割できる</strong>：二分探索は元の問題（配列内での検索）を部分問題（配列の半分での検索）に再帰的に分割し、中間要素とターゲット要素を比較することで実現されます。</li>
+<li><strong>部分問題は独立している</strong>：二分探索では、各ラウンドで一つの部分問題を処理し、他の部分問題に影響されません。</li>
+<li><strong>部分問題の解をマージする必要がない</strong>：二分探索は特定の要素を見つけることを目的としているため、部分問題の解をマージする必要がありません。部分問題が解決されると、元の問題も解決されます。</li>
+</ul>
+<p>分割統治は検索効率を向上させることができます。なぜなら、総当たり検索はラウンドごとに1つの選択肢しか除去できませんが、<strong>分割統治は選択肢の半分を除去できるからです</strong>。</p>
+<h3 id="1">1. &nbsp; 分割統治に基づく二分探索の実装<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<p>前の章では、二分探索は反復に基づいて実装されました。今度は、分割統治（再帰）に基づいて実装します。</p>
+<div class="admonition question">
+<p class="admonition-title">Question</p>
+<p>長さ <span class="arithmatex">\(n\)</span> の順序付けられた配列 <code>nums</code> が与えられ、すべての要素が一意である場合、要素 <code>target</code> を見つけてください。</p>
+</div>
+<p>分割統治の観点から、検索区間 <span class="arithmatex">\([i, j]\)</span> に対応する部分問題を <span class="arithmatex">\(f(i, j)\)</span> と表します。</p>
+<p>元の問題 <span class="arithmatex">\(f(0, n-1)\)</span> から開始して、以下のステップで二分探索を実行します。</p>
+<ol>
+<li>検索区間 <span class="arithmatex">\([i, j]\)</span> の中点 <span class="arithmatex">\(m\)</span> を計算し、それを使用して検索区間の半分を除去します。</li>
+<li>半分のサイズに縮小された部分問題を再帰的に解決します。これは <span class="arithmatex">\(f(i, m-1)\)</span> または <span class="arithmatex">\(f(m+1, j)\)</span> になる可能性があります。</li>
+<li><code>target</code> が見つかるか区間が空になってリターンするまで、ステップ <code>1.</code> と <code>2.</code> を繰り返します。</li>
+</ol>
+<p>以下の図は、配列内で要素 <span class="arithmatex">\(6\)</span> を探す二分探索の分割統治過程を示しています。</p>
+<p><a class="glightbox" href="../binary_search_recur.assets/binary_search_recur.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="二分探索の分割統治過程" class="animation-figure" src="../binary_search_recur.assets/binary_search_recur.png" /></a></p>
+<p align="center"> 図 12-4 &nbsp; 二分探索の分割統治過程 </p>
+
+<p>実装コードでは、問題 <span class="arithmatex">\(f(i, j)\)</span> を解決するために再帰関数 <code>dfs()</code> を宣言します：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:14"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><input id="__tabbed_1_14" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label><label for="__tabbed_1_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_recur.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">target</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">j</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;二分探索：問題 f(i, j)&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># 区間が空の場合、対象要素がないことを示すため、-1 を返す</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="k">if</span> <span class="n">i</span> <span class="o">&gt;</span> <span class="n">j</span><span class="p">:</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>        <span class="k">return</span> <span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="c1"># 中点インデックス m を計算</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>    <span class="n">m</span> <span class="o">=</span> <span class="p">(</span><span class="n">i</span> <span class="o">+</span> <span class="n">j</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>    <span class="k">if</span> <span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span> <span class="o">&lt;</span> <span class="n">target</span><span class="p">:</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>        <span class="c1"># 再帰部分問題 f(m+1, j)</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>        <span class="k">return</span> <span class="n">dfs</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="n">target</span><span class="p">,</span> <span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">j</span><span class="p">)</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>    <span class="k">elif</span> <span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">target</span><span class="p">:</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>        <span class="c1"># 再帰部分問題 f(i, m-1)</span>
+<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>        <span class="k">return</span> <span class="n">dfs</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="n">target</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">m</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>    <span class="k">else</span><span class="p">:</span>
+<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>        <span class="c1"># 対象要素を発見したため、そのインデックスを返す</span>
+<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>        <span class="k">return</span> <span class="n">m</span>
+<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>
+<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a><span class="k">def</span><span class="w"> </span><span class="nf">binary_search</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">target</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;二分探索&quot;&quot;&quot;</span>
+<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a>    <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
+<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a>    <span class="c1"># 問題 f(0, n-1) を解く</span>
+<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a>    <span class="k">return</span> <span class="n">dfs</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="n">target</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_recur.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 二分探索：問題 f(i, j) */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// 区間が空の場合、対象要素が存在しないことを示すため、-1 を返す</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="c1">// 中点インデックス m を計算</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">        </span><span class="c1">// 再帰的な部分問題 f(m+1, j)</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">);</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">        </span><span class="c1">// 再帰的な部分問題 f(i, m-1)</span>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">        </span><span class="c1">// 対象要素が見つかったため、そのインデックスを返す</span>
+<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">m</span><span class="p">;</span>
+<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="p">}</span>
+<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a>
+<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="cm">/* 二分探索 */</span>
+<a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a><span class="kt">int</span><span class="w"> </span><span class="nf">binarySearch</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
+<a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a><span class="w">    </span><span class="c1">// 問題 f(0, n-1) を解く</span>
+<a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-1-26" name="__codelineno-1-26" href="#__codelineno-1-26"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_recur.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 二分探索：問題 f(i, j) */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// 区間が空の場合、対象要素が存在しないことを示すため、-1 を返す</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="c1">// 中点インデックス m を計算</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">        </span><span class="c1">// 再帰的な部分問題 f(m+1, j)</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">);</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">        </span><span class="c1">// 再帰的な部分問題 f(i, m-1)</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">    </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">        </span><span class="c1">// 対象要素が見つかったため、そのインデックスを返す</span>
+<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">m</span><span class="p">;</span>
+<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="p">}</span>
+<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a>
+<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="cm">/* 二分探索 */</span>
+<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a><span class="kt">int</span><span class="w"> </span><span class="nf">binarySearch</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="p">;</span>
+<a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a><span class="w">    </span><span class="c1">// 問題 f(0, n-1) を解く</span>
+<a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_recur.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">binary_search_recur</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">DFS</span><span class="p">}</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">binary_search_recur</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">BinarySearch</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_recur.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">dfs</span><span class="p">}</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">binarySearch</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_recur.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">binarySearch</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_recur.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">dfs</span><span class="p">}</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">binarySearch</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_recur.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">dfs</span><span class="p">}</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">binarySearch</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_recur.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binarySearch</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_recur.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binary_search</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_recur.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binarySearch</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_recur.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">dfs</span><span class="p">}</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">binarySearch</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_recur.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">dfs</span><span class="p">}</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">binary_search</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_recur.zig</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a>
+<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binarySearch</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
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diff --git a/ja/chapter_divide_and_conquer/build_binary_tree_problem.assets/build_tree_division_pointers.png b/ja/chapter_divide_and_conquer/build_binary_tree_problem.assets/build_tree_division_pointers.png
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diff --git a/ja/chapter_divide_and_conquer/build_binary_tree_problem.assets/built_tree_step1.png b/ja/chapter_divide_and_conquer/build_binary_tree_problem.assets/built_tree_step1.png
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diff --git a/ja/chapter_divide_and_conquer/build_binary_tree_problem.assets/built_tree_step5.png b/ja/chapter_divide_and_conquer/build_binary_tree_problem.assets/built_tree_step5.png
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diff --git a/ja/chapter_divide_and_conquer/build_binary_tree_problem.assets/built_tree_step6.png b/ja/chapter_divide_and_conquer/build_binary_tree_problem.assets/built_tree_step6.png
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diff --git a/ja/chapter_divide_and_conquer/build_binary_tree_problem.assets/built_tree_step7.png b/ja/chapter_divide_and_conquer/build_binary_tree_problem.assets/built_tree_step7.png
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+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 分割統治問題かどうかの判定
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; 部分木の分割方法
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#3" class="md-nav__link">
+    <span class="md-ellipsis">
+      3. &nbsp; 変数に基づく部分木範囲の記述
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#4" class="md-nav__link">
+    <span class="md-ellipsis">
+      4. &nbsp; コード実装
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
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+  
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+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
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+    </li>
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+
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+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
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+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
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+  
+
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+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
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+  </span>
+  
+
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+  
+
+              
+            
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+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
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+              
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+      
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+    <span class="md-ellipsis">
+      1. &nbsp; 分割統治問題かどうかの判定
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; 部分木の分割方法
+    </span>
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+      
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+    <span class="md-ellipsis">
+      3. &nbsp; 変数に基づく部分木範囲の記述
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#4" class="md-nav__link">
+    <span class="md-ellipsis">
+      4. &nbsp; コード実装
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+</li>
+      
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+                  </div>
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+<h1 id="123">12.3 &nbsp; 二分木構築問題<a class="headerlink" href="#123" title="Permanent link">&para;</a></h1>
+<div class="admonition question">
+<p class="admonition-title">Question</p>
+<p>二分木の前順走査 <code>preorder</code> シーケンスと中順走査 <code>inorder</code> シーケンスが与えられた場合、二分木を構築してそのルートノードを返してください。二分木に重複するノード値がないと仮定します（以下の図に示すように）。</p>
+</div>
+<p><a class="glightbox" href="../build_binary_tree_problem.assets/build_tree_example.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="二分木構築のサンプルデータ" class="animation-figure" src="../build_binary_tree_problem.assets/build_tree_example.png" /></a></p>
+<p align="center"> 図 12-5 &nbsp; 二分木構築のサンプルデータ </p>
+
+<h3 id="1">1. &nbsp; 分割統治問題かどうかの判定<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<p><code>preorder</code> と <code>inorder</code> シーケンスから二分木を構築する元の問題は、典型的な分割統治問題です。</p>
+<ul>
+<li><strong>問題を分解できる</strong>：分割統治の観点から、元の問題を2つの部分問題（左の部分木の構築と右の部分木の構築）とルートノードの初期化という1つの操作に分割できます。各部分木（部分問題）について、同じアプローチを継続的に適用し、より小さな部分木（部分問題）に分割し、最小の部分問題（空の部分木）に到達するまで続けます。</li>
+<li><strong>部分問題は独立している</strong>：左と右の部分木は重複しません。左の部分木を構築する際、左の部分木に対応する中順走査と前順走査のセグメントのみが必要です。右の部分木にも同じアプローチが適用されます。</li>
+<li><strong>部分問題の解を組み合わせることができる</strong>：左と右の部分木（部分問題の解）を構築したら、それらをルートノードに接続して元の問題の解を取得できます。</li>
+</ul>
+<h3 id="2">2. &nbsp; 部分木の分割方法<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
+<p>上記の分析に基づいて、この問題は分割統治を使用して解決できます。<strong>しかし、前順走査 <code>preorder</code> シーケンスと中順走査 <code>inorder</code> シーケンスを使用して左と右の部分木をどのように分割すればよいでしょうか？</strong></p>
+<p>定義により、<code>preorder</code> と <code>inorder</code> シーケンスの両方を3つの部分に分割できます：</p>
+<ul>
+<li>前順走査：<code>[ ルート | 左の部分木 | 右の部分木 ]</code>。例えば、図では、木は <code>[ 3 | 9 | 2 1 7 ]</code> に対応します。</li>
+<li>中順走査：<code>[ 左の部分木 | ルート | 右の部分木 ]</code>。例えば、図では、木は <code>[ 9 | 3 | 1 2 7 ]</code> に対応します。</li>
+</ul>
+<p>前の図のデータを使用して、次の図に示すステップに従って分割結果を取得できます：</p>
+<ol>
+<li>前順走査の最初の要素3がルートノードの値です。</li>
+<li><code>inorder</code> シーケンス内でルートノード3のインデックスを見つけ、このインデックスを使用して <code>inorder</code> を <code>[ 9 | 3 ｜ 1 2 7 ]</code> に分割します。</li>
+<li><code>inorder</code> シーケンスの分割に従って、左と右の部分木がそれぞれ1個と3個のノードを含むことが簡単に決定できるため、<code>preorder</code> シーケンスを <code>[ 3 | 9 | 2 1 7 ]</code> に対応して分割できます。</li>
+</ol>
+<p><a class="glightbox" href="../build_binary_tree_problem.assets/build_tree_preorder_inorder_division.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="前順走査と中順走査での部分木の分割" class="animation-figure" src="../build_binary_tree_problem.assets/build_tree_preorder_inorder_division.png" /></a></p>
+<p align="center"> 図 12-6 &nbsp; 前順走査と中順走査での部分木の分割 </p>
+
+<h3 id="3">3. &nbsp; 変数に基づく部分木範囲の記述<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
+<p>上記の分割方法に基づいて、<strong><code>preorder</code> と <code>inorder</code> シーケンスにおけるルート、左の部分木、右の部分木のインデックス範囲を取得しました</strong>。これらのインデックス範囲を記述するために、いくつかのポインタ変数を使用します。</p>
+<ul>
+<li>現在の木のルートノードの <code>preorder</code> シーケンスでのインデックスを <span class="arithmatex">\(i\)</span> とします。</li>
+<li>現在の木のルートノードの <code>inorder</code> シーケンスでのインデックスを <span class="arithmatex">\(m\)</span> とします。</li>
+<li>現在の木の <code>inorder</code> シーケンスでのインデックス範囲を <span class="arithmatex">\([l, r]\)</span> とします。</li>
+</ul>
+<p>以下の表に示すように、これらの変数は <code>preorder</code> シーケンスでのルートノードのインデックスと <code>inorder</code> シーケンスでの部分木のインデックス範囲を表します。</p>
+<p align="center"> 表 12-1 &nbsp; 前順走査と中順走査でのルートノードと部分木のインデックス </p>
+
+<div class="center-table">
+<table>
+<thead>
+<tr>
+<th></th>
+<th><code>preorder</code> でのルートノードインデックス</th>
+<th><code>inorder</code> での部分木インデックス範囲</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td>現在の木</td>
+<td><span class="arithmatex">\(i\)</span></td>
+<td><span class="arithmatex">\([l, r]\)</span></td>
+</tr>
+<tr>
+<td>左の部分木</td>
+<td><span class="arithmatex">\(i + 1\)</span></td>
+<td><span class="arithmatex">\([l, m-1]\)</span></td>
+</tr>
+<tr>
+<td>右の部分木</td>
+<td><span class="arithmatex">\(i + 1 + (m - l)\)</span></td>
+<td><span class="arithmatex">\([m+1, r]\)</span></td>
+</tr>
+</tbody>
+</table>
+</div>
+<p>右の部分木のルートインデックスの <span class="arithmatex">\((m-l)\)</span> は「左の部分木のノード数」を表すことに注意してください。より明確な理解のために、以下の図を参照することが役立つ場合があります。</p>
+<p><a class="glightbox" href="../build_binary_tree_problem.assets/build_tree_division_pointers.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="ルートノードと左右の部分木のインデックス" class="animation-figure" src="../build_binary_tree_problem.assets/build_tree_division_pointers.png" /></a></p>
+<p align="center"> 図 12-7 &nbsp; ルートノードと左右の部分木のインデックス </p>
+
+<h3 id="4">4. &nbsp; コード実装<a class="headerlink" href="#4" title="Permanent link">&para;</a></h3>
+<p><span class="arithmatex">\(m\)</span> の問い合わせの効率を向上させるために、ハッシュテーブル <code>hmap</code> を使用して <code>inorder</code> シーケンスの要素からそのインデックスへのマッピングを格納します：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:14"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><input id="__tabbed_1_14" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label><label for="__tabbed_1_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">build_tree.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a>    <span class="n">preorder</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="n">inorder_map</span><span class="p">:</span> <span class="nb">dict</span><span class="p">[</span><span class="nb">int</span><span class="p">,</span> <span class="nb">int</span><span class="p">],</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="n">l</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="n">r</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;二分木の構築：分割統治&quot;&quot;&quot;</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>    <span class="c1"># 部分木の区間が空のとき終了</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>    <span class="k">if</span> <span class="n">r</span> <span class="o">-</span> <span class="n">l</span> <span class="o">&lt;</span> <span class="mi">0</span><span class="p">:</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>        <span class="k">return</span> <span class="kc">None</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>    <span class="c1"># ルートノードを初期化</span>
+<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>    <span class="n">root</span> <span class="o">=</span> <span class="n">TreeNode</span><span class="p">(</span><span class="n">preorder</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>    <span class="c1"># m をクエリして左部分木と右部分木を分割</span>
+<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>    <span class="n">m</span> <span class="o">=</span> <span class="n">inorder_map</span><span class="p">[</span><span class="n">preorder</span><span class="p">[</span><span class="n">i</span><span class="p">]]</span>
+<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>    <span class="c1"># 部分問題：左部分木を構築</span>
+<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>    <span class="n">root</span><span class="o">.</span><span class="n">left</span> <span class="o">=</span> <span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span> <span class="n">inorder_map</span><span class="p">,</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">l</span><span class="p">,</span> <span class="n">m</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a>    <span class="c1"># 部分問題：右部分木を構築</span>
+<a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a>    <span class="n">root</span><span class="o">.</span><span class="n">right</span> <span class="o">=</span> <span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span> <span class="n">inorder_map</span><span class="p">,</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">1</span> <span class="o">+</span> <span class="n">m</span> <span class="o">-</span> <span class="n">l</span><span class="p">,</span> <span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">r</span><span class="p">)</span>
+<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a>    <span class="c1"># ルートノードを返す</span>
+<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a>    <span class="k">return</span> <span class="n">root</span>
+<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a>
+<a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a><span class="k">def</span><span class="w"> </span><span class="nf">build_tree</span><span class="p">(</span><span class="n">preorder</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">inorder</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;二分木を構築&quot;&quot;&quot;</span>
+<a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a>    <span class="c1"># ハッシュテーブルを初期化、中順走査の要素からインデックスへのマッピングを保存</span>
+<a id="__codelineno-0-26" name="__codelineno-0-26" href="#__codelineno-0-26"></a>    <span class="n">inorder_map</span> <span class="o">=</span> <span class="p">{</span><span class="n">val</span><span class="p">:</span> <span class="n">i</span> <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">val</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">inorder</span><span class="p">)}</span>
+<a id="__codelineno-0-27" name="__codelineno-0-27" href="#__codelineno-0-27"></a>    <span class="n">root</span> <span class="o">=</span> <span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span> <span class="n">inorder_map</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">inorder</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-0-28" name="__codelineno-0-28" href="#__codelineno-0-28"></a>    <span class="k">return</span> <span class="n">root</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">build_tree.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 二分木の構築：分割統治 */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">dfs</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">unordered_map</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">r</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// 部分木の区間が空の場合に終了</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="c1">// ルートノードを初期化</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">preorder</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="c1">// m を問い合わせて左右の部分木を分割</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">[</span><span class="n">preorder</span><span class="p">[</span><span class="n">i</span><span class="p">]];</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">    </span><span class="c1">// 部分問題：左の部分木を構築</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">    </span><span class="n">root</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">    </span><span class="c1">// 部分問題：右の部分木を構築</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">    </span><span class="n">root</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">r</span><span class="p">);</span>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">    </span><span class="c1">// ルートノードを返す</span>
+<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
+<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="p">}</span>
+<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a>
+<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="cm">/* 二分木の構築 */</span>
+<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">buildTree</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">inorder</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="w">    </span><span class="c1">// ハッシュテーブルを初期化し、中間順序の要素からインデックスへのマッピングを格納</span>
+<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="w">    </span><span class="n">unordered_map</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">;</span>
+<a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">inorder</span><span class="p">.</span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a><span class="w">        </span><span class="n">inorderMap</span><span class="p">[</span><span class="n">inorder</span><span class="p">[</span><span class="n">i</span><span class="p">]]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">inorder</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-1-26" name="__codelineno-1-26" href="#__codelineno-1-26"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
+<a id="__codelineno-1-27" name="__codelineno-1-27" href="#__codelineno-1-27"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">build_tree.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 二分木の構築：分割統治 */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">Map</span><span class="o">&lt;</span><span class="n">Integer</span><span class="p">,</span><span class="w"> </span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">r</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// 部分木の区間が空の場合に終了</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="c1">// ルートノードを初期化</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">preorder</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">);</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">    </span><span class="c1">// m を問い合わせて左右の部分木を分割</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">preorder</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">);</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">    </span><span class="c1">// 部分問題：左の部分木を構築</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">    </span><span class="n">root</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">    </span><span class="c1">// 部分問題：右の部分木を構築</span>
+<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">    </span><span class="n">root</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">l</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">r</span><span class="p">);</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">    </span><span class="c1">// ルートノードを返す</span>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="p">}</span>
+<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a>
+<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="cm">/* 二分木の構築 */</span>
+<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="n">TreeNode</span><span class="w"> </span><span class="nf">buildTree</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">inorder</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="w">    </span><span class="c1">// ハッシュテーブルを初期化し、中間順序の要素からインデックスへのマッピングを格納</span>
+<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="w">    </span><span class="n">Map</span><span class="o">&lt;</span><span class="n">Integer</span><span class="p">,</span><span class="w"> </span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">inorderMap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">HashMap</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">inorder</span><span class="p">.</span><span class="na">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a><span class="w">        </span><span class="n">inorderMap</span><span class="p">.</span><span class="na">put</span><span class="p">(</span><span class="n">inorder</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">preorder</span><span class="p">,</span><span class="w"> </span><span class="n">inorderMap</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">inorder</span><span class="p">.</span><span class="na">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
+<a id="__codelineno-2-27" name="__codelineno-2-27" href="#__codelineno-2-27"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">build_tree.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">build_tree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">DFS</span><span class="p">}</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">build_tree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">BuildTree</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">build_tree.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">dfsBuildTree</span><span class="p">}</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">buildTree</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">build_tree.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">buildTree</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">build_tree.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">dfs</span><span class="p">}</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">buildTree</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">build_tree.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">dfs</span><span class="p">}</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">buildTree</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">build_tree.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">buildTree</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">build_tree.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">build_tree</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">build_tree.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">buildTree</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">build_tree.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">dfs</span><span class="p">}</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">buildTree</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">build_tree.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">dfs</span><span class="p">}</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">build_tree</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">build_tree.zig</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a>
+<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">buildTree</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>以下の図は、二分木を構築する再帰過程を示しています。各ノードは再帰の「下降」段階で作成され、各エッジ（参照）は「上昇」段階で形成されます。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:9"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">&lt;1&gt;</label><label for="__tabbed_2_2">&lt;2&gt;</label><label for="__tabbed_2_3">&lt;3&gt;</label><label for="__tabbed_2_4">&lt;4&gt;</label><label for="__tabbed_2_5">&lt;5&gt;</label><label for="__tabbed_2_6">&lt;6&gt;</label><label for="__tabbed_2_7">&lt;7&gt;</label><label for="__tabbed_2_8">&lt;8&gt;</label><label for="__tabbed_2_9">&lt;9&gt;</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<p><a class="glightbox" href="../build_binary_tree_problem.assets/built_tree_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="二分木構築の再帰過程" class="animation-figure" src="../build_binary_tree_problem.assets/built_tree_step1.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../build_binary_tree_problem.assets/built_tree_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="built_tree_step2" class="animation-figure" src="../build_binary_tree_problem.assets/built_tree_step2.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../build_binary_tree_problem.assets/built_tree_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="built_tree_step3" class="animation-figure" src="../build_binary_tree_problem.assets/built_tree_step3.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../build_binary_tree_problem.assets/built_tree_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="built_tree_step4" class="animation-figure" src="../build_binary_tree_problem.assets/built_tree_step4.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../build_binary_tree_problem.assets/built_tree_step5.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="built_tree_step5" class="animation-figure" src="../build_binary_tree_problem.assets/built_tree_step5.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../build_binary_tree_problem.assets/built_tree_step6.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="built_tree_step6" class="animation-figure" src="../build_binary_tree_problem.assets/built_tree_step6.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../build_binary_tree_problem.assets/built_tree_step7.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="built_tree_step7" class="animation-figure" src="../build_binary_tree_problem.assets/built_tree_step7.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../build_binary_tree_problem.assets/built_tree_step8.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="built_tree_step8" class="animation-figure" src="../build_binary_tree_problem.assets/built_tree_step8.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../build_binary_tree_problem.assets/built_tree_step9.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="built_tree_step9" class="animation-figure" src="../build_binary_tree_problem.assets/built_tree_step9.png" /></a></p>
+</div>
+</div>
+</div>
+<p align="center"> 図 12-8 &nbsp; 二分木構築の再帰過程 </p>
+
+<p>各再帰関数の <code>preorder</code> と <code>inorder</code> シーケンスの分割は以下の図に示されています。</p>
+<p><a class="glightbox" href="../build_binary_tree_problem.assets/built_tree_overall.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="各再帰関数での分割" class="animation-figure" src="../build_binary_tree_problem.assets/built_tree_overall.png" /></a></p>
+<p align="center"> 図 12-9 &nbsp; 各再帰関数での分割 </p>
+
+<p>二分木が <span class="arithmatex">\(n\)</span> 個のノードを持つと仮定すると、各ノードの初期化（再帰関数 <code>dfs()</code> の呼び出し）には <span class="arithmatex">\(O(1)\)</span> 時間がかかります。<strong>したがって、全体の時間計算量は <span class="arithmatex">\(O(n)\)</span> です</strong>。</p>
+<p>ハッシュテーブルは <code>inorder</code> 要素からそのインデックスへのマッピングを格納するため、<span class="arithmatex">\(O(n)\)</span> スペースが必要です。最悪の場合、二分木が連結リストに退化すると、再帰の深さは <span class="arithmatex">\(n\)</span> に達し、<span class="arithmatex">\(O(n)\)</span> のスタックスペースを消費する可能性があります。<strong>したがって、全体の空間計算量は <span class="arithmatex">\(O(n)\)</span> です</strong>。</p>
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+      <a href="../../chapter_preface/about_the_book/" class="md-nav__link">
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+      <a href="../../chapter_preface/summary/" class="md-nav__link">
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+  
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+    第 1 章 &nbsp; アルゴリズムとの出会い
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+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
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+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
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+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
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+  
+
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+        
+      
+        
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+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
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+            第 2 章 &nbsp; 計算量解析
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+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
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+  
+
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+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
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+    2.2 &nbsp; 反復と再帰
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+  
+
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+    </li>
+  
+
+              
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+  
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+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
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+  
+
+              
+            
+              
+                
+  
+  
+  
+  
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+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
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+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
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+            <a href="../../chapter_data_structure/" class="md-nav__link ">
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+  
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+    第 3 章 &nbsp; データ構造
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+            第 3 章 &nbsp; データ構造
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+            
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+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
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+  
+
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+            
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+  
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+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
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+  
+  
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+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
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+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1211" class="md-nav__link">
+    <span class="md-ellipsis">
+      12.1.1 &nbsp; 分割統治問題を特定する方法
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1212" class="md-nav__link">
+    <span class="md-ellipsis">
+      12.1.2 &nbsp; 分割統治による効率の向上
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="12.1.2   分割統治による効率の向上">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 操作数の最適化
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; 並列計算による最適化
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1213" class="md-nav__link">
+    <span class="md-ellipsis">
+      12.1.3 &nbsp; 分割統治の一般的な応用
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
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+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
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+  
+  
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+      
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+          
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_19" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_reference/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9 3v15h3V3H9m3 2 4 13 3-1-4-13-3 1M5 5v13h3V5H5M3 19v2h18v-2H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    参考文献
+  </span>
+  
+
+            </a>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_19_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_19">
+            <span class="md-nav__icon md-icon"></span>
+            参考文献
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+  </ul>
+</nav>
+                  </div>
+                </div>
+              </div>
+            
+            
+              
+              <div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
+                <div class="md-sidebar__scrollwrap">
+                  <div class="md-sidebar__inner">
+                    
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1211" class="md-nav__link">
+    <span class="md-ellipsis">
+      12.1.1 &nbsp; 分割統治問題を特定する方法
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1212" class="md-nav__link">
+    <span class="md-ellipsis">
+      12.1.2 &nbsp; 分割統治による効率の向上
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="12.1.2   分割統治による効率の向上">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 操作数の最適化
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; 並列計算による最適化
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1213" class="md-nav__link">
+    <span class="md-ellipsis">
+      12.1.3 &nbsp; 分割統治の一般的な応用
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+                  </div>
+                </div>
+              </div>
+            
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+          
+            <div class="md-content" data-md-component="content">
+              <article class="md-content__inner md-typeset">
+                
+                  <!-- Tags -->
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+      title="編集"
+      class="md-content__button md-icon"
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+<h1 id="121">12.1 &nbsp; 分割統治アルゴリズム<a class="headerlink" href="#121" title="Permanent link">&para;</a></h1>
+<p><u>分割統治</u>は重要で人気のあるアルゴリズム戦略です。名前が示すように、アルゴリズムは通常再帰的に実装され、「分割」と「統治」の2つのステップから構成されます。</p>
+<ol>
+<li><strong>分割（分割段階）</strong>：元の問題を再帰的に2つ以上の小さな部分問題に分解し、最小の部分問題に到達するまで続けます。</li>
+<li><strong>統治（マージ段階）</strong>：解決方法が既知の最小の部分問題から開始し、部分問題の解をボトムアップ方式でマージして元の問題の解を構築します。</li>
+</ol>
+<p>以下の図に示すように、「マージソート」は分割統治戦略の典型的な応用の一つです。</p>
+<ol>
+<li><strong>分割</strong>：元の配列（元の問題）を再帰的に2つの副配列（部分問題）に分割し、副配列が1つの要素のみになるまで（最小の部分問題）続けます。</li>
+<li><strong>統治</strong>：順序付けられた副配列（部分問題の解）をボトムアップでマージして、順序付けられた元の配列（元の問題の解）を取得します。</li>
+</ol>
+<p><a class="glightbox" href="../divide_and_conquer.assets/divide_and_conquer_merge_sort.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="マージソートの分割統治戦略" class="animation-figure" src="../divide_and_conquer.assets/divide_and_conquer_merge_sort.png" /></a></p>
+<p align="center"> 図 12-1 &nbsp; マージソートの分割統治戦略 </p>
+
+<h2 id="1211">12.1.1 &nbsp; 分割統治問題を特定する方法<a class="headerlink" href="#1211" title="Permanent link">&para;</a></h2>
+<p>問題が分割統治解決に適しているかどうかは、通常以下の基準に基づいて決定できます。</p>
+<ol>
+<li><strong>問題をより小さなものに分解できる</strong>：元の問題をより小さく類似した部分問題に分割でき、そのような過程を同じ方法で再帰的に実行できます。</li>
+<li><strong>部分問題は独立している</strong>：部分問題間に重複がなく、独立しており、個別に解決できます。</li>
+<li><strong>部分問題の解をマージできる</strong>：元の問題の解は、部分問題の解を組み合わせることで導出されます。</li>
+</ol>
+<p>明らかに、マージソートはこれら3つの基準を満たしています。</p>
+<ol>
+<li><strong>問題をより小さなものに分解できる</strong>：配列（元の問題）を再帰的に2つの副配列（部分問題）に分割します。</li>
+<li><strong>部分問題は独立している</strong>：各副配列は独立してソートできます（部分問題は独立して解決できます）。</li>
+<li><strong>部分問題の解をマージできる</strong>：2つの順序付けられた副配列（部分問題の解）を1つの順序付けられた配列（元の問題の解）にマージできます。</li>
+</ol>
+<h2 id="1212">12.1.2 &nbsp; 分割統治による効率の向上<a class="headerlink" href="#1212" title="Permanent link">&para;</a></h2>
+<p><strong>分割統治戦略はアルゴリズム問題を効果的に解決するだけでなく、しばしば効率を向上させます</strong>。ソートアルゴリズムでは、クイックソート、マージソート、ヒープソートは、分割統治戦略を適用しているため、選択ソート、バブルソート、挿入ソートよりも高速です。</p>
+<p>私たちの心には疑問があるかもしれません：<strong>なぜ分割統治はアルゴリズムの効率を向上させることができ、その根本的な論理は何ですか？</strong> つまり、問題を部分問題に分解し、それらを解決し、それらの解を組み合わせて元の問題に対処することが、元の問題を直接解決するよりも効率的である理由は何ですか？この質問は2つの側面から分析できます：操作数と並列計算。</p>
+<h3 id="1">1. &nbsp; 操作数の最適化<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<p>「バブルソート」を例にとると、長さ <span class="arithmatex">\(n\)</span> の配列を処理するのに <span class="arithmatex">\(O(n^2)\)</span> 時間が必要です。以下の図に示すように、配列を中点から2つの副配列に分割するとします。そのような分割には <span class="arithmatex">\(O(n)\)</span> 時間が必要です。各副配列のソートには <span class="arithmatex">\(O((n / 2)^2)\)</span> 時間が必要です。そして2つの副配列のマージには <span class="arithmatex">\(O(n)\)</span> 時間が必要です。したがって、全体の時間計算量は：</p>
+<div class="arithmatex">\[
+O(n + (\frac{n}{2})^2 \times 2 + n) = O(\frac{n^2}{2} + 2n)
+\]</div>
+<p><a class="glightbox" href="../divide_and_conquer.assets/divide_and_conquer_bubble_sort.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="配列分割前後のバブルソート" class="animation-figure" src="../divide_and_conquer.assets/divide_and_conquer_bubble_sort.png" /></a></p>
+<p align="center"> 図 12-2 &nbsp; 配列分割前後のバブルソート </p>
+
+<p>以下の不等式を計算してみましょう。左側は分割前の総操作数を表し、右側は分割後の総操作数をそれぞれ表します：</p>
+<div class="arithmatex">\[
+\begin{aligned}
+n^2 &amp; &gt; \frac{n^2}{2} + 2n \newline
+n^2 - \frac{n^2}{2} - 2n &amp; &gt; 0 \newline
+n(n - 4) &amp; &gt; 0
+\end{aligned}
+\]</div>
+<p><strong>これは <span class="arithmatex">\(n &gt; 4\)</span> の場合、分割後の操作数が少なく、より良いパフォーマンスにつながることを意味します</strong>。分割後の時間計算量は依然として二次 <span class="arithmatex">\(O(n^2)\)</span> ですが、計算量の定数係数が減少していることに注意してください。</p>
+<p>さらに進むことができます。<strong>副配列をその中点からさらに2つの副配列に分割し続けて、副配列が1つの要素のみになるまで続けたらどうでしょうか？</strong> このアイデアは実際には「マージソート」で、時間計算量は <span class="arithmatex">\(O(n \log n)\)</span> です。</p>
+<p>少し違うことを試してみましょう。<strong>2つではなく、より多くの分割に分割したらどうでしょうか？</strong> 例えば、元の配列を <span class="arithmatex">\(k\)</span> 個の副配列に均等に分割しますか？このアプローチは「バケットソート」と非常に似ており、大量のデータのソートに非常に適しています。理論的には、時間計算量は <span class="arithmatex">\(O(n + k)\)</span> に達することができます。</p>
+<h3 id="2">2. &nbsp; 並列計算による最適化<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
+<p>分割統治によって生成される部分問題は互いに独立していることが分かっています。<strong>これは、それらを並列で解決できることを意味します。</strong> その結果、分割統治はアルゴリズムの時間計算量を減らすだけでなく、<strong>現代のオペレーティングシステムによる並列最適化も促進します。</strong></p>
+<p>並列最適化は、複数のコアやプロセッサを持つ環境で特に効果的です。システムが複数の部分問題を同時に処理できるため、計算リソースを完全に活用し、全体的な実行時間が大幅に短縮されます。</p>
+<p>例えば、以下の図に示す「バケットソート」では、大量のデータを様々なバケットに均等に分解します。各バケットのソート作業は、利用可能な計算ユニットに割り当てることができます。すべての作業が完了すると、すべてのソートされたバケットがマージされて最終結果が生成されます。</p>
+<p><a class="glightbox" href="../divide_and_conquer.assets/divide_and_conquer_parallel_computing.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="バケットソートの並列計算" class="animation-figure" src="../divide_and_conquer.assets/divide_and_conquer_parallel_computing.png" /></a></p>
+<p align="center"> 図 12-3 &nbsp; バケットソートの並列計算 </p>
+
+<h2 id="1213">12.1.3 &nbsp; 分割統治の一般的な応用<a class="headerlink" href="#1213" title="Permanent link">&para;</a></h2>
+<p>分割統治は多くの古典的なアルゴリズム問題を解決するために使用できます。</p>
+<ul>
+<li><strong>最近点対の発見</strong>：このアルゴリズムは点の集合を2つの半分に分割することで動作します。そして各半分で再帰的に最近点対を見つけます。最後に、2つの半分にまたがるペアを考慮して、全体の最近点対を見つけます。</li>
+<li><strong>大整数の乗算</strong>：一つのアルゴリズムはKaratsubaと呼ばれます。大整数の乗算をいくつかの小さな整数の乗算と加算に分解します。</li>
+<li><strong>行列の乗算</strong>：一例はStrassenアルゴリズムです。大きな行列の乗算を複数の小さな行列の乗算と加算に分解します。</li>
+<li><strong>ハノイの塔問題</strong>：ハノイの塔問題は再帰的に解決でき、分割統治戦略の典型的な応用です。</li>
+<li><strong>転倒対の解決</strong>：シーケンスで、前の数が後の数より大きい場合、これら2つの数は転倒対を構成します。転倒対問題の解決は、マージソートの助けを借りて、分割統治のアイデアを利用できます。</li>
+</ul>
+<p>分割統治はアルゴリズムとデータ構造の設計にも広く応用されています。</p>
+<ul>
+<li><strong>二分探索</strong>：二分探索は、ソート済み配列を中点インデックスから2つの半分に分割します。そして、ターゲット値と中間要素値の比較結果に基づいて、一方の半分が破棄されます。同じプロセスで残りの半分で検索が続行され、ターゲットが見つかるか残りの要素がなくなるまで続きます。</li>
+<li><strong>マージソート</strong>：この節の冒頭ですでに紹介したため、さらなる詳述は不要です。</li>
+<li><strong>クイックソート</strong>：クイックソートはピボット値を選択して配列を2つの副配列に分割し、一方はピボットより小さい要素、もう一方はピボットより大きい要素を持ちます。このプロセスは、これら2つの副配列のそれぞれに対して、1つの要素のみを保持するまで続きます。</li>
+<li><strong>バケットソート</strong>：バケットソートの基本的なアイデアは、データを複数のバケットに分散させることです。各バケット内の要素をソートした後、バケットから順序よく要素を取得して順序付けられた配列を取得します。</li>
+<li><strong>木</strong>：例えば、二分探索木、AVL木、赤黒木、B木、B+木など。その操作（検索、挿入、削除）はすべて分割統治戦略の応用と見なすことができます。</li>
+<li><strong>ヒープ</strong>：ヒープは特別なタイプの完全二分木です。その様々な操作（挿入、削除、ヒープ化）は、実際に分割統治のアイデアを含意しています。</li>
+<li><strong>ハッシュテーブル</strong>：ハッシュテーブルは直接分割統治を適用しませんが、一部のハッシュ衝突解決ソリューションは間接的にこの戦略を適用します。例えば、チェイン法の長いリストは、クエリ効率を向上させるために赤黒木に変換される場合があります。</li>
+</ul>
+<p>**分割統治は巧妙に浸透するアルゴリズムアイデア**であり、様々なアルゴリズムとデータ構造に組み込まれていることが分かります。</p>
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+    <li class="md-nav__item">
+      <a href="../../chapter_preface/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_introduction/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 基本ケースを考える
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; 部分問題の分解
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#3" class="md-nav__link">
+    <span class="md-ellipsis">
+      3. &nbsp; コード実装
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
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+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
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+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
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+        
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+    15.4 &nbsp; 最大積切断問題
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+  
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+
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+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
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+<h1 id="124">12.4 &nbsp; ハノイの塔問題<a class="headerlink" href="#124" title="Permanent link">&para;</a></h1>
+<p>マージソートと二分木構築の両方で、元の問題を2つの部分問題に分解し、それぞれが元の問題のサイズの半分でした。しかし、ハノイの塔では、異なる分解戦略を採用します。</p>
+<div class="admonition question">
+<p class="admonition-title">Question</p>
+<p>3つの柱があり、それぞれ <code>A</code>、<code>B</code>、<code>C</code> と表記されます。最初、柱 <code>A</code> には <span class="arithmatex">\(n\)</span> 枚の円盤があり、上から下に向かって昇順のサイズで配置されています。私たちのタスクは、これらの <span class="arithmatex">\(n\)</span> 枚の円盤を柱 <code>C</code> に移動し、元の順序を維持することです（以下の図に示すように）。移動中には以下のルールが適用されます：</p>
+<ol>
+<li>円盤は柱の上部からのみ取り除くことができ、別の柱の上部に置く必要があります。</li>
+<li>一度に移動できるのは1枚の円盤のみです。</li>
+<li>小さい円盤は常に大きい円盤の上にある必要があります。</li>
+</ol>
+</div>
+<p><a class="glightbox" href="../hanota_problem.assets/hanota_example.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="ハノイの塔の例" class="animation-figure" src="../hanota_problem.assets/hanota_example.png" /></a></p>
+<p align="center"> 図 12-10 &nbsp; ハノイの塔の例 </p>
+
+<p><strong>サイズ <span class="arithmatex">\(i\)</span> のハノイの塔問題を <span class="arithmatex">\(f(i)\)</span> と表記します</strong>。例えば、<span class="arithmatex">\(f(3)\)</span> は3枚の円盤を柱 <code>A</code> から柱 <code>C</code> に移動することを表します。</p>
+<h3 id="1">1. &nbsp; 基本ケースを考える<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<p>以下の図に示すように、問題 <span class="arithmatex">\(f(1)\)</span>（円盤が1枚のみ）については、<code>A</code> から <code>C</code> に直接移動できます。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:2"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">&lt;1&gt;</label><label for="__tabbed_1_2">&lt;2&gt;</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<p><a class="glightbox" href="../hanota_problem.assets/hanota_f1_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="サイズ1の問題の解" class="animation-figure" src="../hanota_problem.assets/hanota_f1_step1.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../hanota_problem.assets/hanota_f1_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="hanota_f1_step2" class="animation-figure" src="../hanota_problem.assets/hanota_f1_step2.png" /></a></p>
+</div>
+</div>
+</div>
+<p align="center"> 図 12-11 &nbsp; サイズ1の問題の解 </p>
+
+<p><span class="arithmatex">\(f(2)\)</span>（円盤が2枚）については、**柱 <code>B</code> の助けを借りて小さい円盤を大きい円盤の上に保つ**必要があります。以下の図に示すように：</p>
+<ol>
+<li>まず、小さい円盤を <code>A</code> から <code>B</code> に移動します。</li>
+<li>次に、大きい円盤を <code>A</code> から <code>C</code> に移動します。</li>
+<li>最後に、小さい円盤を <code>B</code> から <code>C</code> に移動します。</li>
+</ol>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:4"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">&lt;1&gt;</label><label for="__tabbed_2_2">&lt;2&gt;</label><label for="__tabbed_2_3">&lt;3&gt;</label><label for="__tabbed_2_4">&lt;4&gt;</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<p><a class="glightbox" href="../hanota_problem.assets/hanota_f2_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="サイズ2の問題の解" class="animation-figure" src="../hanota_problem.assets/hanota_f2_step1.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../hanota_problem.assets/hanota_f2_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="hanota_f2_step2" class="animation-figure" src="../hanota_problem.assets/hanota_f2_step2.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../hanota_problem.assets/hanota_f2_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="hanota_f2_step3" class="animation-figure" src="../hanota_problem.assets/hanota_f2_step3.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../hanota_problem.assets/hanota_f2_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="hanota_f2_step4" class="animation-figure" src="../hanota_problem.assets/hanota_f2_step4.png" /></a></p>
+</div>
+</div>
+</div>
+<p align="center"> 図 12-12 &nbsp; サイズ2の問題の解 </p>
+
+<p><span class="arithmatex">\(f(2)\)</span> を解決する過程は次のように要約できます：<strong><code>B</code> の助けを借りて2枚の円盤を <code>A</code> から <code>C</code> に移動する</strong>。ここで、<code>C</code> をターゲット柱、<code>B</code> をバッファ柱と呼びます。</p>
+<h3 id="2">2. &nbsp; 部分問題の分解<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
+<p>問題 <span class="arithmatex">\(f(3)\)</span>（つまり、円盤が3枚の場合）については、状況がやや複雑になります。</p>
+<p>すでに <span class="arithmatex">\(f(1)\)</span> と <span class="arithmatex">\(f(2)\)</span> の解が分かっているので、分割統治の観点を採用し、<strong><code>A</code> の上の2枚の円盤を1つの単位として扱い</strong>、以下の図に示すステップを実行できます。これにより、3枚の円盤を <code>A</code> から <code>C</code> に正常に移動できます。</p>
+<ol>
+<li><code>B</code> をターゲット柱、<code>C</code> をバッファ柱として、2枚の円盤を <code>A</code> から <code>B</code> に移動します。</li>
+<li>残りの円盤を <code>A</code> から直接 <code>C</code> に移動します。</li>
+<li><code>C</code> をターゲット柱、<code>A</code> をバッファ柱として、2枚の円盤を <code>B</code> から <code>C</code> に移動します。</li>
+</ol>
+<div class="tabbed-set tabbed-alternate" data-tabs="3:4"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">&lt;1&gt;</label><label for="__tabbed_3_2">&lt;2&gt;</label><label for="__tabbed_3_3">&lt;3&gt;</label><label for="__tabbed_3_4">&lt;4&gt;</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<p><a class="glightbox" href="../hanota_problem.assets/hanota_f3_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="サイズ3の問題の解" class="animation-figure" src="../hanota_problem.assets/hanota_f3_step1.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../hanota_problem.assets/hanota_f3_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="hanota_f3_step2" class="animation-figure" src="../hanota_problem.assets/hanota_f3_step2.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../hanota_problem.assets/hanota_f3_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="hanota_f3_step3" class="animation-figure" src="../hanota_problem.assets/hanota_f3_step3.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../hanota_problem.assets/hanota_f3_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="hanota_f3_step4" class="animation-figure" src="../hanota_problem.assets/hanota_f3_step4.png" /></a></p>
+</div>
+</div>
+</div>
+<p align="center"> 図 12-13 &nbsp; サイズ3の問題の解 </p>
+
+<p>本質的に、<strong><span class="arithmatex">\(f(3)\)</span> を2つの <span class="arithmatex">\(f(2)\)</span> 部分問題と1つの <span class="arithmatex">\(f(1)\)</span> 部分問題に分解します</strong>。これら3つの部分問題を順次解決することで、元の問題が解決され、部分問題が独立しており、それらの解をマージできることを示しています。</p>
+<p>ここから、以下の図に示すハノイの塔の分割統治戦略を要約できます。元の問題 <span class="arithmatex">\(f(n)\)</span> を2つの部分問題 <span class="arithmatex">\(f(n-1)\)</span> と1つの部分問題 <span class="arithmatex">\(f(1)\)</span> に分割し、以下の順序でこれら3つの部分問題を解決します：</p>
+<ol>
+<li><code>C</code> をバッファとして使用し、<span class="arithmatex">\(n-1\)</span> 枚の円盤を <code>A</code> から <code>B</code> に移動します。</li>
+<li>残りの円盤を <code>A</code> から直接 <code>C</code> に移動します。</li>
+<li><code>A</code> をバッファとして使用し、<span class="arithmatex">\(n-1\)</span> 枚の円盤を <code>B</code> から <code>C</code> に移動します。</li>
+</ol>
+<p>各 <span class="arithmatex">\(f(n-1)\)</span> 部分問題について、<strong>同じ再帰分割を適用でき</strong>、最小の部分問題 <span class="arithmatex">\(f(1)\)</span> に到達するまで続けます。<span class="arithmatex">\(f(1)\)</span> は単一の移動のみが必要であることがすでに分かっているため、解決するのは簡単です。</p>
+<p><a class="glightbox" href="../hanota_problem.assets/hanota_divide_and_conquer.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="ハノイの塔を解決するための分割統治戦略" class="animation-figure" src="../hanota_problem.assets/hanota_divide_and_conquer.png" /></a></p>
+<p align="center"> 図 12-14 &nbsp; ハノイの塔を解決するための分割統治戦略 </p>
+
+<h3 id="3">3. &nbsp; コード実装<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
+<p>コードでは、再帰関数 <code>dfs(i, src, buf, tar)</code> を定義します。これは柱 <code>src</code> から上の <span class="arithmatex">\(i\)</span> 枚の円盤を柱 <code>tar</code> に移動し、柱 <code>buf</code> をバッファとして使用します：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="4:14"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><input id="__tabbed_4_6" name="__tabbed_4" type="radio" /><input id="__tabbed_4_7" name="__tabbed_4" type="radio" /><input id="__tabbed_4_8" name="__tabbed_4" type="radio" /><input id="__tabbed_4_9" name="__tabbed_4" type="radio" /><input id="__tabbed_4_10" name="__tabbed_4" type="radio" /><input id="__tabbed_4_11" name="__tabbed_4" type="radio" /><input id="__tabbed_4_12" name="__tabbed_4" type="radio" /><input id="__tabbed_4_13" name="__tabbed_4" type="radio" /><input id="__tabbed_4_14" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">Python</label><label for="__tabbed_4_2">C++</label><label for="__tabbed_4_3">Java</label><label for="__tabbed_4_4">C#</label><label for="__tabbed_4_5">Go</label><label for="__tabbed_4_6">Swift</label><label for="__tabbed_4_7">JS</label><label for="__tabbed_4_8">TS</label><label for="__tabbed_4_9">Dart</label><label for="__tabbed_4_10">Rust</label><label for="__tabbed_4_11">C</label><label for="__tabbed_4_12">Kotlin</label><label for="__tabbed_4_13">Ruby</label><label for="__tabbed_4_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hanota.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">move</span><span class="p">(</span><span class="n">src</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">tar</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]):</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;円盤を移動&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># src の上から円盤を取り出す</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="n">pan</span> <span class="o">=</span> <span class="n">src</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="c1"># 円盤を tar の上に置く</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="n">tar</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">pan</span><span class="p">)</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="k">def</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">src</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">buf</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">tar</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]):</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;ハノイの塔問題 f(i) を解く&quot;&quot;&quot;</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>    <span class="c1"># src に円盤が 1 つだけ残っている場合、それを tar に移動</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>    <span class="k">if</span> <span class="n">i</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>        <span class="n">move</span><span class="p">(</span><span class="n">src</span><span class="p">,</span> <span class="n">tar</span><span class="p">)</span>
+<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>        <span class="k">return</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>    <span class="c1"># 部分問題 f(i-1)：tar の助けを借りて src の上の i-1 個の円盤を buf に移動</span>
+<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>    <span class="n">dfs</span><span class="p">(</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">src</span><span class="p">,</span> <span class="n">tar</span><span class="p">,</span> <span class="n">buf</span><span class="p">)</span>
+<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>    <span class="c1"># 部分問題 f(1)：残りの 1 個の円盤を src から tar に移動</span>
+<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>    <span class="n">move</span><span class="p">(</span><span class="n">src</span><span class="p">,</span> <span class="n">tar</span><span class="p">)</span>
+<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a>    <span class="c1"># 部分問題 f(i-1)：src の助けを借りて buf の上の i-1 個の円盤を tar に移動</span>
+<a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a>    <span class="n">dfs</span><span class="p">(</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">buf</span><span class="p">,</span> <span class="n">src</span><span class="p">,</span> <span class="n">tar</span><span class="p">)</span>
+<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a>
+<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a><span class="k">def</span><span class="w"> </span><span class="nf">solve_hanota</span><span class="p">(</span><span class="n">A</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">B</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">C</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]):</span>
+<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;ハノイの塔問題を解く&quot;&quot;&quot;</span>
+<a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a>    <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">A</span><span class="p">)</span>
+<a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a>    <span class="c1"># B の助けを借りて A の上の n 個の円盤を C に移動</span>
+<a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a>    <span class="n">dfs</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">A</span><span class="p">,</span> <span class="n">B</span><span class="p">,</span> <span class="n">C</span><span class="p">)</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hanota.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 円盤を移動 */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">move</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">tar</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// src の最上部から円盤を取り出す</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">pan</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">src</span><span class="p">.</span><span class="n">back</span><span class="p">();</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="n">src</span><span class="p">.</span><span class="n">pop_back</span><span class="p">();</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="c1">// 円盤を tar の最上部に配置</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="n">tar</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">pan</span><span class="p">);</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="p">}</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="cm">/* ハノイの塔問題 f(i) を解く */</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="kt">void</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">buf</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">tar</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">    </span><span class="c1">// src に円盤が1つだけ残っている場合、それを tar に移動</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">        </span><span class="n">move</span><span class="p">(</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">);</span>
+<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w">    </span><span class="c1">// 部分問題 f(i-1)：tar の助けを借りて、上位 i-1 個の円盤を src から buf に移動</span>
+<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">);</span>
+<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="w">    </span><span class="c1">// 部分問題 f(1)：残りの1つの円盤を src から tar に移動</span>
+<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="w">    </span><span class="n">move</span><span class="p">(</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">);</span>
+<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="w">    </span><span class="c1">// 部分問題 f(i-1)：src の助けを借りて、上位 i-1 個の円盤を buf から tar に移動</span>
+<a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">);</span>
+<a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a><span class="p">}</span>
+<a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a>
+<a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a><span class="cm">/* ハノイの塔問題を解く */</span>
+<a id="__codelineno-1-26" name="__codelineno-1-26" href="#__codelineno-1-26"></a><span class="kt">void</span><span class="w"> </span><span class="nf">solveHanota</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">A</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">B</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">C</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-27" name="__codelineno-1-27" href="#__codelineno-1-27"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">A</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
+<a id="__codelineno-1-28" name="__codelineno-1-28" href="#__codelineno-1-28"></a><span class="w">    </span><span class="c1">// B の助けを借りて、上位 n 個の円盤を A から C に移動</span>
+<a id="__codelineno-1-29" name="__codelineno-1-29" href="#__codelineno-1-29"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">A</span><span class="p">,</span><span class="w"> </span><span class="n">B</span><span class="p">,</span><span class="w"> </span><span class="n">C</span><span class="p">);</span>
+<a id="__codelineno-1-30" name="__codelineno-1-30" href="#__codelineno-1-30"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hanota.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 円盤を移動 */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">move</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">tar</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// src の最上部から円盤を取り出す</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="n">Integer</span><span class="w"> </span><span class="n">pan</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">src</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">src</span><span class="p">.</span><span class="na">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="c1">// 円盤を tar の最上部に配置</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="n">tar</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">pan</span><span class="p">);</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="p">}</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="cm">/* ハノイの塔問題 f(i) を解く */</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="kt">void</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">buf</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">tar</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">    </span><span class="c1">// src に円盤が1つだけ残っている場合、それを tar に移動</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">        </span><span class="n">move</span><span class="p">(</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">);</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">    </span><span class="c1">// 部分問題 f(i-1)：tar の助けを借りて、上位 i-1 個の円盤を src から buf に移動</span>
+<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">);</span>
+<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w">    </span><span class="c1">// 部分問題 f(1)：残りの1つの円盤を src から tar に移動</span>
+<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w">    </span><span class="n">move</span><span class="p">(</span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">);</span>
+<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="w">    </span><span class="c1">// 部分問題 f(i-1)：src の助けを借りて、上位 i-1 個の円盤を buf から tar に移動</span>
+<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">buf</span><span class="p">,</span><span class="w"> </span><span class="n">src</span><span class="p">,</span><span class="w"> </span><span class="n">tar</span><span class="p">);</span>
+<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a><span class="p">}</span>
+<a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a>
+<a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a><span class="cm">/* ハノイの塔問題を解く */</span>
+<a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a><span class="kt">void</span><span class="w"> </span><span class="nf">solveHanota</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">A</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">B</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">C</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">A</span><span class="p">.</span><span class="na">size</span><span class="p">();</span>
+<a id="__codelineno-2-27" name="__codelineno-2-27" href="#__codelineno-2-27"></a><span class="w">    </span><span class="c1">// B の助けを借りて、上位 n 個の円盤を A から C に移動</span>
+<a id="__codelineno-2-28" name="__codelineno-2-28" href="#__codelineno-2-28"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">A</span><span class="p">,</span><span class="w"> </span><span class="n">B</span><span class="p">,</span><span class="w"> </span><span class="n">C</span><span class="p">);</span>
+<a id="__codelineno-2-29" name="__codelineno-2-29" href="#__codelineno-2-29"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hanota.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">hanota</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Move</span><span class="p">}</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">hanota</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">DFS</span><span class="p">}</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="na">[class]</span><span class="p">{</span><span class="n">hanota</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">SolveHanota</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hanota.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">move</span><span class="p">}</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">dfsHanota</span><span class="p">}</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">solveHanota</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hanota.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">move</span><span class="p">}</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">solveHanota</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hanota.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">move</span><span class="p">}</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">dfs</span><span class="p">}</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">solveHanota</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hanota.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">move</span><span class="p">}</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">dfs</span><span class="p">}</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">solveHanota</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hanota.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">move</span><span class="p">}</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">solveHanota</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hanota.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">move_pan</span><span class="p">}</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">solve_hanota</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hanota.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">move</span><span class="p">}</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">solveHanota</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hanota.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">move</span><span class="p">}</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">dfs</span><span class="p">}</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">solveHanota</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hanota.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">move</span><span class="p">}</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">dfs</span><span class="p">}</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">solve_hanota</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hanota.zig</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">move</span><span class="p">}</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a>
+<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
+<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a>
+<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">solveHanota</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>以下の図に示すように、ハノイの塔問題は高さ <span class="arithmatex">\(n\)</span> の再帰木として視覚化できます。各ノードは部分問題を表し、<code>dfs()</code> の呼び出しに対応します。<strong>したがって、時間計算量は <span class="arithmatex">\(O(2^n)\)</span>、空間計算量は <span class="arithmatex">\(O(n)\)</span> です。</strong></p>
+<p><a class="glightbox" href="../hanota_problem.assets/hanota_recursive_tree.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="ハノイの塔の再帰木" class="animation-figure" src="../hanota_problem.assets/hanota_recursive_tree.png" /></a></p>
+<p align="center"> 図 12-15 &nbsp; ハノイの塔の再帰木 </p>
+
+<div class="admonition quote">
+<p class="admonition-title">Quote</p>
+<p>ハノイの塔は古代の伝説に由来します。古代インドの寺院で、僧侶たちは3本の高いダイヤモンドの柱と、異なるサイズの <span class="arithmatex">\(64\)</span> 枚の金の円盤を持っていました。彼らは、最後の円盤が正しく置かれたとき、世界が終わると信じていました。</p>
+<p>しかし、僧侶たちが1秒に1枚の円盤を移動したとしても、約 <span class="arithmatex">\(2^{64} \approx 1.84×10^{19}\)</span> —約5850億年—かかり、宇宙の年齢の現在の推定をはるかに超えています。したがって、この伝説が真実であれば、世界の終わりについて心配する必要はおそらくないでしょう。</p>
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+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_1" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_hello_algo/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m13.13 22.19-1.63-3.83c1.57-.58 3.04-1.36 4.4-2.27l-2.77 6.1M5.64 12.5l-3.83-1.63 6.1-2.77C7 9.46 6.22 10.93 5.64 12.5M19.22 4c.28 0 .53 0 .74.05.17 1.39-.02 4.25-3.3 7.53-1.7 1.71-3.73 3.02-6.01 3.89l-2.15-2.1c.92-2.31 2.23-4.34 3.92-6.03C15.18 4.58 17.64 4 19.22 4m0-2c-1.98 0-4.98.69-8.22 3.93-2.19 2.19-3.5 4.6-4.35 6.71-.28.75-.09 1.57.46 2.13l2.13 2.12c.38.38.89.61 1.42.61.23 0 .47-.06.7-.15A19.1 19.1 0 0 0 18.07 13c5.66-5.66 3.54-10.61 3.54-10.61S20.7 2 19.22 2m-4.68 7.46c-.78-.78-.78-2.05 0-2.83s2.05-.78 2.83 0c.77.78.78 2.05 0 2.83-.78.78-2.05.78-2.83 0m-5.66 7.07-1.41-1.41 1.41 1.41M6.24 22l3.64-3.64c-.34-.09-.67-.24-.97-.45L4.83 22h1.41M2 22h1.41l4.77-4.76-1.42-1.41L2 20.59V22m0-2.83 4.09-4.08c-.21-.3-.36-.62-.45-.97L2 17.76v1.41Z"/></svg>
+  
+  <span class="md-ellipsis">
+    はじめに
+  </span>
+  
+
+            </a>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_1_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_1">
+            <span class="md-nav__icon md-icon"></span>
+            はじめに
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_2" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_preface/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M21 4H3a2 2 0 0 0-2 2v13a2 2 0 0 0 2 2h18a2 2 0 0 0 2-2V6a2 2 0 0 0-2-2M3 19V6h8v13H3m18 0h-8V6h8v13m-7-9.5h6V11h-6V9.5m0 2.5h6v1.5h-6V12m0 2.5h6V16h-6v-1.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 0 章 &nbsp; 前書き
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_2" id="__nav_2_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_2_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_2">
+            <span class="md-nav__icon md-icon"></span>
+            第 0 章 &nbsp; 前書き
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_preface/about_the_book/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.1 &nbsp; この本について
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_preface/suggestions/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.2 &nbsp; 本書の使い方
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_preface/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_introduction/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="./" class="md-nav__link md-nav__link--active">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link md-nav__link--active" for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
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+<h1 id="12">第 12 章 &nbsp; 分割統治<a class="headerlink" href="#12" title="Permanent link">&para;</a></h1>
+<p><a class="glightbox" href="../assets/covers/chapter_divide_and_conquer.jpg" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="分割統治" class="cover-image" src="../assets/covers/chapter_divide_and_conquer.jpg" /></a></p>
+<div class="admonition abstract">
+<p class="admonition-title">Abstract</p>
+<p>困難な問題は層を重ねて分解され、各分解によってより単純になります。</p>
+<p>分割統治は深い真理を明らかにします：単純さから始めれば、複雑さは解決される。</p>
+</div>
+<h2 id="_1">章の内容<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h2>
+<ul>
+<li><a href="divide_and_conquer/">12.1 &nbsp; 分割統治アルゴリズム</a></li>
+<li><a href="binary_search_recur/">12.2 &nbsp; 分割統治探索戦略</a></li>
+<li><a href="build_binary_tree_problem/">12.3 &nbsp; 二分木構築問題</a></li>
+<li><a href="hanota_problem/">12.4 &nbsp; ハノイの塔問題</a></li>
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+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+      
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
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+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
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+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
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+      
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+          
+        
+      
+    
+    
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+    
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+      
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+            <a href="../../chapter_reference/" class="md-nav__link ">
+              
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9 3v15h3V3H9m3 2 4 13 3-1-4-13-3 1M5 5v13h3V5H5M3 19v2h18v-2H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    参考文献
+  </span>
+  
+
+            </a>
+            
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+                <div class="md-sidebar__scrollwrap">
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+<h1 id="125">12.5 &nbsp; まとめ<a class="headerlink" href="#125" title="Permanent link">&para;</a></h1>
+<ul>
+<li>分割統治は一般的なアルゴリズム設計戦略で、分割（分割）と統治（マージ）の2つの段階から構成され、一般的に再帰を使用して実装されます。</li>
+<li>問題が分割統治アプローチに適しているかどうかを判断するために、問題が分解可能かどうか、部分問題が独立しているかどうか、部分問題をマージできるかどうかを確認します。</li>
+<li>マージソートは分割統治戦略の典型的な例です。配列を再帰的に2つの等しい長さの副配列に分割し、1つの要素のみが残るまで続け、次にこれらの副配列を層ごとにマージしてソートを完了します。</li>
+<li>分割統治戦略の導入は、しばしばアルゴリズムの効率を向上させます。一方では操作数を減らし、他方では分割後のシステムの並列最適化を促進します。</li>
+<li>分割統治は多数のアルゴリズム問題に適用でき、データ構造とアルゴリズム設計で広く使用され、多くのシナリオに現れます。</li>
+<li>総当たり検索と比較して、適応検索はより効率的です。時間計算量が <span class="arithmatex">\(O(\log n)\)</span> の検索アルゴリズムは、通常分割統治戦略に基づいています。</li>
+<li>二分探索は分割統治戦略のもう一つの古典的な応用です。部分問題の解のマージを含まず、再帰的な分割統治アプローチで実装できます。</li>
+<li>二分木構築問題では、木の構築（元の問題）を左の部分木と右の部分木の構築（部分問題）に分割できます。これは前順走査と中順走査のインデックス範囲を分割することで実現できます。</li>
+<li>ハノイの塔問題では、サイズ <span class="arithmatex">\(n\)</span> の問題をサイズ <span class="arithmatex">\(n-1\)</span> の2つの部分問題とサイズ <span class="arithmatex">\(1\)</span> の1つの部分問題に分解できます。これら3つの部分問題を順次解決することで、元の問題が解決されます。</li>
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+      <a href="../../chapter_preface/summary/" class="md-nav__link">
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+  
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+    第 1 章 &nbsp; アルゴリズムとの出会い
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+  
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+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
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+    1.3 &nbsp; まとめ
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+        
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+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
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+            第 2 章 &nbsp; 計算量解析
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+    2.1 &nbsp; アルゴリズム効率評価
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+    2.2 &nbsp; 反復と再帰
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+  
+
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+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
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+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
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+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
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+    </li>
+  
+
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+  
+  
+  
+  
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+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
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+  
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+    第 3 章 &nbsp; データ構造
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1421" class="md-nav__link">
+    <span class="md-ellipsis">
+      14.2.1 &nbsp; 最適部分構造
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1422" class="md-nav__link">
+    <span class="md-ellipsis">
+      14.2.2 &nbsp; 無記憶性
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
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+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
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+    
+      
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+          
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_19" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_reference/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9 3v15h3V3H9m3 2 4 13 3-1-4-13-3 1M5 5v13h3V5H5M3 19v2h18v-2H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    参考文献
+  </span>
+  
+
+            </a>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_19_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_19">
+            <span class="md-nav__icon md-icon"></span>
+            参考文献
+          </label>
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+      
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+</nav>
+                  </div>
+                </div>
+              </div>
+            
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+              
+              <div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
+                <div class="md-sidebar__scrollwrap">
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+    <span class="md-ellipsis">
+      14.2.1 &nbsp; 最適部分構造
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+      14.2.2 &nbsp; 無記憶性
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+<h1 id="142">14.2 &nbsp; 動的プログラミング問題の特徴<a class="headerlink" href="#142" title="Permanent link">&para;</a></h1>
+<p>前のセクションでは、動的プログラミングが問題を部分問題に分解することで元の問題を解決する方法を学びました。実際、部分問題の分解は一般的なアルゴリズムアプローチであり、分割統治法、動的プログラミング、バックトラッキングでは異なる重点があります。</p>
+<ul>
+<li>分割統治法アルゴリズムは元の問題を複数の独立した部分問題に再帰的に分割し、最小の部分問題に到達するまで続け、バックトラッキング時に部分問題の解を組み合わせて最終的に元の問題の解を得ます。</li>
+<li>動的プログラミングも問題を再帰的に分解しますが、分割統治法アルゴリズムとの主な違いは、動的プログラミングの部分問題が相互依存的であり、分解プロセス中に多くの重複する部分問題が現れることです。</li>
+<li>バックトラッキングアルゴリズムは試行錯誤によってすべての可能な解を網羅し、枝刈りによって不必要な探索分岐を避けます。元の問題の解は一連の決定ステップから構成され、各決定ステップ前の各部分シーケンスを部分問題として考えることができます。</li>
+</ul>
+<p>実際、動的プログラミングは最適化問題を解決するためによく使用され、これらは重複する部分問題を含むだけでなく、他に2つの主要な特徴があります：最適部分構造と無記憶性です。</p>
+<h2 id="1421">14.2.1 &nbsp; 最適部分構造<a class="headerlink" href="#1421" title="Permanent link">&para;</a></h2>
+<p>階段登り問題を少し修正して、最適部分構造の概念を実証するのにより適したものにします。</p>
+<div class="admonition question">
+<p class="admonition-title">階段登りの最小コスト</p>
+<p>階段があり、一度に1段または2段上ることができ、階段の各段にはその段で支払う必要があるコストを表す非負の整数があります。非負の整数配列 <span class="arithmatex">\(cost\)</span> が与えられ、<span class="arithmatex">\(cost[i]\)</span> は <span class="arithmatex">\(i\)</span> 段目で支払う必要があるコストを表し、<span class="arithmatex">\(cost[0]\)</span> は地面（開始点）です。頂上に到達するために必要な最小コストは何ですか？</p>
+</div>
+<p>下の図に示すように、1段目、2段目、3段目のコストがそれぞれ <span class="arithmatex">\(1\)</span>、<span class="arithmatex">\(10\)</span>、<span class="arithmatex">\(1\)</span> の場合、地面から3段目に登る最小コストは <span class="arithmatex">\(2\)</span> です。</p>
+<p><a class="glightbox" href="../dp_problem_features.assets/min_cost_cs_example.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="3段目に登る最小コスト" class="animation-figure" src="../dp_problem_features.assets/min_cost_cs_example.png" /></a></p>
+<p align="center"> 図 14-6 &nbsp; 3段目に登る最小コスト </p>
+
+<p><span class="arithmatex">\(dp[i]\)</span> を <span class="arithmatex">\(i\)</span> 段目に登る累積コストとします。<span class="arithmatex">\(i\)</span> 段目は <span class="arithmatex">\(i-1\)</span> 段目または <span class="arithmatex">\(i-2\)</span> 段目からのみ来ることができるため、<span class="arithmatex">\(dp[i]\)</span> は <span class="arithmatex">\(dp[i-1] + cost[i]\)</span> または <span class="arithmatex">\(dp[i-2] + cost[i]\)</span> のいずれかしかありえません。コストを最小化するために、2つのうち小さい方を選択すべきです：</p>
+<div class="arithmatex">\[
+dp[i] = \min(dp[i-1], dp[i-2]) + cost[i]
+\]</div>
+<p>これにより最適部分構造の意味がわかります：<strong>元の問題の最適解は部分問題の最適解から構築される</strong>。</p>
+<p>この問題は明らかに最適部分構造を持っています：2つの部分問題 <span class="arithmatex">\(dp[i-1]\)</span> と <span class="arithmatex">\(dp[i-2]\)</span> の最適解からより良い方を選択し、それを使用して元の問題 <span class="arithmatex">\(dp[i]\)</span> の最適解を構築します。</p>
+<p>では、前のセクションの階段登り問題は最適部分構造を持っているでしょうか？その目標は解の数を求めることで、これは数え上げ問題のようですが、別の方法で尋ねてみましょう：「解の最大数を求める」。驚くことに、**問題が変わったにもかかわらず、最適部分構造が現れた**ことがわかります：<span class="arithmatex">\(n\)</span> 段目での解の最大数は、<span class="arithmatex">\(n-1\)</span> 段目と <span class="arithmatex">\(n-2\)</span> 段目での解の最大数の和に等しいです。したがって、最適部分構造の解釈は非常に柔軟で、異なる問題では異なる意味を持ちます。</p>
+<p>状態遷移方程式と初期状態 <span class="arithmatex">\(dp[1] = cost[1]\)</span> および <span class="arithmatex">\(dp[2] = cost[2]\)</span> に従って、動的プログラミングコードを得ることができます：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:14"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><input id="__tabbed_1_14" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label><label for="__tabbed_1_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">min_cost_climbing_stairs_dp</span><span class="p">(</span><span class="n">cost</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;最小コスト階段登り：動的プログラミング&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">cost</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">1</span> <span class="ow">or</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">2</span><span class="p">:</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>        <span class="k">return</span> <span class="n">cost</span><span class="p">[</span><span class="n">n</span><span class="p">]</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="c1"># dp テーブルを初期化、部分問題の解を格納するために使用</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>    <span class="n">dp</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>    <span class="c1"># 初期状態：最小の部分問題の解を事前設定</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>    <span class="n">dp</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">dp</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="n">cost</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">cost</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>    <span class="c1"># 状態遷移：小さい部分問題から大きい部分問題を段階的に解く</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>        <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">],</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">2</span><span class="p">])</span> <span class="o">+</span> <span class="n">cost</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>    <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">]</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 最小コスト階段登り：動的プログラミング */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">minCostClimbingStairsDP</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">cost</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="n">n</span><span class="p">];</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化し、部分問題の解を格納するために使用</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">dp</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="c1">// 初期状態：最小の部分問題の解を事前設定</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="mi">2</span><span class="p">];</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">    </span><span class="c1">// 状態遷移：小さな問題から大きな部分問題を段階的に解く</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">];</span>
+<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 最小コスト階段登り：動的プログラミング */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">minCostClimbingStairsDP</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">cost</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="p">.</span><span class="na">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="n">n</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化し、部分問題の解を格納するために使用</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">    </span><span class="c1">// 初期状態：最小の部分問題の解を事前設定</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">    </span><span class="n">dp</span><span class="o">[</span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">    </span><span class="n">dp</span><span class="o">[</span><span class="mi">2</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="mi">2</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">    </span><span class="c1">// 状態遷移：小さな問題から大きな部分問題を段階的に解く</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">min</span><span class="p">(</span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">min_cost_climbing_stairs_dp</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">MinCostClimbingStairsDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">minCostClimbingStairsDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">minCostClimbingStairsDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">minCostClimbingStairsDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">minCostClimbingStairsDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">minCostClimbingStairsDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">min_cost_climbing_stairs_dp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">minCostClimbingStairsDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">minCostClimbingStairsDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">min_cost_climbing_stairs_dp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.zig</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">minCostClimbingStairsDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>下の図は上記コードの動的プログラミングプロセスを示しています。</p>
+<p><a class="glightbox" href="../dp_problem_features.assets/min_cost_cs_dp.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="階段登りの最小コストの動的プログラミングプロセス" class="animation-figure" src="../dp_problem_features.assets/min_cost_cs_dp.png" /></a></p>
+<p align="center"> 図 14-7 &nbsp; 階段登りの最小コストの動的プログラミングプロセス </p>
+
+<p>この問題も空間最適化が可能で、1次元を0に圧縮し、空間計算量を <span class="arithmatex">\(O(n)\)</span> から <span class="arithmatex">\(O(1)\)</span> に削減できます：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:14"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><input id="__tabbed_2_14" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label><label for="__tabbed_2_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.py</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">min_cost_climbing_stairs_dp_comp</span><span class="p">(</span><span class="n">cost</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;最小コスト階段登り：空間最適化動的プログラミング&quot;&quot;&quot;</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a>    <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">cost</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a>    <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">1</span> <span class="ow">or</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">2</span><span class="p">:</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a>        <span class="k">return</span> <span class="n">cost</span><span class="p">[</span><span class="n">n</span><span class="p">]</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a>    <span class="n">a</span><span class="p">,</span> <span class="n">b</span> <span class="o">=</span> <span class="n">cost</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">cost</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span>
+<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a>        <span class="n">a</span><span class="p">,</span> <span class="n">b</span> <span class="o">=</span> <span class="n">b</span><span class="p">,</span> <span class="nb">min</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span> <span class="o">+</span> <span class="n">cost</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a>    <span class="k">return</span> <span class="n">b</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.cpp</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 最小コスト階段登り：空間最適化動的プログラミング */</span>
+<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">minCostClimbingStairsDPComp</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">cost</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="n">n</span><span class="p">];</span>
+<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="mi">2</span><span class="p">];</span>
+<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">b</span><span class="p">;</span>
+<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w">        </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">tmp</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">cost</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="w">        </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
+<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">b</span><span class="p">;</span>
+<a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.java</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 最小コスト階段登り：空間最適化動的プログラミング */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">minCostClimbingStairsDPComp</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">cost</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="p">.</span><span class="na">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="n">n</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="mi">2</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">b</span><span class="p">;</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w">        </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">min</span><span class="p">(</span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">tmp</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">cost</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w">        </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">b</span><span class="p">;</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.cs</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">min_cost_climbing_stairs_dp</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">MinCostClimbingStairsDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.go</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">minCostClimbingStairsDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">minCostClimbingStairsDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.js</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">minCostClimbingStairsDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.ts</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">minCostClimbingStairsDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.dart</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">minCostClimbingStairsDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.rs</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">min_cost_climbing_stairs_dp_comp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.c</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">minCostClimbingStairsDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.kt</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">minCostClimbingStairsDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">min_cost_climbing_stairs_dp_comp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_cost_climbing_stairs_dp.zig</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">minCostClimbingStairsDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h2 id="1422">14.2.2 &nbsp; 無記憶性<a class="headerlink" href="#1422" title="Permanent link">&para;</a></h2>
+<p>無記憶性は動的プログラミングが問題解決に効果的であることを可能にする重要な特徴の1つです。その定義は：<strong>特定の状態が与えられたとき、その将来の発展は現在の状態のみに関連し、過去に経験したすべての状態とは無関係である</strong>。</p>
+<p>階段登り問題を例に取ると、状態 <span class="arithmatex">\(i\)</span> が与えられたとき、それは状態 <span class="arithmatex">\(i+1\)</span> と <span class="arithmatex">\(i+2\)</span> に発展し、それぞれ1段ジャンプと2段ジャンプに対応します。これら2つの選択をするとき、状態 <span class="arithmatex">\(i\)</span> より前の状態を考慮する必要はありません。なぜなら、それらは状態 <span class="arithmatex">\(i\)</span> の将来に影響しないからです。</p>
+<p>しかし、階段登り問題に制約を追加すると、状況が変わります。</p>
+<div class="admonition question">
+<p class="admonition-title">制約付き階段登り</p>
+<p><span class="arithmatex">\(n\)</span> 段の階段があり、毎回1段または2段上ることができますが、<strong>1段を2回連続でジャンプすることはできません</strong>。頂上に登る方法は何通りありますか？</p>
+</div>
+<p>下の図に示すように、3段目に登る実行可能な選択肢は2つだけで、1段を3回連続でジャンプする選択肢は制約条件を満たさないため破棄されます。</p>
+<p><a class="glightbox" href="../dp_problem_features.assets/climbing_stairs_constraint_example.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="制約付きで3段目に登る実行可能な選択肢の数" class="animation-figure" src="../dp_problem_features.assets/climbing_stairs_constraint_example.png" /></a></p>
+<p align="center"> 図 14-8 &nbsp; 制約付きで3段目に登る実行可能な選択肢の数 </p>
+
+<p>この問題では、前回が1段ジャンプだった場合、次回は必ず2段ジャンプでなければなりません。これは**次のステップの選択が現在の状態（現在の階段段数）だけでは独立して決定できず、前の状態（前回の階段段数）にも依存する**ことを意味します。</p>
+<p>この問題がもはや無記憶性を満たさず、状態遷移方程式 <span class="arithmatex">\(dp[i] = dp[i-1] + dp[i-2]\)</span> も失敗することは容易にわかります。なぜなら <span class="arithmatex">\(dp[i-1]\)</span> は今回の1段ジャンプを表しますが、多くの「前回が1段ジャンプだった」選択肢を含んでおり、制約を満たすためにはこれらを直接 <span class="arithmatex">\(dp[i]\)</span> に含めることはできません。</p>
+<p>このため、状態定義を拡張する必要があります：<strong>状態 <span class="arithmatex">\([i, j]\)</span> は <span class="arithmatex">\(i\)</span> 段目にいて、前回が <span class="arithmatex">\(j\)</span> 段ジャンプだったことを表す</strong>。ここで <span class="arithmatex">\(j \in \{1, 2\}\)</span> です。この状態定義は前回が1段ジャンプだったか2段ジャンプだったかを効果的に区別し、現在の状態がどこから来たかを適切に判断できます。</p>
+<ul>
+<li>前回が1段ジャンプだった場合、前々回は必ず2段ジャンプを選択していたはずです。つまり、<span class="arithmatex">\(dp[i, 1]\)</span> は <span class="arithmatex">\(dp[i-1, 2]\)</span> からのみ遷移できます。</li>
+<li>前回が2段ジャンプだった場合、前々回は1段ジャンプまたは2段ジャンプを選択できました。つまり、<span class="arithmatex">\(dp[i, 2]\)</span> は <span class="arithmatex">\(dp[i-2, 1]\)</span> または <span class="arithmatex">\(dp[i-2, 2]\)</span> から遷移できます。</li>
+</ul>
+<p>下の図に示すように、<span class="arithmatex">\(dp[i, j]\)</span> は状態 <span class="arithmatex">\([i, j]\)</span> の解の数を表します。この時点で、状態遷移方程式は次のようになります：</p>
+<div class="arithmatex">\[
+\begin{cases}
+dp[i, 1] = dp[i-1, 2] \\
+dp[i, 2] = dp[i-2, 1] + dp[i-2, 2]
+\end{cases}
+\]</div>
+<p><a class="glightbox" href="../dp_problem_features.assets/climbing_stairs_constraint_state_transfer.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="制約を考慮した再帰関係" class="animation-figure" src="../dp_problem_features.assets/climbing_stairs_constraint_state_transfer.png" /></a></p>
+<p align="center"> 図 14-9 &nbsp; 制約を考慮した再帰関係 </p>
+
+<p>最終的に、<span class="arithmatex">\(dp[n, 1] + dp[n, 2]\)</span> を返せばよく、この2つの合計が <span class="arithmatex">\(n\)</span> 段目に登る解の総数を表します：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="3:14"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><input id="__tabbed_3_14" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label><label for="__tabbed_3_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_constraint_dp.py</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">climbing_stairs_constraint_dp</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;制約付き階段登り：動的プログラミング&quot;&quot;&quot;</span>
+<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a>    <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">1</span> <span class="ow">or</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">2</span><span class="p">:</span>
+<a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a>        <span class="k">return</span> <span class="mi">1</span>
+<a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a>    <span class="c1"># dp テーブルを初期化、部分問題の解を格納するために使用</span>
+<a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a>    <span class="n">dp</span> <span class="o">=</span> <span class="p">[[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="mi">3</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)]</span>
+<a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a>    <span class="c1"># 初期状態：最小の部分問題の解を事前設定</span>
+<a id="__codelineno-28-8" name="__codelineno-28-8" href="#__codelineno-28-8"></a>    <span class="n">dp</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="mi">1</span><span class="p">],</span> <span class="n">dp</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span>
+<a id="__codelineno-28-9" name="__codelineno-28-9" href="#__codelineno-28-9"></a>    <span class="n">dp</span><span class="p">[</span><span class="mi">2</span><span class="p">][</span><span class="mi">1</span><span class="p">],</span> <span class="n">dp</span><span class="p">[</span><span class="mi">2</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span>
+<a id="__codelineno-28-10" name="__codelineno-28-10" href="#__codelineno-28-10"></a>    <span class="c1"># 状態遷移：小さい部分問題から大きい部分問題を段階的に解く</span>
+<a id="__codelineno-28-11" name="__codelineno-28-11" href="#__codelineno-28-11"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-28-12" name="__codelineno-28-12" href="#__codelineno-28-12"></a>        <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span>
+<a id="__codelineno-28-13" name="__codelineno-28-13" href="#__codelineno-28-13"></a>        <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">2</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">2</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span>
+<a id="__codelineno-28-14" name="__codelineno-28-14" href="#__codelineno-28-14"></a>    <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_constraint_dp.cpp</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="cm">/* 制約付き階段登り：動的プログラミング */</span>
+<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">climbingStairsConstraintDP</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化し、部分問題の解を格納するために使用</span>
+<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">dp</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">));</span>
+<a id="__codelineno-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a><span class="w">    </span><span class="c1">// 初期状態：最小の部分問題の解を事前設定</span>
+<a id="__codelineno-29-9" name="__codelineno-29-9" href="#__codelineno-29-9"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-29-10" name="__codelineno-29-10" href="#__codelineno-29-10"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-29-11" name="__codelineno-29-11" href="#__codelineno-29-11"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">2</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-29-12" name="__codelineno-29-12" href="#__codelineno-29-12"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">2</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-29-13" name="__codelineno-29-13" href="#__codelineno-29-13"></a><span class="w">    </span><span class="c1">// 状態遷移：小さな問題から大きな部分問題を段階的に解く</span>
+<a id="__codelineno-29-14" name="__codelineno-29-14" href="#__codelineno-29-14"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-15" name="__codelineno-29-15" href="#__codelineno-29-15"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="mi">2</span><span class="p">];</span>
+<a id="__codelineno-29-16" name="__codelineno-29-16" href="#__codelineno-29-16"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">][</span><span class="mi">2</span><span class="p">];</span>
+<a id="__codelineno-29-17" name="__codelineno-29-17" href="#__codelineno-29-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-18" name="__codelineno-29-18" href="#__codelineno-29-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="mi">2</span><span class="p">];</span>
+<a id="__codelineno-29-19" name="__codelineno-29-19" href="#__codelineno-29-19"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_constraint_dp.java</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* 制約付き階段登り：動的プログラミング */</span>
+<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">climbingStairsConstraintDP</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化し、部分問題の解を格納するために使用</span>
+<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a><span class="w">    </span><span class="kt">int</span><span class="o">[][]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="mi">3</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a><span class="w">    </span><span class="c1">// 初期状態：最小の部分問題の解を事前設定</span>
+<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a><span class="w">    </span><span class="n">dp</span><span class="o">[</span><span class="mi">1</span><span class="o">][</span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-30-10" name="__codelineno-30-10" href="#__codelineno-30-10"></a><span class="w">    </span><span class="n">dp</span><span class="o">[</span><span class="mi">1</span><span class="o">][</span><span class="mi">2</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-30-11" name="__codelineno-30-11" href="#__codelineno-30-11"></a><span class="w">    </span><span class="n">dp</span><span class="o">[</span><span class="mi">2</span><span class="o">][</span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-30-12" name="__codelineno-30-12" href="#__codelineno-30-12"></a><span class="w">    </span><span class="n">dp</span><span class="o">[</span><span class="mi">2</span><span class="o">][</span><span class="mi">2</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-30-13" name="__codelineno-30-13" href="#__codelineno-30-13"></a><span class="w">    </span><span class="c1">// 状態遷移：小さな問題から大きな部分問題を段階的に解く</span>
+<a id="__codelineno-30-14" name="__codelineno-30-14" href="#__codelineno-30-14"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-15" name="__codelineno-30-15" href="#__codelineno-30-15"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="mi">2</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-30-16" name="__codelineno-30-16" href="#__codelineno-30-16"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="mi">2</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="o">][</span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="o">][</span><span class="mi">2</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-30-17" name="__codelineno-30-17" href="#__codelineno-30-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-18" name="__codelineno-30-18" href="#__codelineno-30-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="mi">2</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-30-19" name="__codelineno-30-19" href="#__codelineno-30-19"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_constraint_dp.cs</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">climbing_stairs_constraint_dp</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">ClimbingStairsConstraintDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_constraint_dp.go</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">climbingStairsConstraintDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_constraint_dp.swift</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">climbingStairsConstraintDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_constraint_dp.js</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">climbingStairsConstraintDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_constraint_dp.ts</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">climbingStairsConstraintDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_constraint_dp.dart</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">climbingStairsConstraintDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_constraint_dp.rs</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">climbing_stairs_constraint_dp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_constraint_dp.c</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">climbingStairsConstraintDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_constraint_dp.kt</span><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">climbingStairsConstraintDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_constraint_dp.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">climbing_stairs_constraint_dp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_constraint_dp.zig</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">climbingStairsConstraintDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>上記のケースでは、前の状態のみを考慮すればよいため、状態定義を拡張することで依然として無記憶性を満たすことができます。しかし、一部の問題では非常に深刻な「状態効果」があります。</p>
+<div class="admonition question">
+<p class="admonition-title">障害物生成付き階段登り</p>
+<p><span class="arithmatex">\(n\)</span> 段の階段があり、毎回1段または2段上ることができます。**<span class="arithmatex">\(i\)</span> 段目に登ったとき、システムが自動的に <span class="arithmatex">\(2i\)</span> 段目に障害物を置き、その後のすべてのラウンドで <span class="arithmatex">\(2i\)</span> 段目にジャンプすることが禁止される**と規定されています。例えば、最初の2ラウンドで2段目と3段目にジャンプした場合、その後は4段目と6段目にジャンプできません。頂上に登る方法は何通りありますか？</p>
+</div>
+<p>この問題では、次のジャンプはすべての過去の状態に依存します。各ジャンプがより高い段に障害物を置き、将来のジャンプに影響するからです。このような問題では、動的プログラミングはしばしば解決に苦労します。</p>
+<p>実際、多くの複雑な組み合わせ最適化問題（巡回セールスマン問題など）は無記憶性を満たしません。このような問題に対しては、通常、ヒューリスティック探索、遺伝的アルゴリズム、強化学習などの他の方法を選択して、限られた時間内に使用可能な局所最適解を得ます。</p>
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+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1431" class="md-nav__link">
+    <span class="md-ellipsis">
+      14.3.1 &nbsp; 問題の判定
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1432" class="md-nav__link">
+    <span class="md-ellipsis">
+      14.3.2 &nbsp; 問題解決ステップ
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="14.3.2   問題解決ステップ">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1-1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 方法1：力任せ探索
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2-2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; 方法2：メモ化探索
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#3-3" class="md-nav__link">
+    <span class="md-ellipsis">
+      3. &nbsp; 方法3：動的プログラミング
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#4" class="md-nav__link">
+    <span class="md-ellipsis">
+      4. &nbsp; 空間最適化
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
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+  
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+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
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+    15.2 &nbsp; 分数ナップサック問題
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+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
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+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
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+    15.4 &nbsp; 最大積切断問題
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+  
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+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
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+  <a href="#1431" class="md-nav__link">
+    <span class="md-ellipsis">
+      14.3.1 &nbsp; 問題の判定
+    </span>
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+</li>
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+  <a href="#1432" class="md-nav__link">
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+      14.3.2 &nbsp; 問題解決ステップ
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+</li>
+        
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+  <a href="#2-2" class="md-nav__link">
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+  
+</li>
+        
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+  <a href="#3-3" class="md-nav__link">
+    <span class="md-ellipsis">
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+    </span>
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+  <a href="#4" class="md-nav__link">
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+<h1 id="143">14.3 &nbsp; 動的プログラミング問題解決アプローチ<a class="headerlink" href="#143" title="Permanent link">&para;</a></h1>
+<p>前の2つのセクションでは、動的プログラミング問題の主要な特徴を紹介しました。次に、より実用的な2つの問題を一緒に探索しましょう。</p>
+<ol>
+<li>問題が動的プログラミング問題かどうかをどのように判断するか？</li>
+<li>動的プログラミング問題を解決する完全なステップは何か？</li>
+</ol>
+<h2 id="1431">14.3.1 &nbsp; 問題の判定<a class="headerlink" href="#1431" title="Permanent link">&para;</a></h2>
+<p>一般的に言えば、問題が重複する部分問題、最適部分構造を含み、無記憶性を示す場合、通常動的プログラミング解法に適しています。しかし、問題の説明から直接これらの特徴を抽出することはしばしば困難です。したがって、通常は条件を緩和し、**まず問題がバックトラッキング（全探索）を使用した解決に適しているかどうかを観察**します。</p>
+<p>**バックトラッキングに適した問題は通常「決定木モデル」に適合**し、これは木構造を使用して記述でき、各ノードは決定を表し、各パスは決定のシーケンスを表します。</p>
+<p>言い換えると、問題が明示的な決定概念を含み、解が一連の決定を通じて生成される場合、それは決定木モデルに適合し、通常バックトラッキングを使用して解決できます。</p>
+<p>この基礎の上で、動的プログラミング問題を判定するための「ボーナスポイント」があります。</p>
+<ul>
+<li>問題に最大化（最小化）または最も（最も少ない）最適な解を見つけるという記述が含まれている。</li>
+<li>問題の状態がリスト、多次元行列、または木を使用して表現でき、状態がその周囲の状態と再帰関係を持っている。</li>
+</ul>
+<p>対応して、「ペナルティポイント」もあります。</p>
+<ul>
+<li>問題の目標は最適解だけでなく、すべての可能な解を見つけることである。</li>
+<li>問題の説明に順列と組み合わせの明らかな特徴があり、特定の複数の解を返す必要がある。</li>
+</ul>
+<p>問題が決定木モデルに適合し、比較的明らかな「ボーナスポイント」を持つ場合、それが動的プログラミング問題であると仮定し、解決プロセス中に検証できます。</p>
+<h2 id="1432">14.3.2 &nbsp; 問題解決ステップ<a class="headerlink" href="#1432" title="Permanent link">&para;</a></h2>
+<p>動的プログラミング問題解決プロセスは問題の性質と難易度によって異なりますが、一般的に次のステップに従います：決定の記述、状態の定義、<span class="arithmatex">\(dp\)</span> テーブルの確立、状態遷移方程式の導出、境界条件の決定など。</p>
+<p>問題解決ステップをより具体的に説明するために、古典的な問題「最小経路和」を例として使用します。</p>
+<div class="admonition question">
+<p class="admonition-title">Question</p>
+<p><span class="arithmatex">\(n \times m\)</span> の二次元グリッド <code>grid</code> が与えられ、グリッドの各セルには負でない整数が含まれ、そのセルのコストを表します。ロボットは左上のセルから始まり、各ステップで下または右にのみ移動でき、右下のセルに到達するまで続けます。左上から右下への最小経路和を返してください。</p>
+</div>
+<p>下の図は例を示しており、与えられたグリッドの最小経路和は <span class="arithmatex">\(13\)</span> です。</p>
+<p><a class="glightbox" href="../dp_solution_pipeline.assets/min_path_sum_example.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="最小経路和の例データ" class="animation-figure" src="../dp_solution_pipeline.assets/min_path_sum_example.png" /></a></p>
+<p align="center"> 図 14-10 &nbsp; 最小経路和の例データ </p>
+
+<p><strong>第1ステップ：各ラウンドの決定を考え、状態を定義し、それにより <span class="arithmatex">\(dp\)</span> テーブルを得る</strong></p>
+<p>この問題の各ラウンドの決定は、現在のセルから下または右に1ステップ移動することです。現在のセルの行と列のインデックスが <span class="arithmatex">\([i, j]\)</span> であると仮定すると、下または右に移動した後、インデックスは <span class="arithmatex">\([i+1, j]\)</span> または <span class="arithmatex">\([i, j+1]\)</span> になります。したがって、状態には2つの変数が含まれるべきです：行インデックスと列インデックス、<span class="arithmatex">\([i, j]\)</span> と表記されます。</p>
+<p>状態 <span class="arithmatex">\([i, j]\)</span> は部分問題に対応します：開始点 <span class="arithmatex">\([0, 0]\)</span> から <span class="arithmatex">\([i, j]\)</span> への最小経路和、<span class="arithmatex">\(dp[i, j]\)</span> と表記されます。</p>
+<p>このようにして、下の図に示す二次元 <span class="arithmatex">\(dp\)</span> 行列を得ます。そのサイズは入力グリッド <span class="arithmatex">\(grid\)</span> と同じです。</p>
+<p><a class="glightbox" href="../dp_solution_pipeline.assets/min_path_sum_solution_state_definition.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="状態定義とDPテーブル" class="animation-figure" src="../dp_solution_pipeline.assets/min_path_sum_solution_state_definition.png" /></a></p>
+<p align="center"> 図 14-11 &nbsp; 状態定義とDPテーブル </p>
+
+<div class="admonition note">
+<p class="admonition-title">Note</p>
+<p>動的プログラミングとバックトラッキングは決定のシーケンスとして記述でき、状態はすべての決定変数から構成されます。問題解決の進行を記述するすべての変数を含むべきで、次の状態を導出するのに十分な情報を含んでいる必要があります。</p>
+<p>各状態は部分問題に対応し、すべての部分問題の解を保存するための <span class="arithmatex">\(dp\)</span> テーブルを定義します。状態の各独立変数は <span class="arithmatex">\(dp\)</span> テーブルの次元です。本質的に、<span class="arithmatex">\(dp\)</span> テーブルは状態と部分問題の解の間のマッピングです。</p>
+</div>
+<p><strong>第2ステップ：最適部分構造を特定し、状態遷移方程式を導出する</strong></p>
+<p>状態 <span class="arithmatex">\([i, j]\)</span> について、それは上のセル <span class="arithmatex">\([i-1, j]\)</span> または左のセル <span class="arithmatex">\([i, j-1]\)</span> からのみ導出できます。したがって、最適部分構造は：<span class="arithmatex">\([i, j]\)</span> に到達する最小経路和は、<span class="arithmatex">\([i, j-1]\)</span> と <span class="arithmatex">\([i-1, j]\)</span> の最小経路和の小さい方によって決定されます。</p>
+<p>上記の分析に基づいて、下の図に示す状態遷移方程式を導出できます：</p>
+<div class="arithmatex">\[
+dp[i, j] = \min(dp[i-1, j], dp[i, j-1]) + grid[i, j]
+\]</div>
+<p><a class="glightbox" href="../dp_solution_pipeline.assets/min_path_sum_solution_state_transition.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="最適部分構造と状態遷移方程式" class="animation-figure" src="../dp_solution_pipeline.assets/min_path_sum_solution_state_transition.png" /></a></p>
+<p align="center"> 図 14-12 &nbsp; 最適部分構造と状態遷移方程式 </p>
+
+<div class="admonition note">
+<p class="admonition-title">Note</p>
+<p>定義された <span class="arithmatex">\(dp\)</span> テーブルに基づいて、元の問題と部分問題の関係を考え、部分問題の最適解から元の問題の最適解をどのように構築するか、つまり最適部分構造を見つけます。</p>
+<p>最適部分構造を特定したら、それを使用して状態遷移方程式を構築できます。</p>
+</div>
+<p><strong>第3ステップ：境界条件と状態遷移順序を決定する</strong></p>
+<p>この問題では、最初の行の状態は左の状態からのみ来ることができ、最初の列の状態は上の状態からのみ来ることができるため、最初の行 <span class="arithmatex">\(i = 0\)</span> と最初の列 <span class="arithmatex">\(j = 0\)</span> が境界条件です。</p>
+<p>下の図に示すように、各セルは左のセルと上のセルから導出されるため、ループを使用して行列を走査し、外側のループは行を反復し、内側のループは列を反復します。</p>
+<p><a class="glightbox" href="../dp_solution_pipeline.assets/min_path_sum_solution_initial_state.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="境界条件と状態遷移順序" class="animation-figure" src="../dp_solution_pipeline.assets/min_path_sum_solution_initial_state.png" /></a></p>
+<p align="center"> 図 14-13 &nbsp; 境界条件と状態遷移順序 </p>
+
+<div class="admonition note">
+<p class="admonition-title">Note</p>
+<p>境界条件は動的プログラミングで <span class="arithmatex">\(dp\)</span> テーブルを初期化するために使用され、探索では枝刈りに使用されます。</p>
+<p>状態遷移順序の核心は、現在の問題の解を計算するとき、それが依存するすべての小さな部分問題が既に正しく計算されていることを確保することです。</p>
+</div>
+<p>上記の分析に基づいて、動的プログラミングコードを直接書くことができます。しかし、部分問題の分解はトップダウンアプローチであるため、「力任せ探索 → メモ化探索 → 動的プログラミング」の順序で実装することが習慣的な思考により適合します。</p>
+<h3 id="1-1">1. &nbsp; 方法1：力任せ探索<a class="headerlink" href="#1-1" title="Permanent link">&para;</a></h3>
+<p>状態 <span class="arithmatex">\([i, j]\)</span> から探索を開始し、それを常により小さな状態 <span class="arithmatex">\([i-1, j]\)</span> と <span class="arithmatex">\([i, j-1]\)</span> に分解します。再帰関数には以下の要素が含まれます。</p>
+<ul>
+<li><strong>再帰パラメータ</strong>：状態 <span class="arithmatex">\([i, j]\)</span>。</li>
+<li><strong>戻り値</strong>：<span class="arithmatex">\([0, 0]\)</span> から <span class="arithmatex">\([i, j]\)</span> への最小経路和 <span class="arithmatex">\(dp[i, j]\)</span>。</li>
+<li><strong>終了条件</strong>：<span class="arithmatex">\(i = 0\)</span> かつ <span class="arithmatex">\(j = 0\)</span> のとき、コスト <span class="arithmatex">\(grid[0, 0]\)</span> を返す。</li>
+<li><strong>枝刈り</strong>：<span class="arithmatex">\(i &lt; 0\)</span> または <span class="arithmatex">\(j &lt; 0\)</span> でインデックスが範囲外のとき、コスト <span class="arithmatex">\(+\infty\)</span> を返し、実行不可能性を表す。</li>
+</ul>
+<p>実装コードは以下の通りです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:14"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><input id="__tabbed_1_14" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label><label for="__tabbed_1_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">min_path_sum_dfs</span><span class="p">(</span><span class="n">grid</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]],</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">j</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;最小パス和：ブルートフォース探索&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># 左上のセルの場合、探索を終了</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="k">if</span> <span class="n">i</span> <span class="o">==</span> <span class="mi">0</span> <span class="ow">and</span> <span class="n">j</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>        <span class="k">return</span> <span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="c1"># 行または列のインデックスが範囲外の場合、+∞ コストを返す</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>    <span class="k">if</span> <span class="n">i</span> <span class="o">&lt;</span> <span class="mi">0</span> <span class="ow">or</span> <span class="n">j</span> <span class="o">&lt;</span> <span class="mi">0</span><span class="p">:</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>        <span class="k">return</span> <span class="n">inf</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>    <span class="c1"># 左上から (i-1, j) と (i, j-1) への最小パスコストを計算</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>    <span class="n">up</span> <span class="o">=</span> <span class="n">min_path_sum_dfs</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span> <span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">j</span><span class="p">)</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>    <span class="n">left</span> <span class="o">=</span> <span class="n">min_path_sum_dfs</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>    <span class="c1"># 左上から (i, j) への最小パスコストを返す</span>
+<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>    <span class="k">return</span> <span class="nb">min</span><span class="p">(</span><span class="n">left</span><span class="p">,</span> <span class="n">up</span><span class="p">)</span> <span class="o">+</span> <span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 最小パス和：ブルートフォース探索 */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">minPathSumDFS</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// 左上のセルの場合、探索を終了</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">];</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="c1">// 行または列のインデックスが範囲外の場合、+∞ のコストを返す</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">;</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">    </span><span class="c1">// 左上から (i-1, j) と (i, j-1) への最小パスコストを計算</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">up</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">minPathSumDFS</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">);</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">minPathSumDFS</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">    </span><span class="c1">// 左上から (i, j) への最小パスコストを返す</span>
+<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">up</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 最小パス和：ブルートフォース探索 */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">minPathSumDFS</span><span class="p">(</span><span class="kt">int</span><span class="o">[][]</span><span class="w"> </span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// 左上のセルの場合、探索を終了</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="c1">// 行または列のインデックスが範囲外の場合、+∞ のコストを返す</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">Integer</span><span class="p">.</span><span class="na">MAX_VALUE</span><span class="p">;</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">    </span><span class="c1">// 左上から (i-1, j) と (i, j-1) への最小パスコストを計算</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">up</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">minPathSumDFS</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">);</span>
+<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">minPathSumDFS</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">    </span><span class="c1">// 左上から (i, j) への最小パスコストを返す</span>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">min</span><span class="p">(</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">up</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">min_path_sum</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">MinPathSumDFS</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">minPathSumDFS</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">minPathSumDFS</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">minPathSumDFS</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">minPathSumDFS</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">minPathSumDFS</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">min_path_sum_dfs</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">minPathSumDFS</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">minPathSumDFS</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">min_path_sum_dfs</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.zig</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">minPathSumDFS</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>下の図は <span class="arithmatex">\(dp[2, 1]\)</span> を根とする再帰木を示しており、いくつかの重複する部分問題を含み、その数はグリッド <code>grid</code> のサイズが増加すると急激に増加します。</p>
+<p>本質的に、重複する部分問題の理由は：**左上隅から特定のセルに到達する複数のパスが存在する**ことです。</p>
+<p><a class="glightbox" href="../dp_solution_pipeline.assets/min_path_sum_dfs.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="力任せ探索の再帰木" class="animation-figure" src="../dp_solution_pipeline.assets/min_path_sum_dfs.png" /></a></p>
+<p align="center"> 図 14-14 &nbsp; 力任せ探索の再帰木 </p>
+
+<p>各状態には下と右の2つの選択があるため、左上隅から右下隅までの総ステップ数は <span class="arithmatex">\(m + n - 2\)</span> で、最悪時間計算量は <span class="arithmatex">\(O(2^{m + n})\)</span> です。この計算方法はグリッドエッジ近くの状況を考慮していないことに注意してください。ネットワークエッジに到達したとき、選択肢が1つしか残らないため、実際のパス数はより少なくなります。</p>
+<h3 id="2-2">2. &nbsp; 方法2：メモ化探索<a class="headerlink" href="#2-2" title="Permanent link">&para;</a></h3>
+<p>グリッド <code>grid</code> と同じサイズのメモリスト <code>mem</code> を導入し、様々な部分問題の解を記録し、重複する部分問題を枝刈りします：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:14"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><input id="__tabbed_2_14" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label><label for="__tabbed_2_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.py</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">min_path_sum_dfs_mem</span><span class="p">(</span>
+<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a>    <span class="n">grid</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]],</span> <span class="n">mem</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]],</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">j</span><span class="p">:</span> <span class="nb">int</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;最小パス和：記憶化探索&quot;&quot;&quot;</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a>    <span class="c1"># 左上のセルの場合、探索を終了</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a>    <span class="k">if</span> <span class="n">i</span> <span class="o">==</span> <span class="mi">0</span> <span class="ow">and</span> <span class="n">j</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
+<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a>        <span class="k">return</span> <span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
+<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a>    <span class="c1"># 行または列のインデックスが範囲外の場合、+∞ コストを返す</span>
+<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a>    <span class="k">if</span> <span class="n">i</span> <span class="o">&lt;</span> <span class="mi">0</span> <span class="ow">or</span> <span class="n">j</span> <span class="o">&lt;</span> <span class="mi">0</span><span class="p">:</span>
+<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a>        <span class="k">return</span> <span class="n">inf</span>
+<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a>    <span class="c1"># 記録がある場合、それを返す</span>
+<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a>    <span class="k">if</span> <span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span> <span class="o">!=</span> <span class="o">-</span><span class="mi">1</span><span class="p">:</span>
+<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a>        <span class="k">return</span> <span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span>
+<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a>    <span class="c1"># 左と上のセルからの最小パスコスト</span>
+<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a>    <span class="n">up</span> <span class="o">=</span> <span class="n">min_path_sum_dfs_mem</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span> <span class="n">mem</span><span class="p">,</span> <span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">j</span><span class="p">)</span>
+<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a>    <span class="n">left</span> <span class="o">=</span> <span class="n">min_path_sum_dfs_mem</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span> <span class="n">mem</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a>    <span class="c1"># 左上から (i, j) への最小パスコストを記録して返す</span>
+<a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a>    <span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">left</span><span class="p">,</span> <span class="n">up</span><span class="p">)</span> <span class="o">+</span> <span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span>
+<a id="__codelineno-14-19" name="__codelineno-14-19" href="#__codelineno-14-19"></a>    <span class="k">return</span> <span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.cpp</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="p">[</span><span class="k">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">minPathSumDFSMem</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.java</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 最小パス和：メモ化探索 */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">minPathSumDFSMem</span><span class="p">(</span><span class="kt">int</span><span class="o">[][]</span><span class="w"> </span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">[][]</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="c1">// 左上のセルの場合、探索を終了</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">    </span><span class="c1">// 行または列のインデックスが範囲外の場合、+∞ のコストを返す</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">Integer</span><span class="p">.</span><span class="na">MAX_VALUE</span><span class="p">;</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="w">    </span><span class="c1">// 記録がある場合、それを返す</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="w">    </span><span class="c1">// 左と上のセルからの最小パスコスト</span>
+<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">up</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">minPathSumDFSMem</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">);</span>
+<a id="__codelineno-16-17" name="__codelineno-16-17" href="#__codelineno-16-17"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">minPathSumDFSMem</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-16-18" name="__codelineno-16-18" href="#__codelineno-16-18"></a><span class="w">    </span><span class="c1">// 左上から (i, j) への最小パスコストを記録して返す</span>
+<a id="__codelineno-16-19" name="__codelineno-16-19" href="#__codelineno-16-19"></a><span class="w">    </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">min</span><span class="p">(</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">up</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-16-20" name="__codelineno-16-20" href="#__codelineno-16-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-16-21" name="__codelineno-16-21" href="#__codelineno-16-21"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.cs</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">min_path_sum</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">MinPathSumDFSMem</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.go</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">minPathSumDFSMem</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">minPathSumDFSMem</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.js</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">minPathSumDFSMem</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.ts</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">minPathSumDFSMem</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.dart</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">minPathSumDFSMem</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.rs</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">min_path_sum_dfs_mem</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.c</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">minPathSumDFSMem</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.kt</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">minPathSumDFSMem</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">min_path_sum_dfs_mem</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.zig</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">minPathSumDFSMem</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>下の図に示すように、メモ化を導入した後、すべての部分問題の解は一度だけ計算される必要があるため、時間計算量は状態の総数、つまりグリッドサイズ <span class="arithmatex">\(O(nm)\)</span> に依存します。</p>
+<p><a class="glightbox" href="../dp_solution_pipeline.assets/min_path_sum_dfs_mem.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="メモ化探索の再帰木" class="animation-figure" src="../dp_solution_pipeline.assets/min_path_sum_dfs_mem.png" /></a></p>
+<p align="center"> 図 14-15 &nbsp; メモ化探索の再帰木 </p>
+
+<h3 id="3-3">3. &nbsp; 方法3：動的プログラミング<a class="headerlink" href="#3-3" title="Permanent link">&para;</a></h3>
+<p>動的プログラミング解法を反復的に実装します。コードは以下の通りです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="3:14"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><input id="__tabbed_3_14" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label><label for="__tabbed_3_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.py</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">min_path_sum_dp</span><span class="p">(</span><span class="n">grid</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]])</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;最小パス和：動的プログラミング&quot;&quot;&quot;</span>
+<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a>    <span class="n">n</span><span class="p">,</span> <span class="n">m</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">grid</span><span class="p">),</span> <span class="nb">len</span><span class="p">(</span><span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
+<a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a>    <span class="c1"># dp テーブルを初期化</span>
+<a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a>    <span class="n">dp</span> <span class="o">=</span> <span class="p">[[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">m</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">)]</span>
+<a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a>    <span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
+<a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a>    <span class="c1"># 状態遷移：最初の行</span>
+<a id="__codelineno-28-8" name="__codelineno-28-8" href="#__codelineno-28-8"></a>    <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">m</span><span class="p">):</span>
+<a id="__codelineno-28-9" name="__codelineno-28-9" href="#__codelineno-28-9"></a>        <span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span><span class="p">]</span>
+<a id="__codelineno-28-10" name="__codelineno-28-10" href="#__codelineno-28-10"></a>    <span class="c1"># 状態遷移：最初の列</span>
+<a id="__codelineno-28-11" name="__codelineno-28-11" href="#__codelineno-28-11"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span><span class="p">):</span>
+<a id="__codelineno-28-12" name="__codelineno-28-12" href="#__codelineno-28-12"></a>        <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
+<a id="__codelineno-28-13" name="__codelineno-28-13" href="#__codelineno-28-13"></a>    <span class="c1"># 状態遷移：残りの行と列</span>
+<a id="__codelineno-28-14" name="__codelineno-28-14" href="#__codelineno-28-14"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span><span class="p">):</span>
+<a id="__codelineno-28-15" name="__codelineno-28-15" href="#__codelineno-28-15"></a>        <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">m</span><span class="p">):</span>
+<a id="__codelineno-28-16" name="__codelineno-28-16" href="#__codelineno-28-16"></a>            <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span> <span class="o">-</span> <span class="mi">1</span><span class="p">],</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="n">j</span><span class="p">])</span> <span class="o">+</span> <span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span>
+<a id="__codelineno-28-17" name="__codelineno-28-17" href="#__codelineno-28-17"></a>    <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="n">m</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.cpp</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="cm">/* 最小パス和：動的プログラミング */</span>
+<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">minPathSumDP</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">grid</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="p">.</span><span class="n">size</span><span class="p">(),</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">].</span><span class="n">size</span><span class="p">();</span>
+<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化</span>
+<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">dp</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">(</span><span class="n">m</span><span class="p">));</span>
+<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">];</span>
+<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="w">    </span><span class="c1">// 状態遷移：最初の行</span>
+<a id="__codelineno-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-9" name="__codelineno-29-9" href="#__codelineno-29-9"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-29-10" name="__codelineno-29-10" href="#__codelineno-29-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-11" name="__codelineno-29-11" href="#__codelineno-29-11"></a><span class="w">    </span><span class="c1">// 状態遷移：最初の列</span>
+<a id="__codelineno-29-12" name="__codelineno-29-12" href="#__codelineno-29-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-13" name="__codelineno-29-13" href="#__codelineno-29-13"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">];</span>
+<a id="__codelineno-29-14" name="__codelineno-29-14" href="#__codelineno-29-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-15" name="__codelineno-29-15" href="#__codelineno-29-15"></a><span class="w">    </span><span class="c1">// 状態遷移：残りの行と列</span>
+<a id="__codelineno-29-16" name="__codelineno-29-16" href="#__codelineno-29-16"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-17" name="__codelineno-29-17" href="#__codelineno-29-17"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-18" name="__codelineno-29-18" href="#__codelineno-29-18"></a><span class="w">            </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">j</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">];</span>
+<a id="__codelineno-29-19" name="__codelineno-29-19" href="#__codelineno-29-19"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-29-20" name="__codelineno-29-20" href="#__codelineno-29-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-21" name="__codelineno-29-21" href="#__codelineno-29-21"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-29-22" name="__codelineno-29-22" href="#__codelineno-29-22"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.java</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* 最小パス和：動的プログラミング */</span>
+<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">minPathSumDP</span><span class="p">(</span><span class="kt">int</span><span class="o">[][]</span><span class="w"> </span><span class="n">grid</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="p">.</span><span class="na">length</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="p">.</span><span class="na">length</span><span class="p">;</span>
+<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化</span>
+<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a><span class="w">    </span><span class="kt">int</span><span class="o">[][]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="n">m</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="w">    </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a><span class="w">    </span><span class="c1">// 状態遷移：最初の行</span>
+<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-30-10" name="__codelineno-30-10" href="#__codelineno-30-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-11" name="__codelineno-30-11" href="#__codelineno-30-11"></a><span class="w">    </span><span class="c1">// 状態遷移：最初の列</span>
+<a id="__codelineno-30-12" name="__codelineno-30-12" href="#__codelineno-30-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-13" name="__codelineno-30-13" href="#__codelineno-30-13"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-30-14" name="__codelineno-30-14" href="#__codelineno-30-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-15" name="__codelineno-30-15" href="#__codelineno-30-15"></a><span class="w">    </span><span class="c1">// 状態遷移：残りの行と列</span>
+<a id="__codelineno-30-16" name="__codelineno-30-16" href="#__codelineno-30-16"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-17" name="__codelineno-30-17" href="#__codelineno-30-17"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-18" name="__codelineno-30-18" href="#__codelineno-30-18"></a><span class="w">            </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">min</span><span class="p">(</span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-30-19" name="__codelineno-30-19" href="#__codelineno-30-19"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-30-20" name="__codelineno-30-20" href="#__codelineno-30-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-21" name="__codelineno-30-21" href="#__codelineno-30-21"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-30-22" name="__codelineno-30-22" href="#__codelineno-30-22"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.cs</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">min_path_sum</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">MinPathSumDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.go</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">minPathSumDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.swift</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">minPathSumDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.js</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">minPathSumDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.ts</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">minPathSumDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.dart</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">minPathSumDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.rs</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">min_path_sum_dp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.c</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">minPathSumDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.kt</span><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">minPathSumDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">min_path_sum_dp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.zig</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">minPathSumDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>下の図は最小経路和の状態遷移プロセスを示し、グリッド全体を走査するため、<strong>時間計算量は <span class="arithmatex">\(O(nm)\)</span></strong> です。</p>
+<p>配列 <code>dp</code> のサイズは <span class="arithmatex">\(n \times m\)</span> であるため、<strong>空間計算量は <span class="arithmatex">\(O(nm)\)</span></strong> です。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="4:12"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><input id="__tabbed_4_6" name="__tabbed_4" type="radio" /><input id="__tabbed_4_7" name="__tabbed_4" type="radio" /><input id="__tabbed_4_8" name="__tabbed_4" type="radio" /><input id="__tabbed_4_9" name="__tabbed_4" type="radio" /><input id="__tabbed_4_10" name="__tabbed_4" type="radio" /><input id="__tabbed_4_11" name="__tabbed_4" type="radio" /><input id="__tabbed_4_12" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">&lt;1&gt;</label><label for="__tabbed_4_2">&lt;2&gt;</label><label for="__tabbed_4_3">&lt;3&gt;</label><label for="__tabbed_4_4">&lt;4&gt;</label><label for="__tabbed_4_5">&lt;5&gt;</label><label for="__tabbed_4_6">&lt;6&gt;</label><label for="__tabbed_4_7">&lt;7&gt;</label><label for="__tabbed_4_8">&lt;8&gt;</label><label for="__tabbed_4_9">&lt;9&gt;</label><label for="__tabbed_4_10">&lt;10&gt;</label><label for="__tabbed_4_11">&lt;11&gt;</label><label for="__tabbed_4_12">&lt;12&gt;</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<p><a class="glightbox" href="../dp_solution_pipeline.assets/min_path_sum_dp_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="最小経路和の動的プログラミングプロセス" class="animation-figure" src="../dp_solution_pipeline.assets/min_path_sum_dp_step1.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../dp_solution_pipeline.assets/min_path_sum_dp_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="min_path_sum_dp_step2" class="animation-figure" src="../dp_solution_pipeline.assets/min_path_sum_dp_step2.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../dp_solution_pipeline.assets/min_path_sum_dp_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="min_path_sum_dp_step3" class="animation-figure" src="../dp_solution_pipeline.assets/min_path_sum_dp_step3.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../dp_solution_pipeline.assets/min_path_sum_dp_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="min_path_sum_dp_step4" class="animation-figure" src="../dp_solution_pipeline.assets/min_path_sum_dp_step4.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../dp_solution_pipeline.assets/min_path_sum_dp_step5.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="min_path_sum_dp_step5" class="animation-figure" src="../dp_solution_pipeline.assets/min_path_sum_dp_step5.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../dp_solution_pipeline.assets/min_path_sum_dp_step6.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="min_path_sum_dp_step6" class="animation-figure" src="../dp_solution_pipeline.assets/min_path_sum_dp_step6.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../dp_solution_pipeline.assets/min_path_sum_dp_step7.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="min_path_sum_dp_step7" class="animation-figure" src="../dp_solution_pipeline.assets/min_path_sum_dp_step7.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../dp_solution_pipeline.assets/min_path_sum_dp_step8.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="min_path_sum_dp_step8" class="animation-figure" src="../dp_solution_pipeline.assets/min_path_sum_dp_step8.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../dp_solution_pipeline.assets/min_path_sum_dp_step9.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="min_path_sum_dp_step9" class="animation-figure" src="../dp_solution_pipeline.assets/min_path_sum_dp_step9.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../dp_solution_pipeline.assets/min_path_sum_dp_step10.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="min_path_sum_dp_step10" class="animation-figure" src="../dp_solution_pipeline.assets/min_path_sum_dp_step10.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../dp_solution_pipeline.assets/min_path_sum_dp_step11.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="min_path_sum_dp_step11" class="animation-figure" src="../dp_solution_pipeline.assets/min_path_sum_dp_step11.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../dp_solution_pipeline.assets/min_path_sum_dp_step12.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="min_path_sum_dp_step12" class="animation-figure" src="../dp_solution_pipeline.assets/min_path_sum_dp_step12.png" /></a></p>
+</div>
+</div>
+</div>
+<p align="center"> 図 14-16 &nbsp; 最小経路和の動的プログラミングプロセス </p>
+
+<h3 id="4">4. &nbsp; 空間最適化<a class="headerlink" href="#4" title="Permanent link">&para;</a></h3>
+<p>各セルは左と上のセルのみに関連するため、単一行配列を使用して <span class="arithmatex">\(dp\)</span> テーブルを実装できます。</p>
+<p>配列 <code>dp</code> は1行の状態のみを表現できるため、最初の列の状態を事前に初期化できず、各行を走査するときに更新することに注意してください：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="5:14"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><input id="__tabbed_5_7" name="__tabbed_5" type="radio" /><input id="__tabbed_5_8" name="__tabbed_5" type="radio" /><input id="__tabbed_5_9" name="__tabbed_5" type="radio" /><input id="__tabbed_5_10" name="__tabbed_5" type="radio" /><input id="__tabbed_5_11" name="__tabbed_5" type="radio" /><input id="__tabbed_5_12" name="__tabbed_5" type="radio" /><input id="__tabbed_5_13" name="__tabbed_5" type="radio" /><input id="__tabbed_5_14" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">Python</label><label for="__tabbed_5_2">C++</label><label for="__tabbed_5_3">Java</label><label for="__tabbed_5_4">C#</label><label for="__tabbed_5_5">Go</label><label for="__tabbed_5_6">Swift</label><label for="__tabbed_5_7">JS</label><label for="__tabbed_5_8">TS</label><label for="__tabbed_5_9">Dart</label><label for="__tabbed_5_10">Rust</label><label for="__tabbed_5_11">C</label><label for="__tabbed_5_12">Kotlin</label><label for="__tabbed_5_13">Ruby</label><label for="__tabbed_5_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.py</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">min_path_sum_dp_comp</span><span class="p">(</span><span class="n">grid</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]])</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-42-2" name="__codelineno-42-2" href="#__codelineno-42-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;最小パス和：空間最適化動的プログラミング&quot;&quot;&quot;</span>
+<a id="__codelineno-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></a>    <span class="n">n</span><span class="p">,</span> <span class="n">m</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">grid</span><span class="p">),</span> <span class="nb">len</span><span class="p">(</span><span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
+<a id="__codelineno-42-4" name="__codelineno-42-4" href="#__codelineno-42-4"></a>    <span class="c1"># dp テーブルを初期化</span>
+<a id="__codelineno-42-5" name="__codelineno-42-5" href="#__codelineno-42-5"></a>    <span class="n">dp</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">m</span>
+<a id="__codelineno-42-6" name="__codelineno-42-6" href="#__codelineno-42-6"></a>    <span class="c1"># 状態遷移：最初の行</span>
+<a id="__codelineno-42-7" name="__codelineno-42-7" href="#__codelineno-42-7"></a>    <span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
+<a id="__codelineno-42-8" name="__codelineno-42-8" href="#__codelineno-42-8"></a>    <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">m</span><span class="p">):</span>
+<a id="__codelineno-42-9" name="__codelineno-42-9" href="#__codelineno-42-9"></a>        <span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">j</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="n">grid</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span><span class="p">]</span>
+<a id="__codelineno-42-10" name="__codelineno-42-10" href="#__codelineno-42-10"></a>    <span class="c1"># 状態遷移：残りの行</span>
+<a id="__codelineno-42-11" name="__codelineno-42-11" href="#__codelineno-42-11"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span><span class="p">):</span>
+<a id="__codelineno-42-12" name="__codelineno-42-12" href="#__codelineno-42-12"></a>        <span class="c1"># 状態遷移：最初の列</span>
+<a id="__codelineno-42-13" name="__codelineno-42-13" href="#__codelineno-42-13"></a>        <span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
+<a id="__codelineno-42-14" name="__codelineno-42-14" href="#__codelineno-42-14"></a>        <span class="c1"># 状態遷移：残りの列</span>
+<a id="__codelineno-42-15" name="__codelineno-42-15" href="#__codelineno-42-15"></a>        <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">m</span><span class="p">):</span>
+<a id="__codelineno-42-16" name="__codelineno-42-16" href="#__codelineno-42-16"></a>            <span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">j</span> <span class="o">-</span> <span class="mi">1</span><span class="p">],</span> <span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">])</span> <span class="o">+</span> <span class="n">grid</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span>
+<a id="__codelineno-42-17" name="__codelineno-42-17" href="#__codelineno-42-17"></a>    <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">m</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.cpp</span><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="p">[</span><span class="k">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">minPathSumDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.java</span><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="cm">/* 最小パス和：空間最適化動的プログラミング */</span>
+<a id="__codelineno-44-2" name="__codelineno-44-2" href="#__codelineno-44-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">minPathSumDPComp</span><span class="p">(</span><span class="kt">int</span><span class="o">[][]</span><span class="w"> </span><span class="n">grid</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-3" name="__codelineno-44-3" href="#__codelineno-44-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="p">.</span><span class="na">length</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="p">.</span><span class="na">length</span><span class="p">;</span>
+<a id="__codelineno-44-4" name="__codelineno-44-4" href="#__codelineno-44-4"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化</span>
+<a id="__codelineno-44-5" name="__codelineno-44-5" href="#__codelineno-44-5"></a><span class="w">    </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-44-6" name="__codelineno-44-6" href="#__codelineno-44-6"></a><span class="w">    </span><span class="c1">// 状態遷移：最初の行</span>
+<a id="__codelineno-44-7" name="__codelineno-44-7" href="#__codelineno-44-7"></a><span class="w">    </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-44-8" name="__codelineno-44-8" href="#__codelineno-44-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-9" name="__codelineno-44-9" href="#__codelineno-44-9"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-44-10" name="__codelineno-44-10" href="#__codelineno-44-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-44-11" name="__codelineno-44-11" href="#__codelineno-44-11"></a><span class="w">    </span><span class="c1">// 状態遷移：残りの行</span>
+<a id="__codelineno-44-12" name="__codelineno-44-12" href="#__codelineno-44-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-13" name="__codelineno-44-13" href="#__codelineno-44-13"></a><span class="w">        </span><span class="c1">// 状態遷移：最初の列</span>
+<a id="__codelineno-44-14" name="__codelineno-44-14" href="#__codelineno-44-14"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-44-15" name="__codelineno-44-15" href="#__codelineno-44-15"></a><span class="w">        </span><span class="c1">// 状態遷移：残りの列</span>
+<a id="__codelineno-44-16" name="__codelineno-44-16" href="#__codelineno-44-16"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-17" name="__codelineno-44-17" href="#__codelineno-44-17"></a><span class="w">            </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">min</span><span class="p">(</span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">grid</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-44-18" name="__codelineno-44-18" href="#__codelineno-44-18"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-44-19" name="__codelineno-44-19" href="#__codelineno-44-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-44-20" name="__codelineno-44-20" href="#__codelineno-44-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-44-21" name="__codelineno-44-21" href="#__codelineno-44-21"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.cs</span><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">min_path_sum</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">MinPathSumDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.go</span><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">minPathSumDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.swift</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">minPathSumDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.js</span><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">minPathSumDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.ts</span><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">minPathSumDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.dart</span><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">minPathSumDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.rs</span><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">min_path_sum_dp_comp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.c</span><pre><span></span><code><a id="__codelineno-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">minPathSumDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.kt</span><pre><span></span><code><a id="__codelineno-53-1" name="__codelineno-53-1" href="#__codelineno-53-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">minPathSumDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.rb</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">min_path_sum_dp_comp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">min_path_sum.zig</span><pre><span></span><code><a id="__codelineno-55-1" name="__codelineno-55-1" href="#__codelineno-55-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">minPathSumDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
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+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_1" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hello_algo/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m13.13 22.19-1.63-3.83c1.57-.58 3.04-1.36 4.4-2.27l-2.77 6.1M5.64 12.5l-3.83-1.63 6.1-2.77C7 9.46 6.22 10.93 5.64 12.5M19.22 4c.28 0 .53 0 .74.05.17 1.39-.02 4.25-3.3 7.53-1.7 1.71-3.73 3.02-6.01 3.89l-2.15-2.1c.92-2.31 2.23-4.34 3.92-6.03C15.18 4.58 17.64 4 19.22 4m0-2c-1.98 0-4.98.69-8.22 3.93-2.19 2.19-3.5 4.6-4.35 6.71-.28.75-.09 1.57.46 2.13l2.13 2.12c.38.38.89.61 1.42.61.23 0 .47-.06.7-.15A19.1 19.1 0 0 0 18.07 13c5.66-5.66 3.54-10.61 3.54-10.61S20.7 2 19.22 2m-4.68 7.46c-.78-.78-.78-2.05 0-2.83s2.05-.78 2.83 0c.77.78.78 2.05 0 2.83-.78.78-2.05.78-2.83 0m-5.66 7.07-1.41-1.41 1.41 1.41M6.24 22l3.64-3.64c-.34-.09-.67-.24-.97-.45L4.83 22h1.41M2 22h1.41l4.77-4.76-1.42-1.41L2 20.59V22m0-2.83 4.09-4.08c-.21-.3-.36-.62-.45-.97L2 17.76v1.41Z"/></svg>
+  
+  <span class="md-ellipsis">
+    はじめに
+  </span>
+  
+
+            </a>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_1_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_1">
+            <span class="md-nav__icon md-icon"></span>
+            はじめに
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
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+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
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+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
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+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_preface/" class="md-nav__link ">
+              
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M21 4H3a2 2 0 0 0-2 2v13a2 2 0 0 0 2 2h18a2 2 0 0 0 2-2V6a2 2 0 0 0-2-2M3 19V6h8v13H3m18 0h-8V6h8v13m-7-9.5h6V11h-6V9.5m0 2.5h6v1.5h-6V12m0 2.5h6V16h-6v-1.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 0 章 &nbsp; 前書き
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_2" id="__nav_2_label" tabindex="0">
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_2_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_2">
+            <span class="md-nav__icon md-icon"></span>
+            第 0 章 &nbsp; 前書き
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/about_the_book/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.1 &nbsp; この本について
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/suggestions/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.2 &nbsp; 本書の使い方
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
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+      
+      
+  
+  
+  
+  
+    
+    
+      
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+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_introduction/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
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+  
+
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+
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+      <a href="../knapsack_problem/" class="md-nav__link">
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+  
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+
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+  
+  
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+      <a href="../unbounded_knapsack_problem/" class="md-nav__link">
+        
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+  <a href="#2" class="md-nav__link">
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+  <a href="#3" class="md-nav__link">
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+    15.4 &nbsp; 最大積切断問題
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+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
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+    16.2 &nbsp; 一緒に創作に参加
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+  
+
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+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
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+    16.3 &nbsp; 用語集
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+  <a href="#2" class="md-nav__link">
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+  <a href="#3" class="md-nav__link">
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+    <a
+      href="https://github.com/krahets/hello-algo/tree/main/ja/docs/chapter_dynamic_programming/edit_distance_problem.md"
+      title="編集"
+      class="md-content__button md-icon"
+    >
+      
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
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+<!-- Page content -->
+<h1 id="146">14.6 &nbsp; 編集距離問題<a class="headerlink" href="#146" title="Permanent link">&para;</a></h1>
+<p>編集距離は、レーベンシュタイン距離とも呼ばれ、一つの文字列を別の文字列に変換するために必要な最小修正回数を指し、情報検索や自然言語処理で2つのシーケンス間の類似度を測定するためによく使用されます。</p>
+<div class="admonition question">
+<p class="admonition-title">Question</p>
+<p>2つの文字列 <span class="arithmatex">\(s\)</span> と <span class="arithmatex">\(t\)</span> が与えられたとき、<span class="arithmatex">\(s\)</span> を <span class="arithmatex">\(t\)</span> に変換するために必要な最小編集回数を返してください。</p>
+<p>文字列に対して3種類の編集を実行できます：文字の挿入、文字の削除、または文字を他の任意の文字に置換。</p>
+</div>
+<p>下の図に示すように、<code>kitten</code> を <code>sitting</code> に変換するには3回の編集が必要で、2回の置換と1回の挿入を含みます。<code>hello</code> を <code>algo</code> に変換するには3ステップが必要で、2回の置換と1回の削除を含みます。</p>
+<p><a class="glightbox" href="../edit_distance_problem.assets/edit_distance_example.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="編集距離の例データ" class="animation-figure" src="../edit_distance_problem.assets/edit_distance_example.png" /></a></p>
+<p align="center"> 図 14-27 &nbsp; 編集距離の例データ </p>
+
+<p><strong>編集距離問題は決定木モデルで自然に説明できます</strong>。文字列は木のノードに対応し、1ラウンドの決定（編集操作）は木のエッジに対応します。</p>
+<p>下の図に示すように、操作に制限がない場合、各ノードは多くのエッジを導出でき、それぞれが1つの操作に対応するため、<code>hello</code> を <code>algo</code> に変換する可能な経路は多数あります。</p>
+<p>決定木の観点から、この問題の目標は、ノード <code>hello</code> とノード <code>algo</code> の間の最短経路を見つけることです。</p>
+<p><a class="glightbox" href="../edit_distance_problem.assets/edit_distance_decision_tree.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="決定木モデルに基づいて表現された編集距離問題" class="animation-figure" src="../edit_distance_problem.assets/edit_distance_decision_tree.png" /></a></p>
+<p align="center"> 図 14-28 &nbsp; 決定木モデルに基づいて表現された編集距離問題 </p>
+
+<h3 id="1">1. &nbsp; 動的プログラミングアプローチ<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<p><strong>ステップ1：各ラウンドの決定を考え、状態を定義し、それにより <span class="arithmatex">\(dp\)</span> テーブルを得る</strong></p>
+<p>各ラウンドの決定は、文字列 <span class="arithmatex">\(s\)</span> に対して1つの編集操作を実行することを含みます。</p>
+<p>編集プロセス中に問題のサイズを段階的に縮小することを目指し、これにより部分問題を構築できます。文字列 <span class="arithmatex">\(s\)</span> と <span class="arithmatex">\(t\)</span> の長さをそれぞれ <span class="arithmatex">\(n\)</span> と <span class="arithmatex">\(m\)</span> とします。まず、両方の文字列の末尾文字 <span class="arithmatex">\(s[n-1]\)</span> と <span class="arithmatex">\(t[m-1]\)</span> を考慮します。</p>
+<ul>
+<li><span class="arithmatex">\(s[n-1]\)</span> と <span class="arithmatex">\(t[m-1]\)</span> が同じ場合、それらをスキップして直接 <span class="arithmatex">\(s[n-2]\)</span> と <span class="arithmatex">\(t[m-2]\)</span> を考慮できます。</li>
+<li><span class="arithmatex">\(s[n-1]\)</span> と <span class="arithmatex">\(t[m-1]\)</span> が異なる場合、<span class="arithmatex">\(s\)</span> に対して1つの編集（挿入、削除、置換）を実行して、2つの文字列の末尾文字を一致させ、それらをスキップしてより小規模な問題を考慮できるようにする必要があります。</li>
+</ul>
+<p>したがって、文字列 <span class="arithmatex">\(s\)</span> での各ラウンドの決定（編集操作）は、<span class="arithmatex">\(s\)</span> と <span class="arithmatex">\(t\)</span> でマッチされる残りの文字を変更します。したがって、状態は <span class="arithmatex">\(s\)</span> と <span class="arithmatex">\(t\)</span> で現在考慮されている <span class="arithmatex">\(i\)</span> 番目と <span class="arithmatex">\(j\)</span> 番目の文字であり、<span class="arithmatex">\([i, j]\)</span> と表記されます。</p>
+<p>状態 <span class="arithmatex">\([i, j]\)</span> は部分問題に対応します：<strong><span class="arithmatex">\(s\)</span> の最初の <span class="arithmatex">\(i\)</span> 文字を <span class="arithmatex">\(t\)</span> の最初の <span class="arithmatex">\(j\)</span> 文字に変更するために必要な最小編集回数</strong>。</p>
+<p>これから、サイズ <span class="arithmatex">\((i+1) \times (j+1)\)</span> の二次元 <span class="arithmatex">\(dp\)</span> テーブルを得ます。</p>
+<p><strong>ステップ2：最適部分構造を特定し、状態遷移方程式を導出する</strong></p>
+<p>部分問題 <span class="arithmatex">\(dp[i, j]\)</span> を考慮すると、これに対応する2つの文字列の末尾文字は <span class="arithmatex">\(s[i-1]\)</span> と <span class="arithmatex">\(t[j-1]\)</span> であり、下の図に示すように3つのシナリオに分けることができます。</p>
+<ol>
+<li><span class="arithmatex">\(s[i-1]\)</span> の後に <span class="arithmatex">\(t[j-1]\)</span> を追加すると、残りの部分問題は <span class="arithmatex">\(dp[i, j-1]\)</span> です。</li>
+<li><span class="arithmatex">\(s[i-1]\)</span> を削除すると、残りの部分問題は <span class="arithmatex">\(dp[i-1, j]\)</span> です。</li>
+<li><span class="arithmatex">\(s[i-1]\)</span> を <span class="arithmatex">\(t[j-1]\)</span> に置換すると、残りの部分問題は <span class="arithmatex">\(dp[i-1, j-1]\)</span> です。</li>
+</ol>
+<p><a class="glightbox" href="../edit_distance_problem.assets/edit_distance_state_transfer.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="編集距離の状態遷移" class="animation-figure" src="../edit_distance_problem.assets/edit_distance_state_transfer.png" /></a></p>
+<p align="center"> 図 14-29 &nbsp; 編集距離の状態遷移 </p>
+
+<p>上記の分析に基づいて、最適部分構造を決定できます：<span class="arithmatex">\(dp[i, j]\)</span> の最小編集回数は、<span class="arithmatex">\(dp[i, j-1]\)</span>、<span class="arithmatex">\(dp[i-1, j]\)</span>、<span class="arithmatex">\(dp[i-1, j-1]\)</span> の中の最小値に編集ステップ <span class="arithmatex">\(1\)</span> を加えたものです。対応する状態遷移方程式は：</p>
+<div class="arithmatex">\[
+dp[i, j] = \min(dp[i, j-1], dp[i-1, j], dp[i-1, j-1]) + 1
+\]</div>
+<p>注意してください。<strong><span class="arithmatex">\(s[i-1]\)</span> と <span class="arithmatex">\(t[j-1]\)</span> が同じ場合、現在の文字に対して編集は必要ありません</strong>。この場合、状態遷移方程式は：</p>
+<div class="arithmatex">\[
+dp[i, j] = dp[i-1, j-1]
+\]</div>
+<p><strong>ステップ3：境界条件と状態遷移の順序を決定する</strong></p>
+<p>両方の文字列が空の場合、編集回数は <span class="arithmatex">\(0\)</span> です。つまり、<span class="arithmatex">\(dp[0, 0] = 0\)</span> です。<span class="arithmatex">\(s\)</span> が空で <span class="arithmatex">\(t\)</span> が空でない場合、最小編集回数は <span class="arithmatex">\(t\)</span> の長さに等しく、つまり最初の行 <span class="arithmatex">\(dp[0, j] = j\)</span> です。<span class="arithmatex">\(s\)</span> が空でなく <span class="arithmatex">\(t\)</span> が空の場合、最小編集回数は <span class="arithmatex">\(s\)</span> の長さに等しく、つまり最初の列 <span class="arithmatex">\(dp[i, 0] = i\)</span> です。</p>
+<p>状態遷移方程式を観察すると、<span class="arithmatex">\(dp[i, j]\)</span> の解決は左、上、左上の解に依存するため、二重ループを使用して正しい順序で <span class="arithmatex">\(dp\)</span> テーブル全体を走査できます。</p>
+<h3 id="2">2. &nbsp; コード実装<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:14"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><input id="__tabbed_1_14" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label><label for="__tabbed_1_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">edit_distance.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">edit_distance_dp</span><span class="p">(</span><span class="n">s</span><span class="p">:</span> <span class="nb">str</span><span class="p">,</span> <span class="n">t</span><span class="p">:</span> <span class="nb">str</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;編集距離：動的プログラミング&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="n">n</span><span class="p">,</span> <span class="n">m</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">s</span><span class="p">),</span> <span class="nb">len</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="n">dp</span> <span class="o">=</span> <span class="p">[[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)]</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="c1"># 状態遷移：最初の行と最初の列</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>        <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">i</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>    <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>        <span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">j</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>    <span class="c1"># 状態遷移：残りの行と列</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>        <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>            <span class="k">if</span> <span class="n">s</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">==</span> <span class="n">t</span><span class="p">[</span><span class="n">j</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]:</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>                <span class="c1"># 2 つの文字が等しい場合、これら 2 つの文字をスキップ</span>
+<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>                <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="n">j</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>            <span class="k">else</span><span class="p">:</span>
+<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>                <span class="c1"># 最小編集数 = 3 つの操作（挿入、削除、置換）からの最小編集数 + 1</span>
+<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a>                <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span> <span class="o">-</span> <span class="mi">1</span><span class="p">],</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="n">j</span><span class="p">],</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="n">j</span> <span class="o">-</span> <span class="mi">1</span><span class="p">])</span> <span class="o">+</span> <span class="mi">1</span>
+<a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a>    <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">m</span><span class="p">]</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">edit_distance.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 編集距離：動的プログラミング */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">editDistanceDP</span><span class="p">(</span><span class="n">string</span><span class="w"> </span><span class="n">s</span><span class="p">,</span><span class="w"> </span><span class="n">string</span><span class="w"> </span><span class="n">t</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">s</span><span class="p">.</span><span class="n">length</span><span class="p">(),</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">t</span><span class="p">.</span><span class="n">length</span><span class="p">();</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">dp</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">(</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">));</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="c1">// 状態遷移：最初の行と最初の列</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span><span class="p">;</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">    </span><span class="c1">// 状態遷移：残りの行と列</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">s</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">t</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">                </span><span class="c1">// 2つの文字が等しい場合、これら2つの文字をスキップ</span>
+<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="w">                </span><span class="c1">// 最小編集数 = 3つの操作（挿入、削除、置換）からの最小編集数 + 1</span>
+<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">j</span><span class="p">]),</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">m</span><span class="p">];</span>
+<a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">edit_distance.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 編集距離：動的プログラミング */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">editDistanceDP</span><span class="p">(</span><span class="n">String</span><span class="w"> </span><span class="n">s</span><span class="p">,</span><span class="w"> </span><span class="n">String</span><span class="w"> </span><span class="n">t</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">s</span><span class="p">.</span><span class="na">length</span><span class="p">(),</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">t</span><span class="p">.</span><span class="na">length</span><span class="p">();</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="kt">int</span><span class="o">[][]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="c1">// 状態遷移：最初の行と最初の列</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span><span class="p">;</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">    </span><span class="c1">// 状態遷移：残りの行と列</span>
+<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">s</span><span class="p">.</span><span class="na">charAt</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">t</span><span class="p">.</span><span class="na">charAt</span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">                </span><span class="c1">// 2つの文字が等しい場合、これら2つの文字をスキップ</span>
+<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w">                </span><span class="c1">// 最小編集数 = 3つの操作（挿入、削除、置換）からの最小編集数 + 1</span>
+<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">min</span><span class="p">(</span><span class="n">Math</span><span class="p">.</span><span class="na">min</span><span class="p">(</span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">j</span><span class="o">]</span><span class="p">),</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="n">m</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">edit_distance.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">edit_distance</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">EditDistanceDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">edit_distance.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">editDistanceDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">edit_distance.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">editDistanceDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">edit_distance.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">editDistanceDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">edit_distance.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">editDistanceDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">edit_distance.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">editDistanceDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">edit_distance.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">edit_distance_dp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">edit_distance.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">editDistanceDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">edit_distance.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">editDistanceDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">edit_distance.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">edit_distance_dp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">edit_distance.zig</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">editDistanceDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>下の図に示すように、編集距離問題の状態遷移プロセスはナップサック問題と非常に似ており、二次元グリッドを埋めることと見なすことができます。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:15"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><input id="__tabbed_2_14" name="__tabbed_2" type="radio" /><input id="__tabbed_2_15" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">&lt;1&gt;</label><label for="__tabbed_2_2">&lt;2&gt;</label><label for="__tabbed_2_3">&lt;3&gt;</label><label for="__tabbed_2_4">&lt;4&gt;</label><label for="__tabbed_2_5">&lt;5&gt;</label><label for="__tabbed_2_6">&lt;6&gt;</label><label for="__tabbed_2_7">&lt;7&gt;</label><label for="__tabbed_2_8">&lt;8&gt;</label><label for="__tabbed_2_9">&lt;9&gt;</label><label for="__tabbed_2_10">&lt;10&gt;</label><label for="__tabbed_2_11">&lt;11&gt;</label><label for="__tabbed_2_12">&lt;12&gt;</label><label for="__tabbed_2_13">&lt;13&gt;</label><label for="__tabbed_2_14">&lt;14&gt;</label><label for="__tabbed_2_15">&lt;15&gt;</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<p><a class="glightbox" href="../edit_distance_problem.assets/edit_distance_dp_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="編集距離の動的プログラミングプロセス" class="animation-figure" src="../edit_distance_problem.assets/edit_distance_dp_step1.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../edit_distance_problem.assets/edit_distance_dp_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="edit_distance_dp_step2" class="animation-figure" src="../edit_distance_problem.assets/edit_distance_dp_step2.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../edit_distance_problem.assets/edit_distance_dp_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="edit_distance_dp_step3" class="animation-figure" src="../edit_distance_problem.assets/edit_distance_dp_step3.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../edit_distance_problem.assets/edit_distance_dp_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="edit_distance_dp_step4" class="animation-figure" src="../edit_distance_problem.assets/edit_distance_dp_step4.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../edit_distance_problem.assets/edit_distance_dp_step5.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="edit_distance_dp_step5" class="animation-figure" src="../edit_distance_problem.assets/edit_distance_dp_step5.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../edit_distance_problem.assets/edit_distance_dp_step6.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="edit_distance_dp_step6" class="animation-figure" src="../edit_distance_problem.assets/edit_distance_dp_step6.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../edit_distance_problem.assets/edit_distance_dp_step7.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="edit_distance_dp_step7" class="animation-figure" src="../edit_distance_problem.assets/edit_distance_dp_step7.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../edit_distance_problem.assets/edit_distance_dp_step8.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="edit_distance_dp_step8" class="animation-figure" src="../edit_distance_problem.assets/edit_distance_dp_step8.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../edit_distance_problem.assets/edit_distance_dp_step9.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="edit_distance_dp_step9" class="animation-figure" src="../edit_distance_problem.assets/edit_distance_dp_step9.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../edit_distance_problem.assets/edit_distance_dp_step10.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="edit_distance_dp_step10" class="animation-figure" src="../edit_distance_problem.assets/edit_distance_dp_step10.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../edit_distance_problem.assets/edit_distance_dp_step11.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="edit_distance_dp_step11" class="animation-figure" src="../edit_distance_problem.assets/edit_distance_dp_step11.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../edit_distance_problem.assets/edit_distance_dp_step12.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="edit_distance_dp_step12" class="animation-figure" src="../edit_distance_problem.assets/edit_distance_dp_step12.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../edit_distance_problem.assets/edit_distance_dp_step13.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="edit_distance_dp_step13" class="animation-figure" src="../edit_distance_problem.assets/edit_distance_dp_step13.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../edit_distance_problem.assets/edit_distance_dp_step14.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="edit_distance_dp_step14" class="animation-figure" src="../edit_distance_problem.assets/edit_distance_dp_step14.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../edit_distance_problem.assets/edit_distance_dp_step15.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="edit_distance_dp_step15" class="animation-figure" src="../edit_distance_problem.assets/edit_distance_dp_step15.png" /></a></p>
+</div>
+</div>
+</div>
+<p align="center"> 図 14-30 &nbsp; 編集距離の動的プログラミングプロセス </p>
+
+<h3 id="3">3. &nbsp; 空間最適化<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
+<p><span class="arithmatex">\(dp[i, j]\)</span> は上の <span class="arithmatex">\(dp[i-1, j]\)</span>、左の <span class="arithmatex">\(dp[i, j-1]\)</span>、左上の <span class="arithmatex">\(dp[i-1, j-1]\)</span> の解から導出され、直接走査では左上の解 <span class="arithmatex">\(dp[i-1, j-1]\)</span> が失われ、逆走査では事前に <span class="arithmatex">\(dp[i, j-1]\)</span> を構築できないため、どちらの走査順序も実行可能ではありません。</p>
+<p>この理由で、変数 <code>leftup</code> を使用して左上の <span class="arithmatex">\(dp[i-1, j-1]\)</span> からの解を一時的に保存し、左と上の解のみを考慮すればよくなります。この状況は無制限ナップサック問題と似ており、直接走査が可能です。コードは以下の通りです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="3:14"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><input id="__tabbed_3_14" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label><label for="__tabbed_3_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">edit_distance.py</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">edit_distance_dp_comp</span><span class="p">(</span><span class="n">s</span><span class="p">:</span> <span class="nb">str</span><span class="p">,</span> <span class="n">t</span><span class="p">:</span> <span class="nb">str</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;編集距離：空間最適化動的プログラミング&quot;&quot;&quot;</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a>    <span class="n">n</span><span class="p">,</span> <span class="n">m</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">s</span><span class="p">),</span> <span class="nb">len</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a>    <span class="n">dp</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a>    <span class="c1"># 状態遷移：最初の行</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a>    <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a>        <span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">j</span>
+<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a>    <span class="c1"># 状態遷移：残りの行</span>
+<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a>        <span class="c1"># 状態遷移：最初の列</span>
+<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a>        <span class="n">leftup</span> <span class="o">=</span> <span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>  <span class="c1"># dp[i-1, j-1] を一時的に保存</span>
+<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a>        <span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a>        <span class="c1"># 状態遷移：残りの列</span>
+<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a>        <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a>            <span class="n">temp</span> <span class="o">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
+<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a>            <span class="k">if</span> <span class="n">s</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">==</span> <span class="n">t</span><span class="p">[</span><span class="n">j</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]:</span>
+<a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a>                <span class="c1"># 2 つの文字が等しい場合、これら 2 つの文字をスキップ</span>
+<a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a>                <span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">leftup</span>
+<a id="__codelineno-14-19" name="__codelineno-14-19" href="#__codelineno-14-19"></a>            <span class="k">else</span><span class="p">:</span>
+<a id="__codelineno-14-20" name="__codelineno-14-20" href="#__codelineno-14-20"></a>                <span class="c1"># 最小編集数 = 3 つの操作（挿入、削除、置換）からの最小編集数 + 1</span>
+<a id="__codelineno-14-21" name="__codelineno-14-21" href="#__codelineno-14-21"></a>                <span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">j</span> <span class="o">-</span> <span class="mi">1</span><span class="p">],</span> <span class="n">dp</span><span class="p">[</span><span class="n">j</span><span class="p">],</span> <span class="n">leftup</span><span class="p">)</span> <span class="o">+</span> <span class="mi">1</span>
+<a id="__codelineno-14-22" name="__codelineno-14-22" href="#__codelineno-14-22"></a>            <span class="n">leftup</span> <span class="o">=</span> <span class="n">temp</span>  <span class="c1"># 次の dp[i-1, j-1] のために更新</span>
+<a id="__codelineno-14-23" name="__codelineno-14-23" href="#__codelineno-14-23"></a>    <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">m</span><span class="p">]</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">edit_distance.cpp</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="p">[</span><span class="k">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">editDistanceDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">edit_distance.java</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 編集距離：空間最適化動的プログラミング */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">editDistanceDPComp</span><span class="p">(</span><span class="n">String</span><span class="w"> </span><span class="n">s</span><span class="p">,</span><span class="w"> </span><span class="n">String</span><span class="w"> </span><span class="n">t</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">s</span><span class="p">.</span><span class="na">length</span><span class="p">(),</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">t</span><span class="p">.</span><span class="na">length</span><span class="p">();</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">    </span><span class="c1">// 状態遷移：最初の行</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span><span class="p">;</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w">    </span><span class="c1">// 状態遷移：残りの行</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="w">        </span><span class="c1">// 状態遷移：最初の列</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">leftup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="p">;</span><span class="w"> </span><span class="c1">// dp[i-1, j-1] を一時的に格納</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="w">        </span><span class="c1">// 状態遷移：残りの列</span>
+<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a><span class="w">            </span><span class="kt">int</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-16-17" name="__codelineno-16-17" href="#__codelineno-16-17"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">s</span><span class="p">.</span><span class="na">charAt</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">t</span><span class="p">.</span><span class="na">charAt</span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-18" name="__codelineno-16-18" href="#__codelineno-16-18"></a><span class="w">                </span><span class="c1">// 2つの文字が等しい場合、これら2つの文字をスキップ</span>
+<a id="__codelineno-16-19" name="__codelineno-16-19" href="#__codelineno-16-19"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">leftup</span><span class="p">;</span>
+<a id="__codelineno-16-20" name="__codelineno-16-20" href="#__codelineno-16-20"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-21" name="__codelineno-16-21" href="#__codelineno-16-21"></a><span class="w">                </span><span class="c1">// 最小編集数 = 3つの操作（挿入、削除、置換）からの最小編集数 + 1</span>
+<a id="__codelineno-16-22" name="__codelineno-16-22" href="#__codelineno-16-22"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">min</span><span class="p">(</span><span class="n">Math</span><span class="p">.</span><span class="na">min</span><span class="p">(</span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">),</span><span class="w"> </span><span class="n">leftup</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-16-23" name="__codelineno-16-23" href="#__codelineno-16-23"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-16-24" name="__codelineno-16-24" href="#__codelineno-16-24"></a><span class="w">            </span><span class="n">leftup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="p">;</span><span class="w"> </span><span class="c1">// 次のラウンドの dp[i-1, j-1] のために更新</span>
+<a id="__codelineno-16-25" name="__codelineno-16-25" href="#__codelineno-16-25"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-16-26" name="__codelineno-16-26" href="#__codelineno-16-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-27" name="__codelineno-16-27" href="#__codelineno-16-27"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-16-28" name="__codelineno-16-28" href="#__codelineno-16-28"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">edit_distance.cs</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">edit_distance</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">EditDistanceDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">edit_distance.go</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">editDistanceDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">edit_distance.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">editDistanceDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">edit_distance.js</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">editDistanceDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">edit_distance.ts</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">editDistanceDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">edit_distance.dart</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">editDistanceDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">edit_distance.rs</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">edit_distance_dp_comp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">edit_distance.c</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">editDistanceDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">edit_distance.kt</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">editDistanceDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">edit_distance.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">edit_distance_dp_comp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">edit_distance.zig</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">editDistanceDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
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+  
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+    1.3 &nbsp; まとめ
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+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
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+            第 2 章 &nbsp; 計算量解析
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+    2.1 &nbsp; アルゴリズム効率評価
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+    2.2 &nbsp; 反復と再帰
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+  
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+      <a href="../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
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+    2.3 &nbsp; 時間計算量
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+  
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+      <a href="../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="./" class="md-nav__link md-nav__link--active">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link md-nav__link--active" for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
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+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
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+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
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+          </ul>
+        </nav>
+      
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+          
+        
+      
+    
+    
+    
+    
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+      
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+        
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+          
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+            <a href="../chapter_reference/" class="md-nav__link ">
+              
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9 3v15h3V3H9m3 2 4 13 3-1-4-13-3 1M5 5v13h3V5H5M3 19v2h18v-2H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    参考文献
+  </span>
+  
+
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+            
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+  <a href="#_1" class="md-nav__link">
+    <span class="md-ellipsis">
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+<h1 id="14">第 14 章 &nbsp; 動的プログラミング<a class="headerlink" href="#14" title="Permanent link">&para;</a></h1>
+<p><a class="glightbox" href="../assets/covers/chapter_dynamic_programming.jpg" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="動的プログラミング" class="cover-image" src="../assets/covers/chapter_dynamic_programming.jpg" /></a></p>
+<div class="admonition abstract">
+<p class="admonition-title">Abstract</p>
+<p>川が流れて海に注ぐように、</p>
+<p>動的プログラミングは小さな問題の解を織り合わせて、より大きな問題の解へと導きます。一歩一歩進んで、最終的な答えが待つ彼岸へと向かいます。</p>
+</div>
+<h2 id="_1">章の内容<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h2>
+<ul>
+<li><a href="intro_to_dynamic_programming/">14.1 &nbsp; 動的プログラミング入門</a></li>
+<li><a href="dp_problem_features/">14.2 &nbsp; DP問題の特性</a></li>
+<li><a href="dp_solution_pipeline/">14.3 &nbsp; DP問題解決アプローチ</a></li>
+<li><a href="knapsack_problem/">14.4 &nbsp; 0-1ナップサック問題</a></li>
+<li><a href="unbounded_knapsack_problem/">14.5 &nbsp; 無制限ナップサック問題</a></li>
+<li><a href="edit_distance_problem/">14.6 &nbsp; 編集距離問題</a></li>
+<li><a href="summary/">14.7 &nbsp; まとめ</a></li>
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+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_2" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_preface/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M21 4H3a2 2 0 0 0-2 2v13a2 2 0 0 0 2 2h18a2 2 0 0 0 2-2V6a2 2 0 0 0-2-2M3 19V6h8v13H3m18 0h-8V6h8v13m-7-9.5h6V11h-6V9.5m0 2.5h6v1.5h-6V12m0 2.5h6V16h-6v-1.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 0 章 &nbsp; 前書き
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_2" id="__nav_2_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_2_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_2">
+            <span class="md-nav__icon md-icon"></span>
+            第 0 章 &nbsp; 前書き
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/about_the_book/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.1 &nbsp; この本について
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/suggestions/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.2 &nbsp; 本書の使い方
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_introduction/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1411-1" class="md-nav__link">
+    <span class="md-ellipsis">
+      14.1.1 &nbsp; 方法1：力任せ探索
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1412-2" class="md-nav__link">
+    <span class="md-ellipsis">
+      14.1.2 &nbsp; 方法2：メモ化探索
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1413-3" class="md-nav__link">
+    <span class="md-ellipsis">
+      14.1.3 &nbsp; 方法3：動的プログラミング
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1414" class="md-nav__link">
+    <span class="md-ellipsis">
+      14.1.4 &nbsp; 空間最適化
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
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+
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+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
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+    15.2 &nbsp; 分数ナップサック問題
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+
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+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
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+
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+
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+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
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+  
+
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+
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+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
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+  
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+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
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+    </li>
+  
+
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+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
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+
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+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
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+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
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+  
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+                  <div class="md-sidebar__inner">
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+  
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+  
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+      目次
+    </label>
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+      
+        <li class="md-nav__item">
+  <a href="#1411-1" class="md-nav__link">
+    <span class="md-ellipsis">
+      14.1.1 &nbsp; 方法1：力任せ探索
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1412-2" class="md-nav__link">
+    <span class="md-ellipsis">
+      14.1.2 &nbsp; 方法2：メモ化探索
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1413-3" class="md-nav__link">
+    <span class="md-ellipsis">
+      14.1.3 &nbsp; 方法3：動的プログラミング
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1414" class="md-nav__link">
+    <span class="md-ellipsis">
+      14.1.4 &nbsp; 空間最適化
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+                  </div>
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+              </div>
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+              <article class="md-content__inner md-typeset">
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+<!-- Page content -->
+<h1 id="141">14.1 &nbsp; 動的プログラミングの紹介<a class="headerlink" href="#141" title="Permanent link">&para;</a></h1>
+<p><u>動的プログラミング</u>は重要なアルゴリズムパラダイムであり、問題を一連の小さな部分問題に分解し、これらの部分問題の解を保存することで冗長な計算を避け、時間効率を大幅に向上させます。</p>
+<p>このセクションでは、古典的な問題から始めて、まず力任せの探索法による解法を提示し、重複する部分問題を特定してから、より効率的な動的プログラミング解法を段階的に導出します。</p>
+<div class="admonition question">
+<p class="admonition-title">階段登り</p>
+<p><span class="arithmatex">\(n\)</span> 段の階段があり、一度に <span class="arithmatex">\(1\)</span> 段または <span class="arithmatex">\(2\)</span> 段上ることができます。頂上に到達する方法は何通りありますか？</p>
+</div>
+<p>下の図に示すように、<span class="arithmatex">\(3\)</span> 段の階段の頂上に到達する方法は <span class="arithmatex">\(3\)</span> 通りあります。</p>
+<p><a class="glightbox" href="../intro_to_dynamic_programming.assets/climbing_stairs_example.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="3段目に到達する方法の数" class="animation-figure" src="../intro_to_dynamic_programming.assets/climbing_stairs_example.png" /></a></p>
+<p align="center"> 図 14-1 &nbsp; 3段目に到達する方法の数 </p>
+
+<p>この問題は**バックトラッキングを用いてすべての可能性を網羅**することで方法の数を計算することを目的としています。具体的には、階段登りの問題を多段階選択プロセスとして考えます：地面から始めて、毎回 <span class="arithmatex">\(1\)</span> 段または <span class="arithmatex">\(2\)</span> 段上るかを選択し、階段の頂上に到達したら方法の数をカウントし、頂上を超えた場合はプルーニング（枝刈り）を行います。コードは以下の通りです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:14"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><input id="__tabbed_1_14" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label><label for="__tabbed_1_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_backtrack.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">choices</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">state</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">res</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;バックトラッキング&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># n 段目に登ったとき、解の数に 1 を加える</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="k">if</span> <span class="n">state</span> <span class="o">==</span> <span class="n">n</span><span class="p">:</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>        <span class="n">res</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="c1"># すべての選択肢を走査</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>    <span class="k">for</span> <span class="n">choice</span> <span class="ow">in</span> <span class="n">choices</span><span class="p">:</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>        <span class="c1"># 枝刈り：n 段を超えて登ることを許可しない</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>        <span class="k">if</span> <span class="n">state</span> <span class="o">+</span> <span class="n">choice</span> <span class="o">&gt;</span> <span class="n">n</span><span class="p">:</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>            <span class="k">continue</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>        <span class="c1"># 試行：選択を行い、状態を更新</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>        <span class="n">backtrack</span><span class="p">(</span><span class="n">choices</span><span class="p">,</span> <span class="n">state</span> <span class="o">+</span> <span class="n">choice</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>        <span class="c1"># 撤回</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>
+<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a><span class="k">def</span><span class="w"> </span><span class="nf">climbing_stairs_backtrack</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;階段登り：バックトラッキング&quot;&quot;&quot;</span>
+<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>    <span class="n">choices</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">]</span>  <span class="c1"># 1 段または 2 段登ることを選択可能</span>
+<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a>    <span class="n">state</span> <span class="o">=</span> <span class="mi">0</span>  <span class="c1"># 0 段目から登り始める</span>
+<a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a>    <span class="n">res</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span>  <span class="c1"># res[0] を使用して解の数を記録</span>
+<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a>    <span class="n">backtrack</span><span class="p">(</span><span class="n">choices</span><span class="p">,</span> <span class="n">state</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="n">res</span><span class="p">)</span>
+<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a>    <span class="k">return</span> <span class="n">res</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_backtrack.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* バックトラッキング */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// n段目に到達したとき、解の数に1を加える</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">state</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">        </span><span class="n">res</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="k">auto</span><span class="w"> </span><span class="o">&amp;</span><span class="n">choice</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">        </span><span class="c1">// 剪定：n段を超えて登ることを許可しない</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">state</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">            </span><span class="k">continue</span><span class="p">;</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">        </span><span class="c1">// 試行：選択を行い、状態を更新</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">        </span><span class="n">backtrack</span><span class="p">(</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choice</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">        </span><span class="c1">// 撤回</span>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="p">}</span>
+<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a>
+<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="cm">/* 階段登り：バックトラッキング */</span>
+<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="kt">int</span><span class="w"> </span><span class="nf">climbingStairsBacktrack</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">choices</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">};</span><span class="w"> </span><span class="c1">// 1段または2段登ることを選択可能</span>
+<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">                </span><span class="c1">// 0段目から登り始める</span>
+<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="mi">0</span><span class="p">};</span><span class="w">        </span><span class="c1">// res[0] を使用して解の数を記録</span>
+<a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">[</span><span class="mi">0</span><span class="p">];</span>
+<a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_backtrack.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* バックトラッキング */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">backtrack</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// n段目に到達したとき、解の数に1を加える</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">state</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="na">set</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="c1">// すべての選択肢を走査</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Integer</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">choices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">        </span><span class="c1">// 剪定：n段を超えて登ることを許可しない</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">state</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choice</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">n</span><span class="p">)</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">            </span><span class="k">continue</span><span class="p">;</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">        </span><span class="c1">// 試行：選択を行い、状態を更新</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">        </span><span class="n">backtrack</span><span class="p">(</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">choice</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">        </span><span class="c1">// 撤回</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="p">}</span>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a>
+<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="cm">/* 階段登り：バックトラッキング */</span>
+<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="kt">int</span><span class="w"> </span><span class="nf">climbingStairsBacktrack</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">choices</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Arrays</span><span class="p">.</span><span class="na">asList</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span><span class="w"> </span><span class="c1">// 1段または2段登ることを選択可能</span>
+<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">state</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 0段目から登り始める</span>
+<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a><span class="w">    </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span><span class="w"> </span><span class="c1">// res[0] を使用して解の数を記録</span>
+<a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a><span class="w">    </span><span class="n">backtrack</span><span class="p">(</span><span class="n">choices</span><span class="p">,</span><span class="w"> </span><span class="n">state</span><span class="p">,</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_backtrack.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">climbing_stairs_backtrack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Backtrack</span><span class="p">}</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">climbing_stairs_backtrack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">ClimbingStairsBacktrack</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_backtrack.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">backtrack</span><span class="p">}</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">climbingStairsBacktrack</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_backtrack.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">climbingStairsBacktrack</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_backtrack.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">backtrack</span><span class="p">}</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">climbingStairsBacktrack</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_backtrack.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">backtrack</span><span class="p">}</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">climbingStairsBacktrack</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_backtrack.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">climbingStairsBacktrack</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_backtrack.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">climbing_stairs_backtrack</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_backtrack.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">climbingStairsBacktrack</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_backtrack.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">climbingStairsBacktrack</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_backtrack.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">climbing_stairs_backtrack</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_backtrack.zig</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">backtrack</span><span class="p">}</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a>
+<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">climbingStairsBacktrack</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h2 id="1411-1">14.1.1 &nbsp; 方法1：力任せ探索<a class="headerlink" href="#1411-1" title="Permanent link">&para;</a></h2>
+<p>バックトラッキングアルゴリズムは問題を明示的に部分問題に分解しません。代わりに、問題を一連の決定ステップとして扱い、試行と枝刈りを通じてすべての可能性を探索します。</p>
+<p>この問題を分解アプローチを使って分析できます。<span class="arithmatex">\(dp[i]\)</span> を <span class="arithmatex">\(i\)</span> 段目に到達する方法の数とします。この場合、<span class="arithmatex">\(dp[i]\)</span> が元の問題であり、その部分問題は次のようになります：</p>
+<div class="arithmatex">\[
+dp[i-1], dp[i-2], \dots, dp[2], dp[1]
+\]</div>
+<p>各移動は <span class="arithmatex">\(1\)</span> 段または <span class="arithmatex">\(2\)</span> 段しか進めないため、<span class="arithmatex">\(i\)</span> 段目に立っているとき、前のステップは <span class="arithmatex">\(i-1\)</span> 段目または <span class="arithmatex">\(i-2\)</span> 段目のいずれかにいたはずです。つまり、<span class="arithmatex">\(i\)</span> 段目には <span class="arithmatex">\(i-1\)</span> 段目または <span class="arithmatex">\(i-2\)</span> 段目からしか到達できません。</p>
+<p>これにより重要な結論が得られます：<strong><span class="arithmatex">\(i-1\)</span> 段目に到達する方法の数に <span class="arithmatex">\(i-2\)</span> 段目に到達する方法の数を加えたものが、<span class="arithmatex">\(i\)</span> 段目に到達する方法の数に等しい</strong>。式は以下の通りです：</p>
+<div class="arithmatex">\[
+dp[i] = dp[i-1] + dp[i-2]
+\]</div>
+<p>これは、階段登り問題において部分問題間に再帰関係があることを意味し、<strong>元の問題の解は部分問題の解から構築できます</strong>。下の図はこの再帰関係を示しています。</p>
+<p><a class="glightbox" href="../intro_to_dynamic_programming.assets/climbing_stairs_state_transfer.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="解の数の再帰関係" class="animation-figure" src="../intro_to_dynamic_programming.assets/climbing_stairs_state_transfer.png" /></a></p>
+<p align="center"> 図 14-2 &nbsp; 解の数の再帰関係 </p>
+
+<p>再帰式に従って力任せ探索解法を得ることができます。<span class="arithmatex">\(dp[n]\)</span> から始めて、**より大きな問題を再帰的に2つの小さな部分問題の和に分解**し、解が既知の最小の部分問題 <span class="arithmatex">\(dp[1]\)</span> と <span class="arithmatex">\(dp[2]\)</span> に到達するまで続けます。<span class="arithmatex">\(dp[1] = 1\)</span> と <span class="arithmatex">\(dp[2] = 2\)</span> で、それぞれ1段目と2段目に登る方法が <span class="arithmatex">\(1\)</span> 通りと <span class="arithmatex">\(2\)</span> 通りあることを表します。</p>
+<p>以下のコードを観察すると、標準的なバックトラッキングコードと同様に深さ優先探索に属しますが、より簡潔です：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:14"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><input id="__tabbed_2_14" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label><label for="__tabbed_2_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dfs.py</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;探索&quot;&quot;&quot;</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a>    <span class="c1"># 既知の dp[1] と dp[2] は、それらを返す</span>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a>    <span class="k">if</span> <span class="n">i</span> <span class="o">==</span> <span class="mi">1</span> <span class="ow">or</span> <span class="n">i</span> <span class="o">==</span> <span class="mi">2</span><span class="p">:</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a>        <span class="k">return</span> <span class="n">i</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a>    <span class="c1"># dp[i] = dp[i-1] + dp[i-2]</span>
+<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a>    <span class="n">count</span> <span class="o">=</span> <span class="n">dfs</span><span class="p">(</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">+</span> <span class="n">dfs</span><span class="p">(</span><span class="n">i</span> <span class="o">-</span> <span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a>    <span class="k">return</span> <span class="n">count</span>
+<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a>
+<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="k">def</span><span class="w"> </span><span class="nf">climbing_stairs_dfs</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;階段登り：探索&quot;&quot;&quot;</span>
+<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a>    <span class="k">return</span> <span class="n">dfs</span><span class="p">(</span><span class="n">n</span><span class="p">)</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dfs.cpp</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 探索 */</span>
+<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="c1">// 既知の dp[1] と dp[2] を返す</span>
+<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">    </span><span class="c1">// dp[i] = dp[i-1] + dp[i-2]</span>
+<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="p">}</span>
+<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a>
+<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="cm">/* 階段登り：探索 */</span>
+<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="kt">int</span><span class="w"> </span><span class="nf">climbingStairsDFS</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">n</span><span class="p">);</span>
+<a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dfs.java</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 探索 */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="c1">// 既知の dp[1] と dp[2] を返す</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">    </span><span class="c1">// dp[i] = dp[i-1] + dp[i-2]</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="p">}</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="cm">/* 階段登り：探索 */</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="kt">int</span><span class="w"> </span><span class="nf">climbingStairsDFS</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">n</span><span class="p">);</span>
+<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dfs.cs</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">climbing_stairs_dfs</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">DFS</span><span class="p">}</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">climbing_stairs_dfs</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">ClimbingStairsDFS</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dfs.go</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">dfs</span><span class="p">}</span>
+<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a>
+<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">climbingStairsDFS</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dfs.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
+<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a>
+<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">climbingStairsDFS</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dfs.js</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">dfs</span><span class="p">}</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a>
+<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">climbingStairsDFS</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dfs.ts</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">dfs</span><span class="p">}</span>
+<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a>
+<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">climbingStairsDFS</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dfs.dart</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
+<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">climbingStairsDFS</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dfs.rs</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
+<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a>
+<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">climbing_stairs_dfs</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dfs.c</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
+<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a>
+<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">climbingStairsDFS</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dfs.kt</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">dfs</span><span class="p">}</span>
+<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a>
+<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">climbingStairsDFS</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dfs.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">dfs</span><span class="p">}</span>
+<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a>
+<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">climbing_stairs_dfs</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dfs.zig</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
+<a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a>
+<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">climbingStairsDFS</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>下の図は力任せ探索によって形成される再帰木を示しています。問題 <span class="arithmatex">\(dp[n]\)</span> について、その再帰木の深さは <span class="arithmatex">\(n\)</span> で、時間計算量は <span class="arithmatex">\(O(2^n)\)</span> です。この指数的増加により、<span class="arithmatex">\(n\)</span> が大きいとプログラムの実行がはるかに遅くなり、長い待機時間が生じます。</p>
+<p><a class="glightbox" href="../intro_to_dynamic_programming.assets/climbing_stairs_dfs_tree.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="階段登りの再帰木" class="animation-figure" src="../intro_to_dynamic_programming.assets/climbing_stairs_dfs_tree.png" /></a></p>
+<p align="center"> 図 14-3 &nbsp; 階段登りの再帰木 </p>
+
+<p>上の図を観察すると、**指数時間計算量は「重複する部分問題」によって引き起こされる**ことがわかります。例えば、<span class="arithmatex">\(dp[9]\)</span> は <span class="arithmatex">\(dp[8]\)</span> と <span class="arithmatex">\(dp[7]\)</span> に分解され、<span class="arithmatex">\(dp[8]\)</span> はさらに <span class="arithmatex">\(dp[7]\)</span> と <span class="arithmatex">\(dp[6]\)</span> に分解され、両方とも部分問題 <span class="arithmatex">\(dp[7]\)</span> を含んでいます。</p>
+<p>このように、部分問題にはさらに小さな重複する部分問題が含まれ、これは無限に続きます。計算リソースの大部分がこれらの重複する部分問題に浪費されています。</p>
+<h2 id="1412-2">14.1.2 &nbsp; 方法2：メモ化探索<a class="headerlink" href="#1412-2" title="Permanent link">&para;</a></h2>
+<p>アルゴリズムの効率を向上させるため、**すべての重複する部分問題を一度だけ計算したい**と考えます。この目的のため、各部分問題の解を記録する配列 <code>mem</code> を宣言し、探索プロセス中に重複する部分問題を枝刈りします。</p>
+<ol>
+<li><span class="arithmatex">\(dp[i]\)</span> が初めて計算されるとき、後で使用するために <code>mem[i]</code> に記録します。</li>
+<li><span class="arithmatex">\(dp[i]\)</span> を再度計算する必要があるとき、<code>mem[i]</code> から直接結果を取得でき、その部分問題の冗長な計算を避けられます。</li>
+</ol>
+<p>コードは以下の通りです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="3:14"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><input id="__tabbed_3_14" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label><label for="__tabbed_3_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dfs_mem.py</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">mem</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;記憶化探索&quot;&quot;&quot;</span>
+<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a>    <span class="c1"># 既知の dp[1] と dp[2] は、それらを返す</span>
+<a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a>    <span class="k">if</span> <span class="n">i</span> <span class="o">==</span> <span class="mi">1</span> <span class="ow">or</span> <span class="n">i</span> <span class="o">==</span> <span class="mi">2</span><span class="p">:</span>
+<a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a>        <span class="k">return</span> <span class="n">i</span>
+<a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a>    <span class="c1"># dp[i] の記録がある場合、それを返す</span>
+<a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a>    <span class="k">if</span> <span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">!=</span> <span class="o">-</span><span class="mi">1</span><span class="p">:</span>
+<a id="__codelineno-28-8" name="__codelineno-28-8" href="#__codelineno-28-8"></a>        <span class="k">return</span> <span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+<a id="__codelineno-28-9" name="__codelineno-28-9" href="#__codelineno-28-9"></a>    <span class="c1"># dp[i] = dp[i-1] + dp[i-2]</span>
+<a id="__codelineno-28-10" name="__codelineno-28-10" href="#__codelineno-28-10"></a>    <span class="n">count</span> <span class="o">=</span> <span class="n">dfs</span><span class="p">(</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">mem</span><span class="p">)</span> <span class="o">+</span> <span class="n">dfs</span><span class="p">(</span><span class="n">i</span> <span class="o">-</span> <span class="mi">2</span><span class="p">,</span> <span class="n">mem</span><span class="p">)</span>
+<a id="__codelineno-28-11" name="__codelineno-28-11" href="#__codelineno-28-11"></a>    <span class="c1"># dp[i] を記録</span>
+<a id="__codelineno-28-12" name="__codelineno-28-12" href="#__codelineno-28-12"></a>    <span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">count</span>
+<a id="__codelineno-28-13" name="__codelineno-28-13" href="#__codelineno-28-13"></a>    <span class="k">return</span> <span class="n">count</span>
+<a id="__codelineno-28-14" name="__codelineno-28-14" href="#__codelineno-28-14"></a>
+<a id="__codelineno-28-15" name="__codelineno-28-15" href="#__codelineno-28-15"></a><span class="k">def</span><span class="w"> </span><span class="nf">climbing_stairs_dfs_mem</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-28-16" name="__codelineno-28-16" href="#__codelineno-28-16"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;階段登り：記憶化探索&quot;&quot;&quot;</span>
+<a id="__codelineno-28-17" name="__codelineno-28-17" href="#__codelineno-28-17"></a>    <span class="c1"># mem[i] は i 段目に登る解の総数を記録、-1 は記録なしを意味する</span>
+<a id="__codelineno-28-18" name="__codelineno-28-18" href="#__codelineno-28-18"></a>    <span class="n">mem</span> <span class="o">=</span> <span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-28-19" name="__codelineno-28-19" href="#__codelineno-28-19"></a>    <span class="k">return</span> <span class="n">dfs</span><span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">mem</span><span class="p">)</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dfs_mem.cpp</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="cm">/* メモ化探索 */</span>
+<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">mem</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w">    </span><span class="c1">// 既知の dp[1] と dp[2] を返す</span>
+<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a><span class="w">    </span><span class="c1">// dp[i] の記録がある場合、それを返す</span>
+<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">-1</span><span class="p">)</span>
+<a id="__codelineno-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-29-9" name="__codelineno-29-9" href="#__codelineno-29-9"></a><span class="w">    </span><span class="c1">// dp[i] = dp[i-1] + dp[i-2]</span>
+<a id="__codelineno-29-10" name="__codelineno-29-10" href="#__codelineno-29-10"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">);</span>
+<a id="__codelineno-29-11" name="__codelineno-29-11" href="#__codelineno-29-11"></a><span class="w">    </span><span class="c1">// dp[i] を記録</span>
+<a id="__codelineno-29-12" name="__codelineno-29-12" href="#__codelineno-29-12"></a><span class="w">    </span><span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-29-13" name="__codelineno-29-13" href="#__codelineno-29-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-29-14" name="__codelineno-29-14" href="#__codelineno-29-14"></a><span class="p">}</span>
+<a id="__codelineno-29-15" name="__codelineno-29-15" href="#__codelineno-29-15"></a>
+<a id="__codelineno-29-16" name="__codelineno-29-16" href="#__codelineno-29-16"></a><span class="cm">/* 階段登り：メモ化探索 */</span>
+<a id="__codelineno-29-17" name="__codelineno-29-17" href="#__codelineno-29-17"></a><span class="kt">int</span><span class="w"> </span><span class="nf">climbingStairsDFSMem</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-18" name="__codelineno-29-18" href="#__codelineno-29-18"></a><span class="w">    </span><span class="c1">// mem[i] は i 段目に登る総解数を記録、-1 は記録なしを意味する</span>
+<a id="__codelineno-29-19" name="__codelineno-29-19" href="#__codelineno-29-19"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">mem</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">-1</span><span class="p">);</span>
+<a id="__codelineno-29-20" name="__codelineno-29-20" href="#__codelineno-29-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">);</span>
+<a id="__codelineno-29-21" name="__codelineno-29-21" href="#__codelineno-29-21"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dfs_mem.java</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* メモ化探索 */</span>
+<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">mem</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w">    </span><span class="c1">// 既知の dp[1] と dp[2] を返す</span>
+<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="w">    </span><span class="c1">// dp[i] の記録がある場合、それを返す</span>
+<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a><span class="w">    </span><span class="c1">// dp[i] = dp[i-1] + dp[i-2]</span>
+<a id="__codelineno-30-10" name="__codelineno-30-10" href="#__codelineno-30-10"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">);</span>
+<a id="__codelineno-30-11" name="__codelineno-30-11" href="#__codelineno-30-11"></a><span class="w">    </span><span class="c1">// dp[i] を記録</span>
+<a id="__codelineno-30-12" name="__codelineno-30-12" href="#__codelineno-30-12"></a><span class="w">    </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-30-13" name="__codelineno-30-13" href="#__codelineno-30-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">count</span><span class="p">;</span>
+<a id="__codelineno-30-14" name="__codelineno-30-14" href="#__codelineno-30-14"></a><span class="p">}</span>
+<a id="__codelineno-30-15" name="__codelineno-30-15" href="#__codelineno-30-15"></a>
+<a id="__codelineno-30-16" name="__codelineno-30-16" href="#__codelineno-30-16"></a><span class="cm">/* 階段登り：メモ化探索 */</span>
+<a id="__codelineno-30-17" name="__codelineno-30-17" href="#__codelineno-30-17"></a><span class="kt">int</span><span class="w"> </span><span class="nf">climbingStairsDFSMem</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-18" name="__codelineno-30-18" href="#__codelineno-30-18"></a><span class="w">    </span><span class="c1">// mem[i] は i 段目に登る総解数を記録、-1 は記録なしを意味する</span>
+<a id="__codelineno-30-19" name="__codelineno-30-19" href="#__codelineno-30-19"></a><span class="w">    </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">mem</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-30-20" name="__codelineno-30-20" href="#__codelineno-30-20"></a><span class="w">    </span><span class="n">Arrays</span><span class="p">.</span><span class="na">fill</span><span class="p">(</span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-30-21" name="__codelineno-30-21" href="#__codelineno-30-21"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dfs</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">);</span>
+<a id="__codelineno-30-22" name="__codelineno-30-22" href="#__codelineno-30-22"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dfs_mem.cs</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">climbing_stairs_dfs_mem</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">DFS</span><span class="p">}</span>
+<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a>
+<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">climbing_stairs_dfs_mem</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">ClimbingStairsDFSMem</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dfs_mem.go</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">dfsMem</span><span class="p">}</span>
+<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a>
+<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">climbingStairsDFSMem</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dfs_mem.swift</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
+<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a>
+<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">climbingStairsDFSMem</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dfs_mem.js</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">dfs</span><span class="p">}</span>
+<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a>
+<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">climbingStairsDFSMem</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dfs_mem.ts</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">dfs</span><span class="p">}</span>
+<a id="__codelineno-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></a>
+<a id="__codelineno-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">climbingStairsDFSMem</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dfs_mem.dart</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
+<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a>
+<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">climbingStairsDFSMem</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dfs_mem.rs</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
+<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a>
+<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">climbing_stairs_dfs_mem</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dfs_mem.c</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
+<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a>
+<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">climbingStairsDFSMem</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dfs_mem.kt</span><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">dfs</span><span class="p">}</span>
+<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a>
+<a id="__codelineno-39-3" name="__codelineno-39-3" href="#__codelineno-39-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">climbingStairsDFSMem</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dfs_mem.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">dfs</span><span class="p">}</span>
+<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a>
+<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">climbing_stairs_dfs_mem</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dfs_mem.zig</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
+<a id="__codelineno-41-2" name="__codelineno-41-2" href="#__codelineno-41-2"></a>
+<a id="__codelineno-41-3" name="__codelineno-41-3" href="#__codelineno-41-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">climbingStairsDFSMem</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>下の図を観察すると、**メモ化後、すべての重複する部分問題は一度だけ計算される必要があり、時間計算量を <span class="arithmatex">\(O(n)\)</span> に最適化**します。これは大幅な改善です。</p>
+<p><a class="glightbox" href="../intro_to_dynamic_programming.assets/climbing_stairs_dfs_memo_tree.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="メモ化探索による再帰木" class="animation-figure" src="../intro_to_dynamic_programming.assets/climbing_stairs_dfs_memo_tree.png" /></a></p>
+<p align="center"> 図 14-4 &nbsp; メモ化探索による再帰木 </p>
+
+<h2 id="1413-3">14.1.3 &nbsp; 方法3：動的プログラミング<a class="headerlink" href="#1413-3" title="Permanent link">&para;</a></h2>
+<p>**メモ化探索は「トップダウン」方式**です：元の問題（根ノード）から始めて、より大きな部分問題をより小さなものに再帰的に分解し、最小の既知の部分問題（葉ノード）の解に到達するまで続けます。その後、バックトラッキングにより部分問題の解を収集し、元の問題の解を構築します。</p>
+<p>一方、**動的プログラミングは「ボトムアップ」方式**です：最小の部分問題の解から始めて、元の問題が解決されるまで、より大きな部分問題の解を反復的に構築します。</p>
+<p>動的プログラミングはバックトラッキングを必要としないため、ループを使った反復のみが必要で、再帰は不要です。以下のコードでは、配列 <code>dp</code> を初期化して部分問題の解を保存し、メモ化探索の配列 <code>mem</code> と同じ記録機能を果たします：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="4:14"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><input id="__tabbed_4_6" name="__tabbed_4" type="radio" /><input id="__tabbed_4_7" name="__tabbed_4" type="radio" /><input id="__tabbed_4_8" name="__tabbed_4" type="radio" /><input id="__tabbed_4_9" name="__tabbed_4" type="radio" /><input id="__tabbed_4_10" name="__tabbed_4" type="radio" /><input id="__tabbed_4_11" name="__tabbed_4" type="radio" /><input id="__tabbed_4_12" name="__tabbed_4" type="radio" /><input id="__tabbed_4_13" name="__tabbed_4" type="radio" /><input id="__tabbed_4_14" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">Python</label><label for="__tabbed_4_2">C++</label><label for="__tabbed_4_3">Java</label><label for="__tabbed_4_4">C#</label><label for="__tabbed_4_5">Go</label><label for="__tabbed_4_6">Swift</label><label for="__tabbed_4_7">JS</label><label for="__tabbed_4_8">TS</label><label for="__tabbed_4_9">Dart</label><label for="__tabbed_4_10">Rust</label><label for="__tabbed_4_11">C</label><label for="__tabbed_4_12">Kotlin</label><label for="__tabbed_4_13">Ruby</label><label for="__tabbed_4_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dp.py</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">climbing_stairs_dp</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-42-2" name="__codelineno-42-2" href="#__codelineno-42-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;階段登り：動的プログラミング&quot;&quot;&quot;</span>
+<a id="__codelineno-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></a>    <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">1</span> <span class="ow">or</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">2</span><span class="p">:</span>
+<a id="__codelineno-42-4" name="__codelineno-42-4" href="#__codelineno-42-4"></a>        <span class="k">return</span> <span class="n">n</span>
+<a id="__codelineno-42-5" name="__codelineno-42-5" href="#__codelineno-42-5"></a>    <span class="c1"># dp テーブルを初期化、部分問題の解を格納するため使用</span>
+<a id="__codelineno-42-6" name="__codelineno-42-6" href="#__codelineno-42-6"></a>    <span class="n">dp</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-42-7" name="__codelineno-42-7" href="#__codelineno-42-7"></a>    <span class="c1"># 初期状態：最小の部分問題の解を事前設定</span>
+<a id="__codelineno-42-8" name="__codelineno-42-8" href="#__codelineno-42-8"></a>    <span class="n">dp</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">dp</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span>
+<a id="__codelineno-42-9" name="__codelineno-42-9" href="#__codelineno-42-9"></a>    <span class="c1"># 状態遷移：小さい部分問題から大きい部分問題を段階的に解く</span>
+<a id="__codelineno-42-10" name="__codelineno-42-10" href="#__codelineno-42-10"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-42-11" name="__codelineno-42-11" href="#__codelineno-42-11"></a>        <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">2</span><span class="p">]</span>
+<a id="__codelineno-42-12" name="__codelineno-42-12" href="#__codelineno-42-12"></a>    <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">]</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dp.cpp</span><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="cm">/* 階段登り：動的プログラミング */</span>
+<a id="__codelineno-43-2" name="__codelineno-43-2" href="#__codelineno-43-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">climbingStairsDP</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-3" name="__codelineno-43-3" href="#__codelineno-43-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-43-4" name="__codelineno-43-4" href="#__codelineno-43-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">n</span><span class="p">;</span>
+<a id="__codelineno-43-5" name="__codelineno-43-5" href="#__codelineno-43-5"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化し、部分問題の解を格納するために使用</span>
+<a id="__codelineno-43-6" name="__codelineno-43-6" href="#__codelineno-43-6"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">dp</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-43-7" name="__codelineno-43-7" href="#__codelineno-43-7"></a><span class="w">    </span><span class="c1">// 初期状態：最小の部分問題の解を事前設定</span>
+<a id="__codelineno-43-8" name="__codelineno-43-8" href="#__codelineno-43-8"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-43-9" name="__codelineno-43-9" href="#__codelineno-43-9"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-43-10" name="__codelineno-43-10" href="#__codelineno-43-10"></a><span class="w">    </span><span class="c1">// 状態遷移：小さな問題から大きな部分問題を段階的に解く</span>
+<a id="__codelineno-43-11" name="__codelineno-43-11" href="#__codelineno-43-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-12" name="__codelineno-43-12" href="#__codelineno-43-12"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="p">];</span>
+<a id="__codelineno-43-13" name="__codelineno-43-13" href="#__codelineno-43-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-43-14" name="__codelineno-43-14" href="#__codelineno-43-14"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">];</span>
+<a id="__codelineno-43-15" name="__codelineno-43-15" href="#__codelineno-43-15"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dp.java</span><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="cm">/* 階段登り：動的プログラミング */</span>
+<a id="__codelineno-44-2" name="__codelineno-44-2" href="#__codelineno-44-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">climbingStairsDP</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-3" name="__codelineno-44-3" href="#__codelineno-44-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-44-4" name="__codelineno-44-4" href="#__codelineno-44-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">n</span><span class="p">;</span>
+<a id="__codelineno-44-5" name="__codelineno-44-5" href="#__codelineno-44-5"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化し、部分問題の解を格納するために使用</span>
+<a id="__codelineno-44-6" name="__codelineno-44-6" href="#__codelineno-44-6"></a><span class="w">    </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-44-7" name="__codelineno-44-7" href="#__codelineno-44-7"></a><span class="w">    </span><span class="c1">// 初期状態：最小の部分問題の解を事前設定</span>
+<a id="__codelineno-44-8" name="__codelineno-44-8" href="#__codelineno-44-8"></a><span class="w">    </span><span class="n">dp</span><span class="o">[</span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-44-9" name="__codelineno-44-9" href="#__codelineno-44-9"></a><span class="w">    </span><span class="n">dp</span><span class="o">[</span><span class="mi">2</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-44-10" name="__codelineno-44-10" href="#__codelineno-44-10"></a><span class="w">    </span><span class="c1">// 状態遷移：小さな問題から大きな部分問題を段階的に解く</span>
+<a id="__codelineno-44-11" name="__codelineno-44-11" href="#__codelineno-44-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-12" name="__codelineno-44-12" href="#__codelineno-44-12"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">2</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-44-13" name="__codelineno-44-13" href="#__codelineno-44-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-44-14" name="__codelineno-44-14" href="#__codelineno-44-14"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-44-15" name="__codelineno-44-15" href="#__codelineno-44-15"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dp.cs</span><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">climbing_stairs_dp</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">ClimbingStairsDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dp.go</span><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">climbingStairsDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dp.swift</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">climbingStairsDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dp.js</span><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">climbingStairsDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dp.ts</span><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">climbingStairsDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dp.dart</span><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">climbingStairsDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dp.rs</span><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">climbing_stairs_dp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dp.c</span><pre><span></span><code><a id="__codelineno-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">climbingStairsDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dp.kt</span><pre><span></span><code><a id="__codelineno-53-1" name="__codelineno-53-1" href="#__codelineno-53-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">climbingStairsDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dp.rb</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">climbing_stairs_dp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dp.zig</span><pre><span></span><code><a id="__codelineno-55-1" name="__codelineno-55-1" href="#__codelineno-55-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">climbingStairsDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>下の図は上記コードの実行プロセスをシミュレートしています。</p>
+<p><a class="glightbox" href="../intro_to_dynamic_programming.assets/climbing_stairs_dp.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="階段登りの動的プログラミングプロセス" class="animation-figure" src="../intro_to_dynamic_programming.assets/climbing_stairs_dp.png" /></a></p>
+<p align="center"> 図 14-5 &nbsp; 階段登りの動的プログラミングプロセス </p>
+
+<p>バックトラッキングアルゴリズムと同様に、動的プログラミングも「状態」の概念を使用して問題解決の特定の段階を表現し、各状態は部分問題とその局所最適解に対応します。例えば、階段登り問題の状態は現在のステップ番号 <span class="arithmatex">\(i\)</span> として定義されます。</p>
+<p>上記の内容に基づいて、動的プログラミングでよく使用される用語をまとめることができます。</p>
+<ul>
+<li>配列 <code>dp</code> は<u>DPテーブル</u>と呼ばれ、<span class="arithmatex">\(dp[i]\)</span> は状態 <span class="arithmatex">\(i\)</span> に対応する部分問題の解を表します。</li>
+<li>最小の部分問題（ステップ <span class="arithmatex">\(1\)</span> と <span class="arithmatex">\(2\)</span>）に対応する状態は<u>初期状態</u>と呼ばれます。</li>
+<li>再帰式 <span class="arithmatex">\(dp[i] = dp[i-1] + dp[i-2]\)</span> は<u>状態遷移方程式</u>と呼ばれます。</li>
+</ul>
+<h2 id="1414">14.1.4 &nbsp; 空間最適化<a class="headerlink" href="#1414" title="Permanent link">&para;</a></h2>
+<p>注意深い読者は**<span class="arithmatex">\(dp[i]\)</span> は <span class="arithmatex">\(dp[i-1]\)</span> と <span class="arithmatex">\(dp[i-2]\)</span> のみに関連するため、すべての部分問題の解を保存するために配列 <code>dp</code> を使用する必要がない**ことに気づくでしょう。単に2つの変数を使って反復的に進めることができます。コードは以下の通りです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="5:14"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><input id="__tabbed_5_7" name="__tabbed_5" type="radio" /><input id="__tabbed_5_8" name="__tabbed_5" type="radio" /><input id="__tabbed_5_9" name="__tabbed_5" type="radio" /><input id="__tabbed_5_10" name="__tabbed_5" type="radio" /><input id="__tabbed_5_11" name="__tabbed_5" type="radio" /><input id="__tabbed_5_12" name="__tabbed_5" type="radio" /><input id="__tabbed_5_13" name="__tabbed_5" type="radio" /><input id="__tabbed_5_14" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">Python</label><label for="__tabbed_5_2">C++</label><label for="__tabbed_5_3">Java</label><label for="__tabbed_5_4">C#</label><label for="__tabbed_5_5">Go</label><label for="__tabbed_5_6">Swift</label><label for="__tabbed_5_7">JS</label><label for="__tabbed_5_8">TS</label><label for="__tabbed_5_9">Dart</label><label for="__tabbed_5_10">Rust</label><label for="__tabbed_5_11">C</label><label for="__tabbed_5_12">Kotlin</label><label for="__tabbed_5_13">Ruby</label><label for="__tabbed_5_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dp.py</span><pre><span></span><code><a id="__codelineno-56-1" name="__codelineno-56-1" href="#__codelineno-56-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">climbing_stairs_dp_comp</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-56-2" name="__codelineno-56-2" href="#__codelineno-56-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;階段登り：空間最適化動的プログラミング&quot;&quot;&quot;</span>
+<a id="__codelineno-56-3" name="__codelineno-56-3" href="#__codelineno-56-3"></a>    <span class="k">if</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">1</span> <span class="ow">or</span> <span class="n">n</span> <span class="o">==</span> <span class="mi">2</span><span class="p">:</span>
+<a id="__codelineno-56-4" name="__codelineno-56-4" href="#__codelineno-56-4"></a>        <span class="k">return</span> <span class="n">n</span>
+<a id="__codelineno-56-5" name="__codelineno-56-5" href="#__codelineno-56-5"></a>    <span class="n">a</span><span class="p">,</span> <span class="n">b</span> <span class="o">=</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span>
+<a id="__codelineno-56-6" name="__codelineno-56-6" href="#__codelineno-56-6"></a>    <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-56-7" name="__codelineno-56-7" href="#__codelineno-56-7"></a>        <span class="n">a</span><span class="p">,</span> <span class="n">b</span> <span class="o">=</span> <span class="n">b</span><span class="p">,</span> <span class="n">a</span> <span class="o">+</span> <span class="n">b</span>
+<a id="__codelineno-56-8" name="__codelineno-56-8" href="#__codelineno-56-8"></a>    <span class="k">return</span> <span class="n">b</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dp.cpp</span><pre><span></span><code><a id="__codelineno-57-1" name="__codelineno-57-1" href="#__codelineno-57-1"></a><span class="cm">/* 階段登り：空間最適化動的プログラミング */</span>
+<a id="__codelineno-57-2" name="__codelineno-57-2" href="#__codelineno-57-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">climbingStairsDPComp</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-3" name="__codelineno-57-3" href="#__codelineno-57-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-57-4" name="__codelineno-57-4" href="#__codelineno-57-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">n</span><span class="p">;</span>
+<a id="__codelineno-57-5" name="__codelineno-57-5" href="#__codelineno-57-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-57-6" name="__codelineno-57-6" href="#__codelineno-57-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-7" name="__codelineno-57-7" href="#__codelineno-57-7"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">b</span><span class="p">;</span>
+<a id="__codelineno-57-8" name="__codelineno-57-8" href="#__codelineno-57-8"></a><span class="w">        </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">b</span><span class="p">;</span>
+<a id="__codelineno-57-9" name="__codelineno-57-9" href="#__codelineno-57-9"></a><span class="w">        </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
+<a id="__codelineno-57-10" name="__codelineno-57-10" href="#__codelineno-57-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-57-11" name="__codelineno-57-11" href="#__codelineno-57-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">b</span><span class="p">;</span>
+<a id="__codelineno-57-12" name="__codelineno-57-12" href="#__codelineno-57-12"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dp.java</span><pre><span></span><code><a id="__codelineno-58-1" name="__codelineno-58-1" href="#__codelineno-58-1"></a><span class="cm">/* 階段登り：空間最適化動的プログラミング */</span>
+<a id="__codelineno-58-2" name="__codelineno-58-2" href="#__codelineno-58-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">climbingStairsDPComp</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-3" name="__codelineno-58-3" href="#__codelineno-58-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-58-4" name="__codelineno-58-4" href="#__codelineno-58-4"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">n</span><span class="p">;</span>
+<a id="__codelineno-58-5" name="__codelineno-58-5" href="#__codelineno-58-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-58-6" name="__codelineno-58-6" href="#__codelineno-58-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-7" name="__codelineno-58-7" href="#__codelineno-58-7"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">b</span><span class="p">;</span>
+<a id="__codelineno-58-8" name="__codelineno-58-8" href="#__codelineno-58-8"></a><span class="w">        </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">b</span><span class="p">;</span>
+<a id="__codelineno-58-9" name="__codelineno-58-9" href="#__codelineno-58-9"></a><span class="w">        </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
+<a id="__codelineno-58-10" name="__codelineno-58-10" href="#__codelineno-58-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-58-11" name="__codelineno-58-11" href="#__codelineno-58-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">b</span><span class="p">;</span>
+<a id="__codelineno-58-12" name="__codelineno-58-12" href="#__codelineno-58-12"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dp.cs</span><pre><span></span><code><a id="__codelineno-59-1" name="__codelineno-59-1" href="#__codelineno-59-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">climbing_stairs_dp</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">ClimbingStairsDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dp.go</span><pre><span></span><code><a id="__codelineno-60-1" name="__codelineno-60-1" href="#__codelineno-60-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">climbingStairsDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dp.swift</span><pre><span></span><code><a id="__codelineno-61-1" name="__codelineno-61-1" href="#__codelineno-61-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">climbingStairsDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dp.js</span><pre><span></span><code><a id="__codelineno-62-1" name="__codelineno-62-1" href="#__codelineno-62-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">climbingStairsDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dp.ts</span><pre><span></span><code><a id="__codelineno-63-1" name="__codelineno-63-1" href="#__codelineno-63-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">climbingStairsDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dp.dart</span><pre><span></span><code><a id="__codelineno-64-1" name="__codelineno-64-1" href="#__codelineno-64-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">climbingStairsDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dp.rs</span><pre><span></span><code><a id="__codelineno-65-1" name="__codelineno-65-1" href="#__codelineno-65-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">climbing_stairs_dp_comp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dp.c</span><pre><span></span><code><a id="__codelineno-66-1" name="__codelineno-66-1" href="#__codelineno-66-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">climbingStairsDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dp.kt</span><pre><span></span><code><a id="__codelineno-67-1" name="__codelineno-67-1" href="#__codelineno-67-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">climbingStairsDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dp.rb</span><pre><span></span><code><a id="__codelineno-68-1" name="__codelineno-68-1" href="#__codelineno-68-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">climbing_stairs_dp_comp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">climbing_stairs_dp.zig</span><pre><span></span><code><a id="__codelineno-69-1" name="__codelineno-69-1" href="#__codelineno-69-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">climbingStairsDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>上記のコードを観察すると、配列 <code>dp</code> が占有していた空間が削除されるため、空間計算量は <span class="arithmatex">\(O(n)\)</span> から <span class="arithmatex">\(O(1)\)</span> に削減されます。</p>
+<p>多くの動的プログラミング問題では、現在の状態は限られた数の前の状態のみに依存するため、必要な状態のみを保持し、「次元削減」によってメモリ空間を節約できます。<strong>この空間最適化技術は「ローリング変数」または「ローリング配列」として知られています</strong>。</p>
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+  
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+  
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+      <a href="../../chapter_preface/about_the_book/" class="md-nav__link">
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+      <a href="../../chapter_preface/summary/" class="md-nav__link">
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+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
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+  
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+    1.1 &nbsp; アルゴリズムはどこにでもある
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+  
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+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
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+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
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+    </li>
+  
+
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+              
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+  
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+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
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+    </li>
+  
+
+              
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+          
+        
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+        
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+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
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+  
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+            第 2 章 &nbsp; 計算量解析
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+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
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+    2.1 &nbsp; アルゴリズム効率評価
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+  
+
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+
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+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
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+    2.2 &nbsp; 反復と再帰
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+  
+
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+    </li>
+  
+
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+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
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+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
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+
+              
+            
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+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
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+  
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+    第 3 章 &nbsp; データ構造
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+            第 3 章 &nbsp; データ構造
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+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
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+    3.1 &nbsp; データ構造の分類
+  </span>
+  
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+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
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+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
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+
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+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
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+  </span>
+  
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+    </li>
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+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
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+  </span>
+  
+
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+    </li>
+  
+
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+  
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+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
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+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
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+  
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+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1-1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 方法1：力任せ探索
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#2-2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; 方法2：メモ化探索
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#3-3" class="md-nav__link">
+    <span class="md-ellipsis">
+      3. &nbsp; 方法3：動的プログラミング
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#4" class="md-nav__link">
+    <span class="md-ellipsis">
+      4. &nbsp; 空間最適化
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
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+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_19" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_reference/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9 3v15h3V3H9m3 2 4 13 3-1-4-13-3 1M5 5v13h3V5H5M3 19v2h18v-2H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    参考文献
+  </span>
+  
+
+            </a>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_19_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_19">
+            <span class="md-nav__icon md-icon"></span>
+            参考文献
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+  </ul>
+</nav>
+                  </div>
+                </div>
+              </div>
+            
+            
+              
+              <div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
+                <div class="md-sidebar__scrollwrap">
+                  <div class="md-sidebar__inner">
+                    
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1-1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 方法1：力任せ探索
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#2-2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; 方法2：メモ化探索
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#3-3" class="md-nav__link">
+    <span class="md-ellipsis">
+      3. &nbsp; 方法3：動的プログラミング
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#4" class="md-nav__link">
+    <span class="md-ellipsis">
+      4. &nbsp; 空間最適化
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+                  </div>
+                </div>
+              </div>
+            
+          
+          
+            <div class="md-content" data-md-component="content">
+              <article class="md-content__inner md-typeset">
+                
+                  <!-- Tags -->
+
+
+<!-- Actions -->
+<!-- Actions -->
+
+
+  <!-- Edit button -->
+  
+    <a
+      href="https://github.com/krahets/hello-algo/tree/main/ja/docs/chapter_dynamic_programming/knapsack_problem.md"
+      title="編集"
+      class="md-content__button md-icon"
+    >
+      
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
+    </a>
+  
+
+  <!-- View button -->
+  
+
+
+<!-- Page content -->
+<h1 id="144-0-1">14.4 &nbsp; 0-1ナップサック問題<a class="headerlink" href="#144-0-1" title="Permanent link">&para;</a></h1>
+<p>ナップサック問題は動的プログラミングの優れた入門問題であり、動的プログラミングで最も一般的な問題タイプです。0-1ナップサック問題、無制限ナップサック問題、複数ナップサック問題など、多くの変種があります。</p>
+<p>このセクションでは、まず最も一般的な0-1ナップサック問題を解決します。</p>
+<div class="admonition question">
+<p class="admonition-title">Question</p>
+<p><span class="arithmatex">\(n\)</span> 個のアイテムが与えられ、<span class="arithmatex">\(i\)</span> 番目のアイテムの重量は <span class="arithmatex">\(wgt[i-1]\)</span> で値は <span class="arithmatex">\(val[i-1]\)</span> です。容量が <span class="arithmatex">\(cap\)</span> のナップサックがあります。各アイテムは1回のみ選択できます。容量制限下でナップサックに入れることができるアイテムの最大値は何ですか？</p>
+</div>
+<p>下の図を観察すると、アイテム番号 <span class="arithmatex">\(i\)</span> は1から数え始め、配列インデックスは0から始まるため、アイテム <span class="arithmatex">\(i\)</span> の重量は <span class="arithmatex">\(wgt[i-1]\)</span> に対応し、値は <span class="arithmatex">\(val[i-1]\)</span> に対応します。</p>
+<p><a class="glightbox" href="../knapsack_problem.assets/knapsack_example.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="0-1ナップサックの例データ" class="animation-figure" src="../knapsack_problem.assets/knapsack_example.png" /></a></p>
+<p align="center"> 図 14-17 &nbsp; 0-1ナップサックの例データ </p>
+
+<p>0-1ナップサック問題を <span class="arithmatex">\(n\)</span> ラウンドの決定から構成されるプロセスとして考えることができます。各アイテムについて入れない、または入れるという2つの決定があり、したがって問題は決定木モデルに適合します。</p>
+<p>この問題の目的は「限られた容量の下でナップサックに入れることができるアイテムの値を最大化する」ことであり、動的プログラミング問題である可能性が高いです。</p>
+<p><strong>第1ステップ：各ラウンドの決定を考え、状態を定義し、それにより <span class="arithmatex">\(dp\)</span> テーブルを得る</strong></p>
+<p>各アイテムについて、ナップサックに入れなければ容量は変わらず、入れれば容量は減少します。これから状態定義を得ることができます：現在のアイテム番号 <span class="arithmatex">\(i\)</span> とナップサック容量 <span class="arithmatex">\(c\)</span>、<span class="arithmatex">\([i, c]\)</span> と表記されます。</p>
+<p>状態 <span class="arithmatex">\([i, c]\)</span> は部分問題に対応します：<strong>容量 <span class="arithmatex">\(c\)</span> のナップサックでの最初の <span class="arithmatex">\(i\)</span> 個のアイテムの最大値</strong>、<span class="arithmatex">\(dp[i, c]\)</span> と表記されます。</p>
+<p>探している解は <span class="arithmatex">\(dp[n, cap]\)</span> であるため、サイズ <span class="arithmatex">\((n+1) \times (cap+1)\)</span> の二次元 <span class="arithmatex">\(dp\)</span> テーブルが必要です。</p>
+<p><strong>第2ステップ：最適部分構造を特定し、状態遷移方程式を導出する</strong></p>
+<p>アイテム <span class="arithmatex">\(i\)</span> の決定を行った後、残るのは最初の <span class="arithmatex">\(i-1\)</span> 個のアイテムの決定の部分問題であり、これは2つのケースに分けることができます。</p>
+<ul>
+<li><strong>アイテム <span class="arithmatex">\(i\)</span> を入れない</strong>：ナップサック容量は変わらず、状態は <span class="arithmatex">\([i-1, c]\)</span> に変わります。</li>
+<li><strong>アイテム <span class="arithmatex">\(i\)</span> を入れる</strong>：ナップサック容量は <span class="arithmatex">\(wgt[i-1]\)</span> だけ減少し、値は <span class="arithmatex">\(val[i-1]\)</span> だけ増加し、状態は <span class="arithmatex">\([i-1, c-wgt[i-1]]\)</span> に変わります。</li>
+</ul>
+<p>上記の分析により、この問題の最適部分構造が明らかになります：<strong>最大値 <span class="arithmatex">\(dp[i, c]\)</span> は、アイテム <span class="arithmatex">\(i\)</span> を入れない方案とアイテム <span class="arithmatex">\(i\)</span> を入れる方案の2つのうち、より大きな値に等しい</strong>。これから状態遷移方程式を導出できます：</p>
+<div class="arithmatex">\[
+dp[i, c] = \max(dp[i-1, c], dp[i-1, c - wgt[i-1]] + val[i-1])
+\]</div>
+<p>現在のアイテムの重量 <span class="arithmatex">\(wgt[i - 1]\)</span> が残りのナップサック容量 <span class="arithmatex">\(c\)</span> を超える場合、唯一の選択肢はナップサックに入れないことであることに注意することが重要です。</p>
+<p><strong>第3ステップ：境界条件と状態遷移の順序を決定する</strong></p>
+<p>アイテムがない場合またはナップサック容量が <span class="arithmatex">\(0\)</span> の場合、最大値は <span class="arithmatex">\(0\)</span> です。つまり、最初の列 <span class="arithmatex">\(dp[i, 0]\)</span> と最初の行 <span class="arithmatex">\(dp[0, c]\)</span> はどちらも <span class="arithmatex">\(0\)</span> に等しいです。</p>
+<p>現在の状態 <span class="arithmatex">\([i, c]\)</span> は直接上の状態 <span class="arithmatex">\([i-1, c]\)</span> と左上の状態 <span class="arithmatex">\([i-1, c-wgt[i-1]]\)</span> から遷移するため、2層のループを通じて <span class="arithmatex">\(dp\)</span> テーブル全体を順序通りに走査します。</p>
+<p>上記の分析に従って、次に力任せ探索、メモ化探索、動的プログラミングの順序で解法を実装します。</p>
+<h3 id="1-1">1. &nbsp; 方法1：力任せ探索<a class="headerlink" href="#1-1" title="Permanent link">&para;</a></h3>
+<p>探索コードには以下の要素が含まれます。</p>
+<ul>
+<li><strong>再帰パラメータ</strong>：状態 <span class="arithmatex">\([i, c]\)</span>。</li>
+<li><strong>戻り値</strong>：部分問題 <span class="arithmatex">\(dp[i, c]\)</span> の解。</li>
+<li><strong>終了条件</strong>：アイテム番号が範囲外 <span class="arithmatex">\(i = 0\)</span> またはナップサックの残り容量が <span class="arithmatex">\(0\)</span> のとき、再帰を終了し値 <span class="arithmatex">\(0\)</span> を返す。</li>
+<li><strong>枝刈り</strong>：現在のアイテムの重量がナップサックの残り容量を超える場合、唯一の選択肢はナップサックに入れないことです。</li>
+</ul>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:14"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><input id="__tabbed_1_14" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label><label for="__tabbed_1_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">knapsack_dfs</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">val</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">c</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;0-1 ナップサック：ブルートフォース探索&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># すべてのアイテムが選択されたかナップサックに残り容量がない場合、値 0 を返す</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="k">if</span> <span class="n">i</span> <span class="o">==</span> <span class="mi">0</span> <span class="ow">or</span> <span class="n">c</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>        <span class="k">return</span> <span class="mi">0</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="c1"># ナップサック容量を超える場合、ナップサックに入れないことしか選択できない</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>    <span class="k">if</span> <span class="n">wgt</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">c</span><span class="p">:</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>        <span class="k">return</span> <span class="n">knapsack_dfs</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span> <span class="n">val</span><span class="p">,</span> <span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">c</span><span class="p">)</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>    <span class="c1"># アイテム i を入れないのと入れるのとの最大値を計算</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>    <span class="n">no</span> <span class="o">=</span> <span class="n">knapsack_dfs</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span> <span class="n">val</span><span class="p">,</span> <span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">c</span><span class="p">)</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>    <span class="n">yes</span> <span class="o">=</span> <span class="n">knapsack_dfs</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span> <span class="n">val</span><span class="p">,</span> <span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">c</span> <span class="o">-</span> <span class="n">wgt</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">])</span> <span class="o">+</span> <span class="n">val</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>    <span class="c1"># 2 つの選択肢のうち大きい値を返す</span>
+<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>    <span class="k">return</span> <span class="nb">max</span><span class="p">(</span><span class="n">no</span><span class="p">,</span> <span class="n">yes</span><span class="p">)</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 0-1 ナップサック：ブルートフォース探索 */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">knapsackDFS</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// すべてのアイテムが選択されたか、ナップサックに残り容量がない場合、値 0 を返す</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="c1">// ナップサックの容量を超える場合、ナップサックに入れないことしか選択できない</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">knapsackDFS</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">);</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">    </span><span class="c1">// アイテム i を入れない場合と入れる場合の最大値を計算</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">no</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsackDFS</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">);</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">yes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsackDFS</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">    </span><span class="c1">// 2つの選択肢のより大きい値を返す</span>
+<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">max</span><span class="p">(</span><span class="n">no</span><span class="p">,</span><span class="w"> </span><span class="n">yes</span><span class="p">);</span>
+<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 0-1 ナップサック：ブルートフォース探索 */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">knapsackDFS</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// すべてのアイテムが選択されたか、ナップサックに残り容量がない場合、値 0 を返す</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="c1">// ナップサックの容量を超える場合、ナップサックに入れないことしか選択できない</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">knapsackDFS</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">);</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">    </span><span class="c1">// アイテム i を入れない場合と入れる場合の最大値を計算</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">no</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsackDFS</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">);</span>
+<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">yes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsackDFS</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">    </span><span class="c1">// 2つの選択肢のより大きい値を返す</span>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">max</span><span class="p">(</span><span class="n">no</span><span class="p">,</span><span class="w"> </span><span class="n">yes</span><span class="p">);</span>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">knapsack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">KnapsackDFS</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">knapsackDFS</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">knapsackDFS</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">knapsackDFS</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">knapsackDFS</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">knapsackDFS</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">knapsack_dfs</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">knapsackDFS</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">knapsackDFS</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">knapsack_dfs</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.zig</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">knapsackDFS</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>下の図に示すように、各アイテムは選択しないと選択するという2つの探索分岐を生成するため、時間計算量は <span class="arithmatex">\(O(2^n)\)</span> です。</p>
+<p>再帰木を観察すると、<span class="arithmatex">\(dp[1, 10]\)</span> などの重複する部分問題があることが容易にわかります。アイテムが多く、ナップサック容量が大きい場合、特に同じ重量のアイテムが多い場合、重複する部分問題の数は大幅に増加します。</p>
+<p><a class="glightbox" href="../knapsack_problem.assets/knapsack_dfs.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="0-1ナップサック問題の力任せ探索再帰木" class="animation-figure" src="../knapsack_problem.assets/knapsack_dfs.png" /></a></p>
+<p align="center"> 図 14-18 &nbsp; 0-1ナップサック問題の力任せ探索再帰木 </p>
+
+<h3 id="2-2">2. &nbsp; 方法2：メモ化探索<a class="headerlink" href="#2-2" title="Permanent link">&para;</a></h3>
+<p>重複する部分問題が一度だけ計算されることを確保するために、部分問題の解を記録するメモ化リスト <code>mem</code> を使用します。ここで <code>mem[i][c]</code> は <span class="arithmatex">\(dp[i, c]\)</span> に対応します。</p>
+<p>メモ化を導入した後、**時間計算量は部分問題の数に依存**し、<span class="arithmatex">\(O(n \times cap)\)</span> になります。実装コードは以下の通りです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:14"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><input id="__tabbed_2_14" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label><label for="__tabbed_2_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.py</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">knapsack_dfs_mem</span><span class="p">(</span>
+<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a>    <span class="n">wgt</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">val</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">mem</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]],</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">c</span><span class="p">:</span> <span class="nb">int</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;0-1 ナップサック：記憶化探索&quot;&quot;&quot;</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a>    <span class="c1"># すべてのアイテムが選択されたかナップサックに残り容量がない場合、値 0 を返す</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a>    <span class="k">if</span> <span class="n">i</span> <span class="o">==</span> <span class="mi">0</span> <span class="ow">or</span> <span class="n">c</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
+<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a>        <span class="k">return</span> <span class="mi">0</span>
+<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a>    <span class="c1"># 記録がある場合、それを返す</span>
+<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a>    <span class="k">if</span> <span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span> <span class="o">!=</span> <span class="o">-</span><span class="mi">1</span><span class="p">:</span>
+<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a>        <span class="k">return</span> <span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span>
+<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a>    <span class="c1"># ナップサック容量を超える場合、ナップサックに入れないことしか選択できない</span>
+<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a>    <span class="k">if</span> <span class="n">wgt</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">c</span><span class="p">:</span>
+<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a>        <span class="k">return</span> <span class="n">knapsack_dfs_mem</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span> <span class="n">val</span><span class="p">,</span> <span class="n">mem</span><span class="p">,</span> <span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">c</span><span class="p">)</span>
+<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a>    <span class="c1"># アイテム i を入れないのと入れるのとの最大値を計算</span>
+<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a>    <span class="n">no</span> <span class="o">=</span> <span class="n">knapsack_dfs_mem</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span> <span class="n">val</span><span class="p">,</span> <span class="n">mem</span><span class="p">,</span> <span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">c</span><span class="p">)</span>
+<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a>    <span class="n">yes</span> <span class="o">=</span> <span class="n">knapsack_dfs_mem</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span> <span class="n">val</span><span class="p">,</span> <span class="n">mem</span><span class="p">,</span> <span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">c</span> <span class="o">-</span> <span class="n">wgt</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">])</span> <span class="o">+</span> <span class="n">val</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a>    <span class="c1"># 2 つの選択肢のうち大きい値を記録して返す</span>
+<a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a>    <span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">no</span><span class="p">,</span> <span class="n">yes</span><span class="p">)</span>
+<a id="__codelineno-14-19" name="__codelineno-14-19" href="#__codelineno-14-19"></a>    <span class="k">return</span> <span class="n">mem</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.cpp</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="p">[</span><span class="k">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">knapsackDFSMem</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.java</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 0-1 ナップサック：メモ化探索 */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">knapsackDFSMem</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">[][]</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="c1">// すべてのアイテムが選択されたか、ナップサックに残り容量がない場合、値 0 を返す</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">    </span><span class="c1">// 記録がある場合、それを返す</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="w">    </span><span class="c1">// ナップサックの容量を超える場合、ナップサックに入れないことしか選択できない</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">knapsackDFSMem</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">);</span>
+<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="w">    </span><span class="c1">// アイテム i を入れない場合と入れる場合の最大値を計算</span>
+<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">no</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsackDFSMem</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="p">);</span>
+<a id="__codelineno-16-17" name="__codelineno-16-17" href="#__codelineno-16-17"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">yes</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">knapsackDFSMem</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="n">mem</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-16-18" name="__codelineno-16-18" href="#__codelineno-16-18"></a><span class="w">    </span><span class="c1">// 2つの選択肢のより大きい値を記録して返す</span>
+<a id="__codelineno-16-19" name="__codelineno-16-19" href="#__codelineno-16-19"></a><span class="w">    </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">max</span><span class="p">(</span><span class="n">no</span><span class="p">,</span><span class="w"> </span><span class="n">yes</span><span class="p">);</span>
+<a id="__codelineno-16-20" name="__codelineno-16-20" href="#__codelineno-16-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">mem</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-16-21" name="__codelineno-16-21" href="#__codelineno-16-21"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.cs</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">knapsack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">KnapsackDFSMem</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.go</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">knapsackDFSMem</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">knapsackDFSMem</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.js</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">knapsackDFSMem</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.ts</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">knapsackDFSMem</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.dart</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">knapsackDFSMem</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.rs</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">knapsack_dfs_mem</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.c</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">knapsackDFSMem</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.kt</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">knapsackDFSMem</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">knapsack_dfs_mem</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.zig</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">knapsackDFSMem</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>下の図はメモ化探索で枝刈りされる探索分岐を示しています。</p>
+<p><a class="glightbox" href="../knapsack_problem.assets/knapsack_dfs_mem.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="0-1ナップサック問題のメモ化探索再帰木" class="animation-figure" src="../knapsack_problem.assets/knapsack_dfs_mem.png" /></a></p>
+<p align="center"> 図 14-19 &nbsp; 0-1ナップサック問題のメモ化探索再帰木 </p>
+
+<h3 id="3-3">3. &nbsp; 方法3：動的プログラミング<a class="headerlink" href="#3-3" title="Permanent link">&para;</a></h3>
+<p>動的プログラミングは本質的に状態遷移中に <span class="arithmatex">\(dp\)</span> テーブルを埋めることを含みます。コードは下の図に示されています：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="3:14"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><input id="__tabbed_3_14" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label><label for="__tabbed_3_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.py</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">knapsack_dp</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">val</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">cap</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;0-1 ナップサック：動的プログラミング&quot;&quot;&quot;</span>
+<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a>    <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">wgt</span><span class="p">)</span>
+<a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a>    <span class="c1"># dp テーブルを初期化</span>
+<a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a>    <span class="n">dp</span> <span class="o">=</span> <span class="p">[[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="n">cap</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)]</span>
+<a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a>    <span class="c1"># 状態遷移</span>
+<a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-28-8" name="__codelineno-28-8" href="#__codelineno-28-8"></a>        <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">cap</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-28-9" name="__codelineno-28-9" href="#__codelineno-28-9"></a>            <span class="k">if</span> <span class="n">wgt</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">c</span><span class="p">:</span>
+<a id="__codelineno-28-10" name="__codelineno-28-10" href="#__codelineno-28-10"></a>                <span class="c1"># ナップサック容量を超える場合、アイテム i を選択しない</span>
+<a id="__codelineno-28-11" name="__codelineno-28-11" href="#__codelineno-28-11"></a>                <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span> <span class="o">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="n">c</span><span class="p">]</span>
+<a id="__codelineno-28-12" name="__codelineno-28-12" href="#__codelineno-28-12"></a>            <span class="k">else</span><span class="p">:</span>
+<a id="__codelineno-28-13" name="__codelineno-28-13" href="#__codelineno-28-13"></a>                <span class="c1"># アイテム i を選択しないのと選択するのとで大きい値</span>
+<a id="__codelineno-28-14" name="__codelineno-28-14" href="#__codelineno-28-14"></a>                <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="n">c</span><span class="p">],</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="n">c</span> <span class="o">-</span> <span class="n">wgt</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]]</span> <span class="o">+</span> <span class="n">val</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">])</span>
+<a id="__codelineno-28-15" name="__codelineno-28-15" href="#__codelineno-28-15"></a>    <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">cap</span><span class="p">]</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.cpp</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="cm">/* 0-1 ナップサック：動的プログラミング */</span>
+<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">knapsackDP</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
+<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化</span>
+<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">dp</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">(</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">));</span>
+<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">cap</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-9" name="__codelineno-29-9" href="#__codelineno-29-9"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-10" name="__codelineno-29-10" href="#__codelineno-29-10"></a><span class="w">                </span><span class="c1">// ナップサックの容量を超える場合、アイテム i を選択しない</span>
+<a id="__codelineno-29-11" name="__codelineno-29-11" href="#__codelineno-29-11"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">c</span><span class="p">];</span>
+<a id="__codelineno-29-12" name="__codelineno-29-12" href="#__codelineno-29-12"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-13" name="__codelineno-29-13" href="#__codelineno-29-13"></a><span class="w">                </span><span class="c1">// 選択しない場合とアイテム i を選択する場合のより大きい値</span>
+<a id="__codelineno-29-14" name="__codelineno-29-14" href="#__codelineno-29-14"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">c</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]);</span>
+<a id="__codelineno-29-15" name="__codelineno-29-15" href="#__codelineno-29-15"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-29-16" name="__codelineno-29-16" href="#__codelineno-29-16"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-29-17" name="__codelineno-29-17" href="#__codelineno-29-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-18" name="__codelineno-29-18" href="#__codelineno-29-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">cap</span><span class="p">];</span>
+<a id="__codelineno-29-19" name="__codelineno-29-19" href="#__codelineno-29-19"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.java</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* 0-1 ナップサック：動的プログラミング */</span>
+<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">knapsackDP</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="na">length</span><span class="p">;</span>
+<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化</span>
+<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a><span class="w">    </span><span class="kt">int</span><span class="o">[][]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">cap</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-10" name="__codelineno-30-10" href="#__codelineno-30-10"></a><span class="w">                </span><span class="c1">// ナップサックの容量を超える場合、アイテム i を選択しない</span>
+<a id="__codelineno-30-11" name="__codelineno-30-11" href="#__codelineno-30-11"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-30-12" name="__codelineno-30-12" href="#__codelineno-30-12"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-13" name="__codelineno-30-13" href="#__codelineno-30-13"></a><span class="w">                </span><span class="c1">// 選択しない場合とアイテム i を選択する場合のより大きい値</span>
+<a id="__codelineno-30-14" name="__codelineno-30-14" href="#__codelineno-30-14"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">max</span><span class="p">(</span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">);</span>
+<a id="__codelineno-30-15" name="__codelineno-30-15" href="#__codelineno-30-15"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-30-16" name="__codelineno-30-16" href="#__codelineno-30-16"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-30-17" name="__codelineno-30-17" href="#__codelineno-30-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-18" name="__codelineno-30-18" href="#__codelineno-30-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="n">cap</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-30-19" name="__codelineno-30-19" href="#__codelineno-30-19"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.cs</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">knapsack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">KnapsackDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.go</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">knapsackDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.swift</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">knapsackDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.js</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">knapsackDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.ts</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">knapsackDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.dart</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">knapsackDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.rs</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">knapsack_dp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.c</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">knapsackDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.kt</span><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">knapsackDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">knapsack_dp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.zig</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">knapsackDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>下の図に示すように、時間計算量と空間計算量の両方が配列 <code>dp</code> のサイズ、つまり <span class="arithmatex">\(O(n \times cap)\)</span> によって決定されます。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="4:14"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><input id="__tabbed_4_6" name="__tabbed_4" type="radio" /><input id="__tabbed_4_7" name="__tabbed_4" type="radio" /><input id="__tabbed_4_8" name="__tabbed_4" type="radio" /><input id="__tabbed_4_9" name="__tabbed_4" type="radio" /><input id="__tabbed_4_10" name="__tabbed_4" type="radio" /><input id="__tabbed_4_11" name="__tabbed_4" type="radio" /><input id="__tabbed_4_12" name="__tabbed_4" type="radio" /><input id="__tabbed_4_13" name="__tabbed_4" type="radio" /><input id="__tabbed_4_14" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">&lt;1&gt;</label><label for="__tabbed_4_2">&lt;2&gt;</label><label for="__tabbed_4_3">&lt;3&gt;</label><label for="__tabbed_4_4">&lt;4&gt;</label><label for="__tabbed_4_5">&lt;5&gt;</label><label for="__tabbed_4_6">&lt;6&gt;</label><label for="__tabbed_4_7">&lt;7&gt;</label><label for="__tabbed_4_8">&lt;8&gt;</label><label for="__tabbed_4_9">&lt;9&gt;</label><label for="__tabbed_4_10">&lt;10&gt;</label><label for="__tabbed_4_11">&lt;11&gt;</label><label for="__tabbed_4_12">&lt;12&gt;</label><label for="__tabbed_4_13">&lt;13&gt;</label><label for="__tabbed_4_14">&lt;14&gt;</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<p><a class="glightbox" href="../knapsack_problem.assets/knapsack_dp_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="0-1ナップサック問題の動的プログラミングプロセス" class="animation-figure" src="../knapsack_problem.assets/knapsack_dp_step1.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../knapsack_problem.assets/knapsack_dp_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="knapsack_dp_step2" class="animation-figure" src="../knapsack_problem.assets/knapsack_dp_step2.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../knapsack_problem.assets/knapsack_dp_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="knapsack_dp_step3" class="animation-figure" src="../knapsack_problem.assets/knapsack_dp_step3.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../knapsack_problem.assets/knapsack_dp_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="knapsack_dp_step4" class="animation-figure" src="../knapsack_problem.assets/knapsack_dp_step4.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../knapsack_problem.assets/knapsack_dp_step5.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="knapsack_dp_step5" class="animation-figure" src="../knapsack_problem.assets/knapsack_dp_step5.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../knapsack_problem.assets/knapsack_dp_step6.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="knapsack_dp_step6" class="animation-figure" src="../knapsack_problem.assets/knapsack_dp_step6.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../knapsack_problem.assets/knapsack_dp_step7.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="knapsack_dp_step7" class="animation-figure" src="../knapsack_problem.assets/knapsack_dp_step7.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../knapsack_problem.assets/knapsack_dp_step8.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="knapsack_dp_step8" class="animation-figure" src="../knapsack_problem.assets/knapsack_dp_step8.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../knapsack_problem.assets/knapsack_dp_step9.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="knapsack_dp_step9" class="animation-figure" src="../knapsack_problem.assets/knapsack_dp_step9.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../knapsack_problem.assets/knapsack_dp_step10.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="knapsack_dp_step10" class="animation-figure" src="../knapsack_problem.assets/knapsack_dp_step10.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../knapsack_problem.assets/knapsack_dp_step11.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="knapsack_dp_step11" class="animation-figure" src="../knapsack_problem.assets/knapsack_dp_step11.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../knapsack_problem.assets/knapsack_dp_step12.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="knapsack_dp_step12" class="animation-figure" src="../knapsack_problem.assets/knapsack_dp_step12.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../knapsack_problem.assets/knapsack_dp_step13.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="knapsack_dp_step13" class="animation-figure" src="../knapsack_problem.assets/knapsack_dp_step13.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../knapsack_problem.assets/knapsack_dp_step14.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="knapsack_dp_step14" class="animation-figure" src="../knapsack_problem.assets/knapsack_dp_step14.png" /></a></p>
+</div>
+</div>
+</div>
+<p align="center"> 図 14-20 &nbsp; 0-1ナップサック問題の動的プログラミングプロセス </p>
+
+<h3 id="4">4. &nbsp; 空間最適化<a class="headerlink" href="#4" title="Permanent link">&para;</a></h3>
+<p>各状態は上の行の状態のみに関連するため、2つの配列を使用してローリング前進させ、空間計算量を <span class="arithmatex">\(O(n^2)\)</span> から <span class="arithmatex">\(O(n)\)</span> に削減できます。</p>
+<p>さらに考えてみると、1つの配列だけで空間最適化を達成できるでしょうか？各状態が直接上のセルまたは左上のセルから遷移することが観察できます。配列が1つしかない場合、<span class="arithmatex">\(i\)</span> 行目の走査を開始するとき、その配列はまだ <span class="arithmatex">\(i-1\)</span> 行目の状態を保存しています。</p>
+<ul>
+<li>通常の順序で走査する場合、<span class="arithmatex">\(dp[i, j]\)</span> に走査したとき、左上の <span class="arithmatex">\(dp[i-1, 1]\)</span> ～ <span class="arithmatex">\(dp[i-1, j-1]\)</span> の値がすでに上書きされている可能性があり、正しい状態遷移結果を得ることができません。</li>
+<li>逆順で走査する場合、上書き問題はなく、状態遷移を正しく実行できます。</li>
+</ul>
+<p>下の図は単一配列での <span class="arithmatex">\(i = 1\)</span> 行目から <span class="arithmatex">\(i = 2\)</span> 行目への遷移プロセスを示しています。通常順序走査と逆順走査の違いについて考えてみてください。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="5:6"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">&lt;1&gt;</label><label for="__tabbed_5_2">&lt;2&gt;</label><label for="__tabbed_5_3">&lt;3&gt;</label><label for="__tabbed_5_4">&lt;4&gt;</label><label for="__tabbed_5_5">&lt;5&gt;</label><label for="__tabbed_5_6">&lt;6&gt;</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<p><a class="glightbox" href="../knapsack_problem.assets/knapsack_dp_comp_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="0-1ナップサックの空間最適化動的プログラミングプロセス" class="animation-figure" src="../knapsack_problem.assets/knapsack_dp_comp_step1.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../knapsack_problem.assets/knapsack_dp_comp_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="knapsack_dp_comp_step2" class="animation-figure" src="../knapsack_problem.assets/knapsack_dp_comp_step2.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../knapsack_problem.assets/knapsack_dp_comp_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="knapsack_dp_comp_step3" class="animation-figure" src="../knapsack_problem.assets/knapsack_dp_comp_step3.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../knapsack_problem.assets/knapsack_dp_comp_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="knapsack_dp_comp_step4" class="animation-figure" src="../knapsack_problem.assets/knapsack_dp_comp_step4.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../knapsack_problem.assets/knapsack_dp_comp_step5.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="knapsack_dp_comp_step5" class="animation-figure" src="../knapsack_problem.assets/knapsack_dp_comp_step5.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../knapsack_problem.assets/knapsack_dp_comp_step6.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="knapsack_dp_comp_step6" class="animation-figure" src="../knapsack_problem.assets/knapsack_dp_comp_step6.png" /></a></p>
+</div>
+</div>
+</div>
+<p align="center"> 図 14-21 &nbsp; 0-1ナップサックの空間最適化動的プログラミングプロセス </p>
+
+<p>コード実装では、配列 <code>dp</code> の最初の次元 <span class="arithmatex">\(i\)</span> を削除し、内側のループを逆走査に変更するだけです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="6:14"><input checked="checked" id="__tabbed_6_1" name="__tabbed_6" type="radio" /><input id="__tabbed_6_2" name="__tabbed_6" type="radio" /><input id="__tabbed_6_3" name="__tabbed_6" type="radio" /><input id="__tabbed_6_4" name="__tabbed_6" type="radio" /><input id="__tabbed_6_5" name="__tabbed_6" type="radio" /><input id="__tabbed_6_6" name="__tabbed_6" type="radio" /><input id="__tabbed_6_7" name="__tabbed_6" type="radio" /><input id="__tabbed_6_8" name="__tabbed_6" type="radio" /><input id="__tabbed_6_9" name="__tabbed_6" type="radio" /><input id="__tabbed_6_10" name="__tabbed_6" type="radio" /><input id="__tabbed_6_11" name="__tabbed_6" type="radio" /><input id="__tabbed_6_12" name="__tabbed_6" type="radio" /><input id="__tabbed_6_13" name="__tabbed_6" type="radio" /><input id="__tabbed_6_14" name="__tabbed_6" type="radio" /><div class="tabbed-labels"><label for="__tabbed_6_1">Python</label><label for="__tabbed_6_2">C++</label><label for="__tabbed_6_3">Java</label><label for="__tabbed_6_4">C#</label><label for="__tabbed_6_5">Go</label><label for="__tabbed_6_6">Swift</label><label for="__tabbed_6_7">JS</label><label for="__tabbed_6_8">TS</label><label for="__tabbed_6_9">Dart</label><label for="__tabbed_6_10">Rust</label><label for="__tabbed_6_11">C</label><label for="__tabbed_6_12">Kotlin</label><label for="__tabbed_6_13">Ruby</label><label for="__tabbed_6_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.py</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">knapsack_dp_comp</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">val</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">cap</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-42-2" name="__codelineno-42-2" href="#__codelineno-42-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;0-1 ナップサック：空間最適化動的プログラミング&quot;&quot;&quot;</span>
+<a id="__codelineno-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></a>    <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">wgt</span><span class="p">)</span>
+<a id="__codelineno-42-4" name="__codelineno-42-4" href="#__codelineno-42-4"></a>    <span class="c1"># dp テーブルを初期化</span>
+<a id="__codelineno-42-5" name="__codelineno-42-5" href="#__codelineno-42-5"></a>    <span class="n">dp</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="n">cap</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-42-6" name="__codelineno-42-6" href="#__codelineno-42-6"></a>    <span class="c1"># 状態遷移</span>
+<a id="__codelineno-42-7" name="__codelineno-42-7" href="#__codelineno-42-7"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-42-8" name="__codelineno-42-8" href="#__codelineno-42-8"></a>        <span class="c1"># 逆順で走査</span>
+<a id="__codelineno-42-9" name="__codelineno-42-9" href="#__codelineno-42-9"></a>        <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">cap</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-42-10" name="__codelineno-42-10" href="#__codelineno-42-10"></a>            <span class="k">if</span> <span class="n">wgt</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">c</span><span class="p">:</span>
+<a id="__codelineno-42-11" name="__codelineno-42-11" href="#__codelineno-42-11"></a>                <span class="c1"># ナップサック容量を超える場合、アイテム i を選択しない</span>
+<a id="__codelineno-42-12" name="__codelineno-42-12" href="#__codelineno-42-12"></a>                <span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span> <span class="o">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span>
+<a id="__codelineno-42-13" name="__codelineno-42-13" href="#__codelineno-42-13"></a>            <span class="k">else</span><span class="p">:</span>
+<a id="__codelineno-42-14" name="__codelineno-42-14" href="#__codelineno-42-14"></a>                <span class="c1"># アイテム i を選択しないのと選択するのとで大きい値</span>
+<a id="__codelineno-42-15" name="__codelineno-42-15" href="#__codelineno-42-15"></a>                <span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">],</span> <span class="n">dp</span><span class="p">[</span><span class="n">c</span> <span class="o">-</span> <span class="n">wgt</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]]</span> <span class="o">+</span> <span class="n">val</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">])</span>
+<a id="__codelineno-42-16" name="__codelineno-42-16" href="#__codelineno-42-16"></a>    <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">cap</span><span class="p">]</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.cpp</span><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="cm">/* 0-1 ナップサック：空間最適化動的プログラミング */</span>
+<a id="__codelineno-43-2" name="__codelineno-43-2" href="#__codelineno-43-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">knapsackDPComp</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-3" name="__codelineno-43-3" href="#__codelineno-43-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
+<a id="__codelineno-43-4" name="__codelineno-43-4" href="#__codelineno-43-4"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化</span>
+<a id="__codelineno-43-5" name="__codelineno-43-5" href="#__codelineno-43-5"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">dp</span><span class="p">(</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-43-6" name="__codelineno-43-6" href="#__codelineno-43-6"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-43-7" name="__codelineno-43-7" href="#__codelineno-43-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-8" name="__codelineno-43-8" href="#__codelineno-43-8"></a><span class="w">        </span><span class="c1">// 逆順で走査</span>
+<a id="__codelineno-43-9" name="__codelineno-43-9" href="#__codelineno-43-9"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cap</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-10" name="__codelineno-43-10" href="#__codelineno-43-10"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-11" name="__codelineno-43-11" href="#__codelineno-43-11"></a><span class="w">                </span><span class="c1">// 選択しない場合とアイテム i を選択する場合のより大きい値</span>
+<a id="__codelineno-43-12" name="__codelineno-43-12" href="#__codelineno-43-12"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]);</span>
+<a id="__codelineno-43-13" name="__codelineno-43-13" href="#__codelineno-43-13"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-43-14" name="__codelineno-43-14" href="#__codelineno-43-14"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-43-15" name="__codelineno-43-15" href="#__codelineno-43-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-43-16" name="__codelineno-43-16" href="#__codelineno-43-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">cap</span><span class="p">];</span>
+<a id="__codelineno-43-17" name="__codelineno-43-17" href="#__codelineno-43-17"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.java</span><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="cm">/* 0-1 ナップサック：空間最適化動的プログラミング */</span>
+<a id="__codelineno-44-2" name="__codelineno-44-2" href="#__codelineno-44-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">knapsackDPComp</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-3" name="__codelineno-44-3" href="#__codelineno-44-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="na">length</span><span class="p">;</span>
+<a id="__codelineno-44-4" name="__codelineno-44-4" href="#__codelineno-44-4"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化</span>
+<a id="__codelineno-44-5" name="__codelineno-44-5" href="#__codelineno-44-5"></a><span class="w">    </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-44-6" name="__codelineno-44-6" href="#__codelineno-44-6"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-44-7" name="__codelineno-44-7" href="#__codelineno-44-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-8" name="__codelineno-44-8" href="#__codelineno-44-8"></a><span class="w">        </span><span class="c1">// 逆順で走査</span>
+<a id="__codelineno-44-9" name="__codelineno-44-9" href="#__codelineno-44-9"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cap</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-10" name="__codelineno-44-10" href="#__codelineno-44-10"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-11" name="__codelineno-44-11" href="#__codelineno-44-11"></a><span class="w">                </span><span class="c1">// 選択しない場合とアイテム i を選択する場合のより大きい値</span>
+<a id="__codelineno-44-12" name="__codelineno-44-12" href="#__codelineno-44-12"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">max</span><span class="p">(</span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">);</span>
+<a id="__codelineno-44-13" name="__codelineno-44-13" href="#__codelineno-44-13"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-44-14" name="__codelineno-44-14" href="#__codelineno-44-14"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-44-15" name="__codelineno-44-15" href="#__codelineno-44-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-44-16" name="__codelineno-44-16" href="#__codelineno-44-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">cap</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-44-17" name="__codelineno-44-17" href="#__codelineno-44-17"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.cs</span><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">knapsack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">KnapsackDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.go</span><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">knapsackDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.swift</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">knapsackDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.js</span><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">knapsackDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.ts</span><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">knapsackDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.dart</span><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">knapsackDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.rs</span><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">knapsack_dp_comp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.c</span><pre><span></span><code><a id="__codelineno-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">knapsackDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.kt</span><pre><span></span><code><a id="__codelineno-53-1" name="__codelineno-53-1" href="#__codelineno-53-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">knapsackDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.rb</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">knapsack_dp_comp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">knapsack.zig</span><pre><span></span><code><a id="__codelineno-55-1" name="__codelineno-55-1" href="#__codelineno-55-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">knapsackDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+
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+  
+  <span class="md-ellipsis">
+    0.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_introduction/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+      
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
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+<h1 id="147">14.7 &nbsp; まとめ<a class="headerlink" href="#147" title="Permanent link">&para;</a></h1>
+<ul>
+<li>動的プログラミングは問題を分解し、部分問題の解を保存することで冗長な計算を避け、計算効率を向上させます。</li>
+<li>時間を考慮しなければ、すべての動的プログラミング問題はバックトラッキング（力任せ探索）を使用して解決できますが、再帰木には多くの重複する部分問題があり、効率が非常に低くなります。記憶化リストを導入することで、計算されたすべての部分問題の解を保存し、重複する部分問題が一度だけ計算されることを保証できます。</li>
+<li>記憶化探索はトップダウンの再帰解法であり、動的プログラミングはボトムアップの反復アプローチに対応し、「表を埋める」ことに似ています。現在の状態は特定の局所状態のみに依存するため、dpテーブルの1次元を削除して空間計算量を削減できます。</li>
+<li>部分問題の分解は汎用的なアルゴリズムアプローチであり、分割統治法、動的プログラミング、バックトラッキングで特徴が異なります。</li>
+<li>動的プログラミング問題には3つの主要な特徴があります：重複する部分問題、最適部分構造、無記憶性。</li>
+<li>元の問題の最適解がその部分問題の最適解から構築できる場合、最適部分構造を持ちます。</li>
+<li>無記憶性とは、状態の将来の発展が現在の状態のみに依存し、過去に経験したすべての状態に依存しないことを意味します。多くの組み合わせ最適化問題にはこの特性がなく、動的プログラミングを使用して迅速に解決することはできません。</li>
+</ul>
+<p><strong>ナップサック問題</strong></p>
+<ul>
+<li>ナップサック問題は最も典型的な動的プログラミング問題の1つで、0-1ナップサック、無制限ナップサック、複数ナップサックなどの変種があります。</li>
+<li>0-1ナップサックの状態定義は、最初の <span class="arithmatex">\(i\)</span> 個のアイテムを含む容量 <span class="arithmatex">\(c\)</span> のナップサックでの最大値です。アイテムをナップサックに入れないまたは入れるという決定に基づいて、最適部分構造を特定し、状態遷移方程式を構築できます。空間最適化では、各状態が直接上と左上の状態に依存するため、左上の状態の上書きを避けるためにリストを逆順で走査する必要があります。</li>
+<li>無制限ナップサック問題では、各種類のアイテムを選択できる数に制限がないため、アイテムを含める状態遷移は0-1ナップサックと異なります。状態が直接上と左の状態に依存するため、空間最適化では前方走査を含める必要があります。</li>
+<li>コイン交換問題は無制限ナップサック問題の変種で、「最大」値を求めることから「最小」コイン数を求めることに変わり、状態遷移方程式は <span class="arithmatex">\(\max()\)</span> を <span class="arithmatex">\(\min()\)</span> に変更する必要があります。ナップサックの容量を「超えない」ことを追求することから、正確に目標金額を求めることに変わり、「目標金額を構成できない」無効解を表すために <span class="arithmatex">\(amt + 1\)</span> を使用します。</li>
+<li>コイン交換問題IIは「最小コイン数」を求めることから「コインの組み合わせ数」を求めることに変わり、状態遷移方程式を <span class="arithmatex">\(\min()\)</span> から和算演算子に変更します。</li>
+</ul>
+<p><strong>編集距離問題</strong></p>
+<ul>
+<li>編集距離（レーベンシュタイン距離）は2つの文字列間の類似度を測定し、一つの文字列を別の文字列に変更するために必要な最小編集ステップ数として定義され、編集操作には追加、削除、置換が含まれます。</li>
+<li>編集距離問題の状態定義は、<span class="arithmatex">\(s\)</span> の最初の <span class="arithmatex">\(i\)</span> 文字を <span class="arithmatex">\(t\)</span> の最初の <span class="arithmatex">\(j\)</span> 文字に変更するために必要な最小編集ステップ数です。<span class="arithmatex">\(s[i] \ne t[j]\)</span> の場合、追加、削除、置換の3つの決定があり、それぞれに対応する残余部分問題があります。これから最適部分構造を特定し、状態遷移方程式を構築できます。<span class="arithmatex">\(s[i] = t[j]\)</span> の場合、現在の文字の編集は必要ありません。</li>
+<li>編集距離では、状態が直接上、左、左上の状態に依存します。したがって、空間最適化後、前方走査も逆走査も正しく状態遷移を実行できません。これに対処するため、変数を使用して左上の状態を一時的に保存し、無制限ナップサック問題の状況と同等にし、空間最適化後に前方走査を可能にします。</li>
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diff --git a/ja/chapter_dynamic_programming/unbounded_knapsack_problem.assets/coin_change_dp_step3.png b/ja/chapter_dynamic_programming/unbounded_knapsack_problem.assets/coin_change_dp_step3.png
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diff --git a/ja/chapter_dynamic_programming/unbounded_knapsack_problem.assets/coin_change_ii_example.png b/ja/chapter_dynamic_programming/unbounded_knapsack_problem.assets/coin_change_ii_example.png
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diff --git a/ja/chapter_dynamic_programming/unbounded_knapsack_problem.assets/unbounded_knapsack_dp_comp_step2.png b/ja/chapter_dynamic_programming/unbounded_knapsack_problem.assets/unbounded_knapsack_dp_comp_step2.png
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diff --git a/ja/chapter_dynamic_programming/unbounded_knapsack_problem.assets/unbounded_knapsack_dp_comp_step3.png b/ja/chapter_dynamic_programming/unbounded_knapsack_problem.assets/unbounded_knapsack_dp_comp_step3.png
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+            <span class="md-nav__icon md-icon"></span>
+            はじめに
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_2" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_preface/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M21 4H3a2 2 0 0 0-2 2v13a2 2 0 0 0 2 2h18a2 2 0 0 0 2-2V6a2 2 0 0 0-2-2M3 19V6h8v13H3m18 0h-8V6h8v13m-7-9.5h6V11h-6V9.5m0 2.5h6v1.5h-6V12m0 2.5h6V16h-6v-1.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 0 章 &nbsp; 前書き
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_2" id="__nav_2_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_2_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_2">
+            <span class="md-nav__icon md-icon"></span>
+            第 0 章 &nbsp; 前書き
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/about_the_book/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.1 &nbsp; この本について
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/suggestions/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.2 &nbsp; 本書の使い方
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_introduction/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1451" class="md-nav__link">
+    <span class="md-ellipsis">
+      14.5.1 &nbsp; 無制限ナップサック問題
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="14.5.1   無制限ナップサック問題">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 動的プログラミングアプローチ
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; コード実装
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#3" class="md-nav__link">
+    <span class="md-ellipsis">
+      3. &nbsp; 空間最適化
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+  
+</li>
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+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1452" class="md-nav__link">
+    <span class="md-ellipsis">
+      14.5.2 &nbsp; コイン交換問題
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="14.5.2   コイン交換問題">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1_1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 動的プログラミングアプローチ
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2_1" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; コード実装
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#3_1" class="md-nav__link">
+    <span class="md-ellipsis">
+      3. &nbsp; 空間最適化
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1453-ii" class="md-nav__link">
+    <span class="md-ellipsis">
+      14.5.3 &nbsp; コイン交換問題II
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="14.5.3   コイン交換問題II">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1_2" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 動的プログラミングアプローチ
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2_2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; コード実装
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#3_2" class="md-nav__link">
+    <span class="md-ellipsis">
+      3. &nbsp; 空間最適化
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
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+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
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+          <label class="md-nav__title" for="__nav_17">
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+            
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+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
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+      
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+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
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+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_appendix/" class="md-nav__link ">
+              
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
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+            第 16 章 &nbsp; 付録
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+            
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+  
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+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
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+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
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+
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+  
+
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+        </nav>
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+          
+        
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+            <a href="../../chapter_reference/" class="md-nav__link ">
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9 3v15h3V3H9m3 2 4 13 3-1-4-13-3 1M5 5v13h3V5H5M3 19v2h18v-2H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    参考文献
+  </span>
+  
+
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+            
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+            参考文献
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+      
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+  
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+  </ul>
+</nav>
+                  </div>
+                </div>
+              </div>
+            
+            
+              
+              <div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
+                <div class="md-sidebar__scrollwrap">
+                  <div class="md-sidebar__inner">
+                    
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1451" class="md-nav__link">
+    <span class="md-ellipsis">
+      14.5.1 &nbsp; 無制限ナップサック問題
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="14.5.1   無制限ナップサック問題">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 動的プログラミングアプローチ
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; コード実装
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#3" class="md-nav__link">
+    <span class="md-ellipsis">
+      3. &nbsp; 空間最適化
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1452" class="md-nav__link">
+    <span class="md-ellipsis">
+      14.5.2 &nbsp; コイン交換問題
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="14.5.2   コイン交換問題">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1_1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 動的プログラミングアプローチ
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2_1" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; コード実装
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#3_1" class="md-nav__link">
+    <span class="md-ellipsis">
+      3. &nbsp; 空間最適化
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1453-ii" class="md-nav__link">
+    <span class="md-ellipsis">
+      14.5.3 &nbsp; コイン交換問題II
+    </span>
+  </a>
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+        
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+  <a href="#1_2" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 動的プログラミングアプローチ
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2_2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; コード実装
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#3_2" class="md-nav__link">
+    <span class="md-ellipsis">
+      3. &nbsp; 空間最適化
+    </span>
+  </a>
+  
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+        
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+    </nav>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+                  </div>
+                </div>
+              </div>
+            
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+              <article class="md-content__inner md-typeset">
+                
+                  <!-- Tags -->
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+    <a
+      href="https://github.com/krahets/hello-algo/tree/main/ja/docs/chapter_dynamic_programming/unbounded_knapsack_problem.md"
+      title="編集"
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+      
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
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+
+<!-- Page content -->
+<h1 id="145">14.5 &nbsp; 無制限ナップサック問題<a class="headerlink" href="#145" title="Permanent link">&para;</a></h1>
+<p>このセクションでは、まず別の一般的なナップサック問題である無制限ナップサックを解決し、次にその特殊ケースであるコイン交換問題を探索します。</p>
+<h2 id="1451">14.5.1 &nbsp; 無制限ナップサック問題<a class="headerlink" href="#1451" title="Permanent link">&para;</a></h2>
+<div class="admonition question">
+<p class="admonition-title">Question</p>
+<p><span class="arithmatex">\(n\)</span> 個のアイテムが与えられ、<span class="arithmatex">\(i\)</span> 番目のアイテムの重量は <span class="arithmatex">\(wgt[i-1]\)</span> で値は <span class="arithmatex">\(val[i-1]\)</span> です。容量が <span class="arithmatex">\(cap\)</span> のバックパックがあります。<strong>各アイテムは複数回選択できます</strong>。容量を超えることなくバックパックに入れることができるアイテムの最大値は何ですか？以下の例を参照してください。</p>
+</div>
+<p><a class="glightbox" href="../unbounded_knapsack_problem.assets/unbounded_knapsack_example.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="無制限ナップサック問題の例データ" class="animation-figure" src="../unbounded_knapsack_problem.assets/unbounded_knapsack_example.png" /></a></p>
+<p align="center"> 図 14-22 &nbsp; 無制限ナップサック問題の例データ </p>
+
+<h3 id="1">1. &nbsp; 動的プログラミングアプローチ<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<p>無制限ナップサック問題は0-1ナップサック問題と非常に似ており、<strong>唯一の違いはアイテムを選択できる回数に制限がないことです</strong>。</p>
+<ul>
+<li>0-1ナップサック問題では、各アイテムは1つしかないため、アイテム <span class="arithmatex">\(i\)</span> をバックパックに入れた後は、前の <span class="arithmatex">\(i-1\)</span> 個のアイテムからのみ選択できます。</li>
+<li>無制限ナップサック問題では、各アイテムの数量は無制限であるため、アイテム <span class="arithmatex">\(i\)</span> をバックパックに入れた後も、<strong>前の <span class="arithmatex">\(i\)</span> 個のアイテムから引き続き選択できます</strong>。</li>
+</ul>
+<p>無制限ナップサック問題のルールの下で、状態 <span class="arithmatex">\([i, c]\)</span> は2つの方法で変化できます。</p>
+<ul>
+<li><strong>アイテム <span class="arithmatex">\(i\)</span> を入れない</strong>：0-1ナップサック問題と同様に、<span class="arithmatex">\([i-1, c]\)</span> に遷移します。</li>
+<li><strong>アイテム <span class="arithmatex">\(i\)</span> を入れる</strong>：0-1ナップサック問題とは異なり、<span class="arithmatex">\([i, c-wgt[i-1]]\)</span> に遷移します。</li>
+</ul>
+<p>したがって、状態遷移方程式は次のようになります：</p>
+<div class="arithmatex">\[
+dp[i, c] = \max(dp[i-1, c], dp[i, c - wgt[i-1]] + val[i-1])
+\]</div>
+<h3 id="2">2. &nbsp; コード実装<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
+<p>2つの問題のコードを比較すると、状態遷移が <span class="arithmatex">\(i-1\)</span> から <span class="arithmatex">\(i\)</span> に変わり、残りは完全に同一です：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:14"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><input id="__tabbed_1_14" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label><label for="__tabbed_1_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">unbounded_knapsack.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">unbounded_knapsack_dp</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">val</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">cap</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;完全ナップサック：動的プログラミング&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">wgt</span><span class="p">)</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="c1"># dp テーブルを初期化</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="n">dp</span> <span class="o">=</span> <span class="p">[[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="n">cap</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)]</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="c1"># 状態遷移</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>        <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">cap</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>            <span class="k">if</span> <span class="n">wgt</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">c</span><span class="p">:</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>                <span class="c1"># ナップサック容量を超える場合、アイテム i を選択しない</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>                <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span> <span class="o">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="n">c</span><span class="p">]</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>            <span class="k">else</span><span class="p">:</span>
+<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>                <span class="c1"># アイテム i を選択しないのと選択するのとで大きい値</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>                <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="n">c</span><span class="p">],</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span> <span class="o">-</span> <span class="n">wgt</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]]</span> <span class="o">+</span> <span class="n">val</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">])</span>
+<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>    <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">cap</span><span class="p">]</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">unbounded_knapsack.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 完全ナップサック：動的プログラミング */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">unboundedKnapsackDP</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">dp</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">(</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">));</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">cap</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">                </span><span class="c1">// ナップサックの容量を超える場合、アイテム i を選択しない</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">c</span><span class="p">];</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">                </span><span class="c1">// 選択しない場合とアイテム i を選択する場合のより大きい値</span>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">c</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]);</span>
+<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">cap</span><span class="p">];</span>
+<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">unbounded_knapsack.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 完全ナップサック：動的プログラミング */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">unboundedKnapsackDP</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="na">length</span><span class="p">;</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="kt">int</span><span class="o">[][]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">cap</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">                </span><span class="c1">// ナップサックの容量を超える場合、アイテム i を選択しない</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">                </span><span class="c1">// 選択しない場合とアイテム i を選択する場合のより大きい値</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">max</span><span class="p">(</span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">c</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">);</span>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="n">cap</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">unbounded_knapsack.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">unbounded_knapsack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">UnboundedKnapsackDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">unbounded_knapsack.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">unboundedKnapsackDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">unbounded_knapsack.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">unboundedKnapsackDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">unbounded_knapsack.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">unboundedKnapsackDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">unbounded_knapsack.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">unboundedKnapsackDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">unbounded_knapsack.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">unboundedKnapsackDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">unbounded_knapsack.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">unbounded_knapsack_dp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">unbounded_knapsack.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">unboundedKnapsackDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">unbounded_knapsack.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">unboundedKnapsackDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">unbounded_knapsack.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">unbounded_knapsack_dp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">unbounded_knapsack.zig</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">unboundedKnapsackDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h3 id="3">3. &nbsp; 空間最適化<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
+<p>現在の状態は左と上の状態から来るため、<strong>空間最適化解法は <span class="arithmatex">\(dp\)</span> テーブルの各行に対して前方走査を実行する必要があります</strong>。</p>
+<p>この走査順序は0-1ナップサックの場合とは逆です。違いを理解するために下の図を参照してください。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:6"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">&lt;1&gt;</label><label for="__tabbed_2_2">&lt;2&gt;</label><label for="__tabbed_2_3">&lt;3&gt;</label><label for="__tabbed_2_4">&lt;4&gt;</label><label for="__tabbed_2_5">&lt;5&gt;</label><label for="__tabbed_2_6">&lt;6&gt;</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<p><a class="glightbox" href="../unbounded_knapsack_problem.assets/unbounded_knapsack_dp_comp_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="空間最適化後の無制限ナップサック問題の動的プログラミングプロセス" class="animation-figure" src="../unbounded_knapsack_problem.assets/unbounded_knapsack_dp_comp_step1.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../unbounded_knapsack_problem.assets/unbounded_knapsack_dp_comp_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="unbounded_knapsack_dp_comp_step2" class="animation-figure" src="../unbounded_knapsack_problem.assets/unbounded_knapsack_dp_comp_step2.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../unbounded_knapsack_problem.assets/unbounded_knapsack_dp_comp_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="unbounded_knapsack_dp_comp_step3" class="animation-figure" src="../unbounded_knapsack_problem.assets/unbounded_knapsack_dp_comp_step3.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../unbounded_knapsack_problem.assets/unbounded_knapsack_dp_comp_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="unbounded_knapsack_dp_comp_step4" class="animation-figure" src="../unbounded_knapsack_problem.assets/unbounded_knapsack_dp_comp_step4.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../unbounded_knapsack_problem.assets/unbounded_knapsack_dp_comp_step5.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="unbounded_knapsack_dp_comp_step5" class="animation-figure" src="../unbounded_knapsack_problem.assets/unbounded_knapsack_dp_comp_step5.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../unbounded_knapsack_problem.assets/unbounded_knapsack_dp_comp_step6.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="unbounded_knapsack_dp_comp_step6" class="animation-figure" src="../unbounded_knapsack_problem.assets/unbounded_knapsack_dp_comp_step6.png" /></a></p>
+</div>
+</div>
+</div>
+<p align="center"> 図 14-23 &nbsp; 空間最適化後の無制限ナップサック問題の動的プログラミングプロセス </p>
+
+<p>コード実装は非常に簡単で、配列 <code>dp</code> の最初の次元を削除するだけです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="3:14"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><input id="__tabbed_3_14" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label><label for="__tabbed_3_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">unbounded_knapsack.py</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">unbounded_knapsack_dp_comp</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">val</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">cap</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;完全ナップサック：空間最適化動的プログラミング&quot;&quot;&quot;</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a>    <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">wgt</span><span class="p">)</span>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a>    <span class="c1"># dp テーブルを初期化</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a>    <span class="n">dp</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="n">cap</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a>    <span class="c1"># 状態遷移</span>
+<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a>        <span class="c1"># 順序で走査</span>
+<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a>        <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">cap</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a>            <span class="k">if</span> <span class="n">wgt</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">c</span><span class="p">:</span>
+<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a>                <span class="c1"># ナップサック容量を超える場合、アイテム i を選択しない</span>
+<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a>                <span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span> <span class="o">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span>
+<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a>            <span class="k">else</span><span class="p">:</span>
+<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a>                <span class="c1"># アイテム i を選択しないのと選択するのとで大きい値</span>
+<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a>                <span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">],</span> <span class="n">dp</span><span class="p">[</span><span class="n">c</span> <span class="o">-</span> <span class="n">wgt</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]]</span> <span class="o">+</span> <span class="n">val</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">])</span>
+<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a>    <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">cap</span><span class="p">]</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">unbounded_knapsack.cpp</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 完全ナップサック：空間最適化動的プログラミング */</span>
+<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">unboundedKnapsackDPComp</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
+<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化</span>
+<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">dp</span><span class="p">(</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">cap</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="w">                </span><span class="c1">// ナップサックの容量を超える場合、アイテム i を選択しない</span>
+<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">];</span>
+<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="w">                </span><span class="c1">// 選択しない場合とアイテム i を選択する場合のより大きい値</span>
+<a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]);</span>
+<a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-15-17" name="__codelineno-15-17" href="#__codelineno-15-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-18" name="__codelineno-15-18" href="#__codelineno-15-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">cap</span><span class="p">];</span>
+<a id="__codelineno-15-19" name="__codelineno-15-19" href="#__codelineno-15-19"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">unbounded_knapsack.java</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 完全ナップサック：空間最適化動的プログラミング */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">unboundedKnapsackDPComp</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="na">length</span><span class="p">;</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">    </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">cap</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">cap</span><span class="p">;</span><span class="w"> </span><span class="n">c</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w">                </span><span class="c1">// ナップサックの容量を超える場合、アイテム i を選択しない</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w">                </span><span class="c1">// 選択しない場合とアイテム i を選択する場合のより大きい値</span>
+<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">max</span><span class="p">(</span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">c</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">val</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">);</span>
+<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-16-17" name="__codelineno-16-17" href="#__codelineno-16-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-18" name="__codelineno-16-18" href="#__codelineno-16-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">cap</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-16-19" name="__codelineno-16-19" href="#__codelineno-16-19"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">unbounded_knapsack.cs</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">unbounded_knapsack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">UnboundedKnapsackDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">unbounded_knapsack.go</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">unboundedKnapsackDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">unbounded_knapsack.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">unboundedKnapsackDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">unbounded_knapsack.js</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">unboundedKnapsackDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">unbounded_knapsack.ts</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">unboundedKnapsackDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">unbounded_knapsack.dart</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">unboundedKnapsackDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">unbounded_knapsack.rs</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">unbounded_knapsack_dp_comp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">unbounded_knapsack.c</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">unboundedKnapsackDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">unbounded_knapsack.kt</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">unboundedKnapsackDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">unbounded_knapsack.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">unbounded_knapsack_dp_comp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">unbounded_knapsack.zig</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">unboundedKnapsackDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h2 id="1452">14.5.2 &nbsp; コイン交換問題<a class="headerlink" href="#1452" title="Permanent link">&para;</a></h2>
+<p>ナップサック問題は動的プログラミング問題の大きなクラスの代表であり、コイン交換問題など多くの変種があります。</p>
+<div class="admonition question">
+<p class="admonition-title">Question</p>
+<p><span class="arithmatex">\(n\)</span> 種類のコインが与えられ、<span class="arithmatex">\(i\)</span> 番目の種類のコインの額面は <span class="arithmatex">\(coins[i - 1]\)</span> で、目標金額は <span class="arithmatex">\(amt\)</span> です。<strong>各種類のコインは複数回選択できます</strong>。目標金額を構成するのに必要な最小コイン数は何ですか？目標金額を構成できない場合は <span class="arithmatex">\(-1\)</span> を返してください。以下の例を参照してください。</p>
+</div>
+<p><a class="glightbox" href="../unbounded_knapsack_problem.assets/coin_change_example.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="コイン交換問題の例データ" class="animation-figure" src="../unbounded_knapsack_problem.assets/coin_change_example.png" /></a></p>
+<p align="center"> 図 14-24 &nbsp; コイン交換問題の例データ </p>
+
+<h3 id="1_1">1. &nbsp; 動的プログラミングアプローチ<a class="headerlink" href="#1_1" title="Permanent link">&para;</a></h3>
+<p><strong>コイン交換は無制限ナップサック問題の特殊ケースと見なすことができ</strong>、以下の類似点と相違点を共有しています。</p>
+<ul>
+<li>2つの問題は互いに変換できます：「アイテム」は「コイン」に対応し、「アイテムの重量」は「コインの額面」に対応し、「バックパックの容量」は「目標金額」に対応します。</li>
+<li>最適化目標は逆です：無制限ナップサック問題はアイテムの値を最大化することを目的とし、コイン交換問題はコインの数を最小化することを目的とします。</li>
+<li>無制限ナップサック問題はバックパック容量を「超えない」解を求め、コイン交換は目標金額を「正確に」構成する解を求めます。</li>
+</ul>
+<p><strong>第1ステップ：各ラウンドの意思決定を考え、状態を定義し、それにより <span class="arithmatex">\(dp\)</span> テーブルを導出する</strong></p>
+<p>状態 <span class="arithmatex">\([i, a]\)</span> は部分問題に対応します：<strong>最初の <span class="arithmatex">\(i\)</span> 種類のコインを使用して金額 <span class="arithmatex">\(a\)</span> を構成できる最小コイン数</strong>、<span class="arithmatex">\(dp[i, a]\)</span> と表記されます。</p>
+<p>二次元 <span class="arithmatex">\(dp\)</span> テーブルのサイズは <span class="arithmatex">\((n+1) \times (amt+1)\)</span> です。</p>
+<p><strong>第2ステップ：最適部分構造を特定し、状態遷移方程式を導出する</strong></p>
+<p>この問題は状態遷移方程式の2つの側面で無制限ナップサック問題と異なります。</p>
+<ul>
+<li>この問題は最小値を求めるため、演算子 <span class="arithmatex">\(\max()\)</span> を <span class="arithmatex">\(\min()\)</span> に変更する必要があります。</li>
+<li>最適化はコインの数に焦点を当てているため、コインが選択されたときに単純に <span class="arithmatex">\(+1\)</span> を追加します。</li>
+</ul>
+<div class="arithmatex">\[
+dp[i, a] = \min(dp[i-1, a], dp[i, a - coins[i-1]] + 1)
+\]</div>
+<p><strong>第3ステップ：境界条件と状態遷移順序を定義する</strong></p>
+<p>目標金額が <span class="arithmatex">\(0\)</span> の場合、それを構成するのに必要な最小コイン数は <span class="arithmatex">\(0\)</span> であるため、最初の列のすべての <span class="arithmatex">\(dp[i, 0]\)</span> は <span class="arithmatex">\(0\)</span> です。</p>
+<p>コインがない場合、**任意の金額 &gt;0 を構成することは不可能**であり、これは無効な解です。状態遷移方程式の <span class="arithmatex">\(\min()\)</span> 関数が無効な解を認識してフィルタリングできるように、<span class="arithmatex">\(+\infty\)</span> を使用してそれらを表現することを検討し、つまり最初の行のすべての <span class="arithmatex">\(dp[0, a]\)</span> を <span class="arithmatex">\(+\infty\)</span> に設定します。</p>
+<h3 id="2_1">2. &nbsp; コード実装<a class="headerlink" href="#2_1" title="Permanent link">&para;</a></h3>
+<p>ほとんどのプログラミング言語は <span class="arithmatex">\(+\infty\)</span> 変数を提供しておらず、整数 <code>int</code> の最大値のみを代替として使用できます。これによりオーバーフローが発生する可能性があります：状態遷移方程式の <span class="arithmatex">\(+1\)</span> 演算がオーバーフローする可能性があります。</p>
+<p>この理由で、数値 <span class="arithmatex">\(amt + 1\)</span> を使用して無効な解を表します。なぜなら、<span class="arithmatex">\(amt\)</span> を構成するのに必要な最大コイン数は最大でも <span class="arithmatex">\(amt\)</span> だからです。結果を返す前に、<span class="arithmatex">\(dp[n, amt]\)</span> が <span class="arithmatex">\(amt + 1\)</span> に等しいかどうかを確認し、そうであれば <span class="arithmatex">\(-1\)</span> を返し、目標金額を構成できないことを示します。コードは以下の通りです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="4:14"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><input id="__tabbed_4_6" name="__tabbed_4" type="radio" /><input id="__tabbed_4_7" name="__tabbed_4" type="radio" /><input id="__tabbed_4_8" name="__tabbed_4" type="radio" /><input id="__tabbed_4_9" name="__tabbed_4" type="radio" /><input id="__tabbed_4_10" name="__tabbed_4" type="radio" /><input id="__tabbed_4_11" name="__tabbed_4" type="radio" /><input id="__tabbed_4_12" name="__tabbed_4" type="radio" /><input id="__tabbed_4_13" name="__tabbed_4" type="radio" /><input id="__tabbed_4_14" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">Python</label><label for="__tabbed_4_2">C++</label><label for="__tabbed_4_3">Java</label><label for="__tabbed_4_4">C#</label><label for="__tabbed_4_5">Go</label><label for="__tabbed_4_6">Swift</label><label for="__tabbed_4_7">JS</label><label for="__tabbed_4_8">TS</label><label for="__tabbed_4_9">Dart</label><label for="__tabbed_4_10">Rust</label><label for="__tabbed_4_11">C</label><label for="__tabbed_4_12">Kotlin</label><label for="__tabbed_4_13">Ruby</label><label for="__tabbed_4_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change.py</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">coin_change_dp</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">amt</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;硬貨交換：動的プログラミング&quot;&quot;&quot;</span>
+<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a>    <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">coins</span><span class="p">)</span>
+<a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a>    <span class="n">MAX</span> <span class="o">=</span> <span class="n">amt</span> <span class="o">+</span> <span class="mi">1</span>
+<a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a>    <span class="c1"># dp テーブルを初期化</span>
+<a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a>    <span class="n">dp</span> <span class="o">=</span> <span class="p">[[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="n">amt</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)]</span>
+<a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a>    <span class="c1"># 状態遷移：最初の行と最初の列</span>
+<a id="__codelineno-28-8" name="__codelineno-28-8" href="#__codelineno-28-8"></a>    <span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">amt</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-28-9" name="__codelineno-28-9" href="#__codelineno-28-9"></a>        <span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">a</span><span class="p">]</span> <span class="o">=</span> <span class="n">MAX</span>
+<a id="__codelineno-28-10" name="__codelineno-28-10" href="#__codelineno-28-10"></a>    <span class="c1"># 状態遷移：残りの行と列</span>
+<a id="__codelineno-28-11" name="__codelineno-28-11" href="#__codelineno-28-11"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-28-12" name="__codelineno-28-12" href="#__codelineno-28-12"></a>        <span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">amt</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-28-13" name="__codelineno-28-13" href="#__codelineno-28-13"></a>            <span class="k">if</span> <span class="n">coins</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">a</span><span class="p">:</span>
+<a id="__codelineno-28-14" name="__codelineno-28-14" href="#__codelineno-28-14"></a>                <span class="c1"># 目標金額を超える場合、硬貨 i を選択しない</span>
+<a id="__codelineno-28-15" name="__codelineno-28-15" href="#__codelineno-28-15"></a>                <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="p">]</span> <span class="o">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="n">a</span><span class="p">]</span>
+<a id="__codelineno-28-16" name="__codelineno-28-16" href="#__codelineno-28-16"></a>            <span class="k">else</span><span class="p">:</span>
+<a id="__codelineno-28-17" name="__codelineno-28-17" href="#__codelineno-28-17"></a>                <span class="c1"># 硬貨 i を選択しないのと選択するのとで小さい値</span>
+<a id="__codelineno-28-18" name="__codelineno-28-18" href="#__codelineno-28-18"></a>                <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="p">]</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="n">a</span><span class="p">],</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span> <span class="o">-</span> <span class="n">coins</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]]</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-28-19" name="__codelineno-28-19" href="#__codelineno-28-19"></a>    <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">amt</span><span class="p">]</span> <span class="k">if</span> <span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">amt</span><span class="p">]</span> <span class="o">!=</span> <span class="n">MAX</span> <span class="k">else</span> <span class="o">-</span><span class="mi">1</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change.cpp</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="cm">/* 硬貨両替：動的プログラミング */</span>
+<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">coinChangeDP</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
+<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">MAX</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化</span>
+<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">dp</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">));</span>
+<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="w">    </span><span class="c1">// 状態遷移：最初の行と最初の列</span>
+<a id="__codelineno-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">amt</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-9" name="__codelineno-29-9" href="#__codelineno-29-9"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">MAX</span><span class="p">;</span>
+<a id="__codelineno-29-10" name="__codelineno-29-10" href="#__codelineno-29-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-11" name="__codelineno-29-11" href="#__codelineno-29-11"></a><span class="w">    </span><span class="c1">// 状態遷移：残りの行と列</span>
+<a id="__codelineno-29-12" name="__codelineno-29-12" href="#__codelineno-29-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-13" name="__codelineno-29-13" href="#__codelineno-29-13"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">amt</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-14" name="__codelineno-29-14" href="#__codelineno-29-14"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-15" name="__codelineno-29-15" href="#__codelineno-29-15"></a><span class="w">                </span><span class="c1">// 目標金額を超える場合、硬貨 i を選択しない</span>
+<a id="__codelineno-29-16" name="__codelineno-29-16" href="#__codelineno-29-16"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">a</span><span class="p">];</span>
+<a id="__codelineno-29-17" name="__codelineno-29-17" href="#__codelineno-29-17"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-18" name="__codelineno-29-18" href="#__codelineno-29-18"></a><span class="w">                </span><span class="c1">// 選択しない場合と硬貨 i を選択する場合のより小さい値</span>
+<a id="__codelineno-29-19" name="__codelineno-29-19" href="#__codelineno-29-19"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">a</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-29-20" name="__codelineno-29-20" href="#__codelineno-29-20"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-29-21" name="__codelineno-29-21" href="#__codelineno-29-21"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-29-22" name="__codelineno-29-22" href="#__codelineno-29-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-23" name="__codelineno-29-23" href="#__codelineno-29-23"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">amt</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">MAX</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">amt</span><span class="p">]</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
+<a id="__codelineno-29-24" name="__codelineno-29-24" href="#__codelineno-29-24"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change.java</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* 硬貨両替：動的プログラミング */</span>
+<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">coinChangeDP</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="na">length</span><span class="p">;</span>
+<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">MAX</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化</span>
+<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="w">    </span><span class="kt">int</span><span class="o">[][]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a><span class="w">    </span><span class="c1">// 状態遷移：最初の行と最初の列</span>
+<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">amt</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">][</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">MAX</span><span class="p">;</span>
+<a id="__codelineno-30-10" name="__codelineno-30-10" href="#__codelineno-30-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-11" name="__codelineno-30-11" href="#__codelineno-30-11"></a><span class="w">    </span><span class="c1">// 状態遷移：残りの行と列</span>
+<a id="__codelineno-30-12" name="__codelineno-30-12" href="#__codelineno-30-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-13" name="__codelineno-30-13" href="#__codelineno-30-13"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">amt</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-14" name="__codelineno-30-14" href="#__codelineno-30-14"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-15" name="__codelineno-30-15" href="#__codelineno-30-15"></a><span class="w">                </span><span class="c1">// 目標金額を超える場合、硬貨 i を選択しない</span>
+<a id="__codelineno-30-16" name="__codelineno-30-16" href="#__codelineno-30-16"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">a</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-30-17" name="__codelineno-30-17" href="#__codelineno-30-17"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-18" name="__codelineno-30-18" href="#__codelineno-30-18"></a><span class="w">                </span><span class="c1">// 選択しない場合と硬貨 i を選択する場合のより小さい値</span>
+<a id="__codelineno-30-19" name="__codelineno-30-19" href="#__codelineno-30-19"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">min</span><span class="p">(</span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">a</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-30-20" name="__codelineno-30-20" href="#__codelineno-30-20"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-30-21" name="__codelineno-30-21" href="#__codelineno-30-21"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-30-22" name="__codelineno-30-22" href="#__codelineno-30-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-23" name="__codelineno-30-23" href="#__codelineno-30-23"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="n">amt</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">MAX</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="n">amt</span><span class="o">]</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-30-24" name="__codelineno-30-24" href="#__codelineno-30-24"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change.cs</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">coin_change</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">CoinChangeDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change.go</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">coinChangeDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change.swift</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">coinChangeDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change.js</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">coinChangeDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change.ts</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">coinChangeDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change.dart</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">coinChangeDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change.rs</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">coin_change_dp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change.c</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">coinChangeDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change.kt</span><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">coinChangeDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">coin_change_dp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change.zig</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">coinChangeDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>下の図はコイン交換問題の動的プログラミングプロセスを示しており、無制限ナップサック問題と非常に似ています。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="5:15"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><input id="__tabbed_5_7" name="__tabbed_5" type="radio" /><input id="__tabbed_5_8" name="__tabbed_5" type="radio" /><input id="__tabbed_5_9" name="__tabbed_5" type="radio" /><input id="__tabbed_5_10" name="__tabbed_5" type="radio" /><input id="__tabbed_5_11" name="__tabbed_5" type="radio" /><input id="__tabbed_5_12" name="__tabbed_5" type="radio" /><input id="__tabbed_5_13" name="__tabbed_5" type="radio" /><input id="__tabbed_5_14" name="__tabbed_5" type="radio" /><input id="__tabbed_5_15" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">&lt;1&gt;</label><label for="__tabbed_5_2">&lt;2&gt;</label><label for="__tabbed_5_3">&lt;3&gt;</label><label for="__tabbed_5_4">&lt;4&gt;</label><label for="__tabbed_5_5">&lt;5&gt;</label><label for="__tabbed_5_6">&lt;6&gt;</label><label for="__tabbed_5_7">&lt;7&gt;</label><label for="__tabbed_5_8">&lt;8&gt;</label><label for="__tabbed_5_9">&lt;9&gt;</label><label for="__tabbed_5_10">&lt;10&gt;</label><label for="__tabbed_5_11">&lt;11&gt;</label><label for="__tabbed_5_12">&lt;12&gt;</label><label for="__tabbed_5_13">&lt;13&gt;</label><label for="__tabbed_5_14">&lt;14&gt;</label><label for="__tabbed_5_15">&lt;15&gt;</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<p><a class="glightbox" href="../unbounded_knapsack_problem.assets/coin_change_dp_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="コイン交換問題の動的プログラミングプロセス" class="animation-figure" src="../unbounded_knapsack_problem.assets/coin_change_dp_step1.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../unbounded_knapsack_problem.assets/coin_change_dp_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="coin_change_dp_step2" class="animation-figure" src="../unbounded_knapsack_problem.assets/coin_change_dp_step2.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../unbounded_knapsack_problem.assets/coin_change_dp_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="coin_change_dp_step3" class="animation-figure" src="../unbounded_knapsack_problem.assets/coin_change_dp_step3.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../unbounded_knapsack_problem.assets/coin_change_dp_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="coin_change_dp_step4" class="animation-figure" src="../unbounded_knapsack_problem.assets/coin_change_dp_step4.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../unbounded_knapsack_problem.assets/coin_change_dp_step5.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="coin_change_dp_step5" class="animation-figure" src="../unbounded_knapsack_problem.assets/coin_change_dp_step5.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../unbounded_knapsack_problem.assets/coin_change_dp_step6.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="coin_change_dp_step6" class="animation-figure" src="../unbounded_knapsack_problem.assets/coin_change_dp_step6.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../unbounded_knapsack_problem.assets/coin_change_dp_step7.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="coin_change_dp_step7" class="animation-figure" src="../unbounded_knapsack_problem.assets/coin_change_dp_step7.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../unbounded_knapsack_problem.assets/coin_change_dp_step8.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="coin_change_dp_step8" class="animation-figure" src="../unbounded_knapsack_problem.assets/coin_change_dp_step8.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../unbounded_knapsack_problem.assets/coin_change_dp_step9.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="coin_change_dp_step9" class="animation-figure" src="../unbounded_knapsack_problem.assets/coin_change_dp_step9.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../unbounded_knapsack_problem.assets/coin_change_dp_step10.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="coin_change_dp_step10" class="animation-figure" src="../unbounded_knapsack_problem.assets/coin_change_dp_step10.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../unbounded_knapsack_problem.assets/coin_change_dp_step11.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="coin_change_dp_step11" class="animation-figure" src="../unbounded_knapsack_problem.assets/coin_change_dp_step11.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../unbounded_knapsack_problem.assets/coin_change_dp_step12.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="coin_change_dp_step12" class="animation-figure" src="../unbounded_knapsack_problem.assets/coin_change_dp_step12.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../unbounded_knapsack_problem.assets/coin_change_dp_step13.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="coin_change_dp_step13" class="animation-figure" src="../unbounded_knapsack_problem.assets/coin_change_dp_step13.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../unbounded_knapsack_problem.assets/coin_change_dp_step14.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="coin_change_dp_step14" class="animation-figure" src="../unbounded_knapsack_problem.assets/coin_change_dp_step14.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../unbounded_knapsack_problem.assets/coin_change_dp_step15.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="coin_change_dp_step15" class="animation-figure" src="../unbounded_knapsack_problem.assets/coin_change_dp_step15.png" /></a></p>
+</div>
+</div>
+</div>
+<p align="center"> 図 14-25 &nbsp; コイン交換問題の動的プログラミングプロセス </p>
+
+<h3 id="3_1">3. &nbsp; 空間最適化<a class="headerlink" href="#3_1" title="Permanent link">&para;</a></h3>
+<p>コイン交換問題の空間最適化は無制限ナップサック問題と同じ方法で処理されます：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="6:14"><input checked="checked" id="__tabbed_6_1" name="__tabbed_6" type="radio" /><input id="__tabbed_6_2" name="__tabbed_6" type="radio" /><input id="__tabbed_6_3" name="__tabbed_6" type="radio" /><input id="__tabbed_6_4" name="__tabbed_6" type="radio" /><input id="__tabbed_6_5" name="__tabbed_6" type="radio" /><input id="__tabbed_6_6" name="__tabbed_6" type="radio" /><input id="__tabbed_6_7" name="__tabbed_6" type="radio" /><input id="__tabbed_6_8" name="__tabbed_6" type="radio" /><input id="__tabbed_6_9" name="__tabbed_6" type="radio" /><input id="__tabbed_6_10" name="__tabbed_6" type="radio" /><input id="__tabbed_6_11" name="__tabbed_6" type="radio" /><input id="__tabbed_6_12" name="__tabbed_6" type="radio" /><input id="__tabbed_6_13" name="__tabbed_6" type="radio" /><input id="__tabbed_6_14" name="__tabbed_6" type="radio" /><div class="tabbed-labels"><label for="__tabbed_6_1">Python</label><label for="__tabbed_6_2">C++</label><label for="__tabbed_6_3">Java</label><label for="__tabbed_6_4">C#</label><label for="__tabbed_6_5">Go</label><label for="__tabbed_6_6">Swift</label><label for="__tabbed_6_7">JS</label><label for="__tabbed_6_8">TS</label><label for="__tabbed_6_9">Dart</label><label for="__tabbed_6_10">Rust</label><label for="__tabbed_6_11">C</label><label for="__tabbed_6_12">Kotlin</label><label for="__tabbed_6_13">Ruby</label><label for="__tabbed_6_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change.py</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">coin_change_dp_comp</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">amt</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-42-2" name="__codelineno-42-2" href="#__codelineno-42-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;硬貨交換：空間最適化動的プログラミング&quot;&quot;&quot;</span>
+<a id="__codelineno-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></a>    <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">coins</span><span class="p">)</span>
+<a id="__codelineno-42-4" name="__codelineno-42-4" href="#__codelineno-42-4"></a>    <span class="n">MAX</span> <span class="o">=</span> <span class="n">amt</span> <span class="o">+</span> <span class="mi">1</span>
+<a id="__codelineno-42-5" name="__codelineno-42-5" href="#__codelineno-42-5"></a>    <span class="c1"># dp テーブルを初期化</span>
+<a id="__codelineno-42-6" name="__codelineno-42-6" href="#__codelineno-42-6"></a>    <span class="n">dp</span> <span class="o">=</span> <span class="p">[</span><span class="n">MAX</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="n">amt</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-42-7" name="__codelineno-42-7" href="#__codelineno-42-7"></a>    <span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-42-8" name="__codelineno-42-8" href="#__codelineno-42-8"></a>    <span class="c1"># 状態遷移</span>
+<a id="__codelineno-42-9" name="__codelineno-42-9" href="#__codelineno-42-9"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-42-10" name="__codelineno-42-10" href="#__codelineno-42-10"></a>        <span class="c1"># 順序で走査</span>
+<a id="__codelineno-42-11" name="__codelineno-42-11" href="#__codelineno-42-11"></a>        <span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">amt</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-42-12" name="__codelineno-42-12" href="#__codelineno-42-12"></a>            <span class="k">if</span> <span class="n">coins</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">a</span><span class="p">:</span>
+<a id="__codelineno-42-13" name="__codelineno-42-13" href="#__codelineno-42-13"></a>                <span class="c1"># 目標金額を超える場合、硬貨 i を選択しない</span>
+<a id="__codelineno-42-14" name="__codelineno-42-14" href="#__codelineno-42-14"></a>                <span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span> <span class="o">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span>
+<a id="__codelineno-42-15" name="__codelineno-42-15" href="#__codelineno-42-15"></a>            <span class="k">else</span><span class="p">:</span>
+<a id="__codelineno-42-16" name="__codelineno-42-16" href="#__codelineno-42-16"></a>                <span class="c1"># 硬貨 i を選択しないのと選択するのとで小さい値</span>
+<a id="__codelineno-42-17" name="__codelineno-42-17" href="#__codelineno-42-17"></a>                <span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">],</span> <span class="n">dp</span><span class="p">[</span><span class="n">a</span> <span class="o">-</span> <span class="n">coins</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]]</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-42-18" name="__codelineno-42-18" href="#__codelineno-42-18"></a>    <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">amt</span><span class="p">]</span> <span class="k">if</span> <span class="n">dp</span><span class="p">[</span><span class="n">amt</span><span class="p">]</span> <span class="o">!=</span> <span class="n">MAX</span> <span class="k">else</span> <span class="o">-</span><span class="mi">1</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change.cpp</span><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="cm">/* 硬貨両替：空間最適化動的プログラミング */</span>
+<a id="__codelineno-43-2" name="__codelineno-43-2" href="#__codelineno-43-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">coinChangeDPComp</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-3" name="__codelineno-43-3" href="#__codelineno-43-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
+<a id="__codelineno-43-4" name="__codelineno-43-4" href="#__codelineno-43-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">MAX</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-43-5" name="__codelineno-43-5" href="#__codelineno-43-5"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化</span>
+<a id="__codelineno-43-6" name="__codelineno-43-6" href="#__codelineno-43-6"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">dp</span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">MAX</span><span class="p">);</span>
+<a id="__codelineno-43-7" name="__codelineno-43-7" href="#__codelineno-43-7"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-43-8" name="__codelineno-43-8" href="#__codelineno-43-8"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-43-9" name="__codelineno-43-9" href="#__codelineno-43-9"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-10" name="__codelineno-43-10" href="#__codelineno-43-10"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">amt</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-11" name="__codelineno-43-11" href="#__codelineno-43-11"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-12" name="__codelineno-43-12" href="#__codelineno-43-12"></a><span class="w">                </span><span class="c1">// 目標金額を超える場合、硬貨 i を選択しない</span>
+<a id="__codelineno-43-13" name="__codelineno-43-13" href="#__codelineno-43-13"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">];</span>
+<a id="__codelineno-43-14" name="__codelineno-43-14" href="#__codelineno-43-14"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-15" name="__codelineno-43-15" href="#__codelineno-43-15"></a><span class="w">                </span><span class="c1">// 選択しない場合と硬貨 i を選択する場合のより小さい値</span>
+<a id="__codelineno-43-16" name="__codelineno-43-16" href="#__codelineno-43-16"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">],</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-43-17" name="__codelineno-43-17" href="#__codelineno-43-17"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-43-18" name="__codelineno-43-18" href="#__codelineno-43-18"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-43-19" name="__codelineno-43-19" href="#__codelineno-43-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-43-20" name="__codelineno-43-20" href="#__codelineno-43-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">amt</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">MAX</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">amt</span><span class="p">]</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
+<a id="__codelineno-43-21" name="__codelineno-43-21" href="#__codelineno-43-21"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change.java</span><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="cm">/* 硬貨両替：空間最適化動的プログラミング */</span>
+<a id="__codelineno-44-2" name="__codelineno-44-2" href="#__codelineno-44-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">coinChangeDPComp</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-3" name="__codelineno-44-3" href="#__codelineno-44-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="na">length</span><span class="p">;</span>
+<a id="__codelineno-44-4" name="__codelineno-44-4" href="#__codelineno-44-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">MAX</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-44-5" name="__codelineno-44-5" href="#__codelineno-44-5"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化</span>
+<a id="__codelineno-44-6" name="__codelineno-44-6" href="#__codelineno-44-6"></a><span class="w">    </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-44-7" name="__codelineno-44-7" href="#__codelineno-44-7"></a><span class="w">    </span><span class="n">Arrays</span><span class="p">.</span><span class="na">fill</span><span class="p">(</span><span class="n">dp</span><span class="p">,</span><span class="w"> </span><span class="n">MAX</span><span class="p">);</span>
+<a id="__codelineno-44-8" name="__codelineno-44-8" href="#__codelineno-44-8"></a><span class="w">    </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-44-9" name="__codelineno-44-9" href="#__codelineno-44-9"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-44-10" name="__codelineno-44-10" href="#__codelineno-44-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-11" name="__codelineno-44-11" href="#__codelineno-44-11"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">amt</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-12" name="__codelineno-44-12" href="#__codelineno-44-12"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-13" name="__codelineno-44-13" href="#__codelineno-44-13"></a><span class="w">                </span><span class="c1">// 目標金額を超える場合、硬貨 i を選択しない</span>
+<a id="__codelineno-44-14" name="__codelineno-44-14" href="#__codelineno-44-14"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-44-15" name="__codelineno-44-15" href="#__codelineno-44-15"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-16" name="__codelineno-44-16" href="#__codelineno-44-16"></a><span class="w">                </span><span class="c1">// 選択しない場合と硬貨 i を選択する場合のより小さい値</span>
+<a id="__codelineno-44-17" name="__codelineno-44-17" href="#__codelineno-44-17"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">min</span><span class="p">(</span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-44-18" name="__codelineno-44-18" href="#__codelineno-44-18"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-44-19" name="__codelineno-44-19" href="#__codelineno-44-19"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-44-20" name="__codelineno-44-20" href="#__codelineno-44-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-44-21" name="__codelineno-44-21" href="#__codelineno-44-21"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">amt</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">MAX</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">amt</span><span class="o">]</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-44-22" name="__codelineno-44-22" href="#__codelineno-44-22"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change.cs</span><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">coin_change</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">CoinChangeDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change.go</span><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">coinChangeDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change.swift</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">coinChangeDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change.js</span><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">coinChangeDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change.ts</span><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">coinChangeDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change.dart</span><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">coinChangeDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change.rs</span><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">coin_change_dp_comp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change.c</span><pre><span></span><code><a id="__codelineno-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">coinChangeDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change.kt</span><pre><span></span><code><a id="__codelineno-53-1" name="__codelineno-53-1" href="#__codelineno-53-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">coinChangeDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change.rb</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">coin_change_dp_comp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change.zig</span><pre><span></span><code><a id="__codelineno-55-1" name="__codelineno-55-1" href="#__codelineno-55-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">coinChangeDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h2 id="1453-ii">14.5.3 &nbsp; コイン交換問題II<a class="headerlink" href="#1453-ii" title="Permanent link">&para;</a></h2>
+<div class="admonition question">
+<p class="admonition-title">Question</p>
+<p><span class="arithmatex">\(n\)</span> 種類のコインが与えられ、<span class="arithmatex">\(i\)</span> 番目の種類のコインの額面は <span class="arithmatex">\(coins[i - 1]\)</span> で、目標金額は <span class="arithmatex">\(amt\)</span> です。各種類のコインは複数回選択でき、<strong>目標金額を構成できるコインの組み合わせは何通りありますか</strong>。以下の例を参照してください。</p>
+</div>
+<p><a class="glightbox" href="../unbounded_knapsack_problem.assets/coin_change_ii_example.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="コイン交換問題IIの例データ" class="animation-figure" src="../unbounded_knapsack_problem.assets/coin_change_ii_example.png" /></a></p>
+<p align="center"> 図 14-26 &nbsp; コイン交換問題IIの例データ </p>
+
+<h3 id="1_2">1. &nbsp; 動的プログラミングアプローチ<a class="headerlink" href="#1_2" title="Permanent link">&para;</a></h3>
+<p>前の問題と比較して、この問題の目標は組み合わせの数を決定することであるため、部分問題は次のようになります：<strong>最初の <span class="arithmatex">\(i\)</span> 種類のコインを使用して金額 <span class="arithmatex">\(a\)</span> を構成できる組み合わせの数</strong>。<span class="arithmatex">\(dp\)</span> テーブルはサイズ <span class="arithmatex">\((n+1) \times (amt + 1)\)</span> の二次元行列のまま残ります。</p>
+<p>現在の状態の組み合わせ数は、現在のコインを選択しない組み合わせと現在のコインを選択する組み合わせの合計です。状態遷移方程式は：</p>
+<div class="arithmatex">\[
+dp[i, a] = dp[i-1, a] + dp[i, a - coins[i-1]]
+\]</div>
+<p>目標金額が <span class="arithmatex">\(0\)</span> の場合、目標金額を構成するのにコインは必要ないため、最初の列のすべての <span class="arithmatex">\(dp[i, 0]\)</span> は <span class="arithmatex">\(1\)</span> に初期化されるべきです。コインがない場合、任意の金額 &gt;0 を構成することは不可能であるため、最初の行のすべての <span class="arithmatex">\(dp[0, a]\)</span> は <span class="arithmatex">\(0\)</span> に設定されるべきです。</p>
+<h3 id="2_2">2. &nbsp; コード実装<a class="headerlink" href="#2_2" title="Permanent link">&para;</a></h3>
+<div class="tabbed-set tabbed-alternate" data-tabs="7:14"><input checked="checked" id="__tabbed_7_1" name="__tabbed_7" type="radio" /><input id="__tabbed_7_2" name="__tabbed_7" type="radio" /><input id="__tabbed_7_3" name="__tabbed_7" type="radio" /><input id="__tabbed_7_4" name="__tabbed_7" type="radio" /><input id="__tabbed_7_5" name="__tabbed_7" type="radio" /><input id="__tabbed_7_6" name="__tabbed_7" type="radio" /><input id="__tabbed_7_7" name="__tabbed_7" type="radio" /><input id="__tabbed_7_8" name="__tabbed_7" type="radio" /><input id="__tabbed_7_9" name="__tabbed_7" type="radio" /><input id="__tabbed_7_10" name="__tabbed_7" type="radio" /><input id="__tabbed_7_11" name="__tabbed_7" type="radio" /><input id="__tabbed_7_12" name="__tabbed_7" type="radio" /><input id="__tabbed_7_13" name="__tabbed_7" type="radio" /><input id="__tabbed_7_14" name="__tabbed_7" type="radio" /><div class="tabbed-labels"><label for="__tabbed_7_1">Python</label><label for="__tabbed_7_2">C++</label><label for="__tabbed_7_3">Java</label><label for="__tabbed_7_4">C#</label><label for="__tabbed_7_5">Go</label><label for="__tabbed_7_6">Swift</label><label for="__tabbed_7_7">JS</label><label for="__tabbed_7_8">TS</label><label for="__tabbed_7_9">Dart</label><label for="__tabbed_7_10">Rust</label><label for="__tabbed_7_11">C</label><label for="__tabbed_7_12">Kotlin</label><label for="__tabbed_7_13">Ruby</label><label for="__tabbed_7_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change_ii.py</span><pre><span></span><code><a id="__codelineno-56-1" name="__codelineno-56-1" href="#__codelineno-56-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">coin_change_ii_dp</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">amt</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-56-2" name="__codelineno-56-2" href="#__codelineno-56-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;硬貨交換 II：動的プログラミング&quot;&quot;&quot;</span>
+<a id="__codelineno-56-3" name="__codelineno-56-3" href="#__codelineno-56-3"></a>    <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">coins</span><span class="p">)</span>
+<a id="__codelineno-56-4" name="__codelineno-56-4" href="#__codelineno-56-4"></a>    <span class="c1"># dp テーブルを初期化</span>
+<a id="__codelineno-56-5" name="__codelineno-56-5" href="#__codelineno-56-5"></a>    <span class="n">dp</span> <span class="o">=</span> <span class="p">[[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="n">amt</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)]</span>
+<a id="__codelineno-56-6" name="__codelineno-56-6" href="#__codelineno-56-6"></a>    <span class="c1"># 最初の列を初期化</span>
+<a id="__codelineno-56-7" name="__codelineno-56-7" href="#__codelineno-56-7"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-56-8" name="__codelineno-56-8" href="#__codelineno-56-8"></a>        <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span>
+<a id="__codelineno-56-9" name="__codelineno-56-9" href="#__codelineno-56-9"></a>    <span class="c1"># 状態遷移</span>
+<a id="__codelineno-56-10" name="__codelineno-56-10" href="#__codelineno-56-10"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-56-11" name="__codelineno-56-11" href="#__codelineno-56-11"></a>        <span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">amt</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-56-12" name="__codelineno-56-12" href="#__codelineno-56-12"></a>            <span class="k">if</span> <span class="n">coins</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">a</span><span class="p">:</span>
+<a id="__codelineno-56-13" name="__codelineno-56-13" href="#__codelineno-56-13"></a>                <span class="c1"># 目標金額を超える場合、硬貨 i を選択しない</span>
+<a id="__codelineno-56-14" name="__codelineno-56-14" href="#__codelineno-56-14"></a>                <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="p">]</span> <span class="o">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="n">a</span><span class="p">]</span>
+<a id="__codelineno-56-15" name="__codelineno-56-15" href="#__codelineno-56-15"></a>            <span class="k">else</span><span class="p">:</span>
+<a id="__codelineno-56-16" name="__codelineno-56-16" href="#__codelineno-56-16"></a>                <span class="c1"># 硬貨 i を選択しないのと選択するのとの両方の選択肢の和</span>
+<a id="__codelineno-56-17" name="__codelineno-56-17" href="#__codelineno-56-17"></a>                <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="p">]</span> <span class="o">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">][</span><span class="n">a</span><span class="p">]</span> <span class="o">+</span> <span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span> <span class="o">-</span> <span class="n">coins</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]]</span>
+<a id="__codelineno-56-18" name="__codelineno-56-18" href="#__codelineno-56-18"></a>    <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">amt</span><span class="p">]</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change_ii.cpp</span><pre><span></span><code><a id="__codelineno-57-1" name="__codelineno-57-1" href="#__codelineno-57-1"></a><span class="cm">/* 硬貨両替 II：動的プログラミング */</span>
+<a id="__codelineno-57-2" name="__codelineno-57-2" href="#__codelineno-57-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">coinChangeIIDP</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-3" name="__codelineno-57-3" href="#__codelineno-57-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
+<a id="__codelineno-57-4" name="__codelineno-57-4" href="#__codelineno-57-4"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化</span>
+<a id="__codelineno-57-5" name="__codelineno-57-5" href="#__codelineno-57-5"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">dp</span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">));</span>
+<a id="__codelineno-57-6" name="__codelineno-57-6" href="#__codelineno-57-6"></a><span class="w">    </span><span class="c1">// 最初の列を初期化</span>
+<a id="__codelineno-57-7" name="__codelineno-57-7" href="#__codelineno-57-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-8" name="__codelineno-57-8" href="#__codelineno-57-8"></a><span class="w">        </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-57-9" name="__codelineno-57-9" href="#__codelineno-57-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-57-10" name="__codelineno-57-10" href="#__codelineno-57-10"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-57-11" name="__codelineno-57-11" href="#__codelineno-57-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-12" name="__codelineno-57-12" href="#__codelineno-57-12"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">amt</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-13" name="__codelineno-57-13" href="#__codelineno-57-13"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-14" name="__codelineno-57-14" href="#__codelineno-57-14"></a><span class="w">                </span><span class="c1">// 目標金額を超える場合、硬貨 i を選択しない</span>
+<a id="__codelineno-57-15" name="__codelineno-57-15" href="#__codelineno-57-15"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">a</span><span class="p">];</span>
+<a id="__codelineno-57-16" name="__codelineno-57-16" href="#__codelineno-57-16"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-17" name="__codelineno-57-17" href="#__codelineno-57-17"></a><span class="w">                </span><span class="c1">// 選択しない場合と硬貨 i を選択する場合の2つの選択肢の合計</span>
+<a id="__codelineno-57-18" name="__codelineno-57-18" href="#__codelineno-57-18"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">][</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]];</span>
+<a id="__codelineno-57-19" name="__codelineno-57-19" href="#__codelineno-57-19"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-57-20" name="__codelineno-57-20" href="#__codelineno-57-20"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-57-21" name="__codelineno-57-21" href="#__codelineno-57-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-57-22" name="__codelineno-57-22" href="#__codelineno-57-22"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">n</span><span class="p">][</span><span class="n">amt</span><span class="p">];</span>
+<a id="__codelineno-57-23" name="__codelineno-57-23" href="#__codelineno-57-23"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change_ii.java</span><pre><span></span><code><a id="__codelineno-58-1" name="__codelineno-58-1" href="#__codelineno-58-1"></a><span class="cm">/* 硬貨両替 II：動的プログラミング */</span>
+<a id="__codelineno-58-2" name="__codelineno-58-2" href="#__codelineno-58-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">coinChangeIIDP</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-3" name="__codelineno-58-3" href="#__codelineno-58-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="na">length</span><span class="p">;</span>
+<a id="__codelineno-58-4" name="__codelineno-58-4" href="#__codelineno-58-4"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化</span>
+<a id="__codelineno-58-5" name="__codelineno-58-5" href="#__codelineno-58-5"></a><span class="w">    </span><span class="kt">int</span><span class="o">[][]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">n</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-58-6" name="__codelineno-58-6" href="#__codelineno-58-6"></a><span class="w">    </span><span class="c1">// 最初の列を初期化</span>
+<a id="__codelineno-58-7" name="__codelineno-58-7" href="#__codelineno-58-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-8" name="__codelineno-58-8" href="#__codelineno-58-8"></a><span class="w">        </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-58-9" name="__codelineno-58-9" href="#__codelineno-58-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-58-10" name="__codelineno-58-10" href="#__codelineno-58-10"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-58-11" name="__codelineno-58-11" href="#__codelineno-58-11"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-12" name="__codelineno-58-12" href="#__codelineno-58-12"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">amt</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-13" name="__codelineno-58-13" href="#__codelineno-58-13"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-14" name="__codelineno-58-14" href="#__codelineno-58-14"></a><span class="w">                </span><span class="c1">// 目標金額を超える場合、硬貨 i を選択しない</span>
+<a id="__codelineno-58-15" name="__codelineno-58-15" href="#__codelineno-58-15"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">a</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-58-16" name="__codelineno-58-16" href="#__codelineno-58-16"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-17" name="__codelineno-58-17" href="#__codelineno-58-17"></a><span class="w">                </span><span class="c1">// 選択しない場合と硬貨 i を選択する場合の2つの選択肢の合計</span>
+<a id="__codelineno-58-18" name="__codelineno-58-18" href="#__codelineno-58-18"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">][</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">i</span><span class="o">][</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]]</span><span class="p">;</span>
+<a id="__codelineno-58-19" name="__codelineno-58-19" href="#__codelineno-58-19"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-58-20" name="__codelineno-58-20" href="#__codelineno-58-20"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-58-21" name="__codelineno-58-21" href="#__codelineno-58-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-58-22" name="__codelineno-58-22" href="#__codelineno-58-22"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">n</span><span class="o">][</span><span class="n">amt</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-58-23" name="__codelineno-58-23" href="#__codelineno-58-23"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change_ii.cs</span><pre><span></span><code><a id="__codelineno-59-1" name="__codelineno-59-1" href="#__codelineno-59-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">coin_change_ii</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">CoinChangeIIDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change_ii.go</span><pre><span></span><code><a id="__codelineno-60-1" name="__codelineno-60-1" href="#__codelineno-60-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">coinChangeIIDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change_ii.swift</span><pre><span></span><code><a id="__codelineno-61-1" name="__codelineno-61-1" href="#__codelineno-61-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">coinChangeIIDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change_ii.js</span><pre><span></span><code><a id="__codelineno-62-1" name="__codelineno-62-1" href="#__codelineno-62-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">coinChangeIIDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change_ii.ts</span><pre><span></span><code><a id="__codelineno-63-1" name="__codelineno-63-1" href="#__codelineno-63-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">coinChangeIIDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change_ii.dart</span><pre><span></span><code><a id="__codelineno-64-1" name="__codelineno-64-1" href="#__codelineno-64-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">coinChangeIIDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change_ii.rs</span><pre><span></span><code><a id="__codelineno-65-1" name="__codelineno-65-1" href="#__codelineno-65-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">coin_change_ii_dp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change_ii.c</span><pre><span></span><code><a id="__codelineno-66-1" name="__codelineno-66-1" href="#__codelineno-66-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">coinChangeIIDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change_ii.kt</span><pre><span></span><code><a id="__codelineno-67-1" name="__codelineno-67-1" href="#__codelineno-67-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">coinChangeIIDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change_ii.rb</span><pre><span></span><code><a id="__codelineno-68-1" name="__codelineno-68-1" href="#__codelineno-68-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">coin_change_ii_dp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change_ii.zig</span><pre><span></span><code><a id="__codelineno-69-1" name="__codelineno-69-1" href="#__codelineno-69-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">coinChangeIIDP</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h3 id="3_2">3. &nbsp; 空間最適化<a class="headerlink" href="#3_2" title="Permanent link">&para;</a></h3>
+<p>空間最適化アプローチは同じで、コインの次元を削除するだけです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="8:14"><input checked="checked" id="__tabbed_8_1" name="__tabbed_8" type="radio" /><input id="__tabbed_8_2" name="__tabbed_8" type="radio" /><input id="__tabbed_8_3" name="__tabbed_8" type="radio" /><input id="__tabbed_8_4" name="__tabbed_8" type="radio" /><input id="__tabbed_8_5" name="__tabbed_8" type="radio" /><input id="__tabbed_8_6" name="__tabbed_8" type="radio" /><input id="__tabbed_8_7" name="__tabbed_8" type="radio" /><input id="__tabbed_8_8" name="__tabbed_8" type="radio" /><input id="__tabbed_8_9" name="__tabbed_8" type="radio" /><input id="__tabbed_8_10" name="__tabbed_8" type="radio" /><input id="__tabbed_8_11" name="__tabbed_8" type="radio" /><input id="__tabbed_8_12" name="__tabbed_8" type="radio" /><input id="__tabbed_8_13" name="__tabbed_8" type="radio" /><input id="__tabbed_8_14" name="__tabbed_8" type="radio" /><div class="tabbed-labels"><label for="__tabbed_8_1">Python</label><label for="__tabbed_8_2">C++</label><label for="__tabbed_8_3">Java</label><label for="__tabbed_8_4">C#</label><label for="__tabbed_8_5">Go</label><label for="__tabbed_8_6">Swift</label><label for="__tabbed_8_7">JS</label><label for="__tabbed_8_8">TS</label><label for="__tabbed_8_9">Dart</label><label for="__tabbed_8_10">Rust</label><label for="__tabbed_8_11">C</label><label for="__tabbed_8_12">Kotlin</label><label for="__tabbed_8_13">Ruby</label><label for="__tabbed_8_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change_ii.py</span><pre><span></span><code><a id="__codelineno-70-1" name="__codelineno-70-1" href="#__codelineno-70-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">coin_change_ii_dp_comp</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">amt</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-70-2" name="__codelineno-70-2" href="#__codelineno-70-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;硬貨交換 II：空間最適化動的プログラミング&quot;&quot;&quot;</span>
+<a id="__codelineno-70-3" name="__codelineno-70-3" href="#__codelineno-70-3"></a>    <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">coins</span><span class="p">)</span>
+<a id="__codelineno-70-4" name="__codelineno-70-4" href="#__codelineno-70-4"></a>    <span class="c1"># dp テーブルを初期化</span>
+<a id="__codelineno-70-5" name="__codelineno-70-5" href="#__codelineno-70-5"></a>    <span class="n">dp</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="n">amt</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-70-6" name="__codelineno-70-6" href="#__codelineno-70-6"></a>    <span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span>
+<a id="__codelineno-70-7" name="__codelineno-70-7" href="#__codelineno-70-7"></a>    <span class="c1"># 状態遷移</span>
+<a id="__codelineno-70-8" name="__codelineno-70-8" href="#__codelineno-70-8"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">n</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-70-9" name="__codelineno-70-9" href="#__codelineno-70-9"></a>        <span class="c1"># 順序で走査</span>
+<a id="__codelineno-70-10" name="__codelineno-70-10" href="#__codelineno-70-10"></a>        <span class="k">for</span> <span class="n">a</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="n">amt</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-70-11" name="__codelineno-70-11" href="#__codelineno-70-11"></a>            <span class="k">if</span> <span class="n">coins</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">a</span><span class="p">:</span>
+<a id="__codelineno-70-12" name="__codelineno-70-12" href="#__codelineno-70-12"></a>                <span class="c1"># 目標金額を超える場合、硬貨 i を選択しない</span>
+<a id="__codelineno-70-13" name="__codelineno-70-13" href="#__codelineno-70-13"></a>                <span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span> <span class="o">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span>
+<a id="__codelineno-70-14" name="__codelineno-70-14" href="#__codelineno-70-14"></a>            <span class="k">else</span><span class="p">:</span>
+<a id="__codelineno-70-15" name="__codelineno-70-15" href="#__codelineno-70-15"></a>                <span class="c1"># 硬貨 i を選択しないのと選択するのとの両方の選択肢の和</span>
+<a id="__codelineno-70-16" name="__codelineno-70-16" href="#__codelineno-70-16"></a>                <span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span> <span class="o">=</span> <span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span> <span class="o">+</span> <span class="n">dp</span><span class="p">[</span><span class="n">a</span> <span class="o">-</span> <span class="n">coins</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]]</span>
+<a id="__codelineno-70-17" name="__codelineno-70-17" href="#__codelineno-70-17"></a>    <span class="k">return</span> <span class="n">dp</span><span class="p">[</span><span class="n">amt</span><span class="p">]</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change_ii.cpp</span><pre><span></span><code><a id="__codelineno-71-1" name="__codelineno-71-1" href="#__codelineno-71-1"></a><span class="cm">/* 硬貨両替 II：空間最適化動的プログラミング */</span>
+<a id="__codelineno-71-2" name="__codelineno-71-2" href="#__codelineno-71-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">coinChangeIIDPComp</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-71-3" name="__codelineno-71-3" href="#__codelineno-71-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
+<a id="__codelineno-71-4" name="__codelineno-71-4" href="#__codelineno-71-4"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化</span>
+<a id="__codelineno-71-5" name="__codelineno-71-5" href="#__codelineno-71-5"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">dp</span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-71-6" name="__codelineno-71-6" href="#__codelineno-71-6"></a><span class="w">    </span><span class="n">dp</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-71-7" name="__codelineno-71-7" href="#__codelineno-71-7"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-71-8" name="__codelineno-71-8" href="#__codelineno-71-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-71-9" name="__codelineno-71-9" href="#__codelineno-71-9"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">amt</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-71-10" name="__codelineno-71-10" href="#__codelineno-71-10"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-71-11" name="__codelineno-71-11" href="#__codelineno-71-11"></a><span class="w">                </span><span class="c1">// 目標金額を超える場合、硬貨 i を選択しない</span>
+<a id="__codelineno-71-12" name="__codelineno-71-12" href="#__codelineno-71-12"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">];</span>
+<a id="__codelineno-71-13" name="__codelineno-71-13" href="#__codelineno-71-13"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-71-14" name="__codelineno-71-14" href="#__codelineno-71-14"></a><span class="w">                </span><span class="c1">// 選択しない場合と硬貨 i を選択する場合の2つの選択肢の合計</span>
+<a id="__codelineno-71-15" name="__codelineno-71-15" href="#__codelineno-71-15"></a><span class="w">                </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]];</span>
+<a id="__codelineno-71-16" name="__codelineno-71-16" href="#__codelineno-71-16"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-71-17" name="__codelineno-71-17" href="#__codelineno-71-17"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-71-18" name="__codelineno-71-18" href="#__codelineno-71-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-71-19" name="__codelineno-71-19" href="#__codelineno-71-19"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="p">[</span><span class="n">amt</span><span class="p">];</span>
+<a id="__codelineno-71-20" name="__codelineno-71-20" href="#__codelineno-71-20"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change_ii.java</span><pre><span></span><code><a id="__codelineno-72-1" name="__codelineno-72-1" href="#__codelineno-72-1"></a><span class="cm">/* 硬貨両替 II：空間最適化動的プログラミング */</span>
+<a id="__codelineno-72-2" name="__codelineno-72-2" href="#__codelineno-72-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">coinChangeIIDPComp</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-72-3" name="__codelineno-72-3" href="#__codelineno-72-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="na">length</span><span class="p">;</span>
+<a id="__codelineno-72-4" name="__codelineno-72-4" href="#__codelineno-72-4"></a><span class="w">    </span><span class="c1">// DPテーブルを初期化</span>
+<a id="__codelineno-72-5" name="__codelineno-72-5" href="#__codelineno-72-5"></a><span class="w">    </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">dp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">amt</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-72-6" name="__codelineno-72-6" href="#__codelineno-72-6"></a><span class="w">    </span><span class="n">dp</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-72-7" name="__codelineno-72-7" href="#__codelineno-72-7"></a><span class="w">    </span><span class="c1">// 状態遷移</span>
+<a id="__codelineno-72-8" name="__codelineno-72-8" href="#__codelineno-72-8"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-72-9" name="__codelineno-72-9" href="#__codelineno-72-9"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">amt</span><span class="p">;</span><span class="w"> </span><span class="n">a</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-72-10" name="__codelineno-72-10" href="#__codelineno-72-10"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-72-11" name="__codelineno-72-11" href="#__codelineno-72-11"></a><span class="w">                </span><span class="c1">// 目標金額を超える場合、硬貨 i を選択しない</span>
+<a id="__codelineno-72-12" name="__codelineno-72-12" href="#__codelineno-72-12"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-72-13" name="__codelineno-72-13" href="#__codelineno-72-13"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-72-14" name="__codelineno-72-14" href="#__codelineno-72-14"></a><span class="w">                </span><span class="c1">// 選択しない場合と硬貨 i を選択する場合の2つの選択肢の合計</span>
+<a id="__codelineno-72-15" name="__codelineno-72-15" href="#__codelineno-72-15"></a><span class="w">                </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]]</span><span class="p">;</span>
+<a id="__codelineno-72-16" name="__codelineno-72-16" href="#__codelineno-72-16"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-72-17" name="__codelineno-72-17" href="#__codelineno-72-17"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-72-18" name="__codelineno-72-18" href="#__codelineno-72-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-72-19" name="__codelineno-72-19" href="#__codelineno-72-19"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">dp</span><span class="o">[</span><span class="n">amt</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-72-20" name="__codelineno-72-20" href="#__codelineno-72-20"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change_ii.cs</span><pre><span></span><code><a id="__codelineno-73-1" name="__codelineno-73-1" href="#__codelineno-73-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">coin_change_ii</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">CoinChangeIIDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change_ii.go</span><pre><span></span><code><a id="__codelineno-74-1" name="__codelineno-74-1" href="#__codelineno-74-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">coinChangeIIDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change_ii.swift</span><pre><span></span><code><a id="__codelineno-75-1" name="__codelineno-75-1" href="#__codelineno-75-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">coinChangeIIDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change_ii.js</span><pre><span></span><code><a id="__codelineno-76-1" name="__codelineno-76-1" href="#__codelineno-76-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">coinChangeIIDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change_ii.ts</span><pre><span></span><code><a id="__codelineno-77-1" name="__codelineno-77-1" href="#__codelineno-77-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">coinChangeIIDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change_ii.dart</span><pre><span></span><code><a id="__codelineno-78-1" name="__codelineno-78-1" href="#__codelineno-78-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">coinChangeIIDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change_ii.rs</span><pre><span></span><code><a id="__codelineno-79-1" name="__codelineno-79-1" href="#__codelineno-79-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">coin_change_ii_dp_comp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change_ii.c</span><pre><span></span><code><a id="__codelineno-80-1" name="__codelineno-80-1" href="#__codelineno-80-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">coinChangeIIDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change_ii.kt</span><pre><span></span><code><a id="__codelineno-81-1" name="__codelineno-81-1" href="#__codelineno-81-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">coinChangeIIDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change_ii.rb</span><pre><span></span><code><a id="__codelineno-82-1" name="__codelineno-82-1" href="#__codelineno-82-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">coin_change_ii_dp_comp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change_ii.zig</span><pre><span></span><code><a id="__codelineno-83-1" name="__codelineno-83-1" href="#__codelineno-83-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">coinChangeIIDPComp</span><span class="p">}</span>
+</code></pre></div>
+</div>
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index 000000000..6569d18c0
--- /dev/null
+++ b/ja/chapter_graph/graph/index.html
@@ -0,0 +1,4006 @@
+
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+<html lang="ja" class="no-js">
+  <head>
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+      <meta name="viewport" content="width=device-width,initial-scale=1">
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+        <meta name="description" content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル">
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+      <meta name="generator" content="mkdocs-1.5.3, mkdocs-material-9.5.5">
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+        <title>9.1   グラフ - Hello アルゴリズム</title>
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+    .gslide-title { margin-top: 0px; user-select: text; }
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+    .gdesc-inner { font-size: 0.75rem; }
+    body[data-md-color-scheme="slate"] .gdesc-inner { background: var(--md-default-bg-color);}
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+</div>
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+        <div class="md-header__topic" data-md-component="header-topic">
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+            
+              9.1 &nbsp; グラフ
+            
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+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#911" class="md-nav__link">
+    <span class="md-ellipsis">
+      9.1.1 &nbsp; グラフの一般的な種類と用語
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#912" class="md-nav__link">
+    <span class="md-ellipsis">
+      9.1.2 &nbsp; グラフの表現
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="9.1.2   グラフの表現">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 隣接行列
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; 隣接リスト
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#913" class="md-nav__link">
+    <span class="md-ellipsis">
+      9.1.3 &nbsp; グラフの一般的な応用
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
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+    <span class="md-ellipsis">
+      9.1.1 &nbsp; グラフの一般的な種類と用語
+    </span>
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+    </span>
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+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
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+<h1 id="91">9.1 &nbsp; グラフ<a class="headerlink" href="#91" title="Permanent link">&para;</a></h1>
+<p><u>グラフ</u>は非線形データ構造の一種で、<u>頂点</u>と<u>辺</u>で構成されます。グラフ<span class="arithmatex">\(G\)</span>は、頂点の集合<span class="arithmatex">\(V\)</span>と辺の集合<span class="arithmatex">\(E\)</span>の組み合わせとして抽象的に表現できます。以下の例は、5つの頂点と7つの辺を含むグラフを示しています。</p>
+<div class="arithmatex">\[
+\begin{aligned}
+V &amp; = \{ 1, 2, 3, 4, 5 \} \newline
+E &amp; = \{ (1,2), (1,3), (1,5), (2,3), (2,4), (2,5), (4,5) \} \newline
+G &amp; = \{ V, E \} \newline
+\end{aligned}
+\]</div>
+<p>頂点をノード、辺をノードを接続する参照（ポインタ）と見なすと、グラフは連結リストから拡張されたデータ構造として見ることができます。下図に示すように、<strong>線形関係（連結リスト）や分割統治関係（木）と比較して、ネットワーク関係（グラフ）は自由度が高いため、より複雑です</strong>。</p>
+<p><a class="glightbox" href="../graph.assets/linkedlist_tree_graph.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="連結リスト、木、グラフの関係" class="animation-figure" src="../graph.assets/linkedlist_tree_graph.png" /></a></p>
+<p align="center"> 図 9-1 &nbsp; 連結リスト、木、グラフの関係 </p>
+
+<h2 id="911">9.1.1 &nbsp; グラフの一般的な種類と用語<a class="headerlink" href="#911" title="Permanent link">&para;</a></h2>
+<p>グラフは、辺に方向があるかどうかによって<u>無向グラフ</u>と<u>有向グラフ</u>に分けることができます（下図参照）。</p>
+<ul>
+<li>無向グラフでは、辺は2つの頂点間の「双方向」接続を表します。例えば、Facebookの「友達」関係です。</li>
+<li>有向グラフでは、辺に方向性があります。つまり、辺<span class="arithmatex">\(A \rightarrow B\)</span>と<span class="arithmatex">\(A \leftarrow B\)</span>は互いに独立しています。例えば、InstagramやTikTokの「フォロー」と「フォロワー」の関係です。</li>
+</ul>
+<p><a class="glightbox" href="../graph.assets/directed_graph.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="有向グラフと無向グラフ" class="animation-figure" src="../graph.assets/directed_graph.png" /></a></p>
+<p align="center"> 図 9-2 &nbsp; 有向グラフと無向グラフ </p>
+
+<p>すべての頂点が接続されているかどうかによって、グラフは<u>連結グラフ</u>と<u>非連結グラフ</u>に分けることができます（下図参照）。</p>
+<ul>
+<li>連結グラフでは、任意の頂点から開始して他の任意の頂点に到達することが可能です。</li>
+<li>非連結グラフでは、任意の開始頂点から到達できない頂点が少なくとも1つ存在します。</li>
+</ul>
+<p><a class="glightbox" href="../graph.assets/connected_graph.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="連結グラフと非連結グラフ" class="animation-figure" src="../graph.assets/connected_graph.png" /></a></p>
+<p align="center"> 図 9-3 &nbsp; 連結グラフと非連結グラフ </p>
+
+<p>辺に重み変数を追加することもでき、その結果として<u>重み付きグラフ</u>が生まれます（下図参照）。例えば、Instagramでは、システムがあなたと他のユーザーとの間の相互作用レベル（いいね、閲覧、コメントなど）によってフォロワーとフォロー中のリストをソートします。このような相互作用ネットワークは重み付きグラフで表現できます。</p>
+<p><a class="glightbox" href="../graph.assets/weighted_graph.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="重み付きグラフと重みなしグラフ" class="animation-figure" src="../graph.assets/weighted_graph.png" /></a></p>
+<p align="center"> 図 9-4 &nbsp; 重み付きグラフと重みなしグラフ </p>
+
+<p>グラフデータ構造には、以下のような一般的に使用される用語があります。</p>
+<ul>
+<li><u>隣接</u>：2つの頂点を接続する辺がある場合、これら2つの頂点は「隣接」していると言われます。上図では、頂点1の隣接頂点は頂点2、3、5です。</li>
+<li><u>パス</u>：頂点Aから頂点Bまでに通過する辺のシーケンスを、AからBへのパスと呼びます。上図では、辺のシーケンス1-5-2-4は頂点1から頂点4へのパスです。</li>
+<li><u>次数</u>：頂点が持つ辺の数です。有向グラフの場合、<u>入次数</u>はその頂点を指す辺の数、<u>出次数</u>はその頂点から出る辺の数を指します。</li>
+</ul>
+<h2 id="912">9.1.2 &nbsp; グラフの表現<a class="headerlink" href="#912" title="Permanent link">&para;</a></h2>
+<p>グラフの一般的な表現には「隣接行列」と「隣接リスト」があります。以下の例では無向グラフを使用します。</p>
+<h3 id="1">1. &nbsp; 隣接行列<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<p>グラフの頂点数を<span class="arithmatex">\(n\)</span>とすると、<u>隣接行列</u>は<span class="arithmatex">\(n \times n\)</span>の行列を使用してグラフを表現します。各行（列）は頂点を表し、行列要素は辺を表し、2つの頂点間に辺があるかどうかを<span class="arithmatex">\(1\)</span>または<span class="arithmatex">\(0\)</span>で示します。</p>
+<p>下図に示すように、隣接行列を<span class="arithmatex">\(M\)</span>、頂点のリストを<span class="arithmatex">\(V\)</span>とすると、行列要素<span class="arithmatex">\(M[i, j] = 1\)</span>は頂点<span class="arithmatex">\(V[i]\)</span>と頂点<span class="arithmatex">\(V[j]\)</span>の間に辺があることを示し、逆に<span class="arithmatex">\(M[i, j] = 0\)</span>は2つの頂点間に辺がないことを示します。</p>
+<p><a class="glightbox" href="../graph.assets/adjacency_matrix.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="隣接行列によるグラフの表現" class="animation-figure" src="../graph.assets/adjacency_matrix.png" /></a></p>
+<p align="center"> 図 9-5 &nbsp; 隣接行列によるグラフの表現 </p>
+
+<p>隣接行列には以下の特性があります。</p>
+<ul>
+<li>頂点は自分自身に接続することはできないため、隣接行列の主対角線上の要素は意味がありません。</li>
+<li>無向グラフの場合、両方向の辺は等価であるため、隣接行列は主対角線に関して対称です。</li>
+<li>隣接行列の要素を<span class="arithmatex">\(1\)</span>と<span class="arithmatex">\(0\)</span>から重みに置き換えることで、重み付きグラフを表現できます。</li>
+</ul>
+<p>隣接行列でグラフを表現する場合、行列要素に直接アクセスして辺を取得できるため、追加、削除、検索、変更の操作が効率的で、すべて時間計算量<span class="arithmatex">\(O(1)\)</span>です。ただし、行列の空間計算量は<span class="arithmatex">\(O(n^2)\)</span>で、より多くのメモリを消費します。</p>
+<h3 id="2">2. &nbsp; 隣接リスト<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
+<p><u>隣接リスト</u>は<span class="arithmatex">\(n\)</span>個の連結リストを使用してグラフを表現し、各連結リストノードは頂点を表します。<span class="arithmatex">\(i\)</span>番目の連結リストは頂点<span class="arithmatex">\(i\)</span>に対応し、すべての隣接頂点（その頂点に接続された頂点）を含みます。下図は隣接リストを使用して格納されたグラフの例を示しています。</p>
+<p><a class="glightbox" href="../graph.assets/adjacency_list.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="隣接リストによるグラフの表現" class="animation-figure" src="../graph.assets/adjacency_list.png" /></a></p>
+<p align="center"> 図 9-6 &nbsp; 隣接リストによるグラフの表現 </p>
+
+<p>隣接リストは実際の辺のみを格納し、辺の総数は<span class="arithmatex">\(n^2\)</span>よりもはるかに少ないことが多く、より空間効率的です。ただし、隣接リストで辺を見つけるには連結リストを走査する必要があるため、その時間効率は隣接行列ほど良くありません。</p>
+<p>上図を観察すると、<strong>隣接リストの構造はハッシュテーブルの「チェイン法」と非常に似ているため、同様の方法を使用して効率を最適化できます</strong>。例えば、連結リストが長い場合、それをAVL木や赤黒木に変換して、時間効率を<span class="arithmatex">\(O(n)\)</span>から<span class="arithmatex">\(O(\log n)\)</span>に最適化できます。連結リストをハッシュテーブルに変換することで、時間計算量を<span class="arithmatex">\(O(1)\)</span>に削減することもできます。</p>
+<h2 id="913">9.1.3 &nbsp; グラフの一般的な応用<a class="headerlink" href="#913" title="Permanent link">&para;</a></h2>
+<p>下表に示すように、多くの現実世界のシステムはグラフでモデル化でき、対応する問題はグラフ計算問題に削減できます。</p>
+<p align="center"> 表 9-1 &nbsp; 現実生活の一般的なグラフ </p>
+
+<div class="center-table">
+<table>
+<thead>
+<tr>
+<th></th>
+<th>頂点</th>
+<th>辺</th>
+<th>グラフ計算問題</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td>ソーシャルネットワーク</td>
+<td>ユーザー</td>
+<td>フォロー / フォロワー関係</td>
+<td>潜在的フォロー推薦</td>
+</tr>
+<tr>
+<td>地下鉄路線</td>
+<td>駅</td>
+<td>駅間の接続性</td>
+<td>最短ルート推薦</td>
+</tr>
+<tr>
+<td>太陽系</td>
+<td>天体</td>
+<td>天体間の重力</td>
+<td>惑星軌道計算</td>
+</tr>
+</tbody>
+</table>
+</div>
+
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diff --git a/ja/chapter_graph/graph_operations.assets/adjacency_list_step4_add_vertex.png b/ja/chapter_graph/graph_operations.assets/adjacency_list_step4_add_vertex.png
new file mode 100644
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+      <a href="../../chapter_preface/summary/" class="md-nav__link">
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+  
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+    第 1 章 &nbsp; アルゴリズムとの出会い
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+  
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+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
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+    1.3 &nbsp; まとめ
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+        
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+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
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+            第 2 章 &nbsp; 計算量解析
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+    2.1 &nbsp; アルゴリズム効率評価
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+    2.2 &nbsp; 反復と再帰
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+  
+
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+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
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+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
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+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
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+    </li>
+  
+
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+  
+  
+  
+  
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+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
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+  
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+    第 3 章 &nbsp; データ構造
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#921" class="md-nav__link">
+    <span class="md-ellipsis">
+      9.2.1 &nbsp; 隣接行列に基づく実装
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#922" class="md-nav__link">
+    <span class="md-ellipsis">
+      9.2.2 &nbsp; 隣接リストに基づく実装
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#923" class="md-nav__link">
+    <span class="md-ellipsis">
+      9.2.3 &nbsp; 効率の比較
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_19" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_reference/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9 3v15h3V3H9m3 2 4 13 3-1-4-13-3 1M5 5v13h3V5H5M3 19v2h18v-2H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    参考文献
+  </span>
+  
+
+            </a>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_19_label" aria-expanded="false">
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+            参考文献
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+        </nav>
+      
+    </li>
+  
+
+    
+  </ul>
+</nav>
+                  </div>
+                </div>
+              </div>
+            
+            
+              
+              <div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
+                <div class="md-sidebar__scrollwrap">
+                  <div class="md-sidebar__inner">
+                    
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+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
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+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#921" class="md-nav__link">
+    <span class="md-ellipsis">
+      9.2.1 &nbsp; 隣接行列に基づく実装
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#922" class="md-nav__link">
+    <span class="md-ellipsis">
+      9.2.2 &nbsp; 隣接リストに基づく実装
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#923" class="md-nav__link">
+    <span class="md-ellipsis">
+      9.2.3 &nbsp; 効率の比較
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
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+</nav>
+                  </div>
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+      href="https://github.com/krahets/hello-algo/tree/main/ja/docs/chapter_graph/graph_operations.md"
+      title="編集"
+      class="md-content__button md-icon"
+    >
+      
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
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+<!-- Page content -->
+<h1 id="92">9.2 &nbsp; グラフの基本操作<a class="headerlink" href="#92" title="Permanent link">&para;</a></h1>
+<p>グラフの基本操作は「辺」に対する操作と「頂点」に対する操作に分けることができます。「隣接行列」と「隣接リスト」の2つの表現方法の下では、実装が異なります。</p>
+<h2 id="921">9.2.1 &nbsp; 隣接行列に基づく実装<a class="headerlink" href="#921" title="Permanent link">&para;</a></h2>
+<p><span class="arithmatex">\(n\)</span>個の頂点を持つ無向グラフが与えられた場合、さまざまな操作は下図のように実装されます。</p>
+<ul>
+<li><strong>辺の追加または削除</strong>：隣接行列内の指定された辺を直接変更し、<span class="arithmatex">\(O(1)\)</span>時間を使用します。無向グラフであるため、両方向の辺を同時に更新する必要があります。</li>
+<li><strong>頂点の追加</strong>：隣接行列の末尾に行と列を追加し、すべて<span class="arithmatex">\(0\)</span>で埋めます。<span class="arithmatex">\(O(n)\)</span>時間を使用します。</li>
+<li><strong>頂点の削除</strong>：隣接行列内の行と列を削除します。最悪の場合は最初の行と列が削除されるときで、<span class="arithmatex">\((n-1)^2\)</span>個の要素を「上と左に移動」する必要があり、<span class="arithmatex">\(O(n^2)\)</span>時間を使用します。</li>
+<li><strong>初期化</strong>：<span class="arithmatex">\(n\)</span>個の頂点を渡し、長さ<span class="arithmatex">\(n\)</span>の頂点リスト<code>vertices</code>を初期化し、<span class="arithmatex">\(O(n)\)</span>時間を使用します。<span class="arithmatex">\(n \times n\)</span>サイズの隣接行列<code>adjMat</code>を初期化し、<span class="arithmatex">\(O(n^2)\)</span>時間を使用します。</li>
+</ul>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:5"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">隣接行列の初期化</label><label for="__tabbed_1_2">辺の追加</label><label for="__tabbed_1_3">辺の削除</label><label for="__tabbed_1_4">頂点の追加</label><label for="__tabbed_1_5">頂点の削除</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<p><a class="glightbox" href="../graph_operations.assets/adjacency_matrix_step1_initialization.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="隣接行列での初期化、辺の追加と削除、頂点の追加と削除" class="animation-figure" src="../graph_operations.assets/adjacency_matrix_step1_initialization.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../graph_operations.assets/adjacency_matrix_step2_add_edge.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="adjacency_matrix_add_edge" class="animation-figure" src="../graph_operations.assets/adjacency_matrix_step2_add_edge.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../graph_operations.assets/adjacency_matrix_step3_remove_edge.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="adjacency_matrix_remove_edge" class="animation-figure" src="../graph_operations.assets/adjacency_matrix_step3_remove_edge.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../graph_operations.assets/adjacency_matrix_step4_add_vertex.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="adjacency_matrix_add_vertex" class="animation-figure" src="../graph_operations.assets/adjacency_matrix_step4_add_vertex.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../graph_operations.assets/adjacency_matrix_step5_remove_vertex.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="adjacency_matrix_remove_vertex" class="animation-figure" src="../graph_operations.assets/adjacency_matrix_step5_remove_vertex.png" /></a></p>
+</div>
+</div>
+</div>
+<p align="center"> 図 9-7 &nbsp; 隣接行列での初期化、辺の追加と削除、頂点の追加と削除 </p>
+
+<p>以下は隣接行列を使用して表現されたグラフの実装コードです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:14"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><input id="__tabbed_2_14" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label><label for="__tabbed_2_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_adjacency_matrix.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">GraphAdjMat</span><span class="p">:</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;隣接行列に基づく無向グラフクラス&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">vertices</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">edges</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]]):</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;コンストラクタ&quot;&quot;&quot;</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>        <span class="c1"># 頂点リスト、要素は「頂点値」を表し、インデックスは「頂点インデックス」を表す</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">vertices</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="p">[]</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>        <span class="c1"># 隣接行列、行と列のインデックスは「頂点インデックス」に対応</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">adj_mat</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]]</span> <span class="o">=</span> <span class="p">[]</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>        <span class="c1"># 頂点を追加</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>        <span class="k">for</span> <span class="n">val</span> <span class="ow">in</span> <span class="n">vertices</span><span class="p">:</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">add_vertex</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>        <span class="c1"># 辺を追加</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>        <span class="c1"># edges要素は頂点インデックスを表す</span>
+<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>        <span class="k">for</span> <span class="n">e</span> <span class="ow">in</span> <span class="n">edges</span><span class="p">:</span>
+<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">add_edge</span><span class="p">(</span><span class="n">e</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">e</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
+<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>
+<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">size</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;頂点数を取得&quot;&quot;&quot;</span>
+<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a>        <span class="k">return</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">vertices</span><span class="p">)</span>
+<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a>
+<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">add_vertex</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;頂点を追加&quot;&quot;&quot;</span>
+<a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a>        <span class="n">n</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span>
+<a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a>        <span class="c1"># 頂点リストに新しい頂点値を追加</span>
+<a id="__codelineno-0-26" name="__codelineno-0-26" href="#__codelineno-0-26"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">vertices</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-0-27" name="__codelineno-0-27" href="#__codelineno-0-27"></a>        <span class="c1"># 隣接行列に行を追加</span>
+<a id="__codelineno-0-28" name="__codelineno-0-28" href="#__codelineno-0-28"></a>        <span class="n">new_row</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">n</span>
+<a id="__codelineno-0-29" name="__codelineno-0-29" href="#__codelineno-0-29"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">adj_mat</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">new_row</span><span class="p">)</span>
+<a id="__codelineno-0-30" name="__codelineno-0-30" href="#__codelineno-0-30"></a>        <span class="c1"># 隣接行列に列を追加</span>
+<a id="__codelineno-0-31" name="__codelineno-0-31" href="#__codelineno-0-31"></a>        <span class="k">for</span> <span class="n">row</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">adj_mat</span><span class="p">:</span>
+<a id="__codelineno-0-32" name="__codelineno-0-32" href="#__codelineno-0-32"></a>            <span class="n">row</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-0-33" name="__codelineno-0-33" href="#__codelineno-0-33"></a>
+<a id="__codelineno-0-34" name="__codelineno-0-34" href="#__codelineno-0-34"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">remove_vertex</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">index</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-0-35" name="__codelineno-0-35" href="#__codelineno-0-35"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;頂点を削除&quot;&quot;&quot;</span>
+<a id="__codelineno-0-36" name="__codelineno-0-36" href="#__codelineno-0-36"></a>        <span class="k">if</span> <span class="n">index</span> <span class="o">&gt;=</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">():</span>
+<a id="__codelineno-0-37" name="__codelineno-0-37" href="#__codelineno-0-37"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">()</span>
+<a id="__codelineno-0-38" name="__codelineno-0-38" href="#__codelineno-0-38"></a>        <span class="c1"># 頂点リストから`index`の頂点を削除</span>
+<a id="__codelineno-0-39" name="__codelineno-0-39" href="#__codelineno-0-39"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">vertices</span><span class="o">.</span><span class="n">pop</span><span class="p">(</span><span class="n">index</span><span class="p">)</span>
+<a id="__codelineno-0-40" name="__codelineno-0-40" href="#__codelineno-0-40"></a>        <span class="c1"># 隣接行列から`index`の行を削除</span>
+<a id="__codelineno-0-41" name="__codelineno-0-41" href="#__codelineno-0-41"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">adj_mat</span><span class="o">.</span><span class="n">pop</span><span class="p">(</span><span class="n">index</span><span class="p">)</span>
+<a id="__codelineno-0-42" name="__codelineno-0-42" href="#__codelineno-0-42"></a>        <span class="c1"># 隣接行列から`index`の列を削除</span>
+<a id="__codelineno-0-43" name="__codelineno-0-43" href="#__codelineno-0-43"></a>        <span class="k">for</span> <span class="n">row</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">adj_mat</span><span class="p">:</span>
+<a id="__codelineno-0-44" name="__codelineno-0-44" href="#__codelineno-0-44"></a>            <span class="n">row</span><span class="o">.</span><span class="n">pop</span><span class="p">(</span><span class="n">index</span><span class="p">)</span>
+<a id="__codelineno-0-45" name="__codelineno-0-45" href="#__codelineno-0-45"></a>
+<a id="__codelineno-0-46" name="__codelineno-0-46" href="#__codelineno-0-46"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">add_edge</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">j</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-0-47" name="__codelineno-0-47" href="#__codelineno-0-47"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;辺を追加&quot;&quot;&quot;</span>
+<a id="__codelineno-0-48" name="__codelineno-0-48" href="#__codelineno-0-48"></a>        <span class="c1"># パラメータi、jは頂点要素のインデックスに対応</span>
+<a id="__codelineno-0-49" name="__codelineno-0-49" href="#__codelineno-0-49"></a>        <span class="c1"># インデックスの範囲外と等価性を処理</span>
+<a id="__codelineno-0-50" name="__codelineno-0-50" href="#__codelineno-0-50"></a>        <span class="k">if</span> <span class="n">i</span> <span class="o">&lt;</span> <span class="mi">0</span> <span class="ow">or</span> <span class="n">j</span> <span class="o">&lt;</span> <span class="mi">0</span> <span class="ow">or</span> <span class="n">i</span> <span class="o">&gt;=</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span> <span class="ow">or</span> <span class="n">j</span> <span class="o">&gt;=</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span> <span class="ow">or</span> <span class="n">i</span> <span class="o">==</span> <span class="n">j</span><span class="p">:</span>
+<a id="__codelineno-0-51" name="__codelineno-0-51" href="#__codelineno-0-51"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">()</span>
+<a id="__codelineno-0-52" name="__codelineno-0-52" href="#__codelineno-0-52"></a>        <span class="c1"># 無向グラフでは、隣接行列は主対角線について対称、すなわち (i, j) == (j, i) を満たす</span>
+<a id="__codelineno-0-53" name="__codelineno-0-53" href="#__codelineno-0-53"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">adj_mat</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span>
+<a id="__codelineno-0-54" name="__codelineno-0-54" href="#__codelineno-0-54"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">adj_mat</span><span class="p">[</span><span class="n">j</span><span class="p">][</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span>
+<a id="__codelineno-0-55" name="__codelineno-0-55" href="#__codelineno-0-55"></a>
+<a id="__codelineno-0-56" name="__codelineno-0-56" href="#__codelineno-0-56"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">remove_edge</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">j</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-0-57" name="__codelineno-0-57" href="#__codelineno-0-57"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;辺を削除&quot;&quot;&quot;</span>
+<a id="__codelineno-0-58" name="__codelineno-0-58" href="#__codelineno-0-58"></a>        <span class="c1"># パラメータi、jは頂点要素のインデックスに対応</span>
+<a id="__codelineno-0-59" name="__codelineno-0-59" href="#__codelineno-0-59"></a>        <span class="c1"># インデックスの範囲外と等価性を処理</span>
+<a id="__codelineno-0-60" name="__codelineno-0-60" href="#__codelineno-0-60"></a>        <span class="k">if</span> <span class="n">i</span> <span class="o">&lt;</span> <span class="mi">0</span> <span class="ow">or</span> <span class="n">j</span> <span class="o">&lt;</span> <span class="mi">0</span> <span class="ow">or</span> <span class="n">i</span> <span class="o">&gt;=</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span> <span class="ow">or</span> <span class="n">j</span> <span class="o">&gt;=</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span> <span class="ow">or</span> <span class="n">i</span> <span class="o">==</span> <span class="n">j</span><span class="p">:</span>
+<a id="__codelineno-0-61" name="__codelineno-0-61" href="#__codelineno-0-61"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">()</span>
+<a id="__codelineno-0-62" name="__codelineno-0-62" href="#__codelineno-0-62"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">adj_mat</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-0-63" name="__codelineno-0-63" href="#__codelineno-0-63"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">adj_mat</span><span class="p">[</span><span class="n">j</span><span class="p">][</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-0-64" name="__codelineno-0-64" href="#__codelineno-0-64"></a>
+<a id="__codelineno-0-65" name="__codelineno-0-65" href="#__codelineno-0-65"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">print</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<a id="__codelineno-0-66" name="__codelineno-0-66" href="#__codelineno-0-66"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;隣接行列を出力&quot;&quot;&quot;</span>
+<a id="__codelineno-0-67" name="__codelineno-0-67" href="#__codelineno-0-67"></a>        <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;頂点リスト =&quot;</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">vertices</span><span class="p">)</span>
+<a id="__codelineno-0-68" name="__codelineno-0-68" href="#__codelineno-0-68"></a>        <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;隣接行列 =&quot;</span><span class="p">)</span>
+<a id="__codelineno-0-69" name="__codelineno-0-69" href="#__codelineno-0-69"></a>        <span class="n">print_matrix</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">adj_mat</span><span class="p">)</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_adjacency_matrix.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 隣接行列に基づく無向グラフクラス */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">GraphAdjMat</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">vertices</span><span class="p">;</span><span class="w">       </span><span class="c1">// 頂点リスト、要素は「頂点値」を表し、インデックスは「頂点インデックス」を表す</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">adjMat</span><span class="p">;</span><span class="w"> </span><span class="c1">// 隣接行列、行と列のインデックスは「頂点インデックス」に対応</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">  </span><span class="k">public</span><span class="o">:</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="n">GraphAdjMat</span><span class="p">(</span><span class="k">const</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">vertices</span><span class="p">,</span><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">edges</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">        </span><span class="c1">// 頂点を追加</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">vertices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">            </span><span class="n">addVertex</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">        </span><span class="c1">// 辺を追加</span>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">        </span><span class="c1">// 辺の要素は頂点インデックスを表す</span>
+<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="k">const</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">edge</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">edges</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">            </span><span class="n">addEdge</span><span class="p">(</span><span class="n">edge</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span><span class="w"> </span><span class="n">edge</span><span class="p">[</span><span class="mi">1</span><span class="p">]);</span>
+<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a>
+<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="w">    </span><span class="cm">/* 頂点数を取得 */</span>
+<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="k">const</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">vertices</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
+<a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a>
+<a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a><span class="w">    </span><span class="cm">/* 頂点を追加 */</span>
+<a id="__codelineno-1-26" name="__codelineno-1-26" href="#__codelineno-1-26"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">addVertex</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-27" name="__codelineno-1-27" href="#__codelineno-1-27"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">size</span><span class="p">();</span>
+<a id="__codelineno-1-28" name="__codelineno-1-28" href="#__codelineno-1-28"></a><span class="w">        </span><span class="c1">// 頂点リストに新しい頂点値を追加</span>
+<a id="__codelineno-1-29" name="__codelineno-1-29" href="#__codelineno-1-29"></a><span class="w">        </span><span class="n">vertices</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-1-30" name="__codelineno-1-30" href="#__codelineno-1-30"></a><span class="w">        </span><span class="c1">// 隣接行列に行を追加</span>
+<a id="__codelineno-1-31" name="__codelineno-1-31" href="#__codelineno-1-31"></a><span class="w">        </span><span class="n">adjMat</span><span class="p">.</span><span class="n">emplace_back</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">));</span>
+<a id="__codelineno-1-32" name="__codelineno-1-32" href="#__codelineno-1-32"></a><span class="w">        </span><span class="c1">// 隣接行列に列を追加</span>
+<a id="__codelineno-1-33" name="__codelineno-1-33" href="#__codelineno-1-33"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">row</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">adjMat</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-34" name="__codelineno-1-34" href="#__codelineno-1-34"></a><span class="w">            </span><span class="n">row</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-1-35" name="__codelineno-1-35" href="#__codelineno-1-35"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-1-36" name="__codelineno-1-36" href="#__codelineno-1-36"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-37" name="__codelineno-1-37" href="#__codelineno-1-37"></a>
+<a id="__codelineno-1-38" name="__codelineno-1-38" href="#__codelineno-1-38"></a><span class="w">    </span><span class="cm">/* 頂点を削除 */</span>
+<a id="__codelineno-1-39" name="__codelineno-1-39" href="#__codelineno-1-39"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">removeVertex</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-40" name="__codelineno-1-40" href="#__codelineno-1-40"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-41" name="__codelineno-1-41" href="#__codelineno-1-41"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;Vertex does not exist&quot;</span><span class="p">);</span>
+<a id="__codelineno-1-42" name="__codelineno-1-42" href="#__codelineno-1-42"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-1-43" name="__codelineno-1-43" href="#__codelineno-1-43"></a><span class="w">        </span><span class="c1">// 頂点リストから`index`の頂点を削除</span>
+<a id="__codelineno-1-44" name="__codelineno-1-44" href="#__codelineno-1-44"></a><span class="w">        </span><span class="n">vertices</span><span class="p">.</span><span class="n">erase</span><span class="p">(</span><span class="n">vertices</span><span class="p">.</span><span class="n">begin</span><span class="p">()</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">index</span><span class="p">);</span>
+<a id="__codelineno-1-45" name="__codelineno-1-45" href="#__codelineno-1-45"></a><span class="w">        </span><span class="c1">// 隣接行列から`index`の行を削除</span>
+<a id="__codelineno-1-46" name="__codelineno-1-46" href="#__codelineno-1-46"></a><span class="w">        </span><span class="n">adjMat</span><span class="p">.</span><span class="n">erase</span><span class="p">(</span><span class="n">adjMat</span><span class="p">.</span><span class="n">begin</span><span class="p">()</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">index</span><span class="p">);</span>
+<a id="__codelineno-1-47" name="__codelineno-1-47" href="#__codelineno-1-47"></a><span class="w">        </span><span class="c1">// 隣接行列から`index`の列を削除</span>
+<a id="__codelineno-1-48" name="__codelineno-1-48" href="#__codelineno-1-48"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">row</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">adjMat</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-49" name="__codelineno-1-49" href="#__codelineno-1-49"></a><span class="w">            </span><span class="n">row</span><span class="p">.</span><span class="n">erase</span><span class="p">(</span><span class="n">row</span><span class="p">.</span><span class="n">begin</span><span class="p">()</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">index</span><span class="p">);</span>
+<a id="__codelineno-1-50" name="__codelineno-1-50" href="#__codelineno-1-50"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-1-51" name="__codelineno-1-51" href="#__codelineno-1-51"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-52" name="__codelineno-1-52" href="#__codelineno-1-52"></a>
+<a id="__codelineno-1-53" name="__codelineno-1-53" href="#__codelineno-1-53"></a><span class="w">    </span><span class="cm">/* 辺を追加 */</span>
+<a id="__codelineno-1-54" name="__codelineno-1-54" href="#__codelineno-1-54"></a><span class="w">    </span><span class="c1">// パラメータi、jは頂点要素のインデックスに対応</span>
+<a id="__codelineno-1-55" name="__codelineno-1-55" href="#__codelineno-1-55"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">addEdge</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-56" name="__codelineno-1-56" href="#__codelineno-1-56"></a><span class="w">        </span><span class="c1">// インデックス範囲外と等価性を処理</span>
+<a id="__codelineno-1-57" name="__codelineno-1-57" href="#__codelineno-1-57"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-58" name="__codelineno-1-58" href="#__codelineno-1-58"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;Vertex does not exist&quot;</span><span class="p">);</span>
+<a id="__codelineno-1-59" name="__codelineno-1-59" href="#__codelineno-1-59"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-1-60" name="__codelineno-1-60" href="#__codelineno-1-60"></a><span class="w">        </span><span class="c1">// 無向グラフでは、隣接行列は主対角線について対称、即ち(i, j) == (j, i)を満たす</span>
+<a id="__codelineno-1-61" name="__codelineno-1-61" href="#__codelineno-1-61"></a><span class="w">        </span><span class="n">adjMat</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-1-62" name="__codelineno-1-62" href="#__codelineno-1-62"></a><span class="w">        </span><span class="n">adjMat</span><span class="p">[</span><span class="n">j</span><span class="p">][</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-1-63" name="__codelineno-1-63" href="#__codelineno-1-63"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-64" name="__codelineno-1-64" href="#__codelineno-1-64"></a>
+<a id="__codelineno-1-65" name="__codelineno-1-65" href="#__codelineno-1-65"></a><span class="w">    </span><span class="cm">/* 辺を削除 */</span>
+<a id="__codelineno-1-66" name="__codelineno-1-66" href="#__codelineno-1-66"></a><span class="w">    </span><span class="c1">// パラメータi、jは頂点要素のインデックスに対応</span>
+<a id="__codelineno-1-67" name="__codelineno-1-67" href="#__codelineno-1-67"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">removeEdge</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-68" name="__codelineno-1-68" href="#__codelineno-1-68"></a><span class="w">        </span><span class="c1">// インデックス範囲外と等価性を処理</span>
+<a id="__codelineno-1-69" name="__codelineno-1-69" href="#__codelineno-1-69"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-70" name="__codelineno-1-70" href="#__codelineno-1-70"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;Vertex does not exist&quot;</span><span class="p">);</span>
+<a id="__codelineno-1-71" name="__codelineno-1-71" href="#__codelineno-1-71"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-1-72" name="__codelineno-1-72" href="#__codelineno-1-72"></a><span class="w">        </span><span class="n">adjMat</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-1-73" name="__codelineno-1-73" href="#__codelineno-1-73"></a><span class="w">        </span><span class="n">adjMat</span><span class="p">[</span><span class="n">j</span><span class="p">][</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-1-74" name="__codelineno-1-74" href="#__codelineno-1-74"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-75" name="__codelineno-1-75" href="#__codelineno-1-75"></a>
+<a id="__codelineno-1-76" name="__codelineno-1-76" href="#__codelineno-1-76"></a><span class="w">    </span><span class="cm">/* 隣接行列を印刷 */</span>
+<a id="__codelineno-1-77" name="__codelineno-1-77" href="#__codelineno-1-77"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-78" name="__codelineno-1-78" href="#__codelineno-1-78"></a><span class="w">        </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;頂点リスト = &quot;</span><span class="p">;</span>
+<a id="__codelineno-1-79" name="__codelineno-1-79" href="#__codelineno-1-79"></a><span class="w">        </span><span class="n">printVector</span><span class="p">(</span><span class="n">vertices</span><span class="p">);</span>
+<a id="__codelineno-1-80" name="__codelineno-1-80" href="#__codelineno-1-80"></a><span class="w">        </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;隣接行列 =&quot;</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
+<a id="__codelineno-1-81" name="__codelineno-1-81" href="#__codelineno-1-81"></a><span class="w">        </span><span class="n">printVectorMatrix</span><span class="p">(</span><span class="n">adjMat</span><span class="p">);</span>
+<a id="__codelineno-1-82" name="__codelineno-1-82" href="#__codelineno-1-82"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-83" name="__codelineno-1-83" href="#__codelineno-1-83"></a><span class="p">};</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_adjacency_matrix.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 隣接行列に基づく無向グラフクラス */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kd">class</span> <span class="nc">GraphAdjMat</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">vertices</span><span class="p">;</span><span class="w"> </span><span class="c1">// 頂点リスト、要素は「頂点値」を表し、インデックスは「頂点インデックス」を表す</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">adjMat</span><span class="p">;</span><span class="w"> </span><span class="c1">// 隣接行列、行と列のインデックスは「頂点インデックス」に対応</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="nf">GraphAdjMat</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">vertices</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">[][]</span><span class="w"> </span><span class="n">edges</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="na">vertices</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="na">adjMat</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">        </span><span class="c1">// 頂点を追加</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">vertices</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">            </span><span class="n">addVertex</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">        </span><span class="c1">// 辺を追加</span>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">        </span><span class="c1">// 辺の要素は頂点インデックスを表す</span>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">e</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">edges</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w">            </span><span class="n">addEdge</span><span class="p">(</span><span class="n">e</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">e</span><span class="o">[</span><span class="mi">1</span><span class="o">]</span><span class="p">);</span>
+<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a>
+<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="w">    </span><span class="cm">/* 頂点数を取得 */</span>
+<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">vertices</span><span class="p">.</span><span class="na">size</span><span class="p">();</span>
+<a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a>
+<a id="__codelineno-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></a><span class="w">    </span><span class="cm">/* 頂点を追加 */</span>
+<a id="__codelineno-2-27" name="__codelineno-2-27" href="#__codelineno-2-27"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">addVertex</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-28" name="__codelineno-2-28" href="#__codelineno-2-28"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">size</span><span class="p">();</span>
+<a id="__codelineno-2-29" name="__codelineno-2-29" href="#__codelineno-2-29"></a><span class="w">        </span><span class="c1">// 頂点リストに新しい頂点値を追加</span>
+<a id="__codelineno-2-30" name="__codelineno-2-30" href="#__codelineno-2-30"></a><span class="w">        </span><span class="n">vertices</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-2-31" name="__codelineno-2-31" href="#__codelineno-2-31"></a><span class="w">        </span><span class="c1">// 隣接行列に行を追加</span>
+<a id="__codelineno-2-32" name="__codelineno-2-32" href="#__codelineno-2-32"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">newRow</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">(</span><span class="n">n</span><span class="p">);</span>
+<a id="__codelineno-2-33" name="__codelineno-2-33" href="#__codelineno-2-33"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-34" name="__codelineno-2-34" href="#__codelineno-2-34"></a><span class="w">            </span><span class="n">newRow</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-2-35" name="__codelineno-2-35" href="#__codelineno-2-35"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-2-36" name="__codelineno-2-36" href="#__codelineno-2-36"></a><span class="w">        </span><span class="n">adjMat</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">newRow</span><span class="p">);</span>
+<a id="__codelineno-2-37" name="__codelineno-2-37" href="#__codelineno-2-37"></a><span class="w">        </span><span class="c1">// 隣接行列に列を追加</span>
+<a id="__codelineno-2-38" name="__codelineno-2-38" href="#__codelineno-2-38"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">row</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">adjMat</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-39" name="__codelineno-2-39" href="#__codelineno-2-39"></a><span class="w">            </span><span class="n">row</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-2-40" name="__codelineno-2-40" href="#__codelineno-2-40"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-2-41" name="__codelineno-2-41" href="#__codelineno-2-41"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-42" name="__codelineno-2-42" href="#__codelineno-2-42"></a>
+<a id="__codelineno-2-43" name="__codelineno-2-43" href="#__codelineno-2-43"></a><span class="w">    </span><span class="cm">/* 頂点を削除 */</span>
+<a id="__codelineno-2-44" name="__codelineno-2-44" href="#__codelineno-2-44"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">removeVertex</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-45" name="__codelineno-2-45" href="#__codelineno-2-45"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">())</span>
+<a id="__codelineno-2-46" name="__codelineno-2-46" href="#__codelineno-2-46"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">();</span>
+<a id="__codelineno-2-47" name="__codelineno-2-47" href="#__codelineno-2-47"></a><span class="w">        </span><span class="c1">// 頂点リストから `index` の頂点を削除</span>
+<a id="__codelineno-2-48" name="__codelineno-2-48" href="#__codelineno-2-48"></a><span class="w">        </span><span class="n">vertices</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">index</span><span class="p">);</span>
+<a id="__codelineno-2-49" name="__codelineno-2-49" href="#__codelineno-2-49"></a><span class="w">        </span><span class="c1">// 隣接行列から `index` の行を削除</span>
+<a id="__codelineno-2-50" name="__codelineno-2-50" href="#__codelineno-2-50"></a><span class="w">        </span><span class="n">adjMat</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">index</span><span class="p">);</span>
+<a id="__codelineno-2-51" name="__codelineno-2-51" href="#__codelineno-2-51"></a><span class="w">        </span><span class="c1">// 隣接行列から `index` の列を削除</span>
+<a id="__codelineno-2-52" name="__codelineno-2-52" href="#__codelineno-2-52"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">row</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">adjMat</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-53" name="__codelineno-2-53" href="#__codelineno-2-53"></a><span class="w">            </span><span class="n">row</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">index</span><span class="p">);</span>
+<a id="__codelineno-2-54" name="__codelineno-2-54" href="#__codelineno-2-54"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-2-55" name="__codelineno-2-55" href="#__codelineno-2-55"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-56" name="__codelineno-2-56" href="#__codelineno-2-56"></a>
+<a id="__codelineno-2-57" name="__codelineno-2-57" href="#__codelineno-2-57"></a><span class="w">    </span><span class="cm">/* 辺を追加 */</span>
+<a id="__codelineno-2-58" name="__codelineno-2-58" href="#__codelineno-2-58"></a><span class="w">    </span><span class="c1">// パラメータ i、j は頂点要素のインデックスに対応</span>
+<a id="__codelineno-2-59" name="__codelineno-2-59" href="#__codelineno-2-59"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">addEdge</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-60" name="__codelineno-2-60" href="#__codelineno-2-60"></a><span class="w">        </span><span class="c1">// インデックスの範囲外と等価性を処理</span>
+<a id="__codelineno-2-61" name="__codelineno-2-61" href="#__codelineno-2-61"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">j</span><span class="p">)</span>
+<a id="__codelineno-2-62" name="__codelineno-2-62" href="#__codelineno-2-62"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">();</span>
+<a id="__codelineno-2-63" name="__codelineno-2-63" href="#__codelineno-2-63"></a><span class="w">        </span><span class="c1">// 無向グラフでは、隣接行列は主対角線について対称、すなわち (i, j) == (j, i) を満たす</span>
+<a id="__codelineno-2-64" name="__codelineno-2-64" href="#__codelineno-2-64"></a><span class="w">        </span><span class="n">adjMat</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">i</span><span class="p">).</span><span class="na">set</span><span class="p">(</span><span class="n">j</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-2-65" name="__codelineno-2-65" href="#__codelineno-2-65"></a><span class="w">        </span><span class="n">adjMat</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">j</span><span class="p">).</span><span class="na">set</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-2-66" name="__codelineno-2-66" href="#__codelineno-2-66"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-67" name="__codelineno-2-67" href="#__codelineno-2-67"></a>
+<a id="__codelineno-2-68" name="__codelineno-2-68" href="#__codelineno-2-68"></a><span class="w">    </span><span class="cm">/* 辺を削除 */</span>
+<a id="__codelineno-2-69" name="__codelineno-2-69" href="#__codelineno-2-69"></a><span class="w">    </span><span class="c1">// パラメータ i、j は頂点要素のインデックスに対応</span>
+<a id="__codelineno-2-70" name="__codelineno-2-70" href="#__codelineno-2-70"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">removeEdge</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-71" name="__codelineno-2-71" href="#__codelineno-2-71"></a><span class="w">        </span><span class="c1">// インデックスの範囲外と等価性を処理</span>
+<a id="__codelineno-2-72" name="__codelineno-2-72" href="#__codelineno-2-72"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">j</span><span class="p">)</span>
+<a id="__codelineno-2-73" name="__codelineno-2-73" href="#__codelineno-2-73"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">();</span>
+<a id="__codelineno-2-74" name="__codelineno-2-74" href="#__codelineno-2-74"></a><span class="w">        </span><span class="n">adjMat</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">i</span><span class="p">).</span><span class="na">set</span><span class="p">(</span><span class="n">j</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-2-75" name="__codelineno-2-75" href="#__codelineno-2-75"></a><span class="w">        </span><span class="n">adjMat</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">j</span><span class="p">).</span><span class="na">set</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-2-76" name="__codelineno-2-76" href="#__codelineno-2-76"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-77" name="__codelineno-2-77" href="#__codelineno-2-77"></a>
+<a id="__codelineno-2-78" name="__codelineno-2-78" href="#__codelineno-2-78"></a><span class="w">    </span><span class="cm">/* 隣接行列を出力 */</span>
+<a id="__codelineno-2-79" name="__codelineno-2-79" href="#__codelineno-2-79"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-80" name="__codelineno-2-80" href="#__codelineno-2-80"></a><span class="w">        </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">print</span><span class="p">(</span><span class="s">&quot;頂点リスト = &quot;</span><span class="p">);</span>
+<a id="__codelineno-2-81" name="__codelineno-2-81" href="#__codelineno-2-81"></a><span class="w">        </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="n">vertices</span><span class="p">);</span>
+<a id="__codelineno-2-82" name="__codelineno-2-82" href="#__codelineno-2-82"></a><span class="w">        </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="s">&quot;隣接行列 =&quot;</span><span class="p">);</span>
+<a id="__codelineno-2-83" name="__codelineno-2-83" href="#__codelineno-2-83"></a><span class="w">        </span><span class="n">PrintUtil</span><span class="p">.</span><span class="na">printMatrix</span><span class="p">(</span><span class="n">adjMat</span><span class="p">);</span>
+<a id="__codelineno-2-84" name="__codelineno-2-84" href="#__codelineno-2-84"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-85" name="__codelineno-2-85" href="#__codelineno-2-85"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_adjacency_matrix.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">GraphAdjMat</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_adjacency_matrix.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">graphAdjMat</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_adjacency_matrix.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">GraphAdjMat</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_adjacency_matrix.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">GraphAdjMat</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_adjacency_matrix.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">GraphAdjMat</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_adjacency_matrix.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">GraphAdjMat</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_adjacency_matrix.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">GraphAdjMat</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_adjacency_matrix.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">GraphAdjMat</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_adjacency_matrix.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">GraphAdjMat</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_adjacency_matrix.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">GraphAdjMat</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_adjacency_matrix.zig</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">GraphAdjMat</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h2 id="922">9.2.2 &nbsp; 隣接リストに基づく実装<a class="headerlink" href="#922" title="Permanent link">&para;</a></h2>
+<p>総計<span class="arithmatex">\(n\)</span>個の頂点と<span class="arithmatex">\(m\)</span>個の辺を持つ無向グラフが与えられた場合、さまざまな操作は下図のように実装できます。</p>
+<ul>
+<li><strong>辺の追加</strong>：対応する頂点の連結リストの末尾に辺を追加するだけで、<span class="arithmatex">\(O(1)\)</span>時間を使用します。無向グラフであるため、両方向に同時に辺を追加する必要があります。</li>
+<li><strong>辺の削除</strong>：対応する頂点の連結リスト内で指定された辺を見つけて削除し、<span class="arithmatex">\(O(m)\)</span>時間を使用します。無向グラフでは、両方向の辺を同時に削除する必要があります。</li>
+<li><strong>頂点の追加</strong>：隣接リストに連結リストを追加し、新しい頂点をリストのヘッドノードにし、<span class="arithmatex">\(O(1)\)</span>時間を使用します。</li>
+<li><strong>頂点の削除</strong>：隣接リスト全体を走査し、指定された頂点を含むすべての辺を削除する必要があり、<span class="arithmatex">\(O(n + m)\)</span>時間を使用します。</li>
+<li><strong>初期化</strong>：隣接リストに<span class="arithmatex">\(n\)</span>個の頂点と<span class="arithmatex">\(2m\)</span>個の辺を作成し、<span class="arithmatex">\(O(n + m)\)</span>時間を使用します。</li>
+</ul>
+<div class="tabbed-set tabbed-alternate" data-tabs="3:5"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">隣接リストの初期化</label><label for="__tabbed_3_2">辺の追加</label><label for="__tabbed_3_3">辺の削除</label><label for="__tabbed_3_4">頂点の追加</label><label for="__tabbed_3_5">頂点の削除</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<p><a class="glightbox" href="../graph_operations.assets/adjacency_list_step1_initialization.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="隣接リストでの初期化、辺の追加と削除、頂点の追加と削除" class="animation-figure" src="../graph_operations.assets/adjacency_list_step1_initialization.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../graph_operations.assets/adjacency_list_step2_add_edge.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="adjacency_list_add_edge" class="animation-figure" src="../graph_operations.assets/adjacency_list_step2_add_edge.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../graph_operations.assets/adjacency_list_step3_remove_edge.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="adjacency_list_remove_edge" class="animation-figure" src="../graph_operations.assets/adjacency_list_step3_remove_edge.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../graph_operations.assets/adjacency_list_step4_add_vertex.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="adjacency_list_add_vertex" class="animation-figure" src="../graph_operations.assets/adjacency_list_step4_add_vertex.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../graph_operations.assets/adjacency_list_step5_remove_vertex.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="adjacency_list_remove_vertex" class="animation-figure" src="../graph_operations.assets/adjacency_list_step5_remove_vertex.png" /></a></p>
+</div>
+</div>
+</div>
+<p align="center"> 図 9-8 &nbsp; 隣接リストでの初期化、辺の追加と削除、頂点の追加と削除 </p>
+
+<p>以下は隣接リストのコード実装です。上図と比較して、実際のコードには以下の違いがあります。</p>
+<ul>
+<li>頂点の追加と削除の便宜、およびコードの簡素化のため、連結リストの代わりにリスト（動的配列）を使用します。</li>
+<li>ハッシュテーブルを使用して隣接リストを格納し、<code>key</code>が頂点インスタンス、<code>value</code>がその頂点の隣接頂点のリスト（連結リスト）です。</li>
+</ul>
+<p>さらに、隣接リストで頂点を表現するために<code>Vertex</code>クラスを使用します。その理由は：隣接行列のようにリストインデックスを使用して異なる頂点を区別する場合、インデックス<span class="arithmatex">\(i\)</span>の頂点を削除したい場合、隣接リスト全体を走査し、<span class="arithmatex">\(i\)</span>より大きいすべてのインデックスを1つずつ減少させる必要があり、これは非常に非効率的です。しかし、各頂点が一意の<code>Vertex</code>インスタンスである場合、頂点を削除しても他の頂点に変更を加える必要がありません。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="4:14"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><input id="__tabbed_4_6" name="__tabbed_4" type="radio" /><input id="__tabbed_4_7" name="__tabbed_4" type="radio" /><input id="__tabbed_4_8" name="__tabbed_4" type="radio" /><input id="__tabbed_4_9" name="__tabbed_4" type="radio" /><input id="__tabbed_4_10" name="__tabbed_4" type="radio" /><input id="__tabbed_4_11" name="__tabbed_4" type="radio" /><input id="__tabbed_4_12" name="__tabbed_4" type="radio" /><input id="__tabbed_4_13" name="__tabbed_4" type="radio" /><input id="__tabbed_4_14" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">Python</label><label for="__tabbed_4_2">C++</label><label for="__tabbed_4_3">Java</label><label for="__tabbed_4_4">C#</label><label for="__tabbed_4_5">Go</label><label for="__tabbed_4_6">Swift</label><label for="__tabbed_4_7">JS</label><label for="__tabbed_4_8">TS</label><label for="__tabbed_4_9">Dart</label><label for="__tabbed_4_10">Rust</label><label for="__tabbed_4_11">C</label><label for="__tabbed_4_12">Kotlin</label><label for="__tabbed_4_13">Ruby</label><label for="__tabbed_4_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_adjacency_list.py</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">GraphAdjList</span><span class="p">:</span>
+<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;隣接リストに基づく無向グラフクラス&quot;&quot;&quot;</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">edges</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">list</span><span class="p">[</span><span class="n">Vertex</span><span class="p">]]):</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;コンストラクタ&quot;&quot;&quot;</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a>        <span class="c1"># 隣接リスト、キー: 頂点、値: その頂点の隣接する全頂点</span>
+<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">adj_list</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">[</span><span class="n">Vertex</span><span class="p">,</span> <span class="nb">list</span><span class="p">[</span><span class="n">Vertex</span><span class="p">]]()</span>
+<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a>        <span class="c1"># すべての頂点と辺を追加</span>
+<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a>        <span class="k">for</span> <span class="n">edge</span> <span class="ow">in</span> <span class="n">edges</span><span class="p">:</span>
+<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">add_vertex</span><span class="p">(</span><span class="n">edge</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
+<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">add_vertex</span><span class="p">(</span><span class="n">edge</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
+<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">add_edge</span><span class="p">(</span><span class="n">edge</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">edge</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
+<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a>
+<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">size</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;頂点数を取得&quot;&quot;&quot;</span>
+<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a>        <span class="k">return</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">adj_list</span><span class="p">)</span>
+<a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a>
+<a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">add_edge</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">vet1</span><span class="p">:</span> <span class="n">Vertex</span><span class="p">,</span> <span class="n">vet2</span><span class="p">:</span> <span class="n">Vertex</span><span class="p">):</span>
+<a id="__codelineno-14-19" name="__codelineno-14-19" href="#__codelineno-14-19"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;辺を追加&quot;&quot;&quot;</span>
+<a id="__codelineno-14-20" name="__codelineno-14-20" href="#__codelineno-14-20"></a>        <span class="k">if</span> <span class="n">vet1</span> <span class="ow">not</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">adj_list</span> <span class="ow">or</span> <span class="n">vet2</span> <span class="ow">not</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">adj_list</span> <span class="ow">or</span> <span class="n">vet1</span> <span class="o">==</span> <span class="n">vet2</span><span class="p">:</span>
+<a id="__codelineno-14-21" name="__codelineno-14-21" href="#__codelineno-14-21"></a>            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">()</span>
+<a id="__codelineno-14-22" name="__codelineno-14-22" href="#__codelineno-14-22"></a>        <span class="c1"># 辺 vet1 - vet2 を追加</span>
+<a id="__codelineno-14-23" name="__codelineno-14-23" href="#__codelineno-14-23"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">adj_list</span><span class="p">[</span><span class="n">vet1</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">vet2</span><span class="p">)</span>
+<a id="__codelineno-14-24" name="__codelineno-14-24" href="#__codelineno-14-24"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">adj_list</span><span class="p">[</span><span class="n">vet2</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">vet1</span><span class="p">)</span>
+<a id="__codelineno-14-25" name="__codelineno-14-25" href="#__codelineno-14-25"></a>
+<a id="__codelineno-14-26" name="__codelineno-14-26" href="#__codelineno-14-26"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">remove_edge</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">vet1</span><span class="p">:</span> <span class="n">Vertex</span><span class="p">,</span> <span class="n">vet2</span><span class="p">:</span> <span class="n">Vertex</span><span class="p">):</span>
+<a id="__codelineno-14-27" name="__codelineno-14-27" href="#__codelineno-14-27"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;辺を削除&quot;&quot;&quot;</span>
+<a id="__codelineno-14-28" name="__codelineno-14-28" href="#__codelineno-14-28"></a>        <span class="k">if</span> <span class="n">vet1</span> <span class="ow">not</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">adj_list</span> <span class="ow">or</span> <span class="n">vet2</span> <span class="ow">not</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">adj_list</span> <span class="ow">or</span> <span class="n">vet1</span> <span class="o">==</span> <span class="n">vet2</span><span class="p">:</span>
+<a id="__codelineno-14-29" name="__codelineno-14-29" href="#__codelineno-14-29"></a>            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">()</span>
+<a id="__codelineno-14-30" name="__codelineno-14-30" href="#__codelineno-14-30"></a>        <span class="c1"># 辺 vet1 - vet2 を削除</span>
+<a id="__codelineno-14-31" name="__codelineno-14-31" href="#__codelineno-14-31"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">adj_list</span><span class="p">[</span><span class="n">vet1</span><span class="p">]</span><span class="o">.</span><span class="n">remove</span><span class="p">(</span><span class="n">vet2</span><span class="p">)</span>
+<a id="__codelineno-14-32" name="__codelineno-14-32" href="#__codelineno-14-32"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">adj_list</span><span class="p">[</span><span class="n">vet2</span><span class="p">]</span><span class="o">.</span><span class="n">remove</span><span class="p">(</span><span class="n">vet1</span><span class="p">)</span>
+<a id="__codelineno-14-33" name="__codelineno-14-33" href="#__codelineno-14-33"></a>
+<a id="__codelineno-14-34" name="__codelineno-14-34" href="#__codelineno-14-34"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">add_vertex</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">vet</span><span class="p">:</span> <span class="n">Vertex</span><span class="p">):</span>
+<a id="__codelineno-14-35" name="__codelineno-14-35" href="#__codelineno-14-35"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;頂点を追加&quot;&quot;&quot;</span>
+<a id="__codelineno-14-36" name="__codelineno-14-36" href="#__codelineno-14-36"></a>        <span class="k">if</span> <span class="n">vet</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">adj_list</span><span class="p">:</span>
+<a id="__codelineno-14-37" name="__codelineno-14-37" href="#__codelineno-14-37"></a>            <span class="k">return</span>
+<a id="__codelineno-14-38" name="__codelineno-14-38" href="#__codelineno-14-38"></a>        <span class="c1"># 隣接リストに新しい連結リストを追加</span>
+<a id="__codelineno-14-39" name="__codelineno-14-39" href="#__codelineno-14-39"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">adj_list</span><span class="p">[</span><span class="n">vet</span><span class="p">]</span> <span class="o">=</span> <span class="p">[]</span>
+<a id="__codelineno-14-40" name="__codelineno-14-40" href="#__codelineno-14-40"></a>
+<a id="__codelineno-14-41" name="__codelineno-14-41" href="#__codelineno-14-41"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">remove_vertex</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">vet</span><span class="p">:</span> <span class="n">Vertex</span><span class="p">):</span>
+<a id="__codelineno-14-42" name="__codelineno-14-42" href="#__codelineno-14-42"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;頂点を削除&quot;&quot;&quot;</span>
+<a id="__codelineno-14-43" name="__codelineno-14-43" href="#__codelineno-14-43"></a>        <span class="k">if</span> <span class="n">vet</span> <span class="ow">not</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">adj_list</span><span class="p">:</span>
+<a id="__codelineno-14-44" name="__codelineno-14-44" href="#__codelineno-14-44"></a>            <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">()</span>
+<a id="__codelineno-14-45" name="__codelineno-14-45" href="#__codelineno-14-45"></a>        <span class="c1"># 隣接リストから頂点vetに対応する連結リストを削除</span>
+<a id="__codelineno-14-46" name="__codelineno-14-46" href="#__codelineno-14-46"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">adj_list</span><span class="o">.</span><span class="n">pop</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span>
+<a id="__codelineno-14-47" name="__codelineno-14-47" href="#__codelineno-14-47"></a>        <span class="c1"># 他の頂点の連結リストを走査し、vetを含むすべての辺を削除</span>
+<a id="__codelineno-14-48" name="__codelineno-14-48" href="#__codelineno-14-48"></a>        <span class="k">for</span> <span class="n">vertex</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">adj_list</span><span class="p">:</span>
+<a id="__codelineno-14-49" name="__codelineno-14-49" href="#__codelineno-14-49"></a>            <span class="k">if</span> <span class="n">vet</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">adj_list</span><span class="p">[</span><span class="n">vertex</span><span class="p">]:</span>
+<a id="__codelineno-14-50" name="__codelineno-14-50" href="#__codelineno-14-50"></a>                <span class="bp">self</span><span class="o">.</span><span class="n">adj_list</span><span class="p">[</span><span class="n">vertex</span><span class="p">]</span><span class="o">.</span><span class="n">remove</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span>
+<a id="__codelineno-14-51" name="__codelineno-14-51" href="#__codelineno-14-51"></a>
+<a id="__codelineno-14-52" name="__codelineno-14-52" href="#__codelineno-14-52"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">print</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<a id="__codelineno-14-53" name="__codelineno-14-53" href="#__codelineno-14-53"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;隣接リストを出力&quot;&quot;&quot;</span>
+<a id="__codelineno-14-54" name="__codelineno-14-54" href="#__codelineno-14-54"></a>        <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;隣接リスト =&quot;</span><span class="p">)</span>
+<a id="__codelineno-14-55" name="__codelineno-14-55" href="#__codelineno-14-55"></a>        <span class="k">for</span> <span class="n">vertex</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">adj_list</span><span class="p">:</span>
+<a id="__codelineno-14-56" name="__codelineno-14-56" href="#__codelineno-14-56"></a>            <span class="n">tmp</span> <span class="o">=</span> <span class="p">[</span><span class="n">v</span><span class="o">.</span><span class="n">val</span> <span class="k">for</span> <span class="n">v</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">adj_list</span><span class="p">[</span><span class="n">vertex</span><span class="p">]]</span>
+<a id="__codelineno-14-57" name="__codelineno-14-57" href="#__codelineno-14-57"></a>            <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">&quot;</span><span class="si">{</span><span class="n">vertex</span><span class="o">.</span><span class="n">val</span><span class="si">}</span><span class="s2">: </span><span class="si">{</span><span class="n">tmp</span><span class="si">}</span><span class="s2">,&quot;</span><span class="p">)</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_adjacency_list.cpp</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 隣接リストに基づく無向グラフクラス */</span>
+<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">GraphAdjList</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">  </span><span class="k">public</span><span class="o">:</span>
+<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="c1">// 隣接リスト、キー：頂点、値：その頂点のすべての隣接頂点</span>
+<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">    </span><span class="n">unordered_map</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*&gt;&gt;</span><span class="w"> </span><span class="n">adjList</span><span class="p">;</span>
+<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a>
+<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">    </span><span class="cm">/* ベクターから指定されたノードを削除 */</span>
+<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">vec</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">vec</span><span class="p">.</span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">vec</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="w">                </span><span class="n">vec</span><span class="p">.</span><span class="n">erase</span><span class="p">(</span><span class="n">vec</span><span class="p">.</span><span class="n">begin</span><span class="p">()</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="w">                </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a>
+<a id="__codelineno-15-17" name="__codelineno-15-17" href="#__codelineno-15-17"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-15-18" name="__codelineno-15-18" href="#__codelineno-15-18"></a><span class="w">    </span><span class="n">GraphAdjList</span><span class="p">(</span><span class="k">const</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*&gt;&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">edges</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-19" name="__codelineno-15-19" href="#__codelineno-15-19"></a><span class="w">        </span><span class="c1">// すべての頂点と辺を追加</span>
+<a id="__codelineno-15-20" name="__codelineno-15-20" href="#__codelineno-15-20"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="k">const</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">edge</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">edges</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-21" name="__codelineno-15-21" href="#__codelineno-15-21"></a><span class="w">            </span><span class="n">addVertex</span><span class="p">(</span><span class="n">edge</span><span class="p">[</span><span class="mi">0</span><span class="p">]);</span>
+<a id="__codelineno-15-22" name="__codelineno-15-22" href="#__codelineno-15-22"></a><span class="w">            </span><span class="n">addVertex</span><span class="p">(</span><span class="n">edge</span><span class="p">[</span><span class="mi">1</span><span class="p">]);</span>
+<a id="__codelineno-15-23" name="__codelineno-15-23" href="#__codelineno-15-23"></a><span class="w">            </span><span class="n">addEdge</span><span class="p">(</span><span class="n">edge</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span><span class="w"> </span><span class="n">edge</span><span class="p">[</span><span class="mi">1</span><span class="p">]);</span>
+<a id="__codelineno-15-24" name="__codelineno-15-24" href="#__codelineno-15-24"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-15-25" name="__codelineno-15-25" href="#__codelineno-15-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-26" name="__codelineno-15-26" href="#__codelineno-15-26"></a>
+<a id="__codelineno-15-27" name="__codelineno-15-27" href="#__codelineno-15-27"></a><span class="w">    </span><span class="cm">/* 頂点数を取得 */</span>
+<a id="__codelineno-15-28" name="__codelineno-15-28" href="#__codelineno-15-28"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-29" name="__codelineno-15-29" href="#__codelineno-15-29"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">adjList</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
+<a id="__codelineno-15-30" name="__codelineno-15-30" href="#__codelineno-15-30"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-31" name="__codelineno-15-31" href="#__codelineno-15-31"></a>
+<a id="__codelineno-15-32" name="__codelineno-15-32" href="#__codelineno-15-32"></a><span class="w">    </span><span class="cm">/* 辺を追加 */</span>
+<a id="__codelineno-15-33" name="__codelineno-15-33" href="#__codelineno-15-33"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">addEdge</span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">vet1</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">vet2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-34" name="__codelineno-15-34" href="#__codelineno-15-34"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">adjList</span><span class="p">.</span><span class="n">count</span><span class="p">(</span><span class="n">vet1</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="o">!</span><span class="n">adjList</span><span class="p">.</span><span class="n">count</span><span class="p">(</span><span class="n">vet2</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">vet1</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">vet2</span><span class="p">)</span>
+<a id="__codelineno-15-35" name="__codelineno-15-35" href="#__codelineno-15-35"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">invalid_argument</span><span class="p">(</span><span class="s">&quot;Vertex does not exist&quot;</span><span class="p">);</span>
+<a id="__codelineno-15-36" name="__codelineno-15-36" href="#__codelineno-15-36"></a><span class="w">        </span><span class="c1">// 辺 vet1 - vet2 を追加</span>
+<a id="__codelineno-15-37" name="__codelineno-15-37" href="#__codelineno-15-37"></a><span class="w">        </span><span class="n">adjList</span><span class="p">[</span><span class="n">vet1</span><span class="p">].</span><span class="n">push_back</span><span class="p">(</span><span class="n">vet2</span><span class="p">);</span>
+<a id="__codelineno-15-38" name="__codelineno-15-38" href="#__codelineno-15-38"></a><span class="w">        </span><span class="n">adjList</span><span class="p">[</span><span class="n">vet2</span><span class="p">].</span><span class="n">push_back</span><span class="p">(</span><span class="n">vet1</span><span class="p">);</span>
+<a id="__codelineno-15-39" name="__codelineno-15-39" href="#__codelineno-15-39"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-40" name="__codelineno-15-40" href="#__codelineno-15-40"></a>
+<a id="__codelineno-15-41" name="__codelineno-15-41" href="#__codelineno-15-41"></a><span class="w">    </span><span class="cm">/* 辺を削除 */</span>
+<a id="__codelineno-15-42" name="__codelineno-15-42" href="#__codelineno-15-42"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">removeEdge</span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">vet1</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">vet2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-43" name="__codelineno-15-43" href="#__codelineno-15-43"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">adjList</span><span class="p">.</span><span class="n">count</span><span class="p">(</span><span class="n">vet1</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="o">!</span><span class="n">adjList</span><span class="p">.</span><span class="n">count</span><span class="p">(</span><span class="n">vet2</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">vet1</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">vet2</span><span class="p">)</span>
+<a id="__codelineno-15-44" name="__codelineno-15-44" href="#__codelineno-15-44"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">invalid_argument</span><span class="p">(</span><span class="s">&quot;Vertex does not exist&quot;</span><span class="p">);</span>
+<a id="__codelineno-15-45" name="__codelineno-15-45" href="#__codelineno-15-45"></a><span class="w">        </span><span class="c1">// 辺 vet1 - vet2 を削除</span>
+<a id="__codelineno-15-46" name="__codelineno-15-46" href="#__codelineno-15-46"></a><span class="w">        </span><span class="n">remove</span><span class="p">(</span><span class="n">adjList</span><span class="p">[</span><span class="n">vet1</span><span class="p">],</span><span class="w"> </span><span class="n">vet2</span><span class="p">);</span>
+<a id="__codelineno-15-47" name="__codelineno-15-47" href="#__codelineno-15-47"></a><span class="w">        </span><span class="n">remove</span><span class="p">(</span><span class="n">adjList</span><span class="p">[</span><span class="n">vet2</span><span class="p">],</span><span class="w"> </span><span class="n">vet1</span><span class="p">);</span>
+<a id="__codelineno-15-48" name="__codelineno-15-48" href="#__codelineno-15-48"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-49" name="__codelineno-15-49" href="#__codelineno-15-49"></a>
+<a id="__codelineno-15-50" name="__codelineno-15-50" href="#__codelineno-15-50"></a><span class="w">    </span><span class="cm">/* 頂点を追加 */</span>
+<a id="__codelineno-15-51" name="__codelineno-15-51" href="#__codelineno-15-51"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">addVertex</span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-52" name="__codelineno-15-52" href="#__codelineno-15-52"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">adjList</span><span class="p">.</span><span class="n">count</span><span class="p">(</span><span class="n">vet</span><span class="p">))</span>
+<a id="__codelineno-15-53" name="__codelineno-15-53" href="#__codelineno-15-53"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-15-54" name="__codelineno-15-54" href="#__codelineno-15-54"></a><span class="w">        </span><span class="c1">// 隣接リストに新しい連結リストを追加</span>
+<a id="__codelineno-15-55" name="__codelineno-15-55" href="#__codelineno-15-55"></a><span class="w">        </span><span class="n">adjList</span><span class="p">[</span><span class="n">vet</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*&gt;</span><span class="p">();</span>
+<a id="__codelineno-15-56" name="__codelineno-15-56" href="#__codelineno-15-56"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-57" name="__codelineno-15-57" href="#__codelineno-15-57"></a>
+<a id="__codelineno-15-58" name="__codelineno-15-58" href="#__codelineno-15-58"></a><span class="w">    </span><span class="cm">/* 頂点を削除 */</span>
+<a id="__codelineno-15-59" name="__codelineno-15-59" href="#__codelineno-15-59"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">removeVertex</span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-60" name="__codelineno-15-60" href="#__codelineno-15-60"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">adjList</span><span class="p">.</span><span class="n">count</span><span class="p">(</span><span class="n">vet</span><span class="p">))</span>
+<a id="__codelineno-15-61" name="__codelineno-15-61" href="#__codelineno-15-61"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">invalid_argument</span><span class="p">(</span><span class="s">&quot;Vertex does not exist&quot;</span><span class="p">);</span>
+<a id="__codelineno-15-62" name="__codelineno-15-62" href="#__codelineno-15-62"></a><span class="w">        </span><span class="c1">// 隣接リストから頂点vetに対応する連結リストを削除</span>
+<a id="__codelineno-15-63" name="__codelineno-15-63" href="#__codelineno-15-63"></a><span class="w">        </span><span class="n">adjList</span><span class="p">.</span><span class="n">erase</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span>
+<a id="__codelineno-15-64" name="__codelineno-15-64" href="#__codelineno-15-64"></a><span class="w">        </span><span class="c1">// 他の頂点の連結リストを走査し、vetを含むすべての辺を削除</span>
+<a id="__codelineno-15-65" name="__codelineno-15-65" href="#__codelineno-15-65"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="k">auto</span><span class="w"> </span><span class="o">&amp;</span><span class="n">adj</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">adjList</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-66" name="__codelineno-15-66" href="#__codelineno-15-66"></a><span class="w">            </span><span class="n">remove</span><span class="p">(</span><span class="n">adj</span><span class="p">.</span><span class="n">second</span><span class="p">,</span><span class="w"> </span><span class="n">vet</span><span class="p">);</span>
+<a id="__codelineno-15-67" name="__codelineno-15-67" href="#__codelineno-15-67"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-15-68" name="__codelineno-15-68" href="#__codelineno-15-68"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-69" name="__codelineno-15-69" href="#__codelineno-15-69"></a>
+<a id="__codelineno-15-70" name="__codelineno-15-70" href="#__codelineno-15-70"></a><span class="w">    </span><span class="cm">/* 隣接リストを印刷 */</span>
+<a id="__codelineno-15-71" name="__codelineno-15-71" href="#__codelineno-15-71"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-72" name="__codelineno-15-72" href="#__codelineno-15-72"></a><span class="w">        </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;隣接リスト =&quot;</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
+<a id="__codelineno-15-73" name="__codelineno-15-73" href="#__codelineno-15-73"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="k">auto</span><span class="w"> </span><span class="o">&amp;</span><span class="n">adj</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">adjList</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-74" name="__codelineno-15-74" href="#__codelineno-15-74"></a><span class="w">            </span><span class="k">const</span><span class="w"> </span><span class="k">auto</span><span class="w"> </span><span class="o">&amp;</span><span class="n">key</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">adj</span><span class="p">.</span><span class="n">first</span><span class="p">;</span>
+<a id="__codelineno-15-75" name="__codelineno-15-75" href="#__codelineno-15-75"></a><span class="w">            </span><span class="k">const</span><span class="w"> </span><span class="k">auto</span><span class="w"> </span><span class="o">&amp;</span><span class="n">vec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">adj</span><span class="p">.</span><span class="n">second</span><span class="p">;</span>
+<a id="__codelineno-15-76" name="__codelineno-15-76" href="#__codelineno-15-76"></a><span class="w">            </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">key</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;: &quot;</span><span class="p">;</span>
+<a id="__codelineno-15-77" name="__codelineno-15-77" href="#__codelineno-15-77"></a><span class="w">            </span><span class="n">printVector</span><span class="p">(</span><span class="n">vetsToVals</span><span class="p">(</span><span class="n">vec</span><span class="p">));</span>
+<a id="__codelineno-15-78" name="__codelineno-15-78" href="#__codelineno-15-78"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-15-79" name="__codelineno-15-79" href="#__codelineno-15-79"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-80" name="__codelineno-15-80" href="#__codelineno-15-80"></a><span class="p">};</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_adjacency_list.java</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 隣接リストに基づく無向グラフクラス */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kd">class</span> <span class="nc">GraphAdjList</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="c1">// 隣接リスト、キー: 頂点、値: その頂点のすべての隣接頂点</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="n">Map</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">adjList</span><span class="p">;</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="nf">GraphAdjList</span><span class="p">(</span><span class="n">Vertex</span><span class="o">[][]</span><span class="w"> </span><span class="n">edges</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="na">adjList</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">HashMap</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w">        </span><span class="c1">// すべての頂点と辺を追加</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Vertex</span><span class="o">[]</span><span class="w"> </span><span class="n">edge</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">edges</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="w">            </span><span class="n">addVertex</span><span class="p">(</span><span class="n">edge</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="p">);</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="w">            </span><span class="n">addVertex</span><span class="p">(</span><span class="n">edge</span><span class="o">[</span><span class="mi">1</span><span class="o">]</span><span class="p">);</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w">            </span><span class="n">addEdge</span><span class="p">(</span><span class="n">edge</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">edge</span><span class="o">[</span><span class="mi">1</span><span class="o">]</span><span class="p">);</span>
+<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a>
+<a id="__codelineno-16-17" name="__codelineno-16-17" href="#__codelineno-16-17"></a><span class="w">    </span><span class="cm">/* 頂点数を取得 */</span>
+<a id="__codelineno-16-18" name="__codelineno-16-18" href="#__codelineno-16-18"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-19" name="__codelineno-16-19" href="#__codelineno-16-19"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">adjList</span><span class="p">.</span><span class="na">size</span><span class="p">();</span>
+<a id="__codelineno-16-20" name="__codelineno-16-20" href="#__codelineno-16-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-21" name="__codelineno-16-21" href="#__codelineno-16-21"></a>
+<a id="__codelineno-16-22" name="__codelineno-16-22" href="#__codelineno-16-22"></a><span class="w">    </span><span class="cm">/* 辺を追加 */</span>
+<a id="__codelineno-16-23" name="__codelineno-16-23" href="#__codelineno-16-23"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">addEdge</span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="n">vet1</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="n">vet2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-24" name="__codelineno-16-24" href="#__codelineno-16-24"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">adjList</span><span class="p">.</span><span class="na">containsKey</span><span class="p">(</span><span class="n">vet1</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="o">!</span><span class="n">adjList</span><span class="p">.</span><span class="na">containsKey</span><span class="p">(</span><span class="n">vet2</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">vet1</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">vet2</span><span class="p">)</span>
+<a id="__codelineno-16-25" name="__codelineno-16-25" href="#__codelineno-16-25"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IllegalArgumentException</span><span class="p">();</span>
+<a id="__codelineno-16-26" name="__codelineno-16-26" href="#__codelineno-16-26"></a><span class="w">        </span><span class="c1">// 辺 vet1 - vet2 を追加</span>
+<a id="__codelineno-16-27" name="__codelineno-16-27" href="#__codelineno-16-27"></a><span class="w">        </span><span class="n">adjList</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">vet1</span><span class="p">).</span><span class="na">add</span><span class="p">(</span><span class="n">vet2</span><span class="p">);</span>
+<a id="__codelineno-16-28" name="__codelineno-16-28" href="#__codelineno-16-28"></a><span class="w">        </span><span class="n">adjList</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">vet2</span><span class="p">).</span><span class="na">add</span><span class="p">(</span><span class="n">vet1</span><span class="p">);</span>
+<a id="__codelineno-16-29" name="__codelineno-16-29" href="#__codelineno-16-29"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-30" name="__codelineno-16-30" href="#__codelineno-16-30"></a>
+<a id="__codelineno-16-31" name="__codelineno-16-31" href="#__codelineno-16-31"></a><span class="w">    </span><span class="cm">/* 辺を削除 */</span>
+<a id="__codelineno-16-32" name="__codelineno-16-32" href="#__codelineno-16-32"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">removeEdge</span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="n">vet1</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="n">vet2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-33" name="__codelineno-16-33" href="#__codelineno-16-33"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">adjList</span><span class="p">.</span><span class="na">containsKey</span><span class="p">(</span><span class="n">vet1</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="o">!</span><span class="n">adjList</span><span class="p">.</span><span class="na">containsKey</span><span class="p">(</span><span class="n">vet2</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">vet1</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">vet2</span><span class="p">)</span>
+<a id="__codelineno-16-34" name="__codelineno-16-34" href="#__codelineno-16-34"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IllegalArgumentException</span><span class="p">();</span>
+<a id="__codelineno-16-35" name="__codelineno-16-35" href="#__codelineno-16-35"></a><span class="w">        </span><span class="c1">// 辺 vet1 - vet2 を削除</span>
+<a id="__codelineno-16-36" name="__codelineno-16-36" href="#__codelineno-16-36"></a><span class="w">        </span><span class="n">adjList</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">vet1</span><span class="p">).</span><span class="na">remove</span><span class="p">(</span><span class="n">vet2</span><span class="p">);</span>
+<a id="__codelineno-16-37" name="__codelineno-16-37" href="#__codelineno-16-37"></a><span class="w">        </span><span class="n">adjList</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">vet2</span><span class="p">).</span><span class="na">remove</span><span class="p">(</span><span class="n">vet1</span><span class="p">);</span>
+<a id="__codelineno-16-38" name="__codelineno-16-38" href="#__codelineno-16-38"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-39" name="__codelineno-16-39" href="#__codelineno-16-39"></a>
+<a id="__codelineno-16-40" name="__codelineno-16-40" href="#__codelineno-16-40"></a><span class="w">    </span><span class="cm">/* 頂点を追加 */</span>
+<a id="__codelineno-16-41" name="__codelineno-16-41" href="#__codelineno-16-41"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">addVertex</span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-42" name="__codelineno-16-42" href="#__codelineno-16-42"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">adjList</span><span class="p">.</span><span class="na">containsKey</span><span class="p">(</span><span class="n">vet</span><span class="p">))</span>
+<a id="__codelineno-16-43" name="__codelineno-16-43" href="#__codelineno-16-43"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-16-44" name="__codelineno-16-44" href="#__codelineno-16-44"></a><span class="w">        </span><span class="c1">// 隣接リストに新しい連結リストを追加</span>
+<a id="__codelineno-16-45" name="__codelineno-16-45" href="#__codelineno-16-45"></a><span class="w">        </span><span class="n">adjList</span><span class="p">.</span><span class="na">put</span><span class="p">(</span><span class="n">vet</span><span class="p">,</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">());</span>
+<a id="__codelineno-16-46" name="__codelineno-16-46" href="#__codelineno-16-46"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-47" name="__codelineno-16-47" href="#__codelineno-16-47"></a>
+<a id="__codelineno-16-48" name="__codelineno-16-48" href="#__codelineno-16-48"></a><span class="w">    </span><span class="cm">/* 頂点を削除 */</span>
+<a id="__codelineno-16-49" name="__codelineno-16-49" href="#__codelineno-16-49"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">removeVertex</span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-50" name="__codelineno-16-50" href="#__codelineno-16-50"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">adjList</span><span class="p">.</span><span class="na">containsKey</span><span class="p">(</span><span class="n">vet</span><span class="p">))</span>
+<a id="__codelineno-16-51" name="__codelineno-16-51" href="#__codelineno-16-51"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IllegalArgumentException</span><span class="p">();</span>
+<a id="__codelineno-16-52" name="__codelineno-16-52" href="#__codelineno-16-52"></a><span class="w">        </span><span class="c1">// 隣接リストから頂点 vet に対応する連結リストを削除</span>
+<a id="__codelineno-16-53" name="__codelineno-16-53" href="#__codelineno-16-53"></a><span class="w">        </span><span class="n">adjList</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span>
+<a id="__codelineno-16-54" name="__codelineno-16-54" href="#__codelineno-16-54"></a><span class="w">        </span><span class="c1">// 他の頂点の連結リストを走査し、vet を含むすべての辺を削除</span>
+<a id="__codelineno-16-55" name="__codelineno-16-55" href="#__codelineno-16-55"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="n">list</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">adjList</span><span class="p">.</span><span class="na">values</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-56" name="__codelineno-16-56" href="#__codelineno-16-56"></a><span class="w">            </span><span class="n">list</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span>
+<a id="__codelineno-16-57" name="__codelineno-16-57" href="#__codelineno-16-57"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-16-58" name="__codelineno-16-58" href="#__codelineno-16-58"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-59" name="__codelineno-16-59" href="#__codelineno-16-59"></a>
+<a id="__codelineno-16-60" name="__codelineno-16-60" href="#__codelineno-16-60"></a><span class="w">    </span><span class="cm">/* 隣接リストを出力 */</span>
+<a id="__codelineno-16-61" name="__codelineno-16-61" href="#__codelineno-16-61"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-62" name="__codelineno-16-62" href="#__codelineno-16-62"></a><span class="w">        </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="s">&quot;隣接リスト =&quot;</span><span class="p">);</span>
+<a id="__codelineno-16-63" name="__codelineno-16-63" href="#__codelineno-16-63"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Map</span><span class="p">.</span><span class="na">Entry</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">adjList</span><span class="p">.</span><span class="na">entrySet</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-64" name="__codelineno-16-64" href="#__codelineno-16-64"></a><span class="w">            </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-16-65" name="__codelineno-16-65" href="#__codelineno-16-65"></a><span class="w">            </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="n">vertex</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="na">getValue</span><span class="p">())</span>
+<a id="__codelineno-16-66" name="__codelineno-16-66" href="#__codelineno-16-66"></a><span class="w">                </span><span class="n">tmp</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">vertex</span><span class="p">.</span><span class="na">val</span><span class="p">);</span>
+<a id="__codelineno-16-67" name="__codelineno-16-67" href="#__codelineno-16-67"></a><span class="w">            </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="na">getKey</span><span class="p">().</span><span class="na">val</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s">&quot;: &quot;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s">&quot;,&quot;</span><span class="p">);</span>
+<a id="__codelineno-16-68" name="__codelineno-16-68" href="#__codelineno-16-68"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-16-69" name="__codelineno-16-69" href="#__codelineno-16-69"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-70" name="__codelineno-16-70" href="#__codelineno-16-70"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_adjacency_list.cs</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">GraphAdjList</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_adjacency_list.go</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">graphAdjList</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_adjacency_list.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">GraphAdjList</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_adjacency_list.js</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">GraphAdjList</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_adjacency_list.ts</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">GraphAdjList</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_adjacency_list.dart</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">GraphAdjList</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_adjacency_list.rs</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">GraphAdjList</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_adjacency_list.c</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AdjListNode</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a>
+<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">GraphAdjList</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_adjacency_list.kt</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">GraphAdjList</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_adjacency_list.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">GraphAdjList</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_adjacency_list.zig</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">GraphAdjList</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h2 id="923">9.2.3 &nbsp; 効率の比較<a class="headerlink" href="#923" title="Permanent link">&para;</a></h2>
+<p>グラフに<span class="arithmatex">\(n\)</span>個の頂点と<span class="arithmatex">\(m\)</span>個の辺があると仮定すると、下表は隣接行列と隣接リストの時間効率と空間効率を比較しています。</p>
+<p align="center"> 表 9-2 &nbsp; 隣接行列と隣接リストの比較 </p>
+
+<div class="center-table">
+<table>
+<thead>
+<tr>
+<th></th>
+<th>隣接行列</th>
+<th>隣接リスト（連結リスト）</th>
+<th>隣接リスト（ハッシュテーブル）</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td>隣接性の判定</td>
+<td><span class="arithmatex">\(O(1)\)</span></td>
+<td><span class="arithmatex">\(O(m)\)</span></td>
+<td><span class="arithmatex">\(O(1)\)</span></td>
+</tr>
+<tr>
+<td>辺の追加</td>
+<td><span class="arithmatex">\(O(1)\)</span></td>
+<td><span class="arithmatex">\(O(1)\)</span></td>
+<td><span class="arithmatex">\(O(1)\)</span></td>
+</tr>
+<tr>
+<td>辺の削除</td>
+<td><span class="arithmatex">\(O(1)\)</span></td>
+<td><span class="arithmatex">\(O(m)\)</span></td>
+<td><span class="arithmatex">\(O(1)\)</span></td>
+</tr>
+<tr>
+<td>頂点の追加</td>
+<td><span class="arithmatex">\(O(n)\)</span></td>
+<td><span class="arithmatex">\(O(1)\)</span></td>
+<td><span class="arithmatex">\(O(1)\)</span></td>
+</tr>
+<tr>
+<td>頂点の削除</td>
+<td><span class="arithmatex">\(O(n^2)\)</span></td>
+<td><span class="arithmatex">\(O(n + m)\)</span></td>
+<td><span class="arithmatex">\(O(n)\)</span></td>
+</tr>
+<tr>
+<td>メモリ空間使用量</td>
+<td><span class="arithmatex">\(O(n^2)\)</span></td>
+<td><span class="arithmatex">\(O(n + m)\)</span></td>
+<td><span class="arithmatex">\(O(n + m)\)</span></td>
+</tr>
+</tbody>
+</table>
+</div>
+<p>上表を観察すると、隣接リスト（ハッシュテーブル）が最高の時間効率と空間効率を持っているように見えます。しかし、実際には、隣接行列での辺に対する操作がより効率的で、単一の配列アクセスまたは代入操作のみが必要です。全体的に、隣接行列は「空間と時間のトレードオフ」の原則を例示し、隣接リストは「時間と空間のトレードオフ」を例示しています。</p>
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+  
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+  
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+      <a href="../../chapter_preface/about_the_book/" class="md-nav__link">
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+      <a href="../../chapter_preface/summary/" class="md-nav__link">
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+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
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+  
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+    1.1 &nbsp; アルゴリズムはどこにでもある
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+  
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+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
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+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
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+    </li>
+  
+
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+              
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+  
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+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
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+    </li>
+  
+
+              
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+          
+        
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+        
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+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
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+  
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+            第 2 章 &nbsp; 計算量解析
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+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
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+    2.1 &nbsp; アルゴリズム効率評価
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+  
+
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+
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+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
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+    2.2 &nbsp; 反復と再帰
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+  
+
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+    </li>
+  
+
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+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
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+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
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+
+              
+            
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+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
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+  
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+    第 3 章 &nbsp; データ構造
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+            第 3 章 &nbsp; データ構造
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+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
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+    3.1 &nbsp; データ構造の分類
+  </span>
+  
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+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
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+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
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+
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+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
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+  </span>
+  
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+    </li>
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+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
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+  </span>
+  
+
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+    </li>
+  
+
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+  
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+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
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+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
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+  
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+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
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+            
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+  
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+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#931" class="md-nav__link">
+    <span class="md-ellipsis">
+      9.3.1 &nbsp; 幅優先探索
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="9.3.1   幅優先探索">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; アルゴリズムの実装
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; 計算量分析
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#932" class="md-nav__link">
+    <span class="md-ellipsis">
+      9.3.2 &nbsp; 深さ優先探索
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="9.3.2   深さ優先探索">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1_1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; アルゴリズムの実装
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2_1" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; 計算量分析
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
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+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
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+          
+        
+      
+    
+    
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+      
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+            <a href="../../chapter_reference/" class="md-nav__link ">
+              
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9 3v15h3V3H9m3 2 4 13 3-1-4-13-3 1M5 5v13h3V5H5M3 19v2h18v-2H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    参考文献
+  </span>
+  
+
+            </a>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_19_label" aria-expanded="false">
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+            参考文献
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+</nav>
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+            
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+              
+              <div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
+                <div class="md-sidebar__scrollwrap">
+                  <div class="md-sidebar__inner">
+                    
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#931" class="md-nav__link">
+    <span class="md-ellipsis">
+      9.3.1 &nbsp; 幅優先探索
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="9.3.1   幅優先探索">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; アルゴリズムの実装
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; 計算量分析
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#932" class="md-nav__link">
+    <span class="md-ellipsis">
+      9.3.2 &nbsp; 深さ優先探索
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="9.3.2   深さ優先探索">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1_1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; アルゴリズムの実装
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2_1" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; 計算量分析
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
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+  
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+                </div>
+              </div>
+            
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+              <article class="md-content__inner md-typeset">
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+    >
+      
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+<h1 id="93">9.3 &nbsp; グラフ走査<a class="headerlink" href="#93" title="Permanent link">&para;</a></h1>
+<p>木は「一対多」の関係を表現し、グラフはより高い自由度を持ち、任意の「多対多」の関係を表現できます。したがって、木をグラフの特別なケースと見なすことができます。明らかに、<strong>木の走査操作もグラフ走査操作の特別なケースです</strong>。</p>
+<p>グラフと木の両方で、走査操作を実装するために探索アルゴリズムの応用が必要です。グラフ走査は2つのタイプに分けることができます：<u>幅優先探索（BFS）</u>と<u>深さ優先探索（DFS）</u>です。</p>
+<h2 id="931">9.3.1 &nbsp; 幅優先探索<a class="headerlink" href="#931" title="Permanent link">&para;</a></h2>
+<p><strong>幅優先探索は近くから遠くへの走査方法で、ある頂点から開始し、常に最も近い頂点を優先的に訪問し、層ごとに外側に展開していきます</strong>。下図に示すように、左上の頂点から開始し、まずその頂点のすべての隣接頂点を走査し、次に次の頂点のすべての隣接頂点を走査し、以下同様に、すべての頂点が訪問されるまで続けます。</p>
+<p><a class="glightbox" href="../graph_traversal.assets/graph_bfs.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="グラフの幅優先走査" class="animation-figure" src="../graph_traversal.assets/graph_bfs.png" /></a></p>
+<p align="center"> 図 9-9 &nbsp; グラフの幅優先走査 </p>
+
+<h3 id="1">1. &nbsp; アルゴリズムの実装<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<p>BFSは通常キューの助けを借りて実装されます（下記のコード参照）。キューは「先入先出」で、これは「近くから遠くへ」走査するBFSの考え方と一致します。</p>
+<ol>
+<li>開始頂点<code>startVet</code>をキューに追加し、ループを開始します。</li>
+<li>ループの各反復で、キューの先頭の頂点をポップし、それを訪問済みとして記録し、次にその頂点のすべての隣接頂点をキューの末尾に追加します。</li>
+<li>すべての頂点が訪問されるまで手順<code>2.</code>を繰り返します。</li>
+</ol>
+<p>頂点の再訪問を防ぐために、ハッシュセット<code>visited</code>を使用してどのノードが訪問されたかを記録します。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:14"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><input id="__tabbed_1_14" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label><label for="__tabbed_1_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_bfs.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">graph_bfs</span><span class="p">(</span><span class="n">graph</span><span class="p">:</span> <span class="n">GraphAdjList</span><span class="p">,</span> <span class="n">start_vet</span><span class="p">:</span> <span class="n">Vertex</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="n">Vertex</span><span class="p">]:</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;幅優先走査&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># 隣接リストを使用してグラフを表現し、指定された頂点のすべての隣接頂点を取得</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="c1"># 頂点走査シーケンス</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="c1"># ハッシュセット、訪問済み頂点を記録するために使用</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>    <span class="n">visited</span> <span class="o">=</span> <span class="nb">set</span><span class="p">[</span><span class="n">Vertex</span><span class="p">]([</span><span class="n">start_vet</span><span class="p">])</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>    <span class="c1"># BFSを実装するために使用されるキュー</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>    <span class="n">que</span> <span class="o">=</span> <span class="n">deque</span><span class="p">[</span><span class="n">Vertex</span><span class="p">]([</span><span class="n">start_vet</span><span class="p">])</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>    <span class="c1"># 頂点vetから開始し、すべての頂点が訪問されるまでループ</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>    <span class="k">while</span> <span class="nb">len</span><span class="p">(</span><span class="n">que</span><span class="p">)</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">:</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>        <span class="n">vet</span> <span class="o">=</span> <span class="n">que</span><span class="o">.</span><span class="n">popleft</span><span class="p">()</span>  <span class="c1"># キューの先頭の頂点をデキュー</span>
+<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>        <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span>  <span class="c1"># 訪問済み頂点を記録</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>        <span class="c1"># その頂点のすべての隣接頂点を走査</span>
+<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>        <span class="k">for</span> <span class="n">adj_vet</span> <span class="ow">in</span> <span class="n">graph</span><span class="o">.</span><span class="n">adj_list</span><span class="p">[</span><span class="n">vet</span><span class="p">]:</span>
+<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>            <span class="k">if</span> <span class="n">adj_vet</span> <span class="ow">in</span> <span class="n">visited</span><span class="p">:</span>
+<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>                <span class="k">continue</span>  <span class="c1"># 既に訪問済みの頂点をスキップ</span>
+<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a>            <span class="n">que</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">adj_vet</span><span class="p">)</span>  <span class="c1"># 未訪問の頂点のみをエンキュー</span>
+<a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a>            <span class="n">visited</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">adj_vet</span><span class="p">)</span>  <span class="c1"># 頂点を訪問済みとしてマーク</span>
+<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a>    <span class="c1"># 頂点走査シーケンスを返す</span>
+<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a>    <span class="k">return</span> <span class="n">res</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_bfs.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 幅優先走査 */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="c1">// 隣接リストを使用してグラフを表現し、指定された頂点のすべての隣接頂点を取得</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="n">vector</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="n">graphBFS</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="o">&amp;</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">startVet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="c1">// 頂点走査順序</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="c1">// ハッシュセット、訪問済み頂点を記録するために使用</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="n">unordered_set</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="n">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="n">startVet</span><span class="p">};</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="c1">// BFSを実装するために使用されるキュー</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">    </span><span class="n">queue</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="n">que</span><span class="p">;</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">    </span><span class="n">que</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">startVet</span><span class="p">);</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">    </span><span class="c1">// 頂点vetから開始し、すべての頂点が訪問されるまでループ</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">que</span><span class="p">.</span><span class="n">empty</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">        </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">vet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">que</span><span class="p">.</span><span class="n">front</span><span class="p">();</span>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">        </span><span class="n">que</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span><span class="w">          </span><span class="c1">// キューの先頭の頂点をデキュー</span>
+<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 訪問済み頂点を記録</span>
+<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">        </span><span class="c1">// その頂点のすべての隣接頂点を走査</span>
+<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="k">auto</span><span class="w"> </span><span class="n">adjVet</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">graph</span><span class="p">.</span><span class="n">adjList</span><span class="p">[</span><span class="n">vet</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">visited</span><span class="p">.</span><span class="n">count</span><span class="p">(</span><span class="n">adjVet</span><span class="p">))</span>
+<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="w">                </span><span class="k">continue</span><span class="p">;</span><span class="w">            </span><span class="c1">// すでに訪問済みの頂点をスキップ</span>
+<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="w">            </span><span class="n">que</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">adjVet</span><span class="p">);</span><span class="w">        </span><span class="c1">// 未訪問の頂点のみをエンキュー</span>
+<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="w">            </span><span class="n">visited</span><span class="p">.</span><span class="n">emplace</span><span class="p">(</span><span class="n">adjVet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 頂点を訪問済みとしてマーク</span>
+<a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a><span class="w">    </span><span class="c1">// 頂点走査順序を返す</span>
+<a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-1-26" name="__codelineno-1-26" href="#__codelineno-1-26"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_bfs.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 幅優先走査 */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="c1">// 隣接リストを使用してグラフを表現し、指定した頂点のすべての隣接頂点を取得</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="n">List</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="nf">graphBFS</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="n">startVet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="c1">// 頂点走査順序</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="c1">// ハッシュセット、訪問済みの頂点を記録するために使用</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="n">Set</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="n">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">HashSet</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">    </span><span class="n">visited</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">startVet</span><span class="p">);</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">    </span><span class="c1">// BFS を実装するために使用するキュー</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">    </span><span class="n">Queue</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="n">que</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">LinkedList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">    </span><span class="n">que</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="n">startVet</span><span class="p">);</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">    </span><span class="c1">// 頂点 vet から開始し、すべての頂点が訪問されるまでループ</span>
+<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">que</span><span class="p">.</span><span class="na">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">        </span><span class="n">Vertex</span><span class="w"> </span><span class="n">vet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">que</span><span class="p">.</span><span class="na">poll</span><span class="p">();</span><span class="w"> </span><span class="c1">// キューの先頭の頂点をデキュー</span>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">        </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span><span class="w">            </span><span class="c1">// 訪問した頂点を記録</span>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">        </span><span class="c1">// その頂点のすべての隣接頂点を走査</span>
+<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="n">adjVet</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">graph</span><span class="p">.</span><span class="na">adjList</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">vet</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">visited</span><span class="p">.</span><span class="na">contains</span><span class="p">(</span><span class="n">adjVet</span><span class="p">))</span>
+<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w">                </span><span class="k">continue</span><span class="p">;</span><span class="w">        </span><span class="c1">// すでに訪問済みの頂点をスキップ</span>
+<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="w">            </span><span class="n">que</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="n">adjVet</span><span class="p">);</span><span class="w">   </span><span class="c1">// 未訪問の頂点のみをエンキュー</span>
+<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="w">            </span><span class="n">visited</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">adjVet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 頂点を訪問済みとしてマーク</span>
+<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a><span class="w">    </span><span class="c1">// 頂点走査順序を返す</span>
+<a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_bfs.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">graph_bfs</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">GraphBFS</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_bfs.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">graphBFS</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_bfs.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">graphBFS</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_bfs.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">graphBFS</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_bfs.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">graphBFS</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_bfs.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">graphBFS</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_bfs.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">graph_bfs</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_bfs.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">Queue</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">isVisited</span><span class="p">}</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">graphBFS</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_bfs.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">graphBFS</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_bfs.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">graph_bfs</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_bfs.zig</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">graphBFS</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>コードは比較的抽象的ですが、下図と比較することでより良く理解できます。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:11"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">&lt;1&gt;</label><label for="__tabbed_2_2">&lt;2&gt;</label><label for="__tabbed_2_3">&lt;3&gt;</label><label for="__tabbed_2_4">&lt;4&gt;</label><label for="__tabbed_2_5">&lt;5&gt;</label><label for="__tabbed_2_6">&lt;6&gt;</label><label for="__tabbed_2_7">&lt;7&gt;</label><label for="__tabbed_2_8">&lt;8&gt;</label><label for="__tabbed_2_9">&lt;9&gt;</label><label for="__tabbed_2_10">&lt;10&gt;</label><label for="__tabbed_2_11">&lt;11&gt;</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<p><a class="glightbox" href="../graph_traversal.assets/graph_bfs_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="グラフの幅優先探索の手順" class="animation-figure" src="../graph_traversal.assets/graph_bfs_step1.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../graph_traversal.assets/graph_bfs_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="graph_bfs_step2" class="animation-figure" src="../graph_traversal.assets/graph_bfs_step2.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../graph_traversal.assets/graph_bfs_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="graph_bfs_step3" class="animation-figure" src="../graph_traversal.assets/graph_bfs_step3.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../graph_traversal.assets/graph_bfs_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="graph_bfs_step4" class="animation-figure" src="../graph_traversal.assets/graph_bfs_step4.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../graph_traversal.assets/graph_bfs_step5.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="graph_bfs_step5" class="animation-figure" src="../graph_traversal.assets/graph_bfs_step5.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../graph_traversal.assets/graph_bfs_step6.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="graph_bfs_step6" class="animation-figure" src="../graph_traversal.assets/graph_bfs_step6.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../graph_traversal.assets/graph_bfs_step7.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="graph_bfs_step7" class="animation-figure" src="../graph_traversal.assets/graph_bfs_step7.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../graph_traversal.assets/graph_bfs_step8.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="graph_bfs_step8" class="animation-figure" src="../graph_traversal.assets/graph_bfs_step8.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../graph_traversal.assets/graph_bfs_step9.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="graph_bfs_step9" class="animation-figure" src="../graph_traversal.assets/graph_bfs_step9.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../graph_traversal.assets/graph_bfs_step10.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="graph_bfs_step10" class="animation-figure" src="../graph_traversal.assets/graph_bfs_step10.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../graph_traversal.assets/graph_bfs_step11.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="graph_bfs_step11" class="animation-figure" src="../graph_traversal.assets/graph_bfs_step11.png" /></a></p>
+</div>
+</div>
+</div>
+<p align="center"> 図 9-10 &nbsp; グラフの幅優先探索の手順 </p>
+
+<div class="admonition question">
+<p class="admonition-title">幅優先走査のシーケンスは一意ですか？</p>
+<p>一意ではありません。幅優先走査は「近くから遠く」の順序で走査することのみを要求し、<strong>同じ距離の頂点の走査順序は任意にできます</strong>。例えば、上図では、頂点<span class="arithmatex">\(1\)</span>と<span class="arithmatex">\(3\)</span>の訪問順序を交換できますし、頂点<span class="arithmatex">\(2\)</span>、<span class="arithmatex">\(4\)</span>、<span class="arithmatex">\(6\)</span>の順序も同様です。</p>
+</div>
+<h3 id="2">2. &nbsp; 計算量分析<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
+<p><strong>時間計算量</strong>：すべての頂点が一度ずつエンキューおよびデキューされ、<span class="arithmatex">\(O(|V|)\)</span>時間を使用します。隣接頂点を走査する過程で、無向グラフであるため、すべての辺が<span class="arithmatex">\(2\)</span>回訪問され、<span class="arithmatex">\(O(2|E|)\)</span>時間を使用します。全体で<span class="arithmatex">\(O(|V| + |E|)\)</span>時間を使用します。</p>
+<p><strong>空間計算量</strong>：リスト<code>res</code>、ハッシュセット<code>visited</code>、キュー<code>que</code>の最大頂点数は<span class="arithmatex">\(|V|\)</span>で、<span class="arithmatex">\(O(|V|)\)</span>空間を使用します。</p>
+<h2 id="932">9.3.2 &nbsp; 深さ優先探索<a class="headerlink" href="#932" title="Permanent link">&para;</a></h2>
+<p><strong>深さ優先探索は可能な限り遠くまで行き、それ以上のパスがない場合にバックトラックする走査方法です</strong>。下図に示すように、左上の頂点から開始し、それ以上のパスがなくなるまで現在の頂点のいずれかの隣接頂点を訪問し、次に戻って続行し、すべての頂点が走査されるまで続けます。</p>
+<p><a class="glightbox" href="../graph_traversal.assets/graph_dfs.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="グラフの深さ優先走査" class="animation-figure" src="../graph_traversal.assets/graph_dfs.png" /></a></p>
+<p align="center"> 図 9-11 &nbsp; グラフの深さ優先走査 </p>
+
+<h3 id="1_1">1. &nbsp; アルゴリズムの実装<a class="headerlink" href="#1_1" title="Permanent link">&para;</a></h3>
+<p>この「可能な限り遠くまで行ってから戻る」アルゴリズムパラダイムは通常再帰に基づいて実装されます。幅優先探索と同様に、深さ優先探索でも、再訪問を避けるために訪問済み頂点を記録するハッシュセット<code>visited</code>の助けが必要です。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="3:14"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><input id="__tabbed_3_14" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label><label for="__tabbed_3_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_dfs.py</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">:</span> <span class="n">GraphAdjList</span><span class="p">,</span> <span class="n">visited</span><span class="p">:</span> <span class="nb">set</span><span class="p">[</span><span class="n">Vertex</span><span class="p">],</span> <span class="n">res</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">Vertex</span><span class="p">],</span> <span class="n">vet</span><span class="p">:</span> <span class="n">Vertex</span><span class="p">):</span>
+<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;深さ優先走査のヘルパー関数&quot;&quot;&quot;</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a>    <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span>  <span class="c1"># 訪問済み頂点を記録</span>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a>    <span class="n">visited</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">vet</span><span class="p">)</span>  <span class="c1"># 頂点を訪問済みとしてマーク</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a>    <span class="c1"># その頂点のすべての隣接頂点を走査</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a>    <span class="k">for</span> <span class="n">adjVet</span> <span class="ow">in</span> <span class="n">graph</span><span class="o">.</span><span class="n">adj_list</span><span class="p">[</span><span class="n">vet</span><span class="p">]:</span>
+<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a>        <span class="k">if</span> <span class="n">adjVet</span> <span class="ow">in</span> <span class="n">visited</span><span class="p">:</span>
+<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a>            <span class="k">continue</span>  <span class="c1"># 既に訪問済みの頂点をスキップ</span>
+<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a>        <span class="c1"># 隣接頂点を再帰的に訪問</span>
+<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a>        <span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span> <span class="n">visited</span><span class="p">,</span> <span class="n">res</span><span class="p">,</span> <span class="n">adjVet</span><span class="p">)</span>
+<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a>
+<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="k">def</span><span class="w"> </span><span class="nf">graph_dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">:</span> <span class="n">GraphAdjList</span><span class="p">,</span> <span class="n">start_vet</span><span class="p">:</span> <span class="n">Vertex</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="n">Vertex</span><span class="p">]:</span>
+<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;深さ優先走査&quot;&quot;&quot;</span>
+<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a>    <span class="c1"># 隣接リストを使用してグラフを表現し、指定された頂点のすべての隣接頂点を取得</span>
+<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a>    <span class="c1"># 頂点走査シーケンス</span>
+<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a>    <span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>
+<a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a>    <span class="c1"># ハッシュセット、訪問済み頂点を記録するために使用</span>
+<a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a>    <span class="n">visited</span> <span class="o">=</span> <span class="nb">set</span><span class="p">[</span><span class="n">Vertex</span><span class="p">]()</span>
+<a id="__codelineno-14-19" name="__codelineno-14-19" href="#__codelineno-14-19"></a>    <span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span> <span class="n">visited</span><span class="p">,</span> <span class="n">res</span><span class="p">,</span> <span class="n">start_vet</span><span class="p">)</span>
+<a id="__codelineno-14-20" name="__codelineno-14-20" href="#__codelineno-14-20"></a>    <span class="k">return</span> <span class="n">res</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_dfs.cpp</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 深さ優先走査ヘルパー関数 */</span>
+<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="o">&amp;</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">unordered_set</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span><span class="w">   </span><span class="c1">// 訪問済み頂点を記録</span>
+<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="n">visited</span><span class="p">.</span><span class="n">emplace</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 頂点を訪問済みとしてマーク</span>
+<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">    </span><span class="c1">// その頂点のすべての隣接頂点を走査</span>
+<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">adjVet</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">graph</span><span class="p">.</span><span class="n">adjList</span><span class="p">[</span><span class="n">vet</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">visited</span><span class="p">.</span><span class="n">count</span><span class="p">(</span><span class="n">adjVet</span><span class="p">))</span>
+<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">            </span><span class="k">continue</span><span class="p">;</span><span class="w"> </span><span class="c1">// すでに訪問済みの頂点をスキップ</span>
+<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w">        </span><span class="c1">// 隣接頂点を再帰的に訪問</span>
+<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="w">        </span><span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">adjVet</span><span class="p">);</span>
+<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="p">}</span>
+<a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a>
+<a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="cm">/* 深さ優先走査 */</span>
+<a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="c1">// 隣接リストを使用してグラフを表現し、指定された頂点のすべての隣接頂点を取得</span>
+<a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a><span class="n">vector</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="n">graphDFS</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="o">&amp;</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="o">*</span><span class="n">startVet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-17" name="__codelineno-15-17" href="#__codelineno-15-17"></a><span class="w">    </span><span class="c1">// 頂点走査順序</span>
+<a id="__codelineno-15-18" name="__codelineno-15-18" href="#__codelineno-15-18"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-15-19" name="__codelineno-15-19" href="#__codelineno-15-19"></a><span class="w">    </span><span class="c1">// ハッシュセット、訪問済み頂点を記録するために使用</span>
+<a id="__codelineno-15-20" name="__codelineno-15-20" href="#__codelineno-15-20"></a><span class="w">    </span><span class="n">unordered_set</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="n">visited</span><span class="p">;</span>
+<a id="__codelineno-15-21" name="__codelineno-15-21" href="#__codelineno-15-21"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">startVet</span><span class="p">);</span>
+<a id="__codelineno-15-22" name="__codelineno-15-22" href="#__codelineno-15-22"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-15-23" name="__codelineno-15-23" href="#__codelineno-15-23"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_dfs.java</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 深さ優先走査の補助関数 */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">Set</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="n">vet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span><span class="w">     </span><span class="c1">// 訪問した頂点を記録</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="n">visited</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">vet</span><span class="p">);</span><span class="w"> </span><span class="c1">// 頂点を訪問済みとしてマーク</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">    </span><span class="c1">// その頂点のすべての隣接頂点を走査</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Vertex</span><span class="w"> </span><span class="n">adjVet</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">graph</span><span class="p">.</span><span class="na">adjList</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">vet</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">visited</span><span class="p">.</span><span class="na">contains</span><span class="p">(</span><span class="n">adjVet</span><span class="p">))</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">            </span><span class="k">continue</span><span class="p">;</span><span class="w"> </span><span class="c1">// すでに訪問済みの頂点をスキップ</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w">        </span><span class="c1">// 隣接頂点を再帰的に訪問</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w">        </span><span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">adjVet</span><span class="p">);</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="p">}</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a>
+<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="cm">/* 深さ優先走査 */</span>
+<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="c1">// 隣接リストを使用してグラフを表現し、指定した頂点のすべての隣接頂点を取得</span>
+<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a><span class="n">List</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="nf">graphDFS</span><span class="p">(</span><span class="n">GraphAdjList</span><span class="w"> </span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">Vertex</span><span class="w"> </span><span class="n">startVet</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-17" name="__codelineno-16-17" href="#__codelineno-16-17"></a><span class="w">    </span><span class="c1">// 頂点走査順序</span>
+<a id="__codelineno-16-18" name="__codelineno-16-18" href="#__codelineno-16-18"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-16-19" name="__codelineno-16-19" href="#__codelineno-16-19"></a><span class="w">    </span><span class="c1">// ハッシュセット、訪問済みの頂点を記録するために使用</span>
+<a id="__codelineno-16-20" name="__codelineno-16-20" href="#__codelineno-16-20"></a><span class="w">    </span><span class="n">Set</span><span class="o">&lt;</span><span class="n">Vertex</span><span class="o">&gt;</span><span class="w"> </span><span class="n">visited</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">HashSet</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-16-21" name="__codelineno-16-21" href="#__codelineno-16-21"></a><span class="w">    </span><span class="n">dfs</span><span class="p">(</span><span class="n">graph</span><span class="p">,</span><span class="w"> </span><span class="n">visited</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">startVet</span><span class="p">);</span>
+<a id="__codelineno-16-22" name="__codelineno-16-22" href="#__codelineno-16-22"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-16-23" name="__codelineno-16-23" href="#__codelineno-16-23"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_dfs.cs</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">graph_dfs</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">DFS</span><span class="p">}</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">graph_dfs</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">GraphDFS</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_dfs.go</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">dfs</span><span class="p">}</span>
+<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a>
+<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">graphDFS</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_dfs.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
+<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a>
+<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">graphDFS</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_dfs.js</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">dfs</span><span class="p">}</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a>
+<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">graphDFS</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_dfs.ts</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">dfs</span><span class="p">}</span>
+<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a>
+<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">graphDFS</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_dfs.dart</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
+<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">graphDFS</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_dfs.rs</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
+<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a>
+<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">graph_dfs</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_dfs.c</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">isVisited</span><span class="p">}</span>
+<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a>
+<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
+<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a>
+<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">graphDFS</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_dfs.kt</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">dfs</span><span class="p">}</span>
+<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a>
+<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">graphDFS</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_dfs.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">dfs</span><span class="p">}</span>
+<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a>
+<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">graph_dfs</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">graph_dfs.zig</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">dfs</span><span class="p">}</span>
+<a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a>
+<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">graphDFS</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>深さ優先探索のアルゴリズムプロセスを下図に示します。</p>
+<ul>
+<li><strong>破線は下向きの再帰を表し</strong>、新しい頂点を訪問するために新しい再帰メソッドが開始されたことを示します。</li>
+<li><strong>曲線の破線は上向きのバックトラックを表し</strong>、この再帰メソッドがこのメソッドが開始された位置に戻ったことを示します。</li>
+</ul>
+<p>理解を深めるため、下図とコードを組み合わせて、DFSプロセス全体を頭の中でシミュレート（または描画）することをお勧めします。各再帰メソッドがいつ開始され、いつ戻るかを含めてです。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="4:11"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><input id="__tabbed_4_6" name="__tabbed_4" type="radio" /><input id="__tabbed_4_7" name="__tabbed_4" type="radio" /><input id="__tabbed_4_8" name="__tabbed_4" type="radio" /><input id="__tabbed_4_9" name="__tabbed_4" type="radio" /><input id="__tabbed_4_10" name="__tabbed_4" type="radio" /><input id="__tabbed_4_11" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">&lt;1&gt;</label><label for="__tabbed_4_2">&lt;2&gt;</label><label for="__tabbed_4_3">&lt;3&gt;</label><label for="__tabbed_4_4">&lt;4&gt;</label><label for="__tabbed_4_5">&lt;5&gt;</label><label for="__tabbed_4_6">&lt;6&gt;</label><label for="__tabbed_4_7">&lt;7&gt;</label><label for="__tabbed_4_8">&lt;8&gt;</label><label for="__tabbed_4_9">&lt;9&gt;</label><label for="__tabbed_4_10">&lt;10&gt;</label><label for="__tabbed_4_11">&lt;11&gt;</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<p><a class="glightbox" href="../graph_traversal.assets/graph_dfs_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="グラフの深さ優先探索の手順" class="animation-figure" src="../graph_traversal.assets/graph_dfs_step1.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../graph_traversal.assets/graph_dfs_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="graph_dfs_step2" class="animation-figure" src="../graph_traversal.assets/graph_dfs_step2.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../graph_traversal.assets/graph_dfs_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="graph_dfs_step3" class="animation-figure" src="../graph_traversal.assets/graph_dfs_step3.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../graph_traversal.assets/graph_dfs_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="graph_dfs_step4" class="animation-figure" src="../graph_traversal.assets/graph_dfs_step4.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../graph_traversal.assets/graph_dfs_step5.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="graph_dfs_step5" class="animation-figure" src="../graph_traversal.assets/graph_dfs_step5.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../graph_traversal.assets/graph_dfs_step6.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="graph_dfs_step6" class="animation-figure" src="../graph_traversal.assets/graph_dfs_step6.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../graph_traversal.assets/graph_dfs_step7.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="graph_dfs_step7" class="animation-figure" src="../graph_traversal.assets/graph_dfs_step7.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../graph_traversal.assets/graph_dfs_step8.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="graph_dfs_step8" class="animation-figure" src="../graph_traversal.assets/graph_dfs_step8.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../graph_traversal.assets/graph_dfs_step9.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="graph_dfs_step9" class="animation-figure" src="../graph_traversal.assets/graph_dfs_step9.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../graph_traversal.assets/graph_dfs_step10.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="graph_dfs_step10" class="animation-figure" src="../graph_traversal.assets/graph_dfs_step10.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../graph_traversal.assets/graph_dfs_step11.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="graph_dfs_step11" class="animation-figure" src="../graph_traversal.assets/graph_dfs_step11.png" /></a></p>
+</div>
+</div>
+</div>
+<p align="center"> 図 9-12 &nbsp; グラフの深さ優先探索の手順 </p>
+
+<div class="admonition question">
+<p class="admonition-title">深さ優先走査のシーケンスは一意ですか？</p>
+<p>幅優先走査と同様に、深さ優先走査シーケンスの順序も一意ではありません。ある頂点が与えられた場合、どの方向を最初に探索することも可能です。つまり、隣接頂点の順序は任意にシャッフルできますが、すべて深さ優先走査の一部です。</p>
+<p>木の走査を例に取ると、「根 <span class="arithmatex">\(\rightarrow\)</span> 左 <span class="arithmatex">\(\rightarrow\)</span> 右」、「左 <span class="arithmatex">\(\rightarrow\)</span> 根 <span class="arithmatex">\(\rightarrow\)</span> 右」、「左 <span class="arithmatex">\(\rightarrow\)</span> 右 <span class="arithmatex">\(\rightarrow\)</span> 根」は、それぞれ前順、中順、後順走査に対応します。これらは3つの異なる走査優先度を示していますが、3つすべてが深さ優先走査と見なされます。</p>
+</div>
+<h3 id="2_1">2. &nbsp; 計算量分析<a class="headerlink" href="#2_1" title="Permanent link">&para;</a></h3>
+<p><strong>時間計算量</strong>：すべての頂点が一度訪問され、<span class="arithmatex">\(O(|V|)\)</span>時間を使用します。すべての辺が2回訪問され、<span class="arithmatex">\(O(2|E|)\)</span>時間を使用します。全体で<span class="arithmatex">\(O(|V| + |E|)\)</span>時間を使用します。</p>
+<p><strong>空間計算量</strong>：リスト<code>res</code>、ハッシュセット<code>visited</code>の最大頂点数は<span class="arithmatex">\(|V|\)</span>で、最大再帰深度は<span class="arithmatex">\(|V|\)</span>です。したがって、<span class="arithmatex">\(O(|V|)\)</span>空間を使用します。</p>
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new file mode 100644
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+  
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+    はじめに
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+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="./" class="md-nav__link md-nav__link--active">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link md-nav__link--active" for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
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+<p class="admonition-title">Abstract</p>
+<p>人生の旅路において、私たちの一人一人はノードであり、無数の見えない辺で結ばれています。</p>
+<p>一つ一つの出会いと別れが、この広大な人生のグラフに独特の印を残していきます。</p>
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+<li><a href="graph/">9.1 &nbsp; グラフ</a></li>
+<li><a href="graph_operations/">9.2 &nbsp; グラフの基本操作</a></li>
+<li><a href="graph_traversal/">9.3 &nbsp; グラフの走査</a></li>
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+    1.2 &nbsp; アルゴリズムとは何か
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+  
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+  
+
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+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
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+    1.3 &nbsp; まとめ
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+        
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+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
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+            第 2 章 &nbsp; 計算量解析
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+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
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+    2.1 &nbsp; アルゴリズム効率評価
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+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
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+
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+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
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+    2.3 &nbsp; 時間計算量
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+  
+
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+
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+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
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+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
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+  
+
+              
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+  
+  
+  
+  
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+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
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+            第 3 章 &nbsp; データ構造
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+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
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+    3.1 &nbsp; データ構造の分類
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+  
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+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
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+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
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+
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+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
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+  </span>
+  
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+  
+  
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+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
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+  </span>
+  
+
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+  
+
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+  
+  
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+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 重要な復習
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#2-q-a" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; Q &amp; A
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
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+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
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+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
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+  
+
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+          
+        
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+    
+    
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+      
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+            <a href="../../chapter_reference/" class="md-nav__link ">
+              
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9 3v15h3V3H9m3 2 4 13 3-1-4-13-3 1M5 5v13h3V5H5M3 19v2h18v-2H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    参考文献
+  </span>
+  
+
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+            
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+</nav>
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+            
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+              
+              <div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
+                <div class="md-sidebar__scrollwrap">
+                  <div class="md-sidebar__inner">
+                    
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+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 重要な復習
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#2-q-a" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; Q &amp; A
+    </span>
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+  
+</li>
+      
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+  
+</nav>
+                  </div>
+                </div>
+              </div>
+            
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+          
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+              <article class="md-content__inner md-typeset">
+                
+                  <!-- Tags -->
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+      href="https://github.com/krahets/hello-algo/tree/main/ja/docs/chapter_graph/summary.md"
+      title="編集"
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+    >
+      
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
+    </a>
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+  
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+<!-- Page content -->
+<h1 id="94">9.4 &nbsp; まとめ<a class="headerlink" href="#94" title="Permanent link">&para;</a></h1>
+<h3 id="1">1. &nbsp; 重要な復習<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<ul>
+<li>グラフは頂点と辺で構成されます。頂点の集合と辺の集合として記述できます。</li>
+<li>線形関係（連結リストなど）や階層関係（木など）と比較して、ネットワーク関係（グラフ）はより大きな柔軟性を提供し、より複雑になります。</li>
+<li>有向グラフでは、辺に方向があります。連結グラフでは、任意の頂点から他の任意の頂点に到達できます。重み付きグラフでは、各辺に関連する重み変数があります。</li>
+<li>隣接行列は、行列（2次元配列）を使用してグラフを表現する方法です。行と列は頂点を表します。行列要素の値は、2つの頂点間に辺があるかどうかを示し、辺がある場合は<span class="arithmatex">\(1\)</span>、ない場合は<span class="arithmatex">\(0\)</span>を使用します。隣接行列は辺の追加、削除、チェックなどの操作に非常に効率的ですが、より多くのスペースが必要です。</li>
+<li>隣接リストは、連結リストの集合を使用してグラフを表現するもう一つの一般的な方法です。グラフ内の各頂点には、その隣接するすべての頂点を含むリストがあります。<span class="arithmatex">\(i\)</span>番目のリストは頂点<span class="arithmatex">\(i\)</span>を表します。隣接リストは隣接行列と比較してより少ないスペースを使用します。ただし、辺を見つけるためにリストを走査する必要があるため、時間効率は低くなります。</li>
+<li>隣接リストの連結リストが十分に長くなったとき、ルックアップ効率を向上させるために赤黒木やハッシュテーブルに変換できます。</li>
+<li>アルゴリズム設計の観点から、隣接行列は「空間と時間のトレードオフ」の概念を反映し、隣接リストは「時間と空間のトレードオフ」を反映します。</li>
+<li>グラフは、ソーシャルネットワークや地下鉄路線など、さまざまな現実世界のシステムをモデル化するために使用できます。</li>
+<li>木はグラフの特別なケースであり、木の走査もグラフ走査の特別なケースです。</li>
+<li>グラフの幅優先走査は、近くから遠くへと層ごとに拡張する探索方法で、通常キューを使用します。</li>
+<li>グラフの深さ優先走査は、それ以上のパスがない場合にバックトラックする前に、まず終端に到達することを優先する探索方法です。しばしば再帰を使用して実装されます。</li>
+</ul>
+<h3 id="2-q-a">2. &nbsp; Q &amp; A<a class="headerlink" href="#2-q-a" title="Permanent link">&para;</a></h3>
+<p><strong>Q</strong>: パスは頂点のシーケンスとして定義されますか、それとも辺のシーケンスとして定義されますか？</p>
+<p>グラフ理論では、グラフ内のパスは頂点のシーケンスを結ぶ有限または無限の辺のシーケンスです。</p>
+<p>この文書では、パスは頂点のシーケンスではなく、辺のシーケンスと考えられます。これは、2つの頂点を結ぶ複数の辺がある可能性があり、その場合各辺がパスに対応するためです。</p>
+<p><strong>Q</strong>: 非連結グラフでは、走査できない点がありますか？</p>
+<p>非連結グラフでは、特定の点から到達できない頂点が少なくとも1つあります。非連結グラフを走査するには、グラフのすべての連結成分を走査するために複数の開始点を設定する必要があります。</p>
+<p><strong>Q</strong>: 隣接リストで、「その頂点に接続されたすべての頂点」の順序は重要ですか？</p>
+<p>任意の順序で構いません。ただし、実際のアプリケーションでは、頂点が追加された順序や頂点値の順序など、特定のルールに従ってそれらをソートする必要がある場合があります。これにより、特定の極値を持つ頂点を素早く見つけることができます。</p>
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diff --git a/ja/chapter_greedy/fractional_knapsack_problem.assets/fractional_knapsack_example.png b/ja/chapter_greedy/fractional_knapsack_problem.assets/fractional_knapsack_example.png
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diff --git a/ja/chapter_greedy/fractional_knapsack_problem.assets/fractional_knapsack_greedy_strategy.png b/ja/chapter_greedy/fractional_knapsack_problem.assets/fractional_knapsack_greedy_strategy.png
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+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_2" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_preface/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M21 4H3a2 2 0 0 0-2 2v13a2 2 0 0 0 2 2h18a2 2 0 0 0 2-2V6a2 2 0 0 0-2-2M3 19V6h8v13H3m18 0h-8V6h8v13m-7-9.5h6V11h-6V9.5m0 2.5h6v1.5h-6V12m0 2.5h6V16h-6v-1.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 0 章 &nbsp; 前書き
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_2" id="__nav_2_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_2_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_2">
+            <span class="md-nav__icon md-icon"></span>
+            第 0 章 &nbsp; 前書き
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/about_the_book/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.1 &nbsp; この本について
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/suggestions/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.2 &nbsp; 本書の使い方
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_introduction/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
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+<h1 id="152">15.2 &nbsp; 分数ナップサック問題<a class="headerlink" href="#152" title="Permanent link">&para;</a></h1>
+<div class="admonition question">
+<p class="admonition-title">Question</p>
+<p><span class="arithmatex">\(n\)</span> 個のアイテムが与えられ、<span class="arithmatex">\(i\)</span> 番目のアイテムの重量は <span class="arithmatex">\(wgt[i-1]\)</span> で値は <span class="arithmatex">\(val[i-1]\)</span> です。容量が <span class="arithmatex">\(cap\)</span> のナップサックがあります。各アイテムは1回のみ選択できますが、<strong>アイテムの一部を選択することができ、その値は選択された重量の割合に基づいて計算されます</strong>。限られた容量の下でナップサック内のアイテムの最大値は何ですか？例を下の図に示します。</p>
+</div>
+<p><a class="glightbox" href="../fractional_knapsack_problem.assets/fractional_knapsack_example.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="分数ナップサック問題の例データ" class="animation-figure" src="../fractional_knapsack_problem.assets/fractional_knapsack_example.png" /></a></p>
+<p align="center"> 図 15-3 &nbsp; 分数ナップサック問題の例データ </p>
+
+<p>分数ナップサック問題は全体的に0-1ナップサック問題と非常に似ており、現在のアイテム <span class="arithmatex">\(i\)</span> と容量 <span class="arithmatex">\(c\)</span> を含み、ナップサックの限られた容量内で値を最大化することを目的としています。</p>
+<p>違いは、この問題ではアイテムの一部のみを選択できることです。下の図に示すように、<strong>アイテムを任意に分割し、重量の割合に基づいて対応する値を計算できます</strong>。</p>
+<ol>
+<li>アイテム <span class="arithmatex">\(i\)</span> について、その単位重量あたりの値は <span class="arithmatex">\(val[i-1] / wgt[i-1]\)</span> で、単位値と呼ばれます。</li>
+<li>重量 <span class="arithmatex">\(w\)</span> のアイテム <span class="arithmatex">\(i\)</span> の一部をナップサックに入れるとすると、ナップサックに追加される値は <span class="arithmatex">\(w \times val[i-1] / wgt[i-1]\)</span> です。</li>
+</ol>
+<p><a class="glightbox" href="../fractional_knapsack_problem.assets/fractional_knapsack_unit_value.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="アイテムの単位重量あたりの値" class="animation-figure" src="../fractional_knapsack_problem.assets/fractional_knapsack_unit_value.png" /></a></p>
+<p align="center"> 図 15-4 &nbsp; アイテムの単位重量あたりの値 </p>
+
+<h3 id="1">1. &nbsp; 貪欲戦略の決定<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<p>ナップサック内のアイテムの総値を最大化することは、<strong>本質的に単位重量あたりの値を最大化することを意味します</strong>。これから、下の図に示す貪欲戦略を導出できます。</p>
+<ol>
+<li>アイテムを単位値の高い順から低い順にソートします。</li>
+<li>すべてのアイテムを反復し、**各ラウンドで最も高い単位値を持つアイテムを貪欲に選択**します。</li>
+<li>ナップサックの残り容量が不十分な場合、現在のアイテムの一部を使用してナップサックを満たします。</li>
+</ol>
+<p><a class="glightbox" href="../fractional_knapsack_problem.assets/fractional_knapsack_greedy_strategy.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="分数ナップサック問題の貪欲戦略" class="animation-figure" src="../fractional_knapsack_problem.assets/fractional_knapsack_greedy_strategy.png" /></a></p>
+<p align="center"> 図 15-5 &nbsp; 分数ナップサック問題の貪欲戦略 </p>
+
+<h3 id="2">2. &nbsp; コード実装<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
+<p>アイテムを単位値でソートするために <code>Item</code> クラスを作成しました。ナップサックが満たされるまでループして貪欲な選択を行い、その後終了して解を返します：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:14"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><input id="__tabbed_1_14" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label><label for="__tabbed_1_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">fractional_knapsack.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">Item</span><span class="p">:</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;アイテム&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">w</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">v</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">w</span> <span class="o">=</span> <span class="n">w</span>  <span class="c1"># アイテムの重量</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">v</span> <span class="o">=</span> <span class="n">v</span>  <span class="c1"># アイテムの価値</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="k">def</span><span class="w"> </span><span class="nf">fractional_knapsack</span><span class="p">(</span><span class="n">wgt</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">val</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">cap</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;分数ナップサック：貪欲法&quot;&quot;&quot;</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>    <span class="c1"># アイテムリストを作成、2 つの属性を含む：重量、価値</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>    <span class="n">items</span> <span class="o">=</span> <span class="p">[</span><span class="n">Item</span><span class="p">(</span><span class="n">w</span><span class="p">,</span> <span class="n">v</span><span class="p">)</span> <span class="k">for</span> <span class="n">w</span><span class="p">,</span> <span class="n">v</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">wgt</span><span class="p">,</span> <span class="n">val</span><span class="p">)]</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>    <span class="c1"># 単位価値 item.v / item.w で高い順にソート</span>
+<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>    <span class="n">items</span><span class="o">.</span><span class="n">sort</span><span class="p">(</span><span class="n">key</span><span class="o">=</span><span class="k">lambda</span> <span class="n">item</span><span class="p">:</span> <span class="n">item</span><span class="o">.</span><span class="n">v</span> <span class="o">/</span> <span class="n">item</span><span class="o">.</span><span class="n">w</span><span class="p">,</span> <span class="n">reverse</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>    <span class="c1"># 貪欲選択をループ</span>
+<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>    <span class="n">res</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>    <span class="k">for</span> <span class="n">item</span> <span class="ow">in</span> <span class="n">items</span><span class="p">:</span>
+<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>        <span class="k">if</span> <span class="n">item</span><span class="o">.</span><span class="n">w</span> <span class="o">&lt;=</span> <span class="n">cap</span><span class="p">:</span>
+<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a>            <span class="c1"># 残り容量が十分な場合、アイテム全体をナップサックに入れる</span>
+<a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a>            <span class="n">res</span> <span class="o">+=</span> <span class="n">item</span><span class="o">.</span><span class="n">v</span>
+<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a>            <span class="n">cap</span> <span class="o">-=</span> <span class="n">item</span><span class="o">.</span><span class="n">w</span>
+<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a>        <span class="k">else</span><span class="p">:</span>
+<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a>            <span class="c1"># 残り容量が不十分な場合、アイテムの一部をナップサックに入れる</span>
+<a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a>            <span class="n">res</span> <span class="o">+=</span> <span class="p">(</span><span class="n">item</span><span class="o">.</span><span class="n">v</span> <span class="o">/</span> <span class="n">item</span><span class="o">.</span><span class="n">w</span><span class="p">)</span> <span class="o">*</span> <span class="n">cap</span>
+<a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a>            <span class="c1"># 残り容量がなくなったため、ループを中断</span>
+<a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a>            <span class="k">break</span>
+<a id="__codelineno-0-26" name="__codelineno-0-26" href="#__codelineno-0-26"></a>    <span class="k">return</span> <span class="n">res</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">fractional_knapsack.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* アイテム */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">Item</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">  </span><span class="k">public</span><span class="o">:</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">w</span><span class="p">;</span><span class="w"> </span><span class="c1">// アイテムの重量</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">v</span><span class="p">;</span><span class="w"> </span><span class="c1">// アイテムの価値</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="n">Item</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">w</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">v</span><span class="p">)</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">w</span><span class="p">(</span><span class="n">w</span><span class="p">),</span><span class="w"> </span><span class="n">v</span><span class="p">(</span><span class="n">v</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="p">};</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="cm">/* 分数ナップサック：貪欲法 */</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="kt">double</span><span class="w"> </span><span class="nf">fractionalKnapsack</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">    </span><span class="c1">// アイテムリストを作成、2つの属性を含む：重量、価値</span>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">Item</span><span class="o">&gt;</span><span class="w"> </span><span class="n">items</span><span class="p">;</span>
+<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">        </span><span class="n">items</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">Item</span><span class="p">(</span><span class="n">wgt</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">val</span><span class="p">[</span><span class="n">i</span><span class="p">]));</span>
+<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w">    </span><span class="c1">// 単位価値 item.v / item.w で高い順にソート</span>
+<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="w">    </span><span class="n">sort</span><span class="p">(</span><span class="n">items</span><span class="p">.</span><span class="n">begin</span><span class="p">(),</span><span class="w"> </span><span class="n">items</span><span class="p">.</span><span class="n">end</span><span class="p">(),</span><span class="w"> </span><span class="p">[](</span><span class="n">Item</span><span class="w"> </span><span class="o">&amp;</span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">Item</span><span class="w"> </span><span class="o">&amp;</span><span class="n">b</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">double</span><span class="p">)</span><span class="n">a</span><span class="p">.</span><span class="n">v</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">a</span><span class="p">.</span><span class="n">w</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="p">(</span><span class="kt">double</span><span class="p">)</span><span class="n">b</span><span class="p">.</span><span class="n">v</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">b</span><span class="p">.</span><span class="n">w</span><span class="p">;</span><span class="w"> </span><span class="p">});</span>
+<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="w">    </span><span class="c1">// 貪欲選択をループ</span>
+<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="w">    </span><span class="kt">double</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="k">auto</span><span class="w"> </span><span class="o">&amp;</span><span class="n">item</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">items</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">item</span><span class="p">.</span><span class="n">w</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a><span class="w">            </span><span class="c1">// 残り容量が十分な場合、アイテム全体をナップサックに入れる</span>
+<a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a><span class="w">            </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">item</span><span class="p">.</span><span class="n">v</span><span class="p">;</span>
+<a id="__codelineno-1-26" name="__codelineno-1-26" href="#__codelineno-1-26"></a><span class="w">            </span><span class="n">cap</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="n">item</span><span class="p">.</span><span class="n">w</span><span class="p">;</span>
+<a id="__codelineno-1-27" name="__codelineno-1-27" href="#__codelineno-1-27"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-28" name="__codelineno-1-28" href="#__codelineno-1-28"></a><span class="w">            </span><span class="c1">// 残り容量が不十分な場合、アイテムの一部をナップサックに入れる</span>
+<a id="__codelineno-1-29" name="__codelineno-1-29" href="#__codelineno-1-29"></a><span class="w">            </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="p">(</span><span class="kt">double</span><span class="p">)</span><span class="n">item</span><span class="p">.</span><span class="n">v</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">item</span><span class="p">.</span><span class="n">w</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">cap</span><span class="p">;</span>
+<a id="__codelineno-1-30" name="__codelineno-1-30" href="#__codelineno-1-30"></a><span class="w">            </span><span class="c1">// 残り容量がなくなったため、ループを中断</span>
+<a id="__codelineno-1-31" name="__codelineno-1-31" href="#__codelineno-1-31"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-1-32" name="__codelineno-1-32" href="#__codelineno-1-32"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-1-33" name="__codelineno-1-33" href="#__codelineno-1-33"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-34" name="__codelineno-1-34" href="#__codelineno-1-34"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-1-35" name="__codelineno-1-35" href="#__codelineno-1-35"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">fractional_knapsack.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* アイテム */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kd">class</span> <span class="nc">Item</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">w</span><span class="p">;</span><span class="w"> </span><span class="c1">// アイテムの重量</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">v</span><span class="p">;</span><span class="w"> </span><span class="c1">// アイテムの価値</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="nf">Item</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">w</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">v</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="na">w</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">w</span><span class="p">;</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="na">v</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">v</span><span class="p">;</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="p">}</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="cm">/* 分数ナップサック：貪欲法 */</span>
+<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="kt">double</span><span class="w"> </span><span class="nf">fractionalKnapsack</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">wgt</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">    </span><span class="c1">// アイテムリストを作成、2つの属性を含む：重量、価値</span>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">    </span><span class="n">Item</span><span class="o">[]</span><span class="w"> </span><span class="n">items</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Item</span><span class="o">[</span><span class="n">wgt</span><span class="p">.</span><span class="na">length</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">wgt</span><span class="p">.</span><span class="na">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w">        </span><span class="n">items</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Item</span><span class="p">(</span><span class="n">wgt</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">);</span>
+<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w">    </span><span class="c1">// 単位価値 item.v / item.w で高い順にソート</span>
+<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="w">    </span><span class="n">Arrays</span><span class="p">.</span><span class="na">sort</span><span class="p">(</span><span class="n">items</span><span class="p">,</span><span class="w"> </span><span class="n">Comparator</span><span class="p">.</span><span class="na">comparingDouble</span><span class="p">(</span><span class="n">item</span><span class="w"> </span><span class="o">-&gt;</span><span class="w"> </span><span class="o">-</span><span class="p">((</span><span class="kt">double</span><span class="p">)</span><span class="w"> </span><span class="n">item</span><span class="p">.</span><span class="na">v</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">item</span><span class="p">.</span><span class="na">w</span><span class="p">)));</span>
+<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="w">    </span><span class="c1">// 貪欲選択をループ</span>
+<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a><span class="w">    </span><span class="kt">double</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Item</span><span class="w"> </span><span class="n">item</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">items</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">item</span><span class="p">.</span><span class="na">w</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">cap</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a><span class="w">            </span><span class="c1">// 残り容量が十分な場合、アイテム全体をナップサックに入れる</span>
+<a id="__codelineno-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></a><span class="w">            </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">item</span><span class="p">.</span><span class="na">v</span><span class="p">;</span>
+<a id="__codelineno-2-27" name="__codelineno-2-27" href="#__codelineno-2-27"></a><span class="w">            </span><span class="n">cap</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="n">item</span><span class="p">.</span><span class="na">w</span><span class="p">;</span>
+<a id="__codelineno-2-28" name="__codelineno-2-28" href="#__codelineno-2-28"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-29" name="__codelineno-2-29" href="#__codelineno-2-29"></a><span class="w">            </span><span class="c1">// 残り容量が不十分な場合、アイテムの一部をナップサックに入れる</span>
+<a id="__codelineno-2-30" name="__codelineno-2-30" href="#__codelineno-2-30"></a><span class="w">            </span><span class="n">res</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="p">(</span><span class="kt">double</span><span class="p">)</span><span class="w"> </span><span class="n">item</span><span class="p">.</span><span class="na">v</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">item</span><span class="p">.</span><span class="na">w</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">cap</span><span class="p">;</span>
+<a id="__codelineno-2-31" name="__codelineno-2-31" href="#__codelineno-2-31"></a><span class="w">            </span><span class="c1">// 残り容量がなくなったため、ループを中断</span>
+<a id="__codelineno-2-32" name="__codelineno-2-32" href="#__codelineno-2-32"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-2-33" name="__codelineno-2-33" href="#__codelineno-2-33"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-2-34" name="__codelineno-2-34" href="#__codelineno-2-34"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-35" name="__codelineno-2-35" href="#__codelineno-2-35"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-2-36" name="__codelineno-2-36" href="#__codelineno-2-36"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">fractional_knapsack.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">Item</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">fractional_knapsack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">FractionalKnapsack</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">fractional_knapsack.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">Item</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">fractionalKnapsack</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">fractional_knapsack.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">Item</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">fractionalKnapsack</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">fractional_knapsack.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">Item</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">fractionalKnapsack</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">fractional_knapsack.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">Item</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">fractionalKnapsack</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">fractional_knapsack.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">Item</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">fractionalKnapsack</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">fractional_knapsack.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">Item</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">fractional_knapsack</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">fractional_knapsack.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">Item</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">fractionalKnapsack</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">fractional_knapsack.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">Item</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">fractionalKnapsack</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">fractional_knapsack.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">Item</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">fractional_knapsack</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">fractional_knapsack.zig</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">Item</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a>
+<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">fractionalKnapsack</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>ソート以外に、最悪の場合、アイテムのリスト全体を走査する必要があるため、<strong>時間計算量は <span class="arithmatex">\(O(n)\)</span></strong> です。ここで <span class="arithmatex">\(n\)</span> はアイテムの数です。</p>
+<p><code>Item</code> オブジェクトリストが初期化されるため、<strong>空間計算量は <span class="arithmatex">\(O(n)\)</span></strong> です。</p>
+<h3 id="3">3. &nbsp; 正しさの証明<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
+<p>背理法を使用します。アイテム <span class="arithmatex">\(x\)</span> が最高の単位値を持ち、あるアルゴリズムが最大値 <code>res</code> を生成するが、解にアイテム <span class="arithmatex">\(x\)</span> が含まれていないと仮定します。</p>
+<p>今、ナップサックから任意のアイテムの単位重量を取り除き、アイテム <span class="arithmatex">\(x\)</span> の単位重量で置き換えます。アイテム <span class="arithmatex">\(x\)</span> の単位値が最高であるため、置き換え後の総値は確実に <code>res</code> より大きくなります。<strong>これは <code>res</code> が最適解であるという仮定と矛盾し、最適解には必ずアイテム <span class="arithmatex">\(x\)</span> が含まれることを証明します</strong>。</p>
+<p>この解の他のアイテムについても、上記の矛盾を構築できます。全体的に、**単位値がより大きいアイテムは常により良い選択**であり、貪欲戦略が効果的であることを証明します。</p>
+<p>下の図に示すように、アイテムの重量と単位値をそれぞれ二次元チャートの横軸と縦軸と見なすと、分数ナップサック問題は「限られた横軸範囲内で囲まれる最大面積を求める」ことに変換できます。この類推は、幾何学的観点から貪欲戦略の効果を理解するのに役立ちます。</p>
+<p><a class="glightbox" href="../fractional_knapsack_problem.assets/fractional_knapsack_area_chart.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="分数ナップサック問題の幾何学的表現" class="animation-figure" src="../fractional_knapsack_problem.assets/fractional_knapsack_area_chart.png" /></a></p>
+<p align="center"> 図 15-6 &nbsp; 分数ナップサック問題の幾何学的表現 </p>
+
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+    krahets/hello-algo
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+</a>
+    </div>
+  
+  <ul class="md-nav__list" data-md-scrollfix>
+    
+      
+      
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+  
+  <span class="md-ellipsis">
+    はじめに
+  </span>
+  
+
+            </a>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_1_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_1">
+            <span class="md-nav__icon md-icon"></span>
+            はじめに
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
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+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
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+        
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+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
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+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_2" >
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+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_preface/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M21 4H3a2 2 0 0 0-2 2v13a2 2 0 0 0 2 2h18a2 2 0 0 0 2-2V6a2 2 0 0 0-2-2M3 19V6h8v13H3m18 0h-8V6h8v13m-7-9.5h6V11h-6V9.5m0 2.5h6v1.5h-6V12m0 2.5h6V16h-6v-1.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 0 章 &nbsp; 前書き
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_2" id="__nav_2_label" tabindex="0">
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_2_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_2">
+            <span class="md-nav__icon md-icon"></span>
+            第 0 章 &nbsp; 前書き
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/about_the_book/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.1 &nbsp; この本について
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/suggestions/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.2 &nbsp; 本書の使い方
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
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+      
+      
+  
+  
+  
+  
+    
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+      
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+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_introduction/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
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+    </li>
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+    15.1 &nbsp; 貪欲アルゴリズム
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+  
+
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+        </label>
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+      <a href="./" class="md-nav__link md-nav__link--active">
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+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
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+    
+  
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+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1511" class="md-nav__link">
+    <span class="md-ellipsis">
+      15.1.1 &nbsp; 貪欲アルゴリズムの利点と制限
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1512" class="md-nav__link">
+    <span class="md-ellipsis">
+      15.1.2 &nbsp; 貪欲アルゴリズムの特徴
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1513" class="md-nav__link">
+    <span class="md-ellipsis">
+      15.1.3 &nbsp; 貪欲アルゴリズムによる問題解決のステップ
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1514" class="md-nav__link">
+    <span class="md-ellipsis">
+      15.1.4 &nbsp; 貪欲アルゴリズムで解決される典型的な問題
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
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+    </li>
+  
+
+              
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+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
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+    </li>
+  
+
+              
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+        </nav>
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+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
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+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
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+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
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+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1511" class="md-nav__link">
+    <span class="md-ellipsis">
+      15.1.1 &nbsp; 貪欲アルゴリズムの利点と制限
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1512" class="md-nav__link">
+    <span class="md-ellipsis">
+      15.1.2 &nbsp; 貪欲アルゴリズムの特徴
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1513" class="md-nav__link">
+    <span class="md-ellipsis">
+      15.1.3 &nbsp; 貪欲アルゴリズムによる問題解決のステップ
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1514" class="md-nav__link">
+    <span class="md-ellipsis">
+      15.1.4 &nbsp; 貪欲アルゴリズムで解決される典型的な問題
+    </span>
+  </a>
+  
+</li>
+      
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+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
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+<h1 id="151">15.1 &nbsp; 貪欲アルゴリズム<a class="headerlink" href="#151" title="Permanent link">&para;</a></h1>
+<p><u>貪欲アルゴリズム</u>は最適化問題を解決するための一般的なアルゴリズムで、基本的に問題の各意思決定段階で最も良い選択をすること、つまり局所的に最適な決定を貪欲に行い、グローバルに最適な解を見つけることを望みます。貪欲アルゴリズムは簡潔で効率的であり、多くの実用的な問題で広く使用されています。</p>
+<p>貪欲アルゴリズムと動的プログラミングは、どちらも最適化問題を解決するためによく使用されます。両者は最適部分構造の性質に依存するなど、いくつかの類似点を共有していますが、動作方法が異なります。</p>
+<ul>
+<li>動的プログラミングは現在の決定段階ですべての以前の決定を考慮し、過去の部分問題の解を使用して現在の部分問題の解を構築します。</li>
+<li>貪欲アルゴリズムは過去の決定を考慮せず、代わりに貪欲な選択を続け、問題が解決されるまで問題の範囲を継続的に狭めます。</li>
+</ul>
+<p>まず、「完全ナップサック問題」の章で紹介された「コイン交換」の例を通じて貪欲アルゴリズムの動作原理を理解しましょう。すでによく知っていると思います。</p>
+<div class="admonition question">
+<p class="admonition-title">Question</p>
+<p><span class="arithmatex">\(n\)</span> 種類のコインが与えられ、<span class="arithmatex">\(i\)</span> 番目の種類のコインの額面は <span class="arithmatex">\(coins[i - 1]\)</span> で、目標金額は <span class="arithmatex">\(amt\)</span> です。各種類のコインは無制限に利用可能で、目標金額を構成するのに必要な最小コイン数は何ですか？目標金額を構成できない場合は <span class="arithmatex">\(-1\)</span> を返してください。</p>
+</div>
+<p>この問題で採用される貪欲戦略を下の図に示します。目標金額が与えられたとき、**それに最も近く、それを超えないコインを貪欲に選択**し、目標金額が満たされるまでこのステップを繰り返します。</p>
+<p><a class="glightbox" href="../greedy_algorithm.assets/coin_change_greedy_strategy.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="コイン交換の貪欲戦略" class="animation-figure" src="../greedy_algorithm.assets/coin_change_greedy_strategy.png" /></a></p>
+<p align="center"> 図 15-1 &nbsp; コイン交換の貪欲戦略 </p>
+
+<p>実装コードは以下の通りです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:14"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><input id="__tabbed_1_14" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label><label for="__tabbed_1_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change_greedy.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">coin_change_greedy</span><span class="p">(</span><span class="n">coins</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">amt</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;硬貨交換：貪欲法&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># coins リストがソートされていると仮定</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="n">i</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">coins</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="n">count</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="c1"># 残り金額がなくなるまで貪欲選択をループ</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>    <span class="k">while</span> <span class="n">amt</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">:</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>        <span class="c1"># 残り金額に最も近く、それより小さい硬貨を見つける</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>        <span class="k">while</span> <span class="n">i</span> <span class="o">&gt;</span> <span class="mi">0</span> <span class="ow">and</span> <span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">amt</span><span class="p">:</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>            <span class="n">i</span> <span class="o">-=</span> <span class="mi">1</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>        <span class="c1"># coins[i] を選択</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>        <span class="n">amt</span> <span class="o">-=</span> <span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>        <span class="n">count</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>    <span class="c1"># 実行可能な解が見つからない場合、-1 を返す</span>
+<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>    <span class="k">return</span> <span class="n">count</span> <span class="k">if</span> <span class="n">amt</span> <span class="o">==</span> <span class="mi">0</span> <span class="k">else</span> <span class="o">-</span><span class="mi">1</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change_greedy.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 硬貨両替：貪欲法 */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">coinChangeGreedy</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// 硬貨リストが順序付けされていると仮定</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="c1">// 残り金額がなくなるまで貪欲選択をループ</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">        </span><span class="c1">// 残り金額に近く、それ以下の最小硬貨を見つける</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">            </span><span class="n">i</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">        </span><span class="c1">// coins[i] を選択</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">        </span><span class="n">amt</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="n">coins</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">    </span><span class="c1">// 実行可能な解が見つからない場合、-1 を返す</span>
+<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
+<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change_greedy.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 硬貨両替：貪欲法 */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">coinChangeGreedy</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">coins</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// 硬貨リストが順序付けされていると仮定</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">coins</span><span class="p">.</span><span class="na">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="c1">// 残り金額がなくなるまで貪欲選択をループ</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">amt</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">        </span><span class="c1">// 残り金額に近く、それ以下の最小硬貨を見つける</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">amt</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">            </span><span class="n">i</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">        </span><span class="c1">// coins[i] を選択</span>
+<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">        </span><span class="n">amt</span><span class="w"> </span><span class="o">-=</span><span class="w"> </span><span class="n">coins</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">        </span><span class="n">count</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">    </span><span class="c1">// 実行可能な解が見つからない場合、-1 を返す</span>
+<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">amt</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">count</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change_greedy.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">coin_change_greedy</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">CoinChangeGreedy</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change_greedy.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">coinChangeGreedy</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change_greedy.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">coinChangeGreedy</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change_greedy.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">coinChangeGreedy</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change_greedy.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">coinChangeGreedy</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change_greedy.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">coinChangeGreedy</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change_greedy.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">coin_change_greedy</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change_greedy.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">coinChangeGreedy</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change_greedy.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">coinChangeGreedy</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change_greedy.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">coin_change_greedy</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">coin_change_greedy.zig</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">coinChangeGreedy</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>感嘆するかもしれません：なんて簡潔なんだ！貪欲アルゴリズムは約10行のコードでコイン交換問題を解決します。</p>
+<h2 id="1511">15.1.1 &nbsp; 貪欲アルゴリズムの利点と制限<a class="headerlink" href="#1511" title="Permanent link">&para;</a></h2>
+<p><strong>貪欲アルゴリズムは直接的で実装が簡単であるだけでなく、通常非常に効率的でもあります</strong>。上記のコードで、最小のコイン額面を <span class="arithmatex">\(\min(coins)\)</span> とすると、貪欲な選択ループは最大 <span class="arithmatex">\(amt / \min(coins)\)</span> 回実行され、時間計算量は <span class="arithmatex">\(O(amt / \min(coins))\)</span> になります。これは動的プログラミング解法の時間計算量 <span class="arithmatex">\(O(n \times amt)\)</span> よりも一桁小さいです。</p>
+<p>しかし、<strong>一部のコイン額面の組み合わせでは、貪欲アルゴリズムは最適解を見つけることができません</strong>。下の図は2つの例を示しています。</p>
+<ul>
+<li><strong>正の例 <span class="arithmatex">\(coins = [1, 5, 10, 20, 50, 100]\)</span></strong>：このコインの組み合わせでは、任意の <span class="arithmatex">\(amt\)</span> に対して、貪欲アルゴリズムは最適解を見つけることができます。</li>
+<li><strong>負の例 <span class="arithmatex">\(coins = [1, 20, 50]\)</span></strong>：<span class="arithmatex">\(amt = 60\)</span> とすると、貪欲アルゴリズムは組み合わせ <span class="arithmatex">\(50 + 1 \times 10\)</span> しか見つけられず、合計11枚のコインですが、動的プログラミングは最適解 <span class="arithmatex">\(20 + 20 + 20\)</span> を見つけることができ、3枚のコインのみが必要です。</li>
+<li><strong>負の例 <span class="arithmatex">\(coins = [1, 49, 50]\)</span></strong>：<span class="arithmatex">\(amt = 98\)</span> とすると、貪欲アルゴリズムは組み合わせ <span class="arithmatex">\(50 + 1 \times 48\)</span> しか見つけられず、合計49枚のコインですが、動的プログラミングは最適解 <span class="arithmatex">\(49 + 49\)</span> を見つけることができ、2枚のコインのみが必要です。</li>
+</ul>
+<p><a class="glightbox" href="../greedy_algorithm.assets/coin_change_greedy_vs_dp.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="貪欲アルゴリズムが最適解を見つけられない例" class="animation-figure" src="../greedy_algorithm.assets/coin_change_greedy_vs_dp.png" /></a></p>
+<p align="center"> 図 15-2 &nbsp; 貪欲アルゴリズムが最適解を見つけられない例 </p>
+
+<p>これは、コイン交換問題において、貪欲アルゴリズムがグローバルに最適な解を見つけることを保証できず、非常に悪い解を見つける可能性があることを意味します。動的プログラミングの方が適しています。</p>
+<p>一般的に、貪欲アルゴリズムの適用性は2つのカテゴリに分類されます。</p>
+<ol>
+<li><strong>最適解を見つけることが保証される</strong>：これらの場合、貪欲アルゴリズムはしばしば最良の選択で、バックトラッキングや動的プログラミングよりも効率的である傾向があります。</li>
+<li><strong>準最適解を見つけることができる</strong>：貪欲アルゴリズムはここでも適用可能です。多くの複雑な問題では、グローバル最適解を見つけることは非常に困難であり、高効率の準最適解を見つけることも非常に価値があります。</li>
+</ol>
+<h2 id="1512">15.1.2 &nbsp; 貪欲アルゴリズムの特徴<a class="headerlink" href="#1512" title="Permanent link">&para;</a></h2>
+<p>それでは、どのような問題が貪欲アルゴリズムで解決するのに適しているのでしょうか？言い換えれば、どのような条件下で貪欲アルゴリズムは最適解を見つけることを保証できるのでしょうか？</p>
+<p>動的プログラミングと比較して、貪欲アルゴリズムはより厳しい使用条件を持ち、主に問題の2つの性質に焦点を当てています。</p>
+<ul>
+<li><strong>貪欲選択性</strong>：局所的に最適な選択が常にグローバルに最適な解に導くことができる場合のみ、貪欲アルゴリズムは最適解を得ることを保証できます。</li>
+<li><strong>最適部分構造</strong>：元の問題の最適解はその部分問題の最適解を含みます。</li>
+</ul>
+<p>最適部分構造は「動的プログラミング」の章ですでに紹介されているため、ここではこれ以上議論しません。一部の問題には明らかな最適部分構造がありませんが、それでも貪欲アルゴリズムを使用して解決できることに注意することが重要です。</p>
+<p>主に貪欲選択性を決定する方法を探索します。その記述は単純に見えますが、<strong>実際には、多くの問題の貪欲選択性を証明することは容易ではありません</strong>。</p>
+<p>例えば、コイン交換問題では、貪欲選択性を反証するために反例を簡単に挙げることができますが、それを証明することははるかに困難です。**コインの組み合わせが貪欲アルゴリズムを使用して解決できるためには、どのような条件を満たす必要があるか**と尋ねられた場合、厳密な数学的証明を提供することが困難であるため、しばしば直感や例に頼って曖昧な答えを提供しなければなりません。</p>
+<div class="admonition quote">
+<p class="admonition-title">Quote</p>
+<p>ある論文では、コインの組み合わせが任意の金額に対して貪欲アルゴリズムを使用して最適解を見つけることができるかどうかを判定するための時間計算量 <span class="arithmatex">\(O(n^3)\)</span> のアルゴリズムが提示されています。</p>
+<p>Pearson, D. A polynomial-time algorithm for the change-making problem[J]. Operations Research Letters, 2005, 33(3): 231-234.</p>
+</div>
+<h2 id="1513">15.1.3 &nbsp; 貪欲アルゴリズムによる問題解決のステップ<a class="headerlink" href="#1513" title="Permanent link">&para;</a></h2>
+<p>貪欲問題の問題解決プロセスは、一般的に以下の3つのステップに分けることができます。</p>
+<ol>
+<li><strong>問題分析</strong>：問題の特徴を整理し理解する。状態定義、最適化目標、制約などを含みます。このステップはバックトラッキングや動的プログラミングでも関与します。</li>
+<li><strong>貪欲戦略の決定</strong>：各ステップで貪欲な選択をする方法を決定する。この戦略は各ステップで問題の規模を縮小し、最終的に問題全体を解決できます。</li>
+<li><strong>正確性の証明</strong>：通常、問題が貪欲選択性と最適部分構造の両方を持つことを証明する必要があります。このステップには、帰納法や背理法などの数学的証明が必要な場合があります。</li>
+</ol>
+<p>貪欲戦略の決定は問題解決の核心ステップですが、実装は容易ではない場合があります。主な理由は以下の通りです。</p>
+<ul>
+<li><strong>異なる問題間で貪欲戦略は大きく異なる</strong>。多くの問題では、貪欲戦略はかなり直接的で、一般的な思考と試行を通じて思いつくことができます。しかし、一部の複雑な問題では、貪欲戦略は非常に見つけにくく、これは個人の問題解決経験とアルゴリズム能力の真のテストです。</li>
+<li><strong>一部の貪欲戦略は非常に誤解を招く</strong>。自信を持って貪欲戦略を設計し、コードを書いてテストに提出したとき、一部のテストケースが通らない可能性が高いです。これは設計された貪欲戦略が「部分的に正しい」だけであるためで、上記のコイン交換の例で説明した通りです。</li>
+</ul>
+<p>正確性を確保するために、貪欲戦略に対して厳密な数学的証明を提供すべきで、<strong>通常は背理法や数学的帰納法を含みます</strong>。</p>
+<p>しかし、正確性を証明することは容易な作業ではない場合があります。途方に暮れた場合、通常はテストケースに基づいてコードをデバッグし、貪欲戦略を段階的に修正し検証することを選択します。</p>
+<h2 id="1514">15.1.4 &nbsp; 貪欲アルゴリズムで解決される典型的な問題<a class="headerlink" href="#1514" title="Permanent link">&para;</a></h2>
+<p>貪欲アルゴリズムは、貪欲選択と最適部分構造の性質を満たす最適化問題によく適用されます。以下は典型的な貪欲アルゴリズム問題のいくつかです。</p>
+<ul>
+<li><strong>コイン交換問題</strong>：一部のコインの組み合わせでは、貪欲アルゴリズムは常に最適解を提供します。</li>
+<li><strong>区間スケジューリング問題</strong>：いくつかのタスクがあり、それぞれが一定期間にわたって行われるとします。目標はできるだけ多くのタスクを完了することです。常に最も早く終了するタスクを選択すると、貪欲アルゴリズムは最適解を達成できます。</li>
+<li><strong>分数ナップサック問題</strong>：アイテムのセットと運搬容量が与えられ、目標は総重量が運搬容量を超えず、総価値が最大化されるようなアイテムのセットを選択することです。常に最高の価値対重量比（価値/重量）のアイテムを選択すると、貪欲アルゴリズムは一部のケースで最適解を達成できます。</li>
+<li><strong>株式取引問題</strong>：株価の履歴のセットが与えられ、複数回の取引を行うことができますが、すでに株式を所有している場合は売却後でないと再度購入できません。目標は最大利益を達成することです。</li>
+<li><strong>ハフマン符号化</strong>：ハフマン符号化は無損失データ圧縮に使用される貪欲アルゴリズムです。ハフマン木を構築することにより、常に最低頻度の2つのノードを統合し、最小重み付きパス長（符号化長）のハフマン木を生成します。</li>
+<li><strong>ダイクストラのアルゴリズム</strong>：これは与えられたソース頂点から他のすべての頂点への最短経路問題を解決するための貪欲アルゴリズムです。</li>
+</ul>
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+  
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+      <a href="../chapter_preface/about_the_book/" class="md-nav__link">
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+      <a href="../chapter_preface/summary/" class="md-nav__link">
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+  
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+  
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+    1.3 &nbsp; まとめ
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+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
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+            第 2 章 &nbsp; 計算量解析
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+    2.1 &nbsp; アルゴリズム効率評価
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+      <a href="../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
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+    2.2 &nbsp; 反復と再帰
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+  
+
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+      <a href="../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
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+    2.3 &nbsp; 時間計算量
+  </span>
+  
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+      <a href="../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
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+    </li>
+  
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+  
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+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
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+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="./" class="md-nav__link md-nav__link--active">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link md-nav__link--active" for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
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+  
+  
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+      
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+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
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+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_appendix/" class="md-nav__link ">
+              
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
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+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
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+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
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+            
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
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+  
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+      
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+            <a href="../chapter_reference/" class="md-nav__link ">
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+  
+  <span class="md-ellipsis">
+    参考文献
+  </span>
+  
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+<h1 id="15">第 15 章 &nbsp; 貪欲法<a class="headerlink" href="#15" title="Permanent link">&para;</a></h1>
+<p><a class="glightbox" href="../assets/covers/chapter_greedy.jpg" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="貪欲法" class="cover-image" src="../assets/covers/chapter_greedy.jpg" /></a></p>
+<div class="admonition abstract">
+<p class="admonition-title">Abstract</p>
+<p>ひまわりは太陽の方を向き、常に自分にとって最大の成長を求めます。</p>
+<p>貪欲な戦略は、一連の単純な選択を通じて、段階的に最良の答えへと導きます。</p>
+</div>
+<h2 id="_1">章の内容<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h2>
+<ul>
+<li><a href="greedy_algorithm/">15.1 &nbsp; 貪欲アルゴリズム</a></li>
+<li><a href="fractional_knapsack_problem/">15.2 &nbsp; 分数ナップサック問題</a></li>
+<li><a href="max_capacity_problem/">15.3 &nbsp; 最大容量問題</a></li>
+<li><a href="max_product_cutting_problem/">15.4 &nbsp; 最大積切断問題</a></li>
+<li><a href="summary/">15.5 &nbsp; まとめ</a></li>
+</ul>
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+        
+  
+  <span class="md-ellipsis">
+    0.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_introduction/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
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+      <a href="../max_product_cutting_problem/" class="md-nav__link">
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+  
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+<h1 id="153">15.3 &nbsp; 最大容量問題<a class="headerlink" href="#153" title="Permanent link">&para;</a></h1>
+<div class="admonition question">
+<p class="admonition-title">Question</p>
+<p>配列 <span class="arithmatex">\(ht\)</span> を入力します。各要素は垂直仕切りの高さを表します。配列内の任意の2つの仕切りと、それらの間のスペースによってコンテナを形成できます。</p>
+<p>コンテナの容量は高さと幅の積（面積）で、高さは短い方の仕切りによって決定され、幅は2つの仕切りの配列インデックスの差です。</p>
+<p>コンテナの容量を最大化する2つの仕切りを配列から選択し、この最大容量を返してください。例を下の図に示します。</p>
+</div>
+<p><a class="glightbox" href="../max_capacity_problem.assets/max_capacity_example.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="最大容量問題の例データ" class="animation-figure" src="../max_capacity_problem.assets/max_capacity_example.png" /></a></p>
+<p align="center"> 図 15-7 &nbsp; 最大容量問題の例データ </p>
+
+<p>コンテナは任意の2つの仕切りによって形成されるため、<strong>この問題の状態は2つの仕切りのインデックスで表現され、<span class="arithmatex">\([i, j]\)</span> と表記されます</strong>。</p>
+<p>問題の記述によれば、容量は高さと幅の積に等しく、高さは短い方の仕切りによって決定され、幅は2つの仕切りの配列インデックスの差です。容量 <span class="arithmatex">\(cap[i, j]\)</span> の式は：</p>
+<div class="arithmatex">\[
+cap[i, j] = \min(ht[i], ht[j]) \times (j - i)
+\]</div>
+<p>配列の長さを <span class="arithmatex">\(n\)</span> と仮定すると、2つの仕切りの組み合わせ数（状態の総数）は <span class="arithmatex">\(C_n^2 = \frac{n(n - 1)}{2}\)</span> です。最も直接的なアプローチは**すべての可能な状態を列挙する**ことで、時間計算量は <span class="arithmatex">\(O(n^2)\)</span> になります。</p>
+<h3 id="1">1. &nbsp; 貪欲戦略の決定<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<p>この問題にはより効率的な解法があります。下の図に示すように、インデックス <span class="arithmatex">\(i &lt; j\)</span> かつ高さ <span class="arithmatex">\(ht[i] &lt; ht[j]\)</span> の状態 <span class="arithmatex">\([i, j]\)</span> を選択します。つまり、<span class="arithmatex">\(i\)</span> は短い仕切り、<span class="arithmatex">\(j\)</span> は高い仕切りです。</p>
+<p><a class="glightbox" href="../max_capacity_problem.assets/max_capacity_initial_state.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="初期状態" class="animation-figure" src="../max_capacity_problem.assets/max_capacity_initial_state.png" /></a></p>
+<p align="center"> 図 15-8 &nbsp; 初期状態 </p>
+
+<p>下の図に示すように、<strong>高い仕切り <span class="arithmatex">\(j\)</span> を短い仕切り <span class="arithmatex">\(i\)</span> に近づけて移動すると、容量は確実に減少します</strong>。</p>
+<p>これは、高い仕切り <span class="arithmatex">\(j\)</span> を移動すると、幅 <span class="arithmatex">\(j-i\)</span> が確実に減少するためです。高さは短い仕切りによって決定されるため、高さは同じまま（<span class="arithmatex">\(i\)</span> が短い仕切りのまま）か減少（移動した <span class="arithmatex">\(j\)</span> が短い仕切りになる）しかありません。</p>
+<p><a class="glightbox" href="../max_capacity_problem.assets/max_capacity_moving_long_board.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="高い仕切りを内側に移動した後の状態" class="animation-figure" src="../max_capacity_problem.assets/max_capacity_moving_long_board.png" /></a></p>
+<p align="center"> 図 15-9 &nbsp; 高い仕切りを内側に移動した後の状態 </p>
+
+<p>逆に、<strong>短い仕切り <span class="arithmatex">\(i\)</span> を内側に移動することによってのみ容量を増加させることが可能です</strong>。幅は確実に減少しますが、<strong>高さが増加する可能性があります</strong>（移動した短い仕切り <span class="arithmatex">\(i\)</span> が高くなる場合）。例えば、下の図では、短い仕切りを移動した後に面積が増加しています。</p>
+<p><a class="glightbox" href="../max_capacity_problem.assets/max_capacity_moving_short_board.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="短い仕切りを内側に移動した後の状態" class="animation-figure" src="../max_capacity_problem.assets/max_capacity_moving_short_board.png" /></a></p>
+<p align="center"> 図 15-10 &nbsp; 短い仕切りを内側に移動した後の状態 </p>
+
+<p>これにより、この問題の貪欲戦略が導かれます：コンテナの両端に2つのポインタを初期化し、各ラウンドで短い仕切りに対応するポインタを内側に移動し、2つのポインタが出会うまで続けます。</p>
+<p>下の図は貪欲戦略の実行を示しています。</p>
+<ol>
+<li>最初に、ポインタ <span class="arithmatex">\(i\)</span> と <span class="arithmatex">\(j\)</span> が配列の両端に配置されます。</li>
+<li>現在の状態の容量 <span class="arithmatex">\(cap[i, j]\)</span> を計算し、最大容量を更新します。</li>
+<li>仕切り <span class="arithmatex">\(i\)</span> と <span class="arithmatex">\(j\)</span> の高さを比較し、短い仕切りを1ステップ内側に移動します。</li>
+<li><span class="arithmatex">\(i\)</span> と <span class="arithmatex">\(j\)</span> が出会うまでステップ <code>2.</code> と <code>3.</code> を繰り返します。</li>
+</ol>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:9"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">&lt;1&gt;</label><label for="__tabbed_1_2">&lt;2&gt;</label><label for="__tabbed_1_3">&lt;3&gt;</label><label for="__tabbed_1_4">&lt;4&gt;</label><label for="__tabbed_1_5">&lt;5&gt;</label><label for="__tabbed_1_6">&lt;6&gt;</label><label for="__tabbed_1_7">&lt;7&gt;</label><label for="__tabbed_1_8">&lt;8&gt;</label><label for="__tabbed_1_9">&lt;9&gt;</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<p><a class="glightbox" href="../max_capacity_problem.assets/max_capacity_greedy_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="最大容量問題の貪欲プロセス" class="animation-figure" src="../max_capacity_problem.assets/max_capacity_greedy_step1.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../max_capacity_problem.assets/max_capacity_greedy_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="max_capacity_greedy_step2" class="animation-figure" src="../max_capacity_problem.assets/max_capacity_greedy_step2.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../max_capacity_problem.assets/max_capacity_greedy_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="max_capacity_greedy_step3" class="animation-figure" src="../max_capacity_problem.assets/max_capacity_greedy_step3.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../max_capacity_problem.assets/max_capacity_greedy_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="max_capacity_greedy_step4" class="animation-figure" src="../max_capacity_problem.assets/max_capacity_greedy_step4.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../max_capacity_problem.assets/max_capacity_greedy_step5.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="max_capacity_greedy_step5" class="animation-figure" src="../max_capacity_problem.assets/max_capacity_greedy_step5.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../max_capacity_problem.assets/max_capacity_greedy_step6.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="max_capacity_greedy_step6" class="animation-figure" src="../max_capacity_problem.assets/max_capacity_greedy_step6.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../max_capacity_problem.assets/max_capacity_greedy_step7.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="max_capacity_greedy_step7" class="animation-figure" src="../max_capacity_problem.assets/max_capacity_greedy_step7.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../max_capacity_problem.assets/max_capacity_greedy_step8.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="max_capacity_greedy_step8" class="animation-figure" src="../max_capacity_problem.assets/max_capacity_greedy_step8.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../max_capacity_problem.assets/max_capacity_greedy_step9.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="max_capacity_greedy_step9" class="animation-figure" src="../max_capacity_problem.assets/max_capacity_greedy_step9.png" /></a></p>
+</div>
+</div>
+</div>
+<p align="center"> 図 15-11 &nbsp; 最大容量問題の貪欲プロセス </p>
+
+<h3 id="2">2. &nbsp; 実装<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
+<p>コードは最大 <span class="arithmatex">\(n\)</span> 回ループするため、<strong>時間計算量は <span class="arithmatex">\(O(n)\)</span></strong> です。</p>
+<p>変数 <span class="arithmatex">\(i\)</span>、<span class="arithmatex">\(j\)</span>、<span class="arithmatex">\(res\)</span> は一定量の追加スペースを使用するため、<strong>空間計算量は <span class="arithmatex">\(O(1)\)</span></strong> です。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:14"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><input id="__tabbed_2_14" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label><label for="__tabbed_2_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">max_capacity.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">max_capacity</span><span class="p">(</span><span class="n">ht</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">])</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;最大容量：貪欲法&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># i、j を初期化、配列の両端で分割させる</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">ht</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="c1"># 初期最大容量は 0</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="n">res</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>    <span class="c1"># 2 つの板が出会うまで貪欲選択をループ</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>    <span class="k">while</span> <span class="n">i</span> <span class="o">&lt;</span> <span class="n">j</span><span class="p">:</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>        <span class="c1"># 最大容量を更新</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>        <span class="n">cap</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">ht</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">ht</span><span class="p">[</span><span class="n">j</span><span class="p">])</span> <span class="o">*</span> <span class="p">(</span><span class="n">j</span> <span class="o">-</span> <span class="n">i</span><span class="p">)</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>        <span class="n">res</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">res</span><span class="p">,</span> <span class="n">cap</span><span class="p">)</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>        <span class="c1"># 短い板を内側に移動</span>
+<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>        <span class="k">if</span> <span class="n">ht</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">&lt;</span> <span class="n">ht</span><span class="p">[</span><span class="n">j</span><span class="p">]:</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>            <span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>        <span class="k">else</span><span class="p">:</span>
+<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>            <span class="n">j</span> <span class="o">-=</span> <span class="mi">1</span>
+<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>    <span class="k">return</span> <span class="n">res</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">max_capacity.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 最大容量：貪欲法 */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">maxCapacity</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">ht</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// i、j を初期化し、配列の両端で分割させる</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ht</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="c1">// 初期最大容量は 0</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="c1">// 2つの板が出会うまで貪欲選択をループ</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">        </span><span class="c1">// 最大容量を更新</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">cap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">min</span><span class="p">(</span><span class="n">ht</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">ht</span><span class="p">[</span><span class="n">j</span><span class="p">])</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">cap</span><span class="p">);</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">        </span><span class="c1">// より短い板を内側に移動</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ht</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">ht</span><span class="p">[</span><span class="n">j</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">            </span><span class="n">i</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">            </span><span class="n">j</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">max_capacity.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 最大容量：貪欲法 */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">maxCapacity</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">ht</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// i、j を初期化し、配列の両端で分割させる</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ht</span><span class="p">.</span><span class="na">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="c1">// 初期最大容量は 0</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="c1">// 2つの板が出会うまで貪欲選択をループ</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">        </span><span class="c1">// 最大容量を更新</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">cap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">min</span><span class="p">(</span><span class="n">ht</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">ht</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">        </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">max</span><span class="p">(</span><span class="n">res</span><span class="p">,</span><span class="w"> </span><span class="n">cap</span><span class="p">);</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">        </span><span class="c1">// より短い板を内側に移動</span>
+<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ht</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">ht</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">            </span><span class="n">i</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">            </span><span class="n">j</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">max_capacity.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">max_capacity</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">MaxCapacity</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">max_capacity.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">maxCapacity</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">max_capacity.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">maxCapacity</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">max_capacity.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">maxCapacity</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">max_capacity.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">maxCapacity</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">max_capacity.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">maxCapacity</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">max_capacity.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">max_capacity</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">max_capacity.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">maxCapacity</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">max_capacity.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">maxCapacity</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">max_capacity.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">max_capacity</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">max_capacity.zig</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">maxCapacity</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h3 id="3">3. &nbsp; 正しさの証明<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
+<p>貪欲法が列挙よりも高速である理由は、各ラウンドの貪欲選択が一部の状態を「スキップ」するからです。</p>
+<p>例えば、<span class="arithmatex">\(i\)</span> が短い仕切りで <span class="arithmatex">\(j\)</span> が高い仕切りである状態 <span class="arithmatex">\(cap[i, j]\)</span> の下で、短い仕切り <span class="arithmatex">\(i\)</span> を貪欲に1ステップ内側に移動すると、下の図に示す「スキップされた」状態につながります。<strong>これは、これらの状態の容量を後で検証できないことを意味します</strong>。</p>
+<div class="arithmatex">\[
+cap[i, i+1], cap[i, i+2], \dots, cap[i, j-2], cap[i, j-1]
+\]</div>
+<p><a class="glightbox" href="../max_capacity_problem.assets/max_capacity_skipped_states.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="短い仕切りの移動によってスキップされる状態" class="animation-figure" src="../max_capacity_problem.assets/max_capacity_skipped_states.png" /></a></p>
+<p align="center"> 図 15-12 &nbsp; 短い仕切りの移動によってスキップされる状態 </p>
+
+<p>観察すると、<strong>これらのスキップされた状態は実際には高い仕切り <span class="arithmatex">\(j\)</span> が内側に移動したすべての状態**です。高い仕切りを内側に移動すると容量が確実に減少することをすでに証明しました。したがって、スキップされた状態は最適解である可能性がなく、**それらをスキップしても最適解を見逃すことはありません</strong>。</p>
+<p>分析により、短い仕切りを移動する操作は「安全」であり、貪欲戦略が効果的であることが示されます。</p>
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diff --git a/ja/chapter_greedy/max_product_cutting_problem.assets/max_product_cutting_greedy_infer2.png b/ja/chapter_greedy/max_product_cutting_problem.assets/max_product_cutting_greedy_infer2.png
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+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_introduction/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
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+<h1 id="154">15.4 &nbsp; 最大積切断問題<a class="headerlink" href="#154" title="Permanent link">&para;</a></h1>
+<div class="admonition question">
+<p class="admonition-title">Question</p>
+<p>正の整数 <span class="arithmatex">\(n\)</span> が与えられたとき、それを合計が <span class="arithmatex">\(n\)</span> になる少なくとも2つの正の整数に分割し、これらの整数の最大積を求めてください。下の図に示すとおりです。</p>
+</div>
+<p><a class="glightbox" href="../max_product_cutting_problem.assets/max_product_cutting_definition.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="最大積切断問題の定義" class="animation-figure" src="../max_product_cutting_problem.assets/max_product_cutting_definition.png" /></a></p>
+<p align="center"> 図 15-13 &nbsp; 最大積切断問題の定義 </p>
+
+<p><span class="arithmatex">\(n\)</span> を <span class="arithmatex">\(m\)</span> 個の整数因子に分割すると仮定し、<span class="arithmatex">\(i\)</span> 番目の因子を <span class="arithmatex">\(n_i\)</span> と表記すると、</p>
+<div class="arithmatex">\[
+n = \sum_{i=1}^{m}n_i
+\]</div>
+<p>この問題の目標は、すべての整数因子の最大積を見つけることです。すなわち、</p>
+<div class="arithmatex">\[
+\max(\prod_{i=1}^{m}n_i)
+\]</div>
+<p>考慮すべき点：分割数 <span class="arithmatex">\(m\)</span> はどの程度大きくすべきか、各 <span class="arithmatex">\(n_i\)</span> は何であるべきか？</p>
+<h3 id="1">1. &nbsp; 貪欲戦略の決定<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<p>経験的に、2つの整数の積は多くの場合その和よりも大きくなります。<span class="arithmatex">\(n\)</span> から因子 <span class="arithmatex">\(2\)</span> を分割すると仮定すると、その積は <span class="arithmatex">\(2(n-2)\)</span> です。この積を <span class="arithmatex">\(n\)</span> と比較します：</p>
+<div class="arithmatex">\[
+\begin{aligned}
+2(n-2) &amp; \geq n \newline
+2n - n - 4 &amp; \geq 0 \newline
+n &amp; \geq 4
+\end{aligned}
+\]</div>
+<p>下の図に示すように、<span class="arithmatex">\(n \geq 4\)</span> のとき、<span class="arithmatex">\(2\)</span> を分割すると積が増加します。<strong>これは4以上の整数を分割すべきであることを示しています</strong>。</p>
+<p><strong>貪欲戦略1</strong>：分割スキームが <span class="arithmatex">\(\geq 4\)</span> の因子を含む場合、それらはさらに分割されるべきです。最終的な分割は因子 <span class="arithmatex">\(1\)</span>、<span class="arithmatex">\(2\)</span>、<span class="arithmatex">\(3\)</span> のみを含むべきです。</p>
+<p><a class="glightbox" href="../max_product_cutting_problem.assets/max_product_cutting_greedy_infer1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="分割による積の増加" class="animation-figure" src="../max_product_cutting_problem.assets/max_product_cutting_greedy_infer1.png" /></a></p>
+<p align="center"> 図 15-14 &nbsp; 分割による積の増加 </p>
+
+<p>次に、どの因子が最適かを考慮します。因子 <span class="arithmatex">\(1\)</span>、<span class="arithmatex">\(2\)</span>、<span class="arithmatex">\(3\)</span> の中で、明らかに <span class="arithmatex">\(1\)</span> が最悪です。<span class="arithmatex">\(1 \times (n-1) &lt; n\)</span> が常に成り立つため、<span class="arithmatex">\(1\)</span> を分割すると実際に積が減少します。</p>
+<p>下の図に示すように、<span class="arithmatex">\(n = 6\)</span> のとき、<span class="arithmatex">\(3 \times 3 &gt; 2 \times 2 \times 2\)</span> です。<strong>これは <span class="arithmatex">\(3\)</span> を分割する方が <span class="arithmatex">\(2\)</span> を分割するよりも良いことを意味します</strong>。</p>
+<p><strong>貪欲戦略2</strong>：分割スキームには最大で2つの <span class="arithmatex">\(2\)</span> があるべきです。3つの <span class="arithmatex">\(2\)</span> は常に2つの <span class="arithmatex">\(3\)</span> に置き換えてより高い積を得ることができるからです。</p>
+<p><a class="glightbox" href="../max_product_cutting_problem.assets/max_product_cutting_greedy_infer2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="最適な分割因子" class="animation-figure" src="../max_product_cutting_problem.assets/max_product_cutting_greedy_infer2.png" /></a></p>
+<p align="center"> 図 15-15 &nbsp; 最適な分割因子 </p>
+
+<p>上記から、以下の貪欲戦略を導出できます。</p>
+<ol>
+<li>入力整数 <span class="arithmatex">\(n\)</span> について、余りが <span class="arithmatex">\(0\)</span>、<span class="arithmatex">\(1\)</span>、または <span class="arithmatex">\(2\)</span> になるまで因子 <span class="arithmatex">\(3\)</span> を継続的に分割します。</li>
+<li>余りが <span class="arithmatex">\(0\)</span> の場合、<span class="arithmatex">\(n\)</span> が <span class="arithmatex">\(3\)</span> の倍数であることを意味するため、それ以上の行動は取りません。</li>
+<li>余りが <span class="arithmatex">\(2\)</span> の場合、さらに分割を続けず、そのまま保持します。</li>
+<li>余りが <span class="arithmatex">\(1\)</span> の場合、<span class="arithmatex">\(2 \times 2 &gt; 1 \times 3\)</span> であるため、最後の <span class="arithmatex">\(3\)</span> を <span class="arithmatex">\(2\)</span> に置き換えるべきです。</li>
+</ol>
+<h3 id="2">2. &nbsp; コード実装<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
+<p>下の図に示すように、整数を分割するためにループを使用する必要はなく、床除算演算を使用して <span class="arithmatex">\(3\)</span> の数 <span class="arithmatex">\(a\)</span> を取得し、剰余演算を使用して余り <span class="arithmatex">\(b\)</span> を取得できます。したがって：</p>
+<div class="arithmatex">\[
+n = 3a + b
+\]</div>
+<p><span class="arithmatex">\(n \leq 3\)</span> の境界ケースでは、<span class="arithmatex">\(1\)</span> を分割する必要があり、積は <span class="arithmatex">\(1 \times (n - 1)\)</span> であることに注意してください。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:14"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><input id="__tabbed_1_14" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label><label for="__tabbed_1_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">max_product_cutting.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">max_product_cutting</span><span class="p">(</span><span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;切断の最大積：貪欲法&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># n &lt;= 3 の場合、1 を切り出す必要がある</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="k">if</span> <span class="n">n</span> <span class="o">&lt;=</span> <span class="mi">3</span><span class="p">:</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>        <span class="k">return</span> <span class="mi">1</span> <span class="o">*</span> <span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="c1"># 貪欲的に 3 を切り出す、a は 3 の個数、b は余り</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>    <span class="n">a</span><span class="p">,</span> <span class="n">b</span> <span class="o">=</span> <span class="n">n</span> <span class="o">//</span> <span class="mi">3</span><span class="p">,</span> <span class="n">n</span> <span class="o">%</span> <span class="mi">3</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>    <span class="k">if</span> <span class="n">b</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>        <span class="c1"># 余りが 1 の場合、1 * 3 のペアを 2 * 2 に変換</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>        <span class="k">return</span> <span class="nb">int</span><span class="p">(</span><span class="n">math</span><span class="o">.</span><span class="n">pow</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">a</span> <span class="o">-</span> <span class="mi">1</span><span class="p">))</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">*</span> <span class="mi">2</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>    <span class="k">if</span> <span class="n">b</span> <span class="o">==</span> <span class="mi">2</span><span class="p">:</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>        <span class="c1"># 余りが 2 の場合、何もしない</span>
+<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>        <span class="k">return</span> <span class="nb">int</span><span class="p">(</span><span class="n">math</span><span class="o">.</span><span class="n">pow</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">a</span><span class="p">))</span> <span class="o">*</span> <span class="mi">2</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>    <span class="c1"># 余りが 0 の場合、何もしない</span>
+<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>    <span class="k">return</span> <span class="nb">int</span><span class="p">(</span><span class="n">math</span><span class="o">.</span><span class="n">pow</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="n">a</span><span class="p">))</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">max_product_cutting.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 最大積切断：貪欲法 */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">maxProductCutting</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// n &lt;= 3 の場合、1 を切り出す必要がある</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">3</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="c1">// 貪欲に 3 を切り出す。a は 3 の個数、b は余り</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">b</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">        </span><span class="c1">// 余りが 1 の場合、1 * 3 のペアを 2 * 2 に変換</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">pow</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">b</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">        </span><span class="c1">// 余りが 2 の場合、何もしない</span>
+<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">pow</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w">    </span><span class="c1">// 余りが 0 の場合、何もしない</span>
+<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">pow</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">);</span>
+<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">max_product_cutting.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 最大積切断：貪欲法 */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">maxProductCutting</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// n &lt;= 3 の場合、1 を切り出す必要がある</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">3</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">1</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="p">(</span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="c1">// 貪欲に 3 を切り出す。a は 3 の個数、b は余り</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">b</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">        </span><span class="c1">// 余りが 1 の場合、1 * 3 のペアを 2 * 2 に変換</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">pow</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">b</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">        </span><span class="c1">// 余りが 2 の場合、何もしない</span>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">pow</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w">    </span><span class="c1">// 余りが 0 の場合、何もしない</span>
+<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">pow</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="n">a</span><span class="p">);</span>
+<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">max_product_cutting.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">max_product_cutting</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">MaxProductCutting</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">max_product_cutting.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">maxProductCutting</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">max_product_cutting.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">maxProductCutting</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">max_product_cutting.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">maxProductCutting</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">max_product_cutting.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">maxProductCutting</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">max_product_cutting.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">maxProductCutting</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">max_product_cutting.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">max_product_cutting</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">max_product_cutting.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">maxProductCutting</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">max_product_cutting.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">maxProductCutting</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">max_product_cutting.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">max_product_cutting</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">max_product_cutting.zig</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">maxProductCutting</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p><a class="glightbox" href="../max_product_cutting_problem.assets/max_product_cutting_greedy_calculation.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="切断後の最大積の計算方法" class="animation-figure" src="../max_product_cutting_problem.assets/max_product_cutting_greedy_calculation.png" /></a></p>
+<p align="center"> 図 15-16 &nbsp; 切断後の最大積の計算方法 </p>
+
+<p><strong>時間計算量はプログラミング言語のべき乗演算の実装に依存します</strong>。Pythonでは、よく使用されるべき乗計算関数は3種類あります：</p>
+<ul>
+<li>演算子 <code>**</code> と関数 <code>pow()</code> の両方の時間計算量は <span class="arithmatex">\(O(\log⁡ a)\)</span> です。</li>
+<li><code>math.pow()</code> 関数は内部でC言語ライブラリの <code>pow()</code> 関数を呼び出し、浮動小数点べき乗を実行し、時間計算量は <span class="arithmatex">\(O(1)\)</span> です。</li>
+</ul>
+<p>変数 <span class="arithmatex">\(a\)</span> と <span class="arithmatex">\(b\)</span> は一定サイズの追加スペースを使用するため、<strong>空間計算量は <span class="arithmatex">\(O(1)\)</span></strong> です。</p>
+<h3 id="3">3. &nbsp; 正しさの証明<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
+<p>背理法を使用し、<span class="arithmatex">\(n \geq 3\)</span> のケースのみを分析します。</p>
+<ol>
+<li><strong>すべての因子 <span class="arithmatex">\(\leq 3\)</span></strong>：最適分割スキームが因子 <span class="arithmatex">\(x \geq 4\)</span> を含むと仮定すると、それを確実に <span class="arithmatex">\(2(x-2)\)</span> にさらに分割でき、より大きな積を得られます。これは仮定と矛盾します。</li>
+<li><strong>分割スキームに <span class="arithmatex">\(1\)</span> が含まれない</strong>：最適分割スキームが因子 <span class="arithmatex">\(1\)</span> を含むと仮定すると、それを確実に別の因子と結合してより大きな積を得られます。これは仮定と矛盾します。</li>
+<li><strong>分割スキームには最大で2つの <span class="arithmatex">\(2\)</span> が含まれる</strong>：最適分割スキームが3つの <span class="arithmatex">\(2\)</span> を含むと仮定すると、それらを確実に2つの <span class="arithmatex">\(3\)</span> に置き換えて、より高い積を達成できます。これは仮定と矛盾します。</li>
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+            
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_2" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_preface/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M21 4H3a2 2 0 0 0-2 2v13a2 2 0 0 0 2 2h18a2 2 0 0 0 2-2V6a2 2 0 0 0-2-2M3 19V6h8v13H3m18 0h-8V6h8v13m-7-9.5h6V11h-6V9.5m0 2.5h6v1.5h-6V12m0 2.5h6V16h-6v-1.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 0 章 &nbsp; 前書き
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_2" id="__nav_2_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_2_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_2">
+            <span class="md-nav__icon md-icon"></span>
+            第 0 章 &nbsp; 前書き
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/about_the_book/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.1 &nbsp; この本について
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/suggestions/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.2 &nbsp; 本書の使い方
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_introduction/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
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+<h1 id="155">15.5 &nbsp; まとめ<a class="headerlink" href="#155" title="Permanent link">&para;</a></h1>
+<ul>
+<li>貪欲アルゴリズムは最適化問題を解決するためによく使用され、原理は各決定段階で局所的に最適な決定を行い、グローバルに最適な解を達成することです。</li>
+<li>貪欲アルゴリズムは貪欲な選択を次々と反復的に行い、各ラウンドで問題をより小さな部分問題に変換し、問題が解決されるまで続けます。</li>
+<li>貪欲アルゴリズムは実装が簡単なだけでなく、問題解決効率も高いです。動的プログラミングと比較して、貪欲アルゴリズムは一般的により低い時間計算量を持ちます。</li>
+<li>コイン交換問題において、貪欲アルゴリズムは特定のコインの組み合わせに対して最適解を保証できますが、他の組み合わせでは貪欲アルゴリズムが非常に悪い解を見つける可能性があります。</li>
+<li>貪欲アルゴリズム解法に適した問題は2つの主要な性質を持ちます：貪欲選択性と最適部分構造。貪欲選択性は貪欲戦略の効果を表します。</li>
+<li>一部の複雑な問題では、貪欲選択性を証明することは簡単ではありません。逆に、無効性を証明することはしばしばより容易で、コイン交換問題などがその例です。</li>
+<li>貪欲問題の解決は主に3つのステップから構成されます：問題分析、貪欲戦略の決定、正しさの証明。このうち、貪欲戦略の決定が重要なステップであり、正しさの証明がしばしば挑戦となります。</li>
+<li>分数ナップサック問題は0-1ナップサック問題に基づいてアイテムの一部の選択を可能にし、したがって貪欲アルゴリズムを使用して解決できます。貪欲戦略の正しさは背理法によって証明できます。</li>
+<li>最大容量問題は全探索法で解決でき、時間計算量は <span class="arithmatex">\(O(n^2)\)</span> です。貪欲戦略を設計することで、各ラウンドで短い板を内側に移動し、時間計算量を <span class="arithmatex">\(O(n)\)</span> に最適化します。</li>
+<li>切断後の最大積問題において、2つの貪欲戦略を導出します：<span class="arithmatex">\(\geq 4\)</span> の整数は継続的に切断されるべきで、最適な切断因子は <span class="arithmatex">\(3\)</span> です。コードにはべき乗演算が含まれ、時間計算量はべき乗演算の実装方法に依存し、一般的に <span class="arithmatex">\(O(1)\)</span> または <span class="arithmatex">\(O(\log n)\)</span> です。</li>
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+  
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+  
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+      <a href="../../chapter_preface/about_the_book/" class="md-nav__link">
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+      <a href="../../chapter_preface/summary/" class="md-nav__link">
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+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
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+  
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+    1.1 &nbsp; アルゴリズムはどこにでもある
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+  
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+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
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+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
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+    </li>
+  
+
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+              
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+  
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+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
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+    </li>
+  
+
+              
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+          
+        
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+        
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+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
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+  
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+            第 2 章 &nbsp; 計算量解析
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+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
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+    2.1 &nbsp; アルゴリズム効率評価
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+  
+
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+
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+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
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+    2.2 &nbsp; 反復と再帰
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+  
+
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+    </li>
+  
+
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+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
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+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
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+
+              
+            
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+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
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+  
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+    第 3 章 &nbsp; データ構造
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+            第 3 章 &nbsp; データ構造
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+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
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+    3.1 &nbsp; データ構造の分類
+  </span>
+  
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+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
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+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
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+
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+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
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+  </span>
+  
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+    </li>
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+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
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+  </span>
+  
+
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+    </li>
+  
+
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+  
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+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
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+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
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+  
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+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
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+              
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+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
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+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
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+  </span>
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+  
+
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+  
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+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
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+      
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+  
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+  
+  
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+    
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+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
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+        
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+        
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+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#631" class="md-nav__link">
+    <span class="md-ellipsis">
+      6.3.1 &nbsp; ハッシュアルゴリズムの目標
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#632" class="md-nav__link">
+    <span class="md-ellipsis">
+      6.3.2 &nbsp; ハッシュアルゴリズムの設計
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#633" class="md-nav__link">
+    <span class="md-ellipsis">
+      6.3.3 &nbsp; 一般的なハッシュアルゴリズム
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
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+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
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+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
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+    15.4 &nbsp; 最大積切断問題
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+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
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+    <span class="md-ellipsis">
+      6.3.3 &nbsp; 一般的なハッシュアルゴリズム
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+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
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+<h1 id="63">6.3 &nbsp; ハッシュアルゴリズム<a class="headerlink" href="#63" title="Permanent link">&para;</a></h1>
+<p>前の2つの節では、ハッシュ表の動作原理とハッシュ衝突を処理する方法を紹介しました。しかし、オープンアドレス法と連鎖法はどちらも**衝突が発生した際にハッシュ表が正常に機能することのみを保証でき、ハッシュ衝突の発生頻度を減らすことはできません**。</p>
+<p>ハッシュ衝突があまりにも頻繁に発生すると、ハッシュ表の性能は劇的に悪化します。下図に示すように、連鎖法ハッシュ表では、理想的なケースではキー値ペアがバケット間に均等に分散され、最適なクエリ効率を実現します。最悪のケースでは、すべてのキー値ペアが同じバケットに格納され、時間計算量が<span class="arithmatex">\(O(n)\)</span>に悪化します。</p>
+<p><a class="glightbox" href="../hash_algorithm.assets/hash_collision_best_worst_condition.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="ハッシュ衝突の理想的および最悪のケース" class="animation-figure" src="../hash_algorithm.assets/hash_collision_best_worst_condition.png" /></a></p>
+<p align="center"> 図 6-8 &nbsp; ハッシュ衝突の理想的および最悪のケース </p>
+
+<p><strong>キー値ペアの分布はハッシュ関数によって決定されます</strong>。ハッシュ関数の計算ステップを思い出すと、まずハッシュ値を計算し、次に配列長で剰余を取ります：</p>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="nv">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span>hash<span class="o">(</span>key<span class="o">)</span><span class="w"> </span>%<span class="w"> </span>capacity
+</code></pre></div>
+<p>上記の式を観察すると、ハッシュ表の容量<code>capacity</code>が固定されている場合、<strong>ハッシュアルゴリズム<code>hash()</code>が出力値を決定し</strong>、それによってハッシュ表におけるキー値ペアの分布を決定します。</p>
+<p>これは、ハッシュ衝突の確率を減らすために、ハッシュアルゴリズム<code>hash()</code>の設計に焦点を当てるべきであることを意味します。</p>
+<h2 id="631">6.3.1 &nbsp; ハッシュアルゴリズムの目標<a class="headerlink" href="#631" title="Permanent link">&para;</a></h2>
+<p>「高速で安定した」ハッシュ表データ構造を実現するために、ハッシュアルゴリズムは以下の特性を持つべきです：</p>
+<ul>
+<li><strong>決定性</strong>: 同じ入力に対して、ハッシュアルゴリズムは常に同じ出力を生成するべきです。そうでなければハッシュ表は信頼できません。</li>
+<li><strong>高効率</strong>: ハッシュ値を計算するプロセスは十分に高速である必要があります。計算オーバーヘッドが小さいほど、ハッシュ表はより実用的になります。</li>
+<li><strong>均等分散</strong>: ハッシュアルゴリズムはキー値ペアがハッシュ表に均等に分散されることを保証するべきです。分散が均等であるほど、ハッシュ衝突の確率は低くなります。</li>
+</ul>
+<p>実際、ハッシュアルゴリズムはハッシュ表の実装だけでなく、他の分野でも広く応用されています。</p>
+<ul>
+<li><strong>パスワード保存</strong>: ユーザーパスワードのセキュリティを保護するために、システムは通常平文パスワードを保存せず、パスワードのハッシュ値を保存します。ユーザーがパスワードを入力すると、システムは入力のハッシュ値を計算し、保存されているハッシュ値と比較します。一致すれば、パスワードは正しいと見なされます。</li>
+<li><strong>データ整合性チェック</strong>: データ送信者はデータのハッシュ値を計算して一緒に送信できます。受信者は受信したデータのハッシュ値を再計算し、受信したハッシュ値と比較できます。一致すれば、データは完全であると見なされます。</li>
+</ul>
+<p>暗号化アプリケーションでは、ハッシュ値から元のパスワードを推測するなどの逆行分析を防ぐために、ハッシュアルゴリズムはより高いレベルのセキュリティ機能が必要です。</p>
+<ul>
+<li><strong>一方向性</strong>: ハッシュ値から入力データに関する情報を推測することは不可能であるべきです。</li>
+<li><strong>衝突耐性</strong>: 同じハッシュ値を生成する2つの異なる入力を見つけることは極めて困難であるべきです。</li>
+<li><strong>雪崩効果</strong>: 入力の小さな変更は、出力に大きく予測不可能な変化をもたらすべきです。</li>
+</ul>
+<p>**「均等分散」と「衝突耐性」は2つの別々の概念**であることに注意してください。均等分散を満たしても、必ずしも衝突耐性があるとは限りません。例えば、ランダムな入力<code>key</code>の下で、ハッシュ関数<code>key % 100</code>は均等に分散された出力を生成できます。しかし、このハッシュアルゴリズムは過度にシンプルで、下二桁が同じすべての<code>key</code>は同じ出力を持つため、ハッシュ値から使用可能な<code>key</code>を簡単に推測でき、パスワードを破ることができます。</p>
+<h2 id="632">6.3.2 &nbsp; ハッシュアルゴリズムの設計<a class="headerlink" href="#632" title="Permanent link">&para;</a></h2>
+<p>ハッシュアルゴリズムの設計は多くの要因を考慮する必要がある複雑な問題です。しかし、要求が少ない一部のシナリオでは、いくつかの簡単なハッシュアルゴリズムを設計することもできます。</p>
+<ul>
+<li><strong>加算ハッシュ</strong>: 入力の各文字のASCIIコードを合計し、合計をハッシュ値として使用します。</li>
+<li><strong>乗算ハッシュ</strong>: 乗算の非相関性を利用し、各ラウンドで定数を乗算し、各文字のASCIIコードをハッシュ値に累積します。</li>
+<li><strong>XORハッシュ</strong>: 入力データの各要素をXORすることでハッシュ値を累積します。</li>
+<li><strong>回転ハッシュ</strong>: 各文字のASCIIコードをハッシュ値に累積し、各累積前にハッシュ値に回転操作を実行します。</li>
+</ul>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:14"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><input id="__tabbed_1_14" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label><label for="__tabbed_1_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">simple_hash.py</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">add_hash</span><span class="p">(</span><span class="n">key</span><span class="p">:</span> <span class="nb">str</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;加法ハッシュ&quot;&quot;&quot;</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a>    <span class="nb">hash</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a>    <span class="n">modulus</span> <span class="o">=</span> <span class="mi">1000000007</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a>    <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="n">key</span><span class="p">:</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a>        <span class="nb">hash</span> <span class="o">+=</span> <span class="nb">ord</span><span class="p">(</span><span class="n">c</span><span class="p">)</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a>    <span class="k">return</span> <span class="nb">hash</span> <span class="o">%</span> <span class="n">modulus</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="k">def</span><span class="w"> </span><span class="nf">mul_hash</span><span class="p">(</span><span class="n">key</span><span class="p">:</span> <span class="nb">str</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;乗法ハッシュ&quot;&quot;&quot;</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a>    <span class="nb">hash</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a>    <span class="n">modulus</span> <span class="o">=</span> <span class="mi">1000000007</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a>    <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="n">key</span><span class="p">:</span>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a>        <span class="nb">hash</span> <span class="o">=</span> <span class="mi">31</span> <span class="o">*</span> <span class="nb">hash</span> <span class="o">+</span> <span class="nb">ord</span><span class="p">(</span><span class="n">c</span><span class="p">)</span>
+<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a>    <span class="k">return</span> <span class="nb">hash</span> <span class="o">%</span> <span class="n">modulus</span>
+<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a>
+<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="k">def</span><span class="w"> </span><span class="nf">xor_hash</span><span class="p">(</span><span class="n">key</span><span class="p">:</span> <span class="nb">str</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;XORハッシュ&quot;&quot;&quot;</span>
+<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a>    <span class="nb">hash</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a>    <span class="n">modulus</span> <span class="o">=</span> <span class="mi">1000000007</span>
+<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a>    <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="n">key</span><span class="p">:</span>
+<a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a>        <span class="nb">hash</span> <span class="o">^=</span> <span class="nb">ord</span><span class="p">(</span><span class="n">c</span><span class="p">)</span>
+<a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a>    <span class="k">return</span> <span class="nb">hash</span> <span class="o">%</span> <span class="n">modulus</span>
+<a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a>
+<a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a><span class="k">def</span><span class="w"> </span><span class="nf">rot_hash</span><span class="p">(</span><span class="n">key</span><span class="p">:</span> <span class="nb">str</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-1-26" name="__codelineno-1-26" href="#__codelineno-1-26"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;回転ハッシュ&quot;&quot;&quot;</span>
+<a id="__codelineno-1-27" name="__codelineno-1-27" href="#__codelineno-1-27"></a>    <span class="nb">hash</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-1-28" name="__codelineno-1-28" href="#__codelineno-1-28"></a>    <span class="n">modulus</span> <span class="o">=</span> <span class="mi">1000000007</span>
+<a id="__codelineno-1-29" name="__codelineno-1-29" href="#__codelineno-1-29"></a>    <span class="k">for</span> <span class="n">c</span> <span class="ow">in</span> <span class="n">key</span><span class="p">:</span>
+<a id="__codelineno-1-30" name="__codelineno-1-30" href="#__codelineno-1-30"></a>        <span class="nb">hash</span> <span class="o">=</span> <span class="p">(</span><span class="nb">hash</span> <span class="o">&lt;&lt;</span> <span class="mi">4</span><span class="p">)</span> <span class="o">^</span> <span class="p">(</span><span class="nb">hash</span> <span class="o">&gt;&gt;</span> <span class="mi">28</span><span class="p">)</span> <span class="o">^</span> <span class="nb">ord</span><span class="p">(</span><span class="n">c</span><span class="p">)</span>
+<a id="__codelineno-1-31" name="__codelineno-1-31" href="#__codelineno-1-31"></a>    <span class="k">return</span> <span class="nb">hash</span> <span class="o">%</span> <span class="n">modulus</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">simple_hash.cpp</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 加算ハッシュ */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">addHash</span><span class="p">(</span><span class="n">string</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="kt">long</span><span class="w"> </span><span class="kt">long</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1000000007</span><span class="p">;</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">unsigned</span><span class="w"> </span><span class="kt">char</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">        </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">hash</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">;</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">hash</span><span class="p">;</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="p">}</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="cm">/* 乗算ハッシュ */</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="kt">int</span><span class="w"> </span><span class="nf">mulHash</span><span class="p">(</span><span class="n">string</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">    </span><span class="kt">long</span><span class="w"> </span><span class="kt">long</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">    </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1000000007</span><span class="p">;</span>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">unsigned</span><span class="w"> </span><span class="kt">char</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">        </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="mi">31</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">;</span>
+<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">hash</span><span class="p">;</span>
+<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="p">}</span>
+<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a>
+<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="cm">/* XORハッシュ */</span>
+<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a><span class="kt">int</span><span class="w"> </span><span class="nf">xorHash</span><span class="p">(</span><span class="n">string</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a><span class="w">    </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1000000007</span><span class="p">;</span>
+<a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">unsigned</span><span class="w"> </span><span class="kt">char</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></a><span class="w">        </span><span class="n">hash</span><span class="w"> </span><span class="o">^=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">c</span><span class="p">;</span>
+<a id="__codelineno-2-27" name="__codelineno-2-27" href="#__codelineno-2-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-28" name="__codelineno-2-28" href="#__codelineno-2-28"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">&amp;</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">;</span>
+<a id="__codelineno-2-29" name="__codelineno-2-29" href="#__codelineno-2-29"></a><span class="p">}</span>
+<a id="__codelineno-2-30" name="__codelineno-2-30" href="#__codelineno-2-30"></a>
+<a id="__codelineno-2-31" name="__codelineno-2-31" href="#__codelineno-2-31"></a><span class="cm">/* 回転ハッシュ */</span>
+<a id="__codelineno-2-32" name="__codelineno-2-32" href="#__codelineno-2-32"></a><span class="kt">int</span><span class="w"> </span><span class="nf">rotHash</span><span class="p">(</span><span class="n">string</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-33" name="__codelineno-2-33" href="#__codelineno-2-33"></a><span class="w">    </span><span class="kt">long</span><span class="w"> </span><span class="kt">long</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-2-34" name="__codelineno-2-34" href="#__codelineno-2-34"></a><span class="w">    </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1000000007</span><span class="p">;</span>
+<a id="__codelineno-2-35" name="__codelineno-2-35" href="#__codelineno-2-35"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">unsigned</span><span class="w"> </span><span class="kt">char</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-36" name="__codelineno-2-36" href="#__codelineno-2-36"></a><span class="w">        </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">((</span><span class="n">hash</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">4</span><span class="p">)</span><span class="w"> </span><span class="o">^</span><span class="w"> </span><span class="p">(</span><span class="n">hash</span><span class="w"> </span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="mi">28</span><span class="p">)</span><span class="w"> </span><span class="o">^</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">;</span>
+<a id="__codelineno-2-37" name="__codelineno-2-37" href="#__codelineno-2-37"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-38" name="__codelineno-2-38" href="#__codelineno-2-38"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="n">hash</span><span class="p">;</span>
+<a id="__codelineno-2-39" name="__codelineno-2-39" href="#__codelineno-2-39"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">simple_hash.java</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 加算ハッシュ */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">addHash</span><span class="p">(</span><span class="n">String</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="kt">long</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="kd">final</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1000000007</span><span class="p">;</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">char</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">key</span><span class="p">.</span><span class="na">toCharArray</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">        </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">hash</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">;</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="n">hash</span><span class="p">;</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="p">}</span>
+<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a>
+<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="cm">/* 乗算ハッシュ */</span>
+<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="kt">int</span><span class="w"> </span><span class="nf">mulHash</span><span class="p">(</span><span class="n">String</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="w">    </span><span class="kt">long</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="w">    </span><span class="kd">final</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1000000007</span><span class="p">;</span>
+<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">char</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">key</span><span class="p">.</span><span class="na">toCharArray</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="w">        </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="mi">31</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">;</span>
+<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="n">hash</span><span class="p">;</span>
+<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="p">}</span>
+<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a>
+<a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a><span class="cm">/* XORハッシュ */</span>
+<a id="__codelineno-3-22" name="__codelineno-3-22" href="#__codelineno-3-22"></a><span class="kt">int</span><span class="w"> </span><span class="nf">xorHash</span><span class="p">(</span><span class="n">String</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-23" name="__codelineno-3-23" href="#__codelineno-3-23"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-3-24" name="__codelineno-3-24" href="#__codelineno-3-24"></a><span class="w">    </span><span class="kd">final</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1000000007</span><span class="p">;</span>
+<a id="__codelineno-3-25" name="__codelineno-3-25" href="#__codelineno-3-25"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">char</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">key</span><span class="p">.</span><span class="na">toCharArray</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-26" name="__codelineno-3-26" href="#__codelineno-3-26"></a><span class="w">        </span><span class="n">hash</span><span class="w"> </span><span class="o">^=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="n">c</span><span class="p">;</span>
+<a id="__codelineno-3-27" name="__codelineno-3-27" href="#__codelineno-3-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-28" name="__codelineno-3-28" href="#__codelineno-3-28"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">&amp;</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">;</span>
+<a id="__codelineno-3-29" name="__codelineno-3-29" href="#__codelineno-3-29"></a><span class="p">}</span>
+<a id="__codelineno-3-30" name="__codelineno-3-30" href="#__codelineno-3-30"></a>
+<a id="__codelineno-3-31" name="__codelineno-3-31" href="#__codelineno-3-31"></a><span class="cm">/* 回転ハッシュ */</span>
+<a id="__codelineno-3-32" name="__codelineno-3-32" href="#__codelineno-3-32"></a><span class="kt">int</span><span class="w"> </span><span class="nf">rotHash</span><span class="p">(</span><span class="n">String</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-33" name="__codelineno-3-33" href="#__codelineno-3-33"></a><span class="w">    </span><span class="kt">long</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-3-34" name="__codelineno-3-34" href="#__codelineno-3-34"></a><span class="w">    </span><span class="kd">final</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">MODULUS</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1000000007</span><span class="p">;</span>
+<a id="__codelineno-3-35" name="__codelineno-3-35" href="#__codelineno-3-35"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">char</span><span class="w"> </span><span class="n">c</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">key</span><span class="p">.</span><span class="na">toCharArray</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-36" name="__codelineno-3-36" href="#__codelineno-3-36"></a><span class="w">        </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">((</span><span class="n">hash</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="mi">4</span><span class="p">)</span><span class="w"> </span><span class="o">^</span><span class="w"> </span><span class="p">(</span><span class="n">hash</span><span class="w"> </span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="mi">28</span><span class="p">)</span><span class="w"> </span><span class="o">^</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="n">c</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">MODULUS</span><span class="p">;</span>
+<a id="__codelineno-3-37" name="__codelineno-3-37" href="#__codelineno-3-37"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-3-38" name="__codelineno-3-38" href="#__codelineno-3-38"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="n">hash</span><span class="p">;</span>
+<a id="__codelineno-3-39" name="__codelineno-3-39" href="#__codelineno-3-39"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">simple_hash.cs</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">simple_hash</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">AddHash</span><span class="p">}</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">simple_hash</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">MulHash</span><span class="p">}</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="na">[class]</span><span class="p">{</span><span class="n">simple_hash</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">XorHash</span><span class="p">}</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="na">[class]</span><span class="p">{</span><span class="n">simple_hash</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">RotHash</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">simple_hash.go</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">addHash</span><span class="p">}</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">mulHash</span><span class="p">}</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">xorHash</span><span class="p">}</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">rotHash</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">simple_hash.swift</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">addHash</span><span class="p">}</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">mulHash</span><span class="p">}</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">xorHash</span><span class="p">}</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">rotHash</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">simple_hash.js</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">addHash</span><span class="p">}</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">mulHash</span><span class="p">}</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">xorHash</span><span class="p">}</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">rotHash</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">simple_hash.ts</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">addHash</span><span class="p">}</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">mulHash</span><span class="p">}</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">xorHash</span><span class="p">}</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">rotHash</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">simple_hash.dart</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">addHash</span><span class="p">}</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">mulHash</span><span class="p">}</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">xorHash</span><span class="p">}</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">rotHash</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">simple_hash.rs</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">add_hash</span><span class="p">}</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">mul_hash</span><span class="p">}</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">xor_hash</span><span class="p">}</span>
+<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">rot_hash</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">simple_hash.c</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">addHash</span><span class="p">}</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">mulHash</span><span class="p">}</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">xorHash</span><span class="p">}</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">rotHash</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">simple_hash.kt</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">addHash</span><span class="p">}</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">mulHash</span><span class="p">}</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">xorHash</span><span class="p">}</span>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a>
+<a id="__codelineno-12-7" name="__codelineno-12-7" href="#__codelineno-12-7"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">rotHash</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">simple_hash.rb</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">add_hash</span><span class="p">}</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a>
+<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">mul_hash</span><span class="p">}</span>
+<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a>
+<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">xor_hash</span><span class="p">}</span>
+<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a>
+<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">rot_hash</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">simple_hash.zig</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">addHash</span><span class="p">}</span>
+<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">mulHash</span><span class="p">}</span>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">xorHash</span><span class="p">}</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a>
+<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">rotHash</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>各ハッシュアルゴリズムの最後のステップが大きな素数<span class="arithmatex">\(1000000007\)</span>の剰余を取ることで、ハッシュ値が適切な範囲内にあることを保証していることが観察されます。なぜ素数の剰余を取ることが強調されるのか、または合成数の剰余を取ることの欠点は何かを考える価値があります。これは興味深い質問です。</p>
+<p>結論として：<strong>大きな素数を剰余として使用することで、ハッシュ値の均等分散を最大化できます</strong>。素数は他の数と共通因子を持たないため、剰余演算によって引き起こされる周期的パターンを減らし、ハッシュ衝突を回避できます。</p>
+<p>例えば、合成数<span class="arithmatex">\(9\)</span>を剰余として選択するとします。これは<span class="arithmatex">\(3\)</span>で割り切れるため、<span class="arithmatex">\(3\)</span>で割り切れるすべての<code>key</code>はハッシュ値<span class="arithmatex">\(0\)</span>、<span class="arithmatex">\(3\)</span>、<span class="arithmatex">\(6\)</span>にマッピングされます。</p>
+<div class="arithmatex">\[
+\begin{aligned}
+\text{modulus} &amp; = 9 \newline
+\text{key} &amp; = \{ 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, \dots \} \newline
+\text{hash} &amp; = \{ 0, 3, 6, 0, 3, 6, 0, 3, 6, 0, 3, 6,\dots \}
+\end{aligned}
+\]</div>
+<p>入力<code>key</code>がたまたまこの種の等差数列分布を持つ場合、ハッシュ値がクラスターし、ハッシュ衝突を悪化させます。今度は<code>modulus</code>を素数<span class="arithmatex">\(13\)</span>に置き換えるとします。<code>key</code>と<code>modulus</code>の間に共通因子がないため、出力ハッシュ値の均等性が大幅に改善されます。</p>
+<div class="arithmatex">\[
+\begin{aligned}
+\text{modulus} &amp; = 13 \newline
+\text{key} &amp; = \{ 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, \dots \} \newline
+\text{hash} &amp; = \{ 0, 3, 6, 9, 12, 2, 5, 8, 11, 1, 4, 7, \dots \}
+\end{aligned}
+\]</div>
+<p><code>key</code>がランダムで均等に分散されることが保証されている場合、剰余として素数または合成数を選択しても、両方とも均等に分散されたハッシュ値を生成できることは注目に値します。しかし、<code>key</code>の分布にある種の周期性がある場合、合成数の剰余はクラスタリングを引き起こしやすくなります。</p>
+<p>要約すると、通常は素数を剰余として選択し、この素数は周期的パターンを可能な限り排除し、ハッシュアルゴリズムの堅牢性を向上させるために十分大きくある必要があります。</p>
+<h2 id="633">6.3.3 &nbsp; 一般的なハッシュアルゴリズム<a class="headerlink" href="#633" title="Permanent link">&para;</a></h2>
+<p>上記で言及した簡単なハッシュアルゴリズムはかなり「脆弱」で、ハッシュアルゴリズムの設計目標から程遠いことは難しくありません。例えば、加算とXORは交換法則に従うため、加算ハッシュとXORハッシュは同じ内容だが順序が異なる文字列を区別できず、ハッシュ衝突を悪化させ、セキュリティ問題を引き起こす可能性があります。</p>
+<p>実際には、通常MD5、SHA-1、SHA-2、SHA-3などの標準ハッシュアルゴリズムを使用します。これらは任意の長さの入力データを固定長のハッシュ値にマッピングできます。</p>
+<p>過去1世紀にわたって、ハッシュアルゴリズムは継続的なアップグレードと最適化のプロセスにありました。一部の研究者はハッシュアルゴリズムの性能向上に努め、ハッカーを含む他の人々はハッシュアルゴリズムのセキュリティ問題を見つけることに専念しています。以下の表は、実用的なアプリケーションで一般的に使用されるハッシュアルゴリズムを示しています。</p>
+<ul>
+<li>MD5とSHA-1は複数回攻撃に成功しており、さまざまなセキュリティアプリケーションで放棄されています。</li>
+<li>SHA-2シリーズ、特にSHA-256は、現在最も安全なハッシュアルゴリズムの1つで、成功した攻撃は報告されておらず、さまざまなセキュリティアプリケーションとプロトコルで一般的に使用されています。</li>
+<li>SHA-3はSHA-2と比較して実装コストが低く、計算効率が高いですが、現在の使用範囲はSHA-2シリーズほど広範囲ではありません。</li>
+</ul>
+<p align="center"> 表 6-2 &nbsp; 一般的なハッシュアルゴリズム </p>
+
+<div class="center-table">
+<table>
+<thead>
+<tr>
+<th></th>
+<th>MD5</th>
+<th>SHA-1</th>
+<th>SHA-2</th>
+<th>SHA-3</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td>リリース年</td>
+<td>1992</td>
+<td>1995</td>
+<td>2002</td>
+<td>2008</td>
+</tr>
+<tr>
+<td>出力長</td>
+<td>128 bit</td>
+<td>160 bit</td>
+<td>256/512 bit</td>
+<td>224/256/384/512 bit</td>
+</tr>
+<tr>
+<td>ハッシュ衝突</td>
+<td>頻繁</td>
+<td>頻繁</td>
+<td>まれ</td>
+<td>まれ</td>
+</tr>
+<tr>
+<td>セキュリティレベル</td>
+<td>低、攻撃に成功している</td>
+<td>低、攻撃に成功している</td>
+<td>高</td>
+<td>高</td>
+</tr>
+<tr>
+<td>アプリケーション</td>
+<td>放棄、データ整合性チェックにまだ使用</td>
+<td>放棄</td>
+<td>暗号通貨取引検証、デジタル署名など</td>
+<td>SHA-2の代替として使用可能</td>
+</tr>
+</tbody>
+</table>
+</div>
+<h1 id="_1">データ構造におけるハッシュ値<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h1>
+<p>ハッシュ表のキーは整数、小数、文字列などのさまざまなデータ型にできることを知っています。プログラミング言語は通常、これらのデータ型に対して組み込みのハッシュアルゴリズムを提供し、ハッシュ表のバケットインデックスを計算します。Pythonを例に取ると、<code>hash()</code>関数を使用してさまざまなデータ型のハッシュ値を計算できます。</p>
+<ul>
+<li>整数とブール値のハッシュ値は、それら自身の値です。</li>
+<li>浮動小数点数と文字列のハッシュ値の計算はより複雑で、興味のある読者は自分で研究することをお勧めします。</li>
+<li>タプルのハッシュ値は、その各要素のハッシュ値の組み合わせで、単一のハッシュ値になります。</li>
+<li>オブジェクトのハッシュ値は、そのメモリアドレスに基づいて生成されます。オブジェクトのハッシュメソッドをオーバーライドすることで、内容に基づいてハッシュ値を生成できます。</li>
+</ul>
+<div class="admonition tip">
+<p class="admonition-title">Tip</p>
+<p>異なるプログラミング言語における組み込みハッシュ値計算関数の定義と方法は異なることに注意してください。</p>
+</div>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:13"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">built_in_hash.py</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="n">num</span> <span class="o">=</span> <span class="mi">3</span>
+<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="n">hash_num</span> <span class="o">=</span> <span class="nb">hash</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="c1"># 整数3のハッシュ値は3</span>
+<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a>
+<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="n">bol</span> <span class="o">=</span> <span class="kc">True</span>
+<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="n">hash_bol</span> <span class="o">=</span> <span class="nb">hash</span><span class="p">(</span><span class="n">bol</span><span class="p">)</span>
+<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="c1"># ブール値Trueのハッシュ値は1</span>
+<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a>
+<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="n">dec</span> <span class="o">=</span> <span class="mf">3.14159</span>
+<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="n">hash_dec</span> <span class="o">=</span> <span class="nb">hash</span><span class="p">(</span><span class="n">dec</span><span class="p">)</span>
+<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="c1"># 小数3.14159のハッシュ値は326484311674566659</span>
+<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a>
+<a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="nb">str</span> <span class="o">=</span> <span class="s2">&quot;Hello 算法&quot;</span>
+<a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="n">hash_str</span> <span class="o">=</span> <span class="nb">hash</span><span class="p">(</span><span class="nb">str</span><span class="p">)</span>
+<a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="c1"># 文字列&quot;Hello 算法&quot;のハッシュ値は4617003410720528961</span>
+<a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a>
+<a id="__codelineno-15-17" name="__codelineno-15-17" href="#__codelineno-15-17"></a><span class="n">tup</span> <span class="o">=</span> <span class="p">(</span><span class="mi">12836</span><span class="p">,</span> <span class="s2">&quot;小哈&quot;</span><span class="p">)</span>
+<a id="__codelineno-15-18" name="__codelineno-15-18" href="#__codelineno-15-18"></a><span class="n">hash_tup</span> <span class="o">=</span> <span class="nb">hash</span><span class="p">(</span><span class="n">tup</span><span class="p">)</span>
+<a id="__codelineno-15-19" name="__codelineno-15-19" href="#__codelineno-15-19"></a><span class="c1"># タプル(12836, &#39;小哈&#39;)のハッシュ値は1029005403108185979</span>
+<a id="__codelineno-15-20" name="__codelineno-15-20" href="#__codelineno-15-20"></a>
+<a id="__codelineno-15-21" name="__codelineno-15-21" href="#__codelineno-15-21"></a><span class="n">obj</span> <span class="o">=</span> <span class="n">ListNode</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-15-22" name="__codelineno-15-22" href="#__codelineno-15-22"></a><span class="n">hash_obj</span> <span class="o">=</span> <span class="nb">hash</span><span class="p">(</span><span class="n">obj</span><span class="p">)</span>
+<a id="__codelineno-15-23" name="__codelineno-15-23" href="#__codelineno-15-23"></a><span class="c1"># ListNodeオブジェクト0x1058fd810のハッシュ値は274267521</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">built_in_hash.cpp</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kt">size_t</span><span class="w"> </span><span class="n">hashNum</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hash</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">()(</span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="c1">// 整数3のハッシュ値は3</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="kt">bool</span><span class="w"> </span><span class="n">bol</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">true</span><span class="p">;</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="kt">size_t</span><span class="w"> </span><span class="n">hashBol</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hash</span><span class="o">&lt;</span><span class="kt">bool</span><span class="o">&gt;</span><span class="p">()(</span><span class="n">bol</span><span class="p">);</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="c1">// ブール値1のハッシュ値は1</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="kt">double</span><span class="w"> </span><span class="n">dec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">3.14159</span><span class="p">;</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="kt">size_t</span><span class="w"> </span><span class="n">hashDec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hash</span><span class="o">&lt;</span><span class="kt">double</span><span class="o">&gt;</span><span class="p">()(</span><span class="n">dec</span><span class="p">);</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="c1">// 小数3.14159のハッシュ値は4614256650576692846</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="n">string</span><span class="w"> </span><span class="n">str</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;Hello 算法&quot;</span><span class="p">;</span>
+<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="kt">size_t</span><span class="w"> </span><span class="n">hashStr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hash</span><span class="o">&lt;</span><span class="n">string</span><span class="o">&gt;</span><span class="p">()(</span><span class="n">str</span><span class="p">);</span>
+<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="c1">// 文字列&quot;Hello 算法&quot;のハッシュ値は15466937326284535026</span>
+<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a>
+<a id="__codelineno-16-17" name="__codelineno-16-17" href="#__codelineno-16-17"></a><span class="c1">// C++では、組み込みstd::hash()は基本データ型のハッシュ値のみを提供</span>
+<a id="__codelineno-16-18" name="__codelineno-16-18" href="#__codelineno-16-18"></a><span class="c1">// 配列とオブジェクトのハッシュ値は別途実装が必要</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">built_in_hash.java</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashNum</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Integer</span><span class="p">.</span><span class="na">hashCode</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="c1">// 整数3のハッシュ値は3</span>
+<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a>
+<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="kt">boolean</span><span class="w"> </span><span class="n">bol</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span><span class="p">;</span>
+<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashBol</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Boolean</span><span class="p">.</span><span class="na">hashCode</span><span class="p">(</span><span class="n">bol</span><span class="p">);</span>
+<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="c1">// ブール値trueのハッシュ値は1231</span>
+<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a>
+<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="kt">double</span><span class="w"> </span><span class="n">dec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">3.14159</span><span class="p">;</span>
+<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashDec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Double</span><span class="p">.</span><span class="na">hashCode</span><span class="p">(</span><span class="n">dec</span><span class="p">);</span>
+<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="c1">// 小数3.14159のハッシュ値は-1340954729</span>
+<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a>
+<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a><span class="n">String</span><span class="w"> </span><span class="n">str</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;Hello 算法&quot;</span><span class="p">;</span>
+<a id="__codelineno-17-14" name="__codelineno-17-14" href="#__codelineno-17-14"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashStr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">str</span><span class="p">.</span><span class="na">hashCode</span><span class="p">();</span>
+<a id="__codelineno-17-15" name="__codelineno-17-15" href="#__codelineno-17-15"></a><span class="c1">// 文字列&quot;Hello 算法&quot;のハッシュ値は-727081396</span>
+<a id="__codelineno-17-16" name="__codelineno-17-16" href="#__codelineno-17-16"></a>
+<a id="__codelineno-17-17" name="__codelineno-17-17" href="#__codelineno-17-17"></a><span class="n">Object</span><span class="o">[]</span><span class="w"> </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="mi">12836</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;小哈&quot;</span><span class="w"> </span><span class="p">};</span>
+<a id="__codelineno-17-18" name="__codelineno-17-18" href="#__codelineno-17-18"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashTup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Arrays</span><span class="p">.</span><span class="na">hashCode</span><span class="p">(</span><span class="n">arr</span><span class="p">);</span>
+<a id="__codelineno-17-19" name="__codelineno-17-19" href="#__codelineno-17-19"></a><span class="c1">// 配列[12836, 小哈]のハッシュ値は1151158</span>
+<a id="__codelineno-17-20" name="__codelineno-17-20" href="#__codelineno-17-20"></a>
+<a id="__codelineno-17-21" name="__codelineno-17-21" href="#__codelineno-17-21"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">obj</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-17-22" name="__codelineno-17-22" href="#__codelineno-17-22"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashObj</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">obj</span><span class="p">.</span><span class="na">hashCode</span><span class="p">();</span>
+<a id="__codelineno-17-23" name="__codelineno-17-23" href="#__codelineno-17-23"></a><span class="c1">// ListNodeオブジェクトutils.ListNode@7dc5e7b4のハッシュ値は2110121908</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">built_in_hash.cs</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span>
+<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashNum</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">.</span><span class="n">GetHashCode</span><span class="p">();</span>
+<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="c1">// 整数3のハッシュ値は3;</span>
+<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a>
+<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="kt">bool</span><span class="w"> </span><span class="n">bol</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">true</span><span class="p">;</span>
+<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashBol</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">bol</span><span class="p">.</span><span class="n">GetHashCode</span><span class="p">();</span>
+<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="c1">// ブール値trueのハッシュ値は1;</span>
+<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a>
+<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="kt">double</span><span class="w"> </span><span class="n">dec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">3.14159</span><span class="p">;</span>
+<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashDec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dec</span><span class="p">.</span><span class="n">GetHashCode</span><span class="p">();</span>
+<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="c1">// 小数3.14159のハッシュ値は-1340954729;</span>
+<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a>
+<a id="__codelineno-18-13" name="__codelineno-18-13" href="#__codelineno-18-13"></a><span class="kt">string</span><span class="w"> </span><span class="n">str</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;Hello 算法&quot;</span><span class="p">;</span>
+<a id="__codelineno-18-14" name="__codelineno-18-14" href="#__codelineno-18-14"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashStr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">str</span><span class="p">.</span><span class="n">GetHashCode</span><span class="p">();</span>
+<a id="__codelineno-18-15" name="__codelineno-18-15" href="#__codelineno-18-15"></a><span class="c1">// 文字列&quot;Hello 算法&quot;のハッシュ値は-586107568;</span>
+<a id="__codelineno-18-16" name="__codelineno-18-16" href="#__codelineno-18-16"></a>
+<a id="__codelineno-18-17" name="__codelineno-18-17" href="#__codelineno-18-17"></a><span class="kt">object</span><span class="p">[]</span><span class="w"> </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mi">12836</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;小哈&quot;</span><span class="p">];</span>
+<a id="__codelineno-18-18" name="__codelineno-18-18" href="#__codelineno-18-18"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashTup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="p">.</span><span class="n">GetHashCode</span><span class="p">();</span>
+<a id="__codelineno-18-19" name="__codelineno-18-19" href="#__codelineno-18-19"></a><span class="c1">// 配列[12836, 小哈]のハッシュ値は42931033;</span>
+<a id="__codelineno-18-20" name="__codelineno-18-20" href="#__codelineno-18-20"></a>
+<a id="__codelineno-18-21" name="__codelineno-18-21" href="#__codelineno-18-21"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">obj</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-18-22" name="__codelineno-18-22" href="#__codelineno-18-22"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashObj</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">obj</span><span class="p">.</span><span class="n">GetHashCode</span><span class="p">();</span>
+<a id="__codelineno-18-23" name="__codelineno-18-23" href="#__codelineno-18-23"></a><span class="c1">// ListNodeオブジェクト0のハッシュ値は39053774;</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">built_in_hash.go</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="c1">// Goには組み込みのハッシュコード関数が提供されていません</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">built_in_hash.swift</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="kd">let</span><span class="w"> </span><span class="nv">num</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">3</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="kd">let</span><span class="w"> </span><span class="nv">hashNum</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">num</span><span class="p">.</span><span class="n">hashValue</span>
+<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="c1">// 整数3のハッシュ値は9047044699613009734</span>
+<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a>
+<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="kd">let</span><span class="w"> </span><span class="nv">bol</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="kc">true</span>
+<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="kd">let</span><span class="w"> </span><span class="nv">hashBol</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">bol</span><span class="p">.</span><span class="n">hashValue</span>
+<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="c1">// ブール値trueのハッシュ値は-4431640247352757451</span>
+<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a>
+<a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a><span class="kd">let</span><span class="w"> </span><span class="nv">dec</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mf">3.14159</span>
+<a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a><span class="kd">let</span><span class="w"> </span><span class="nv">hashDec</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">dec</span><span class="p">.</span><span class="n">hashValue</span>
+<a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a><span class="c1">// 小数3.14159のハッシュ値は-2465384235396674631</span>
+<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a>
+<a id="__codelineno-20-13" name="__codelineno-20-13" href="#__codelineno-20-13"></a><span class="kd">let</span><span class="w"> </span><span class="nv">str</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">&quot;Hello 算法&quot;</span>
+<a id="__codelineno-20-14" name="__codelineno-20-14" href="#__codelineno-20-14"></a><span class="kd">let</span><span class="w"> </span><span class="nv">hashStr</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">str</span><span class="p">.</span><span class="n">hashValue</span>
+<a id="__codelineno-20-15" name="__codelineno-20-15" href="#__codelineno-20-15"></a><span class="c1">// 文字列&quot;Hello 算法&quot;のハッシュ値は-7850626797806988787</span>
+<a id="__codelineno-20-16" name="__codelineno-20-16" href="#__codelineno-20-16"></a>
+<a id="__codelineno-20-17" name="__codelineno-20-17" href="#__codelineno-20-17"></a><span class="kd">let</span><span class="w"> </span><span class="nv">arr</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[</span><span class="n">AnyHashable</span><span class="p">(</span><span class="mi">12836</span><span class="p">),</span><span class="w"> </span><span class="n">AnyHashable</span><span class="p">(</span><span class="s">&quot;小哈&quot;</span><span class="p">)]</span>
+<a id="__codelineno-20-18" name="__codelineno-20-18" href="#__codelineno-20-18"></a><span class="kd">let</span><span class="w"> </span><span class="nv">hashTup</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">arr</span><span class="p">.</span><span class="n">hashValue</span>
+<a id="__codelineno-20-19" name="__codelineno-20-19" href="#__codelineno-20-19"></a><span class="c1">// 配列[AnyHashable(12836), AnyHashable(&quot;小哈&quot;)]のハッシュ値は-2308633508154532996</span>
+<a id="__codelineno-20-20" name="__codelineno-20-20" href="#__codelineno-20-20"></a>
+<a id="__codelineno-20-21" name="__codelineno-20-21" href="#__codelineno-20-21"></a><span class="kd">let</span><span class="w"> </span><span class="nv">obj</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-20-22" name="__codelineno-20-22" href="#__codelineno-20-22"></a><span class="kd">let</span><span class="w"> </span><span class="nv">hashObj</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">obj</span><span class="p">.</span><span class="n">hashValue</span>
+<a id="__codelineno-20-23" name="__codelineno-20-23" href="#__codelineno-20-23"></a><span class="c1">// ListNodeオブジェクトutils.ListNodeのハッシュ値は-2434780518035996159</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">built_in_hash.js</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="c1">// JavaScriptには組み込みのハッシュコード関数が提供されていません</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">built_in_hash.ts</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="c1">// TypeScriptには組み込みのハッシュコード関数が提供されていません</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">built_in_hash.dart</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="kt">int</span><span class="w"> </span><span class="kt">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">3</span><span class="p">;</span>
+<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashNum</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kt">num</span><span class="p">.</span><span class="n">hashCode</span><span class="p">;</span>
+<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="c1">// 整数3のハッシュ値は34803</span>
+<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a>
+<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="kt">bool</span><span class="w"> </span><span class="n">bol</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span><span class="p">;</span>
+<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashBol</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">bol</span><span class="p">.</span><span class="n">hashCode</span><span class="p">;</span>
+<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="c1">// ブール値trueのハッシュ値は1231</span>
+<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a>
+<a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></a><span class="kt">double</span><span class="w"> </span><span class="n">dec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">3.14159</span><span class="p">;</span>
+<a id="__codelineno-23-10" name="__codelineno-23-10" href="#__codelineno-23-10"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashDec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dec</span><span class="p">.</span><span class="n">hashCode</span><span class="p">;</span>
+<a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a><span class="c1">// 小数3.14159のハッシュ値は2570631074981783</span>
+<a id="__codelineno-23-12" name="__codelineno-23-12" href="#__codelineno-23-12"></a>
+<a id="__codelineno-23-13" name="__codelineno-23-13" href="#__codelineno-23-13"></a><span class="kt">String</span><span class="w"> </span><span class="n">str</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s2">&quot;Hello 算法&quot;</span><span class="p">;</span>
+<a id="__codelineno-23-14" name="__codelineno-23-14" href="#__codelineno-23-14"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashStr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">str</span><span class="p">.</span><span class="n">hashCode</span><span class="p">;</span>
+<a id="__codelineno-23-15" name="__codelineno-23-15" href="#__codelineno-23-15"></a><span class="c1">// 文字列&quot;Hello 算法&quot;のハッシュ値は468167534</span>
+<a id="__codelineno-23-16" name="__codelineno-23-16" href="#__codelineno-23-16"></a>
+<a id="__codelineno-23-17" name="__codelineno-23-17" href="#__codelineno-23-17"></a><span class="n">List</span><span class="w"> </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="m">12836</span><span class="p">,</span><span class="w"> </span><span class="s2">&quot;小哈&quot;</span><span class="p">];</span>
+<a id="__codelineno-23-18" name="__codelineno-23-18" href="#__codelineno-23-18"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashArr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="p">.</span><span class="n">hashCode</span><span class="p">;</span>
+<a id="__codelineno-23-19" name="__codelineno-23-19" href="#__codelineno-23-19"></a><span class="c1">// 配列[12836, 小哈]のハッシュ値は976512528</span>
+<a id="__codelineno-23-20" name="__codelineno-23-20" href="#__codelineno-23-20"></a>
+<a id="__codelineno-23-21" name="__codelineno-23-21" href="#__codelineno-23-21"></a><span class="n">ListNode</span><span class="w"> </span><span class="n">obj</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
+<a id="__codelineno-23-22" name="__codelineno-23-22" href="#__codelineno-23-22"></a><span class="kt">int</span><span class="w"> </span><span class="n">hashObj</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">obj</span><span class="p">.</span><span class="n">hashCode</span><span class="p">;</span>
+<a id="__codelineno-23-23" name="__codelineno-23-23" href="#__codelineno-23-23"></a><span class="c1">// ListNodeオブジェクトInstance of &#39;ListNode&#39;のハッシュ値は1033450432</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">built_in_hash.rs</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="k">use</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">collections</span><span class="p">::</span><span class="n">hash_map</span><span class="p">::</span><span class="n">DefaultHasher</span><span class="p">;</span>
+<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="k">use</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">hash</span><span class="p">::{</span><span class="n">Hash</span><span class="p">,</span><span class="w"> </span><span class="n">Hasher</span><span class="p">};</span>
+<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a>
+<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a><span class="kd">let</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">3</span><span class="p">;</span>
+<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">num_hasher</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">DefaultHasher</span><span class="p">::</span><span class="n">new</span><span class="p">();</span>
+<a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a><span class="n">num</span><span class="p">.</span><span class="n">hash</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">num_hasher</span><span class="p">);</span>
+<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></a><span class="kd">let</span><span class="w"> </span><span class="n">hash_num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num_hasher</span><span class="p">.</span><span class="n">finish</span><span class="p">();</span>
+<a id="__codelineno-24-8" name="__codelineno-24-8" href="#__codelineno-24-8"></a><span class="c1">// 整数3のハッシュ値は568126464209439262</span>
+<a id="__codelineno-24-9" name="__codelineno-24-9" href="#__codelineno-24-9"></a>
+<a id="__codelineno-24-10" name="__codelineno-24-10" href="#__codelineno-24-10"></a><span class="kd">let</span><span class="w"> </span><span class="n">bol</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span><span class="p">;</span>
+<a id="__codelineno-24-11" name="__codelineno-24-11" href="#__codelineno-24-11"></a><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">bol_hasher</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">DefaultHasher</span><span class="p">::</span><span class="n">new</span><span class="p">();</span>
+<a id="__codelineno-24-12" name="__codelineno-24-12" href="#__codelineno-24-12"></a><span class="n">bol</span><span class="p">.</span><span class="n">hash</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">bol_hasher</span><span class="p">);</span>
+<a id="__codelineno-24-13" name="__codelineno-24-13" href="#__codelineno-24-13"></a><span class="kd">let</span><span class="w"> </span><span class="n">hash_bol</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">bol_hasher</span><span class="p">.</span><span class="n">finish</span><span class="p">();</span>
+<a id="__codelineno-24-14" name="__codelineno-24-14" href="#__codelineno-24-14"></a><span class="c1">// ブール値trueのハッシュ値は4952851536318644461</span>
+<a id="__codelineno-24-15" name="__codelineno-24-15" href="#__codelineno-24-15"></a>
+<a id="__codelineno-24-16" name="__codelineno-24-16" href="#__codelineno-24-16"></a><span class="kd">let</span><span class="w"> </span><span class="n">dec</span><span class="p">:</span><span class="w"> </span><span class="kt">f32</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">3.14159</span><span class="p">;</span>
+<a id="__codelineno-24-17" name="__codelineno-24-17" href="#__codelineno-24-17"></a><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">dec_hasher</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">DefaultHasher</span><span class="p">::</span><span class="n">new</span><span class="p">();</span>
+<a id="__codelineno-24-18" name="__codelineno-24-18" href="#__codelineno-24-18"></a><span class="n">dec</span><span class="p">.</span><span class="n">to_bits</span><span class="p">().</span><span class="n">hash</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">dec_hasher</span><span class="p">);</span>
+<a id="__codelineno-24-19" name="__codelineno-24-19" href="#__codelineno-24-19"></a><span class="kd">let</span><span class="w"> </span><span class="n">hash_dec</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">dec_hasher</span><span class="p">.</span><span class="n">finish</span><span class="p">();</span>
+<a id="__codelineno-24-20" name="__codelineno-24-20" href="#__codelineno-24-20"></a><span class="c1">// 小数3.14159のハッシュ値は2566941990314602357</span>
+<a id="__codelineno-24-21" name="__codelineno-24-21" href="#__codelineno-24-21"></a>
+<a id="__codelineno-24-22" name="__codelineno-24-22" href="#__codelineno-24-22"></a><span class="kd">let</span><span class="w"> </span><span class="kt">str</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;Hello 算法&quot;</span><span class="p">;</span>
+<a id="__codelineno-24-23" name="__codelineno-24-23" href="#__codelineno-24-23"></a><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">str_hasher</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">DefaultHasher</span><span class="p">::</span><span class="n">new</span><span class="p">();</span>
+<a id="__codelineno-24-24" name="__codelineno-24-24" href="#__codelineno-24-24"></a><span class="kt">str</span><span class="p">.</span><span class="n">hash</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">str_hasher</span><span class="p">);</span>
+<a id="__codelineno-24-25" name="__codelineno-24-25" href="#__codelineno-24-25"></a><span class="kd">let</span><span class="w"> </span><span class="n">hash_str</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">str_hasher</span><span class="p">.</span><span class="n">finish</span><span class="p">();</span>
+<a id="__codelineno-24-26" name="__codelineno-24-26" href="#__codelineno-24-26"></a><span class="c1">// 文字列&quot;Hello 算法&quot;のハッシュ値は16092673739211250988</span>
+<a id="__codelineno-24-27" name="__codelineno-24-27" href="#__codelineno-24-27"></a>
+<a id="__codelineno-24-28" name="__codelineno-24-28" href="#__codelineno-24-28"></a><span class="kd">let</span><span class="w"> </span><span class="n">arr</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="o">&amp;</span><span class="mi">12836</span><span class="p">,</span><span class="w"> </span><span class="o">&amp;</span><span class="s">&quot;小哈&quot;</span><span class="p">);</span>
+<a id="__codelineno-24-29" name="__codelineno-24-29" href="#__codelineno-24-29"></a><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">tup_hasher</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">DefaultHasher</span><span class="p">::</span><span class="n">new</span><span class="p">();</span>
+<a id="__codelineno-24-30" name="__codelineno-24-30" href="#__codelineno-24-30"></a><span class="n">arr</span><span class="p">.</span><span class="n">hash</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">tup_hasher</span><span class="p">);</span>
+<a id="__codelineno-24-31" name="__codelineno-24-31" href="#__codelineno-24-31"></a><span class="kd">let</span><span class="w"> </span><span class="n">hash_tup</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tup_hasher</span><span class="p">.</span><span class="n">finish</span><span class="p">();</span>
+<a id="__codelineno-24-32" name="__codelineno-24-32" href="#__codelineno-24-32"></a><span class="c1">// タプル(12836, &quot;小哈&quot;)のハッシュ値は1885128010422702749</span>
+<a id="__codelineno-24-33" name="__codelineno-24-33" href="#__codelineno-24-33"></a>
+<a id="__codelineno-24-34" name="__codelineno-24-34" href="#__codelineno-24-34"></a><span class="kd">let</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ListNode</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="mi">42</span><span class="p">);</span>
+<a id="__codelineno-24-35" name="__codelineno-24-35" href="#__codelineno-24-35"></a><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">hasher</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">DefaultHasher</span><span class="p">::</span><span class="n">new</span><span class="p">();</span>
+<a id="__codelineno-24-36" name="__codelineno-24-36" href="#__codelineno-24-36"></a><span class="n">node</span><span class="p">.</span><span class="n">borrow</span><span class="p">().</span><span class="n">val</span><span class="p">.</span><span class="n">hash</span><span class="p">(</span><span class="o">&amp;</span><span class="k">mut</span><span class="w"> </span><span class="n">hasher</span><span class="p">);</span>
+<a id="__codelineno-24-37" name="__codelineno-24-37" href="#__codelineno-24-37"></a><span class="kd">let</span><span class="w"> </span><span class="n">hash</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hasher</span><span class="p">.</span><span class="n">finish</span><span class="p">();</span>
+<a id="__codelineno-24-38" name="__codelineno-24-38" href="#__codelineno-24-38"></a><span class="c1">// ListNodeオブジェクトRefCell { value: ListNode { val: 42, next: None } }のハッシュ値は15387811073369036852</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">built_in_hash.c</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="c1">// Cには組み込みのハッシュコード関数が提供されていません</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">built_in_hash.kt</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">built_in_hash.zig</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>多くのプログラミング言語では、<strong>不変オブジェクトのみがハッシュ表の<code>key</code>として機能できます</strong>。リスト（動的配列）を<code>key</code>として使用する場合、リストの内容が変更されると、そのハッシュ値も変更され、ハッシュ表で元の<code>value</code>を見つけることができなくなります。</p>
+<p>カスタムオブジェクト（連結リストノードなど）のメンバー変数は可変ですが、ハッシュ可能です。<strong>これは、オブジェクトのハッシュ値が通常そのメモリアドレスに基づいて生成されるためです</strong>。オブジェクトの内容が変更されても、メモリアドレスは同じままなので、ハッシュ値は変更されません。</p>
+<p>異なるコンソールで出力されるハッシュ値が異なることに気づいたかもしれません。<strong>これは、Pythonインタープリターが起動するたびに文字列ハッシュ関数にランダムソルトを追加するためです</strong>。このアプローチはHashDoS攻撃を効果的に防ぎ、ハッシュアルゴリズムのセキュリティを向上させます。</p>
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diff --git a/ja/chapter_hashing/hash_collision.assets/hash_table_open_addressing_deletion.png b/ja/chapter_hashing/hash_collision.assets/hash_table_open_addressing_deletion.png
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+  
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+  
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+      <a href="../../chapter_preface/about_the_book/" class="md-nav__link">
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+      <a href="../../chapter_preface/summary/" class="md-nav__link">
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+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
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+  
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+    1.1 &nbsp; アルゴリズムはどこにでもある
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+  
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+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
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+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
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+    </li>
+  
+
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+              
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+  
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+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
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+    </li>
+  
+
+              
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+          
+        
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+        
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+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
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+  
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+            第 2 章 &nbsp; 計算量解析
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+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
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+    2.1 &nbsp; アルゴリズム効率評価
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+  
+
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+
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+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
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+    2.2 &nbsp; 反復と再帰
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+  
+
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+    </li>
+  
+
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+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
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+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
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+
+              
+            
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+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
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+  
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+    第 3 章 &nbsp; データ構造
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+            第 3 章 &nbsp; データ構造
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+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
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+    3.1 &nbsp; データ構造の分類
+  </span>
+  
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+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
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+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
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+
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+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
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+  </span>
+  
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+    </li>
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+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
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+  </span>
+  
+
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+    </li>
+  
+
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+  
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+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
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+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
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+  
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+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
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+        
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+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
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+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
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+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
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+          <label class="md-nav__title" for="__nav_7">
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+            第 5 章 &nbsp; スタックとキュー
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+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
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+  </span>
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+
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+  
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+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
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+    </li>
+  
+
+              
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
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+    </li>
+  
+
+              
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+              
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+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
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+      
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+  
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+  
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+    
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+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
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+        
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+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
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+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#621" class="md-nav__link">
+    <span class="md-ellipsis">
+      6.2.1 &nbsp; 連鎖法
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#622" class="md-nav__link">
+    <span class="md-ellipsis">
+      6.2.2 &nbsp; オープンアドレス法
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="6.2.2   オープンアドレス法">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 線形プローブ
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; 二次プローブ
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#3" class="md-nav__link">
+    <span class="md-ellipsis">
+      3. &nbsp; 二重ハッシュ
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#623" class="md-nav__link">
+    <span class="md-ellipsis">
+      6.2.3 &nbsp; プログラミング言語の選択
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
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+            
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+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
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+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
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+        
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+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
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+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
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+      
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+  
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+    
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+      
+        
+          
+        
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+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
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+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
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+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
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+      
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+          
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_19" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_reference/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9 3v15h3V3H9m3 2 4 13 3-1-4-13-3 1M5 5v13h3V5H5M3 19v2h18v-2H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    参考文献
+  </span>
+  
+
+            </a>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_19_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_19">
+            <span class="md-nav__icon md-icon"></span>
+            参考文献
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
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+        </nav>
+      
+    </li>
+  
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+    
+  </ul>
+</nav>
+                  </div>
+                </div>
+              </div>
+            
+            
+              
+              <div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
+                <div class="md-sidebar__scrollwrap">
+                  <div class="md-sidebar__inner">
+                    
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#621" class="md-nav__link">
+    <span class="md-ellipsis">
+      6.2.1 &nbsp; 連鎖法
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#622" class="md-nav__link">
+    <span class="md-ellipsis">
+      6.2.2 &nbsp; オープンアドレス法
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="6.2.2   オープンアドレス法">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 線形プローブ
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; 二次プローブ
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#3" class="md-nav__link">
+    <span class="md-ellipsis">
+      3. &nbsp; 二重ハッシュ
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#623" class="md-nav__link">
+    <span class="md-ellipsis">
+      6.2.3 &nbsp; プログラミング言語の選択
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+                  </div>
+                </div>
+              </div>
+            
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+          
+            <div class="md-content" data-md-component="content">
+              <article class="md-content__inner md-typeset">
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+      title="編集"
+      class="md-content__button md-icon"
+    >
+      
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+<h1 id="62">6.2 &nbsp; ハッシュ衝突<a class="headerlink" href="#62" title="Permanent link">&para;</a></h1>
+<p>前節で述べたように、**ほとんどの場合、ハッシュ関数の入力空間は出力空間よりもはるかに大きい**ため、理論的にはハッシュ衝突は避けられません。例えば、入力空間がすべての整数で、出力空間が配列容量のサイズの場合、複数の整数が必然的に同じバケットインデックスにマッピングされます。</p>
+<p>ハッシュ衝突は誤ったクエリ結果につながり、ハッシュ表の使いやすさに深刻な影響を与える可能性があります。この問題に対処するために、ハッシュ衝突が発生するたびに、衝突が消えるまでハッシュ表のリサイズを実行します。このアプローチは非常にシンプルで直接的であり、うまく機能します。しかし、テーブルの拡張には大量のデータ移行とハッシュコードの再計算が含まれ、これらは高コストであるため、非常に非効率的に見えます。効率を向上させるために、以下の戦略を採用できます：</p>
+<ol>
+<li>**ハッシュ衝突が発生した場合でも、ターゲット要素の検索が適切に機能する**ようにハッシュ表のデータ構造を改善する。</li>
+<li>深刻な衝突が観察され、必要になる前に、拡張は最後の手段とする。</li>
+</ol>
+<p>ハッシュ表の構造を改善する主な方法は2つあります：「連鎖法」と「オープンアドレス法」です。</p>
+<h2 id="621">6.2.1 &nbsp; 連鎖法<a class="headerlink" href="#621" title="Permanent link">&para;</a></h2>
+<p>元のハッシュ表では、各バケットは1つのキー値ペアのみを格納できます。<u>連鎖法</u>は単一の要素を連結リストに変換し、キー値ペアをリストノードとして扱い、衝突するすべてのキー値ペアを同じ連結リストに格納します。下図は連鎖法を使用したハッシュ表の例を示しています。</p>
+<p><a class="glightbox" href="../hash_collision.assets/hash_table_chaining.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="連鎖法ハッシュ表" class="animation-figure" src="../hash_collision.assets/hash_table_chaining.png" /></a></p>
+<p align="center"> 図 6-5 &nbsp; 連鎖法ハッシュ表 </p>
+
+<p>連鎖法で実装されたハッシュ表の操作は以下のように変更されます：</p>
+<ul>
+<li><strong>要素のクエリ</strong>: <code>key</code>を入力し、ハッシュ関数を通してバケットインデックスを取得し、連結リストのヘッドノードにアクセスします。連結リストを走査してキーを比較し、ターゲットキー値ペアを見つけます。</li>
+<li><strong>要素の追加</strong>: ハッシュ関数を通して連結リストのヘッドノードにアクセスし、ノード（キー値ペア）をリストに追加します。</li>
+<li><strong>要素の削除</strong>: ハッシュ関数の結果に基づいて連結リストのヘッドにアクセスし、連結リストを走査してターゲットノードを見つけて削除します。</li>
+</ul>
+<p>連鎖法には以下の制限があります：</p>
+<ul>
+<li><strong>空間使用量の増加</strong>: 連結リストにはノードポインタが含まれており、配列よりも多くのメモリ空間を消費します。</li>
+<li><strong>クエリ効率の低下</strong>: 対応する要素を見つけるために連結リストの線形走査が必要になるためです。</li>
+</ul>
+<p>以下のコードは連鎖法ハッシュ表の簡単な実装を提供し、注意すべき2つの点があります：</p>
+<ul>
+<li>簡単にするために、連結リストの代わりにリスト（動的配列）を使用します。この設定では、ハッシュ表（配列）は複数のバケットを含み、各バケットはリストです。</li>
+<li>この実装にはハッシュ表のリサイズメソッドが含まれています。負荷率が<span class="arithmatex">\(\frac{2}{3}\)</span>を超えると、ハッシュ表を元のサイズの2倍に拡張します。</li>
+</ul>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:14"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><input id="__tabbed_1_14" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label><label for="__tabbed_1_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map_chaining.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">HashMapChaining</span><span class="p">:</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;チェーンアドレス法ハッシュテーブル&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;コンストラクタ&quot;&quot;&quot;</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">size</span> <span class="o">=</span> <span class="mi">0</span>  <span class="c1"># キー値ペアの数</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span> <span class="o">=</span> <span class="mi">4</span>  <span class="c1"># ハッシュテーブルの容量</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">load_thres</span> <span class="o">=</span> <span class="mf">2.0</span> <span class="o">/</span> <span class="mf">3.0</span>  <span class="c1"># 拡張をトリガーする負荷率の閾値</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">extend_ratio</span> <span class="o">=</span> <span class="mi">2</span>  <span class="c1"># 拡張の倍数</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span> <span class="o">=</span> <span class="p">[[]</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">capacity</span><span class="p">)]</span>  <span class="c1"># バケット配列</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">hash_func</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;ハッシュ関数&quot;&quot;&quot;</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>        <span class="k">return</span> <span class="n">key</span> <span class="o">%</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span>
+<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>
+<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">load_factor</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">float</span><span class="p">:</span>
+<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;負荷率&quot;&quot;&quot;</span>
+<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span>
+<a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a>
+<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">get</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">str</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;照会操作&quot;&quot;&quot;</span>
+<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a>        <span class="n">index</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">hash_func</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a>        <span class="n">bucket</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span>
+<a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a>        <span class="c1"># バケットを走査し、キーが見つかれば対応する val を返す</span>
+<a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a>        <span class="k">for</span> <span class="n">pair</span> <span class="ow">in</span> <span class="n">bucket</span><span class="p">:</span>
+<a id="__codelineno-0-26" name="__codelineno-0-26" href="#__codelineno-0-26"></a>            <span class="k">if</span> <span class="n">pair</span><span class="o">.</span><span class="n">key</span> <span class="o">==</span> <span class="n">key</span><span class="p">:</span>
+<a id="__codelineno-0-27" name="__codelineno-0-27" href="#__codelineno-0-27"></a>                <span class="k">return</span> <span class="n">pair</span><span class="o">.</span><span class="n">val</span>
+<a id="__codelineno-0-28" name="__codelineno-0-28" href="#__codelineno-0-28"></a>        <span class="c1"># キーが見つからない場合、None を返す</span>
+<a id="__codelineno-0-29" name="__codelineno-0-29" href="#__codelineno-0-29"></a>        <span class="k">return</span> <span class="kc">None</span>
+<a id="__codelineno-0-30" name="__codelineno-0-30" href="#__codelineno-0-30"></a>
+<a id="__codelineno-0-31" name="__codelineno-0-31" href="#__codelineno-0-31"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">put</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">str</span><span class="p">):</span>
+<a id="__codelineno-0-32" name="__codelineno-0-32" href="#__codelineno-0-32"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;追加操作&quot;&quot;&quot;</span>
+<a id="__codelineno-0-33" name="__codelineno-0-33" href="#__codelineno-0-33"></a>        <span class="c1"># 負荷率が閾値を超えた場合、拡張を実行</span>
+<a id="__codelineno-0-34" name="__codelineno-0-34" href="#__codelineno-0-34"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">load_factor</span><span class="p">()</span> <span class="o">&gt;</span> <span class="bp">self</span><span class="o">.</span><span class="n">load_thres</span><span class="p">:</span>
+<a id="__codelineno-0-35" name="__codelineno-0-35" href="#__codelineno-0-35"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">extend</span><span class="p">()</span>
+<a id="__codelineno-0-36" name="__codelineno-0-36" href="#__codelineno-0-36"></a>        <span class="n">index</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">hash_func</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-0-37" name="__codelineno-0-37" href="#__codelineno-0-37"></a>        <span class="n">bucket</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span>
+<a id="__codelineno-0-38" name="__codelineno-0-38" href="#__codelineno-0-38"></a>        <span class="c1"># バケットを走査し、指定されたキーに遭遇した場合、対応する val を更新して返す</span>
+<a id="__codelineno-0-39" name="__codelineno-0-39" href="#__codelineno-0-39"></a>        <span class="k">for</span> <span class="n">pair</span> <span class="ow">in</span> <span class="n">bucket</span><span class="p">:</span>
+<a id="__codelineno-0-40" name="__codelineno-0-40" href="#__codelineno-0-40"></a>            <span class="k">if</span> <span class="n">pair</span><span class="o">.</span><span class="n">key</span> <span class="o">==</span> <span class="n">key</span><span class="p">:</span>
+<a id="__codelineno-0-41" name="__codelineno-0-41" href="#__codelineno-0-41"></a>                <span class="n">pair</span><span class="o">.</span><span class="n">val</span> <span class="o">=</span> <span class="n">val</span>
+<a id="__codelineno-0-42" name="__codelineno-0-42" href="#__codelineno-0-42"></a>                <span class="k">return</span>
+<a id="__codelineno-0-43" name="__codelineno-0-43" href="#__codelineno-0-43"></a>        <span class="c1"># キーが見つからない場合、キー値ペアを末尾に追加</span>
+<a id="__codelineno-0-44" name="__codelineno-0-44" href="#__codelineno-0-44"></a>        <span class="n">pair</span> <span class="o">=</span> <span class="n">Pair</span><span class="p">(</span><span class="n">key</span><span class="p">,</span> <span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-0-45" name="__codelineno-0-45" href="#__codelineno-0-45"></a>        <span class="n">bucket</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">pair</span><span class="p">)</span>
+<a id="__codelineno-0-46" name="__codelineno-0-46" href="#__codelineno-0-46"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">size</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-0-47" name="__codelineno-0-47" href="#__codelineno-0-47"></a>
+<a id="__codelineno-0-48" name="__codelineno-0-48" href="#__codelineno-0-48"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-0-49" name="__codelineno-0-49" href="#__codelineno-0-49"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;削除操作&quot;&quot;&quot;</span>
+<a id="__codelineno-0-50" name="__codelineno-0-50" href="#__codelineno-0-50"></a>        <span class="n">index</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">hash_func</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-0-51" name="__codelineno-0-51" href="#__codelineno-0-51"></a>        <span class="n">bucket</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span>
+<a id="__codelineno-0-52" name="__codelineno-0-52" href="#__codelineno-0-52"></a>        <span class="c1"># バケットを走査し、その中からキー値ペアを削除</span>
+<a id="__codelineno-0-53" name="__codelineno-0-53" href="#__codelineno-0-53"></a>        <span class="k">for</span> <span class="n">pair</span> <span class="ow">in</span> <span class="n">bucket</span><span class="p">:</span>
+<a id="__codelineno-0-54" name="__codelineno-0-54" href="#__codelineno-0-54"></a>            <span class="k">if</span> <span class="n">pair</span><span class="o">.</span><span class="n">key</span> <span class="o">==</span> <span class="n">key</span><span class="p">:</span>
+<a id="__codelineno-0-55" name="__codelineno-0-55" href="#__codelineno-0-55"></a>                <span class="n">bucket</span><span class="o">.</span><span class="n">remove</span><span class="p">(</span><span class="n">pair</span><span class="p">)</span>
+<a id="__codelineno-0-56" name="__codelineno-0-56" href="#__codelineno-0-56"></a>                <span class="bp">self</span><span class="o">.</span><span class="n">size</span> <span class="o">-=</span> <span class="mi">1</span>
+<a id="__codelineno-0-57" name="__codelineno-0-57" href="#__codelineno-0-57"></a>                <span class="k">break</span>
+<a id="__codelineno-0-58" name="__codelineno-0-58" href="#__codelineno-0-58"></a>
+<a id="__codelineno-0-59" name="__codelineno-0-59" href="#__codelineno-0-59"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">extend</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<a id="__codelineno-0-60" name="__codelineno-0-60" href="#__codelineno-0-60"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;ハッシュテーブルを拡張&quot;&quot;&quot;</span>
+<a id="__codelineno-0-61" name="__codelineno-0-61" href="#__codelineno-0-61"></a>        <span class="c1"># 元のハッシュテーブルを一時的に保存</span>
+<a id="__codelineno-0-62" name="__codelineno-0-62" href="#__codelineno-0-62"></a>        <span class="n">buckets</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span>
+<a id="__codelineno-0-63" name="__codelineno-0-63" href="#__codelineno-0-63"></a>        <span class="c1"># 拡張された新しいハッシュテーブルを初期化</span>
+<a id="__codelineno-0-64" name="__codelineno-0-64" href="#__codelineno-0-64"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span> <span class="o">*=</span> <span class="bp">self</span><span class="o">.</span><span class="n">extend_ratio</span>
+<a id="__codelineno-0-65" name="__codelineno-0-65" href="#__codelineno-0-65"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span> <span class="o">=</span> <span class="p">[[]</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">capacity</span><span class="p">)]</span>
+<a id="__codelineno-0-66" name="__codelineno-0-66" href="#__codelineno-0-66"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">size</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-0-67" name="__codelineno-0-67" href="#__codelineno-0-67"></a>        <span class="c1"># 元のハッシュテーブルから新しいハッシュテーブルにキー値ペアを移動</span>
+<a id="__codelineno-0-68" name="__codelineno-0-68" href="#__codelineno-0-68"></a>        <span class="k">for</span> <span class="n">bucket</span> <span class="ow">in</span> <span class="n">buckets</span><span class="p">:</span>
+<a id="__codelineno-0-69" name="__codelineno-0-69" href="#__codelineno-0-69"></a>            <span class="k">for</span> <span class="n">pair</span> <span class="ow">in</span> <span class="n">bucket</span><span class="p">:</span>
+<a id="__codelineno-0-70" name="__codelineno-0-70" href="#__codelineno-0-70"></a>                <span class="bp">self</span><span class="o">.</span><span class="n">put</span><span class="p">(</span><span class="n">pair</span><span class="o">.</span><span class="n">key</span><span class="p">,</span> <span class="n">pair</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-0-71" name="__codelineno-0-71" href="#__codelineno-0-71"></a>
+<a id="__codelineno-0-72" name="__codelineno-0-72" href="#__codelineno-0-72"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">print</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<a id="__codelineno-0-73" name="__codelineno-0-73" href="#__codelineno-0-73"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;ハッシュテーブルを出力&quot;&quot;&quot;</span>
+<a id="__codelineno-0-74" name="__codelineno-0-74" href="#__codelineno-0-74"></a>        <span class="k">for</span> <span class="n">bucket</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">:</span>
+<a id="__codelineno-0-75" name="__codelineno-0-75" href="#__codelineno-0-75"></a>            <span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>
+<a id="__codelineno-0-76" name="__codelineno-0-76" href="#__codelineno-0-76"></a>            <span class="k">for</span> <span class="n">pair</span> <span class="ow">in</span> <span class="n">bucket</span><span class="p">:</span>
+<a id="__codelineno-0-77" name="__codelineno-0-77" href="#__codelineno-0-77"></a>                <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">str</span><span class="p">(</span><span class="n">pair</span><span class="o">.</span><span class="n">key</span><span class="p">)</span> <span class="o">+</span> <span class="s2">&quot; -&gt; &quot;</span> <span class="o">+</span> <span class="n">pair</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-0-78" name="__codelineno-0-78" href="#__codelineno-0-78"></a>            <span class="nb">print</span><span class="p">(</span><span class="n">res</span><span class="p">)</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map_chaining.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* チェイン法ハッシュテーブル */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">HashMapChaining</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">  </span><span class="k">private</span><span class="o">:</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w">                       </span><span class="c1">// キー値ペアの数</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span><span class="w">                   </span><span class="c1">// ハッシュテーブルの容量</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="kt">double</span><span class="w"> </span><span class="n">loadThres</span><span class="p">;</span><span class="w">               </span><span class="c1">// 拡張をトリガーする負荷率の閾値</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">extendRatio</span><span class="p">;</span><span class="w">                </span><span class="c1">// 拡張倍率</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="n">Pair</span><span class="w"> </span><span class="o">*&gt;&gt;</span><span class="w"> </span><span class="n">buckets</span><span class="p">;</span><span class="w"> </span><span class="c1">// バケット配列</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">  </span><span class="k">public</span><span class="o">:</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">    </span><span class="n">HashMapChaining</span><span class="p">()</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">size</span><span class="p">(</span><span class="mi">0</span><span class="p">),</span><span class="w"> </span><span class="n">capacity</span><span class="p">(</span><span class="mi">4</span><span class="p">),</span><span class="w"> </span><span class="n">loadThres</span><span class="p">(</span><span class="mf">2.0</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">3.0</span><span class="p">),</span><span class="w"> </span><span class="n">extendRatio</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">        </span><span class="n">buckets</span><span class="p">.</span><span class="n">resize</span><span class="p">(</span><span class="n">capacity</span><span class="p">);</span>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a>
+<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">    </span><span class="cm">/* デストラクタ */</span>
+<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w">    </span><span class="o">~</span><span class="n">HashMapChaining</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="k">auto</span><span class="w"> </span><span class="o">&amp;</span><span class="n">bucket</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="w">            </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">pair</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="w">                </span><span class="c1">// メモリを解放</span>
+<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="w">                </span><span class="k">delete</span><span class="w"> </span><span class="n">pair</span><span class="p">;</span>
+<a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a>
+<a id="__codelineno-1-26" name="__codelineno-1-26" href="#__codelineno-1-26"></a><span class="w">    </span><span class="cm">/* ハッシュ関数 */</span>
+<a id="__codelineno-1-27" name="__codelineno-1-27" href="#__codelineno-1-27"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-28" name="__codelineno-1-28" href="#__codelineno-1-28"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span>
+<a id="__codelineno-1-29" name="__codelineno-1-29" href="#__codelineno-1-29"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-30" name="__codelineno-1-30" href="#__codelineno-1-30"></a>
+<a id="__codelineno-1-31" name="__codelineno-1-31" href="#__codelineno-1-31"></a><span class="w">    </span><span class="cm">/* 負荷率 */</span>
+<a id="__codelineno-1-32" name="__codelineno-1-32" href="#__codelineno-1-32"></a><span class="w">    </span><span class="kt">double</span><span class="w"> </span><span class="n">loadFactor</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-33" name="__codelineno-1-33" href="#__codelineno-1-33"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">double</span><span class="p">)</span><span class="n">size</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="p">(</span><span class="kt">double</span><span class="p">)</span><span class="n">capacity</span><span class="p">;</span>
+<a id="__codelineno-1-34" name="__codelineno-1-34" href="#__codelineno-1-34"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-35" name="__codelineno-1-35" href="#__codelineno-1-35"></a>
+<a id="__codelineno-1-36" name="__codelineno-1-36" href="#__codelineno-1-36"></a><span class="w">    </span><span class="cm">/* クエリ操作 */</span>
+<a id="__codelineno-1-37" name="__codelineno-1-37" href="#__codelineno-1-37"></a><span class="w">    </span><span class="n">string</span><span class="w"> </span><span class="n">get</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-38" name="__codelineno-1-38" href="#__codelineno-1-38"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-1-39" name="__codelineno-1-39" href="#__codelineno-1-39"></a><span class="w">        </span><span class="c1">// バケットを走査、キーが見つかった場合、対応するvalを返却</span>
+<a id="__codelineno-1-40" name="__codelineno-1-40" href="#__codelineno-1-40"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">pair</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-41" name="__codelineno-1-41" href="#__codelineno-1-41"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-42" name="__codelineno-1-42" href="#__codelineno-1-42"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-1-43" name="__codelineno-1-43" href="#__codelineno-1-43"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-1-44" name="__codelineno-1-44" href="#__codelineno-1-44"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-1-45" name="__codelineno-1-45" href="#__codelineno-1-45"></a><span class="w">        </span><span class="c1">// キーが見つからない場合、空文字列を返却</span>
+<a id="__codelineno-1-46" name="__codelineno-1-46" href="#__codelineno-1-46"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="s">&quot;&quot;</span><span class="p">;</span>
+<a id="__codelineno-1-47" name="__codelineno-1-47" href="#__codelineno-1-47"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-48" name="__codelineno-1-48" href="#__codelineno-1-48"></a>
+<a id="__codelineno-1-49" name="__codelineno-1-49" href="#__codelineno-1-49"></a><span class="w">    </span><span class="cm">/* 追加操作 */</span>
+<a id="__codelineno-1-50" name="__codelineno-1-50" href="#__codelineno-1-50"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">put</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">string</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-51" name="__codelineno-1-51" href="#__codelineno-1-51"></a><span class="w">        </span><span class="c1">// 負荷率が閾値を超えた場合、拡張を実行</span>
+<a id="__codelineno-1-52" name="__codelineno-1-52" href="#__codelineno-1-52"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">loadFactor</span><span class="p">()</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">loadThres</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-53" name="__codelineno-1-53" href="#__codelineno-1-53"></a><span class="w">            </span><span class="n">extend</span><span class="p">();</span>
+<a id="__codelineno-1-54" name="__codelineno-1-54" href="#__codelineno-1-54"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-1-55" name="__codelineno-1-55" href="#__codelineno-1-55"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-1-56" name="__codelineno-1-56" href="#__codelineno-1-56"></a><span class="w">        </span><span class="c1">// バケットを走査、指定キーに遭遇した場合、対応するvalを更新して返却</span>
+<a id="__codelineno-1-57" name="__codelineno-1-57" href="#__codelineno-1-57"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">pair</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-58" name="__codelineno-1-58" href="#__codelineno-1-58"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-59" name="__codelineno-1-59" href="#__codelineno-1-59"></a><span class="w">                </span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-1-60" name="__codelineno-1-60" href="#__codelineno-1-60"></a><span class="w">                </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-1-61" name="__codelineno-1-61" href="#__codelineno-1-61"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-1-62" name="__codelineno-1-62" href="#__codelineno-1-62"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-1-63" name="__codelineno-1-63" href="#__codelineno-1-63"></a><span class="w">        </span><span class="c1">// キーが見つからない場合、キー値ペアを末尾に追加</span>
+<a id="__codelineno-1-64" name="__codelineno-1-64" href="#__codelineno-1-64"></a><span class="w">        </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">].</span><span class="n">push_back</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">Pair</span><span class="p">(</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">));</span>
+<a id="__codelineno-1-65" name="__codelineno-1-65" href="#__codelineno-1-65"></a><span class="w">        </span><span class="n">size</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-1-66" name="__codelineno-1-66" href="#__codelineno-1-66"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-67" name="__codelineno-1-67" href="#__codelineno-1-67"></a>
+<a id="__codelineno-1-68" name="__codelineno-1-68" href="#__codelineno-1-68"></a><span class="w">    </span><span class="cm">/* 削除操作 */</span>
+<a id="__codelineno-1-69" name="__codelineno-1-69" href="#__codelineno-1-69"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-70" name="__codelineno-1-70" href="#__codelineno-1-70"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-1-71" name="__codelineno-1-71" href="#__codelineno-1-71"></a><span class="w">        </span><span class="k">auto</span><span class="w"> </span><span class="o">&amp;</span><span class="n">bucket</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
+<a id="__codelineno-1-72" name="__codelineno-1-72" href="#__codelineno-1-72"></a><span class="w">        </span><span class="c1">// バケットを走査、キー値ペアを削除</span>
+<a id="__codelineno-1-73" name="__codelineno-1-73" href="#__codelineno-1-73"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">bucket</span><span class="p">.</span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-74" name="__codelineno-1-74" href="#__codelineno-1-74"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">bucket</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">-&gt;</span><span class="n">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-75" name="__codelineno-1-75" href="#__codelineno-1-75"></a><span class="w">                </span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">bucket</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-1-76" name="__codelineno-1-76" href="#__codelineno-1-76"></a><span class="w">                </span><span class="n">bucket</span><span class="p">.</span><span class="n">erase</span><span class="p">(</span><span class="n">bucket</span><span class="p">.</span><span class="n">begin</span><span class="p">()</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">i</span><span class="p">);</span><span class="w"> </span><span class="c1">// キー値ペアを削除</span>
+<a id="__codelineno-1-77" name="__codelineno-1-77" href="#__codelineno-1-77"></a><span class="w">                </span><span class="k">delete</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span><span class="w">                       </span><span class="c1">// メモリを解放</span>
+<a id="__codelineno-1-78" name="__codelineno-1-78" href="#__codelineno-1-78"></a><span class="w">                </span><span class="n">size</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-1-79" name="__codelineno-1-79" href="#__codelineno-1-79"></a><span class="w">                </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-1-80" name="__codelineno-1-80" href="#__codelineno-1-80"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-1-81" name="__codelineno-1-81" href="#__codelineno-1-81"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-1-82" name="__codelineno-1-82" href="#__codelineno-1-82"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-83" name="__codelineno-1-83" href="#__codelineno-1-83"></a>
+<a id="__codelineno-1-84" name="__codelineno-1-84" href="#__codelineno-1-84"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを拡張 */</span>
+<a id="__codelineno-1-85" name="__codelineno-1-85" href="#__codelineno-1-85"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">extend</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-86" name="__codelineno-1-86" href="#__codelineno-1-86"></a><span class="w">        </span><span class="c1">// 元のハッシュテーブルを一時保存</span>
+<a id="__codelineno-1-87" name="__codelineno-1-87" href="#__codelineno-1-87"></a><span class="w">        </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="n">Pair</span><span class="w"> </span><span class="o">*&gt;&gt;</span><span class="w"> </span><span class="n">bucketsTmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="p">;</span>
+<a id="__codelineno-1-88" name="__codelineno-1-88" href="#__codelineno-1-88"></a><span class="w">        </span><span class="c1">// 拡張された新しいハッシュテーブルを初期化</span>
+<a id="__codelineno-1-89" name="__codelineno-1-89" href="#__codelineno-1-89"></a><span class="w">        </span><span class="n">capacity</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="n">extendRatio</span><span class="p">;</span>
+<a id="__codelineno-1-90" name="__codelineno-1-90" href="#__codelineno-1-90"></a><span class="w">        </span><span class="n">buckets</span><span class="p">.</span><span class="n">clear</span><span class="p">();</span>
+<a id="__codelineno-1-91" name="__codelineno-1-91" href="#__codelineno-1-91"></a><span class="w">        </span><span class="n">buckets</span><span class="p">.</span><span class="n">resize</span><span class="p">(</span><span class="n">capacity</span><span class="p">);</span>
+<a id="__codelineno-1-92" name="__codelineno-1-92" href="#__codelineno-1-92"></a><span class="w">        </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-1-93" name="__codelineno-1-93" href="#__codelineno-1-93"></a><span class="w">        </span><span class="c1">// 元のハッシュテーブルから新しいハッシュテーブルにキー値ペアを移動</span>
+<a id="__codelineno-1-94" name="__codelineno-1-94" href="#__codelineno-1-94"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="k">auto</span><span class="w"> </span><span class="o">&amp;</span><span class="n">bucket</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">bucketsTmp</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-95" name="__codelineno-1-95" href="#__codelineno-1-95"></a><span class="w">            </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">pair</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-96" name="__codelineno-1-96" href="#__codelineno-1-96"></a><span class="w">                </span><span class="n">put</span><span class="p">(</span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-1-97" name="__codelineno-1-97" href="#__codelineno-1-97"></a><span class="w">                </span><span class="c1">// メモリを解放</span>
+<a id="__codelineno-1-98" name="__codelineno-1-98" href="#__codelineno-1-98"></a><span class="w">                </span><span class="k">delete</span><span class="w"> </span><span class="n">pair</span><span class="p">;</span>
+<a id="__codelineno-1-99" name="__codelineno-1-99" href="#__codelineno-1-99"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-1-100" name="__codelineno-1-100" href="#__codelineno-1-100"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-1-101" name="__codelineno-1-101" href="#__codelineno-1-101"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-102" name="__codelineno-1-102" href="#__codelineno-1-102"></a>
+<a id="__codelineno-1-103" name="__codelineno-1-103" href="#__codelineno-1-103"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを印刷 */</span>
+<a id="__codelineno-1-104" name="__codelineno-1-104" href="#__codelineno-1-104"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-105" name="__codelineno-1-105" href="#__codelineno-1-105"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="k">auto</span><span class="w"> </span><span class="o">&amp;</span><span class="n">bucket</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-106" name="__codelineno-1-106" href="#__codelineno-1-106"></a><span class="w">            </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;[&quot;</span><span class="p">;</span>
+<a id="__codelineno-1-107" name="__codelineno-1-107" href="#__codelineno-1-107"></a><span class="w">            </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">pair</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-108" name="__codelineno-1-108" href="#__codelineno-1-108"></a><span class="w">                </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">key</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot; -&gt; &quot;</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;, &quot;</span><span class="p">;</span>
+<a id="__codelineno-1-109" name="__codelineno-1-109" href="#__codelineno-1-109"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-1-110" name="__codelineno-1-110" href="#__codelineno-1-110"></a><span class="w">            </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;]</span><span class="se">\n</span><span class="s">&quot;</span><span class="p">;</span>
+<a id="__codelineno-1-111" name="__codelineno-1-111" href="#__codelineno-1-111"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-1-112" name="__codelineno-1-112" href="#__codelineno-1-112"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-113" name="__codelineno-1-113" href="#__codelineno-1-113"></a><span class="p">};</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map_chaining.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* チェイン法ハッシュテーブル */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kd">class</span> <span class="nc">HashMapChaining</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="c1">// キー値ペアの数</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span><span class="w"> </span><span class="c1">// ハッシュテーブルの容量</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="kt">double</span><span class="w"> </span><span class="n">loadThres</span><span class="p">;</span><span class="w"> </span><span class="c1">// 拡張をトリガーする負荷率の閾値</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">extendRatio</span><span class="p">;</span><span class="w"> </span><span class="c1">// 拡張倍率</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">buckets</span><span class="p">;</span><span class="w"> </span><span class="c1">// バケット配列</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="nf">HashMapChaining</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">        </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">        </span><span class="n">capacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">4</span><span class="p">;</span>
+<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">        </span><span class="n">loadThres</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2.0</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">3.0</span><span class="p">;</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">        </span><span class="n">extendRatio</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">        </span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">(</span><span class="n">capacity</span><span class="p">);</span>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w">            </span><span class="n">buckets</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">());</span>
+<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a>
+<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="w">    </span><span class="cm">/* ハッシュ関数 */</span>
+<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="nf">hashFunc</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span>
+<a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a>
+<a id="__codelineno-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></a><span class="w">    </span><span class="cm">/* 負荷率 */</span>
+<a id="__codelineno-2-27" name="__codelineno-2-27" href="#__codelineno-2-27"></a><span class="w">    </span><span class="kt">double</span><span class="w"> </span><span class="nf">loadFactor</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-28" name="__codelineno-2-28" href="#__codelineno-2-28"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">double</span><span class="p">)</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span>
+<a id="__codelineno-2-29" name="__codelineno-2-29" href="#__codelineno-2-29"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-30" name="__codelineno-2-30" href="#__codelineno-2-30"></a>
+<a id="__codelineno-2-31" name="__codelineno-2-31" href="#__codelineno-2-31"></a><span class="w">    </span><span class="cm">/* クエリ操作 */</span>
+<a id="__codelineno-2-32" name="__codelineno-2-32" href="#__codelineno-2-32"></a><span class="w">    </span><span class="n">String</span><span class="w"> </span><span class="nf">get</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-33" name="__codelineno-2-33" href="#__codelineno-2-33"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-2-34" name="__codelineno-2-34" href="#__codelineno-2-34"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;</span><span class="w"> </span><span class="n">bucket</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">index</span><span class="p">);</span>
+<a id="__codelineno-2-35" name="__codelineno-2-35" href="#__codelineno-2-35"></a><span class="w">        </span><span class="c1">// バケットを走査、キーが見つかった場合対応するvalを返す</span>
+<a id="__codelineno-2-36" name="__codelineno-2-36" href="#__codelineno-2-36"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-37" name="__codelineno-2-37" href="#__codelineno-2-37"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="na">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-38" name="__codelineno-2-38" href="#__codelineno-2-38"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="na">val</span><span class="p">;</span>
+<a id="__codelineno-2-39" name="__codelineno-2-39" href="#__codelineno-2-39"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-2-40" name="__codelineno-2-40" href="#__codelineno-2-40"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-2-41" name="__codelineno-2-41" href="#__codelineno-2-41"></a><span class="w">        </span><span class="c1">// キーが見つからない場合、nullを返す</span>
+<a id="__codelineno-2-42" name="__codelineno-2-42" href="#__codelineno-2-42"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-2-43" name="__codelineno-2-43" href="#__codelineno-2-43"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-44" name="__codelineno-2-44" href="#__codelineno-2-44"></a>
+<a id="__codelineno-2-45" name="__codelineno-2-45" href="#__codelineno-2-45"></a><span class="w">    </span><span class="cm">/* 追加操作 */</span>
+<a id="__codelineno-2-46" name="__codelineno-2-46" href="#__codelineno-2-46"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="nf">put</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">String</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-47" name="__codelineno-2-47" href="#__codelineno-2-47"></a><span class="w">        </span><span class="c1">// 負荷率が閾値を超えた場合、拡張を実行</span>
+<a id="__codelineno-2-48" name="__codelineno-2-48" href="#__codelineno-2-48"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">loadFactor</span><span class="p">()</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">loadThres</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-49" name="__codelineno-2-49" href="#__codelineno-2-49"></a><span class="w">            </span><span class="n">extend</span><span class="p">();</span>
+<a id="__codelineno-2-50" name="__codelineno-2-50" href="#__codelineno-2-50"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-2-51" name="__codelineno-2-51" href="#__codelineno-2-51"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-2-52" name="__codelineno-2-52" href="#__codelineno-2-52"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;</span><span class="w"> </span><span class="n">bucket</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">index</span><span class="p">);</span>
+<a id="__codelineno-2-53" name="__codelineno-2-53" href="#__codelineno-2-53"></a><span class="w">        </span><span class="c1">// バケットを走査、指定したキーに遭遇した場合、対応するvalを更新して戻る</span>
+<a id="__codelineno-2-54" name="__codelineno-2-54" href="#__codelineno-2-54"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-55" name="__codelineno-2-55" href="#__codelineno-2-55"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="na">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-56" name="__codelineno-2-56" href="#__codelineno-2-56"></a><span class="w">                </span><span class="n">pair</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-2-57" name="__codelineno-2-57" href="#__codelineno-2-57"></a><span class="w">                </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-2-58" name="__codelineno-2-58" href="#__codelineno-2-58"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-2-59" name="__codelineno-2-59" href="#__codelineno-2-59"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-2-60" name="__codelineno-2-60" href="#__codelineno-2-60"></a><span class="w">        </span><span class="c1">// キーが見つからない場合、キー値ペアを末尾に追加</span>
+<a id="__codelineno-2-61" name="__codelineno-2-61" href="#__codelineno-2-61"></a><span class="w">        </span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Pair</span><span class="p">(</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-2-62" name="__codelineno-2-62" href="#__codelineno-2-62"></a><span class="w">        </span><span class="n">bucket</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">pair</span><span class="p">);</span>
+<a id="__codelineno-2-63" name="__codelineno-2-63" href="#__codelineno-2-63"></a><span class="w">        </span><span class="n">size</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-2-64" name="__codelineno-2-64" href="#__codelineno-2-64"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-65" name="__codelineno-2-65" href="#__codelineno-2-65"></a>
+<a id="__codelineno-2-66" name="__codelineno-2-66" href="#__codelineno-2-66"></a><span class="w">    </span><span class="cm">/* 削除操作 */</span>
+<a id="__codelineno-2-67" name="__codelineno-2-67" href="#__codelineno-2-67"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-68" name="__codelineno-2-68" href="#__codelineno-2-68"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-2-69" name="__codelineno-2-69" href="#__codelineno-2-69"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;</span><span class="w"> </span><span class="n">bucket</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">index</span><span class="p">);</span>
+<a id="__codelineno-2-70" name="__codelineno-2-70" href="#__codelineno-2-70"></a><span class="w">        </span><span class="c1">// バケットを走査、その中からキー値ペアを削除</span>
+<a id="__codelineno-2-71" name="__codelineno-2-71" href="#__codelineno-2-71"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-72" name="__codelineno-2-72" href="#__codelineno-2-72"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="na">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-73" name="__codelineno-2-73" href="#__codelineno-2-73"></a><span class="w">                </span><span class="n">bucket</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">pair</span><span class="p">);</span>
+<a id="__codelineno-2-74" name="__codelineno-2-74" href="#__codelineno-2-74"></a><span class="w">                </span><span class="n">size</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-2-75" name="__codelineno-2-75" href="#__codelineno-2-75"></a><span class="w">                </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-2-76" name="__codelineno-2-76" href="#__codelineno-2-76"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-2-77" name="__codelineno-2-77" href="#__codelineno-2-77"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-2-78" name="__codelineno-2-78" href="#__codelineno-2-78"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-79" name="__codelineno-2-79" href="#__codelineno-2-79"></a>
+<a id="__codelineno-2-80" name="__codelineno-2-80" href="#__codelineno-2-80"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを拡張 */</span>
+<a id="__codelineno-2-81" name="__codelineno-2-81" href="#__codelineno-2-81"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="nf">extend</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-82" name="__codelineno-2-82" href="#__codelineno-2-82"></a><span class="w">        </span><span class="c1">// 元のハッシュテーブルを一時的に保存</span>
+<a id="__codelineno-2-83" name="__codelineno-2-83" href="#__codelineno-2-83"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">bucketsTmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="p">;</span>
+<a id="__codelineno-2-84" name="__codelineno-2-84" href="#__codelineno-2-84"></a><span class="w">        </span><span class="c1">// 拡張された新しいハッシュテーブルを初期化</span>
+<a id="__codelineno-2-85" name="__codelineno-2-85" href="#__codelineno-2-85"></a><span class="w">        </span><span class="n">capacity</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="n">extendRatio</span><span class="p">;</span>
+<a id="__codelineno-2-86" name="__codelineno-2-86" href="#__codelineno-2-86"></a><span class="w">        </span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">(</span><span class="n">capacity</span><span class="p">);</span>
+<a id="__codelineno-2-87" name="__codelineno-2-87" href="#__codelineno-2-87"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-88" name="__codelineno-2-88" href="#__codelineno-2-88"></a><span class="w">            </span><span class="n">buckets</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">());</span>
+<a id="__codelineno-2-89" name="__codelineno-2-89" href="#__codelineno-2-89"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-2-90" name="__codelineno-2-90" href="#__codelineno-2-90"></a><span class="w">        </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-2-91" name="__codelineno-2-91" href="#__codelineno-2-91"></a><span class="w">        </span><span class="c1">// 元のハッシュテーブルから新しいハッシュテーブルにキー値ペアを移動</span>
+<a id="__codelineno-2-92" name="__codelineno-2-92" href="#__codelineno-2-92"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;</span><span class="w"> </span><span class="n">bucket</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">bucketsTmp</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-93" name="__codelineno-2-93" href="#__codelineno-2-93"></a><span class="w">            </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-94" name="__codelineno-2-94" href="#__codelineno-2-94"></a><span class="w">                </span><span class="n">put</span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="na">key</span><span class="p">,</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="na">val</span><span class="p">);</span>
+<a id="__codelineno-2-95" name="__codelineno-2-95" href="#__codelineno-2-95"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-2-96" name="__codelineno-2-96" href="#__codelineno-2-96"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-2-97" name="__codelineno-2-97" href="#__codelineno-2-97"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-98" name="__codelineno-2-98" href="#__codelineno-2-98"></a>
+<a id="__codelineno-2-99" name="__codelineno-2-99" href="#__codelineno-2-99"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを印刷 */</span>
+<a id="__codelineno-2-100" name="__codelineno-2-100" href="#__codelineno-2-100"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="nf">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-101" name="__codelineno-2-101" href="#__codelineno-2-101"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;</span><span class="w"> </span><span class="n">bucket</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-102" name="__codelineno-2-102" href="#__codelineno-2-102"></a><span class="w">            </span><span class="n">List</span><span class="o">&lt;</span><span class="n">String</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-2-103" name="__codelineno-2-103" href="#__codelineno-2-103"></a><span class="w">            </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-104" name="__codelineno-2-104" href="#__codelineno-2-104"></a><span class="w">                </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="na">key</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s">&quot; -&gt; &quot;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="na">val</span><span class="p">);</span>
+<a id="__codelineno-2-105" name="__codelineno-2-105" href="#__codelineno-2-105"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-2-106" name="__codelineno-2-106" href="#__codelineno-2-106"></a><span class="w">            </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-2-107" name="__codelineno-2-107" href="#__codelineno-2-107"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-2-108" name="__codelineno-2-108" href="#__codelineno-2-108"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-109" name="__codelineno-2-109" href="#__codelineno-2-109"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map_chaining.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">HashMapChaining</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map_chaining.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">hashMapChaining</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map_chaining.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">HashMapChaining</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map_chaining.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">HashMapChaining</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map_chaining.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">HashMapChaining</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map_chaining.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">HashMapChaining</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map_chaining.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">HashMapChaining</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map_chaining.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">Node</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">HashMapChaining</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map_chaining.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">HashMapChaining</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map_chaining.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">HashMapChaining</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map_chaining.zig</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">HashMapChaining</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>連結リストが非常に長い場合、クエリ効率<span class="arithmatex">\(O(n)\)</span>が悪いことは注目に値します。<strong>この場合、リストを「AVL木」または「赤黒木」に変換して</strong>、クエリ操作の時間計算量を<span class="arithmatex">\(O(\log n)\)</span>に最適化できます。</p>
+<h2 id="622">6.2.2 &nbsp; オープンアドレス法<a class="headerlink" href="#622" title="Permanent link">&para;</a></h2>
+<p><u>オープンアドレス法</u>は追加のデータ構造を導入せず、代わりに「複数回プローブ」を通してハッシュ衝突を処理します。プローブ方法には主に線形プローブ、二次プローブ、二重ハッシュがあります。</p>
+<p>線形プローブを例にして、オープンアドレス法ハッシュ表のメカニズムを紹介しましょう。</p>
+<h3 id="1">1. &nbsp; 線形プローブ<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<p>線形プローブは固定ステップの線形検索をプローブに使用し、通常のハッシュ表とは異なります。</p>
+<ul>
+<li><strong>要素の挿入</strong>: ハッシュ関数を使用してバケットインデックスを計算します。バケットに既に要素が含まれている場合、衝突位置から線形に前方に走査し（通常ステップサイズは<span class="arithmatex">\(1\)</span>）、空のバケットが見つかるまで進み、要素を挿入します。</li>
+<li><strong>要素の検索</strong>: ハッシュ衝突に遭遇した場合、同じステップサイズを使用して線形に前方に走査し、対応する要素が見つかったら<code>value</code>を返します。空のバケットに遭遇した場合、ターゲット要素がハッシュ表にないことを意味するため、<code>None</code>を返します。</li>
+</ul>
+<p>下図はオープンアドレス法（線形プローブ）ハッシュ表におけるキー値ペアの分布を示しています。このハッシュ関数によると、下二桁が同じキーは同じバケットにマッピングされます。線形プローブを通して、それらはそのバケットとその下のバケットに順次格納されます。</p>
+<p><a class="glightbox" href="../hash_collision.assets/hash_table_linear_probing.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="オープンアドレス法（線形プローブ）ハッシュ表におけるキー値ペアの分布" class="animation-figure" src="../hash_collision.assets/hash_table_linear_probing.png" /></a></p>
+<p align="center"> 図 6-6 &nbsp; オープンアドレス法（線形プローブ）ハッシュ表におけるキー値ペアの分布 </p>
+
+<p>しかし、<strong>線形プローブは「クラスタリング」を作りやすい傾向があります</strong>。具体的には、配列内の連続的に占有された位置が長いほど、これらの連続した位置でハッシュ衝突が発生する確率が高くなり、その位置でのクラスタリングの成長をさらに促進し、悪循環を形成し、最終的に挿入、削除、クエリ、更新操作の効率低下につながります。</p>
+<p>**オープンアドレス法ハッシュ表では要素を直接削除できない**ことに注意することが重要です。要素を削除すると、配列に空のバケット<code>None</code>が作成されます。要素を検索する際、線形プローブがこの空のバケットに遭遇すると戻ってしまい、このバケットの下の要素にアクセスできなくなります。プログラムはこれらの要素が存在しないと誤って仮定する可能性があります。下図に示すとおりです。</p>
+<p><a class="glightbox" href="../hash_collision.assets/hash_table_open_addressing_deletion.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="オープンアドレス法での削除によるクエリ問題" class="animation-figure" src="../hash_collision.assets/hash_table_open_addressing_deletion.png" /></a></p>
+<p align="center"> 図 6-7 &nbsp; オープンアドレス法での削除によるクエリ問題 </p>
+
+<p>この問題を解決するために、<u>遅延削除</u>メカニズムを採用できます：ハッシュ表から要素を直接削除する代わりに、<strong>定数<code>TOMBSTONE</code>を使用してバケットをマークします</strong>。このメカニズムでは、<code>None</code>と<code>TOMBSTONE</code>の両方が空のバケットを表し、キー値ペアを保持できます。ただし、線形プローブが<code>TOMBSTONE</code>に遭遇した場合、その下にまだキー値ペアがある可能性があるため、走査を続ける必要があります。</p>
+<p>しかし、<strong>遅延削除はハッシュ表の性能劣化を加速する可能性があります</strong>。削除操作のたびに削除マークが生成され、<code>TOMBSTONE</code>が増加すると、線形プローブがターゲット要素を見つけるために複数の<code>TOMBSTONE</code>をスキップする必要がある可能性があるため、検索時間も増加します。</p>
+<p>これに対処するために、線形プローブ中に最初に遭遇した<code>TOMBSTONE</code>のインデックスを記録し、検索されたターゲット要素とその<code>TOMBSTONE</code>の位置を交換することを検討してください。これを行う利点は、要素がクエリまたは追加されるたびに、要素がその理想的な位置（プローブの開始点）により近いバケットに移動され、クエリ効率が最適化されることです。</p>
+<p>以下のコードは、遅延削除を使用したオープンアドレス法（線形プローブ）ハッシュ表を実装しています。ハッシュ表の空間をより有効に活用するために、ハッシュ表を「循環配列」として扱います。配列の終わりを超えると、最初に戻って走査を続けます。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:14"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><input id="__tabbed_2_14" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label><label for="__tabbed_2_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map_open_addressing.py</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">HashMapOpenAddressing</span><span class="p">:</span>
+<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;オープンアドレス法ハッシュテーブル&quot;&quot;&quot;</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;コンストラクタ&quot;&quot;&quot;</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">size</span> <span class="o">=</span> <span class="mi">0</span>  <span class="c1"># キー値ペアの数</span>
+<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span> <span class="o">=</span> <span class="mi">4</span>  <span class="c1"># ハッシュテーブルの容量</span>
+<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">load_thres</span> <span class="o">=</span> <span class="mf">2.0</span> <span class="o">/</span> <span class="mf">3.0</span>  <span class="c1"># 拡張をトリガーする負荷率の閾値</span>
+<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">extend_ratio</span> <span class="o">=</span> <span class="mi">2</span>  <span class="c1"># 拡張の倍数</span>
+<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">Pair</span> <span class="o">|</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="kc">None</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span>  <span class="c1"># バケット配列</span>
+<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">TOMBSTONE</span> <span class="o">=</span> <span class="n">Pair</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="s2">&quot;-1&quot;</span><span class="p">)</span>  <span class="c1"># 削除マーク</span>
+<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a>
+<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">hash_func</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;ハッシュ関数&quot;&quot;&quot;</span>
+<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a>        <span class="k">return</span> <span class="n">key</span> <span class="o">%</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span>
+<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a>
+<a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">load_factor</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">float</span><span class="p">:</span>
+<a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;負荷率&quot;&quot;&quot;</span>
+<a id="__codelineno-14-19" name="__codelineno-14-19" href="#__codelineno-14-19"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span> <span class="o">/</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span>
+<a id="__codelineno-14-20" name="__codelineno-14-20" href="#__codelineno-14-20"></a>
+<a id="__codelineno-14-21" name="__codelineno-14-21" href="#__codelineno-14-21"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">find_bucket</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-14-22" name="__codelineno-14-22" href="#__codelineno-14-22"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;key に対応するバケットインデックスを検索&quot;&quot;&quot;</span>
+<a id="__codelineno-14-23" name="__codelineno-14-23" href="#__codelineno-14-23"></a>        <span class="n">index</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">hash_func</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-14-24" name="__codelineno-14-24" href="#__codelineno-14-24"></a>        <span class="n">first_tombstone</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-14-25" name="__codelineno-14-25" href="#__codelineno-14-25"></a>        <span class="c1"># 線形探査、空のバケットに遭遇したらブレーク</span>
+<a id="__codelineno-14-26" name="__codelineno-14-26" href="#__codelineno-14-26"></a>        <span class="k">while</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-14-27" name="__codelineno-14-27" href="#__codelineno-14-27"></a>            <span class="c1"># キーに遭遇した場合、対応するバケットインデックスを返す</span>
+<a id="__codelineno-14-28" name="__codelineno-14-28" href="#__codelineno-14-28"></a>            <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="o">.</span><span class="n">key</span> <span class="o">==</span> <span class="n">key</span><span class="p">:</span>
+<a id="__codelineno-14-29" name="__codelineno-14-29" href="#__codelineno-14-29"></a>                <span class="c1"># 削除マークが以前に遭遇していた場合、キー値ペアをそのインデックスに移動</span>
+<a id="__codelineno-14-30" name="__codelineno-14-30" href="#__codelineno-14-30"></a>                <span class="k">if</span> <span class="n">first_tombstone</span> <span class="o">!=</span> <span class="o">-</span><span class="mi">1</span><span class="p">:</span>
+<a id="__codelineno-14-31" name="__codelineno-14-31" href="#__codelineno-14-31"></a>                    <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">first_tombstone</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span>
+<a id="__codelineno-14-32" name="__codelineno-14-32" href="#__codelineno-14-32"></a>                    <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">TOMBSTONE</span>
+<a id="__codelineno-14-33" name="__codelineno-14-33" href="#__codelineno-14-33"></a>                    <span class="k">return</span> <span class="n">first_tombstone</span>  <span class="c1"># 移動されたバケットインデックスを返す</span>
+<a id="__codelineno-14-34" name="__codelineno-14-34" href="#__codelineno-14-34"></a>                <span class="k">return</span> <span class="n">index</span>  <span class="c1"># バケットインデックスを返す</span>
+<a id="__codelineno-14-35" name="__codelineno-14-35" href="#__codelineno-14-35"></a>            <span class="c1"># 最初に遭遇した削除マークを記録</span>
+<a id="__codelineno-14-36" name="__codelineno-14-36" href="#__codelineno-14-36"></a>            <span class="k">if</span> <span class="n">first_tombstone</span> <span class="o">==</span> <span class="o">-</span><span class="mi">1</span> <span class="ow">and</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="ow">is</span> <span class="bp">self</span><span class="o">.</span><span class="n">TOMBSTONE</span><span class="p">:</span>
+<a id="__codelineno-14-37" name="__codelineno-14-37" href="#__codelineno-14-37"></a>                <span class="n">first_tombstone</span> <span class="o">=</span> <span class="n">index</span>
+<a id="__codelineno-14-38" name="__codelineno-14-38" href="#__codelineno-14-38"></a>            <span class="c1"># バケットインデックスを計算、末尾を超えた場合は先頭に戻る</span>
+<a id="__codelineno-14-39" name="__codelineno-14-39" href="#__codelineno-14-39"></a>            <span class="n">index</span> <span class="o">=</span> <span class="p">(</span><span class="n">index</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">%</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span>
+<a id="__codelineno-14-40" name="__codelineno-14-40" href="#__codelineno-14-40"></a>        <span class="c1"># キーが存在しない場合、挿入ポイントのインデックスを返す</span>
+<a id="__codelineno-14-41" name="__codelineno-14-41" href="#__codelineno-14-41"></a>        <span class="k">return</span> <span class="n">index</span> <span class="k">if</span> <span class="n">first_tombstone</span> <span class="o">==</span> <span class="o">-</span><span class="mi">1</span> <span class="k">else</span> <span class="n">first_tombstone</span>
+<a id="__codelineno-14-42" name="__codelineno-14-42" href="#__codelineno-14-42"></a>
+<a id="__codelineno-14-43" name="__codelineno-14-43" href="#__codelineno-14-43"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">get</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">str</span><span class="p">:</span>
+<a id="__codelineno-14-44" name="__codelineno-14-44" href="#__codelineno-14-44"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;照会操作&quot;&quot;&quot;</span>
+<a id="__codelineno-14-45" name="__codelineno-14-45" href="#__codelineno-14-45"></a>        <span class="c1"># key に対応するバケットインデックスを検索</span>
+<a id="__codelineno-14-46" name="__codelineno-14-46" href="#__codelineno-14-46"></a>        <span class="n">index</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">find_bucket</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-14-47" name="__codelineno-14-47" href="#__codelineno-14-47"></a>        <span class="c1"># キー値ペアが見つかれば、対応する val を返す</span>
+<a id="__codelineno-14-48" name="__codelineno-14-48" href="#__codelineno-14-48"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">[</span><span class="kc">None</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">TOMBSTONE</span><span class="p">]:</span>
+<a id="__codelineno-14-49" name="__codelineno-14-49" href="#__codelineno-14-49"></a>            <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="o">.</span><span class="n">val</span>
+<a id="__codelineno-14-50" name="__codelineno-14-50" href="#__codelineno-14-50"></a>        <span class="c1"># キー値ペアが存在しない場合、None を返す</span>
+<a id="__codelineno-14-51" name="__codelineno-14-51" href="#__codelineno-14-51"></a>        <span class="k">return</span> <span class="kc">None</span>
+<a id="__codelineno-14-52" name="__codelineno-14-52" href="#__codelineno-14-52"></a>
+<a id="__codelineno-14-53" name="__codelineno-14-53" href="#__codelineno-14-53"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">put</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">str</span><span class="p">):</span>
+<a id="__codelineno-14-54" name="__codelineno-14-54" href="#__codelineno-14-54"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;追加操作&quot;&quot;&quot;</span>
+<a id="__codelineno-14-55" name="__codelineno-14-55" href="#__codelineno-14-55"></a>        <span class="c1"># 負荷率が閾値を超えた場合、拡張を実行</span>
+<a id="__codelineno-14-56" name="__codelineno-14-56" href="#__codelineno-14-56"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">load_factor</span><span class="p">()</span> <span class="o">&gt;</span> <span class="bp">self</span><span class="o">.</span><span class="n">load_thres</span><span class="p">:</span>
+<a id="__codelineno-14-57" name="__codelineno-14-57" href="#__codelineno-14-57"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">extend</span><span class="p">()</span>
+<a id="__codelineno-14-58" name="__codelineno-14-58" href="#__codelineno-14-58"></a>        <span class="c1"># key に対応するバケットインデックスを検索</span>
+<a id="__codelineno-14-59" name="__codelineno-14-59" href="#__codelineno-14-59"></a>        <span class="n">index</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">find_bucket</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-14-60" name="__codelineno-14-60" href="#__codelineno-14-60"></a>        <span class="c1"># キー値ペアが見つかれば、val を上書きして返す</span>
+<a id="__codelineno-14-61" name="__codelineno-14-61" href="#__codelineno-14-61"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">[</span><span class="kc">None</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">TOMBSTONE</span><span class="p">]:</span>
+<a id="__codelineno-14-62" name="__codelineno-14-62" href="#__codelineno-14-62"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="o">.</span><span class="n">val</span> <span class="o">=</span> <span class="n">val</span>
+<a id="__codelineno-14-63" name="__codelineno-14-63" href="#__codelineno-14-63"></a>            <span class="k">return</span>
+<a id="__codelineno-14-64" name="__codelineno-14-64" href="#__codelineno-14-64"></a>        <span class="c1"># キー値ペアが存在しない場合、キー値ペアを追加</span>
+<a id="__codelineno-14-65" name="__codelineno-14-65" href="#__codelineno-14-65"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">=</span> <span class="n">Pair</span><span class="p">(</span><span class="n">key</span><span class="p">,</span> <span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-14-66" name="__codelineno-14-66" href="#__codelineno-14-66"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">size</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-14-67" name="__codelineno-14-67" href="#__codelineno-14-67"></a>
+<a id="__codelineno-14-68" name="__codelineno-14-68" href="#__codelineno-14-68"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-14-69" name="__codelineno-14-69" href="#__codelineno-14-69"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;削除操作&quot;&quot;&quot;</span>
+<a id="__codelineno-14-70" name="__codelineno-14-70" href="#__codelineno-14-70"></a>        <span class="c1"># key に対応するバケットインデックスを検索</span>
+<a id="__codelineno-14-71" name="__codelineno-14-71" href="#__codelineno-14-71"></a>        <span class="n">index</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">find_bucket</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-14-72" name="__codelineno-14-72" href="#__codelineno-14-72"></a>        <span class="c1"># キー値ペアが見つかれば、削除マークで覆う</span>
+<a id="__codelineno-14-73" name="__codelineno-14-73" href="#__codelineno-14-73"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">[</span><span class="kc">None</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">TOMBSTONE</span><span class="p">]:</span>
+<a id="__codelineno-14-74" name="__codelineno-14-74" href="#__codelineno-14-74"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">TOMBSTONE</span>
+<a id="__codelineno-14-75" name="__codelineno-14-75" href="#__codelineno-14-75"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">size</span> <span class="o">-=</span> <span class="mi">1</span>
+<a id="__codelineno-14-76" name="__codelineno-14-76" href="#__codelineno-14-76"></a>
+<a id="__codelineno-14-77" name="__codelineno-14-77" href="#__codelineno-14-77"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">extend</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<a id="__codelineno-14-78" name="__codelineno-14-78" href="#__codelineno-14-78"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;ハッシュテーブルを拡張&quot;&quot;&quot;</span>
+<a id="__codelineno-14-79" name="__codelineno-14-79" href="#__codelineno-14-79"></a>        <span class="c1"># 元のハッシュテーブルを一時的に保存</span>
+<a id="__codelineno-14-80" name="__codelineno-14-80" href="#__codelineno-14-80"></a>        <span class="n">buckets_tmp</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span>
+<a id="__codelineno-14-81" name="__codelineno-14-81" href="#__codelineno-14-81"></a>        <span class="c1"># 拡張された新しいハッシュテーブルを初期化</span>
+<a id="__codelineno-14-82" name="__codelineno-14-82" href="#__codelineno-14-82"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span> <span class="o">*=</span> <span class="bp">self</span><span class="o">.</span><span class="n">extend_ratio</span>
+<a id="__codelineno-14-83" name="__codelineno-14-83" href="#__codelineno-14-83"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span> <span class="o">=</span> <span class="p">[</span><span class="kc">None</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span>
+<a id="__codelineno-14-84" name="__codelineno-14-84" href="#__codelineno-14-84"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">size</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-14-85" name="__codelineno-14-85" href="#__codelineno-14-85"></a>        <span class="c1"># 元のハッシュテーブルから新しいハッシュテーブルにキー値ペアを移動</span>
+<a id="__codelineno-14-86" name="__codelineno-14-86" href="#__codelineno-14-86"></a>        <span class="k">for</span> <span class="n">pair</span> <span class="ow">in</span> <span class="n">buckets_tmp</span><span class="p">:</span>
+<a id="__codelineno-14-87" name="__codelineno-14-87" href="#__codelineno-14-87"></a>            <span class="k">if</span> <span class="n">pair</span> <span class="ow">not</span> <span class="ow">in</span> <span class="p">[</span><span class="kc">None</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">TOMBSTONE</span><span class="p">]:</span>
+<a id="__codelineno-14-88" name="__codelineno-14-88" href="#__codelineno-14-88"></a>                <span class="bp">self</span><span class="o">.</span><span class="n">put</span><span class="p">(</span><span class="n">pair</span><span class="o">.</span><span class="n">key</span><span class="p">,</span> <span class="n">pair</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-14-89" name="__codelineno-14-89" href="#__codelineno-14-89"></a>
+<a id="__codelineno-14-90" name="__codelineno-14-90" href="#__codelineno-14-90"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">print</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<a id="__codelineno-14-91" name="__codelineno-14-91" href="#__codelineno-14-91"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;ハッシュテーブルを出力&quot;&quot;&quot;</span>
+<a id="__codelineno-14-92" name="__codelineno-14-92" href="#__codelineno-14-92"></a>        <span class="k">for</span> <span class="n">pair</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">:</span>
+<a id="__codelineno-14-93" name="__codelineno-14-93" href="#__codelineno-14-93"></a>            <span class="k">if</span> <span class="n">pair</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-14-94" name="__codelineno-14-94" href="#__codelineno-14-94"></a>                <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;None&quot;</span><span class="p">)</span>
+<a id="__codelineno-14-95" name="__codelineno-14-95" href="#__codelineno-14-95"></a>            <span class="k">elif</span> <span class="n">pair</span> <span class="ow">is</span> <span class="bp">self</span><span class="o">.</span><span class="n">TOMBSTONE</span><span class="p">:</span>
+<a id="__codelineno-14-96" name="__codelineno-14-96" href="#__codelineno-14-96"></a>                <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;TOMBSTONE&quot;</span><span class="p">)</span>
+<a id="__codelineno-14-97" name="__codelineno-14-97" href="#__codelineno-14-97"></a>            <span class="k">else</span><span class="p">:</span>
+<a id="__codelineno-14-98" name="__codelineno-14-98" href="#__codelineno-14-98"></a>                <span class="nb">print</span><span class="p">(</span><span class="n">pair</span><span class="o">.</span><span class="n">key</span><span class="p">,</span> <span class="s2">&quot;-&gt;&quot;</span><span class="p">,</span> <span class="n">pair</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map_open_addressing.cpp</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* オープンアドレス法ハッシュテーブル */</span>
+<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">HashMapOpenAddressing</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">  </span><span class="k">private</span><span class="o">:</span>
+<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w">                             </span><span class="c1">// キー値ペアの数</span>
+<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">4</span><span class="p">;</span><span class="w">                     </span><span class="c1">// ハッシュテーブルの容量</span>
+<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">    </span><span class="k">const</span><span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="n">loadThres</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2.0</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">3.0</span><span class="p">;</span><span class="w">     </span><span class="c1">// 拡張をトリガーする負荷率の閾値</span>
+<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">    </span><span class="k">const</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">extendRatio</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w">            </span><span class="c1">// 拡張倍率</span>
+<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">Pair</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="n">buckets</span><span class="p">;</span><span class="w">               </span><span class="c1">// バケット配列</span>
+<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w">    </span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">TOMBSTONE</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Pair</span><span class="p">(</span><span class="mi">-1</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;-1&quot;</span><span class="p">);</span><span class="w"> </span><span class="c1">// 削除マーク</span>
+<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a>
+<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="w">  </span><span class="k">public</span><span class="o">:</span>
+<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="w">    </span><span class="n">HashMapOpenAddressing</span><span class="p">()</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">size</span><span class="p">(</span><span class="mi">0</span><span class="p">),</span><span class="w"> </span><span class="n">buckets</span><span class="p">(</span><span class="n">capacity</span><span class="p">,</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a>
+<a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a><span class="w">    </span><span class="cm">/* デストラクタ */</span>
+<a id="__codelineno-15-17" name="__codelineno-15-17" href="#__codelineno-15-17"></a><span class="w">    </span><span class="o">~</span><span class="n">HashMapOpenAddressing</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-18" name="__codelineno-15-18" href="#__codelineno-15-18"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">pair</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-19" name="__codelineno-15-19" href="#__codelineno-15-19"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-20" name="__codelineno-15-20" href="#__codelineno-15-20"></a><span class="w">                </span><span class="k">delete</span><span class="w"> </span><span class="n">pair</span><span class="p">;</span>
+<a id="__codelineno-15-21" name="__codelineno-15-21" href="#__codelineno-15-21"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-15-22" name="__codelineno-15-22" href="#__codelineno-15-22"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-15-23" name="__codelineno-15-23" href="#__codelineno-15-23"></a><span class="w">        </span><span class="k">delete</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">;</span>
+<a id="__codelineno-15-24" name="__codelineno-15-24" href="#__codelineno-15-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-25" name="__codelineno-15-25" href="#__codelineno-15-25"></a>
+<a id="__codelineno-15-26" name="__codelineno-15-26" href="#__codelineno-15-26"></a><span class="w">    </span><span class="cm">/* ハッシュ関数 */</span>
+<a id="__codelineno-15-27" name="__codelineno-15-27" href="#__codelineno-15-27"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-28" name="__codelineno-15-28" href="#__codelineno-15-28"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span>
+<a id="__codelineno-15-29" name="__codelineno-15-29" href="#__codelineno-15-29"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-30" name="__codelineno-15-30" href="#__codelineno-15-30"></a>
+<a id="__codelineno-15-31" name="__codelineno-15-31" href="#__codelineno-15-31"></a><span class="w">    </span><span class="cm">/* 負荷率 */</span>
+<a id="__codelineno-15-32" name="__codelineno-15-32" href="#__codelineno-15-32"></a><span class="w">    </span><span class="kt">double</span><span class="w"> </span><span class="n">loadFactor</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-33" name="__codelineno-15-33" href="#__codelineno-15-33"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">double</span><span class="p">)</span><span class="n">size</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span>
+<a id="__codelineno-15-34" name="__codelineno-15-34" href="#__codelineno-15-34"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-35" name="__codelineno-15-35" href="#__codelineno-15-35"></a>
+<a id="__codelineno-15-36" name="__codelineno-15-36" href="#__codelineno-15-36"></a><span class="w">    </span><span class="cm">/* keyに対応するバケットインデックスを検索 */</span>
+<a id="__codelineno-15-37" name="__codelineno-15-37" href="#__codelineno-15-37"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">findBucket</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-38" name="__codelineno-15-38" href="#__codelineno-15-38"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-15-39" name="__codelineno-15-39" href="#__codelineno-15-39"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
+<a id="__codelineno-15-40" name="__codelineno-15-40" href="#__codelineno-15-40"></a><span class="w">        </span><span class="c1">// 線形探査、空のバケットに遭遇したら中断</span>
+<a id="__codelineno-15-41" name="__codelineno-15-41" href="#__codelineno-15-41"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-42" name="__codelineno-15-42" href="#__codelineno-15-42"></a><span class="w">            </span><span class="c1">// keyに遭遇した場合、対応するバケットインデックスを返却</span>
+<a id="__codelineno-15-43" name="__codelineno-15-43" href="#__codelineno-15-43"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="o">-&gt;</span><span class="n">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-44" name="__codelineno-15-44" href="#__codelineno-15-44"></a><span class="w">                </span><span class="c1">// 以前に削除マークに遭遇していた場合、キー値ペアをそのインデックスに移動</span>
+<a id="__codelineno-15-45" name="__codelineno-15-45" href="#__codelineno-15-45"></a><span class="w">                </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="mi">-1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-46" name="__codelineno-15-46" href="#__codelineno-15-46"></a><span class="w">                    </span><span class="n">buckets</span><span class="p">[</span><span class="n">firstTombstone</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
+<a id="__codelineno-15-47" name="__codelineno-15-47" href="#__codelineno-15-47"></a><span class="w">                    </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">;</span>
+<a id="__codelineno-15-48" name="__codelineno-15-48" href="#__codelineno-15-48"></a><span class="w">                    </span><span class="k">return</span><span class="w"> </span><span class="n">firstTombstone</span><span class="p">;</span><span class="w"> </span><span class="c1">// 移動されたバケットインデックスを返却</span>
+<a id="__codelineno-15-49" name="__codelineno-15-49" href="#__codelineno-15-49"></a><span class="w">                </span><span class="p">}</span>
+<a id="__codelineno-15-50" name="__codelineno-15-50" href="#__codelineno-15-50"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="c1">// バケットインデックスを返却</span>
+<a id="__codelineno-15-51" name="__codelineno-15-51" href="#__codelineno-15-51"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-15-52" name="__codelineno-15-52" href="#__codelineno-15-52"></a><span class="w">            </span><span class="c1">// 最初に遭遇した削除マークを記録</span>
+<a id="__codelineno-15-53" name="__codelineno-15-53" href="#__codelineno-15-53"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">-1</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-54" name="__codelineno-15-54" href="#__codelineno-15-54"></a><span class="w">                </span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span>
+<a id="__codelineno-15-55" name="__codelineno-15-55" href="#__codelineno-15-55"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-15-56" name="__codelineno-15-56" href="#__codelineno-15-56"></a><span class="w">            </span><span class="c1">// バケットインデックスを計算、末尾を超えた場合は先頭に戻る</span>
+<a id="__codelineno-15-57" name="__codelineno-15-57" href="#__codelineno-15-57"></a><span class="w">            </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span>
+<a id="__codelineno-15-58" name="__codelineno-15-58" href="#__codelineno-15-58"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-15-59" name="__codelineno-15-59" href="#__codelineno-15-59"></a><span class="w">        </span><span class="c1">// keyが存在しない場合、挿入ポイントのインデックスを返却</span>
+<a id="__codelineno-15-60" name="__codelineno-15-60" href="#__codelineno-15-60"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">-1</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">firstTombstone</span><span class="p">;</span>
+<a id="__codelineno-15-61" name="__codelineno-15-61" href="#__codelineno-15-61"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-62" name="__codelineno-15-62" href="#__codelineno-15-62"></a>
+<a id="__codelineno-15-63" name="__codelineno-15-63" href="#__codelineno-15-63"></a><span class="w">    </span><span class="cm">/* クエリ操作 */</span>
+<a id="__codelineno-15-64" name="__codelineno-15-64" href="#__codelineno-15-64"></a><span class="w">    </span><span class="n">string</span><span class="w"> </span><span class="n">get</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-65" name="__codelineno-15-65" href="#__codelineno-15-65"></a><span class="w">        </span><span class="c1">// keyに対応するバケットインデックスを検索</span>
+<a id="__codelineno-15-66" name="__codelineno-15-66" href="#__codelineno-15-66"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">findBucket</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-15-67" name="__codelineno-15-67" href="#__codelineno-15-67"></a><span class="w">        </span><span class="c1">// キー値ペアが見つかった場合、対応するvalを返却</span>
+<a id="__codelineno-15-68" name="__codelineno-15-68" href="#__codelineno-15-68"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-69" name="__codelineno-15-69" href="#__codelineno-15-69"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-15-70" name="__codelineno-15-70" href="#__codelineno-15-70"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-15-71" name="__codelineno-15-71" href="#__codelineno-15-71"></a><span class="w">        </span><span class="c1">// キー値ペアが存在しない場合、空文字列を返却</span>
+<a id="__codelineno-15-72" name="__codelineno-15-72" href="#__codelineno-15-72"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="s">&quot;&quot;</span><span class="p">;</span>
+<a id="__codelineno-15-73" name="__codelineno-15-73" href="#__codelineno-15-73"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-74" name="__codelineno-15-74" href="#__codelineno-15-74"></a>
+<a id="__codelineno-15-75" name="__codelineno-15-75" href="#__codelineno-15-75"></a><span class="w">    </span><span class="cm">/* 追加操作 */</span>
+<a id="__codelineno-15-76" name="__codelineno-15-76" href="#__codelineno-15-76"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">put</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">string</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-77" name="__codelineno-15-77" href="#__codelineno-15-77"></a><span class="w">        </span><span class="c1">// 負荷率が閾値を超えた場合、拡張を実行</span>
+<a id="__codelineno-15-78" name="__codelineno-15-78" href="#__codelineno-15-78"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">loadFactor</span><span class="p">()</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">loadThres</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-79" name="__codelineno-15-79" href="#__codelineno-15-79"></a><span class="w">            </span><span class="n">extend</span><span class="p">();</span>
+<a id="__codelineno-15-80" name="__codelineno-15-80" href="#__codelineno-15-80"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-15-81" name="__codelineno-15-81" href="#__codelineno-15-81"></a><span class="w">        </span><span class="c1">// keyに対応するバケットインデックスを検索</span>
+<a id="__codelineno-15-82" name="__codelineno-15-82" href="#__codelineno-15-82"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">findBucket</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-15-83" name="__codelineno-15-83" href="#__codelineno-15-83"></a><span class="w">        </span><span class="c1">// キー値ペアが見つかった場合、valを上書きして返却</span>
+<a id="__codelineno-15-84" name="__codelineno-15-84" href="#__codelineno-15-84"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-85" name="__codelineno-15-85" href="#__codelineno-15-85"></a><span class="w">            </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-15-86" name="__codelineno-15-86" href="#__codelineno-15-86"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-15-87" name="__codelineno-15-87" href="#__codelineno-15-87"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-15-88" name="__codelineno-15-88" href="#__codelineno-15-88"></a><span class="w">        </span><span class="c1">// キー値ペアが存在しない場合、キー値ペアを追加</span>
+<a id="__codelineno-15-89" name="__codelineno-15-89" href="#__codelineno-15-89"></a><span class="w">        </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Pair</span><span class="p">(</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-15-90" name="__codelineno-15-90" href="#__codelineno-15-90"></a><span class="w">        </span><span class="n">size</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-15-91" name="__codelineno-15-91" href="#__codelineno-15-91"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-92" name="__codelineno-15-92" href="#__codelineno-15-92"></a>
+<a id="__codelineno-15-93" name="__codelineno-15-93" href="#__codelineno-15-93"></a><span class="w">    </span><span class="cm">/* 削除操作 */</span>
+<a id="__codelineno-15-94" name="__codelineno-15-94" href="#__codelineno-15-94"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-95" name="__codelineno-15-95" href="#__codelineno-15-95"></a><span class="w">        </span><span class="c1">// keyに対応するバケットインデックスを検索</span>
+<a id="__codelineno-15-96" name="__codelineno-15-96" href="#__codelineno-15-96"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">findBucket</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-15-97" name="__codelineno-15-97" href="#__codelineno-15-97"></a><span class="w">        </span><span class="c1">// キー値ペアが見つかった場合、削除マークで覆う</span>
+<a id="__codelineno-15-98" name="__codelineno-15-98" href="#__codelineno-15-98"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-99" name="__codelineno-15-99" href="#__codelineno-15-99"></a><span class="w">            </span><span class="k">delete</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
+<a id="__codelineno-15-100" name="__codelineno-15-100" href="#__codelineno-15-100"></a><span class="w">            </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">;</span>
+<a id="__codelineno-15-101" name="__codelineno-15-101" href="#__codelineno-15-101"></a><span class="w">            </span><span class="n">size</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-15-102" name="__codelineno-15-102" href="#__codelineno-15-102"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-15-103" name="__codelineno-15-103" href="#__codelineno-15-103"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-104" name="__codelineno-15-104" href="#__codelineno-15-104"></a>
+<a id="__codelineno-15-105" name="__codelineno-15-105" href="#__codelineno-15-105"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを拡張 */</span>
+<a id="__codelineno-15-106" name="__codelineno-15-106" href="#__codelineno-15-106"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">extend</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-107" name="__codelineno-15-107" href="#__codelineno-15-107"></a><span class="w">        </span><span class="c1">// 元のハッシュテーブルを一時保存</span>
+<a id="__codelineno-15-108" name="__codelineno-15-108" href="#__codelineno-15-108"></a><span class="w">        </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">Pair</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="n">bucketsTmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="p">;</span>
+<a id="__codelineno-15-109" name="__codelineno-15-109" href="#__codelineno-15-109"></a><span class="w">        </span><span class="c1">// 拡張された新しいハッシュテーブルを初期化</span>
+<a id="__codelineno-15-110" name="__codelineno-15-110" href="#__codelineno-15-110"></a><span class="w">        </span><span class="n">capacity</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="n">extendRatio</span><span class="p">;</span>
+<a id="__codelineno-15-111" name="__codelineno-15-111" href="#__codelineno-15-111"></a><span class="w">        </span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">Pair</span><span class="w"> </span><span class="o">*&gt;</span><span class="p">(</span><span class="n">capacity</span><span class="p">,</span><span class="w"> </span><span class="k">nullptr</span><span class="p">);</span>
+<a id="__codelineno-15-112" name="__codelineno-15-112" href="#__codelineno-15-112"></a><span class="w">        </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-15-113" name="__codelineno-15-113" href="#__codelineno-15-113"></a><span class="w">        </span><span class="c1">// 元のハッシュテーブルから新しいハッシュテーブルにキー値ペアを移動</span>
+<a id="__codelineno-15-114" name="__codelineno-15-114" href="#__codelineno-15-114"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">pair</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">bucketsTmp</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-115" name="__codelineno-15-115" href="#__codelineno-15-115"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-116" name="__codelineno-15-116" href="#__codelineno-15-116"></a><span class="w">                </span><span class="n">put</span><span class="p">(</span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-15-117" name="__codelineno-15-117" href="#__codelineno-15-117"></a><span class="w">                </span><span class="k">delete</span><span class="w"> </span><span class="n">pair</span><span class="p">;</span>
+<a id="__codelineno-15-118" name="__codelineno-15-118" href="#__codelineno-15-118"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-15-119" name="__codelineno-15-119" href="#__codelineno-15-119"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-15-120" name="__codelineno-15-120" href="#__codelineno-15-120"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-121" name="__codelineno-15-121" href="#__codelineno-15-121"></a>
+<a id="__codelineno-15-122" name="__codelineno-15-122" href="#__codelineno-15-122"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを印刷 */</span>
+<a id="__codelineno-15-123" name="__codelineno-15-123" href="#__codelineno-15-123"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-124" name="__codelineno-15-124" href="#__codelineno-15-124"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">pair</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-125" name="__codelineno-15-125" href="#__codelineno-15-125"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-126" name="__codelineno-15-126" href="#__codelineno-15-126"></a><span class="w">                </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;nullptr&quot;</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
+<a id="__codelineno-15-127" name="__codelineno-15-127" href="#__codelineno-15-127"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-128" name="__codelineno-15-128" href="#__codelineno-15-128"></a><span class="w">                </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;TOMBSTONE&quot;</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
+<a id="__codelineno-15-129" name="__codelineno-15-129" href="#__codelineno-15-129"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-130" name="__codelineno-15-130" href="#__codelineno-15-130"></a><span class="w">                </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">key</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot; -&gt; &quot;</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
+<a id="__codelineno-15-131" name="__codelineno-15-131" href="#__codelineno-15-131"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-15-132" name="__codelineno-15-132" href="#__codelineno-15-132"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-15-133" name="__codelineno-15-133" href="#__codelineno-15-133"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-134" name="__codelineno-15-134" href="#__codelineno-15-134"></a><span class="p">};</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map_open_addressing.java</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* オープンアドレス法ハッシュテーブル */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kd">class</span> <span class="nc">HashMapOpenAddressing</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="c1">// キー値ペアの数</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">4</span><span class="p">;</span><span class="w"> </span><span class="c1">// ハッシュテーブルの容量</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">final</span><span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="n">loadThres</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mf">2.0</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mf">3.0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 拡張をトリガーする負荷率の閾値</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">final</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">extendRatio</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 拡張倍率</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="n">Pair</span><span class="o">[]</span><span class="w"> </span><span class="n">buckets</span><span class="p">;</span><span class="w"> </span><span class="c1">// バケット配列</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kd">final</span><span class="w"> </span><span class="n">Pair</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Pair</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;-1&quot;</span><span class="p">);</span><span class="w"> </span><span class="c1">// 削除マーク</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="nf">HashMapOpenAddressing</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="w">        </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w">        </span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Pair</span><span class="o">[</span><span class="n">capacity</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a>
+<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a><span class="w">    </span><span class="cm">/* ハッシュ関数 */</span>
+<a id="__codelineno-16-17" name="__codelineno-16-17" href="#__codelineno-16-17"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">hashFunc</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-18" name="__codelineno-16-18" href="#__codelineno-16-18"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span>
+<a id="__codelineno-16-19" name="__codelineno-16-19" href="#__codelineno-16-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-20" name="__codelineno-16-20" href="#__codelineno-16-20"></a>
+<a id="__codelineno-16-21" name="__codelineno-16-21" href="#__codelineno-16-21"></a><span class="w">    </span><span class="cm">/* 負荷率 */</span>
+<a id="__codelineno-16-22" name="__codelineno-16-22" href="#__codelineno-16-22"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">double</span><span class="w"> </span><span class="nf">loadFactor</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-23" name="__codelineno-16-23" href="#__codelineno-16-23"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="kt">double</span><span class="p">)</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span>
+<a id="__codelineno-16-24" name="__codelineno-16-24" href="#__codelineno-16-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-25" name="__codelineno-16-25" href="#__codelineno-16-25"></a>
+<a id="__codelineno-16-26" name="__codelineno-16-26" href="#__codelineno-16-26"></a><span class="w">    </span><span class="cm">/* keyに対応するバケットインデックスを検索 */</span>
+<a id="__codelineno-16-27" name="__codelineno-16-27" href="#__codelineno-16-27"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">findBucket</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-28" name="__codelineno-16-28" href="#__codelineno-16-28"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-16-29" name="__codelineno-16-29" href="#__codelineno-16-29"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-16-30" name="__codelineno-16-30" href="#__codelineno-16-30"></a><span class="w">        </span><span class="c1">// 線形探査、空のバケットに遭遇したら終了</span>
+<a id="__codelineno-16-31" name="__codelineno-16-31" href="#__codelineno-16-31"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-32" name="__codelineno-16-32" href="#__codelineno-16-32"></a><span class="w">            </span><span class="c1">// keyに遭遇した場合、対応するバケットインデックスを返す</span>
+<a id="__codelineno-16-33" name="__codelineno-16-33" href="#__codelineno-16-33"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="p">.</span><span class="na">key</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-34" name="__codelineno-16-34" href="#__codelineno-16-34"></a><span class="w">                </span><span class="c1">// 以前に削除マークに遭遇していた場合、キー値ペアをそのインデックスに移動</span>
+<a id="__codelineno-16-35" name="__codelineno-16-35" href="#__codelineno-16-35"></a><span class="w">                </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-36" name="__codelineno-16-36" href="#__codelineno-16-36"></a><span class="w">                    </span><span class="n">buckets</span><span class="o">[</span><span class="n">firstTombstone</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-16-37" name="__codelineno-16-37" href="#__codelineno-16-37"></a><span class="w">                    </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">;</span>
+<a id="__codelineno-16-38" name="__codelineno-16-38" href="#__codelineno-16-38"></a><span class="w">                    </span><span class="k">return</span><span class="w"> </span><span class="n">firstTombstone</span><span class="p">;</span><span class="w"> </span><span class="c1">// 移動後のバケットインデックスを返す</span>
+<a id="__codelineno-16-39" name="__codelineno-16-39" href="#__codelineno-16-39"></a><span class="w">                </span><span class="p">}</span>
+<a id="__codelineno-16-40" name="__codelineno-16-40" href="#__codelineno-16-40"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="n">index</span><span class="p">;</span><span class="w"> </span><span class="c1">// バケットインデックスを返す</span>
+<a id="__codelineno-16-41" name="__codelineno-16-41" href="#__codelineno-16-41"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-16-42" name="__codelineno-16-42" href="#__codelineno-16-42"></a><span class="w">            </span><span class="c1">// 最初に遭遇した削除マークを記録</span>
+<a id="__codelineno-16-43" name="__codelineno-16-43" href="#__codelineno-16-43"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-44" name="__codelineno-16-44" href="#__codelineno-16-44"></a><span class="w">                </span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">;</span>
+<a id="__codelineno-16-45" name="__codelineno-16-45" href="#__codelineno-16-45"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-16-46" name="__codelineno-16-46" href="#__codelineno-16-46"></a><span class="w">            </span><span class="c1">// バケットインデックスを計算、末尾を超えた場合は先頭に戻る</span>
+<a id="__codelineno-16-47" name="__codelineno-16-47" href="#__codelineno-16-47"></a><span class="w">            </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">index</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span>
+<a id="__codelineno-16-48" name="__codelineno-16-48" href="#__codelineno-16-48"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-16-49" name="__codelineno-16-49" href="#__codelineno-16-49"></a><span class="w">        </span><span class="c1">// keyが存在しない場合、挿入ポイントのインデックスを返す</span>
+<a id="__codelineno-16-50" name="__codelineno-16-50" href="#__codelineno-16-50"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">firstTombstone</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">firstTombstone</span><span class="p">;</span>
+<a id="__codelineno-16-51" name="__codelineno-16-51" href="#__codelineno-16-51"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-52" name="__codelineno-16-52" href="#__codelineno-16-52"></a>
+<a id="__codelineno-16-53" name="__codelineno-16-53" href="#__codelineno-16-53"></a><span class="w">    </span><span class="cm">/* クエリ操作 */</span>
+<a id="__codelineno-16-54" name="__codelineno-16-54" href="#__codelineno-16-54"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="n">String</span><span class="w"> </span><span class="nf">get</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-55" name="__codelineno-16-55" href="#__codelineno-16-55"></a><span class="w">        </span><span class="c1">// keyに対応するバケットインデックスを検索</span>
+<a id="__codelineno-16-56" name="__codelineno-16-56" href="#__codelineno-16-56"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">findBucket</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-16-57" name="__codelineno-16-57" href="#__codelineno-16-57"></a><span class="w">        </span><span class="c1">// キー値ペアが見つかった場合、対応するvalを返す</span>
+<a id="__codelineno-16-58" name="__codelineno-16-58" href="#__codelineno-16-58"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-59" name="__codelineno-16-59" href="#__codelineno-16-59"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="p">.</span><span class="na">val</span><span class="p">;</span>
+<a id="__codelineno-16-60" name="__codelineno-16-60" href="#__codelineno-16-60"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-16-61" name="__codelineno-16-61" href="#__codelineno-16-61"></a><span class="w">        </span><span class="c1">// キー値ペアが存在しない場合、nullを返す</span>
+<a id="__codelineno-16-62" name="__codelineno-16-62" href="#__codelineno-16-62"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-16-63" name="__codelineno-16-63" href="#__codelineno-16-63"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-64" name="__codelineno-16-64" href="#__codelineno-16-64"></a>
+<a id="__codelineno-16-65" name="__codelineno-16-65" href="#__codelineno-16-65"></a><span class="w">    </span><span class="cm">/* 追加操作 */</span>
+<a id="__codelineno-16-66" name="__codelineno-16-66" href="#__codelineno-16-66"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">put</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">String</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-67" name="__codelineno-16-67" href="#__codelineno-16-67"></a><span class="w">        </span><span class="c1">// 負荷率が閾値を超えた場合、拡張を実行</span>
+<a id="__codelineno-16-68" name="__codelineno-16-68" href="#__codelineno-16-68"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">loadFactor</span><span class="p">()</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">loadThres</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-69" name="__codelineno-16-69" href="#__codelineno-16-69"></a><span class="w">            </span><span class="n">extend</span><span class="p">();</span>
+<a id="__codelineno-16-70" name="__codelineno-16-70" href="#__codelineno-16-70"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-16-71" name="__codelineno-16-71" href="#__codelineno-16-71"></a><span class="w">        </span><span class="c1">// keyに対応するバケットインデックスを検索</span>
+<a id="__codelineno-16-72" name="__codelineno-16-72" href="#__codelineno-16-72"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">findBucket</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-16-73" name="__codelineno-16-73" href="#__codelineno-16-73"></a><span class="w">        </span><span class="c1">// キー値ペアが見つかった場合、valを上書きして戻る</span>
+<a id="__codelineno-16-74" name="__codelineno-16-74" href="#__codelineno-16-74"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-75" name="__codelineno-16-75" href="#__codelineno-16-75"></a><span class="w">            </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-16-76" name="__codelineno-16-76" href="#__codelineno-16-76"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-16-77" name="__codelineno-16-77" href="#__codelineno-16-77"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-16-78" name="__codelineno-16-78" href="#__codelineno-16-78"></a><span class="w">        </span><span class="c1">// キー値ペアが存在しない場合、キー値ペアを追加</span>
+<a id="__codelineno-16-79" name="__codelineno-16-79" href="#__codelineno-16-79"></a><span class="w">        </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Pair</span><span class="p">(</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-16-80" name="__codelineno-16-80" href="#__codelineno-16-80"></a><span class="w">        </span><span class="n">size</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-16-81" name="__codelineno-16-81" href="#__codelineno-16-81"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-82" name="__codelineno-16-82" href="#__codelineno-16-82"></a>
+<a id="__codelineno-16-83" name="__codelineno-16-83" href="#__codelineno-16-83"></a><span class="w">    </span><span class="cm">/* 削除操作 */</span>
+<a id="__codelineno-16-84" name="__codelineno-16-84" href="#__codelineno-16-84"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-85" name="__codelineno-16-85" href="#__codelineno-16-85"></a><span class="w">        </span><span class="c1">// keyに対応するバケットインデックスを検索</span>
+<a id="__codelineno-16-86" name="__codelineno-16-86" href="#__codelineno-16-86"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">findBucket</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-16-87" name="__codelineno-16-87" href="#__codelineno-16-87"></a><span class="w">        </span><span class="c1">// キー値ペアが見つかった場合、削除マークで覆う</span>
+<a id="__codelineno-16-88" name="__codelineno-16-88" href="#__codelineno-16-88"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-89" name="__codelineno-16-89" href="#__codelineno-16-89"></a><span class="w">            </span><span class="n">buckets</span><span class="o">[</span><span class="n">index</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">;</span>
+<a id="__codelineno-16-90" name="__codelineno-16-90" href="#__codelineno-16-90"></a><span class="w">            </span><span class="n">size</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-16-91" name="__codelineno-16-91" href="#__codelineno-16-91"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-16-92" name="__codelineno-16-92" href="#__codelineno-16-92"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-93" name="__codelineno-16-93" href="#__codelineno-16-93"></a>
+<a id="__codelineno-16-94" name="__codelineno-16-94" href="#__codelineno-16-94"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを拡張 */</span>
+<a id="__codelineno-16-95" name="__codelineno-16-95" href="#__codelineno-16-95"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">extend</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-96" name="__codelineno-16-96" href="#__codelineno-16-96"></a><span class="w">        </span><span class="c1">// 元のハッシュテーブルを一時的に保存</span>
+<a id="__codelineno-16-97" name="__codelineno-16-97" href="#__codelineno-16-97"></a><span class="w">        </span><span class="n">Pair</span><span class="o">[]</span><span class="w"> </span><span class="n">bucketsTmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="p">;</span>
+<a id="__codelineno-16-98" name="__codelineno-16-98" href="#__codelineno-16-98"></a><span class="w">        </span><span class="c1">// 拡張された新しいハッシュテーブルを初期化</span>
+<a id="__codelineno-16-99" name="__codelineno-16-99" href="#__codelineno-16-99"></a><span class="w">        </span><span class="n">capacity</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="n">extendRatio</span><span class="p">;</span>
+<a id="__codelineno-16-100" name="__codelineno-16-100" href="#__codelineno-16-100"></a><span class="w">        </span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Pair</span><span class="o">[</span><span class="n">capacity</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-16-101" name="__codelineno-16-101" href="#__codelineno-16-101"></a><span class="w">        </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-16-102" name="__codelineno-16-102" href="#__codelineno-16-102"></a><span class="w">        </span><span class="c1">// 元のハッシュテーブルから新しいハッシュテーブルにキー値ペアを移動</span>
+<a id="__codelineno-16-103" name="__codelineno-16-103" href="#__codelineno-16-103"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">bucketsTmp</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-104" name="__codelineno-16-104" href="#__codelineno-16-104"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-105" name="__codelineno-16-105" href="#__codelineno-16-105"></a><span class="w">                </span><span class="n">put</span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="na">key</span><span class="p">,</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="na">val</span><span class="p">);</span>
+<a id="__codelineno-16-106" name="__codelineno-16-106" href="#__codelineno-16-106"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-16-107" name="__codelineno-16-107" href="#__codelineno-16-107"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-16-108" name="__codelineno-16-108" href="#__codelineno-16-108"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-109" name="__codelineno-16-109" href="#__codelineno-16-109"></a>
+<a id="__codelineno-16-110" name="__codelineno-16-110" href="#__codelineno-16-110"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを印刷 */</span>
+<a id="__codelineno-16-111" name="__codelineno-16-111" href="#__codelineno-16-111"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-112" name="__codelineno-16-112" href="#__codelineno-16-112"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-113" name="__codelineno-16-113" href="#__codelineno-16-113"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-114" name="__codelineno-16-114" href="#__codelineno-16-114"></a><span class="w">                </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="s">&quot;null&quot;</span><span class="p">);</span>
+<a id="__codelineno-16-115" name="__codelineno-16-115" href="#__codelineno-16-115"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">TOMBSTONE</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-116" name="__codelineno-16-116" href="#__codelineno-16-116"></a><span class="w">                </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="s">&quot;TOMBSTONE&quot;</span><span class="p">);</span>
+<a id="__codelineno-16-117" name="__codelineno-16-117" href="#__codelineno-16-117"></a><span class="w">            </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-118" name="__codelineno-16-118" href="#__codelineno-16-118"></a><span class="w">                </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="na">key</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s">&quot; -&gt; &quot;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="na">val</span><span class="p">);</span>
+<a id="__codelineno-16-119" name="__codelineno-16-119" href="#__codelineno-16-119"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-16-120" name="__codelineno-16-120" href="#__codelineno-16-120"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-16-121" name="__codelineno-16-121" href="#__codelineno-16-121"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-122" name="__codelineno-16-122" href="#__codelineno-16-122"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map_open_addressing.cs</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">HashMapOpenAddressing</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map_open_addressing.go</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">hashMapOpenAddressing</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map_open_addressing.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">HashMapOpenAddressing</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map_open_addressing.js</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">HashMapOpenAddressing</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map_open_addressing.ts</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">HashMapOpenAddressing</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map_open_addressing.dart</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">HashMapOpenAddressing</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map_open_addressing.rs</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">HashMapOpenAddressing</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map_open_addressing.c</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">HashMapOpenAddressing</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map_open_addressing.kt</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">HashMapOpenAddressing</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map_open_addressing.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">HashMapOpenAddressing</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map_open_addressing.zig</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">HashMapOpenAddressing</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h3 id="2">2. &nbsp; 二次プローブ<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
+<p>二次プローブは線形プローブに似ており、オープンアドレス法の一般的な戦略の1つです。衝突が発生した場合、二次プローブは単純に固定ステップ数をスキップするのではなく、「プローブ回数の二乗」に等しいステップ数、つまり<span class="arithmatex">\(1, 4, 9, \dots\)</span>ステップをスキップします。</p>
+<p>二次プローブには以下の利点があります：</p>
+<ul>
+<li>二次プローブは、プローブ回数の二乗の距離をスキップすることで、線形プローブのクラスタリング効果を軽減しようとします。</li>
+<li>二次プローブはより大きな距離をスキップして空の位置を見つけ、データをより均等に分散するのに役立ちます。</li>
+</ul>
+<p>しかし、二次プローブは完璧ではありません：</p>
+<ul>
+<li>クラスタリングは依然として存在し、つまり一部の位置は他の位置よりも占有される可能性が高いです。</li>
+<li>二乗の成長により、二次プローブはハッシュ表全体をプローブできない可能性があり、ハッシュ表に空のバケットがあっても、二次プローブがアクセスできない可能性があります。</li>
+</ul>
+<h3 id="3">3. &nbsp; 二重ハッシュ<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
+<p>名前が示すように、二重ハッシュ法は複数のハッシュ関数<span class="arithmatex">\(f_1(x)\)</span>、<span class="arithmatex">\(f_2(x)\)</span>、<span class="arithmatex">\(f_3(x)\)</span>、<span class="arithmatex">\(\dots\)</span>をプローブに使用します。</p>
+<ul>
+<li><strong>要素の挿入</strong>: ハッシュ関数<span class="arithmatex">\(f_1(x)\)</span>が衝突に遭遇した場合、<span class="arithmatex">\(f_2(x)\)</span>を試し、以下同様に、空の位置が見つかって要素が挿入されるまで続けます。</li>
+<li><strong>要素の検索</strong>: 同じハッシュ関数の順序で検索し、ターゲット要素が見つかって返されるまで、または空の位置に遭遇するかすべてのハッシュ関数が試されるまで続け、要素がハッシュ表にないことを示し、<code>None</code>を返します。</li>
+</ul>
+<p>線形プローブと比較して、二重ハッシュ法はクラスタリングが起こりにくいですが、複数のハッシュ関数は追加の計算オーバーヘッドを導入します。</p>
+<div class="admonition tip">
+<p class="admonition-title">Tip</p>
+<p>オープンアドレス法（線形プローブ、二次プローブ、二重ハッシュ）ハッシュ表はすべて「要素を直接削除できない」という問題があることに注意してください。</p>
+</div>
+<h2 id="623">6.2.3 &nbsp; プログラミング言語の選択<a class="headerlink" href="#623" title="Permanent link">&para;</a></h2>
+<p>異なるプログラミング言語は異なるハッシュ表実装戦略を採用しています。以下にいくつかの例を示します：</p>
+<ul>
+<li>Pythonはオープンアドレス法を使用します。<code>dict</code>辞書はプローブに疑似乱数を使用します。</li>
+<li>Javaは連鎖法を使用します。JDK 1.8以降、<code>HashMap</code>の配列長が64に達し、連結リストの長さが8に達すると、連結リストは検索性能を向上させるために赤黒木に変換されます。</li>
+<li>Goは連鎖法を使用します。Goは各バケットが最大8つのキー値ペアを格納できることを規定し、容量を超えた場合はオーバーフローバケットが連結されます。オーバーフローバケットが多すぎる場合、性能を確保するために特別な等容量リサイズ操作が実行されます。</li>
+</ul>
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diff --git a/ja/chapter_hashing/hash_map.assets/hash_table_lookup.png b/ja/chapter_hashing/hash_map.assets/hash_table_lookup.png
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diff --git a/ja/chapter_hashing/hash_map.assets/hash_table_reshash.png b/ja/chapter_hashing/hash_map.assets/hash_table_reshash.png
new file mode 100644
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+      <div class="md-header__ellipsis">
+        <div class="md-header__topic">
+          <span class="md-ellipsis">
+            Hello アルゴリズム
+          </span>
+        </div>
+        <div class="md-header__topic" data-md-component="header-topic">
+          <span class="md-ellipsis">
+            
+              6.1 &nbsp; ハッシュ表
+            
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+        </div>
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+    
+      
+        <form class="md-header__option" data-md-component="palette">
+  
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+    
+    <input class="md-option" data-md-color-media="" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="teal"  aria-label="ダークモード"  type="radio" name="__palette" id="__palette_0">
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+      <label class="md-header__button md-icon" title="ダークモード" for="__palette_1" hidden>
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+      </label>
+    
+  
+    
+    
+    
+    <input class="md-option" data-md-color-media="" data-md-color-scheme="slate" data-md-color-primary="black" data-md-color-accent="teal"  aria-label="ライトモード"  type="radio" name="__palette" id="__palette_1">
+    
+      <label class="md-header__button md-icon" title="ライトモード" for="__palette_0" hidden>
+        <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07 19.07 3.5m-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13.51 1.67m-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87.4 1.31M19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35-2.53-2.2m4.33-2.7 1.15-2.77 2.2 2.54-3.35.23m1.15-4.96-1.14-2.78 3.34.24-2.2 2.54M9.63 18.93l2.77 1.15-2.53 2.19-.24-3.34Z"/></svg>
+      </label>
+    
+  
+</form>
+      
+    
+    
+      <script>var media,input,key,value,palette=__md_get("__palette");if(palette&&palette.color){"(prefers-color-scheme)"===palette.color.media&&(media=matchMedia("(prefers-color-scheme: light)"),input=document.querySelector(media.matches?"[data-md-color-media='(prefers-color-scheme: light)']":"[data-md-color-media='(prefers-color-scheme: dark)']"),palette.color.media=input.getAttribute("data-md-color-media"),palette.color.scheme=input.getAttribute("data-md-color-scheme"),palette.color.primary=input.getAttribute("data-md-color-primary"),palette.color.accent=input.getAttribute("data-md-color-accent"));for([key,value]of Object.entries(palette.color))document.body.setAttribute("data-md-color-"+key,value)}</script>
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+            
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+        <div class="md-search__suggest" data-md-component="search-suggest"></div>
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+    </form>
+    <div class="md-search__output">
+      <div class="md-search__scrollwrap" data-md-scrollfix>
+        <div class="md-search-result" data-md-component="search-result">
+          <div class="md-search-result__meta">
+            検索を初期化
+          </div>
+          <ol class="md-search-result__list" role="presentation"></ol>
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+</div>
+    
+    
+      <div class="md-header__source">
+        <a href="https://github.com/krahets/hello-algo" title="リポジトリへ" class="md-source" data-md-component="source">
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m13.13 22.19-1.63-3.83c1.57-.58 3.04-1.36 4.4-2.27l-2.77 6.1M5.64 12.5l-3.83-1.63 6.1-2.77C7 9.46 6.22 10.93 5.64 12.5M19.22 4c.28 0 .53 0 .74.05.17 1.39-.02 4.25-3.3 7.53-1.7 1.71-3.73 3.02-6.01 3.89l-2.15-2.1c.92-2.31 2.23-4.34 3.92-6.03C15.18 4.58 17.64 4 19.22 4m0-2c-1.98 0-4.98.69-8.22 3.93-2.19 2.19-3.5 4.6-4.35 6.71-.28.75-.09 1.57.46 2.13l2.13 2.12c.38.38.89.61 1.42.61.23 0 .47-.06.7-.15A19.1 19.1 0 0 0 18.07 13c5.66-5.66 3.54-10.61 3.54-10.61S20.7 2 19.22 2m-4.68 7.46c-.78-.78-.78-2.05 0-2.83s2.05-.78 2.83 0c.77.78.78 2.05 0 2.83-.78.78-2.05.78-2.83 0m-5.66 7.07-1.41-1.41 1.41 1.41M6.24 22l3.64-3.64c-.34-.09-.67-.24-.97-.45L4.83 22h1.41M2 22h1.41l4.77-4.76-1.42-1.41L2 20.59V22m0-2.83 4.09-4.08c-.21-.3-.36-.62-.45-.97L2 17.76v1.41Z"/></svg>
+  
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M21 4H3a2 2 0 0 0-2 2v13a2 2 0 0 0 2 2h18a2 2 0 0 0 2-2V6a2 2 0 0 0-2-2M3 19V6h8v13H3m18 0h-8V6h8v13m-7-9.5h6V11h-6V9.5m0 2.5h6v1.5h-6V12m0 2.5h6V16h-6v-1.5Z"/></svg>
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+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/about_the_book/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.1 &nbsp; この本について
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/suggestions/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.2 &nbsp; 本書の使い方
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_introduction/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#611" class="md-nav__link">
+    <span class="md-ellipsis">
+      6.1.1 &nbsp; ハッシュ表の一般的な操作
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#612" class="md-nav__link">
+    <span class="md-ellipsis">
+      6.1.2 &nbsp; ハッシュ表の簡単な実装
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#613" class="md-nav__link">
+    <span class="md-ellipsis">
+      6.1.3 &nbsp; ハッシュ衝突とリサイズ
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
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+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
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+    <span class="md-ellipsis">
+      6.1.1 &nbsp; ハッシュ表の一般的な操作
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#612" class="md-nav__link">
+    <span class="md-ellipsis">
+      6.1.2 &nbsp; ハッシュ表の簡単な実装
+    </span>
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+  
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+      
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+  <a href="#613" class="md-nav__link">
+    <span class="md-ellipsis">
+      6.1.3 &nbsp; ハッシュ衝突とリサイズ
+    </span>
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+<h1 id="61">6.1 &nbsp; ハッシュ表<a class="headerlink" href="#61" title="Permanent link">&para;</a></h1>
+<p><u>ハッシュ表</u>は<u>ハッシュマップ</u>とも呼ばれ、キーと値の間のマッピングを確立し、効率的な要素の取得を可能にするデータ構造です。具体的には、ハッシュ表に<code>key</code>を入力すると、<span class="arithmatex">\(O(1)\)</span>の時間計算量で対応する<code>value</code>を取得できます。</p>
+<p>下図に示すように、<span class="arithmatex">\(n\)</span>人の学生がいて、各学生には「名前」と「学籍番号」の2つのデータフィールドがあるとします。学籍番号を入力として対応する名前を返すクエリ機能を実装したい場合、下図に示すハッシュ表を使用できます。</p>
+<p><a class="glightbox" href="../hash_map.assets/hash_table_lookup.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="ハッシュ表の抽象的な表現" class="animation-figure" src="../hash_map.assets/hash_table_lookup.png" /></a></p>
+<p align="center"> 図 6-1 &nbsp; ハッシュ表の抽象的な表現 </p>
+
+<p>ハッシュ表に加えて、配列や連結リストもクエリ機能の実装に使用できますが、時間計算量が異なります。効率は以下の表で比較されています：</p>
+<ul>
+<li><strong>要素の挿入</strong>: 配列（または連結リスト）の末尾に要素を追加するだけです。この操作の時間計算量は<span class="arithmatex">\(O(1)\)</span>です。</li>
+<li><strong>要素の検索</strong>: 配列（または連結リスト）がソートされていないため、要素を検索するにはすべての要素を走査する必要があります。この操作の時間計算量は<span class="arithmatex">\(O(n)\)</span>です。</li>
+<li><strong>要素の削除</strong>: 要素を削除するには、まずその要素を見つけてから、配列（または連結リスト）から削除します。この操作の時間計算量は<span class="arithmatex">\(O(n)\)</span>です。</li>
+</ul>
+<p align="center"> 表 6-1 &nbsp; 一般的な操作の時間効率の比較 </p>
+
+<div class="center-table">
+<table>
+<thead>
+<tr>
+<th></th>
+<th>配列</th>
+<th>連結リスト</th>
+<th>ハッシュ表</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td>要素の検索</td>
+<td><span class="arithmatex">\(O(n)\)</span></td>
+<td><span class="arithmatex">\(O(n)\)</span></td>
+<td><span class="arithmatex">\(O(1)\)</span></td>
+</tr>
+<tr>
+<td>要素の挿入</td>
+<td><span class="arithmatex">\(O(1)\)</span></td>
+<td><span class="arithmatex">\(O(1)\)</span></td>
+<td><span class="arithmatex">\(O(1)\)</span></td>
+</tr>
+<tr>
+<td>要素の削除</td>
+<td><span class="arithmatex">\(O(n)\)</span></td>
+<td><span class="arithmatex">\(O(n)\)</span></td>
+<td><span class="arithmatex">\(O(1)\)</span></td>
+</tr>
+</tbody>
+</table>
+</div>
+<p>観察されるように、**ハッシュ表における操作（挿入、削除、検索、変更）の時間計算量は<span class="arithmatex">\(O(1)\)</span>**で、非常に効率的です。</p>
+<h2 id="611">6.1.1 &nbsp; ハッシュ表の一般的な操作<a class="headerlink" href="#611" title="Permanent link">&para;</a></h2>
+<p>ハッシュ表の一般的な操作には、初期化、クエリ、キー値ペアの追加、キー値ペアの削除があります。以下はコード例です：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="c1"># ハッシュ表を初期化</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="n">hmap</span><span class="p">:</span> <span class="nb">dict</span> <span class="o">=</span> <span class="p">{}</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="c1"># 追加操作</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a><span class="c1"># ハッシュ表にキー値ペア (key, value) を追加</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a><span class="n">hmap</span><span class="p">[</span><span class="mi">12836</span><span class="p">]</span> <span class="o">=</span> <span class="s2">&quot;小哈&quot;</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="n">hmap</span><span class="p">[</span><span class="mi">15937</span><span class="p">]</span> <span class="o">=</span> <span class="s2">&quot;小啰&quot;</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="n">hmap</span><span class="p">[</span><span class="mi">16750</span><span class="p">]</span> <span class="o">=</span> <span class="s2">&quot;小算&quot;</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a><span class="n">hmap</span><span class="p">[</span><span class="mi">13276</span><span class="p">]</span> <span class="o">=</span> <span class="s2">&quot;小法&quot;</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a><span class="n">hmap</span><span class="p">[</span><span class="mi">10583</span><span class="p">]</span> <span class="o">=</span> <span class="s2">&quot;小鸭&quot;</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a><span class="c1"># クエリ操作</span>
+<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a><span class="c1"># ハッシュ表にキーを入力し、値を取得</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a><span class="n">name</span><span class="p">:</span> <span class="nb">str</span> <span class="o">=</span> <span class="n">hmap</span><span class="p">[</span><span class="mi">15937</span><span class="p">]</span>
+<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>
+<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a><span class="c1"># 削除操作</span>
+<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a><span class="c1"># ハッシュ表からキー値ペア (key, value) を削除</span>
+<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a><span class="n">hmap</span><span class="o">.</span><span class="n">pop</span><span class="p">(</span><span class="mi">10583</span><span class="p">)</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* ハッシュ表を初期化 */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="n">unordered_map</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="n">string</span><span class="o">&gt;</span><span class="w"> </span><span class="n">map</span><span class="p">;</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="cm">/* 追加操作 */</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="c1">// ハッシュ表にキー値ペア (key, value) を追加</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="n">map</span><span class="p">[</span><span class="mi">12836</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;小哈&quot;</span><span class="p">;</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="n">map</span><span class="p">[</span><span class="mi">15937</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;小啰&quot;</span><span class="p">;</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="n">map</span><span class="p">[</span><span class="mi">16750</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;小算&quot;</span><span class="p">;</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="n">map</span><span class="p">[</span><span class="mi">13276</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;小法&quot;</span><span class="p">;</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="n">map</span><span class="p">[</span><span class="mi">10583</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s">&quot;小鸭&quot;</span><span class="p">;</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="cm">/* クエリ操作 */</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="c1">// ハッシュ表にキーを入力し、値を取得</span>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="n">string</span><span class="w"> </span><span class="n">name</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">map</span><span class="p">[</span><span class="mi">15937</span><span class="p">];</span>
+<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a>
+<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="cm">/* 削除操作 */</span>
+<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="c1">// ハッシュ表からキー値ペア (key, value) を削除</span>
+<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="n">map</span><span class="p">.</span><span class="n">erase</span><span class="p">(</span><span class="mi">10583</span><span class="p">);</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* ハッシュ表を初期化 */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="n">Map</span><span class="o">&lt;</span><span class="n">Integer</span><span class="p">,</span><span class="w"> </span><span class="n">String</span><span class="o">&gt;</span><span class="w"> </span><span class="n">map</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">HashMap</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="cm">/* 追加操作 */</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="c1">// ハッシュ表にキー値ペア (key, value) を追加</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="n">map</span><span class="p">.</span><span class="na">put</span><span class="p">(</span><span class="mi">12836</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;小哈&quot;</span><span class="p">);</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="n">map</span><span class="p">.</span><span class="na">put</span><span class="p">(</span><span class="mi">15937</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;小啰&quot;</span><span class="p">);</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="n">map</span><span class="p">.</span><span class="na">put</span><span class="p">(</span><span class="mi">16750</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;小算&quot;</span><span class="p">);</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="n">map</span><span class="p">.</span><span class="na">put</span><span class="p">(</span><span class="mi">13276</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;小法&quot;</span><span class="p">);</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="n">map</span><span class="p">.</span><span class="na">put</span><span class="p">(</span><span class="mi">10583</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;小鸭&quot;</span><span class="p">);</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="cm">/* クエリ操作 */</span>
+<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="c1">// ハッシュ表にキーを入力し、値を取得</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="n">String</span><span class="w"> </span><span class="n">name</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="mi">15937</span><span class="p">);</span>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="cm">/* 削除操作 */</span>
+<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="c1">// ハッシュ表からキー値ペア (key, value) を削除</span>
+<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="n">map</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="mi">10583</span><span class="p">);</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* ハッシュ表を初期化 */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="n">Dictionary</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">string</span><span class="o">&gt;</span><span class="w"> </span><span class="n">map</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="cm">/* 追加操作 */</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="c1">// ハッシュ表にキー値ペア (key, value) を追加</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">    </span><span class="p">{</span><span class="w"> </span><span class="mi">12836</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;小哈&quot;</span><span class="w"> </span><span class="p">},</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">    </span><span class="p">{</span><span class="w"> </span><span class="mi">15937</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;小啰&quot;</span><span class="w"> </span><span class="p">},</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="w">    </span><span class="p">{</span><span class="w"> </span><span class="mi">16750</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;小算&quot;</span><span class="w"> </span><span class="p">},</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="w">    </span><span class="p">{</span><span class="w"> </span><span class="mi">13276</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;小法&quot;</span><span class="w"> </span><span class="p">},</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="w">    </span><span class="p">{</span><span class="w"> </span><span class="mi">10583</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;小鸭&quot;</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="p">};</span>
+<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a>
+<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="cm">/* クエリ操作 */</span>
+<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="c1">// ハッシュ表にキーを入力し、値を取得</span>
+<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="kt">string</span><span class="w"> </span><span class="n">name</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">map</span><span class="p">[</span><span class="mi">15937</span><span class="p">];</span>
+<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a>
+<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="cm">/* 削除操作 */</span>
+<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="c1">// ハッシュ表からキー値ペア (key, value) を削除</span>
+<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="n">map</span><span class="p">.</span><span class="n">Remove</span><span class="p">(</span><span class="mi">10583</span><span class="p">);</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map_test.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* ハッシュ表を初期化 */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="nx">hmap</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">make</span><span class="p">(</span><span class="kd">map</span><span class="p">[</span><span class="kt">int</span><span class="p">]</span><span class="kt">string</span><span class="p">)</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="cm">/* 追加操作 */</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="c1">// ハッシュ表にキー値ペア (key, value) を追加</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="nx">hmap</span><span class="p">[</span><span class="mi">12836</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">&quot;小哈&quot;</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="nx">hmap</span><span class="p">[</span><span class="mi">15937</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">&quot;小啰&quot;</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="nx">hmap</span><span class="p">[</span><span class="mi">16750</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">&quot;小算&quot;</span>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="nx">hmap</span><span class="p">[</span><span class="mi">13276</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">&quot;小法&quot;</span>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="nx">hmap</span><span class="p">[</span><span class="mi">10583</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">&quot;小鸭&quot;</span>
+<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a>
+<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="cm">/* クエリ操作 */</span>
+<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="c1">// ハッシュ表にキーを入力し、値を取得</span>
+<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="nx">name</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">hmap</span><span class="p">[</span><span class="mi">15937</span><span class="p">]</span>
+<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a>
+<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="cm">/* 削除操作 */</span>
+<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="c1">// ハッシュ表からキー値ペア (key, value) を削除</span>
+<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="nb">delete</span><span class="p">(</span><span class="nx">hmap</span><span class="p">,</span><span class="w"> </span><span class="mi">10583</span><span class="p">)</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* ハッシュ表を初期化 */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">var</span><span class="w"> </span><span class="nv">map</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">:</span><span class="w"> </span><span class="nb">String</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[:]</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="cm">/* 追加操作 */</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="c1">// ハッシュ表にキー値ペア (key, value) を追加</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="bp">map</span><span class="p">[</span><span class="mi">12836</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">&quot;小哈&quot;</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="bp">map</span><span class="p">[</span><span class="mi">15937</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">&quot;小啰&quot;</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="bp">map</span><span class="p">[</span><span class="mi">16750</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">&quot;小算&quot;</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="bp">map</span><span class="p">[</span><span class="mi">13276</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">&quot;小法&quot;</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="bp">map</span><span class="p">[</span><span class="mi">10583</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="s">&quot;小鸭&quot;</span>
+<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="cm">/* クエリ操作 */</span>
+<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="c1">// ハッシュ表にキーを入力し、値を取得</span>
+<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="kd">let</span><span class="w"> </span><span class="nv">name</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="bp">map</span><span class="p">[</span><span class="mi">15937</span><span class="p">]</span><span class="o">!</span>
+<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a>
+<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="cm">/* 削除操作 */</span>
+<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="c1">// ハッシュ表からキー値ペア (key, value) を削除</span>
+<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="bp">map</span><span class="p">.</span><span class="n">removeValue</span><span class="p">(</span><span class="n">forKey</span><span class="p">:</span><span class="w"> </span><span class="mi">10583</span><span class="p">)</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* ハッシュ表を初期化 */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">const</span><span class="w"> </span><span class="nx">map</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Map</span><span class="p">();</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="cm">/* 追加操作 */</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="c1">// ハッシュ表にキー値ペア (key, value) を追加</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="nx">map</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="mf">12836</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;小哈&#39;</span><span class="p">);</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="nx">map</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="mf">15937</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;小啰&#39;</span><span class="p">);</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="nx">map</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="mf">16750</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;小算&#39;</span><span class="p">);</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="nx">map</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="mf">13276</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;小法&#39;</span><span class="p">);</span>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="nx">map</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="mf">10583</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;小鸭&#39;</span><span class="p">);</span>
+<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a>
+<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="cm">/* クエリ操作 */</span>
+<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="c1">// ハッシュ表にキーを入力し、値を取得</span>
+<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="kd">let</span><span class="w"> </span><span class="nx">name</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">map</span><span class="p">.</span><span class="nx">get</span><span class="p">(</span><span class="mf">15937</span><span class="p">);</span>
+<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a>
+<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="cm">/* 削除操作 */</span>
+<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a><span class="c1">// ハッシュ表からキー値ペア (key, value) を削除</span>
+<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="nx">map</span><span class="p">.</span><span class="ow">delete</span><span class="p">(</span><span class="mf">10583</span><span class="p">);</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* ハッシュ表を初期化 */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">const</span><span class="w"> </span><span class="nx">map</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nb">Map</span><span class="o">&lt;</span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="kt">string</span><span class="o">&gt;</span><span class="p">();</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="cm">/* 追加操作 */</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="c1">// ハッシュ表にキー値ペア (key, value) を追加</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="nx">map</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="mf">12836</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;小哈&#39;</span><span class="p">);</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="nx">map</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="mf">15937</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;小啰&#39;</span><span class="p">);</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="nx">map</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="mf">16750</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;小算&#39;</span><span class="p">);</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="nx">map</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="mf">13276</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;小法&#39;</span><span class="p">);</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="nx">map</span><span class="p">.</span><span class="nx">set</span><span class="p">(</span><span class="mf">10583</span><span class="p">,</span><span class="w"> </span><span class="s1">&#39;小鸭&#39;</span><span class="p">);</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="s1">&#39;\n追加後、ハッシュ表は\nKey -&gt; Value&#39;</span><span class="p">);</span>
+<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="nx">map</span><span class="p">);</span>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a>
+<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="cm">/* クエリ操作 */</span>
+<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="c1">// ハッシュ表にキーを入力し、値を取得</span>
+<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="kd">let</span><span class="w"> </span><span class="nx">name</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">map</span><span class="p">.</span><span class="nx">get</span><span class="p">(</span><span class="mf">15937</span><span class="p">);</span>
+<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="s1">&#39;\n学籍番号15937を入力、名前を問い合わせ &#39;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">name</span><span class="p">);</span>
+<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a>
+<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="cm">/* 削除操作 */</span>
+<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="c1">// ハッシュ表からキー値ペア (key, value) を削除</span>
+<a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a><span class="nx">map</span><span class="p">.</span><span class="ow">delete</span><span class="p">(</span><span class="mf">10583</span><span class="p">);</span>
+<a id="__codelineno-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></a><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="s1">&#39;\n10583を削除後、ハッシュ表は\nKey -&gt; Value&#39;</span><span class="p">);</span>
+<a id="__codelineno-7-22" name="__codelineno-7-22" href="#__codelineno-7-22"></a><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="nx">map</span><span class="p">);</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* ハッシュ表を初期化 */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="n">Map</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">String</span><span class="o">&gt;</span><span class="w"> </span><span class="n">map</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{};</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="cm">/* 追加操作 */</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="c1">// ハッシュ表にキー値ペア (key, value) を追加</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="n">map</span><span class="p">[</span><span class="m">12836</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s2">&quot;小哈&quot;</span><span class="p">;</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="n">map</span><span class="p">[</span><span class="m">15937</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s2">&quot;小啰&quot;</span><span class="p">;</span>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="n">map</span><span class="p">[</span><span class="m">16750</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s2">&quot;小算&quot;</span><span class="p">;</span>
+<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="n">map</span><span class="p">[</span><span class="m">13276</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s2">&quot;小法&quot;</span><span class="p">;</span>
+<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="n">map</span><span class="p">[</span><span class="m">10583</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="s2">&quot;小鸭&quot;</span><span class="p">;</span>
+<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a>
+<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="cm">/* クエリ操作 */</span>
+<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="c1">// ハッシュ表にキーを入力し、値を取得</span>
+<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="kt">String</span><span class="w"> </span><span class="n">name</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">map</span><span class="p">[</span><span class="m">15937</span><span class="p">];</span>
+<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a>
+<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="cm">/* 削除操作 */</span>
+<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a><span class="c1">// ハッシュ表からキー値ペア (key, value) を削除</span>
+<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a><span class="n">map</span><span class="p">.</span><span class="n">remove</span><span class="p">(</span><span class="m">10583</span><span class="p">);</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="k">use</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">collections</span><span class="p">::</span><span class="n">HashMap</span><span class="p">;</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="cm">/* ハッシュ表を初期化 */</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">map</span><span class="p">:</span><span class="w"> </span><span class="nc">HashMap</span><span class="o">&lt;</span><span class="kt">i32</span><span class="p">,</span><span class="w"> </span><span class="nb">String</span><span class="o">&gt;</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">HashMap</span><span class="p">::</span><span class="n">new</span><span class="p">();</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="cm">/* 追加操作 */</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="c1">// ハッシュ表にキー値ペア (key, value) を追加</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="n">map</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="mi">12836</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;小哈&quot;</span><span class="p">.</span><span class="n">to_string</span><span class="p">());</span>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="n">map</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="mi">15937</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;小啰&quot;</span><span class="p">.</span><span class="n">to_string</span><span class="p">());</span>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="n">map</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="mi">16750</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;小算&quot;</span><span class="p">.</span><span class="n">to_string</span><span class="p">());</span>
+<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="n">map</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="mi">13279</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;小法&quot;</span><span class="p">.</span><span class="n">to_string</span><span class="p">());</span>
+<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="n">map</span><span class="p">.</span><span class="n">insert</span><span class="p">(</span><span class="mi">10583</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;小鸭&quot;</span><span class="p">.</span><span class="n">to_string</span><span class="p">());</span>
+<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a>
+<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="cm">/* クエリ操作 */</span>
+<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="c1">// ハッシュ表にキーを入力し、値を取得</span>
+<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="kd">let</span><span class="w"> </span><span class="n">_name</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;&amp;</span><span class="nb">String</span><span class="o">&gt;</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="n">get</span><span class="p">(</span><span class="o">&amp;</span><span class="mi">15937</span><span class="p">);</span>
+<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a>
+<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="cm">/* 削除操作 */</span>
+<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="c1">// ハッシュ表からキー値ペア (key, value) を削除</span>
+<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="kd">let</span><span class="w"> </span><span class="n">_removed_value</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="nb">String</span><span class="o">&gt;</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="n">remove</span><span class="p">(</span><span class="o">&amp;</span><span class="mi">10583</span><span class="p">);</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="c1">// Cには組み込みのハッシュ表が提供されていません</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map.zig</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>ハッシュ表を走査する一般的な方法は3つあります：キー値ペアの走査、キーの走査、値の走査。以下はコード例です：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:13"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map.py</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="c1"># ハッシュ表を走査</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="c1"># キー値ペア key-&gt;value を走査</span>
+<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="k">for</span> <span class="n">key</span><span class="p">,</span> <span class="n">value</span> <span class="ow">in</span> <span class="n">hmap</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
+<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a>    <span class="nb">print</span><span class="p">(</span><span class="n">key</span><span class="p">,</span> <span class="s2">&quot;-&gt;&quot;</span><span class="p">,</span> <span class="n">value</span><span class="p">)</span>
+<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a><span class="c1"># キーのみを走査</span>
+<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a><span class="k">for</span> <span class="n">key</span> <span class="ow">in</span> <span class="n">hmap</span><span class="o">.</span><span class="n">keys</span><span class="p">():</span>
+<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a>    <span class="nb">print</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a><span class="c1"># 値のみを走査</span>
+<a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a><span class="k">for</span> <span class="n">value</span> <span class="ow">in</span> <span class="n">hmap</span><span class="o">.</span><span class="n">values</span><span class="p">():</span>
+<a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a>    <span class="nb">print</span><span class="p">(</span><span class="n">value</span><span class="p">)</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* ハッシュ表を走査 */</span>
+<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="c1">// キー値ペア key-&gt;value を走査</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="k">auto</span><span class="w"> </span><span class="n">kv</span><span class="o">:</span><span class="w"> </span><span class="n">map</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">kv</span><span class="p">.</span><span class="n">first</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot; -&gt; &quot;</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">kv</span><span class="p">.</span><span class="n">second</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="p">}</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="c1">// イテレータを使用してキー値ペア key-&gt;value を走査</span>
+<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="k">auto</span><span class="w"> </span><span class="n">iter</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="n">begin</span><span class="p">();</span><span class="w"> </span><span class="n">iter</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="n">end</span><span class="p">();</span><span class="w"> </span><span class="n">iter</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w">    </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">iter</span><span class="o">-&gt;</span><span class="n">first</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;-&gt;&quot;</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">iter</span><span class="o">-&gt;</span><span class="n">second</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
+<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* ハッシュ表を走査 */</span>
+<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="c1">// キー値ペア key-&gt;value を走査</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Map</span><span class="p">.</span><span class="na">Entry</span><span class="o">&lt;</span><span class="n">Integer</span><span class="p">,</span><span class="w"> </span><span class="n">String</span><span class="o">&gt;</span><span class="w"> </span><span class="n">kv</span><span class="p">:</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="na">entrySet</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="n">kv</span><span class="p">.</span><span class="na">getKey</span><span class="p">()</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s">&quot; -&gt; &quot;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">kv</span><span class="p">.</span><span class="na">getValue</span><span class="p">());</span>
+<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="p">}</span>
+<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="c1">// キーのみを走査</span>
+<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">:</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="na">keySet</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">    </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="p">}</span>
+<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="c1">// 値のみを走査</span>
+<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">String</span><span class="w"> </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="na">values</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="w">    </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* ハッシュ表を走査 */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="c1">// キー値ペア Key-&gt;Value を走査</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="kt">var</span><span class="w"> </span><span class="n">kv</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">map</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="n">kv</span><span class="p">.</span><span class="n">Key</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s">&quot; -&gt; &quot;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">kv</span><span class="p">.</span><span class="n">Value</span><span class="p">);</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="p">}</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="c1">// キーのみを走査</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="n">Keys</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">    </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="p">}</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="c1">// 値のみを走査</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="k">foreach</span><span class="w"> </span><span class="p">(</span><span class="kt">string</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="n">Values</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="w">    </span><span class="n">Console</span><span class="p">.</span><span class="n">WriteLine</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map_test.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* ハッシュ表を走査 */</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="c1">// キー値ペア key-&gt;value を走査</span>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="k">for</span><span class="w"> </span><span class="nx">key</span><span class="p">,</span><span class="w"> </span><span class="nx">value</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">hmap</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="w">    </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="nx">key</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;-&gt;&quot;</span><span class="p">,</span><span class="w"> </span><span class="nx">value</span><span class="p">)</span>
+<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="p">}</span>
+<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="c1">// キーのみを走査</span>
+<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="k">for</span><span class="w"> </span><span class="nx">key</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">hmap</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="w">    </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="nx">key</span><span class="p">)</span>
+<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="p">}</span>
+<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="c1">// 値のみを走査</span>
+<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="k">for</span><span class="w"> </span><span class="nx">_</span><span class="p">,</span><span class="w"> </span><span class="nx">value</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="k">range</span><span class="w"> </span><span class="nx">hmap</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="w">    </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Println</span><span class="p">(</span><span class="nx">value</span><span class="p">)</span>
+<a id="__codelineno-17-13" name="__codelineno-17-13" href="#__codelineno-17-13"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* ハッシュ表を走査 */</span>
+<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="c1">// キー値ペア Key-&gt;Value を走査</span>
+<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">value</span><span class="p">)</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="bp">map</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="w">    </span><span class="bp">print</span><span class="p">(</span><span class="s">&quot;</span><span class="si">\(</span><span class="n">key</span><span class="si">)</span><span class="s"> -&gt; </span><span class="si">\(</span><span class="n">value</span><span class="si">)</span><span class="s">&quot;</span><span class="p">)</span>
+<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="p">}</span>
+<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="c1">// キーのみを走査</span>
+<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="k">for</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="bp">map</span><span class="p">.</span><span class="n">keys</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="w">    </span><span class="bp">print</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="p">}</span>
+<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a><span class="c1">// 値のみを走査</span>
+<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="k">for</span><span class="w"> </span><span class="n">value</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="bp">map</span><span class="p">.</span><span class="n">values</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a><span class="w">    </span><span class="bp">print</span><span class="p">(</span><span class="n">value</span><span class="p">)</span>
+<a id="__codelineno-18-13" name="__codelineno-18-13" href="#__codelineno-18-13"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="cm">/* ハッシュ表を走査 */</span>
+<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="s1">&#39;\nキー値ペア Key-&gt;Value を走査&#39;</span><span class="p">);</span>
+<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="p">[</span><span class="nx">k</span><span class="p">,</span><span class="w"> </span><span class="nx">v</span><span class="p">]</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">map</span><span class="p">.</span><span class="nx">entries</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="w">    </span><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="nx">k</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s1">&#39; -&gt; &#39;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">v</span><span class="p">);</span>
+<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="p">}</span>
+<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="s1">&#39;\nキーのみを走査 Key&#39;</span><span class="p">);</span>
+<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">k</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">map</span><span class="p">.</span><span class="nx">keys</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a><span class="w">    </span><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="nx">k</span><span class="p">);</span>
+<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a><span class="p">}</span>
+<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="s1">&#39;\n値のみを走査 Value&#39;</span><span class="p">);</span>
+<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">v</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">map</span><span class="p">.</span><span class="nx">values</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-19-12" name="__codelineno-19-12" href="#__codelineno-19-12"></a><span class="w">    </span><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="nx">v</span><span class="p">);</span>
+<a id="__codelineno-19-13" name="__codelineno-19-13" href="#__codelineno-19-13"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* ハッシュ表を走査 */</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="s1">&#39;\nキー値ペア Key-&gt;Value を走査&#39;</span><span class="p">);</span>
+<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="p">[</span><span class="nx">k</span><span class="p">,</span><span class="w"> </span><span class="nx">v</span><span class="p">]</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">map</span><span class="p">.</span><span class="nx">entries</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="w">    </span><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="nx">k</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s1">&#39; -&gt; &#39;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="nx">v</span><span class="p">);</span>
+<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="p">}</span>
+<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="s1">&#39;\nキーのみを走査 Key&#39;</span><span class="p">);</span>
+<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">k</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">map</span><span class="p">.</span><span class="nx">keys</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="w">    </span><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="nx">k</span><span class="p">);</span>
+<a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a><span class="p">}</span>
+<a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="s1">&#39;\n値のみを走査 Value&#39;</span><span class="p">);</span>
+<a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kd">const</span><span class="w"> </span><span class="nx">v</span><span class="w"> </span><span class="k">of</span><span class="w"> </span><span class="nx">map</span><span class="p">.</span><span class="nx">values</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a><span class="w">    </span><span class="nx">console</span><span class="p">.</span><span class="nx">info</span><span class="p">(</span><span class="nx">v</span><span class="p">);</span>
+<a id="__codelineno-20-13" name="__codelineno-20-13" href="#__codelineno-20-13"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* ハッシュ表を走査 */</span>
+<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="c1">// キー値ペア Key-&gt;Value を走査</span>
+<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="n">map</span><span class="p">.</span><span class="n">forEach</span><span class="p">((</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">value</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="n">print</span><span class="p">(</span><span class="s1">&#39;</span><span class="si">$</span><span class="n">key</span><span class="s1"> -&gt; </span><span class="si">$</span><span class="n">value</span><span class="s1">&#39;</span><span class="p">);</span>
+<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="p">});</span>
+<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a>
+<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="c1">// キーのみを走査 Key</span>
+<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="n">map</span><span class="p">.</span><span class="n">keys</span><span class="p">.</span><span class="n">forEach</span><span class="p">((</span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a><span class="n">print</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a><span class="p">});</span>
+<a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a>
+<a id="__codelineno-21-12" name="__codelineno-21-12" href="#__codelineno-21-12"></a><span class="c1">// 値のみを走査 Value</span>
+<a id="__codelineno-21-13" name="__codelineno-21-13" href="#__codelineno-21-13"></a><span class="n">map</span><span class="p">.</span><span class="n">values</span><span class="p">.</span><span class="n">forEach</span><span class="p">((</span><span class="n">value</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-21-14" name="__codelineno-21-14" href="#__codelineno-21-14"></a><span class="n">print</span><span class="p">(</span><span class="n">value</span><span class="p">);</span>
+<a id="__codelineno-21-15" name="__codelineno-21-15" href="#__codelineno-21-15"></a><span class="p">});</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="cm">/* ハッシュ表を走査 */</span>
+<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="c1">// キー値ペア Key-&gt;Value を走査</span>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">value</span><span class="p">)</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="o">&amp;</span><span class="n">map</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="w">    </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;{key} -&gt; {value}&quot;</span><span class="p">);</span>
+<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="p">}</span>
+<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a>
+<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="c1">// キーのみを走査 Key</span>
+<a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a><span class="k">for</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="n">keys</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a><span class="w">    </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;{key}&quot;</span><span class="p">);</span>
+<a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a><span class="p">}</span>
+<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a>
+<a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="c1">// 値のみを走査 Value</span>
+<a id="__codelineno-22-13" name="__codelineno-22-13" href="#__codelineno-22-13"></a><span class="k">for</span><span class="w"> </span><span class="n">value</span><span class="w"> </span><span class="k">in</span><span class="w"> </span><span class="n">map</span><span class="p">.</span><span class="n">values</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-22-14" name="__codelineno-22-14" href="#__codelineno-22-14"></a><span class="w">    </span><span class="fm">println!</span><span class="p">(</span><span class="s">&quot;{value}&quot;</span><span class="p">);</span>
+<a id="__codelineno-22-15" name="__codelineno-22-15" href="#__codelineno-22-15"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="c1">// Cには組み込みのハッシュ表が提供されていません</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">hash_map.zig</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="c1">// Zigの例は提供されていません</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h2 id="612">6.1.2 &nbsp; ハッシュ表の簡単な実装<a class="headerlink" href="#612" title="Permanent link">&para;</a></h2>
+<p>まず、最も簡単なケースを考えてみましょう：<strong>配列のみを使ってハッシュ表を実装すること</strong>。ハッシュ表において、配列の各空きスロットは<u>バケット</u>と呼ばれ、各バケットはキー値ペアを格納できます。したがって、クエリ操作は<code>key</code>に対応するバケットを見つけ、そこから<code>value</code>を取得することになります。</p>
+<p>では、<code>key</code>に基づいて対応するバケットをどのように特定するのでしょうか？これは<u>ハッシュ関数</u>によって実現されます。ハッシュ関数の役割は、より大きな入力空間をより小さな出力空間にマッピングすることです。ハッシュ表では、入力空間はすべてのキーで構成され、出力空間はすべてのバケット（配列インデックス）で構成されます。つまり、<code>key</code>が与えられた場合、<strong>ハッシュ関数を使用して対応するキー値ペアの配列内の格納位置を決定できます</strong>。</p>
+<p>与えられた<code>key</code>に対して、ハッシュ関数の計算は2つのステップで構成されます：</p>
+<ol>
+<li>特定のハッシュアルゴリズム<code>hash()</code>を使用してハッシュ値を計算します。</li>
+<li>ハッシュ値をバケット数（配列長）<code>capacity</code>で剰余を取り、キーに対応する配列<code>index</code>を取得します。</li>
+</ol>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="nv">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span>hash<span class="o">(</span>key<span class="o">)</span><span class="w"> </span>%<span class="w"> </span>capacity
+</code></pre></div>
+<p>その後、<code>index</code>を使用してハッシュ表内の対応するバケットにアクセスし、<code>value</code>を取得できます。</p>
+<p>配列長が<code>capacity = 100</code>で、ハッシュアルゴリズムが<code>hash(key) = key</code>として定義されているとします。したがって、ハッシュ関数は<code>key % 100</code>として表現できます。以下の図は、<code>key</code>を学籍番号、<code>value</code>を名前として、ハッシュ関数の動作原理を示しています。</p>
+<p><a class="glightbox" href="../hash_map.assets/hash_function.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="ハッシュ関数の動作原理" class="animation-figure" src="../hash_map.assets/hash_function.png" /></a></p>
+<p align="center"> 図 6-2 &nbsp; ハッシュ関数の動作原理 </p>
+
+<p>以下のコードは簡単なハッシュ表を実装しています。ここでは、<code>key</code>と<code>value</code>を<code>Pair</code>クラスにカプセル化してキー値ペアを表現しています。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="3:14"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><input id="__tabbed_3_14" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label><label for="__tabbed_3_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_hash_map.py</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">Pair</span><span class="p">:</span>
+<a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;キー値ペア&quot;&quot;&quot;</span>
+<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a>
+<a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">str</span><span class="p">):</span>
+<a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">key</span> <span class="o">=</span> <span class="n">key</span>
+<a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">val</span> <span class="o">=</span> <span class="n">val</span>
+<a id="__codelineno-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a>
+<a id="__codelineno-27-8" name="__codelineno-27-8" href="#__codelineno-27-8"></a><span class="k">class</span><span class="w"> </span><span class="nc">ArrayHashMap</span><span class="p">:</span>
+<a id="__codelineno-27-9" name="__codelineno-27-9" href="#__codelineno-27-9"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;配列実装に基づくハッシュテーブル&quot;&quot;&quot;</span>
+<a id="__codelineno-27-10" name="__codelineno-27-10" href="#__codelineno-27-10"></a>
+<a id="__codelineno-27-11" name="__codelineno-27-11" href="#__codelineno-27-11"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<a id="__codelineno-27-12" name="__codelineno-27-12" href="#__codelineno-27-12"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;コンストラクタ&quot;&quot;&quot;</span>
+<a id="__codelineno-27-13" name="__codelineno-27-13" href="#__codelineno-27-13"></a>        <span class="c1"># 100個のバケットを含む配列を初期化</span>
+<a id="__codelineno-27-14" name="__codelineno-27-14" href="#__codelineno-27-14"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">Pair</span> <span class="o">|</span> <span class="kc">None</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="kc">None</span><span class="p">]</span> <span class="o">*</span> <span class="mi">100</span>
+<a id="__codelineno-27-15" name="__codelineno-27-15" href="#__codelineno-27-15"></a>
+<a id="__codelineno-27-16" name="__codelineno-27-16" href="#__codelineno-27-16"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">hash_func</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-27-17" name="__codelineno-27-17" href="#__codelineno-27-17"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;ハッシュ関数&quot;&quot;&quot;</span>
+<a id="__codelineno-27-18" name="__codelineno-27-18" href="#__codelineno-27-18"></a>        <span class="n">index</span> <span class="o">=</span> <span class="n">key</span> <span class="o">%</span> <span class="mi">100</span>
+<a id="__codelineno-27-19" name="__codelineno-27-19" href="#__codelineno-27-19"></a>        <span class="k">return</span> <span class="n">index</span>
+<a id="__codelineno-27-20" name="__codelineno-27-20" href="#__codelineno-27-20"></a>
+<a id="__codelineno-27-21" name="__codelineno-27-21" href="#__codelineno-27-21"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">get</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">str</span><span class="p">:</span>
+<a id="__codelineno-27-22" name="__codelineno-27-22" href="#__codelineno-27-22"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;照会操作&quot;&quot;&quot;</span>
+<a id="__codelineno-27-23" name="__codelineno-27-23" href="#__codelineno-27-23"></a>        <span class="n">index</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">hash_func</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-27-24" name="__codelineno-27-24" href="#__codelineno-27-24"></a>        <span class="n">pair</span><span class="p">:</span> <span class="n">Pair</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span>
+<a id="__codelineno-27-25" name="__codelineno-27-25" href="#__codelineno-27-25"></a>        <span class="k">if</span> <span class="n">pair</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-27-26" name="__codelineno-27-26" href="#__codelineno-27-26"></a>            <span class="k">return</span> <span class="kc">None</span>
+<a id="__codelineno-27-27" name="__codelineno-27-27" href="#__codelineno-27-27"></a>        <span class="k">return</span> <span class="n">pair</span><span class="o">.</span><span class="n">val</span>
+<a id="__codelineno-27-28" name="__codelineno-27-28" href="#__codelineno-27-28"></a>
+<a id="__codelineno-27-29" name="__codelineno-27-29" href="#__codelineno-27-29"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">put</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">str</span><span class="p">):</span>
+<a id="__codelineno-27-30" name="__codelineno-27-30" href="#__codelineno-27-30"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;追加操作&quot;&quot;&quot;</span>
+<a id="__codelineno-27-31" name="__codelineno-27-31" href="#__codelineno-27-31"></a>        <span class="n">pair</span> <span class="o">=</span> <span class="n">Pair</span><span class="p">(</span><span class="n">key</span><span class="p">,</span> <span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-27-32" name="__codelineno-27-32" href="#__codelineno-27-32"></a>        <span class="n">index</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">hash_func</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-27-33" name="__codelineno-27-33" href="#__codelineno-27-33"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">=</span> <span class="n">pair</span>
+<a id="__codelineno-27-34" name="__codelineno-27-34" href="#__codelineno-27-34"></a>
+<a id="__codelineno-27-35" name="__codelineno-27-35" href="#__codelineno-27-35"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">key</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-27-36" name="__codelineno-27-36" href="#__codelineno-27-36"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;削除操作&quot;&quot;&quot;</span>
+<a id="__codelineno-27-37" name="__codelineno-27-37" href="#__codelineno-27-37"></a>        <span class="n">index</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">hash_func</span><span class="p">(</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-27-38" name="__codelineno-27-38" href="#__codelineno-27-38"></a>        <span class="c1"># None に設定し、削除を表現</span>
+<a id="__codelineno-27-39" name="__codelineno-27-39" href="#__codelineno-27-39"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span> <span class="o">=</span> <span class="kc">None</span>
+<a id="__codelineno-27-40" name="__codelineno-27-40" href="#__codelineno-27-40"></a>
+<a id="__codelineno-27-41" name="__codelineno-27-41" href="#__codelineno-27-41"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">entry_set</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="n">Pair</span><span class="p">]:</span>
+<a id="__codelineno-27-42" name="__codelineno-27-42" href="#__codelineno-27-42"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;すべてのキー値ペアを取得&quot;&quot;&quot;</span>
+<a id="__codelineno-27-43" name="__codelineno-27-43" href="#__codelineno-27-43"></a>        <span class="n">result</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="n">Pair</span><span class="p">]</span> <span class="o">=</span> <span class="p">[]</span>
+<a id="__codelineno-27-44" name="__codelineno-27-44" href="#__codelineno-27-44"></a>        <span class="k">for</span> <span class="n">pair</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">:</span>
+<a id="__codelineno-27-45" name="__codelineno-27-45" href="#__codelineno-27-45"></a>            <span class="k">if</span> <span class="n">pair</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-27-46" name="__codelineno-27-46" href="#__codelineno-27-46"></a>                <span class="n">result</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">pair</span><span class="p">)</span>
+<a id="__codelineno-27-47" name="__codelineno-27-47" href="#__codelineno-27-47"></a>        <span class="k">return</span> <span class="n">result</span>
+<a id="__codelineno-27-48" name="__codelineno-27-48" href="#__codelineno-27-48"></a>
+<a id="__codelineno-27-49" name="__codelineno-27-49" href="#__codelineno-27-49"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">key_set</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
+<a id="__codelineno-27-50" name="__codelineno-27-50" href="#__codelineno-27-50"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;すべてのキーを取得&quot;&quot;&quot;</span>
+<a id="__codelineno-27-51" name="__codelineno-27-51" href="#__codelineno-27-51"></a>        <span class="n">result</span> <span class="o">=</span> <span class="p">[]</span>
+<a id="__codelineno-27-52" name="__codelineno-27-52" href="#__codelineno-27-52"></a>        <span class="k">for</span> <span class="n">pair</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">:</span>
+<a id="__codelineno-27-53" name="__codelineno-27-53" href="#__codelineno-27-53"></a>            <span class="k">if</span> <span class="n">pair</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-27-54" name="__codelineno-27-54" href="#__codelineno-27-54"></a>                <span class="n">result</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">pair</span><span class="o">.</span><span class="n">key</span><span class="p">)</span>
+<a id="__codelineno-27-55" name="__codelineno-27-55" href="#__codelineno-27-55"></a>        <span class="k">return</span> <span class="n">result</span>
+<a id="__codelineno-27-56" name="__codelineno-27-56" href="#__codelineno-27-56"></a>
+<a id="__codelineno-27-57" name="__codelineno-27-57" href="#__codelineno-27-57"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">value_set</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">str</span><span class="p">]:</span>
+<a id="__codelineno-27-58" name="__codelineno-27-58" href="#__codelineno-27-58"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;すべての値を取得&quot;&quot;&quot;</span>
+<a id="__codelineno-27-59" name="__codelineno-27-59" href="#__codelineno-27-59"></a>        <span class="n">result</span> <span class="o">=</span> <span class="p">[]</span>
+<a id="__codelineno-27-60" name="__codelineno-27-60" href="#__codelineno-27-60"></a>        <span class="k">for</span> <span class="n">pair</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">:</span>
+<a id="__codelineno-27-61" name="__codelineno-27-61" href="#__codelineno-27-61"></a>            <span class="k">if</span> <span class="n">pair</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-27-62" name="__codelineno-27-62" href="#__codelineno-27-62"></a>                <span class="n">result</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">pair</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-27-63" name="__codelineno-27-63" href="#__codelineno-27-63"></a>        <span class="k">return</span> <span class="n">result</span>
+<a id="__codelineno-27-64" name="__codelineno-27-64" href="#__codelineno-27-64"></a>
+<a id="__codelineno-27-65" name="__codelineno-27-65" href="#__codelineno-27-65"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">print</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<a id="__codelineno-27-66" name="__codelineno-27-66" href="#__codelineno-27-66"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;ハッシュテーブルを出力&quot;&quot;&quot;</span>
+<a id="__codelineno-27-67" name="__codelineno-27-67" href="#__codelineno-27-67"></a>        <span class="k">for</span> <span class="n">pair</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">buckets</span><span class="p">:</span>
+<a id="__codelineno-27-68" name="__codelineno-27-68" href="#__codelineno-27-68"></a>            <span class="k">if</span> <span class="n">pair</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-27-69" name="__codelineno-27-69" href="#__codelineno-27-69"></a>                <span class="nb">print</span><span class="p">(</span><span class="n">pair</span><span class="o">.</span><span class="n">key</span><span class="p">,</span> <span class="s2">&quot;-&gt;&quot;</span><span class="p">,</span> <span class="n">pair</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_hash_map.cpp</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="cm">/* キー値ペア */</span>
+<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="k">struct</span><span class="w"> </span><span class="nc">Pair</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a><span class="w">  </span><span class="k">public</span><span class="o">:</span>
+<a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">;</span>
+<a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a><span class="w">    </span><span class="n">string</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a><span class="w">    </span><span class="n">Pair</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">string</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a><span class="w">        </span><span class="k">this</span><span class="o">-&gt;</span><span class="n">key</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">key</span><span class="p">;</span>
+<a id="__codelineno-28-8" name="__codelineno-28-8" href="#__codelineno-28-8"></a><span class="w">        </span><span class="k">this</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-28-9" name="__codelineno-28-9" href="#__codelineno-28-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-10" name="__codelineno-28-10" href="#__codelineno-28-10"></a><span class="p">};</span>
+<a id="__codelineno-28-11" name="__codelineno-28-11" href="#__codelineno-28-11"></a>
+<a id="__codelineno-28-12" name="__codelineno-28-12" href="#__codelineno-28-12"></a><span class="cm">/* 配列実装に基づくハッシュテーブル */</span>
+<a id="__codelineno-28-13" name="__codelineno-28-13" href="#__codelineno-28-13"></a><span class="k">class</span><span class="w"> </span><span class="nc">ArrayHashMap</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-14" name="__codelineno-28-14" href="#__codelineno-28-14"></a><span class="w">  </span><span class="k">private</span><span class="o">:</span>
+<a id="__codelineno-28-15" name="__codelineno-28-15" href="#__codelineno-28-15"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">Pair</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="n">buckets</span><span class="p">;</span>
+<a id="__codelineno-28-16" name="__codelineno-28-16" href="#__codelineno-28-16"></a>
+<a id="__codelineno-28-17" name="__codelineno-28-17" href="#__codelineno-28-17"></a><span class="w">  </span><span class="k">public</span><span class="o">:</span>
+<a id="__codelineno-28-18" name="__codelineno-28-18" href="#__codelineno-28-18"></a><span class="w">    </span><span class="n">ArrayHashMap</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-19" name="__codelineno-28-19" href="#__codelineno-28-19"></a><span class="w">        </span><span class="c1">// 配列を初期化、100個のバケットを含む</span>
+<a id="__codelineno-28-20" name="__codelineno-28-20" href="#__codelineno-28-20"></a><span class="w">        </span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">Pair</span><span class="w"> </span><span class="o">*&gt;</span><span class="p">(</span><span class="mi">100</span><span class="p">);</span>
+<a id="__codelineno-28-21" name="__codelineno-28-21" href="#__codelineno-28-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-22" name="__codelineno-28-22" href="#__codelineno-28-22"></a>
+<a id="__codelineno-28-23" name="__codelineno-28-23" href="#__codelineno-28-23"></a><span class="w">    </span><span class="o">~</span><span class="n">ArrayHashMap</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-24" name="__codelineno-28-24" href="#__codelineno-28-24"></a><span class="w">        </span><span class="c1">// メモリを解放</span>
+<a id="__codelineno-28-25" name="__codelineno-28-25" href="#__codelineno-28-25"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="k">const</span><span class="w"> </span><span class="k">auto</span><span class="w"> </span><span class="o">&amp;</span><span class="n">bucket</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-26" name="__codelineno-28-26" href="#__codelineno-28-26"></a><span class="w">            </span><span class="k">delete</span><span class="w"> </span><span class="n">bucket</span><span class="p">;</span>
+<a id="__codelineno-28-27" name="__codelineno-28-27" href="#__codelineno-28-27"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-28-28" name="__codelineno-28-28" href="#__codelineno-28-28"></a><span class="w">        </span><span class="n">buckets</span><span class="p">.</span><span class="n">clear</span><span class="p">();</span>
+<a id="__codelineno-28-29" name="__codelineno-28-29" href="#__codelineno-28-29"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-30" name="__codelineno-28-30" href="#__codelineno-28-30"></a>
+<a id="__codelineno-28-31" name="__codelineno-28-31" href="#__codelineno-28-31"></a><span class="w">    </span><span class="cm">/* ハッシュ関数 */</span>
+<a id="__codelineno-28-32" name="__codelineno-28-32" href="#__codelineno-28-32"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-33" name="__codelineno-28-33" href="#__codelineno-28-33"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mi">100</span><span class="p">;</span>
+<a id="__codelineno-28-34" name="__codelineno-28-34" href="#__codelineno-28-34"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">index</span><span class="p">;</span>
+<a id="__codelineno-28-35" name="__codelineno-28-35" href="#__codelineno-28-35"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-36" name="__codelineno-28-36" href="#__codelineno-28-36"></a>
+<a id="__codelineno-28-37" name="__codelineno-28-37" href="#__codelineno-28-37"></a><span class="w">    </span><span class="cm">/* クエリ操作 */</span>
+<a id="__codelineno-28-38" name="__codelineno-28-38" href="#__codelineno-28-38"></a><span class="w">    </span><span class="n">string</span><span class="w"> </span><span class="n">get</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-39" name="__codelineno-28-39" href="#__codelineno-28-39"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-28-40" name="__codelineno-28-40" href="#__codelineno-28-40"></a><span class="w">        </span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">pair</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
+<a id="__codelineno-28-41" name="__codelineno-28-41" href="#__codelineno-28-41"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span>
+<a id="__codelineno-28-42" name="__codelineno-28-42" href="#__codelineno-28-42"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="s">&quot;&quot;</span><span class="p">;</span>
+<a id="__codelineno-28-43" name="__codelineno-28-43" href="#__codelineno-28-43"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-28-44" name="__codelineno-28-44" href="#__codelineno-28-44"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-45" name="__codelineno-28-45" href="#__codelineno-28-45"></a>
+<a id="__codelineno-28-46" name="__codelineno-28-46" href="#__codelineno-28-46"></a><span class="w">    </span><span class="cm">/* 追加操作 */</span>
+<a id="__codelineno-28-47" name="__codelineno-28-47" href="#__codelineno-28-47"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">put</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">string</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-48" name="__codelineno-28-48" href="#__codelineno-28-48"></a><span class="w">        </span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">pair</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Pair</span><span class="p">(</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-28-49" name="__codelineno-28-49" href="#__codelineno-28-49"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-28-50" name="__codelineno-28-50" href="#__codelineno-28-50"></a><span class="w">        </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">pair</span><span class="p">;</span>
+<a id="__codelineno-28-51" name="__codelineno-28-51" href="#__codelineno-28-51"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-52" name="__codelineno-28-52" href="#__codelineno-28-52"></a>
+<a id="__codelineno-28-53" name="__codelineno-28-53" href="#__codelineno-28-53"></a><span class="w">    </span><span class="cm">/* 削除操作 */</span>
+<a id="__codelineno-28-54" name="__codelineno-28-54" href="#__codelineno-28-54"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-55" name="__codelineno-28-55" href="#__codelineno-28-55"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-28-56" name="__codelineno-28-56" href="#__codelineno-28-56"></a><span class="w">        </span><span class="c1">// メモリを解放してnullptrに設定</span>
+<a id="__codelineno-28-57" name="__codelineno-28-57" href="#__codelineno-28-57"></a><span class="w">        </span><span class="k">delete</span><span class="w"> </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">];</span>
+<a id="__codelineno-28-58" name="__codelineno-28-58" href="#__codelineno-28-58"></a><span class="w">        </span><span class="n">buckets</span><span class="p">[</span><span class="n">index</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">;</span>
+<a id="__codelineno-28-59" name="__codelineno-28-59" href="#__codelineno-28-59"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-60" name="__codelineno-28-60" href="#__codelineno-28-60"></a>
+<a id="__codelineno-28-61" name="__codelineno-28-61" href="#__codelineno-28-61"></a><span class="w">    </span><span class="cm">/* すべてのキー値ペアを取得 */</span>
+<a id="__codelineno-28-62" name="__codelineno-28-62" href="#__codelineno-28-62"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">Pair</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="n">pairSet</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-63" name="__codelineno-28-63" href="#__codelineno-28-63"></a><span class="w">        </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">Pair</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="n">pairSet</span><span class="p">;</span>
+<a id="__codelineno-28-64" name="__codelineno-28-64" href="#__codelineno-28-64"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">pair</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-65" name="__codelineno-28-65" href="#__codelineno-28-65"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-66" name="__codelineno-28-66" href="#__codelineno-28-66"></a><span class="w">                </span><span class="n">pairSet</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">pair</span><span class="p">);</span>
+<a id="__codelineno-28-67" name="__codelineno-28-67" href="#__codelineno-28-67"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-28-68" name="__codelineno-28-68" href="#__codelineno-28-68"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-28-69" name="__codelineno-28-69" href="#__codelineno-28-69"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">pairSet</span><span class="p">;</span>
+<a id="__codelineno-28-70" name="__codelineno-28-70" href="#__codelineno-28-70"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-71" name="__codelineno-28-71" href="#__codelineno-28-71"></a>
+<a id="__codelineno-28-72" name="__codelineno-28-72" href="#__codelineno-28-72"></a><span class="w">    </span><span class="cm">/* すべてのキーを取得 */</span>
+<a id="__codelineno-28-73" name="__codelineno-28-73" href="#__codelineno-28-73"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">keySet</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-74" name="__codelineno-28-74" href="#__codelineno-28-74"></a><span class="w">        </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">keySet</span><span class="p">;</span>
+<a id="__codelineno-28-75" name="__codelineno-28-75" href="#__codelineno-28-75"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">pair</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-76" name="__codelineno-28-76" href="#__codelineno-28-76"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-77" name="__codelineno-28-77" href="#__codelineno-28-77"></a><span class="w">                </span><span class="n">keySet</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-28-78" name="__codelineno-28-78" href="#__codelineno-28-78"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-28-79" name="__codelineno-28-79" href="#__codelineno-28-79"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-28-80" name="__codelineno-28-80" href="#__codelineno-28-80"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">keySet</span><span class="p">;</span>
+<a id="__codelineno-28-81" name="__codelineno-28-81" href="#__codelineno-28-81"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-82" name="__codelineno-28-82" href="#__codelineno-28-82"></a>
+<a id="__codelineno-28-83" name="__codelineno-28-83" href="#__codelineno-28-83"></a><span class="w">    </span><span class="cm">/* すべての値を取得 */</span>
+<a id="__codelineno-28-84" name="__codelineno-28-84" href="#__codelineno-28-84"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">string</span><span class="o">&gt;</span><span class="w"> </span><span class="n">valueSet</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-85" name="__codelineno-28-85" href="#__codelineno-28-85"></a><span class="w">        </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">string</span><span class="o">&gt;</span><span class="w"> </span><span class="n">valueSet</span><span class="p">;</span>
+<a id="__codelineno-28-86" name="__codelineno-28-86" href="#__codelineno-28-86"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">pair</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-87" name="__codelineno-28-87" href="#__codelineno-28-87"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-88" name="__codelineno-28-88" href="#__codelineno-28-88"></a><span class="w">                </span><span class="n">valueSet</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">pair</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-28-89" name="__codelineno-28-89" href="#__codelineno-28-89"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-28-90" name="__codelineno-28-90" href="#__codelineno-28-90"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-28-91" name="__codelineno-28-91" href="#__codelineno-28-91"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">valueSet</span><span class="p">;</span>
+<a id="__codelineno-28-92" name="__codelineno-28-92" href="#__codelineno-28-92"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-93" name="__codelineno-28-93" href="#__codelineno-28-93"></a>
+<a id="__codelineno-28-94" name="__codelineno-28-94" href="#__codelineno-28-94"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを印刷 */</span>
+<a id="__codelineno-28-95" name="__codelineno-28-95" href="#__codelineno-28-95"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-96" name="__codelineno-28-96" href="#__codelineno-28-96"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="o">*</span><span class="n">kv</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">pairSet</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-97" name="__codelineno-28-97" href="#__codelineno-28-97"></a><span class="w">            </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">kv</span><span class="o">-&gt;</span><span class="n">key</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot; -&gt; &quot;</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">kv</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
+<a id="__codelineno-28-98" name="__codelineno-28-98" href="#__codelineno-28-98"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-28-99" name="__codelineno-28-99" href="#__codelineno-28-99"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-100" name="__codelineno-28-100" href="#__codelineno-28-100"></a><span class="p">};</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_hash_map.java</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="cm">/* キー値ペア */</span>
+<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="kd">class</span> <span class="nc">Pair</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">;</span>
+<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="n">String</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a>
+<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="nf">Pair</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">String</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="na">key</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">key</span><span class="p">;</span>
+<a id="__codelineno-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-29-9" name="__codelineno-29-9" href="#__codelineno-29-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-10" name="__codelineno-29-10" href="#__codelineno-29-10"></a><span class="p">}</span>
+<a id="__codelineno-29-11" name="__codelineno-29-11" href="#__codelineno-29-11"></a>
+<a id="__codelineno-29-12" name="__codelineno-29-12" href="#__codelineno-29-12"></a><span class="cm">/* 配列実装に基づくハッシュテーブル */</span>
+<a id="__codelineno-29-13" name="__codelineno-29-13" href="#__codelineno-29-13"></a><span class="kd">class</span> <span class="nc">ArrayHashMap</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-14" name="__codelineno-29-14" href="#__codelineno-29-14"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;</span><span class="w"> </span><span class="n">buckets</span><span class="p">;</span>
+<a id="__codelineno-29-15" name="__codelineno-29-15" href="#__codelineno-29-15"></a>
+<a id="__codelineno-29-16" name="__codelineno-29-16" href="#__codelineno-29-16"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="nf">ArrayHashMap</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-17" name="__codelineno-29-17" href="#__codelineno-29-17"></a><span class="w">        </span><span class="c1">// 100個のバケットを含む配列を初期化</span>
+<a id="__codelineno-29-18" name="__codelineno-29-18" href="#__codelineno-29-18"></a><span class="w">        </span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-29-19" name="__codelineno-29-19" href="#__codelineno-29-19"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">100</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-20" name="__codelineno-29-20" href="#__codelineno-29-20"></a><span class="w">            </span><span class="n">buckets</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="kc">null</span><span class="p">);</span>
+<a id="__codelineno-29-21" name="__codelineno-29-21" href="#__codelineno-29-21"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-29-22" name="__codelineno-29-22" href="#__codelineno-29-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-23" name="__codelineno-29-23" href="#__codelineno-29-23"></a>
+<a id="__codelineno-29-24" name="__codelineno-29-24" href="#__codelineno-29-24"></a><span class="w">    </span><span class="cm">/* ハッシュ関数 */</span>
+<a id="__codelineno-29-25" name="__codelineno-29-25" href="#__codelineno-29-25"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">hashFunc</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-26" name="__codelineno-29-26" href="#__codelineno-29-26"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">key</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mi">100</span><span class="p">;</span>
+<a id="__codelineno-29-27" name="__codelineno-29-27" href="#__codelineno-29-27"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">index</span><span class="p">;</span>
+<a id="__codelineno-29-28" name="__codelineno-29-28" href="#__codelineno-29-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-29" name="__codelineno-29-29" href="#__codelineno-29-29"></a>
+<a id="__codelineno-29-30" name="__codelineno-29-30" href="#__codelineno-29-30"></a><span class="w">    </span><span class="cm">/* クエリ操作 */</span>
+<a id="__codelineno-29-31" name="__codelineno-29-31" href="#__codelineno-29-31"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="n">String</span><span class="w"> </span><span class="nf">get</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-32" name="__codelineno-29-32" href="#__codelineno-29-32"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-29-33" name="__codelineno-29-33" href="#__codelineno-29-33"></a><span class="w">        </span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">buckets</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">index</span><span class="p">);</span>
+<a id="__codelineno-29-34" name="__codelineno-29-34" href="#__codelineno-29-34"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
+<a id="__codelineno-29-35" name="__codelineno-29-35" href="#__codelineno-29-35"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-29-36" name="__codelineno-29-36" href="#__codelineno-29-36"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">pair</span><span class="p">.</span><span class="na">val</span><span class="p">;</span>
+<a id="__codelineno-29-37" name="__codelineno-29-37" href="#__codelineno-29-37"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-38" name="__codelineno-29-38" href="#__codelineno-29-38"></a>
+<a id="__codelineno-29-39" name="__codelineno-29-39" href="#__codelineno-29-39"></a><span class="w">    </span><span class="cm">/* 追加操作 */</span>
+<a id="__codelineno-29-40" name="__codelineno-29-40" href="#__codelineno-29-40"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">put</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">String</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-41" name="__codelineno-29-41" href="#__codelineno-29-41"></a><span class="w">        </span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Pair</span><span class="p">(</span><span class="n">key</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-29-42" name="__codelineno-29-42" href="#__codelineno-29-42"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-29-43" name="__codelineno-29-43" href="#__codelineno-29-43"></a><span class="w">        </span><span class="n">buckets</span><span class="p">.</span><span class="na">set</span><span class="p">(</span><span class="n">index</span><span class="p">,</span><span class="w"> </span><span class="n">pair</span><span class="p">);</span>
+<a id="__codelineno-29-44" name="__codelineno-29-44" href="#__codelineno-29-44"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-45" name="__codelineno-29-45" href="#__codelineno-29-45"></a>
+<a id="__codelineno-29-46" name="__codelineno-29-46" href="#__codelineno-29-46"></a><span class="w">    </span><span class="cm">/* 削除操作 */</span>
+<a id="__codelineno-29-47" name="__codelineno-29-47" href="#__codelineno-29-47"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">key</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-48" name="__codelineno-29-48" href="#__codelineno-29-48"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">hashFunc</span><span class="p">(</span><span class="n">key</span><span class="p">);</span>
+<a id="__codelineno-29-49" name="__codelineno-29-49" href="#__codelineno-29-49"></a><span class="w">        </span><span class="c1">// nullに設定して削除を示す</span>
+<a id="__codelineno-29-50" name="__codelineno-29-50" href="#__codelineno-29-50"></a><span class="w">        </span><span class="n">buckets</span><span class="p">.</span><span class="na">set</span><span class="p">(</span><span class="n">index</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">);</span>
+<a id="__codelineno-29-51" name="__codelineno-29-51" href="#__codelineno-29-51"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-52" name="__codelineno-29-52" href="#__codelineno-29-52"></a>
+<a id="__codelineno-29-53" name="__codelineno-29-53" href="#__codelineno-29-53"></a><span class="w">    </span><span class="cm">/* すべてのキー値ペアを取得 */</span>
+<a id="__codelineno-29-54" name="__codelineno-29-54" href="#__codelineno-29-54"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;</span><span class="w"> </span><span class="nf">pairSet</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-55" name="__codelineno-29-55" href="#__codelineno-29-55"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Pair</span><span class="o">&gt;</span><span class="w"> </span><span class="n">pairSet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-29-56" name="__codelineno-29-56" href="#__codelineno-29-56"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-57" name="__codelineno-29-57" href="#__codelineno-29-57"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
+<a id="__codelineno-29-58" name="__codelineno-29-58" href="#__codelineno-29-58"></a><span class="w">                </span><span class="n">pairSet</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">pair</span><span class="p">);</span>
+<a id="__codelineno-29-59" name="__codelineno-29-59" href="#__codelineno-29-59"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-29-60" name="__codelineno-29-60" href="#__codelineno-29-60"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">pairSet</span><span class="p">;</span>
+<a id="__codelineno-29-61" name="__codelineno-29-61" href="#__codelineno-29-61"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-62" name="__codelineno-29-62" href="#__codelineno-29-62"></a>
+<a id="__codelineno-29-63" name="__codelineno-29-63" href="#__codelineno-29-63"></a><span class="w">    </span><span class="cm">/* すべてのキーを取得 */</span>
+<a id="__codelineno-29-64" name="__codelineno-29-64" href="#__codelineno-29-64"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="nf">keySet</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-65" name="__codelineno-29-65" href="#__codelineno-29-65"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">keySet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-29-66" name="__codelineno-29-66" href="#__codelineno-29-66"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-67" name="__codelineno-29-67" href="#__codelineno-29-67"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
+<a id="__codelineno-29-68" name="__codelineno-29-68" href="#__codelineno-29-68"></a><span class="w">                </span><span class="n">keySet</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="na">key</span><span class="p">);</span>
+<a id="__codelineno-29-69" name="__codelineno-29-69" href="#__codelineno-29-69"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-29-70" name="__codelineno-29-70" href="#__codelineno-29-70"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">keySet</span><span class="p">;</span>
+<a id="__codelineno-29-71" name="__codelineno-29-71" href="#__codelineno-29-71"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-72" name="__codelineno-29-72" href="#__codelineno-29-72"></a>
+<a id="__codelineno-29-73" name="__codelineno-29-73" href="#__codelineno-29-73"></a><span class="w">    </span><span class="cm">/* すべての値を取得 */</span>
+<a id="__codelineno-29-74" name="__codelineno-29-74" href="#__codelineno-29-74"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">String</span><span class="o">&gt;</span><span class="w"> </span><span class="nf">valueSet</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-75" name="__codelineno-29-75" href="#__codelineno-29-75"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="n">String</span><span class="o">&gt;</span><span class="w"> </span><span class="n">valueSet</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-29-76" name="__codelineno-29-76" href="#__codelineno-29-76"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">pair</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-77" name="__codelineno-29-77" href="#__codelineno-29-77"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pair</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
+<a id="__codelineno-29-78" name="__codelineno-29-78" href="#__codelineno-29-78"></a><span class="w">                </span><span class="n">valueSet</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">pair</span><span class="p">.</span><span class="na">val</span><span class="p">);</span>
+<a id="__codelineno-29-79" name="__codelineno-29-79" href="#__codelineno-29-79"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-29-80" name="__codelineno-29-80" href="#__codelineno-29-80"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">valueSet</span><span class="p">;</span>
+<a id="__codelineno-29-81" name="__codelineno-29-81" href="#__codelineno-29-81"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-82" name="__codelineno-29-82" href="#__codelineno-29-82"></a>
+<a id="__codelineno-29-83" name="__codelineno-29-83" href="#__codelineno-29-83"></a><span class="w">    </span><span class="cm">/* ハッシュテーブルを印刷 */</span>
+<a id="__codelineno-29-84" name="__codelineno-29-84" href="#__codelineno-29-84"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">print</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-85" name="__codelineno-29-85" href="#__codelineno-29-85"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">Pair</span><span class="w"> </span><span class="n">kv</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">pairSet</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-86" name="__codelineno-29-86" href="#__codelineno-29-86"></a><span class="w">            </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="n">kv</span><span class="p">.</span><span class="na">key</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="s">&quot; -&gt; &quot;</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">kv</span><span class="p">.</span><span class="na">val</span><span class="p">);</span>
+<a id="__codelineno-29-87" name="__codelineno-29-87" href="#__codelineno-29-87"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-29-88" name="__codelineno-29-88" href="#__codelineno-29-88"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-89" name="__codelineno-29-89" href="#__codelineno-29-89"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_hash_map.cs</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">Pair</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a>
+<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">ArrayHashMap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_hash_map.go</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">pair</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a>
+<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">arrayHashMap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_hash_map.swift</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="p">[</span><span class="n">file</span><span class="p">]{</span><span class="n">utils</span><span class="o">/</span><span class="n">pair</span><span class="p">.</span><span class="n">swift</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">Pair</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a>
+<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">ArrayHashMap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_hash_map.js</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">Pair</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a>
+<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">ArrayHashMap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_hash_map.ts</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">Pair</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a>
+<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">ArrayHashMap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_hash_map.dart</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">Pair</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<a id="__codelineno-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></a>
+<a id="__codelineno-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ArrayHashMap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_hash_map.rs</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">Pair</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a>
+<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ArrayHashMap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_hash_map.c</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">Pair</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a>
+<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ArrayHashMap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_hash_map.kt</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">Pair</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a>
+<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">ArrayHashMap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_hash_map.rb</span><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">Pair</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a>
+<a id="__codelineno-39-3" name="__codelineno-39-3" href="#__codelineno-39-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">ArrayHashMap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_hash_map.zig</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">Pair</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a>
+<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ArrayHashMap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h2 id="613">6.1.3 &nbsp; ハッシュ衝突とリサイズ<a class="headerlink" href="#613" title="Permanent link">&para;</a></h2>
+<p>本質的に、ハッシュ関数の役割は、すべてのキーの入力空間全体を、すべての配列インデックスの出力空間にマッピングすることです。しかし、入力空間は出力空間よりもはるかに大きいことがよくあります。したがって、<strong>理論的には、「複数の入力が同じ出力に対応する」ケースが常に存在します</strong>。</p>
+<p>上記の例では、与えられたハッシュ関数で、入力<code>key</code>の下二桁が同じ場合、ハッシュ関数は同じ出力を生成します。例えば、学籍番号12836と20336の2人の学生をクエリすると、以下のことがわかります：</p>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="m">12836</span><span class="w"> </span>%<span class="w"> </span><span class="nv">100</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">36</span>
+<a id="__codelineno-41-2" name="__codelineno-41-2" href="#__codelineno-41-2"></a><span class="m">20336</span><span class="w"> </span>%<span class="w"> </span><span class="nv">100</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">36</span>
+</code></pre></div>
+<p>下図に示すように、両方の学籍番号が同じ名前を指しており、これは明らかに間違っています。この複数の入力が同じ出力に対応する状況を<u>ハッシュ衝突</u>と呼びます。</p>
+<p><a class="glightbox" href="../hash_map.assets/hash_collision.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="ハッシュ衝突の例" class="animation-figure" src="../hash_map.assets/hash_collision.png" /></a></p>
+<p align="center"> 図 6-3 &nbsp; ハッシュ衝突の例 </p>
+
+<p>ハッシュ表の容量<span class="arithmatex">\(n\)</span>が増加するにつれて、複数のキーが同じバケットに割り当てられる確率が減少し、衝突が少なくなることは理解しやすいです。したがって、<strong>ハッシュ表をリサイズすることでハッシュ衝突を減らすことができます</strong>。</p>
+<p>下図に示すように、リサイズ前は、キー値ペア<code>(136, A)</code>と<code>(236, D)</code>が衝突していました。しかし、リサイズ後は衝突が解決されています。</p>
+<p><a class="glightbox" href="../hash_map.assets/hash_table_reshash.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="ハッシュ表のリサイズ" class="animation-figure" src="../hash_map.assets/hash_table_reshash.png" /></a></p>
+<p align="center"> 図 6-4 &nbsp; ハッシュ表のリサイズ </p>
+
+<p>配列の拡張と同様に、ハッシュ表のリサイズにはすべてのキー値ペアを元のハッシュ表から新しいものに移行する必要があり、時間がかかります。さらに、ハッシュ表の<code>capacity</code>が変更されるため、ハッシュ関数を使用してすべてのキー値ペアの格納位置を再計算する必要があり、リサイズプロセスの計算オーバーヘッドがさらに増加します。したがって、プログラミング言語は頻繁なリサイズを防ぐために、ハッシュ表に十分大きな容量を割り当てることがよくあります。</p>
+<p><u>負荷率</u>はハッシュ表の重要な概念です。ハッシュ表内の要素数とバケット数の比率として定義されます。ハッシュ衝突の深刻度を測定するために使用され、<strong>しばしばハッシュ表のリサイズのトリガーとしても機能します</strong>。例えば、Javaでは、負荷率が<span class="arithmatex">\(0.75\)</span>を超えると、システムはハッシュ表を元のサイズの2倍にリサイズします。</p>
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+  
+  <span class="md-ellipsis">
+    0.1 &nbsp; この本について
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_preface/suggestions/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.2 &nbsp; 本書の使い方
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_preface/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_introduction/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="./" class="md-nav__link md-nav__link--active">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link md-nav__link--active" for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
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+      <a href="../chapter_greedy/summary/" class="md-nav__link">
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+<p><a class="glightbox" href="../assets/covers/chapter_hashing.jpg" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="ハッシュ表" class="cover-image" src="../assets/covers/chapter_hashing.jpg" /></a></p>
+<div class="admonition abstract">
+<p class="admonition-title">Abstract</p>
+<p>コンピューティングの世界において、ハッシュ表は賢い司書のようなものです。</p>
+<p>インデックス番号の計算方法を理解し、目的の本を迅速に取得することを可能にします。</p>
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+<h2 id="_1">章の内容<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h2>
+<ul>
+<li><a href="hash_map/">6.1 &nbsp; ハッシュ表</a></li>
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+      <a href="../../chapter_preface/summary/" class="md-nav__link">
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+  
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+    第 1 章 &nbsp; アルゴリズムとの出会い
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+  
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+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
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+    1.3 &nbsp; まとめ
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+        
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+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
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+            第 2 章 &nbsp; 計算量解析
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+    2.1 &nbsp; アルゴリズム効率評価
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+    2.2 &nbsp; 反復と再帰
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+  
+
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+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
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+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
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+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
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+    </li>
+  
+
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+  
+  
+  
+  
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+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
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+  
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+    第 3 章 &nbsp; データ構造
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+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 重要なポイント
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#2-q-a" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; Q &amp; A
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
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+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
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+      
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+          
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_19" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_reference/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9 3v15h3V3H9m3 2 4 13 3-1-4-13-3 1M5 5v13h3V5H5M3 19v2h18v-2H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    参考文献
+  </span>
+  
+
+            </a>
+            
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_19_label" aria-expanded="false">
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+            参考文献
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+            
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+              <div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
+                <div class="md-sidebar__scrollwrap">
+                  <div class="md-sidebar__inner">
+                    
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+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
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+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 重要なポイント
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#2-q-a" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; Q &amp; A
+    </span>
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+  
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+      
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+  
+</nav>
+                  </div>
+                </div>
+              </div>
+            
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+<h1 id="64">6.4 &nbsp; まとめ<a class="headerlink" href="#64" title="Permanent link">&para;</a></h1>
+<h3 id="1">1. &nbsp; 重要なポイント<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<ul>
+<li>入力<code>key</code>が与えられると、ハッシュ表は<span class="arithmatex">\(O(1)\)</span>の時間で対応する<code>value</code>を取得でき、非常に効率的です。</li>
+<li>一般的なハッシュ表の操作には、クエリ、キー値ペアの追加、キー値ペアの削除、ハッシュ表の走査があります。</li>
+<li>ハッシュ関数は<code>key</code>を配列インデックスにマッピングし、対応するバケットにアクセスして<code>value</code>を取得できるようにします。</li>
+<li>2つの異なるキーがハッシュ化後に同じ配列インデックスになる場合があり、誤ったクエリ結果につながります。この現象はハッシュ衝突として知られています。</li>
+<li>ハッシュ表の容量が大きいほど、ハッシュ衝突の確率は低くなります。したがって、ハッシュ表のリサイズはハッシュ衝突を緩和できます。配列のリサイズと同様に、ハッシュ表のリサイズはコストが高いです。</li>
+<li>要素数をバケット数で割った負荷率は、ハッシュ衝突の深刻度を反映し、しばしばハッシュ表リサイズのトリガー条件として使用されます。</li>
+<li>連鎖法は各要素を連結リストに変換し、衝突するすべての要素を同じリストに格納することでハッシュ衝突に対処します。ただし、過度に長いリストはクエリ効率を低下させる可能性があり、リストを赤黒木に変換することで改善できます。</li>
+<li>オープンアドレス法は複数回のプローブを通してハッシュ衝突を処理します。線形プローブは固定ステップサイズを使用しますが、要素を削除できず、クラスタリングを起こしやすい傾向があります。多重ハッシュはプローブに複数のハッシュ関数を使用し、線形プローブと比較してクラスタリングを減らしますが、計算オーバーヘッドが増加します。</li>
+<li>異なるプログラミング言語はさまざまなハッシュ表実装を採用しています。例えば、Javaの<code>HashMap</code>は連鎖法を使用し、Pythonの<code>dict</code>はオープンアドレス法を採用しています。</li>
+<li>ハッシュ表では、決定性、高効率、均等分散を持つハッシュアルゴリズムが望まれます。暗号化では、ハッシュアルゴリズムは衝突耐性と雪崩効果も持つべきです。</li>
+<li>ハッシュアルゴリズムは通常、ハッシュ値の均等分散を保証し、ハッシュ衝突を減らすために、大きな素数を剰余として使用します。</li>
+<li>一般的なハッシュアルゴリズムには、MD5、SHA-1、SHA-2、SHA-3があります。MD5はファイル整合性チェックによく使用され、SHA-2は安全なアプリケーションとプロトコルで一般的に使用されます。</li>
+<li>プログラミング言語は通常、ハッシュ表のバケットインデックスを計算するために、データ型に対して組み込みのハッシュアルゴリズムを提供します。一般的に、不変オブジェクトのみがハッシュ可能です。</li>
+</ul>
+<h3 id="2-q-a">2. &nbsp; Q &amp; A<a class="headerlink" href="#2-q-a" title="Permanent link">&para;</a></h3>
+<p><strong>Q</strong>: ハッシュ表の時間計算量が<span class="arithmatex">\(O(n)\)</span>に悪化するのはいつですか？</p>
+<p>ハッシュ表の時間計算量は、ハッシュ衝突が深刻な場合に<span class="arithmatex">\(O(n)\)</span>に悪化する可能性があります。ハッシュ関数が適切に設計され、容量が適切に設定され、衝突が均等に分散されている場合、時間計算量は<span class="arithmatex">\(O(1)\)</span>です。プログラミング言語の組み込みハッシュ表を使用する場合、通常は時間計算量を<span class="arithmatex">\(O(1)\)</span>と考えます。</p>
+<p><strong>Q</strong>: なぜハッシュ関数<span class="arithmatex">\(f(x) = x\)</span>を使用しないのですか？これなら衝突を排除できます。</p>
+<p>ハッシュ関数<span class="arithmatex">\(f(x) = x\)</span>では、各要素が一意のバケットインデックスに対応し、これは配列と同等です。しかし、入力空間は通常出力空間（配列長）よりもはるかに大きいため、ハッシュ関数の最後のステップは配列長の剰余を取ることがよくあります。言い換えると、ハッシュ表の目標は、<span class="arithmatex">\(O(1)\)</span>のクエリ効率を提供しながら、より大きな状態空間をより小さなものにマッピングすることです。</p>
+<p><strong>Q</strong>: ハッシュ表がこれらの構造を使って実装されているにもかかわらず、なぜ配列、連結リスト、二分木よりも効率的になれるのですか？</p>
+<p>まず、ハッシュ表は時間効率が高いですが、空間効率は低いです。ハッシュ表のメモリの大部分は未使用のままです。</p>
+<p>次に、ハッシュ表は特定のユースケースでのみ時間効率が高いです。配列や連結リストを使用して同じ時間計算量で機能を実装できる場合、通常はハッシュ表を使用するよりも高速です。これは、ハッシュ関数の計算がオーバーヘッドを発生させ、時間計算量の定数因子が大きくなるためです。</p>
+<p>最後に、ハッシュ表の時間計算量は悪化する可能性があります。例えば、連鎖法では、連結リストや赤黒木で検索操作を実行し、これは依然として<span class="arithmatex">\(O(n)\)</span>時間に悪化するリスクがあります。</p>
+<p><strong>Q</strong>: 多重ハッシュにも要素を直接削除できないという欠陥がありますか？削除としてマークされた空間は再利用できますか？</p>
+<p>多重ハッシュはオープンアドレス法の一形態であり、すべてのオープンアドレス法には要素を直接削除できないという欠点があります。要素を削除済みとしてマークする必要があります。マークされた空間は再利用できます。ハッシュ表に新しい要素を挿入する際、ハッシュ関数が削除済みとしてマークされた位置を指している場合、その位置は新しい要素によって使用できます。これにより、ハッシュ表のプローブシーケンスを維持しながら、空間の効率的な使用が保証されます。</p>
+<p><strong>Q</strong>: なぜ線形プローブの検索プロセス中にハッシュ衝突が発生するのですか？</p>
+<p>検索プロセス中、ハッシュ関数は対応するバケットとキー値ペアを指します。<code>key</code>が一致しない場合、ハッシュ衝突を示します。したがって、線形プローブは正しいキー値ペアが見つかるか検索が失敗するまで、事前に決められたステップサイズで下方向に検索します。</p>
+<p><strong>Q</strong>: なぜハッシュ表のリサイズがハッシュ衝突を緩和できるのですか？</p>
+<p>ハッシュ関数の最後のステップは、出力を配列インデックス範囲内に保つために、配列長<span class="arithmatex">\(n\)</span>の剰余を取ることがよくあります。リサイズ時、配列長<span class="arithmatex">\(n\)</span>が変化し、キーに対応するインデックスも変化する可能性があります。以前に同じバケットにマッピングされていたキーが、リサイズ後に複数のバケットに分散される可能性があり、それによってハッシュ衝突が緩和されます。</p>
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+    <a href="../.." title="Hello アルゴリズム" class="md-header__button md-logo" aria-label="Hello アルゴリズム" data-md-component="logo">
+      
+  <img src="../../assets/images/logo.svg" alt="logo">
+
+    </a>
+    <label class="md-header__button md-icon" for="__drawer">
+      
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 6h18v2H3V6m0 5h18v2H3v-2m0 5h18v2H3v-2Z"/></svg>
+    </label>
+    <div class="md-header__title" data-md-component="header-title">
+      <div class="md-header__ellipsis">
+        <div class="md-header__topic">
+          <span class="md-ellipsis">
+            Hello アルゴリズム
+          </span>
+        </div>
+        <div class="md-header__topic" data-md-component="header-topic">
+          <span class="md-ellipsis">
+            
+              8.2 &nbsp; ヒープの構築
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+    
+      
+        <form class="md-header__option" data-md-component="palette">
+  
+    
+    
+    
+    <input class="md-option" data-md-color-media="" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="teal"  aria-label="ダークモード"  type="radio" name="__palette" id="__palette_0">
+    
+      <label class="md-header__button md-icon" title="ダークモード" for="__palette_1" hidden>
+        <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07 19.07 3.5m-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13.51 1.67m-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87.4 1.31M19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35-2.53-2.2m4.33-2.7 1.15-2.77 2.2 2.54-3.35.23m1.15-4.96-1.14-2.78 3.34.24-2.2 2.54M9.63 18.93l2.77 1.15-2.53 2.19-.24-3.34Z"/></svg>
+      </label>
+    
+  
+    
+    
+    
+    <input class="md-option" data-md-color-media="" data-md-color-scheme="slate" data-md-color-primary="black" data-md-color-accent="teal"  aria-label="ライトモード"  type="radio" name="__palette" id="__palette_1">
+    
+      <label class="md-header__button md-icon" title="ライトモード" for="__palette_0" hidden>
+        <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07 19.07 3.5m-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13.51 1.67m-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87.4 1.31M19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35-2.53-2.2m4.33-2.7 1.15-2.77 2.2 2.54-3.35.23m1.15-4.96-1.14-2.78 3.34.24-2.2 2.54M9.63 18.93l2.77 1.15-2.53 2.19-.24-3.34Z"/></svg>
+      </label>
+    
+  
+</form>
+      
+    
+    
+      <script>var media,input,key,value,palette=__md_get("__palette");if(palette&&palette.color){"(prefers-color-scheme)"===palette.color.media&&(media=matchMedia("(prefers-color-scheme: light)"),input=document.querySelector(media.matches?"[data-md-color-media='(prefers-color-scheme: light)']":"[data-md-color-media='(prefers-color-scheme: dark)']"),palette.color.media=input.getAttribute("data-md-color-media"),palette.color.scheme=input.getAttribute("data-md-color-scheme"),palette.color.primary=input.getAttribute("data-md-color-primary"),palette.color.accent=input.getAttribute("data-md-color-accent"));for([key,value]of Object.entries(palette.color))document.body.setAttribute("data-md-color-"+key,value)}</script>
+    
+    
+      <div class="md-header__option">
+  <div class="md-select">
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+    <button class="md-header__button md-icon" aria-label="言語切り替え">
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12.87 15.07-2.54-2.51.03-.03A17.52 17.52 0 0 0 14.07 6H17V4h-7V2H8v2H1v2h11.17C11.5 7.92 10.44 9.75 9 11.35 8.07 10.32 7.3 9.19 6.69 8h-2c.73 1.63 1.73 3.17 2.98 4.56l-5.09 5.02L4 19l5-5 3.11 3.11.76-2.04M18.5 10h-2L12 22h2l1.12-3h4.75L21 22h2l-4.5-12m-2.62 7 1.62-4.33L19.12 17h-3.24Z"/></svg>
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+    <div class="md-select__inner">
+      <ul class="md-select__list">
+        
+          <li class="md-select__item">
+            <a href="/chapter_heap/build_heap/" hreflang="zh" class="md-select__link">
+              简体中文
+            </a>
+          </li>
+        
+          <li class="md-select__item">
+            <a href="/zh-hant/chapter_heap/build_heap/" hreflang="zh-Hant" class="md-select__link">
+              繁體中文
+            </a>
+          </li>
+        
+          <li class="md-select__item">
+            <a href="/en/chapter_heap/build_heap/" hreflang="en" class="md-select__link">
+              English
+            </a>
+          </li>
+        
+          <li class="md-select__item">
+            <a href="/ja/chapter_heap/build_heap/" hreflang="ja" class="md-select__link">
+              日本語
+            </a>
+          </li>
+        
+      </ul>
+    </div>
+  </div>
+</div>
+    
+    
+      <label class="md-header__button md-icon" for="__search">
+        
+        <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.516 6.516 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5Z"/></svg>
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+      <div class="md-search" data-md-component="search" role="dialog">
+  <label class="md-search__overlay" for="__search"></label>
+  <div class="md-search__inner" role="search">
+    <form class="md-search__form" name="search">
+      <input type="text" class="md-search__input" name="query" aria-label="検索" placeholder="検索" autocapitalize="off" autocorrect="off" autocomplete="off" spellcheck="false" data-md-component="search-query" required>
+      <label class="md-search__icon md-icon" for="__search">
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+        <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.516 6.516 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5Z"/></svg>
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+        <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M20 11v2H8l5.5 5.5-1.42 1.42L4.16 12l7.92-7.92L13.5 5.5 8 11h12Z"/></svg>
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+      <nav class="md-search__options" aria-label="検索">
+        
+          <a href="javascript:void(0)" class="md-search__icon md-icon" title="共有" aria-label="共有" data-clipboard data-clipboard-text="" data-md-component="search-share" tabindex="-1">
+            
+            <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 16.08c-.76 0-1.44.3-1.96.77L8.91 12.7c.05-.23.09-.46.09-.7 0-.24-.04-.47-.09-.7l7.05-4.11c.54.5 1.25.81 2.04.81a3 3 0 0 0 3-3 3 3 0 0 0-3-3 3 3 0 0 0-3 3c0 .24.04.47.09.7L8.04 9.81C7.5 9.31 6.79 9 6 9a3 3 0 0 0-3 3 3 3 0 0 0 3 3c.79 0 1.5-.31 2.04-.81l7.12 4.15c-.05.21-.08.43-.08.66 0 1.61 1.31 2.91 2.92 2.91 1.61 0 2.92-1.3 2.92-2.91A2.92 2.92 0 0 0 18 16.08Z"/></svg>
+          </a>
+        
+        <button type="reset" class="md-search__icon md-icon" title="クリア" aria-label="クリア" tabindex="-1">
+          
+          <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 6.41 17.59 5 12 10.59 6.41 5 5 6.41 10.59 12 5 17.59 6.41 19 12 13.41 17.59 19 19 17.59 13.41 12 19 6.41Z"/></svg>
+        </button>
+      </nav>
+      
+        <div class="md-search__suggest" data-md-component="search-suggest"></div>
+      
+    </form>
+    <div class="md-search__output">
+      <div class="md-search__scrollwrap" data-md-scrollfix>
+        <div class="md-search-result" data-md-component="search-result">
+          <div class="md-search-result__meta">
+            検索を初期化
+          </div>
+          <ol class="md-search-result__list" role="presentation"></ol>
+        </div>
+      </div>
+    </div>
+  </div>
+</div>
+    
+    
+      <div class="md-header__source">
+        <a href="https://github.com/krahets/hello-algo" title="リポジトリへ" class="md-source" data-md-component="source">
+  <div class="md-source__icon md-icon">
+    
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 496 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"/></svg>
+  </div>
+  <div class="md-source__repository">
+    krahets/hello-algo
+  </div>
+</a>
+      </div>
+    
+  </nav>
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+</header>
+    
+    <div class="md-container" data-md-component="container">
+      
+      
+        
+          
+        
+      
+      <main class="md-main" data-md-component="main">
+        <div class="md-main__inner md-grid">
+          
+            
+              
+              <div class="md-sidebar md-sidebar--primary" data-md-component="sidebar" data-md-type="navigation" >
+                <div class="md-sidebar__scrollwrap">
+                  <div class="md-sidebar__inner">
+                    
+
+
+
+<nav class="md-nav md-nav--primary" aria-label="ナビゲーション" data-md-level="0">
+  <label class="md-nav__title" for="__drawer">
+    <a href="../.." title="Hello アルゴリズム" class="md-nav__button md-logo" aria-label="Hello アルゴリズム" data-md-component="logo">
+      
+  <img src="../../assets/images/logo.svg" alt="logo">
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+    </a>
+    Hello アルゴリズム
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+  
+    <div class="md-nav__source">
+      <a href="https://github.com/krahets/hello-algo" title="リポジトリへ" class="md-source" data-md-component="source">
+  <div class="md-source__icon md-icon">
+    
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 496 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"/></svg>
+  </div>
+  <div class="md-source__repository">
+    krahets/hello-algo
+  </div>
+</a>
+    </div>
+  
+  <ul class="md-nav__list" data-md-scrollfix>
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
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+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_1" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hello_algo/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m13.13 22.19-1.63-3.83c1.57-.58 3.04-1.36 4.4-2.27l-2.77 6.1M5.64 12.5l-3.83-1.63 6.1-2.77C7 9.46 6.22 10.93 5.64 12.5M19.22 4c.28 0 .53 0 .74.05.17 1.39-.02 4.25-3.3 7.53-1.7 1.71-3.73 3.02-6.01 3.89l-2.15-2.1c.92-2.31 2.23-4.34 3.92-6.03C15.18 4.58 17.64 4 19.22 4m0-2c-1.98 0-4.98.69-8.22 3.93-2.19 2.19-3.5 4.6-4.35 6.71-.28.75-.09 1.57.46 2.13l2.13 2.12c.38.38.89.61 1.42.61.23 0 .47-.06.7-.15A19.1 19.1 0 0 0 18.07 13c5.66-5.66 3.54-10.61 3.54-10.61S20.7 2 19.22 2m-4.68 7.46c-.78-.78-.78-2.05 0-2.83s2.05-.78 2.83 0c.77.78.78 2.05 0 2.83-.78.78-2.05.78-2.83 0m-5.66 7.07-1.41-1.41 1.41 1.41M6.24 22l3.64-3.64c-.34-.09-.67-.24-.97-.45L4.83 22h1.41M2 22h1.41l4.77-4.76-1.42-1.41L2 20.59V22m0-2.83 4.09-4.08c-.21-.3-.36-.62-.45-.97L2 17.76v1.41Z"/></svg>
+  
+  <span class="md-ellipsis">
+    はじめに
+  </span>
+  
+
+            </a>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_1_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_1">
+            <span class="md-nav__icon md-icon"></span>
+            はじめに
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+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
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+  
+  
+  
+  
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+      
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+          
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+    
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+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_2" >
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+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_preface/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M21 4H3a2 2 0 0 0-2 2v13a2 2 0 0 0 2 2h18a2 2 0 0 0 2-2V6a2 2 0 0 0-2-2M3 19V6h8v13H3m18 0h-8V6h8v13m-7-9.5h6V11h-6V9.5m0 2.5h6v1.5h-6V12m0 2.5h6V16h-6v-1.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 0 章 &nbsp; 前書き
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_2" id="__nav_2_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_2_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_2">
+            <span class="md-nav__icon md-icon"></span>
+            第 0 章 &nbsp; 前書き
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/about_the_book/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.1 &nbsp; この本について
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/suggestions/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.2 &nbsp; 本書の使い方
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_introduction/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#821" class="md-nav__link">
+    <span class="md-ellipsis">
+      8.2.1 &nbsp; ヒープ挿入操作による実装
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#822" class="md-nav__link">
+    <span class="md-ellipsis">
+      8.2.2 &nbsp; 走査によるヒープ化の実装
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#823" class="md-nav__link">
+    <span class="md-ellipsis">
+      8.2.3 &nbsp; 計算量分析
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
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+    <span class="md-ellipsis">
+      8.2.1 &nbsp; ヒープ挿入操作による実装
+    </span>
+  </a>
+  
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+      
+        <li class="md-nav__item">
+  <a href="#822" class="md-nav__link">
+    <span class="md-ellipsis">
+      8.2.2 &nbsp; 走査によるヒープ化の実装
+    </span>
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+      
+        <li class="md-nav__item">
+  <a href="#823" class="md-nav__link">
+    <span class="md-ellipsis">
+      8.2.3 &nbsp; 計算量分析
+    </span>
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+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
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+<h1 id="82">8.2 &nbsp; ヒープ構築操作<a class="headerlink" href="#82" title="Permanent link">&para;</a></h1>
+<p>場合によっては、リストのすべての要素を使用してヒープを構築したいことがあり、このプロセスは「ヒープ構築操作」として知られています。</p>
+<h2 id="821">8.2.1 &nbsp; ヒープ挿入操作による実装<a class="headerlink" href="#821" title="Permanent link">&para;</a></h2>
+<p>まず、空のヒープを作成し、次にリストを反復処理して、各要素に対して順番に「ヒープ挿入操作」を実行します。これは、要素をヒープの末尾に追加し、次に下から上に「ヒープ化」することを意味します。</p>
+<p>ヒープに要素が追加されるたびに、ヒープの長さは1つずつ増加します。ノードは二分木に上から下に追加されるため、ヒープは「上から下に」構築されます。</p>
+<p>要素数を<span class="arithmatex">\(n\)</span>とすると、各要素の挿入操作は<span class="arithmatex">\(O(\log{n})\)</span>時間かかるため、このヒープ構築方法の時間計算量は<span class="arithmatex">\(O(n \log n)\)</span>です。</p>
+<h2 id="822">8.2.2 &nbsp; 走査によるヒープ化の実装<a class="headerlink" href="#822" title="Permanent link">&para;</a></h2>
+<p>実際には、2つのステップでより効率的なヒープ構築方法を実装できます。</p>
+<ol>
+<li>リストのすべての要素をそのままヒープに追加します。この時点では、ヒープの性質はまだ満たされていません。</li>
+<li>ヒープを逆順（レベル順走査の逆）で走査し、各非葉ノードに対して「上から下のヒープ化」を実行します。</li>
+</ol>
+<p><strong>ノードをヒープ化した後、そのノードを根とする部分木は有効な部分ヒープになります</strong>。走査が逆順であるため、ヒープは「下から上に」構築されます。</p>
+<p>逆走査を選択する理由は、現在のノードの下の部分木がすでに有効な部分ヒープであることを保証し、現在のノードのヒープ化を効果的にするためです。</p>
+<p>言及する価値があるのは、**葉ノードは子を持たないため、自然に有効な部分ヒープを形成し、ヒープ化する必要がない**ということです。以下のコードに示すように、最後の非葉ノードは最後のノードの親です。そこから開始して逆順に走査してヒープ化を実行します：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:14"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><input id="__tabbed_1_14" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label><label for="__tabbed_1_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]):</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;コンストラクタ、入力リストに基づいてヒープを構築&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># すべてのリスト要素をヒープに追加</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span> <span class="o">=</span> <span class="n">nums</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="c1"># 葉以外のすべてのノードをヒープ化</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">parent</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span> <span class="o">-</span> <span class="mi">1</span><span class="p">),</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">sift_down</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* コンストラクタ、入力リストに基づいてヒープを構築 */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="n">MaxHeap</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// すべてのリスト要素をヒープに追加</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="n">maxHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">;</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="c1">// 葉以外のすべてのノードをヒープ化</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">parent</span><span class="p">(</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">        </span><span class="n">siftDown</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* コンストラクタ、入力リストに基づいてヒープを構築 */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="n">MaxHeap</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// すべてのリスト要素をヒープに追加</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="n">maxHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">(</span><span class="n">nums</span><span class="p">);</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="c1">// 葉を除くすべてのノードをヒープ化</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">parent</span><span class="p">(</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">        </span><span class="n">siftDown</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">maxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">newMaxHeap</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="kd">init</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="kr">constructor</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="kr">constructor</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">new</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">newMaxHeap</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">MaxHeap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="kp">initialize</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.zig</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">init</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h2 id="823">8.2.3 &nbsp; 計算量分析<a class="headerlink" href="#823" title="Permanent link">&para;</a></h2>
+<p>次に、この第2のヒープ構築方法の時間計算量を計算してみましょう。</p>
+<ul>
+<li>完備二分木のノード数を<span class="arithmatex">\(n\)</span>と仮定すると、葉ノードの数は<span class="arithmatex">\((n + 1) / 2\)</span>です。ここで<span class="arithmatex">\(/\)</span> は整数除算です。したがって、ヒープ化が必要なノードの数は<span class="arithmatex">\((n - 1) / 2\)</span>です。</li>
+<li>「上から下のヒープ化」のプロセスでは、各ノードは最大で葉ノードまでヒープ化されるため、最大反復回数は二分木の高さ<span class="arithmatex">\(\log n\)</span>です。</li>
+</ul>
+<p>この2つを掛け合わせると、ヒープ構築プロセスの時間計算量は<span class="arithmatex">\(O(n \log n)\)</span>となります。<strong>しかし、この推定は正確ではありません。二分木の下位レベルには上位よりもはるかに多くのノードがあるという性質を考慮していないからです。</strong></p>
+<p>より正確な計算を行いましょう。計算を簡素化するため、<span class="arithmatex">\(n\)</span>個のノードと高さ<span class="arithmatex">\(h\)</span>を持つ「完全二分木」を仮定します。この仮定は結果の正確性に影響しません。</p>
+<p><a class="glightbox" href="../build_heap.assets/heapify_operations_count.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="完全二分木の各レベルのノード数" class="animation-figure" src="../build_heap.assets/heapify_operations_count.png" /></a></p>
+<p align="center"> 図 8-5 &nbsp; 完全二分木の各レベルのノード数 </p>
+
+<p>上図に示すように、ノードが「上から下にヒープ化される」最大反復回数は、そのノードから葉ノードまでの距離と等しく、これは正確に「ノードの高さ」です。したがって、各レベルで「ノード数×ノードの高さ」を合計して、**すべてのノードの総ヒープ化反復回数を得る**ことができます。</p>
+<div class="arithmatex">\[
+T(h) = 2^0h + 2^1(h-1) + 2^2(h-2) + \dots + 2^{(h-1)}\times1
+\]</div>
+<p>上記の方程式を簡素化するために、高校の数列の知識を使用する必要があります。まず<span class="arithmatex">\(T(h)\)</span>に<span class="arithmatex">\(2\)</span>を掛けて以下を得ます：</p>
+<div class="arithmatex">\[
+\begin{aligned}
+T(h) &amp; = 2^0h + 2^1(h-1) + 2^2(h-2) + \dots + 2^{h-1}\times1 \newline
+2T(h) &amp; = 2^1h + 2^2(h-1) + 2^3(h-2) + \dots + 2^h\times1 \newline
+\end{aligned}
+\]</div>
+<p>変位法を使用して<span class="arithmatex">\(2T(h)\)</span>から<span class="arithmatex">\(T(h)\)</span>を減算すると、以下を得ます：</p>
+<div class="arithmatex">\[
+2T(h) - T(h) = T(h) = -2^0h + 2^1 + 2^2 + \dots + 2^{h-1} + 2^h
+\]</div>
+<p>方程式を観察すると、<span class="arithmatex">\(T(h)\)</span>は等比数列であり、和の公式を使用して直接計算でき、時間計算量は以下になります：</p>
+<div class="arithmatex">\[
+\begin{aligned}
+T(h) &amp; = 2 \frac{1 - 2^h}{1 - 2} - h \newline
+&amp; = 2^{h+1} - h - 2 \newline
+&amp; = O(2^h)
+\end{aligned}
+\]</div>
+<p>さらに、高さ<span class="arithmatex">\(h\)</span>の完全二分木は<span class="arithmatex">\(n = 2^{h+1} - 1\)</span>個のノードを持つため、計算量は<span class="arithmatex">\(O(2^h) = O(n)\)</span>です。この計算は、**リストを入力してヒープを構築する時間計算量が<span class="arithmatex">\(O(n)\)</span>であり、非常に効率的である**ことを示しています。</p>
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BtJwem

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diff --git a/ja/chapter_heap/heap.assets/heap_push_step3.png b/ja/chapter_heap/heap.assets/heap_push_step3.png
new file mode 100644
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diff --git a/ja/chapter_heap/heap.assets/min_heap_and_max_heap.png b/ja/chapter_heap/heap.assets/min_heap_and_max_heap.png
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+    <div data-md-component="skip">
+      
+        
+        <a href="#81" class="md-skip">
+          コンテンツにスキップ
+        </a>
+      
+    </div>
+    <div data-md-component="announce">
+      
+        <aside class="md-banner">
+          <div class="md-banner__inner md-grid md-typeset">
+            
+            
+
+    
+
+<div class="banner-svg">
+    <svg xmlns="http://www.w3.org/2000/svg"
+        viewBox="0 0 512 512"><!--!Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free Copyright 2024 Fonticons, Inc.-->
+        <path
+            d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
+    </svg>
+    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+</div>
+
+          </div>
+          
+        </aside>
+      
+    </div>
+    
+    
+      
+
+  
+
+<header class="md-header md-header--shadow" data-md-component="header">
+  <nav class="md-header__inner md-grid" aria-label="ヘッダー">
+    <a href="../.." title="Hello アルゴリズム" class="md-header__button md-logo" aria-label="Hello アルゴリズム" data-md-component="logo">
+      
+  <img src="../../assets/images/logo.svg" alt="logo">
+
+    </a>
+    <label class="md-header__button md-icon" for="__drawer">
+      
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 6h18v2H3V6m0 5h18v2H3v-2m0 5h18v2H3v-2Z"/></svg>
+    </label>
+    <div class="md-header__title" data-md-component="header-title">
+      <div class="md-header__ellipsis">
+        <div class="md-header__topic">
+          <span class="md-ellipsis">
+            Hello アルゴリズム
+          </span>
+        </div>
+        <div class="md-header__topic" data-md-component="header-topic">
+          <span class="md-ellipsis">
+            
+              8.1 &nbsp; ヒープ
+            
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+    </div>
+    
+      
+        <form class="md-header__option" data-md-component="palette">
+  
+    
+    
+    
+    <input class="md-option" data-md-color-media="" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="teal"  aria-label="ダークモード"  type="radio" name="__palette" id="__palette_0">
+    
+      <label class="md-header__button md-icon" title="ダークモード" for="__palette_1" hidden>
+        <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07 19.07 3.5m-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13.51 1.67m-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87.4 1.31M19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35-2.53-2.2m4.33-2.7 1.15-2.77 2.2 2.54-3.35.23m1.15-4.96-1.14-2.78 3.34.24-2.2 2.54M9.63 18.93l2.77 1.15-2.53 2.19-.24-3.34Z"/></svg>
+      </label>
+    
+  
+    
+    
+    
+    <input class="md-option" data-md-color-media="" data-md-color-scheme="slate" data-md-color-primary="black" data-md-color-accent="teal"  aria-label="ライトモード"  type="radio" name="__palette" id="__palette_1">
+    
+      <label class="md-header__button md-icon" title="ライトモード" for="__palette_0" hidden>
+        <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07 19.07 3.5m-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13.51 1.67m-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87.4 1.31M19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35-2.53-2.2m4.33-2.7 1.15-2.77 2.2 2.54-3.35.23m1.15-4.96-1.14-2.78 3.34.24-2.2 2.54M9.63 18.93l2.77 1.15-2.53 2.19-.24-3.34Z"/></svg>
+      </label>
+    
+  
+</form>
+      
+    
+    
+      <script>var media,input,key,value,palette=__md_get("__palette");if(palette&&palette.color){"(prefers-color-scheme)"===palette.color.media&&(media=matchMedia("(prefers-color-scheme: light)"),input=document.querySelector(media.matches?"[data-md-color-media='(prefers-color-scheme: light)']":"[data-md-color-media='(prefers-color-scheme: dark)']"),palette.color.media=input.getAttribute("data-md-color-media"),palette.color.scheme=input.getAttribute("data-md-color-scheme"),palette.color.primary=input.getAttribute("data-md-color-primary"),palette.color.accent=input.getAttribute("data-md-color-accent"));for([key,value]of Object.entries(palette.color))document.body.setAttribute("data-md-color-"+key,value)}</script>
+    
+    
+      <div class="md-header__option">
+  <div class="md-select">
+    
+    <button class="md-header__button md-icon" aria-label="言語切り替え">
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12.87 15.07-2.54-2.51.03-.03A17.52 17.52 0 0 0 14.07 6H17V4h-7V2H8v2H1v2h11.17C11.5 7.92 10.44 9.75 9 11.35 8.07 10.32 7.3 9.19 6.69 8h-2c.73 1.63 1.73 3.17 2.98 4.56l-5.09 5.02L4 19l5-5 3.11 3.11.76-2.04M18.5 10h-2L12 22h2l1.12-3h4.75L21 22h2l-4.5-12m-2.62 7 1.62-4.33L19.12 17h-3.24Z"/></svg>
+    </button>
+    <div class="md-select__inner">
+      <ul class="md-select__list">
+        
+          <li class="md-select__item">
+            <a href="/chapter_heap/heap/" hreflang="zh" class="md-select__link">
+              简体中文
+            </a>
+          </li>
+        
+          <li class="md-select__item">
+            <a href="/zh-hant/chapter_heap/heap/" hreflang="zh-Hant" class="md-select__link">
+              繁體中文
+            </a>
+          </li>
+        
+          <li class="md-select__item">
+            <a href="/en/chapter_heap/heap/" hreflang="en" class="md-select__link">
+              English
+            </a>
+          </li>
+        
+          <li class="md-select__item">
+            <a href="/ja/chapter_heap/heap/" hreflang="ja" class="md-select__link">
+              日本語
+            </a>
+          </li>
+        
+      </ul>
+    </div>
+  </div>
+</div>
+    
+    
+      <label class="md-header__button md-icon" for="__search">
+        
+        <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.516 6.516 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5Z"/></svg>
+      </label>
+      <div class="md-search" data-md-component="search" role="dialog">
+  <label class="md-search__overlay" for="__search"></label>
+  <div class="md-search__inner" role="search">
+    <form class="md-search__form" name="search">
+      <input type="text" class="md-search__input" name="query" aria-label="検索" placeholder="検索" autocapitalize="off" autocorrect="off" autocomplete="off" spellcheck="false" data-md-component="search-query" required>
+      <label class="md-search__icon md-icon" for="__search">
+        
+        <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.516 6.516 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5Z"/></svg>
+        
+        <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M20 11v2H8l5.5 5.5-1.42 1.42L4.16 12l7.92-7.92L13.5 5.5 8 11h12Z"/></svg>
+      </label>
+      <nav class="md-search__options" aria-label="検索">
+        
+          <a href="javascript:void(0)" class="md-search__icon md-icon" title="共有" aria-label="共有" data-clipboard data-clipboard-text="" data-md-component="search-share" tabindex="-1">
+            
+            <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 16.08c-.76 0-1.44.3-1.96.77L8.91 12.7c.05-.23.09-.46.09-.7 0-.24-.04-.47-.09-.7l7.05-4.11c.54.5 1.25.81 2.04.81a3 3 0 0 0 3-3 3 3 0 0 0-3-3 3 3 0 0 0-3 3c0 .24.04.47.09.7L8.04 9.81C7.5 9.31 6.79 9 6 9a3 3 0 0 0-3 3 3 3 0 0 0 3 3c.79 0 1.5-.31 2.04-.81l7.12 4.15c-.05.21-.08.43-.08.66 0 1.61 1.31 2.91 2.92 2.91 1.61 0 2.92-1.3 2.92-2.91A2.92 2.92 0 0 0 18 16.08Z"/></svg>
+          </a>
+        
+        <button type="reset" class="md-search__icon md-icon" title="クリア" aria-label="クリア" tabindex="-1">
+          
+          <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 6.41 17.59 5 12 10.59 6.41 5 5 6.41 10.59 12 5 17.59 6.41 19 12 13.41 17.59 19 19 17.59 13.41 12 19 6.41Z"/></svg>
+        </button>
+      </nav>
+      
+        <div class="md-search__suggest" data-md-component="search-suggest"></div>
+      
+    </form>
+    <div class="md-search__output">
+      <div class="md-search__scrollwrap" data-md-scrollfix>
+        <div class="md-search-result" data-md-component="search-result">
+          <div class="md-search-result__meta">
+            検索を初期化
+          </div>
+          <ol class="md-search-result__list" role="presentation"></ol>
+        </div>
+      </div>
+    </div>
+  </div>
+</div>
+    
+    
+      <div class="md-header__source">
+        <a href="https://github.com/krahets/hello-algo" title="リポジトリへ" class="md-source" data-md-component="source">
+  <div class="md-source__icon md-icon">
+    
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 496 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"/></svg>
+  </div>
+  <div class="md-source__repository">
+    krahets/hello-algo
+  </div>
+</a>
+      </div>
+    
+  </nav>
+  
+</header>
+    
+    <div class="md-container" data-md-component="container">
+      
+      
+        
+          
+        
+      
+      <main class="md-main" data-md-component="main">
+        <div class="md-main__inner md-grid">
+          
+            
+              
+              <div class="md-sidebar md-sidebar--primary" data-md-component="sidebar" data-md-type="navigation" >
+                <div class="md-sidebar__scrollwrap">
+                  <div class="md-sidebar__inner">
+                    
+
+
+
+<nav class="md-nav md-nav--primary" aria-label="ナビゲーション" data-md-level="0">
+  <label class="md-nav__title" for="__drawer">
+    <a href="../.." title="Hello アルゴリズム" class="md-nav__button md-logo" aria-label="Hello アルゴリズム" data-md-component="logo">
+      
+  <img src="../../assets/images/logo.svg" alt="logo">
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+    Hello アルゴリズム
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+    <div class="md-nav__source">
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+    
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 496 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"/></svg>
+  </div>
+  <div class="md-source__repository">
+    krahets/hello-algo
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+</a>
+    </div>
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+  <ul class="md-nav__list" data-md-scrollfix>
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+    <li class="md-nav__item md-nav__item--nested">
+      
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+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_1" >
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+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hello_algo/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m13.13 22.19-1.63-3.83c1.57-.58 3.04-1.36 4.4-2.27l-2.77 6.1M5.64 12.5l-3.83-1.63 6.1-2.77C7 9.46 6.22 10.93 5.64 12.5M19.22 4c.28 0 .53 0 .74.05.17 1.39-.02 4.25-3.3 7.53-1.7 1.71-3.73 3.02-6.01 3.89l-2.15-2.1c.92-2.31 2.23-4.34 3.92-6.03C15.18 4.58 17.64 4 19.22 4m0-2c-1.98 0-4.98.69-8.22 3.93-2.19 2.19-3.5 4.6-4.35 6.71-.28.75-.09 1.57.46 2.13l2.13 2.12c.38.38.89.61 1.42.61.23 0 .47-.06.7-.15A19.1 19.1 0 0 0 18.07 13c5.66-5.66 3.54-10.61 3.54-10.61S20.7 2 19.22 2m-4.68 7.46c-.78-.78-.78-2.05 0-2.83s2.05-.78 2.83 0c.77.78.78 2.05 0 2.83-.78.78-2.05.78-2.83 0m-5.66 7.07-1.41-1.41 1.41 1.41M6.24 22l3.64-3.64c-.34-.09-.67-.24-.97-.45L4.83 22h1.41M2 22h1.41l4.77-4.76-1.42-1.41L2 20.59V22m0-2.83 4.09-4.08c-.21-.3-.36-.62-.45-.97L2 17.76v1.41Z"/></svg>
+  
+  <span class="md-ellipsis">
+    はじめに
+  </span>
+  
+
+            </a>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_1_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_1">
+            <span class="md-nav__icon md-icon"></span>
+            はじめに
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
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+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_2" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_preface/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M21 4H3a2 2 0 0 0-2 2v13a2 2 0 0 0 2 2h18a2 2 0 0 0 2-2V6a2 2 0 0 0-2-2M3 19V6h8v13H3m18 0h-8V6h8v13m-7-9.5h6V11h-6V9.5m0 2.5h6v1.5h-6V12m0 2.5h6V16h-6v-1.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 0 章 &nbsp; 前書き
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_2" id="__nav_2_label" tabindex="0">
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_2_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_2">
+            <span class="md-nav__icon md-icon"></span>
+            第 0 章 &nbsp; 前書き
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/about_the_book/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.1 &nbsp; この本について
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/suggestions/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.2 &nbsp; 本書の使い方
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_introduction/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#811" class="md-nav__link">
+    <span class="md-ellipsis">
+      8.1.1 &nbsp; ヒープの一般的な操作
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#812" class="md-nav__link">
+    <span class="md-ellipsis">
+      8.1.2 &nbsp; ヒープの実装
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="8.1.2   ヒープの実装">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; ヒープの格納と表現
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; ヒープの先頭要素へのアクセス
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#3" class="md-nav__link">
+    <span class="md-ellipsis">
+      3. &nbsp; ヒープへの要素挿入
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#4" class="md-nav__link">
+    <span class="md-ellipsis">
+      4. &nbsp; ヒープからの先頭要素削除
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#813" class="md-nav__link">
+    <span class="md-ellipsis">
+      8.1.3 &nbsp; ヒープの一般的な応用
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
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+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
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+  </span>
+  
+
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+    </li>
+  
+
+              
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+              
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+  
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+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
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+  
+  
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+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
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+              
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+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
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+
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+    15.2 &nbsp; 分数ナップサック問題
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+  
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+
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+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
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+    15.3 &nbsp; 最大容量問題
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+  
+
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+    </li>
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+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
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+  
+
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+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
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+  
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+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
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+
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+
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+    16.2 &nbsp; 一緒に創作に参加
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+  
+
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+
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+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
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+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
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+                <div class="md-sidebar__scrollwrap">
+                  <div class="md-sidebar__inner">
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+  
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+      目次
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+      
+        <li class="md-nav__item">
+  <a href="#811" class="md-nav__link">
+    <span class="md-ellipsis">
+      8.1.1 &nbsp; ヒープの一般的な操作
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#812" class="md-nav__link">
+    <span class="md-ellipsis">
+      8.1.2 &nbsp; ヒープの実装
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="8.1.2   ヒープの実装">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; ヒープの格納と表現
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; ヒープの先頭要素へのアクセス
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#3" class="md-nav__link">
+    <span class="md-ellipsis">
+      3. &nbsp; ヒープへの要素挿入
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#4" class="md-nav__link">
+    <span class="md-ellipsis">
+      4. &nbsp; ヒープからの先頭要素削除
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#813" class="md-nav__link">
+    <span class="md-ellipsis">
+      8.1.3 &nbsp; ヒープの一般的な応用
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+                  </div>
+                </div>
+              </div>
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+      
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
+    </a>
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+  
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+<!-- Page content -->
+<h1 id="81">8.1 &nbsp; ヒープ<a class="headerlink" href="#81" title="Permanent link">&para;</a></h1>
+<p><u>ヒープ</u>は特定の条件を満たす完備二分木で、主に次の2つのタイプに分類されます（下図参照）。</p>
+<ul>
+<li><u>最小ヒープ</u>：任意のノードの値 <span class="arithmatex">\(\leq\)</span> その子ノードの値。</li>
+<li><u>最大ヒープ</u>：任意のノードの値 <span class="arithmatex">\(\geq\)</span> その子ノードの値。</li>
+</ul>
+<p><a class="glightbox" href="../heap.assets/min_heap_and_max_heap.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="最小ヒープと最大ヒープ" class="animation-figure" src="../heap.assets/min_heap_and_max_heap.png" /></a></p>
+<p align="center"> 図 8-1 &nbsp; 最小ヒープと最大ヒープ </p>
+
+<p>完備二分木の特別なケースとして、ヒープには以下の特性があります：</p>
+<ul>
+<li>最下位層のノードは左から右に埋められ、他の層のノードは完全に埋められています。</li>
+<li>二分木の根ノードをヒープの「先頭」と呼び、最も右下のノードをヒープの「末尾」と呼びます。</li>
+<li>最大ヒープ（最小ヒープ）の場合、先頭要素（根）の値はすべての要素の中で最大（最小）です。</li>
+</ul>
+<h2 id="811">8.1.1 &nbsp; ヒープの一般的な操作<a class="headerlink" href="#811" title="Permanent link">&para;</a></h2>
+<p>多くのプログラミング言語が<u>優先度キュー</u>を提供していることに注意してください。これは優先度付きソートを持つキューとして定義される抽象データ構造です。</p>
+<p>実際には、<strong>ヒープは優先度キューを実装するためによく使用されます。最大ヒープは、要素が降順でデキューされる優先度キューに対応します</strong>。使用の観点から、「優先度キュー」と「ヒープ」を同等のデータ構造と考えることができます。したがって、この本では両者を特別に区別せず、統一して「ヒープ」と呼びます。</p>
+<p>ヒープの一般的な操作を下表に示します。メソッド名はプログラミング言語によって異なる場合があります。</p>
+<p align="center"> 表 8-1 &nbsp; ヒープ操作の効率 </p>
+
+<div class="center-table">
+<table>
+<thead>
+<tr>
+<th>メソッド名</th>
+<th>説明</th>
+<th>時間計算量</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td><code>push()</code></td>
+<td>ヒープに要素を追加</td>
+<td><span class="arithmatex">\(O(\log n)\)</span></td>
+</tr>
+<tr>
+<td><code>pop()</code></td>
+<td>ヒープから先頭要素を削除</td>
+<td><span class="arithmatex">\(O(\log n)\)</span></td>
+</tr>
+<tr>
+<td><code>peek()</code></td>
+<td>先頭要素にアクセス（最大/最小ヒープの場合、最大/最小値）</td>
+<td><span class="arithmatex">\(O(1)\)</span></td>
+</tr>
+<tr>
+<td><code>size()</code></td>
+<td>ヒープ内の要素数を取得</td>
+<td><span class="arithmatex">\(O(1)\)</span></td>
+</tr>
+<tr>
+<td><code>isEmpty()</code></td>
+<td>ヒープが空かどうかをチェック</td>
+<td><span class="arithmatex">\(O(1)\)</span></td>
+</tr>
+</tbody>
+</table>
+</div>
+<p>実際には、プログラミング言語によって提供されるヒープクラス（または優先度キュークラス）を直接使用できます。</p>
+<p>ソートアルゴリズムで「昇順」と「降順」があるように、<code>flag</code>を設定するか<code>Comparator</code>を変更することで「最小ヒープ」と「最大ヒープ」を切り替えることができます。コードは以下の通りです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:14"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><input id="__tabbed_1_14" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label><label for="__tabbed_1_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">heap.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="c1"># 最小ヒープの初期化</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="n">min_heap</span><span class="p">,</span> <span class="n">flag</span> <span class="o">=</span> <span class="p">[],</span> <span class="mi">1</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="c1"># 最大ヒープの初期化</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="n">max_heap</span><span class="p">,</span> <span class="n">flag</span> <span class="o">=</span> <span class="p">[],</span> <span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a><span class="c1"># Pythonのheapqモジュールはデフォルトで最小ヒープを実装</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="c1"># 要素をヒープにプッシュする前に負の値にすることで、順序を反転させ、最大ヒープを実装</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="c1"># この例では、flag = 1は最小ヒープに対応し、flag = -1は最大ヒープに対応</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a><span class="c1"># ヒープに要素をプッシュ</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a><span class="n">heapq</span><span class="o">.</span><span class="n">heappush</span><span class="p">(</span><span class="n">max_heap</span><span class="p">,</span> <span class="n">flag</span> <span class="o">*</span> <span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a><span class="n">heapq</span><span class="o">.</span><span class="n">heappush</span><span class="p">(</span><span class="n">max_heap</span><span class="p">,</span> <span class="n">flag</span> <span class="o">*</span> <span class="mi">3</span><span class="p">)</span>
+<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a><span class="n">heapq</span><span class="o">.</span><span class="n">heappush</span><span class="p">(</span><span class="n">max_heap</span><span class="p">,</span> <span class="n">flag</span> <span class="o">*</span> <span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a><span class="n">heapq</span><span class="o">.</span><span class="n">heappush</span><span class="p">(</span><span class="n">max_heap</span><span class="p">,</span> <span class="n">flag</span> <span class="o">*</span> <span class="mi">5</span><span class="p">)</span>
+<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a><span class="n">heapq</span><span class="o">.</span><span class="n">heappush</span><span class="p">(</span><span class="n">max_heap</span><span class="p">,</span> <span class="n">flag</span> <span class="o">*</span> <span class="mi">4</span><span class="p">)</span>
+<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>
+<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a><span class="c1"># ヒープの先頭要素を取得</span>
+<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a><span class="n">peek</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">flag</span> <span class="o">*</span> <span class="n">max_heap</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="c1"># 5</span>
+<a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a>
+<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a><span class="c1"># ヒープの先頭要素をポップ</span>
+<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a><span class="c1"># ポップされた要素は降順のシーケンスを形成</span>
+<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a><span class="n">val</span> <span class="o">=</span> <span class="n">flag</span> <span class="o">*</span> <span class="n">heapq</span><span class="o">.</span><span class="n">heappop</span><span class="p">(</span><span class="n">max_heap</span><span class="p">)</span> <span class="c1"># 5</span>
+<a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a><span class="n">val</span> <span class="o">=</span> <span class="n">flag</span> <span class="o">*</span> <span class="n">heapq</span><span class="o">.</span><span class="n">heappop</span><span class="p">(</span><span class="n">max_heap</span><span class="p">)</span> <span class="c1"># 4</span>
+<a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a><span class="n">val</span> <span class="o">=</span> <span class="n">flag</span> <span class="o">*</span> <span class="n">heapq</span><span class="o">.</span><span class="n">heappop</span><span class="p">(</span><span class="n">max_heap</span><span class="p">)</span> <span class="c1"># 3</span>
+<a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a><span class="n">val</span> <span class="o">=</span> <span class="n">flag</span> <span class="o">*</span> <span class="n">heapq</span><span class="o">.</span><span class="n">heappop</span><span class="p">(</span><span class="n">max_heap</span><span class="p">)</span> <span class="c1"># 2</span>
+<a id="__codelineno-0-26" name="__codelineno-0-26" href="#__codelineno-0-26"></a><span class="n">val</span> <span class="o">=</span> <span class="n">flag</span> <span class="o">*</span> <span class="n">heapq</span><span class="o">.</span><span class="n">heappop</span><span class="p">(</span><span class="n">max_heap</span><span class="p">)</span> <span class="c1"># 1</span>
+<a id="__codelineno-0-27" name="__codelineno-0-27" href="#__codelineno-0-27"></a>
+<a id="__codelineno-0-28" name="__codelineno-0-28" href="#__codelineno-0-28"></a><span class="c1"># ヒープのサイズを取得</span>
+<a id="__codelineno-0-29" name="__codelineno-0-29" href="#__codelineno-0-29"></a><span class="n">size</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">max_heap</span><span class="p">)</span>
+<a id="__codelineno-0-30" name="__codelineno-0-30" href="#__codelineno-0-30"></a>
+<a id="__codelineno-0-31" name="__codelineno-0-31" href="#__codelineno-0-31"></a><span class="c1"># ヒープが空かどうかをチェック</span>
+<a id="__codelineno-0-32" name="__codelineno-0-32" href="#__codelineno-0-32"></a><span class="n">is_empty</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="ow">not</span> <span class="n">max_heap</span>
+<a id="__codelineno-0-33" name="__codelineno-0-33" href="#__codelineno-0-33"></a>
+<a id="__codelineno-0-34" name="__codelineno-0-34" href="#__codelineno-0-34"></a><span class="c1"># リストからヒープを作成</span>
+<a id="__codelineno-0-35" name="__codelineno-0-35" href="#__codelineno-0-35"></a><span class="n">min_heap</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">4</span><span class="p">]</span>
+<a id="__codelineno-0-36" name="__codelineno-0-36" href="#__codelineno-0-36"></a><span class="n">heapq</span><span class="o">.</span><span class="n">heapify</span><span class="p">(</span><span class="n">min_heap</span><span class="p">)</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">heap.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* ヒープの初期化 */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="c1">// 最小ヒープの初期化</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="n">priority_queue</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">greater</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">minHeap</span><span class="p">;</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="c1">// 最大ヒープの初期化</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="n">priority_queue</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">less</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">;</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="cm">/* ヒープに要素をプッシュ */</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="cm">/* ヒープの先頭要素を取得 */</span>
+<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="kt">int</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">top</span><span class="p">();</span><span class="w"> </span><span class="c1">// 5</span>
+<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a>
+<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="cm">/* ヒープの先頭要素をポップ */</span>
+<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="c1">// ポップされた要素は降順のシーケンスを形成</span>
+<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span><span class="w"> </span><span class="c1">// 5</span>
+<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span><span class="w"> </span><span class="c1">// 4</span>
+<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span><span class="w"> </span><span class="c1">// 3</span>
+<a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span><span class="w"> </span><span class="c1">// 2</span>
+<a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span><span class="w"> </span><span class="c1">// 1</span>
+<a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a>
+<a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a><span class="cm">/* ヒープのサイズを取得 */</span>
+<a id="__codelineno-1-26" name="__codelineno-1-26" href="#__codelineno-1-26"></a><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
+<a id="__codelineno-1-27" name="__codelineno-1-27" href="#__codelineno-1-27"></a>
+<a id="__codelineno-1-28" name="__codelineno-1-28" href="#__codelineno-1-28"></a><span class="cm">/* ヒープが空かどうかをチェック */</span>
+<a id="__codelineno-1-29" name="__codelineno-1-29" href="#__codelineno-1-29"></a><span class="kt">bool</span><span class="w"> </span><span class="n">isEmpty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">empty</span><span class="p">();</span>
+<a id="__codelineno-1-30" name="__codelineno-1-30" href="#__codelineno-1-30"></a>
+<a id="__codelineno-1-31" name="__codelineno-1-31" href="#__codelineno-1-31"></a><span class="cm">/* リストからヒープを作成 */</span>
+<a id="__codelineno-1-32" name="__codelineno-1-32" href="#__codelineno-1-32"></a><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">input</span><span class="p">{</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">};</span>
+<a id="__codelineno-1-33" name="__codelineno-1-33" href="#__codelineno-1-33"></a><span class="n">priority_queue</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">greater</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">minHeap</span><span class="p">(</span><span class="n">input</span><span class="p">.</span><span class="n">begin</span><span class="p">(),</span><span class="w"> </span><span class="n">input</span><span class="p">.</span><span class="n">end</span><span class="p">());</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">heap.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* ヒープの初期化 */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="c1">// 最小ヒープの初期化</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="n">Queue</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">minHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">PriorityQueue</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="c1">// 最大ヒープの初期化（ラムダ式でComparatorを変更するだけ）</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="n">Queue</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">maxHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">PriorityQueue</span><span class="o">&lt;&gt;</span><span class="p">((</span><span class="n">a</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="p">)</span><span class="w"> </span><span class="o">-&gt;</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">a</span><span class="p">);</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="cm">/* ヒープに要素をプッシュ */</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="n">maxHeap</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="n">maxHeap</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="n">maxHeap</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="n">maxHeap</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="n">maxHeap</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
+<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="cm">/* ヒープの先頭要素を取得 */</span>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="kt">int</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">peek</span><span class="p">();</span><span class="w"> </span><span class="c1">// 5</span>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a>
+<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="cm">/* ヒープの先頭要素をポップ */</span>
+<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="c1">// ポップされた要素は降順のシーケンスを形成</span>
+<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">poll</span><span class="p">();</span><span class="w"> </span><span class="c1">// 5</span>
+<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">poll</span><span class="p">();</span><span class="w"> </span><span class="c1">// 4</span>
+<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">poll</span><span class="p">();</span><span class="w"> </span><span class="c1">// 3</span>
+<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">poll</span><span class="p">();</span><span class="w"> </span><span class="c1">// 2</span>
+<a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">poll</span><span class="p">();</span><span class="w"> </span><span class="c1">// 1</span>
+<a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a>
+<a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a><span class="cm">/* ヒープのサイズを取得 */</span>
+<a id="__codelineno-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></a><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">size</span><span class="p">();</span>
+<a id="__codelineno-2-27" name="__codelineno-2-27" href="#__codelineno-2-27"></a>
+<a id="__codelineno-2-28" name="__codelineno-2-28" href="#__codelineno-2-28"></a><span class="cm">/* ヒープが空かどうかをチェック */</span>
+<a id="__codelineno-2-29" name="__codelineno-2-29" href="#__codelineno-2-29"></a><span class="kt">boolean</span><span class="w"> </span><span class="n">isEmpty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">isEmpty</span><span class="p">();</span>
+<a id="__codelineno-2-30" name="__codelineno-2-30" href="#__codelineno-2-30"></a>
+<a id="__codelineno-2-31" name="__codelineno-2-31" href="#__codelineno-2-31"></a><span class="cm">/* リストからヒープを作成 */</span>
+<a id="__codelineno-2-32" name="__codelineno-2-32" href="#__codelineno-2-32"></a><span class="n">minHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">PriorityQueue</span><span class="o">&lt;&gt;</span><span class="p">(</span><span class="n">Arrays</span><span class="p">.</span><span class="na">asList</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">));</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">heap.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* ヒープの初期化 */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="c1">// 最小ヒープの初期化</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="n">PriorityQueue</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">minHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">();</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="c1">// 最大ヒープの初期化（ラムダ式でComparatorを変更するだけ）</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="n">PriorityQueue</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">maxHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="n">Comparer</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">.</span><span class="n">Create</span><span class="p">((</span><span class="n">x</span><span class="p">,</span><span class="w"> </span><span class="n">y</span><span class="p">)</span><span class="w"> </span><span class="o">=&gt;</span><span class="w"> </span><span class="n">y</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">x</span><span class="p">));</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="cm">/* ヒープに要素をプッシュ */</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">Enqueue</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">Enqueue</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">);</span>
+<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">Enqueue</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">Enqueue</span><span class="p">(</span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">);</span>
+<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="n">maxHeap</span><span class="p">.</span><span class="n">Enqueue</span><span class="p">(</span><span class="mi">4</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">);</span>
+<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a>
+<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="cm">/* ヒープの先頭要素を取得 */</span>
+<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="kt">int</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">Peek</span><span class="p">();</span><span class="c1">//5</span>
+<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a>
+<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="cm">/* ヒープの先頭要素をポップ */</span>
+<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="c1">// ポップされた要素は降順のシーケンスを形成</span>
+<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">Dequeue</span><span class="p">();</span><span class="w">  </span><span class="c1">// 5</span>
+<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">Dequeue</span><span class="p">();</span><span class="w">  </span><span class="c1">// 4</span>
+<a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">Dequeue</span><span class="p">();</span><span class="w">  </span><span class="c1">// 3</span>
+<a id="__codelineno-3-22" name="__codelineno-3-22" href="#__codelineno-3-22"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">Dequeue</span><span class="p">();</span><span class="w">  </span><span class="c1">// 2</span>
+<a id="__codelineno-3-23" name="__codelineno-3-23" href="#__codelineno-3-23"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">Dequeue</span><span class="p">();</span><span class="w">  </span><span class="c1">// 1</span>
+<a id="__codelineno-3-24" name="__codelineno-3-24" href="#__codelineno-3-24"></a>
+<a id="__codelineno-3-25" name="__codelineno-3-25" href="#__codelineno-3-25"></a><span class="cm">/* ヒープのサイズを取得 */</span>
+<a id="__codelineno-3-26" name="__codelineno-3-26" href="#__codelineno-3-26"></a><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">Count</span><span class="p">;</span>
+<a id="__codelineno-3-27" name="__codelineno-3-27" href="#__codelineno-3-27"></a>
+<a id="__codelineno-3-28" name="__codelineno-3-28" href="#__codelineno-3-28"></a><span class="cm">/* ヒープが空かどうかをチェック */</span>
+<a id="__codelineno-3-29" name="__codelineno-3-29" href="#__codelineno-3-29"></a><span class="kt">bool</span><span class="w"> </span><span class="n">isEmpty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">Count</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-3-30" name="__codelineno-3-30" href="#__codelineno-3-30"></a>
+<a id="__codelineno-3-31" name="__codelineno-3-31" href="#__codelineno-3-31"></a><span class="cm">/* リストからヒープを作成 */</span>
+<a id="__codelineno-3-32" name="__codelineno-3-32" href="#__codelineno-3-32"></a><span class="n">minHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">PriorityQueue</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">&gt;</span><span class="p">([(</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span><span class="p">),</span><span class="w"> </span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">),</span><span class="w"> </span><span class="p">(</span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">),</span><span class="w"> </span><span class="p">(</span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">),</span><span class="w"> </span><span class="p">(</span><span class="mi">4</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">)]);</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">heap.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="c1">// Goでは、heap.Interfaceを実装することで整数の最大ヒープを構築できます</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="c1">// heap.Interfaceを実装するには、sort.Interfaceも実装する必要があります</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="kd">type</span><span class="w"> </span><span class="nx">intHeap</span><span class="w"> </span><span class="p">[]</span><span class="kt">any</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="c1">// heap.InterfaceのPushメソッド、要素をヒープにプッシュ</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">intHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">Push</span><span class="p">(</span><span class="nx">x</span><span class="w"> </span><span class="kt">any</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="w">    </span><span class="c1">// PushとPopの両方でポインタレシーバーを使用</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="w">    </span><span class="c1">// スライスの要素を調整するだけでなく、その長さも変更するため</span>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w">    </span><span class="o">*</span><span class="nx">h</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">,</span><span class="w"> </span><span class="nx">x</span><span class="p">.(</span><span class="kt">int</span><span class="p">))</span>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="p">}</span>
+<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a>
+<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="c1">// heap.InterfaceのPopメソッド、ヒープの先頭要素を削除</span>
+<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">intHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">Pop</span><span class="p">()</span><span class="w"> </span><span class="kt">any</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="w">    </span><span class="c1">// ヒープからポップする要素は末尾に格納</span>
+<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="w">    </span><span class="nx">last</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)[</span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="w">    </span><span class="o">*</span><span class="nx">h</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)[:</span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nx">last</span>
+<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="p">}</span>
+<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a>
+<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="c1">// sort.InterfaceのLenメソッド</span>
+<a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">intHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">Len</span><span class="p">()</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-22" name="__codelineno-4-22" href="#__codelineno-4-22"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)</span>
+<a id="__codelineno-4-23" name="__codelineno-4-23" href="#__codelineno-4-23"></a><span class="p">}</span>
+<a id="__codelineno-4-24" name="__codelineno-4-24" href="#__codelineno-4-24"></a>
+<a id="__codelineno-4-25" name="__codelineno-4-25" href="#__codelineno-4-25"></a><span class="c1">// sort.InterfaceのLessメソッド</span>
+<a id="__codelineno-4-26" name="__codelineno-4-26" href="#__codelineno-4-26"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">intHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">Less</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-27" name="__codelineno-4-27" href="#__codelineno-4-27"></a><span class="w">    </span><span class="c1">// 最小ヒープを実装したい場合は、これを小なり比較に変更</span>
+<a id="__codelineno-4-28" name="__codelineno-4-28" href="#__codelineno-4-28"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)[</span><span class="nx">i</span><span class="p">].(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">&gt;</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)[</span><span class="nx">j</span><span class="p">].(</span><span class="kt">int</span><span class="p">)</span>
+<a id="__codelineno-4-29" name="__codelineno-4-29" href="#__codelineno-4-29"></a><span class="p">}</span>
+<a id="__codelineno-4-30" name="__codelineno-4-30" href="#__codelineno-4-30"></a>
+<a id="__codelineno-4-31" name="__codelineno-4-31" href="#__codelineno-4-31"></a><span class="c1">// sort.InterfaceのSwapメソッド</span>
+<a id="__codelineno-4-32" name="__codelineno-4-32" href="#__codelineno-4-32"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">intHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">Swap</span><span class="p">(</span><span class="nx">i</span><span class="p">,</span><span class="w"> </span><span class="nx">j</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-33" name="__codelineno-4-33" href="#__codelineno-4-33"></a><span class="w">    </span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)[</span><span class="nx">i</span><span class="p">],</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)[</span><span class="nx">j</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)[</span><span class="nx">j</span><span class="p">],</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)[</span><span class="nx">i</span><span class="p">]</span>
+<a id="__codelineno-4-34" name="__codelineno-4-34" href="#__codelineno-4-34"></a><span class="p">}</span>
+<a id="__codelineno-4-35" name="__codelineno-4-35" href="#__codelineno-4-35"></a>
+<a id="__codelineno-4-36" name="__codelineno-4-36" href="#__codelineno-4-36"></a><span class="c1">// Top ヒープの先頭要素を取得</span>
+<a id="__codelineno-4-37" name="__codelineno-4-37" href="#__codelineno-4-37"></a><span class="kd">func</span><span class="w"> </span><span class="p">(</span><span class="nx">h</span><span class="w"> </span><span class="o">*</span><span class="nx">intHeap</span><span class="p">)</span><span class="w"> </span><span class="nx">Top</span><span class="p">()</span><span class="w"> </span><span class="kt">any</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-38" name="__codelineno-4-38" href="#__codelineno-4-38"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="o">*</span><span class="nx">h</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
+<a id="__codelineno-4-39" name="__codelineno-4-39" href="#__codelineno-4-39"></a><span class="p">}</span>
+<a id="__codelineno-4-40" name="__codelineno-4-40" href="#__codelineno-4-40"></a>
+<a id="__codelineno-4-41" name="__codelineno-4-41" href="#__codelineno-4-41"></a><span class="cm">/* ドライバーコード */</span>
+<a id="__codelineno-4-42" name="__codelineno-4-42" href="#__codelineno-4-42"></a><span class="kd">func</span><span class="w"> </span><span class="nx">TestHeap</span><span class="p">(</span><span class="nx">t</span><span class="w"> </span><span class="o">*</span><span class="nx">testing</span><span class="p">.</span><span class="nx">T</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-43" name="__codelineno-4-43" href="#__codelineno-4-43"></a><span class="w">    </span><span class="cm">/* ヒープの初期化 */</span>
+<a id="__codelineno-4-44" name="__codelineno-4-44" href="#__codelineno-4-44"></a><span class="w">    </span><span class="c1">// 最大ヒープの初期化</span>
+<a id="__codelineno-4-45" name="__codelineno-4-45" href="#__codelineno-4-45"></a><span class="w">    </span><span class="nx">maxHeap</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">intHeap</span><span class="p">{}</span>
+<a id="__codelineno-4-46" name="__codelineno-4-46" href="#__codelineno-4-46"></a><span class="w">    </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Init</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">)</span>
+<a id="__codelineno-4-47" name="__codelineno-4-47" href="#__codelineno-4-47"></a><span class="w">    </span><span class="cm">/* ヒープに要素をプッシュ */</span>
+<a id="__codelineno-4-48" name="__codelineno-4-48" href="#__codelineno-4-48"></a><span class="w">    </span><span class="c1">// heap.Interfaceのメソッドを呼び出して要素を追加</span>
+<a id="__codelineno-4-49" name="__codelineno-4-49" href="#__codelineno-4-49"></a><span class="w">    </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Push</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-4-50" name="__codelineno-4-50" href="#__codelineno-4-50"></a><span class="w">    </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Push</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">)</span>
+<a id="__codelineno-4-51" name="__codelineno-4-51" href="#__codelineno-4-51"></a><span class="w">    </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Push</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-4-52" name="__codelineno-4-52" href="#__codelineno-4-52"></a><span class="w">    </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Push</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">)</span>
+<a id="__codelineno-4-53" name="__codelineno-4-53" href="#__codelineno-4-53"></a><span class="w">    </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Push</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">)</span>
+<a id="__codelineno-4-54" name="__codelineno-4-54" href="#__codelineno-4-54"></a>
+<a id="__codelineno-4-55" name="__codelineno-4-55" href="#__codelineno-4-55"></a><span class="w">    </span><span class="cm">/* ヒープの先頭要素を取得 */</span>
+<a id="__codelineno-4-56" name="__codelineno-4-56" href="#__codelineno-4-56"></a><span class="w">    </span><span class="nx">top</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">maxHeap</span><span class="p">.</span><span class="nx">Top</span><span class="p">()</span>
+<a id="__codelineno-4-57" name="__codelineno-4-57" href="#__codelineno-4-57"></a><span class="w">    </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Printf</span><span class="p">(</span><span class="s">&quot;ヒープの先頭要素は %d\n&quot;</span><span class="p">,</span><span class="w"> </span><span class="nx">top</span><span class="p">)</span>
+<a id="__codelineno-4-58" name="__codelineno-4-58" href="#__codelineno-4-58"></a>
+<a id="__codelineno-4-59" name="__codelineno-4-59" href="#__codelineno-4-59"></a><span class="w">    </span><span class="cm">/* ヒープの先頭要素をポップ */</span>
+<a id="__codelineno-4-60" name="__codelineno-4-60" href="#__codelineno-4-60"></a><span class="w">    </span><span class="c1">// heap.Interfaceのメソッドを呼び出して要素を削除</span>
+<a id="__codelineno-4-61" name="__codelineno-4-61" href="#__codelineno-4-61"></a><span class="w">    </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Pop</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="c1">// 5</span>
+<a id="__codelineno-4-62" name="__codelineno-4-62" href="#__codelineno-4-62"></a><span class="w">    </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Pop</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="c1">// 4</span>
+<a id="__codelineno-4-63" name="__codelineno-4-63" href="#__codelineno-4-63"></a><span class="w">    </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Pop</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="c1">// 3</span>
+<a id="__codelineno-4-64" name="__codelineno-4-64" href="#__codelineno-4-64"></a><span class="w">    </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Pop</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="c1">// 2</span>
+<a id="__codelineno-4-65" name="__codelineno-4-65" href="#__codelineno-4-65"></a><span class="w">    </span><span class="nx">heap</span><span class="p">.</span><span class="nx">Pop</span><span class="p">(</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="c1">// 1</span>
+<a id="__codelineno-4-66" name="__codelineno-4-66" href="#__codelineno-4-66"></a>
+<a id="__codelineno-4-67" name="__codelineno-4-67" href="#__codelineno-4-67"></a><span class="w">    </span><span class="cm">/* ヒープのサイズを取得 */</span>
+<a id="__codelineno-4-68" name="__codelineno-4-68" href="#__codelineno-4-68"></a><span class="w">    </span><span class="nx">size</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">maxHeap</span><span class="p">)</span>
+<a id="__codelineno-4-69" name="__codelineno-4-69" href="#__codelineno-4-69"></a><span class="w">    </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Printf</span><span class="p">(</span><span class="s">&quot;ヒープ内の要素数は %d\n&quot;</span><span class="p">,</span><span class="w"> </span><span class="nx">size</span><span class="p">)</span>
+<a id="__codelineno-4-70" name="__codelineno-4-70" href="#__codelineno-4-70"></a>
+<a id="__codelineno-4-71" name="__codelineno-4-71" href="#__codelineno-4-71"></a><span class="w">    </span><span class="cm">/* ヒープが空かどうかをチェック */</span>
+<a id="__codelineno-4-72" name="__codelineno-4-72" href="#__codelineno-4-72"></a><span class="w">    </span><span class="nx">isEmpty</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="o">*</span><span class="nx">maxHeap</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-4-73" name="__codelineno-4-73" href="#__codelineno-4-73"></a><span class="w">    </span><span class="nx">fmt</span><span class="p">.</span><span class="nx">Printf</span><span class="p">(</span><span class="s">&quot;ヒープは空ですか？ %t\n&quot;</span><span class="p">,</span><span class="w"> </span><span class="nx">isEmpty</span><span class="p">)</span>
+<a id="__codelineno-4-74" name="__codelineno-4-74" href="#__codelineno-4-74"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">heap.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* ヒープの初期化 */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="c1">// SwiftのHeap型は最大ヒープと最小ヒープの両方をサポートし、swift-collectionsライブラリが必要</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="kd">var</span><span class="w"> </span><span class="nv">heap</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">Heap</span><span class="p">&lt;</span><span class="nb">Int</span><span class="p">&gt;()</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="cm">/* ヒープに要素をプッシュ */</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="n">heap</span><span class="p">.</span><span class="bp">insert</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="n">heap</span><span class="p">.</span><span class="bp">insert</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="n">heap</span><span class="p">.</span><span class="bp">insert</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="n">heap</span><span class="p">.</span><span class="bp">insert</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="n">heap</span><span class="p">.</span><span class="bp">insert</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
+<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="cm">/* ヒープの先頭要素を取得 */</span>
+<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="kd">var</span><span class="w"> </span><span class="nv">peek</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">heap</span><span class="p">.</span><span class="bp">max</span><span class="p">()</span><span class="o">!</span>
+<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a>
+<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="cm">/* ヒープの先頭要素をポップ */</span>
+<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="n">peek</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">heap</span><span class="p">.</span><span class="n">removeMax</span><span class="p">()</span><span class="w"> </span><span class="c1">// 5</span>
+<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="n">peek</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">heap</span><span class="p">.</span><span class="n">removeMax</span><span class="p">()</span><span class="w"> </span><span class="c1">// 4</span>
+<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="n">peek</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">heap</span><span class="p">.</span><span class="n">removeMax</span><span class="p">()</span><span class="w"> </span><span class="c1">// 3</span>
+<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="n">peek</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">heap</span><span class="p">.</span><span class="n">removeMax</span><span class="p">()</span><span class="w"> </span><span class="c1">// 2</span>
+<a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a><span class="n">peek</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">heap</span><span class="p">.</span><span class="n">removeMax</span><span class="p">()</span><span class="w"> </span><span class="c1">// 1</span>
+<a id="__codelineno-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></a>
+<a id="__codelineno-5-22" name="__codelineno-5-22" href="#__codelineno-5-22"></a><span class="cm">/* ヒープのサイズを取得 */</span>
+<a id="__codelineno-5-23" name="__codelineno-5-23" href="#__codelineno-5-23"></a><span class="kd">let</span><span class="w"> </span><span class="nv">size</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">heap</span><span class="p">.</span><span class="bp">count</span>
+<a id="__codelineno-5-24" name="__codelineno-5-24" href="#__codelineno-5-24"></a>
+<a id="__codelineno-5-25" name="__codelineno-5-25" href="#__codelineno-5-25"></a><span class="cm">/* ヒープが空かどうかをチェック */</span>
+<a id="__codelineno-5-26" name="__codelineno-5-26" href="#__codelineno-5-26"></a><span class="kd">let</span><span class="w"> </span><span class="nv">isEmpty</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">heap</span><span class="p">.</span><span class="bp">isEmpty</span>
+<a id="__codelineno-5-27" name="__codelineno-5-27" href="#__codelineno-5-27"></a>
+<a id="__codelineno-5-28" name="__codelineno-5-28" href="#__codelineno-5-28"></a><span class="cm">/* リストからヒープを作成 */</span>
+<a id="__codelineno-5-29" name="__codelineno-5-29" href="#__codelineno-5-29"></a><span class="kd">let</span><span class="w"> </span><span class="nv">heap2</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">Heap</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">])</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">heap.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="c1">// JavaScriptは組み込みのHeapクラスを提供していません</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">heap.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="c1">// TypeScriptは組み込みのHeapクラスを提供していません</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">heap.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="c1">// Dartは組み込みのHeapクラスを提供していません</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">heap.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="k">use</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">collections</span><span class="p">::</span><span class="n">BinaryHeap</span><span class="p">;</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">use</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">cmp</span><span class="p">::</span><span class="n">Reverse</span><span class="p">;</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="cm">/* ヒープの初期化 */</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="c1">// 最小ヒープの初期化</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">min_heap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">BinaryHeap</span><span class="p">::</span><span class="o">&lt;</span><span class="n">Reverse</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;&gt;</span><span class="p">::</span><span class="n">new</span><span class="p">();</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="c1">// 最大ヒープの初期化</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">max_heap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">BinaryHeap</span><span class="p">::</span><span class="n">new</span><span class="p">();</span>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="cm">/* ヒープに要素をプッシュ */</span>
+<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="n">max_heap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="n">max_heap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
+<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="n">max_heap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="n">max_heap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
+<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="n">max_heap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
+<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a>
+<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="cm">/* ヒープの先頭要素を取得 */</span>
+<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="kd">let</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max_heap</span><span class="p">.</span><span class="n">peek</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span><span class="w">  </span><span class="c1">// 5</span>
+<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a>
+<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="cm">/* ヒープの先頭要素をポップ */</span>
+<a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="c1">// ポップされた要素は降順のシーケンスを形成</span>
+<a id="__codelineno-9-22" name="__codelineno-9-22" href="#__codelineno-9-22"></a><span class="kd">let</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max_heap</span><span class="p">.</span><span class="n">pop</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span><span class="w">   </span><span class="c1">// 5</span>
+<a id="__codelineno-9-23" name="__codelineno-9-23" href="#__codelineno-9-23"></a><span class="kd">let</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max_heap</span><span class="p">.</span><span class="n">pop</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span><span class="w">   </span><span class="c1">// 4</span>
+<a id="__codelineno-9-24" name="__codelineno-9-24" href="#__codelineno-9-24"></a><span class="kd">let</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max_heap</span><span class="p">.</span><span class="n">pop</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span><span class="w">   </span><span class="c1">// 3</span>
+<a id="__codelineno-9-25" name="__codelineno-9-25" href="#__codelineno-9-25"></a><span class="kd">let</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max_heap</span><span class="p">.</span><span class="n">pop</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span><span class="w">   </span><span class="c1">// 2</span>
+<a id="__codelineno-9-26" name="__codelineno-9-26" href="#__codelineno-9-26"></a><span class="kd">let</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max_heap</span><span class="p">.</span><span class="n">pop</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span><span class="w">   </span><span class="c1">// 1</span>
+<a id="__codelineno-9-27" name="__codelineno-9-27" href="#__codelineno-9-27"></a>
+<a id="__codelineno-9-28" name="__codelineno-9-28" href="#__codelineno-9-28"></a><span class="cm">/* ヒープのサイズを取得 */</span>
+<a id="__codelineno-9-29" name="__codelineno-9-29" href="#__codelineno-9-29"></a><span class="kd">let</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max_heap</span><span class="p">.</span><span class="n">len</span><span class="p">();</span>
+<a id="__codelineno-9-30" name="__codelineno-9-30" href="#__codelineno-9-30"></a>
+<a id="__codelineno-9-31" name="__codelineno-9-31" href="#__codelineno-9-31"></a><span class="cm">/* ヒープが空かどうかをチェック */</span>
+<a id="__codelineno-9-32" name="__codelineno-9-32" href="#__codelineno-9-32"></a><span class="kd">let</span><span class="w"> </span><span class="n">is_empty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max_heap</span><span class="p">.</span><span class="n">is_empty</span><span class="p">();</span>
+<a id="__codelineno-9-33" name="__codelineno-9-33" href="#__codelineno-9-33"></a>
+<a id="__codelineno-9-34" name="__codelineno-9-34" href="#__codelineno-9-34"></a><span class="cm">/* リストからヒープを作成 */</span>
+<a id="__codelineno-9-35" name="__codelineno-9-35" href="#__codelineno-9-35"></a><span class="kd">let</span><span class="w"> </span><span class="n">min_heap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">BinaryHeap</span><span class="p">::</span><span class="n">from</span><span class="p">(</span><span class="fm">vec!</span><span class="p">[</span><span class="n">Reverse</span><span class="p">(</span><span class="mi">1</span><span class="p">),</span><span class="w"> </span><span class="n">Reverse</span><span class="p">(</span><span class="mi">3</span><span class="p">),</span><span class="w"> </span><span class="n">Reverse</span><span class="p">(</span><span class="mi">2</span><span class="p">),</span><span class="w"> </span><span class="n">Reverse</span><span class="p">(</span><span class="mi">5</span><span class="p">),</span><span class="w"> </span><span class="n">Reverse</span><span class="p">(</span><span class="mi">4</span><span class="p">)]);</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">heap.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="c1">// Cは組み込みのHeapクラスを提供していません</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">heap.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* ヒープの初期化 */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="c1">// 最小ヒープの初期化</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="kd">var</span><span class="w"> </span><span class="nv">minHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">PriorityQueue</span><span class="o">&lt;</span><span class="kt">Int</span><span class="o">&gt;</span><span class="p">()</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="c1">// 最大ヒープの初期化（ラムダ式でComparatorを変更するだけ）</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="kd">val</span><span class="w"> </span><span class="nv">maxHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">PriorityQueue</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">a</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">,</span><span class="w"> </span><span class="n">b</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="o">-&gt;</span><span class="w"> </span><span class="n">b</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">a</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="cm">/* ヒープに要素をプッシュ */</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="n">maxHeap</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-11-9" name="__codelineno-11-9" href="#__codelineno-11-9"></a><span class="n">maxHeap</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="m">3</span><span class="p">)</span>
+<a id="__codelineno-11-10" name="__codelineno-11-10" href="#__codelineno-11-10"></a><span class="n">maxHeap</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="m">2</span><span class="p">)</span>
+<a id="__codelineno-11-11" name="__codelineno-11-11" href="#__codelineno-11-11"></a><span class="n">maxHeap</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="m">5</span><span class="p">)</span>
+<a id="__codelineno-11-12" name="__codelineno-11-12" href="#__codelineno-11-12"></a><span class="n">maxHeap</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="m">4</span><span class="p">)</span>
+<a id="__codelineno-11-13" name="__codelineno-11-13" href="#__codelineno-11-13"></a>
+<a id="__codelineno-11-14" name="__codelineno-11-14" href="#__codelineno-11-14"></a><span class="cm">/* ヒープの先頭要素を取得 */</span>
+<a id="__codelineno-11-15" name="__codelineno-11-15" href="#__codelineno-11-15"></a><span class="kd">var</span><span class="w"> </span><span class="nv">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">peek</span><span class="p">()</span><span class="w"> </span><span class="c1">// 5</span>
+<a id="__codelineno-11-16" name="__codelineno-11-16" href="#__codelineno-11-16"></a>
+<a id="__codelineno-11-17" name="__codelineno-11-17" href="#__codelineno-11-17"></a><span class="cm">/* ヒープの先頭要素をポップ */</span>
+<a id="__codelineno-11-18" name="__codelineno-11-18" href="#__codelineno-11-18"></a><span class="c1">// ポップされた要素は降順のシーケンスを形成</span>
+<a id="__codelineno-11-19" name="__codelineno-11-19" href="#__codelineno-11-19"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">poll</span><span class="p">()</span><span class="w"> </span><span class="c1">// 5</span>
+<a id="__codelineno-11-20" name="__codelineno-11-20" href="#__codelineno-11-20"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">poll</span><span class="p">()</span><span class="w"> </span><span class="c1">// 4</span>
+<a id="__codelineno-11-21" name="__codelineno-11-21" href="#__codelineno-11-21"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">poll</span><span class="p">()</span><span class="w"> </span><span class="c1">// 3</span>
+<a id="__codelineno-11-22" name="__codelineno-11-22" href="#__codelineno-11-22"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">poll</span><span class="p">()</span><span class="w"> </span><span class="c1">// 2</span>
+<a id="__codelineno-11-23" name="__codelineno-11-23" href="#__codelineno-11-23"></a><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">poll</span><span class="p">()</span><span class="w"> </span><span class="c1">// 1</span>
+<a id="__codelineno-11-24" name="__codelineno-11-24" href="#__codelineno-11-24"></a>
+<a id="__codelineno-11-25" name="__codelineno-11-25" href="#__codelineno-11-25"></a><span class="cm">/* ヒープのサイズを取得 */</span>
+<a id="__codelineno-11-26" name="__codelineno-11-26" href="#__codelineno-11-26"></a><span class="kd">val</span><span class="w"> </span><span class="nv">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">size</span>
+<a id="__codelineno-11-27" name="__codelineno-11-27" href="#__codelineno-11-27"></a>
+<a id="__codelineno-11-28" name="__codelineno-11-28" href="#__codelineno-11-28"></a><span class="cm">/* ヒープが空かどうかをチェック */</span>
+<a id="__codelineno-11-29" name="__codelineno-11-29" href="#__codelineno-11-29"></a><span class="kd">val</span><span class="w"> </span><span class="nv">isEmpty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">isEmpty</span><span class="p">()</span>
+<a id="__codelineno-11-30" name="__codelineno-11-30" href="#__codelineno-11-30"></a>
+<a id="__codelineno-11-31" name="__codelineno-11-31" href="#__codelineno-11-31"></a><span class="cm">/* リストからヒープを作成 */</span>
+<a id="__codelineno-11-32" name="__codelineno-11-32" href="#__codelineno-11-32"></a><span class="n">minHeap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">PriorityQueue</span><span class="p">(</span><span class="n">mutableListOf</span><span class="p">(</span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="m">3</span><span class="p">,</span><span class="w"> </span><span class="m">2</span><span class="p">,</span><span class="w"> </span><span class="m">5</span><span class="p">,</span><span class="w"> </span><span class="m">4</span><span class="p">))</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">heap.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">heap.zig</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h2 id="812">8.1.2 &nbsp; ヒープの実装<a class="headerlink" href="#812" title="Permanent link">&para;</a></h2>
+<p>以下の実装は最大ヒープです。最小ヒープに変換するには、すべてのサイズ論理比較を反転させるだけです（例えば、<span class="arithmatex">\(\geq\)</span>を<span class="arithmatex">\(\leq\)</span>に置き換える）。興味のある読者は自分で実装することをお勧めします。</p>
+<h3 id="1">1. &nbsp; ヒープの格納と表現<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<p>「二分木」の節で述べたように、完備二分木は配列表現に非常に適しています。ヒープは完備二分木の一種なので、<strong>配列を使用してヒープを格納します</strong>。</p>
+<p>配列を使用して二分木を表現する場合、要素はノード値を表し、インデックスは二分木内のノード位置を表します。<strong>ノードポインタはインデックスマッピング公式を通じて実装されます</strong>。</p>
+<p>下図に示すように、インデックス<span class="arithmatex">\(i\)</span>が与えられた場合、その左の子のインデックスは<span class="arithmatex">\(2i + 1\)</span>、右の子のインデックスは<span class="arithmatex">\(2i + 2\)</span>、親のインデックスは<span class="arithmatex">\((i - 1) / 2\)</span>（床除算）です。インデックスが範囲外の場合、nullノードまたはノードが存在しないことを意味します。</p>
+<p><a class="glightbox" href="../heap.assets/representation_of_heap.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="ヒープの表現と格納" class="animation-figure" src="../heap.assets/representation_of_heap.png" /></a></p>
+<p align="center"> 図 8-2 &nbsp; ヒープの表現と格納 </p>
+
+<p>後で便利に使用するため、インデックスマッピング公式を関数にカプセル化できます：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:14"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><input id="__tabbed_2_14" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label><label for="__tabbed_2_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.py</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">left</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;左の子ノードのインデックスを取得&quot;&quot;&quot;</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a>    <span class="k">return</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">1</span>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="k">def</span><span class="w"> </span><span class="nf">right</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;右の子ノードのインデックスを取得&quot;&quot;&quot;</span>
+<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a>    <span class="k">return</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">2</span>
+<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a>
+<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="k">def</span><span class="w"> </span><span class="nf">parent</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;親ノードのインデックスを取得&quot;&quot;&quot;</span>
+<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a>    <span class="k">return</span> <span class="p">(</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span>  <span class="c1"># 整数除算で切り下げ</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.cpp</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 左の子ノードのインデックスを取得 */</span>
+<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">left</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="p">}</span>
+<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a>
+<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="cm">/* 右の子ノードのインデックスを取得 */</span>
+<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="kt">int</span><span class="w"> </span><span class="nf">right</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="p">}</span>
+<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a>
+<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="cm">/* 親ノードのインデックスを取得 */</span>
+<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="kt">int</span><span class="w"> </span><span class="nf">parent</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 整数除算で切り下げ</span>
+<a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.java</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 左の子ノードのインデックスを取得 */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">left</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="p">}</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="cm">/* 右の子ノードのインデックスを取得 */</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="kt">int</span><span class="w"> </span><span class="nf">right</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="p">}</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="cm">/* 親ノードのインデックスを取得 */</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="kt">int</span><span class="w"> </span><span class="nf">parent</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 整数除算で切り下げ</span>
+<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.cs</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Left</span><span class="p">}</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Right</span><span class="p">}</span>
+<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a>
+<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="na">[class]</span><span class="p">{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Parent</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.go</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">maxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">left</span><span class="p">}</span>
+<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a>
+<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">maxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">right</span><span class="p">}</span>
+<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a>
+<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">maxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">parent</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="kr">left</span><span class="p">}</span>
+<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a>
+<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="kr">right</span><span class="p">}</span>
+<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a>
+<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">parent</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.js</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">left</span><span class="p">}</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a>
+<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">right</span><span class="p">}</span>
+<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a>
+<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">parent</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.ts</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">left</span><span class="p">}</span>
+<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a>
+<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">right</span><span class="p">}</span>
+<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a>
+<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">parent</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.dart</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">_left</span><span class="p">}</span>
+<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">_right</span><span class="p">}</span>
+<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a>
+<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">_parent</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.rs</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">left</span><span class="p">}</span>
+<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a>
+<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">right</span><span class="p">}</span>
+<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a>
+<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">parent</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.c</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">left</span><span class="p">}</span>
+<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a>
+<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">right</span><span class="p">}</span>
+<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a>
+<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">parent</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.kt</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">left</span><span class="p">}</span>
+<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a>
+<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">right</span><span class="p">}</span>
+<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a>
+<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">parent</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">MaxHeap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">left</span><span class="p">}</span>
+<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a>
+<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">MaxHeap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">right</span><span class="p">}</span>
+<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a>
+<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">MaxHeap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">parent</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.zig</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">left</span><span class="p">}</span>
+<a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a>
+<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">right</span><span class="p">}</span>
+<a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a>
+<a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">parent</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h3 id="2">2. &nbsp; ヒープの先頭要素へのアクセス<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
+<p>ヒープの先頭要素は二分木の根ノードで、リストの最初の要素でもあります：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="3:14"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><input id="__tabbed_3_14" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label><label for="__tabbed_3_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.py</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">peek</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;ヒープの先頭要素にアクセス&quot;&quot;&quot;</span>
+<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a>    <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.cpp</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="cm">/* ヒープの先頭要素にアクセス */</span>
+<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="mi">0</span><span class="p">];</span>
+<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.java</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* ヒープの先頭要素にアクセス */</span>
+<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.cs</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Peek</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.go</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">maxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">peek</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.swift</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">peek</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.js</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">peek</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.ts</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">peek</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.dart</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">peek</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.rs</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">peek</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.c</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">peek</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.kt</span><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">peek</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">MaxHeap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">peek</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.zig</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">peek</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h3 id="3">3. &nbsp; ヒープへの要素挿入<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
+<p>要素<code>val</code>が与えられた場合、まずそれをヒープの底に追加します。追加後、<code>val</code>がヒープ内の他の要素より大きい可能性があるため、ヒープの完全性が損なわれる可能性があります。<strong>したがって、挿入されたノードから根ノードまでのパスを修復する必要があります</strong>。この操作は<u>ヒープ化</u>と呼ばれます。</p>
+<p>挿入されたノードから開始して、<strong>下から上にヒープ化を実行します</strong>。下図に示すように、挿入されたノードの値をその親ノードと比較し、挿入されたノードが大きい場合はそれらを交換します。次にこの操作を続行し、根に到達するか、交換が不要なノードに遭遇するまで、下から上にヒープ内の各ノードを修復します。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="4:9"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><input id="__tabbed_4_6" name="__tabbed_4" type="radio" /><input id="__tabbed_4_7" name="__tabbed_4" type="radio" /><input id="__tabbed_4_8" name="__tabbed_4" type="radio" /><input id="__tabbed_4_9" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">&lt;1&gt;</label><label for="__tabbed_4_2">&lt;2&gt;</label><label for="__tabbed_4_3">&lt;3&gt;</label><label for="__tabbed_4_4">&lt;4&gt;</label><label for="__tabbed_4_5">&lt;5&gt;</label><label for="__tabbed_4_6">&lt;6&gt;</label><label for="__tabbed_4_7">&lt;7&gt;</label><label for="__tabbed_4_8">&lt;8&gt;</label><label for="__tabbed_4_9">&lt;9&gt;</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<p><a class="glightbox" href="../heap.assets/heap_push_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="ヒープへの要素挿入の手順" class="animation-figure" src="../heap.assets/heap_push_step1.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../heap.assets/heap_push_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_push_step2" class="animation-figure" src="../heap.assets/heap_push_step2.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../heap.assets/heap_push_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_push_step3" class="animation-figure" src="../heap.assets/heap_push_step3.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../heap.assets/heap_push_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_push_step4" class="animation-figure" src="../heap.assets/heap_push_step4.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../heap.assets/heap_push_step5.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_push_step5" class="animation-figure" src="../heap.assets/heap_push_step5.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../heap.assets/heap_push_step6.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_push_step6" class="animation-figure" src="../heap.assets/heap_push_step6.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../heap.assets/heap_push_step7.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_push_step7" class="animation-figure" src="../heap.assets/heap_push_step7.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../heap.assets/heap_push_step8.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_push_step8" class="animation-figure" src="../heap.assets/heap_push_step8.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../heap.assets/heap_push_step9.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_push_step9" class="animation-figure" src="../heap.assets/heap_push_step9.png" /></a></p>
+</div>
+</div>
+</div>
+<p align="center"> 図 8-3 &nbsp; ヒープへの要素挿入の手順 </p>
+
+<p>総ノード数を<span class="arithmatex">\(n\)</span>とすると、木の高さは<span class="arithmatex">\(O(\log n)\)</span>です。したがって、ヒープ化操作のループ反復回数は最大<span class="arithmatex">\(O(\log n)\)</span>で、<strong>要素挿入操作の時間計算量は<span class="arithmatex">\(O(\log n)\)</span>になります</strong>。コードは以下の通りです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="5:14"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><input id="__tabbed_5_7" name="__tabbed_5" type="radio" /><input id="__tabbed_5_8" name="__tabbed_5" type="radio" /><input id="__tabbed_5_9" name="__tabbed_5" type="radio" /><input id="__tabbed_5_10" name="__tabbed_5" type="radio" /><input id="__tabbed_5_11" name="__tabbed_5" type="radio" /><input id="__tabbed_5_12" name="__tabbed_5" type="radio" /><input id="__tabbed_5_13" name="__tabbed_5" type="radio" /><input id="__tabbed_5_14" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">Python</label><label for="__tabbed_5_2">C++</label><label for="__tabbed_5_3">Java</label><label for="__tabbed_5_4">C#</label><label for="__tabbed_5_5">Go</label><label for="__tabbed_5_6">Swift</label><label for="__tabbed_5_7">JS</label><label for="__tabbed_5_8">TS</label><label for="__tabbed_5_9">Dart</label><label for="__tabbed_5_10">Rust</label><label for="__tabbed_5_11">C</label><label for="__tabbed_5_12">Kotlin</label><label for="__tabbed_5_13">Ruby</label><label for="__tabbed_5_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.py</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-42-2" name="__codelineno-42-2" href="#__codelineno-42-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;ヒープに要素をプッシュ&quot;&quot;&quot;</span>
+<a id="__codelineno-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></a>    <span class="c1"># ノードを追加</span>
+<a id="__codelineno-42-4" name="__codelineno-42-4" href="#__codelineno-42-4"></a>    <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-42-5" name="__codelineno-42-5" href="#__codelineno-42-5"></a>    <span class="c1"># 下から上へヒープ化</span>
+<a id="__codelineno-42-6" name="__codelineno-42-6" href="#__codelineno-42-6"></a>    <span class="bp">self</span><span class="o">.</span><span class="n">sift_up</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-42-7" name="__codelineno-42-7" href="#__codelineno-42-7"></a>
+<a id="__codelineno-42-8" name="__codelineno-42-8" href="#__codelineno-42-8"></a><span class="k">def</span><span class="w"> </span><span class="nf">sift_up</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-42-9" name="__codelineno-42-9" href="#__codelineno-42-9"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;ノードiから開始して、下から上へヒープ化&quot;&quot;&quot;</span>
+<a id="__codelineno-42-10" name="__codelineno-42-10" href="#__codelineno-42-10"></a>    <span class="k">while</span> <span class="kc">True</span><span class="p">:</span>
+<a id="__codelineno-42-11" name="__codelineno-42-11" href="#__codelineno-42-11"></a>        <span class="c1"># ノードiの親ノードを取得</span>
+<a id="__codelineno-42-12" name="__codelineno-42-12" href="#__codelineno-42-12"></a>        <span class="n">p</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">parent</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
+<a id="__codelineno-42-13" name="__codelineno-42-13" href="#__codelineno-42-13"></a>        <span class="c1"># 「ルートノードを越える」または「ノードが修復不要」の場合、ヒープ化を終了</span>
+<a id="__codelineno-42-14" name="__codelineno-42-14" href="#__codelineno-42-14"></a>        <span class="k">if</span> <span class="n">p</span> <span class="o">&lt;</span> <span class="mi">0</span> <span class="ow">or</span> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">&lt;=</span> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">p</span><span class="p">]:</span>
+<a id="__codelineno-42-15" name="__codelineno-42-15" href="#__codelineno-42-15"></a>            <span class="k">break</span>
+<a id="__codelineno-42-16" name="__codelineno-42-16" href="#__codelineno-42-16"></a>        <span class="c1"># 2つのノードを交換</span>
+<a id="__codelineno-42-17" name="__codelineno-42-17" href="#__codelineno-42-17"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">p</span><span class="p">)</span>
+<a id="__codelineno-42-18" name="__codelineno-42-18" href="#__codelineno-42-18"></a>        <span class="c1"># 上向きのループヒープ化</span>
+<a id="__codelineno-42-19" name="__codelineno-42-19" href="#__codelineno-42-19"></a>        <span class="n">i</span> <span class="o">=</span> <span class="n">p</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.cpp</span><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="cm">/* ヒープに要素をプッシュ */</span>
+<a id="__codelineno-43-2" name="__codelineno-43-2" href="#__codelineno-43-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-3" name="__codelineno-43-3" href="#__codelineno-43-3"></a><span class="w">    </span><span class="c1">// ノードを追加</span>
+<a id="__codelineno-43-4" name="__codelineno-43-4" href="#__codelineno-43-4"></a><span class="w">    </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-43-5" name="__codelineno-43-5" href="#__codelineno-43-5"></a><span class="w">    </span><span class="c1">// 下から上へヒープ化</span>
+<a id="__codelineno-43-6" name="__codelineno-43-6" href="#__codelineno-43-6"></a><span class="w">    </span><span class="n">siftUp</span><span class="p">(</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-43-7" name="__codelineno-43-7" href="#__codelineno-43-7"></a><span class="p">}</span>
+<a id="__codelineno-43-8" name="__codelineno-43-8" href="#__codelineno-43-8"></a>
+<a id="__codelineno-43-9" name="__codelineno-43-9" href="#__codelineno-43-9"></a><span class="cm">/* ノードiから上向きにヒープ化を開始 */</span>
+<a id="__codelineno-43-10" name="__codelineno-43-10" href="#__codelineno-43-10"></a><span class="kt">void</span><span class="w"> </span><span class="nf">siftUp</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-11" name="__codelineno-43-11" href="#__codelineno-43-11"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nb">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-12" name="__codelineno-43-12" href="#__codelineno-43-12"></a><span class="w">        </span><span class="c1">// ノードiの親ノードを取得</span>
+<a id="__codelineno-43-13" name="__codelineno-43-13" href="#__codelineno-43-13"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">parent</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-43-14" name="__codelineno-43-14" href="#__codelineno-43-14"></a><span class="w">        </span><span class="c1">// 「ルートノードを超える」または「ノードが修復不要」の場合、ヒープ化を終了</span>
+<a id="__codelineno-43-15" name="__codelineno-43-15" href="#__codelineno-43-15"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">p</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">p</span><span class="p">])</span>
+<a id="__codelineno-43-16" name="__codelineno-43-16" href="#__codelineno-43-16"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-43-17" name="__codelineno-43-17" href="#__codelineno-43-17"></a><span class="w">        </span><span class="c1">// 2つのノードを交換</span>
+<a id="__codelineno-43-18" name="__codelineno-43-18" href="#__codelineno-43-18"></a><span class="w">        </span><span class="n">swap</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">p</span><span class="p">]);</span>
+<a id="__codelineno-43-19" name="__codelineno-43-19" href="#__codelineno-43-19"></a><span class="w">        </span><span class="c1">// 上向きにループしてヒープ化</span>
+<a id="__codelineno-43-20" name="__codelineno-43-20" href="#__codelineno-43-20"></a><span class="w">        </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">p</span><span class="p">;</span>
+<a id="__codelineno-43-21" name="__codelineno-43-21" href="#__codelineno-43-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-43-22" name="__codelineno-43-22" href="#__codelineno-43-22"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.java</span><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="cm">/* 要素をヒープにプッシュ */</span>
+<a id="__codelineno-44-2" name="__codelineno-44-2" href="#__codelineno-44-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-3" name="__codelineno-44-3" href="#__codelineno-44-3"></a><span class="w">    </span><span class="c1">// ノードを追加</span>
+<a id="__codelineno-44-4" name="__codelineno-44-4" href="#__codelineno-44-4"></a><span class="w">    </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-44-5" name="__codelineno-44-5" href="#__codelineno-44-5"></a><span class="w">    </span><span class="c1">// 下から上へヒープ化</span>
+<a id="__codelineno-44-6" name="__codelineno-44-6" href="#__codelineno-44-6"></a><span class="w">    </span><span class="n">siftUp</span><span class="p">(</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-44-7" name="__codelineno-44-7" href="#__codelineno-44-7"></a><span class="p">}</span>
+<a id="__codelineno-44-8" name="__codelineno-44-8" href="#__codelineno-44-8"></a>
+<a id="__codelineno-44-9" name="__codelineno-44-9" href="#__codelineno-44-9"></a><span class="cm">/* ノード i から上向きにヒープ化を開始 */</span>
+<a id="__codelineno-44-10" name="__codelineno-44-10" href="#__codelineno-44-10"></a><span class="kt">void</span><span class="w"> </span><span class="nf">siftUp</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-11" name="__codelineno-44-11" href="#__codelineno-44-11"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-12" name="__codelineno-44-12" href="#__codelineno-44-12"></a><span class="w">        </span><span class="c1">// ノード i の親ノードを取得</span>
+<a id="__codelineno-44-13" name="__codelineno-44-13" href="#__codelineno-44-13"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">parent</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-44-14" name="__codelineno-44-14" href="#__codelineno-44-14"></a><span class="w">        </span><span class="c1">// 「根ノードを越える」または「ノードが修復不要」の場合、ヒープ化を終了</span>
+<a id="__codelineno-44-15" name="__codelineno-44-15" href="#__codelineno-44-15"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">p</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">p</span><span class="p">))</span>
+<a id="__codelineno-44-16" name="__codelineno-44-16" href="#__codelineno-44-16"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-44-17" name="__codelineno-44-17" href="#__codelineno-44-17"></a><span class="w">        </span><span class="c1">// 2つのノードを交換</span>
+<a id="__codelineno-44-18" name="__codelineno-44-18" href="#__codelineno-44-18"></a><span class="w">        </span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">p</span><span class="p">);</span>
+<a id="__codelineno-44-19" name="__codelineno-44-19" href="#__codelineno-44-19"></a><span class="w">        </span><span class="c1">// 上向きにヒープ化をループ</span>
+<a id="__codelineno-44-20" name="__codelineno-44-20" href="#__codelineno-44-20"></a><span class="w">        </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">p</span><span class="p">;</span>
+<a id="__codelineno-44-21" name="__codelineno-44-21" href="#__codelineno-44-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-44-22" name="__codelineno-44-22" href="#__codelineno-44-22"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.cs</span><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Push</span><span class="p">}</span>
+<a id="__codelineno-45-2" name="__codelineno-45-2" href="#__codelineno-45-2"></a>
+<a id="__codelineno-45-3" name="__codelineno-45-3" href="#__codelineno-45-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">SiftUp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.go</span><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">maxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">push</span><span class="p">}</span>
+<a id="__codelineno-46-2" name="__codelineno-46-2" href="#__codelineno-46-2"></a>
+<a id="__codelineno-46-3" name="__codelineno-46-3" href="#__codelineno-46-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">maxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">siftUp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.swift</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">push</span><span class="p">}</span>
+<a id="__codelineno-47-2" name="__codelineno-47-2" href="#__codelineno-47-2"></a>
+<a id="__codelineno-47-3" name="__codelineno-47-3" href="#__codelineno-47-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">siftUp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.js</span><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">push</span><span class="p">}</span>
+<a id="__codelineno-48-2" name="__codelineno-48-2" href="#__codelineno-48-2"></a>
+<a id="__codelineno-48-3" name="__codelineno-48-3" href="#__codelineno-48-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">siftUp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.ts</span><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">push</span><span class="p">}</span>
+<a id="__codelineno-49-2" name="__codelineno-49-2" href="#__codelineno-49-2"></a>
+<a id="__codelineno-49-3" name="__codelineno-49-3" href="#__codelineno-49-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">siftUp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.dart</span><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">push</span><span class="p">}</span>
+<a id="__codelineno-50-2" name="__codelineno-50-2" href="#__codelineno-50-2"></a>
+<a id="__codelineno-50-3" name="__codelineno-50-3" href="#__codelineno-50-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">siftUp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.rs</span><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">push</span><span class="p">}</span>
+<a id="__codelineno-51-2" name="__codelineno-51-2" href="#__codelineno-51-2"></a>
+<a id="__codelineno-51-3" name="__codelineno-51-3" href="#__codelineno-51-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">sift_up</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.c</span><pre><span></span><code><a id="__codelineno-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">push</span><span class="p">}</span>
+<a id="__codelineno-52-2" name="__codelineno-52-2" href="#__codelineno-52-2"></a>
+<a id="__codelineno-52-3" name="__codelineno-52-3" href="#__codelineno-52-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">siftUp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.kt</span><pre><span></span><code><a id="__codelineno-53-1" name="__codelineno-53-1" href="#__codelineno-53-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">push</span><span class="p">}</span>
+<a id="__codelineno-53-2" name="__codelineno-53-2" href="#__codelineno-53-2"></a>
+<a id="__codelineno-53-3" name="__codelineno-53-3" href="#__codelineno-53-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">siftUp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.rb</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">MaxHeap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">push</span><span class="p">}</span>
+<a id="__codelineno-54-2" name="__codelineno-54-2" href="#__codelineno-54-2"></a>
+<a id="__codelineno-54-3" name="__codelineno-54-3" href="#__codelineno-54-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">MaxHeap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">sift_up</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.zig</span><pre><span></span><code><a id="__codelineno-55-1" name="__codelineno-55-1" href="#__codelineno-55-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">push</span><span class="p">}</span>
+<a id="__codelineno-55-2" name="__codelineno-55-2" href="#__codelineno-55-2"></a>
+<a id="__codelineno-55-3" name="__codelineno-55-3" href="#__codelineno-55-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">siftUp</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h3 id="4">4. &nbsp; ヒープからの先頭要素削除<a class="headerlink" href="#4" title="Permanent link">&para;</a></h3>
+<p>ヒープの先頭要素は二分木の根ノード、つまりリストの最初の要素です。リストから最初の要素を直接削除すると、二分木内のすべてのノードインデックスが変更され、後続の修復にヒープ化を使用することが困難になります。要素インデックスの変更を最小限に抑えるため、次の手順を使用します。</p>
+<ol>
+<li>ヒープの先頭要素と底の要素を交換します（根ノードと最も右の葉ノードを交換）。</li>
+<li>交換後、リストからヒープの底を削除します（交換されているため、実際には元の先頭要素が削除される）。</li>
+<li>根ノードから開始して、<strong>上から下にヒープ化を実行します</strong>。</li>
+</ol>
+<p>下図に示すように、<strong>「上から下のヒープ化」の方向は「下から上のヒープ化」と反対です</strong>。根ノードの値をその2つの子と比較し、最大の子と交換します。次に、葉ノードに到達するか、交換が不要なノードに遭遇するまで、この操作を繰り返します。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="6:10"><input checked="checked" id="__tabbed_6_1" name="__tabbed_6" type="radio" /><input id="__tabbed_6_2" name="__tabbed_6" type="radio" /><input id="__tabbed_6_3" name="__tabbed_6" type="radio" /><input id="__tabbed_6_4" name="__tabbed_6" type="radio" /><input id="__tabbed_6_5" name="__tabbed_6" type="radio" /><input id="__tabbed_6_6" name="__tabbed_6" type="radio" /><input id="__tabbed_6_7" name="__tabbed_6" type="radio" /><input id="__tabbed_6_8" name="__tabbed_6" type="radio" /><input id="__tabbed_6_9" name="__tabbed_6" type="radio" /><input id="__tabbed_6_10" name="__tabbed_6" type="radio" /><div class="tabbed-labels"><label for="__tabbed_6_1">&lt;1&gt;</label><label for="__tabbed_6_2">&lt;2&gt;</label><label for="__tabbed_6_3">&lt;3&gt;</label><label for="__tabbed_6_4">&lt;4&gt;</label><label for="__tabbed_6_5">&lt;5&gt;</label><label for="__tabbed_6_6">&lt;6&gt;</label><label for="__tabbed_6_7">&lt;7&gt;</label><label for="__tabbed_6_8">&lt;8&gt;</label><label for="__tabbed_6_9">&lt;9&gt;</label><label for="__tabbed_6_10">&lt;10&gt;</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<p><a class="glightbox" href="../heap.assets/heap_pop_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="ヒープからの先頭要素削除の手順" class="animation-figure" src="../heap.assets/heap_pop_step1.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../heap.assets/heap_pop_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_pop_step2" class="animation-figure" src="../heap.assets/heap_pop_step2.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../heap.assets/heap_pop_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_pop_step3" class="animation-figure" src="../heap.assets/heap_pop_step3.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../heap.assets/heap_pop_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_pop_step4" class="animation-figure" src="../heap.assets/heap_pop_step4.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../heap.assets/heap_pop_step5.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_pop_step5" class="animation-figure" src="../heap.assets/heap_pop_step5.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../heap.assets/heap_pop_step6.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_pop_step6" class="animation-figure" src="../heap.assets/heap_pop_step6.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../heap.assets/heap_pop_step7.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_pop_step7" class="animation-figure" src="../heap.assets/heap_pop_step7.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../heap.assets/heap_pop_step8.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_pop_step8" class="animation-figure" src="../heap.assets/heap_pop_step8.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../heap.assets/heap_pop_step9.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_pop_step9" class="animation-figure" src="../heap.assets/heap_pop_step9.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../heap.assets/heap_pop_step10.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_pop_step10" class="animation-figure" src="../heap.assets/heap_pop_step10.png" /></a></p>
+</div>
+</div>
+</div>
+<p align="center"> 図 8-4 &nbsp; ヒープからの先頭要素削除の手順 </p>
+
+<p>要素挿入操作と同様に、先頭要素削除操作の時間計算量も<span class="arithmatex">\(O(\log n)\)</span>です。コードは以下の通りです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="7:14"><input checked="checked" id="__tabbed_7_1" name="__tabbed_7" type="radio" /><input id="__tabbed_7_2" name="__tabbed_7" type="radio" /><input id="__tabbed_7_3" name="__tabbed_7" type="radio" /><input id="__tabbed_7_4" name="__tabbed_7" type="radio" /><input id="__tabbed_7_5" name="__tabbed_7" type="radio" /><input id="__tabbed_7_6" name="__tabbed_7" type="radio" /><input id="__tabbed_7_7" name="__tabbed_7" type="radio" /><input id="__tabbed_7_8" name="__tabbed_7" type="radio" /><input id="__tabbed_7_9" name="__tabbed_7" type="radio" /><input id="__tabbed_7_10" name="__tabbed_7" type="radio" /><input id="__tabbed_7_11" name="__tabbed_7" type="radio" /><input id="__tabbed_7_12" name="__tabbed_7" type="radio" /><input id="__tabbed_7_13" name="__tabbed_7" type="radio" /><input id="__tabbed_7_14" name="__tabbed_7" type="radio" /><div class="tabbed-labels"><label for="__tabbed_7_1">Python</label><label for="__tabbed_7_2">C++</label><label for="__tabbed_7_3">Java</label><label for="__tabbed_7_4">C#</label><label for="__tabbed_7_5">Go</label><label for="__tabbed_7_6">Swift</label><label for="__tabbed_7_7">JS</label><label for="__tabbed_7_8">TS</label><label for="__tabbed_7_9">Dart</label><label for="__tabbed_7_10">Rust</label><label for="__tabbed_7_11">C</label><label for="__tabbed_7_12">Kotlin</label><label for="__tabbed_7_13">Ruby</label><label for="__tabbed_7_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.py</span><pre><span></span><code><a id="__codelineno-56-1" name="__codelineno-56-1" href="#__codelineno-56-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">pop</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-56-2" name="__codelineno-56-2" href="#__codelineno-56-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;要素をヒープから出す&quot;&quot;&quot;</span>
+<a id="__codelineno-56-3" name="__codelineno-56-3" href="#__codelineno-56-3"></a>    <span class="c1"># 空の処理</span>
+<a id="__codelineno-56-4" name="__codelineno-56-4" href="#__codelineno-56-4"></a>    <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">is_empty</span><span class="p">():</span>
+<a id="__codelineno-56-5" name="__codelineno-56-5" href="#__codelineno-56-5"></a>        <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;Heap is empty&quot;</span><span class="p">)</span>
+<a id="__codelineno-56-6" name="__codelineno-56-6" href="#__codelineno-56-6"></a>    <span class="c1"># ルートノードと最右端の葉ノードを交換（最初の要素と最後の要素を交換）</span>
+<a id="__codelineno-56-7" name="__codelineno-56-7" href="#__codelineno-56-7"></a>    <span class="bp">self</span><span class="o">.</span><span class="n">swap</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-56-8" name="__codelineno-56-8" href="#__codelineno-56-8"></a>    <span class="c1"># ノードを削除</span>
+<a id="__codelineno-56-9" name="__codelineno-56-9" href="#__codelineno-56-9"></a>    <span class="n">val</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
+<a id="__codelineno-56-10" name="__codelineno-56-10" href="#__codelineno-56-10"></a>    <span class="c1"># 上から下へヒープ化</span>
+<a id="__codelineno-56-11" name="__codelineno-56-11" href="#__codelineno-56-11"></a>    <span class="bp">self</span><span class="o">.</span><span class="n">sift_down</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-56-12" name="__codelineno-56-12" href="#__codelineno-56-12"></a>    <span class="c1"># ヒープの先頭要素を返す</span>
+<a id="__codelineno-56-13" name="__codelineno-56-13" href="#__codelineno-56-13"></a>    <span class="k">return</span> <span class="n">val</span>
+<a id="__codelineno-56-14" name="__codelineno-56-14" href="#__codelineno-56-14"></a>
+<a id="__codelineno-56-15" name="__codelineno-56-15" href="#__codelineno-56-15"></a><span class="k">def</span><span class="w"> </span><span class="nf">sift_down</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-56-16" name="__codelineno-56-16" href="#__codelineno-56-16"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;ノードiから開始して、上から下へヒープ化&quot;&quot;&quot;</span>
+<a id="__codelineno-56-17" name="__codelineno-56-17" href="#__codelineno-56-17"></a>    <span class="k">while</span> <span class="kc">True</span><span class="p">:</span>
+<a id="__codelineno-56-18" name="__codelineno-56-18" href="#__codelineno-56-18"></a>        <span class="c1"># i、l、rの中で最大のノードを決定し、maとする</span>
+<a id="__codelineno-56-19" name="__codelineno-56-19" href="#__codelineno-56-19"></a>        <span class="n">l</span><span class="p">,</span> <span class="n">r</span><span class="p">,</span> <span class="n">ma</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span> <span class="bp">self</span><span class="o">.</span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span> <span class="n">i</span>
+<a id="__codelineno-56-20" name="__codelineno-56-20" href="#__codelineno-56-20"></a>        <span class="k">if</span> <span class="n">l</span> <span class="o">&lt;</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span> <span class="ow">and</span> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">l</span><span class="p">]</span> <span class="o">&gt;</span> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">ma</span><span class="p">]:</span>
+<a id="__codelineno-56-21" name="__codelineno-56-21" href="#__codelineno-56-21"></a>            <span class="n">ma</span> <span class="o">=</span> <span class="n">l</span>
+<a id="__codelineno-56-22" name="__codelineno-56-22" href="#__codelineno-56-22"></a>        <span class="k">if</span> <span class="n">r</span> <span class="o">&lt;</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span> <span class="ow">and</span> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">r</span><span class="p">]</span> <span class="o">&gt;</span> <span class="bp">self</span><span class="o">.</span><span class="n">max_heap</span><span class="p">[</span><span class="n">ma</span><span class="p">]:</span>
+<a id="__codelineno-56-23" name="__codelineno-56-23" href="#__codelineno-56-23"></a>            <span class="n">ma</span> <span class="o">=</span> <span class="n">r</span>
+<a id="__codelineno-56-24" name="__codelineno-56-24" href="#__codelineno-56-24"></a>        <span class="c1"># ノードiが最大またはインデックスl、rが範囲外の場合、さらなるヒープ化は不要、ブレーク</span>
+<a id="__codelineno-56-25" name="__codelineno-56-25" href="#__codelineno-56-25"></a>        <span class="k">if</span> <span class="n">ma</span> <span class="o">==</span> <span class="n">i</span><span class="p">:</span>
+<a id="__codelineno-56-26" name="__codelineno-56-26" href="#__codelineno-56-26"></a>            <span class="k">break</span>
+<a id="__codelineno-56-27" name="__codelineno-56-27" href="#__codelineno-56-27"></a>        <span class="c1"># 2つのノードを交換</span>
+<a id="__codelineno-56-28" name="__codelineno-56-28" href="#__codelineno-56-28"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">ma</span><span class="p">)</span>
+<a id="__codelineno-56-29" name="__codelineno-56-29" href="#__codelineno-56-29"></a>        <span class="c1"># 下向きのループヒープ化</span>
+<a id="__codelineno-56-30" name="__codelineno-56-30" href="#__codelineno-56-30"></a>        <span class="n">i</span> <span class="o">=</span> <span class="n">ma</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.cpp</span><pre><span></span><code><a id="__codelineno-57-1" name="__codelineno-57-1" href="#__codelineno-57-1"></a><span class="cm">/* 要素がヒープから退出 */</span>
+<a id="__codelineno-57-2" name="__codelineno-57-2" href="#__codelineno-57-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-3" name="__codelineno-57-3" href="#__codelineno-57-3"></a><span class="w">    </span><span class="c1">// 空の処理</span>
+<a id="__codelineno-57-4" name="__codelineno-57-4" href="#__codelineno-57-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-5" name="__codelineno-57-5" href="#__codelineno-57-5"></a><span class="w">        </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;Heap is empty&quot;</span><span class="p">);</span>
+<a id="__codelineno-57-6" name="__codelineno-57-6" href="#__codelineno-57-6"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-57-7" name="__codelineno-57-7" href="#__codelineno-57-7"></a><span class="w">    </span><span class="c1">// ルートノードを最も右の葉ノードと交換（最初の要素と最後の要素を交換）</span>
+<a id="__codelineno-57-8" name="__codelineno-57-8" href="#__codelineno-57-8"></a><span class="w">    </span><span class="n">swap</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]);</span>
+<a id="__codelineno-57-9" name="__codelineno-57-9" href="#__codelineno-57-9"></a><span class="w">    </span><span class="c1">// ノードを削除</span>
+<a id="__codelineno-57-10" name="__codelineno-57-10" href="#__codelineno-57-10"></a><span class="w">    </span><span class="n">maxHeap</span><span class="p">.</span><span class="n">pop_back</span><span class="p">();</span>
+<a id="__codelineno-57-11" name="__codelineno-57-11" href="#__codelineno-57-11"></a><span class="w">    </span><span class="c1">// 上から下へヒープ化</span>
+<a id="__codelineno-57-12" name="__codelineno-57-12" href="#__codelineno-57-12"></a><span class="w">    </span><span class="n">siftDown</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-57-13" name="__codelineno-57-13" href="#__codelineno-57-13"></a><span class="p">}</span>
+<a id="__codelineno-57-14" name="__codelineno-57-14" href="#__codelineno-57-14"></a>
+<a id="__codelineno-57-15" name="__codelineno-57-15" href="#__codelineno-57-15"></a><span class="cm">/* ノードiから下向きにヒープ化を開始 */</span>
+<a id="__codelineno-57-16" name="__codelineno-57-16" href="#__codelineno-57-16"></a><span class="kt">void</span><span class="w"> </span><span class="nf">siftDown</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-17" name="__codelineno-57-17" href="#__codelineno-57-17"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nb">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-18" name="__codelineno-57-18" href="#__codelineno-57-18"></a><span class="w">        </span><span class="c1">// i、l、rの中で最大のノードを決定し、maとして記録</span>
+<a id="__codelineno-57-19" name="__codelineno-57-19" href="#__codelineno-57-19"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-57-20" name="__codelineno-57-20" href="#__codelineno-57-20"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">l</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span>
+<a id="__codelineno-57-21" name="__codelineno-57-21" href="#__codelineno-57-21"></a><span class="w">            </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span><span class="p">;</span>
+<a id="__codelineno-57-22" name="__codelineno-57-22" href="#__codelineno-57-22"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">r</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span>
+<a id="__codelineno-57-23" name="__codelineno-57-23" href="#__codelineno-57-23"></a><span class="w">            </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span><span class="p">;</span>
+<a id="__codelineno-57-24" name="__codelineno-57-24" href="#__codelineno-57-24"></a><span class="w">        </span><span class="c1">// ノードiが最大、またはインデックスl、rが範囲外の場合、これ以上のヒープ化は不要、ブレーク</span>
+<a id="__codelineno-57-25" name="__codelineno-57-25" href="#__codelineno-57-25"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span><span class="p">)</span>
+<a id="__codelineno-57-26" name="__codelineno-57-26" href="#__codelineno-57-26"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-57-27" name="__codelineno-57-27" href="#__codelineno-57-27"></a><span class="w">        </span><span class="n">swap</span><span class="p">(</span><span class="n">maxHeap</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">[</span><span class="n">ma</span><span class="p">]);</span>
+<a id="__codelineno-57-28" name="__codelineno-57-28" href="#__codelineno-57-28"></a><span class="w">        </span><span class="c1">// 下向きにループしてヒープ化</span>
+<a id="__codelineno-57-29" name="__codelineno-57-29" href="#__codelineno-57-29"></a><span class="w">        </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ma</span><span class="p">;</span>
+<a id="__codelineno-57-30" name="__codelineno-57-30" href="#__codelineno-57-30"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-57-31" name="__codelineno-57-31" href="#__codelineno-57-31"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.java</span><pre><span></span><code><a id="__codelineno-58-1" name="__codelineno-58-1" href="#__codelineno-58-1"></a><span class="cm">/* 要素がヒープから退出 */</span>
+<a id="__codelineno-58-2" name="__codelineno-58-2" href="#__codelineno-58-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-3" name="__codelineno-58-3" href="#__codelineno-58-3"></a><span class="w">    </span><span class="c1">// 空の処理</span>
+<a id="__codelineno-58-4" name="__codelineno-58-4" href="#__codelineno-58-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
+<a id="__codelineno-58-5" name="__codelineno-58-5" href="#__codelineno-58-5"></a><span class="w">        </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">();</span>
+<a id="__codelineno-58-6" name="__codelineno-58-6" href="#__codelineno-58-6"></a><span class="w">    </span><span class="c1">// 根ノードを最も右の葉ノードと交換（最初の要素を最後の要素と交換）</span>
+<a id="__codelineno-58-7" name="__codelineno-58-7" href="#__codelineno-58-7"></a><span class="w">    </span><span class="n">swap</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-58-8" name="__codelineno-58-8" href="#__codelineno-58-8"></a><span class="w">    </span><span class="c1">// ノードを削除</span>
+<a id="__codelineno-58-9" name="__codelineno-58-9" href="#__codelineno-58-9"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-58-10" name="__codelineno-58-10" href="#__codelineno-58-10"></a><span class="w">    </span><span class="c1">// 上から下へヒープ化</span>
+<a id="__codelineno-58-11" name="__codelineno-58-11" href="#__codelineno-58-11"></a><span class="w">    </span><span class="n">siftDown</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-58-12" name="__codelineno-58-12" href="#__codelineno-58-12"></a><span class="w">    </span><span class="c1">// ヒープの先頭要素を返す</span>
+<a id="__codelineno-58-13" name="__codelineno-58-13" href="#__codelineno-58-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-58-14" name="__codelineno-58-14" href="#__codelineno-58-14"></a><span class="p">}</span>
+<a id="__codelineno-58-15" name="__codelineno-58-15" href="#__codelineno-58-15"></a>
+<a id="__codelineno-58-16" name="__codelineno-58-16" href="#__codelineno-58-16"></a><span class="cm">/* ノード i から下向きにヒープ化を開始 */</span>
+<a id="__codelineno-58-17" name="__codelineno-58-17" href="#__codelineno-58-17"></a><span class="kt">void</span><span class="w"> </span><span class="nf">siftDown</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-18" name="__codelineno-58-18" href="#__codelineno-58-18"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-19" name="__codelineno-58-19" href="#__codelineno-58-19"></a><span class="w">        </span><span class="c1">// i、l、r の中で最大のノードを決定し、ma とする</span>
+<a id="__codelineno-58-20" name="__codelineno-58-20" href="#__codelineno-58-20"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-58-21" name="__codelineno-58-21" href="#__codelineno-58-21"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">l</span><span class="p">)</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">ma</span><span class="p">))</span>
+<a id="__codelineno-58-22" name="__codelineno-58-22" href="#__codelineno-58-22"></a><span class="w">            </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span><span class="p">;</span>
+<a id="__codelineno-58-23" name="__codelineno-58-23" href="#__codelineno-58-23"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">r</span><span class="p">)</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">maxHeap</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">ma</span><span class="p">))</span>
+<a id="__codelineno-58-24" name="__codelineno-58-24" href="#__codelineno-58-24"></a><span class="w">            </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span><span class="p">;</span>
+<a id="__codelineno-58-25" name="__codelineno-58-25" href="#__codelineno-58-25"></a><span class="w">        </span><span class="c1">// ノード i が最大の場合、またはインデックス l、r が範囲外の場合、さらなるヒープ化は不要、終了</span>
+<a id="__codelineno-58-26" name="__codelineno-58-26" href="#__codelineno-58-26"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span><span class="p">)</span>
+<a id="__codelineno-58-27" name="__codelineno-58-27" href="#__codelineno-58-27"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-58-28" name="__codelineno-58-28" href="#__codelineno-58-28"></a><span class="w">        </span><span class="c1">// 2つのノードを交換</span>
+<a id="__codelineno-58-29" name="__codelineno-58-29" href="#__codelineno-58-29"></a><span class="w">        </span><span class="n">swap</span><span class="p">(</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">ma</span><span class="p">);</span>
+<a id="__codelineno-58-30" name="__codelineno-58-30" href="#__codelineno-58-30"></a><span class="w">        </span><span class="c1">// 下向きにヒープ化をループ</span>
+<a id="__codelineno-58-31" name="__codelineno-58-31" href="#__codelineno-58-31"></a><span class="w">        </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ma</span><span class="p">;</span>
+<a id="__codelineno-58-32" name="__codelineno-58-32" href="#__codelineno-58-32"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-58-33" name="__codelineno-58-33" href="#__codelineno-58-33"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.cs</span><pre><span></span><code><a id="__codelineno-59-1" name="__codelineno-59-1" href="#__codelineno-59-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Pop</span><span class="p">}</span>
+<a id="__codelineno-59-2" name="__codelineno-59-2" href="#__codelineno-59-2"></a>
+<a id="__codelineno-59-3" name="__codelineno-59-3" href="#__codelineno-59-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">SiftDown</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.go</span><pre><span></span><code><a id="__codelineno-60-1" name="__codelineno-60-1" href="#__codelineno-60-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">maxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">pop</span><span class="p">}</span>
+<a id="__codelineno-60-2" name="__codelineno-60-2" href="#__codelineno-60-2"></a>
+<a id="__codelineno-60-3" name="__codelineno-60-3" href="#__codelineno-60-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">maxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">siftDown</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.swift</span><pre><span></span><code><a id="__codelineno-61-1" name="__codelineno-61-1" href="#__codelineno-61-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">pop</span><span class="p">}</span>
+<a id="__codelineno-61-2" name="__codelineno-61-2" href="#__codelineno-61-2"></a>
+<a id="__codelineno-61-3" name="__codelineno-61-3" href="#__codelineno-61-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">siftDown</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.js</span><pre><span></span><code><a id="__codelineno-62-1" name="__codelineno-62-1" href="#__codelineno-62-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">pop</span><span class="p">}</span>
+<a id="__codelineno-62-2" name="__codelineno-62-2" href="#__codelineno-62-2"></a>
+<a id="__codelineno-62-3" name="__codelineno-62-3" href="#__codelineno-62-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">siftDown</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.ts</span><pre><span></span><code><a id="__codelineno-63-1" name="__codelineno-63-1" href="#__codelineno-63-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">pop</span><span class="p">}</span>
+<a id="__codelineno-63-2" name="__codelineno-63-2" href="#__codelineno-63-2"></a>
+<a id="__codelineno-63-3" name="__codelineno-63-3" href="#__codelineno-63-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">siftDown</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.dart</span><pre><span></span><code><a id="__codelineno-64-1" name="__codelineno-64-1" href="#__codelineno-64-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">pop</span><span class="p">}</span>
+<a id="__codelineno-64-2" name="__codelineno-64-2" href="#__codelineno-64-2"></a>
+<a id="__codelineno-64-3" name="__codelineno-64-3" href="#__codelineno-64-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">siftDown</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.rs</span><pre><span></span><code><a id="__codelineno-65-1" name="__codelineno-65-1" href="#__codelineno-65-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">pop</span><span class="p">}</span>
+<a id="__codelineno-65-2" name="__codelineno-65-2" href="#__codelineno-65-2"></a>
+<a id="__codelineno-65-3" name="__codelineno-65-3" href="#__codelineno-65-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">sift_down</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.c</span><pre><span></span><code><a id="__codelineno-66-1" name="__codelineno-66-1" href="#__codelineno-66-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">pop</span><span class="p">}</span>
+<a id="__codelineno-66-2" name="__codelineno-66-2" href="#__codelineno-66-2"></a>
+<a id="__codelineno-66-3" name="__codelineno-66-3" href="#__codelineno-66-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">siftDown</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.kt</span><pre><span></span><code><a id="__codelineno-67-1" name="__codelineno-67-1" href="#__codelineno-67-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">pop</span><span class="p">}</span>
+<a id="__codelineno-67-2" name="__codelineno-67-2" href="#__codelineno-67-2"></a>
+<a id="__codelineno-67-3" name="__codelineno-67-3" href="#__codelineno-67-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">siftDown</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.rb</span><pre><span></span><code><a id="__codelineno-68-1" name="__codelineno-68-1" href="#__codelineno-68-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">MaxHeap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">pop</span><span class="p">}</span>
+<a id="__codelineno-68-2" name="__codelineno-68-2" href="#__codelineno-68-2"></a>
+<a id="__codelineno-68-3" name="__codelineno-68-3" href="#__codelineno-68-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">MaxHeap</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">sift_down</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">my_heap.zig</span><pre><span></span><code><a id="__codelineno-69-1" name="__codelineno-69-1" href="#__codelineno-69-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">pop</span><span class="p">}</span>
+<a id="__codelineno-69-2" name="__codelineno-69-2" href="#__codelineno-69-2"></a>
+<a id="__codelineno-69-3" name="__codelineno-69-3" href="#__codelineno-69-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">MaxHeap</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">siftDown</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h2 id="813">8.1.3 &nbsp; ヒープの一般的な応用<a class="headerlink" href="#813" title="Permanent link">&para;</a></h2>
+<ul>
+<li><strong>優先度キュー</strong>：ヒープは優先度キューを実装するための好ましいデータ構造で、エンキュー操作とデキュー操作の両方の時間計算量が<span class="arithmatex">\(O(\log n)\)</span>、キュー構築の時間計算量が<span class="arithmatex">\(O(n)\)</span>で、すべて非常に効率的です。</li>
+<li><strong>ヒープソート</strong>：データセットが与えられた場合、それらからヒープを作成し、次に要素削除操作を継続的に実行して順序付けされたデータを取得できます。ただし、ヒープソートを実装するより洗練された方法があり、「ヒープソート」の章で説明されています。</li>
+<li><strong>最大<span class="arithmatex">\(k\)</span>個の要素の発見</strong>：これは古典的なアルゴリズム問題であり、一般的な使用例でもあります。Weiboホット検索のトップ10ホットニュースの選択や、トップ10の売れ筋商品の選択などです。</li>
+</ul>
+
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+  
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+    はじめに
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M21 4H3a2 2 0 0 0-2 2v13a2 2 0 0 0 2 2h18a2 2 0 0 0 2-2V6a2 2 0 0 0-2-2M3 19V6h8v13H3m18 0h-8V6h8v13m-7-9.5h6V11h-6V9.5m0 2.5h6v1.5h-6V12m0 2.5h6V16h-6v-1.5Z"/></svg>
+  
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+    第 0 章 &nbsp; 前書き
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+      <a href="../chapter_preface/about_the_book/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    0.1 &nbsp; この本について
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+  
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+      <a href="../chapter_preface/suggestions/" class="md-nav__link">
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+    0.2 &nbsp; 本書の使い方
+  </span>
+  
+
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+      <a href="../chapter_preface/summary/" class="md-nav__link">
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+    0.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_introduction/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="./" class="md-nav__link md-nav__link--active">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link md-nav__link--active" for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
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+<div class="admonition abstract">
+<p class="admonition-title">Abstract</p>
+<p>ヒープは山とその険しい峰のように、層をなして起伏し、それぞれが独特の形を持っています。</p>
+<p>各山の頂は散らばった高さで上下しますが、最も高いものが常に最初に注目を集めます。</p>
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+<ul>
+<li><a href="heap/">8.1 &nbsp; ヒープ</a></li>
+<li><a href="build_heap/">8.2 &nbsp; ヒープの構築</a></li>
+<li><a href="top_k/">8.3 &nbsp; Top-k問題</a></li>
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+      <a href="../../chapter_preface/about_the_book/" class="md-nav__link">
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+      <a href="../../chapter_preface/summary/" class="md-nav__link">
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+  
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+    第 1 章 &nbsp; アルゴリズムとの出会い
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+    1.1 &nbsp; アルゴリズムはどこにでもある
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+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
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+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
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+  
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+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
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+    </li>
+  
+
+              
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+          
+        
+      
+        
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+            <a href="../../chapter_computational_complexity/" class="md-nav__link ">
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+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
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+  
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+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
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+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
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+    </li>
+  
+
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+            
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+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
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+  
+
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+    </li>
+  
+
+              
+            
+              
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+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
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+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
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+      
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+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
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+            第 3 章 &nbsp; データ構造
+          </label>
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+            
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+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
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+    </li>
+  
+
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+            
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+  
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+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
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+  
+  
+  
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+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
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+  
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+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
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+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
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+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
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+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
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+            
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+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
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+        
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+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
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+  
+  
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+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 重要な復習
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#2-q-a" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; Q &amp; A
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
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+          
+        
+      
+    
+    
+    
+    
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+      
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+        
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+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_19" >
+        
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+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_reference/" class="md-nav__link ">
+              
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9 3v15h3V3H9m3 2 4 13 3-1-4-13-3 1M5 5v13h3V5H5M3 19v2h18v-2H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    参考文献
+  </span>
+  
+
+            </a>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_19_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_19">
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+            参考文献
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+</nav>
+                  </div>
+                </div>
+              </div>
+            
+            
+              
+              <div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
+                <div class="md-sidebar__scrollwrap">
+                  <div class="md-sidebar__inner">
+                    
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 重要な復習
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#2-q-a" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; Q &amp; A
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+                  </div>
+                </div>
+              </div>
+            
+          
+          
+            <div class="md-content" data-md-component="content">
+              <article class="md-content__inner md-typeset">
+                
+                  <!-- Tags -->
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+
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+<!-- Actions -->
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+
+  <!-- Edit button -->
+  
+    <a
+      href="https://github.com/krahets/hello-algo/tree/main/ja/docs/chapter_heap/summary.md"
+      title="編集"
+      class="md-content__button md-icon"
+    >
+      
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
+    </a>
+  
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+  
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+
+<!-- Page content -->
+<h1 id="84">8.4 &nbsp; まとめ<a class="headerlink" href="#84" title="Permanent link">&para;</a></h1>
+<h3 id="1">1. &nbsp; 重要な復習<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<ul>
+<li>ヒープは完備二分木で、その構築性質に基づいて最大ヒープまたは最小ヒープに分類できます。最大ヒープの先頭要素は最大で、最小ヒープの先頭要素は最小です。</li>
+<li>優先度キューは、デキューの優先度を持つキューとして定義され、通常ヒープを使用して実装されます。</li>
+<li>ヒープの一般的な操作とそれに対応する時間計算量には以下があります：ヒープへの要素挿入<span class="arithmatex">\(O(\log n)\)</span>、ヒープからの先頭要素削除<span class="arithmatex">\(O(\log n)\)</span>、ヒープの先頭要素へのアクセス<span class="arithmatex">\(O(1)\)</span>。</li>
+<li>完備二分木は配列で表現するのに適しているため、ヒープは一般的に配列を使用して格納されます。</li>
+<li>ヒープ化操作はヒープの性質を維持するために使用され、ヒープの挿入操作と削除操作の両方で使用されます。</li>
+<li><span class="arithmatex">\(n\)</span>個の要素が入力として与えられた場合のヒープ構築の時間計算量は<span class="arithmatex">\(O(n)\)</span>に最適化でき、これは非常に効率的です。</li>
+<li>Top-kは古典的なアルゴリズム問題で、ヒープデータ構造を使用して効率的に解決でき、時間計算量は<span class="arithmatex">\(O(n \log k)\)</span>です。</li>
+</ul>
+<h3 id="2-q-a">2. &nbsp; Q &amp; A<a class="headerlink" href="#2-q-a" title="Permanent link">&para;</a></h3>
+<p><strong>Q</strong>: データ構造の「ヒープ」とメモリ管理の「ヒープ」は同じ概念ですか？</p>
+<p>この2つは、どちらも「ヒープ」と呼ばれますが、同じ概念ではありません。コンピュータシステムメモリのヒープは動的メモリ割り当ての一部で、プログラムが実行中にデータを格納するために使用できます。プログラムは、オブジェクトや配列などの複雑な構造を格納するために、一定量のヒープメモリを要求できます。割り当てられたデータが不要になったときは、メモリリークを防ぐためにプログラムがこのメモリを解放する必要があります。スタックメモリと比較して、ヒープメモリの管理と使用にはより多くの注意が必要で、不適切な使用はメモリリークやダングリングポインタにつながる可能性があります。</p>
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+<div class="banner-svg">
+    <svg xmlns="http://www.w3.org/2000/svg"
+        viewBox="0 0 512 512"><!--!Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free Copyright 2024 Fonticons, Inc.-->
+        <path
+            d="M480 32c0-12.9-7.8-24.6-19.8-29.6s-25.7-2.2-34.9 6.9L381.7 53c-48 48-113.1 75-181 75H192 160 64c-35.3 0-64 28.7-64 64v96c0 35.3 28.7 64 64 64l0 128c0 17.7 14.3 32 32 32h64c17.7 0 32-14.3 32-32V352l8.7 0c67.9 0 133 27 181 75l43.6 43.6c9.2 9.2 22.9 11.9 34.9 6.9s19.8-16.6 19.8-29.6V300.4c18.6-8.8 32-32.5 32-60.4s-13.4-51.6-32-60.4V32zm-64 76.7V240 371.3C357.2 317.8 280.5 288 200.7 288H192V192h8.7c79.8 0 156.5-29.8 215.3-83.3z" />
+    </svg>
+    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
+</div>
+
+          </div>
+          
+        </aside>
+      
+    </div>
+    
+    
+      
+
+  
+
+<header class="md-header md-header--shadow" data-md-component="header">
+  <nav class="md-header__inner md-grid" aria-label="ヘッダー">
+    <a href="../.." title="Hello アルゴリズム" class="md-header__button md-logo" aria-label="Hello アルゴリズム" data-md-component="logo">
+      
+  <img src="../../assets/images/logo.svg" alt="logo">
+
+    </a>
+    <label class="md-header__button md-icon" for="__drawer">
+      
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 6h18v2H3V6m0 5h18v2H3v-2m0 5h18v2H3v-2Z"/></svg>
+    </label>
+    <div class="md-header__title" data-md-component="header-title">
+      <div class="md-header__ellipsis">
+        <div class="md-header__topic">
+          <span class="md-ellipsis">
+            Hello アルゴリズム
+          </span>
+        </div>
+        <div class="md-header__topic" data-md-component="header-topic">
+          <span class="md-ellipsis">
+            
+              8.3 &nbsp; Top-k問題
+            
+          </span>
+        </div>
+      </div>
+    </div>
+    
+      
+        <form class="md-header__option" data-md-component="palette">
+  
+    
+    
+    
+    <input class="md-option" data-md-color-media="" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="teal"  aria-label="ダークモード"  type="radio" name="__palette" id="__palette_0">
+    
+      <label class="md-header__button md-icon" title="ダークモード" for="__palette_1" hidden>
+        <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07 19.07 3.5m-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13.51 1.67m-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87.4 1.31M19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35-2.53-2.2m4.33-2.7 1.15-2.77 2.2 2.54-3.35.23m1.15-4.96-1.14-2.78 3.34.24-2.2 2.54M9.63 18.93l2.77 1.15-2.53 2.19-.24-3.34Z"/></svg>
+      </label>
+    
+  
+    
+    
+    
+    <input class="md-option" data-md-color-media="" data-md-color-scheme="slate" data-md-color-primary="black" data-md-color-accent="teal"  aria-label="ライトモード"  type="radio" name="__palette" id="__palette_1">
+    
+      <label class="md-header__button md-icon" title="ライトモード" for="__palette_0" hidden>
+        <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07 19.07 3.5m-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13.51 1.67m-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87.4 1.31M19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35-2.53-2.2m4.33-2.7 1.15-2.77 2.2 2.54-3.35.23m1.15-4.96-1.14-2.78 3.34.24-2.2 2.54M9.63 18.93l2.77 1.15-2.53 2.19-.24-3.34Z"/></svg>
+      </label>
+    
+  
+</form>
+      
+    
+    
+      <script>var media,input,key,value,palette=__md_get("__palette");if(palette&&palette.color){"(prefers-color-scheme)"===palette.color.media&&(media=matchMedia("(prefers-color-scheme: light)"),input=document.querySelector(media.matches?"[data-md-color-media='(prefers-color-scheme: light)']":"[data-md-color-media='(prefers-color-scheme: dark)']"),palette.color.media=input.getAttribute("data-md-color-media"),palette.color.scheme=input.getAttribute("data-md-color-scheme"),palette.color.primary=input.getAttribute("data-md-color-primary"),palette.color.accent=input.getAttribute("data-md-color-accent"));for([key,value]of Object.entries(palette.color))document.body.setAttribute("data-md-color-"+key,value)}</script>
+    
+    
+      <div class="md-header__option">
+  <div class="md-select">
+    
+    <button class="md-header__button md-icon" aria-label="言語切り替え">
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12.87 15.07-2.54-2.51.03-.03A17.52 17.52 0 0 0 14.07 6H17V4h-7V2H8v2H1v2h11.17C11.5 7.92 10.44 9.75 9 11.35 8.07 10.32 7.3 9.19 6.69 8h-2c.73 1.63 1.73 3.17 2.98 4.56l-5.09 5.02L4 19l5-5 3.11 3.11.76-2.04M18.5 10h-2L12 22h2l1.12-3h4.75L21 22h2l-4.5-12m-2.62 7 1.62-4.33L19.12 17h-3.24Z"/></svg>
+    </button>
+    <div class="md-select__inner">
+      <ul class="md-select__list">
+        
+          <li class="md-select__item">
+            <a href="/chapter_heap/top_k/" hreflang="zh" class="md-select__link">
+              简体中文
+            </a>
+          </li>
+        
+          <li class="md-select__item">
+            <a href="/zh-hant/chapter_heap/top_k/" hreflang="zh-Hant" class="md-select__link">
+              繁體中文
+            </a>
+          </li>
+        
+          <li class="md-select__item">
+            <a href="/en/chapter_heap/top_k/" hreflang="en" class="md-select__link">
+              English
+            </a>
+          </li>
+        
+          <li class="md-select__item">
+            <a href="/ja/chapter_heap/top_k/" hreflang="ja" class="md-select__link">
+              日本語
+            </a>
+          </li>
+        
+      </ul>
+    </div>
+  </div>
+</div>
+    
+    
+      <label class="md-header__button md-icon" for="__search">
+        
+        <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.516 6.516 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5Z"/></svg>
+      </label>
+      <div class="md-search" data-md-component="search" role="dialog">
+  <label class="md-search__overlay" for="__search"></label>
+  <div class="md-search__inner" role="search">
+    <form class="md-search__form" name="search">
+      <input type="text" class="md-search__input" name="query" aria-label="検索" placeholder="検索" autocapitalize="off" autocorrect="off" autocomplete="off" spellcheck="false" data-md-component="search-query" required>
+      <label class="md-search__icon md-icon" for="__search">
+        
+        <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.516 6.516 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5Z"/></svg>
+        
+        <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M20 11v2H8l5.5 5.5-1.42 1.42L4.16 12l7.92-7.92L13.5 5.5 8 11h12Z"/></svg>
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+      <nav class="md-search__options" aria-label="検索">
+        
+          <a href="javascript:void(0)" class="md-search__icon md-icon" title="共有" aria-label="共有" data-clipboard data-clipboard-text="" data-md-component="search-share" tabindex="-1">
+            
+            <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 16.08c-.76 0-1.44.3-1.96.77L8.91 12.7c.05-.23.09-.46.09-.7 0-.24-.04-.47-.09-.7l7.05-4.11c.54.5 1.25.81 2.04.81a3 3 0 0 0 3-3 3 3 0 0 0-3-3 3 3 0 0 0-3 3c0 .24.04.47.09.7L8.04 9.81C7.5 9.31 6.79 9 6 9a3 3 0 0 0-3 3 3 3 0 0 0 3 3c.79 0 1.5-.31 2.04-.81l7.12 4.15c-.05.21-.08.43-.08.66 0 1.61 1.31 2.91 2.92 2.91 1.61 0 2.92-1.3 2.92-2.91A2.92 2.92 0 0 0 18 16.08Z"/></svg>
+          </a>
+        
+        <button type="reset" class="md-search__icon md-icon" title="クリア" aria-label="クリア" tabindex="-1">
+          
+          <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 6.41 17.59 5 12 10.59 6.41 5 5 6.41 10.59 12 5 17.59 6.41 19 12 13.41 17.59 19 19 17.59 13.41 12 19 6.41Z"/></svg>
+        </button>
+      </nav>
+      
+        <div class="md-search__suggest" data-md-component="search-suggest"></div>
+      
+    </form>
+    <div class="md-search__output">
+      <div class="md-search__scrollwrap" data-md-scrollfix>
+        <div class="md-search-result" data-md-component="search-result">
+          <div class="md-search-result__meta">
+            検索を初期化
+          </div>
+          <ol class="md-search-result__list" role="presentation"></ol>
+        </div>
+      </div>
+    </div>
+  </div>
+</div>
+    
+    
+      <div class="md-header__source">
+        <a href="https://github.com/krahets/hello-algo" title="リポジトリへ" class="md-source" data-md-component="source">
+  <div class="md-source__icon md-icon">
+    
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 496 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"/></svg>
+  </div>
+  <div class="md-source__repository">
+    krahets/hello-algo
+  </div>
+</a>
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+  </nav>
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+</header>
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+    <div class="md-container" data-md-component="container">
+      
+      
+        
+          
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+      <main class="md-main" data-md-component="main">
+        <div class="md-main__inner md-grid">
+          
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+              
+              <div class="md-sidebar md-sidebar--primary" data-md-component="sidebar" data-md-type="navigation" >
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+    Hello アルゴリズム
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+    
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 496 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"/></svg>
+  </div>
+  <div class="md-source__repository">
+    krahets/hello-algo
+  </div>
+</a>
+    </div>
+  
+  <ul class="md-nav__list" data-md-scrollfix>
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+      
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+    
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+    
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+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
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+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_1" >
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+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hello_algo/" class="md-nav__link ">
+              
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m13.13 22.19-1.63-3.83c1.57-.58 3.04-1.36 4.4-2.27l-2.77 6.1M5.64 12.5l-3.83-1.63 6.1-2.77C7 9.46 6.22 10.93 5.64 12.5M19.22 4c.28 0 .53 0 .74.05.17 1.39-.02 4.25-3.3 7.53-1.7 1.71-3.73 3.02-6.01 3.89l-2.15-2.1c.92-2.31 2.23-4.34 3.92-6.03C15.18 4.58 17.64 4 19.22 4m0-2c-1.98 0-4.98.69-8.22 3.93-2.19 2.19-3.5 4.6-4.35 6.71-.28.75-.09 1.57.46 2.13l2.13 2.12c.38.38.89.61 1.42.61.23 0 .47-.06.7-.15A19.1 19.1 0 0 0 18.07 13c5.66-5.66 3.54-10.61 3.54-10.61S20.7 2 19.22 2m-4.68 7.46c-.78-.78-.78-2.05 0-2.83s2.05-.78 2.83 0c.77.78.78 2.05 0 2.83-.78.78-2.05.78-2.83 0m-5.66 7.07-1.41-1.41 1.41 1.41M6.24 22l3.64-3.64c-.34-.09-.67-.24-.97-.45L4.83 22h1.41M2 22h1.41l4.77-4.76-1.42-1.41L2 20.59V22m0-2.83 4.09-4.08c-.21-.3-.36-.62-.45-.97L2 17.76v1.41Z"/></svg>
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+            はじめに
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_2" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_preface/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M21 4H3a2 2 0 0 0-2 2v13a2 2 0 0 0 2 2h18a2 2 0 0 0 2-2V6a2 2 0 0 0-2-2M3 19V6h8v13H3m18 0h-8V6h8v13m-7-9.5h6V11h-6V9.5m0 2.5h6v1.5h-6V12m0 2.5h6V16h-6v-1.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 0 章 &nbsp; 前書き
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_2" id="__nav_2_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_2_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_2">
+            <span class="md-nav__icon md-icon"></span>
+            第 0 章 &nbsp; 前書き
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/about_the_book/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.1 &nbsp; この本について
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/suggestions/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.2 &nbsp; 本書の使い方
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_introduction/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#831-1" class="md-nav__link">
+    <span class="md-ellipsis">
+      8.3.1 &nbsp; 方法1：反復選択
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#832-2" class="md-nav__link">
+    <span class="md-ellipsis">
+      8.3.2 &nbsp; 方法2：ソート
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#833-3" class="md-nav__link">
+    <span class="md-ellipsis">
+      8.3.3 &nbsp; 方法3：ヒープ
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
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+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
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+    14.4 &nbsp; 0-1ナップサック問題
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+  
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+    </li>
+  
+
+              
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+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
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+    </li>
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+
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+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
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+    14.6 &nbsp; 編集距離問題
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+  
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+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
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+    15.3 &nbsp; 最大容量問題
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+    15.4 &nbsp; 最大積切断問題
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+  </span>
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+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
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+    16.3 &nbsp; 用語集
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+                <div class="md-sidebar__scrollwrap">
+                  <div class="md-sidebar__inner">
+                    
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+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
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+  
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+    <label class="md-nav__title" for="__toc">
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+      目次
+    </label>
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+      
+        <li class="md-nav__item">
+  <a href="#831-1" class="md-nav__link">
+    <span class="md-ellipsis">
+      8.3.1 &nbsp; 方法1：反復選択
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#832-2" class="md-nav__link">
+    <span class="md-ellipsis">
+      8.3.2 &nbsp; 方法2：ソート
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#833-3" class="md-nav__link">
+    <span class="md-ellipsis">
+      8.3.3 &nbsp; 方法3：ヒープ
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+                  </div>
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+                
+                  <!-- Tags -->
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+<!-- Actions -->
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+  
+    <a
+      href="https://github.com/krahets/hello-algo/tree/main/ja/docs/chapter_heap/top_k.md"
+      title="編集"
+      class="md-content__button md-icon"
+    >
+      
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
+    </a>
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+  
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+
+<!-- Page content -->
+<h1 id="83-top-k">8.3 &nbsp; Top-k問題<a class="headerlink" href="#83-top-k" title="Permanent link">&para;</a></h1>
+<div class="admonition question">
+<p class="admonition-title">Question</p>
+<p>長さ<span class="arithmatex">\(n\)</span>の順序付けられていない配列<code>nums</code>が与えられたとき、配列内の最大<span class="arithmatex">\(k\)</span>個の要素を返してください。</p>
+</div>
+<p>この問題について、まず2つの直接的な解法を紹介し、次により効率的なヒープベースの方法を説明します。</p>
+<h2 id="831-1">8.3.1 &nbsp; 方法1：反復選択<a class="headerlink" href="#831-1" title="Permanent link">&para;</a></h2>
+<p>下図に示すように、<span class="arithmatex">\(k\)</span>回の反復を実行し、各回で<span class="arithmatex">\(1\)</span>番目、<span class="arithmatex">\(2\)</span>番目、<span class="arithmatex">\(\dots\)</span>、<span class="arithmatex">\(k\)</span>番目に大きい要素を抽出できます。時間計算量は<span class="arithmatex">\(O(nk)\)</span>です。</p>
+<p>この方法は<span class="arithmatex">\(k \ll n\)</span>の場合にのみ適しています。<span class="arithmatex">\(k\)</span>が<span class="arithmatex">\(n\)</span>に近い場合、時間計算量は<span class="arithmatex">\(O(n^2)\)</span>に近づき、非常に時間がかかります。</p>
+<p><a class="glightbox" href="../top_k.assets/top_k_traversal.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="最大k個の要素を反復的に見つける" class="animation-figure" src="../top_k.assets/top_k_traversal.png" /></a></p>
+<p align="center"> 図 8-6 &nbsp; 最大k個の要素を反復的に見つける </p>
+
+<div class="admonition tip">
+<p class="admonition-title">Tip</p>
+<p><span class="arithmatex">\(k = n\)</span>の場合、完全に順序付けられたシーケンスを得ることができ、これは「選択ソート」アルゴリズムと同等です。</p>
+</div>
+<h2 id="832-2">8.3.2 &nbsp; 方法2：ソート<a class="headerlink" href="#832-2" title="Permanent link">&para;</a></h2>
+<p>下図に示すように、まず配列<code>nums</code>をソートし、次に最後の<span class="arithmatex">\(k\)</span>個の要素を返すことができます。時間計算量は<span class="arithmatex">\(O(n \log n)\)</span>です。</p>
+<p>明らかに、この方法はタスクを「やりすぎ」ています。最大<span class="arithmatex">\(k\)</span>個の要素を見つけるだけでよく、他の要素をソートする必要はありません。</p>
+<p><a class="glightbox" href="../top_k.assets/top_k_sorting.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="ソートによる最大k個の要素の発見" class="animation-figure" src="../top_k.assets/top_k_sorting.png" /></a></p>
+<p align="center"> 図 8-7 &nbsp; ソートによる最大k個の要素の発見 </p>
+
+<h2 id="833-3">8.3.3 &nbsp; 方法3：ヒープ<a class="headerlink" href="#833-3" title="Permanent link">&para;</a></h2>
+<p>以下のプロセスに示すように、ヒープに基づいてTop-k問題をより効率的に解決できます。</p>
+<ol>
+<li>最小ヒープを初期化します。先頭要素が最小になります。</li>
+<li>まず、配列の最初の<span class="arithmatex">\(k\)</span>個の要素をヒープに挿入します。</li>
+<li><span class="arithmatex">\(k + 1\)</span>番目の要素から開始し、現在の要素がヒープの先頭要素より大きい場合、ヒープの先頭要素を削除し、現在の要素をヒープに挿入します。</li>
+<li>走査を完了した後、ヒープには最大<span class="arithmatex">\(k\)</span>個の要素が含まれています。</li>
+</ol>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:9"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">&lt;1&gt;</label><label for="__tabbed_1_2">&lt;2&gt;</label><label for="__tabbed_1_3">&lt;3&gt;</label><label for="__tabbed_1_4">&lt;4&gt;</label><label for="__tabbed_1_5">&lt;5&gt;</label><label for="__tabbed_1_6">&lt;6&gt;</label><label for="__tabbed_1_7">&lt;7&gt;</label><label for="__tabbed_1_8">&lt;8&gt;</label><label for="__tabbed_1_9">&lt;9&gt;</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<p><a class="glightbox" href="../top_k.assets/top_k_heap_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="ヒープに基づく最大k個の要素の発見" class="animation-figure" src="../top_k.assets/top_k_heap_step1.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../top_k.assets/top_k_heap_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="top_k_heap_step2" class="animation-figure" src="../top_k.assets/top_k_heap_step2.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../top_k.assets/top_k_heap_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="top_k_heap_step3" class="animation-figure" src="../top_k.assets/top_k_heap_step3.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../top_k.assets/top_k_heap_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="top_k_heap_step4" class="animation-figure" src="../top_k.assets/top_k_heap_step4.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../top_k.assets/top_k_heap_step5.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="top_k_heap_step5" class="animation-figure" src="../top_k.assets/top_k_heap_step5.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../top_k.assets/top_k_heap_step6.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="top_k_heap_step6" class="animation-figure" src="../top_k.assets/top_k_heap_step6.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../top_k.assets/top_k_heap_step7.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="top_k_heap_step7" class="animation-figure" src="../top_k.assets/top_k_heap_step7.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../top_k.assets/top_k_heap_step8.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="top_k_heap_step8" class="animation-figure" src="../top_k.assets/top_k_heap_step8.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../top_k.assets/top_k_heap_step9.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="top_k_heap_step9" class="animation-figure" src="../top_k.assets/top_k_heap_step9.png" /></a></p>
+</div>
+</div>
+</div>
+<p align="center"> 図 8-8 &nbsp; ヒープに基づく最大k個の要素の発見 </p>
+
+<p>サンプルコードは以下の通りです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:14"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><input id="__tabbed_2_14" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label><label for="__tabbed_2_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">top_k.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">top_k_heap</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">k</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;ヒープを使用して配列内の最大k個の要素を見つける&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># 最小ヒープを初期化</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="n">heap</span> <span class="o">=</span> <span class="p">[]</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="c1"># 配列の最初のk個の要素をヒープに入力</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">k</span><span class="p">):</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>        <span class="n">heapq</span><span class="o">.</span><span class="n">heappush</span><span class="p">(</span><span class="n">heap</span><span class="p">,</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>    <span class="c1"># k+1番目の要素から、ヒープの長さをkに保つ</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">k</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)):</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>        <span class="c1"># 現在の要素がヒープの先頭要素より大きい場合、ヒープの先頭要素を削除し、現在の要素をヒープに入力</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>        <span class="k">if</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">heap</span><span class="p">[</span><span class="mi">0</span><span class="p">]:</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>            <span class="n">heapq</span><span class="o">.</span><span class="n">heappop</span><span class="p">(</span><span class="n">heap</span><span class="p">)</span>
+<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>            <span class="n">heapq</span><span class="o">.</span><span class="n">heappush</span><span class="p">(</span><span class="n">heap</span><span class="p">,</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>    <span class="k">return</span> <span class="n">heap</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">top_k.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* ヒープを使用して配列内の最大k個の要素を見つける */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="n">priority_queue</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">greater</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">topKHeap</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">k</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// 最小ヒープを初期化</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="n">priority_queue</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">,</span><span class="w"> </span><span class="n">greater</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">heap</span><span class="p">;</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="c1">// 配列の最初のk個の要素をヒープに入力</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">k</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">        </span><span class="n">heap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">    </span><span class="c1">// k+1番目の要素から、ヒープの長さをkに保つ</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">k</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">        </span><span class="c1">// 現在の要素がヒープの先頭要素より大きい場合、ヒープの先頭要素を削除し、現在の要素をヒープに入力</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">heap</span><span class="p">.</span><span class="n">top</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">            </span><span class="n">heap</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">            </span><span class="n">heap</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
+<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">heap</span><span class="p">;</span>
+<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">top_k.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* ヒープを使用して配列内の最大 k 個の要素を検索 */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="n">Queue</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="nf">topKHeap</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">k</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// 最小ヒープを初期化</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="n">Queue</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">heap</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">PriorityQueue</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="p">();</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="c1">// 配列の最初の k 個の要素をヒープに入力</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">k</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">        </span><span class="n">heap</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">);</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">    </span><span class="c1">// k+1 番目の要素から、ヒープの長さを k に保つ</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">k</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">        </span><span class="c1">// 現在の要素がヒープの先頭要素より大きい場合、ヒープの先頭要素を削除し、現在の要素をヒープに入力</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">heap</span><span class="p">.</span><span class="na">peek</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">            </span><span class="n">heap</span><span class="p">.</span><span class="na">poll</span><span class="p">();</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">            </span><span class="n">heap</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">);</span>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">heap</span><span class="p">;</span>
+<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">top_k.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">top_k</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">TopKHeap</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">top_k.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">topKHeap</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">top_k.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">topKHeap</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">top_k.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">pushMinHeap</span><span class="p">}</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">popMinHeap</span><span class="p">}</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">peekMinHeap</span><span class="p">}</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">getMinHeap</span><span class="p">}</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">topKHeap</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">top_k.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">pushMinHeap</span><span class="p">}</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">popMinHeap</span><span class="p">}</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">peekMinHeap</span><span class="p">}</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">getMinHeap</span><span class="p">}</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">topKHeap</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">top_k.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">topKHeap</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">top_k.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">top_k_heap</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">top_k.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">pushMinHeap</span><span class="p">}</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">popMinHeap</span><span class="p">}</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">peekMinHeap</span><span class="p">}</span>
+<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">getMinHeap</span><span class="p">}</span>
+<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a>
+<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">topKHeap</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">top_k.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">topKHeap</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">top_k.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">top_k_heap</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">top_k.zig</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">topKHeap</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>合計<span class="arithmatex">\(n\)</span>回のヒープ挿入と削除が実行され、最大ヒープサイズが<span class="arithmatex">\(k\)</span>であるため、時間計算量は<span class="arithmatex">\(O(n \log k)\)</span>です。この方法は非常に効率的で、<span class="arithmatex">\(k\)</span>が小さい場合、時間計算量は<span class="arithmatex">\(O(n)\)</span>に近づき、<span class="arithmatex">\(k\)</span>が大きい場合でも、時間計算量は<span class="arithmatex">\(O(n \log n)\)</span>を超えません。</p>
+<p>さらに、この方法は動的データストリームのシナリオに適しています。データを継続的に追加することで、ヒープ内の要素を維持し、最大<span class="arithmatex">\(k\)</span>個の要素の動的更新を実現できます。</p>
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diff --git a/ja/chapter_hello_algo/index.html b/ja/chapter_hello_algo/index.html
new file mode 100644
index 000000000..6e09e2142
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@@ -0,0 +1,3734 @@
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+    第 1 章 &nbsp; アルゴリズムとの出会い
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+    1.2 &nbsp; アルゴリズムとは何か
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+      <a href="../chapter_introduction/summary/" class="md-nav__link">
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+    1.3 &nbsp; まとめ
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+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
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+            第 2 章 &nbsp; 計算量解析
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+    2.1 &nbsp; アルゴリズム効率評価
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+      <a href="../chapter_computational_complexity/time_complexity/" class="md-nav__link">
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+  
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+      <a href="../chapter_computational_complexity/space_complexity/" class="md-nav__link">
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+    2.4 &nbsp; 空間計算量
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+  
+
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+
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+  
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+      <a href="../chapter_computational_complexity/summary/" class="md-nav__link">
+        
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+    第 3 章 &nbsp; データ構造
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+            第 3 章 &nbsp; データ構造
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+      <a href="../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
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+      <a href="../chapter_data_structure/basic_data_types/" class="md-nav__link">
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+    3.2 &nbsp; 基本データ型
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+      <a href="../chapter_data_structure/number_encoding/" class="md-nav__link">
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+  
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+      <a href="../chapter_data_structure/character_encoding/" class="md-nav__link">
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+  
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+      <a href="../chapter_data_structure/summary/" class="md-nav__link">
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+    3.5 &nbsp; まとめ
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+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_19" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_reference/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9 3v15h3V3H9m3 2 4 13 3-1-4-13-3 1M5 5v13h3V5H5M3 19v2h18v-2H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    参考文献
+  </span>
+  
+
+            </a>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_19_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_19">
+            <span class="md-nav__icon md-icon"></span>
+            参考文献
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
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+            
+          </ul>
+        </nav>
+      
+    </li>
+  
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+    
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+</nav>
+                  </div>
+                </div>
+              </div>
+            
+            
+              
+              <div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
+                <div class="md-sidebar__scrollwrap">
+                  <div class="md-sidebar__inner">
+                    
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+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+</nav>
+                  </div>
+                </div>
+              </div>
+            
+          
+          
+            <div class="md-content" data-md-component="content">
+              <article class="md-content__inner md-typeset">
+                
+                  <!-- Tags -->
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+<!-- Actions -->
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+  <!-- Edit button -->
+  
+    <a
+      href="https://github.com/krahets/hello-algo/tree/main/ja/docs/chapter_hello_algo/index.md"
+      title="編集"
+      class="md-content__button md-icon"
+    >
+      
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
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+  
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+
+<!-- Page content -->
+<h1 id="_1">はじめに<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h1>
+<p>数年前、私はLeetCodeで「剣指Offer」の問題解答を共有し、多くの読者から励ましとサポートを受けました。読者とのやり取りの中で、最もよく聞かれた質問は「アルゴリズムの勉強をどう始めたらよいか」でした。次第に、私はこの質問に強い関心を抱くようになりました。</p>
+<p>問題を直接解くことが最も人気のある方法のようです。これはシンプルで直接的で効果的です。しかし、問題解決はマインスイーパーをプレイするようなものです。自学自習の能力が高い人は、地雷を一つずつ回避していくことができますが、しっかりとした基礎がない人は、何度もつまずいて挫折しながら後退することになるかもしれません。教科書を読むことも一般的な方法ですが、就職活動中の人にとって、卒業論文の執筆、履歴書の提出、筆記試験や面接の準備が既にエネルギーの大部分を消費しており、分厚い本を読むことはしばしば困難な挑戦となります。</p>
+<p>もしあなたが同様の悩みを抱えているなら、この本があなたを見つけることができて幸運です。この本は、この質問に対する私の答えです。これが最良の解決策ではないかもしれませんが、少なくとも積極的な試みです。この本があなたに直接内定をもたらすことはできませんが、データ構造とアルゴリズムの「知識地図」を探索する手引きとなり、さまざまな「地雷」の形、大きさ、位置を理解し、さまざまな「地雷除去方法」をマスターできるようお手伝いします。これらのスキルがあれば、より快適に問題を解き、文献を読むことができ、徐々に知識体系を構築できると信じています。</p>
+<p>私は、ファインマン教授の言葉に深く同感します。「知識は無料ではありません。注意を払わなければならないのです。」この意味で、この本は完全に「無料」ではありません。この本に対するあなたの貴重な「注意」に応えるために、私は最善を尽くし、最大の「注意」を払ってこの本を書きます。</p>
+<p>自分の限界を認識しており、この本の内容が時間をかけて洗練されたにもかかわらず、間違いは確実に残っていることを理解しています。先生方や学生の皆様からの批評と訂正を心から歓迎いたします。</p>
+<p><a class="glightbox" href="../assets/covers/chapter_hello_algo.jpg" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Hello Algo" class="cover-image" src="../assets/covers/chapter_hello_algo.jpg" /></a></p>
+<div style="text-align: center;">
+    <h2 style="margin-top: 0.8em; margin-bottom: 0.8em;">Hello, Algo!</h2>
+</div>
+
+<p>コンピュータの出現は世界に大きな変化をもたらしました。高速な計算能力と優れたプログラム可能性により、コンピュータはアルゴリズムを実行しデータを処理するための理想的な媒体となりました。ビデオゲームのリアルなグラフィックス、自動運転の知的な判断、AlphaGoの見事な囲碁ゲーム、ChatGPTの自然な対話など、これらのアプリケーションはすべて、コンピュータ上で動作するアルゴリズムの精巧な実演です。</p>
+<p>実際、コンピュータの出現以前から、アルゴリズムとデータ構造は世界の至る所に存在していました。初期のアルゴリズムは比較的シンプルで、古代の計数方法や道具作りの手順などがありました。文明が進歩するにつれて、アルゴリズムはより洗練され複雑になりました。職人の精巧な技術から、生産力を解放する工業製品、宇宙を支配する科学法則まで、ほぼすべての平凡または驚異的なことの背後には、アルゴリズムの巧妙な思考があります。</p>
+<p>同様に、データ構造は至る所にあります。ソーシャルネットワークから地下鉄路線まで、多くのシステムは「グラフ」としてモデル化できます。国から家族まで、社会組織の主要な形態は「木」の特徴を示します。冬服は「スタック」のようで、最初に着たものが最後に脱がれます。バドミントンのシャトル筒は「キュー」に似ており、一方の端で挿入し、もう一方の端で取り出します。辞書は「ハッシュテーブル」のようで、目標エントリを素早く検索できます。</p>
+<p>この本は、明確で理解しやすいアニメーション図解と実行可能なコード例を通じて、読者がアルゴリズムとデータ構造の核心概念を理解し、プログラミングを通じてそれらを実装できるようになることを目指しています。この基盤の上で、この本は複雑な世界におけるアルゴリズムの生き生きとした現れを明らかにし、アルゴリズムの美しさを示すことに努めています。この本があなたのお役に立てることを願っています！</p>
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+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_19" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_reference/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9 3v15h3V3H9m3 2 4 13 3-1-4-13-3 1M5 5v13h3V5H5M3 19v2h18v-2H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    参考文献
+  </span>
+  
+
+            </a>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_19_label" aria-expanded="false">
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+            参考文献
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+                  </div>
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+            
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+              <div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
+                <div class="md-sidebar__scrollwrap">
+                  <div class="md-sidebar__inner">
+                    
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+  
+  
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+  
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+                  </div>
+                </div>
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+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
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+<h1 id="11">1.1 &nbsp; アルゴリズムは至る所にある<a class="headerlink" href="#11" title="Permanent link">&para;</a></h1>
+<p>「アルゴリズム」という言葉を聞くと、自然に数学を思い浮かべます。しかし、多くのアルゴリズムは複雑な数学を含まず、基本的な論理により多く依存しており、これは私たちの日常生活の至る所で見ることができます。</p>
+<p>アルゴリズムについて正式に議論を始める前に、興味深い事実を共有する価値があります。<strong>あなたは無意識のうちに多くのアルゴリズムを学び、日常生活でそれらを応用することに慣れています</strong>。ここで、この点を証明するためにいくつかの具体的な例を挙げます。</p>
+<p><strong>例1：辞書の引き方</strong>。英語の辞書では、単語がアルファベット順に並んでいます。<span class="arithmatex">\(r\)</span>で始まる単語を探していると仮定すると、通常は以下の方法で行います：</p>
+<ol>
+<li>辞書を大体半分ぐらいのところで開き、そのページの最初の語彙を確認します。例えば<span class="arithmatex">\(m\)</span>で始まる文字だとしましょう。</li>
+<li><span class="arithmatex">\(r\)</span>はアルファベットで<span class="arithmatex">\(m\)</span>の後に来るので、前半を無視して、探索空間を後半に絞ります。</li>
+<li><span class="arithmatex">\(r\)</span>で始まる単語を見つけるまで、ステップ<code>1.</code>と<code>2.</code>を繰り返します。</li>
+</ol>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:5"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">&lt;1&gt;</label><label for="__tabbed_1_2">&lt;2&gt;</label><label for="__tabbed_1_3">&lt;3&gt;</label><label for="__tabbed_1_4">&lt;4&gt;</label><label for="__tabbed_1_5">&lt;5&gt;</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<p><a class="glightbox" href="../algorithms_are_everywhere.assets/binary_search_dictionary_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="辞書を引く過程" class="animation-figure" src="../algorithms_are_everywhere.assets/binary_search_dictionary_step1.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../algorithms_are_everywhere.assets/binary_search_dictionary_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="辞書での二分探索ステップ2" class="animation-figure" src="../algorithms_are_everywhere.assets/binary_search_dictionary_step2.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../algorithms_are_everywhere.assets/binary_search_dictionary_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="辞書での二分探索ステップ3" class="animation-figure" src="../algorithms_are_everywhere.assets/binary_search_dictionary_step3.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../algorithms_are_everywhere.assets/binary_search_dictionary_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="辞書での二分探索ステップ4" class="animation-figure" src="../algorithms_are_everywhere.assets/binary_search_dictionary_step4.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../algorithms_are_everywhere.assets/binary_search_dictionary_step5.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="辞書での二分探索ステップ5" class="animation-figure" src="../algorithms_are_everywhere.assets/binary_search_dictionary_step5.png" /></a></p>
+</div>
+</div>
+</div>
+<p align="center"> 図 1-1 &nbsp; 辞書を引く過程 </p>
+
+<p>辞書を引くことは、小学生にとって必須のスキルですが、実際には有名な「二分探索」アルゴリズムです。データ構造の観点から、辞書をソートされた「配列」と考えることができます。アルゴリズムの観点から、辞書で単語を探すために取られる一連の行動は、「二分探索」アルゴリズムと見なすことができます。</p>
+<p><strong>例2：トランプの整理</strong>。トランプをプレイするとき、手札を昇順に並べる必要があります。以下の過程で示されます。</p>
+<ol>
+<li>トランプを「整列済み」と「未整列」のセクションに分けます。最初は一番左のカードが既に整列していると仮定します。</li>
+<li>未整列セクションからカードを1枚取り出し、整列済みセクションの正しい位置に挿入します。この後、左端の2枚のカードが整列します。</li>
+<li>すべてのカードが整列するまで、ステップ<code>2</code>を繰り返します。</li>
+</ol>
+<p><a class="glightbox" href="../algorithms_are_everywhere.assets/playing_cards_sorting.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="トランプの整理過程" class="animation-figure" src="../algorithms_are_everywhere.assets/playing_cards_sorting.png" /></a></p>
+<p align="center"> 図 1-2 &nbsp; トランプの整理過程 </p>
+
+<p>上記のトランプを整理する方法は、実質的に「挿入ソート」アルゴリズムであり、小さなデータセットに対して非常に効率的です。多くのプログラミング言語のソート関数には挿入ソートが含まれています。</p>
+<p><strong>例3：お釣りの計算</strong>。スーパーマーケットで<span class="arithmatex">\(69\)</span>の買い物をしたと仮定します。レジ係に<span class="arithmatex">\(100\)</span>を渡すと、<span class="arithmatex">\(31\)</span>のお釣りを提供する必要があります。この過程は以下の図で明確に理解できます。</p>
+<ol>
+<li>選択肢は<span class="arithmatex">\(31\)</span>以下の価値のある通貨で、<span class="arithmatex">\(1\)</span>、<span class="arithmatex">\(5\)</span>、<span class="arithmatex">\(10\)</span>、<span class="arithmatex">\(20\)</span>が含まれます。</li>
+<li>選択肢から最大の<span class="arithmatex">\(20\)</span>を取り出し、<span class="arithmatex">\(31 - 20 = 11\)</span>が残ります。</li>
+<li>残りの選択肢から最大の<span class="arithmatex">\(10\)</span>を取り出し、<span class="arithmatex">\(11 - 10 = 1\)</span>が残ります。</li>
+<li>残りの選択肢から最大の<span class="arithmatex">\(1\)</span>を取り出し、<span class="arithmatex">\(1 - 1 = 0\)</span>が残ります。</li>
+<li>お釣りの計算が完了し、解答は<span class="arithmatex">\(20 + 10 + 1 = 31\)</span>です。</li>
+</ol>
+<p><a class="glightbox" href="../algorithms_are_everywhere.assets/greedy_change.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="お釣りの計算過程" class="animation-figure" src="../algorithms_are_everywhere.assets/greedy_change.png" /></a></p>
+<p align="center"> 図 1-3 &nbsp; お釣りの計算過程 </p>
+
+<p>記述されたステップでは、利用可能な最大の額面を使用して各段階で最良の選択肢を選ぶことで、効果的なお釣り計算戦略につながります。データ構造とアルゴリズムの観点から、このアプローチは「貪欲」アルゴリズムとして知られています。</p>
+<p>料理の準備から宇宙旅行まで、ほぼすべての問題解決にはアルゴリズムが関わっています。コンピュータの出現により、メモリにデータ構造を格納し、CPUとGPUを呼び出してアルゴリズムを実行するコードを書くことができるようになりました。このようにして、現実世界の問題をコンピュータに移し、より効率的な方法でさまざまな複雑な問題を解決できます。</p>
+<div class="admonition tip">
+<p class="admonition-title">Tip</p>
+<p>データ構造、アルゴリズム、配列、二分探索などの概念についてまだ混乱している場合は、読み続けることをお勧めします。この本は、データ構造とアルゴリズムの理解の領域へと優しく導いてくれるでしょう。</p>
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+  
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+    はじめに
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+  
+  <span class="md-ellipsis">
+    第 0 章 &nbsp; 前書き
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+            第 0 章 &nbsp; 前書き
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+  
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+  
+    <li class="md-nav__item">
+      <a href="../chapter_preface/about_the_book/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    0.1 &nbsp; この本について
+  </span>
+  
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+    <li class="md-nav__item">
+      <a href="../chapter_preface/suggestions/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    0.2 &nbsp; 本書の使い方
+  </span>
+  
+
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+
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+  
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+    <li class="md-nav__item">
+      <a href="../chapter_preface/summary/" class="md-nav__link">
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+  
+  <span class="md-ellipsis">
+    0.3 &nbsp; まとめ
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
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+    1.1 &nbsp; アルゴリズムはどこにでもある
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+  
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+      <a href="what_is_dsa/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
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+    </li>
+  
+
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+            
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+  
+    <li class="md-nav__item">
+      <a href="summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
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+  
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+          
+        
+      
+        
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+        
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+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
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+            第 2 章 &nbsp; 計算量解析
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+      <a href="../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
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+    2.1 &nbsp; アルゴリズム効率評価
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+  
+
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+      <a href="../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
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+  
+
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+  
+
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+      <a href="../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
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+    </li>
+  
+
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+              
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+  
+  
+  
+  
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+      <a href="../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
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+    </li>
+  
+
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+              
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+  
+  
+  
+  
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+      <a href="../chapter_computational_complexity/summary/" class="md-nav__link">
+        
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+            <a href="../chapter_data_structure/" class="md-nav__link ">
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
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+  
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+      
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+          
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_19" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_reference/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9 3v15h3V3H9m3 2 4 13 3-1-4-13-3 1M5 5v13h3V5H5M3 19v2h18v-2H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    参考文献
+  </span>
+  
+
+            </a>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_19_label" aria-expanded="false">
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+            参考文献
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+            
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+              <div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
+                <div class="md-sidebar__scrollwrap">
+                  <div class="md-sidebar__inner">
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+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
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+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#_1" class="md-nav__link">
+    <span class="md-ellipsis">
+      章の内容
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+      
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+  
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+                  </div>
+                </div>
+              </div>
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+    >
+      
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
+    </a>
+  
+
+  <!-- View button -->
+  
+
+
+<!-- Page content -->
+<h1 id="1">第 1 章 &nbsp; アルゴリズムとの出会い<a class="headerlink" href="#1" title="Permanent link">&para;</a></h1>
+<p><a class="glightbox" href="../assets/covers/chapter_introduction.jpg" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="アルゴリズムとの出会い" class="cover-image" src="../assets/covers/chapter_introduction.jpg" /></a></p>
+<div class="admonition abstract">
+<p class="admonition-title">Abstract</p>
+<p>優雅な乙女が踊ります。データと絡み合い、アルゴリズムのメロディーに合わせてスカートをなびかせながら。</p>
+<p>彼女があなたをダンスに誘います。彼女のステップに従って、論理と美に満ちたアルゴリズムの世界に入りましょう。</p>
+</div>
+<h2 id="_1">章の内容<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h2>
+<ul>
+<li><a href="algorithms_are_everywhere/">1.1 &nbsp; アルゴリズムはどこにでもある</a></li>
+<li><a href="what_is_dsa/">1.2 &nbsp; アルゴリズムとは何か</a></li>
+<li><a href="summary/">1.3 &nbsp; まとめ</a></li>
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+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_2" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_preface/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M21 4H3a2 2 0 0 0-2 2v13a2 2 0 0 0 2 2h18a2 2 0 0 0 2-2V6a2 2 0 0 0-2-2M3 19V6h8v13H3m18 0h-8V6h8v13m-7-9.5h6V11h-6V9.5m0 2.5h6v1.5h-6V12m0 2.5h6V16h-6v-1.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 0 章 &nbsp; 前書き
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_2" id="__nav_2_label" tabindex="0">
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+          <label class="md-nav__title" for="__nav_2">
+            <span class="md-nav__icon md-icon"></span>
+            第 0 章 &nbsp; 前書き
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/about_the_book/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.1 &nbsp; この本について
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/suggestions/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.2 &nbsp; 本書の使い方
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
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+      
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+  
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+  
+  
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+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1-q-a" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; Q &amp; A
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
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+  
+
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+
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+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
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+<h1 id="13">1.3 &nbsp; まとめ<a class="headerlink" href="#13" title="Permanent link">&para;</a></h1>
+<ul>
+<li>アルゴリズムは日常生活にありふれており、思っているほどアクセスしにくく複雑なものではありません。実際、私たちは既に無意識のうちに多くのアルゴリズムを学び、生活の様々な問題を解決するために使用しています。</li>
+<li>辞書で単語を引く原理は二分探索アルゴリズムと一致しています。二分探索アルゴリズムは分割統治という重要なアルゴリズム概念を体現しています。</li>
+<li>トランプを整理する過程は挿入ソートアルゴリズムと非常に似ています。挿入ソートアルゴリズムは小さなデータセットのソートに適しています。</li>
+<li>通貨でお釣りを計算するステップは本質的に貪欲アルゴリズムに従っており、各ステップでその時点での最良の選択をします。</li>
+<li>アルゴリズムは有限時間内で特定の問題を解決するための段階的な指示のセットですが、データ構造はコンピュータでのデータの組織化と保存方法を定義します。</li>
+<li>データ構造とアルゴリズムは密接に関連しています。データ構造はアルゴリズムの基礎であり、アルゴリズムはデータ構造の機能を活用するステージです。</li>
+<li>データ構造とアルゴリズムをブロックの組み立てに例えることができます。ブロックはデータを表し、ブロックの形状と接続方法はデータ構造を表し、ブロックを組み立てるステップはアルゴリズムに対応します。</li>
+</ul>
+<h3 id="1-q-a">1. &nbsp; Q &amp; A<a class="headerlink" href="#1-q-a" title="Permanent link">&para;</a></h3>
+<p><strong>Q</strong>：プログラマーとして、日常の仕事でアルゴリズムを手動で実装する必要があることはめったにありません。最も一般的に使用されるアルゴリズムは、既にプログラミング言語とライブラリに組み込まれており、すぐに使用できます。これは、私たちが仕事で遭遇する問題が、カスタムアルゴリズム設計を必要とする複雑さのレベルにまだ達していないことを示唆していますか？</p>
+<p>特定の仕事スキルが武術の「技」のようなものだとすれば、基礎科目は「内功」のようなものです。</p>
+<p>アルゴリズム（およびその他の基礎科目）を学ぶ意義は、必ずしも仕事でそれらを一から実装することではなく、概念の確固たる理解に基づいて、より専門的な意思決定と問題解決を可能にし、それによって仕事の全体的な質を向上させることだと私は信じています。例えば、すべてのプログラミング言語には組み込みのソート関数があります：</p>
+<ul>
+<li>データ構造とアルゴリズムを学んでいない場合、どんなデータが与えられても、このソート関数に渡すだけかもしれません。スムーズに動作し、良いパフォーマンスを示し、問題がないように見えます。</li>
+<li>しかし、アルゴリズムを学んだことがあれば、組み込みのソート関数の時間複雑度は通常<span class="arithmatex">\(O(n \log n)\)</span>であることを理解しています。さらに、データが固定桁数の整数（学生IDなど）で構成されている場合、基数ソートのようなより効率的なアプローチを適用でき、時間複雑度をO(nk)に削減できます。ここでkは桁数です。大量のデータを処理する際、節約された時間は重要な価値に変わります — コストの削減、ユーザーエクスペリエンスの向上、システムパフォーマンスの向上。</li>
+</ul>
+<p>エンジニアリングでは、多くの問題を最適に解決することは困難です。ほとんどは「準最適」解決策で対処されます。問題の難しさは、その固有の複雑さだけでなく、それに取り組む人の知識と経験にも依存します。専門知識と経験が深いほど、分析がより徹底的になり、問題をより優雅に解決できます。</p>
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+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_2" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_preface/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M21 4H3a2 2 0 0 0-2 2v13a2 2 0 0 0 2 2h18a2 2 0 0 0 2-2V6a2 2 0 0 0-2-2M3 19V6h8v13H3m18 0h-8V6h8v13m-7-9.5h6V11h-6V9.5m0 2.5h6v1.5h-6V12m0 2.5h6V16h-6v-1.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 0 章 &nbsp; 前書き
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_2" id="__nav_2_label" tabindex="0">
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+          <label class="md-nav__title" for="__nav_2">
+            <span class="md-nav__icon md-icon"></span>
+            第 0 章 &nbsp; 前書き
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
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+            
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/about_the_book/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.1 &nbsp; この本について
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/suggestions/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.2 &nbsp; 本書の使い方
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
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+          </ul>
+        </nav>
+      
+    </li>
+  
+
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+      
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+  
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+  
+  
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+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#121" class="md-nav__link">
+    <span class="md-ellipsis">
+      1.2.1 &nbsp; アルゴリズムの定義
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#122" class="md-nav__link">
+    <span class="md-ellipsis">
+      1.2.2 &nbsp; データ構造の定義
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#123" class="md-nav__link">
+    <span class="md-ellipsis">
+      1.2.3 &nbsp; データ構造とアルゴリズムの関係
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
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+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
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+  
+
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+    </li>
+  
+
+              
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+        </nav>
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+          
+        
+      
+        
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+  </span>
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+
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+      
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+  <a href="#121" class="md-nav__link">
+    <span class="md-ellipsis">
+      1.2.1 &nbsp; アルゴリズムの定義
+    </span>
+  </a>
+  
+</li>
+      
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+  <a href="#122" class="md-nav__link">
+    <span class="md-ellipsis">
+      1.2.2 &nbsp; データ構造の定義
+    </span>
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+      
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+  <a href="#123" class="md-nav__link">
+    <span class="md-ellipsis">
+      1.2.3 &nbsp; データ構造とアルゴリズムの関係
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
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+<!-- Page content -->
+<h1 id="12">1.2 &nbsp; アルゴリズムとは何か<a class="headerlink" href="#12" title="Permanent link">&para;</a></h1>
+<h2 id="121">1.2.1 &nbsp; アルゴリズムの定義<a class="headerlink" href="#121" title="Permanent link">&para;</a></h2>
+<p><u>アルゴリズム</u>は、有限時間内で特定の問題を解決するための一連の指示またはステップです。以下の特徴があります：</p>
+<ul>
+<li>問題が明確に定義されており、入力と出力の明確な定義が含まれています。</li>
+<li>アルゴリズムは実行可能で、有限の回数のステップ、時間、メモリ空間内で完了できることを意味します。</li>
+<li>各ステップには明確な意味があります。同じ入力と条件の下で出力は一貫して同じです。</li>
+</ul>
+<h2 id="122">1.2.2 &nbsp; データ構造の定義<a class="headerlink" href="#122" title="Permanent link">&para;</a></h2>
+<p><u>データ構造</u>は、コンピュータ内でデータを組織し保存する方法で、以下の設計目標があります：</p>
+<ul>
+<li>コンピュータのメモリを節約するために空間占有を最小化する。</li>
+<li>データ操作を可能な限り高速にし、データのアクセス、追加、削除、更新などをカバーする。</li>
+<li>効率的なアルゴリズム実行を可能にするために、簡潔なデータ表現と論理情報を提供する。</li>
+</ul>
+<p><strong>データ構造の設計はバランスを取る行為であり、しばしばトレードオフが必要です</strong>。一つの側面を改善したい場合、しばしば別の側面で妥協する必要があります。以下は2つの例です：</p>
+<ul>
+<li>配列と比較して、連結リストはデータの追加と削除においてより便利ですが、データアクセス速度を犠牲にします。</li>
+<li>連結リストと比較して、グラフはより豊富な論理情報を提供しますが、より多くのメモリ空間が必要です。</li>
+</ul>
+<h2 id="123">1.2.3 &nbsp; データ構造とアルゴリズムの関係<a class="headerlink" href="#123" title="Permanent link">&para;</a></h2>
+<p>以下の図に示すように、データ構造とアルゴリズムは高度に関連し、密接に統合されており、具体的には以下の3つの側面があります：</p>
+<ul>
+<li>データ構造はアルゴリズムの基礎です。構造化されたデータ保存とアルゴリズムのためのデータ操作方法を提供します。</li>
+<li>アルゴリズムはデータ構造に活力を注入します。データ構造だけではデータ情報を保存するだけです。アルゴリズムの応用によって、特定の問題を解決できます。</li>
+<li>アルゴリズムは異なるデータ構造に基づいて実装できることが多いですが、実行効率は大きく異なることがあります。適切なデータ構造を選択することが鍵です。</li>
+</ul>
+<p><a class="glightbox" href="../what_is_dsa.assets/relationship_between_data_structure_and_algorithm.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="データ構造とアルゴリズムの関係" class="animation-figure" src="../what_is_dsa.assets/relationship_between_data_structure_and_algorithm.png" /></a></p>
+<p align="center"> 図 1-4 &nbsp; データ構造とアルゴリズムの関係 </p>
+
+<p>データ構造とアルゴリズムは、以下の図に示すように、ブロックのセットに例えることができます。ブロックセットには多数のピースが含まれ、詳細な組み立て説明書が付いています。これらの説明書に段階的に従うことで、複雑なブロックモデルを構築できます。</p>
+<p><a class="glightbox" href="../what_is_dsa.assets/assembling_blocks.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="ブロックの組み立て" class="animation-figure" src="../what_is_dsa.assets/assembling_blocks.png" /></a></p>
+<p align="center"> 図 1-5 &nbsp; ブロックの組み立て </p>
+
+<p>両者の詳細な対応関係は以下の表に示されています。</p>
+<p align="center"> 表 1-1 &nbsp; データ構造とアルゴリズムをブロックと比較 </p>
+
+<div class="center-table">
+<table>
+<thead>
+<tr>
+<th>データ構造とアルゴリズム</th>
+<th>ブロック</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td>入力データ</td>
+<td>未組み立てのブロック</td>
+</tr>
+<tr>
+<td>データ構造</td>
+<td>ブロックの組織、形状、サイズ、接続などを含む</td>
+</tr>
+<tr>
+<td>アルゴリズム</td>
+<td>ブロックを望ましい形状に組み立てる一連のステップ</td>
+</tr>
+<tr>
+<td>出力データ</td>
+<td>完成したブロックモデル</td>
+</tr>
+</tbody>
+</table>
+</div>
+<p>データ構造とアルゴリズムはプログラミング言語から独立していることは注目に値します。この理由により、この本は複数のプログラミング言語での実装を提供できます。</p>
+<div class="admonition tip">
+<p class="admonition-title">慣習的な略語</p>
+<p>実生活の議論では、「データ構造とアルゴリズム」を単純に「アルゴリズム」と呼ぶことがよくあります。例えば、よく知られたLeetCodeアルゴリズム問題は、実際にはデータ構造とアルゴリズムの両方の知識をテストしています。</p>
+</div>
+
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+  <span class="md-ellipsis">
+    第 0 章 &nbsp; 前書き
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_2" id="__nav_2_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_2_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_2">
+            <span class="md-nav__icon md-icon"></span>
+            第 0 章 &nbsp; 前書き
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
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+            
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+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    0.1 &nbsp; この本について
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    0.1 &nbsp; この本について
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#011" class="md-nav__link">
+    <span class="md-ellipsis">
+      0.1.1 &nbsp; 対象読者
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#012" class="md-nav__link">
+    <span class="md-ellipsis">
+      0.1.2 &nbsp; 内容構成
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#013" class="md-nav__link">
+    <span class="md-ellipsis">
+      0.1.3 &nbsp; 謝辞
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../suggestions/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.2 &nbsp; 本書の使い方
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_introduction/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
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+      </a>
+    </li>
+  
+
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+  
+  
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+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
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+              
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+        </nav>
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+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
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+            
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+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
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+          <label class="md-nav__title" for="__nav_17">
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+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
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+  
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+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
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+    </li>
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+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
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+    </li>
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+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
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+    </li>
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+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
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+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
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+      </a>
+    </li>
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+        </nav>
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+      
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+        
+          
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+            <a href="../../chapter_appendix/" class="md-nav__link ">
+              
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
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+            第 16 章 &nbsp; 付録
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+            
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+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
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+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
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+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
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+  
+  <span class="md-ellipsis">
+    参考文献
+  </span>
+  
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+            
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+</nav>
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+            
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+                <div class="md-sidebar__scrollwrap">
+                  <div class="md-sidebar__inner">
+                    
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+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#011" class="md-nav__link">
+    <span class="md-ellipsis">
+      0.1.1 &nbsp; 対象読者
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#012" class="md-nav__link">
+    <span class="md-ellipsis">
+      0.1.2 &nbsp; 内容構成
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#013" class="md-nav__link">
+    <span class="md-ellipsis">
+      0.1.3 &nbsp; 謝辞
+    </span>
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+  
+</li>
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+  
+</nav>
+                  </div>
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+      title="編集"
+      class="md-content__button md-icon"
+    >
+      
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
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+<!-- Page content -->
+<h1 id="01">0.1 &nbsp; この本について<a class="headerlink" href="#01" title="Permanent link">&para;</a></h1>
+<p>このオープンソースプロジェクトは、データ構造とアルゴリズムに関する無料で初心者にやさしいクラッシュコースの作成を目指しています。</p>
+<ul>
+<li>アニメーション付きの図解、理解しやすい内容、滑らかな学習曲線により、初心者がデータ構造とアルゴリズムの「知識マップ」を探索するのに役立ちます。</li>
+<li>ワンクリックでコードを実行できるため、読者のプログラミングスキルの向上と、アルゴリズムの動作原理およびデータ構造の基礎実装の理解に役立ちます。</li>
+<li>教えることによる学習を促進し、質問や洞察の共有を自由に行ってください。議論を通じて一緒に成長しましょう。</li>
+</ul>
+<h2 id="011">0.1.1 &nbsp; 対象読者<a class="headerlink" href="#011" title="Permanent link">&para;</a></h2>
+<p>もしあなたがアルゴリズムに触れたばかりで経験が限られている場合、またはアルゴリズムである程度の経験を積んでいても、データ構造とアルゴリズムについて曖昧な理解しかなく、常に「分かった」と「うーん」の間を行き来している場合、この本はあなたのためのものです！</p>
+<p>すでにある程度の問題解決経験を積んでおり、ほとんどのタイプの問題に精通している場合、この本はアルゴリズムの知識体系を復習し整理するのに役立ちます。リポジトリのソースコードは「問題解決ツールキット」や「アルゴリズムチートシート」として使用できます。</p>
+<p>もしあなたがアルゴリズムの専門家であれば、貴重な提案をいただくか、<a href="https://www.hello-algo.com/chapter_appendix/contribution/">参加して協力</a>していただければと思います。</p>
+<div class="admonition success">
+<p class="admonition-title">前提条件</p>
+<p>少なくとも一つのプログラミング言語で簡単なコードを書いて読むことができる必要があります。</p>
+</div>
+<h2 id="012">0.1.2 &nbsp; 内容構成<a class="headerlink" href="#012" title="Permanent link">&para;</a></h2>
+<p>本書の主な内容を下図に示します。</p>
+<ul>
+<li><strong>計算量解析</strong>: データ構造とアルゴリズムを評価する側面と方法を探求します。時間計算量と空間計算量を導出する方法、および一般的なタイプと例を扱います。</li>
+<li><strong>データ構造</strong>: 基本的なデータ型、分類方法、定義、長所と短所、一般的な操作、タイプ、応用、および配列、連結リスト、スタック、キュー、ハッシュテーブル、木、ヒープ、グラフなどのデータ構造の実装方法に焦点を当てます。</li>
+<li><strong>アルゴリズム</strong>: アルゴリズムを定義し、その長所と短所、効率性、応用シナリオ、問題解決ステップについて議論し、検索、ソート、分割統治、バックトラッキング、動的プログラミング、貪欲アルゴリズムなど、さまざまなアルゴリズムのサンプル問題を含みます。</li>
+</ul>
+<p><a class="glightbox" href="../about_the_book.assets/hello_algo_mindmap.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="本書の主な内容" class="animation-figure" src="../about_the_book.assets/hello_algo_mindmap.png" /></a></p>
+<p align="center"> 図 0-1 &nbsp; 本書の主な内容 </p>
+
+<h2 id="013">0.1.3 &nbsp; 謝辞<a class="headerlink" href="#013" title="Permanent link">&para;</a></h2>
+<p>この本は、オープンソースコミュニティの多くの貢献者の共同努力により継続的に改善されています。時間とエネルギーを投資してくださった各執筆者に感謝いたします。GitHubで生成された順序で記載されています: krahets, coderonion, Gonglja, nuomi1, Reanon, justin-tse, hpstory, danielsss, curtishd, night-cruise, S-N-O-R-L-A-X, msk397, gvenusleo, khoaxuantu, RiverTwilight, rongyi, gyt95, zhuoqinyue, K3v123, Zuoxun, mingXta, hello-ikun, FangYuan33, GN-Yu, yuelinxin, longsizhuo, Cathay-Chen, guowei-gong, xBLACKICEx, IsChristina, JoseHung, qualifier1024, QiLOL, pengchzn, Guanngxu, L-Super, WSL0809, Slone123c, lhxsm, yuan0221, what-is-me, theNefelibatas, longranger2, cy-by-side, xiongsp, JeffersonHuang, Transmigration-zhou, magentaqin, Wonderdch, malone6, xiaomiusa87, gaofer, bluebean-cloud, a16su, Shyam-Chen, nanlei, hongyun-robot, Phoenix0415, MolDuM, Nigh, he-weilai, junminhong, mgisr, iron-irax, yd-j, XiaChuerwu, XC-Zero, seven1240, SamJin98, wodray, reeswell, NI-SW, Horbin-Magician, Enlightenus, xjr7670, YangXuanyi, DullSword, boloboloda, iStig, qq909244296, jiaxianhua, wenjianmin, keshida, kilikilikid, lclc6, lwbaptx, liuxjerry, lucaswangdev, lyl625760, hts0000, gledfish, fbigm, echo1937, szu17dmy, dshlstarr, Yucao-cy, coderlef, czruby, bongbongbakudan, beintentional, ZongYangL, ZhongYuuu, luluxia, xb534, bitsmi, ElaBosak233, baagod, zhouLion, yishangzhang, yi427, yabo083, weibk, wangwang105, th1nk3r-ing, tao363, 4yDX3906, syd168, steventimes, sslmj2020, smilelsb, siqyka, selear, sdshaoda, Xi-Row, popozhu, nuquist19, noobcodemaker, XiaoK29, chadyi, ZhongGuanbin, shanghai-Jerry, JackYang-hellobobo, Javesun99, lipusheng, BlindTerran, ShiMaRing, FreddieLi, FloranceYeh, iFleey, fanchenggang, gltianwen, goerll, Dr-XYZ, nedchu, curly210102, CuB3y0nd, KraHsu, CarrotDLaw, youshaoXG, bubble9um, fanenr, eagleanurag, LifeGoesOnionOnionOnion, 52coder, foursevenlove, KorsChen, hezhizhen, linzeyan, ZJKung, GaochaoZhu, hopkings2008, yang-le, Evilrabbit520, Turing-1024-Lee, thomasq0, Suremotoo, Allen-Scai, Risuntsy, Richard-Zhang1019, qingpeng9802, primexiao, nidhoggfgg, 1ch0, MwumLi, martinx, ZnYang2018, hugtyftg, logan-qiu, psychelzh, Keynman, KeiichiKasai and 0130w.</p>
+<p>この本のコードレビュー作業は、coderonion, Gonglja, gvenusleo, hpstory, justin‐tse, khoaxuantu, krahets, night-cruise, nuomi1, Reanon and rongyi（アルファベット順）によって完了されました。彼らの時間と努力に感謝し、様々な言語でのコードの標準化と統一性を確保してくださいました。</p>
+<p>この本の繁体字中国語版は Shyam-Chen と Dr-XYZ によってレビューされ、英語版は yuelinxin, K3v123, QiLOL, Phoenix0415, SamJin98, yanedie, RafaelCaso, pengchzn, thomasq0, and magentaqin によってレビューされました。彼らの継続的な貢献により、この本がより広い読者に届き、役立つことができます。</p>
+<p>この本の制作過程において、多くの方々から貴重な支援をいただきました。これらに限定されませんが：</p>
+<ul>
+<li>会社でのメンター、李熙博士に感謝します。ある会話で「早く行動しろ」と励ましていただき、この本を書く決意を固めることができました。</li>
+<li>ガールフレンドのBubbleに感謝します。この本の最初の読者として、アルゴリズム初心者の視点から多くの貴重な提案をいただき、この本を初心者により適したものにしてくださいました。</li>
+<li>Tengbao、Qibao、Feibaoに感謝します。この本のクリエイティブな名前を考えてくださり、みんなが初めて「Hello World!」を書いた時の素晴らしい思い出を呼び起こしてくれました。</li>
+<li>Xiaoquanに感謝します。知的財産に関する専門的な支援を提供してくださり、このオープンソース本の開発において重要な役割を果たしてくださいました。</li>
+<li>Sutongに感謝します。この本の美しいカバーとロゴをデザインしてくださり、私の要求で何度も修正を辛抱強く行ってくださいました。</li>
+<li>@squidfunk に感謝します。執筆と組版の提案、および彼が開発したオープンソースドキュメントテーマ <a href="https://github.com/squidfunk/mkdocs-material/tree/master">Material-for-MkDocs</a> を提供してくださいました。</li>
+</ul>
+<p>執筆の過程で、データ構造とアルゴリズムに関する多数の教科書や記事を深く研究しました。これらの作品は模範的なモデルとして機能し、この本の内容の正確性と品質を確保してくださいました。先人の方々の貴重な貢献に感謝いたします！</p>
+<p>この本は、理論と実践を組み合わせた学習を提唱しており、この点で <a href="https://github.com/d2l-ai/d2l-en">"Dive into Deep Learning"</a> からインスピレーションを受けています。この優れた本をすべての読者に強くお勧めします。</p>
+<p><strong>継続的な支援と励ましにより、この興味深い仕事をすることを可能にしてくださった両親に心から感謝いたします</strong>。</p>
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+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 6h18v2H3V6m0 5h18v2H3v-2m0 5h18v2H3v-2Z"/></svg>
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+    <div class="md-header__title" data-md-component="header-title">
+      <div class="md-header__ellipsis">
+        <div class="md-header__topic">
+          <span class="md-ellipsis">
+            Hello アルゴリズム
+          </span>
+        </div>
+        <div class="md-header__topic" data-md-component="header-topic">
+          <span class="md-ellipsis">
+            
+              第 0 章 &nbsp; 序文
+            
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+    
+      
+        <form class="md-header__option" data-md-component="palette">
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+    
+    
+    
+    <input class="md-option" data-md-color-media="" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="teal"  aria-label="ダークモード"  type="radio" name="__palette" id="__palette_0">
+    
+      <label class="md-header__button md-icon" title="ダークモード" for="__palette_1" hidden>
+        <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07 19.07 3.5m-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13.51 1.67m-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87.4 1.31M19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35-2.53-2.2m4.33-2.7 1.15-2.77 2.2 2.54-3.35.23m1.15-4.96-1.14-2.78 3.34.24-2.2 2.54M9.63 18.93l2.77 1.15-2.53 2.19-.24-3.34Z"/></svg>
+      </label>
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+  
+    
+    
+    
+    <input class="md-option" data-md-color-media="" data-md-color-scheme="slate" data-md-color-primary="black" data-md-color-accent="teal"  aria-label="ライトモード"  type="radio" name="__palette" id="__palette_1">
+    
+      <label class="md-header__button md-icon" title="ライトモード" for="__palette_0" hidden>
+        <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07 19.07 3.5m-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13.51 1.67m-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87.4 1.31M19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35-2.53-2.2m4.33-2.7 1.15-2.77 2.2 2.54-3.35.23m1.15-4.96-1.14-2.78 3.34.24-2.2 2.54M9.63 18.93l2.77 1.15-2.53 2.19-.24-3.34Z"/></svg>
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+    
+  
+</form>
+      
+    
+    
+      <script>var media,input,key,value,palette=__md_get("__palette");if(palette&&palette.color){"(prefers-color-scheme)"===palette.color.media&&(media=matchMedia("(prefers-color-scheme: light)"),input=document.querySelector(media.matches?"[data-md-color-media='(prefers-color-scheme: light)']":"[data-md-color-media='(prefers-color-scheme: dark)']"),palette.color.media=input.getAttribute("data-md-color-media"),palette.color.scheme=input.getAttribute("data-md-color-scheme"),palette.color.primary=input.getAttribute("data-md-color-primary"),palette.color.accent=input.getAttribute("data-md-color-accent"));for([key,value]of Object.entries(palette.color))document.body.setAttribute("data-md-color-"+key,value)}</script>
+    
+    
+      <div class="md-header__option">
+  <div class="md-select">
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+    <button class="md-header__button md-icon" aria-label="言語切り替え">
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12.87 15.07-2.54-2.51.03-.03A17.52 17.52 0 0 0 14.07 6H17V4h-7V2H8v2H1v2h11.17C11.5 7.92 10.44 9.75 9 11.35 8.07 10.32 7.3 9.19 6.69 8h-2c.73 1.63 1.73 3.17 2.98 4.56l-5.09 5.02L4 19l5-5 3.11 3.11.76-2.04M18.5 10h-2L12 22h2l1.12-3h4.75L21 22h2l-4.5-12m-2.62 7 1.62-4.33L19.12 17h-3.24Z"/></svg>
+    </button>
+    <div class="md-select__inner">
+      <ul class="md-select__list">
+        
+          <li class="md-select__item">
+            <a href="/chapter_preface/" hreflang="zh" class="md-select__link">
+              简体中文
+            </a>
+          </li>
+        
+          <li class="md-select__item">
+            <a href="/zh-hant/chapter_preface/" hreflang="zh-Hant" class="md-select__link">
+              繁體中文
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+          </li>
+        
+          <li class="md-select__item">
+            <a href="/en/chapter_preface/" hreflang="en" class="md-select__link">
+              English
+            </a>
+          </li>
+        
+          <li class="md-select__item">
+            <a href="/ja/chapter_preface/" hreflang="ja" class="md-select__link">
+              日本語
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+        
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+</div>
+    
+    
+      <label class="md-header__button md-icon" for="__search">
+        
+        <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.516 6.516 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5Z"/></svg>
+      </label>
+      <div class="md-search" data-md-component="search" role="dialog">
+  <label class="md-search__overlay" for="__search"></label>
+  <div class="md-search__inner" role="search">
+    <form class="md-search__form" name="search">
+      <input type="text" class="md-search__input" name="query" aria-label="検索" placeholder="検索" autocapitalize="off" autocorrect="off" autocomplete="off" spellcheck="false" data-md-component="search-query" required>
+      <label class="md-search__icon md-icon" for="__search">
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+        <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.516 6.516 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5Z"/></svg>
+        
+        <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M20 11v2H8l5.5 5.5-1.42 1.42L4.16 12l7.92-7.92L13.5 5.5 8 11h12Z"/></svg>
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+      <nav class="md-search__options" aria-label="検索">
+        
+          <a href="javascript:void(0)" class="md-search__icon md-icon" title="共有" aria-label="共有" data-clipboard data-clipboard-text="" data-md-component="search-share" tabindex="-1">
+            
+            <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 16.08c-.76 0-1.44.3-1.96.77L8.91 12.7c.05-.23.09-.46.09-.7 0-.24-.04-.47-.09-.7l7.05-4.11c.54.5 1.25.81 2.04.81a3 3 0 0 0 3-3 3 3 0 0 0-3-3 3 3 0 0 0-3 3c0 .24.04.47.09.7L8.04 9.81C7.5 9.31 6.79 9 6 9a3 3 0 0 0-3 3 3 3 0 0 0 3 3c.79 0 1.5-.31 2.04-.81l7.12 4.15c-.05.21-.08.43-.08.66 0 1.61 1.31 2.91 2.92 2.91 1.61 0 2.92-1.3 2.92-2.91A2.92 2.92 0 0 0 18 16.08Z"/></svg>
+          </a>
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+        <button type="reset" class="md-search__icon md-icon" title="クリア" aria-label="クリア" tabindex="-1">
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+          <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 6.41 17.59 5 12 10.59 6.41 5 5 6.41 10.59 12 5 17.59 6.41 19 12 13.41 17.59 19 19 17.59 13.41 12 19 6.41Z"/></svg>
+        </button>
+      </nav>
+      
+        <div class="md-search__suggest" data-md-component="search-suggest"></div>
+      
+    </form>
+    <div class="md-search__output">
+      <div class="md-search__scrollwrap" data-md-scrollfix>
+        <div class="md-search-result" data-md-component="search-result">
+          <div class="md-search-result__meta">
+            検索を初期化
+          </div>
+          <ol class="md-search-result__list" role="presentation"></ol>
+        </div>
+      </div>
+    </div>
+  </div>
+</div>
+    
+    
+      <div class="md-header__source">
+        <a href="https://github.com/krahets/hello-algo" title="リポジトリへ" class="md-source" data-md-component="source">
+  <div class="md-source__icon md-icon">
+    
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 496 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"/></svg>
+  </div>
+  <div class="md-source__repository">
+    krahets/hello-algo
+  </div>
+</a>
+      </div>
+    
+  </nav>
+  
+</header>
+    
+    <div class="md-container" data-md-component="container">
+      
+      
+        
+          
+        
+      
+      <main class="md-main" data-md-component="main">
+        <div class="md-main__inner md-grid">
+          
+            
+              
+              <div class="md-sidebar md-sidebar--primary" data-md-component="sidebar" data-md-type="navigation" >
+                <div class="md-sidebar__scrollwrap">
+                  <div class="md-sidebar__inner">
+                    
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+
+<nav class="md-nav md-nav--primary" aria-label="ナビゲーション" data-md-level="0">
+  <label class="md-nav__title" for="__drawer">
+    <a href=".." title="Hello アルゴリズム" class="md-nav__button md-logo" aria-label="Hello アルゴリズム" data-md-component="logo">
+      
+  <img src="../assets/images/logo.svg" alt="logo">
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+    Hello アルゴリズム
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+      <a href="https://github.com/krahets/hello-algo" title="リポジトリへ" class="md-source" data-md-component="source">
+  <div class="md-source__icon md-icon">
+    
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 496 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"/></svg>
+  </div>
+  <div class="md-source__repository">
+    krahets/hello-algo
+  </div>
+</a>
+    </div>
+  
+  <ul class="md-nav__list" data-md-scrollfix>
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_1" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_hello_algo/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m13.13 22.19-1.63-3.83c1.57-.58 3.04-1.36 4.4-2.27l-2.77 6.1M5.64 12.5l-3.83-1.63 6.1-2.77C7 9.46 6.22 10.93 5.64 12.5M19.22 4c.28 0 .53 0 .74.05.17 1.39-.02 4.25-3.3 7.53-1.7 1.71-3.73 3.02-6.01 3.89l-2.15-2.1c.92-2.31 2.23-4.34 3.92-6.03C15.18 4.58 17.64 4 19.22 4m0-2c-1.98 0-4.98.69-8.22 3.93-2.19 2.19-3.5 4.6-4.35 6.71-.28.75-.09 1.57.46 2.13l2.13 2.12c.38.38.89.61 1.42.61.23 0 .47-.06.7-.15A19.1 19.1 0 0 0 18.07 13c5.66-5.66 3.54-10.61 3.54-10.61S20.7 2 19.22 2m-4.68 7.46c-.78-.78-.78-2.05 0-2.83s2.05-.78 2.83 0c.77.78.78 2.05 0 2.83-.78.78-2.05.78-2.83 0m-5.66 7.07-1.41-1.41 1.41 1.41M6.24 22l3.64-3.64c-.34-.09-.67-.24-.97-.45L4.83 22h1.41M2 22h1.41l4.77-4.76-1.42-1.41L2 20.59V22m0-2.83 4.09-4.08c-.21-.3-.36-.62-.45-.97L2 17.76v1.41Z"/></svg>
+  
+  <span class="md-ellipsis">
+    はじめに
+  </span>
+  
+
+            </a>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_1_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_1">
+            <span class="md-nav__icon md-icon"></span>
+            はじめに
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_2" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="./" class="md-nav__link md-nav__link--active">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M21 4H3a2 2 0 0 0-2 2v13a2 2 0 0 0 2 2h18a2 2 0 0 0 2-2V6a2 2 0 0 0-2-2M3 19V6h8v13H3m18 0h-8V6h8v13m-7-9.5h6V11h-6V9.5m0 2.5h6v1.5h-6V12m0 2.5h6V16h-6v-1.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 0 章 &nbsp; 前書き
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link md-nav__link--active" for="__nav_2" id="__nav_2_label" tabindex="0">
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+              </label>
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_2_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_2">
+            <span class="md-nav__icon md-icon"></span>
+            第 0 章 &nbsp; 前書き
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="about_the_book/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.1 &nbsp; この本について
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="suggestions/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.2 &nbsp; 本書の使い方
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_introduction/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
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+      
+    </li>
+  
+
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+      
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+  
+  
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+  
+  
+  
+    
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+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_2" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M21 4H3a2 2 0 0 0-2 2v13a2 2 0 0 0 2 2h18a2 2 0 0 0 2-2V6a2 2 0 0 0-2-2M3 19V6h8v13H3m18 0h-8V6h8v13m-7-9.5h6V11h-6V9.5m0 2.5h6v1.5h-6V12m0 2.5h6V16h-6v-1.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 0 章 &nbsp; 前書き
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_2" id="__nav_2_label" tabindex="0">
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+          <label class="md-nav__title" for="__nav_2">
+            <span class="md-nav__icon md-icon"></span>
+            第 0 章 &nbsp; 前書き
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../about_the_book/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.1 &nbsp; この本について
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
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+    <li class="md-nav__item md-nav__item--active">
+      
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+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    0.2 &nbsp; 本書の使い方
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    0.2 &nbsp; 本書の使い方
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#021" class="md-nav__link">
+    <span class="md-ellipsis">
+      0.2.1 &nbsp; 記述規則
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#022" class="md-nav__link">
+    <span class="md-ellipsis">
+      0.2.2 &nbsp; アニメーション図解による効率的学習
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#023" class="md-nav__link">
+    <span class="md-ellipsis">
+      0.2.3 &nbsp; コーディング実践による理解の深化
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#024" class="md-nav__link">
+    <span class="md-ellipsis">
+      0.2.4 &nbsp; 議論による共同学習
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#025" class="md-nav__link">
+    <span class="md-ellipsis">
+      0.2.5 &nbsp; アルゴリズム学習パス
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
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+      
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+  
+  
+  
+  
+    
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+      
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+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_introduction/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
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+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
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+          <label class="md-nav__title" for="__nav_17">
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+            第 15 章 &nbsp; 貪欲法
+          </label>
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+            
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+  
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+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
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+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
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+  
+    
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+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
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+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
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+            
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+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
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+          </ul>
+        </nav>
+      
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+    
+    
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+      
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+            <a href="../../chapter_reference/" class="md-nav__link ">
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9 3v15h3V3H9m3 2 4 13 3-1-4-13-3 1M5 5v13h3V5H5M3 19v2h18v-2H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    参考文献
+  </span>
+  
+
+            </a>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_19_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_19">
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+            参考文献
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+            
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+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+  </ul>
+</nav>
+                  </div>
+                </div>
+              </div>
+            
+            
+              
+              <div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
+                <div class="md-sidebar__scrollwrap">
+                  <div class="md-sidebar__inner">
+                    
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#021" class="md-nav__link">
+    <span class="md-ellipsis">
+      0.2.1 &nbsp; 記述規則
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#022" class="md-nav__link">
+    <span class="md-ellipsis">
+      0.2.2 &nbsp; アニメーション図解による効率的学習
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#023" class="md-nav__link">
+    <span class="md-ellipsis">
+      0.2.3 &nbsp; コーディング実践による理解の深化
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#024" class="md-nav__link">
+    <span class="md-ellipsis">
+      0.2.4 &nbsp; 議論による共同学習
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#025" class="md-nav__link">
+    <span class="md-ellipsis">
+      0.2.5 &nbsp; アルゴリズム学習パス
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+                  </div>
+                </div>
+              </div>
+            
+          
+          
+            <div class="md-content" data-md-component="content">
+              <article class="md-content__inner md-typeset">
+                
+                  <!-- Tags -->
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+  
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+      href="https://github.com/krahets/hello-algo/tree/main/ja/docs/chapter_preface/suggestions.md"
+      title="編集"
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+    >
+      
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
+    </a>
+  
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+  
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+<!-- Page content -->
+<h1 id="02">0.2 &nbsp; 読み方<a class="headerlink" href="#02" title="Permanent link">&para;</a></h1>
+<div class="admonition tip">
+<p class="admonition-title">Tip</p>
+<p>最良の読書体験のために、このセクションを通読することをお勧めします。</p>
+</div>
+<h2 id="021">0.2.1 &nbsp; 記述規則<a class="headerlink" href="#021" title="Permanent link">&para;</a></h2>
+<ul>
+<li>タイトルの後に「*」が付いた章は任意であり、比較的難易度の高い内容が含まれています。時間に制約がある場合は、これらをスキップすることをお勧めします。</li>
+<li>技術用語は太字（印刷版およびPDF版）または下線（Web版）で表示されます。例えば、<u>配列</u>などです。技術文書をより良く理解するために、これらに慣れることをお勧めします。</li>
+<li>**太字のテキスト**は重要な内容や要約文を示し、特別な注意を払う価値があります。</li>
+<li>特定の意味を持つ単語や句は「引用符」で示され、曖昧さを避けます。</li>
+<li>プログラミング言語間で一致しない用語については、この本はPythonに従います。例えば、<code>null</code>を意味するために<code>None</code>を使用します。</li>
+<li>この本は、よりコンパクトなコンテンツレイアウトと引き換えに、プログラミング言語のコメント規約を部分的に無視しています。コメントは主に3つのタイプで構成されています：タイトルコメント、内容コメント、複数行コメント。</li>
+</ul>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="sd">&quot;&quot;&quot;関数、クラス、テストサンプルなどをラベル付けするためのヘッダーコメント&quot;&quot;&quot;</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="c1"># 詳細を説明するためのコメント</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a><span class="sd">&quot;&quot;&quot;</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a><span class="sd">複数行</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="sd">コメント</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="sd">&quot;&quot;&quot;</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 関数、クラス、テストサンプルなどをラベル付けするためのヘッダーコメント */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="c1">// 詳細を説明するためのコメント</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="cm">/**</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="cm"> * 複数行</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="cm"> * コメント</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="cm"> */</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 関数、クラス、テストサンプルなどをラベル付けするためのヘッダーコメント */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="c1">// 詳細を説明するためのコメント</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="cm">/**</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="cm"> * 複数行</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="cm"> * コメント</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="cm"> */</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 関数、クラス、テストサンプルなどをラベル付けするためのヘッダーコメント */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="c1">// 詳細を説明するためのコメント</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="cm">/**</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="cm"> * 複数行</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="cm"> * コメント</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="cm"> */</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 関数、クラス、テストサンプルなどをラベル付けするためのヘッダーコメント */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="c1">// 詳細を説明するためのコメント</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="cm">/**</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="cm"> * 複数行</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="cm"> * コメント</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="cm"> */</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 関数、クラス、テストサンプルなどをラベル付けするためのヘッダーコメント */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="c1">// 詳細を説明するためのコメント</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="cm">/**</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="cm"> * 複数行</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="cm"> * コメント</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="cm"> */</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 関数、クラス、テストサンプルなどをラベル付けするためのヘッダーコメント */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="c1">// 詳細を説明するためのコメント</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="cm">/**</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="cm"> * 複数行</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="cm"> * コメント</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="cm"> */</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 関数、クラス、テストサンプルなどをラベル付けするためのヘッダーコメント */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="c1">// 詳細を説明するためのコメント</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="cm">/**</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="cm"> * 複数行</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="cm"> * コメント</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="cm"> */</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 関数、クラス、テストサンプルなどをラベル付けするためのヘッダーコメント */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="c1">// 詳細を説明するためのコメント</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="cm">/**</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="cm"> * 複数行</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="cm"> * コメント</span>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="cm"> */</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 関数、クラス、テストサンプルなどをラベル付けするためのヘッダーコメント */</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="c1">// 詳細を説明するためのコメント</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="sd">/**</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="sd"> * 複数行</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="sd"> * コメント</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="sd"> */</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 関数、クラス、テストサンプルなどをラベル付けするためのヘッダーコメント */</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="c1">// 詳細を説明するためのコメント</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="cm">/**</span>
+<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="cm"> * 複数行</span>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="cm"> * コメント</span>
+<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a><span class="cm"> */</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 関数、クラス、テストサンプルなどをラベル付けするためのヘッダーコメント */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="c1">// 詳細を説明するためのコメント</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="cm">/**</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="cm"> * 複数行</span>
+<a id="__codelineno-11-7" name="__codelineno-11-7" href="#__codelineno-11-7"></a><span class="cm"> * コメント</span>
+<a id="__codelineno-11-8" name="__codelineno-11-8" href="#__codelineno-11-8"></a><span class="cm"> */</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="c1">// 関数、クラス、テストサンプルなどをラベル付けするためのヘッダーコメント</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="c1">// 詳細を説明するためのコメント</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="c1">// 複数行</span>
+<a id="__codelineno-12-6" name="__codelineno-12-6" href="#__codelineno-12-6"></a><span class="c1">// コメント</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h2 id="022">0.2.2 &nbsp; アニメーション図解による効率的学習<a class="headerlink" href="#022" title="Permanent link">&para;</a></h2>
+<p>テキストと比較して、動画や画像は情報密度が高く、より構造化されており、理解しやすくなっています。この本では、<strong>重要で難しい概念は主にアニメーションと図解を通じて提示され</strong>、テキストは説明と補足として機能します。</p>
+<p>下図に示すようなアニメーションや図解のある内容に遭遇した場合、<strong>図の理解を優先し、テキストを補足として</strong>、両方を統合して包括的な理解を得てください。</p>
+<p><a class="glightbox" href="../../index.assets/animation.gif" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="アニメーション図解の例" class="animation-figure" src="../../index.assets/animation.gif" /></a></p>
+<p align="center"> 図 0-2 &nbsp; アニメーション図解の例 </p>
+
+<h2 id="023">0.2.3 &nbsp; コーディング実践による理解の深化<a class="headerlink" href="#023" title="Permanent link">&para;</a></h2>
+<p>この本のソースコードは<a href="https://github.com/krahets/hello-algo">GitHubリポジトリ</a>でホストされています。下図に示すように、<strong>ソースコードにはテスト例が付属しており、ワンクリックで実行できます</strong>。</p>
+<p>時間に余裕がある場合は、<strong>自分でコードをタイプすることをお勧めします</strong>。時間がない場合は、少なくともすべてのコードを読んで実行してください。</p>
+<p>コードを読むだけと比較して、コードを書くことは多くの場合、より多くの学習をもたらします。<strong>実践による学習こそが真の学習方法です。</strong></p>
+<p><a class="glightbox" href="../../index.assets/running_code.gif" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="コード実行例" class="animation-figure" src="../../index.assets/running_code.gif" /></a></p>
+<p align="center"> 図 0-3 &nbsp; コード実行例 </p>
+
+<p>コードを実行するための設定には、主に3つのステップが含まれます。</p>
+<p><strong>ステップ1：ローカルプログラミング環境をインストール</strong>。付録の<a href="https://www.hello-algo.com/chapter_appendix/installation/">チュートリアル</a>に従ってインストールするか、すでにインストールされている場合はこのステップをスキップしてください。</p>
+<p><strong>ステップ2：コードリポジトリをクローンまたはダウンロード</strong>。<a href="https://github.com/krahets/hello-algo">GitHubリポジトリ</a>を訪問してください。</p>
+<p><a href="https://git-scm.com/downloads">Git</a>がインストールされている場合は、次のコマンドを使用してリポジトリをクローンします：</p>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a>git<span class="w"> </span>clone<span class="w"> </span>https://github.com/krahets/hello-algo.git
+</code></pre></div>
+<p>または、下図に示す場所にある「Download ZIP」ボタンをクリックして、コードを圧縮ZIPファイルとして直接ダウンロードすることもできます。その後、ローカルで展開するだけです。</p>
+<p><a class="glightbox" href="../suggestions.assets/download_code.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="リポジトリのクローンとコードのダウンロード" class="animation-figure" src="../suggestions.assets/download_code.png" /></a></p>
+<p align="center"> 図 0-4 &nbsp; リポジトリのクローンとコードのダウンロード </p>
+
+<p><strong>ステップ3：ソースコードを実行</strong>。下図に示すように、上部にファイル名が記載されたコードブロックについては、リポジトリの<code>codes</code>フォルダで対応するソースコードファイルを見つけることができます。これらのファイルはワンクリックで実行でき、不要なデバッグ時間を節約し、学習に集中できます。</p>
+<p><a class="glightbox" href="../suggestions.assets/code_md_to_repo.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="コードブロックと対応するソースコードファイル" class="animation-figure" src="../suggestions.assets/code_md_to_repo.png" /></a></p>
+<p align="center"> 図 0-5 &nbsp; コードブロックと対応するソースコードファイル </p>
+
+<h2 id="024">0.2.4 &nbsp; 議論による共同学習<a class="headerlink" href="#024" title="Permanent link">&para;</a></h2>
+<p>この本を読んでいる間、学べなかった点を飛ばさないでください。<strong>コメントセクションで気軽に質問してください</strong>。喜んでお答えし、通常2日以内に回答できます。</p>
+<p>下図に示すように、各章の下部にコメントセクションがあります。これらのコメントに注意を払うことをお勧めします。他の人が遭遇した問題を知ることで、知識のギャップを特定し、より深い思索を促すだけでなく、仲間の読者の質問に答えたり、洞察を共有したり、相互の向上を促進したりすることで寛大に貢献することも招待します。</p>
+<p><a class="glightbox" href="../../index.assets/comment.gif" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="コメントセクションの例" class="animation-figure" src="../../index.assets/comment.gif" /></a></p>
+<p align="center"> 図 0-6 &nbsp; コメントセクションの例 </p>
+
+<h2 id="025">0.2.5 &nbsp; アルゴリズム学習パス<a class="headerlink" href="#025" title="Permanent link">&para;</a></h2>
+<p>全体的に、データ構造とアルゴリズムをマスターする旅は3つの段階に分けることができます：</p>
+<ol>
+<li><strong>段階1：アルゴリズムの入門</strong>。さまざまなデータ構造の特性と使用法に慣れ、異なるアルゴリズムの原理、プロセス、用途、効率について学ぶ必要があります。</li>
+<li><strong>段階2：アルゴリズム問題の練習</strong>。<a href="https://leetcode.cn/studyplan/coding-interviews/">Sword for Offer</a>や<a href="https://leetcode.cn/studyplan/top-100-liked/">LeetCode Hot 100</a>などの人気のある問題から始めることをお勧めし、少なくとも100問を蓄積して主流のアルゴリズム問題に慣れることです。練習を始めると忘却が課題になる可能性がありますが、これは正常なことですのでご安心ください。「エビングハウスの忘却曲線」に従って問題を復習することができ、通常3〜5回の反復の後、それらを覚えることができるでしょう。</li>
+<li><strong>段階3：知識体系の構築</strong>。学習の面では、アルゴリズムコラム記事、解法フレームワーク、アルゴリズム教科書を読んで知識体系を継続的に豊かにすることができます。練習の面では、トピック別分類、一つの問題に対する複数の解法、複数の問題に対する一つの解法など、高度な戦略を試すことができます。これらの戦略に関する洞察は、さまざまなコミュニティで見つけることができます。</li>
+</ol>
+<p>下図に示すように、この本は主に「段階1」をカバーしており、段階2と3により効率的に取り組むのに役立つことを目的としています。</p>
+<p><a class="glightbox" href="../suggestions.assets/learning_route.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="アルゴリズム学習パス" class="animation-figure" src="../suggestions.assets/learning_route.png" /></a></p>
+<p align="center"> 図 0-7 &nbsp; アルゴリズム学習パス </p>
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+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    0.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+      
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_introduction/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
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+  
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+  
+  <span class="md-ellipsis">
+    第 0 章 &nbsp; 前書き
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+            第 0 章 &nbsp; 前書き
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+            
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+  
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+    <li class="md-nav__item">
+      <a href="../chapter_preface/about_the_book/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    0.1 &nbsp; この本について
+  </span>
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+      <a href="../chapter_preface/suggestions/" class="md-nav__link">
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+    0.2 &nbsp; 本書の使い方
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+  
+
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+
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+      <a href="../chapter_preface/summary/" class="md-nav__link">
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+  <span class="md-ellipsis">
+    0.3 &nbsp; まとめ
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+            <a href="../chapter_introduction/" class="md-nav__link ">
+              
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+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
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+  
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+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
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+      <a href="../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
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+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
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+  
+
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+            
+              
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+  
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+  
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+      <a href="../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
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+      
+      
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+  
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+      
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+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
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+      
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+        
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+          
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+            <a href="../chapter_computational_complexity/" class="md-nav__link ">
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+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
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+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
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+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
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+            
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+            
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+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
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+    </li>
+  
+
+              
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+        </nav>
+      
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+          
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+        
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+        
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+    
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+      
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+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
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+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
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+        </nav>
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+          
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+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
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+    </li>
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+
+              
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+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
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+  
+
+              
+            
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+  
+  
+  
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+      <a href="../chapter_backtracking/n_queens_problem/" class="md-nav__link">
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+
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+  
+
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+              
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+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
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+
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+  
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+      <a href="../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
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+  
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+  
+
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+      <a href="../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
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+  
+
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+
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+      <a href="../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
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+  
+
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+
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+      <a href="../chapter_dynamic_programming/summary/" class="md-nav__link">
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+  <span class="md-ellipsis">
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+
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+      <a href="../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
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+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
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+
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+      <a href="../chapter_greedy/summary/" class="md-nav__link">
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+<h1 id="_1">参考文献<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h1>
+<p>[1] Thomas H. Cormen, et al. Introduction to Algorithms (3<sup>rd</sup> Edition).</p>
+<p>[2] Aditya Bhargava. Grokking Algorithms: An Illustrated Guide for Programmers and Other Curious People (1<sup>st</sup> Edition).</p>
+<p>[3] Robert Sedgewick, et al. Algorithms (4<sup>th</sup> Edition).</p>
+<p>[4] Yan Weimin. Data Structures (C Language Version).</p>
+<p>[5] Deng Junhui. Data Structures (C++ Language Version, Third Edition).</p>
+<p>[6] Mark Allen Weiss, translated by Chen Yue. Data Structures and Algorithm Analysis in Java (Third Edition).</p>
+<p>[7] Cheng Jie. Speaking of Data Structures.</p>
+<p>[8] Wang Zheng. The Beauty of Data Structures and Algorithms.</p>
+<p>[9] Gayle Laakmann McDowell. Cracking the Coding Interview: 189 Programming Questions and Solutions (6<sup>th</sup> Edition).</p>
+<p>[10] Aston Zhang, et al. Dive into Deep Learning.</p>
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+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1011" class="md-nav__link">
+    <span class="md-ellipsis">
+      10.1.1 &nbsp; 区間表現方法
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1012" class="md-nav__link">
+    <span class="md-ellipsis">
+      10.1.2 &nbsp; 利点と制限
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
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+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
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+  <a href="#1011" class="md-nav__link">
+    <span class="md-ellipsis">
+      10.1.1 &nbsp; 区間表現方法
+    </span>
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+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1012" class="md-nav__link">
+    <span class="md-ellipsis">
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+      title="編集"
+      class="md-content__button md-icon"
+    >
+      
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
+    </a>
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+
+<!-- Page content -->
+<h1 id="101">10.1 &nbsp; 二分探索<a class="headerlink" href="#101" title="Permanent link">&para;</a></h1>
+<p><u>二分探索</u>は分割統治戦略を用いる効率的な探索アルゴリズムです。配列内の要素の整列順序を利用し、各反復で探索区間を半分に減らしながら、目標要素が見つかるか探索区間が空になるまで続行します。</p>
+<div class="admonition question">
+<p class="admonition-title">Question</p>
+<p>長さ<span class="arithmatex">\(n\)</span>の配列<code>nums</code>が与えられ、要素は重複なしで昇順に配列されています。この配列内の要素<code>target</code>のインデックスを見つけて返してください。配列に要素が含まれていない場合は<span class="arithmatex">\(-1\)</span>を返してください。例を下図に示します。</p>
+</div>
+<p><a class="glightbox" href="../binary_search.assets/binary_search_example.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Binary search example data" class="animation-figure" src="../binary_search.assets/binary_search_example.png" /></a></p>
+<p align="center"> 図 10-1 &nbsp; Binary search example data </p>
+
+<p>下図に示すように、まず<span class="arithmatex">\(i = 0\)</span>と<span class="arithmatex">\(j = n - 1\)</span>でポインタを初期化し、それぞれ配列の最初と最後の要素を指します。これらはまた全体の探索区間<span class="arithmatex">\([0, n - 1]\)</span>を表します。角括弧は閉区間を示し、境界値自身も含むことに注意してください。</p>
+<p>そして、以下の2つのステップをループで実行する可能性があります。</p>
+<ol>
+<li>中点インデックス<span class="arithmatex">\(m = \lfloor {(i + j) / 2} \rfloor\)</span>を計算します。ここで<span class="arithmatex">\(\lfloor \: \rfloor\)</span>は床関数を表します。</li>
+<li><code>nums[m]</code>と<code>target</code>の比較に基づいて、以下の3つのケースのうち1つを選択して実行します。<ol>
+<li><code>nums[m] &lt; target</code>の場合、<code>target</code>は区間<span class="arithmatex">\([m + 1, j]\)</span>にあることを示すため、<span class="arithmatex">\(i = m + 1\)</span>とします。</li>
+<li><code>nums[m] &gt; target</code>の場合、<code>target</code>は区間<span class="arithmatex">\([i, m - 1]\)</span>にあることを示すため、<span class="arithmatex">\(j = m - 1\)</span>とします。</li>
+<li><code>nums[m] = target</code>の場合、<code>target</code>が見つかったことを示すため、インデックス<span class="arithmatex">\(m\)</span>を返します。</li>
+</ol>
+</li>
+</ol>
+<p>配列に目標要素が含まれていない場合、探索区間は最終的に空になり、<span class="arithmatex">\(-1\)</span>を返して終了します。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:7"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">&lt;1&gt;</label><label for="__tabbed_1_2">&lt;2&gt;</label><label for="__tabbed_1_3">&lt;3&gt;</label><label for="__tabbed_1_4">&lt;4&gt;</label><label for="__tabbed_1_5">&lt;5&gt;</label><label for="__tabbed_1_6">&lt;6&gt;</label><label for="__tabbed_1_7">&lt;7&gt;</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<p><a class="glightbox" href="../binary_search.assets/binary_search_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Binary search process" class="animation-figure" src="../binary_search.assets/binary_search_step1.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../binary_search.assets/binary_search_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="binary_search_step2" class="animation-figure" src="../binary_search.assets/binary_search_step2.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../binary_search.assets/binary_search_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="binary_search_step3" class="animation-figure" src="../binary_search.assets/binary_search_step3.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../binary_search.assets/binary_search_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="binary_search_step4" class="animation-figure" src="../binary_search.assets/binary_search_step4.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../binary_search.assets/binary_search_step5.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="binary_search_step5" class="animation-figure" src="../binary_search.assets/binary_search_step5.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../binary_search.assets/binary_search_step6.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="binary_search_step6" class="animation-figure" src="../binary_search.assets/binary_search_step6.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../binary_search.assets/binary_search_step7.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="binary_search_step7" class="animation-figure" src="../binary_search.assets/binary_search_step7.png" /></a></p>
+</div>
+</div>
+</div>
+<p align="center"> 図 10-2 &nbsp; Binary search process </p>
+
+<p><span class="arithmatex">\(i\)</span>と<span class="arithmatex">\(j\)</span>が両方とも<code>int</code>型であるため、**<span class="arithmatex">\(i + j\)</span>は<code>int</code>型の範囲を超える可能性がある**ことは注目に値します。大きな数のオーバーフローを避けるため、通常は式<span class="arithmatex">\(m = \lfloor {i + (j - i) / 2} \rfloor\)</span>を使用して中点を計算します。</p>
+<p>コードは以下の通りです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:14"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><input id="__tabbed_2_14" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label><label for="__tabbed_2_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">binary_search</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">target</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;二分探索（両端閉区間）&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># 両端閉区間 [0, n-1] を初期化、すなわち i, j はそれぞれ配列の最初の要素と最後の要素を指す</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="c1"># 検索区間が空になるまでループ（i &gt; j のとき空）</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="k">while</span> <span class="n">i</span> <span class="o">&lt;=</span> <span class="n">j</span><span class="p">:</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>        <span class="c1"># 理論的には、Pythonの数値は無限に大きくなることができる（メモリサイズに依存）ため、大きな数のオーバーフローを考慮する必要はない</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>        <span class="n">m</span> <span class="o">=</span> <span class="n">i</span> <span class="o">+</span> <span class="p">(</span><span class="n">j</span> <span class="o">-</span> <span class="n">i</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span>  <span class="c1"># 中点インデックス m を計算</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>        <span class="k">if</span> <span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span> <span class="o">&lt;</span> <span class="n">target</span><span class="p">:</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>            <span class="n">i</span> <span class="o">=</span> <span class="n">m</span> <span class="o">+</span> <span class="mi">1</span>  <span class="c1"># この場合、target は区間 [m+1, j] にあることを示す</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>        <span class="k">elif</span> <span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">target</span><span class="p">:</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>            <span class="n">j</span> <span class="o">=</span> <span class="n">m</span> <span class="o">-</span> <span class="mi">1</span>  <span class="c1"># この場合、target は区間 [i, m-1] にあることを示す</span>
+<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>        <span class="k">else</span><span class="p">:</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>            <span class="k">return</span> <span class="n">m</span>  <span class="c1"># ターゲット要素が見つかったため、そのインデックスを返す</span>
+<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>    <span class="k">return</span> <span class="o">-</span><span class="mi">1</span>  <span class="c1"># ターゲット要素が見つからなかったため、-1 を返す</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 二分探索（両端閉区間） */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">binarySearch</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// 両端閉区間[0, n-1]を初期化、すなわちi、jはそれぞれ配列の最初の要素と最後の要素を指す</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="c1">// 探索区間が空になるまでループ（i &gt; jの時空になる）</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 中点インデックスmを計算</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w">    </span><span class="c1">// この状況はtargetが区間[m+1, j]にあることを示す</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="c1">// この状況はtargetが区間[i, m-1]にあることを示す</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="c1">// ターゲット要素が見つかったため、そのインデックスを返す</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">m</span><span class="p">;</span>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">    </span><span class="c1">// ターゲット要素が見つからなかったため、-1を返す</span>
+<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
+<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 二分探索（両端閉区間） */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">binarySearch</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// 両端閉区間 [0, n-1] を初期化、すなわち i, j はそれぞれ配列の最初の要素と最後の要素を指す</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="c1">// 探索区間が空になるまでループ（i &gt; j のとき空）</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 中点インデックス m を計算</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="c1">// この状況は target が区間 [m+1, j] にあることを示す</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="c1">// この状況は target が区間 [i, m-1] にあることを示す</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="c1">// 目標要素を見つけたので、そのインデックスを返す</span>
+<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">m</span><span class="p">;</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">    </span><span class="c1">// 目標要素を見つけられなかったので、-1 を返す</span>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">binary_search</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">BinarySearch</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">binarySearch</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">binarySearch</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">binarySearch</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">binarySearch</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binarySearch</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binary_search</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binarySearch</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">binarySearch</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">binary_search</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search.zig</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binarySearch</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p><strong>時間計算量は<span class="arithmatex">\(O(\log n)\)</span>です</strong>：二分ループにおいて、区間は各ラウンドで半分に減少するため、反復回数は<span class="arithmatex">\(\log_2 n\)</span>となります。</p>
+<p><strong>空間計算量は<span class="arithmatex">\(O(1)\)</span>です</strong>：ポインタ<span class="arithmatex">\(i\)</span>と<span class="arithmatex">\(j\)</span>は定数サイズの空間を占有します。</p>
+<h2 id="1011">10.1.1 &nbsp; 区間表現方法<a class="headerlink" href="#1011" title="Permanent link">&para;</a></h2>
+<p>上記の閉区間の他に、もう一つの一般的な区間表現は「左閉右開」区間で、<span class="arithmatex">\([0, n)\)</span>として定義され、左境界は自身を含み、右境界は含みません。この表現では、<span class="arithmatex">\(i = j\)</span>のとき区間<span class="arithmatex">\([i, j)\)</span>は空になります。</p>
+<p>この表現に基づいて同じ機能を持つ二分探索アルゴリズムを実装できます：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="3:14"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><input id="__tabbed_3_14" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label><label for="__tabbed_3_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search.py</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">binary_search_lcro</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">target</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;二分探索（左閉右開区間）&quot;&quot;&quot;</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a>    <span class="c1"># 左閉右開区間 [0, n) を初期化、すなわち i, j はそれぞれ配列の最初の要素と最後の要素+1を指す</span>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a>    <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a>    <span class="c1"># 検索区間が空になるまでループ（i = j のとき空）</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a>    <span class="k">while</span> <span class="n">i</span> <span class="o">&lt;</span> <span class="n">j</span><span class="p">:</span>
+<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a>        <span class="n">m</span> <span class="o">=</span> <span class="n">i</span> <span class="o">+</span> <span class="p">(</span><span class="n">j</span> <span class="o">-</span> <span class="n">i</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span>  <span class="c1"># 中点インデックス m を計算</span>
+<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a>        <span class="k">if</span> <span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span> <span class="o">&lt;</span> <span class="n">target</span><span class="p">:</span>
+<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a>            <span class="n">i</span> <span class="o">=</span> <span class="n">m</span> <span class="o">+</span> <span class="mi">1</span>  <span class="c1"># この場合、target は区間 [m+1, j) にあることを示す</span>
+<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a>        <span class="k">elif</span> <span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">target</span><span class="p">:</span>
+<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a>            <span class="n">j</span> <span class="o">=</span> <span class="n">m</span>  <span class="c1"># この場合、target は区間 [i, m) にあることを示す</span>
+<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a>        <span class="k">else</span><span class="p">:</span>
+<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a>            <span class="k">return</span> <span class="n">m</span>  <span class="c1"># ターゲット要素が見つかったため、そのインデックスを返す</span>
+<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a>    <span class="k">return</span> <span class="o">-</span><span class="mi">1</span>  <span class="c1"># ターゲット要素が見つからなかったため、-1 を返す</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search.cpp</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 二分探索（左閉右開区間） */</span>
+<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">binarySearchLCRO</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="c1">// 左閉右開区間[0, n)を初期化、すなわちi、jはそれぞれ配列の最初の要素と最後の要素+1を指す</span>
+<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
+<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">    </span><span class="c1">// 探索区間が空になるまでループ（i = jの時空になる）</span>
+<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 中点インデックスmを計算</span>
+<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w">    </span><span class="c1">// この状況はtargetが区間[m+1, j)にあることを示す</span>
+<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="c1">// この状況はtargetが区間[i, m)にあることを示す</span>
+<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span>
+<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="c1">// ターゲット要素が見つかったため、そのインデックスを返す</span>
+<a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">m</span><span class="p">;</span>
+<a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="w">    </span><span class="c1">// ターゲット要素が見つからなかったため、-1を返す</span>
+<a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
+<a id="__codelineno-15-17" name="__codelineno-15-17" href="#__codelineno-15-17"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search.java</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 二分探索（左閉右開区間） */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">binarySearchLCRO</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="c1">// 左閉右開区間 [0, n) を初期化、すなわち i, j はそれぞれ配列の最初の要素と最後の要素+1を指す</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="p">;</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">    </span><span class="c1">// 探索区間が空になるまでループ（i = j のとき空）</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 中点インデックス m を計算</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="c1">// この状況は target が区間 [m+1, j) にあることを示す</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="c1">// この状況は target が区間 [i, m) にあることを示す</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="c1">// 目標要素を見つけたので、そのインデックスを返す</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">m</span><span class="p">;</span>
+<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="w">    </span><span class="c1">// 目標要素を見つけられなかったので、-1 を返す</span>
+<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-16-17" name="__codelineno-16-17" href="#__codelineno-16-17"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search.cs</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">binary_search</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">BinarySearchLCRO</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search.go</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">binarySearchLCRO</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">binarySearchLCRO</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search.js</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">binarySearchLCRO</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search.ts</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">binarySearchLCRO</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search.dart</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binarySearchLCRO</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search.rs</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binary_search_lcro</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search.c</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binarySearchLCRO</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search.kt</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">binarySearchLCRO</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">binary_search_lcro</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search.zig</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binarySearchLCRO</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>下図に示すように、2つの区間表現タイプにおいて、二分探索アルゴリズムの初期化、ループ条件、区間縮小操作が異なります。</p>
+<p>「閉区間」表現では両方の境界が包含的であるため、ポインタ<span class="arithmatex">\(i\)</span>と<span class="arithmatex">\(j\)</span>による区間縮小操作も対称的です。これによりエラーが発生しにくくなるため、<strong>一般的に「閉区間」アプローチの使用が推奨されます</strong>。</p>
+<p><a class="glightbox" href="../binary_search.assets/binary_search_ranges.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Two types of interval definitions" class="animation-figure" src="../binary_search.assets/binary_search_ranges.png" /></a></p>
+<p align="center"> 図 10-3 &nbsp; Two types of interval definitions </p>
+
+<h2 id="1012">10.1.2 &nbsp; 利点と制限<a class="headerlink" href="#1012" title="Permanent link">&para;</a></h2>
+<p>二分探索は時間と空間の両方の面で良好な性能を示します。</p>
+<ul>
+<li>二分探索は時間効率が良いです。大きなデータセットでは、対数時間計算量が大きな利点を提供します。例えば、サイズ<span class="arithmatex">\(n = 2^{20}\)</span>のデータセットが与えられた場合、線形探索は<span class="arithmatex">\(2^{20} = 1048576\)</span>回の反復が必要ですが、二分探索は<span class="arithmatex">\(\log_2 2^{20} = 20\)</span>回のループのみで済みます。</li>
+<li>二分探索には追加の空間が必要ありません。追加の空間に依存する探索アルゴリズム（ハッシュ探索など）と比較して、二分探索はより空間効率的です。</li>
+</ul>
+<p>しかし、二分探索は以下の懸念により、すべてのシナリオに適しているとは限りません。</p>
+<ul>
+<li>二分探索はソート済みデータにのみ適用できます。未ソートのデータは二分探索を適用する前にソートする必要があり、ソートアルゴリズムは通常<span class="arithmatex">\(O(n \log n)\)</span>の時間計算量を持つため、これは価値がないかもしれません。このコストは線形探索よりも高く、二分探索自体は言うまでもありません。頻繁な挿入があるシナリオでは、配列を順序に保つコストは非常に高く、特定の位置に新しい要素を挿入する時間計算量は<span class="arithmatex">\(O(n)\)</span>です。</li>
+<li>二分探索は配列のみを使用できます。二分探索には非連続（ジャンプ）要素アクセスが必要で、これは連結リストでは非効率的です。そのため、連結リストや連結リストに基づくデータ構造はこのアルゴリズムに適していない可能性があります。</li>
+<li>線形探索は小さなデータセットでより良い性能を示します。線形探索では各反復で1つの判定操作のみが必要ですが、二分探索では1つの加算、1つの除算、1つから3つの判定操作、1つの加算（減算）を含み、合計4つから6つの操作が必要です。そのため、データサイズ<span class="arithmatex">\(n\)</span>が小さい場合、線形探索は二分探索よりも高速です。</li>
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+  
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+  
+  <span class="md-ellipsis">
+    第 0 章 &nbsp; 前書き
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+      <a href="../../chapter_preface/about_the_book/" class="md-nav__link">
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+      <a href="../../chapter_preface/suggestions/" class="md-nav__link">
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+
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+      <a href="../../chapter_preface/summary/" class="md-nav__link">
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+    0.3 &nbsp; まとめ
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+            <a href="../../chapter_introduction/" class="md-nav__link ">
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+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
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+  
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+            第 1 章 &nbsp; アルゴリズムとの出会い
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+      <a href="../../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
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+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
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+  
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+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
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+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
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+    </li>
+  
+
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+            
+              
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+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
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+    </li>
+  
+
+              
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+          
+        
+      
+        
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+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
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+  
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+            第 2 章 &nbsp; 計算量解析
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+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
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+    2.1 &nbsp; アルゴリズム効率評価
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+  
+
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+
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+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
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+    2.2 &nbsp; 反復と再帰
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+  
+
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+    </li>
+  
+
+              
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+  
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+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
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+  
+  
+  
+  
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+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
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+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
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+            第 3 章 &nbsp; データ構造
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+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
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+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
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+
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+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
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+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
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+    </li>
+  
+
+              
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+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
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+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
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+  
+  
+  
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+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
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+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
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+    </li>
+  
+
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+              
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+  
+  
+  
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+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
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+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
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+  
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+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1031" class="md-nav__link">
+    <span class="md-ellipsis">
+      10.3.1 &nbsp; 左境界を見つける
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1032" class="md-nav__link">
+    <span class="md-ellipsis">
+      10.3.2 &nbsp; 右境界を見つける
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="10.3.2   右境界を見つける">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 左境界探索を再利用する
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; 要素探索に変換する
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
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+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
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+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
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+          </ul>
+        </nav>
+      
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+  
+
+    
+      
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+          
+        
+      
+    
+    
+    
+    
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+      
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+        
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+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_19" >
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+          
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+            <a href="../../chapter_reference/" class="md-nav__link ">
+              
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9 3v15h3V3H9m3 2 4 13 3-1-4-13-3 1M5 5v13h3V5H5M3 19v2h18v-2H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    参考文献
+  </span>
+  
+
+            </a>
+            
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_19_label" aria-expanded="false">
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+            <span class="md-nav__icon md-icon"></span>
+            参考文献
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+</nav>
+                  </div>
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+            
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+              
+              <div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
+                <div class="md-sidebar__scrollwrap">
+                  <div class="md-sidebar__inner">
+                    
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+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1031" class="md-nav__link">
+    <span class="md-ellipsis">
+      10.3.1 &nbsp; 左境界を見つける
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1032" class="md-nav__link">
+    <span class="md-ellipsis">
+      10.3.2 &nbsp; 右境界を見つける
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="10.3.2   右境界を見つける">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 左境界探索を再利用する
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; 要素探索に変換する
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+                  </div>
+                </div>
+              </div>
+            
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+            <div class="md-content" data-md-component="content">
+              <article class="md-content__inner md-typeset">
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+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
+    </a>
+  
+
+  <!-- View button -->
+  
+
+
+<!-- Page content -->
+<h1 id="103">10.3 &nbsp; 二分探索の境界<a class="headerlink" href="#103" title="Permanent link">&para;</a></h1>
+<h2 id="1031">10.3.1 &nbsp; 左境界を見つける<a class="headerlink" href="#1031" title="Permanent link">&para;</a></h2>
+<div class="admonition question">
+<p class="admonition-title">Question</p>
+<p>重複要素を含む可能性がある長さ<span class="arithmatex">\(n\)</span>のソート済み配列<code>nums</code>が与えられ、最も左の要素<code>target</code>のインデックスを返してください。要素が配列に存在しない場合は、<span class="arithmatex">\(-1\)</span>を返してください。</p>
+</div>
+<p>挿入位置の二分探索方法を思い出すと、探索完了後、インデックス<span class="arithmatex">\(i\)</span>は<code>target</code>の最も左の出現を指します。したがって、<strong>挿入位置の探索は本質的に最も左の<code>target</code>のインデックスを見つけることと同じです</strong>。</p>
+<p>挿入位置を見つける関数を使用して<code>target</code>の左境界を見つけることができます。配列に<code>target</code>が含まれていない可能性があることに注意してください。これは以下の2つの結果につながる可能性があります：</p>
+<ul>
+<li>挿入位置のインデックス<span class="arithmatex">\(i\)</span>が範囲外です。</li>
+<li>要素<code>nums[i]</code>が<code>target</code>と等しくありません。</li>
+</ul>
+<p>これらの場合、単に<span class="arithmatex">\(-1\)</span>を返します。コードは以下の通りです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:14"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><input id="__tabbed_1_14" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label><label for="__tabbed_1_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_edge.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">binary_search_left_edge</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">target</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;最左端のターゲットの二分探索&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># ターゲットの挿入位置を見つけることと同等</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="n">i</span> <span class="o">=</span> <span class="n">binary_search_insertion</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="n">target</span><span class="p">)</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="c1"># ターゲットが見つからなかった場合、-1 を返す</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="k">if</span> <span class="n">i</span> <span class="o">==</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span> <span class="ow">or</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">!=</span> <span class="n">target</span><span class="p">:</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>        <span class="k">return</span> <span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>    <span class="c1"># ターゲットが見つかった場合、インデックス i を返す</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>    <span class="k">return</span> <span class="n">i</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_edge.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 最左のターゲットの二分探索 */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">binarySearchLeftEdge</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// targetの挿入ポイントを見つけることと等価</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">binarySearchInsertion</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">);</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="c1">// targetが見つからなかったため、-1を返す</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">    </span><span class="c1">// targetが見つかったため、インデックスiを返す</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_edge.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 最も左の target を二分探索 */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">binarySearchLeftEdge</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// target の挿入点を見つけることと等価</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">binary_search_insertion</span><span class="p">.</span><span class="na">binarySearchInsertion</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="p">);</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="c1">// target を見つけられなかったので、-1 を返す</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">    </span><span class="c1">// target を見つけたので、インデックス i を返す</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_edge.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">binary_search_edge</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">BinarySearchLeftEdge</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_edge.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">binarySearchLeftEdge</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_edge.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">binarySearchLeftEdge</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_edge.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">binarySearchLeftEdge</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_edge.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">binarySearchLeftEdge</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_edge.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binarySearchLeftEdge</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_edge.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binary_search_left_edge</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_edge.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binarySearchLeftEdge</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_edge.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">binarySearchLeftEdge</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_edge.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">binary_search_left_edge</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_edge.zig</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binarySearchLeftEdge</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h2 id="1032">10.3.2 &nbsp; 右境界を見つける<a class="headerlink" href="#1032" title="Permanent link">&para;</a></h2>
+<p><code>target</code>の最も右の出現をどのように見つけるでしょうか？最も直接的な方法は、<code>nums[m] == target</code>の場合に探索境界を調整する方法を変更して、従来の二分探索ロジックを修正することです。コードはここでは省略されています。興味がある場合は、自分でコードを実装してみてください。</p>
+<p>以下では、さらに2つの巧妙な方法を紹介します。</p>
+<h3 id="1">1. &nbsp; 左境界探索を再利用する<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<p><code>target</code>の最も右の出現を見つけるには、最も左の<code>target</code>を見つけるために使用された関数を再利用できます。具体的には、最も右のターゲットの探索を最も左のターゲット + 1の探索に変換します。</p>
+<p>下図に示すように、探索完了後、ポインタ<span class="arithmatex">\(i\)</span>は最も左の<code>target + 1</code>（存在する場合）を指し、ポインタ<span class="arithmatex">\(j\)</span>は<code>target</code>の最も右の出現を指します。したがって、<span class="arithmatex">\(j\)</span>を返すことで右境界が得られます。</p>
+<p><a class="glightbox" href="../binary_search_edge.assets/binary_search_right_edge_by_left_edge.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Transforming the search for the right boundary into the search for the left boundary" class="animation-figure" src="../binary_search_edge.assets/binary_search_right_edge_by_left_edge.png" /></a></p>
+<p align="center"> 図 10-7 &nbsp; Transforming the search for the right boundary into the search for the left boundary </p>
+
+<p>返される挿入位置は<span class="arithmatex">\(i\)</span>であることに注意してください。したがって、<span class="arithmatex">\(j\)</span>を得るためには1を引く必要があります：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:14"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><input id="__tabbed_2_14" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label><label for="__tabbed_2_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_edge.py</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">binary_search_right_edge</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">target</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;最右端のターゲットの二分探索&quot;&quot;&quot;</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a>    <span class="c1"># 最左端のターゲット + 1 を見つけることに変換</span>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a>    <span class="n">i</span> <span class="o">=</span> <span class="n">binary_search_insertion</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="n">target</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a>    <span class="c1"># j は最右端のターゲットを指し、i はターゲットより大きい最初の要素を指す</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a>    <span class="n">j</span> <span class="o">=</span> <span class="n">i</span> <span class="o">-</span> <span class="mi">1</span>
+<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a>    <span class="c1"># ターゲットが見つからなかった場合、-1 を返す</span>
+<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a>    <span class="k">if</span> <span class="n">j</span> <span class="o">==</span> <span class="o">-</span><span class="mi">1</span> <span class="ow">or</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">!=</span> <span class="n">target</span><span class="p">:</span>
+<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a>        <span class="k">return</span> <span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a>    <span class="c1"># ターゲットが見つかった場合、インデックス j を返す</span>
+<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a>    <span class="k">return</span> <span class="n">j</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_edge.cpp</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 最右のターゲットの二分探索 */</span>
+<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">binarySearchRightEdge</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="c1">// 最左のtarget + 1を見つけることに変換</span>
+<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">binarySearchInsertion</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">    </span><span class="c1">// jは最右のターゲットを指し、iはtargetより大きい最初の要素を指す</span>
+<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">    </span><span class="c1">// targetが見つからなかったため、-1を返す</span>
+<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">-1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">-1</span><span class="p">;</span>
+<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="w">    </span><span class="c1">// targetが見つかったため、インデックスjを返す</span>
+<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">j</span><span class="p">;</span>
+<a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_edge.java</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 最も右の target を二分探索 */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">binarySearchRightEdge</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="c1">// 最も左の target + 1 を見つけることに変換</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">binary_search_insertion</span><span class="p">.</span><span class="na">binarySearchInsertion</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">target</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">    </span><span class="c1">// j は最も右の target を指し、i は target より大きい最初の要素を指す</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">    </span><span class="c1">// target を見つけられなかったので、-1 を返す</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="w">    </span><span class="c1">// target を見つけたので、インデックス j を返す</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">j</span><span class="p">;</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_edge.cs</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">binary_search_edge</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">BinarySearchRightEdge</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_edge.go</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">binarySearchRightEdge</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_edge.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">binarySearchRightEdge</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_edge.js</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">binarySearchRightEdge</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_edge.ts</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">binarySearchRightEdge</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_edge.dart</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binarySearchRightEdge</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_edge.rs</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binary_search_right_edge</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_edge.c</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binarySearchRightEdge</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_edge.kt</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">binarySearchRightEdge</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_edge.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">binary_search_right_edge</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_edge.zig</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binarySearchRightEdge</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h3 id="2">2. &nbsp; 要素探索に変換する<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
+<p>配列に<code>target</code>が含まれていない場合、<span class="arithmatex">\(i\)</span>と<span class="arithmatex">\(j\)</span>は最終的に<code>target</code>より大きい最初の要素と小さい最初の要素をそれぞれ指します。</p>
+<p>したがって、下図に示すように、配列に存在しない要素を構築して、左と右の境界を探索できます。</p>
+<ul>
+<li>最も左の<code>target</code>を見つけるには：<code>target - 0.5</code>を探索することに変換でき、ポインタ<span class="arithmatex">\(i\)</span>を返します。</li>
+<li>最も右の<code>target</code>を見つけるには：<code>target + 0.5</code>を探索することに変換でき、ポインタ<span class="arithmatex">\(j\)</span>を返します。</li>
+</ul>
+<p><a class="glightbox" href="../binary_search_edge.assets/binary_search_edge_by_element.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Transforming the search for boundaries into the search for an element" class="animation-figure" src="../binary_search_edge.assets/binary_search_edge_by_element.png" /></a></p>
+<p align="center"> 図 10-8 &nbsp; Transforming the search for boundaries into the search for an element </p>
+
+<p>コードはここでは省略されていますが、このアプローチについて注意すべき2つの重要な点があります。</p>
+<ul>
+<li>与えられた配列<code>nums</code>には小数が含まれていないため、等しい場合の処理は心配ありません。</li>
+<li>ただし、このアプローチで小数を導入するには、<code>target</code>変数を浮動小数点型に変更する必要があります（Pythonでは変更は不要です）。</li>
+</ul>
+
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diff --git a/ja/chapter_searching/binary_search_insertion.assets/binary_search_insertion_step4.png b/ja/chapter_searching/binary_search_insertion.assets/binary_search_insertion_step4.png
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+        <div class="md-header__topic" data-md-component="header-topic">
+          <span class="md-ellipsis">
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+              10.2 &nbsp; 二分探索挿入点
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+            検索を初期化
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+        <a href="https://github.com/krahets/hello-algo" title="リポジトリへ" class="md-source" data-md-component="source">
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+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/suggestions/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.2 &nbsp; 本書の使い方
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_introduction/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1021" class="md-nav__link">
+    <span class="md-ellipsis">
+      10.2.1 &nbsp; 重複要素がない場合
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1022" class="md-nav__link">
+    <span class="md-ellipsis">
+      10.2.2 &nbsp; 重複要素がある場合
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
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+    </span>
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+      10.2.2 &nbsp; 重複要素がある場合
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+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
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+<h1 id="102">10.2 &nbsp; 二分探索による挿入<a class="headerlink" href="#102" title="Permanent link">&para;</a></h1>
+<p>二分探索は目標要素を探索するだけでなく、目標要素の挿入位置を探索するなど、多くの変種問題を解決するためにも使用されます。</p>
+<h2 id="1021">10.2.1 &nbsp; 重複要素がない場合<a class="headerlink" href="#1021" title="Permanent link">&para;</a></h2>
+<div class="admonition question">
+<p class="admonition-title">Question</p>
+<p>一意の要素を持つ長さ<span class="arithmatex">\(n\)</span>のソート済み配列<code>nums</code>と要素<code>target</code>が与えられ、ソート順を維持しながら<code>target</code>を<code>nums</code>に挿入します。<code>target</code>が配列にすでに存在する場合は、既存の要素の左側に挿入します。挿入後の配列における<code>target</code>のインデックスを返してください。下図に示す例を参照してください。</p>
+</div>
+<p><a class="glightbox" href="../binary_search_insertion.assets/binary_search_insertion_example.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Example data for binary search insertion point" class="animation-figure" src="../binary_search_insertion.assets/binary_search_insertion_example.png" /></a></p>
+<p align="center"> 図 10-4 &nbsp; Example data for binary search insertion point </p>
+
+<p>前のセクションの二分探索コードを再利用したい場合、以下の2つの質問に答える必要があります。</p>
+<p><strong>質問1</strong>：配列にすでに<code>target</code>が含まれている場合、挿入位置は既存要素のインデックスになりますか？</p>
+<p><code>target</code>を等しい要素の左側に挿入するという要件は、新しく挿入される<code>target</code>が元の<code>target</code>の位置を置き換えることを意味します。つまり、<strong>配列に<code>target</code>が含まれている場合、挿入位置は確かにその<code>target</code>のインデックスです</strong>。</p>
+<p><strong>質問2</strong>：配列に<code>target</code>が含まれていない場合、どのインデックスに挿入されますか？</p>
+<p>二分探索プロセスをさらに考えてみましょう：<code>nums[m] &lt; target</code>のとき、ポインタ<span class="arithmatex">\(i\)</span>が移動します。これは、ポインタ<span class="arithmatex">\(i\)</span>が<code>target</code>以上の要素に近づいていることを意味します。同様に、ポインタ<span class="arithmatex">\(j\)</span>は常に<code>target</code>以下の要素に近づいています。</p>
+<p>したがって、二分の終了時には確実に：<span class="arithmatex">\(i\)</span>は<code>target</code>より大きい最初の要素を指し、<span class="arithmatex">\(j\)</span>は<code>target</code>より小さい最初の要素を指します。<strong>配列に<code>target</code>が含まれていない場合、挿入位置は<span class="arithmatex">\(i\)</span>であることは明らかです</strong>。コードは以下の通りです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:14"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><input id="__tabbed_1_14" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label><label for="__tabbed_1_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_insertion.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">binary_search_insertion_simple</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">target</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;挿入位置の二分探索（重複要素なし）&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span>  <span class="c1"># 両端閉区間 [0, n-1] を初期化</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="k">while</span> <span class="n">i</span> <span class="o">&lt;=</span> <span class="n">j</span><span class="p">:</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>        <span class="n">m</span> <span class="o">=</span> <span class="n">i</span> <span class="o">+</span> <span class="p">(</span><span class="n">j</span> <span class="o">-</span> <span class="n">i</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span>  <span class="c1"># 中点インデックス m を計算</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>        <span class="k">if</span> <span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span> <span class="o">&lt;</span> <span class="n">target</span><span class="p">:</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>            <span class="n">i</span> <span class="o">=</span> <span class="n">m</span> <span class="o">+</span> <span class="mi">1</span>  <span class="c1"># ターゲットは区間 [m+1, j] にある</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>        <span class="k">elif</span> <span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">target</span><span class="p">:</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>            <span class="n">j</span> <span class="o">=</span> <span class="n">m</span> <span class="o">-</span> <span class="mi">1</span>  <span class="c1"># ターゲットは区間 [i, m-1] にある</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>        <span class="k">else</span><span class="p">:</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>            <span class="k">return</span> <span class="n">m</span>  <span class="c1"># ターゲットが見つかった場合、挿入位置 m を返す</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>    <span class="c1"># ターゲットが見つからなかった場合、挿入位置 i を返す</span>
+<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>    <span class="k">return</span> <span class="n">i</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_insertion.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 挿入ポイントの二分探索（重複要素なし） */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">binarySearchInsertionSimple</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 両端閉区間[0, n-1]を初期化</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 中点インデックスmを計算</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// ターゲットは区間[m+1, j]にある</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// ターゲットは区間[i, m-1]にある</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="c1">// ターゲットが見つかったため、挿入ポイントmを返す</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">    </span><span class="c1">// ターゲットが見つからなかったため、挿入ポイントiを返す</span>
+<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_insertion.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 挿入点の二分探索（重複要素なし） */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">binarySearchInsertionSimple</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 両端閉区間 [0, n-1] を初期化</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 中点インデックス m を計算</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target は区間 [m+1, j] にある</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target は区間 [i, m-1] にある</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="c1">// target を見つけたので、挿入点 m を返す</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">    </span><span class="c1">// target を見つけられなかったので、挿入点 i を返す</span>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_insertion.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">binary_search_insertion</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">BinarySearchInsertionSimple</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_insertion.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">binarySearchInsertionSimple</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_insertion.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">binarySearchInsertionSimple</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_insertion.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">binarySearchInsertionSimple</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_insertion.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">binarySearchInsertionSimple</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_insertion.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binarySearchInsertionSimple</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_insertion.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binary_search_insertion_simple</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_insertion.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binarySearchInsertionSimple</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_insertion.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">binarySearchInsertionSimple</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_insertion.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">binary_search_insertion_simple</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_insertion.zig</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binarySearchInsertionSimple</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h2 id="1022">10.2.2 &nbsp; 重複要素がある場合<a class="headerlink" href="#1022" title="Permanent link">&para;</a></h2>
+<div class="admonition question">
+<p class="admonition-title">Question</p>
+<p>前の質問に基づいて、配列に重複要素が含まれている可能性があると仮定し、他はすべて同じとします。</p>
+</div>
+<p>配列に<code>target</code>の複数の出現がある場合、通常の二分探索は<code>target</code>の1つの出現のインデックスのみを返すことができ、<strong>その位置の左右に<code>target</code>の出現がいくつあるかを特定することはできません</strong>。</p>
+<p>問題では目標要素を最も左の位置に挿入することが要求されているため、<strong>配列内の最も左の<code>target</code>のインデックスを見つける必要があります</strong>。最初に下図に示すステップを通してこれを実装することを考えてみましょう。</p>
+<ol>
+<li>二分探索を実行して<code>target</code>の任意のインデックス、例えば<span class="arithmatex">\(k\)</span>を見つけます。</li>
+<li>インデックス<span class="arithmatex">\(k\)</span>から開始して、最も左の<code>target</code>の出現が見つかるまで左に線形探索を行い、このインデックスを返します。</li>
+</ol>
+<p><a class="glightbox" href="../binary_search_insertion.assets/binary_search_insertion_naive.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Linear search for the insertion point of duplicate elements" class="animation-figure" src="../binary_search_insertion.assets/binary_search_insertion_naive.png" /></a></p>
+<p align="center"> 図 10-5 &nbsp; Linear search for the insertion point of duplicate elements </p>
+
+<p>この方法は実現可能ですが、線形探索を含むため、時間計算量は<span class="arithmatex">\(O(n)\)</span>です。この方法は、配列に多くの重複する<code>target</code>が含まれている場合に非効率です。</p>
+<p>今度は二分探索コードを拡張することを考えてみましょう。下図に示すように、全体的なプロセスは同じままです。各ラウンドで、まず中間インデックス<span class="arithmatex">\(m\)</span>を計算し、次に<code>target</code>と<code>nums[m]</code>の値を比較して、以下のケースになります。</p>
+<ul>
+<li><code>nums[m] &lt; target</code>または<code>nums[m] &gt; target</code>のとき、これは<code>target</code>がまだ見つかっていないことを意味するため、通常の二分探索を使用して探索範囲を狭め、<strong>ポインタ<span class="arithmatex">\(i\)</span>と<span class="arithmatex">\(j\)</span>を<code>target</code>に近づけます</strong>。</li>
+<li><code>nums[m] == target</code>のとき、これは<code>target</code>より小さい要素が範囲<span class="arithmatex">\([i, m - 1]\)</span>にあることを示すため、<span class="arithmatex">\(j = m - 1\)</span>を使用して範囲を狭め、<strong>ポインタ<span class="arithmatex">\(j\)</span>を<code>target</code>より小さい要素に近づけます</strong>。</li>
+</ul>
+<p>ループ後、<span class="arithmatex">\(i\)</span>は最も左の<code>target</code>を指し、<span class="arithmatex">\(j\)</span>は<code>target</code>より小さい最初の要素を指すため、<strong>インデックス<span class="arithmatex">\(i\)</span>が挿入位置です</strong>。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:8"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">&lt;1&gt;</label><label for="__tabbed_2_2">&lt;2&gt;</label><label for="__tabbed_2_3">&lt;3&gt;</label><label for="__tabbed_2_4">&lt;4&gt;</label><label for="__tabbed_2_5">&lt;5&gt;</label><label for="__tabbed_2_6">&lt;6&gt;</label><label for="__tabbed_2_7">&lt;7&gt;</label><label for="__tabbed_2_8">&lt;8&gt;</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<p><a class="glightbox" href="../binary_search_insertion.assets/binary_search_insertion_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Steps for binary search insertion point of duplicate elements" class="animation-figure" src="../binary_search_insertion.assets/binary_search_insertion_step1.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../binary_search_insertion.assets/binary_search_insertion_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="binary_search_insertion_step2" class="animation-figure" src="../binary_search_insertion.assets/binary_search_insertion_step2.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../binary_search_insertion.assets/binary_search_insertion_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="binary_search_insertion_step3" class="animation-figure" src="../binary_search_insertion.assets/binary_search_insertion_step3.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../binary_search_insertion.assets/binary_search_insertion_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="binary_search_insertion_step4" class="animation-figure" src="../binary_search_insertion.assets/binary_search_insertion_step4.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../binary_search_insertion.assets/binary_search_insertion_step5.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="binary_search_insertion_step5" class="animation-figure" src="../binary_search_insertion.assets/binary_search_insertion_step5.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../binary_search_insertion.assets/binary_search_insertion_step6.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="binary_search_insertion_step6" class="animation-figure" src="../binary_search_insertion.assets/binary_search_insertion_step6.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../binary_search_insertion.assets/binary_search_insertion_step7.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="binary_search_insertion_step7" class="animation-figure" src="../binary_search_insertion.assets/binary_search_insertion_step7.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../binary_search_insertion.assets/binary_search_insertion_step8.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="binary_search_insertion_step8" class="animation-figure" src="../binary_search_insertion.assets/binary_search_insertion_step8.png" /></a></p>
+</div>
+</div>
+</div>
+<p align="center"> 図 10-6 &nbsp; Steps for binary search insertion point of duplicate elements </p>
+
+<p>以下のコードを観察してください。分岐<code>nums[m] &gt; target</code>と<code>nums[m] == target</code>の操作は同じであるため、これら2つの分岐をマージできます。</p>
+<p>それでも、ロジックがより明確になり、可読性が向上するため、条件を展開したままにしておくことができます。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="3:14"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><input id="__tabbed_3_14" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label><label for="__tabbed_3_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_insertion.py</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">binary_search_insertion</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">target</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;挿入位置の二分探索（重複要素あり）&quot;&quot;&quot;</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a>    <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="o">=</span> <span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span>  <span class="c1"># 両端閉区間 [0, n-1] を初期化</span>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a>    <span class="k">while</span> <span class="n">i</span> <span class="o">&lt;=</span> <span class="n">j</span><span class="p">:</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a>        <span class="n">m</span> <span class="o">=</span> <span class="n">i</span> <span class="o">+</span> <span class="p">(</span><span class="n">j</span> <span class="o">-</span> <span class="n">i</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span>  <span class="c1"># 中点インデックス m を計算</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a>        <span class="k">if</span> <span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span> <span class="o">&lt;</span> <span class="n">target</span><span class="p">:</span>
+<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a>            <span class="n">i</span> <span class="o">=</span> <span class="n">m</span> <span class="o">+</span> <span class="mi">1</span>  <span class="c1"># ターゲットは区間 [m+1, j] にある</span>
+<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a>        <span class="k">elif</span> <span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">target</span><span class="p">:</span>
+<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a>            <span class="n">j</span> <span class="o">=</span> <span class="n">m</span> <span class="o">-</span> <span class="mi">1</span>  <span class="c1"># ターゲットは区間 [i, m-1] にある</span>
+<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a>        <span class="k">else</span><span class="p">:</span>
+<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a>            <span class="n">j</span> <span class="o">=</span> <span class="n">m</span> <span class="o">-</span> <span class="mi">1</span>  <span class="c1"># ターゲット未満の最初の要素は区間 [i, m-1] にある</span>
+<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a>    <span class="c1"># 挿入位置 i を返す</span>
+<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a>    <span class="k">return</span> <span class="n">i</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_insertion.cpp</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 挿入ポイントの二分探索（重複要素あり） */</span>
+<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">binarySearchInsertion</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 両端閉区間[0, n-1]を初期化</span>
+<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 中点インデックスmを計算</span>
+<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// ターゲットは区間[m+1, j]にある</span>
+<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">m</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// ターゲットは区間[i, m-1]にある</span>
+<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// ターゲット未満の最初の要素は区間[i, m-1]にある</span>
+<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="w">    </span><span class="c1">// 挿入ポイントiを返す</span>
+<a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_insertion.java</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 挿入点の二分探索（重複要素あり） */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">binarySearchInsertion</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 両端閉区間 [0, n-1] を初期化</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 中点インデックス m を計算</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">            </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target は区間 [m+1, j] にある</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">m</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target は区間 [i, m-1] にある</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="w">            </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// target より小さい最初の要素は区間 [i, m-1] にある</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="w">    </span><span class="c1">// 挿入点 i を返す</span>
+<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_insertion.cs</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">binary_search_insertion</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">BinarySearchInsertion</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_insertion.go</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">binarySearchInsertion</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_insertion.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">binarySearchInsertion</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_insertion.js</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">binarySearchInsertion</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_insertion.ts</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">binarySearchInsertion</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_insertion.dart</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binarySearchInsertion</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_insertion.rs</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binary_search_insertion</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_insertion.c</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binarySearchInsertion</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_insertion.kt</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">binarySearchInsertion</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_insertion.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">binary_search_insertion</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_insertion.zig</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">binarySearchInsertion</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<div class="admonition tip">
+<p class="admonition-title">Tip</p>
+<p>このセクションのコードは「閉区間」を使用しています。「左閉右開」に興味がある場合は、自分でコードを実装してみてください。</p>
+</div>
+<p>要約すると、二分探索は本質的にポインタ<span class="arithmatex">\(i\)</span>と<span class="arithmatex">\(j\)</span>の探索目標を設定することです。これらの目標は特定の要素（<code>target</code>など）または要素の範囲（<code>target</code>より小さいものなど）である可能性があります。</p>
+<p>二分探索の連続ループにおいて、ポインタ<span class="arithmatex">\(i\)</span>と<span class="arithmatex">\(j\)</span>は段階的に事前定義された目標に近づきます。最終的に、それらは答えを見つけるか、境界を越えた後に停止します。</p>
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new file mode 100644
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+  
+  <span class="md-ellipsis">
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+            第 0 章 &nbsp; 前書き
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+      <a href="../chapter_preface/about_the_book/" class="md-nav__link">
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+      <a href="../chapter_preface/suggestions/" class="md-nav__link">
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+      <a href="../chapter_preface/summary/" class="md-nav__link">
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+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
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+    1.1 &nbsp; アルゴリズムはどこにでもある
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+      <a href="../chapter_introduction/what_is_dsa/" class="md-nav__link">
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+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
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+  
+  
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+    <li class="md-nav__item">
+      <a href="../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
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+    </li>
+  
+
+              
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+
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+          
+        
+      
+        
+      
+        
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+        
+      
+        
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+            <a href="../chapter_computational_complexity/" class="md-nav__link ">
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+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
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+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
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+      <a href="../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
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+    </li>
+  
+
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+            
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+      <a href="../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
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+      <a href="../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
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+      
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+            <a href="../chapter_data_structure/" class="md-nav__link ">
+              
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
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+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
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+            
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+  
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+  
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+      <a href="../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
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+  
+
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+            
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+  
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+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
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+  
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+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="./" class="md-nav__link md-nav__link--active">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link md-nav__link--active" for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
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+          </ul>
+        </nav>
+      
+    </li>
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+
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+          
+        
+      
+        
+      
+        
+      
+        
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+        
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+      
+        
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+        
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+    
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+      
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+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_dynamic_programming/" class="md-nav__link ">
+              
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+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
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+            第 14 章 &nbsp; 動的プログラミング
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+            
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+            
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+  
+  
+  
+  
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+      <a href="../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
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+        </nav>
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+    </li>
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+          
+        
+      
+        
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+            <a href="../chapter_greedy/" class="md-nav__link ">
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
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+      <a href="../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
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+  
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+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
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+  
+
+              
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+        </nav>
+      
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+
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+          
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+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
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+            第 16 章 &nbsp; 付録
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+            
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+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
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+
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+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_appendix/contribution/" class="md-nav__link">
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+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
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+    </li>
+  
+
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+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_appendix/terminology/" class="md-nav__link">
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+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
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+<h1 id="10">第 10 章 &nbsp; 探索<a class="headerlink" href="#10" title="Permanent link">&para;</a></h1>
+<p><a class="glightbox" href="../assets/covers/chapter_searching.jpg" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Searching" class="cover-image" src="../assets/covers/chapter_searching.jpg" /></a></p>
+<div class="admonition abstract">
+<p class="admonition-title">Abstract</p>
+<p>探索は未知への冒険です。神秘的な空間の隅々まで巡る必要があるかもしれませんし、あるいはすぐに目標を見つけることができるかもしれません。</p>
+<p>この発見の旅において、それぞれの探査は予期しない答えで終わるかもしれません。</p>
+</div>
+<h2 id="_1">章の内容<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h2>
+<ul>
+<li><a href="binary_search/">10.1 &nbsp; 二分探索</a></li>
+<li><a href="binary_search_insertion/">10.2 &nbsp; 二分探索挿入点</a></li>
+<li><a href="binary_search_edge/">10.3 &nbsp; 二分探索の境界</a></li>
+<li><a href="replace_linear_by_hashing/">10.4 &nbsp; ハッシュ最適化戦略</a></li>
+<li><a href="searching_algorithm_revisited/">10.5 &nbsp; 探索アルゴリズム再考</a></li>
+<li><a href="summary/">10.6 &nbsp; まとめ</a></li>
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+      <a href="../../chapter_preface/summary/" class="md-nav__link">
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+  
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+    第 1 章 &nbsp; アルゴリズムとの出会い
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+  
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+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
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+    1.3 &nbsp; まとめ
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+        
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+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
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+            第 2 章 &nbsp; 計算量解析
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+    2.1 &nbsp; アルゴリズム効率評価
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+    2.2 &nbsp; 反復と再帰
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+  
+
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+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
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+    2.3 &nbsp; 時間計算量
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+  
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+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
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+
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+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
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+    第 3 章 &nbsp; データ構造
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+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1041" class="md-nav__link">
+    <span class="md-ellipsis">
+      10.4.1 &nbsp; 線形探索：時間を空間と交換
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1042" class="md-nav__link">
+    <span class="md-ellipsis">
+      10.4.2 &nbsp; ハッシュ探索：空間を時間と交換
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_19" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_reference/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9 3v15h3V3H9m3 2 4 13 3-1-4-13-3 1M5 5v13h3V5H5M3 19v2h18v-2H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    参考文献
+  </span>
+  
+
+            </a>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_19_label" aria-expanded="false">
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+            参考文献
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+      
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+</nav>
+                  </div>
+                </div>
+              </div>
+            
+            
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+              <div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
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+    <span class="md-ellipsis">
+      10.4.1 &nbsp; 線形探索：時間を空間と交換
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1042" class="md-nav__link">
+    <span class="md-ellipsis">
+      10.4.2 &nbsp; ハッシュ探索：空間を時間と交換
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
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+      title="編集"
+      class="md-content__button md-icon"
+    >
+      
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
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+<h1 id="104">10.4 &nbsp; ハッシュ最適化戦略<a class="headerlink" href="#104" title="Permanent link">&para;</a></h1>
+<p>アルゴリズム問題において、<strong>線形探索をハッシュベースの探索に置き換えることで、アルゴリズムの時間計算量を削減することがよくあります</strong>。アルゴリズム問題を使用して理解を深めましょう。</p>
+<div class="admonition question">
+<p class="admonition-title">Question</p>
+<p>整数配列<code>nums</code>と目標要素<code>target</code>が与えられ、配列内で「和」が<code>target</code>に等しい2つの要素を探索し、それらの配列インデックスを返してください。任意の解が受け入れられます。</p>
+</div>
+<h2 id="1041">10.4.1 &nbsp; 線形探索：時間を空間と交換<a class="headerlink" href="#1041" title="Permanent link">&para;</a></h2>
+<p>すべての可能な組み合わせを直接横断することを考えてみます。下図に示すように、ネストしたループを開始し、各反復で2つの整数の和が<code>target</code>に等しいかどうかを判断します。そうであれば、それらのインデックスを返します。</p>
+<p><a class="glightbox" href="../replace_linear_by_hashing.assets/two_sum_brute_force.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Linear search solution for two-sum problem" class="animation-figure" src="../replace_linear_by_hashing.assets/two_sum_brute_force.png" /></a></p>
+<p align="center"> 図 10-9 &nbsp; Linear search solution for two-sum problem </p>
+
+<p>コードは以下の通りです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:14"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><input id="__tabbed_1_14" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label><label for="__tabbed_1_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">two_sum.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">two_sum_brute_force</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">target</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;方法一：ブルートフォース列挙&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># 二重ループ、時間計算量は O(n^2)</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>        <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)):</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>            <span class="k">if</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">+</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">==</span> <span class="n">target</span><span class="p">:</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>                <span class="k">return</span> <span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>    <span class="k">return</span> <span class="p">[]</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">two_sum.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 方法一：ブルートフォース列挙 */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">twoSumBruteForce</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="c1">// 二重ループ、時間計算量はO(n^2)</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">target</span><span class="p">)</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="p">{</span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">};</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">{};</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">two_sum.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 方法一: 暴力列挙 */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="nf">twoSumBruteForce</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="p">;</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="c1">// 二重ループ、時間計算量は O(n^2)</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">target</span><span class="p">)</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="p">};</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">two_sum.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">two_sum</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">TwoSumBruteForce</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">two_sum.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">twoSumBruteForce</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">two_sum.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">twoSumBruteForce</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">two_sum.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">twoSumBruteForce</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">two_sum.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">twoSumBruteForce</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">two_sum.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">twoSumBruteForce</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">two_sum.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">two_sum_brute_force</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">two_sum.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">twoSumBruteForce</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">two_sum.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">twoSumBruteForce</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">two_sum.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">two_sum_brute_force</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">two_sum.zig</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">twoSumBruteForce</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>この方法の時間計算量は<span class="arithmatex">\(O(n^2)\)</span>、空間計算量は<span class="arithmatex">\(O(1)\)</span>で、大容量データでは非常に時間がかかる可能性があります。</p>
+<h2 id="1042">10.4.2 &nbsp; ハッシュ探索：空間を時間と交換<a class="headerlink" href="#1042" title="Permanent link">&para;</a></h2>
+<p>ハッシュテーブルの使用を考えてみましょう。キーと値のペアはそれぞれ配列要素とそのインデックスです。配列をループし、各反復中に下図に示すステップを実行します。</p>
+<ol>
+<li>数値<code>target - nums[i]</code>がハッシュテーブルにあるかどうかを確認します。ある場合は、これら2つの要素のインデックスを直接返します。</li>
+<li>キーと値のペア<code>nums[i]</code>とインデックス<code>i</code>をハッシュテーブルに追加します。</li>
+</ol>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:3"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">&lt;1&gt;</label><label for="__tabbed_2_2">&lt;2&gt;</label><label for="__tabbed_2_3">&lt;3&gt;</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<p><a class="glightbox" href="../replace_linear_by_hashing.assets/two_sum_hashtable_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Help hash table solve two-sum" class="animation-figure" src="../replace_linear_by_hashing.assets/two_sum_hashtable_step1.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../replace_linear_by_hashing.assets/two_sum_hashtable_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="two_sum_hashtable_step2" class="animation-figure" src="../replace_linear_by_hashing.assets/two_sum_hashtable_step2.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../replace_linear_by_hashing.assets/two_sum_hashtable_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="two_sum_hashtable_step3" class="animation-figure" src="../replace_linear_by_hashing.assets/two_sum_hashtable_step3.png" /></a></p>
+</div>
+</div>
+</div>
+<p align="center"> 図 10-10 &nbsp; Help hash table solve two-sum </p>
+
+<p>実装コードは以下に示され、単一のループのみが必要です：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="3:14"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><input id="__tabbed_3_14" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label><label for="__tabbed_3_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">two_sum.py</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">two_sum_hash_table</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">target</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
+<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;方法二：補助ハッシュテーブル&quot;&quot;&quot;</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a>    <span class="c1"># 補助ハッシュテーブル、空間計算量は O(n)</span>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a>    <span class="n">dic</span> <span class="o">=</span> <span class="p">{}</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a>    <span class="c1"># 単一ループ、時間計算量は O(n)</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)):</span>
+<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a>        <span class="k">if</span> <span class="n">target</span> <span class="o">-</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="ow">in</span> <span class="n">dic</span><span class="p">:</span>
+<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a>            <span class="k">return</span> <span class="p">[</span><span class="n">dic</span><span class="p">[</span><span class="n">target</span> <span class="o">-</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]],</span> <span class="n">i</span><span class="p">]</span>
+<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a>        <span class="n">dic</span><span class="p">[</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]]</span> <span class="o">=</span> <span class="n">i</span>
+<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a>    <span class="k">return</span> <span class="p">[]</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">two_sum.cpp</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 方法二：補助ハッシュテーブル */</span>
+<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">twoSumHashTable</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
+<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="c1">// 補助ハッシュテーブル、空間計算量はO(n)</span>
+<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">    </span><span class="n">unordered_map</span><span class="o">&lt;</span><span class="kt">int</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">dic</span><span class="p">;</span>
+<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">    </span><span class="c1">// 単層ループ、時間計算量はO(n)</span>
+<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">dic</span><span class="p">.</span><span class="n">find</span><span class="p">(</span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">])</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">dic</span><span class="p">.</span><span class="n">end</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="p">{</span><span class="n">dic</span><span class="p">[</span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]],</span><span class="w"> </span><span class="n">i</span><span class="p">};</span>
+<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="w">        </span><span class="n">dic</span><span class="p">.</span><span class="n">emplace</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">{};</span>
+<a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">two_sum.java</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 方法二: 補助ハッシュテーブル */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="nf">twoSumHashTable</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">target</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="p">;</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="c1">// 補助ハッシュテーブル、空間計算量は O(n)</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">    </span><span class="n">Map</span><span class="o">&lt;</span><span class="n">Integer</span><span class="p">,</span><span class="w"> </span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">dic</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">HashMap</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">    </span><span class="c1">// 単一層ループ、時間計算量は O(n)</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">dic</span><span class="p">.</span><span class="na">containsKey</span><span class="p">(</span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">))</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">dic</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">target</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">),</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="p">};</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="w">        </span><span class="n">dic</span><span class="p">.</span><span class="na">put</span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">two_sum.cs</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">two_sum</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">TwoSumHashTable</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">two_sum.go</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">twoSumHashTable</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">two_sum.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">twoSumHashTable</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">two_sum.js</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">twoSumHashTable</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">two_sum.ts</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">twoSumHashTable</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">two_sum.dart</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">twoSumHashTable</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">two_sum.rs</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">two_sum_hash_table</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">two_sum.c</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">HashTable</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a>
+<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">twoSumHashTable</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">two_sum.kt</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">twoSumHashTable</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">two_sum.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">two_sum_hash_table</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">two_sum.zig</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">twoSumHashTable</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>この方法は、ハッシュ探索を使用することで時間計算量を<span class="arithmatex">\(O(n^2)\)</span>から<span class="arithmatex">\(O(n)\)</span>に削減し、実行時効率を大幅に向上させます。</p>
+<p>追加のハッシュテーブルを維持する必要があるため、空間計算量は<span class="arithmatex">\(O(n)\)</span>です。<strong>それにもかかわらず、この方法は全体的により均衡のとれた時空間効率を持ち、この問題の最適解となります</strong>。</p>
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+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1051" class="md-nav__link">
+    <span class="md-ellipsis">
+      10.5.1 &nbsp; 総当たり探索
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1052" class="md-nav__link">
+    <span class="md-ellipsis">
+      10.5.2 &nbsp; 適応的探索
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1053" class="md-nav__link">
+    <span class="md-ellipsis">
+      10.5.3 &nbsp; 探索方法の選択
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
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+    <span class="md-ellipsis">
+      10.5.1 &nbsp; 総当たり探索
+    </span>
+  </a>
+  
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+      
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+      10.5.3 &nbsp; 探索方法の選択
+    </span>
+  </a>
+  
+</li>
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+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
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+<h1 id="105">10.5 &nbsp; 探索アルゴリズムの再検討<a class="headerlink" href="#105" title="Permanent link">&para;</a></h1>
+<p><u>探索アルゴリズム（検索アルゴリズム）</u>は、配列、連結リスト、木、グラフなどのデータ構造内で特定の基準を満たす1つ以上の要素を取得するために使用されます。</p>
+<p>探索アルゴリズムは、そのアプローチに基づいて以下の2つのカテゴリに分けることができます。</p>
+<ul>
+<li><strong>データ構造を横断することで目標要素を特定する</strong>：配列、連結リスト、木、グラフの横断など。</li>
+<li><strong>データの組織構造や既存のデータを使用して効率的な要素探索を実現する</strong>：二分探索、ハッシュ探索、二分探索木探索など。</li>
+</ul>
+<p>これらのトピックは前の章で紹介されたため、私たちには馴染みのないものではありません。このセクションでは、より体系的な観点から探索アルゴリズムを再検討します。</p>
+<h2 id="1051">10.5.1 &nbsp; 総当たり探索<a class="headerlink" href="#1051" title="Permanent link">&para;</a></h2>
+<p>総当たり探索は、データ構造のすべての要素を横断することで目標要素を特定します。</p>
+<ul>
+<li>「線形探索」は配列や連結リストなどの線形データ構造に適しています。データ構造の一端から開始し、目標要素が見つかるか、目標要素を見つけることなく他端に到達するまで、各要素に一つずつアクセスします。</li>
+<li>「幅優先探索」と「深さ優先探索」は、グラフと木の2つの横断戦略です。幅優先探索は初期ノードから開始し、層ごと（左から右へ）に探索し、近くから遠くのノードにアクセスします。深さ優先探索は初期ノードから開始し、パスの終端（上から下へ）まで追跡し、その後バックトラックして他のパスを試し、データ構造全体が横断されるまで続行します。</li>
+</ul>
+<p>総当たり探索の利点は、その単純さと汎用性であり、**データの前処理や追加のデータ構造の助けが不要**です。</p>
+<p>ただし、**このタイプのアルゴリズムの時間計算量は<span class="arithmatex">\(O(n)\)</span>**で、<span class="arithmatex">\(n\)</span>は要素数であるため、大規模なデータセットでは性能が悪くなります。</p>
+<h2 id="1052">10.5.2 &nbsp; 適応的探索<a class="headerlink" href="#1052" title="Permanent link">&para;</a></h2>
+<p>適応的探索は、データの固有の性質（順序など）を使用して探索プロセスを最適化し、それにより目標要素をより効率的に特定します。</p>
+<ul>
+<li>「二分探索」はデータの整列性を使用して効率的な探索を実現し、配列にのみ適用可能です。</li>
+<li>「ハッシュ探索」はハッシュテーブルを使用して探索データと目標データの間にキーと値のマッピングを確立し、それによりクエリ操作を実装します。</li>
+<li>特定の木構造（二分探索木など）での「木探索」は、ノード値の比較に基づいてノードを迅速に除外し、それにより目標要素を特定します。</li>
+</ul>
+<p>これらのアルゴリズムの利点は高効率であり、<strong>時間計算量が<span class="arithmatex">\(O(\log n)\)</span>または<span class="arithmatex">\(O(1)\)</span>にまで達します</strong>。</p>
+<p>ただし、<strong>これらのアルゴリズムを使用するには、多くの場合データの前処理が必要です</strong>。例えば、二分探索では事前に配列をソートする必要があり、ハッシュ探索と木探索の両方で追加のデータ構造の助けが必要です。これらの構造を維持することも、時間と空間の面でより多くのオーバーヘッドが必要です。</p>
+<div class="admonition tip">
+<p class="admonition-title">Tip</p>
+<p>適応的探索アルゴリズムは、多くの場合探索アルゴリズムと呼ばれ、<strong>主に特定のデータ構造内で目標要素を迅速に取得するために使用されます</strong>。</p>
+</div>
+<h2 id="1053">10.5.3 &nbsp; 探索方法の選択<a class="headerlink" href="#1053" title="Permanent link">&para;</a></h2>
+<p>サイズ<span class="arithmatex">\(n\)</span>のデータセットが与えられた場合、線形探索、二分探索、木探索、ハッシュ探索、またはその他の方法を使用して目標要素を取得できます。これらの方法の動作原理を下図に示します。</p>
+<p><a class="glightbox" href="../searching_algorithm_revisited.assets/searching_algorithms.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Various search strategies" class="animation-figure" src="../searching_algorithm_revisited.assets/searching_algorithms.png" /></a></p>
+<p align="center"> 図 10-11 &nbsp; Various search strategies </p>
+
+<p>前述の方法の特性と操作効率を以下の表に示します。</p>
+<p align="center"> 表 10-1 &nbsp; 探索アルゴリズム効率の比較 </p>
+
+<div class="center-table">
+<table>
+<thead>
+<tr>
+<th></th>
+<th>線形探索</th>
+<th>二分探索</th>
+<th>木探索</th>
+<th>ハッシュ探索</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td>要素探索</td>
+<td><span class="arithmatex">\(O(n)\)</span></td>
+<td><span class="arithmatex">\(O(\log n)\)</span></td>
+<td><span class="arithmatex">\(O(\log n)\)</span></td>
+<td><span class="arithmatex">\(O(1)\)</span></td>
+</tr>
+<tr>
+<td>要素挿入</td>
+<td><span class="arithmatex">\(O(1)\)</span></td>
+<td><span class="arithmatex">\(O(n)\)</span></td>
+<td><span class="arithmatex">\(O(\log n)\)</span></td>
+<td><span class="arithmatex">\(O(1)\)</span></td>
+</tr>
+<tr>
+<td>要素削除</td>
+<td><span class="arithmatex">\(O(n)\)</span></td>
+<td><span class="arithmatex">\(O(n)\)</span></td>
+<td><span class="arithmatex">\(O(\log n)\)</span></td>
+<td><span class="arithmatex">\(O(1)\)</span></td>
+</tr>
+<tr>
+<td>追加空間</td>
+<td><span class="arithmatex">\(O(1)\)</span></td>
+<td><span class="arithmatex">\(O(1)\)</span></td>
+<td><span class="arithmatex">\(O(n)\)</span></td>
+<td><span class="arithmatex">\(O(n)\)</span></td>
+</tr>
+<tr>
+<td>データ前処理</td>
+<td>/</td>
+<td>ソート <span class="arithmatex">\(O(n \log n)\)</span></td>
+<td>木構築 <span class="arithmatex">\(O(n \log n)\)</span></td>
+<td>ハッシュテーブル構築 <span class="arithmatex">\(O(n)\)</span></td>
+</tr>
+<tr>
+<td>データ順序性</td>
+<td>無順序</td>
+<td>順序</td>
+<td>順序</td>
+<td>無順序</td>
+</tr>
+</tbody>
+</table>
+</div>
+<p>探索アルゴリズムの選択は、データ量、探索性能要件、データクエリと更新の頻度などにも依存します。</p>
+<p><strong>線形探索</strong></p>
+<ul>
+<li>汎用性が良く、データ前処理操作が不要です。データを一度だけクエリする必要がある場合、他の3つの方法のデータ前処理時間は線形探索の時間よりも長くなります。</li>
+<li>小容量のデータに適しており、時間計算量が効率に与える影響は小さいです。</li>
+<li>データ更新が非常に頻繁なシナリオに適しています。この方法はデータの追加メンテナンスを必要としないためです。</li>
+</ul>
+<p><strong>二分探索</strong></p>
+<ul>
+<li>より大きなデータ量に適しており、安定した性能と最悪ケースの時間計算量<span class="arithmatex">\(O(\log n)\)</span>を持ちます。</li>
+<li>ただし、データ量が大きすぎることはできません。配列の保存には連続したメモリ空間が必要だからです。</li>
+<li>頻繁な追加と削除があるシナリオには適していません。順序付き配列の維持に多くのオーバーヘッドが発生するためです。</li>
+</ul>
+<p><strong>ハッシュ探索</strong></p>
+<ul>
+<li>高速クエリ性能が不可欠なシナリオに適しており、平均時間計算量は<span class="arithmatex">\(O(1)\)</span>です。</li>
+<li>順序付きデータや範囲探索が必要なシナリオには適していません。ハッシュテーブルはデータの順序性を維持できないためです。</li>
+<li>ハッシュ関数とハッシュ衝突処理戦略への依存度が高く、性能劣化のリスクが大きいです。</li>
+<li>過度に大容量のデータには適していません。ハッシュテーブルは衝突を最小化し、良好なクエリ性能を提供するために追加の空間が必要だからです。</li>
+</ul>
+<p><strong>木探索</strong></p>
+<ul>
+<li>大容量データに適しています。木ノードはメモリ内に分散して保存されるためです。</li>
+<li>順序付きデータの維持や範囲探索に適しています。</li>
+<li>ノードの継続的な追加と削除により、二分探索木は偏る可能性があり、時間計算量が<span class="arithmatex">\(O(n)\)</span>に劣化する可能性があります。</li>
+<li>AVL木や赤黒木を使用する場合、操作は<span class="arithmatex">\(O(\log n)\)</span>効率で安定して実行できますが、木のバランスを維持する操作により追加のオーバーヘッドが追加されます。</li>
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+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+      
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_19" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_reference/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9 3v15h3V3H9m3 2 4 13 3-1-4-13-3 1M5 5v13h3V5H5M3 19v2h18v-2H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    参考文献
+  </span>
+  
+
+            </a>
+            
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+<h1 id="106">10.6 &nbsp; まとめ<a class="headerlink" href="#106" title="Permanent link">&para;</a></h1>
+<ul>
+<li>二分探索はデータの順序に依存し、探索区間を反復的に半分にすることで探索を実行します。入力データがソート済みである必要があり、配列または配列ベースのデータ構造にのみ適用可能です。</li>
+<li>無順序データセット内のエントリを見つけるには、総当たり探索が必要な場合があります。データ構造に基づいて異なる探索アルゴリズムを適用できます：線形探索は配列と連結リストに適しており、幅優先探索（BFS）と深さ優先探索（DFS）はグラフと木に適しています。これらのアルゴリズムは非常に汎用性が高く、データの前処理が不要ですが、<span class="arithmatex">\(O(n)\)</span>という高い時間計算量を持ちます。</li>
+<li>ハッシュ探索、木探索、二分探索は効率的な探索方法で、特定のデータ構造内で目標要素を迅速に特定できます。これらのアルゴリズムは非常に効率的で、時間計算量が<span class="arithmatex">\(O(\log n)\)</span>または<span class="arithmatex">\(O(1)\)</span>にまで達しますが、通常は追加のデータ構造を収容するために追加の空間が必要です。</li>
+<li>実際には、データ量、探索性能要件、データクエリと更新頻度などの要因を分析して、適切な探索方法を選択する必要があります。</li>
+<li>線形探索は小さなデータや頻繁に更新される（変動性の高い）データに理想的です。二分探索は大きくてソート済みのデータに適しています。ハッシュ探索は高いクエリ効率が必要で範囲クエリが不要なデータに適しています。木探索は順序を維持し、範囲クエリをサポートする必要がある大きな動的データに最も適しています。</li>
+<li>線形探索をハッシュ探索に置き換えることは、実行時性能を最適化する一般的な戦略で、時間計算量を<span class="arithmatex">\(O(n)\)</span>から<span class="arithmatex">\(O(1)\)</span>に削減します。</li>
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+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1131" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.3.1 &nbsp; アルゴリズムプロセス
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1132" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.3.2 &nbsp; 効率の最適化
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1133" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.3.3 &nbsp; アルゴリズムの特性
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_19" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_reference/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9 3v15h3V3H9m3 2 4 13 3-1-4-13-3 1M5 5v13h3V5H5M3 19v2h18v-2H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    参考文献
+  </span>
+  
+
+            </a>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_19_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_19">
+            <span class="md-nav__icon md-icon"></span>
+            参考文献
+          </label>
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+            
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+        </nav>
+      
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+    
+  </ul>
+</nav>
+                  </div>
+                </div>
+              </div>
+            
+            
+              
+              <div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
+                <div class="md-sidebar__scrollwrap">
+                  <div class="md-sidebar__inner">
+                    
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1131" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.3.1 &nbsp; アルゴリズムプロセス
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1132" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.3.2 &nbsp; 効率の最適化
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1133" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.3.3 &nbsp; アルゴリズムの特性
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+                  </div>
+                </div>
+              </div>
+            
+          
+          
+            <div class="md-content" data-md-component="content">
+              <article class="md-content__inner md-typeset">
+                
+                  <!-- Tags -->
+
+
+<!-- Actions -->
+<!-- Actions -->
+
+
+  <!-- Edit button -->
+  
+    <a
+      href="https://github.com/krahets/hello-algo/tree/main/ja/docs/chapter_sorting/bubble_sort.md"
+      title="編集"
+      class="md-content__button md-icon"
+    >
+      
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
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+<!-- Page content -->
+<h1 id="113">11.3 &nbsp; バブルソート<a class="headerlink" href="#113" title="Permanent link">&para;</a></h1>
+<p><u>バブルソート</u>は、隣接する要素を継続的に比較し交換することで動作します。このプロセスは泡が底から上に上昇するようなものなので、「バブルソート」と名付けられました。</p>
+<p>下図に示すように、バブリングプロセスは要素交換を使用してシミュレートできます：配列の左端から開始して右に移動し、隣接する要素の各ペアを比較します。左の要素が右の要素より大きい場合は、それらを交換します。横断後、最大要素は配列の右端にバブルアップします。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:7"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">&lt;1&gt;</label><label for="__tabbed_1_2">&lt;2&gt;</label><label for="__tabbed_1_3">&lt;3&gt;</label><label for="__tabbed_1_4">&lt;4&gt;</label><label for="__tabbed_1_5">&lt;5&gt;</label><label for="__tabbed_1_6">&lt;6&gt;</label><label for="__tabbed_1_7">&lt;7&gt;</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<p><a class="glightbox" href="../bubble_sort.assets/bubble_operation_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Simulating bubble process using element swap" class="animation-figure" src="../bubble_sort.assets/bubble_operation_step1.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../bubble_sort.assets/bubble_operation_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="bubble_operation_step2" class="animation-figure" src="../bubble_sort.assets/bubble_operation_step2.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../bubble_sort.assets/bubble_operation_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="bubble_operation_step3" class="animation-figure" src="../bubble_sort.assets/bubble_operation_step3.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../bubble_sort.assets/bubble_operation_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="bubble_operation_step4" class="animation-figure" src="../bubble_sort.assets/bubble_operation_step4.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../bubble_sort.assets/bubble_operation_step5.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="bubble_operation_step5" class="animation-figure" src="../bubble_sort.assets/bubble_operation_step5.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../bubble_sort.assets/bubble_operation_step6.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="bubble_operation_step6" class="animation-figure" src="../bubble_sort.assets/bubble_operation_step6.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../bubble_sort.assets/bubble_operation_step7.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="bubble_operation_step7" class="animation-figure" src="../bubble_sort.assets/bubble_operation_step7.png" /></a></p>
+</div>
+</div>
+</div>
+<p align="center"> 図 11-4 &nbsp; Simulating bubble process using element swap </p>
+
+<h2 id="1131">11.3.1 &nbsp; アルゴリズムプロセス<a class="headerlink" href="#1131" title="Permanent link">&para;</a></h2>
+<p>配列の長さを<span class="arithmatex">\(n\)</span>とします。バブルソートのステップは下図に示されます：</p>
+<ol>
+<li>まず、<span class="arithmatex">\(n\)</span>個の要素に対して1回の「バブル」パスを実行し、<strong>最大要素を正しい位置に交換します</strong>。</li>
+<li>次に、残りの<span class="arithmatex">\(n - 1\)</span>個の要素に対して「バブル」パスを実行し、<strong>2番目に大きい要素を正しい位置に交換します</strong>。</li>
+<li>この方法で続行します；<span class="arithmatex">\(n - 1\)</span>回のパスの後、<strong>最大<span class="arithmatex">\(n - 1\)</span>個の要素が正しい位置に移動されます</strong>。</li>
+<li>残りの唯一の要素は**必ず**最小であるため、**さらなる**ソートは必要ありません。この時点で、配列はソートされます。</li>
+</ol>
+<p><a class="glightbox" href="../bubble_sort.assets/bubble_sort_overview.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Bubble sort process" class="animation-figure" src="../bubble_sort.assets/bubble_sort_overview.png" /></a></p>
+<p align="center"> 図 11-5 &nbsp; Bubble sort process </p>
+
+<p>コード例は以下の通りです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:14"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><input id="__tabbed_2_14" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label><label for="__tabbed_2_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">bubble_sort.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">bubble_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]):</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;バブルソート&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="c1"># 外側のループ：未ソート範囲は [0, i]</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>        <span class="c1"># 内側のループ：未ソート範囲 [0, i] の最大要素を範囲の右端に移動</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>        <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">i</span><span class="p">):</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>            <span class="k">if</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]:</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>                <span class="c1"># nums[j] と nums[j + 1] を交換</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>                <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">],</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="mi">1</span><span class="p">],</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">bubble_sort.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* バブルソート */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">bubbleSort</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// 外側ループ：未ソート範囲は[0, i]</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">        </span><span class="c1">// 内側ループ：未ソート範囲[0, i]内の最大要素を範囲の右端に交換</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">                </span><span class="c1">// nums[j]とnums[j + 1]を交換</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">                </span><span class="c1">// ここではstdのswapを使用</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">                </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">],</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]);</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">bubble_sort.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* バブルソート */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">bubbleSort</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// 外側ループ: 未ソート範囲は [0, i]</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">        </span><span class="c1">// 内側ループ: 未ソート範囲 [0, i] の最大要素を範囲の右端に交換</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">                </span><span class="c1">// nums[j] と nums[j + 1] を交換</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">                </span><span class="kt">int</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">                </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">                </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">bubble_sort.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">bubble_sort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">BubbleSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">bubble_sort.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">bubbleSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">bubble_sort.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">bubbleSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">bubble_sort.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">bubbleSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">bubble_sort.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">bubbleSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">bubble_sort.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">bubbleSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">bubble_sort.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">bubble_sort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">bubble_sort.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">bubbleSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">bubble_sort.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">bubbleSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">bubble_sort.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">bubble_sort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">bubble_sort.zig</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">bubbleSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h2 id="1132">11.3.2 &nbsp; 効率の最適化<a class="headerlink" href="#1132" title="Permanent link">&para;</a></h2>
+<p>「バブリング」のラウンド中に交換が発生しない場合、配列はすでにソートされているため、すぐに戻ることができます。これを検出するために、<code>flag</code>変数を追加できます；パスで交換が行われない場合は、フラグを設定して早期に戻ります。</p>
+<p>この最適化があっても、バブルソートの最悪時間計算量と平均時間計算量は<span class="arithmatex">\(O(n^2)\)</span>のままです。ただし、入力配列がすでにソートされている場合、最良ケース時間計算量は<span class="arithmatex">\(O(n)\)</span>まで低くなる可能性があります。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="3:14"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><input id="__tabbed_3_14" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label><label for="__tabbed_3_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">bubble_sort.py</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">bubble_sort_with_flag</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]):</span>
+<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;バブルソート（フラグによる最適化）&quot;&quot;&quot;</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a>    <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a>    <span class="c1"># 外側のループ：未ソート範囲は [0, i]</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a>        <span class="n">flag</span> <span class="o">=</span> <span class="kc">False</span>  <span class="c1"># フラグを初期化</span>
+<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a>        <span class="c1"># 内側のループ：未ソート範囲 [0, i] の最大要素を範囲の右端に移動</span>
+<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a>        <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">i</span><span class="p">):</span>
+<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a>            <span class="k">if</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]:</span>
+<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a>                <span class="c1"># nums[j] と nums[j + 1] を交換</span>
+<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a>                <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">],</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="mi">1</span><span class="p">],</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
+<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a>                <span class="n">flag</span> <span class="o">=</span> <span class="kc">True</span>  <span class="c1"># 要素を交換したことを記録</span>
+<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a>        <span class="k">if</span> <span class="ow">not</span> <span class="n">flag</span><span class="p">:</span>
+<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a>            <span class="k">break</span>  <span class="c1"># この回の「バブリング」で要素が交換されなかった場合、終了</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">bubble_sort.cpp</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* バブルソート（フラグ最適化版）*/</span>
+<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">bubbleSortWithFlag</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="c1">// 外側ループ：未ソート範囲は[0, i]</span>
+<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">        </span><span class="kt">bool</span><span class="w"> </span><span class="n">flag</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">false</span><span class="p">;</span><span class="w"> </span><span class="c1">// フラグを初期化</span>
+<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">        </span><span class="c1">// 内側ループ：未ソート範囲[0, i]内の最大要素を範囲の右端に交換</span>
+<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">])</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w">                </span><span class="c1">// nums[j]とnums[j + 1]を交換</span>
+<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="w">                </span><span class="c1">// ここではstdのswapを使用</span>
+<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="w">                </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">],</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]);</span>
+<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="w">                </span><span class="n">flag</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">true</span><span class="p">;</span><span class="w"> </span><span class="c1">// 交換された要素を記録</span>
+<a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">flag</span><span class="p">)</span>
+<a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span><span class="w"> </span><span class="c1">// この回の「バブリング」で要素が交換されなかった場合、終了</span>
+<a id="__codelineno-15-17" name="__codelineno-15-17" href="#__codelineno-15-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-18" name="__codelineno-15-18" href="#__codelineno-15-18"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">bubble_sort.java</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* バブルソート（フラグによる最適化） */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">bubbleSortWithFlag</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="c1">// 外側ループ: 未ソート範囲は [0, i]</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">        </span><span class="kt">boolean</span><span class="w"> </span><span class="n">flag</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">false</span><span class="p">;</span><span class="w"> </span><span class="c1">// フラグを初期化</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">        </span><span class="c1">// 内側ループ: 未ソート範囲 [0, i] の最大要素を範囲の右端に交換</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w">                </span><span class="c1">// nums[j] と nums[j + 1] を交換</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w">                </span><span class="kt">int</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="w">                </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="w">                </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w">                </span><span class="n">flag</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">true</span><span class="p">;</span><span class="w"> </span><span class="c1">// 交換された要素を記録</span>
+<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">flag</span><span class="p">)</span>
+<a id="__codelineno-16-17" name="__codelineno-16-17" href="#__codelineno-16-17"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span><span class="w"> </span><span class="c1">// この「バブリング」ラウンドで要素が交換されなかった場合、終了</span>
+<a id="__codelineno-16-18" name="__codelineno-16-18" href="#__codelineno-16-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-19" name="__codelineno-16-19" href="#__codelineno-16-19"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">bubble_sort.cs</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">bubble_sort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">BubbleSortWithFlag</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">bubble_sort.go</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">bubbleSortWithFlag</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">bubble_sort.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">bubbleSortWithFlag</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">bubble_sort.js</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">bubbleSortWithFlag</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">bubble_sort.ts</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">bubbleSortWithFlag</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">bubble_sort.dart</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">bubbleSortWithFlag</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">bubble_sort.rs</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">bubble_sort_with_flag</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">bubble_sort.c</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">bubbleSortWithFlag</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">bubble_sort.kt</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">bubbleSortWithFlag</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">bubble_sort.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">bubble_sort_with_flag</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">bubble_sort.zig</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">bubbleSortWithFlag</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h2 id="1133">11.3.3 &nbsp; アルゴリズムの特性<a class="headerlink" href="#1133" title="Permanent link">&para;</a></h2>
+<ul>
+<li><strong><span class="arithmatex">\(O(n^2)\)</span>の時間計算量、適応ソート。</strong> 各「バブリング」ラウンドは長さ<span class="arithmatex">\(n - 1\)</span>、<span class="arithmatex">\(n - 2\)</span>、<span class="arithmatex">\(\dots\)</span>、<span class="arithmatex">\(2\)</span>、<span class="arithmatex">\(1\)</span>の配列セグメントを横断し、合計は<span class="arithmatex">\((n - 1) n / 2\)</span>となります。<code>flag</code>最適化により、配列がすでにソートされている場合、最良ケース時間計算量は<span class="arithmatex">\(O(n)\)</span>に達する可能性があります。</li>
+<li><strong><span class="arithmatex">\(O(1)\)</span>の空間計算量、インプレースソート。</strong> ポインタ<span class="arithmatex">\(i\)</span>と<span class="arithmatex">\(j\)</span>によって定数量の追加空間のみが使用されます。</li>
+<li><strong>安定ソート。</strong> 等しい要素は「バブリング」中に交換されないため、元の順序が保持され、これは安定ソートになります。</li>
+</ul>
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index 000000000..c192f0a27
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+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/suggestions/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.2 &nbsp; 本書の使い方
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_introduction/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1181" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.8.1 &nbsp; アルゴリズムの過程
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1182" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.8.2 &nbsp; アルゴリズムの特徴
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1183" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.8.3 &nbsp; 均等分散を達成する方法
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
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+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
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+  
+
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+    </li>
+  
+
+              
+            
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+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
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+  
+  
+  
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+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
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+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
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+
+              
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+  
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+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
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+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
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+
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+
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+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
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+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
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+  
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+      
+        <li class="md-nav__item">
+  <a href="#1181" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.8.1 &nbsp; アルゴリズムの過程
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1182" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.8.2 &nbsp; アルゴリズムの特徴
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1183" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.8.3 &nbsp; 均等分散を達成する方法
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
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+    >
+      
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
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+<h1 id="118">11.8 &nbsp; バケットソート<a class="headerlink" href="#118" title="Permanent link">&para;</a></h1>
+<p>前述のソートアルゴリズムはすべて「比較ベースのソートアルゴリズム」で、値を比較することで要素をソートします。このようなソートアルゴリズムは <span class="arithmatex">\(O(n \log n)\)</span> より良い時間計算量を持つことはできません。次に、線形時間計算量を達成できるいくつかの「非比較ソートアルゴリズム」について議論します。</p>
+<p><u>バケットソート</u>は分割統治戦略の典型的な応用です。一連の順序付けられたバケットを設定し、各バケットがデータの範囲を含み、入力データをこれらのバケットに均等に分散させることで動作します。そして、各バケット内のデータを個別にソートします。最後に、すべてのバケットからのソート済みデータを順次マージして最終結果を生成します。</p>
+<h2 id="1181">11.8.1 &nbsp; アルゴリズムの過程<a class="headerlink" href="#1181" title="Permanent link">&para;</a></h2>
+<p>長さ <span class="arithmatex">\(n\)</span> の配列で、<span class="arithmatex">\([0, 1)\)</span> の範囲の浮動小数点数を考えてみます。バケットソートの過程は以下の図に示されています。</p>
+<ol>
+<li><span class="arithmatex">\(k\)</span> 個のバケットを初期化し、<span class="arithmatex">\(n\)</span> 個の要素をこれらの <span class="arithmatex">\(k\)</span> 個のバケットに分散させます。</li>
+<li>各バケットを個別にソートします（プログラミング言語の組み込みソート関数を使用）。</li>
+<li>最小から最大のバケットの順序で結果をマージします。</li>
+</ol>
+<p><a class="glightbox" href="../bucket_sort.assets/bucket_sort_overview.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="バケットソートアルゴリズムの過程" class="animation-figure" src="../bucket_sort.assets/bucket_sort_overview.png" /></a></p>
+<p align="center"> 図 11-13 &nbsp; バケットソートアルゴリズムの過程 </p>
+
+<p>コードは以下の通りです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:14"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><input id="__tabbed_1_14" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label><label for="__tabbed_1_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">bucket_sort.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">bucket_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">float</span><span class="p">]):</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;バケットソート&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># k = n/2 個のバケットを初期化、各バケットに平均2個の要素を配置することを期待</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="n">k</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="n">buckets</span> <span class="o">=</span> <span class="p">[[]</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">k</span><span class="p">)]</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="c1"># 1. 配列要素を各バケットに分散</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>    <span class="k">for</span> <span class="n">num</span> <span class="ow">in</span> <span class="n">nums</span><span class="p">:</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>        <span class="c1"># 入力データ範囲は [0, 1)、num * k を使用してインデックス範囲 [0, k-1] にマッピング</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>        <span class="n">i</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">num</span> <span class="o">*</span> <span class="n">k</span><span class="p">)</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>        <span class="c1"># num をバケット i に追加</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>        <span class="n">buckets</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>    <span class="c1"># 2. 各バケットをソート</span>
+<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>    <span class="k">for</span> <span class="n">bucket</span> <span class="ow">in</span> <span class="n">buckets</span><span class="p">:</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>        <span class="c1"># 組み込みソート関数を使用、他のソートアルゴリズムに置き換えることも可能</span>
+<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>        <span class="n">bucket</span><span class="o">.</span><span class="n">sort</span><span class="p">()</span>
+<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>    <span class="c1"># 3. バケットを走査して結果をマージ</span>
+<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>    <span class="n">i</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a>    <span class="k">for</span> <span class="n">bucket</span> <span class="ow">in</span> <span class="n">buckets</span><span class="p">:</span>
+<a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a>        <span class="k">for</span> <span class="n">num</span> <span class="ow">in</span> <span class="n">bucket</span><span class="p">:</span>
+<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a>            <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">num</span>
+<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a>            <span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">bucket_sort.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* バケットソート */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">bucketSort</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">float</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// k = n/2個のバケットを初期化、各バケットに2つの要素を割り当てることを期待</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">float</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">buckets</span><span class="p">(</span><span class="n">k</span><span class="p">);</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="c1">// 1. 配列要素を各バケットに分配</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">float</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">        </span><span class="c1">// 入力データ範囲は[0, 1)、num * kを使用してインデックス範囲[0, k-1]にマップ</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">k</span><span class="p">;</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">        </span><span class="c1">// bucket_idxバケットに数値を追加</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">        </span><span class="n">buckets</span><span class="p">[</span><span class="n">i</span><span class="p">].</span><span class="n">push_back</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">    </span><span class="c1">// 2. 各バケットをソート</span>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">float</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">bucket</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">        </span><span class="c1">// 組み込みソート関数を使用、他のソートアルゴリズムに置き換えることも可能</span>
+<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">        </span><span class="n">sort</span><span class="p">(</span><span class="n">bucket</span><span class="p">.</span><span class="n">begin</span><span class="p">(),</span><span class="w"> </span><span class="n">bucket</span><span class="p">.</span><span class="n">end</span><span class="p">());</span>
+<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w">    </span><span class="c1">// 3. バケットを走査して結果をマージ</span>
+<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">float</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">bucket</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">float</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a><span class="w">            </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">bucket_sort.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* バケットソート */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">bucketSort</span><span class="p">(</span><span class="kt">float</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// k = n/2 個のバケットを初期化、各バケットに期待される要素数は 2 個</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Float</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="n">buckets</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">k</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">        </span><span class="n">buckets</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">());</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">    </span><span class="c1">// 1. 配列要素を各バケットに分散</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">float</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">        </span><span class="c1">// 入力データ範囲は [0, 1)、num * k を使ってインデックス範囲 [0, k-1] にマッピング</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="p">(</span><span class="n">num</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">k</span><span class="p">);</span>
+<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">        </span><span class="c1">// num をバケット i に追加</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">        </span><span class="n">buckets</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">i</span><span class="p">).</span><span class="na">add</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">    </span><span class="c1">// 2. 各バケットをソート</span>
+<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Float</span><span class="o">&gt;</span><span class="w"> </span><span class="n">bucket</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w">        </span><span class="c1">// 組み込みソート関数を使用、他のソートアルゴリズムに置き換えることも可能</span>
+<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w">        </span><span class="n">Collections</span><span class="p">.</span><span class="na">sort</span><span class="p">(</span><span class="n">bucket</span><span class="p">);</span>
+<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="w">    </span><span class="c1">// 3. バケットを走査して結果をマージ</span>
+<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Float</span><span class="o">&gt;</span><span class="w"> </span><span class="n">bucket</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">buckets</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">float</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">bucket</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a><span class="w">            </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">++]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-2-27" name="__codelineno-2-27" href="#__codelineno-2-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-28" name="__codelineno-2-28" href="#__codelineno-2-28"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">bucket_sort.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">bucket_sort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">BucketSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">bucket_sort.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">bucketSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">bucket_sort.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">bucketSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">bucket_sort.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">bucketSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">bucket_sort.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">bucketSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">bucket_sort.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">bucketSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">bucket_sort.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">bucket_sort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">bucket_sort.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">bucketSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">bucket_sort.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">bucketSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">bucket_sort.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">bucket_sort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">bucket_sort.zig</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">bucketSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h2 id="1182">11.8.2 &nbsp; アルゴリズムの特徴<a class="headerlink" href="#1182" title="Permanent link">&para;</a></h2>
+<p>バケットソートは非常に大きなデータセットの処理に適しています。例えば、入力データに100万個の要素が含まれ、システムメモリの制限によりすべてのデータを同時にロードできない場合、データを1,000個のバケットに分割し、各バケットを個別にソートしてから結果をマージできます。</p>
+<ul>
+<li><strong>時間計算量は <span class="arithmatex">\(O(n + k)\)</span></strong>：要素がバケット間で均等に分散されていると仮定すると、各バケット内の要素数は <span class="arithmatex">\(n/k\)</span> です。単一のバケットのソートに <span class="arithmatex">\(O(n/k \log(n/k))\)</span> 時間がかかると仮定すると、すべてのバケットのソートに <span class="arithmatex">\(O(n \log(n/k))\)</span> 時間がかかります。<strong>バケット数 <span class="arithmatex">\(k\)</span> が比較的大きいとき、時間計算量は <span class="arithmatex">\(O(n)\)</span> に近づきます</strong>。結果のマージには、すべてのバケットと要素を走査する必要があり、<span class="arithmatex">\(O(n + k)\)</span> 時間がかかります。最悪の場合、すべてのデータが単一のバケットに分散され、そのバケットのソートには <span class="arithmatex">\(O(n^2)\)</span> 時間がかかります。</li>
+<li><strong>空間計算量は <span class="arithmatex">\(O(n + k)\)</span>、非インプレースソート</strong>：<span class="arithmatex">\(k\)</span> 個のバケットと合計 <span class="arithmatex">\(n\)</span> 個の要素のための追加スペースが必要です。</li>
+<li>バケットソートが安定かどうかは、各バケット内で使用されるソートアルゴリズムが安定かどうかに依存します。</li>
+</ul>
+<h2 id="1183">11.8.3 &nbsp; 均等分散を達成する方法<a class="headerlink" href="#1183" title="Permanent link">&para;</a></h2>
+<p>バケットソートの理論的時間計算量は <span class="arithmatex">\(O(n)\)</span> に達することができます。<strong>重要なことは、すべてのバケットに要素を均等に分散させることです</strong>。実世界のデータはしばしば均一に分散されていないからです。例えば、eBayのすべての商品を価格範囲で10個のバケットに均等に分散させたいとします。しかし、商品価格の分散は均等でない可能性があり、100ドル未満の商品が多く、500ドル以上の商品が少ないかもしれません。価格範囲を均等に10分割すると、各バケットの商品数の差が大きくなります。</p>
+<p>均等分散を達成するために、最初におおよその境界を設定して、データを3つのバケットに大まかに分割できます。<strong>分散が完了した後、より多くのアイテムを持つバケットをさらに3つのバケットに分割し、すべてのバケットの要素数がほぼ等しくなるまで続けます</strong>。</p>
+<p>以下の図に示すように、この方法は本質的に再帰木を構築し、葉ノードの要素数ができるだけ均等になることを目指します。もちろん、各ラウンドでデータを3つのバケットに分割する必要はありません - 分割戦略はデータの独特な特性に適応的に調整できます。</p>
+<p><a class="glightbox" href="../bucket_sort.assets/scatter_in_buckets_recursively.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="バケットの再帰的分割" class="animation-figure" src="../bucket_sort.assets/scatter_in_buckets_recursively.png" /></a></p>
+<p align="center"> 図 11-14 &nbsp; バケットの再帰的分割 </p>
+
+<p>商品価格の確率分布を事前に知っている場合、<strong>データの確率分布に基づいて各バケットの価格境界を設定できます</strong>。データ分布を具体的に計算する必要は必ずしもなく、代わりに確率モデルを使用してデータ特性に基づいて近似できることに注意してください。</p>
+<p>以下の図に示すように、商品価格が正規分布に従うと仮定すると、バケット間でアイテムの分散のバランスを取るために合理的な価格区間を定義できます。</p>
+<p><a class="glightbox" href="../bucket_sort.assets/scatter_in_buckets_distribution.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="確率分布に基づくバケット分割" class="animation-figure" src="../bucket_sort.assets/scatter_in_buckets_distribution.png" /></a></p>
+<p align="center"> 図 11-15 &nbsp; 確率分布に基づくバケット分割 </p>
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+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1191" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.9.1 &nbsp; 簡単な実装
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1192" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.9.2 &nbsp; 完全な実装
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1193" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.9.3 &nbsp; アルゴリズムの特徴
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1194" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.9.4 &nbsp; 制限事項
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+    
+    
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+      
+        <li class="md-nav__item">
+  <a href="#1191" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.9.1 &nbsp; 簡単な実装
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1192" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.9.2 &nbsp; 完全な実装
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1193" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.9.3 &nbsp; アルゴリズムの特徴
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1194" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.9.4 &nbsp; 制限事項
+    </span>
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+<h1 id="119">11.9 &nbsp; 計数ソート<a class="headerlink" href="#119" title="Permanent link">&para;</a></h1>
+<p><u>計数ソート</u>は要素の数をカウントすることでソートを実現し、通常は整数配列に適用されます。</p>
+<h2 id="1191">11.9.1 &nbsp; 簡単な実装<a class="headerlink" href="#1191" title="Permanent link">&para;</a></h2>
+<p>簡単な例から始めましょう。長さ <span class="arithmatex">\(n\)</span> の配列 <code>nums</code> が与えられ、すべての要素が「非負整数」である場合、計数ソートの全体的な過程は以下の図に示されています。</p>
+<ol>
+<li>配列を走査して最大数を見つけ、それを <span class="arithmatex">\(m\)</span> とし、長さ <span class="arithmatex">\(m + 1\)</span> の補助配列 <code>counter</code> を作成します。</li>
+<li><strong><code>counter</code> を使用して <code>nums</code> 内の各数の出現回数をカウントします</strong>。ここで <code>counter[num]</code> は数 <code>num</code> の出現回数に対応します。カウント方法は簡単で、<code>nums</code> を走査し（現在の数を <code>num</code> とする）、各ラウンドで <code>counter[num]</code> を <span class="arithmatex">\(1\)</span> 増やします。</li>
+<li><strong><code>counter</code> のインデックスは自然に順序付けられているため、すべての数は本質的にすでにソートされています</strong>。次に、<code>counter</code> を走査し、出現順に <code>nums</code> を昇順で埋めます。</li>
+</ol>
+<p><a class="glightbox" href="../counting_sort.assets/counting_sort_overview.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="計数ソートの過程" class="animation-figure" src="../counting_sort.assets/counting_sort_overview.png" /></a></p>
+<p align="center"> 図 11-16 &nbsp; 計数ソートの過程 </p>
+
+<p>コードは以下の通りです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:14"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><input id="__tabbed_1_14" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label><label for="__tabbed_1_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">counting_sort.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">counting_sort_naive</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]):</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;計数ソート&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># シンプルな実装、オブジェクトのソートには使用できない</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="c1"># 1. 配列内の最大要素 m を統計</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="n">m</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="k">for</span> <span class="n">num</span> <span class="ow">in</span> <span class="n">nums</span><span class="p">:</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>        <span class="n">m</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">m</span><span class="p">,</span> <span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>    <span class="c1"># 2. 各数字の出現回数を統計</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>    <span class="c1"># counter[num] は num の出現回数を表す</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>    <span class="n">counter</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>    <span class="k">for</span> <span class="n">num</span> <span class="ow">in</span> <span class="n">nums</span><span class="p">:</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>        <span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>    <span class="c1"># 3. counter を走査し、各要素を元の配列 nums に埋め戻し</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>    <span class="n">i</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>    <span class="k">for</span> <span class="n">num</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>        <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="p">]):</span>
+<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>            <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">num</span>
+<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a>            <span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">counting_sort.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* カウントソート */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="c1">// 簡単な実装、オブジェクトのソートには使用できない</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="kt">void</span><span class="w"> </span><span class="nf">countingSortNaive</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="c1">// 1. 配列の最大要素mを統計</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">        </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max</span><span class="p">(</span><span class="n">m</span><span class="p">,</span><span class="w"> </span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">    </span><span class="c1">// 2. 各数字の出現回数を統計</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">    </span><span class="c1">// counter[num]はnumの出現回数を表す</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">counter</span><span class="p">(</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">        </span><span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="p">]</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">    </span><span class="c1">// 3. counterを走査し、各要素を元の配列numsに戻す</span>
+<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">num</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="p">];</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="w">            </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">counting_sort.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 計数ソート */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="c1">// 簡単な実装、オブジェクトのソートには使用できない</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="kt">void</span><span class="w"> </span><span class="nf">countingSortNaive</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="c1">// 1. 配列の最大要素 m を統計</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">        </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">max</span><span class="p">(</span><span class="n">m</span><span class="p">,</span><span class="w"> </span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">    </span><span class="c1">// 2. 各数字の出現回数を統計</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">    </span><span class="c1">// counter[num] は num の出現回数を表す</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">    </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">counter</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">        </span><span class="n">counter</span><span class="o">[</span><span class="n">num</span><span class="o">]++</span><span class="p">;</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">    </span><span class="c1">// 3. counter を走査し、各要素を元の配列 nums に戻す</span>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">num</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">counter</span><span class="o">[</span><span class="n">num</span><span class="o">]</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w">            </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">counting_sort.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">counting_sort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">CountingSortNaive</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">counting_sort.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">countingSortNaive</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">counting_sort.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">countingSortNaive</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">counting_sort.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">countingSortNaive</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">counting_sort.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">countingSortNaive</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">counting_sort.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">countingSortNaive</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">counting_sort.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">counting_sort_naive</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">counting_sort.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">countingSortNaive</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">counting_sort.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">countingSortNaive</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">counting_sort.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">counting_sort_naive</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">counting_sort.zig</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">countingSortNaive</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<div class="admonition note">
+<p class="admonition-title">計数ソートとバケットソートの関係</p>
+<p>バケットソートの観点から、計数ソートにおける計数配列 <code>counter</code> の各インデックスをバケットと考え、カウントの過程を要素を対応するバケットに分散させることと考えることができます。本質的に、計数ソートは整数データのためのバケットソートの特別なケースです。</p>
+</div>
+<h2 id="1192">11.9.2 &nbsp; 完全な実装<a class="headerlink" href="#1192" title="Permanent link">&para;</a></h2>
+<p>注意深い読者は気付くかもしれませんが、<strong>入力データがオブジェクトの場合、上記の手順 <code>3.</code> は無効です</strong>。入力データが商品オブジェクトで、価格（クラスメンバ変数）で商品をソートしたいとします。しかし、上記のアルゴリズムは結果としてソート済みの価格のみを提供できます。</p>
+<p>では、元のデータのソート結果をどのように取得できるでしょうか？まず、<code>counter</code> の「前置和」を計算します。名前が示すように、インデックス <code>i</code> での前置和 <code>prefix[i]</code> は、配列の最初の <code>i</code> 個の要素の和に等しいです：</p>
+<div class="arithmatex">\[
+\text{prefix}[i] = \sum_{j=0}^i \text{counter[j]}
+\]</div>
+<p><strong>前置和には明確な意味があります。<code>prefix[num] - 1</code> は結果配列 <code>res</code> における要素 <code>num</code> の最後の出現のインデックスを表します</strong>。この情報は重要で、各要素が結果配列のどこに現れるべきかを教えてくれます。次に、元の配列 <code>nums</code> の各要素 <code>num</code> を逆順で走査し、各反復で以下の2つの手順を実行します。</p>
+<ol>
+<li>インデックス <code>prefix[num] - 1</code> で配列 <code>res</code> に <code>num</code> を埋めます。</li>
+<li>前置和 <code>prefix[num]</code> を <span class="arithmatex">\(1\)</span> 減らして、<code>num</code> を配置する次のインデックスを取得します。</li>
+</ol>
+<p>走査後、配列 <code>res</code> にはソートされた結果が含まれ、最後に <code>res</code> が元の配列 <code>nums</code> を置き換えます。完全な計数ソートの過程は以下の図に示されています。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:8"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">&lt;1&gt;</label><label for="__tabbed_2_2">&lt;2&gt;</label><label for="__tabbed_2_3">&lt;3&gt;</label><label for="__tabbed_2_4">&lt;4&gt;</label><label for="__tabbed_2_5">&lt;5&gt;</label><label for="__tabbed_2_6">&lt;6&gt;</label><label for="__tabbed_2_7">&lt;7&gt;</label><label for="__tabbed_2_8">&lt;8&gt;</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<p><a class="glightbox" href="../counting_sort.assets/counting_sort_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="計数ソートの過程" class="animation-figure" src="../counting_sort.assets/counting_sort_step1.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../counting_sort.assets/counting_sort_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="counting_sort_step2" class="animation-figure" src="../counting_sort.assets/counting_sort_step2.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../counting_sort.assets/counting_sort_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="counting_sort_step3" class="animation-figure" src="../counting_sort.assets/counting_sort_step3.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../counting_sort.assets/counting_sort_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="counting_sort_step4" class="animation-figure" src="../counting_sort.assets/counting_sort_step4.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../counting_sort.assets/counting_sort_step5.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="counting_sort_step5" class="animation-figure" src="../counting_sort.assets/counting_sort_step5.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../counting_sort.assets/counting_sort_step6.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="counting_sort_step6" class="animation-figure" src="../counting_sort.assets/counting_sort_step6.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../counting_sort.assets/counting_sort_step7.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="counting_sort_step7" class="animation-figure" src="../counting_sort.assets/counting_sort_step7.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../counting_sort.assets/counting_sort_step8.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="counting_sort_step8" class="animation-figure" src="../counting_sort.assets/counting_sort_step8.png" /></a></p>
+</div>
+</div>
+</div>
+<p align="center"> 図 11-17 &nbsp; 計数ソートの過程 </p>
+
+<p>計数ソートの実装コードは以下の通りです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="3:14"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><input id="__tabbed_3_14" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label><label for="__tabbed_3_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">counting_sort.py</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">counting_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]):</span>
+<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;計数ソート&quot;&quot;&quot;</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a>    <span class="c1"># 完全な実装、オブジェクトのソートが可能で、安定ソート</span>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a>    <span class="c1"># 1. 配列内の最大要素 m を統計</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a>    <span class="n">m</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a>    <span class="c1"># 2. 各数字の出現回数を統計</span>
+<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a>    <span class="c1"># counter[num] は num の出現回数を表す</span>
+<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a>    <span class="n">counter</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="n">m</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a>    <span class="k">for</span> <span class="n">num</span> <span class="ow">in</span> <span class="n">nums</span><span class="p">:</span>
+<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a>        <span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a>    <span class="c1"># 3. counter の前置和を計算し、「出現回数」を「末尾インデックス」に変換</span>
+<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a>    <span class="c1"># counter[num]-1 は res において num が最後に出現するインデックス</span>
+<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">m</span><span class="p">):</span>
+<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a>        <span class="n">counter</span><span class="p">[</span><span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">+=</span> <span class="n">counter</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a>    <span class="c1"># 4. nums を逆順に走査し、各要素を結果配列 res に配置</span>
+<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a>    <span class="c1"># 結果を記録するための配列 res を初期化</span>
+<a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a>    <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
+<a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a>    <span class="n">res</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">n</span>
+<a id="__codelineno-14-19" name="__codelineno-14-19" href="#__codelineno-14-19"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-14-20" name="__codelineno-14-20" href="#__codelineno-14-20"></a>        <span class="n">num</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+<a id="__codelineno-14-21" name="__codelineno-14-21" href="#__codelineno-14-21"></a>        <span class="n">res</span><span class="p">[</span><span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="p">]</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">num</span>  <span class="c1"># num を対応するインデックスに配置</span>
+<a id="__codelineno-14-22" name="__codelineno-14-22" href="#__codelineno-14-22"></a>        <span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="p">]</span> <span class="o">-=</span> <span class="mi">1</span>  <span class="c1"># 前置和を1減らし、num を配置する次のインデックスを取得</span>
+<a id="__codelineno-14-23" name="__codelineno-14-23" href="#__codelineno-14-23"></a>    <span class="c1"># 結果配列 res を使用して元の配列 nums を上書き</span>
+<a id="__codelineno-14-24" name="__codelineno-14-24" href="#__codelineno-14-24"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
+<a id="__codelineno-14-25" name="__codelineno-14-25" href="#__codelineno-14-25"></a>        <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">counting_sort.cpp</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* カウントソート */</span>
+<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="c1">// 完全な実装、オブジェクトのソートが可能で安定ソート</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="kt">void</span><span class="w"> </span><span class="nf">countingSort</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="c1">// 1. 配列の最大要素mを統計</span>
+<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">        </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max</span><span class="p">(</span><span class="n">m</span><span class="p">,</span><span class="w"> </span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w">    </span><span class="c1">// 2. 各数字の出現回数を統計</span>
+<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="w">    </span><span class="c1">// counter[num]はnumの出現回数を表す</span>
+<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">counter</span><span class="p">(</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="w">        </span><span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="p">]</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="w">    </span><span class="c1">// 3. counterの前缀和を計算し、「出現回数」を「末尾インデックス」に変換</span>
+<a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a><span class="w">    </span><span class="c1">// counter[num]-1はnumがresで現れる最後のインデックス</span>
+<a id="__codelineno-15-17" name="__codelineno-15-17" href="#__codelineno-15-17"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-18" name="__codelineno-15-18" href="#__codelineno-15-18"></a><span class="w">        </span><span class="n">counter</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">counter</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-15-19" name="__codelineno-15-19" href="#__codelineno-15-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-20" name="__codelineno-15-20" href="#__codelineno-15-20"></a><span class="w">    </span><span class="c1">// 4. numsを逆順で走査し、各要素を結果配列resに配置</span>
+<a id="__codelineno-15-21" name="__codelineno-15-21" href="#__codelineno-15-21"></a><span class="w">    </span><span class="c1">// 結果を記録する配列resを初期化</span>
+<a id="__codelineno-15-22" name="__codelineno-15-22" href="#__codelineno-15-22"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
+<a id="__codelineno-15-23" name="__codelineno-15-23" href="#__codelineno-15-23"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">(</span><span class="n">n</span><span class="p">);</span>
+<a id="__codelineno-15-24" name="__codelineno-15-24" href="#__codelineno-15-24"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-25" name="__codelineno-15-25" href="#__codelineno-15-25"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-15-26" name="__codelineno-15-26" href="#__codelineno-15-26"></a><span class="w">        </span><span class="n">res</span><span class="p">[</span><span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="p">]</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span><span class="w"> </span><span class="c1">// numを対応するインデックスに配置</span>
+<a id="__codelineno-15-27" name="__codelineno-15-27" href="#__codelineno-15-27"></a><span class="w">        </span><span class="n">counter</span><span class="p">[</span><span class="n">num</span><span class="p">]</span><span class="o">--</span><span class="p">;</span><span class="w">              </span><span class="c1">// 前缀和を1減らし、numを配置する次のインデックスを取得</span>
+<a id="__codelineno-15-28" name="__codelineno-15-28" href="#__codelineno-15-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-29" name="__codelineno-15-29" href="#__codelineno-15-29"></a><span class="w">    </span><span class="c1">// 結果配列resで元の配列numsを上書き</span>
+<a id="__codelineno-15-30" name="__codelineno-15-30" href="#__codelineno-15-30"></a><span class="w">    </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-15-31" name="__codelineno-15-31" href="#__codelineno-15-31"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">counting_sort.java</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 計数ソート */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="c1">// 完全な実装、オブジェクトをソートでき、安定ソート</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="kt">void</span><span class="w"> </span><span class="nf">countingSort</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="c1">// 1. 配列の最大要素 m を統計</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">        </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">max</span><span class="p">(</span><span class="n">m</span><span class="p">,</span><span class="w"> </span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w">    </span><span class="c1">// 2. 各数字の出現回数を統計</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w">    </span><span class="c1">// counter[num] は num の出現回数を表す</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="w">    </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">counter</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">m</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w">        </span><span class="n">counter</span><span class="o">[</span><span class="n">num</span><span class="o">]++</span><span class="p">;</span>
+<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="w">    </span><span class="c1">// 3. counter の累積和を計算し、「出現回数」を「尻尾インデックス」に変換</span>
+<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a><span class="w">    </span><span class="c1">// counter[num]-1 は res 内で num が出現する最後のインデックス</span>
+<a id="__codelineno-16-17" name="__codelineno-16-17" href="#__codelineno-16-17"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-18" name="__codelineno-16-18" href="#__codelineno-16-18"></a><span class="w">        </span><span class="n">counter</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">counter</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-16-19" name="__codelineno-16-19" href="#__codelineno-16-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-20" name="__codelineno-16-20" href="#__codelineno-16-20"></a><span class="w">    </span><span class="c1">// 4. nums を逆順に走査し、各要素を結果配列 res に配置</span>
+<a id="__codelineno-16-21" name="__codelineno-16-21" href="#__codelineno-16-21"></a><span class="w">    </span><span class="c1">// 結果を記録する配列 res を初期化</span>
+<a id="__codelineno-16-22" name="__codelineno-16-22" href="#__codelineno-16-22"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="p">;</span>
+<a id="__codelineno-16-23" name="__codelineno-16-23" href="#__codelineno-16-23"></a><span class="w">    </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">n</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-16-24" name="__codelineno-16-24" href="#__codelineno-16-24"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-25" name="__codelineno-16-25" href="#__codelineno-16-25"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-16-26" name="__codelineno-16-26" href="#__codelineno-16-26"></a><span class="w">        </span><span class="n">res</span><span class="o">[</span><span class="n">counter</span><span class="o">[</span><span class="n">num</span><span class="o">]</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span><span class="w"> </span><span class="c1">// num を対応するインデックスに配置</span>
+<a id="__codelineno-16-27" name="__codelineno-16-27" href="#__codelineno-16-27"></a><span class="w">        </span><span class="n">counter</span><span class="o">[</span><span class="n">num</span><span class="o">]--</span><span class="p">;</span><span class="w"> </span><span class="c1">// 累積和を 1 減算し、num を配置する次のインデックスを取得</span>
+<a id="__codelineno-16-28" name="__codelineno-16-28" href="#__codelineno-16-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-29" name="__codelineno-16-29" href="#__codelineno-16-29"></a><span class="w">    </span><span class="c1">// 結果配列 res を使って元の配列 nums を上書き</span>
+<a id="__codelineno-16-30" name="__codelineno-16-30" href="#__codelineno-16-30"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-31" name="__codelineno-16-31" href="#__codelineno-16-31"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">res</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-16-32" name="__codelineno-16-32" href="#__codelineno-16-32"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-33" name="__codelineno-16-33" href="#__codelineno-16-33"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">counting_sort.cs</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">counting_sort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">CountingSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">counting_sort.go</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">countingSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">counting_sort.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">countingSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">counting_sort.js</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">countingSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">counting_sort.ts</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">countingSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">counting_sort.dart</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">countingSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">counting_sort.rs</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">counting_sort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">counting_sort.c</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">countingSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">counting_sort.kt</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">countingSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">counting_sort.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">counting_sort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">counting_sort.zig</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">countingSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h2 id="1193">11.9.3 &nbsp; アルゴリズムの特徴<a class="headerlink" href="#1193" title="Permanent link">&para;</a></h2>
+<ul>
+<li><strong>時間計算量は <span class="arithmatex">\(O(n + m)\)</span>、非適応ソート</strong>：<code>nums</code> と <code>counter</code> の走査が含まれ、どちらも線形時間を使用します。一般的に、<span class="arithmatex">\(n \gg m\)</span> であり、時間計算量は <span class="arithmatex">\(O(n)\)</span> に近づきます。</li>
+<li><strong>空間計算量は <span class="arithmatex">\(O(n + m)\)</span>、非インプレースソート</strong>：長さ <span class="arithmatex">\(n\)</span> の配列 <code>res</code> と長さ <span class="arithmatex">\(m\)</span> の配列 <code>counter</code> をそれぞれ使用します。</li>
+<li><strong>安定ソート</strong>：要素が「右から左」の順序で <code>res</code> に埋められるため、<code>nums</code> の走査を逆順にすることで、等しい要素間の相対位置の変化を防ぎ、安定したソートを実現できます。実際、<code>nums</code> を順番に走査しても正しいソート結果を生成できますが、結果は不安定です。</li>
+</ul>
+<h2 id="1194">11.9.4 &nbsp; 制限事項<a class="headerlink" href="#1194" title="Permanent link">&para;</a></h2>
+<p>今までに、計数ソートは非常に巧妙だと感じるかもしれません。単に量をカウントするだけで効率的なソートを実現できるからです。しかし、計数ソートを使用するための前提条件は比較的厳しいです。</p>
+<p><strong>計数ソートは非負整数にのみ適用できます</strong>。他のタイプのデータに適用したい場合、これらのデータが要素の元の順序を変更することなく非負整数に変換できることを保証する必要があります。例えば、負の整数を含む配列の場合、最初にすべての数に定数を加えて、すべてを正の数に変換し、ソート完了後に元に戻すことができます。</p>
+<p><strong>計数ソートは値の範囲が小さい大きなデータセットに適しています</strong>。例えば、上記の例では、<span class="arithmatex">\(m\)</span> は大きすぎるべきではありません。そうでなければ、あまりにも多くのスペースを占有してしまいます。そして <span class="arithmatex">\(n \ll m\)</span> の場合、計数ソートは <span class="arithmatex">\(O(m)\)</span> 時間を使用し、<span class="arithmatex">\(O(n \log n)\)</span> ソートアルゴリズムより遅い可能性があります。</p>
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+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1171" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.7.1 &nbsp; アルゴリズムの流れ
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1172" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.7.2 &nbsp; アルゴリズムの特徴
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_19" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_reference/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9 3v15h3V3H9m3 2 4 13 3-1-4-13-3 1M5 5v13h3V5H5M3 19v2h18v-2H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    参考文献
+  </span>
+  
+
+            </a>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_19_label" aria-expanded="false">
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+            参考文献
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+      
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+</nav>
+                  </div>
+                </div>
+              </div>
+            
+            
+              
+              <div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
+                <div class="md-sidebar__scrollwrap">
+                  <div class="md-sidebar__inner">
+                    
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1171" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.7.1 &nbsp; アルゴリズムの流れ
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1172" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.7.2 &nbsp; アルゴリズムの特徴
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+                  </div>
+                </div>
+              </div>
+            
+          
+          
+            <div class="md-content" data-md-component="content">
+              <article class="md-content__inner md-typeset">
+                
+                  <!-- Tags -->
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+<!-- Actions -->
+<!-- Actions -->
+
+
+  <!-- Edit button -->
+  
+    <a
+      href="https://github.com/krahets/hello-algo/tree/main/ja/docs/chapter_sorting/heap_sort.md"
+      title="編集"
+      class="md-content__button md-icon"
+    >
+      
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
+    </a>
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+  <!-- View button -->
+  
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+<!-- Page content -->
+<h1 id="117">11.7 &nbsp; ヒープソート<a class="headerlink" href="#117" title="Permanent link">&para;</a></h1>
+<div class="admonition tip">
+<p class="admonition-title">Tip</p>
+<p>この節を読む前に、「ヒープ」の章を必ず完了させてください。</p>
+</div>
+<p><u>ヒープソート</u>は、ヒープデータ構造に基づく効率的なソートアルゴリズムです。すでに学習した「ヒープの構築」と「要素の抽出」操作を使用してヒープソートを実装できます。</p>
+<ol>
+<li>配列を入力し、最小ヒープを構築します。ここで、最小要素がヒープの頂上に位置します。</li>
+<li>継続的に抽出操作を実行し、抽出された要素を順次記録して、最小から最大までのソート済みリストを取得します。</li>
+</ol>
+<p>上記の方法は実現可能ですが、ポップされた要素を格納するための追加の配列が必要で、やや空間を消費します。実際には、通常、より優雅な実装を使用します。</p>
+<h2 id="1171">11.7.1 &nbsp; アルゴリズムの流れ<a class="headerlink" href="#1171" title="Permanent link">&para;</a></h2>
+<p>配列の長さを <span class="arithmatex">\(n\)</span> とすると、ヒープソートの過程は以下の通りです。</p>
+<ol>
+<li>配列を入力し、最大ヒープを構築します。この手順の後、最大要素がヒープの頂上に位置します。</li>
+<li>ヒープの頂上要素（最初の要素）とヒープの底部要素（最後の要素）を交換します。この交換の後、ヒープの長さを <span class="arithmatex">\(1\)</span> 減らし、ソート済み要素の数を <span class="arithmatex">\(1\)</span> 増やします。</li>
+<li>ヒープの頂上から開始して、上から下へのsift-down操作を実行します。sift-downの後、ヒープの性質が復元されます。</li>
+<li>手順 <code>2.</code> と <code>3.</code> を繰り返します。<span class="arithmatex">\(n - 1\)</span> ラウンドループして、配列のソートを完了します。</li>
+</ol>
+<div class="admonition tip">
+<p class="admonition-title">Tip</p>
+<p>実際、要素抽出操作も手順 <code>2.</code> と <code>3.</code> を含み、抽出された要素をヒープから削除する追加の手順があります。</p>
+</div>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:12"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">&lt;1&gt;</label><label for="__tabbed_1_2">&lt;2&gt;</label><label for="__tabbed_1_3">&lt;3&gt;</label><label for="__tabbed_1_4">&lt;4&gt;</label><label for="__tabbed_1_5">&lt;5&gt;</label><label for="__tabbed_1_6">&lt;6&gt;</label><label for="__tabbed_1_7">&lt;7&gt;</label><label for="__tabbed_1_8">&lt;8&gt;</label><label for="__tabbed_1_9">&lt;9&gt;</label><label for="__tabbed_1_10">&lt;10&gt;</label><label for="__tabbed_1_11">&lt;11&gt;</label><label for="__tabbed_1_12">&lt;12&gt;</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<p><a class="glightbox" href="../heap_sort.assets/heap_sort_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="ヒープソートの過程" class="animation-figure" src="../heap_sort.assets/heap_sort_step1.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../heap_sort.assets/heap_sort_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_sort_step2" class="animation-figure" src="../heap_sort.assets/heap_sort_step2.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../heap_sort.assets/heap_sort_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_sort_step3" class="animation-figure" src="../heap_sort.assets/heap_sort_step3.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../heap_sort.assets/heap_sort_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_sort_step4" class="animation-figure" src="../heap_sort.assets/heap_sort_step4.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../heap_sort.assets/heap_sort_step5.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_sort_step5" class="animation-figure" src="../heap_sort.assets/heap_sort_step5.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../heap_sort.assets/heap_sort_step6.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_sort_step6" class="animation-figure" src="../heap_sort.assets/heap_sort_step6.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../heap_sort.assets/heap_sort_step7.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_sort_step7" class="animation-figure" src="../heap_sort.assets/heap_sort_step7.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../heap_sort.assets/heap_sort_step8.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_sort_step8" class="animation-figure" src="../heap_sort.assets/heap_sort_step8.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../heap_sort.assets/heap_sort_step9.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_sort_step9" class="animation-figure" src="../heap_sort.assets/heap_sort_step9.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../heap_sort.assets/heap_sort_step10.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_sort_step10" class="animation-figure" src="../heap_sort.assets/heap_sort_step10.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../heap_sort.assets/heap_sort_step11.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_sort_step11" class="animation-figure" src="../heap_sort.assets/heap_sort_step11.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../heap_sort.assets/heap_sort_step12.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="heap_sort_step12" class="animation-figure" src="../heap_sort.assets/heap_sort_step12.png" /></a></p>
+</div>
+</div>
+</div>
+<p align="center"> 図 11-12 &nbsp; ヒープソートの過程 </p>
+
+<p>コードの実装では、「ヒープ」の章からのsift-down関数 <code>sift_down()</code> を使用しました。最大要素が抽出されるにつれてヒープの長さが減少するため、<code>sift_down()</code> 関数に長さパラメータ <span class="arithmatex">\(n\)</span> を追加して、ヒープの現在の有効長を指定する必要があることに注意することが重要です。コードは以下の通りです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:14"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><input id="__tabbed_2_14" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label><label for="__tabbed_2_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">heap_sort.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">sift_down</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">n</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;ヒープの長さが n、ノード i から上から下へヒープ化を開始&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="k">while</span> <span class="kc">True</span><span class="p">:</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>        <span class="c1"># i、l、r の中で最大のノードを判定し、ma とする</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>        <span class="n">l</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">1</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>        <span class="n">r</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">2</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>        <span class="n">ma</span> <span class="o">=</span> <span class="n">i</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>        <span class="k">if</span> <span class="n">l</span> <span class="o">&lt;</span> <span class="n">n</span> <span class="ow">and</span> <span class="n">nums</span><span class="p">[</span><span class="n">l</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">nums</span><span class="p">[</span><span class="n">ma</span><span class="p">]:</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>            <span class="n">ma</span> <span class="o">=</span> <span class="n">l</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>        <span class="k">if</span> <span class="n">r</span> <span class="o">&lt;</span> <span class="n">n</span> <span class="ow">and</span> <span class="n">nums</span><span class="p">[</span><span class="n">r</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">nums</span><span class="p">[</span><span class="n">ma</span><span class="p">]:</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>            <span class="n">ma</span> <span class="o">=</span> <span class="n">r</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>        <span class="c1"># ノード i が最大または l、r のインデックスが範囲外の場合、さらなるヒープ化は不要、ループを抜ける</span>
+<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>        <span class="k">if</span> <span class="n">ma</span> <span class="o">==</span> <span class="n">i</span><span class="p">:</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>            <span class="k">break</span>
+<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>        <span class="c1"># 2つのノードを交換</span>
+<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>        <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">nums</span><span class="p">[</span><span class="n">ma</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">ma</span><span class="p">],</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>        <span class="c1"># 下向きにヒープ化をループ</span>
+<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a>        <span class="n">i</span> <span class="o">=</span> <span class="n">ma</span>
+<a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a>
+<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a><span class="k">def</span><span class="w"> </span><span class="nf">heap_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]):</span>
+<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;ヒープソート&quot;&quot;&quot;</span>
+<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a>    <span class="c1"># ヒープ構築操作：葉ノード以外のすべてのノードをヒープ化</span>
+<a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a>        <span class="n">sift_down</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">),</span> <span class="n">i</span><span class="p">)</span>
+<a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a>    <span class="c1"># ヒープから最大要素を抽出し、n-1 回繰り返す</span>
+<a id="__codelineno-0-26" name="__codelineno-0-26" href="#__codelineno-0-26"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-0-27" name="__codelineno-0-27" href="#__codelineno-0-27"></a>        <span class="c1"># ルートノードと最も右の葉ノードを交換（最初の要素と最後の要素を交換）</span>
+<a id="__codelineno-0-28" name="__codelineno-0-28" href="#__codelineno-0-28"></a>        <span class="n">nums</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">nums</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+<a id="__codelineno-0-29" name="__codelineno-0-29" href="#__codelineno-0-29"></a>        <span class="c1"># ルートノードから上から下へヒープ化を開始</span>
+<a id="__codelineno-0-30" name="__codelineno-0-30" href="#__codelineno-0-30"></a>        <span class="n">sift_down</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">heap_sort.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* ヒープの長さはn、ノードiから上から下へヒープ化を開始 */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">siftDown</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="nb">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">        </span><span class="c1">// i、l、r の中で最大のノードを決定し、maとして記録</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">l</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">            </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span><span class="p">;</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">r</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">ma</span><span class="p">])</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">            </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span><span class="p">;</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">        </span><span class="c1">// ノードiが最大か、インデックスl、rが境界外の場合、それ以上のヒープ化は不要で終了</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">        </span><span class="c1">// 二つのノードを交換</span>
+<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w">        </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">ma</span><span class="p">]);</span>
+<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w">        </span><span class="c1">// 下向きにヒープ化をループ</span>
+<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="w">        </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ma</span><span class="p">;</span>
+<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="p">}</span>
+<a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a>
+<a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a><span class="cm">/* ヒープソート */</span>
+<a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a><span class="kt">void</span><span class="w"> </span><span class="nf">heapSort</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a><span class="w">    </span><span class="c1">// ヒープ構築操作：葉以外のすべてのノードをヒープ化</span>
+<a id="__codelineno-1-26" name="__codelineno-1-26" href="#__codelineno-1-26"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="o">--</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-27" name="__codelineno-1-27" href="#__codelineno-1-27"></a><span class="w">        </span><span class="n">siftDown</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">(),</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-1-28" name="__codelineno-1-28" href="#__codelineno-1-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-29" name="__codelineno-1-29" href="#__codelineno-1-29"></a><span class="w">    </span><span class="c1">// ヒープから最大要素を抽出し、n-1回繰り返す</span>
+<a id="__codelineno-1-30" name="__codelineno-1-30" href="#__codelineno-1-30"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="o">--</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-31" name="__codelineno-1-31" href="#__codelineno-1-31"></a><span class="w">        </span><span class="c1">// ルートノードを最右葉ノードと交換（最初の要素を最後の要素と交換）</span>
+<a id="__codelineno-1-32" name="__codelineno-1-32" href="#__codelineno-1-32"></a><span class="w">        </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]);</span>
+<a id="__codelineno-1-33" name="__codelineno-1-33" href="#__codelineno-1-33"></a><span class="w">        </span><span class="c1">// ルートノードから上から下へヒープ化を開始</span>
+<a id="__codelineno-1-34" name="__codelineno-1-34" href="#__codelineno-1-34"></a><span class="w">        </span><span class="n">siftDown</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-1-35" name="__codelineno-1-35" href="#__codelineno-1-35"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-36" name="__codelineno-1-36" href="#__codelineno-1-36"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">heap_sort.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* ヒープの長さは n、ノード i から上から下へヒープ化開始 */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">siftDown</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="kc">true</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">        </span><span class="c1">// i, l, r の中で最大のノードを判定し、ma とする</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">l</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">l</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">ma</span><span class="o">]</span><span class="p">)</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">            </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">l</span><span class="p">;</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">r</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">ma</span><span class="o">]</span><span class="p">)</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">            </span><span class="n">ma</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">r</span><span class="p">;</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">        </span><span class="c1">// ノード i が最大、またはインデックス l, r が範囲外の場合、さらなるヒープ化は不要、ブレーク</span>
+<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">ma</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">i</span><span class="p">)</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">        </span><span class="c1">// 2つのノードを交換</span>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">ma</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">ma</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="p">;</span>
+<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w">        </span><span class="c1">// 下向きにヒープ化をループ</span>
+<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="w">        </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">ma</span><span class="p">;</span>
+<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a><span class="p">}</span>
+<a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a>
+<a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a><span class="cm">/* ヒープソート */</span>
+<a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a><span class="kt">void</span><span class="w"> </span><span class="nf">heapSort</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></a><span class="w">    </span><span class="c1">// ヒープ構築操作: 葉ノード以外のすべてのノードをヒープ化</span>
+<a id="__codelineno-2-27" name="__codelineno-2-27" href="#__codelineno-2-27"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-28" name="__codelineno-2-28" href="#__codelineno-2-28"></a><span class="w">        </span><span class="n">siftDown</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-2-29" name="__codelineno-2-29" href="#__codelineno-2-29"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-30" name="__codelineno-2-30" href="#__codelineno-2-30"></a><span class="w">    </span><span class="c1">// ヒープから最大要素を抽出し、n-1 回繰り返し</span>
+<a id="__codelineno-2-31" name="__codelineno-2-31" href="#__codelineno-2-31"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-32" name="__codelineno-2-32" href="#__codelineno-2-32"></a><span class="w">        </span><span class="c1">// ルートノードと最も右の葉ノードを交換（最初の要素と最後の要素を交換）</span>
+<a id="__codelineno-2-33" name="__codelineno-2-33" href="#__codelineno-2-33"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-2-34" name="__codelineno-2-34" href="#__codelineno-2-34"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="mi">0</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-2-35" name="__codelineno-2-35" href="#__codelineno-2-35"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
+<a id="__codelineno-2-36" name="__codelineno-2-36" href="#__codelineno-2-36"></a><span class="w">        </span><span class="c1">// ルートノードから上から下へヒープ化開始</span>
+<a id="__codelineno-2-37" name="__codelineno-2-37" href="#__codelineno-2-37"></a><span class="w">        </span><span class="n">siftDown</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-2-38" name="__codelineno-2-38" href="#__codelineno-2-38"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-39" name="__codelineno-2-39" href="#__codelineno-2-39"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">heap_sort.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">heap_sort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">SiftDown</span><span class="p">}</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">heap_sort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">HeapSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">heap_sort.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">siftDown</span><span class="p">}</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">heapSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">heap_sort.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">siftDown</span><span class="p">}</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">heapSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">heap_sort.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">siftDown</span><span class="p">}</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">heapSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">heap_sort.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">siftDown</span><span class="p">}</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">heapSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">heap_sort.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">siftDown</span><span class="p">}</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">heapSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">heap_sort.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">sift_down</span><span class="p">}</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">heap_sort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">heap_sort.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">siftDown</span><span class="p">}</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">heapSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">heap_sort.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">siftDown</span><span class="p">}</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">heapSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">heap_sort.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">sift_down</span><span class="p">}</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">heap_sort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">heap_sort.zig</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">siftDown</span><span class="p">}</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a>
+<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">heapSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h2 id="1172">11.7.2 &nbsp; アルゴリズムの特徴<a class="headerlink" href="#1172" title="Permanent link">&para;</a></h2>
+<ul>
+<li><strong>時間計算量は <span class="arithmatex">\(O(n \log n)\)</span>、非適応ソート</strong>：ヒープの構築は <span class="arithmatex">\(O(n)\)</span> 時間を使用します。ヒープから最大要素を抽出するには <span class="arithmatex">\(O(\log n)\)</span> 時間がかかり、<span class="arithmatex">\(n - 1\)</span> ラウンドループします。</li>
+<li><strong>空間計算量は <span class="arithmatex">\(O(1)\)</span>、インプレースソート</strong>：いくつかのポインタ変数が <span class="arithmatex">\(O(1)\)</span> 空間を使用します。要素の交換とヒープ化操作は元の配列で実行されます。</li>
+<li><strong>非安定ソート</strong>：ヒープの頂上と底部要素の交換中に、等しい要素の相対位置が変わる可能性があります。</li>
+</ul>
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diff --git a/ja/chapter_sorting/index.html b/ja/chapter_sorting/index.html
new file mode 100644
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+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="./" class="md-nav__link md-nav__link--active">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link md-nav__link--active" for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
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+<h1 id="11">第 11 章 &nbsp; ソート<a class="headerlink" href="#11" title="Permanent link">&para;</a></h1>
+<p><a class="glightbox" href="../assets/covers/chapter_sorting.jpg" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Sorting" class="cover-image" src="../assets/covers/chapter_sorting.jpg" /></a></p>
+<div class="admonition abstract">
+<p class="admonition-title">Abstract</p>
+<p>ソートは混沌を秩序に変える魔法の鍵のようなもので、データをより効率的に理解し処理することを可能にします。</p>
+<p>単純な昇順であろうと複雑なカテゴリ配列であろうと、ソートはデータの調和美を明らかにします。</p>
+</div>
+<h2 id="_1">章の内容<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h2>
+<ul>
+<li><a href="sorting_algorithm/">11.1 &nbsp; ソートアルゴリズム</a></li>
+<li><a href="selection_sort/">11.2 &nbsp; 選択ソート</a></li>
+<li><a href="bubble_sort/">11.3 &nbsp; バブルソート</a></li>
+<li><a href="insertion_sort/">11.4 &nbsp; 挿入ソート</a></li>
+<li><a href="quick_sort/">11.5 &nbsp; クイックソート</a></li>
+<li><a href="merge_sort/">11.6 &nbsp; マージソート</a></li>
+<li><a href="heap_sort/">11.7 &nbsp; ヒープソート</a></li>
+<li><a href="bucket_sort/">11.8 &nbsp; バケットソート</a></li>
+<li><a href="counting_sort/">11.9 &nbsp; 計数ソート</a></li>
+<li><a href="radix_sort/">11.10 &nbsp; 基数ソート</a></li>
+<li><a href="summary/">11.11 &nbsp; まとめ</a></li>
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+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
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+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1141" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.4.1 &nbsp; アルゴリズムプロセス
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1142" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.4.2 &nbsp; アルゴリズムの特性
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1143" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.4.3 &nbsp; 挿入ソートの利点
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_19" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_reference/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9 3v15h3V3H9m3 2 4 13 3-1-4-13-3 1M5 5v13h3V5H5M3 19v2h18v-2H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    参考文献
+  </span>
+  
+
+            </a>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_19_label" aria-expanded="false">
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+            参考文献
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+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+  </ul>
+</nav>
+                  </div>
+                </div>
+              </div>
+            
+            
+              
+              <div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
+                <div class="md-sidebar__scrollwrap">
+                  <div class="md-sidebar__inner">
+                    
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1141" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.4.1 &nbsp; アルゴリズムプロセス
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1142" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.4.2 &nbsp; アルゴリズムの特性
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1143" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.4.3 &nbsp; 挿入ソートの利点
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+                  </div>
+                </div>
+              </div>
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+    <a
+      href="https://github.com/krahets/hello-algo/tree/main/ja/docs/chapter_sorting/insertion_sort.md"
+      title="編集"
+      class="md-content__button md-icon"
+    >
+      
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
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+<h1 id="114">11.4 &nbsp; 挿入ソート<a class="headerlink" href="#114" title="Permanent link">&para;</a></h1>
+<p><u>挿入ソート</u>は、トランプのデッキを手動でソートするプロセスによく似た動作をするシンプルなソートアルゴリズムです。</p>
+<p>具体的には、未ソート区間からベース要素を選択し、その左側のソート済み区間の要素と比較して、要素を正しい位置に挿入します。</p>
+<p>下図は、要素が配列に挿入される方法を示しています。ベース要素を<code>base</code>とすると、ターゲットインデックスから<code>base</code>までのすべての要素を右に1つずつシフトし、その後<code>base</code>をターゲットインデックスに割り当てる必要があります。</p>
+<p><a class="glightbox" href="../insertion_sort.assets/insertion_operation.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Single insertion operation" class="animation-figure" src="../insertion_sort.assets/insertion_operation.png" /></a></p>
+<p align="center"> 図 11-6 &nbsp; Single insertion operation </p>
+
+<h2 id="1141">11.4.1 &nbsp; アルゴリズムプロセス<a class="headerlink" href="#1141" title="Permanent link">&para;</a></h2>
+<p>挿入ソートの全体的なプロセスは下図に示されます。</p>
+<ol>
+<li>配列の最初の要素をソート済みとみなします。</li>
+<li>2番目の要素を<code>base</code>として選択し、正しい位置に挿入して、<strong>最初の2つの要素をソート済みにします</strong>。</li>
+<li>3番目の要素を<code>base</code>として選択し、正しい位置に挿入して、<strong>最初の3つの要素をソート済みにします</strong>。</li>
+<li>この方法で続行し、最後の反復では、最後の要素を<code>base</code>として取り、正しい位置に挿入した後、<strong>すべての要素がソートされます</strong>。</li>
+</ol>
+<p><a class="glightbox" href="../insertion_sort.assets/insertion_sort_overview.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Insertion sort process" class="animation-figure" src="../insertion_sort.assets/insertion_sort_overview.png" /></a></p>
+<p align="center"> 図 11-7 &nbsp; Insertion sort process </p>
+
+<p>コード例は以下の通りです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:14"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><input id="__tabbed_1_14" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label><label for="__tabbed_1_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">insertion_sort.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">insertion_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]):</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;挿入ソート&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># 外側のループ：ソート済み範囲は [0, i-1]</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)):</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>        <span class="n">base</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>        <span class="n">j</span> <span class="o">=</span> <span class="n">i</span> <span class="o">-</span> <span class="mi">1</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>        <span class="c1"># 内側のループ：base をソート済み範囲 [0, i-1] の正しい位置に挿入</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>        <span class="k">while</span> <span class="n">j</span> <span class="o">&gt;=</span> <span class="mi">0</span> <span class="ow">and</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">&gt;</span> <span class="n">base</span><span class="p">:</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>            <span class="n">nums</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>  <span class="c1"># nums[j] を右に1つ移動</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>            <span class="n">j</span> <span class="o">-=</span> <span class="mi">1</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>        <span class="n">nums</span><span class="p">[</span><span class="n">j</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">base</span>  <span class="c1"># base を正しい位置に代入</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">insertion_sort.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 挿入ソート */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">insertionSort</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// 外側ループ：ソート済み範囲は[0, i-1]</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">        </span><span class="c1">// 内側ループ：baseをソート済み範囲[0, i-1]内の正しい位置に挿入</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">base</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">            </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">];</span><span class="w"> </span><span class="c1">// nums[j]を一つ右に移動</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">            </span><span class="n">j</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">base</span><span class="p">;</span><span class="w"> </span><span class="c1">// baseを正しい位置に代入</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">insertion_sort.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 挿入ソート */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">insertionSort</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// 外側ループ: ソート済み範囲は [0, i-1]</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">base</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">        </span><span class="c1">// 内側ループ: base をソート済み範囲 [0, i-1] の正しい位置に挿入</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">base</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">            </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">;</span><span class="w"> </span><span class="c1">// nums[j] を右に1つ移動</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">            </span><span class="n">j</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">base</span><span class="p">;</span><span class="w">        </span><span class="c1">// base を正しい位置に代入</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">insertion_sort.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">insertion_sort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">InsertionSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">insertion_sort.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">insertionSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">insertion_sort.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">insertionSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">insertion_sort.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">insertionSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">insertion_sort.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">insertionSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">insertion_sort.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">insertionSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">insertion_sort.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">insertion_sort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">insertion_sort.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">insertionSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">insertion_sort.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">insertionSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">insertion_sort.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">insertion_sort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">insertion_sort.zig</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">insertionSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h2 id="1142">11.4.2 &nbsp; アルゴリズムの特性<a class="headerlink" href="#1142" title="Permanent link">&para;</a></h2>
+<ul>
+<li><strong>時間計算量は<span class="arithmatex">\(O(n^2)\)</span>、適応ソート</strong>：最悪の場合、各挿入操作には<span class="arithmatex">\(n - 1\)</span>、<span class="arithmatex">\(n-2\)</span>、...、<span class="arithmatex">\(2\)</span>、<span class="arithmatex">\(1\)</span>のループが必要で、合計は<span class="arithmatex">\((n - 1) n / 2\)</span>となり、時間計算量は<span class="arithmatex">\(O(n^2)\)</span>です。順序付きデータの場合、挿入操作は早期に終了します。入力配列が完全に順序付けられている場合、挿入ソートは最良時間計算量<span class="arithmatex">\(O(n)\)</span>を実現します。</li>
+<li><strong>空間計算量は<span class="arithmatex">\(O(1)\)</span>、インプレースソート</strong>：ポインタ<span class="arithmatex">\(i\)</span>と<span class="arithmatex">\(j\)</span>は定数量の追加空間を使用します。</li>
+<li><strong>安定ソート</strong>：挿入操作中、等しい要素の右側に要素を挿入し、順序を変更しません。</li>
+</ul>
+<h2 id="1143">11.4.3 &nbsp; 挿入ソートの利点<a class="headerlink" href="#1143" title="Permanent link">&para;</a></h2>
+<p>挿入ソートの時間計算量は<span class="arithmatex">\(O(n^2)\)</span>で、次に学習するクイックソートの時間計算量は<span class="arithmatex">\(O(n \log n)\)</span>です。挿入ソートはより高い時間計算量を持ちますが、<strong>小さな入力サイズでは通常より高速です</strong>。</p>
+<p>この結論は線形探索と二分探索の結論と似ています。時間計算量が<span class="arithmatex">\(O(n \log n)\)</span>で分割統治戦略に基づくクイックソートなどのアルゴリズムは、多くの場合より多くの単位操作を含みます。小さな入力サイズでは、<span class="arithmatex">\(n^2\)</span>と<span class="arithmatex">\(n \log n\)</span>の数値は近く、計算量が支配的でなく、ラウンドあたりの単位操作数が決定的な役割を果たします。</p>
+<p>実際、多くのプログラミング言語（Javaなど）は、組み込みソート関数内で挿入ソートを使用しています。一般的なアプローチは：長い配列に対しては、クイックソートなどの分割統治戦略に基づくソートアルゴリズムを使用し、短い配列に対しては挿入ソートを直接使用します。</p>
+<p>バブルソート、選択ソート、挿入ソートはすべて時間計算量<span class="arithmatex">\(O(n^2)\)</span>を持ちますが、実際には、<strong>挿入ソートはバブルソートや選択ソートよりも一般的に使用されます</strong>。主な理由は以下の通りです。</p>
+<ul>
+<li>バブルソートは要素交換に基づき、一時変数の使用が必要で、3つの単位操作を含みます；挿入ソートは要素代入に基づき、1つの単位操作のみが必要です。したがって、<strong>バブルソートの計算オーバーヘッドは一般的に挿入ソートよりも高くなります</strong>。</li>
+<li>選択ソートの時間計算量は常に<span class="arithmatex">\(O(n^2)\)</span>です。<strong>部分的に順序付けられたデータのセットが与えられた場合、挿入ソートは通常選択ソートよりも効率的です</strong>。</li>
+<li>選択ソートは不安定で、マルチレベルソートに適用できません。</li>
+</ul>
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+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1161" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.6.1 &nbsp; アルゴリズムワークフロー
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1162" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.6.2 &nbsp; アルゴリズムの特性
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1163" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.6.3 &nbsp; 連結リストのソート
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
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+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
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+  
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+              
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+        </nav>
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+  </span>
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+            参考文献
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
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+        </nav>
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+  
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+  </ul>
+</nav>
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+              </div>
+            
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+              <div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
+                <div class="md-sidebar__scrollwrap">
+                  <div class="md-sidebar__inner">
+                    
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1161" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.6.1 &nbsp; アルゴリズムワークフロー
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1162" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.6.2 &nbsp; アルゴリズムの特性
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1163" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.6.3 &nbsp; 連結リストのソート
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
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+</nav>
+                  </div>
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+    <a
+      href="https://github.com/krahets/hello-algo/tree/main/ja/docs/chapter_sorting/merge_sort.md"
+      title="編集"
+      class="md-content__button md-icon"
+    >
+      
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
+    </a>
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+  
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+<!-- Page content -->
+<h1 id="116">11.6 &nbsp; マージソート<a class="headerlink" href="#116" title="Permanent link">&para;</a></h1>
+<p><u>マージソート</u>は分割統治戦略に基づくソートアルゴリズムで、下図に示す「分割」と「マージ」フェーズを含みます。</p>
+<ol>
+<li><strong>分割フェーズ</strong>：中点から配列を再帰的に分割し、長い配列のソート問題をより短い配列に変換します。</li>
+<li><strong>マージフェーズ</strong>：サブ配列の長さが1になったときに分割を停止し、その後マージを開始します。2つの短いソート済み配列を連続的により長いソート済み配列にマージし、プロセスが完了するまで続行します。</li>
+</ol>
+<p><a class="glightbox" href="../merge_sort.assets/merge_sort_overview.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="The divide and merge phases of merge sort" class="animation-figure" src="../merge_sort.assets/merge_sort_overview.png" /></a></p>
+<p align="center"> 図 11-10 &nbsp; The divide and merge phases of merge sort </p>
+
+<h2 id="1161">11.6.1 &nbsp; アルゴリズムワークフロー<a class="headerlink" href="#1161" title="Permanent link">&para;</a></h2>
+<p>下図に示すように、「分割フェーズ」は中点から配列を上から下に2つのサブ配列に再帰的に分割します。</p>
+<ol>
+<li>中点<code>mid</code>を計算し、左サブ配列（区間<code>[left, mid]</code>）と右サブ配列（区間<code>[mid + 1, right]</code>）を再帰的に分割します。</li>
+<li>サブ配列の長さが1になるまでステップ<code>1.</code>を再帰的に続行し、その後停止します。</li>
+</ol>
+<p>「マージフェーズ」は左と右のサブ配列を下から上にソート済み配列に結合します。重要なのは、マージが長さ1のサブ配列から開始され、マージフェーズ中に各サブ配列がソートされることです。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:10"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">&lt;1&gt;</label><label for="__tabbed_1_2">&lt;2&gt;</label><label for="__tabbed_1_3">&lt;3&gt;</label><label for="__tabbed_1_4">&lt;4&gt;</label><label for="__tabbed_1_5">&lt;5&gt;</label><label for="__tabbed_1_6">&lt;6&gt;</label><label for="__tabbed_1_7">&lt;7&gt;</label><label for="__tabbed_1_8">&lt;8&gt;</label><label for="__tabbed_1_9">&lt;9&gt;</label><label for="__tabbed_1_10">&lt;10&gt;</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<p><a class="glightbox" href="../merge_sort.assets/merge_sort_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Merge sort process" class="animation-figure" src="../merge_sort.assets/merge_sort_step1.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../merge_sort.assets/merge_sort_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="merge_sort_step2" class="animation-figure" src="../merge_sort.assets/merge_sort_step2.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../merge_sort.assets/merge_sort_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="merge_sort_step3" class="animation-figure" src="../merge_sort.assets/merge_sort_step3.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../merge_sort.assets/merge_sort_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="merge_sort_step4" class="animation-figure" src="../merge_sort.assets/merge_sort_step4.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../merge_sort.assets/merge_sort_step5.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="merge_sort_step5" class="animation-figure" src="../merge_sort.assets/merge_sort_step5.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../merge_sort.assets/merge_sort_step6.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="merge_sort_step6" class="animation-figure" src="../merge_sort.assets/merge_sort_step6.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../merge_sort.assets/merge_sort_step7.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="merge_sort_step7" class="animation-figure" src="../merge_sort.assets/merge_sort_step7.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../merge_sort.assets/merge_sort_step8.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="merge_sort_step8" class="animation-figure" src="../merge_sort.assets/merge_sort_step8.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../merge_sort.assets/merge_sort_step9.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="merge_sort_step9" class="animation-figure" src="../merge_sort.assets/merge_sort_step9.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../merge_sort.assets/merge_sort_step10.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="merge_sort_step10" class="animation-figure" src="../merge_sort.assets/merge_sort_step10.png" /></a></p>
+</div>
+</div>
+</div>
+<p align="center"> 図 11-11 &nbsp; Merge sort process </p>
+
+<p>マージソートの再帰順序は二分木の後順横断と一致することが観察できます。</p>
+<ul>
+<li><strong>後順横断</strong>：まず左のサブツリーを再帰的に横断し、次に右のサブツリーを横断し、最後にルートノードを処理します。</li>
+<li><strong>マージソート</strong>：まず左のサブ配列を再帰的に処理し、次に右のサブ配列を処理し、最後にマージを実行します。</li>
+</ul>
+<p>マージソートの実装は以下のコードに示されます。<code>nums</code>でマージされる区間は<code>[left, right]</code>で、<code>tmp</code>の対応する区間は<code>[0, right - left]</code>であることに注意してください。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:14"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><input id="__tabbed_2_14" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label><label for="__tabbed_2_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">merge_sort.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">merge</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">left</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">mid</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">right</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;左サブ配列と右サブ配列をマージ&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># 左サブ配列区間は [left, mid]、右サブ配列区間は [mid+1, right]</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="c1"># 一時配列 tmp を作成してマージ結果を格納</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="n">tmp</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="n">right</span> <span class="o">-</span> <span class="n">left</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="c1"># 左右サブ配列の開始インデックスを初期化</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>    <span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">,</span> <span class="n">k</span> <span class="o">=</span> <span class="n">left</span><span class="p">,</span> <span class="n">mid</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>    <span class="c1"># 両方のサブ配列に要素が残っている間、より小さい要素を一時配列にコピー</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>    <span class="k">while</span> <span class="n">i</span> <span class="o">&lt;=</span> <span class="n">mid</span> <span class="ow">and</span> <span class="n">j</span> <span class="o">&lt;=</span> <span class="n">right</span><span class="p">:</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>        <span class="k">if</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">&lt;=</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]:</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>            <span class="n">tmp</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>            <span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>        <span class="k">else</span><span class="p">:</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>            <span class="n">tmp</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
+<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>            <span class="n">j</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>        <span class="n">k</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>    <span class="c1"># 残った左右サブ配列の要素を一時配列にコピー</span>
+<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a>    <span class="k">while</span> <span class="n">i</span> <span class="o">&lt;=</span> <span class="n">mid</span><span class="p">:</span>
+<a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a>        <span class="n">tmp</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a>        <span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a>        <span class="n">k</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a>    <span class="k">while</span> <span class="n">j</span> <span class="o">&lt;=</span> <span class="n">right</span><span class="p">:</span>
+<a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a>        <span class="n">tmp</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span>
+<a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a>        <span class="n">j</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a>        <span class="n">k</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-0-26" name="__codelineno-0-26" href="#__codelineno-0-26"></a>    <span class="c1"># 一時配列 tmp の要素を元の配列 nums の対応する区間にコピーバック</span>
+<a id="__codelineno-0-27" name="__codelineno-0-27" href="#__codelineno-0-27"></a>    <span class="k">for</span> <span class="n">k</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">tmp</span><span class="p">)):</span>
+<a id="__codelineno-0-28" name="__codelineno-0-28" href="#__codelineno-0-28"></a>        <span class="n">nums</span><span class="p">[</span><span class="n">left</span> <span class="o">+</span> <span class="n">k</span><span class="p">]</span> <span class="o">=</span> <span class="n">tmp</span><span class="p">[</span><span class="n">k</span><span class="p">]</span>
+<a id="__codelineno-0-29" name="__codelineno-0-29" href="#__codelineno-0-29"></a>
+<a id="__codelineno-0-30" name="__codelineno-0-30" href="#__codelineno-0-30"></a><span class="k">def</span><span class="w"> </span><span class="nf">merge_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">left</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">right</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-0-31" name="__codelineno-0-31" href="#__codelineno-0-31"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;マージソート&quot;&quot;&quot;</span>
+<a id="__codelineno-0-32" name="__codelineno-0-32" href="#__codelineno-0-32"></a>    <span class="c1"># 終了条件</span>
+<a id="__codelineno-0-33" name="__codelineno-0-33" href="#__codelineno-0-33"></a>    <span class="k">if</span> <span class="n">left</span> <span class="o">&gt;=</span> <span class="n">right</span><span class="p">:</span>
+<a id="__codelineno-0-34" name="__codelineno-0-34" href="#__codelineno-0-34"></a>        <span class="k">return</span>  <span class="c1"># サブ配列の長さが1のときに再帰を終了</span>
+<a id="__codelineno-0-35" name="__codelineno-0-35" href="#__codelineno-0-35"></a>    <span class="c1"># 分割段階</span>
+<a id="__codelineno-0-36" name="__codelineno-0-36" href="#__codelineno-0-36"></a>    <span class="n">mid</span> <span class="o">=</span> <span class="n">left</span> <span class="o">+</span> <span class="p">(</span><span class="n">right</span> <span class="o">-</span> <span class="n">left</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span>  <span class="c1"># 中点を計算</span>
+<a id="__codelineno-0-37" name="__codelineno-0-37" href="#__codelineno-0-37"></a>    <span class="n">merge_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="n">left</span><span class="p">,</span> <span class="n">mid</span><span class="p">)</span>  <span class="c1"># 左サブ配列を再帰的に処理</span>
+<a id="__codelineno-0-38" name="__codelineno-0-38" href="#__codelineno-0-38"></a>    <span class="n">merge_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="n">mid</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">right</span><span class="p">)</span>  <span class="c1"># 右サブ配列を再帰的に処理</span>
+<a id="__codelineno-0-39" name="__codelineno-0-39" href="#__codelineno-0-39"></a>    <span class="c1"># マージ段階</span>
+<a id="__codelineno-0-40" name="__codelineno-0-40" href="#__codelineno-0-40"></a>    <span class="n">merge</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="n">left</span><span class="p">,</span> <span class="n">mid</span><span class="p">,</span> <span class="n">right</span><span class="p">)</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">merge_sort.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 左サブ配列と右サブ配列をマージ */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">merge</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">mid</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// 左サブ配列の区間は[left, mid]、右サブ配列の区間は[mid+1, right]</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="c1">// マージ結果を保存する一時配列tmpを作成</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">tmp</span><span class="p">(</span><span class="n">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="c1">// 左右サブ配列の開始インデックスを初期化</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="c1">// 両サブ配列に要素がある間、小さい方の要素を一時配列にコピー</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">])</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">            </span><span class="n">tmp</span><span class="p">[</span><span class="n">k</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="o">++</span><span class="p">];</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">        </span><span class="k">else</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">            </span><span class="n">tmp</span><span class="p">[</span><span class="n">k</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="o">++</span><span class="p">];</span>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">    </span><span class="c1">// 左右サブ配列の残りの要素を一時配列にコピー</span>
+<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">mid</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w">        </span><span class="n">tmp</span><span class="p">[</span><span class="n">k</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="o">++</span><span class="p">];</span>
+<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="w">        </span><span class="n">tmp</span><span class="p">[</span><span class="n">k</span><span class="o">++</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="o">++</span><span class="p">];</span>
+<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a><span class="w">    </span><span class="c1">// 一時配列tmpの要素を元の配列numsの対応する区間にコピー</span>
+<a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">tmp</span><span class="p">.</span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">k</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">k</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">[</span><span class="n">k</span><span class="p">];</span>
+<a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-26" name="__codelineno-1-26" href="#__codelineno-1-26"></a><span class="p">}</span>
+<a id="__codelineno-1-27" name="__codelineno-1-27" href="#__codelineno-1-27"></a>
+<a id="__codelineno-1-28" name="__codelineno-1-28" href="#__codelineno-1-28"></a><span class="cm">/* マージソート */</span>
+<a id="__codelineno-1-29" name="__codelineno-1-29" href="#__codelineno-1-29"></a><span class="kt">void</span><span class="w"> </span><span class="nf">mergeSort</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-30" name="__codelineno-1-30" href="#__codelineno-1-30"></a><span class="w">    </span><span class="c1">// 終了条件</span>
+<a id="__codelineno-1-31" name="__codelineno-1-31" href="#__codelineno-1-31"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">right</span><span class="p">)</span>
+<a id="__codelineno-1-32" name="__codelineno-1-32" href="#__codelineno-1-32"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span><span class="w"> </span><span class="c1">// サブ配列の長さが1の時、再帰を終了</span>
+<a id="__codelineno-1-33" name="__codelineno-1-33" href="#__codelineno-1-33"></a><span class="w">    </span><span class="c1">// 分割段階</span>
+<a id="__codelineno-1-34" name="__codelineno-1-34" href="#__codelineno-1-34"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w">    </span><span class="c1">// 中点を計算</span>
+<a id="__codelineno-1-35" name="__codelineno-1-35" href="#__codelineno-1-35"></a><span class="w">    </span><span class="n">mergeSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">);</span><span class="w">      </span><span class="c1">// 左サブ配列を再帰的に処理</span>
+<a id="__codelineno-1-36" name="__codelineno-1-36" href="#__codelineno-1-36"></a><span class="w">    </span><span class="n">mergeSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span><span class="w"> </span><span class="c1">// 右サブ配列を再帰的に処理</span>
+<a id="__codelineno-1-37" name="__codelineno-1-37" href="#__codelineno-1-37"></a><span class="w">    </span><span class="c1">// マージ段階</span>
+<a id="__codelineno-1-38" name="__codelineno-1-38" href="#__codelineno-1-38"></a><span class="w">    </span><span class="n">merge</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-1-39" name="__codelineno-1-39" href="#__codelineno-1-39"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">merge_sort.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 左部分配列と右部分配列をマージ */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">merge</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">mid</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// 左部分配列区間は [left, mid]、右部分配列区間は [mid+1, right]</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="c1">// 一時配列 tmp を作成してマージ結果を格納</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="c1">// 左右部分配列の開始インデックスを初期化</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">    </span><span class="c1">// 両部分配列にまだ要素がある間、比較してより小さい要素を一時配列にコピー</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">)</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">            </span><span class="n">tmp</span><span class="o">[</span><span class="n">k</span><span class="o">++]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">++]</span><span class="p">;</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">        </span><span class="k">else</span>
+<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">            </span><span class="n">tmp</span><span class="o">[</span><span class="n">k</span><span class="o">++]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">++]</span><span class="p">;</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">    </span><span class="c1">// 左右部分配列の残りの要素を一時配列にコピー</span>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">mid</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w">        </span><span class="n">tmp</span><span class="o">[</span><span class="n">k</span><span class="o">++]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">++]</span><span class="p">;</span>
+<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">j</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="w">        </span><span class="n">tmp</span><span class="o">[</span><span class="n">k</span><span class="o">++]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">++]</span><span class="p">;</span>
+<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a><span class="w">    </span><span class="c1">// 一時配列 tmp の要素を元の配列 nums の対応する区間にコピーバック</span>
+<a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">tmp</span><span class="p">.</span><span class="na">length</span><span class="p">;</span><span class="w"> </span><span class="n">k</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">k</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="o">[</span><span class="n">k</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></a><span class="p">}</span>
+<a id="__codelineno-2-27" name="__codelineno-2-27" href="#__codelineno-2-27"></a>
+<a id="__codelineno-2-28" name="__codelineno-2-28" href="#__codelineno-2-28"></a><span class="cm">/* マージソート */</span>
+<a id="__codelineno-2-29" name="__codelineno-2-29" href="#__codelineno-2-29"></a><span class="kt">void</span><span class="w"> </span><span class="nf">mergeSort</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-30" name="__codelineno-2-30" href="#__codelineno-2-30"></a><span class="w">    </span><span class="c1">// 終了条件</span>
+<a id="__codelineno-2-31" name="__codelineno-2-31" href="#__codelineno-2-31"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">right</span><span class="p">)</span>
+<a id="__codelineno-2-32" name="__codelineno-2-32" href="#__codelineno-2-32"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span><span class="w"> </span><span class="c1">// 部分配列の長さが 1 のとき再帰を終了</span>
+<a id="__codelineno-2-33" name="__codelineno-2-33" href="#__codelineno-2-33"></a><span class="w">    </span><span class="c1">// 分割段階</span>
+<a id="__codelineno-2-34" name="__codelineno-2-34" href="#__codelineno-2-34"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="p">(</span><span class="n">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span><span class="w"> </span><span class="c1">// 中点を計算</span>
+<a id="__codelineno-2-35" name="__codelineno-2-35" href="#__codelineno-2-35"></a><span class="w">    </span><span class="n">mergeSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">);</span><span class="w"> </span><span class="c1">// 左部分配列を再帰的に処理</span>
+<a id="__codelineno-2-36" name="__codelineno-2-36" href="#__codelineno-2-36"></a><span class="w">    </span><span class="n">mergeSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span><span class="w"> </span><span class="c1">// 右部分配列を再帰的に処理</span>
+<a id="__codelineno-2-37" name="__codelineno-2-37" href="#__codelineno-2-37"></a><span class="w">    </span><span class="c1">// マージ段階</span>
+<a id="__codelineno-2-38" name="__codelineno-2-38" href="#__codelineno-2-38"></a><span class="w">    </span><span class="n">merge</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">mid</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-2-39" name="__codelineno-2-39" href="#__codelineno-2-39"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">merge_sort.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">merge_sort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Merge</span><span class="p">}</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">merge_sort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">MergeSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">merge_sort.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">merge</span><span class="p">}</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">mergeSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">merge_sort.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">merge</span><span class="p">}</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">mergeSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">merge_sort.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">merge</span><span class="p">}</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">mergeSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">merge_sort.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">merge</span><span class="p">}</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">mergeSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">merge_sort.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">merge</span><span class="p">}</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">mergeSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">merge_sort.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">merge</span><span class="p">}</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">merge_sort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">merge_sort.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">merge</span><span class="p">}</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">mergeSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">merge_sort.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">merge</span><span class="p">}</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">mergeSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">merge_sort.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">merge</span><span class="p">}</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">merge_sort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">merge_sort.zig</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">merge</span><span class="p">}</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a>
+<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">mergeSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h2 id="1162">11.6.2 &nbsp; アルゴリズムの特性<a class="headerlink" href="#1162" title="Permanent link">&para;</a></h2>
+<ul>
+<li><strong><span class="arithmatex">\(O(n \log n)\)</span>の時間計算量、非適応ソート</strong>：分割により高さ<span class="arithmatex">\(\log n\)</span>の再帰ツリーが作成され、各層で合計<span class="arithmatex">\(n\)</span>回の操作をマージし、全体的な時間計算量は<span class="arithmatex">\(O(n \log n)\)</span>となります。</li>
+<li><strong><span class="arithmatex">\(O(n)\)</span>の空間計算量、非インプレースソート</strong>：再帰深度は<span class="arithmatex">\(\log n\)</span>で、<span class="arithmatex">\(O(\log n)\)</span>のスタックフレーム空間を使用します。マージ操作には補助配列が必要で、追加の<span class="arithmatex">\(O(n)\)</span>空間を使用します。</li>
+<li><strong>安定ソート</strong>：マージプロセス中、等しい要素の順序は変更されません。</li>
+</ul>
+<h2 id="1163">11.6.3 &nbsp; 連結リストのソート<a class="headerlink" href="#1163" title="Permanent link">&para;</a></h2>
+<p>連結リストの場合、マージソートは他のソートアルゴリズムよりも大きな利点があります。<strong>連結リストソートタスクの空間計算量を<span class="arithmatex">\(O(1)\)</span>に最適化できます</strong>。</p>
+<ul>
+<li><strong>分割フェーズ</strong>：「再帰」の代わりに「反復」を使用して連結リスト分割作業を実行できるため、再帰で使用されるスタックフレーム空間を節約できます。</li>
+<li><strong>マージフェーズ</strong>：連結リストでは、ノードの挿入と削除操作は参照（ポインタ）を変更することで実現できるため、マージフェーズ（2つの短い順序付きリストを1つの長い順序付きリストに結合）中に追加のリストを作成する必要がありません。</li>
+</ul>
+<p>実装の詳細は比較的複雑で、興味のある読者は関連資料を参照して学習してください。</p>
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+      <a href="../../chapter_preface/summary/" class="md-nav__link">
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+  
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+    第 1 章 &nbsp; アルゴリズムとの出会い
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+  
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+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
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+    1.3 &nbsp; まとめ
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+        
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+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
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+            第 2 章 &nbsp; 計算量解析
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+    2.1 &nbsp; アルゴリズム効率評価
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+    2.2 &nbsp; 反復と再帰
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+  
+
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+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
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+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
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+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
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+    </li>
+  
+
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+  
+  
+  
+  
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+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
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+  
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+    第 3 章 &nbsp; データ構造
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1151" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.5.1 &nbsp; アルゴリズムプロセス
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1152" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.5.2 &nbsp; アルゴリズムの特徴
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1153" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.5.3 &nbsp; なぜクイックソートは高速なのか
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1154" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.5.4 &nbsp; ピボット最適化
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1155" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.5.5 &nbsp; 末尾再帰最適化
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_19" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_reference/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9 3v15h3V3H9m3 2 4 13 3-1-4-13-3 1M5 5v13h3V5H5M3 19v2h18v-2H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    参考文献
+  </span>
+  
+
+            </a>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_19_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_19">
+            <span class="md-nav__icon md-icon"></span>
+            参考文献
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+  </ul>
+</nav>
+                  </div>
+                </div>
+              </div>
+            
+            
+              
+              <div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
+                <div class="md-sidebar__scrollwrap">
+                  <div class="md-sidebar__inner">
+                    
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1151" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.5.1 &nbsp; アルゴリズムプロセス
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1152" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.5.2 &nbsp; アルゴリズムの特徴
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1153" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.5.3 &nbsp; なぜクイックソートは高速なのか
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1154" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.5.4 &nbsp; ピボット最適化
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1155" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.5.5 &nbsp; 末尾再帰最適化
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+                  </div>
+                </div>
+              </div>
+            
+          
+          
+            <div class="md-content" data-md-component="content">
+              <article class="md-content__inner md-typeset">
+                
+                  <!-- Tags -->
+
+
+<!-- Actions -->
+<!-- Actions -->
+
+
+  <!-- Edit button -->
+  
+    <a
+      href="https://github.com/krahets/hello-algo/tree/main/ja/docs/chapter_sorting/quick_sort.md"
+      title="編集"
+      class="md-content__button md-icon"
+    >
+      
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
+    </a>
+  
+
+  <!-- View button -->
+  
+
+
+<!-- Page content -->
+<h1 id="115">11.5 &nbsp; クイックソート<a class="headerlink" href="#115" title="Permanent link">&para;</a></h1>
+<p><u>クイックソート</u>は分割統治戦略に基づくソートアルゴリズムで、その効率性と幅広い応用で知られています。</p>
+<p>クイックソートのコア操作は「ピボット分割」で、配列から要素を「ピボット」として選択し、ピボットより小さいすべての要素をその左側に移動し、ピボットより大きいすべての要素をその右側に移動することを目的としています。具体的に、ピボット分割のプロセスは下図に示されます。</p>
+<ol>
+<li>配列の最も左の要素をピボットとして選択し、2つのポインタ<code>i</code>と<code>j</code>を初期化して配列の両端をそれぞれ指すようにします。</li>
+<li>各ラウンドで<code>i</code>（<code>j</code>）を使用してピボットより大きい（小さい）最初の要素を探索し、次にこれら2つの要素を交換するループを設定します。</li>
+<li><code>i</code>と<code>j</code>が出会うまでステップ<code>2.</code>を繰り返し、最後にピボットを2つのサブ配列の境界に交換します。</li>
+</ol>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:9"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">&lt;1&gt;</label><label for="__tabbed_1_2">&lt;2&gt;</label><label for="__tabbed_1_3">&lt;3&gt;</label><label for="__tabbed_1_4">&lt;4&gt;</label><label for="__tabbed_1_5">&lt;5&gt;</label><label for="__tabbed_1_6">&lt;6&gt;</label><label for="__tabbed_1_7">&lt;7&gt;</label><label for="__tabbed_1_8">&lt;8&gt;</label><label for="__tabbed_1_9">&lt;9&gt;</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<p><a class="glightbox" href="../quick_sort.assets/pivot_division_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Pivot division process" class="animation-figure" src="../quick_sort.assets/pivot_division_step1.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../quick_sort.assets/pivot_division_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="pivot_division_step2" class="animation-figure" src="../quick_sort.assets/pivot_division_step2.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../quick_sort.assets/pivot_division_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="pivot_division_step3" class="animation-figure" src="../quick_sort.assets/pivot_division_step3.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../quick_sort.assets/pivot_division_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="pivot_division_step4" class="animation-figure" src="../quick_sort.assets/pivot_division_step4.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../quick_sort.assets/pivot_division_step5.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="pivot_division_step5" class="animation-figure" src="../quick_sort.assets/pivot_division_step5.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../quick_sort.assets/pivot_division_step6.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="pivot_division_step6" class="animation-figure" src="../quick_sort.assets/pivot_division_step6.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../quick_sort.assets/pivot_division_step7.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="pivot_division_step7" class="animation-figure" src="../quick_sort.assets/pivot_division_step7.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../quick_sort.assets/pivot_division_step8.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="pivot_division_step8" class="animation-figure" src="../quick_sort.assets/pivot_division_step8.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../quick_sort.assets/pivot_division_step9.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="pivot_division_step9" class="animation-figure" src="../quick_sort.assets/pivot_division_step9.png" /></a></p>
+</div>
+</div>
+</div>
+<p align="center"> 図 11-8 &nbsp; Pivot division process </p>
+
+<p>ピボット分割後、元の配列は3つの部分に分割されます：左サブ配列、ピボット、右サブ配列で、「左サブ配列の任意の要素 <span class="arithmatex">\(\leq\)</span> ピボット <span class="arithmatex">\(\leq\)</span> 右サブ配列の任意の要素」を満たします。したがって、これら2つのサブ配列のみをソートすればよいのです。</p>
+<div class="admonition note">
+<p class="admonition-title">クイックソートの分割統治戦略</p>
+<p>ピボット分割の本質は、より長い配列のソート問題をより短い2つの配列に簡素化することです。</p>
+</div>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:14"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><input id="__tabbed_2_14" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label><label for="__tabbed_2_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">partition</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">left</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">right</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;分割&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># nums[left] をピボットとして使用</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="o">=</span> <span class="n">left</span><span class="p">,</span> <span class="n">right</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="k">while</span> <span class="n">i</span> <span class="o">&lt;</span> <span class="n">j</span><span class="p">:</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>        <span class="k">while</span> <span class="n">i</span> <span class="o">&lt;</span> <span class="n">j</span> <span class="ow">and</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">&gt;=</span> <span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">]:</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>            <span class="n">j</span> <span class="o">-=</span> <span class="mi">1</span>  <span class="c1"># 右から左へピボットより小さい最初の要素を探す</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>        <span class="k">while</span> <span class="n">i</span> <span class="o">&lt;</span> <span class="n">j</span> <span class="ow">and</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">&lt;=</span> <span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">]:</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>            <span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>  <span class="c1"># 左から右へピボットより大きい最初の要素を探す</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>        <span class="c1"># 要素を交換</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>        <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">],</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>    <span class="c1"># ピボットを2つのサブ配列の境界に交換</span>
+<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>    <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">],</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>    <span class="k">return</span> <span class="n">i</span>  <span class="c1"># ピボットのインデックスを返す</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 分割 */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">partition</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// nums[left]をピボットとして使用</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">])</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">            </span><span class="n">j</span><span class="o">--</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右から左へピボットより小さい最初の要素を検索</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">])</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">            </span><span class="n">i</span><span class="o">++</span><span class="p">;</span><span class="w">          </span><span class="c1">// 左から右へピボットより大きい最初の要素を検索</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">        </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">);</span><span class="w"> </span><span class="c1">// これら二つの要素を交換</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">    </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">);</span><span class="w"> </span><span class="c1">// ピボットを二つのサブ配列の境界に交換</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w">            </span><span class="c1">// ピボットのインデックスを返す</span>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 要素を交換 */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">swap</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="p">}</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="cm">/* 分割 */</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="kt">int</span><span class="w"> </span><span class="nf">partition</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">    </span><span class="c1">// nums[left] を基準値として使用</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">left</span><span class="o">]</span><span class="p">)</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">            </span><span class="n">j</span><span class="o">--</span><span class="p">;</span><span class="w">          </span><span class="c1">// 右から左へ、基準値より小さい最初の要素を検索</span>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">left</span><span class="o">]</span><span class="p">)</span>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">            </span><span class="n">i</span><span class="o">++</span><span class="p">;</span><span class="w">          </span><span class="c1">// 左から右へ、基準値より大きい最初の要素を検索</span>
+<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w">        </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">);</span><span class="w"> </span><span class="c1">// これら2つの要素を交換</span>
+<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w">    </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">);</span><span class="w">  </span><span class="c1">// 基準値を2つの部分配列の境界に交換</span>
+<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w">             </span><span class="c1">// 基準値のインデックスを返す</span>
+<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">quickSort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Swap</span><span class="p">}</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">quickSort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Partition</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">quickSort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">partition</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="bp">partition</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">QuickSort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">swap</span><span class="p">}</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">QuickSort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">partition</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">QuickSort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">swap</span><span class="p">}</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">QuickSort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">partition</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">QuickSort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">_swap</span><span class="p">}</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">QuickSort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">_partition</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">QuickSort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">partition</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">swap</span><span class="p">}</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">partition</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">swap</span><span class="p">}</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">partition</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">QuickSort</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">partition</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.zig</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">QuickSort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">swap</span><span class="p">}</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a>
+<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">QuickSort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">partition</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h2 id="1151">11.5.1 &nbsp; アルゴリズムプロセス<a class="headerlink" href="#1151" title="Permanent link">&para;</a></h2>
+<p>クイックソートの全体的なプロセスは下図に示されます。</p>
+<ol>
+<li>まず、元の配列に対して「ピボット分割」を実行し、未ソートの左と右のサブ配列を取得します。</li>
+<li>次に、左と右のサブ配列に対してそれぞれ再帰的に「ピボット分割」を実行します。</li>
+<li>サブ配列の長さが1になるまで再帰を続け、配列全体のソートを完了します。</li>
+</ol>
+<p><a class="glightbox" href="../quick_sort.assets/quick_sort_overview.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Quick sort process" class="animation-figure" src="../quick_sort.assets/quick_sort_overview.png" /></a></p>
+<p align="center"> 図 11-9 &nbsp; Quick sort process </p>
+
+<div class="tabbed-set tabbed-alternate" data-tabs="3:14"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><input id="__tabbed_3_14" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label><label for="__tabbed_3_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.py</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">quick_sort</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">left</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">right</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;クイックソート&quot;&quot;&quot;</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a>    <span class="c1"># サブ配列の長さが1のときに再帰を終了</span>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a>    <span class="k">if</span> <span class="n">left</span> <span class="o">&gt;=</span> <span class="n">right</span><span class="p">:</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a>        <span class="k">return</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a>    <span class="c1"># 分割</span>
+<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a>    <span class="n">pivot</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">partition</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="n">left</span><span class="p">,</span> <span class="n">right</span><span class="p">)</span>
+<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a>    <span class="c1"># 左サブ配列と右サブ配列を再帰的に処理</span>
+<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a>    <span class="bp">self</span><span class="o">.</span><span class="n">quick_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="n">left</span><span class="p">,</span> <span class="n">pivot</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a>    <span class="bp">self</span><span class="o">.</span><span class="n">quick_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="n">pivot</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">right</span><span class="p">)</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.cpp</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* クイックソート */</span>
+<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">quickSort</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="c1">// サブ配列の長さが1の時、再帰を終了</span>
+<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">right</span><span class="p">)</span>
+<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">    </span><span class="c1">// 分割</span>
+<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">partition</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">    </span><span class="c1">// 左サブ配列と右サブ配列を再帰的に処理</span>
+<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w">    </span><span class="n">quickSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="w">    </span><span class="n">quickSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.java</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* クイックソート */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">quickSort</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="c1">// 部分配列の長さが 1 のとき再帰を終了</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">right</span><span class="p">)</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">    </span><span class="c1">// 分割</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">partition</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">    </span><span class="c1">// 左部分配列と右部分配列を再帰的に処理</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w">    </span><span class="n">quickSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w">    </span><span class="n">quickSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.cs</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">quickSort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">QuickSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.go</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">quickSort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">quickSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">quickSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.js</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">QuickSort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">quickSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.ts</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">QuickSort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">quickSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.dart</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">QuickSort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">quickSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.rs</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">QuickSort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">quick_sort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.c</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">quickSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.kt</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">quickSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">QuickSort</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">quick_sort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.zig</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">QuickSort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">quickSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h2 id="1152">11.5.2 &nbsp; アルゴリズムの特徴<a class="headerlink" href="#1152" title="Permanent link">&para;</a></h2>
+<ul>
+<li><strong><span class="arithmatex">\(O(n \log n)\)</span>の時間計算量、非適応ソート</strong>：平均的なケースでは、ピボット分割の再帰レベルは<span class="arithmatex">\(\log n\)</span>で、レベルあたりのループの総数は<span class="arithmatex">\(n\)</span>であり、全体で<span class="arithmatex">\(O(n \log n)\)</span>の時間を使用します。最悪の場合、各ラウンドのピボット分割は長さ<span class="arithmatex">\(n\)</span>の配列を長さ<span class="arithmatex">\(0\)</span>と<span class="arithmatex">\(n - 1\)</span>の2つのサブ配列に分割し、再帰レベル数が<span class="arithmatex">\(n\)</span>に達すると、各レベルのループ数は<span class="arithmatex">\(n\)</span>で、使用される総時間は<span class="arithmatex">\(O(n^2)\)</span>です。</li>
+<li><strong><span class="arithmatex">\(O(n)\)</span>の空間計算量、インプレースソート</strong>：入力配列が完全に逆順の場合、最悪の再帰深度は<span class="arithmatex">\(n\)</span>に達し、<span class="arithmatex">\(O(n)\)</span>のスタックフレーム空間を使用します。ソート操作は追加の配列の助けなしに元の配列で実行されます。</li>
+<li><strong>非安定ソート</strong>：ピボット分割の最終ステップで、ピボットは等しい要素の右側に交換される可能性があります。</li>
+</ul>
+<h2 id="1153">11.5.3 &nbsp; なぜクイックソートは高速なのか<a class="headerlink" href="#1153" title="Permanent link">&para;</a></h2>
+<p>名前が示すように、クイックソートは効率性の面で一定の利点を持つべきです。クイックソートの平均時間計算量は「マージソート」や「ヒープソート」と同じですが、以下の理由で一般的により効率的です。</p>
+<ul>
+<li><strong>最悪ケースシナリオの低い確率</strong>：クイックソートの最悪時間計算量は<span class="arithmatex">\(O(n^2)\)</span>で、マージソートほど安定していませんが、ほとんどの場合、クイックソートは<span class="arithmatex">\(O(n \log n)\)</span>の時間計算量で動作できます。</li>
+<li><strong>高いキャッシュ利用率</strong>：ピボット分割操作中、システムはサブ配列全体をキャッシュにロードできるため、要素により効率的にアクセスできます。対照的に、「ヒープソート」などのアルゴリズムは要素にジャンプ方式でアクセスする必要があり、この特徴を欠いています。</li>
+<li><strong>計算量の小さな定数係数</strong>：上記3つのアルゴリズムの中で、クイックソートは比較、代入、交換などの操作の総数が最も少ないです。これは「挿入ソート」が「バブルソート」よりも高速な理由と似ています。</li>
+</ul>
+<h2 id="1154">11.5.4 &nbsp; ピボット最適化<a class="headerlink" href="#1154" title="Permanent link">&para;</a></h2>
+<p><strong>クイックソートの時間効率は特定の入力で劣化する可能性があります</strong>。例えば、入力配列が完全に逆順の場合、最も左の要素をピボットとして選択するため、ピボット分割後、ピボットは配列の右端に交換され、左サブ配列の長さが<span class="arithmatex">\(n - 1\)</span>、右サブ配列の長さが<span class="arithmatex">\(0\)</span>になります。この方法を続けると、各ラウンドのピボット分割でサブ配列の長さが<span class="arithmatex">\(0\)</span>になり、分割統治戦略が失敗し、クイックソートは「バブルソート」に似た形に劣化します。</p>
+<p>この状況を避けるため、<strong>ピボット分割でピボット選択戦略を最適化できます</strong>。例えば、要素をランダムに選択してピボットとすることができます。ただし、運が悪く、一貫して最適でないピボットを選択した場合、効率はまだ満足できません。</p>
+<p>プログラミング言語は通常「疑似乱数」を生成することに注意することが重要です。疑似乱数シーケンスに対して特定のテストケースを構築すると、クイックソートの効率はまだ劣化する可能性があります。</p>
+<p>さらなる改善のため、3つの候補要素（通常は配列の最初、最後、中点の要素）を選択し、**これら3つの候補要素の中央値をピボットとして使用**できます。この方法で、ピボットが「小さすぎず大きすぎない」確率が大幅に増加します。もちろん、さらに多くの候補要素を選択してアルゴリズムの堅牢性をさらに向上させることもできます。この方法により、時間計算量が<span class="arithmatex">\(O(n^2)\)</span>に劣化する確率が大幅に削減されます。</p>
+<p>サンプルコードは以下の通りです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="4:14"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><input id="__tabbed_4_6" name="__tabbed_4" type="radio" /><input id="__tabbed_4_7" name="__tabbed_4" type="radio" /><input id="__tabbed_4_8" name="__tabbed_4" type="radio" /><input id="__tabbed_4_9" name="__tabbed_4" type="radio" /><input id="__tabbed_4_10" name="__tabbed_4" type="radio" /><input id="__tabbed_4_11" name="__tabbed_4" type="radio" /><input id="__tabbed_4_12" name="__tabbed_4" type="radio" /><input id="__tabbed_4_13" name="__tabbed_4" type="radio" /><input id="__tabbed_4_14" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">Python</label><label for="__tabbed_4_2">C++</label><label for="__tabbed_4_3">Java</label><label for="__tabbed_4_4">C#</label><label for="__tabbed_4_5">Go</label><label for="__tabbed_4_6">Swift</label><label for="__tabbed_4_7">JS</label><label for="__tabbed_4_8">TS</label><label for="__tabbed_4_9">Dart</label><label for="__tabbed_4_10">Rust</label><label for="__tabbed_4_11">C</label><label for="__tabbed_4_12">Kotlin</label><label for="__tabbed_4_13">Ruby</label><label for="__tabbed_4_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.py</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">median_three</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">left</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">mid</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">right</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;3つの候補要素の中央値を選択&quot;&quot;&quot;</span>
+<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a>    <span class="n">l</span><span class="p">,</span> <span class="n">m</span><span class="p">,</span> <span class="n">r</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">],</span> <span class="n">nums</span><span class="p">[</span><span class="n">mid</span><span class="p">],</span> <span class="n">nums</span><span class="p">[</span><span class="n">right</span><span class="p">]</span>
+<a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a>    <span class="k">if</span> <span class="p">(</span><span class="n">l</span> <span class="o">&lt;=</span> <span class="n">m</span> <span class="o">&lt;=</span> <span class="n">r</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="n">r</span> <span class="o">&lt;=</span> <span class="n">m</span> <span class="o">&lt;=</span> <span class="n">l</span><span class="p">):</span>
+<a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a>        <span class="k">return</span> <span class="n">mid</span>  <span class="c1"># m は l と r の間</span>
+<a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a>    <span class="k">if</span> <span class="p">(</span><span class="n">m</span> <span class="o">&lt;=</span> <span class="n">l</span> <span class="o">&lt;=</span> <span class="n">r</span><span class="p">)</span> <span class="ow">or</span> <span class="p">(</span><span class="n">r</span> <span class="o">&lt;=</span> <span class="n">l</span> <span class="o">&lt;=</span> <span class="n">m</span><span class="p">):</span>
+<a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a>        <span class="k">return</span> <span class="n">left</span>  <span class="c1"># l は m と r の間</span>
+<a id="__codelineno-28-8" name="__codelineno-28-8" href="#__codelineno-28-8"></a>    <span class="k">return</span> <span class="n">right</span>
+<a id="__codelineno-28-9" name="__codelineno-28-9" href="#__codelineno-28-9"></a>
+<a id="__codelineno-28-10" name="__codelineno-28-10" href="#__codelineno-28-10"></a><span class="k">def</span><span class="w"> </span><span class="nf">partition</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">left</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">right</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-28-11" name="__codelineno-28-11" href="#__codelineno-28-11"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;分割（三点中央値）&quot;&quot;&quot;</span>
+<a id="__codelineno-28-12" name="__codelineno-28-12" href="#__codelineno-28-12"></a>    <span class="c1"># nums[left] をピボットとして使用</span>
+<a id="__codelineno-28-13" name="__codelineno-28-13" href="#__codelineno-28-13"></a>    <span class="n">med</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">median_three</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="n">left</span><span class="p">,</span> <span class="p">(</span><span class="n">left</span> <span class="o">+</span> <span class="n">right</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span><span class="p">,</span> <span class="n">right</span><span class="p">)</span>
+<a id="__codelineno-28-14" name="__codelineno-28-14" href="#__codelineno-28-14"></a>    <span class="c1"># 中央値を配列の最左端に交換</span>
+<a id="__codelineno-28-15" name="__codelineno-28-15" href="#__codelineno-28-15"></a>    <span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">],</span> <span class="n">nums</span><span class="p">[</span><span class="n">med</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">med</span><span class="p">],</span> <span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">]</span>
+<a id="__codelineno-28-16" name="__codelineno-28-16" href="#__codelineno-28-16"></a>    <span class="c1"># nums[left] をピボットとして使用</span>
+<a id="__codelineno-28-17" name="__codelineno-28-17" href="#__codelineno-28-17"></a>    <span class="n">i</span><span class="p">,</span> <span class="n">j</span> <span class="o">=</span> <span class="n">left</span><span class="p">,</span> <span class="n">right</span>
+<a id="__codelineno-28-18" name="__codelineno-28-18" href="#__codelineno-28-18"></a>    <span class="k">while</span> <span class="n">i</span> <span class="o">&lt;</span> <span class="n">j</span><span class="p">:</span>
+<a id="__codelineno-28-19" name="__codelineno-28-19" href="#__codelineno-28-19"></a>        <span class="k">while</span> <span class="n">i</span> <span class="o">&lt;</span> <span class="n">j</span> <span class="ow">and</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">&gt;=</span> <span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">]:</span>
+<a id="__codelineno-28-20" name="__codelineno-28-20" href="#__codelineno-28-20"></a>            <span class="n">j</span> <span class="o">-=</span> <span class="mi">1</span>  <span class="c1"># 右から左へピボットより小さい最初の要素を探す</span>
+<a id="__codelineno-28-21" name="__codelineno-28-21" href="#__codelineno-28-21"></a>        <span class="k">while</span> <span class="n">i</span> <span class="o">&lt;</span> <span class="n">j</span> <span class="ow">and</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">&lt;=</span> <span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">]:</span>
+<a id="__codelineno-28-22" name="__codelineno-28-22" href="#__codelineno-28-22"></a>            <span class="n">i</span> <span class="o">+=</span> <span class="mi">1</span>  <span class="c1"># 左から右へピボットより大きい最初の要素を探す</span>
+<a id="__codelineno-28-23" name="__codelineno-28-23" href="#__codelineno-28-23"></a>        <span class="c1"># 要素を交換</span>
+<a id="__codelineno-28-24" name="__codelineno-28-24" href="#__codelineno-28-24"></a>        <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">],</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+<a id="__codelineno-28-25" name="__codelineno-28-25" href="#__codelineno-28-25"></a>    <span class="c1"># ピボットを2つのサブ配列の境界に交換</span>
+<a id="__codelineno-28-26" name="__codelineno-28-26" href="#__codelineno-28-26"></a>    <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">],</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+<a id="__codelineno-28-27" name="__codelineno-28-27" href="#__codelineno-28-27"></a>    <span class="k">return</span> <span class="n">i</span>  <span class="c1"># ピボットのインデックスを返す</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.cpp</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="cm">/* 三つの候補要素の中央値を選択 */</span>
+<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">medianThree</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">mid</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">],</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">mid</span><span class="p">],</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">right</span><span class="p">];</span>
+<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">((</span><span class="n">l</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">r</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">l</span><span class="p">))</span>
+<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">mid</span><span class="p">;</span><span class="w"> </span><span class="c1">// mはlとrの間</span>
+<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">((</span><span class="n">m</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">r</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">))</span>
+<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">left</span><span class="p">;</span><span class="w"> </span><span class="c1">// lはmとrの間</span>
+<a id="__codelineno-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-29-9" name="__codelineno-29-9" href="#__codelineno-29-9"></a><span class="p">}</span>
+<a id="__codelineno-29-10" name="__codelineno-29-10" href="#__codelineno-29-10"></a>
+<a id="__codelineno-29-11" name="__codelineno-29-11" href="#__codelineno-29-11"></a><span class="cm">/* 分割（三つの中央値） */</span>
+<a id="__codelineno-29-12" name="__codelineno-29-12" href="#__codelineno-29-12"></a><span class="kt">int</span><span class="w"> </span><span class="nf">partition</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-13" name="__codelineno-29-13" href="#__codelineno-29-13"></a><span class="w">    </span><span class="c1">// 三つの候補要素の中央値を選択</span>
+<a id="__codelineno-29-14" name="__codelineno-29-14" href="#__codelineno-29-14"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">med</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">medianThree</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-29-15" name="__codelineno-29-15" href="#__codelineno-29-15"></a><span class="w">    </span><span class="c1">// 中央値を配列の最左位置に交換</span>
+<a id="__codelineno-29-16" name="__codelineno-29-16" href="#__codelineno-29-16"></a><span class="w">    </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">med</span><span class="p">);</span>
+<a id="__codelineno-29-17" name="__codelineno-29-17" href="#__codelineno-29-17"></a><span class="w">    </span><span class="c1">// nums[left]をピボットとして使用</span>
+<a id="__codelineno-29-18" name="__codelineno-29-18" href="#__codelineno-29-18"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-29-19" name="__codelineno-29-19" href="#__codelineno-29-19"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-20" name="__codelineno-29-20" href="#__codelineno-29-20"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">])</span>
+<a id="__codelineno-29-21" name="__codelineno-29-21" href="#__codelineno-29-21"></a><span class="w">            </span><span class="n">j</span><span class="o">--</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右から左へピボットより小さい最初の要素を検索</span>
+<a id="__codelineno-29-22" name="__codelineno-29-22" href="#__codelineno-29-22"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">left</span><span class="p">])</span>
+<a id="__codelineno-29-23" name="__codelineno-29-23" href="#__codelineno-29-23"></a><span class="w">            </span><span class="n">i</span><span class="o">++</span><span class="p">;</span><span class="w">          </span><span class="c1">// 左から右へピボットより大きい最初の要素を検索</span>
+<a id="__codelineno-29-24" name="__codelineno-29-24" href="#__codelineno-29-24"></a><span class="w">        </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">);</span><span class="w"> </span><span class="c1">// これら二つの要素を交換</span>
+<a id="__codelineno-29-25" name="__codelineno-29-25" href="#__codelineno-29-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-26" name="__codelineno-29-26" href="#__codelineno-29-26"></a><span class="w">    </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">);</span><span class="w"> </span><span class="c1">// ピボットを二つのサブ配列の境界に交換</span>
+<a id="__codelineno-29-27" name="__codelineno-29-27" href="#__codelineno-29-27"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w">            </span><span class="c1">// ピボットのインデックスを返す</span>
+<a id="__codelineno-29-28" name="__codelineno-29-28" href="#__codelineno-29-28"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.java</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* 3つの候補要素の中央値を選択 */</span>
+<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">medianThree</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">mid</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">left</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">mid</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">r</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">right</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">((</span><span class="n">l</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">r</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">l</span><span class="p">))</span>
+<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">mid</span><span class="p">;</span><span class="w"> </span><span class="c1">// m は l と r の間</span>
+<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">((</span><span class="n">m</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">r</span><span class="p">)</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="p">(</span><span class="n">r</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">l</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">))</span>
+<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">left</span><span class="p">;</span><span class="w"> </span><span class="c1">// l は m と r の間</span>
+<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a><span class="p">}</span>
+<a id="__codelineno-30-10" name="__codelineno-30-10" href="#__codelineno-30-10"></a>
+<a id="__codelineno-30-11" name="__codelineno-30-11" href="#__codelineno-30-11"></a><span class="cm">/* 分割（3つの中央値） */</span>
+<a id="__codelineno-30-12" name="__codelineno-30-12" href="#__codelineno-30-12"></a><span class="kt">int</span><span class="w"> </span><span class="nf">partition</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-13" name="__codelineno-30-13" href="#__codelineno-30-13"></a><span class="w">    </span><span class="c1">// 3つの候補要素の中央値を選択</span>
+<a id="__codelineno-30-14" name="__codelineno-30-14" href="#__codelineno-30-14"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">med</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">medianThree</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-30-15" name="__codelineno-30-15" href="#__codelineno-30-15"></a><span class="w">    </span><span class="c1">// 中央値を配列の最左端の位置に交換</span>
+<a id="__codelineno-30-16" name="__codelineno-30-16" href="#__codelineno-30-16"></a><span class="w">    </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">med</span><span class="p">);</span>
+<a id="__codelineno-30-17" name="__codelineno-30-17" href="#__codelineno-30-17"></a><span class="w">    </span><span class="c1">// nums[left] を基準値として使用</span>
+<a id="__codelineno-30-18" name="__codelineno-30-18" href="#__codelineno-30-18"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-30-19" name="__codelineno-30-19" href="#__codelineno-30-19"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-20" name="__codelineno-30-20" href="#__codelineno-30-20"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">left</span><span class="o">]</span><span class="p">)</span>
+<a id="__codelineno-30-21" name="__codelineno-30-21" href="#__codelineno-30-21"></a><span class="w">            </span><span class="n">j</span><span class="o">--</span><span class="p">;</span><span class="w">          </span><span class="c1">// 右から左へ、基準値より小さい最初の要素を検索</span>
+<a id="__codelineno-30-22" name="__codelineno-30-22" href="#__codelineno-30-22"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&amp;&amp;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">left</span><span class="o">]</span><span class="p">)</span>
+<a id="__codelineno-30-23" name="__codelineno-30-23" href="#__codelineno-30-23"></a><span class="w">            </span><span class="n">i</span><span class="o">++</span><span class="p">;</span><span class="w">          </span><span class="c1">// 左から右へ、基準値より大きい最初の要素を検索</span>
+<a id="__codelineno-30-24" name="__codelineno-30-24" href="#__codelineno-30-24"></a><span class="w">        </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="p">);</span><span class="w"> </span><span class="c1">// これら2つの要素を交換</span>
+<a id="__codelineno-30-25" name="__codelineno-30-25" href="#__codelineno-30-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-26" name="__codelineno-30-26" href="#__codelineno-30-26"></a><span class="w">    </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">);</span><span class="w">  </span><span class="c1">// 基準値を2つの部分配列の境界に交換</span>
+<a id="__codelineno-30-27" name="__codelineno-30-27" href="#__codelineno-30-27"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">i</span><span class="p">;</span><span class="w">             </span><span class="c1">// 基準値のインデックスを返す</span>
+<a id="__codelineno-30-28" name="__codelineno-30-28" href="#__codelineno-30-28"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.cs</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">QuickSortMedian</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">MedianThree</span><span class="p">}</span>
+<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a>
+<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">QuickSortMedian</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Partition</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.go</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">quickSortMedian</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">medianThree</span><span class="p">}</span>
+<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a>
+<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">quickSortMedian</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">partition</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.swift</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">medianThree</span><span class="p">}</span>
+<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a>
+<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">partitionMedian</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.js</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">QuickSortMedian</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">medianThree</span><span class="p">}</span>
+<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a>
+<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">QuickSortMedian</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">partition</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.ts</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">QuickSortMedian</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">medianThree</span><span class="p">}</span>
+<a id="__codelineno-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></a>
+<a id="__codelineno-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">QuickSortMedian</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">partition</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.dart</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">QuickSortMedian</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">_medianThree</span><span class="p">}</span>
+<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a>
+<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">QuickSortMedian</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">_partition</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.rs</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">QuickSortMedian</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">median_three</span><span class="p">}</span>
+<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a>
+<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">QuickSortMedian</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">partition</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.c</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">medianThree</span><span class="p">}</span>
+<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a>
+<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">partitionMedian</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.kt</span><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">medianThree</span><span class="p">}</span>
+<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a>
+<a id="__codelineno-39-3" name="__codelineno-39-3" href="#__codelineno-39-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">partitionMedian</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">QuickSortMedian</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">median_three</span><span class="p">}</span>
+<a id="__codelineno-40-2" name="__codelineno-40-2" href="#__codelineno-40-2"></a>
+<a id="__codelineno-40-3" name="__codelineno-40-3" href="#__codelineno-40-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">QuickSortMedian</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">partition</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.zig</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">QuickSortMedian</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">medianThree</span><span class="p">}</span>
+<a id="__codelineno-41-2" name="__codelineno-41-2" href="#__codelineno-41-2"></a>
+<a id="__codelineno-41-3" name="__codelineno-41-3" href="#__codelineno-41-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">QuickSortMedian</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">partition</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h2 id="1155">11.5.5 &nbsp; 末尾再帰最適化<a class="headerlink" href="#1155" title="Permanent link">&para;</a></h2>
+<p><strong>特定の入力では、クイックソートはより多くの空間を占有する可能性があります</strong>。例えば、完全に順序付けられた入力配列を考えてみましょう。再帰でのサブ配列の長さを<span class="arithmatex">\(m\)</span>とします。各ラウンドのピボット分割で、長さ<span class="arithmatex">\(0\)</span>の左サブ配列と長さ<span class="arithmatex">\(m - 1\)</span>の右サブ配列が生成されます。これは、再帰呼び出しごとに問題サイズが1つの要素のみ減少することを意味し、各レベルの再帰での削減が非常に小さくなります。
+結果として、再帰ツリーの高さは<span class="arithmatex">\(n − 1\)</span>に達する可能性があり、これには<span class="arithmatex">\(O(n)\)</span>のスタックフレーム空間が必要です。</p>
+<p>スタックフレーム空間の蓄積を防ぐため、各ラウンドのピボットソート後に2つのサブ配列の長さを比較し、**より短いサブ配列のみを再帰的にソート**できます。より短いサブ配列の長さは<span class="arithmatex">\(n / 2\)</span>を超えないため、この方法は再帰深度が<span class="arithmatex">\(\log n\)</span>を超えないことを保証し、最悪空間計算量を<span class="arithmatex">\(O(\log n)\)</span>に最適化します。コードは以下の通りです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="5:14"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><input id="__tabbed_5_7" name="__tabbed_5" type="radio" /><input id="__tabbed_5_8" name="__tabbed_5" type="radio" /><input id="__tabbed_5_9" name="__tabbed_5" type="radio" /><input id="__tabbed_5_10" name="__tabbed_5" type="radio" /><input id="__tabbed_5_11" name="__tabbed_5" type="radio" /><input id="__tabbed_5_12" name="__tabbed_5" type="radio" /><input id="__tabbed_5_13" name="__tabbed_5" type="radio" /><input id="__tabbed_5_14" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">Python</label><label for="__tabbed_5_2">C++</label><label for="__tabbed_5_3">Java</label><label for="__tabbed_5_4">C#</label><label for="__tabbed_5_5">Go</label><label for="__tabbed_5_6">Swift</label><label for="__tabbed_5_7">JS</label><label for="__tabbed_5_8">TS</label><label for="__tabbed_5_9">Dart</label><label for="__tabbed_5_10">Rust</label><label for="__tabbed_5_11">C</label><label for="__tabbed_5_12">Kotlin</label><label for="__tabbed_5_13">Ruby</label><label for="__tabbed_5_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.py</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">quick_sort</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">left</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">right</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-42-2" name="__codelineno-42-2" href="#__codelineno-42-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;クイックソート（末尾再帰最適化）&quot;&quot;&quot;</span>
+<a id="__codelineno-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></a>    <span class="c1"># サブ配列の長さが1のときに終了</span>
+<a id="__codelineno-42-4" name="__codelineno-42-4" href="#__codelineno-42-4"></a>    <span class="k">while</span> <span class="n">left</span> <span class="o">&lt;</span> <span class="n">right</span><span class="p">:</span>
+<a id="__codelineno-42-5" name="__codelineno-42-5" href="#__codelineno-42-5"></a>        <span class="c1"># 分割操作</span>
+<a id="__codelineno-42-6" name="__codelineno-42-6" href="#__codelineno-42-6"></a>        <span class="n">pivot</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">partition</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="n">left</span><span class="p">,</span> <span class="n">right</span><span class="p">)</span>
+<a id="__codelineno-42-7" name="__codelineno-42-7" href="#__codelineno-42-7"></a>        <span class="c1"># 2つのサブ配列のうち短い方に対してクイックソートを実行</span>
+<a id="__codelineno-42-8" name="__codelineno-42-8" href="#__codelineno-42-8"></a>        <span class="k">if</span> <span class="n">pivot</span> <span class="o">-</span> <span class="n">left</span> <span class="o">&lt;</span> <span class="n">right</span> <span class="o">-</span> <span class="n">pivot</span><span class="p">:</span>
+<a id="__codelineno-42-9" name="__codelineno-42-9" href="#__codelineno-42-9"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">quick_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="n">left</span><span class="p">,</span> <span class="n">pivot</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>  <span class="c1"># 左サブ配列を再帰的にソート</span>
+<a id="__codelineno-42-10" name="__codelineno-42-10" href="#__codelineno-42-10"></a>            <span class="n">left</span> <span class="o">=</span> <span class="n">pivot</span> <span class="o">+</span> <span class="mi">1</span>  <span class="c1"># 残りの未ソート区間は [pivot + 1, right]</span>
+<a id="__codelineno-42-11" name="__codelineno-42-11" href="#__codelineno-42-11"></a>        <span class="k">else</span><span class="p">:</span>
+<a id="__codelineno-42-12" name="__codelineno-42-12" href="#__codelineno-42-12"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">quick_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="n">pivot</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">right</span><span class="p">)</span>  <span class="c1"># 右サブ配列を再帰的にソート</span>
+<a id="__codelineno-42-13" name="__codelineno-42-13" href="#__codelineno-42-13"></a>            <span class="n">right</span> <span class="o">=</span> <span class="n">pivot</span> <span class="o">-</span> <span class="mi">1</span>  <span class="c1"># 残りの未ソート区間は [left, pivot - 1]</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.cpp</span><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="cm">/* クイックソート（末尾再帰最適化） */</span>
+<a id="__codelineno-43-2" name="__codelineno-43-2" href="#__codelineno-43-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">quickSort</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-3" name="__codelineno-43-3" href="#__codelineno-43-3"></a><span class="w">    </span><span class="c1">// サブ配列の長さが1の時終了</span>
+<a id="__codelineno-43-4" name="__codelineno-43-4" href="#__codelineno-43-4"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-5" name="__codelineno-43-5" href="#__codelineno-43-5"></a><span class="w">        </span><span class="c1">// 分割操作</span>
+<a id="__codelineno-43-6" name="__codelineno-43-6" href="#__codelineno-43-6"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">partition</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-43-7" name="__codelineno-43-7" href="#__codelineno-43-7"></a><span class="w">        </span><span class="c1">// 二つのサブ配列のうち短い方でクイックソートを実行</span>
+<a id="__codelineno-43-8" name="__codelineno-43-8" href="#__codelineno-43-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">pivot</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-9" name="__codelineno-43-9" href="#__codelineno-43-9"></a><span class="w">            </span><span class="n">quickSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span><span class="w"> </span><span class="c1">// 左サブ配列を再帰的にソート</span>
+<a id="__codelineno-43-10" name="__codelineno-43-10" href="#__codelineno-43-10"></a><span class="w">            </span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">                 </span><span class="c1">// 残りの未ソート区間は[pivot + 1, right]</span>
+<a id="__codelineno-43-11" name="__codelineno-43-11" href="#__codelineno-43-11"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-12" name="__codelineno-43-12" href="#__codelineno-43-12"></a><span class="w">            </span><span class="n">quickSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span><span class="w"> </span><span class="c1">// 右サブ配列を再帰的にソート</span>
+<a id="__codelineno-43-13" name="__codelineno-43-13" href="#__codelineno-43-13"></a><span class="w">            </span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w">                 </span><span class="c1">// 残りの未ソート区間は[left, pivot - 1]</span>
+<a id="__codelineno-43-14" name="__codelineno-43-14" href="#__codelineno-43-14"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-43-15" name="__codelineno-43-15" href="#__codelineno-43-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-43-16" name="__codelineno-43-16" href="#__codelineno-43-16"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.java</span><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="cm">/* クイックソート（末尾再帰最適化） */</span>
+<a id="__codelineno-44-2" name="__codelineno-44-2" href="#__codelineno-44-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">quickSort</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-3" name="__codelineno-44-3" href="#__codelineno-44-3"></a><span class="w">    </span><span class="c1">// 部分配列の長さが 1 のとき終了</span>
+<a id="__codelineno-44-4" name="__codelineno-44-4" href="#__codelineno-44-4"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">left</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-5" name="__codelineno-44-5" href="#__codelineno-44-5"></a><span class="w">        </span><span class="c1">// 分割操作</span>
+<a id="__codelineno-44-6" name="__codelineno-44-6" href="#__codelineno-44-6"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">partition</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-44-7" name="__codelineno-44-7" href="#__codelineno-44-7"></a><span class="w">        </span><span class="c1">// 2つの部分配列のうち短い方にクイックソートを実行</span>
+<a id="__codelineno-44-8" name="__codelineno-44-8" href="#__codelineno-44-8"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">left</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">right</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">pivot</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-9" name="__codelineno-44-9" href="#__codelineno-44-9"></a><span class="w">            </span><span class="n">quickSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span><span class="w"> </span><span class="c1">// 左部分配列を再帰的にソート</span>
+<a id="__codelineno-44-10" name="__codelineno-44-10" href="#__codelineno-44-10"></a><span class="w">            </span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 残りの未ソート区間は [pivot + 1, right]</span>
+<a id="__codelineno-44-11" name="__codelineno-44-11" href="#__codelineno-44-11"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-12" name="__codelineno-44-12" href="#__codelineno-44-12"></a><span class="w">            </span><span class="n">quickSort</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">right</span><span class="p">);</span><span class="w"> </span><span class="c1">// 右部分配列を再帰的にソート</span>
+<a id="__codelineno-44-13" name="__codelineno-44-13" href="#__codelineno-44-13"></a><span class="w">            </span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">pivot</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 残りの未ソート区間は [left, pivot - 1]</span>
+<a id="__codelineno-44-14" name="__codelineno-44-14" href="#__codelineno-44-14"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-44-15" name="__codelineno-44-15" href="#__codelineno-44-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-44-16" name="__codelineno-44-16" href="#__codelineno-44-16"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.cs</span><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">QuickSortTailCall</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">QuickSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.go</span><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">quickSortTailCall</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">quickSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.swift</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">quickSortTailCall</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.js</span><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">QuickSortTailCall</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">quickSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.ts</span><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">QuickSortTailCall</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">quickSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.dart</span><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">QuickSortTailCall</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">quickSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.rs</span><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">QuickSortTailCall</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">quick_sort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.c</span><pre><span></span><code><a id="__codelineno-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">quickSortTailCall</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.kt</span><pre><span></span><code><a id="__codelineno-53-1" name="__codelineno-53-1" href="#__codelineno-53-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">quickSortTailCall</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.rb</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">QuickSortTailCall</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">quick_sort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">quick_sort.zig</span><pre><span></span><code><a id="__codelineno-55-1" name="__codelineno-55-1" href="#__codelineno-55-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">QuickSortTailCall</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">quickSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
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+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/suggestions/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.2 &nbsp; 本書の使い方
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_introduction/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#11101" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.10.1 &nbsp; アルゴリズムの過程
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#11102" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.10.2 &nbsp; アルゴリズムの特徴
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
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+      11.10.1 &nbsp; アルゴリズムの過程
+    </span>
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+      
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+  <a href="#11102" class="md-nav__link">
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+<h1 id="1110">11.10 &nbsp; 基数ソート<a class="headerlink" href="#1110" title="Permanent link">&para;</a></h1>
+<p>前の節では計数ソートを紹介しました。これは、データサイズ <span class="arithmatex">\(n\)</span> が大きいがデータ範囲 <span class="arithmatex">\(m\)</span> が小さいシナリオに適しています。<span class="arithmatex">\(n = 10^6\)</span> の学生IDをソートする必要があり、各IDが <span class="arithmatex">\(8\)</span> 桁の数字であるとします。これは、データ範囲 <span class="arithmatex">\(m = 10^8\)</span> が非常に大きいことを意味します。この場合、計数ソートを使用すると、大量のメモリスペースが必要になります。基数ソートはこの状況を回避できます。</p>
+<p><u>基数ソート</u>は計数ソートと同じ核心概念を共有し、要素の頻度をカウントすることでソートします。同時に、基数ソートは数字の桁間の漸進的関係を利用してこれを基盤としています。桁を一度に一つずつ処理してソートし、最終的なソート順序を達成します。</p>
+<h2 id="11101">11.10.1 &nbsp; アルゴリズムの過程<a class="headerlink" href="#11101" title="Permanent link">&para;</a></h2>
+<p>学生IDデータを例として、最下位桁を <span class="arithmatex">\(1\)</span> 番目、最上位桁を <span class="arithmatex">\(8\)</span> 番目とすると、基数ソートの過程は以下の図に示されています。</p>
+<ol>
+<li>桁 <span class="arithmatex">\(k = 1\)</span> を初期化します。</li>
+<li>学生IDの <span class="arithmatex">\(k\)</span> 番目の桁に対して「計数ソート」を実行します。完了後、データは <span class="arithmatex">\(k\)</span> 番目の桁に基づいて最小から最大までソートされます。</li>
+<li><span class="arithmatex">\(k\)</span> を <span class="arithmatex">\(1\)</span> 増やし、手順 <code>2.</code> に戻って反復を続け、すべての桁がソートされるまで続けます。この時点で過程が終了します。</li>
+</ol>
+<p><a class="glightbox" href="../radix_sort.assets/radix_sort_overview.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="基数ソートアルゴリズムの過程" class="animation-figure" src="../radix_sort.assets/radix_sort_overview.png" /></a></p>
+<p align="center"> 図 11-18 &nbsp; 基数ソートアルゴリズムの過程 </p>
+
+<p>以下、コード実装を詳しく見てみます。基数 <span class="arithmatex">\(d\)</span> での数 <span class="arithmatex">\(x\)</span> に対して、その <span class="arithmatex">\(k\)</span> 番目の桁 <span class="arithmatex">\(x_k\)</span> を取得するには、以下の計算式を使用できます：</p>
+<div class="arithmatex">\[
+x_k = \lfloor\frac{x}{d^{k-1}}\rfloor \bmod d
+\]</div>
+<p>ここで <span class="arithmatex">\(\lfloor a \rfloor\)</span> は浮動小数点数 <span class="arithmatex">\(a\)</span> の切り捨てを表し、<span class="arithmatex">\(\bmod \: d\)</span> は <span class="arithmatex">\(d\)</span> による剰余を表します。学生IDデータの場合、<span class="arithmatex">\(d = 10\)</span> で <span class="arithmatex">\(k \in [1, 8]\)</span> です。</p>
+<p>さらに、<span class="arithmatex">\(k\)</span> 番目の桁に基づいてソートできるように、計数ソートのコードを少し修正する必要があります：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:14"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><input id="__tabbed_1_14" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label><label for="__tabbed_1_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">radix_sort.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">digit</span><span class="p">(</span><span class="n">num</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">exp</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;要素 num の k 番目の桁を取得、exp = 10^(k-1)&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># k の代わりに exp を渡すことで、ここでコストの高い累乗計算を避けることができる</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="k">return</span> <span class="p">(</span><span class="n">num</span> <span class="o">//</span> <span class="n">exp</span><span class="p">)</span> <span class="o">%</span> <span class="mi">10</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a><span class="k">def</span><span class="w"> </span><span class="nf">counting_sort_digit</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">],</span> <span class="n">exp</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;計数ソート（nums の k 番目の桁に基づく）&quot;&quot;&quot;</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>    <span class="c1"># 10進数の桁の範囲は 0~9、したがって長さ10のバケット配列が必要</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>    <span class="n">counter</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="mi">10</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>    <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>    <span class="c1"># 数字 0~9 の出現回数を統計</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
+<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>        <span class="n">d</span> <span class="o">=</span> <span class="n">digit</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">exp</span><span class="p">)</span>  <span class="c1"># nums[i] の k 番目の桁を取得、d とする</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>        <span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">1</span>  <span class="c1"># 数字 d の出現回数を統計</span>
+<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>    <span class="c1"># 前置和を計算し、「出現回数」を「配列インデックス」に変換</span>
+<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">10</span><span class="p">):</span>
+<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>        <span class="n">counter</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">+=</span> <span class="n">counter</span><span class="p">[</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a>    <span class="c1"># 逆順に走査し、バケット統計に基づいて各要素を res に配置</span>
+<a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a>    <span class="n">res</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">n</span>
+<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a>        <span class="n">d</span> <span class="o">=</span> <span class="n">digit</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">exp</span><span class="p">)</span>
+<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a>        <span class="n">j</span> <span class="o">=</span> <span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span> <span class="o">-</span> <span class="mi">1</span>  <span class="c1"># 配列内の d のインデックス j を取得</span>
+<a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a>        <span class="n">res</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>  <span class="c1"># 現在の要素をインデックス j に配置</span>
+<a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a>        <span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span> <span class="o">-=</span> <span class="mi">1</span>  <span class="c1"># d の数を1減らす</span>
+<a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a>    <span class="c1"># 結果を使用して元の配列 nums を上書き</span>
+<a id="__codelineno-0-26" name="__codelineno-0-26" href="#__codelineno-0-26"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
+<a id="__codelineno-0-27" name="__codelineno-0-27" href="#__codelineno-0-27"></a>        <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+<a id="__codelineno-0-28" name="__codelineno-0-28" href="#__codelineno-0-28"></a>
+<a id="__codelineno-0-29" name="__codelineno-0-29" href="#__codelineno-0-29"></a><span class="k">def</span><span class="w"> </span><span class="nf">radix_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]):</span>
+<a id="__codelineno-0-30" name="__codelineno-0-30" href="#__codelineno-0-30"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;基数ソート&quot;&quot;&quot;</span>
+<a id="__codelineno-0-31" name="__codelineno-0-31" href="#__codelineno-0-31"></a>    <span class="c1"># 配列の最大要素を取得し、最大桁数を判定するために使用</span>
+<a id="__codelineno-0-32" name="__codelineno-0-32" href="#__codelineno-0-32"></a>    <span class="n">m</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
+<a id="__codelineno-0-33" name="__codelineno-0-33" href="#__codelineno-0-33"></a>    <span class="c1"># 最下位桁から最上位桁まで走査</span>
+<a id="__codelineno-0-34" name="__codelineno-0-34" href="#__codelineno-0-34"></a>    <span class="n">exp</span> <span class="o">=</span> <span class="mi">1</span>
+<a id="__codelineno-0-35" name="__codelineno-0-35" href="#__codelineno-0-35"></a>    <span class="k">while</span> <span class="n">exp</span> <span class="o">&lt;=</span> <span class="n">m</span><span class="p">:</span>
+<a id="__codelineno-0-36" name="__codelineno-0-36" href="#__codelineno-0-36"></a>        <span class="c1"># 配列要素の k 番目の桁に対して計数ソートを実行</span>
+<a id="__codelineno-0-37" name="__codelineno-0-37" href="#__codelineno-0-37"></a>        <span class="c1"># k = 1 -&gt; exp = 1</span>
+<a id="__codelineno-0-38" name="__codelineno-0-38" href="#__codelineno-0-38"></a>        <span class="c1"># k = 2 -&gt; exp = 10</span>
+<a id="__codelineno-0-39" name="__codelineno-0-39" href="#__codelineno-0-39"></a>        <span class="c1"># つまり、exp = 10^(k-1)</span>
+<a id="__codelineno-0-40" name="__codelineno-0-40" href="#__codelineno-0-40"></a>        <span class="n">counting_sort_digit</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span> <span class="n">exp</span><span class="p">)</span>
+<a id="__codelineno-0-41" name="__codelineno-0-41" href="#__codelineno-0-41"></a>        <span class="n">exp</span> <span class="o">*=</span> <span class="mi">10</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">radix_sort.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 要素numのk番目の桁を取得、exp = 10^(k-1) */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">digit</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// kの代わりにexpを渡すことで、ここで繰り返される高価な冪乗計算を避けることができる</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">num</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mi">10</span><span class="p">;</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="p">}</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="cm">/* カウントソート（numsのk番目の桁に基づく） */</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="kt">void</span><span class="w"> </span><span class="nf">countingSortDigit</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">    </span><span class="c1">// 10進数の桁範囲は0~9なので、長さ10のバケット配列が必要</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">counter</span><span class="p">(</span><span class="mi">10</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">    </span><span class="c1">// 数字0~9の出現回数を統計</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">d</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">digit</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">exp</span><span class="p">);</span><span class="w"> </span><span class="c1">// nums[i]のk番目の桁を取得、dとして記録</span>
+<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">        </span><span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span><span class="o">++</span><span class="p">;</span><span class="w">                </span><span class="c1">// 数字dの出現回数を統計</span>
+<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w">    </span><span class="c1">// 前缀和を計算し、「出現回数」を「配列インデックス」に変換</span>
+<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">10</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="w">        </span><span class="n">counter</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">counter</span><span class="p">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">];</span>
+<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="w">    </span><span class="c1">// 逆順で走査し、バケット統計に基づいて各要素をresに配置</span>
+<a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">(</span><span class="n">n</span><span class="p">,</span><span class="w"> </span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-24" name="__codelineno-1-24" href="#__codelineno-1-24"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">d</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">digit</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">exp</span><span class="p">);</span>
+<a id="__codelineno-1-25" name="__codelineno-1-25" href="#__codelineno-1-25"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// dが配列内にあるインデックスjを取得</span>
+<a id="__codelineno-1-26" name="__codelineno-1-26" href="#__codelineno-1-26"></a><span class="w">        </span><span class="n">res</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">];</span><span class="w">       </span><span class="c1">// 現在の要素をインデックスjに配置</span>
+<a id="__codelineno-1-27" name="__codelineno-1-27" href="#__codelineno-1-27"></a><span class="w">        </span><span class="n">counter</span><span class="p">[</span><span class="n">d</span><span class="p">]</span><span class="o">--</span><span class="p">;</span><span class="w">           </span><span class="c1">// dのカウントを1減らす</span>
+<a id="__codelineno-1-28" name="__codelineno-1-28" href="#__codelineno-1-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-29" name="__codelineno-1-29" href="#__codelineno-1-29"></a><span class="w">    </span><span class="c1">// 結果で元の配列numsを上書き</span>
+<a id="__codelineno-1-30" name="__codelineno-1-30" href="#__codelineno-1-30"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span>
+<a id="__codelineno-1-31" name="__codelineno-1-31" href="#__codelineno-1-31"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-1-32" name="__codelineno-1-32" href="#__codelineno-1-32"></a><span class="p">}</span>
+<a id="__codelineno-1-33" name="__codelineno-1-33" href="#__codelineno-1-33"></a>
+<a id="__codelineno-1-34" name="__codelineno-1-34" href="#__codelineno-1-34"></a><span class="cm">/* 基数ソート */</span>
+<a id="__codelineno-1-35" name="__codelineno-1-35" href="#__codelineno-1-35"></a><span class="kt">void</span><span class="w"> </span><span class="nf">radixSort</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-36" name="__codelineno-1-36" href="#__codelineno-1-36"></a><span class="w">    </span><span class="c1">// 配列の最大要素を取得、最大桁数を判定するために使用</span>
+<a id="__codelineno-1-37" name="__codelineno-1-37" href="#__codelineno-1-37"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="o">*</span><span class="n">max_element</span><span class="p">(</span><span class="n">nums</span><span class="p">.</span><span class="n">begin</span><span class="p">(),</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">end</span><span class="p">());</span>
+<a id="__codelineno-1-38" name="__codelineno-1-38" href="#__codelineno-1-38"></a><span class="w">    </span><span class="c1">// 最下位桁から最上位桁まで走査</span>
+<a id="__codelineno-1-39" name="__codelineno-1-39" href="#__codelineno-1-39"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">exp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">exp</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">exp</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">10</span><span class="p">)</span>
+<a id="__codelineno-1-40" name="__codelineno-1-40" href="#__codelineno-1-40"></a><span class="w">        </span><span class="c1">// 配列要素のk番目の桁でカウントソートを実行</span>
+<a id="__codelineno-1-41" name="__codelineno-1-41" href="#__codelineno-1-41"></a><span class="w">        </span><span class="c1">// k = 1 -&gt; exp = 1</span>
+<a id="__codelineno-1-42" name="__codelineno-1-42" href="#__codelineno-1-42"></a><span class="w">        </span><span class="c1">// k = 2 -&gt; exp = 10</span>
+<a id="__codelineno-1-43" name="__codelineno-1-43" href="#__codelineno-1-43"></a><span class="w">        </span><span class="c1">// つまり、exp = 10^(k-1)</span>
+<a id="__codelineno-1-44" name="__codelineno-1-44" href="#__codelineno-1-44"></a><span class="w">        </span><span class="n">countingSortDigit</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">exp</span><span class="p">);</span>
+<a id="__codelineno-1-45" name="__codelineno-1-45" href="#__codelineno-1-45"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">radix_sort.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 要素 num の k 番目の桁を取得、exp = 10^(k-1) */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">digit</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// k の代わりに exp を渡すことで、ここでコストの高い累乗計算の繰り返しを避けることができる</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">num</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="mi">10</span><span class="p">;</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="p">}</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="cm">/* 計数ソート（nums の k 番目の桁に基づく） */</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="kt">void</span><span class="w"> </span><span class="nf">countingSortDigit</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">exp</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">    </span><span class="c1">// 10進数の桁の範囲は 0~9、したがって長さ 10 のバケット配列が必要</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">    </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">counter</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="mi">10</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="p">;</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">    </span><span class="c1">// 桁 0~9 の出現回数を統計</span>
+<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">d</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">digit</span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">exp</span><span class="p">);</span><span class="w"> </span><span class="c1">// nums[i] の k 番目の桁を取得、d とする</span>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">        </span><span class="n">counter</span><span class="o">[</span><span class="n">d</span><span class="o">]++</span><span class="p">;</span><span class="w">                </span><span class="c1">// 桁 d の出現回数を統計</span>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w">    </span><span class="c1">// 累積和を計算し、「出現回数」を「配列インデックス」に変換</span>
+<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">10</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="w">        </span><span class="n">counter</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">+=</span><span class="w"> </span><span class="n">counter</span><span class="o">[</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="w">    </span><span class="c1">// 逆順に走査し、バケット統計に基づいて各要素を res に配置</span>
+<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a><span class="w">    </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">n</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-24" name="__codelineno-2-24" href="#__codelineno-2-24"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">d</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">digit</span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">,</span><span class="w"> </span><span class="n">exp</span><span class="p">);</span>
+<a id="__codelineno-2-25" name="__codelineno-2-25" href="#__codelineno-2-25"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">counter</span><span class="o">[</span><span class="n">d</span><span class="o">]</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="c1">// 配列内での d のインデックス j を取得</span>
+<a id="__codelineno-2-26" name="__codelineno-2-26" href="#__codelineno-2-26"></a><span class="w">        </span><span class="n">res</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">;</span><span class="w">       </span><span class="c1">// 現在の要素をインデックス j に配置</span>
+<a id="__codelineno-2-27" name="__codelineno-2-27" href="#__codelineno-2-27"></a><span class="w">        </span><span class="n">counter</span><span class="o">[</span><span class="n">d</span><span class="o">]--</span><span class="p">;</span><span class="w">           </span><span class="c1">// d のカウントを 1 減らす</span>
+<a id="__codelineno-2-28" name="__codelineno-2-28" href="#__codelineno-2-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-29" name="__codelineno-2-29" href="#__codelineno-2-29"></a><span class="w">    </span><span class="c1">// 結果で元の配列 nums を上書き</span>
+<a id="__codelineno-2-30" name="__codelineno-2-30" href="#__codelineno-2-30"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span>
+<a id="__codelineno-2-31" name="__codelineno-2-31" href="#__codelineno-2-31"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">res</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-2-32" name="__codelineno-2-32" href="#__codelineno-2-32"></a><span class="p">}</span>
+<a id="__codelineno-2-33" name="__codelineno-2-33" href="#__codelineno-2-33"></a>
+<a id="__codelineno-2-34" name="__codelineno-2-34" href="#__codelineno-2-34"></a><span class="cm">/* 基数ソート */</span>
+<a id="__codelineno-2-35" name="__codelineno-2-35" href="#__codelineno-2-35"></a><span class="kt">void</span><span class="w"> </span><span class="nf">radixSort</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-36" name="__codelineno-2-36" href="#__codelineno-2-36"></a><span class="w">    </span><span class="c1">// 配列の最大要素を取得し、最大桁数を判定するために使用</span>
+<a id="__codelineno-2-37" name="__codelineno-2-37" href="#__codelineno-2-37"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Integer</span><span class="p">.</span><span class="na">MIN_VALUE</span><span class="p">;</span>
+<a id="__codelineno-2-38" name="__codelineno-2-38" href="#__codelineno-2-38"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span>
+<a id="__codelineno-2-39" name="__codelineno-2-39" href="#__codelineno-2-39"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">num</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">m</span><span class="p">)</span>
+<a id="__codelineno-2-40" name="__codelineno-2-40" href="#__codelineno-2-40"></a><span class="w">            </span><span class="n">m</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-2-41" name="__codelineno-2-41" href="#__codelineno-2-41"></a><span class="w">    </span><span class="c1">// 最下位桁から最上位桁まで走査</span>
+<a id="__codelineno-2-42" name="__codelineno-2-42" href="#__codelineno-2-42"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">exp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">exp</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="n">m</span><span class="p">;</span><span class="w"> </span><span class="n">exp</span><span class="w"> </span><span class="o">*=</span><span class="w"> </span><span class="mi">10</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-43" name="__codelineno-2-43" href="#__codelineno-2-43"></a><span class="w">        </span><span class="c1">// 配列要素の k 番目の桁に対して計数ソートを実行</span>
+<a id="__codelineno-2-44" name="__codelineno-2-44" href="#__codelineno-2-44"></a><span class="w">        </span><span class="c1">// k = 1 -&gt; exp = 1</span>
+<a id="__codelineno-2-45" name="__codelineno-2-45" href="#__codelineno-2-45"></a><span class="w">        </span><span class="c1">// k = 2 -&gt; exp = 10</span>
+<a id="__codelineno-2-46" name="__codelineno-2-46" href="#__codelineno-2-46"></a><span class="w">        </span><span class="c1">// すなわち exp = 10^(k-1)</span>
+<a id="__codelineno-2-47" name="__codelineno-2-47" href="#__codelineno-2-47"></a><span class="w">        </span><span class="n">countingSortDigit</span><span class="p">(</span><span class="n">nums</span><span class="p">,</span><span class="w"> </span><span class="n">exp</span><span class="p">);</span>
+<a id="__codelineno-2-48" name="__codelineno-2-48" href="#__codelineno-2-48"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-49" name="__codelineno-2-49" href="#__codelineno-2-49"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">radix_sort.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">radix_sort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Digit</span><span class="p">}</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">radix_sort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">CountingSortDigit</span><span class="p">}</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="na">[class]</span><span class="p">{</span><span class="n">radix_sort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">RadixSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">radix_sort.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">digit</span><span class="p">}</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">countingSortDigit</span><span class="p">}</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">radixSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">radix_sort.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">digit</span><span class="p">}</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">countingSortDigit</span><span class="p">}</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">radixSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">radix_sort.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">digit</span><span class="p">}</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">countingSortDigit</span><span class="p">}</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">radixSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">radix_sort.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">digit</span><span class="p">}</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">countingSortDigit</span><span class="p">}</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">radixSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">radix_sort.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">digit</span><span class="p">}</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">countingSortDigit</span><span class="p">}</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">radixSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">radix_sort.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">digit</span><span class="p">}</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">counting_sort_digit</span><span class="p">}</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">radix_sort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">radix_sort.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">digit</span><span class="p">}</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">countingSortDigit</span><span class="p">}</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">radixSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">radix_sort.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">digit</span><span class="p">}</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">countingSortDigit</span><span class="p">}</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">radixSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">radix_sort.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">digit</span><span class="p">}</span>
+<a id="__codelineno-12-2" name="__codelineno-12-2" href="#__codelineno-12-2"></a>
+<a id="__codelineno-12-3" name="__codelineno-12-3" href="#__codelineno-12-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">counting_sort_digit</span><span class="p">}</span>
+<a id="__codelineno-12-4" name="__codelineno-12-4" href="#__codelineno-12-4"></a>
+<a id="__codelineno-12-5" name="__codelineno-12-5" href="#__codelineno-12-5"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">radix_sort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">radix_sort.zig</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">digit</span><span class="p">}</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a>
+<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">countingSortDigit</span><span class="p">}</span>
+<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a>
+<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">radixSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<div class="admonition question">
+<p class="admonition-title">なぜ最下位桁から開始するのか？</p>
+<p>連続するソートラウンドでは、後のラウンドの結果が前のラウンドの結果を上書きします。例えば、最初のラウンドの結果が <span class="arithmatex">\(a &lt; b\)</span> で、2番目のラウンドが <span class="arithmatex">\(a &gt; b\)</span> の場合、2番目のラウンドの結果が最初のラウンドの結果を置き換えます。上位桁は下位桁より優先されるため、上位桁の前に下位桁をソートすることが理にかなっています。</p>
+</div>
+<h2 id="11102">11.10.2 &nbsp; アルゴリズムの特徴<a class="headerlink" href="#11102" title="Permanent link">&para;</a></h2>
+<p>計数ソートと比較して、基数ソートはより大きな数値範囲に適していますが、<strong>データが固定桁数で表現でき、桁数があまり大きくないことを前提としています</strong>。例えば、浮動小数点数は桁数 <span class="arithmatex">\(k\)</span> が大きい可能性があり、時間計算量 <span class="arithmatex">\(O(nk) \gg O(n^2)\)</span> につながる可能性があるため、基数ソートには適していません。</p>
+<ul>
+<li><strong>時間計算量は <span class="arithmatex">\(O(nk)\)</span>、非適応ソート</strong>：データサイズを <span class="arithmatex">\(n\)</span>、データが基数 <span class="arithmatex">\(d\)</span>、最大桁数を <span class="arithmatex">\(k\)</span> とすると、単一桁のソートには <span class="arithmatex">\(O(n + d)\)</span> 時間がかかり、すべての <span class="arithmatex">\(k\)</span> 桁のソートには <span class="arithmatex">\(O((n + d)k)\)</span> 時間がかかります。一般的に、<span class="arithmatex">\(d\)</span> と <span class="arithmatex">\(k\)</span> はどちらも比較的小さく、時間計算量は <span class="arithmatex">\(O(n)\)</span> に近づきます。</li>
+<li><strong>空間計算量は <span class="arithmatex">\(O(n + d)\)</span>、非インプレースソート</strong>：計数ソートと同様に、基数ソートは長さ <span class="arithmatex">\(n\)</span> と <span class="arithmatex">\(d\)</span> の配列 <code>res</code> と <code>counter</code> にそれぞれ依存します。</li>
+<li><strong>安定ソート</strong>：計数ソートが安定な場合、基数ソートも安定です。計数ソートが不安定な場合、基数ソートは正しいソート順序を保証できません。</li>
+</ul>
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diff --git a/ja/chapter_sorting/selection_sort.assets/selection_sort_step4.png b/ja/chapter_sorting/selection_sort.assets/selection_sort_step4.png
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diff --git a/ja/chapter_sorting/selection_sort.assets/selection_sort_step8.png b/ja/chapter_sorting/selection_sort.assets/selection_sort_step8.png
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diff --git a/ja/chapter_sorting/selection_sort/index.html b/ja/chapter_sorting/selection_sort/index.html
new file mode 100644
index 000000000..1074584eb
--- /dev/null
+++ b/ja/chapter_sorting/selection_sort/index.html
@@ -0,0 +1,3983 @@
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+  
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+  
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+      <a href="../../chapter_preface/about_the_book/" class="md-nav__link">
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+      <a href="../../chapter_preface/summary/" class="md-nav__link">
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+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
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+  
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+    1.1 &nbsp; アルゴリズムはどこにでもある
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+  
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+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
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+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
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+    </li>
+  
+
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+              
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+  
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+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
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+    </li>
+  
+
+              
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+          
+        
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+        
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+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
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+  
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+            第 2 章 &nbsp; 計算量解析
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+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
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+    2.1 &nbsp; アルゴリズム効率評価
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+  
+
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+
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+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
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+    2.2 &nbsp; 反復と再帰
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+  
+
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+    </li>
+  
+
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+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
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+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
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+
+              
+            
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+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
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+  
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+    第 3 章 &nbsp; データ構造
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+            第 3 章 &nbsp; データ構造
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+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
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+    3.1 &nbsp; データ構造の分類
+  </span>
+  
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+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
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+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
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+
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+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
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+  </span>
+  
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+    </li>
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+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
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+  </span>
+  
+
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+    </li>
+  
+
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+  
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+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
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+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
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+  
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+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1121" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.2.1 &nbsp; アルゴリズムの特性
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
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+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
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+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
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+            
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+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
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+          
+        
+      
+        
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+        
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+      
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+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
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+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
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+            
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+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
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+      
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+          
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+      
+        
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+    
+    
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+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
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+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_appendix/" class="md-nav__link ">
+              
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
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+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
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+            
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+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
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+              
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
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+              
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+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
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+  
+  <span class="md-ellipsis">
+    参考文献
+  </span>
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+                  <div class="md-sidebar__inner">
+                    
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+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
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+      目次
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+      
+        <li class="md-nav__item">
+  <a href="#1121" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.2.1 &nbsp; アルゴリズムの特性
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+                  </div>
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+              </div>
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+      
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
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+
+<!-- Page content -->
+<h1 id="112">11.2 &nbsp; 選択ソート<a class="headerlink" href="#112" title="Permanent link">&para;</a></h1>
+<p><u>選択ソート</u>は非常にシンプルな原理で動作します：各反復で未ソート区間から最小要素を選択し、ソート済みセクションの末尾に移動するループを使用します。</p>
+<p>配列の長さを<span class="arithmatex">\(n\)</span>とすると、選択ソートのステップは下図に示されます。</p>
+<ol>
+<li>最初に、すべての要素は未ソートで、つまり未ソート（インデックス）区間は<span class="arithmatex">\([0, n-1]\)</span>です。</li>
+<li>区間<span class="arithmatex">\([0, n-1]\)</span>の最小要素を選択し、インデックス<span class="arithmatex">\(0\)</span>の要素と交換します。この後、配列の最初の要素がソートされます。</li>
+<li>区間<span class="arithmatex">\([1, n-1]\)</span>の最小要素を選択し、インデックス<span class="arithmatex">\(1\)</span>の要素と交換します。この後、配列の最初の2つの要素がソートされます。</li>
+<li>この方法で続行します。<span class="arithmatex">\(n - 1\)</span>ラウンドの選択と交換の後、最初の<span class="arithmatex">\(n - 1\)</span>個の要素がソートされます。</li>
+<li>残りの唯一の要素は結果的に最大要素であり、ソートする必要がないため、配列はソートされます。</li>
+</ol>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:11"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">&lt;1&gt;</label><label for="__tabbed_1_2">&lt;2&gt;</label><label for="__tabbed_1_3">&lt;3&gt;</label><label for="__tabbed_1_4">&lt;4&gt;</label><label for="__tabbed_1_5">&lt;5&gt;</label><label for="__tabbed_1_6">&lt;6&gt;</label><label for="__tabbed_1_7">&lt;7&gt;</label><label for="__tabbed_1_8">&lt;8&gt;</label><label for="__tabbed_1_9">&lt;9&gt;</label><label for="__tabbed_1_10">&lt;10&gt;</label><label for="__tabbed_1_11">&lt;11&gt;</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<p><a class="glightbox" href="../selection_sort.assets/selection_sort_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Selection sort process" class="animation-figure" src="../selection_sort.assets/selection_sort_step1.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../selection_sort.assets/selection_sort_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="selection_sort_step2" class="animation-figure" src="../selection_sort.assets/selection_sort_step2.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../selection_sort.assets/selection_sort_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="selection_sort_step3" class="animation-figure" src="../selection_sort.assets/selection_sort_step3.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../selection_sort.assets/selection_sort_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="selection_sort_step4" class="animation-figure" src="../selection_sort.assets/selection_sort_step4.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../selection_sort.assets/selection_sort_step5.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="selection_sort_step5" class="animation-figure" src="../selection_sort.assets/selection_sort_step5.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../selection_sort.assets/selection_sort_step6.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="selection_sort_step6" class="animation-figure" src="../selection_sort.assets/selection_sort_step6.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../selection_sort.assets/selection_sort_step7.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="selection_sort_step7" class="animation-figure" src="../selection_sort.assets/selection_sort_step7.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../selection_sort.assets/selection_sort_step8.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="selection_sort_step8" class="animation-figure" src="../selection_sort.assets/selection_sort_step8.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../selection_sort.assets/selection_sort_step9.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="selection_sort_step9" class="animation-figure" src="../selection_sort.assets/selection_sort_step9.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../selection_sort.assets/selection_sort_step10.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="selection_sort_step10" class="animation-figure" src="../selection_sort.assets/selection_sort_step10.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../selection_sort.assets/selection_sort_step11.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="selection_sort_step11" class="animation-figure" src="../selection_sort.assets/selection_sort_step11.png" /></a></p>
+</div>
+</div>
+</div>
+<p align="center"> 図 11-2 &nbsp; Selection sort process </p>
+
+<p>コードでは、<span class="arithmatex">\(k\)</span>を使用して未ソート区間内の最小要素を記録します：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:14"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><input id="__tabbed_2_14" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label><label for="__tabbed_2_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">selection_sort.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">selection_sort</span><span class="p">(</span><span class="n">nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]):</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;選択ソート&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">nums</span><span class="p">)</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="c1"># 外側のループ：未ソート範囲は [i, n-1]</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span> <span class="o">-</span> <span class="mi">1</span><span class="p">):</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>        <span class="c1"># 内側のループ：未ソート範囲内で最小要素を見つける</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>        <span class="n">k</span> <span class="o">=</span> <span class="n">i</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>        <span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">n</span><span class="p">):</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>            <span class="k">if</span> <span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span> <span class="o">&lt;</span> <span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">]:</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>                <span class="n">k</span> <span class="o">=</span> <span class="n">j</span>  <span class="c1"># 最小要素のインデックスを記録</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>        <span class="c1"># 最小要素を未ソート範囲の先頭要素と交換</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>        <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">=</span> <span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">],</span> <span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">selection_sort.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 選択ソート */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">selectionSort</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="c1">// 外側ループ：未ソート範囲は[i, n-1]</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">        </span><span class="c1">// 内側ループ：未ソート範囲内で最小要素を見つける</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="p">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">])</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">                </span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span><span class="p">;</span><span class="w"> </span><span class="c1">// 最小要素のインデックスを記録</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">        </span><span class="c1">// 最小要素を未ソート範囲の最初の要素と交換</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">        </span><span class="n">swap</span><span class="p">(</span><span class="n">nums</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">k</span><span class="p">]);</span>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">selection_sort.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 選択ソート */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">selectionSort</span><span class="p">(</span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="p">;</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="c1">// 外側ループ: 未ソート範囲は [i, n-1]</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">        </span><span class="c1">// 内側ループ: 未ソート範囲内で最小要素を見つける</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="p">;</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">n</span><span class="p">;</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="o">]</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">k</span><span class="o">]</span><span class="p">)</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">                </span><span class="n">k</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">j</span><span class="p">;</span><span class="w"> </span><span class="c1">// 最小要素のインデックスを記録</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">        </span><span class="c1">// 最小要素と未ソート範囲の最初の要素を交換</span>
+<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">k</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">k</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="p">;</span>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">selection_sort.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">selection_sort</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">SelectionSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">selection_sort.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">selectionSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">selection_sort.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">selectionSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">selection_sort.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">selectionSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">selection_sort.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">selectionSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">selection_sort.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">selectionSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">selection_sort.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">selection_sort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">selection_sort.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">selectionSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">selection_sort.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">selectionSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">selection_sort.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">selection_sort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">selection_sort.zig</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">selectionSort</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h2 id="1121">11.2.1 &nbsp; アルゴリズムの特性<a class="headerlink" href="#1121" title="Permanent link">&para;</a></h2>
+<ul>
+<li><strong><span class="arithmatex">\(O(n^2)\)</span>の時間計算量、非適応ソート</strong>：外側ループに<span class="arithmatex">\(n - 1\)</span>回の反復があり、未ソートセクションの長さは最初の反復で<span class="arithmatex">\(n\)</span>から始まり、最後の反復で<span class="arithmatex">\(2\)</span>まで減少します。つまり、各外側ループ反復にはそれぞれ<span class="arithmatex">\(n\)</span>、<span class="arithmatex">\(n - 1\)</span>、<span class="arithmatex">\(\dots\)</span>、<span class="arithmatex">\(3\)</span>、<span class="arithmatex">\(2\)</span>回の内側ループ反復が含まれ、合計は<span class="arithmatex">\(\frac{(n - 1)(n + 2)}{2}\)</span>となります。</li>
+<li><strong><span class="arithmatex">\(O(1)\)</span>の空間計算量、インプレースソート</strong>：ポインタ<span class="arithmatex">\(i\)</span>と<span class="arithmatex">\(j\)</span>で定数の追加空間を使用します。</li>
+<li><strong>非安定ソート</strong>：下図に示すように、要素<code>nums[i]</code>は等しい要素の右側に交換される可能性があり、相対順序が変わる原因となります。</li>
+</ul>
+<p><a class="glightbox" href="../selection_sort.assets/selection_sort_instability.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Selection sort instability example" class="animation-figure" src="../selection_sort.assets/selection_sort_instability.png" /></a></p>
+<p align="center"> 図 11-3 &nbsp; Selection sort instability example </p>
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+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1111" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.1.1 &nbsp; 評価次元
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#1112" class="md-nav__link">
+    <span class="md-ellipsis">
+      11.1.2 &nbsp; 理想的なソートアルゴリズム
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_19" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_reference/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9 3v15h3V3H9m3 2 4 13 3-1-4-13-3 1M5 5v13h3V5H5M3 19v2h18v-2H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    参考文献
+  </span>
+  
+
+            </a>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_19_label" aria-expanded="false">
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+            参考文献
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+      
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+</nav>
+                  </div>
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+<h1 id="111">11.1 &nbsp; ソートアルゴリズム<a class="headerlink" href="#111" title="Permanent link">&para;</a></h1>
+<p><u>ソートアルゴリズム</u>は、データセットを特定の順序で配列するために使用されます。ソートアルゴリズムは、順序付けられたデータは通常、より効率的に探索、分析、処理できるため、幅広い応用があります。</p>
+<p>下図に示すように、ソートアルゴリズムのデータ型は整数、浮動小数点数、文字、文字列などです。ソート基準は、数値サイズ、文字ASCII順序、またはカスタム基準など、必要に応じて設定できます。</p>
+<p><a class="glightbox" href="../sorting_algorithm.assets/sorting_examples.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="Data types and comparator examples" class="animation-figure" src="../sorting_algorithm.assets/sorting_examples.png" /></a></p>
+<p align="center"> 図 11-1 &nbsp; Data types and comparator examples </p>
+
+<h2 id="1111">11.1.1 &nbsp; 評価次元<a class="headerlink" href="#1111" title="Permanent link">&para;</a></h2>
+<p><strong>実行効率</strong>：ソートアルゴリズムの時間計算量ができるだけ低いことを期待し、全体的な操作数も少ないこと（時間計算量の定数項を下げる）を望みます。大容量データでは、実行効率が特に重要です。</p>
+<p><strong>インプレース性</strong>：名前が示すとおり、<u>インプレースソート</u>は元の配列を直接操作することで実現され、追加のヘルパー配列が不要であるため、メモリを節約します。一般的に、インプレースソートはデータ移動操作が少なく、高速です。</p>
+<p><strong>安定性</strong>：<u>安定ソート</u>は、ソート後に配列内の等しい要素の相対順序が変わらないことを保証します。</p>
+<p>安定ソートは、マルチキーソートシナリオにおいて必要条件です。学生情報を格納するテーブルがあり、第1列と第2列がそれぞれ名前と年齢であるとします。この場合、<u>不安定ソート</u>は入力データの順序を失う可能性があります：</p>
+<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="c1"># 入力データは名前でソート済み</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="c1"># (名前, 年齢)</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="w">  </span><span class="o">(</span><span class="s1">&#39;A&#39;</span>,<span class="w"> </span><span class="m">19</span><span class="o">)</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="w">  </span><span class="o">(</span><span class="s1">&#39;B&#39;</span>,<span class="w"> </span><span class="m">18</span><span class="o">)</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a><span class="w">  </span><span class="o">(</span><span class="s1">&#39;C&#39;</span>,<span class="w"> </span><span class="m">21</span><span class="o">)</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a><span class="w">  </span><span class="o">(</span><span class="s1">&#39;D&#39;</span>,<span class="w"> </span><span class="m">19</span><span class="o">)</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="w">  </span><span class="o">(</span><span class="s1">&#39;E&#39;</span>,<span class="w"> </span><span class="m">23</span><span class="o">)</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a><span class="c1"># 不安定ソートアルゴリズムを使用してリストを年齢でソートすると仮定すると、</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a><span class="c1"># 結果は(&#39;D&#39;, 19)と(&#39;A&#39;, 19)の相対位置を変更し、</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a><span class="c1"># 入力データが名前でソート済みであるという性質が失われる</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a><span class="w">  </span><span class="o">(</span><span class="s1">&#39;B&#39;</span>,<span class="w"> </span><span class="m">18</span><span class="o">)</span>
+<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a><span class="w">  </span><span class="o">(</span><span class="s1">&#39;D&#39;</span>,<span class="w"> </span><span class="m">19</span><span class="o">)</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a><span class="w">  </span><span class="o">(</span><span class="s1">&#39;A&#39;</span>,<span class="w"> </span><span class="m">19</span><span class="o">)</span>
+<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a><span class="w">  </span><span class="o">(</span><span class="s1">&#39;C&#39;</span>,<span class="w"> </span><span class="m">21</span><span class="o">)</span>
+<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a><span class="w">  </span><span class="o">(</span><span class="s1">&#39;E&#39;</span>,<span class="w"> </span><span class="m">23</span><span class="o">)</span>
+</code></pre></div>
+<p><strong>適応性</strong>：<u>適応ソート</u>は入力データ内の既存の順序情報を活用して計算負荷を削減し、より最適な時間効率を実現します。適応ソートアルゴリズムの最良ケース時間計算量は、通常平均ケース時間計算量よりも優れています。</p>
+<p><strong>比較ベースまたは非比較ベース</strong>：<u>比較ベースソート</u>は比較演算子（<span class="arithmatex">\(&lt;\)</span>、<span class="arithmatex">\(=\)</span>、<span class="arithmatex">\(&gt;\)</span>）に依存して要素の相対順序を決定し、配列全体をソートします。理論的最適時間計算量は<span class="arithmatex">\(O(n \log n)\)</span>です。一方、<u>非比較ソート</u>は比較演算子を使用せず、<span class="arithmatex">\(O(n)\)</span>の時間計算量を実現できますが、汎用性は比較的劣ります。</p>
+<h2 id="1112">11.1.2 &nbsp; 理想的なソートアルゴリズム<a class="headerlink" href="#1112" title="Permanent link">&para;</a></h2>
+<p><strong>高速実行、インプレース、安定、適応、汎用</strong>。明らかに、これらのすべての特徴を組み合わせたソートアルゴリズムは今日まで見つかっていません。したがって、ソートアルゴリズムを選択する際は、データの特定の特徴と問題の要件に基づいて決定する必要があります。</p>
+<p>次に、さまざまなソートアルゴリズムを一緒に学び、上記の評価次元に基づいてそれぞれの利点と欠点を分析します。</p>
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+  
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+  
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+      <a href="../../chapter_preface/about_the_book/" class="md-nav__link">
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+      <a href="../../chapter_preface/summary/" class="md-nav__link">
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+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
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+  
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+    1.1 &nbsp; アルゴリズムはどこにでもある
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+  
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+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
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+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
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+    </li>
+  
+
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+              
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+  
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+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
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+    </li>
+  
+
+              
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+          
+        
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+        
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+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
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+  
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+            第 2 章 &nbsp; 計算量解析
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+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
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+    2.1 &nbsp; アルゴリズム効率評価
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+  
+
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+
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+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
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+    2.2 &nbsp; 反復と再帰
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+  
+
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+    </li>
+  
+
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+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
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+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
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+
+              
+            
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+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
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+  
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+    第 3 章 &nbsp; データ構造
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+            第 3 章 &nbsp; データ構造
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+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
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+    3.1 &nbsp; データ構造の分類
+  </span>
+  
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+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
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+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
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+
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+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
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+  </span>
+  
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+    </li>
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+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
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+  </span>
+  
+
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+    </li>
+  
+
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+  
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+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
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+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
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+  
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+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 重要な復習
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#2-q-a" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; Q &amp; A
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
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+      
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+          
+        
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+    
+    
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+      
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+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_19" >
+        
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+            <a href="../../chapter_reference/" class="md-nav__link ">
+              
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9 3v15h3V3H9m3 2 4 13 3-1-4-13-3 1M5 5v13h3V5H5M3 19v2h18v-2H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    参考文献
+  </span>
+  
+
+            </a>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_19_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_19">
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+            参考文献
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+            
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+      
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+  
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+    
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+</nav>
+                  </div>
+                </div>
+              </div>
+            
+            
+              
+              <div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
+                <div class="md-sidebar__scrollwrap">
+                  <div class="md-sidebar__inner">
+                    
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 重要な復習
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#2-q-a" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; Q &amp; A
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+                  </div>
+                </div>
+              </div>
+            
+          
+          
+            <div class="md-content" data-md-component="content">
+              <article class="md-content__inner md-typeset">
+                
+                  <!-- Tags -->
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+
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+
+  <!-- Edit button -->
+  
+    <a
+      href="https://github.com/krahets/hello-algo/tree/main/ja/docs/chapter_sorting/summary.md"
+      title="編集"
+      class="md-content__button md-icon"
+    >
+      
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
+    </a>
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+  <!-- View button -->
+  
+
+
+<!-- Page content -->
+<h1 id="1111">11.11 &nbsp; まとめ<a class="headerlink" href="#1111" title="Permanent link">&para;</a></h1>
+<h3 id="1">1. &nbsp; 重要な復習<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<ul>
+<li>バブルソートは隣接する要素を交換することで動作します。フラグを追加して早期リターンを可能にすることで、バブルソートの最良ケースの時間計算量を <span class="arithmatex">\(O(n)\)</span> に最適化できます。</li>
+<li>挿入ソートは、未ソート区間から要素を取り出してソート済み区間の正しい位置に挿入することで各ラウンドをソートします。挿入ソートの時間計算量は <span class="arithmatex">\(O(n^2)\)</span> ですが、単位あたりの操作が比較的少ないため、少量のデータのソートでは非常に人気があります。</li>
+<li>クイックソートは歩哨分割操作に基づいています。歩哨分割では、常に最悪のピボットを選ぶ可能性があり、時間計算量が <span class="arithmatex">\(O(n^2)\)</span> に劣化する可能性があります。中央値やランダムピボットを導入することで、そのような劣化の確率を減らすことができます。末尾再帰は再帰の深さを効果的に減らし、空間計算量を <span class="arithmatex">\(O(\log n)\)</span> に最適化します。</li>
+<li>マージソートには分割とマージの2つの段階があり、通常分割統治戦略を体現しています。マージソートでは、配列のソートには補助配列の作成が必要で、空間計算量は <span class="arithmatex">\(O(n)\)</span> になります。しかし、リストのソートの空間計算量は <span class="arithmatex">\(O(1)\)</span> に最適化できます。</li>
+<li>バケットソートは3つの手順から構成されます：データをバケットに分散、各バケット内でのソート、バケット順での結果のマージ。これも分割統治戦略を体現し、非常に大きなデータセットに適しています。バケットソートの鍵はデータの均等分散です。</li>
+<li>計数ソートはバケットソートの変形で、各データポイントの出現回数をカウントすることでソートします。計数ソートは限られた範囲のデータを持つ大きなデータセットに適しており、データを正の整数に変換する必要があります。</li>
+<li>基数ソートは桁ごとにソートすることでデータを処理し、データが固定長の数値として表現される必要があります。</li>
+<li>全体的に、私たちは高効率、安定性、インプレース操作、適応性を持つソートアルゴリズムを求めています。しかし、他のデータ構造やアルゴリズムと同様に、これらすべての条件を同時に満たすソートアルゴリズムは存在しません。実際の応用では、データの特性に基づいて適切なソートアルゴリズムを選択する必要があります。</li>
+<li>以下の図は、効率性、安定性、インプレース性、適応性の観点から主流のソートアルゴリズムを比較しています。</li>
+</ul>
+<p><a class="glightbox" href="../summary.assets/sorting_algorithms_comparison.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="ソートアルゴリズムの比較" class="animation-figure" src="../summary.assets/sorting_algorithms_comparison.png" /></a></p>
+<p align="center"> 図 11-19 &nbsp; ソートアルゴリズムの比較 </p>
+
+<h3 id="2-q-a">2. &nbsp; Q &amp; A<a class="headerlink" href="#2-q-a" title="Permanent link">&para;</a></h3>
+<p><strong>Q</strong>: ソートアルゴリズムの安定性はいつ必要ですか？</p>
+<p>実際には、オブジェクトの一つの属性に基づいてソートする場合があります。例えば、学生は名前と身長の属性を持ち、多段階ソートを実装することを目指します：最初に名前で <code>(A, 180) (B, 185) (C, 170) (D, 170)</code> を取得し、次に身長で。ソートアルゴリズムが不安定なため、<code>(D, 170) (C, 170) (A, 180) (B, 185)</code> になってしまう可能性があります。</p>
+<p>学生DとCの位置が交換され、名前の順序性が破られているのが分かります。これは望ましくありません。</p>
+<p><strong>Q</strong>: 歩哨分割での「右から左への検索」と「左から右への検索」の順序を交換できますか？</p>
+<p>いいえ、最左要素をピボットとして使用する場合、最初に「右から左への検索」を行い、次に「左から右への検索」を行う必要があります。この結論はやや直観に反するので、理由を分析してみましょう。</p>
+<p>歩哨分割 <code>partition()</code> の最後のステップは <code>nums[left]</code> と <code>nums[i]</code> を交換することです。交換後、ピボットの左側の要素はすべてピボット以下になります。<strong>これには最後の交換前に <code>nums[left] &gt;= nums[i]</code> が成り立つ必要があります</strong>。「左から右への検索」を最初に行い、ピボットより大きい要素が見つからない場合、<strong><code>i == j</code> でループを終了し、<code>nums[j] == nums[i] &gt; nums[left]</code> となる可能性があります</strong>。つまり、最終交換操作はピボットより大きい要素を配列の左端に交換し、歩哨分割を失敗させます。</p>
+<p>例えば、配列 <code>[0, 0, 0, 0, 1]</code> が与えられた場合、最初に「左から右への検索」を行うと、歩哨分割後の配列は <code>[1, 0, 0, 0, 0]</code> となり、これは正しくありません。</p>
+<p>さらに考えると、<code>nums[right]</code> をピボットとして選択する場合、まったく逆で、最初に「左から右への検索」を行う必要があります。</p>
+<p><strong>Q</strong>: 末尾再帰最適化について、短い配列を選択することで再帰の深さが <span class="arithmatex">\(\log n\)</span> を超えないことを保証するのはなぜですか？</p>
+<p>再帰の深さは現在リターンしていない再帰メソッドの数です。歩哨分割の各ラウンドは元の配列を2つの副配列に分割します。末尾再帰最適化により、再帰的に続行する副配列の長さは最大でも元の配列長の半分です。最悪の場合常に長さを半分にすると仮定すると、最終的な再帰の深さは <span class="arithmatex">\(\log n\)</span> になります。</p>
+<p>元のクイックソートを見直すと、より大きな配列を継続的に再帰処理する可能性があり、最悪の場合 <span class="arithmatex">\(n\)</span>、<span class="arithmatex">\(n - 1\)</span>、...、<span class="arithmatex">\(2\)</span>、<span class="arithmatex">\(1\)</span> で、再帰の深さは <span class="arithmatex">\(n\)</span> になります。末尾再帰最適化はこのシナリオを回避できます。</p>
+<p><strong>Q</strong>: 配列のすべての要素が等しい場合、クイックソートの時間計算量は <span class="arithmatex">\(O(n^2)\)</span> ですか？この劣化ケースをどう処理すべきですか？</p>
+<p>はい。この状況については、歩哨分割を使用して配列をピボットより小さい、等しい、大きいの3つの部分に分割することを検討してください。小さい部分と大きい部分のみを再帰的に進めます。この方法では、すべての入力要素が等しい配列を1ラウンドの歩哨分割だけでソートできます。</p>
+<p><strong>Q</strong>: なぜバケットソートの最悪ケース時間計算量は <span class="arithmatex">\(O(n^2)\)</span> ですか？</p>
+<p>最悪の場合、すべての要素が同じバケットに配置されます。これらの要素をソートするために <span class="arithmatex">\(O(n^2)\)</span> アルゴリズムを使用する場合、時間計算量は <span class="arithmatex">\(O(n^2)\)</span> になります。</p>
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+    body[data-md-color-scheme="slate"] .gdesc-inner { background: var(--md-default-bg-color);}
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+  
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+  
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+      <a href="../../chapter_preface/about_the_book/" class="md-nav__link">
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+      <a href="../../chapter_preface/summary/" class="md-nav__link">
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+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
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+  
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+    1.1 &nbsp; アルゴリズムはどこにでもある
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+  
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+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
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+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
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+    </li>
+  
+
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+              
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+  
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+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
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+    </li>
+  
+
+              
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+          
+        
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+        
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+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
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+  
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+            第 2 章 &nbsp; 計算量解析
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+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
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+    2.1 &nbsp; アルゴリズム効率評価
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+  
+
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+
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+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
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+    2.2 &nbsp; 反復と再帰
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+  
+
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+    </li>
+  
+
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+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
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+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
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+
+              
+            
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+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
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+  
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+    第 3 章 &nbsp; データ構造
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+            第 3 章 &nbsp; データ構造
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+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
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+    3.1 &nbsp; データ構造の分類
+  </span>
+  
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+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
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+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
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+
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+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
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+  </span>
+  
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+    </li>
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+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
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+  </span>
+  
+
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+    </li>
+  
+
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+  
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+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
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+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
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+  
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+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
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+  
+  
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+  
+  
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+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
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+        
+          
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+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
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+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
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+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
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+  
+    <li class="md-nav__item">
+      <a href="../stack/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
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+  
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+  
+    <li class="md-nav__item">
+      <a href="../queue/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
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+  
+
+      </a>
+    </li>
+  
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+  
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+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
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+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#531" class="md-nav__link">
+    <span class="md-ellipsis">
+      5.3.1 &nbsp; 両端キューの一般的な操作
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#532" class="md-nav__link">
+    <span class="md-ellipsis">
+      5.3.2 &nbsp; 両端キューの実装 *
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="5.3.2   両端キューの実装 *">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 双方向連結リストに基づく実装
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; 配列に基づく実装
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#533" class="md-nav__link">
+    <span class="md-ellipsis">
+      5.3.3 &nbsp; 両端キューの応用
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
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+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
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+      
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+  
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+  
+    
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+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
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+    
+    
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+    <li class="md-nav__item md-nav__item--nested">
+      
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+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
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+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
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+  
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+      
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+          
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
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+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_19" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_reference/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9 3v15h3V3H9m3 2 4 13 3-1-4-13-3 1M5 5v13h3V5H5M3 19v2h18v-2H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    参考文献
+  </span>
+  
+
+            </a>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_19_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_19">
+            <span class="md-nav__icon md-icon"></span>
+            参考文献
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
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+    
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+</nav>
+                  </div>
+                </div>
+              </div>
+            
+            
+              
+              <div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
+                <div class="md-sidebar__scrollwrap">
+                  <div class="md-sidebar__inner">
+                    
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#531" class="md-nav__link">
+    <span class="md-ellipsis">
+      5.3.1 &nbsp; 両端キューの一般的な操作
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#532" class="md-nav__link">
+    <span class="md-ellipsis">
+      5.3.2 &nbsp; 両端キューの実装 *
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="5.3.2   両端キューの実装 *">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 双方向連結リストに基づく実装
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; 配列に基づく実装
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#533" class="md-nav__link">
+    <span class="md-ellipsis">
+      5.3.3 &nbsp; 両端キューの応用
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+                  </div>
+                </div>
+              </div>
+            
+          
+          
+            <div class="md-content" data-md-component="content">
+              <article class="md-content__inner md-typeset">
+                
+                  <!-- Tags -->
+
+
+<!-- Actions -->
+<!-- Actions -->
+
+
+  <!-- Edit button -->
+  
+    <a
+      href="https://github.com/krahets/hello-algo/tree/main/ja/docs/chapter_stack_and_queue/deque.md"
+      title="編集"
+      class="md-content__button md-icon"
+    >
+      
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
+    </a>
+  
+
+  <!-- View button -->
+  
+
+
+<!-- Page content -->
+<h1 id="53">5.3 &nbsp; 両端キュー<a class="headerlink" href="#53" title="Permanent link">&para;</a></h1>
+<p>キューでは、先頭からの要素の削除や末尾への要素の追加のみが可能です。下図に示すように、<u>両端キュー（deque）</u>はより柔軟性を提供し、先頭と末尾の両方で要素の追加や削除を可能にします。</p>
+<p><a class="glightbox" href="../deque.assets/deque_operations.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="両端キューの操作" class="animation-figure" src="../deque.assets/deque_operations.png" /></a></p>
+<p align="center"> 図 5-7 &nbsp; 両端キューの操作 </p>
+
+<h2 id="531">5.3.1 &nbsp; 両端キューの一般的な操作<a class="headerlink" href="#531" title="Permanent link">&para;</a></h2>
+<p>両端キューの一般的な操作は以下の通りです。具体的なメソッド名は使用するプログラミング言語によって異なります。</p>
+<p align="center"> 表 5-3 &nbsp; 両端キューの操作効率 </p>
+
+<div class="center-table">
+<table>
+<thead>
+<tr>
+<th>メソッド名</th>
+<th>説明</th>
+<th>時間計算量</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td><code>pushFirst()</code></td>
+<td>先頭に要素を追加</td>
+<td><span class="arithmatex">\(O(1)\)</span></td>
+</tr>
+<tr>
+<td><code>pushLast()</code></td>
+<td>末尾に要素を追加</td>
+<td><span class="arithmatex">\(O(1)\)</span></td>
+</tr>
+<tr>
+<td><code>popFirst()</code></td>
+<td>先頭要素を削除</td>
+<td><span class="arithmatex">\(O(1)\)</span></td>
+</tr>
+<tr>
+<td><code>popLast()</code></td>
+<td>末尾要素を削除</td>
+<td><span class="arithmatex">\(O(1)\)</span></td>
+</tr>
+<tr>
+<td><code>peekFirst()</code></td>
+<td>先頭要素にアクセス</td>
+<td><span class="arithmatex">\(O(1)\)</span></td>
+</tr>
+<tr>
+<td><code>peekLast()</code></td>
+<td>末尾要素にアクセス</td>
+<td><span class="arithmatex">\(O(1)\)</span></td>
+</tr>
+</tbody>
+</table>
+</div>
+<p>同様に、プログラミング言語で実装された両端キュークラスを直接使用することができます：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">deque.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="kn">from</span><span class="w"> </span><span class="nn">collections</span><span class="w"> </span><span class="kn">import</span> <span class="n">deque</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="c1"># 両端キューを初期化</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="n">deq</span><span class="p">:</span> <span class="n">deque</span><span class="p">[</span><span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="n">deque</span><span class="p">()</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a><span class="c1"># 要素をエンキュー</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="n">deq</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>      <span class="c1"># 末尾に追加</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="n">deq</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a><span class="n">deq</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a><span class="n">deq</span><span class="o">.</span><span class="n">appendleft</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>  <span class="c1"># 先頭に追加</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a><span class="n">deq</span><span class="o">.</span><span class="n">appendleft</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>
+<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a><span class="c1"># 要素にアクセス</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a><span class="n">front</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">deq</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>  <span class="c1"># 先頭要素</span>
+<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a><span class="n">rear</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">deq</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>  <span class="c1"># 末尾要素</span>
+<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a>
+<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a><span class="c1"># 要素をデキュー</span>
+<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a><span class="n">pop_front</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">deq</span><span class="o">.</span><span class="n">popleft</span><span class="p">()</span>  <span class="c1"># 先頭要素をデキュー</span>
+<a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a><span class="n">pop_rear</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">deq</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>       <span class="c1"># 末尾要素をデキュー</span>
+<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a>
+<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a><span class="c1"># 両端キューの長さを取得</span>
+<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a><span class="n">size</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">deq</span><span class="p">)</span>
+<a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a>
+<a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a><span class="c1"># 両端キューが空かどうかを確認</span>
+<a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a><span class="n">is_empty</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">deq</span><span class="p">)</span> <span class="o">==</span> <span class="mi">0</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">deque.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 両端キューを初期化 */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="n">deque</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">deque</span><span class="p">;</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="cm">/* 要素をエンキュー */</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="n">deque</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span><span class="w">   </span><span class="c1">// 末尾に追加</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="n">deque</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="n">deque</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="n">deque</span><span class="p">.</span><span class="n">push_front</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span><span class="w">  </span><span class="c1">// 先頭に追加</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="n">deque</span><span class="p">.</span><span class="n">push_front</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="cm">/* 要素にアクセス */</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="kt">int</span><span class="w"> </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">front</span><span class="p">();</span><span class="w"> </span><span class="c1">// 先頭要素</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="kt">int</span><span class="w"> </span><span class="n">back</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">back</span><span class="p">();</span><span class="w">   </span><span class="c1">// 末尾要素</span>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a>
+<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="cm">/* 要素をデキュー */</span>
+<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="n">deque</span><span class="p">.</span><span class="n">pop_front</span><span class="p">();</span><span class="w">  </span><span class="c1">// 先頭要素をデキュー</span>
+<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="n">deque</span><span class="p">.</span><span class="n">pop_back</span><span class="p">();</span><span class="w">   </span><span class="c1">// 末尾要素をデキュー</span>
+<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a>
+<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a><span class="cm">/* 両端キューの長さを取得 */</span>
+<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
+<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a>
+<a id="__codelineno-1-22" name="__codelineno-1-22" href="#__codelineno-1-22"></a><span class="cm">/* 両端キューが空かどうかを確認 */</span>
+<a id="__codelineno-1-23" name="__codelineno-1-23" href="#__codelineno-1-23"></a><span class="kt">bool</span><span class="w"> </span><span class="n">empty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">empty</span><span class="p">();</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">deque.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 両端キューを初期化 */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="n">Deque</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">deque</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">LinkedList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="cm">/* 要素をエンキュー */</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="n">deque</span><span class="p">.</span><span class="na">offerLast</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span><span class="w">   </span><span class="c1">// 末尾に追加</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="n">deque</span><span class="p">.</span><span class="na">offerLast</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="n">deque</span><span class="p">.</span><span class="na">offerLast</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="n">deque</span><span class="p">.</span><span class="na">offerFirst</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span><span class="w">  </span><span class="c1">// 先頭に追加</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="n">deque</span><span class="p">.</span><span class="na">offerFirst</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="cm">/* 要素にアクセス */</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="kt">int</span><span class="w"> </span><span class="n">peekFirst</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="na">peekFirst</span><span class="p">();</span><span class="w">  </span><span class="c1">// 先頭要素</span>
+<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="kt">int</span><span class="w"> </span><span class="n">peekLast</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="na">peekLast</span><span class="p">();</span><span class="w">    </span><span class="c1">// 末尾要素</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="cm">/* 要素をデキュー */</span>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="kt">int</span><span class="w"> </span><span class="n">popFirst</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="na">pollFirst</span><span class="p">();</span><span class="w">  </span><span class="c1">// 先頭要素をデキュー</span>
+<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="kt">int</span><span class="w"> </span><span class="n">popLast</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="na">pollLast</span><span class="p">();</span><span class="w">    </span><span class="c1">// 末尾要素をデキュー</span>
+<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a>
+<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a><span class="cm">/* 両端キューの長さを取得 */</span>
+<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="na">size</span><span class="p">();</span>
+<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a>
+<a id="__codelineno-2-22" name="__codelineno-2-22" href="#__codelineno-2-22"></a><span class="cm">/* 両端キューが空かどうかを確認 */</span>
+<a id="__codelineno-2-23" name="__codelineno-2-23" href="#__codelineno-2-23"></a><span class="kt">boolean</span><span class="w"> </span><span class="n">isEmpty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="na">isEmpty</span><span class="p">();</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">deque.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 両端キューを初期化 */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="c1">// C#では、LinkedListを両端キューとして使用</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="n">LinkedList</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">deque</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">();</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="cm">/* 要素をエンキュー */</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="n">deque</span><span class="p">.</span><span class="n">AddLast</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span><span class="w">   </span><span class="c1">// 末尾に追加</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="n">deque</span><span class="p">.</span><span class="n">AddLast</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="n">deque</span><span class="p">.</span><span class="n">AddLast</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="n">deque</span><span class="p">.</span><span class="n">AddFirst</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span><span class="w">  </span><span class="c1">// 先頭に追加</span>
+<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a><span class="n">deque</span><span class="p">.</span><span class="n">AddFirst</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a>
+<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="cm">/* 要素にアクセス */</span>
+<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a><span class="kt">int</span><span class="w"> </span><span class="n">peekFirst</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">First</span><span class="p">.</span><span class="n">Value</span><span class="p">;</span><span class="w">  </span><span class="c1">// 先頭要素</span>
+<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="kt">int</span><span class="w"> </span><span class="n">peekLast</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">Last</span><span class="p">.</span><span class="n">Value</span><span class="p">;</span><span class="w">    </span><span class="c1">// 末尾要素</span>
+<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a>
+<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a><span class="cm">/* 要素をデキュー */</span>
+<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="n">deque</span><span class="p">.</span><span class="n">RemoveFirst</span><span class="p">();</span><span class="w">  </span><span class="c1">// 先頭要素をデキュー</span>
+<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="n">deque</span><span class="p">.</span><span class="n">RemoveLast</span><span class="p">();</span><span class="w">   </span><span class="c1">// 末尾要素をデキュー</span>
+<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a>
+<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="cm">/* 両端キューの長さを取得 */</span>
+<a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">Count</span><span class="p">;</span>
+<a id="__codelineno-3-22" name="__codelineno-3-22" href="#__codelineno-3-22"></a>
+<a id="__codelineno-3-23" name="__codelineno-3-23" href="#__codelineno-3-23"></a><span class="cm">/* 両端キューが空かどうかを確認 */</span>
+<a id="__codelineno-3-24" name="__codelineno-3-24" href="#__codelineno-3-24"></a><span class="kt">bool</span><span class="w"> </span><span class="n">isEmpty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">Count</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">deque_test.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 両端キューを初期化 */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="c1">// Goでは、listを両端キューとして使用</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="nx">deque</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">list</span><span class="p">.</span><span class="nx">New</span><span class="p">()</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="cm">/* 要素をエンキュー */</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="nx">deque</span><span class="p">.</span><span class="nx">PushBack</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="w">      </span><span class="c1">// 末尾に追加</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="nx">deque</span><span class="p">.</span><span class="nx">PushBack</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="nx">deque</span><span class="p">.</span><span class="nx">PushBack</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="nx">deque</span><span class="p">.</span><span class="nx">PushFront</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span><span class="w">     </span><span class="c1">// 先頭に追加</span>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="nx">deque</span><span class="p">.</span><span class="nx">PushFront</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a>
+<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="cm">/* 要素にアクセス */</span>
+<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="nx">front</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">deque</span><span class="p">.</span><span class="nx">Front</span><span class="p">()</span><span class="w"> </span><span class="c1">// 先頭要素</span>
+<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="nx">rear</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">deque</span><span class="p">.</span><span class="nx">Back</span><span class="p">()</span><span class="w">   </span><span class="c1">// 末尾要素</span>
+<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a>
+<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="cm">/* 要素をデキュー */</span>
+<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="nx">deque</span><span class="p">.</span><span class="nx">Remove</span><span class="p">(</span><span class="nx">front</span><span class="p">)</span><span class="w">    </span><span class="c1">// 先頭要素をデキュー</span>
+<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a><span class="nx">deque</span><span class="p">.</span><span class="nx">Remove</span><span class="p">(</span><span class="nx">rear</span><span class="p">)</span><span class="w">     </span><span class="c1">// 末尾要素をデキュー</span>
+<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a>
+<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="cm">/* 両端キューの長さを取得 */</span>
+<a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a><span class="nx">size</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">deque</span><span class="p">.</span><span class="nx">Len</span><span class="p">()</span>
+<a id="__codelineno-4-22" name="__codelineno-4-22" href="#__codelineno-4-22"></a>
+<a id="__codelineno-4-23" name="__codelineno-4-23" href="#__codelineno-4-23"></a><span class="cm">/* 両端キューが空かどうかを確認 */</span>
+<a id="__codelineno-4-24" name="__codelineno-4-24" href="#__codelineno-4-24"></a><span class="nx">isEmpty</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">deque</span><span class="p">.</span><span class="nx">Len</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">deque.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 両端キューを初期化 */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="c1">// Swiftには組み込みの両端キュークラスがないため、Arrayを両端キューとして使用</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="kd">var</span><span class="w"> </span><span class="nv">deque</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[]</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="cm">/* 要素をエンキュー */</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="n">deque</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span><span class="w"> </span><span class="c1">// 末尾に追加</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="n">deque</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="n">deque</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="n">deque</span><span class="p">.</span><span class="bp">insert</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="n">at</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="c1">// 先頭に追加</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="n">deque</span><span class="p">.</span><span class="bp">insert</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="n">at</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="cm">/* 要素にアクセス */</span>
+<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="kd">let</span><span class="w"> </span><span class="nv">peekFirst</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="bp">first</span><span class="p">!</span><span class="w"> </span><span class="c1">// 先頭要素</span>
+<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a><span class="kd">let</span><span class="w"> </span><span class="nv">peekLast</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="bp">last</span><span class="p">!</span><span class="w">   </span><span class="c1">// 末尾要素</span>
+<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a>
+<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="cm">/* 要素をデキュー */</span>
+<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="c1">// Arrayを使用する場合、popFirstの計算量はO(n)</span>
+<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="kd">let</span><span class="w"> </span><span class="nv">popFirst</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">removeFirst</span><span class="p">()</span><span class="w"> </span><span class="c1">// 先頭要素をデキュー</span>
+<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="kd">let</span><span class="w"> </span><span class="nv">popLast</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="bp">removeLast</span><span class="p">()</span><span class="w">   </span><span class="c1">// 末尾要素をデキュー</span>
+<a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a>
+<a id="__codelineno-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></a><span class="cm">/* 両端キューの長さを取得 */</span>
+<a id="__codelineno-5-22" name="__codelineno-5-22" href="#__codelineno-5-22"></a><span class="kd">let</span><span class="w"> </span><span class="nv">size</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="bp">count</span>
+<a id="__codelineno-5-23" name="__codelineno-5-23" href="#__codelineno-5-23"></a>
+<a id="__codelineno-5-24" name="__codelineno-5-24" href="#__codelineno-5-24"></a><span class="cm">/* 両端キューが空かどうかを確認 */</span>
+<a id="__codelineno-5-25" name="__codelineno-5-25" href="#__codelineno-5-25"></a><span class="kd">let</span><span class="w"> </span><span class="nv">isEmpty</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="bp">isEmpty</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">deque.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 両端キューを初期化 */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="c1">// JavaScriptには組み込みの両端キューがないため、Arrayを両端キューとして使用</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="kd">const</span><span class="w"> </span><span class="nx">deque</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="cm">/* 要素をエンキュー */</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="nx">deque</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">2</span><span class="p">);</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="nx">deque</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">5</span><span class="p">);</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="nx">deque</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">4</span><span class="p">);</span>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="c1">// 注意：unshift()は配列のため時間計算量がO(n)</span>
+<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="nx">deque</span><span class="p">.</span><span class="nx">unshift</span><span class="p">(</span><span class="mf">3</span><span class="p">);</span>
+<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="nx">deque</span><span class="p">.</span><span class="nx">unshift</span><span class="p">(</span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a>
+<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="cm">/* 要素にアクセス */</span>
+<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a><span class="kd">const</span><span class="w"> </span><span class="nx">peekFirst</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deque</span><span class="p">[</span><span class="mf">0</span><span class="p">];</span><span class="w"> </span><span class="c1">// 先頭要素</span>
+<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="kd">const</span><span class="w"> </span><span class="nx">peekLast</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deque</span><span class="p">[</span><span class="nx">deque</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">];</span><span class="w"> </span><span class="c1">// 末尾要素</span>
+<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a>
+<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="cm">/* 要素をデキュー */</span>
+<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a><span class="c1">// 注意：shift()は配列のため時間計算量がO(n)</span>
+<a id="__codelineno-6-19" name="__codelineno-6-19" href="#__codelineno-6-19"></a><span class="kd">const</span><span class="w"> </span><span class="nx">popFront</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deque</span><span class="p">.</span><span class="nx">shift</span><span class="p">();</span><span class="w"> </span><span class="c1">// 先頭要素をデキュー</span>
+<a id="__codelineno-6-20" name="__codelineno-6-20" href="#__codelineno-6-20"></a><span class="kd">const</span><span class="w"> </span><span class="nx">popBack</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deque</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span><span class="w">    </span><span class="c1">// 末尾要素をデキュー</span>
+<a id="__codelineno-6-21" name="__codelineno-6-21" href="#__codelineno-6-21"></a>
+<a id="__codelineno-6-22" name="__codelineno-6-22" href="#__codelineno-6-22"></a><span class="cm">/* 両端キューの長さを取得 */</span>
+<a id="__codelineno-6-23" name="__codelineno-6-23" href="#__codelineno-6-23"></a><span class="kd">const</span><span class="w"> </span><span class="nx">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deque</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-6-24" name="__codelineno-6-24" href="#__codelineno-6-24"></a>
+<a id="__codelineno-6-25" name="__codelineno-6-25" href="#__codelineno-6-25"></a><span class="cm">/* 両端キューが空かどうかを確認 */</span>
+<a id="__codelineno-6-26" name="__codelineno-6-26" href="#__codelineno-6-26"></a><span class="kd">const</span><span class="w"> </span><span class="nx">isEmpty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">size</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">deque.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 両端キューを初期化 */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="c1">// TypeScriptには組み込みの両端キューがないため、Arrayを両端キューとして使用</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="kd">const</span><span class="w"> </span><span class="nx">deque</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="cm">/* 要素をエンキュー */</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="nx">deque</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">2</span><span class="p">);</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="nx">deque</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">5</span><span class="p">);</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="nx">deque</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">4</span><span class="p">);</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="c1">// 注意：unshift()は配列のため時間計算量がO(n)</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="nx">deque</span><span class="p">.</span><span class="nx">unshift</span><span class="p">(</span><span class="mf">3</span><span class="p">);</span>
+<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="nx">deque</span><span class="p">.</span><span class="nx">unshift</span><span class="p">(</span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a>
+<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="cm">/* 要素にアクセス */</span>
+<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a><span class="kd">const</span><span class="w"> </span><span class="nx">peekFirst</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deque</span><span class="p">[</span><span class="mf">0</span><span class="p">];</span><span class="w"> </span><span class="c1">// 先頭要素</span>
+<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="kd">const</span><span class="w"> </span><span class="nx">peekLast</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deque</span><span class="p">[</span><span class="nx">deque</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">];</span><span class="w"> </span><span class="c1">// 末尾要素</span>
+<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a>
+<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="cm">/* 要素をデキュー */</span>
+<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="c1">// 注意：shift()は配列のため時間計算量がO(n)</span>
+<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="kd">const</span><span class="w"> </span><span class="nx">popFront</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deque</span><span class="p">.</span><span class="nx">shift</span><span class="p">()</span><span class="w"> </span><span class="kr">as</span><span class="w"> </span><span class="kt">number</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭要素をデキュー</span>
+<a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a><span class="kd">const</span><span class="w"> </span><span class="nx">popBack</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deque</span><span class="p">.</span><span class="nx">pop</span><span class="p">()</span><span class="w"> </span><span class="kr">as</span><span class="w"> </span><span class="kt">number</span><span class="p">;</span><span class="w">    </span><span class="c1">// 末尾要素をデキュー</span>
+<a id="__codelineno-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></a>
+<a id="__codelineno-7-22" name="__codelineno-7-22" href="#__codelineno-7-22"></a><span class="cm">/* 両端キューの長さを取得 */</span>
+<a id="__codelineno-7-23" name="__codelineno-7-23" href="#__codelineno-7-23"></a><span class="kd">const</span><span class="w"> </span><span class="nx">size</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">deque</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-7-24" name="__codelineno-7-24" href="#__codelineno-7-24"></a>
+<a id="__codelineno-7-25" name="__codelineno-7-25" href="#__codelineno-7-25"></a><span class="cm">/* 両端キューが空かどうかを確認 */</span>
+<a id="__codelineno-7-26" name="__codelineno-7-26" href="#__codelineno-7-26"></a><span class="kd">const</span><span class="w"> </span><span class="nx">isEmpty</span><span class="o">:</span><span class="w"> </span><span class="kt">boolean</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">size</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">deque.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 両端キューを初期化 */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="c1">// Dartでは、Queueが両端キューとして定義される</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="n">Queue</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">deque</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Queue</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="p">();</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="cm">/* 要素をエンキュー */</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="n">deque</span><span class="p">.</span><span class="n">addLast</span><span class="p">(</span><span class="m">2</span><span class="p">);</span><span class="w">  </span><span class="c1">// 末尾に追加</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="n">deque</span><span class="p">.</span><span class="n">addLast</span><span class="p">(</span><span class="m">5</span><span class="p">);</span>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="n">deque</span><span class="p">.</span><span class="n">addLast</span><span class="p">(</span><span class="m">4</span><span class="p">);</span>
+<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="n">deque</span><span class="p">.</span><span class="n">addFirst</span><span class="p">(</span><span class="m">3</span><span class="p">);</span><span class="w"> </span><span class="c1">// 先頭に追加</span>
+<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="n">deque</span><span class="p">.</span><span class="n">addFirst</span><span class="p">(</span><span class="m">1</span><span class="p">);</span>
+<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a>
+<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="cm">/* 要素にアクセス */</span>
+<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="kt">int</span><span class="w"> </span><span class="n">peekFirst</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">first</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭要素</span>
+<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a><span class="kt">int</span><span class="w"> </span><span class="n">peekLast</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">last</span><span class="p">;</span><span class="w">   </span><span class="c1">// 末尾要素</span>
+<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a>
+<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="cm">/* 要素をデキュー */</span>
+<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a><span class="kt">int</span><span class="w"> </span><span class="n">popFirst</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">removeFirst</span><span class="p">();</span><span class="w"> </span><span class="c1">// 先頭要素をデキュー</span>
+<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a><span class="kt">int</span><span class="w"> </span><span class="n">popLast</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">removeLast</span><span class="p">();</span><span class="w">   </span><span class="c1">// 末尾要素をデキュー</span>
+<a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a>
+<a id="__codelineno-8-20" name="__codelineno-8-20" href="#__codelineno-8-20"></a><span class="cm">/* 両端キューの長さを取得 */</span>
+<a id="__codelineno-8-21" name="__codelineno-8-21" href="#__codelineno-8-21"></a><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">length</span><span class="p">;</span>
+<a id="__codelineno-8-22" name="__codelineno-8-22" href="#__codelineno-8-22"></a>
+<a id="__codelineno-8-23" name="__codelineno-8-23" href="#__codelineno-8-23"></a><span class="cm">/* 両端キューが空かどうかを確認 */</span>
+<a id="__codelineno-8-24" name="__codelineno-8-24" href="#__codelineno-8-24"></a><span class="kt">bool</span><span class="w"> </span><span class="n">isEmpty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">isEmpty</span><span class="p">;</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">deque.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 両端キューを初期化 */</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">deque</span><span class="p">:</span><span class="w"> </span><span class="nc">VecDeque</span><span class="o">&lt;</span><span class="kt">u32</span><span class="o">&gt;</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">VecDeque</span><span class="p">::</span><span class="n">new</span><span class="p">();</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="cm">/* 要素をエンキュー */</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="n">deque</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span><span class="w">  </span><span class="c1">// 末尾に追加</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="n">deque</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="n">deque</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="n">deque</span><span class="p">.</span><span class="n">push_front</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span><span class="w"> </span><span class="c1">// 先頭に追加</span>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="n">deque</span><span class="p">.</span><span class="n">push_front</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a>
+<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="cm">/* 要素にアクセス */</span>
+<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">front</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">front</span><span class="p">()</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 先頭要素</span>
+<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="p">}</span>
+<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">rear</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">back</span><span class="p">()</span><span class="w"> </span><span class="p">{</span><span class="w">   </span><span class="c1">// 末尾要素</span>
+<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="p">}</span>
+<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a>
+<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="cm">/* 要素をデキュー */</span>
+<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">pop_front</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">pop_front</span><span class="p">()</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="c1">// 先頭要素をデキュー</span>
+<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="p">}</span>
+<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">pop_rear</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">pop_back</span><span class="p">()</span><span class="w"> </span><span class="p">{</span><span class="w">   </span><span class="c1">// 末尾要素をデキュー</span>
+<a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="p">}</span>
+<a id="__codelineno-9-22" name="__codelineno-9-22" href="#__codelineno-9-22"></a>
+<a id="__codelineno-9-23" name="__codelineno-9-23" href="#__codelineno-9-23"></a><span class="cm">/* 両端キューの長さを取得 */</span>
+<a id="__codelineno-9-24" name="__codelineno-9-24" href="#__codelineno-9-24"></a><span class="kd">let</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">len</span><span class="p">();</span>
+<a id="__codelineno-9-25" name="__codelineno-9-25" href="#__codelineno-9-25"></a>
+<a id="__codelineno-9-26" name="__codelineno-9-26" href="#__codelineno-9-26"></a><span class="cm">/* 両端キューが空かどうかを確認 */</span>
+<a id="__codelineno-9-27" name="__codelineno-9-27" href="#__codelineno-9-27"></a><span class="kd">let</span><span class="w"> </span><span class="n">is_empty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">is_empty</span><span class="p">();</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">deque.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="c1">// Cには組み込みの両端キューが提供されていません</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">deque.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">deque.zig</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h2 id="532">5.3.2 &nbsp; 両端キューの実装 *<a class="headerlink" href="#532" title="Permanent link">&para;</a></h2>
+<p>両端キューの実装は通常のキューの実装と似ており、連結リストまたは配列を基盤となるデータ構造として使用できます。</p>
+<h3 id="1">1. &nbsp; 双方向連結リストに基づく実装<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<p>前節で、通常の単一連結リストを使ってキューを実装したことを思い出してください。これは先頭からの削除（デキュー操作に対応）と末尾への新しい要素の追加（エンキュー操作に対応）を便利に行えるためでした。</p>
+<p>両端キューでは、先頭と末尾の両方でエンキューとデキュー操作を実行できます。つまり、両端キューは逆方向の操作も実装する必要があります。このため、両端キューの基盤となるデータ構造として「双方向連結リスト」を使用します。</p>
+<p>下図に示すように、双方向連結リストの先頭ノードと末尾ノードをそれぞれ両端キューの前端と後端として扱い、両端でのノードの追加と削除機能を実装します。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:5"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">LinkedListDeque</label><label for="__tabbed_2_2">pushLast()</label><label for="__tabbed_2_3">pushFirst()</label><label for="__tabbed_2_4">popLast()</label><label for="__tabbed_2_5">popFirst()</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<p><a class="glightbox" href="../deque.assets/linkedlist_deque_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="双方向連結リストによる両端キューのエンキューとデキュー操作の実装" class="animation-figure" src="../deque.assets/linkedlist_deque_step1.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../deque.assets/linkedlist_deque_step2_push_last.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="linkedlist_deque_push_last" class="animation-figure" src="../deque.assets/linkedlist_deque_step2_push_last.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../deque.assets/linkedlist_deque_step3_push_first.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="linkedlist_deque_push_first" class="animation-figure" src="../deque.assets/linkedlist_deque_step3_push_first.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../deque.assets/linkedlist_deque_step4_pop_last.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="linkedlist_deque_pop_last" class="animation-figure" src="../deque.assets/linkedlist_deque_step4_pop_last.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../deque.assets/linkedlist_deque_step5_pop_first.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="linkedlist_deque_pop_first" class="animation-figure" src="../deque.assets/linkedlist_deque_step5_pop_first.png" /></a></p>
+</div>
+</div>
+</div>
+<p align="center"> 図 5-8 &nbsp; 双方向連結リストによる両端キューのエンキューとデキュー操作の実装 </p>
+
+<p>実装コードは以下の通りです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="3:14"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><input id="__tabbed_3_14" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label><label for="__tabbed_3_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linkedlist_deque.py</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">ListNode</span><span class="p">:</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;双方向連結リストノード&quot;&quot;&quot;</span>
+<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>
+<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;コンストラクタ&quot;&quot;&quot;</span>
+<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">val</span>
+<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">next</span><span class="p">:</span> <span class="n">ListNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span>  <span class="c1"># 後続ノードへの参照</span>
+<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">prev</span><span class="p">:</span> <span class="n">ListNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span>  <span class="c1"># 前駆ノードへの参照</span>
+<a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a>
+<a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a><span class="k">class</span><span class="w"> </span><span class="nc">LinkedListDeque</span><span class="p">:</span>
+<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;双方向連結リストベースの双端キュークラス&quot;&quot;&quot;</span>
+<a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a>
+<a id="__codelineno-13-13" name="__codelineno-13-13" href="#__codelineno-13-13"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;コンストラクタ&quot;&quot;&quot;</span>
+<a id="__codelineno-13-15" name="__codelineno-13-15" href="#__codelineno-13-15"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_front</span><span class="p">:</span> <span class="n">ListNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span>  <span class="c1"># ヘッドノード front</span>
+<a id="__codelineno-13-16" name="__codelineno-13-16" href="#__codelineno-13-16"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_rear</span><span class="p">:</span> <span class="n">ListNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span>  <span class="c1"># テールノード rear</span>
+<a id="__codelineno-13-17" name="__codelineno-13-17" href="#__codelineno-13-17"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">0</span>  <span class="c1"># 双端キューの長さ</span>
+<a id="__codelineno-13-18" name="__codelineno-13-18" href="#__codelineno-13-18"></a>
+<a id="__codelineno-13-19" name="__codelineno-13-19" href="#__codelineno-13-19"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">size</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-13-20" name="__codelineno-13-20" href="#__codelineno-13-20"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;双端キューの長さを取得&quot;&quot;&quot;</span>
+<a id="__codelineno-13-21" name="__codelineno-13-21" href="#__codelineno-13-21"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span>
+<a id="__codelineno-13-22" name="__codelineno-13-22" href="#__codelineno-13-22"></a>
+<a id="__codelineno-13-23" name="__codelineno-13-23" href="#__codelineno-13-23"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">is_empty</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">bool</span><span class="p">:</span>
+<a id="__codelineno-13-24" name="__codelineno-13-24" href="#__codelineno-13-24"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;双端キューが空かどうかを判定&quot;&quot;&quot;</span>
+<a id="__codelineno-13-25" name="__codelineno-13-25" href="#__codelineno-13-25"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">==</span> <span class="mi">0</span>
+<a id="__codelineno-13-26" name="__codelineno-13-26" href="#__codelineno-13-26"></a>
+<a id="__codelineno-13-27" name="__codelineno-13-27" href="#__codelineno-13-27"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">num</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">is_front</span><span class="p">:</span> <span class="nb">bool</span><span class="p">):</span>
+<a id="__codelineno-13-28" name="__codelineno-13-28" href="#__codelineno-13-28"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;エンキュー操作&quot;&quot;&quot;</span>
+<a id="__codelineno-13-29" name="__codelineno-13-29" href="#__codelineno-13-29"></a>        <span class="n">node</span> <span class="o">=</span> <span class="n">ListNode</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-13-30" name="__codelineno-13-30" href="#__codelineno-13-30"></a>        <span class="c1"># リストが空の場合、front と rear の両方を node に向ける</span>
+<a id="__codelineno-13-31" name="__codelineno-13-31" href="#__codelineno-13-31"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">is_empty</span><span class="p">():</span>
+<a id="__codelineno-13-32" name="__codelineno-13-32" href="#__codelineno-13-32"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_rear</span> <span class="o">=</span> <span class="n">node</span>
+<a id="__codelineno-13-33" name="__codelineno-13-33" href="#__codelineno-13-33"></a>        <span class="c1"># 前端エンキュー操作</span>
+<a id="__codelineno-13-34" name="__codelineno-13-34" href="#__codelineno-13-34"></a>        <span class="k">elif</span> <span class="n">is_front</span><span class="p">:</span>
+<a id="__codelineno-13-35" name="__codelineno-13-35" href="#__codelineno-13-35"></a>            <span class="c1"># ノードをリストの先頭に追加</span>
+<a id="__codelineno-13-36" name="__codelineno-13-36" href="#__codelineno-13-36"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">_front</span><span class="o">.</span><span class="n">prev</span> <span class="o">=</span> <span class="n">node</span>
+<a id="__codelineno-13-37" name="__codelineno-13-37" href="#__codelineno-13-37"></a>            <span class="n">node</span><span class="o">.</span><span class="n">next</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_front</span>
+<a id="__codelineno-13-38" name="__codelineno-13-38" href="#__codelineno-13-38"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="o">=</span> <span class="n">node</span>  <span class="c1"># ヘッドノードを更新</span>
+<a id="__codelineno-13-39" name="__codelineno-13-39" href="#__codelineno-13-39"></a>        <span class="c1"># 後端エンキュー操作</span>
+<a id="__codelineno-13-40" name="__codelineno-13-40" href="#__codelineno-13-40"></a>        <span class="k">else</span><span class="p">:</span>
+<a id="__codelineno-13-41" name="__codelineno-13-41" href="#__codelineno-13-41"></a>            <span class="c1"># ノードをリストの末尾に追加</span>
+<a id="__codelineno-13-42" name="__codelineno-13-42" href="#__codelineno-13-42"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">_rear</span><span class="o">.</span><span class="n">next</span> <span class="o">=</span> <span class="n">node</span>
+<a id="__codelineno-13-43" name="__codelineno-13-43" href="#__codelineno-13-43"></a>            <span class="n">node</span><span class="o">.</span><span class="n">prev</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_rear</span>
+<a id="__codelineno-13-44" name="__codelineno-13-44" href="#__codelineno-13-44"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">_rear</span> <span class="o">=</span> <span class="n">node</span>  <span class="c1"># テールノードを更新</span>
+<a id="__codelineno-13-45" name="__codelineno-13-45" href="#__codelineno-13-45"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">+=</span> <span class="mi">1</span>  <span class="c1"># キューの長さを更新</span>
+<a id="__codelineno-13-46" name="__codelineno-13-46" href="#__codelineno-13-46"></a>
+<a id="__codelineno-13-47" name="__codelineno-13-47" href="#__codelineno-13-47"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">push_first</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">num</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-13-48" name="__codelineno-13-48" href="#__codelineno-13-48"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;前端エンキュー&quot;&quot;&quot;</span>
+<a id="__codelineno-13-49" name="__codelineno-13-49" href="#__codelineno-13-49"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">push</span><span class="p">(</span><span class="n">num</span><span class="p">,</span> <span class="kc">True</span><span class="p">)</span>
+<a id="__codelineno-13-50" name="__codelineno-13-50" href="#__codelineno-13-50"></a>
+<a id="__codelineno-13-51" name="__codelineno-13-51" href="#__codelineno-13-51"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">push_last</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">num</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-13-52" name="__codelineno-13-52" href="#__codelineno-13-52"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;後端エンキュー&quot;&quot;&quot;</span>
+<a id="__codelineno-13-53" name="__codelineno-13-53" href="#__codelineno-13-53"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">push</span><span class="p">(</span><span class="n">num</span><span class="p">,</span> <span class="kc">False</span><span class="p">)</span>
+<a id="__codelineno-13-54" name="__codelineno-13-54" href="#__codelineno-13-54"></a>
+<a id="__codelineno-13-55" name="__codelineno-13-55" href="#__codelineno-13-55"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">pop</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">is_front</span><span class="p">:</span> <span class="nb">bool</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-13-56" name="__codelineno-13-56" href="#__codelineno-13-56"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;デキュー操作&quot;&quot;&quot;</span>
+<a id="__codelineno-13-57" name="__codelineno-13-57" href="#__codelineno-13-57"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">is_empty</span><span class="p">():</span>
+<a id="__codelineno-13-58" name="__codelineno-13-58" href="#__codelineno-13-58"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;Double-ended queue is empty&quot;</span><span class="p">)</span>
+<a id="__codelineno-13-59" name="__codelineno-13-59" href="#__codelineno-13-59"></a>        <span class="c1"># 前端デキュー操作</span>
+<a id="__codelineno-13-60" name="__codelineno-13-60" href="#__codelineno-13-60"></a>        <span class="k">if</span> <span class="n">is_front</span><span class="p">:</span>
+<a id="__codelineno-13-61" name="__codelineno-13-61" href="#__codelineno-13-61"></a>            <span class="n">val</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_front</span><span class="o">.</span><span class="n">val</span>  <span class="c1"># ヘッドノードの値を一時的に保存</span>
+<a id="__codelineno-13-62" name="__codelineno-13-62" href="#__codelineno-13-62"></a>            <span class="c1"># ヘッドノードを削除</span>
+<a id="__codelineno-13-63" name="__codelineno-13-63" href="#__codelineno-13-63"></a>            <span class="n">fnext</span><span class="p">:</span> <span class="n">ListNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_front</span><span class="o">.</span><span class="n">next</span>
+<a id="__codelineno-13-64" name="__codelineno-13-64" href="#__codelineno-13-64"></a>            <span class="k">if</span> <span class="n">fnext</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-13-65" name="__codelineno-13-65" href="#__codelineno-13-65"></a>                <span class="n">fnext</span><span class="o">.</span><span class="n">prev</span> <span class="o">=</span> <span class="kc">None</span>
+<a id="__codelineno-13-66" name="__codelineno-13-66" href="#__codelineno-13-66"></a>                <span class="bp">self</span><span class="o">.</span><span class="n">_front</span><span class="o">.</span><span class="n">next</span> <span class="o">=</span> <span class="kc">None</span>
+<a id="__codelineno-13-67" name="__codelineno-13-67" href="#__codelineno-13-67"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="o">=</span> <span class="n">fnext</span>  <span class="c1"># ヘッドノードを更新</span>
+<a id="__codelineno-13-68" name="__codelineno-13-68" href="#__codelineno-13-68"></a>        <span class="c1"># 後端デキュー操作</span>
+<a id="__codelineno-13-69" name="__codelineno-13-69" href="#__codelineno-13-69"></a>        <span class="k">else</span><span class="p">:</span>
+<a id="__codelineno-13-70" name="__codelineno-13-70" href="#__codelineno-13-70"></a>            <span class="n">val</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_rear</span><span class="o">.</span><span class="n">val</span>  <span class="c1"># テールノードの値を一時的に保存</span>
+<a id="__codelineno-13-71" name="__codelineno-13-71" href="#__codelineno-13-71"></a>            <span class="c1"># テールノードを削除</span>
+<a id="__codelineno-13-72" name="__codelineno-13-72" href="#__codelineno-13-72"></a>            <span class="n">rprev</span><span class="p">:</span> <span class="n">ListNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_rear</span><span class="o">.</span><span class="n">prev</span>
+<a id="__codelineno-13-73" name="__codelineno-13-73" href="#__codelineno-13-73"></a>            <span class="k">if</span> <span class="n">rprev</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-13-74" name="__codelineno-13-74" href="#__codelineno-13-74"></a>                <span class="n">rprev</span><span class="o">.</span><span class="n">next</span> <span class="o">=</span> <span class="kc">None</span>
+<a id="__codelineno-13-75" name="__codelineno-13-75" href="#__codelineno-13-75"></a>                <span class="bp">self</span><span class="o">.</span><span class="n">_rear</span><span class="o">.</span><span class="n">prev</span> <span class="o">=</span> <span class="kc">None</span>
+<a id="__codelineno-13-76" name="__codelineno-13-76" href="#__codelineno-13-76"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">_rear</span> <span class="o">=</span> <span class="n">rprev</span>  <span class="c1"># テールノードを更新</span>
+<a id="__codelineno-13-77" name="__codelineno-13-77" href="#__codelineno-13-77"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">-=</span> <span class="mi">1</span>  <span class="c1"># キューの長さを更新</span>
+<a id="__codelineno-13-78" name="__codelineno-13-78" href="#__codelineno-13-78"></a>        <span class="k">return</span> <span class="n">val</span>
+<a id="__codelineno-13-79" name="__codelineno-13-79" href="#__codelineno-13-79"></a>
+<a id="__codelineno-13-80" name="__codelineno-13-80" href="#__codelineno-13-80"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">pop_first</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-13-81" name="__codelineno-13-81" href="#__codelineno-13-81"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;前端デキュー&quot;&quot;&quot;</span>
+<a id="__codelineno-13-82" name="__codelineno-13-82" href="#__codelineno-13-82"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">pop</span><span class="p">(</span><span class="kc">True</span><span class="p">)</span>
+<a id="__codelineno-13-83" name="__codelineno-13-83" href="#__codelineno-13-83"></a>
+<a id="__codelineno-13-84" name="__codelineno-13-84" href="#__codelineno-13-84"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">pop_last</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-13-85" name="__codelineno-13-85" href="#__codelineno-13-85"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;後端デキュー&quot;&quot;&quot;</span>
+<a id="__codelineno-13-86" name="__codelineno-13-86" href="#__codelineno-13-86"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">pop</span><span class="p">(</span><span class="kc">False</span><span class="p">)</span>
+<a id="__codelineno-13-87" name="__codelineno-13-87" href="#__codelineno-13-87"></a>
+<a id="__codelineno-13-88" name="__codelineno-13-88" href="#__codelineno-13-88"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">peek_first</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-13-89" name="__codelineno-13-89" href="#__codelineno-13-89"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;前端要素にアクセス&quot;&quot;&quot;</span>
+<a id="__codelineno-13-90" name="__codelineno-13-90" href="#__codelineno-13-90"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">is_empty</span><span class="p">():</span>
+<a id="__codelineno-13-91" name="__codelineno-13-91" href="#__codelineno-13-91"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;Double-ended queue is empty&quot;</span><span class="p">)</span>
+<a id="__codelineno-13-92" name="__codelineno-13-92" href="#__codelineno-13-92"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_front</span><span class="o">.</span><span class="n">val</span>
+<a id="__codelineno-13-93" name="__codelineno-13-93" href="#__codelineno-13-93"></a>
+<a id="__codelineno-13-94" name="__codelineno-13-94" href="#__codelineno-13-94"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">peek_last</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-13-95" name="__codelineno-13-95" href="#__codelineno-13-95"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;後端要素にアクセス&quot;&quot;&quot;</span>
+<a id="__codelineno-13-96" name="__codelineno-13-96" href="#__codelineno-13-96"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">is_empty</span><span class="p">():</span>
+<a id="__codelineno-13-97" name="__codelineno-13-97" href="#__codelineno-13-97"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;Double-ended queue is empty&quot;</span><span class="p">)</span>
+<a id="__codelineno-13-98" name="__codelineno-13-98" href="#__codelineno-13-98"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_rear</span><span class="o">.</span><span class="n">val</span>
+<a id="__codelineno-13-99" name="__codelineno-13-99" href="#__codelineno-13-99"></a>
+<a id="__codelineno-13-100" name="__codelineno-13-100" href="#__codelineno-13-100"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">to_array</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
+<a id="__codelineno-13-101" name="__codelineno-13-101" href="#__codelineno-13-101"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;出力用の配列を返す&quot;&quot;&quot;</span>
+<a id="__codelineno-13-102" name="__codelineno-13-102" href="#__codelineno-13-102"></a>        <span class="n">node</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_front</span>
+<a id="__codelineno-13-103" name="__codelineno-13-103" href="#__codelineno-13-103"></a>        <span class="n">res</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span>
+<a id="__codelineno-13-104" name="__codelineno-13-104" href="#__codelineno-13-104"></a>        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()):</span>
+<a id="__codelineno-13-105" name="__codelineno-13-105" href="#__codelineno-13-105"></a>            <span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">node</span><span class="o">.</span><span class="n">val</span>
+<a id="__codelineno-13-106" name="__codelineno-13-106" href="#__codelineno-13-106"></a>            <span class="n">node</span> <span class="o">=</span> <span class="n">node</span><span class="o">.</span><span class="n">next</span>
+<a id="__codelineno-13-107" name="__codelineno-13-107" href="#__codelineno-13-107"></a>        <span class="k">return</span> <span class="n">res</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linkedlist_deque.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 双方向連結リストノード */</span>
+<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="k">struct</span><span class="w"> </span><span class="nc">DoublyListNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w">              </span><span class="c1">// ノードの値</span>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="n">DoublyListNode</span><span class="w"> </span><span class="o">*</span><span class="n">next</span><span class="p">;</span><span class="w"> </span><span class="c1">// 後続ノードへのポインタ</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w">    </span><span class="n">DoublyListNode</span><span class="w"> </span><span class="o">*</span><span class="n">prev</span><span class="p">;</span><span class="w"> </span><span class="c1">// 前続ノードへのポインタ</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="w">    </span><span class="n">DoublyListNode</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">val</span><span class="p">),</span><span class="w"> </span><span class="n">prev</span><span class="p">(</span><span class="k">nullptr</span><span class="p">),</span><span class="w"> </span><span class="n">next</span><span class="p">(</span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="p">};</span>
+<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a>
+<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="cm">/* 双方向連結リストに基づく両端キュークラス */</span>
+<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="k">class</span><span class="w"> </span><span class="nc">LinkedListDeque</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="w">  </span><span class="k">private</span><span class="o">:</span>
+<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="w">    </span><span class="n">DoublyListNode</span><span class="w"> </span><span class="o">*</span><span class="n">front</span><span class="p">,</span><span class="w"> </span><span class="o">*</span><span class="n">rear</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノードfront、末尾ノードrear</span>
+<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">              </span><span class="c1">// 両端キューの長さ</span>
+<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a>
+<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a><span class="w">  </span><span class="k">public</span><span class="o">:</span>
+<a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a><span class="w">    </span><span class="n">LinkedListDeque</span><span class="p">()</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">front</span><span class="p">(</span><span class="k">nullptr</span><span class="p">),</span><span class="w"> </span><span class="n">rear</span><span class="p">(</span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-19" name="__codelineno-14-19" href="#__codelineno-14-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-20" name="__codelineno-14-20" href="#__codelineno-14-20"></a>
+<a id="__codelineno-14-21" name="__codelineno-14-21" href="#__codelineno-14-21"></a><span class="w">    </span><span class="cm">/* デストラクタ */</span>
+<a id="__codelineno-14-22" name="__codelineno-14-22" href="#__codelineno-14-22"></a><span class="w">    </span><span class="o">~</span><span class="n">LinkedListDeque</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-23" name="__codelineno-14-23" href="#__codelineno-14-23"></a><span class="w">        </span><span class="c1">// 連結リストを走査、ノードを削除、メモリを解放</span>
+<a id="__codelineno-14-24" name="__codelineno-14-24" href="#__codelineno-14-24"></a><span class="w">        </span><span class="n">DoublyListNode</span><span class="w"> </span><span class="o">*</span><span class="n">pre</span><span class="p">,</span><span class="w"> </span><span class="o">*</span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">;</span>
+<a id="__codelineno-14-25" name="__codelineno-14-25" href="#__codelineno-14-25"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-26" name="__codelineno-14-26" href="#__codelineno-14-26"></a><span class="w">            </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">;</span>
+<a id="__codelineno-14-27" name="__codelineno-14-27" href="#__codelineno-14-27"></a><span class="w">            </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-14-28" name="__codelineno-14-28" href="#__codelineno-14-28"></a><span class="w">            </span><span class="k">delete</span><span class="w"> </span><span class="n">pre</span><span class="p">;</span>
+<a id="__codelineno-14-29" name="__codelineno-14-29" href="#__codelineno-14-29"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-14-30" name="__codelineno-14-30" href="#__codelineno-14-30"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-31" name="__codelineno-14-31" href="#__codelineno-14-31"></a>
+<a id="__codelineno-14-32" name="__codelineno-14-32" href="#__codelineno-14-32"></a><span class="w">    </span><span class="cm">/* 両端キューの長さを取得 */</span>
+<a id="__codelineno-14-33" name="__codelineno-14-33" href="#__codelineno-14-33"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-34" name="__codelineno-14-34" href="#__codelineno-14-34"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span>
+<a id="__codelineno-14-35" name="__codelineno-14-35" href="#__codelineno-14-35"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-36" name="__codelineno-14-36" href="#__codelineno-14-36"></a>
+<a id="__codelineno-14-37" name="__codelineno-14-37" href="#__codelineno-14-37"></a><span class="w">    </span><span class="cm">/* 両端キューが空かどうかを判定 */</span>
+<a id="__codelineno-14-38" name="__codelineno-14-38" href="#__codelineno-14-38"></a><span class="w">    </span><span class="kt">bool</span><span class="w"> </span><span class="n">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-39" name="__codelineno-14-39" href="#__codelineno-14-39"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-14-40" name="__codelineno-14-40" href="#__codelineno-14-40"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-41" name="__codelineno-14-41" href="#__codelineno-14-41"></a>
+<a id="__codelineno-14-42" name="__codelineno-14-42" href="#__codelineno-14-42"></a><span class="w">    </span><span class="cm">/* エンキュー操作 */</span>
+<a id="__codelineno-14-43" name="__codelineno-14-43" href="#__codelineno-14-43"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="kt">bool</span><span class="w"> </span><span class="n">isFront</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-44" name="__codelineno-14-44" href="#__codelineno-14-44"></a><span class="w">        </span><span class="n">DoublyListNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">DoublyListNode</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-14-45" name="__codelineno-14-45" href="#__codelineno-14-45"></a><span class="w">        </span><span class="c1">// リストが空の場合、frontとrearの両方をnodeに向ける</span>
+<a id="__codelineno-14-46" name="__codelineno-14-46" href="#__codelineno-14-46"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
+<a id="__codelineno-14-47" name="__codelineno-14-47" href="#__codelineno-14-47"></a><span class="w">            </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-14-48" name="__codelineno-14-48" href="#__codelineno-14-48"></a><span class="w">        </span><span class="c1">// 先頭エンキュー操作</span>
+<a id="__codelineno-14-49" name="__codelineno-14-49" href="#__codelineno-14-49"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isFront</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-50" name="__codelineno-14-50" href="#__codelineno-14-50"></a><span class="w">            </span><span class="c1">// ノードをリストの先頭に追加</span>
+<a id="__codelineno-14-51" name="__codelineno-14-51" href="#__codelineno-14-51"></a><span class="w">            </span><span class="n">front</span><span class="o">-&gt;</span><span class="n">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-14-52" name="__codelineno-14-52" href="#__codelineno-14-52"></a><span class="w">            </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">;</span>
+<a id="__codelineno-14-53" name="__codelineno-14-53" href="#__codelineno-14-53"></a><span class="w">            </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノードを更新</span>
+<a id="__codelineno-14-54" name="__codelineno-14-54" href="#__codelineno-14-54"></a><span class="w">        </span><span class="c1">// 末尾エンキュー操作</span>
+<a id="__codelineno-14-55" name="__codelineno-14-55" href="#__codelineno-14-55"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-56" name="__codelineno-14-56" href="#__codelineno-14-56"></a><span class="w">            </span><span class="c1">// ノードをリストの末尾に追加</span>
+<a id="__codelineno-14-57" name="__codelineno-14-57" href="#__codelineno-14-57"></a><span class="w">            </span><span class="n">rear</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-14-58" name="__codelineno-14-58" href="#__codelineno-14-58"></a><span class="w">            </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rear</span><span class="p">;</span>
+<a id="__codelineno-14-59" name="__codelineno-14-59" href="#__codelineno-14-59"></a><span class="w">            </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span><span class="w"> </span><span class="c1">// 末尾ノードを更新</span>
+<a id="__codelineno-14-60" name="__codelineno-14-60" href="#__codelineno-14-60"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-14-61" name="__codelineno-14-61" href="#__codelineno-14-61"></a><span class="w">        </span><span class="n">queSize</span><span class="o">++</span><span class="p">;</span><span class="w"> </span><span class="c1">// キュー長を更新</span>
+<a id="__codelineno-14-62" name="__codelineno-14-62" href="#__codelineno-14-62"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-63" name="__codelineno-14-63" href="#__codelineno-14-63"></a>
+<a id="__codelineno-14-64" name="__codelineno-14-64" href="#__codelineno-14-64"></a><span class="w">    </span><span class="cm">/* 先頭エンキュー */</span>
+<a id="__codelineno-14-65" name="__codelineno-14-65" href="#__codelineno-14-65"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">pushFirst</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-66" name="__codelineno-14-66" href="#__codelineno-14-66"></a><span class="w">        </span><span class="n">push</span><span class="p">(</span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="nb">true</span><span class="p">);</span>
+<a id="__codelineno-14-67" name="__codelineno-14-67" href="#__codelineno-14-67"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-68" name="__codelineno-14-68" href="#__codelineno-14-68"></a>
+<a id="__codelineno-14-69" name="__codelineno-14-69" href="#__codelineno-14-69"></a><span class="w">    </span><span class="cm">/* 末尾エンキュー */</span>
+<a id="__codelineno-14-70" name="__codelineno-14-70" href="#__codelineno-14-70"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">pushLast</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-71" name="__codelineno-14-71" href="#__codelineno-14-71"></a><span class="w">        </span><span class="n">push</span><span class="p">(</span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="nb">false</span><span class="p">);</span>
+<a id="__codelineno-14-72" name="__codelineno-14-72" href="#__codelineno-14-72"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-73" name="__codelineno-14-73" href="#__codelineno-14-73"></a>
+<a id="__codelineno-14-74" name="__codelineno-14-74" href="#__codelineno-14-74"></a><span class="w">    </span><span class="cm">/* デキュー操作 */</span>
+<a id="__codelineno-14-75" name="__codelineno-14-75" href="#__codelineno-14-75"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">pop</span><span class="p">(</span><span class="kt">bool</span><span class="w"> </span><span class="n">isFront</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-76" name="__codelineno-14-76" href="#__codelineno-14-76"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
+<a id="__codelineno-14-77" name="__codelineno-14-77" href="#__codelineno-14-77"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;Queue is empty&quot;</span><span class="p">);</span>
+<a id="__codelineno-14-78" name="__codelineno-14-78" href="#__codelineno-14-78"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-14-79" name="__codelineno-14-79" href="#__codelineno-14-79"></a><span class="w">        </span><span class="c1">// 先頭デキュー操作</span>
+<a id="__codelineno-14-80" name="__codelineno-14-80" href="#__codelineno-14-80"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isFront</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-81" name="__codelineno-14-81" href="#__codelineno-14-81"></a><span class="w">            </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノードの値を一時保存</span>
+<a id="__codelineno-14-82" name="__codelineno-14-82" href="#__codelineno-14-82"></a><span class="w">            </span><span class="c1">// 先頭ノードを削除</span>
+<a id="__codelineno-14-83" name="__codelineno-14-83" href="#__codelineno-14-83"></a><span class="w">            </span><span class="n">DoublyListNode</span><span class="w"> </span><span class="o">*</span><span class="n">fNext</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-14-84" name="__codelineno-14-84" href="#__codelineno-14-84"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">fNext</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-85" name="__codelineno-14-85" href="#__codelineno-14-85"></a><span class="w">                </span><span class="n">fNext</span><span class="o">-&gt;</span><span class="n">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">;</span>
+<a id="__codelineno-14-86" name="__codelineno-14-86" href="#__codelineno-14-86"></a><span class="w">                </span><span class="n">front</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">;</span>
+<a id="__codelineno-14-87" name="__codelineno-14-87" href="#__codelineno-14-87"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-14-88" name="__codelineno-14-88" href="#__codelineno-14-88"></a><span class="w">            </span><span class="k">delete</span><span class="w"> </span><span class="n">front</span><span class="p">;</span>
+<a id="__codelineno-14-89" name="__codelineno-14-89" href="#__codelineno-14-89"></a><span class="w">            </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">fNext</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノードを更新</span>
+<a id="__codelineno-14-90" name="__codelineno-14-90" href="#__codelineno-14-90"></a><span class="w">        </span><span class="c1">// 末尾デキュー操作</span>
+<a id="__codelineno-14-91" name="__codelineno-14-91" href="#__codelineno-14-91"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-92" name="__codelineno-14-92" href="#__codelineno-14-92"></a><span class="w">            </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rear</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span><span class="w"> </span><span class="c1">// 末尾ノードの値を一時保存</span>
+<a id="__codelineno-14-93" name="__codelineno-14-93" href="#__codelineno-14-93"></a><span class="w">            </span><span class="c1">// 末尾ノードを削除</span>
+<a id="__codelineno-14-94" name="__codelineno-14-94" href="#__codelineno-14-94"></a><span class="w">            </span><span class="n">DoublyListNode</span><span class="w"> </span><span class="o">*</span><span class="n">rPrev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rear</span><span class="o">-&gt;</span><span class="n">prev</span><span class="p">;</span>
+<a id="__codelineno-14-95" name="__codelineno-14-95" href="#__codelineno-14-95"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">rPrev</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-96" name="__codelineno-14-96" href="#__codelineno-14-96"></a><span class="w">                </span><span class="n">rPrev</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">;</span>
+<a id="__codelineno-14-97" name="__codelineno-14-97" href="#__codelineno-14-97"></a><span class="w">                </span><span class="n">rear</span><span class="o">-&gt;</span><span class="n">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">;</span>
+<a id="__codelineno-14-98" name="__codelineno-14-98" href="#__codelineno-14-98"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-14-99" name="__codelineno-14-99" href="#__codelineno-14-99"></a><span class="w">            </span><span class="k">delete</span><span class="w"> </span><span class="n">rear</span><span class="p">;</span>
+<a id="__codelineno-14-100" name="__codelineno-14-100" href="#__codelineno-14-100"></a><span class="w">            </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rPrev</span><span class="p">;</span><span class="w"> </span><span class="c1">// 末尾ノードを更新</span>
+<a id="__codelineno-14-101" name="__codelineno-14-101" href="#__codelineno-14-101"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-14-102" name="__codelineno-14-102" href="#__codelineno-14-102"></a><span class="w">        </span><span class="n">queSize</span><span class="o">--</span><span class="p">;</span><span class="w"> </span><span class="c1">// キュー長を更新</span>
+<a id="__codelineno-14-103" name="__codelineno-14-103" href="#__codelineno-14-103"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-14-104" name="__codelineno-14-104" href="#__codelineno-14-104"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-105" name="__codelineno-14-105" href="#__codelineno-14-105"></a>
+<a id="__codelineno-14-106" name="__codelineno-14-106" href="#__codelineno-14-106"></a><span class="w">    </span><span class="cm">/* 先頭デキュー */</span>
+<a id="__codelineno-14-107" name="__codelineno-14-107" href="#__codelineno-14-107"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">popFirst</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-108" name="__codelineno-14-108" href="#__codelineno-14-108"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">pop</span><span class="p">(</span><span class="nb">true</span><span class="p">);</span>
+<a id="__codelineno-14-109" name="__codelineno-14-109" href="#__codelineno-14-109"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-110" name="__codelineno-14-110" href="#__codelineno-14-110"></a>
+<a id="__codelineno-14-111" name="__codelineno-14-111" href="#__codelineno-14-111"></a><span class="w">    </span><span class="cm">/* 末尾デキュー */</span>
+<a id="__codelineno-14-112" name="__codelineno-14-112" href="#__codelineno-14-112"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">popLast</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-113" name="__codelineno-14-113" href="#__codelineno-14-113"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">pop</span><span class="p">(</span><span class="nb">false</span><span class="p">);</span>
+<a id="__codelineno-14-114" name="__codelineno-14-114" href="#__codelineno-14-114"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-115" name="__codelineno-14-115" href="#__codelineno-14-115"></a>
+<a id="__codelineno-14-116" name="__codelineno-14-116" href="#__codelineno-14-116"></a><span class="w">    </span><span class="cm">/* 先頭要素にアクセス */</span>
+<a id="__codelineno-14-117" name="__codelineno-14-117" href="#__codelineno-14-117"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">peekFirst</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-118" name="__codelineno-14-118" href="#__codelineno-14-118"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
+<a id="__codelineno-14-119" name="__codelineno-14-119" href="#__codelineno-14-119"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;Double-ended queue is empty&quot;</span><span class="p">);</span>
+<a id="__codelineno-14-120" name="__codelineno-14-120" href="#__codelineno-14-120"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">front</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-14-121" name="__codelineno-14-121" href="#__codelineno-14-121"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-122" name="__codelineno-14-122" href="#__codelineno-14-122"></a>
+<a id="__codelineno-14-123" name="__codelineno-14-123" href="#__codelineno-14-123"></a><span class="w">    </span><span class="cm">/* 末尾要素にアクセス */</span>
+<a id="__codelineno-14-124" name="__codelineno-14-124" href="#__codelineno-14-124"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">peekLast</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-125" name="__codelineno-14-125" href="#__codelineno-14-125"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
+<a id="__codelineno-14-126" name="__codelineno-14-126" href="#__codelineno-14-126"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;Double-ended queue is empty&quot;</span><span class="p">);</span>
+<a id="__codelineno-14-127" name="__codelineno-14-127" href="#__codelineno-14-127"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">rear</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-14-128" name="__codelineno-14-128" href="#__codelineno-14-128"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-129" name="__codelineno-14-129" href="#__codelineno-14-129"></a>
+<a id="__codelineno-14-130" name="__codelineno-14-130" href="#__codelineno-14-130"></a><span class="w">    </span><span class="cm">/* 印刷用に配列を返却 */</span>
+<a id="__codelineno-14-131" name="__codelineno-14-131" href="#__codelineno-14-131"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">toVector</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-132" name="__codelineno-14-132" href="#__codelineno-14-132"></a><span class="w">        </span><span class="n">DoublyListNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">;</span>
+<a id="__codelineno-14-133" name="__codelineno-14-133" href="#__codelineno-14-133"></a><span class="w">        </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">(</span><span class="n">size</span><span class="p">());</span>
+<a id="__codelineno-14-134" name="__codelineno-14-134" href="#__codelineno-14-134"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-135" name="__codelineno-14-135" href="#__codelineno-14-135"></a><span class="w">            </span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-14-136" name="__codelineno-14-136" href="#__codelineno-14-136"></a><span class="w">            </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-14-137" name="__codelineno-14-137" href="#__codelineno-14-137"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-14-138" name="__codelineno-14-138" href="#__codelineno-14-138"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-14-139" name="__codelineno-14-139" href="#__codelineno-14-139"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-140" name="__codelineno-14-140" href="#__codelineno-14-140"></a><span class="p">};</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linkedlist_deque.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 双方向連結リストノード */</span>
+<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kd">class</span> <span class="nc">ListNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w"> </span><span class="c1">// ノード値</span>
+<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="n">next</span><span class="p">;</span><span class="w"> </span><span class="c1">// 後続ノードへの参照</span>
+<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="n">prev</span><span class="p">;</span><span class="w"> </span><span class="c1">// 前任ノードへの参照</span>
+<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a>
+<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">    </span><span class="n">ListNode</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w">        </span><span class="n">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="p">}</span>
+<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a>
+<a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="cm">/* 双方向連結リストに基づく両端キュークラス */</span>
+<a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="kd">class</span> <span class="nc">LinkedListDeque</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="n">ListNode</span><span class="w"> </span><span class="n">front</span><span class="p">,</span><span class="w"> </span><span class="n">rear</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノード front、末尾ノード rear</span>
+<a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// 両端キューの長さ</span>
+<a id="__codelineno-15-17" name="__codelineno-15-17" href="#__codelineno-15-17"></a>
+<a id="__codelineno-15-18" name="__codelineno-15-18" href="#__codelineno-15-18"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="nf">LinkedListDeque</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-19" name="__codelineno-15-19" href="#__codelineno-15-19"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-15-20" name="__codelineno-15-20" href="#__codelineno-15-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-21" name="__codelineno-15-21" href="#__codelineno-15-21"></a>
+<a id="__codelineno-15-22" name="__codelineno-15-22" href="#__codelineno-15-22"></a><span class="w">    </span><span class="cm">/* 両端キューの長さを取得 */</span>
+<a id="__codelineno-15-23" name="__codelineno-15-23" href="#__codelineno-15-23"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-24" name="__codelineno-15-24" href="#__codelineno-15-24"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span>
+<a id="__codelineno-15-25" name="__codelineno-15-25" href="#__codelineno-15-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-26" name="__codelineno-15-26" href="#__codelineno-15-26"></a>
+<a id="__codelineno-15-27" name="__codelineno-15-27" href="#__codelineno-15-27"></a><span class="w">    </span><span class="cm">/* 両端キューが空かどうかを判定 */</span>
+<a id="__codelineno-15-28" name="__codelineno-15-28" href="#__codelineno-15-28"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">boolean</span><span class="w"> </span><span class="nf">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-29" name="__codelineno-15-29" href="#__codelineno-15-29"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-15-30" name="__codelineno-15-30" href="#__codelineno-15-30"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-31" name="__codelineno-15-31" href="#__codelineno-15-31"></a>
+<a id="__codelineno-15-32" name="__codelineno-15-32" href="#__codelineno-15-32"></a><span class="w">    </span><span class="cm">/* エンキュー操作 */</span>
+<a id="__codelineno-15-33" name="__codelineno-15-33" href="#__codelineno-15-33"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="kt">boolean</span><span class="w"> </span><span class="n">isFront</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-34" name="__codelineno-15-34" href="#__codelineno-15-34"></a><span class="w">        </span><span class="n">ListNode</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-15-35" name="__codelineno-15-35" href="#__codelineno-15-35"></a><span class="w">        </span><span class="c1">// リストが空の場合、front と rear の両方を node に指す</span>
+<a id="__codelineno-15-36" name="__codelineno-15-36" href="#__codelineno-15-36"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
+<a id="__codelineno-15-37" name="__codelineno-15-37" href="#__codelineno-15-37"></a><span class="w">            </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-15-38" name="__codelineno-15-38" href="#__codelineno-15-38"></a><span class="w">        </span><span class="c1">// 先頭エンキュー操作</span>
+<a id="__codelineno-15-39" name="__codelineno-15-39" href="#__codelineno-15-39"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isFront</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-40" name="__codelineno-15-40" href="#__codelineno-15-40"></a><span class="w">            </span><span class="c1">// node をリストの先頭に追加</span>
+<a id="__codelineno-15-41" name="__codelineno-15-41" href="#__codelineno-15-41"></a><span class="w">            </span><span class="n">front</span><span class="p">.</span><span class="na">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-15-42" name="__codelineno-15-42" href="#__codelineno-15-42"></a><span class="w">            </span><span class="n">node</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">;</span>
+<a id="__codelineno-15-43" name="__codelineno-15-43" href="#__codelineno-15-43"></a><span class="w">            </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span><span class="w"> </span><span class="c1">// front を更新</span>
+<a id="__codelineno-15-44" name="__codelineno-15-44" href="#__codelineno-15-44"></a><span class="w">        </span><span class="c1">// 末尾エンキュー操作</span>
+<a id="__codelineno-15-45" name="__codelineno-15-45" href="#__codelineno-15-45"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-46" name="__codelineno-15-46" href="#__codelineno-15-46"></a><span class="w">            </span><span class="c1">// node をリストの末尾に追加</span>
+<a id="__codelineno-15-47" name="__codelineno-15-47" href="#__codelineno-15-47"></a><span class="w">            </span><span class="n">rear</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-15-48" name="__codelineno-15-48" href="#__codelineno-15-48"></a><span class="w">            </span><span class="n">node</span><span class="p">.</span><span class="na">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rear</span><span class="p">;</span>
+<a id="__codelineno-15-49" name="__codelineno-15-49" href="#__codelineno-15-49"></a><span class="w">            </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span><span class="w"> </span><span class="c1">// rear を更新</span>
+<a id="__codelineno-15-50" name="__codelineno-15-50" href="#__codelineno-15-50"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-15-51" name="__codelineno-15-51" href="#__codelineno-15-51"></a><span class="w">        </span><span class="n">queSize</span><span class="o">++</span><span class="p">;</span><span class="w"> </span><span class="c1">// 長さを更新</span>
+<a id="__codelineno-15-52" name="__codelineno-15-52" href="#__codelineno-15-52"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-53" name="__codelineno-15-53" href="#__codelineno-15-53"></a>
+<a id="__codelineno-15-54" name="__codelineno-15-54" href="#__codelineno-15-54"></a><span class="w">    </span><span class="cm">/* 先頭エンキュー */</span>
+<a id="__codelineno-15-55" name="__codelineno-15-55" href="#__codelineno-15-55"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">pushFirst</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-56" name="__codelineno-15-56" href="#__codelineno-15-56"></a><span class="w">        </span><span class="n">push</span><span class="p">(</span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="kc">true</span><span class="p">);</span>
+<a id="__codelineno-15-57" name="__codelineno-15-57" href="#__codelineno-15-57"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-58" name="__codelineno-15-58" href="#__codelineno-15-58"></a>
+<a id="__codelineno-15-59" name="__codelineno-15-59" href="#__codelineno-15-59"></a><span class="w">    </span><span class="cm">/* 末尾エンキュー */</span>
+<a id="__codelineno-15-60" name="__codelineno-15-60" href="#__codelineno-15-60"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">pushLast</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-61" name="__codelineno-15-61" href="#__codelineno-15-61"></a><span class="w">        </span><span class="n">push</span><span class="p">(</span><span class="n">num</span><span class="p">,</span><span class="w"> </span><span class="kc">false</span><span class="p">);</span>
+<a id="__codelineno-15-62" name="__codelineno-15-62" href="#__codelineno-15-62"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-63" name="__codelineno-15-63" href="#__codelineno-15-63"></a>
+<a id="__codelineno-15-64" name="__codelineno-15-64" href="#__codelineno-15-64"></a><span class="w">    </span><span class="cm">/* デキュー操作 */</span>
+<a id="__codelineno-15-65" name="__codelineno-15-65" href="#__codelineno-15-65"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">pop</span><span class="p">(</span><span class="kt">boolean</span><span class="w"> </span><span class="n">isFront</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-66" name="__codelineno-15-66" href="#__codelineno-15-66"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
+<a id="__codelineno-15-67" name="__codelineno-15-67" href="#__codelineno-15-67"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">();</span>
+<a id="__codelineno-15-68" name="__codelineno-15-68" href="#__codelineno-15-68"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-15-69" name="__codelineno-15-69" href="#__codelineno-15-69"></a><span class="w">        </span><span class="c1">// 先頭デキュー操作</span>
+<a id="__codelineno-15-70" name="__codelineno-15-70" href="#__codelineno-15-70"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isFront</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-71" name="__codelineno-15-71" href="#__codelineno-15-71"></a><span class="w">            </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">.</span><span class="na">val</span><span class="p">;</span><span class="w"> </span><span class="c1">// 一時的に先頭ノード値を保存</span>
+<a id="__codelineno-15-72" name="__codelineno-15-72" href="#__codelineno-15-72"></a><span class="w">            </span><span class="c1">// 次のノードを削除</span>
+<a id="__codelineno-15-73" name="__codelineno-15-73" href="#__codelineno-15-73"></a><span class="w">            </span><span class="n">ListNode</span><span class="w"> </span><span class="n">fNext</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">.</span><span class="na">next</span><span class="p">;</span>
+<a id="__codelineno-15-74" name="__codelineno-15-74" href="#__codelineno-15-74"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">fNext</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-75" name="__codelineno-15-75" href="#__codelineno-15-75"></a><span class="w">                </span><span class="n">fNext</span><span class="p">.</span><span class="na">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-15-76" name="__codelineno-15-76" href="#__codelineno-15-76"></a><span class="w">                </span><span class="n">front</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-15-77" name="__codelineno-15-77" href="#__codelineno-15-77"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-15-78" name="__codelineno-15-78" href="#__codelineno-15-78"></a><span class="w">            </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">fNext</span><span class="p">;</span><span class="w"> </span><span class="c1">// front を更新</span>
+<a id="__codelineno-15-79" name="__codelineno-15-79" href="#__codelineno-15-79"></a><span class="w">        </span><span class="c1">// 末尾デキュー操作</span>
+<a id="__codelineno-15-80" name="__codelineno-15-80" href="#__codelineno-15-80"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-81" name="__codelineno-15-81" href="#__codelineno-15-81"></a><span class="w">            </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rear</span><span class="p">.</span><span class="na">val</span><span class="p">;</span><span class="w"> </span><span class="c1">// 一時的に末尾ノード値を保存</span>
+<a id="__codelineno-15-82" name="__codelineno-15-82" href="#__codelineno-15-82"></a><span class="w">            </span><span class="c1">// 前のノードを削除</span>
+<a id="__codelineno-15-83" name="__codelineno-15-83" href="#__codelineno-15-83"></a><span class="w">            </span><span class="n">ListNode</span><span class="w"> </span><span class="n">rPrev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rear</span><span class="p">.</span><span class="na">prev</span><span class="p">;</span>
+<a id="__codelineno-15-84" name="__codelineno-15-84" href="#__codelineno-15-84"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">rPrev</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-85" name="__codelineno-15-85" href="#__codelineno-15-85"></a><span class="w">                </span><span class="n">rPrev</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-15-86" name="__codelineno-15-86" href="#__codelineno-15-86"></a><span class="w">                </span><span class="n">rear</span><span class="p">.</span><span class="na">prev</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-15-87" name="__codelineno-15-87" href="#__codelineno-15-87"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-15-88" name="__codelineno-15-88" href="#__codelineno-15-88"></a><span class="w">            </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rPrev</span><span class="p">;</span><span class="w"> </span><span class="c1">// rear を更新</span>
+<a id="__codelineno-15-89" name="__codelineno-15-89" href="#__codelineno-15-89"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-15-90" name="__codelineno-15-90" href="#__codelineno-15-90"></a><span class="w">        </span><span class="n">queSize</span><span class="o">--</span><span class="p">;</span><span class="w"> </span><span class="c1">// 長さを更新</span>
+<a id="__codelineno-15-91" name="__codelineno-15-91" href="#__codelineno-15-91"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-15-92" name="__codelineno-15-92" href="#__codelineno-15-92"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-93" name="__codelineno-15-93" href="#__codelineno-15-93"></a>
+<a id="__codelineno-15-94" name="__codelineno-15-94" href="#__codelineno-15-94"></a><span class="w">    </span><span class="cm">/* 先頭デキュー */</span>
+<a id="__codelineno-15-95" name="__codelineno-15-95" href="#__codelineno-15-95"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">popFirst</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-96" name="__codelineno-15-96" href="#__codelineno-15-96"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">pop</span><span class="p">(</span><span class="kc">true</span><span class="p">);</span>
+<a id="__codelineno-15-97" name="__codelineno-15-97" href="#__codelineno-15-97"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-98" name="__codelineno-15-98" href="#__codelineno-15-98"></a>
+<a id="__codelineno-15-99" name="__codelineno-15-99" href="#__codelineno-15-99"></a><span class="w">    </span><span class="cm">/* 末尾デキュー */</span>
+<a id="__codelineno-15-100" name="__codelineno-15-100" href="#__codelineno-15-100"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">popLast</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-101" name="__codelineno-15-101" href="#__codelineno-15-101"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">pop</span><span class="p">(</span><span class="kc">false</span><span class="p">);</span>
+<a id="__codelineno-15-102" name="__codelineno-15-102" href="#__codelineno-15-102"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-103" name="__codelineno-15-103" href="#__codelineno-15-103"></a>
+<a id="__codelineno-15-104" name="__codelineno-15-104" href="#__codelineno-15-104"></a><span class="w">    </span><span class="cm">/* 先頭要素にアクセス */</span>
+<a id="__codelineno-15-105" name="__codelineno-15-105" href="#__codelineno-15-105"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">peekFirst</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-106" name="__codelineno-15-106" href="#__codelineno-15-106"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
+<a id="__codelineno-15-107" name="__codelineno-15-107" href="#__codelineno-15-107"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">();</span>
+<a id="__codelineno-15-108" name="__codelineno-15-108" href="#__codelineno-15-108"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">front</span><span class="p">.</span><span class="na">val</span><span class="p">;</span>
+<a id="__codelineno-15-109" name="__codelineno-15-109" href="#__codelineno-15-109"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-110" name="__codelineno-15-110" href="#__codelineno-15-110"></a>
+<a id="__codelineno-15-111" name="__codelineno-15-111" href="#__codelineno-15-111"></a><span class="w">    </span><span class="cm">/* 末尾要素にアクセス */</span>
+<a id="__codelineno-15-112" name="__codelineno-15-112" href="#__codelineno-15-112"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">peekLast</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-113" name="__codelineno-15-113" href="#__codelineno-15-113"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
+<a id="__codelineno-15-114" name="__codelineno-15-114" href="#__codelineno-15-114"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">();</span>
+<a id="__codelineno-15-115" name="__codelineno-15-115" href="#__codelineno-15-115"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">rear</span><span class="p">.</span><span class="na">val</span><span class="p">;</span>
+<a id="__codelineno-15-116" name="__codelineno-15-116" href="#__codelineno-15-116"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-117" name="__codelineno-15-117" href="#__codelineno-15-117"></a>
+<a id="__codelineno-15-118" name="__codelineno-15-118" href="#__codelineno-15-118"></a><span class="w">    </span><span class="cm">/* 配列を返す */</span>
+<a id="__codelineno-15-119" name="__codelineno-15-119" href="#__codelineno-15-119"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="nf">toArray</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-120" name="__codelineno-15-120" href="#__codelineno-15-120"></a><span class="w">        </span><span class="n">ListNode</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">;</span>
+<a id="__codelineno-15-121" name="__codelineno-15-121" href="#__codelineno-15-121"></a><span class="w">        </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">size</span><span class="p">()</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-15-122" name="__codelineno-15-122" href="#__codelineno-15-122"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="na">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-123" name="__codelineno-15-123" href="#__codelineno-15-123"></a><span class="w">            </span><span class="n">res</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">val</span><span class="p">;</span>
+<a id="__codelineno-15-124" name="__codelineno-15-124" href="#__codelineno-15-124"></a><span class="w">            </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">next</span><span class="p">;</span>
+<a id="__codelineno-15-125" name="__codelineno-15-125" href="#__codelineno-15-125"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-15-126" name="__codelineno-15-126" href="#__codelineno-15-126"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-15-127" name="__codelineno-15-127" href="#__codelineno-15-127"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-128" name="__codelineno-15-128" href="#__codelineno-15-128"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linkedlist_deque.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">ListNode</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">LinkedListDeque</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linkedlist_deque.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">linkedListDeque</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linkedlist_deque.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">ListNode</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a>
+<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">LinkedListDeque</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linkedlist_deque.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">ListNode</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a>
+<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">LinkedListDeque</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linkedlist_deque.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">ListNode</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a>
+<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">LinkedListDeque</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linkedlist_deque.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ListNode</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a>
+<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">LinkedListDeque</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linkedlist_deque.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ListNode</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">LinkedListDeque</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linkedlist_deque.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">DoublyListNode</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a>
+<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">LinkedListDeque</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linkedlist_deque.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">ListNode</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a>
+<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">LinkedListDeque</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linkedlist_deque.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">ListNode</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a>
+<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">LinkedListDeque</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linkedlist_deque.zig</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ListNode</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a>
+<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">LinkedListDeque</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h3 id="2">2. &nbsp; 配列に基づく実装<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
+<p>下図に示すように、配列でキューを実装するのと同様に、循環配列を使って両端キューを実装することもできます。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="4:5"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><input id="__tabbed_4_5" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">ArrayDeque</label><label for="__tabbed_4_2">pushLast()</label><label for="__tabbed_4_3">pushFirst()</label><label for="__tabbed_4_4">popLast()</label><label for="__tabbed_4_5">popFirst()</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<p><a class="glightbox" href="../deque.assets/array_deque_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="配列による両端キューのエンキューとデキュー操作の実装" class="animation-figure" src="../deque.assets/array_deque_step1.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../deque.assets/array_deque_step2_push_last.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="array_deque_push_last" class="animation-figure" src="../deque.assets/array_deque_step2_push_last.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../deque.assets/array_deque_step3_push_first.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="array_deque_push_first" class="animation-figure" src="../deque.assets/array_deque_step3_push_first.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../deque.assets/array_deque_step4_pop_last.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="array_deque_pop_last" class="animation-figure" src="../deque.assets/array_deque_step4_pop_last.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../deque.assets/array_deque_step5_pop_first.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="array_deque_pop_first" class="animation-figure" src="../deque.assets/array_deque_step5_pop_first.png" /></a></p>
+</div>
+</div>
+</div>
+<p align="center"> 図 5-9 &nbsp; 配列による両端キューのエンキューとデキュー操作の実装 </p>
+
+<p>実装では「前端エンキュー」と「後端デキュー」のメソッドを追加するだけです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="5:14"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><input id="__tabbed_5_7" name="__tabbed_5" type="radio" /><input id="__tabbed_5_8" name="__tabbed_5" type="radio" /><input id="__tabbed_5_9" name="__tabbed_5" type="radio" /><input id="__tabbed_5_10" name="__tabbed_5" type="radio" /><input id="__tabbed_5_11" name="__tabbed_5" type="radio" /><input id="__tabbed_5_12" name="__tabbed_5" type="radio" /><input id="__tabbed_5_13" name="__tabbed_5" type="radio" /><input id="__tabbed_5_14" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">Python</label><label for="__tabbed_5_2">C++</label><label for="__tabbed_5_3">Java</label><label for="__tabbed_5_4">C#</label><label for="__tabbed_5_5">Go</label><label for="__tabbed_5_6">Swift</label><label for="__tabbed_5_7">JS</label><label for="__tabbed_5_8">TS</label><label for="__tabbed_5_9">Dart</label><label for="__tabbed_5_10">Rust</label><label for="__tabbed_5_11">C</label><label for="__tabbed_5_12">Kotlin</label><label for="__tabbed_5_13">Ruby</label><label for="__tabbed_5_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_deque.py</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">ArrayDeque</span><span class="p">:</span>
+<a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;循環配列ベースの双端キュークラス&quot;&quot;&quot;</span>
+<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a>
+<a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">capacity</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;コンストラクタ&quot;&quot;&quot;</span>
+<a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">capacity</span>
+<a id="__codelineno-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_front</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-27-8" name="__codelineno-27-8" href="#__codelineno-27-8"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-27-9" name="__codelineno-27-9" href="#__codelineno-27-9"></a>
+<a id="__codelineno-27-10" name="__codelineno-27-10" href="#__codelineno-27-10"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">capacity</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-27-11" name="__codelineno-27-11" href="#__codelineno-27-11"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;双端キューの容量を取得&quot;&quot;&quot;</span>
+<a id="__codelineno-27-12" name="__codelineno-27-12" href="#__codelineno-27-12"></a>        <span class="k">return</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_nums</span><span class="p">)</span>
+<a id="__codelineno-27-13" name="__codelineno-27-13" href="#__codelineno-27-13"></a>
+<a id="__codelineno-27-14" name="__codelineno-27-14" href="#__codelineno-27-14"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">size</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-27-15" name="__codelineno-27-15" href="#__codelineno-27-15"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;双端キューの長さを取得&quot;&quot;&quot;</span>
+<a id="__codelineno-27-16" name="__codelineno-27-16" href="#__codelineno-27-16"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span>
+<a id="__codelineno-27-17" name="__codelineno-27-17" href="#__codelineno-27-17"></a>
+<a id="__codelineno-27-18" name="__codelineno-27-18" href="#__codelineno-27-18"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">is_empty</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">bool</span><span class="p">:</span>
+<a id="__codelineno-27-19" name="__codelineno-27-19" href="#__codelineno-27-19"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;双端キューが空かどうかを判定&quot;&quot;&quot;</span>
+<a id="__codelineno-27-20" name="__codelineno-27-20" href="#__codelineno-27-20"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">==</span> <span class="mi">0</span>
+<a id="__codelineno-27-21" name="__codelineno-27-21" href="#__codelineno-27-21"></a>
+<a id="__codelineno-27-22" name="__codelineno-27-22" href="#__codelineno-27-22"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">index</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-27-23" name="__codelineno-27-23" href="#__codelineno-27-23"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;循環配列のインデックスを計算&quot;&quot;&quot;</span>
+<a id="__codelineno-27-24" name="__codelineno-27-24" href="#__codelineno-27-24"></a>        <span class="c1"># モジュロ演算によって循環配列を実装</span>
+<a id="__codelineno-27-25" name="__codelineno-27-25" href="#__codelineno-27-25"></a>        <span class="c1"># i が配列の末尾を超えた場合、先頭に戻る</span>
+<a id="__codelineno-27-26" name="__codelineno-27-26" href="#__codelineno-27-26"></a>        <span class="c1"># i が配列の先頭を超えた場合、末尾に戻る</span>
+<a id="__codelineno-27-27" name="__codelineno-27-27" href="#__codelineno-27-27"></a>        <span class="k">return</span> <span class="p">(</span><span class="n">i</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span><span class="p">())</span> <span class="o">%</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span><span class="p">()</span>
+<a id="__codelineno-27-28" name="__codelineno-27-28" href="#__codelineno-27-28"></a>
+<a id="__codelineno-27-29" name="__codelineno-27-29" href="#__codelineno-27-29"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">push_first</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">num</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-27-30" name="__codelineno-27-30" href="#__codelineno-27-30"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;前端エンキュー&quot;&quot;&quot;</span>
+<a id="__codelineno-27-31" name="__codelineno-27-31" href="#__codelineno-27-31"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">==</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span><span class="p">():</span>
+<a id="__codelineno-27-32" name="__codelineno-27-32" href="#__codelineno-27-32"></a>            <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;双端キューが満杯です&quot;</span><span class="p">)</span>
+<a id="__codelineno-27-33" name="__codelineno-27-33" href="#__codelineno-27-33"></a>            <span class="k">return</span>
+<a id="__codelineno-27-34" name="__codelineno-27-34" href="#__codelineno-27-34"></a>        <span class="c1"># フロントポインタを左に1つ移動</span>
+<a id="__codelineno-27-35" name="__codelineno-27-35" href="#__codelineno-27-35"></a>        <span class="c1"># モジュロ演算によってフロントが配列の先頭を超えて末尾に戻ることを実装</span>
+<a id="__codelineno-27-36" name="__codelineno-27-36" href="#__codelineno-27-36"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">index</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-27-37" name="__codelineno-27-37" href="#__codelineno-27-37"></a>        <span class="c1"># num を前端に追加</span>
+<a id="__codelineno-27-38" name="__codelineno-27-38" href="#__codelineno-27-38"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_nums</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">_front</span><span class="p">]</span> <span class="o">=</span> <span class="n">num</span>
+<a id="__codelineno-27-39" name="__codelineno-27-39" href="#__codelineno-27-39"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-27-40" name="__codelineno-27-40" href="#__codelineno-27-40"></a>
+<a id="__codelineno-27-41" name="__codelineno-27-41" href="#__codelineno-27-41"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">push_last</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">num</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-27-42" name="__codelineno-27-42" href="#__codelineno-27-42"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;後端エンキュー&quot;&quot;&quot;</span>
+<a id="__codelineno-27-43" name="__codelineno-27-43" href="#__codelineno-27-43"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">==</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span><span class="p">():</span>
+<a id="__codelineno-27-44" name="__codelineno-27-44" href="#__codelineno-27-44"></a>            <span class="nb">print</span><span class="p">(</span><span class="s2">&quot;双端キューが満杯です&quot;</span><span class="p">)</span>
+<a id="__codelineno-27-45" name="__codelineno-27-45" href="#__codelineno-27-45"></a>            <span class="k">return</span>
+<a id="__codelineno-27-46" name="__codelineno-27-46" href="#__codelineno-27-46"></a>        <span class="c1"># リアポインタを計算、リアインデックス + 1 を指す</span>
+<a id="__codelineno-27-47" name="__codelineno-27-47" href="#__codelineno-27-47"></a>        <span class="n">rear</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">index</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span><span class="p">)</span>
+<a id="__codelineno-27-48" name="__codelineno-27-48" href="#__codelineno-27-48"></a>        <span class="c1"># num を後端に追加</span>
+<a id="__codelineno-27-49" name="__codelineno-27-49" href="#__codelineno-27-49"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_nums</span><span class="p">[</span><span class="n">rear</span><span class="p">]</span> <span class="o">=</span> <span class="n">num</span>
+<a id="__codelineno-27-50" name="__codelineno-27-50" href="#__codelineno-27-50"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-27-51" name="__codelineno-27-51" href="#__codelineno-27-51"></a>
+<a id="__codelineno-27-52" name="__codelineno-27-52" href="#__codelineno-27-52"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">pop_first</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-27-53" name="__codelineno-27-53" href="#__codelineno-27-53"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;前端デキュー&quot;&quot;&quot;</span>
+<a id="__codelineno-27-54" name="__codelineno-27-54" href="#__codelineno-27-54"></a>        <span class="n">num</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">peek_first</span><span class="p">()</span>
+<a id="__codelineno-27-55" name="__codelineno-27-55" href="#__codelineno-27-55"></a>        <span class="c1"># フロントポインタを1つ後ろに移動</span>
+<a id="__codelineno-27-56" name="__codelineno-27-56" href="#__codelineno-27-56"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">index</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-27-57" name="__codelineno-27-57" href="#__codelineno-27-57"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">-=</span> <span class="mi">1</span>
+<a id="__codelineno-27-58" name="__codelineno-27-58" href="#__codelineno-27-58"></a>        <span class="k">return</span> <span class="n">num</span>
+<a id="__codelineno-27-59" name="__codelineno-27-59" href="#__codelineno-27-59"></a>
+<a id="__codelineno-27-60" name="__codelineno-27-60" href="#__codelineno-27-60"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">pop_last</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-27-61" name="__codelineno-27-61" href="#__codelineno-27-61"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;後端デキュー&quot;&quot;&quot;</span>
+<a id="__codelineno-27-62" name="__codelineno-27-62" href="#__codelineno-27-62"></a>        <span class="n">num</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">peek_last</span><span class="p">()</span>
+<a id="__codelineno-27-63" name="__codelineno-27-63" href="#__codelineno-27-63"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">-=</span> <span class="mi">1</span>
+<a id="__codelineno-27-64" name="__codelineno-27-64" href="#__codelineno-27-64"></a>        <span class="k">return</span> <span class="n">num</span>
+<a id="__codelineno-27-65" name="__codelineno-27-65" href="#__codelineno-27-65"></a>
+<a id="__codelineno-27-66" name="__codelineno-27-66" href="#__codelineno-27-66"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">peek_first</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-27-67" name="__codelineno-27-67" href="#__codelineno-27-67"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;前端要素にアクセス&quot;&quot;&quot;</span>
+<a id="__codelineno-27-68" name="__codelineno-27-68" href="#__codelineno-27-68"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">is_empty</span><span class="p">():</span>
+<a id="__codelineno-27-69" name="__codelineno-27-69" href="#__codelineno-27-69"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;Double-ended queue is empty&quot;</span><span class="p">)</span>
+<a id="__codelineno-27-70" name="__codelineno-27-70" href="#__codelineno-27-70"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_nums</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">_front</span><span class="p">]</span>
+<a id="__codelineno-27-71" name="__codelineno-27-71" href="#__codelineno-27-71"></a>
+<a id="__codelineno-27-72" name="__codelineno-27-72" href="#__codelineno-27-72"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">peek_last</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-27-73" name="__codelineno-27-73" href="#__codelineno-27-73"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;後端要素にアクセス&quot;&quot;&quot;</span>
+<a id="__codelineno-27-74" name="__codelineno-27-74" href="#__codelineno-27-74"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">is_empty</span><span class="p">():</span>
+<a id="__codelineno-27-75" name="__codelineno-27-75" href="#__codelineno-27-75"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;Double-ended queue is empty&quot;</span><span class="p">)</span>
+<a id="__codelineno-27-76" name="__codelineno-27-76" href="#__codelineno-27-76"></a>        <span class="c1"># 後端要素のインデックスを計算</span>
+<a id="__codelineno-27-77" name="__codelineno-27-77" href="#__codelineno-27-77"></a>        <span class="n">last</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">index</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-27-78" name="__codelineno-27-78" href="#__codelineno-27-78"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_nums</span><span class="p">[</span><span class="n">last</span><span class="p">]</span>
+<a id="__codelineno-27-79" name="__codelineno-27-79" href="#__codelineno-27-79"></a>
+<a id="__codelineno-27-80" name="__codelineno-27-80" href="#__codelineno-27-80"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">to_array</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
+<a id="__codelineno-27-81" name="__codelineno-27-81" href="#__codelineno-27-81"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;出力用の配列を返す&quot;&quot;&quot;</span>
+<a id="__codelineno-27-82" name="__codelineno-27-82" href="#__codelineno-27-82"></a>        <span class="c1"># 有効な長さ範囲内の要素のみを変換</span>
+<a id="__codelineno-27-83" name="__codelineno-27-83" href="#__codelineno-27-83"></a>        <span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>
+<a id="__codelineno-27-84" name="__codelineno-27-84" href="#__codelineno-27-84"></a>        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_size</span><span class="p">):</span>
+<a id="__codelineno-27-85" name="__codelineno-27-85" href="#__codelineno-27-85"></a>            <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_nums</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">index</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="o">+</span> <span class="n">i</span><span class="p">)])</span>
+<a id="__codelineno-27-86" name="__codelineno-27-86" href="#__codelineno-27-86"></a>        <span class="k">return</span> <span class="n">res</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_deque.cpp</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="cm">/* 循環配列に基づく両端キュークラス */</span>
+<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">ArrayDeque</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a><span class="w">  </span><span class="k">private</span><span class="o">:</span>
+<a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">nums</span><span class="p">;</span><span class="w"> </span><span class="c1">// 両端キューの要素を格納する配列</span>
+<a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">front</span><span class="p">;</span><span class="w">        </span><span class="c1">// 先頭ポインタ、先頭要素を指す</span>
+<a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span><span class="w">      </span><span class="c1">// 両端キューの長さ</span>
+<a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a>
+<a id="__codelineno-28-8" name="__codelineno-28-8" href="#__codelineno-28-8"></a><span class="w">  </span><span class="k">public</span><span class="o">:</span>
+<a id="__codelineno-28-9" name="__codelineno-28-9" href="#__codelineno-28-9"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-28-10" name="__codelineno-28-10" href="#__codelineno-28-10"></a><span class="w">    </span><span class="n">ArrayDeque</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-11" name="__codelineno-28-11" href="#__codelineno-28-11"></a><span class="w">        </span><span class="n">nums</span><span class="p">.</span><span class="n">resize</span><span class="p">(</span><span class="n">capacity</span><span class="p">);</span>
+<a id="__codelineno-28-12" name="__codelineno-28-12" href="#__codelineno-28-12"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-28-13" name="__codelineno-28-13" href="#__codelineno-28-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-14" name="__codelineno-28-14" href="#__codelineno-28-14"></a>
+<a id="__codelineno-28-15" name="__codelineno-28-15" href="#__codelineno-28-15"></a><span class="w">    </span><span class="cm">/* 両端キューの容量を取得 */</span>
+<a id="__codelineno-28-16" name="__codelineno-28-16" href="#__codelineno-28-16"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-17" name="__codelineno-28-17" href="#__codelineno-28-17"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
+<a id="__codelineno-28-18" name="__codelineno-28-18" href="#__codelineno-28-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-19" name="__codelineno-28-19" href="#__codelineno-28-19"></a>
+<a id="__codelineno-28-20" name="__codelineno-28-20" href="#__codelineno-28-20"></a><span class="w">    </span><span class="cm">/* 両端キューの長さを取得 */</span>
+<a id="__codelineno-28-21" name="__codelineno-28-21" href="#__codelineno-28-21"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-22" name="__codelineno-28-22" href="#__codelineno-28-22"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span>
+<a id="__codelineno-28-23" name="__codelineno-28-23" href="#__codelineno-28-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-24" name="__codelineno-28-24" href="#__codelineno-28-24"></a>
+<a id="__codelineno-28-25" name="__codelineno-28-25" href="#__codelineno-28-25"></a><span class="w">    </span><span class="cm">/* 両端キューが空かどうかを判定 */</span>
+<a id="__codelineno-28-26" name="__codelineno-28-26" href="#__codelineno-28-26"></a><span class="w">    </span><span class="kt">bool</span><span class="w"> </span><span class="n">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-27" name="__codelineno-28-27" href="#__codelineno-28-27"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-28-28" name="__codelineno-28-28" href="#__codelineno-28-28"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-29" name="__codelineno-28-29" href="#__codelineno-28-29"></a>
+<a id="__codelineno-28-30" name="__codelineno-28-30" href="#__codelineno-28-30"></a><span class="w">    </span><span class="cm">/* 循環配列のインデックスを計算 */</span>
+<a id="__codelineno-28-31" name="__codelineno-28-31" href="#__codelineno-28-31"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">index</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-32" name="__codelineno-28-32" href="#__codelineno-28-32"></a><span class="w">        </span><span class="c1">// 剰余演算で循環配列を実現</span>
+<a id="__codelineno-28-33" name="__codelineno-28-33" href="#__codelineno-28-33"></a><span class="w">        </span><span class="c1">// iが配列の末尾を超えた場合、先頭に戻る</span>
+<a id="__codelineno-28-34" name="__codelineno-28-34" href="#__codelineno-28-34"></a><span class="w">        </span><span class="c1">// iが配列の先頭を超えた場合、末尾に戻る</span>
+<a id="__codelineno-28-35" name="__codelineno-28-35" href="#__codelineno-28-35"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">capacity</span><span class="p">())</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">();</span>
+<a id="__codelineno-28-36" name="__codelineno-28-36" href="#__codelineno-28-36"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-37" name="__codelineno-28-37" href="#__codelineno-28-37"></a>
+<a id="__codelineno-28-38" name="__codelineno-28-38" href="#__codelineno-28-38"></a><span class="w">    </span><span class="cm">/* 先頭エンキュー */</span>
+<a id="__codelineno-28-39" name="__codelineno-28-39" href="#__codelineno-28-39"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">pushFirst</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-40" name="__codelineno-28-40" href="#__codelineno-28-40"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">capacity</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-41" name="__codelineno-28-41" href="#__codelineno-28-41"></a><span class="w">            </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;Double-ended queue is full&quot;</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
+<a id="__codelineno-28-42" name="__codelineno-28-42" href="#__codelineno-28-42"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-28-43" name="__codelineno-28-43" href="#__codelineno-28-43"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-28-44" name="__codelineno-28-44" href="#__codelineno-28-44"></a><span class="w">        </span><span class="c1">// 先頭ポインタを1つ左に移動</span>
+<a id="__codelineno-28-45" name="__codelineno-28-45" href="#__codelineno-28-45"></a><span class="w">        </span><span class="c1">// 剰余演算でfrontが配列の先頭を越えて末尾に戻ることを実現</span>
+<a id="__codelineno-28-46" name="__codelineno-28-46" href="#__codelineno-28-46"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-28-47" name="__codelineno-28-47" href="#__codelineno-28-47"></a><span class="w">        </span><span class="c1">// numを先頭に追加</span>
+<a id="__codelineno-28-48" name="__codelineno-28-48" href="#__codelineno-28-48"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">front</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-28-49" name="__codelineno-28-49" href="#__codelineno-28-49"></a><span class="w">        </span><span class="n">queSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-28-50" name="__codelineno-28-50" href="#__codelineno-28-50"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-51" name="__codelineno-28-51" href="#__codelineno-28-51"></a>
+<a id="__codelineno-28-52" name="__codelineno-28-52" href="#__codelineno-28-52"></a><span class="w">    </span><span class="cm">/* 末尾エンキュー */</span>
+<a id="__codelineno-28-53" name="__codelineno-28-53" href="#__codelineno-28-53"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">pushLast</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-54" name="__codelineno-28-54" href="#__codelineno-28-54"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">capacity</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-55" name="__codelineno-28-55" href="#__codelineno-28-55"></a><span class="w">            </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;Double-ended queue is full&quot;</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
+<a id="__codelineno-28-56" name="__codelineno-28-56" href="#__codelineno-28-56"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-28-57" name="__codelineno-28-57" href="#__codelineno-28-57"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-28-58" name="__codelineno-28-58" href="#__codelineno-28-58"></a><span class="w">        </span><span class="c1">// 末尾ポインタを計算、末尾インデックス + 1を指す</span>
+<a id="__codelineno-28-59" name="__codelineno-28-59" href="#__codelineno-28-59"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">queSize</span><span class="p">);</span>
+<a id="__codelineno-28-60" name="__codelineno-28-60" href="#__codelineno-28-60"></a><span class="w">        </span><span class="c1">// numを末尾に追加</span>
+<a id="__codelineno-28-61" name="__codelineno-28-61" href="#__codelineno-28-61"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">rear</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-28-62" name="__codelineno-28-62" href="#__codelineno-28-62"></a><span class="w">        </span><span class="n">queSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-28-63" name="__codelineno-28-63" href="#__codelineno-28-63"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-64" name="__codelineno-28-64" href="#__codelineno-28-64"></a>
+<a id="__codelineno-28-65" name="__codelineno-28-65" href="#__codelineno-28-65"></a><span class="w">    </span><span class="cm">/* 先頭デキュー */</span>
+<a id="__codelineno-28-66" name="__codelineno-28-66" href="#__codelineno-28-66"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">popFirst</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-67" name="__codelineno-28-67" href="#__codelineno-28-67"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peekFirst</span><span class="p">();</span>
+<a id="__codelineno-28-68" name="__codelineno-28-68" href="#__codelineno-28-68"></a><span class="w">        </span><span class="c1">// 先頭ポインタを1つ後ろに移動</span>
+<a id="__codelineno-28-69" name="__codelineno-28-69" href="#__codelineno-28-69"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-28-70" name="__codelineno-28-70" href="#__codelineno-28-70"></a><span class="w">        </span><span class="n">queSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-28-71" name="__codelineno-28-71" href="#__codelineno-28-71"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-28-72" name="__codelineno-28-72" href="#__codelineno-28-72"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-73" name="__codelineno-28-73" href="#__codelineno-28-73"></a>
+<a id="__codelineno-28-74" name="__codelineno-28-74" href="#__codelineno-28-74"></a><span class="w">    </span><span class="cm">/* 末尾デキュー */</span>
+<a id="__codelineno-28-75" name="__codelineno-28-75" href="#__codelineno-28-75"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">popLast</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-76" name="__codelineno-28-76" href="#__codelineno-28-76"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peekLast</span><span class="p">();</span>
+<a id="__codelineno-28-77" name="__codelineno-28-77" href="#__codelineno-28-77"></a><span class="w">        </span><span class="n">queSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-28-78" name="__codelineno-28-78" href="#__codelineno-28-78"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-28-79" name="__codelineno-28-79" href="#__codelineno-28-79"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-80" name="__codelineno-28-80" href="#__codelineno-28-80"></a>
+<a id="__codelineno-28-81" name="__codelineno-28-81" href="#__codelineno-28-81"></a><span class="w">    </span><span class="cm">/* 先頭要素にアクセス */</span>
+<a id="__codelineno-28-82" name="__codelineno-28-82" href="#__codelineno-28-82"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">peekFirst</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-83" name="__codelineno-28-83" href="#__codelineno-28-83"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
+<a id="__codelineno-28-84" name="__codelineno-28-84" href="#__codelineno-28-84"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;Double-ended queue is empty&quot;</span><span class="p">);</span>
+<a id="__codelineno-28-85" name="__codelineno-28-85" href="#__codelineno-28-85"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">front</span><span class="p">];</span>
+<a id="__codelineno-28-86" name="__codelineno-28-86" href="#__codelineno-28-86"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-87" name="__codelineno-28-87" href="#__codelineno-28-87"></a>
+<a id="__codelineno-28-88" name="__codelineno-28-88" href="#__codelineno-28-88"></a><span class="w">    </span><span class="cm">/* 末尾要素にアクセス */</span>
+<a id="__codelineno-28-89" name="__codelineno-28-89" href="#__codelineno-28-89"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">peekLast</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-90" name="__codelineno-28-90" href="#__codelineno-28-90"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
+<a id="__codelineno-28-91" name="__codelineno-28-91" href="#__codelineno-28-91"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;Double-ended queue is empty&quot;</span><span class="p">);</span>
+<a id="__codelineno-28-92" name="__codelineno-28-92" href="#__codelineno-28-92"></a><span class="w">        </span><span class="c1">// 末尾要素のインデックスを計算</span>
+<a id="__codelineno-28-93" name="__codelineno-28-93" href="#__codelineno-28-93"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">last</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-28-94" name="__codelineno-28-94" href="#__codelineno-28-94"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">last</span><span class="p">];</span>
+<a id="__codelineno-28-95" name="__codelineno-28-95" href="#__codelineno-28-95"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-96" name="__codelineno-28-96" href="#__codelineno-28-96"></a>
+<a id="__codelineno-28-97" name="__codelineno-28-97" href="#__codelineno-28-97"></a><span class="w">    </span><span class="cm">/* 印刷用に配列を返却 */</span>
+<a id="__codelineno-28-98" name="__codelineno-28-98" href="#__codelineno-28-98"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">toVector</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-99" name="__codelineno-28-99" href="#__codelineno-28-99"></a><span class="w">        </span><span class="c1">// 有効な長さ範囲内の要素のみを変換</span>
+<a id="__codelineno-28-100" name="__codelineno-28-100" href="#__codelineno-28-100"></a><span class="w">        </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">(</span><span class="n">queSize</span><span class="p">);</span>
+<a id="__codelineno-28-101" name="__codelineno-28-101" href="#__codelineno-28-101"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-102" name="__codelineno-28-102" href="#__codelineno-28-102"></a><span class="w">            </span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">index</span><span class="p">(</span><span class="n">j</span><span class="p">)];</span>
+<a id="__codelineno-28-103" name="__codelineno-28-103" href="#__codelineno-28-103"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-28-104" name="__codelineno-28-104" href="#__codelineno-28-104"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-28-105" name="__codelineno-28-105" href="#__codelineno-28-105"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-106" name="__codelineno-28-106" href="#__codelineno-28-106"></a><span class="p">};</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_deque.java</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="cm">/* 循環配列に基づく両端キュークラス */</span>
+<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="kd">class</span> <span class="nc">ArrayDeque</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">;</span><span class="w"> </span><span class="c1">// 両端キューの要素を格納する配列</span>
+<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">front</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ポインタ、先頭要素を指す</span>
+<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span><span class="w"> </span><span class="c1">// 両端キューの長さ</span>
+<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a>
+<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="nf">ArrayDeque</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-9" name="__codelineno-29-9" href="#__codelineno-29-9"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="na">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">capacity</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-29-10" name="__codelineno-29-10" href="#__codelineno-29-10"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-29-11" name="__codelineno-29-11" href="#__codelineno-29-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-12" name="__codelineno-29-12" href="#__codelineno-29-12"></a>
+<a id="__codelineno-29-13" name="__codelineno-29-13" href="#__codelineno-29-13"></a><span class="w">    </span><span class="cm">/* 両端キューの容量を取得 */</span>
+<a id="__codelineno-29-14" name="__codelineno-29-14" href="#__codelineno-29-14"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">capacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-15" name="__codelineno-29-15" href="#__codelineno-29-15"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="p">;</span>
+<a id="__codelineno-29-16" name="__codelineno-29-16" href="#__codelineno-29-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-17" name="__codelineno-29-17" href="#__codelineno-29-17"></a>
+<a id="__codelineno-29-18" name="__codelineno-29-18" href="#__codelineno-29-18"></a><span class="w">    </span><span class="cm">/* 両端キューの長さを取得 */</span>
+<a id="__codelineno-29-19" name="__codelineno-29-19" href="#__codelineno-29-19"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-20" name="__codelineno-29-20" href="#__codelineno-29-20"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span>
+<a id="__codelineno-29-21" name="__codelineno-29-21" href="#__codelineno-29-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-22" name="__codelineno-29-22" href="#__codelineno-29-22"></a>
+<a id="__codelineno-29-23" name="__codelineno-29-23" href="#__codelineno-29-23"></a><span class="w">    </span><span class="cm">/* 両端キューが空かどうかを判定 */</span>
+<a id="__codelineno-29-24" name="__codelineno-29-24" href="#__codelineno-29-24"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">boolean</span><span class="w"> </span><span class="nf">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-25" name="__codelineno-29-25" href="#__codelineno-29-25"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-29-26" name="__codelineno-29-26" href="#__codelineno-29-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-27" name="__codelineno-29-27" href="#__codelineno-29-27"></a>
+<a id="__codelineno-29-28" name="__codelineno-29-28" href="#__codelineno-29-28"></a><span class="w">    </span><span class="cm">/* 循環配列インデックスを計算 */</span>
+<a id="__codelineno-29-29" name="__codelineno-29-29" href="#__codelineno-29-29"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">index</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-30" name="__codelineno-29-30" href="#__codelineno-29-30"></a><span class="w">        </span><span class="c1">// モジュロ演算により循環配列を実装</span>
+<a id="__codelineno-29-31" name="__codelineno-29-31" href="#__codelineno-29-31"></a><span class="w">        </span><span class="c1">// i が配列の末尾を超える場合、先頭に戻る</span>
+<a id="__codelineno-29-32" name="__codelineno-29-32" href="#__codelineno-29-32"></a><span class="w">        </span><span class="c1">// i が配列の先頭を超える場合、末尾に戻る</span>
+<a id="__codelineno-29-33" name="__codelineno-29-33" href="#__codelineno-29-33"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">capacity</span><span class="p">())</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">();</span>
+<a id="__codelineno-29-34" name="__codelineno-29-34" href="#__codelineno-29-34"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-35" name="__codelineno-29-35" href="#__codelineno-29-35"></a>
+<a id="__codelineno-29-36" name="__codelineno-29-36" href="#__codelineno-29-36"></a><span class="w">    </span><span class="cm">/* 先頭エンキュー */</span>
+<a id="__codelineno-29-37" name="__codelineno-29-37" href="#__codelineno-29-37"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">pushFirst</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-38" name="__codelineno-29-38" href="#__codelineno-29-38"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">capacity</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-39" name="__codelineno-29-39" href="#__codelineno-29-39"></a><span class="w">            </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="s">&quot;両端キューが満杯です&quot;</span><span class="p">);</span>
+<a id="__codelineno-29-40" name="__codelineno-29-40" href="#__codelineno-29-40"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-29-41" name="__codelineno-29-41" href="#__codelineno-29-41"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-29-42" name="__codelineno-29-42" href="#__codelineno-29-42"></a><span class="w">        </span><span class="c1">// 先頭ポインタを左に移動し、境界を越える場合は配列の末尾に回る</span>
+<a id="__codelineno-29-43" name="__codelineno-29-43" href="#__codelineno-29-43"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-29-44" name="__codelineno-29-44" href="#__codelineno-29-44"></a><span class="w">        </span><span class="c1">// 先頭に num を追加</span>
+<a id="__codelineno-29-45" name="__codelineno-29-45" href="#__codelineno-29-45"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">front</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-29-46" name="__codelineno-29-46" href="#__codelineno-29-46"></a><span class="w">        </span><span class="n">queSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-29-47" name="__codelineno-29-47" href="#__codelineno-29-47"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-48" name="__codelineno-29-48" href="#__codelineno-29-48"></a>
+<a id="__codelineno-29-49" name="__codelineno-29-49" href="#__codelineno-29-49"></a><span class="w">    </span><span class="cm">/* 末尾エンキュー */</span>
+<a id="__codelineno-29-50" name="__codelineno-29-50" href="#__codelineno-29-50"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">pushLast</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-51" name="__codelineno-29-51" href="#__codelineno-29-51"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">capacity</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-52" name="__codelineno-29-52" href="#__codelineno-29-52"></a><span class="w">            </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="s">&quot;両端キューが満杯です&quot;</span><span class="p">);</span>
+<a id="__codelineno-29-53" name="__codelineno-29-53" href="#__codelineno-29-53"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-29-54" name="__codelineno-29-54" href="#__codelineno-29-54"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-29-55" name="__codelineno-29-55" href="#__codelineno-29-55"></a><span class="w">        </span><span class="c1">// 末尾ポインタを計算し、末尾に要素を追加</span>
+<a id="__codelineno-29-56" name="__codelineno-29-56" href="#__codelineno-29-56"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">queSize</span><span class="p">);</span>
+<a id="__codelineno-29-57" name="__codelineno-29-57" href="#__codelineno-29-57"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">rear</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-29-58" name="__codelineno-29-58" href="#__codelineno-29-58"></a><span class="w">        </span><span class="n">queSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-29-59" name="__codelineno-29-59" href="#__codelineno-29-59"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-60" name="__codelineno-29-60" href="#__codelineno-29-60"></a>
+<a id="__codelineno-29-61" name="__codelineno-29-61" href="#__codelineno-29-61"></a><span class="w">    </span><span class="cm">/* 先頭デキュー */</span>
+<a id="__codelineno-29-62" name="__codelineno-29-62" href="#__codelineno-29-62"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">popFirst</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-63" name="__codelineno-29-63" href="#__codelineno-29-63"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peekFirst</span><span class="p">();</span>
+<a id="__codelineno-29-64" name="__codelineno-29-64" href="#__codelineno-29-64"></a><span class="w">        </span><span class="c1">// 先頭ポインタを右に移動</span>
+<a id="__codelineno-29-65" name="__codelineno-29-65" href="#__codelineno-29-65"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-29-66" name="__codelineno-29-66" href="#__codelineno-29-66"></a><span class="w">        </span><span class="n">queSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-29-67" name="__codelineno-29-67" href="#__codelineno-29-67"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-29-68" name="__codelineno-29-68" href="#__codelineno-29-68"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-69" name="__codelineno-29-69" href="#__codelineno-29-69"></a>
+<a id="__codelineno-29-70" name="__codelineno-29-70" href="#__codelineno-29-70"></a><span class="w">    </span><span class="cm">/* 末尾デキュー */</span>
+<a id="__codelineno-29-71" name="__codelineno-29-71" href="#__codelineno-29-71"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">popLast</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-72" name="__codelineno-29-72" href="#__codelineno-29-72"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peekLast</span><span class="p">();</span>
+<a id="__codelineno-29-73" name="__codelineno-29-73" href="#__codelineno-29-73"></a><span class="w">        </span><span class="n">queSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-29-74" name="__codelineno-29-74" href="#__codelineno-29-74"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-29-75" name="__codelineno-29-75" href="#__codelineno-29-75"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-76" name="__codelineno-29-76" href="#__codelineno-29-76"></a>
+<a id="__codelineno-29-77" name="__codelineno-29-77" href="#__codelineno-29-77"></a><span class="w">    </span><span class="cm">/* 先頭要素にアクセス */</span>
+<a id="__codelineno-29-78" name="__codelineno-29-78" href="#__codelineno-29-78"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">peekFirst</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-79" name="__codelineno-29-79" href="#__codelineno-29-79"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
+<a id="__codelineno-29-80" name="__codelineno-29-80" href="#__codelineno-29-80"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">();</span>
+<a id="__codelineno-29-81" name="__codelineno-29-81" href="#__codelineno-29-81"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">front</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-29-82" name="__codelineno-29-82" href="#__codelineno-29-82"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-83" name="__codelineno-29-83" href="#__codelineno-29-83"></a>
+<a id="__codelineno-29-84" name="__codelineno-29-84" href="#__codelineno-29-84"></a><span class="w">    </span><span class="cm">/* 末尾要素にアクセス */</span>
+<a id="__codelineno-29-85" name="__codelineno-29-85" href="#__codelineno-29-85"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">peekLast</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-86" name="__codelineno-29-86" href="#__codelineno-29-86"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
+<a id="__codelineno-29-87" name="__codelineno-29-87" href="#__codelineno-29-87"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">();</span>
+<a id="__codelineno-29-88" name="__codelineno-29-88" href="#__codelineno-29-88"></a><span class="w">        </span><span class="c1">// 末尾要素のインデックスを計算</span>
+<a id="__codelineno-29-89" name="__codelineno-29-89" href="#__codelineno-29-89"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">last</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">index</span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-29-90" name="__codelineno-29-90" href="#__codelineno-29-90"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">last</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-29-91" name="__codelineno-29-91" href="#__codelineno-29-91"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-92" name="__codelineno-29-92" href="#__codelineno-29-92"></a>
+<a id="__codelineno-29-93" name="__codelineno-29-93" href="#__codelineno-29-93"></a><span class="w">    </span><span class="cm">/* 配列を返す */</span>
+<a id="__codelineno-29-94" name="__codelineno-29-94" href="#__codelineno-29-94"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="nf">toArray</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-95" name="__codelineno-29-95" href="#__codelineno-29-95"></a><span class="w">        </span><span class="c1">// front から開始して queSize 個の要素のみをコピー</span>
+<a id="__codelineno-29-96" name="__codelineno-29-96" href="#__codelineno-29-96"></a><span class="w">        </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">queSize</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-29-97" name="__codelineno-29-97" href="#__codelineno-29-97"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-98" name="__codelineno-29-98" href="#__codelineno-29-98"></a><span class="w">            </span><span class="n">res</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">index</span><span class="p">(</span><span class="n">j</span><span class="p">)</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-29-99" name="__codelineno-29-99" href="#__codelineno-29-99"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-29-100" name="__codelineno-29-100" href="#__codelineno-29-100"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-29-101" name="__codelineno-29-101" href="#__codelineno-29-101"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-102" name="__codelineno-29-102" href="#__codelineno-29-102"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_deque.cs</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">ArrayDeque</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_deque.go</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">arrayDeque</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_deque.swift</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">ArrayDeque</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_deque.js</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">ArrayDeque</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_deque.ts</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">ArrayDeque</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_deque.dart</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ArrayDeque</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_deque.rs</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ArrayDeque</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_deque.c</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ArrayDeque</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_deque.kt</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">ArrayDeque</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_deque.rb</span><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">ArrayDeque</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_deque.zig</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ArrayDeque</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h2 id="533">5.3.3 &nbsp; 両端キューの応用<a class="headerlink" href="#533" title="Permanent link">&para;</a></h2>
+<p>両端キューはスタックとキューの両方のロジックを組み合わせているため、<strong>それぞれのすべてのユースケースを実装でき、より大きな柔軟性を提供します</strong>。</p>
+<p>ソフトウェアの「元に戻す」機能は通常スタックを使って実装されることを知っています：システムは各変更操作をスタックに<code>push</code>し、次に<code>pop</code>して元に戻すことを実装します。しかし、システムリソースの制限を考慮して、ソフトウェアは元に戻すステップの数を制限することがよくあります（例えば、最後の50ステップのみを許可）。スタックの長さが50を超えた場合、ソフトウェアはスタックの底部（キューの前端）で削除操作を実行する必要があります。<strong>しかし、通常のスタックではこの機能を実行できないため、両端キューが必要になります</strong>。「元に戻す」のコアロジックは依然としてスタックの後入れ先出し原則に従いますが、両端キューはより柔軟にいくつかの追加ロジックを実装できることに注意してください。</p>
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+  
+  <span class="md-ellipsis">
+    はじめに
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+            はじめに
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M21 4H3a2 2 0 0 0-2 2v13a2 2 0 0 0 2 2h18a2 2 0 0 0 2-2V6a2 2 0 0 0-2-2M3 19V6h8v13H3m18 0h-8V6h8v13m-7-9.5h6V11h-6V9.5m0 2.5h6v1.5h-6V12m0 2.5h6V16h-6v-1.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 0 章 &nbsp; 前書き
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+            第 0 章 &nbsp; 前書き
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+            
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+  
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+  
+    <li class="md-nav__item">
+      <a href="../chapter_preface/about_the_book/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.1 &nbsp; この本について
+  </span>
+  
+
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+
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+  
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+    <li class="md-nav__item">
+      <a href="../chapter_preface/suggestions/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    0.2 &nbsp; 本書の使い方
+  </span>
+  
+
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+    </li>
+  
+
+              
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+  
+  
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+  
+    <li class="md-nav__item">
+      <a href="../chapter_preface/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.3 &nbsp; まとめ
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+            <a href="../chapter_introduction/" class="md-nav__link ">
+              
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
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+  
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+            第 1 章 &nbsp; アルゴリズムとの出会い
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+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
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+
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+      <a href="../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
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+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
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+    </li>
+  
+
+              
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+
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+      
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+  
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+      
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+          
+        
+      
+        
+      
+        
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+        
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+        
+      
+        
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+    
+    
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+            <a href="../chapter_computational_complexity/" class="md-nav__link ">
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
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+            
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+          <label class="md-nav__title" for="__nav_4">
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+            第 2 章 &nbsp; 計算量解析
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+            
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+      <a href="../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
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+    </li>
+  
+
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+            
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+  
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+      <a href="../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
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+            <a href="../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="./" class="md-nav__link md-nav__link--active">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link md-nav__link--active" for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
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+    
+      
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+          
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_19" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_reference/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9 3v15h3V3H9m3 2 4 13 3-1-4-13-3 1M5 5v13h3V5H5M3 19v2h18v-2H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    参考文献
+  </span>
+  
+
+            </a>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_19_label" aria-expanded="false">
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+            参考文献
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+            
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+              <div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
+                <div class="md-sidebar__scrollwrap">
+                  <div class="md-sidebar__inner">
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+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
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+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#_1" class="md-nav__link">
+    <span class="md-ellipsis">
+      章の内容
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+      
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+  
+</nav>
+                  </div>
+                </div>
+              </div>
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+    </a>
+  
+
+  <!-- View button -->
+  
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+
+<!-- Page content -->
+<h1 id="5">第 5 章 &nbsp; スタックとキュー<a class="headerlink" href="#5" title="Permanent link">&para;</a></h1>
+<p><a class="glightbox" href="../assets/covers/chapter_stack_and_queue.jpg" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="スタックとキュー" class="cover-image" src="../assets/covers/chapter_stack_and_queue.jpg" /></a></p>
+<div class="admonition abstract">
+<p class="admonition-title">Abstract</p>
+<p>スタックは積み重ねられた猫のようなもので、キューは一列に並んだ猫のようなものです。</p>
+<p>それらはそれぞれ、後入先出（LIFO）と先入先出（FIFO）の論理関係を表しています。</p>
+</div>
+<h2 id="_1">章の内容<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h2>
+<ul>
+<li><a href="stack/">5.1 &nbsp; スタック</a></li>
+<li><a href="queue/">5.2 &nbsp; キュー</a></li>
+<li><a href="deque/">5.3 &nbsp; 両端キュー</a></li>
+<li><a href="summary/">5.4 &nbsp; まとめ</a></li>
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+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
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+  
+  
+  
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+    
+      
+        
+          
+        
+      
+        
+      
+        
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+        
+      
+        
+      
+        
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+    
+    
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+    <li class="md-nav__item md-nav__item--nested">
+      
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+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
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+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
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+          <label class="md-nav__title" for="__nav_5">
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+            第 3 章 &nbsp; データ構造
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+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
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+    </li>
+  
+
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+  
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+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
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+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
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+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
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+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
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+            
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+  
+  
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+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
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+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
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+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
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+            
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
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+    <li class="md-nav__item md-nav__item--active">
+      
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+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#521" class="md-nav__link">
+    <span class="md-ellipsis">
+      5.2.1 &nbsp; キューの一般的な操作
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#522" class="md-nav__link">
+    <span class="md-ellipsis">
+      5.2.2 &nbsp; キューの実装
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="5.2.2   キューの実装">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 連結リストベースの実装
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; 配列ベースの実装
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#523" class="md-nav__link">
+    <span class="md-ellipsis">
+      5.2.3 &nbsp; キューの典型的な応用
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
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+            
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+  
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+  
+  
+    <li class="md-nav__item">
+      <a href="../deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
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+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
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+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
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+            第 6 章 &nbsp; ハッシュ表
+          </label>
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+            
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+  
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+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
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+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
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+      
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+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
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+            
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+              
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_19" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_reference/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9 3v15h3V3H9m3 2 4 13 3-1-4-13-3 1M5 5v13h3V5H5M3 19v2h18v-2H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    参考文献
+  </span>
+  
+
+            </a>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_19_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_19">
+            <span class="md-nav__icon md-icon"></span>
+            参考文献
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+  </ul>
+</nav>
+                  </div>
+                </div>
+              </div>
+            
+            
+              
+              <div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
+                <div class="md-sidebar__scrollwrap">
+                  <div class="md-sidebar__inner">
+                    
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#521" class="md-nav__link">
+    <span class="md-ellipsis">
+      5.2.1 &nbsp; キューの一般的な操作
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#522" class="md-nav__link">
+    <span class="md-ellipsis">
+      5.2.2 &nbsp; キューの実装
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="5.2.2   キューの実装">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 連結リストベースの実装
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; 配列ベースの実装
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#523" class="md-nav__link">
+    <span class="md-ellipsis">
+      5.2.3 &nbsp; キューの典型的な応用
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+                  </div>
+                </div>
+              </div>
+            
+          
+          
+            <div class="md-content" data-md-component="content">
+              <article class="md-content__inner md-typeset">
+                
+                  <!-- Tags -->
+
+
+<!-- Actions -->
+<!-- Actions -->
+
+
+  <!-- Edit button -->
+  
+    <a
+      href="https://github.com/krahets/hello-algo/tree/main/ja/docs/chapter_stack_and_queue/queue.md"
+      title="編集"
+      class="md-content__button md-icon"
+    >
+      
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
+    </a>
+  
+
+  <!-- View button -->
+  
+
+
+<!-- Page content -->
+<h1 id="52">5.2 &nbsp; キュー<a class="headerlink" href="#52" title="Permanent link">&para;</a></h1>
+<p><u>キュー</u>は、先入先出（FIFO）ルールに従う線形データ構造です。名前が示すように、キューは行列の現象をシミュレートし、新参者は列の後ろに並び、前の人が最初に列を離れます。</p>
+<p>下図に示すように、キューの前面を「ヘッド」、後面を「テール」と呼びます。キューの後ろに要素を追加する操作を「エンキュー」、前から要素を削除する操作を「デキュー」と呼びます。</p>
+<p><a class="glightbox" href="../queue.assets/queue_operations.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="キューの先入先出ルール" class="animation-figure" src="../queue.assets/queue_operations.png" /></a></p>
+<p align="center"> 図 5-4 &nbsp; キューの先入先出ルール </p>
+
+<h2 id="521">5.2.1 &nbsp; キューの一般的な操作<a class="headerlink" href="#521" title="Permanent link">&para;</a></h2>
+<p>キューの一般的な操作を下表に示します。メソッド名はプログラミング言語によって異なる場合があることに注意してください。ここでは、スタックで使用したのと同じ命名規則を使用します。</p>
+<p align="center"> 表 5-2 &nbsp; キュー操作の効率 </p>
+
+<div class="center-table">
+<table>
+<thead>
+<tr>
+<th>メソッド名</th>
+<th>説明</th>
+<th>時間計算量</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td><code>push()</code></td>
+<td>要素をエンキュー、テールに追加</td>
+<td><span class="arithmatex">\(O(1)\)</span></td>
+</tr>
+<tr>
+<td><code>pop()</code></td>
+<td>ヘッド要素をデキュー</td>
+<td><span class="arithmatex">\(O(1)\)</span></td>
+</tr>
+<tr>
+<td><code>peek()</code></td>
+<td>ヘッド要素にアクセス</td>
+<td><span class="arithmatex">\(O(1)\)</span></td>
+</tr>
+</tbody>
+</table>
+</div>
+<p>プログラミング言語で用意されているキュークラスを直接使用できます：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">queue.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="kn">from</span><span class="w"> </span><span class="nn">collections</span><span class="w"> </span><span class="kn">import</span> <span class="n">deque</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="c1"># キューを初期化</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a><span class="c1"># Pythonでは、一般的にdequeクラスをキューとして使用します</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a><span class="c1"># queue.Queue()は純粋なキュークラスですが、使いにくいため推奨されません</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a><span class="n">que</span><span class="p">:</span> <span class="n">deque</span><span class="p">[</span><span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="n">deque</span><span class="p">()</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="c1"># 要素をエンキュー</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a><span class="n">que</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a><span class="n">que</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a><span class="n">que</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a><span class="n">que</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
+<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a><span class="n">que</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>
+<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a><span class="c1"># 最初の要素にアクセス</span>
+<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a><span class="n">front</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">que</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>
+<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a><span class="c1"># 要素をデキュー</span>
+<a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a><span class="n">pop</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">que</span><span class="o">.</span><span class="n">popleft</span><span class="p">()</span>
+<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a>
+<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a><span class="c1"># キューの長さを取得</span>
+<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a><span class="n">size</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">que</span><span class="p">)</span>
+<a id="__codelineno-0-23" name="__codelineno-0-23" href="#__codelineno-0-23"></a>
+<a id="__codelineno-0-24" name="__codelineno-0-24" href="#__codelineno-0-24"></a><span class="c1"># キューが空かどうかチェック</span>
+<a id="__codelineno-0-25" name="__codelineno-0-25" href="#__codelineno-0-25"></a><span class="n">is_empty</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">que</span><span class="p">)</span> <span class="o">==</span> <span class="mi">0</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">queue.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* キューを初期化 */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="n">queue</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">queue</span><span class="p">;</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="cm">/* 要素をエンキュー */</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="n">queue</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="n">queue</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="n">queue</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="n">queue</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="n">queue</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="cm">/* 最初の要素にアクセス */</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="kt">int</span><span class="w"> </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="n">front</span><span class="p">();</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="cm">/* 要素をデキュー */</span>
+<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="n">queue</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span>
+<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a>
+<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="cm">/* キューの長さを取得 */</span>
+<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
+<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a>
+<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="cm">/* キューが空かどうかチェック */</span>
+<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="kt">bool</span><span class="w"> </span><span class="n">empty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="n">empty</span><span class="p">();</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">queue.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* キューを初期化 */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="n">Queue</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">queue</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">LinkedList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="cm">/* 要素をエンキュー */</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="n">queue</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="n">queue</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="n">queue</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="n">queue</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="n">queue</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="cm">/* 最初の要素にアクセス */</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="kt">int</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="na">peek</span><span class="p">();</span>
+<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="cm">/* 要素をデキュー */</span>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="kt">int</span><span class="w"> </span><span class="n">pop</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="na">poll</span><span class="p">();</span>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a>
+<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="cm">/* キューの長さを取得 */</span>
+<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="na">size</span><span class="p">();</span>
+<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a>
+<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="cm">/* キューが空かどうかチェック */</span>
+<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="kt">boolean</span><span class="w"> </span><span class="n">isEmpty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="na">isEmpty</span><span class="p">();</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">queue.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* キューを初期化 */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="n">Queue</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">queue</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">();</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="cm">/* 要素をエンキュー */</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="n">queue</span><span class="p">.</span><span class="n">Enqueue</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="n">queue</span><span class="p">.</span><span class="n">Enqueue</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="n">queue</span><span class="p">.</span><span class="n">Enqueue</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="n">queue</span><span class="p">.</span><span class="n">Enqueue</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="n">queue</span><span class="p">.</span><span class="n">Enqueue</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
+<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a>
+<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="cm">/* 最初の要素にアクセス */</span>
+<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="kt">int</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="n">Peek</span><span class="p">();</span>
+<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a>
+<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="cm">/* 要素をデキュー */</span>
+<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="kt">int</span><span class="w"> </span><span class="n">pop</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="n">Dequeue</span><span class="p">();</span>
+<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a>
+<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="cm">/* キューの長さを取得 */</span>
+<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="n">Count</span><span class="p">;</span>
+<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a>
+<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="cm">/* キューが空かどうかチェック */</span>
+<a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a><span class="kt">bool</span><span class="w"> </span><span class="n">isEmpty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="n">Count</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">queue_test.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* キューを初期化 */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="c1">// Goでは、listをキューとして使用</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="nx">queue</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">list</span><span class="p">.</span><span class="nx">New</span><span class="p">()</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="cm">/* 要素をエンキュー */</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="nx">queue</span><span class="p">.</span><span class="nx">PushBack</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="nx">queue</span><span class="p">.</span><span class="nx">PushBack</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="nx">queue</span><span class="p">.</span><span class="nx">PushBack</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="nx">queue</span><span class="p">.</span><span class="nx">PushBack</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="nx">queue</span><span class="p">.</span><span class="nx">PushBack</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
+<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a>
+<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="cm">/* 最初の要素にアクセス */</span>
+<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="nx">peek</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">queue</span><span class="p">.</span><span class="nx">Front</span><span class="p">()</span>
+<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a>
+<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="cm">/* 要素をデキュー */</span>
+<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="nx">pop</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">queue</span><span class="p">.</span><span class="nx">Front</span><span class="p">()</span>
+<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="nx">queue</span><span class="p">.</span><span class="nx">Remove</span><span class="p">(</span><span class="nx">pop</span><span class="p">)</span>
+<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a>
+<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="cm">/* キューの長さを取得 */</span>
+<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="nx">size</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">queue</span><span class="p">.</span><span class="nx">Len</span><span class="p">()</span>
+<a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a>
+<a id="__codelineno-4-22" name="__codelineno-4-22" href="#__codelineno-4-22"></a><span class="cm">/* キューが空かどうかチェック */</span>
+<a id="__codelineno-4-23" name="__codelineno-4-23" href="#__codelineno-4-23"></a><span class="nx">isEmpty</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">queue</span><span class="p">.</span><span class="nx">Len</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">queue.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* キューを初期化 */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="c1">// Swiftには組み込みのキュークラスがないため、Arrayをキューとして使用</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="kd">var</span><span class="w"> </span><span class="nv">queue</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[]</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="cm">/* 要素をエンキュー */</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="n">queue</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="n">queue</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="n">queue</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="n">queue</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="n">queue</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
+<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="cm">/* 最初の要素にアクセス */</span>
+<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="kd">let</span><span class="w"> </span><span class="nv">peek</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="bp">first</span><span class="p">!</span>
+<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a>
+<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="cm">/* 要素をデキュー */</span>
+<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="c1">// 配列なので、removeFirstの計算量はO(n)</span>
+<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a><span class="kd">let</span><span class="w"> </span><span class="nv">pool</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="n">removeFirst</span><span class="p">()</span>
+<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a>
+<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="cm">/* キューの長さを取得 */</span>
+<a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a><span class="kd">let</span><span class="w"> </span><span class="nv">size</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="bp">count</span>
+<a id="__codelineno-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></a>
+<a id="__codelineno-5-22" name="__codelineno-5-22" href="#__codelineno-5-22"></a><span class="cm">/* キューが空かどうかチェック */</span>
+<a id="__codelineno-5-23" name="__codelineno-5-23" href="#__codelineno-5-23"></a><span class="kd">let</span><span class="w"> </span><span class="nv">isEmpty</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="bp">isEmpty</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">queue.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* キューを初期化 */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="c1">// JavaScriptには組み込みのキューがないため、Arrayをキューとして使用</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="kd">const</span><span class="w"> </span><span class="nx">queue</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="cm">/* 要素をエンキュー */</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="nx">queue</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="nx">queue</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">3</span><span class="p">);</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="nx">queue</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">2</span><span class="p">);</span>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="nx">queue</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">5</span><span class="p">);</span>
+<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="nx">queue</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">4</span><span class="p">);</span>
+<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a>
+<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="cm">/* 最初の要素にアクセス */</span>
+<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="kd">const</span><span class="w"> </span><span class="nx">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">queue</span><span class="p">[</span><span class="mf">0</span><span class="p">];</span>
+<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a>
+<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="cm">/* 要素をデキュー */</span>
+<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a><span class="c1">// 基礎構造が配列なので、shift()メソッドの時間計算量はO(n)</span>
+<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a><span class="kd">const</span><span class="w"> </span><span class="nx">pop</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">queue</span><span class="p">.</span><span class="nx">shift</span><span class="p">();</span>
+<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a>
+<a id="__codelineno-6-19" name="__codelineno-6-19" href="#__codelineno-6-19"></a><span class="cm">/* キューの長さを取得 */</span>
+<a id="__codelineno-6-20" name="__codelineno-6-20" href="#__codelineno-6-20"></a><span class="kd">const</span><span class="w"> </span><span class="nx">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">queue</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-6-21" name="__codelineno-6-21" href="#__codelineno-6-21"></a>
+<a id="__codelineno-6-22" name="__codelineno-6-22" href="#__codelineno-6-22"></a><span class="cm">/* キューが空かどうかチェック */</span>
+<a id="__codelineno-6-23" name="__codelineno-6-23" href="#__codelineno-6-23"></a><span class="kd">const</span><span class="w"> </span><span class="nx">empty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">queue</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">queue.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* キューを初期化 */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="c1">// TypeScriptには組み込みのキューがないため、Arrayをキューとして使用</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="kd">const</span><span class="w"> </span><span class="nx">queue</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="cm">/* 要素をエンキュー */</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="nx">queue</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="nx">queue</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">3</span><span class="p">);</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="nx">queue</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">2</span><span class="p">);</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="nx">queue</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">5</span><span class="p">);</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="nx">queue</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">4</span><span class="p">);</span>
+<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="cm">/* 最初の要素にアクセス */</span>
+<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="kd">const</span><span class="w"> </span><span class="nx">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">queue</span><span class="p">[</span><span class="mf">0</span><span class="p">];</span>
+<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a>
+<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="cm">/* 要素をデキュー */</span>
+<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="c1">// 基礎構造が配列なので、shift()メソッドの時間計算量はO(n)</span>
+<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a><span class="kd">const</span><span class="w"> </span><span class="nx">pop</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">queue</span><span class="p">.</span><span class="nx">shift</span><span class="p">();</span>
+<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a>
+<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="cm">/* キューの長さを取得 */</span>
+<a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a><span class="kd">const</span><span class="w"> </span><span class="nx">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">queue</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></a>
+<a id="__codelineno-7-22" name="__codelineno-7-22" href="#__codelineno-7-22"></a><span class="cm">/* キューが空かどうかチェック */</span>
+<a id="__codelineno-7-23" name="__codelineno-7-23" href="#__codelineno-7-23"></a><span class="kd">const</span><span class="w"> </span><span class="nx">empty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">queue</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">queue.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* キューを初期化 */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="c1">// DartのQueueクラスは双方向キューですが、キューとして使用できます</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="n">Queue</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">queue</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Queue</span><span class="p">();</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="cm">/* 要素をエンキュー */</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="n">queue</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="m">1</span><span class="p">);</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="n">queue</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="m">3</span><span class="p">);</span>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="n">queue</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="m">2</span><span class="p">);</span>
+<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="n">queue</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="m">5</span><span class="p">);</span>
+<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="n">queue</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="m">4</span><span class="p">);</span>
+<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a>
+<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="cm">/* 最初の要素にアクセス */</span>
+<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="kt">int</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="n">first</span><span class="p">;</span>
+<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a>
+<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="cm">/* 要素をデキュー */</span>
+<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="kt">int</span><span class="w"> </span><span class="n">pop</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="n">removeFirst</span><span class="p">();</span>
+<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a>
+<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a><span class="cm">/* キューの長さを取得 */</span>
+<a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="n">length</span><span class="p">;</span>
+<a id="__codelineno-8-20" name="__codelineno-8-20" href="#__codelineno-8-20"></a>
+<a id="__codelineno-8-21" name="__codelineno-8-21" href="#__codelineno-8-21"></a><span class="cm">/* キューが空かどうかチェック */</span>
+<a id="__codelineno-8-22" name="__codelineno-8-22" href="#__codelineno-8-22"></a><span class="kt">bool</span><span class="w"> </span><span class="n">isEmpty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="n">isEmpty</span><span class="p">;</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">queue.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 双方向キューを初期化 */</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="c1">// Rustでは、双方向キューを通常のキューとして使用</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">deque</span><span class="p">:</span><span class="w"> </span><span class="nc">VecDeque</span><span class="o">&lt;</span><span class="kt">u32</span><span class="o">&gt;</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">VecDeque</span><span class="p">::</span><span class="n">new</span><span class="p">();</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="cm">/* 要素をエンキュー */</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="n">deque</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="n">deque</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="n">deque</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="n">deque</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="n">deque</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
+<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a>
+<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="cm">/* 最初の要素にアクセス */</span>
+<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">front</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">front</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="p">}</span>
+<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a>
+<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="cm">/* 要素をデキュー */</span>
+<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="k">if</span><span class="w"> </span><span class="kd">let</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">pop</span><span class="p">)</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">pop_front</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="p">}</span>
+<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a>
+<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="cm">/* キューの長さを取得 */</span>
+<a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="kd">let</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">len</span><span class="p">();</span>
+<a id="__codelineno-9-22" name="__codelineno-9-22" href="#__codelineno-9-22"></a>
+<a id="__codelineno-9-23" name="__codelineno-9-23" href="#__codelineno-9-23"></a><span class="cm">/* キューが空かどうかチェック */</span>
+<a id="__codelineno-9-24" name="__codelineno-9-24" href="#__codelineno-9-24"></a><span class="kd">let</span><span class="w"> </span><span class="n">is_empty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">deque</span><span class="p">.</span><span class="n">is_empty</span><span class="p">();</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">queue.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="c1">// Cは組み込みのキューを提供していません</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">queue.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">queue.zig</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h2 id="522">5.2.2 &nbsp; キューの実装<a class="headerlink" href="#522" title="Permanent link">&para;</a></h2>
+<p>キューを実装するには、一方の端で要素を追加し、もう一方の端で要素を削除できるデータ構造が必要です。連結リストと配列の両方がこの要件を満たします。</p>
+<h3 id="1">1. &nbsp; 連結リストベースの実装<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<p>下図に示すように、連結リストの「ヘッドノード」と「テールノード」をそれぞれキューの「フロント」と「リア」と考えることができます。ノードは後ろでのみ追加でき、前でのみ削除できるように規定されています。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:3"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">LinkedListQueue</label><label for="__tabbed_2_2">push()</label><label for="__tabbed_2_3">pop()</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<p><a class="glightbox" href="../queue.assets/linkedlist_queue_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="連結リストによるキュー実装のエンキューとデキュー操作" class="animation-figure" src="../queue.assets/linkedlist_queue_step1.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../queue.assets/linkedlist_queue_step2_push.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="linkedlist_queue_push" class="animation-figure" src="../queue.assets/linkedlist_queue_step2_push.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../queue.assets/linkedlist_queue_step3_pop.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="linkedlist_queue_pop" class="animation-figure" src="../queue.assets/linkedlist_queue_step3_pop.png" /></a></p>
+</div>
+</div>
+</div>
+<p align="center"> 図 5-5 &nbsp; 連結リストによるキュー実装のエンキューとデキュー操作 </p>
+
+<p>以下は、連結リストを使用してキューを実装するコードです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="3:14"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><input id="__tabbed_3_14" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label><label for="__tabbed_3_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linkedlist_queue.py</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">LinkedListQueue</span><span class="p">:</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;連結リストベースのキュークラス&quot;&quot;&quot;</span>
+<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>
+<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;コンストラクタ&quot;&quot;&quot;</span>
+<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_front</span><span class="p">:</span> <span class="n">ListNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span>  <span class="c1"># ヘッドノード front</span>
+<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_rear</span><span class="p">:</span> <span class="n">ListNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span>  <span class="c1"># テールノード rear</span>
+<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a>
+<a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">size</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;キューの長さを取得&quot;&quot;&quot;</span>
+<a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span>
+<a id="__codelineno-13-13" name="__codelineno-13-13" href="#__codelineno-13-13"></a>
+<a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">is_empty</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">bool</span><span class="p">:</span>
+<a id="__codelineno-13-15" name="__codelineno-13-15" href="#__codelineno-13-15"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;キューが空かどうかを判定&quot;&quot;&quot;</span>
+<a id="__codelineno-13-16" name="__codelineno-13-16" href="#__codelineno-13-16"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">==</span> <span class="mi">0</span>
+<a id="__codelineno-13-17" name="__codelineno-13-17" href="#__codelineno-13-17"></a>
+<a id="__codelineno-13-18" name="__codelineno-13-18" href="#__codelineno-13-18"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">num</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-13-19" name="__codelineno-13-19" href="#__codelineno-13-19"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;エンキュー&quot;&quot;&quot;</span>
+<a id="__codelineno-13-20" name="__codelineno-13-20" href="#__codelineno-13-20"></a>        <span class="c1"># テールノードの後ろに num を追加</span>
+<a id="__codelineno-13-21" name="__codelineno-13-21" href="#__codelineno-13-21"></a>        <span class="n">node</span> <span class="o">=</span> <span class="n">ListNode</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-13-22" name="__codelineno-13-22" href="#__codelineno-13-22"></a>        <span class="c1"># キューが空の場合、ヘッドとテールノードの両方をそのノードに向ける</span>
+<a id="__codelineno-13-23" name="__codelineno-13-23" href="#__codelineno-13-23"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-13-24" name="__codelineno-13-24" href="#__codelineno-13-24"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="o">=</span> <span class="n">node</span>
+<a id="__codelineno-13-25" name="__codelineno-13-25" href="#__codelineno-13-25"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">_rear</span> <span class="o">=</span> <span class="n">node</span>
+<a id="__codelineno-13-26" name="__codelineno-13-26" href="#__codelineno-13-26"></a>        <span class="c1"># キューが空でない場合、そのノードをテールノードの後ろに追加</span>
+<a id="__codelineno-13-27" name="__codelineno-13-27" href="#__codelineno-13-27"></a>        <span class="k">else</span><span class="p">:</span>
+<a id="__codelineno-13-28" name="__codelineno-13-28" href="#__codelineno-13-28"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">_rear</span><span class="o">.</span><span class="n">next</span> <span class="o">=</span> <span class="n">node</span>
+<a id="__codelineno-13-29" name="__codelineno-13-29" href="#__codelineno-13-29"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">_rear</span> <span class="o">=</span> <span class="n">node</span>
+<a id="__codelineno-13-30" name="__codelineno-13-30" href="#__codelineno-13-30"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-13-31" name="__codelineno-13-31" href="#__codelineno-13-31"></a>
+<a id="__codelineno-13-32" name="__codelineno-13-32" href="#__codelineno-13-32"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">pop</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-13-33" name="__codelineno-13-33" href="#__codelineno-13-33"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;デキュー&quot;&quot;&quot;</span>
+<a id="__codelineno-13-34" name="__codelineno-13-34" href="#__codelineno-13-34"></a>        <span class="n">num</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">peek</span><span class="p">()</span>
+<a id="__codelineno-13-35" name="__codelineno-13-35" href="#__codelineno-13-35"></a>        <span class="c1"># ヘッドノードを削除</span>
+<a id="__codelineno-13-36" name="__codelineno-13-36" href="#__codelineno-13-36"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_front</span><span class="o">.</span><span class="n">next</span>
+<a id="__codelineno-13-37" name="__codelineno-13-37" href="#__codelineno-13-37"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">-=</span> <span class="mi">1</span>
+<a id="__codelineno-13-38" name="__codelineno-13-38" href="#__codelineno-13-38"></a>        <span class="k">return</span> <span class="n">num</span>
+<a id="__codelineno-13-39" name="__codelineno-13-39" href="#__codelineno-13-39"></a>
+<a id="__codelineno-13-40" name="__codelineno-13-40" href="#__codelineno-13-40"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">peek</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-13-41" name="__codelineno-13-41" href="#__codelineno-13-41"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;フロント要素にアクセス&quot;&quot;&quot;</span>
+<a id="__codelineno-13-42" name="__codelineno-13-42" href="#__codelineno-13-42"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">is_empty</span><span class="p">():</span>
+<a id="__codelineno-13-43" name="__codelineno-13-43" href="#__codelineno-13-43"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;Queue is empty&quot;</span><span class="p">)</span>
+<a id="__codelineno-13-44" name="__codelineno-13-44" href="#__codelineno-13-44"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_front</span><span class="o">.</span><span class="n">val</span>
+<a id="__codelineno-13-45" name="__codelineno-13-45" href="#__codelineno-13-45"></a>
+<a id="__codelineno-13-46" name="__codelineno-13-46" href="#__codelineno-13-46"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">to_list</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
+<a id="__codelineno-13-47" name="__codelineno-13-47" href="#__codelineno-13-47"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;出力用のリストに変換&quot;&quot;&quot;</span>
+<a id="__codelineno-13-48" name="__codelineno-13-48" href="#__codelineno-13-48"></a>        <span class="n">queue</span> <span class="o">=</span> <span class="p">[]</span>
+<a id="__codelineno-13-49" name="__codelineno-13-49" href="#__codelineno-13-49"></a>        <span class="n">temp</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_front</span>
+<a id="__codelineno-13-50" name="__codelineno-13-50" href="#__codelineno-13-50"></a>        <span class="k">while</span> <span class="n">temp</span><span class="p">:</span>
+<a id="__codelineno-13-51" name="__codelineno-13-51" href="#__codelineno-13-51"></a>            <span class="n">queue</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">temp</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-13-52" name="__codelineno-13-52" href="#__codelineno-13-52"></a>            <span class="n">temp</span> <span class="o">=</span> <span class="n">temp</span><span class="o">.</span><span class="n">next</span>
+<a id="__codelineno-13-53" name="__codelineno-13-53" href="#__codelineno-13-53"></a>        <span class="k">return</span> <span class="n">queue</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linkedlist_queue.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 連結リストに基づくキュークラス */</span>
+<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">LinkedListQueue</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">  </span><span class="k">private</span><span class="o">:</span>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">front</span><span class="p">,</span><span class="w"> </span><span class="o">*</span><span class="n">rear</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノードfront、末尾ノードrear</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a>
+<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w">  </span><span class="k">public</span><span class="o">:</span>
+<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w">    </span><span class="n">LinkedListQueue</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">;</span>
+<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="w">        </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">;</span>
+<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="w">        </span><span class="n">queSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a>
+<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="w">    </span><span class="o">~</span><span class="n">LinkedListQueue</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a><span class="w">        </span><span class="c1">// 連結リストを走査、ノードを削除、メモリを解放</span>
+<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a><span class="w">        </span><span class="n">freeMemoryLinkedList</span><span class="p">(</span><span class="n">front</span><span class="p">);</span>
+<a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a>
+<a id="__codelineno-14-19" name="__codelineno-14-19" href="#__codelineno-14-19"></a><span class="w">    </span><span class="cm">/* キューの長さを取得 */</span>
+<a id="__codelineno-14-20" name="__codelineno-14-20" href="#__codelineno-14-20"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-21" name="__codelineno-14-21" href="#__codelineno-14-21"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span>
+<a id="__codelineno-14-22" name="__codelineno-14-22" href="#__codelineno-14-22"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-23" name="__codelineno-14-23" href="#__codelineno-14-23"></a>
+<a id="__codelineno-14-24" name="__codelineno-14-24" href="#__codelineno-14-24"></a><span class="w">    </span><span class="cm">/* キューが空かどうかを判定 */</span>
+<a id="__codelineno-14-25" name="__codelineno-14-25" href="#__codelineno-14-25"></a><span class="w">    </span><span class="kt">bool</span><span class="w"> </span><span class="n">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-26" name="__codelineno-14-26" href="#__codelineno-14-26"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-14-27" name="__codelineno-14-27" href="#__codelineno-14-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-28" name="__codelineno-14-28" href="#__codelineno-14-28"></a>
+<a id="__codelineno-14-29" name="__codelineno-14-29" href="#__codelineno-14-29"></a><span class="w">    </span><span class="cm">/* エンキュー */</span>
+<a id="__codelineno-14-30" name="__codelineno-14-30" href="#__codelineno-14-30"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-31" name="__codelineno-14-31" href="#__codelineno-14-31"></a><span class="w">        </span><span class="c1">// 末尾ノードの後ろにnumを追加</span>
+<a id="__codelineno-14-32" name="__codelineno-14-32" href="#__codelineno-14-32"></a><span class="w">        </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-14-33" name="__codelineno-14-33" href="#__codelineno-14-33"></a><span class="w">        </span><span class="c1">// キューが空の場合、先頭と末尾ノードの両方をそのノードに向ける</span>
+<a id="__codelineno-14-34" name="__codelineno-14-34" href="#__codelineno-14-34"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-35" name="__codelineno-14-35" href="#__codelineno-14-35"></a><span class="w">            </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-14-36" name="__codelineno-14-36" href="#__codelineno-14-36"></a><span class="w">            </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-14-37" name="__codelineno-14-37" href="#__codelineno-14-37"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-14-38" name="__codelineno-14-38" href="#__codelineno-14-38"></a><span class="w">        </span><span class="c1">// キューが空でない場合、そのノードを末尾ノードの後ろに追加</span>
+<a id="__codelineno-14-39" name="__codelineno-14-39" href="#__codelineno-14-39"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-40" name="__codelineno-14-40" href="#__codelineno-14-40"></a><span class="w">            </span><span class="n">rear</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-14-41" name="__codelineno-14-41" href="#__codelineno-14-41"></a><span class="w">            </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-14-42" name="__codelineno-14-42" href="#__codelineno-14-42"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-14-43" name="__codelineno-14-43" href="#__codelineno-14-43"></a><span class="w">        </span><span class="n">queSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-14-44" name="__codelineno-14-44" href="#__codelineno-14-44"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-45" name="__codelineno-14-45" href="#__codelineno-14-45"></a>
+<a id="__codelineno-14-46" name="__codelineno-14-46" href="#__codelineno-14-46"></a><span class="w">    </span><span class="cm">/* デキュー */</span>
+<a id="__codelineno-14-47" name="__codelineno-14-47" href="#__codelineno-14-47"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-48" name="__codelineno-14-48" href="#__codelineno-14-48"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peek</span><span class="p">();</span>
+<a id="__codelineno-14-49" name="__codelineno-14-49" href="#__codelineno-14-49"></a><span class="w">        </span><span class="c1">// 先頭ノードを削除</span>
+<a id="__codelineno-14-50" name="__codelineno-14-50" href="#__codelineno-14-50"></a><span class="w">        </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">;</span>
+<a id="__codelineno-14-51" name="__codelineno-14-51" href="#__codelineno-14-51"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-14-52" name="__codelineno-14-52" href="#__codelineno-14-52"></a><span class="w">        </span><span class="c1">// メモリを解放</span>
+<a id="__codelineno-14-53" name="__codelineno-14-53" href="#__codelineno-14-53"></a><span class="w">        </span><span class="k">delete</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
+<a id="__codelineno-14-54" name="__codelineno-14-54" href="#__codelineno-14-54"></a><span class="w">        </span><span class="n">queSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-14-55" name="__codelineno-14-55" href="#__codelineno-14-55"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-14-56" name="__codelineno-14-56" href="#__codelineno-14-56"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-57" name="__codelineno-14-57" href="#__codelineno-14-57"></a>
+<a id="__codelineno-14-58" name="__codelineno-14-58" href="#__codelineno-14-58"></a><span class="w">    </span><span class="cm">/* 先頭要素にアクセス */</span>
+<a id="__codelineno-14-59" name="__codelineno-14-59" href="#__codelineno-14-59"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-60" name="__codelineno-14-60" href="#__codelineno-14-60"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-14-61" name="__codelineno-14-61" href="#__codelineno-14-61"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;Queue is empty&quot;</span><span class="p">);</span>
+<a id="__codelineno-14-62" name="__codelineno-14-62" href="#__codelineno-14-62"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">front</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-14-63" name="__codelineno-14-63" href="#__codelineno-14-63"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-64" name="__codelineno-14-64" href="#__codelineno-14-64"></a>
+<a id="__codelineno-14-65" name="__codelineno-14-65" href="#__codelineno-14-65"></a><span class="w">    </span><span class="cm">/* 連結リストをVectorに変換して返却 */</span>
+<a id="__codelineno-14-66" name="__codelineno-14-66" href="#__codelineno-14-66"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">toVector</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-67" name="__codelineno-14-67" href="#__codelineno-14-67"></a><span class="w">        </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">;</span>
+<a id="__codelineno-14-68" name="__codelineno-14-68" href="#__codelineno-14-68"></a><span class="w">        </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">(</span><span class="n">size</span><span class="p">());</span>
+<a id="__codelineno-14-69" name="__codelineno-14-69" href="#__codelineno-14-69"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-70" name="__codelineno-14-70" href="#__codelineno-14-70"></a><span class="w">            </span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-14-71" name="__codelineno-14-71" href="#__codelineno-14-71"></a><span class="w">            </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-14-72" name="__codelineno-14-72" href="#__codelineno-14-72"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-14-73" name="__codelineno-14-73" href="#__codelineno-14-73"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-14-74" name="__codelineno-14-74" href="#__codelineno-14-74"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-75" name="__codelineno-14-75" href="#__codelineno-14-75"></a><span class="p">};</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linkedlist_queue.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 連結リストに基づくキュークラス */</span>
+<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kd">class</span> <span class="nc">LinkedListQueue</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="n">ListNode</span><span class="w"> </span><span class="n">front</span><span class="p">,</span><span class="w"> </span><span class="n">rear</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノード front、末尾ノード rear</span>
+<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a>
+<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="nf">LinkedListQueue</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">        </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a>
+<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="w">    </span><span class="cm">/* キューの長さを取得 */</span>
+<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span>
+<a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a>
+<a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a><span class="w">    </span><span class="cm">/* キューが空かどうかを判定 */</span>
+<a id="__codelineno-15-17" name="__codelineno-15-17" href="#__codelineno-15-17"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">boolean</span><span class="w"> </span><span class="nf">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-18" name="__codelineno-15-18" href="#__codelineno-15-18"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-15-19" name="__codelineno-15-19" href="#__codelineno-15-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-20" name="__codelineno-15-20" href="#__codelineno-15-20"></a>
+<a id="__codelineno-15-21" name="__codelineno-15-21" href="#__codelineno-15-21"></a><span class="w">    </span><span class="cm">/* エンキュー */</span>
+<a id="__codelineno-15-22" name="__codelineno-15-22" href="#__codelineno-15-22"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-23" name="__codelineno-15-23" href="#__codelineno-15-23"></a><span class="w">        </span><span class="c1">// 末尾ノードの後ろに num を追加</span>
+<a id="__codelineno-15-24" name="__codelineno-15-24" href="#__codelineno-15-24"></a><span class="w">        </span><span class="n">ListNode</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-15-25" name="__codelineno-15-25" href="#__codelineno-15-25"></a><span class="w">        </span><span class="c1">// キューが空の場合、先頭と末尾ノードの両方をそのノードにポイント</span>
+<a id="__codelineno-15-26" name="__codelineno-15-26" href="#__codelineno-15-26"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-27" name="__codelineno-15-27" href="#__codelineno-15-27"></a><span class="w">            </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-15-28" name="__codelineno-15-28" href="#__codelineno-15-28"></a><span class="w">            </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-15-29" name="__codelineno-15-29" href="#__codelineno-15-29"></a><span class="w">        </span><span class="c1">// キューが空でない場合、そのノードを末尾ノードの後ろに追加</span>
+<a id="__codelineno-15-30" name="__codelineno-15-30" href="#__codelineno-15-30"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-31" name="__codelineno-15-31" href="#__codelineno-15-31"></a><span class="w">            </span><span class="n">rear</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-15-32" name="__codelineno-15-32" href="#__codelineno-15-32"></a><span class="w">            </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-15-33" name="__codelineno-15-33" href="#__codelineno-15-33"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-15-34" name="__codelineno-15-34" href="#__codelineno-15-34"></a><span class="w">        </span><span class="n">queSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-15-35" name="__codelineno-15-35" href="#__codelineno-15-35"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-36" name="__codelineno-15-36" href="#__codelineno-15-36"></a>
+<a id="__codelineno-15-37" name="__codelineno-15-37" href="#__codelineno-15-37"></a><span class="w">    </span><span class="cm">/* デキュー */</span>
+<a id="__codelineno-15-38" name="__codelineno-15-38" href="#__codelineno-15-38"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-39" name="__codelineno-15-39" href="#__codelineno-15-39"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peek</span><span class="p">();</span>
+<a id="__codelineno-15-40" name="__codelineno-15-40" href="#__codelineno-15-40"></a><span class="w">        </span><span class="c1">// 先頭ノードを削除</span>
+<a id="__codelineno-15-41" name="__codelineno-15-41" href="#__codelineno-15-41"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">.</span><span class="na">next</span><span class="p">;</span>
+<a id="__codelineno-15-42" name="__codelineno-15-42" href="#__codelineno-15-42"></a><span class="w">        </span><span class="n">queSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-15-43" name="__codelineno-15-43" href="#__codelineno-15-43"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-15-44" name="__codelineno-15-44" href="#__codelineno-15-44"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-45" name="__codelineno-15-45" href="#__codelineno-15-45"></a>
+<a id="__codelineno-15-46" name="__codelineno-15-46" href="#__codelineno-15-46"></a><span class="w">    </span><span class="cm">/* 先頭要素にアクセス */</span>
+<a id="__codelineno-15-47" name="__codelineno-15-47" href="#__codelineno-15-47"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-48" name="__codelineno-15-48" href="#__codelineno-15-48"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
+<a id="__codelineno-15-49" name="__codelineno-15-49" href="#__codelineno-15-49"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">();</span>
+<a id="__codelineno-15-50" name="__codelineno-15-50" href="#__codelineno-15-50"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">front</span><span class="p">.</span><span class="na">val</span><span class="p">;</span>
+<a id="__codelineno-15-51" name="__codelineno-15-51" href="#__codelineno-15-51"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-52" name="__codelineno-15-52" href="#__codelineno-15-52"></a>
+<a id="__codelineno-15-53" name="__codelineno-15-53" href="#__codelineno-15-53"></a><span class="w">    </span><span class="cm">/* 連結リストを配列に変換して返す */</span>
+<a id="__codelineno-15-54" name="__codelineno-15-54" href="#__codelineno-15-54"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="nf">toArray</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-55" name="__codelineno-15-55" href="#__codelineno-15-55"></a><span class="w">        </span><span class="n">ListNode</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">;</span>
+<a id="__codelineno-15-56" name="__codelineno-15-56" href="#__codelineno-15-56"></a><span class="w">        </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">size</span><span class="p">()</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-15-57" name="__codelineno-15-57" href="#__codelineno-15-57"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="na">length</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-58" name="__codelineno-15-58" href="#__codelineno-15-58"></a><span class="w">            </span><span class="n">res</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">val</span><span class="p">;</span>
+<a id="__codelineno-15-59" name="__codelineno-15-59" href="#__codelineno-15-59"></a><span class="w">            </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">next</span><span class="p">;</span>
+<a id="__codelineno-15-60" name="__codelineno-15-60" href="#__codelineno-15-60"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-15-61" name="__codelineno-15-61" href="#__codelineno-15-61"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-15-62" name="__codelineno-15-62" href="#__codelineno-15-62"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-63" name="__codelineno-15-63" href="#__codelineno-15-63"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linkedlist_queue.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">LinkedListQueue</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linkedlist_queue.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">linkedListQueue</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linkedlist_queue.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">LinkedListQueue</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linkedlist_queue.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">LinkedListQueue</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linkedlist_queue.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">LinkedListQueue</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linkedlist_queue.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">LinkedListQueue</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linkedlist_queue.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">LinkedListQueue</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linkedlist_queue.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">LinkedListQueue</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linkedlist_queue.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">LinkedListQueue</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linkedlist_queue.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">LinkedListQueue</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linkedlist_queue.zig</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">LinkedListQueue</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h3 id="2">2. &nbsp; 配列ベースの実装<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
+<p>配列の最初の要素を削除する時間計算量は<span class="arithmatex">\(O(n)\)</span>で、デキュー操作が非効率になります。しかし、この問題は以下のように巧妙に回避できます。</p>
+<p>変数<code>front</code>を使用してフロント要素のインデックスを示し、変数<code>size</code>を維持してキューの長さを記録します。<code>rear = front + size</code>を定義し、これはテール要素の直後の位置を指します。</p>
+<p>この設計により、<strong>配列内の要素の有効な間隔は<code>[front, rear - 1]</code>です</strong>。各操作の実装方法を下図に示します。</p>
+<ul>
+<li>エンキュー操作：入力要素を<code>rear</code>インデックスに割り当て、<code>size</code>を1増加させます。</li>
+<li>デキュー操作：単に<code>front</code>を1増加させ、<code>size</code>を1減少させます。</li>
+</ul>
+<p>エンキューとデキュー操作は両方とも単一の操作のみを必要とし、それぞれの時間計算量は<span class="arithmatex">\(O(1)\)</span>です。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="4:3"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">ArrayQueue</label><label for="__tabbed_4_2">push()</label><label for="__tabbed_4_3">pop()</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<p><a class="glightbox" href="../queue.assets/array_queue_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="配列によるキュー実装のエンキューとデキュー操作" class="animation-figure" src="../queue.assets/array_queue_step1.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../queue.assets/array_queue_step2_push.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="array_queue_push" class="animation-figure" src="../queue.assets/array_queue_step2_push.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../queue.assets/array_queue_step3_pop.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="array_queue_pop" class="animation-figure" src="../queue.assets/array_queue_step3_pop.png" /></a></p>
+</div>
+</div>
+</div>
+<p align="center"> 図 5-6 &nbsp; 配列によるキュー実装のエンキューとデキュー操作 </p>
+
+<p>問題に気づくかもしれません：エンキューとデキュー操作が継続的に実行されると、<code>front</code>と<code>rear</code>の両方が右に移動し、<strong>最終的に配列の末尾に到達してそれ以上移動できなくなります</strong>。これを解決するために、配列を「循環配列」として扱い、配列の末尾を先頭に接続します。</p>
+<p>循環配列では、<code>front</code>または<code>rear</code>が末尾に到達すると、配列の先頭にループバックする必要があります。この循環パターンは、以下のコードに示すように「剰余演算」で実現できます：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="5:14"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><input id="__tabbed_5_7" name="__tabbed_5" type="radio" /><input id="__tabbed_5_8" name="__tabbed_5" type="radio" /><input id="__tabbed_5_9" name="__tabbed_5" type="radio" /><input id="__tabbed_5_10" name="__tabbed_5" type="radio" /><input id="__tabbed_5_11" name="__tabbed_5" type="radio" /><input id="__tabbed_5_12" name="__tabbed_5" type="radio" /><input id="__tabbed_5_13" name="__tabbed_5" type="radio" /><input id="__tabbed_5_14" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">Python</label><label for="__tabbed_5_2">C++</label><label for="__tabbed_5_3">Java</label><label for="__tabbed_5_4">C#</label><label for="__tabbed_5_5">Go</label><label for="__tabbed_5_6">Swift</label><label for="__tabbed_5_7">JS</label><label for="__tabbed_5_8">TS</label><label for="__tabbed_5_9">Dart</label><label for="__tabbed_5_10">Rust</label><label for="__tabbed_5_11">C</label><label for="__tabbed_5_12">Kotlin</label><label for="__tabbed_5_13">Ruby</label><label for="__tabbed_5_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_queue.py</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">ArrayQueue</span><span class="p">:</span>
+<a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;循環配列ベースのキュークラス&quot;&quot;&quot;</span>
+<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a>
+<a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">size</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;コンストラクタ&quot;&quot;&quot;</span>
+<a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_nums</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">size</span>  <span class="c1"># キュー要素を格納する配列</span>
+<a id="__codelineno-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_front</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">0</span>  <span class="c1"># フロントポインタ、フロント要素を指す</span>
+<a id="__codelineno-27-8" name="__codelineno-27-8" href="#__codelineno-27-8"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">0</span>  <span class="c1"># キューの長さ</span>
+<a id="__codelineno-27-9" name="__codelineno-27-9" href="#__codelineno-27-9"></a>
+<a id="__codelineno-27-10" name="__codelineno-27-10" href="#__codelineno-27-10"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">capacity</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-27-11" name="__codelineno-27-11" href="#__codelineno-27-11"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;キューの容量を取得&quot;&quot;&quot;</span>
+<a id="__codelineno-27-12" name="__codelineno-27-12" href="#__codelineno-27-12"></a>        <span class="k">return</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_nums</span><span class="p">)</span>
+<a id="__codelineno-27-13" name="__codelineno-27-13" href="#__codelineno-27-13"></a>
+<a id="__codelineno-27-14" name="__codelineno-27-14" href="#__codelineno-27-14"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">size</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-27-15" name="__codelineno-27-15" href="#__codelineno-27-15"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;キューの長さを取得&quot;&quot;&quot;</span>
+<a id="__codelineno-27-16" name="__codelineno-27-16" href="#__codelineno-27-16"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span>
+<a id="__codelineno-27-17" name="__codelineno-27-17" href="#__codelineno-27-17"></a>
+<a id="__codelineno-27-18" name="__codelineno-27-18" href="#__codelineno-27-18"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">is_empty</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">bool</span><span class="p">:</span>
+<a id="__codelineno-27-19" name="__codelineno-27-19" href="#__codelineno-27-19"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;キューが空かどうかを判定&quot;&quot;&quot;</span>
+<a id="__codelineno-27-20" name="__codelineno-27-20" href="#__codelineno-27-20"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">==</span> <span class="mi">0</span>
+<a id="__codelineno-27-21" name="__codelineno-27-21" href="#__codelineno-27-21"></a>
+<a id="__codelineno-27-22" name="__codelineno-27-22" href="#__codelineno-27-22"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">num</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-27-23" name="__codelineno-27-23" href="#__codelineno-27-23"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;エンキュー&quot;&quot;&quot;</span>
+<a id="__codelineno-27-24" name="__codelineno-27-24" href="#__codelineno-27-24"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">==</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span><span class="p">():</span>
+<a id="__codelineno-27-25" name="__codelineno-27-25" href="#__codelineno-27-25"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;Queue is full&quot;</span><span class="p">)</span>
+<a id="__codelineno-27-26" name="__codelineno-27-26" href="#__codelineno-27-26"></a>        <span class="c1"># リアポインタを計算、リアインデックス + 1 を指す</span>
+<a id="__codelineno-27-27" name="__codelineno-27-27" href="#__codelineno-27-27"></a>        <span class="c1"># モジュロ演算を使用してリアポインタを配列の末尾から先頭に戻す</span>
+<a id="__codelineno-27-28" name="__codelineno-27-28" href="#__codelineno-27-28"></a>        <span class="n">rear</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span><span class="p">)</span> <span class="o">%</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span><span class="p">()</span>
+<a id="__codelineno-27-29" name="__codelineno-27-29" href="#__codelineno-27-29"></a>        <span class="c1"># num をリアに追加</span>
+<a id="__codelineno-27-30" name="__codelineno-27-30" href="#__codelineno-27-30"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_nums</span><span class="p">[</span><span class="n">rear</span><span class="p">]</span> <span class="o">=</span> <span class="n">num</span>
+<a id="__codelineno-27-31" name="__codelineno-27-31" href="#__codelineno-27-31"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-27-32" name="__codelineno-27-32" href="#__codelineno-27-32"></a>
+<a id="__codelineno-27-33" name="__codelineno-27-33" href="#__codelineno-27-33"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">pop</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-27-34" name="__codelineno-27-34" href="#__codelineno-27-34"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;デキュー&quot;&quot;&quot;</span>
+<a id="__codelineno-27-35" name="__codelineno-27-35" href="#__codelineno-27-35"></a>        <span class="n">num</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">peek</span><span class="p">()</span>
+<a id="__codelineno-27-36" name="__codelineno-27-36" href="#__codelineno-27-36"></a>        <span class="c1"># フロントポインタを1つ後ろに移動、末尾を超えた場合は配列の先頭に戻る</span>
+<a id="__codelineno-27-37" name="__codelineno-27-37" href="#__codelineno-27-37"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="o">=</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_front</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">%</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span><span class="p">()</span>
+<a id="__codelineno-27-38" name="__codelineno-27-38" href="#__codelineno-27-38"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">-=</span> <span class="mi">1</span>
+<a id="__codelineno-27-39" name="__codelineno-27-39" href="#__codelineno-27-39"></a>        <span class="k">return</span> <span class="n">num</span>
+<a id="__codelineno-27-40" name="__codelineno-27-40" href="#__codelineno-27-40"></a>
+<a id="__codelineno-27-41" name="__codelineno-27-41" href="#__codelineno-27-41"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">peek</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-27-42" name="__codelineno-27-42" href="#__codelineno-27-42"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;フロント要素にアクセス&quot;&quot;&quot;</span>
+<a id="__codelineno-27-43" name="__codelineno-27-43" href="#__codelineno-27-43"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">is_empty</span><span class="p">():</span>
+<a id="__codelineno-27-44" name="__codelineno-27-44" href="#__codelineno-27-44"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;Queue is empty&quot;</span><span class="p">)</span>
+<a id="__codelineno-27-45" name="__codelineno-27-45" href="#__codelineno-27-45"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_nums</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">_front</span><span class="p">]</span>
+<a id="__codelineno-27-46" name="__codelineno-27-46" href="#__codelineno-27-46"></a>
+<a id="__codelineno-27-47" name="__codelineno-27-47" href="#__codelineno-27-47"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">to_list</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
+<a id="__codelineno-27-48" name="__codelineno-27-48" href="#__codelineno-27-48"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;出力用の配列を返す&quot;&quot;&quot;</span>
+<a id="__codelineno-27-49" name="__codelineno-27-49" href="#__codelineno-27-49"></a>        <span class="n">res</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span>
+<a id="__codelineno-27-50" name="__codelineno-27-50" href="#__codelineno-27-50"></a>        <span class="n">j</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_front</span>
+<a id="__codelineno-27-51" name="__codelineno-27-51" href="#__codelineno-27-51"></a>        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()):</span>
+<a id="__codelineno-27-52" name="__codelineno-27-52" href="#__codelineno-27-52"></a>            <span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_nums</span><span class="p">[(</span><span class="n">j</span> <span class="o">%</span> <span class="bp">self</span><span class="o">.</span><span class="n">capacity</span><span class="p">())]</span>
+<a id="__codelineno-27-53" name="__codelineno-27-53" href="#__codelineno-27-53"></a>            <span class="n">j</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-27-54" name="__codelineno-27-54" href="#__codelineno-27-54"></a>        <span class="k">return</span> <span class="n">res</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_queue.cpp</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="cm">/* 循環配列に基づくキュークラス */</span>
+<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">ArrayQueue</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a><span class="w">  </span><span class="k">private</span><span class="o">:</span>
+<a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="o">*</span><span class="n">nums</span><span class="p">;</span><span class="w">       </span><span class="c1">// キュー要素を格納する配列</span>
+<a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">front</span><span class="p">;</span><span class="w">       </span><span class="c1">// 先頭ポインタ、先頭要素を指す</span>
+<a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span><span class="w">     </span><span class="c1">// キューの長さ</span>
+<a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">queCapacity</span><span class="p">;</span><span class="w"> </span><span class="c1">// キューの容量</span>
+<a id="__codelineno-28-8" name="__codelineno-28-8" href="#__codelineno-28-8"></a>
+<a id="__codelineno-28-9" name="__codelineno-28-9" href="#__codelineno-28-9"></a><span class="w">  </span><span class="k">public</span><span class="o">:</span>
+<a id="__codelineno-28-10" name="__codelineno-28-10" href="#__codelineno-28-10"></a><span class="w">    </span><span class="n">ArrayQueue</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-11" name="__codelineno-28-11" href="#__codelineno-28-11"></a><span class="w">        </span><span class="c1">// 配列を初期化</span>
+<a id="__codelineno-28-12" name="__codelineno-28-12" href="#__codelineno-28-12"></a><span class="w">        </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="p">[</span><span class="n">capacity</span><span class="p">];</span>
+<a id="__codelineno-28-13" name="__codelineno-28-13" href="#__codelineno-28-13"></a><span class="w">        </span><span class="n">queCapacity</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">capacity</span><span class="p">;</span>
+<a id="__codelineno-28-14" name="__codelineno-28-14" href="#__codelineno-28-14"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-28-15" name="__codelineno-28-15" href="#__codelineno-28-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-16" name="__codelineno-28-16" href="#__codelineno-28-16"></a>
+<a id="__codelineno-28-17" name="__codelineno-28-17" href="#__codelineno-28-17"></a><span class="w">    </span><span class="o">~</span><span class="n">ArrayQueue</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-18" name="__codelineno-28-18" href="#__codelineno-28-18"></a><span class="w">        </span><span class="k">delete</span><span class="p">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">;</span>
+<a id="__codelineno-28-19" name="__codelineno-28-19" href="#__codelineno-28-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-20" name="__codelineno-28-20" href="#__codelineno-28-20"></a>
+<a id="__codelineno-28-21" name="__codelineno-28-21" href="#__codelineno-28-21"></a><span class="w">    </span><span class="cm">/* キューの容量を取得 */</span>
+<a id="__codelineno-28-22" name="__codelineno-28-22" href="#__codelineno-28-22"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-23" name="__codelineno-28-23" href="#__codelineno-28-23"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queCapacity</span><span class="p">;</span>
+<a id="__codelineno-28-24" name="__codelineno-28-24" href="#__codelineno-28-24"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-25" name="__codelineno-28-25" href="#__codelineno-28-25"></a>
+<a id="__codelineno-28-26" name="__codelineno-28-26" href="#__codelineno-28-26"></a><span class="w">    </span><span class="cm">/* キューの長さを取得 */</span>
+<a id="__codelineno-28-27" name="__codelineno-28-27" href="#__codelineno-28-27"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-28" name="__codelineno-28-28" href="#__codelineno-28-28"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span>
+<a id="__codelineno-28-29" name="__codelineno-28-29" href="#__codelineno-28-29"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-30" name="__codelineno-28-30" href="#__codelineno-28-30"></a>
+<a id="__codelineno-28-31" name="__codelineno-28-31" href="#__codelineno-28-31"></a><span class="w">    </span><span class="cm">/* キューが空かどうかを判定 */</span>
+<a id="__codelineno-28-32" name="__codelineno-28-32" href="#__codelineno-28-32"></a><span class="w">    </span><span class="kt">bool</span><span class="w"> </span><span class="n">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-33" name="__codelineno-28-33" href="#__codelineno-28-33"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-28-34" name="__codelineno-28-34" href="#__codelineno-28-34"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-35" name="__codelineno-28-35" href="#__codelineno-28-35"></a>
+<a id="__codelineno-28-36" name="__codelineno-28-36" href="#__codelineno-28-36"></a><span class="w">    </span><span class="cm">/* エンキュー */</span>
+<a id="__codelineno-28-37" name="__codelineno-28-37" href="#__codelineno-28-37"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-38" name="__codelineno-28-38" href="#__codelineno-28-38"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">queCapacity</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-39" name="__codelineno-28-39" href="#__codelineno-28-39"></a><span class="w">            </span><span class="n">cout</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="s">&quot;Queue is full&quot;</span><span class="w"> </span><span class="o">&lt;&lt;</span><span class="w"> </span><span class="n">endl</span><span class="p">;</span>
+<a id="__codelineno-28-40" name="__codelineno-28-40" href="#__codelineno-28-40"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-28-41" name="__codelineno-28-41" href="#__codelineno-28-41"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-28-42" name="__codelineno-28-42" href="#__codelineno-28-42"></a><span class="w">        </span><span class="c1">// 末尾ポインタを計算、末尾インデックス + 1を指す</span>
+<a id="__codelineno-28-43" name="__codelineno-28-43" href="#__codelineno-28-43"></a><span class="w">        </span><span class="c1">// 剰余演算を使用して末尾ポインタが配列の末尾から先頭に戻るようにラップ</span>
+<a id="__codelineno-28-44" name="__codelineno-28-44" href="#__codelineno-28-44"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">queSize</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">queCapacity</span><span class="p">;</span>
+<a id="__codelineno-28-45" name="__codelineno-28-45" href="#__codelineno-28-45"></a><span class="w">        </span><span class="c1">// numを末尾に追加</span>
+<a id="__codelineno-28-46" name="__codelineno-28-46" href="#__codelineno-28-46"></a><span class="w">        </span><span class="n">nums</span><span class="p">[</span><span class="n">rear</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-28-47" name="__codelineno-28-47" href="#__codelineno-28-47"></a><span class="w">        </span><span class="n">queSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-28-48" name="__codelineno-28-48" href="#__codelineno-28-48"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-49" name="__codelineno-28-49" href="#__codelineno-28-49"></a>
+<a id="__codelineno-28-50" name="__codelineno-28-50" href="#__codelineno-28-50"></a><span class="w">    </span><span class="cm">/* デキュー */</span>
+<a id="__codelineno-28-51" name="__codelineno-28-51" href="#__codelineno-28-51"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-52" name="__codelineno-28-52" href="#__codelineno-28-52"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peek</span><span class="p">();</span>
+<a id="__codelineno-28-53" name="__codelineno-28-53" href="#__codelineno-28-53"></a><span class="w">        </span><span class="c1">// 先頭ポインタを1つ後ろに移動、末尾を超えた場合は配列の先頭に戻る</span>
+<a id="__codelineno-28-54" name="__codelineno-28-54" href="#__codelineno-28-54"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">queCapacity</span><span class="p">;</span>
+<a id="__codelineno-28-55" name="__codelineno-28-55" href="#__codelineno-28-55"></a><span class="w">        </span><span class="n">queSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-28-56" name="__codelineno-28-56" href="#__codelineno-28-56"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-28-57" name="__codelineno-28-57" href="#__codelineno-28-57"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-58" name="__codelineno-28-58" href="#__codelineno-28-58"></a>
+<a id="__codelineno-28-59" name="__codelineno-28-59" href="#__codelineno-28-59"></a><span class="w">    </span><span class="cm">/* 先頭要素にアクセス */</span>
+<a id="__codelineno-28-60" name="__codelineno-28-60" href="#__codelineno-28-60"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-61" name="__codelineno-28-61" href="#__codelineno-28-61"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
+<a id="__codelineno-28-62" name="__codelineno-28-62" href="#__codelineno-28-62"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;Queue is empty&quot;</span><span class="p">);</span>
+<a id="__codelineno-28-63" name="__codelineno-28-63" href="#__codelineno-28-63"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">front</span><span class="p">];</span>
+<a id="__codelineno-28-64" name="__codelineno-28-64" href="#__codelineno-28-64"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-65" name="__codelineno-28-65" href="#__codelineno-28-65"></a>
+<a id="__codelineno-28-66" name="__codelineno-28-66" href="#__codelineno-28-66"></a><span class="w">    </span><span class="cm">/* 配列をVectorに変換して返却 */</span>
+<a id="__codelineno-28-67" name="__codelineno-28-67" href="#__codelineno-28-67"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">toVector</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-68" name="__codelineno-28-68" href="#__codelineno-28-68"></a><span class="w">        </span><span class="c1">// 有効な長さ範囲内の要素のみを変換</span>
+<a id="__codelineno-28-69" name="__codelineno-28-69" href="#__codelineno-28-69"></a><span class="w">        </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">arr</span><span class="p">(</span><span class="n">queSize</span><span class="p">);</span>
+<a id="__codelineno-28-70" name="__codelineno-28-70" href="#__codelineno-28-70"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-71" name="__codelineno-28-71" href="#__codelineno-28-71"></a><span class="w">            </span><span class="n">arr</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="p">[</span><span class="n">j</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">queCapacity</span><span class="p">];</span>
+<a id="__codelineno-28-72" name="__codelineno-28-72" href="#__codelineno-28-72"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-28-73" name="__codelineno-28-73" href="#__codelineno-28-73"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">arr</span><span class="p">;</span>
+<a id="__codelineno-28-74" name="__codelineno-28-74" href="#__codelineno-28-74"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-75" name="__codelineno-28-75" href="#__codelineno-28-75"></a><span class="p">};</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_queue.java</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="cm">/* 配列に基づくキュークラス */</span>
+<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="kd">class</span> <span class="nc">ArrayQueue</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">nums</span><span class="p">;</span><span class="w"> </span><span class="c1">// 要素を格納する配列</span>
+<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">front</span><span class="p">;</span><span class="w"> </span><span class="c1">// キューヘッドポインタ、最初の要素を指す</span>
+<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span><span class="w"> </span><span class="c1">// キューの長さ</span>
+<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a>
+<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="nf">ArrayQueue</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">capacity</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a><span class="w">        </span><span class="n">nums</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">capacity</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-29-9" name="__codelineno-29-9" href="#__codelineno-29-9"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-29-10" name="__codelineno-29-10" href="#__codelineno-29-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-11" name="__codelineno-29-11" href="#__codelineno-29-11"></a>
+<a id="__codelineno-29-12" name="__codelineno-29-12" href="#__codelineno-29-12"></a><span class="w">    </span><span class="cm">/* キューの容量を取得 */</span>
+<a id="__codelineno-29-13" name="__codelineno-29-13" href="#__codelineno-29-13"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">capacity</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-14" name="__codelineno-29-14" href="#__codelineno-29-14"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="p">.</span><span class="na">length</span><span class="p">;</span>
+<a id="__codelineno-29-15" name="__codelineno-29-15" href="#__codelineno-29-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-16" name="__codelineno-29-16" href="#__codelineno-29-16"></a>
+<a id="__codelineno-29-17" name="__codelineno-29-17" href="#__codelineno-29-17"></a><span class="w">    </span><span class="cm">/* キューの長さを取得 */</span>
+<a id="__codelineno-29-18" name="__codelineno-29-18" href="#__codelineno-29-18"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-19" name="__codelineno-29-19" href="#__codelineno-29-19"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span>
+<a id="__codelineno-29-20" name="__codelineno-29-20" href="#__codelineno-29-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-21" name="__codelineno-29-21" href="#__codelineno-29-21"></a>
+<a id="__codelineno-29-22" name="__codelineno-29-22" href="#__codelineno-29-22"></a><span class="w">    </span><span class="cm">/* キューが空かどうかを判定 */</span>
+<a id="__codelineno-29-23" name="__codelineno-29-23" href="#__codelineno-29-23"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">boolean</span><span class="w"> </span><span class="nf">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-24" name="__codelineno-29-24" href="#__codelineno-29-24"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-29-25" name="__codelineno-29-25" href="#__codelineno-29-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-26" name="__codelineno-29-26" href="#__codelineno-29-26"></a>
+<a id="__codelineno-29-27" name="__codelineno-29-27" href="#__codelineno-29-27"></a><span class="w">    </span><span class="cm">/* エンキュー */</span>
+<a id="__codelineno-29-28" name="__codelineno-29-28" href="#__codelineno-29-28"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-29" name="__codelineno-29-29" href="#__codelineno-29-29"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">queSize</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">capacity</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-30" name="__codelineno-29-30" href="#__codelineno-29-30"></a><span class="w">            </span><span class="n">System</span><span class="p">.</span><span class="na">out</span><span class="p">.</span><span class="na">println</span><span class="p">(</span><span class="s">&quot;キューが満杯です&quot;</span><span class="p">);</span>
+<a id="__codelineno-29-31" name="__codelineno-29-31" href="#__codelineno-29-31"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-29-32" name="__codelineno-29-32" href="#__codelineno-29-32"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-29-33" name="__codelineno-29-33" href="#__codelineno-29-33"></a><span class="w">        </span><span class="c1">// リアポインタを計算：front + queSize</span>
+<a id="__codelineno-29-34" name="__codelineno-29-34" href="#__codelineno-29-34"></a><span class="w">        </span><span class="c1">// モジュロ操作により rear が配列の長さを超えることを回避</span>
+<a id="__codelineno-29-35" name="__codelineno-29-35" href="#__codelineno-29-35"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">rear</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="n">queSize</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">();</span>
+<a id="__codelineno-29-36" name="__codelineno-29-36" href="#__codelineno-29-36"></a><span class="w">        </span><span class="c1">// 要素をキューリアに追加</span>
+<a id="__codelineno-29-37" name="__codelineno-29-37" href="#__codelineno-29-37"></a><span class="w">        </span><span class="n">nums</span><span class="o">[</span><span class="n">rear</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-29-38" name="__codelineno-29-38" href="#__codelineno-29-38"></a><span class="w">        </span><span class="n">queSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-29-39" name="__codelineno-29-39" href="#__codelineno-29-39"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-40" name="__codelineno-29-40" href="#__codelineno-29-40"></a>
+<a id="__codelineno-29-41" name="__codelineno-29-41" href="#__codelineno-29-41"></a><span class="w">    </span><span class="cm">/* デキュー */</span>
+<a id="__codelineno-29-42" name="__codelineno-29-42" href="#__codelineno-29-42"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-43" name="__codelineno-29-43" href="#__codelineno-29-43"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peek</span><span class="p">();</span>
+<a id="__codelineno-29-44" name="__codelineno-29-44" href="#__codelineno-29-44"></a><span class="w">        </span><span class="c1">// キューヘッドポインタを後ろに1つ移動、モジュロ操作により範囲を超えることを回避</span>
+<a id="__codelineno-29-45" name="__codelineno-29-45" href="#__codelineno-29-45"></a><span class="w">        </span><span class="n">front</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">front</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">();</span>
+<a id="__codelineno-29-46" name="__codelineno-29-46" href="#__codelineno-29-46"></a><span class="w">        </span><span class="n">queSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-29-47" name="__codelineno-29-47" href="#__codelineno-29-47"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-29-48" name="__codelineno-29-48" href="#__codelineno-29-48"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-49" name="__codelineno-29-49" href="#__codelineno-29-49"></a>
+<a id="__codelineno-29-50" name="__codelineno-29-50" href="#__codelineno-29-50"></a><span class="w">    </span><span class="cm">/* キューヘッド要素にアクセス */</span>
+<a id="__codelineno-29-51" name="__codelineno-29-51" href="#__codelineno-29-51"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-52" name="__codelineno-29-52" href="#__codelineno-29-52"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
+<a id="__codelineno-29-53" name="__codelineno-29-53" href="#__codelineno-29-53"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">();</span>
+<a id="__codelineno-29-54" name="__codelineno-29-54" href="#__codelineno-29-54"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">front</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-29-55" name="__codelineno-29-55" href="#__codelineno-29-55"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-56" name="__codelineno-29-56" href="#__codelineno-29-56"></a>
+<a id="__codelineno-29-57" name="__codelineno-29-57" href="#__codelineno-29-57"></a><span class="w">    </span><span class="cm">/* 配列を返す */</span>
+<a id="__codelineno-29-58" name="__codelineno-29-58" href="#__codelineno-29-58"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="nf">toArray</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-59" name="__codelineno-29-59" href="#__codelineno-29-59"></a><span class="w">        </span><span class="c1">// front から開始して queSize 個の要素のみをコピー</span>
+<a id="__codelineno-29-60" name="__codelineno-29-60" href="#__codelineno-29-60"></a><span class="w">        </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">queSize</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-29-61" name="__codelineno-29-61" href="#__codelineno-29-61"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">front</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">queSize</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">,</span><span class="w"> </span><span class="n">j</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-62" name="__codelineno-29-62" href="#__codelineno-29-62"></a><span class="w">            </span><span class="n">res</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">nums</span><span class="o">[</span><span class="n">j</span><span class="w"> </span><span class="o">%</span><span class="w"> </span><span class="n">capacity</span><span class="p">()</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-29-63" name="__codelineno-29-63" href="#__codelineno-29-63"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-29-64" name="__codelineno-29-64" href="#__codelineno-29-64"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-29-65" name="__codelineno-29-65" href="#__codelineno-29-65"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-66" name="__codelineno-29-66" href="#__codelineno-29-66"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_queue.cs</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">ArrayQueue</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_queue.go</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">arrayQueue</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_queue.swift</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">ArrayQueue</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_queue.js</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">ArrayQueue</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_queue.ts</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">ArrayQueue</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_queue.dart</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ArrayQueue</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_queue.rs</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ArrayQueue</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_queue.c</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ArrayQueue</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_queue.kt</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">ArrayQueue</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_queue.rb</span><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">ArrayQueue</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_queue.zig</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ArrayQueue</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>上記のキュー実装にはまだ制限があります：長さが固定されています。しかし、この問題は解決が困難ではありません。配列を必要に応じて自動拡張できる動的配列に置き換えることができます。興味のある読者は自分で実装してみてください。</p>
+<p>2つの実装の比較はスタックの場合と一貫しており、ここでは繰り返しません。</p>
+<h2 id="523">5.2.3 &nbsp; キューの典型的な応用<a class="headerlink" href="#523" title="Permanent link">&para;</a></h2>
+<ul>
+<li><strong>Amazonの注文</strong>：買い物客が注文を行った後、これらの注文はキューに参加し、システムは順番に処理します。独身の日などのイベント中は、短時間で大量の注文が生成され、高い同時実行性がエンジニアにとって重要な課題となります。</li>
+<li><strong>様々なToDoリスト</strong>：「先着順」機能が必要なシナリオ、例えばプリンターのタスクキューやレストランの配達キューなど、キューで処理順序を効果的に維持できます。</li>
+</ul>
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+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
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+          </ul>
+        </nav>
+      
+    </li>
+  
+
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+      
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+  
+  
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+      
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+          
+        
+      
+        
+      
+        
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+        
+      
+        
+      
+        
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+    
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+      
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+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
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+          <label class="md-nav__title" for="__nav_5">
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+            第 3 章 &nbsp; データ構造
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+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
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+    </li>
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+
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+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
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+          </ul>
+        </nav>
+      
+    </li>
+  
+
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+      
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+  
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+      
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+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
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+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
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+          
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+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
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+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
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+            
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+  
+  
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+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
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+  
+  
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+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
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+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" checked>
+        
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+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
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+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
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+      
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+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#511" class="md-nav__link">
+    <span class="md-ellipsis">
+      5.1.1 &nbsp; スタックの一般的な操作
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#512" class="md-nav__link">
+    <span class="md-ellipsis">
+      5.1.2 &nbsp; スタックの実装
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="5.1.2   スタックの実装">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 連結リストベースの実装
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; 配列ベースの実装
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#513-2" class="md-nav__link">
+    <span class="md-ellipsis">
+      5.1.3 &nbsp; 2つの実装の比較
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#514" class="md-nav__link">
+    <span class="md-ellipsis">
+      5.1.4 &nbsp; スタックの典型的な応用
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
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+          <label class="md-nav__title" for="__nav_8">
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+            第 6 章 &nbsp; ハッシュ表
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+            
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+  
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+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
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+    
+    
+    
+    
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+      
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+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
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+              
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
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+      
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+</nav>
+                  </div>
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+              <div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
+                <div class="md-sidebar__scrollwrap">
+                  <div class="md-sidebar__inner">
+                    
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+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#511" class="md-nav__link">
+    <span class="md-ellipsis">
+      5.1.1 &nbsp; スタックの一般的な操作
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#512" class="md-nav__link">
+    <span class="md-ellipsis">
+      5.1.2 &nbsp; スタックの実装
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="5.1.2   スタックの実装">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 連結リストベースの実装
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; 配列ベースの実装
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#513-2" class="md-nav__link">
+    <span class="md-ellipsis">
+      5.1.3 &nbsp; 2つの実装の比較
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#514" class="md-nav__link">
+    <span class="md-ellipsis">
+      5.1.4 &nbsp; スタックの典型的な応用
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+                  </div>
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+      
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
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+<!-- Page content -->
+<h1 id="51">5.1 &nbsp; スタック<a class="headerlink" href="#51" title="Permanent link">&para;</a></h1>
+<p><u>スタック</u>は、後入先出（LIFO）の原則に従う線形データ構造です。</p>
+<p>スタックをテーブル上の皿の山に例えることができます。底の皿にアクセスするには、まず上の皿を取り除く必要があります。皿を様々な種類の要素（整数、文字、オブジェクトなど）に置き換えることで、スタックと呼ばれるデータ構造を得ることができます。</p>
+<p>下図に示すように、要素の山の上部を「スタックのトップ」、下部を「スタックのボトム」と呼びます。スタックのトップに要素を追加する操作を「プッシュ」、トップ要素を削除する操作を「ポップ」と呼びます。</p>
+<p><a class="glightbox" href="../stack.assets/stack_operations.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="スタックの後入先出ルール" class="animation-figure" src="../stack.assets/stack_operations.png" /></a></p>
+<p align="center"> 図 5-1 &nbsp; スタックの後入先出ルール </p>
+
+<h2 id="511">5.1.1 &nbsp; スタックの一般的な操作<a class="headerlink" href="#511" title="Permanent link">&para;</a></h2>
+<p>スタックの一般的な操作を下表に示します。具体的なメソッド名は使用するプログラミング言語によって異なります。ここでは、例として<code>push()</code>、<code>pop()</code>、<code>peek()</code>を使用します。</p>
+<p align="center"> 表 5-1 &nbsp; スタック操作の効率 </p>
+
+<div class="center-table">
+<table>
+<thead>
+<tr>
+<th>メソッド</th>
+<th>説明</th>
+<th>時間計算量</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td><code>push()</code></td>
+<td>要素をスタックにプッシュ（トップに追加）</td>
+<td><span class="arithmatex">\(O(1)\)</span></td>
+</tr>
+<tr>
+<td><code>pop()</code></td>
+<td>スタックからトップ要素をポップ</td>
+<td><span class="arithmatex">\(O(1)\)</span></td>
+</tr>
+<tr>
+<td><code>peek()</code></td>
+<td>スタックのトップ要素にアクセス</td>
+<td><span class="arithmatex">\(O(1)\)</span></td>
+</tr>
+</tbody>
+</table>
+</div>
+<p>通常、プログラミング言語に組み込まれているスタッククラスを直接使用できます。ただし、一部の言語では具体的にスタッククラスを提供していない場合があります。これらの場合、言語の「配列」または「連結リスト」をスタックとして使用し、プログラムでスタックロジックに関連しない操作を無視できます。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:13"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">stack.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="c1"># スタックを初期化</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="c1"># Pythonには組み込みのスタッククラスがないため、listをスタックとして使用</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="n">stack</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="p">[]</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a><span class="c1"># 要素をスタックにプッシュ</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a><span class="n">stack</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a><span class="n">stack</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a><span class="n">stack</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a><span class="n">stack</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a><span class="n">stack</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a><span class="c1"># スタックのトップ要素にアクセス</span>
+<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a><span class="n">peek</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">stack</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>
+<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a><span class="c1"># スタックから要素をポップ</span>
+<a id="__codelineno-0-16" name="__codelineno-0-16" href="#__codelineno-0-16"></a><span class="n">pop</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">stack</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
+<a id="__codelineno-0-17" name="__codelineno-0-17" href="#__codelineno-0-17"></a>
+<a id="__codelineno-0-18" name="__codelineno-0-18" href="#__codelineno-0-18"></a><span class="c1"># スタックの長さを取得</span>
+<a id="__codelineno-0-19" name="__codelineno-0-19" href="#__codelineno-0-19"></a><span class="n">size</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">stack</span><span class="p">)</span>
+<a id="__codelineno-0-20" name="__codelineno-0-20" href="#__codelineno-0-20"></a>
+<a id="__codelineno-0-21" name="__codelineno-0-21" href="#__codelineno-0-21"></a><span class="c1"># スタックが空かどうかチェック</span>
+<a id="__codelineno-0-22" name="__codelineno-0-22" href="#__codelineno-0-22"></a><span class="n">is_empty</span><span class="p">:</span> <span class="nb">bool</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">stack</span><span class="p">)</span> <span class="o">==</span> <span class="mi">0</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">stack.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* スタックを初期化 */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="n">stack</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">stack</span><span class="p">;</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="cm">/* 要素をスタックにプッシュ */</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="n">stack</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="n">stack</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="n">stack</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="n">stack</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="n">stack</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="cm">/* スタックのトップ要素にアクセス */</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="kt">int</span><span class="w"> </span><span class="n">top</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="n">top</span><span class="p">();</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="cm">/* スタックから要素をポップ */</span>
+<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="n">stack</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span><span class="w"> </span><span class="c1">// 戻り値なし</span>
+<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a>
+<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="cm">/* スタックの長さを取得 */</span>
+<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
+<a id="__codelineno-1-19" name="__codelineno-1-19" href="#__codelineno-1-19"></a>
+<a id="__codelineno-1-20" name="__codelineno-1-20" href="#__codelineno-1-20"></a><span class="cm">/* スタックが空かどうかチェック */</span>
+<a id="__codelineno-1-21" name="__codelineno-1-21" href="#__codelineno-1-21"></a><span class="kt">bool</span><span class="w"> </span><span class="n">empty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="n">empty</span><span class="p">();</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">stack.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* スタックを初期化 */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="n">Stack</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">stack</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">Stack</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="cm">/* 要素をスタックにプッシュ */</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="n">stack</span><span class="p">.</span><span class="na">push</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="n">stack</span><span class="p">.</span><span class="na">push</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="n">stack</span><span class="p">.</span><span class="na">push</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="n">stack</span><span class="p">.</span><span class="na">push</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="n">stack</span><span class="p">.</span><span class="na">push</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="cm">/* スタックのトップ要素にアクセス */</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="kt">int</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="na">peek</span><span class="p">();</span>
+<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="cm">/* スタックから要素をポップ */</span>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="kt">int</span><span class="w"> </span><span class="n">pop</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="na">pop</span><span class="p">();</span>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a>
+<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="cm">/* スタックの長さを取得 */</span>
+<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="na">size</span><span class="p">();</span>
+<a id="__codelineno-2-19" name="__codelineno-2-19" href="#__codelineno-2-19"></a>
+<a id="__codelineno-2-20" name="__codelineno-2-20" href="#__codelineno-2-20"></a><span class="cm">/* スタックが空かどうかチェック */</span>
+<a id="__codelineno-2-21" name="__codelineno-2-21" href="#__codelineno-2-21"></a><span class="kt">boolean</span><span class="w"> </span><span class="n">isEmpty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="na">isEmpty</span><span class="p">();</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">stack.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* スタックを初期化 */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="n">Stack</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">stack</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">();</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="cm">/* 要素をスタックにプッシュ */</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="n">stack</span><span class="p">.</span><span class="n">Push</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="n">stack</span><span class="p">.</span><span class="n">Push</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="n">stack</span><span class="p">.</span><span class="n">Push</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-3-8" name="__codelineno-3-8" href="#__codelineno-3-8"></a><span class="n">stack</span><span class="p">.</span><span class="n">Push</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
+<a id="__codelineno-3-9" name="__codelineno-3-9" href="#__codelineno-3-9"></a><span class="n">stack</span><span class="p">.</span><span class="n">Push</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
+<a id="__codelineno-3-10" name="__codelineno-3-10" href="#__codelineno-3-10"></a>
+<a id="__codelineno-3-11" name="__codelineno-3-11" href="#__codelineno-3-11"></a><span class="cm">/* スタックのトップ要素にアクセス */</span>
+<a id="__codelineno-3-12" name="__codelineno-3-12" href="#__codelineno-3-12"></a><span class="kt">int</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="n">Peek</span><span class="p">();</span>
+<a id="__codelineno-3-13" name="__codelineno-3-13" href="#__codelineno-3-13"></a>
+<a id="__codelineno-3-14" name="__codelineno-3-14" href="#__codelineno-3-14"></a><span class="cm">/* スタックから要素をポップ */</span>
+<a id="__codelineno-3-15" name="__codelineno-3-15" href="#__codelineno-3-15"></a><span class="kt">int</span><span class="w"> </span><span class="n">pop</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="n">Pop</span><span class="p">();</span>
+<a id="__codelineno-3-16" name="__codelineno-3-16" href="#__codelineno-3-16"></a>
+<a id="__codelineno-3-17" name="__codelineno-3-17" href="#__codelineno-3-17"></a><span class="cm">/* スタックの長さを取得 */</span>
+<a id="__codelineno-3-18" name="__codelineno-3-18" href="#__codelineno-3-18"></a><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="n">Count</span><span class="p">;</span>
+<a id="__codelineno-3-19" name="__codelineno-3-19" href="#__codelineno-3-19"></a>
+<a id="__codelineno-3-20" name="__codelineno-3-20" href="#__codelineno-3-20"></a><span class="cm">/* スタックが空かどうかチェック */</span>
+<a id="__codelineno-3-21" name="__codelineno-3-21" href="#__codelineno-3-21"></a><span class="kt">bool</span><span class="w"> </span><span class="n">isEmpty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="n">Count</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">stack_test.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* スタックを初期化 */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="c1">// Goでは、Sliceをスタックとして使用することが推奨されます</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="kd">var</span><span class="w"> </span><span class="nx">stack</span><span class="w"> </span><span class="p">[]</span><span class="kt">int</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="cm">/* 要素をスタックにプッシュ */</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="nx">stack</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">stack</span><span class="p">,</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="nx">stack</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">stack</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">)</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="nx">stack</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">stack</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="nx">stack</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">stack</span><span class="p">,</span><span class="w"> </span><span class="mi">5</span><span class="p">)</span>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="nx">stack</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nb">append</span><span class="p">(</span><span class="nx">stack</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">)</span>
+<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a>
+<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="cm">/* スタックのトップ要素にアクセス */</span>
+<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="nx">peek</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">stack</span><span class="p">[</span><span class="nb">len</span><span class="p">(</span><span class="nx">stack</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a>
+<a id="__codelineno-4-15" name="__codelineno-4-15" href="#__codelineno-4-15"></a><span class="cm">/* スタックから要素をポップ */</span>
+<a id="__codelineno-4-16" name="__codelineno-4-16" href="#__codelineno-4-16"></a><span class="nx">pop</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">stack</span><span class="p">[</span><span class="nb">len</span><span class="p">(</span><span class="nx">stack</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-4-17" name="__codelineno-4-17" href="#__codelineno-4-17"></a><span class="nx">stack</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">stack</span><span class="p">[:</span><span class="nb">len</span><span class="p">(</span><span class="nx">stack</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-4-18" name="__codelineno-4-18" href="#__codelineno-4-18"></a>
+<a id="__codelineno-4-19" name="__codelineno-4-19" href="#__codelineno-4-19"></a><span class="cm">/* スタックの長さを取得 */</span>
+<a id="__codelineno-4-20" name="__codelineno-4-20" href="#__codelineno-4-20"></a><span class="nx">size</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">stack</span><span class="p">)</span>
+<a id="__codelineno-4-21" name="__codelineno-4-21" href="#__codelineno-4-21"></a>
+<a id="__codelineno-4-22" name="__codelineno-4-22" href="#__codelineno-4-22"></a><span class="cm">/* スタックが空かどうかチェック */</span>
+<a id="__codelineno-4-23" name="__codelineno-4-23" href="#__codelineno-4-23"></a><span class="nx">isEmpty</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nb">len</span><span class="p">(</span><span class="nx">stack</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">stack.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* スタックを初期化 */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="c1">// Swiftには組み込みのスタッククラスがないため、Arrayをスタックとして使用</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="kd">var</span><span class="w"> </span><span class="nv">stack</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[]</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="cm">/* 要素をスタックにプッシュ */</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="n">stack</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="n">stack</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="n">stack</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="n">stack</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="n">stack</span><span class="p">.</span><span class="n">append</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
+<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="cm">/* スタックのトップ要素にアクセス */</span>
+<a id="__codelineno-5-13" name="__codelineno-5-13" href="#__codelineno-5-13"></a><span class="kd">let</span><span class="w"> </span><span class="nv">peek</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="bp">last</span><span class="p">!</span>
+<a id="__codelineno-5-14" name="__codelineno-5-14" href="#__codelineno-5-14"></a>
+<a id="__codelineno-5-15" name="__codelineno-5-15" href="#__codelineno-5-15"></a><span class="cm">/* スタックから要素をポップ */</span>
+<a id="__codelineno-5-16" name="__codelineno-5-16" href="#__codelineno-5-16"></a><span class="kd">let</span><span class="w"> </span><span class="nv">pop</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="bp">removeLast</span><span class="p">()</span>
+<a id="__codelineno-5-17" name="__codelineno-5-17" href="#__codelineno-5-17"></a>
+<a id="__codelineno-5-18" name="__codelineno-5-18" href="#__codelineno-5-18"></a><span class="cm">/* スタックの長さを取得 */</span>
+<a id="__codelineno-5-19" name="__codelineno-5-19" href="#__codelineno-5-19"></a><span class="kd">let</span><span class="w"> </span><span class="nv">size</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="bp">count</span>
+<a id="__codelineno-5-20" name="__codelineno-5-20" href="#__codelineno-5-20"></a>
+<a id="__codelineno-5-21" name="__codelineno-5-21" href="#__codelineno-5-21"></a><span class="cm">/* スタックが空かどうかチェック */</span>
+<a id="__codelineno-5-22" name="__codelineno-5-22" href="#__codelineno-5-22"></a><span class="kd">let</span><span class="w"> </span><span class="nv">isEmpty</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="bp">isEmpty</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">stack.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* スタックを初期化 */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="c1">// JavaScriptには組み込みのスタッククラスがないため、Arrayをスタックとして使用</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="kd">const</span><span class="w"> </span><span class="nx">stack</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="cm">/* 要素をスタックにプッシュ */</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="nx">stack</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="nx">stack</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">3</span><span class="p">);</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="nx">stack</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">2</span><span class="p">);</span>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="nx">stack</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">5</span><span class="p">);</span>
+<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="nx">stack</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">4</span><span class="p">);</span>
+<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a>
+<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="cm">/* スタックのトップ要素にアクセス */</span>
+<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="kd">const</span><span class="w"> </span><span class="nx">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">stack</span><span class="p">[</span><span class="nx">stack</span><span class="p">.</span><span class="nx">length</span><span class="o">-</span><span class="mf">1</span><span class="p">];</span>
+<a id="__codelineno-6-14" name="__codelineno-6-14" href="#__codelineno-6-14"></a>
+<a id="__codelineno-6-15" name="__codelineno-6-15" href="#__codelineno-6-15"></a><span class="cm">/* スタックから要素をポップ */</span>
+<a id="__codelineno-6-16" name="__codelineno-6-16" href="#__codelineno-6-16"></a><span class="kd">const</span><span class="w"> </span><span class="nx">pop</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">stack</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
+<a id="__codelineno-6-17" name="__codelineno-6-17" href="#__codelineno-6-17"></a>
+<a id="__codelineno-6-18" name="__codelineno-6-18" href="#__codelineno-6-18"></a><span class="cm">/* スタックの長さを取得 */</span>
+<a id="__codelineno-6-19" name="__codelineno-6-19" href="#__codelineno-6-19"></a><span class="kd">const</span><span class="w"> </span><span class="nx">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">stack</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-6-20" name="__codelineno-6-20" href="#__codelineno-6-20"></a>
+<a id="__codelineno-6-21" name="__codelineno-6-21" href="#__codelineno-6-21"></a><span class="cm">/* スタックが空かどうかチェック */</span>
+<a id="__codelineno-6-22" name="__codelineno-6-22" href="#__codelineno-6-22"></a><span class="kd">const</span><span class="w"> </span><span class="nx">is_empty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">stack</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">stack.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* スタックを初期化 */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="c1">// TypeScriptには組み込みのスタッククラスがないため、Arrayをスタックとして使用</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="kd">const</span><span class="w"> </span><span class="nx">stack</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="cm">/* 要素をスタックにプッシュ */</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="nx">stack</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">1</span><span class="p">);</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="nx">stack</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">3</span><span class="p">);</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="nx">stack</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">2</span><span class="p">);</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="nx">stack</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">5</span><span class="p">);</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="nx">stack</span><span class="p">.</span><span class="nx">push</span><span class="p">(</span><span class="mf">4</span><span class="p">);</span>
+<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="cm">/* スタックのトップ要素にアクセス */</span>
+<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="kd">const</span><span class="w"> </span><span class="nx">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">stack</span><span class="p">[</span><span class="nx">stack</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mf">1</span><span class="p">];</span>
+<a id="__codelineno-7-14" name="__codelineno-7-14" href="#__codelineno-7-14"></a>
+<a id="__codelineno-7-15" name="__codelineno-7-15" href="#__codelineno-7-15"></a><span class="cm">/* スタックから要素をポップ */</span>
+<a id="__codelineno-7-16" name="__codelineno-7-16" href="#__codelineno-7-16"></a><span class="kd">const</span><span class="w"> </span><span class="nx">pop</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">stack</span><span class="p">.</span><span class="nx">pop</span><span class="p">();</span>
+<a id="__codelineno-7-17" name="__codelineno-7-17" href="#__codelineno-7-17"></a>
+<a id="__codelineno-7-18" name="__codelineno-7-18" href="#__codelineno-7-18"></a><span class="cm">/* スタックの長さを取得 */</span>
+<a id="__codelineno-7-19" name="__codelineno-7-19" href="#__codelineno-7-19"></a><span class="kd">const</span><span class="w"> </span><span class="nx">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">stack</span><span class="p">.</span><span class="nx">length</span><span class="p">;</span>
+<a id="__codelineno-7-20" name="__codelineno-7-20" href="#__codelineno-7-20"></a>
+<a id="__codelineno-7-21" name="__codelineno-7-21" href="#__codelineno-7-21"></a><span class="cm">/* スタックが空かどうかチェック */</span>
+<a id="__codelineno-7-22" name="__codelineno-7-22" href="#__codelineno-7-22"></a><span class="kd">const</span><span class="w"> </span><span class="nx">is_empty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">stack</span><span class="p">.</span><span class="nx">length</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="mf">0</span><span class="p">;</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">stack.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* スタックを初期化 */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="c1">// Dartには組み込みのスタッククラスがないため、Listをスタックとして使用</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">stack</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[];</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="cm">/* 要素をスタックにプッシュ */</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="n">stack</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="m">1</span><span class="p">);</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="n">stack</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="m">3</span><span class="p">);</span>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="n">stack</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="m">2</span><span class="p">);</span>
+<a id="__codelineno-8-9" name="__codelineno-8-9" href="#__codelineno-8-9"></a><span class="n">stack</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="m">5</span><span class="p">);</span>
+<a id="__codelineno-8-10" name="__codelineno-8-10" href="#__codelineno-8-10"></a><span class="n">stack</span><span class="p">.</span><span class="n">add</span><span class="p">(</span><span class="m">4</span><span class="p">);</span>
+<a id="__codelineno-8-11" name="__codelineno-8-11" href="#__codelineno-8-11"></a>
+<a id="__codelineno-8-12" name="__codelineno-8-12" href="#__codelineno-8-12"></a><span class="cm">/* スタックのトップ要素にアクセス */</span>
+<a id="__codelineno-8-13" name="__codelineno-8-13" href="#__codelineno-8-13"></a><span class="kt">int</span><span class="w"> </span><span class="n">peek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="n">last</span><span class="p">;</span>
+<a id="__codelineno-8-14" name="__codelineno-8-14" href="#__codelineno-8-14"></a>
+<a id="__codelineno-8-15" name="__codelineno-8-15" href="#__codelineno-8-15"></a><span class="cm">/* スタックから要素をポップ */</span>
+<a id="__codelineno-8-16" name="__codelineno-8-16" href="#__codelineno-8-16"></a><span class="kt">int</span><span class="w"> </span><span class="n">pop</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="n">removeLast</span><span class="p">();</span>
+<a id="__codelineno-8-17" name="__codelineno-8-17" href="#__codelineno-8-17"></a>
+<a id="__codelineno-8-18" name="__codelineno-8-18" href="#__codelineno-8-18"></a><span class="cm">/* スタックの長さを取得 */</span>
+<a id="__codelineno-8-19" name="__codelineno-8-19" href="#__codelineno-8-19"></a><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="n">length</span><span class="p">;</span>
+<a id="__codelineno-8-20" name="__codelineno-8-20" href="#__codelineno-8-20"></a>
+<a id="__codelineno-8-21" name="__codelineno-8-21" href="#__codelineno-8-21"></a><span class="cm">/* スタックが空かどうかチェック */</span>
+<a id="__codelineno-8-22" name="__codelineno-8-22" href="#__codelineno-8-22"></a><span class="kt">bool</span><span class="w"> </span><span class="n">isEmpty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="n">isEmpty</span><span class="p">;</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">stack.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* スタックを初期化 */</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="c1">// Vecをスタックとして使用</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="kd">let</span><span class="w"> </span><span class="k">mut</span><span class="w"> </span><span class="n">stack</span><span class="p">:</span><span class="w"> </span><span class="nb">Vec</span><span class="o">&lt;</span><span class="kt">i32</span><span class="o">&gt;</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Vec</span><span class="p">::</span><span class="n">new</span><span class="p">();</span>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="cm">/* 要素をスタックにプッシュ */</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="n">stack</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="n">stack</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="n">stack</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="n">stack</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="n">stack</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
+<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a>
+<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="cm">/* スタックのトップ要素にアクセス */</span>
+<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="kd">let</span><span class="w"> </span><span class="n">top</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="n">last</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span>
+<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a>
+<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="cm">/* スタックから要素をポップ */</span>
+<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="kd">let</span><span class="w"> </span><span class="n">pop</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="n">pop</span><span class="p">().</span><span class="n">unwrap</span><span class="p">();</span>
+<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a>
+<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="cm">/* スタックの長さを取得 */</span>
+<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="kd">let</span><span class="w"> </span><span class="n">size</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="n">len</span><span class="p">();</span>
+<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a>
+<a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="cm">/* スタックが空かどうかチェック */</span>
+<a id="__codelineno-9-22" name="__codelineno-9-22" href="#__codelineno-9-22"></a><span class="kd">let</span><span class="w"> </span><span class="n">is_empty</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="n">is_empty</span><span class="p">();</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">stack.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="c1">// Cは組み込みのスタックを提供していません</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">stack.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">stack.zig</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h2 id="512">5.1.2 &nbsp; スタックの実装<a class="headerlink" href="#512" title="Permanent link">&para;</a></h2>
+<p>スタックがどのように動作するかをより深く理解するために、自分でスタッククラスを実装してみましょう。</p>
+<p>スタックは後入先出の原則に従うため、スタックのトップでのみ要素を追加または削除できます。しかし、配列と連結リストの両方は任意の位置で要素を追加・削除できるため、<strong>スタックは制限された配列または連結リストと見なすことができます</strong>。言い換えれば、配列や連結リストの特定の無関係な操作を「遮蔽」して、外部の動作をスタックの特性に合わせることができます。</p>
+<h3 id="1">1. &nbsp; 連結リストベースの実装<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<p>連結リストを使用してスタックを実装する場合、リストのヘッドノードをスタックのトップ、テールノードをスタックのボトムと考えることができます。</p>
+<p>下図に示すように、プッシュ操作では、単に連結リストのヘッドに要素を挿入します。このノード挿入方法は「ヘッド挿入」として知られています。ポップ操作では、リストからヘッドノードを削除するだけです。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:3"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">LinkedListStack</label><label for="__tabbed_2_2">push()</label><label for="__tabbed_2_3">pop()</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<p><a class="glightbox" href="../stack.assets/linkedlist_stack_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="連結リストによるスタック実装のプッシュとポップ操作" class="animation-figure" src="../stack.assets/linkedlist_stack_step1.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../stack.assets/linkedlist_stack_step2_push.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="linkedlist_stack_push" class="animation-figure" src="../stack.assets/linkedlist_stack_step2_push.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../stack.assets/linkedlist_stack_step3_pop.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="linkedlist_stack_pop" class="animation-figure" src="../stack.assets/linkedlist_stack_step3_pop.png" /></a></p>
+</div>
+</div>
+</div>
+<p align="center"> 図 5-2 &nbsp; 連結リストによるスタック実装のプッシュとポップ操作 </p>
+
+<p>以下は、連結リストに基づくスタック実装のサンプルコードです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="3:14"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><input id="__tabbed_3_14" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label><label for="__tabbed_3_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linkedlist_stack.py</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">LinkedListStack</span><span class="p">:</span>
+<a id="__codelineno-13-2" name="__codelineno-13-2" href="#__codelineno-13-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;連結リストベースのスタッククラス&quot;&quot;&quot;</span>
+<a id="__codelineno-13-3" name="__codelineno-13-3" href="#__codelineno-13-3"></a>
+<a id="__codelineno-13-4" name="__codelineno-13-4" href="#__codelineno-13-4"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<a id="__codelineno-13-5" name="__codelineno-13-5" href="#__codelineno-13-5"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;コンストラクタ&quot;&quot;&quot;</span>
+<a id="__codelineno-13-6" name="__codelineno-13-6" href="#__codelineno-13-6"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_peek</span><span class="p">:</span> <span class="n">ListNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span>
+<a id="__codelineno-13-7" name="__codelineno-13-7" href="#__codelineno-13-7"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">0</span>
+<a id="__codelineno-13-8" name="__codelineno-13-8" href="#__codelineno-13-8"></a>
+<a id="__codelineno-13-9" name="__codelineno-13-9" href="#__codelineno-13-9"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">size</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-13-10" name="__codelineno-13-10" href="#__codelineno-13-10"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;スタックの長さを取得&quot;&quot;&quot;</span>
+<a id="__codelineno-13-11" name="__codelineno-13-11" href="#__codelineno-13-11"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span>
+<a id="__codelineno-13-12" name="__codelineno-13-12" href="#__codelineno-13-12"></a>
+<a id="__codelineno-13-13" name="__codelineno-13-13" href="#__codelineno-13-13"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">is_empty</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">bool</span><span class="p">:</span>
+<a id="__codelineno-13-14" name="__codelineno-13-14" href="#__codelineno-13-14"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;スタックが空かどうかを判定&quot;&quot;&quot;</span>
+<a id="__codelineno-13-15" name="__codelineno-13-15" href="#__codelineno-13-15"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">==</span> <span class="mi">0</span>
+<a id="__codelineno-13-16" name="__codelineno-13-16" href="#__codelineno-13-16"></a>
+<a id="__codelineno-13-17" name="__codelineno-13-17" href="#__codelineno-13-17"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-13-18" name="__codelineno-13-18" href="#__codelineno-13-18"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;プッシュ&quot;&quot;&quot;</span>
+<a id="__codelineno-13-19" name="__codelineno-13-19" href="#__codelineno-13-19"></a>        <span class="n">node</span> <span class="o">=</span> <span class="n">ListNode</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-13-20" name="__codelineno-13-20" href="#__codelineno-13-20"></a>        <span class="n">node</span><span class="o">.</span><span class="n">next</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_peek</span>
+<a id="__codelineno-13-21" name="__codelineno-13-21" href="#__codelineno-13-21"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_peek</span> <span class="o">=</span> <span class="n">node</span>
+<a id="__codelineno-13-22" name="__codelineno-13-22" href="#__codelineno-13-22"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">+=</span> <span class="mi">1</span>
+<a id="__codelineno-13-23" name="__codelineno-13-23" href="#__codelineno-13-23"></a>
+<a id="__codelineno-13-24" name="__codelineno-13-24" href="#__codelineno-13-24"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">pop</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-13-25" name="__codelineno-13-25" href="#__codelineno-13-25"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;ポップ&quot;&quot;&quot;</span>
+<a id="__codelineno-13-26" name="__codelineno-13-26" href="#__codelineno-13-26"></a>        <span class="n">num</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">peek</span><span class="p">()</span>
+<a id="__codelineno-13-27" name="__codelineno-13-27" href="#__codelineno-13-27"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_peek</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_peek</span><span class="o">.</span><span class="n">next</span>
+<a id="__codelineno-13-28" name="__codelineno-13-28" href="#__codelineno-13-28"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_size</span> <span class="o">-=</span> <span class="mi">1</span>
+<a id="__codelineno-13-29" name="__codelineno-13-29" href="#__codelineno-13-29"></a>        <span class="k">return</span> <span class="n">num</span>
+<a id="__codelineno-13-30" name="__codelineno-13-30" href="#__codelineno-13-30"></a>
+<a id="__codelineno-13-31" name="__codelineno-13-31" href="#__codelineno-13-31"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">peek</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-13-32" name="__codelineno-13-32" href="#__codelineno-13-32"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;スタックトップ要素にアクセス&quot;&quot;&quot;</span>
+<a id="__codelineno-13-33" name="__codelineno-13-33" href="#__codelineno-13-33"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">is_empty</span><span class="p">():</span>
+<a id="__codelineno-13-34" name="__codelineno-13-34" href="#__codelineno-13-34"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;Stack is empty&quot;</span><span class="p">)</span>
+<a id="__codelineno-13-35" name="__codelineno-13-35" href="#__codelineno-13-35"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_peek</span><span class="o">.</span><span class="n">val</span>
+<a id="__codelineno-13-36" name="__codelineno-13-36" href="#__codelineno-13-36"></a>
+<a id="__codelineno-13-37" name="__codelineno-13-37" href="#__codelineno-13-37"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">to_list</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
+<a id="__codelineno-13-38" name="__codelineno-13-38" href="#__codelineno-13-38"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;出力用のリストに変換&quot;&quot;&quot;</span>
+<a id="__codelineno-13-39" name="__codelineno-13-39" href="#__codelineno-13-39"></a>        <span class="n">arr</span> <span class="o">=</span> <span class="p">[]</span>
+<a id="__codelineno-13-40" name="__codelineno-13-40" href="#__codelineno-13-40"></a>        <span class="n">node</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_peek</span>
+<a id="__codelineno-13-41" name="__codelineno-13-41" href="#__codelineno-13-41"></a>        <span class="k">while</span> <span class="n">node</span><span class="p">:</span>
+<a id="__codelineno-13-42" name="__codelineno-13-42" href="#__codelineno-13-42"></a>            <span class="n">arr</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-13-43" name="__codelineno-13-43" href="#__codelineno-13-43"></a>            <span class="n">node</span> <span class="o">=</span> <span class="n">node</span><span class="o">.</span><span class="n">next</span>
+<a id="__codelineno-13-44" name="__codelineno-13-44" href="#__codelineno-13-44"></a>        <span class="n">arr</span><span class="o">.</span><span class="n">reverse</span><span class="p">()</span>
+<a id="__codelineno-13-45" name="__codelineno-13-45" href="#__codelineno-13-45"></a>        <span class="k">return</span> <span class="n">arr</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linkedlist_stack.cpp</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="cm">/* 連結リストに基づくスタッククラス */</span>
+<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">LinkedListStack</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="w">  </span><span class="k">private</span><span class="o">:</span>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="w">    </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">stackTop</span><span class="p">;</span><span class="w"> </span><span class="c1">// 先頭ノードをスタックトップとして使用</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">stkSize</span><span class="p">;</span><span class="w">        </span><span class="c1">// スタックの長さ</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a>
+<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="w">  </span><span class="k">public</span><span class="o">:</span>
+<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="w">    </span><span class="n">LinkedListStack</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w">        </span><span class="n">stackTop</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">;</span>
+<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="w">        </span><span class="n">stkSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a>
+<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="w">    </span><span class="o">~</span><span class="n">LinkedListStack</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a><span class="w">        </span><span class="c1">// 連結リストを走査、ノードを削除、メモリを解放</span>
+<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a><span class="w">        </span><span class="n">freeMemoryLinkedList</span><span class="p">(</span><span class="n">stackTop</span><span class="p">);</span>
+<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a>
+<a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a><span class="w">    </span><span class="cm">/* スタックの長さを取得 */</span>
+<a id="__codelineno-14-19" name="__codelineno-14-19" href="#__codelineno-14-19"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-20" name="__codelineno-14-20" href="#__codelineno-14-20"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">stkSize</span><span class="p">;</span>
+<a id="__codelineno-14-21" name="__codelineno-14-21" href="#__codelineno-14-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-22" name="__codelineno-14-22" href="#__codelineno-14-22"></a>
+<a id="__codelineno-14-23" name="__codelineno-14-23" href="#__codelineno-14-23"></a><span class="w">    </span><span class="cm">/* スタックが空かどうかを判定 */</span>
+<a id="__codelineno-14-24" name="__codelineno-14-24" href="#__codelineno-14-24"></a><span class="w">    </span><span class="kt">bool</span><span class="w"> </span><span class="n">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-25" name="__codelineno-14-25" href="#__codelineno-14-25"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-14-26" name="__codelineno-14-26" href="#__codelineno-14-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-27" name="__codelineno-14-27" href="#__codelineno-14-27"></a>
+<a id="__codelineno-14-28" name="__codelineno-14-28" href="#__codelineno-14-28"></a><span class="w">    </span><span class="cm">/* プッシュ */</span>
+<a id="__codelineno-14-29" name="__codelineno-14-29" href="#__codelineno-14-29"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-30" name="__codelineno-14-30" href="#__codelineno-14-30"></a><span class="w">        </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-14-31" name="__codelineno-14-31" href="#__codelineno-14-31"></a><span class="w">        </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stackTop</span><span class="p">;</span>
+<a id="__codelineno-14-32" name="__codelineno-14-32" href="#__codelineno-14-32"></a><span class="w">        </span><span class="n">stackTop</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-14-33" name="__codelineno-14-33" href="#__codelineno-14-33"></a><span class="w">        </span><span class="n">stkSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-14-34" name="__codelineno-14-34" href="#__codelineno-14-34"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-35" name="__codelineno-14-35" href="#__codelineno-14-35"></a>
+<a id="__codelineno-14-36" name="__codelineno-14-36" href="#__codelineno-14-36"></a><span class="w">    </span><span class="cm">/* ポップ */</span>
+<a id="__codelineno-14-37" name="__codelineno-14-37" href="#__codelineno-14-37"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-38" name="__codelineno-14-38" href="#__codelineno-14-38"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">top</span><span class="p">();</span>
+<a id="__codelineno-14-39" name="__codelineno-14-39" href="#__codelineno-14-39"></a><span class="w">        </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stackTop</span><span class="p">;</span>
+<a id="__codelineno-14-40" name="__codelineno-14-40" href="#__codelineno-14-40"></a><span class="w">        </span><span class="n">stackTop</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stackTop</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-14-41" name="__codelineno-14-41" href="#__codelineno-14-41"></a><span class="w">        </span><span class="c1">// メモリを解放</span>
+<a id="__codelineno-14-42" name="__codelineno-14-42" href="#__codelineno-14-42"></a><span class="w">        </span><span class="k">delete</span><span class="w"> </span><span class="n">tmp</span><span class="p">;</span>
+<a id="__codelineno-14-43" name="__codelineno-14-43" href="#__codelineno-14-43"></a><span class="w">        </span><span class="n">stkSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-14-44" name="__codelineno-14-44" href="#__codelineno-14-44"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-14-45" name="__codelineno-14-45" href="#__codelineno-14-45"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-46" name="__codelineno-14-46" href="#__codelineno-14-46"></a>
+<a id="__codelineno-14-47" name="__codelineno-14-47" href="#__codelineno-14-47"></a><span class="w">    </span><span class="cm">/* スタックトップ要素にアクセス */</span>
+<a id="__codelineno-14-48" name="__codelineno-14-48" href="#__codelineno-14-48"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">top</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-49" name="__codelineno-14-49" href="#__codelineno-14-49"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
+<a id="__codelineno-14-50" name="__codelineno-14-50" href="#__codelineno-14-50"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;Stack is empty&quot;</span><span class="p">);</span>
+<a id="__codelineno-14-51" name="__codelineno-14-51" href="#__codelineno-14-51"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">stackTop</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-14-52" name="__codelineno-14-52" href="#__codelineno-14-52"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-53" name="__codelineno-14-53" href="#__codelineno-14-53"></a>
+<a id="__codelineno-14-54" name="__codelineno-14-54" href="#__codelineno-14-54"></a><span class="w">    </span><span class="cm">/* リストを配列に変換して返却 */</span>
+<a id="__codelineno-14-55" name="__codelineno-14-55" href="#__codelineno-14-55"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">toVector</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-56" name="__codelineno-14-56" href="#__codelineno-14-56"></a><span class="w">        </span><span class="n">ListNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stackTop</span><span class="p">;</span>
+<a id="__codelineno-14-57" name="__codelineno-14-57" href="#__codelineno-14-57"></a><span class="w">        </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">(</span><span class="n">size</span><span class="p">());</span>
+<a id="__codelineno-14-58" name="__codelineno-14-58" href="#__codelineno-14-58"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-14-59" name="__codelineno-14-59" href="#__codelineno-14-59"></a><span class="w">            </span><span class="n">res</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-14-60" name="__codelineno-14-60" href="#__codelineno-14-60"></a><span class="w">            </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">next</span><span class="p">;</span>
+<a id="__codelineno-14-61" name="__codelineno-14-61" href="#__codelineno-14-61"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-14-62" name="__codelineno-14-62" href="#__codelineno-14-62"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-14-63" name="__codelineno-14-63" href="#__codelineno-14-63"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-14-64" name="__codelineno-14-64" href="#__codelineno-14-64"></a><span class="p">};</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linkedlist_stack.java</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 連結リストに基づくスタッククラス */</span>
+<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kd">class</span> <span class="nc">LinkedListStack</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="n">ListNode</span><span class="w"> </span><span class="n">stackPeek</span><span class="p">;</span><span class="w"> </span><span class="c1">// ヘッドノードをスタックトップとして使用</span>
+<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">stkSize</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="c1">// スタックの長さ</span>
+<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a>
+<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="nf">LinkedListStack</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">        </span><span class="n">stackPeek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a>
+<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="w">    </span><span class="cm">/* スタックの長さを取得 */</span>
+<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">stkSize</span><span class="p">;</span>
+<a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a>
+<a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="w">    </span><span class="cm">/* スタックが空かどうかを判定 */</span>
+<a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">boolean</span><span class="w"> </span><span class="nf">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-17" name="__codelineno-15-17" href="#__codelineno-15-17"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-15-18" name="__codelineno-15-18" href="#__codelineno-15-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-19" name="__codelineno-15-19" href="#__codelineno-15-19"></a>
+<a id="__codelineno-15-20" name="__codelineno-15-20" href="#__codelineno-15-20"></a><span class="w">    </span><span class="cm">/* プッシュ */</span>
+<a id="__codelineno-15-21" name="__codelineno-15-21" href="#__codelineno-15-21"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-22" name="__codelineno-15-22" href="#__codelineno-15-22"></a><span class="w">        </span><span class="n">ListNode</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ListNode</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-15-23" name="__codelineno-15-23" href="#__codelineno-15-23"></a><span class="w">        </span><span class="n">node</span><span class="p">.</span><span class="na">next</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stackPeek</span><span class="p">;</span>
+<a id="__codelineno-15-24" name="__codelineno-15-24" href="#__codelineno-15-24"></a><span class="w">        </span><span class="n">stackPeek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-15-25" name="__codelineno-15-25" href="#__codelineno-15-25"></a><span class="w">        </span><span class="n">stkSize</span><span class="o">++</span><span class="p">;</span>
+<a id="__codelineno-15-26" name="__codelineno-15-26" href="#__codelineno-15-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-27" name="__codelineno-15-27" href="#__codelineno-15-27"></a>
+<a id="__codelineno-15-28" name="__codelineno-15-28" href="#__codelineno-15-28"></a><span class="w">    </span><span class="cm">/* ポップ */</span>
+<a id="__codelineno-15-29" name="__codelineno-15-29" href="#__codelineno-15-29"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-30" name="__codelineno-15-30" href="#__codelineno-15-30"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">peek</span><span class="p">();</span>
+<a id="__codelineno-15-31" name="__codelineno-15-31" href="#__codelineno-15-31"></a><span class="w">        </span><span class="n">stackPeek</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stackPeek</span><span class="p">.</span><span class="na">next</span><span class="p">;</span>
+<a id="__codelineno-15-32" name="__codelineno-15-32" href="#__codelineno-15-32"></a><span class="w">        </span><span class="n">stkSize</span><span class="o">--</span><span class="p">;</span>
+<a id="__codelineno-15-33" name="__codelineno-15-33" href="#__codelineno-15-33"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-15-34" name="__codelineno-15-34" href="#__codelineno-15-34"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-35" name="__codelineno-15-35" href="#__codelineno-15-35"></a>
+<a id="__codelineno-15-36" name="__codelineno-15-36" href="#__codelineno-15-36"></a><span class="w">    </span><span class="cm">/* スタックトップ要素にアクセス */</span>
+<a id="__codelineno-15-37" name="__codelineno-15-37" href="#__codelineno-15-37"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-38" name="__codelineno-15-38" href="#__codelineno-15-38"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
+<a id="__codelineno-15-39" name="__codelineno-15-39" href="#__codelineno-15-39"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">();</span>
+<a id="__codelineno-15-40" name="__codelineno-15-40" href="#__codelineno-15-40"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">stackPeek</span><span class="p">.</span><span class="na">val</span><span class="p">;</span>
+<a id="__codelineno-15-41" name="__codelineno-15-41" href="#__codelineno-15-41"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-42" name="__codelineno-15-42" href="#__codelineno-15-42"></a>
+<a id="__codelineno-15-43" name="__codelineno-15-43" href="#__codelineno-15-43"></a><span class="w">    </span><span class="cm">/* List を Array に変換して返す */</span>
+<a id="__codelineno-15-44" name="__codelineno-15-44" href="#__codelineno-15-44"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="nf">toArray</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-45" name="__codelineno-15-45" href="#__codelineno-15-45"></a><span class="w">        </span><span class="n">ListNode</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">stackPeek</span><span class="p">;</span>
+<a id="__codelineno-15-46" name="__codelineno-15-46" href="#__codelineno-15-46"></a><span class="w">        </span><span class="kt">int</span><span class="o">[]</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="kt">int</span><span class="o">[</span><span class="n">size</span><span class="p">()</span><span class="o">]</span><span class="p">;</span>
+<a id="__codelineno-15-47" name="__codelineno-15-47" href="#__codelineno-15-47"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">res</span><span class="p">.</span><span class="na">length</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="o">--</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-48" name="__codelineno-15-48" href="#__codelineno-15-48"></a><span class="w">            </span><span class="n">res</span><span class="o">[</span><span class="n">i</span><span class="o">]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">val</span><span class="p">;</span>
+<a id="__codelineno-15-49" name="__codelineno-15-49" href="#__codelineno-15-49"></a><span class="w">            </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">next</span><span class="p">;</span>
+<a id="__codelineno-15-50" name="__codelineno-15-50" href="#__codelineno-15-50"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-15-51" name="__codelineno-15-51" href="#__codelineno-15-51"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-15-52" name="__codelineno-15-52" href="#__codelineno-15-52"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-53" name="__codelineno-15-53" href="#__codelineno-15-53"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linkedlist_stack.cs</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">LinkedListStack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linkedlist_stack.go</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">linkedListStack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linkedlist_stack.swift</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">LinkedListStack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linkedlist_stack.js</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">LinkedListStack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linkedlist_stack.ts</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">LinkedListStack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linkedlist_stack.dart</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">LinkedListStack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linkedlist_stack.rs</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">LinkedListStack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linkedlist_stack.c</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">LinkedListStack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linkedlist_stack.kt</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">LinkedListStack</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linkedlist_stack.rb</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">LinkedListStack</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">linkedlist_stack.zig</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">LinkedListStack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h3 id="2">2. &nbsp; 配列ベースの実装<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
+<p>配列を使用してスタックを実装する場合、配列の末尾をスタックのトップと考えることができます。下図に示すように、プッシュとポップ操作は、それぞれ配列の末尾での要素の追加と削除に対応し、どちらも時間計算量<span class="arithmatex">\(O(1)\)</span>です。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="4:3"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">ArrayStack</label><label for="__tabbed_4_2">push()</label><label for="__tabbed_4_3">pop()</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<p><a class="glightbox" href="../stack.assets/array_stack_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="配列によるスタック実装のプッシュとポップ操作" class="animation-figure" src="../stack.assets/array_stack_step1.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../stack.assets/array_stack_step2_push.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="array_stack_push" class="animation-figure" src="../stack.assets/array_stack_step2_push.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../stack.assets/array_stack_step3_pop.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="array_stack_pop" class="animation-figure" src="../stack.assets/array_stack_step3_pop.png" /></a></p>
+</div>
+</div>
+</div>
+<p align="center"> 図 5-3 &nbsp; 配列によるスタック実装のプッシュとポップ操作 </p>
+
+<p>スタックにプッシュされる要素が継続的に増加する可能性があるため、動的配列を使用でき、配列拡張を自分で処理する必要がありません。以下はサンプルコードです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="5:14"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><input id="__tabbed_5_7" name="__tabbed_5" type="radio" /><input id="__tabbed_5_8" name="__tabbed_5" type="radio" /><input id="__tabbed_5_9" name="__tabbed_5" type="radio" /><input id="__tabbed_5_10" name="__tabbed_5" type="radio" /><input id="__tabbed_5_11" name="__tabbed_5" type="radio" /><input id="__tabbed_5_12" name="__tabbed_5" type="radio" /><input id="__tabbed_5_13" name="__tabbed_5" type="radio" /><input id="__tabbed_5_14" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">Python</label><label for="__tabbed_5_2">C++</label><label for="__tabbed_5_3">Java</label><label for="__tabbed_5_4">C#</label><label for="__tabbed_5_5">Go</label><label for="__tabbed_5_6">Swift</label><label for="__tabbed_5_7">JS</label><label for="__tabbed_5_8">TS</label><label for="__tabbed_5_9">Dart</label><label for="__tabbed_5_10">Rust</label><label for="__tabbed_5_11">C</label><label for="__tabbed_5_12">Kotlin</label><label for="__tabbed_5_13">Ruby</label><label for="__tabbed_5_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_stack.py</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">ArrayStack</span><span class="p">:</span>
+<a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;配列ベースのスタッククラス&quot;&quot;&quot;</span>
+<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a>
+<a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;コンストラクタ&quot;&quot;&quot;</span>
+<a id="__codelineno-27-6" name="__codelineno-27-6" href="#__codelineno-27-6"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_stack</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]</span> <span class="o">=</span> <span class="p">[]</span>
+<a id="__codelineno-27-7" name="__codelineno-27-7" href="#__codelineno-27-7"></a>
+<a id="__codelineno-27-8" name="__codelineno-27-8" href="#__codelineno-27-8"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">size</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-27-9" name="__codelineno-27-9" href="#__codelineno-27-9"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;スタックの長さを取得&quot;&quot;&quot;</span>
+<a id="__codelineno-27-10" name="__codelineno-27-10" href="#__codelineno-27-10"></a>        <span class="k">return</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_stack</span><span class="p">)</span>
+<a id="__codelineno-27-11" name="__codelineno-27-11" href="#__codelineno-27-11"></a>
+<a id="__codelineno-27-12" name="__codelineno-27-12" href="#__codelineno-27-12"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">is_empty</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">bool</span><span class="p">:</span>
+<a id="__codelineno-27-13" name="__codelineno-27-13" href="#__codelineno-27-13"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;スタックが空かどうかを判定&quot;&quot;&quot;</span>
+<a id="__codelineno-27-14" name="__codelineno-27-14" href="#__codelineno-27-14"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()</span> <span class="o">==</span> <span class="mi">0</span>
+<a id="__codelineno-27-15" name="__codelineno-27-15" href="#__codelineno-27-15"></a>
+<a id="__codelineno-27-16" name="__codelineno-27-16" href="#__codelineno-27-16"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">item</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-27-17" name="__codelineno-27-17" href="#__codelineno-27-17"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;プッシュ&quot;&quot;&quot;</span>
+<a id="__codelineno-27-18" name="__codelineno-27-18" href="#__codelineno-27-18"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_stack</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">item</span><span class="p">)</span>
+<a id="__codelineno-27-19" name="__codelineno-27-19" href="#__codelineno-27-19"></a>
+<a id="__codelineno-27-20" name="__codelineno-27-20" href="#__codelineno-27-20"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">pop</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-27-21" name="__codelineno-27-21" href="#__codelineno-27-21"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;ポップ&quot;&quot;&quot;</span>
+<a id="__codelineno-27-22" name="__codelineno-27-22" href="#__codelineno-27-22"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">is_empty</span><span class="p">():</span>
+<a id="__codelineno-27-23" name="__codelineno-27-23" href="#__codelineno-27-23"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;Stack is empty&quot;</span><span class="p">)</span>
+<a id="__codelineno-27-24" name="__codelineno-27-24" href="#__codelineno-27-24"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_stack</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
+<a id="__codelineno-27-25" name="__codelineno-27-25" href="#__codelineno-27-25"></a>
+<a id="__codelineno-27-26" name="__codelineno-27-26" href="#__codelineno-27-26"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">peek</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-27-27" name="__codelineno-27-27" href="#__codelineno-27-27"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;スタックトップ要素にアクセス&quot;&quot;&quot;</span>
+<a id="__codelineno-27-28" name="__codelineno-27-28" href="#__codelineno-27-28"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">is_empty</span><span class="p">():</span>
+<a id="__codelineno-27-29" name="__codelineno-27-29" href="#__codelineno-27-29"></a>            <span class="k">raise</span> <span class="ne">IndexError</span><span class="p">(</span><span class="s2">&quot;Stack is empty&quot;</span><span class="p">)</span>
+<a id="__codelineno-27-30" name="__codelineno-27-30" href="#__codelineno-27-30"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_stack</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+<a id="__codelineno-27-31" name="__codelineno-27-31" href="#__codelineno-27-31"></a>
+<a id="__codelineno-27-32" name="__codelineno-27-32" href="#__codelineno-27-32"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">to_list</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
+<a id="__codelineno-27-33" name="__codelineno-27-33" href="#__codelineno-27-33"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;出力用の配列を返す&quot;&quot;&quot;</span>
+<a id="__codelineno-27-34" name="__codelineno-27-34" href="#__codelineno-27-34"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_stack</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_stack.cpp</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="cm">/* 配列に基づくスタッククラス */</span>
+<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">ArrayStack</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a><span class="w">  </span><span class="k">private</span><span class="o">:</span>
+<a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">stack</span><span class="p">;</span>
+<a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a>
+<a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a><span class="w">  </span><span class="k">public</span><span class="o">:</span>
+<a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a><span class="w">    </span><span class="cm">/* スタックの長さを取得 */</span>
+<a id="__codelineno-28-8" name="__codelineno-28-8" href="#__codelineno-28-8"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-9" name="__codelineno-28-9" href="#__codelineno-28-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
+<a id="__codelineno-28-10" name="__codelineno-28-10" href="#__codelineno-28-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-11" name="__codelineno-28-11" href="#__codelineno-28-11"></a>
+<a id="__codelineno-28-12" name="__codelineno-28-12" href="#__codelineno-28-12"></a><span class="w">    </span><span class="cm">/* スタックが空かどうかを判定 */</span>
+<a id="__codelineno-28-13" name="__codelineno-28-13" href="#__codelineno-28-13"></a><span class="w">    </span><span class="kt">bool</span><span class="w"> </span><span class="n">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-14" name="__codelineno-28-14" href="#__codelineno-28-14"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-28-15" name="__codelineno-28-15" href="#__codelineno-28-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-16" name="__codelineno-28-16" href="#__codelineno-28-16"></a>
+<a id="__codelineno-28-17" name="__codelineno-28-17" href="#__codelineno-28-17"></a><span class="w">    </span><span class="cm">/* プッシュ */</span>
+<a id="__codelineno-28-18" name="__codelineno-28-18" href="#__codelineno-28-18"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="n">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-19" name="__codelineno-28-19" href="#__codelineno-28-19"></a><span class="w">        </span><span class="n">stack</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-28-20" name="__codelineno-28-20" href="#__codelineno-28-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-21" name="__codelineno-28-21" href="#__codelineno-28-21"></a>
+<a id="__codelineno-28-22" name="__codelineno-28-22" href="#__codelineno-28-22"></a><span class="w">    </span><span class="cm">/* ポップ */</span>
+<a id="__codelineno-28-23" name="__codelineno-28-23" href="#__codelineno-28-23"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-24" name="__codelineno-28-24" href="#__codelineno-28-24"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">top</span><span class="p">();</span>
+<a id="__codelineno-28-25" name="__codelineno-28-25" href="#__codelineno-28-25"></a><span class="w">        </span><span class="n">stack</span><span class="p">.</span><span class="n">pop_back</span><span class="p">();</span>
+<a id="__codelineno-28-26" name="__codelineno-28-26" href="#__codelineno-28-26"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">num</span><span class="p">;</span>
+<a id="__codelineno-28-27" name="__codelineno-28-27" href="#__codelineno-28-27"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-28" name="__codelineno-28-28" href="#__codelineno-28-28"></a>
+<a id="__codelineno-28-29" name="__codelineno-28-29" href="#__codelineno-28-29"></a><span class="w">    </span><span class="cm">/* スタックトップ要素にアクセス */</span>
+<a id="__codelineno-28-30" name="__codelineno-28-30" href="#__codelineno-28-30"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">top</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-31" name="__codelineno-28-31" href="#__codelineno-28-31"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
+<a id="__codelineno-28-32" name="__codelineno-28-32" href="#__codelineno-28-32"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="n">out_of_range</span><span class="p">(</span><span class="s">&quot;Stack is empty&quot;</span><span class="p">);</span>
+<a id="__codelineno-28-33" name="__codelineno-28-33" href="#__codelineno-28-33"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="n">back</span><span class="p">();</span>
+<a id="__codelineno-28-34" name="__codelineno-28-34" href="#__codelineno-28-34"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-35" name="__codelineno-28-35" href="#__codelineno-28-35"></a>
+<a id="__codelineno-28-36" name="__codelineno-28-36" href="#__codelineno-28-36"></a><span class="w">    </span><span class="cm">/* Vectorを返却 */</span>
+<a id="__codelineno-28-37" name="__codelineno-28-37" href="#__codelineno-28-37"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">toVector</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-28-38" name="__codelineno-28-38" href="#__codelineno-28-38"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">stack</span><span class="p">;</span>
+<a id="__codelineno-28-39" name="__codelineno-28-39" href="#__codelineno-28-39"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-28-40" name="__codelineno-28-40" href="#__codelineno-28-40"></a><span class="p">};</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_stack.java</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="cm">/* 配列に基づくスタッククラス */</span>
+<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="kd">class</span> <span class="nc">ArrayStack</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">stack</span><span class="p">;</span>
+<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a>
+<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="nf">ArrayStack</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a><span class="w">        </span><span class="c1">// リスト（動的配列）を初期化</span>
+<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="w">        </span><span class="n">stack</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-9" name="__codelineno-29-9" href="#__codelineno-29-9"></a>
+<a id="__codelineno-29-10" name="__codelineno-29-10" href="#__codelineno-29-10"></a><span class="w">    </span><span class="cm">/* スタックの長さを取得 */</span>
+<a id="__codelineno-29-11" name="__codelineno-29-11" href="#__codelineno-29-11"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-12" name="__codelineno-29-12" href="#__codelineno-29-12"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="na">size</span><span class="p">();</span>
+<a id="__codelineno-29-13" name="__codelineno-29-13" href="#__codelineno-29-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-14" name="__codelineno-29-14" href="#__codelineno-29-14"></a>
+<a id="__codelineno-29-15" name="__codelineno-29-15" href="#__codelineno-29-15"></a><span class="w">    </span><span class="cm">/* スタックが空かどうかを判定 */</span>
+<a id="__codelineno-29-16" name="__codelineno-29-16" href="#__codelineno-29-16"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">boolean</span><span class="w"> </span><span class="nf">isEmpty</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-17" name="__codelineno-29-17" href="#__codelineno-29-17"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-29-18" name="__codelineno-29-18" href="#__codelineno-29-18"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-19" name="__codelineno-29-19" href="#__codelineno-29-19"></a>
+<a id="__codelineno-29-20" name="__codelineno-29-20" href="#__codelineno-29-20"></a><span class="w">    </span><span class="cm">/* プッシュ */</span>
+<a id="__codelineno-29-21" name="__codelineno-29-21" href="#__codelineno-29-21"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">push</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-22" name="__codelineno-29-22" href="#__codelineno-29-22"></a><span class="w">        </span><span class="n">stack</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-29-23" name="__codelineno-29-23" href="#__codelineno-29-23"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-24" name="__codelineno-29-24" href="#__codelineno-29-24"></a>
+<a id="__codelineno-29-25" name="__codelineno-29-25" href="#__codelineno-29-25"></a><span class="w">    </span><span class="cm">/* ポップ */</span>
+<a id="__codelineno-29-26" name="__codelineno-29-26" href="#__codelineno-29-26"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">pop</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-27" name="__codelineno-29-27" href="#__codelineno-29-27"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
+<a id="__codelineno-29-28" name="__codelineno-29-28" href="#__codelineno-29-28"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">();</span>
+<a id="__codelineno-29-29" name="__codelineno-29-29" href="#__codelineno-29-29"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="na">remove</span><span class="p">(</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-29-30" name="__codelineno-29-30" href="#__codelineno-29-30"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-31" name="__codelineno-29-31" href="#__codelineno-29-31"></a>
+<a id="__codelineno-29-32" name="__codelineno-29-32" href="#__codelineno-29-32"></a><span class="w">    </span><span class="cm">/* スタックトップ要素にアクセス */</span>
+<a id="__codelineno-29-33" name="__codelineno-29-33" href="#__codelineno-29-33"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">peek</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-34" name="__codelineno-29-34" href="#__codelineno-29-34"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">isEmpty</span><span class="p">())</span>
+<a id="__codelineno-29-35" name="__codelineno-29-35" href="#__codelineno-29-35"></a><span class="w">            </span><span class="k">throw</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">IndexOutOfBoundsException</span><span class="p">();</span>
+<a id="__codelineno-29-36" name="__codelineno-29-36" href="#__codelineno-29-36"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-29-37" name="__codelineno-29-37" href="#__codelineno-29-37"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-38" name="__codelineno-29-38" href="#__codelineno-29-38"></a>
+<a id="__codelineno-29-39" name="__codelineno-29-39" href="#__codelineno-29-39"></a><span class="w">    </span><span class="cm">/* List を Array に変換して返す */</span>
+<a id="__codelineno-29-40" name="__codelineno-29-40" href="#__codelineno-29-40"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="n">Object</span><span class="o">[]</span><span class="w"> </span><span class="nf">toArray</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-41" name="__codelineno-29-41" href="#__codelineno-29-41"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">stack</span><span class="p">.</span><span class="na">toArray</span><span class="p">();</span>
+<a id="__codelineno-29-42" name="__codelineno-29-42" href="#__codelineno-29-42"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-43" name="__codelineno-29-43" href="#__codelineno-29-43"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_stack.cs</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">ArrayStack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_stack.go</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">arrayStack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_stack.swift</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">ArrayStack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_stack.js</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">ArrayStack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_stack.ts</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">ArrayStack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_stack.dart</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ArrayStack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_stack.rs</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ArrayStack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_stack.c</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ArrayStack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_stack.kt</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">ArrayStack</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_stack.rb</span><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">ArrayStack</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_stack.zig</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ArrayStack</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h2 id="513-2">5.1.3 &nbsp; 2つの実装の比較<a class="headerlink" href="#513-2" title="Permanent link">&para;</a></h2>
+<p><strong>サポートされる操作</strong></p>
+<p>両方の実装は、スタックで定義されたすべての操作をサポートします。配列実装はさらにランダムアクセスをサポートしますが、これはスタック定義の範囲を超えており、一般的には使用されません。</p>
+<p><strong>時間効率</strong></p>
+<p>配列ベースの実装では、プッシュとポップ操作の両方が事前に割り当てられた連続メモリで発生し、良好なキャッシュ局所性があるため効率が高くなります。しかし、プッシュ操作が配列容量を超える場合、リサイズメカニズムがトリガーされ、そのプッシュ操作の時間計算量は<span class="arithmatex">\(O(n)\)</span>になります。</p>
+<p>連結リスト実装では、リスト拡張は非常に柔軟で、配列拡張のような効率低下の問題はありません。しかし、プッシュ操作にはノードオブジェクトの初期化とポインタの変更が必要なため、効率は比較的低くなります。プッシュされる要素がすでにノードオブジェクトの場合、初期化ステップをスキップでき、効率が向上します。</p>
+<p>したがって、プッシュとポップ操作の要素が<code>int</code>や<code>double</code>などの基本データ型の場合、以下の結論を導くことができます：</p>
+<ul>
+<li>配列ベースのスタック実装は拡張時に効率が低下しますが、拡張は低頻度操作であるため、平均効率は高くなります。</li>
+<li>連結リストベースのスタック実装はより安定した効率パフォーマンスを提供します。</li>
+</ul>
+<p><strong>空間効率</strong></p>
+<p>リストを初期化する際、システムは「初期容量」を割り当てますが、これは実際の必要量を超える可能性があります。さらに、拡張メカニズムは通常、特定の係数（2倍など）で容量を増加させ、これも実際の必要量を超える可能性があります。したがって、<strong>配列ベースのスタックは一部の空間を無駄にする可能性があります</strong>。</p>
+<p>しかし、連結リストノードはポインタを格納するための追加空間が必要なため、<strong>連結リストノードが占有する空間は比較的大きくなります</strong>。</p>
+<p>まとめると、どちらの実装がよりメモリ効率的かを単純に判断することはできません。特定の状況に基づく分析が必要です。</p>
+<h2 id="514">5.1.4 &nbsp; スタックの典型的な応用<a class="headerlink" href="#514" title="Permanent link">&para;</a></h2>
+<ul>
+<li><strong>ブラウザの戻ると進む、ソフトウェアの元に戻すとやり直し</strong>。新しいWebページを開くたびに、ブラウザは前のページをスタックにプッシュし、戻る操作（本質的にはポップ操作）を通じて前のページに戻ることができます。戻ると進むの両方をサポートするには、2つのスタックが連携して動作する必要があります。</li>
+<li><strong>プログラムのメモリ管理</strong>。関数が呼び出されるたびに、システムはスタックのトップにスタックフレームを追加して関数のコンテキスト情報を記録します。再帰関数では、下方向の再帰フェーズはスタックへのプッシュを続け、上方向のバックトラッキングフェーズはスタックからのポップを続けます。</li>
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+        <a href="https://github.com/krahets/hello-algo" title="リポジトリへ" class="md-source" data-md-component="source">
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+  
+  <span class="md-ellipsis">
+    はじめに
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M21 4H3a2 2 0 0 0-2 2v13a2 2 0 0 0 2 2h18a2 2 0 0 0 2-2V6a2 2 0 0 0-2-2M3 19V6h8v13H3m18 0h-8V6h8v13m-7-9.5h6V11h-6V9.5m0 2.5h6v1.5h-6V12m0 2.5h6V16h-6v-1.5Z"/></svg>
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+    第 0 章 &nbsp; 前書き
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+            
+              
+              <label class="md-nav__link " for="__nav_2" id="__nav_2_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_2_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_2">
+            <span class="md-nav__icon md-icon"></span>
+            第 0 章 &nbsp; 前書き
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/about_the_book/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.1 &nbsp; この本について
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/suggestions/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.2 &nbsp; 本書の使い方
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_introduction/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 重要なポイント
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#2-q-a" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; Q &amp; A
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_tree/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_tree/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
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+<h1 id="54">5.4 &nbsp; まとめ<a class="headerlink" href="#54" title="Permanent link">&para;</a></h1>
+<h3 id="1">1. &nbsp; 重要なポイント<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<ul>
+<li>スタックは後入れ先出し（LIFO）の原則に従うデータ構造で、配列または連結リストを使って実装できます。</li>
+<li>時間効率の観点では、スタックの配列実装の方が平均的な効率が高いです。ただし、拡張時には単一のプッシュ操作の時間計算量が<span class="arithmatex">\(O(n)\)</span>に悪化する可能性があります。対照的に、スタックの連結リスト実装はより安定した効率を提供します。</li>
+<li>空間効率に関しては、スタックの配列実装は一定程度の空間の無駄につながる可能性があります。ただし、連結リストのノードが占有するメモリ空間は一般的に配列の要素よりも大きいことに注意することが重要です。</li>
+<li>キューは先入れ先出し（FIFO）の原則に従うデータ構造で、同様に配列または連結リストを使って実装できます。キューの時間と空間効率に関する結論は、スタックと似ています。</li>
+<li>両端キュー（deque）はより柔軟なキューの種類で、両端での要素の追加と削除を可能にします。</li>
+</ul>
+<h3 id="2-q-a">2. &nbsp; Q &amp; A<a class="headerlink" href="#2-q-a" title="Permanent link">&para;</a></h3>
+<p><strong>Q</strong>: ブラウザの進む・戻る機能は双方向連結リストで実装されているのですか？</p>
+<p>ブラウザの進む・戻るナビゲーションは本質的に「スタック」概念の現れです。ユーザーが新しいページを訪問すると、そのページがスタックの先頭に追加されます。戻るボタンをクリックすると、ページがスタックの先頭からポップされます。両端キュー（deque）は、「両端キュー」の章で述べたように、いくつかの追加操作を便利に実装できます。</p>
+<p><strong>Q</strong>: スタックからポップした後、ポップされたノードのメモリを解放する必要がありますか？</p>
+<p>ポップされたノードが後で使用される場合は、そのメモリを解放する必要はありません。自動ガベージコレクションを持つJavaやPythonなどの言語では、手動のメモリ解放は必要ありません。CやC++では、手動のメモリ解放が必要です。</p>
+<p><strong>Q</strong>: 両端キューは2つのスタックを結合したもののように見えます。その用途は何ですか？</p>
+<p>両端キューは、スタックとキューの組み合わせまたは2つのスタックを結合したもので、スタックとキューの両方のロジックを示します。したがって、スタックとキューのすべてのアプリケーションを実装でき、より大きな柔軟性を提供します。</p>
+<p><strong>Q</strong>: 元に戻すとやり直しは具体的にどのように実装されるのですか？</p>
+<p>元に戻すとやり直しの操作は2つのスタックを使って実装されます：元に戻す用のスタック<code>A</code>とやり直し用のスタック<code>B</code>です。</p>
+<ol>
+<li>ユーザーが操作を実行するたびに、それがスタック<code>A</code>にプッシュされ、スタック<code>B</code>がクリアされます。</li>
+<li>ユーザーが「元に戻す」を実行すると、最新の操作がスタック<code>A</code>からポップされ、スタック<code>B</code>にプッシュされます。</li>
+<li>ユーザーが「やり直し」を実行すると、最新の操作がスタック<code>B</code>からポップされ、スタック<code>A</code>に戻されます。</li>
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+  
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+  
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+      <a href="../../chapter_preface/about_the_book/" class="md-nav__link">
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+      <a href="../../chapter_preface/summary/" class="md-nav__link">
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+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
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+  
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+    1.1 &nbsp; アルゴリズムはどこにでもある
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+  
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+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
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+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
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+    </li>
+  
+
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+              
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+  
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+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
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+    </li>
+  
+
+              
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+          
+        
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+        
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+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
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+  
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+            第 2 章 &nbsp; 計算量解析
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+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
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+    2.1 &nbsp; アルゴリズム効率評価
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+  
+
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+
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+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
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+    2.2 &nbsp; 反復と再帰
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+  
+
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+    </li>
+  
+
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+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
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+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
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+
+              
+            
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+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
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+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
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+  
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+    第 3 章 &nbsp; データ構造
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+            第 3 章 &nbsp; データ構造
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+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
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+    3.1 &nbsp; データ構造の分類
+  </span>
+  
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+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
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+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
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+
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+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
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+  </span>
+  
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+    </li>
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+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
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+  </span>
+  
+
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+    </li>
+  
+
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+  
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+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
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+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
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+  
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+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#731" class="md-nav__link">
+    <span class="md-ellipsis">
+      7.3.1 &nbsp; 完全二分木の表現
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#732" class="md-nav__link">
+    <span class="md-ellipsis">
+      7.3.2 &nbsp; 任意の二分木の表現
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#733" class="md-nav__link">
+    <span class="md-ellipsis">
+      7.3.3 &nbsp; 利点と制限
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
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+
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+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
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+
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+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
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+
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+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
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+    15.3 &nbsp; 最大容量問題
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+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
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+    15.4 &nbsp; 最大積切断問題
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+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
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+  <a href="#731" class="md-nav__link">
+    <span class="md-ellipsis">
+      7.3.1 &nbsp; 完全二分木の表現
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+  
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+      
+        <li class="md-nav__item">
+  <a href="#732" class="md-nav__link">
+    <span class="md-ellipsis">
+      7.3.2 &nbsp; 任意の二分木の表現
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+  
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+      
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+  <a href="#733" class="md-nav__link">
+    <span class="md-ellipsis">
+      7.3.3 &nbsp; 利点と制限
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+      
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
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+<!-- Page content -->
+<h1 id="73">7.3 &nbsp; 二分木の配列表現<a class="headerlink" href="#73" title="Permanent link">&para;</a></h1>
+<p>連結リスト表現では、二分木の格納単位はノード<code>TreeNode</code>であり、ノードはポインタによって接続されます。連結リスト表現での二分木の基本操作については前の節で紹介しました。</p>
+<p>では、配列を使って二分木を表現することはできるでしょうか？答えはイエスです。</p>
+<h2 id="731">7.3.1 &nbsp; 完全二分木の表現<a class="headerlink" href="#731" title="Permanent link">&para;</a></h2>
+<p>まず簡単なケースから分析してみましょう。完全二分木が与えられたとき、レベル順探索の順序に従ってすべてのノードを配列に格納し、各ノードは一意の配列インデックスに対応します。</p>
+<p>レベル順探索の特性に基づいて、親ノードのインデックスとその子ノードの間の「マッピング公式」を導き出すことができます：<strong>ノードのインデックスが<span class="arithmatex">\(i\)</span>の場合、その左の子のインデックスは<span class="arithmatex">\(2i + 1\)</span>、右の子のインデックスは<span class="arithmatex">\(2i + 2\)</span>です</strong>。下図は、さまざまなノードのインデックス間のマッピング関係を示しています。</p>
+<p><a class="glightbox" href="../array_representation_of_tree.assets/array_representation_binary_tree.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="完全二分木の配列表現" class="animation-figure" src="../array_representation_of_tree.assets/array_representation_binary_tree.png" /></a></p>
+<p align="center"> 図 7-12 &nbsp; 完全二分木の配列表現 </p>
+
+<p><strong>マッピング公式は、連結リストのノード参照（ポインタ）と同様の役割を果たします</strong>。配列内の任意のノードが与えられたとき、マッピング公式を使用してその左（右）の子ノードにアクセスできます。</p>
+<h2 id="732">7.3.2 &nbsp; 任意の二分木の表現<a class="headerlink" href="#732" title="Permanent link">&para;</a></h2>
+<p>完全二分木は特別なケースです。二分木の中間レベルには多くの<code>None</code>値が存在することがよくあります。レベル順探索のシーケンスにはこれらの<code>None</code>値が含まれないため、このシーケンスだけに依存して<code>None</code>値の数と分布を推測することはできません。<strong>つまり、複数の二分木構造が同じレベル順探索シーケンスと一致する可能性があります</strong>。</p>
+<p>下図に示すように、完全でない二分木が与えられた場合、上記の配列表現方法は失敗します。</p>
+<p><a class="glightbox" href="../array_representation_of_tree.assets/array_representation_without_empty.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="レベル順探索シーケンスが複数の二分木の可能性に対応" class="animation-figure" src="../array_representation_of_tree.assets/array_representation_without_empty.png" /></a></p>
+<p align="center"> 図 7-13 &nbsp; レベル順探索シーケンスが複数の二分木の可能性に対応 </p>
+
+<p>この問題を解決するために、<strong>レベル順探索シーケンスですべての<code>None</code>値を明示的に書き出すことを検討できます</strong>。下図に示すように、この処理後、レベル順探索シーケンスは二分木を一意に表現できます。サンプルコードは以下の通りです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:14"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><input id="__tabbed_1_14" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label><label for="__tabbed_1_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="c1"># 二分木の配列表現</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="c1"># Noneを使用して空のスロットを表現</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a><span class="n">tree</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">9</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="mi">12</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="mi">15</span><span class="p">]</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 二分木の配列表現 */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="c1">// 最大整数値INT_MAXを使用して空のスロットをマーク</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">,</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">,</span><span class="w"> </span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="p">,</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">,</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">,</span><span class="w"> </span><span class="mi">12</span><span class="p">,</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">,</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">,</span><span class="w"> </span><span class="mi">15</span><span class="p">};</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 二分木の配列表現 */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="c1">// Integerラッパークラスを使用してnullで空のスロットをマーク</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="n">Integer</span><span class="o">[]</span><span class="w"> </span><span class="n">tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="mi">12</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="mi">15</span><span class="w"> </span><span class="p">};</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 二分木の配列表現 */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="c1">// nullable int (int?)を使用してnullで空のスロットをマーク</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="kt">int?</span><span class="p">[]</span><span class="w"> </span><span class="n">tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">,</span><span class="w"> </span><span class="k">null</span><span class="p">,</span><span class="w"> </span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="p">,</span><span class="w"> </span><span class="k">null</span><span class="p">,</span><span class="w"> </span><span class="k">null</span><span class="p">,</span><span class="w"> </span><span class="mi">12</span><span class="p">,</span><span class="w"> </span><span class="k">null</span><span class="p">,</span><span class="w"> </span><span class="k">null</span><span class="p">,</span><span class="w"> </span><span class="mi">15</span><span class="p">];</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 二分木の配列表現 */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="c1">// any型スライスを使用してnilで空のスロットをマーク</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="nx">tree</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="p">[]</span><span class="kt">any</span><span class="p">{</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">,</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span><span class="w"> </span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="p">,</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span><span class="w"> </span><span class="mi">12</span><span class="p">,</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span><span class="w"> </span><span class="mi">15</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 二分木の配列表現 */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="c1">// optional Int (Int?)を使用してnilで空のスロットをマーク</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="kd">let</span><span class="w"> </span><span class="nv">tree</span><span class="p">:</span><span class="w"> </span><span class="p">[</span><span class="nb">Int</span><span class="p">?]</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">,</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span><span class="w"> </span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="p">,</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span><span class="w"> </span><span class="mi">12</span><span class="p">,</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span><span class="w"> </span><span class="mi">15</span><span class="p">]</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 二分木の配列表現 */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="c1">// nullを使用して空のスロットを表現</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="kd">let</span><span class="w"> </span><span class="nx">tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="mf">2</span><span class="p">,</span><span class="w"> </span><span class="mf">3</span><span class="p">,</span><span class="w"> </span><span class="mf">4</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="mf">6</span><span class="p">,</span><span class="w"> </span><span class="mf">7</span><span class="p">,</span><span class="w"> </span><span class="mf">8</span><span class="p">,</span><span class="w"> </span><span class="mf">9</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="mf">12</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="mf">15</span><span class="p">];</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 二分木の配列表現 */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="c1">// nullを使用して空のスロットを表現</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="kd">let</span><span class="w"> </span><span class="nx">tree</span><span class="o">:</span><span class="w"> </span><span class="p">(</span><span class="kt">number</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">)[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="mf">1</span><span class="p">,</span><span class="w"> </span><span class="mf">2</span><span class="p">,</span><span class="w"> </span><span class="mf">3</span><span class="p">,</span><span class="w"> </span><span class="mf">4</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="mf">6</span><span class="p">,</span><span class="w"> </span><span class="mf">7</span><span class="p">,</span><span class="w"> </span><span class="mf">8</span><span class="p">,</span><span class="w"> </span><span class="mf">9</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="mf">12</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="mf">15</span><span class="p">];</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 二分木の配列表現 */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="c1">// nullable int (int?)を使用してnullで空のスロットをマーク</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="n">List</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">?&gt;</span><span class="w"> </span><span class="n">tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="m">2</span><span class="p">,</span><span class="w"> </span><span class="m">3</span><span class="p">,</span><span class="w"> </span><span class="m">4</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="m">6</span><span class="p">,</span><span class="w"> </span><span class="m">7</span><span class="p">,</span><span class="w"> </span><span class="m">8</span><span class="p">,</span><span class="w"> </span><span class="m">9</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="m">12</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="m">15</span><span class="p">];</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="cm">/* 二分木の配列表現 */</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="c1">// Noneを使用して空のスロットをマーク</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a><span class="kd">let</span><span class="w"> </span><span class="n">tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">[</span><span class="nb">Some</span><span class="p">(</span><span class="mi">1</span><span class="p">),</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="mi">2</span><span class="p">),</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="mi">3</span><span class="p">),</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="mi">4</span><span class="p">),</span><span class="w"> </span><span class="nb">None</span><span class="p">,</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="mi">6</span><span class="p">),</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="mi">7</span><span class="p">),</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="mi">8</span><span class="p">),</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="mi">9</span><span class="p">),</span><span class="w"> </span><span class="nb">None</span><span class="p">,</span><span class="w"> </span><span class="nb">None</span><span class="p">,</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="mi">12</span><span class="p">),</span><span class="w"> </span><span class="nb">None</span><span class="p">,</span><span class="w"> </span><span class="nb">None</span><span class="p">,</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="mi">15</span><span class="p">)];</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 二分木の配列表現 */</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="c1">// 最大int値を使用して空のスロットをマーク、したがってノード値はINT_MAXであってはならない</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="kt">int</span><span class="w"> </span><span class="n">tree</span><span class="p">[]</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">{</span><span class="mi">1</span><span class="p">,</span><span class="w"> </span><span class="mi">2</span><span class="p">,</span><span class="w"> </span><span class="mi">3</span><span class="p">,</span><span class="w"> </span><span class="mi">4</span><span class="p">,</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">,</span><span class="w"> </span><span class="mi">6</span><span class="p">,</span><span class="w"> </span><span class="mi">7</span><span class="p">,</span><span class="w"> </span><span class="mi">8</span><span class="p">,</span><span class="w"> </span><span class="mi">9</span><span class="p">,</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">,</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">,</span><span class="w"> </span><span class="mi">12</span><span class="p">,</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">,</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">,</span><span class="w"> </span><span class="mi">15</span><span class="p">};</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 二分木の配列表現 */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="c1">// nullを使用して空のスロットを表現</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="kd">val</span><span class="w"> </span><span class="nv">tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">mutableListOf</span><span class="p">(</span><span class="w"> </span><span class="m">1</span><span class="p">,</span><span class="w"> </span><span class="m">2</span><span class="p">,</span><span class="w"> </span><span class="m">3</span><span class="p">,</span><span class="w"> </span><span class="m">4</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="m">6</span><span class="p">,</span><span class="w"> </span><span class="m">7</span><span class="p">,</span><span class="w"> </span><span class="m">8</span><span class="p">,</span><span class="w"> </span><span class="m">9</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="m">12</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="m">15</span><span class="w"> </span><span class="p">)</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p><a class="glightbox" href="../array_representation_of_tree.assets/array_representation_with_empty.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="任意の種類の二分木の配列表現" class="animation-figure" src="../array_representation_of_tree.assets/array_representation_with_empty.png" /></a></p>
+<p align="center"> 図 7-14 &nbsp; 任意の種類の二分木の配列表現 </p>
+
+<p>注目すべきは、<strong>完備二分木は配列表現に非常に適している**ということです。完備二分木の定義を思い出すと、<code>None</code>は最下位レベルでのみ、かつ右側に向かって現れます。**つまり、すべての<code>None</code>値は確実にレベル順探索シーケンスの最後に現れます</strong>。</p>
+<p>これは、配列を使用して完備二分木を表現する際、すべての<code>None</code>値の格納を省略できることを意味し、非常に便利です。下図に例を示します。</p>
+<p><a class="glightbox" href="../array_representation_of_tree.assets/array_representation_complete_binary_tree.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="完備二分木の配列表現" class="animation-figure" src="../array_representation_of_tree.assets/array_representation_complete_binary_tree.png" /></a></p>
+<p align="center"> 図 7-15 &nbsp; 完備二分木の配列表現 </p>
+
+<p>以下のコードは、配列表現に基づく二分木を実装し、次の操作を含みます：</p>
+<ul>
+<li>ノードが与えられたとき、その値、左（右）の子ノード、および親ノードを取得する。</li>
+<li>前順、中順、後順、およびレベル順探索シーケンスを取得する。</li>
+</ul>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:14"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><input id="__tabbed_2_14" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label><label for="__tabbed_2_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_binary_tree.py</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">ArrayBinaryTree</span><span class="p">:</span>
+<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;配列ベースの二分木クラス&quot;&quot;&quot;</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">arr</span><span class="p">:</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span> <span class="o">|</span> <span class="kc">None</span><span class="p">]):</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;コンストラクタ&quot;&quot;&quot;</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_tree</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">arr</span><span class="p">)</span>
+<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a>
+<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">size</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;リストの容量&quot;&quot;&quot;</span>
+<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a>        <span class="k">return</span> <span class="nb">len</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_tree</span><span class="p">)</span>
+<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a>
+<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">val</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;インデックスiのノードの値を取得&quot;&quot;&quot;</span>
+<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a>        <span class="c1"># インデックスが範囲外の場合、Noneを返し、空席を表す</span>
+<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a>        <span class="k">if</span> <span class="n">i</span> <span class="o">&lt;</span> <span class="mi">0</span> <span class="ow">or</span> <span class="n">i</span> <span class="o">&gt;=</span> <span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">():</span>
+<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a>            <span class="k">return</span> <span class="kc">None</span>
+<a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">_tree</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+<a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a>
+<a id="__codelineno-14-19" name="__codelineno-14-19" href="#__codelineno-14-19"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">left</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-14-20" name="__codelineno-14-20" href="#__codelineno-14-20"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;インデックスiのノードの左の子のインデックスを取得&quot;&quot;&quot;</span>
+<a id="__codelineno-14-21" name="__codelineno-14-21" href="#__codelineno-14-21"></a>        <span class="k">return</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">1</span>
+<a id="__codelineno-14-22" name="__codelineno-14-22" href="#__codelineno-14-22"></a>
+<a id="__codelineno-14-23" name="__codelineno-14-23" href="#__codelineno-14-23"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">right</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-14-24" name="__codelineno-14-24" href="#__codelineno-14-24"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;インデックスiのノードの右の子のインデックスを取得&quot;&quot;&quot;</span>
+<a id="__codelineno-14-25" name="__codelineno-14-25" href="#__codelineno-14-25"></a>        <span class="k">return</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">2</span>
+<a id="__codelineno-14-26" name="__codelineno-14-26" href="#__codelineno-14-26"></a>
+<a id="__codelineno-14-27" name="__codelineno-14-27" href="#__codelineno-14-27"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">parent</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-14-28" name="__codelineno-14-28" href="#__codelineno-14-28"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;インデックスiのノードの親のインデックスを取得&quot;&quot;&quot;</span>
+<a id="__codelineno-14-29" name="__codelineno-14-29" href="#__codelineno-14-29"></a>        <span class="k">return</span> <span class="p">(</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span>
+<a id="__codelineno-14-30" name="__codelineno-14-30" href="#__codelineno-14-30"></a>
+<a id="__codelineno-14-31" name="__codelineno-14-31" href="#__codelineno-14-31"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">level_order</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
+<a id="__codelineno-14-32" name="__codelineno-14-32" href="#__codelineno-14-32"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;レベル順走査&quot;&quot;&quot;</span>
+<a id="__codelineno-14-33" name="__codelineno-14-33" href="#__codelineno-14-33"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>
+<a id="__codelineno-14-34" name="__codelineno-14-34" href="#__codelineno-14-34"></a>        <span class="c1"># 配列を走査</span>
+<a id="__codelineno-14-35" name="__codelineno-14-35" href="#__codelineno-14-35"></a>        <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">size</span><span class="p">()):</span>
+<a id="__codelineno-14-36" name="__codelineno-14-36" href="#__codelineno-14-36"></a>            <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-14-37" name="__codelineno-14-37" href="#__codelineno-14-37"></a>                <span class="bp">self</span><span class="o">.</span><span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">))</span>
+<a id="__codelineno-14-38" name="__codelineno-14-38" href="#__codelineno-14-38"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">res</span>
+<a id="__codelineno-14-39" name="__codelineno-14-39" href="#__codelineno-14-39"></a>
+<a id="__codelineno-14-40" name="__codelineno-14-40" href="#__codelineno-14-40"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">i</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">order</span><span class="p">:</span> <span class="nb">str</span><span class="p">):</span>
+<a id="__codelineno-14-41" name="__codelineno-14-41" href="#__codelineno-14-41"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;深さ優先走査&quot;&quot;&quot;</span>
+<a id="__codelineno-14-42" name="__codelineno-14-42" href="#__codelineno-14-42"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-14-43" name="__codelineno-14-43" href="#__codelineno-14-43"></a>            <span class="k">return</span>
+<a id="__codelineno-14-44" name="__codelineno-14-44" href="#__codelineno-14-44"></a>        <span class="c1"># 前順走査</span>
+<a id="__codelineno-14-45" name="__codelineno-14-45" href="#__codelineno-14-45"></a>        <span class="k">if</span> <span class="n">order</span> <span class="o">==</span> <span class="s2">&quot;pre&quot;</span><span class="p">:</span>
+<a id="__codelineno-14-46" name="__codelineno-14-46" href="#__codelineno-14-46"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">))</span>
+<a id="__codelineno-14-47" name="__codelineno-14-47" href="#__codelineno-14-47"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">dfs</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span> <span class="n">order</span><span class="p">)</span>
+<a id="__codelineno-14-48" name="__codelineno-14-48" href="#__codelineno-14-48"></a>        <span class="c1"># 中順走査</span>
+<a id="__codelineno-14-49" name="__codelineno-14-49" href="#__codelineno-14-49"></a>        <span class="k">if</span> <span class="n">order</span> <span class="o">==</span> <span class="s2">&quot;in&quot;</span><span class="p">:</span>
+<a id="__codelineno-14-50" name="__codelineno-14-50" href="#__codelineno-14-50"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">))</span>
+<a id="__codelineno-14-51" name="__codelineno-14-51" href="#__codelineno-14-51"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">dfs</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span> <span class="n">order</span><span class="p">)</span>
+<a id="__codelineno-14-52" name="__codelineno-14-52" href="#__codelineno-14-52"></a>        <span class="c1"># 後順走査</span>
+<a id="__codelineno-14-53" name="__codelineno-14-53" href="#__codelineno-14-53"></a>        <span class="k">if</span> <span class="n">order</span> <span class="o">==</span> <span class="s2">&quot;post&quot;</span><span class="p">:</span>
+<a id="__codelineno-14-54" name="__codelineno-14-54" href="#__codelineno-14-54"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">))</span>
+<a id="__codelineno-14-55" name="__codelineno-14-55" href="#__codelineno-14-55"></a>
+<a id="__codelineno-14-56" name="__codelineno-14-56" href="#__codelineno-14-56"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">pre_order</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
+<a id="__codelineno-14-57" name="__codelineno-14-57" href="#__codelineno-14-57"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;前順走査&quot;&quot;&quot;</span>
+<a id="__codelineno-14-58" name="__codelineno-14-58" href="#__codelineno-14-58"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>
+<a id="__codelineno-14-59" name="__codelineno-14-59" href="#__codelineno-14-59"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">order</span><span class="o">=</span><span class="s2">&quot;pre&quot;</span><span class="p">)</span>
+<a id="__codelineno-14-60" name="__codelineno-14-60" href="#__codelineno-14-60"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">res</span>
+<a id="__codelineno-14-61" name="__codelineno-14-61" href="#__codelineno-14-61"></a>
+<a id="__codelineno-14-62" name="__codelineno-14-62" href="#__codelineno-14-62"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">in_order</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
+<a id="__codelineno-14-63" name="__codelineno-14-63" href="#__codelineno-14-63"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;中順走査&quot;&quot;&quot;</span>
+<a id="__codelineno-14-64" name="__codelineno-14-64" href="#__codelineno-14-64"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>
+<a id="__codelineno-14-65" name="__codelineno-14-65" href="#__codelineno-14-65"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">order</span><span class="o">=</span><span class="s2">&quot;in&quot;</span><span class="p">)</span>
+<a id="__codelineno-14-66" name="__codelineno-14-66" href="#__codelineno-14-66"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">res</span>
+<a id="__codelineno-14-67" name="__codelineno-14-67" href="#__codelineno-14-67"></a>
+<a id="__codelineno-14-68" name="__codelineno-14-68" href="#__codelineno-14-68"></a>    <span class="k">def</span><span class="w"> </span><span class="nf">post_order</span><span class="p">(</span><span class="bp">self</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
+<a id="__codelineno-14-69" name="__codelineno-14-69" href="#__codelineno-14-69"></a><span class="w">        </span><span class="sd">&quot;&quot;&quot;後順走査&quot;&quot;&quot;</span>
+<a id="__codelineno-14-70" name="__codelineno-14-70" href="#__codelineno-14-70"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>
+<a id="__codelineno-14-71" name="__codelineno-14-71" href="#__codelineno-14-71"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">order</span><span class="o">=</span><span class="s2">&quot;post&quot;</span><span class="p">)</span>
+<a id="__codelineno-14-72" name="__codelineno-14-72" href="#__codelineno-14-72"></a>        <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">res</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_binary_tree.cpp</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 配列ベースの二分木クラス */</span>
+<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="k">class</span><span class="w"> </span><span class="nc">ArrayBinaryTree</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">  </span><span class="k">public</span><span class="o">:</span>
+<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">    </span><span class="n">ArrayBinaryTree</span><span class="p">(</span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">arr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">        </span><span class="n">tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">arr</span><span class="p">;</span>
+<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a>
+<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w">    </span><span class="cm">/* リストの容量 */</span>
+<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">tree</span><span class="p">.</span><span class="n">size</span><span class="p">();</span>
+<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a>
+<a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="w">    </span><span class="cm">/* インデックス i のノードの値を取得 */</span>
+<a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a><span class="w">        </span><span class="c1">// インデックスが範囲外の場合、INT_MAX を返す（null を表す）</span>
+<a id="__codelineno-15-17" name="__codelineno-15-17" href="#__codelineno-15-17"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">())</span>
+<a id="__codelineno-15-18" name="__codelineno-15-18" href="#__codelineno-15-18"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">;</span>
+<a id="__codelineno-15-19" name="__codelineno-15-19" href="#__codelineno-15-19"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">tree</span><span class="p">[</span><span class="n">i</span><span class="p">];</span>
+<a id="__codelineno-15-20" name="__codelineno-15-20" href="#__codelineno-15-20"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-21" name="__codelineno-15-21" href="#__codelineno-15-21"></a>
+<a id="__codelineno-15-22" name="__codelineno-15-22" href="#__codelineno-15-22"></a><span class="w">    </span><span class="cm">/* インデックス i のノードの左の子のインデックスを取得 */</span>
+<a id="__codelineno-15-23" name="__codelineno-15-23" href="#__codelineno-15-23"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">left</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-24" name="__codelineno-15-24" href="#__codelineno-15-24"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-15-25" name="__codelineno-15-25" href="#__codelineno-15-25"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-26" name="__codelineno-15-26" href="#__codelineno-15-26"></a>
+<a id="__codelineno-15-27" name="__codelineno-15-27" href="#__codelineno-15-27"></a><span class="w">    </span><span class="cm">/* インデックス i のノードの右の子のインデックスを取得 */</span>
+<a id="__codelineno-15-28" name="__codelineno-15-28" href="#__codelineno-15-28"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">right</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-29" name="__codelineno-15-29" href="#__codelineno-15-29"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-15-30" name="__codelineno-15-30" href="#__codelineno-15-30"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-31" name="__codelineno-15-31" href="#__codelineno-15-31"></a>
+<a id="__codelineno-15-32" name="__codelineno-15-32" href="#__codelineno-15-32"></a><span class="w">    </span><span class="cm">/* インデックス i のノードの親のインデックスを取得 */</span>
+<a id="__codelineno-15-33" name="__codelineno-15-33" href="#__codelineno-15-33"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">parent</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-34" name="__codelineno-15-34" href="#__codelineno-15-34"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-15-35" name="__codelineno-15-35" href="#__codelineno-15-35"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-36" name="__codelineno-15-36" href="#__codelineno-15-36"></a>
+<a id="__codelineno-15-37" name="__codelineno-15-37" href="#__codelineno-15-37"></a><span class="w">    </span><span class="cm">/* レベル順走査 */</span>
+<a id="__codelineno-15-38" name="__codelineno-15-38" href="#__codelineno-15-38"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">levelOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-39" name="__codelineno-15-39" href="#__codelineno-15-39"></a><span class="w">        </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-15-40" name="__codelineno-15-40" href="#__codelineno-15-40"></a><span class="w">        </span><span class="c1">// 配列を走査</span>
+<a id="__codelineno-15-41" name="__codelineno-15-41" href="#__codelineno-15-41"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-42" name="__codelineno-15-42" href="#__codelineno-15-42"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">)</span>
+<a id="__codelineno-15-43" name="__codelineno-15-43" href="#__codelineno-15-43"></a><span class="w">                </span><span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
+<a id="__codelineno-15-44" name="__codelineno-15-44" href="#__codelineno-15-44"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-15-45" name="__codelineno-15-45" href="#__codelineno-15-45"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-15-46" name="__codelineno-15-46" href="#__codelineno-15-46"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-47" name="__codelineno-15-47" href="#__codelineno-15-47"></a>
+<a id="__codelineno-15-48" name="__codelineno-15-48" href="#__codelineno-15-48"></a><span class="w">    </span><span class="cm">/* 前順走査 */</span>
+<a id="__codelineno-15-49" name="__codelineno-15-49" href="#__codelineno-15-49"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">preOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-50" name="__codelineno-15-50" href="#__codelineno-15-50"></a><span class="w">        </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-15-51" name="__codelineno-15-51" href="#__codelineno-15-51"></a><span class="w">        </span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;pre&quot;</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-15-52" name="__codelineno-15-52" href="#__codelineno-15-52"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-15-53" name="__codelineno-15-53" href="#__codelineno-15-53"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-54" name="__codelineno-15-54" href="#__codelineno-15-54"></a>
+<a id="__codelineno-15-55" name="__codelineno-15-55" href="#__codelineno-15-55"></a><span class="w">    </span><span class="cm">/* 中順走査 */</span>
+<a id="__codelineno-15-56" name="__codelineno-15-56" href="#__codelineno-15-56"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">inOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-57" name="__codelineno-15-57" href="#__codelineno-15-57"></a><span class="w">        </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-15-58" name="__codelineno-15-58" href="#__codelineno-15-58"></a><span class="w">        </span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;in&quot;</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-15-59" name="__codelineno-15-59" href="#__codelineno-15-59"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-15-60" name="__codelineno-15-60" href="#__codelineno-15-60"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-61" name="__codelineno-15-61" href="#__codelineno-15-61"></a>
+<a id="__codelineno-15-62" name="__codelineno-15-62" href="#__codelineno-15-62"></a><span class="w">    </span><span class="cm">/* 後順走査 */</span>
+<a id="__codelineno-15-63" name="__codelineno-15-63" href="#__codelineno-15-63"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">postOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-64" name="__codelineno-15-64" href="#__codelineno-15-64"></a><span class="w">        </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-15-65" name="__codelineno-15-65" href="#__codelineno-15-65"></a><span class="w">        </span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;post&quot;</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-15-66" name="__codelineno-15-66" href="#__codelineno-15-66"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-15-67" name="__codelineno-15-67" href="#__codelineno-15-67"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-68" name="__codelineno-15-68" href="#__codelineno-15-68"></a>
+<a id="__codelineno-15-69" name="__codelineno-15-69" href="#__codelineno-15-69"></a><span class="w">  </span><span class="k">private</span><span class="o">:</span>
+<a id="__codelineno-15-70" name="__codelineno-15-70" href="#__codelineno-15-70"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">tree</span><span class="p">;</span>
+<a id="__codelineno-15-71" name="__codelineno-15-71" href="#__codelineno-15-71"></a>
+<a id="__codelineno-15-72" name="__codelineno-15-72" href="#__codelineno-15-72"></a><span class="w">    </span><span class="cm">/* 深さ優先走査 */</span>
+<a id="__codelineno-15-73" name="__codelineno-15-73" href="#__codelineno-15-73"></a><span class="w">    </span><span class="kt">void</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">string</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="o">&amp;</span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-74" name="__codelineno-15-74" href="#__codelineno-15-74"></a><span class="w">        </span><span class="c1">// 空の位置の場合、戻る</span>
+<a id="__codelineno-15-75" name="__codelineno-15-75" href="#__codelineno-15-75"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">INT_MAX</span><span class="p">)</span>
+<a id="__codelineno-15-76" name="__codelineno-15-76" href="#__codelineno-15-76"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-15-77" name="__codelineno-15-77" href="#__codelineno-15-77"></a><span class="w">        </span><span class="c1">// 前順走査</span>
+<a id="__codelineno-15-78" name="__codelineno-15-78" href="#__codelineno-15-78"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="s">&quot;pre&quot;</span><span class="p">)</span>
+<a id="__codelineno-15-79" name="__codelineno-15-79" href="#__codelineno-15-79"></a><span class="w">            </span><span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
+<a id="__codelineno-15-80" name="__codelineno-15-80" href="#__codelineno-15-80"></a><span class="w">        </span><span class="n">dfs</span><span class="p">(</span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-15-81" name="__codelineno-15-81" href="#__codelineno-15-81"></a><span class="w">        </span><span class="c1">// 中順走査</span>
+<a id="__codelineno-15-82" name="__codelineno-15-82" href="#__codelineno-15-82"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="s">&quot;in&quot;</span><span class="p">)</span>
+<a id="__codelineno-15-83" name="__codelineno-15-83" href="#__codelineno-15-83"></a><span class="w">            </span><span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
+<a id="__codelineno-15-84" name="__codelineno-15-84" href="#__codelineno-15-84"></a><span class="w">        </span><span class="n">dfs</span><span class="p">(</span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-15-85" name="__codelineno-15-85" href="#__codelineno-15-85"></a><span class="w">        </span><span class="c1">// 後順走査</span>
+<a id="__codelineno-15-86" name="__codelineno-15-86" href="#__codelineno-15-86"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">order</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="s">&quot;post&quot;</span><span class="p">)</span>
+<a id="__codelineno-15-87" name="__codelineno-15-87" href="#__codelineno-15-87"></a><span class="w">            </span><span class="n">res</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
+<a id="__codelineno-15-88" name="__codelineno-15-88" href="#__codelineno-15-88"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-89" name="__codelineno-15-89" href="#__codelineno-15-89"></a><span class="p">};</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_binary_tree.java</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 配列ベースの二分木クラス */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kd">class</span> <span class="nc">ArrayBinaryTree</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">tree</span><span class="p">;</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="nf">ArrayBinaryTree</span><span class="p">(</span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">arr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">        </span><span class="n">tree</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">(</span><span class="n">arr</span><span class="p">);</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w">    </span><span class="cm">/* リストの容量 */</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="nf">size</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">tree</span><span class="p">.</span><span class="na">size</span><span class="p">();</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a>
+<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="w">    </span><span class="cm">/* インデックス i のノードの値を取得 */</span>
+<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="n">Integer</span><span class="w"> </span><span class="nf">val</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-17" name="__codelineno-16-17" href="#__codelineno-16-17"></a><span class="w">        </span><span class="c1">// インデックスが範囲外の場合、null を返す（空の位置を表す）</span>
+<a id="__codelineno-16-18" name="__codelineno-16-18" href="#__codelineno-16-18"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">0</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="n">size</span><span class="p">())</span>
+<a id="__codelineno-16-19" name="__codelineno-16-19" href="#__codelineno-16-19"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-16-20" name="__codelineno-16-20" href="#__codelineno-16-20"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">tree</span><span class="p">.</span><span class="na">get</span><span class="p">(</span><span class="n">i</span><span class="p">);</span>
+<a id="__codelineno-16-21" name="__codelineno-16-21" href="#__codelineno-16-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-22" name="__codelineno-16-22" href="#__codelineno-16-22"></a>
+<a id="__codelineno-16-23" name="__codelineno-16-23" href="#__codelineno-16-23"></a><span class="w">    </span><span class="cm">/* インデックス i のノードの左の子のインデックスを取得 */</span>
+<a id="__codelineno-16-24" name="__codelineno-16-24" href="#__codelineno-16-24"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="n">Integer</span><span class="w"> </span><span class="nf">left</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-25" name="__codelineno-16-25" href="#__codelineno-16-25"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-16-26" name="__codelineno-16-26" href="#__codelineno-16-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-27" name="__codelineno-16-27" href="#__codelineno-16-27"></a>
+<a id="__codelineno-16-28" name="__codelineno-16-28" href="#__codelineno-16-28"></a><span class="w">    </span><span class="cm">/* インデックス i のノードの右の子のインデックスを取得 */</span>
+<a id="__codelineno-16-29" name="__codelineno-16-29" href="#__codelineno-16-29"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="n">Integer</span><span class="w"> </span><span class="nf">right</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-30" name="__codelineno-16-30" href="#__codelineno-16-30"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">2</span><span class="w"> </span><span class="o">*</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-16-31" name="__codelineno-16-31" href="#__codelineno-16-31"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-32" name="__codelineno-16-32" href="#__codelineno-16-32"></a>
+<a id="__codelineno-16-33" name="__codelineno-16-33" href="#__codelineno-16-33"></a><span class="w">    </span><span class="cm">/* インデックス i のノードの親のインデックスを取得 */</span>
+<a id="__codelineno-16-34" name="__codelineno-16-34" href="#__codelineno-16-34"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="n">Integer</span><span class="w"> </span><span class="nf">parent</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-35" name="__codelineno-16-35" href="#__codelineno-16-35"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="p">(</span><span class="n">i</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="o">/</span><span class="w"> </span><span class="mi">2</span><span class="p">;</span>
+<a id="__codelineno-16-36" name="__codelineno-16-36" href="#__codelineno-16-36"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-37" name="__codelineno-16-37" href="#__codelineno-16-37"></a>
+<a id="__codelineno-16-38" name="__codelineno-16-38" href="#__codelineno-16-38"></a><span class="w">    </span><span class="cm">/* レベル順走査 */</span>
+<a id="__codelineno-16-39" name="__codelineno-16-39" href="#__codelineno-16-39"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="nf">levelOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-40" name="__codelineno-16-40" href="#__codelineno-16-40"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-16-41" name="__codelineno-16-41" href="#__codelineno-16-41"></a><span class="w">        </span><span class="c1">// 配列を走査</span>
+<a id="__codelineno-16-42" name="__codelineno-16-42" href="#__codelineno-16-42"></a><span class="w">        </span><span class="k">for</span><span class="w"> </span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w"> </span><span class="n">i</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">size</span><span class="p">();</span><span class="w"> </span><span class="n">i</span><span class="o">++</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-43" name="__codelineno-16-43" href="#__codelineno-16-43"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
+<a id="__codelineno-16-44" name="__codelineno-16-44" href="#__codelineno-16-44"></a><span class="w">                </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
+<a id="__codelineno-16-45" name="__codelineno-16-45" href="#__codelineno-16-45"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-16-46" name="__codelineno-16-46" href="#__codelineno-16-46"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-16-47" name="__codelineno-16-47" href="#__codelineno-16-47"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-48" name="__codelineno-16-48" href="#__codelineno-16-48"></a>
+<a id="__codelineno-16-49" name="__codelineno-16-49" href="#__codelineno-16-49"></a><span class="w">    </span><span class="cm">/* 深さ優先走査 */</span>
+<a id="__codelineno-16-50" name="__codelineno-16-50" href="#__codelineno-16-50"></a><span class="w">    </span><span class="kd">private</span><span class="w"> </span><span class="kt">void</span><span class="w"> </span><span class="nf">dfs</span><span class="p">(</span><span class="n">Integer</span><span class="w"> </span><span class="n">i</span><span class="p">,</span><span class="w"> </span><span class="n">String</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-51" name="__codelineno-16-51" href="#__codelineno-16-51"></a><span class="w">        </span><span class="c1">// 空の位置の場合、戻る</span>
+<a id="__codelineno-16-52" name="__codelineno-16-52" href="#__codelineno-16-52"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">)</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
+<a id="__codelineno-16-53" name="__codelineno-16-53" href="#__codelineno-16-53"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-16-54" name="__codelineno-16-54" href="#__codelineno-16-54"></a><span class="w">        </span><span class="c1">// 前順走査</span>
+<a id="__codelineno-16-55" name="__codelineno-16-55" href="#__codelineno-16-55"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="s">&quot;pre&quot;</span><span class="p">.</span><span class="na">equals</span><span class="p">(</span><span class="n">order</span><span class="p">))</span>
+<a id="__codelineno-16-56" name="__codelineno-16-56" href="#__codelineno-16-56"></a><span class="w">            </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
+<a id="__codelineno-16-57" name="__codelineno-16-57" href="#__codelineno-16-57"></a><span class="w">        </span><span class="n">dfs</span><span class="p">(</span><span class="n">left</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-16-58" name="__codelineno-16-58" href="#__codelineno-16-58"></a><span class="w">        </span><span class="c1">// 中順走査</span>
+<a id="__codelineno-16-59" name="__codelineno-16-59" href="#__codelineno-16-59"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="s">&quot;in&quot;</span><span class="p">.</span><span class="na">equals</span><span class="p">(</span><span class="n">order</span><span class="p">))</span>
+<a id="__codelineno-16-60" name="__codelineno-16-60" href="#__codelineno-16-60"></a><span class="w">            </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
+<a id="__codelineno-16-61" name="__codelineno-16-61" href="#__codelineno-16-61"></a><span class="w">        </span><span class="n">dfs</span><span class="p">(</span><span class="n">right</span><span class="p">(</span><span class="n">i</span><span class="p">),</span><span class="w"> </span><span class="n">order</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-16-62" name="__codelineno-16-62" href="#__codelineno-16-62"></a><span class="w">        </span><span class="c1">// 後順走査</span>
+<a id="__codelineno-16-63" name="__codelineno-16-63" href="#__codelineno-16-63"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="s">&quot;post&quot;</span><span class="p">.</span><span class="na">equals</span><span class="p">(</span><span class="n">order</span><span class="p">))</span>
+<a id="__codelineno-16-64" name="__codelineno-16-64" href="#__codelineno-16-64"></a><span class="w">            </span><span class="n">res</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">val</span><span class="p">(</span><span class="n">i</span><span class="p">));</span>
+<a id="__codelineno-16-65" name="__codelineno-16-65" href="#__codelineno-16-65"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-66" name="__codelineno-16-66" href="#__codelineno-16-66"></a>
+<a id="__codelineno-16-67" name="__codelineno-16-67" href="#__codelineno-16-67"></a><span class="w">    </span><span class="cm">/* 前順走査 */</span>
+<a id="__codelineno-16-68" name="__codelineno-16-68" href="#__codelineno-16-68"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-69" name="__codelineno-16-69" href="#__codelineno-16-69"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-16-70" name="__codelineno-16-70" href="#__codelineno-16-70"></a><span class="w">        </span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;pre&quot;</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-16-71" name="__codelineno-16-71" href="#__codelineno-16-71"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-16-72" name="__codelineno-16-72" href="#__codelineno-16-72"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-73" name="__codelineno-16-73" href="#__codelineno-16-73"></a>
+<a id="__codelineno-16-74" name="__codelineno-16-74" href="#__codelineno-16-74"></a><span class="w">    </span><span class="cm">/* 中順走査 */</span>
+<a id="__codelineno-16-75" name="__codelineno-16-75" href="#__codelineno-16-75"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="nf">inOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-76" name="__codelineno-16-76" href="#__codelineno-16-76"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-16-77" name="__codelineno-16-77" href="#__codelineno-16-77"></a><span class="w">        </span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;in&quot;</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-16-78" name="__codelineno-16-78" href="#__codelineno-16-78"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-16-79" name="__codelineno-16-79" href="#__codelineno-16-79"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-80" name="__codelineno-16-80" href="#__codelineno-16-80"></a>
+<a id="__codelineno-16-81" name="__codelineno-16-81" href="#__codelineno-16-81"></a><span class="w">    </span><span class="cm">/* 後順走査 */</span>
+<a id="__codelineno-16-82" name="__codelineno-16-82" href="#__codelineno-16-82"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="nf">postOrder</span><span class="p">()</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-83" name="__codelineno-16-83" href="#__codelineno-16-83"></a><span class="w">        </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">res</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-16-84" name="__codelineno-16-84" href="#__codelineno-16-84"></a><span class="w">        </span><span class="n">dfs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="w"> </span><span class="s">&quot;post&quot;</span><span class="p">,</span><span class="w"> </span><span class="n">res</span><span class="p">);</span>
+<a id="__codelineno-16-85" name="__codelineno-16-85" href="#__codelineno-16-85"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">res</span><span class="p">;</span>
+<a id="__codelineno-16-86" name="__codelineno-16-86" href="#__codelineno-16-86"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-87" name="__codelineno-16-87" href="#__codelineno-16-87"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_binary_tree.cs</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">ArrayBinaryTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_binary_tree.go</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">arrayBinaryTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_binary_tree.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">ArrayBinaryTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_binary_tree.js</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">ArrayBinaryTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_binary_tree.ts</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">ArrayBinaryTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_binary_tree.dart</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ArrayBinaryTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_binary_tree.rs</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ArrayBinaryTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_binary_tree.c</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ArrayBinaryTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_binary_tree.kt</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">ArrayBinaryTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_binary_tree.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">ArrayBinaryTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">array_binary_tree.zig</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">ArrayBinaryTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h2 id="733">7.3.3 &nbsp; 利点と制限<a class="headerlink" href="#733" title="Permanent link">&para;</a></h2>
+<p>二分木の配列表現には以下の利点があります：</p>
+<ul>
+<li>配列は連続したメモリ空間に格納されるため、キャッシュフレンドリーで、より高速なアクセスと探索が可能です。</li>
+<li>ポインタを格納する必要がないため、スペースを節約できます。</li>
+<li>ノードへのランダムアクセスが可能です。</li>
+</ul>
+<p>しかし、配列表現にはいくつかの制限もあります：</p>
+<ul>
+<li>配列格納には連続したメモリ空間が必要なため、大量のデータを持つ木の格納には適していません。</li>
+<li>ノードの追加や削除には配列の挿入や削除操作が必要で、効率が低くなります。</li>
+<li>二分木に多くの<code>None</code>値がある場合、配列に含まれるノードデータの割合が低くなり、空間利用率が低下します。</li>
+</ul>
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+    <span>日本語版審閱者を募集しています！詳細は <a href="https://github.com/krahets/hello-algo/blob/main/ja/CONTRIBUTING.md">CONTRIBUTING.md</a> を参照してください。</span>
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+        </aside>
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+      </label>
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+    
+    
+    <input class="md-option" data-md-color-media="" data-md-color-scheme="slate" data-md-color-primary="black" data-md-color-accent="teal"  aria-label="ライトモード"  type="radio" name="__palette" id="__palette_1">
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+      </label>
+    
+  
+</form>
+      
+    
+    
+      <script>var media,input,key,value,palette=__md_get("__palette");if(palette&&palette.color){"(prefers-color-scheme)"===palette.color.media&&(media=matchMedia("(prefers-color-scheme: light)"),input=document.querySelector(media.matches?"[data-md-color-media='(prefers-color-scheme: light)']":"[data-md-color-media='(prefers-color-scheme: dark)']"),palette.color.media=input.getAttribute("data-md-color-media"),palette.color.scheme=input.getAttribute("data-md-color-scheme"),palette.color.primary=input.getAttribute("data-md-color-primary"),palette.color.accent=input.getAttribute("data-md-color-accent"));for([key,value]of Object.entries(palette.color))document.body.setAttribute("data-md-color-"+key,value)}</script>
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+    <div class="md-select__inner">
+      <ul class="md-select__list">
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+          <li class="md-select__item">
+            <a href="/chapter_tree/avl_tree/" hreflang="zh" class="md-select__link">
+              简体中文
+            </a>
+          </li>
+        
+          <li class="md-select__item">
+            <a href="/zh-hant/chapter_tree/avl_tree/" hreflang="zh-Hant" class="md-select__link">
+              繁體中文
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+          </li>
+        
+          <li class="md-select__item">
+            <a href="/en/chapter_tree/avl_tree/" hreflang="en" class="md-select__link">
+              English
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+  <label class="md-search__overlay" for="__search"></label>
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+      <div class="md-search__scrollwrap" data-md-scrollfix>
+        <div class="md-search-result" data-md-component="search-result">
+          <div class="md-search-result__meta">
+            検索を初期化
+          </div>
+          <ol class="md-search-result__list" role="presentation"></ol>
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+      </div>
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+  </div>
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+    
+    
+      <div class="md-header__source">
+        <a href="https://github.com/krahets/hello-algo" title="リポジトリへ" class="md-source" data-md-component="source">
+  <div class="md-source__icon md-icon">
+    
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 496 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"/></svg>
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+            はじめに
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+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_2" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_preface/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M21 4H3a2 2 0 0 0-2 2v13a2 2 0 0 0 2 2h18a2 2 0 0 0 2-2V6a2 2 0 0 0-2-2M3 19V6h8v13H3m18 0h-8V6h8v13m-7-9.5h6V11h-6V9.5m0 2.5h6v1.5h-6V12m0 2.5h6V16h-6v-1.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 0 章 &nbsp; 前書き
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_2" id="__nav_2_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_2_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_2">
+            <span class="md-nav__icon md-icon"></span>
+            第 0 章 &nbsp; 前書き
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/about_the_book/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.1 &nbsp; この本について
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/suggestions/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.2 &nbsp; 本書の使い方
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_introduction/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#751-avl" class="md-nav__link">
+    <span class="md-ellipsis">
+      7.5.1 &nbsp; AVL木の一般的な用語
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="7.5.1   AVL木の一般的な用語">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; ノードの高さ
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; ノードの平衡因子
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#752-avl" class="md-nav__link">
+    <span class="md-ellipsis">
+      7.5.2 &nbsp; AVL木の回転
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="7.5.2   AVL木の回転">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1_1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 右回転
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2_1" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; 左回転
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#3" class="md-nav__link">
+    <span class="md-ellipsis">
+      3. &nbsp; 左右回転
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#4" class="md-nav__link">
+    <span class="md-ellipsis">
+      4. &nbsp; 右左回転
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#5" class="md-nav__link">
+    <span class="md-ellipsis">
+      5. &nbsp; 回転の選択
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#753-avl" class="md-nav__link">
+    <span class="md-ellipsis">
+      7.5.3 &nbsp; AVL木の一般的な操作
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="7.5.3   AVL木の一般的な操作">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1_2" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; ノードの挿入
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2_2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; ノードの削除
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#3_1" class="md-nav__link">
+    <span class="md-ellipsis">
+      3. &nbsp; ノードの検索
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#754-avl" class="md-nav__link">
+    <span class="md-ellipsis">
+      7.5.4 &nbsp; AVL木の典型的な応用
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_19" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_reference/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9 3v15h3V3H9m3 2 4 13 3-1-4-13-3 1M5 5v13h3V5H5M3 19v2h18v-2H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    参考文献
+  </span>
+  
+
+            </a>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_19_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_19">
+            <span class="md-nav__icon md-icon"></span>
+            参考文献
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+  </ul>
+</nav>
+                  </div>
+                </div>
+              </div>
+            
+            
+              
+              <div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
+                <div class="md-sidebar__scrollwrap">
+                  <div class="md-sidebar__inner">
+                    
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#751-avl" class="md-nav__link">
+    <span class="md-ellipsis">
+      7.5.1 &nbsp; AVL木の一般的な用語
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="7.5.1   AVL木の一般的な用語">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; ノードの高さ
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; ノードの平衡因子
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#752-avl" class="md-nav__link">
+    <span class="md-ellipsis">
+      7.5.2 &nbsp; AVL木の回転
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="7.5.2   AVL木の回転">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1_1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 右回転
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2_1" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; 左回転
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#3" class="md-nav__link">
+    <span class="md-ellipsis">
+      3. &nbsp; 左右回転
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#4" class="md-nav__link">
+    <span class="md-ellipsis">
+      4. &nbsp; 右左回転
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#5" class="md-nav__link">
+    <span class="md-ellipsis">
+      5. &nbsp; 回転の選択
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#753-avl" class="md-nav__link">
+    <span class="md-ellipsis">
+      7.5.3 &nbsp; AVL木の一般的な操作
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="7.5.3   AVL木の一般的な操作">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1_2" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; ノードの挿入
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2_2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; ノードの削除
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#3_1" class="md-nav__link">
+    <span class="md-ellipsis">
+      3. &nbsp; ノードの検索
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#754-avl" class="md-nav__link">
+    <span class="md-ellipsis">
+      7.5.4 &nbsp; AVL木の典型的な応用
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+                  </div>
+                </div>
+              </div>
+            
+          
+          
+            <div class="md-content" data-md-component="content">
+              <article class="md-content__inner md-typeset">
+                
+                  <!-- Tags -->
+
+
+<!-- Actions -->
+<!-- Actions -->
+
+
+  <!-- Edit button -->
+  
+    <a
+      href="https://github.com/krahets/hello-algo/tree/main/ja/docs/chapter_tree/avl_tree.md"
+      title="編集"
+      class="md-content__button md-icon"
+    >
+      
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
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+<h1 id="75-avl">7.5 &nbsp; AVL木 *<a class="headerlink" href="#75-avl" title="Permanent link">&para;</a></h1>
+<p>「二分探索木」の節では、複数の挿入と削除の後、二分探索木が連結リストに退化する可能性があることを述べました。このような場合、すべての操作の時間計算量が<span class="arithmatex">\(O(\log n)\)</span>から<span class="arithmatex">\(O(n)\)</span>に悪化します。</p>
+<p>下図に示すように、2つのノード削除操作の後、この二分探索木は連結リストに退化します。</p>
+<p><a class="glightbox" href="../avl_tree.assets/avltree_degradation_from_removing_node.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="ノード削除後のAVL木の退化" class="animation-figure" src="../avl_tree.assets/avltree_degradation_from_removing_node.png" /></a></p>
+<p align="center"> 図 7-24 &nbsp; ノード削除後のAVL木の退化 </p>
+
+<p>例えば、下図に示す完全二分木では、2つのノードを挿入した後、木が左に大きく傾き、検索操作の時間計算量も悪化します。</p>
+<p><a class="glightbox" href="../avl_tree.assets/avltree_degradation_from_inserting_node.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="ノード挿入後のAVL木の退化" class="animation-figure" src="../avl_tree.assets/avltree_degradation_from_inserting_node.png" /></a></p>
+<p align="center"> 図 7-25 &nbsp; ノード挿入後のAVL木の退化 </p>
+
+<p>1962年、G. M. Adelson-VelskyとE. M. Landisが論文「An algorithm for the organization of information」で<u>AVL木</u>を提案しました。この論文では、ノードの継続的な追加と削除の後もAVL木が退化しないことを保証する一連の操作について詳述し、さまざまな操作の時間計算量を<span class="arithmatex">\(O(\log n)\)</span>レベルに維持しました。つまり、頻繁な追加、削除、検索、変更が必要なシナリオで、AVL木は常に効率的なデータ操作性能を維持でき、大きな応用価値があります。</p>
+<h2 id="751-avl">7.5.1 &nbsp; AVL木の一般的な用語<a class="headerlink" href="#751-avl" title="Permanent link">&para;</a></h2>
+<p>AVL木は二分探索木でありかつ平衡二分木でもあり、これら2つの種類の二分木のすべての性質を満たしているため、<u>平衡二分探索木</u>です。</p>
+<h3 id="1">1. &nbsp; ノードの高さ<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<p>AVL木に関連する操作ではノードの高さを取得する必要があるため、ノードクラスに<code>height</code>変数を追加する必要があります：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:14"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><input id="__tabbed_1_14" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label><label for="__tabbed_1_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">TreeNode</span><span class="p">:</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;AVL木ノード&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">val</span>                 <span class="c1"># ノード値</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">height</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">0</span>                <span class="c1"># ノードの高さ</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">left</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span>   <span class="c1"># 左の子への参照</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">right</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span>  <span class="c1"># 右の子への参照</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* AVL木ノード */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="k">struct</span><span class="w"> </span><span class="nc">TreeNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">{};</span><span class="w">          </span><span class="c1">// ノード値</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">height</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span><span class="w">     </span><span class="c1">// ノードの高さ</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">left</span><span class="p">{};</span><span class="w">   </span><span class="c1">// 左の子</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">right</span><span class="p">{};</span><span class="w">  </span><span class="c1">// 右の子</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="n">TreeNode</span><span class="p">()</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">default</span><span class="p">;</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="k">explicit</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">x</span><span class="p">)</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">x</span><span class="p">){}</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="p">};</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* AVL木ノード */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kd">class</span> <span class="nc">TreeNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w">        </span><span class="c1">// ノード値</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">height</span><span class="p">;</span><span class="w">     </span><span class="c1">// ノードの高さ</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">left</span><span class="p">;</span><span class="w">  </span><span class="c1">// 左の子</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">right</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右の子</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="kd">public</span><span class="w"> </span><span class="nf">TreeNode</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">x</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">x</span><span class="p">;</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* AVL木ノード */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="k">class</span><span class="w"> </span><span class="nf">TreeNode</span><span class="p">(</span><span class="kt">int?</span><span class="w"> </span><span class="n">x</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int?</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">x</span><span class="p">;</span><span class="w">    </span><span class="c1">// ノード値</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">height</span><span class="p">;</span><span class="w">      </span><span class="c1">// ノードの高さ</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">left</span><span class="p">;</span><span class="w">  </span><span class="c1">// 左の子への参照</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">right</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右の子への参照</span>
+<a id="__codelineno-3-7" name="__codelineno-3-7" href="#__codelineno-3-7"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* AVL木ノード */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">type</span><span class="w"> </span><span class="nx">TreeNode</span><span class="w"> </span><span class="kd">struct</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="nx">Val</span><span class="w">    </span><span class="kt">int</span><span class="w">       </span><span class="c1">// ノード値</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="nx">Height</span><span class="w"> </span><span class="kt">int</span><span class="w">       </span><span class="c1">// ノードの高さ</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w">    </span><span class="nx">Left</span><span class="w">   </span><span class="o">*</span><span class="nx">TreeNode</span><span class="w"> </span><span class="c1">// 左の子への参照</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="w">    </span><span class="nx">Right</span><span class="w">  </span><span class="o">*</span><span class="nx">TreeNode</span><span class="w"> </span><span class="c1">// 右の子への参照</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* AVL木ノード */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">TreeNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">val</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="c1">// ノード値</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">height</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="c1">// ノードの高さ</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">left</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">?</span><span class="w"> </span><span class="c1">// 左の子</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">right</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">?</span><span class="w"> </span><span class="c1">// 右の子</span>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w">    </span><span class="kd">init</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w">        </span><span class="n">val</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">x</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="w">        </span><span class="n">height</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="mi">0</span>
+<a id="__codelineno-5-11" name="__codelineno-5-11" href="#__codelineno-5-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-12" name="__codelineno-5-12" href="#__codelineno-5-12"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* AVL木ノード */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">TreeNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w">    </span><span class="nx">val</span><span class="p">;</span><span class="w"> </span><span class="c1">// ノード値</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">    </span><span class="nx">height</span><span class="p">;</span><span class="w"> </span><span class="c1">// ノードの高さ</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">    </span><span class="nx">left</span><span class="p">;</span><span class="w"> </span><span class="c1">// 左の子ポインタ</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">    </span><span class="nx">right</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右の子ポインタ</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">(</span><span class="nx">val</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="p">,</span><span class="w"> </span><span class="nx">height</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="nx">val</span><span class="p">;</span>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">height</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">height</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="nx">height</span><span class="p">;</span>
+<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">left</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="nx">left</span><span class="p">;</span>
+<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">right</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="nx">right</span><span class="p">;</span>
+<a id="__codelineno-6-12" name="__codelineno-6-12" href="#__codelineno-6-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-13" name="__codelineno-6-13" href="#__codelineno-6-13"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* AVL木ノード */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">TreeNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w">    </span><span class="nx">val</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">;</span><span class="w">            </span><span class="c1">// ノード値</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">    </span><span class="nx">height</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">;</span><span class="w">         </span><span class="c1">// ノードの高さ</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">    </span><span class="nx">left</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span><span class="w">  </span><span class="c1">// 左の子ポインタ</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a><span class="w">    </span><span class="nx">right</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右の子ポインタ</span>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">(</span><span class="nx">val?</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="nx">height?</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="nx">left?</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="nx">right?</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">0</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">val</span><span class="p">;</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">height</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">height</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">0</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">height</span><span class="p">;</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">left</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">null</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">left</span><span class="p">;</span>
+<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">right</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">null</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">right</span><span class="p">;</span>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-13" name="__codelineno-7-13" href="#__codelineno-7-13"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* AVL木ノード */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">TreeNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w">         </span><span class="c1">// ノード値</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">height</span><span class="p">;</span><span class="w">      </span><span class="c1">// ノードの高さ</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">  </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">left</span><span class="p">;</span><span class="w">  </span><span class="c1">// 左の子</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w">  </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">right</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右の子</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="w">  </span><span class="n">TreeNode</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="p">[</span><span class="k">this</span><span class="p">.</span><span class="n">height</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="p">,</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">right</span><span class="p">]);</span>
+<a id="__codelineno-8-8" name="__codelineno-8-8" href="#__codelineno-8-8"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="k">use</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">rc</span><span class="p">::</span><span class="n">Rc</span><span class="p">;</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">use</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">cell</span><span class="p">::</span><span class="n">RefCell</span><span class="p">;</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="cm">/* AVL木ノード */</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="k">struct</span><span class="w"> </span><span class="nc">TreeNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">    </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span><span class="w">                               </span><span class="c1">// ノード値</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">    </span><span class="n">height</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span><span class="w">                            </span><span class="c1">// ノードの高さ</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w">    </span><span class="n">left</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;</span><span class="p">,</span><span class="w">    </span><span class="c1">// 左の子</span>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="w">    </span><span class="n">right</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;</span><span class="p">,</span><span class="w">   </span><span class="c1">// 右の子</span>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a><span class="p">}</span>
+<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a>
+<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="k">impl</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">new</span><span class="p">(</span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nc">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="bp">Self</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="w">        </span><span class="n">Rc</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="n">RefCell</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="bp">Self</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="w">            </span><span class="n">val</span><span class="p">,</span>
+<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="w">            </span><span class="n">height</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">,</span>
+<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="w">            </span><span class="n">left</span><span class="p">:</span><span class="w"> </span><span class="nb">None</span><span class="p">,</span>
+<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="w">            </span><span class="n">right</span><span class="p">:</span><span class="w"> </span><span class="nb">None</span>
+<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="w">        </span><span class="p">}))</span>
+<a id="__codelineno-9-21" name="__codelineno-9-21" href="#__codelineno-9-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-22" name="__codelineno-9-22" href="#__codelineno-9-22"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* AVL木ノード */</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="nc">TreeNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">height</span><span class="p">;</span>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w">    </span><span class="k">struct</span><span class="w"> </span><span class="nc">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">left</span><span class="p">;</span>
+<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w">    </span><span class="k">struct</span><span class="w"> </span><span class="nc">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="p">}</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">;</span>
+<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a>
+<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">newTreeNode</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a>
+<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="w">    </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">TreeNode</span><span class="p">));</span>
+<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="w">    </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a><span class="w">    </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">height</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="w">    </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
+<a id="__codelineno-10-17" name="__codelineno-10-17" href="#__codelineno-10-17"></a><span class="w">    </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
+<a id="__codelineno-10-18" name="__codelineno-10-18" href="#__codelineno-10-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-10-19" name="__codelineno-10-19" href="#__codelineno-10-19"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* AVL木ノード */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">TreeNode</span><span class="p">(</span><span class="kd">val</span><span class="w"> </span><span class="nv">_val</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w">  </span><span class="c1">// ノード値</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">height</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="m">0</span><span class="w">          </span><span class="c1">// ノードの高さ</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">left</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode? </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="w">   </span><span class="c1">// 左の子</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">right</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode? </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="w">  </span><span class="c1">// 右の子</span>
+<a id="__codelineno-11-6" name="__codelineno-11-6" href="#__codelineno-11-6"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>「ノードの高さ」とは、そのノードから最も遠い葉ノードまでの距離、つまり通過する「辺」の数を指します。重要なのは、葉ノードの高さは<span class="arithmatex">\(0\)</span>で、nullノードの高さは<span class="arithmatex">\(-1\)</span>であることです。ノードの高さを取得し、更新するための2つのユーティリティ関数を作成します：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:14"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><input id="__tabbed_2_14" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label><label for="__tabbed_2_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.py</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">height</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">node</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;ノードの高さを取得&quot;&quot;&quot;</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a>    <span class="c1"># 空ノードの高さは-1、葉ノードの高さは0</span>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a>    <span class="k">if</span> <span class="n">node</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a>        <span class="k">return</span> <span class="n">node</span><span class="o">.</span><span class="n">height</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a>    <span class="k">return</span> <span class="o">-</span><span class="mi">1</span>
+<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a>
+<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="k">def</span><span class="w"> </span><span class="nf">update_height</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">node</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">):</span>
+<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;ノードの高さを更新&quot;&quot;&quot;</span>
+<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a>    <span class="c1"># ノードの高さ = 最も高い部分木の高さ + 1</span>
+<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a>    <span class="n">node</span><span class="o">.</span><span class="n">height</span> <span class="o">=</span> <span class="nb">max</span><span class="p">([</span><span class="bp">self</span><span class="o">.</span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="p">),</span> <span class="bp">self</span><span class="o">.</span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">)])</span> <span class="o">+</span> <span class="mi">1</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.cpp</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* ノードの高さを取得 */</span>
+<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">height</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="c1">// 空ノードの高さは-1、葉ノードの高さは0</span>
+<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="mi">-1</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">height</span><span class="p">;</span>
+<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="p">}</span>
+<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a>
+<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="cm">/* ノードの高さを更新 */</span>
+<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="kt">void</span><span class="w"> </span><span class="nf">updateHeight</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w">    </span><span class="c1">// ノードの高さ = 最も高い部分木の高さ + 1</span>
+<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="w">    </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">height</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">max</span><span class="p">(</span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">),</span><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">))</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.java</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* ノードの高さを取得 */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">height</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="c1">// 空ノードの高さは -1、葉ノードの高さは 0</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">height</span><span class="p">;</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="p">}</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="cm">/* ノードの高さを更新 */</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="kt">void</span><span class="w"> </span><span class="nf">updateHeight</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w">    </span><span class="c1">// ノードの高さは最も高い部分木の高さ + 1</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w">    </span><span class="n">node</span><span class="p">.</span><span class="na">height</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">Math</span><span class="p">.</span><span class="na">max</span><span class="p">(</span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="p">),</span><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="p">))</span><span class="w"> </span><span class="o">+</span><span class="w"> </span><span class="mi">1</span><span class="p">;</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.cs</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Height</span><span class="p">}</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">UpdateHeight</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.go</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">aVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">height</span><span class="p">}</span>
+<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a>
+<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">aVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">updateHeight</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">height</span><span class="p">}</span>
+<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a>
+<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">updateHeight</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.js</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">height</span><span class="p">}</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a>
+<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">updateHeight</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.ts</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">height</span><span class="p">}</span>
+<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a>
+<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">updateHeight</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.dart</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">height</span><span class="p">}</span>
+<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">updateHeight</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.rs</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">height</span><span class="p">}</span>
+<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a>
+<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">update_height</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.c</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">height</span><span class="p">}</span>
+<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a>
+<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">updateHeight</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.kt</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">height</span><span class="p">}</span>
+<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a>
+<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">updateHeight</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">height</span><span class="p">}</span>
+<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a>
+<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">update_height</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.zig</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">height</span><span class="p">}</span>
+<a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a>
+<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">updateHeight</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h3 id="2">2. &nbsp; ノードの平衡因子<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
+<p>ノードの<u>平衡因子</u>は、そのノードの左部分木の高さから右部分木の高さを引いた値として定義され、nullノードの平衡因子は<span class="arithmatex">\(0\)</span>として定義されます。後で使いやすくするため、ノードの平衡因子を取得する機能も関数にカプセル化します：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="3:14"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><input id="__tabbed_3_14" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label><label for="__tabbed_3_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.py</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">balance_factor</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">node</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">int</span><span class="p">:</span>
+<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;バランス因子を取得&quot;&quot;&quot;</span>
+<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a>    <span class="c1"># 空ノードのバランス因子は0</span>
+<a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a>    <span class="k">if</span> <span class="n">node</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a>        <span class="k">return</span> <span class="mi">0</span>
+<a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a>    <span class="c1"># ノードのバランス因子 = 左部分木の高さ - 右部分木の高さ</span>
+<a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a>    <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="p">)</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.cpp</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="cm">/* 平衡因子を取得 */</span>
+<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">balanceFactor</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w">    </span><span class="c1">// 空ノードの平衡因子は0</span>
+<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span>
+<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a><span class="w">    </span><span class="c1">// ノードの平衡因子 = 左部分木の高さ - 右部分木の高さ</span>
+<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.java</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* 平衡因子を取得 */</span>
+<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="kt">int</span><span class="w"> </span><span class="nf">balanceFactor</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w">    </span><span class="c1">// 空ノードの平衡因子は 0</span>
+<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
+<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="w">    </span><span class="c1">// ノードの平衡因子 = 左部分木の高さ - 右部分木の高さ</span>
+<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="p">)</span><span class="w"> </span><span class="o">-</span><span class="w"> </span><span class="n">height</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="p">);</span>
+<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.cs</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">BalanceFactor</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.go</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">aVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">balanceFactor</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.swift</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">balanceFactor</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.js</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">balanceFactor</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.ts</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">balanceFactor</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.dart</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">balanceFactor</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.rs</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">balance_factor</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.c</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">balanceFactor</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.kt</span><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">balanceFactor</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">balance_factor</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.zig</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">balanceFactor</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<div class="admonition tip">
+<p class="admonition-title">Tip</p>
+<p>平衡因子を<span class="arithmatex">\(f\)</span>とすると、AVL木の任意のノードの平衡因子は<span class="arithmatex">\(-1 \le f \le 1\)</span>を満たします。</p>
+</div>
+<h2 id="752-avl">7.5.2 &nbsp; AVL木の回転<a class="headerlink" href="#752-avl" title="Permanent link">&para;</a></h2>
+<p>AVL木の特徴的な機能は「回転」操作で、これは二分木の中順探索シーケンスに影響を与えることなく、不平衡なノードのバランスを回復できます。つまり、<strong>回転操作は「二分探索木」の性質を維持しながら、木を「平衡二分木」に戻すことができます</strong>。</p>
+<p>絶対平衡因子が<span class="arithmatex">\(&gt; 1\)</span>のノードを「不平衡ノード」と呼びます。不平衡のタイプに応じて、4種類の回転があります：右回転、左回転、右左回転、左右回転です。以下、これらの回転操作について詳しく説明します。</p>
+<h3 id="1_1">1. &nbsp; 右回転<a class="headerlink" href="#1_1" title="Permanent link">&para;</a></h3>
+<p>下図に示すように、二分木で下から上への最初の不平衡ノードは「ノード3」です。この不平衡ノードを根とする部分木に焦点を当て、これを<code>node</code>とし、その左の子を<code>child</code>として、「右回転」を実行します。右回転後、部分木は再びバランスが取れ、同時に二分探索木の性質も維持されます。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="4:4"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">&lt;1&gt;</label><label for="__tabbed_4_2">&lt;2&gt;</label><label for="__tabbed_4_3">&lt;3&gt;</label><label for="__tabbed_4_4">&lt;4&gt;</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<p><a class="glightbox" href="../avl_tree.assets/avltree_right_rotate_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="右回転の手順" class="animation-figure" src="../avl_tree.assets/avltree_right_rotate_step1.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../avl_tree.assets/avltree_right_rotate_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="avltree_right_rotate_step2" class="animation-figure" src="../avl_tree.assets/avltree_right_rotate_step2.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../avl_tree.assets/avltree_right_rotate_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="avltree_right_rotate_step3" class="animation-figure" src="../avl_tree.assets/avltree_right_rotate_step3.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../avl_tree.assets/avltree_right_rotate_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="avltree_right_rotate_step4" class="animation-figure" src="../avl_tree.assets/avltree_right_rotate_step4.png" /></a></p>
+</div>
+</div>
+</div>
+<p align="center"> 図 7-26 &nbsp; 右回転の手順 </p>
+
+<p>下図に示すように、<code>child</code>ノードに右の子（<code>grand_child</code>と表記）がある場合、右回転で手順を追加する必要があります：<code>grand_child</code>を<code>node</code>の左の子に設定します。</p>
+<p><a class="glightbox" href="../avl_tree.assets/avltree_right_rotate_with_grandchild.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="grand_childがある右回転" class="animation-figure" src="../avl_tree.assets/avltree_right_rotate_with_grandchild.png" /></a></p>
+<p align="center"> 図 7-27 &nbsp; grand_childがある右回転 </p>
+
+<p>「右回転」は比喩的な用語で、実際にはノードポインタを変更することで実現されます。以下のコードで示されます：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="5:14"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><input id="__tabbed_5_7" name="__tabbed_5" type="radio" /><input id="__tabbed_5_8" name="__tabbed_5" type="radio" /><input id="__tabbed_5_9" name="__tabbed_5" type="radio" /><input id="__tabbed_5_10" name="__tabbed_5" type="radio" /><input id="__tabbed_5_11" name="__tabbed_5" type="radio" /><input id="__tabbed_5_12" name="__tabbed_5" type="radio" /><input id="__tabbed_5_13" name="__tabbed_5" type="radio" /><input id="__tabbed_5_14" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">Python</label><label for="__tabbed_5_2">C++</label><label for="__tabbed_5_3">Java</label><label for="__tabbed_5_4">C#</label><label for="__tabbed_5_5">Go</label><label for="__tabbed_5_6">Swift</label><label for="__tabbed_5_7">JS</label><label for="__tabbed_5_8">TS</label><label for="__tabbed_5_9">Dart</label><label for="__tabbed_5_10">Rust</label><label for="__tabbed_5_11">C</label><label for="__tabbed_5_12">Kotlin</label><label for="__tabbed_5_13">Ruby</label><label for="__tabbed_5_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.py</span><pre><span></span><code><a id="__codelineno-42-1" name="__codelineno-42-1" href="#__codelineno-42-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">right_rotate</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">node</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-42-2" name="__codelineno-42-2" href="#__codelineno-42-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;右回転操作&quot;&quot;&quot;</span>
+<a id="__codelineno-42-3" name="__codelineno-42-3" href="#__codelineno-42-3"></a>    <span class="n">child</span> <span class="o">=</span> <span class="n">node</span><span class="o">.</span><span class="n">left</span>
+<a id="__codelineno-42-4" name="__codelineno-42-4" href="#__codelineno-42-4"></a>    <span class="n">grand_child</span> <span class="o">=</span> <span class="n">child</span><span class="o">.</span><span class="n">right</span>
+<a id="__codelineno-42-5" name="__codelineno-42-5" href="#__codelineno-42-5"></a>    <span class="c1"># childを中心にnodeを右に回転</span>
+<a id="__codelineno-42-6" name="__codelineno-42-6" href="#__codelineno-42-6"></a>    <span class="n">child</span><span class="o">.</span><span class="n">right</span> <span class="o">=</span> <span class="n">node</span>
+<a id="__codelineno-42-7" name="__codelineno-42-7" href="#__codelineno-42-7"></a>    <span class="n">node</span><span class="o">.</span><span class="n">left</span> <span class="o">=</span> <span class="n">grand_child</span>
+<a id="__codelineno-42-8" name="__codelineno-42-8" href="#__codelineno-42-8"></a>    <span class="c1"># ノードの高さを更新</span>
+<a id="__codelineno-42-9" name="__codelineno-42-9" href="#__codelineno-42-9"></a>    <span class="bp">self</span><span class="o">.</span><span class="n">update_height</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
+<a id="__codelineno-42-10" name="__codelineno-42-10" href="#__codelineno-42-10"></a>    <span class="bp">self</span><span class="o">.</span><span class="n">update_height</span><span class="p">(</span><span class="n">child</span><span class="p">)</span>
+<a id="__codelineno-42-11" name="__codelineno-42-11" href="#__codelineno-42-11"></a>    <span class="c1"># 回転後の部分木のルートを返す</span>
+<a id="__codelineno-42-12" name="__codelineno-42-12" href="#__codelineno-42-12"></a>    <span class="k">return</span> <span class="n">child</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.cpp</span><pre><span></span><code><a id="__codelineno-43-1" name="__codelineno-43-1" href="#__codelineno-43-1"></a><span class="cm">/* 右回転操作 */</span>
+<a id="__codelineno-43-2" name="__codelineno-43-2" href="#__codelineno-43-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">rightRotate</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-43-3" name="__codelineno-43-3" href="#__codelineno-43-3"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">;</span>
+<a id="__codelineno-43-4" name="__codelineno-43-4" href="#__codelineno-43-4"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">grandChild</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-43-5" name="__codelineno-43-5" href="#__codelineno-43-5"></a><span class="w">    </span><span class="c1">// childを中心にnodeを右に回転</span>
+<a id="__codelineno-43-6" name="__codelineno-43-6" href="#__codelineno-43-6"></a><span class="w">    </span><span class="n">child</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-43-7" name="__codelineno-43-7" href="#__codelineno-43-7"></a><span class="w">    </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grandChild</span><span class="p">;</span>
+<a id="__codelineno-43-8" name="__codelineno-43-8" href="#__codelineno-43-8"></a><span class="w">    </span><span class="c1">// ノードの高さを更新</span>
+<a id="__codelineno-43-9" name="__codelineno-43-9" href="#__codelineno-43-9"></a><span class="w">    </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-43-10" name="__codelineno-43-10" href="#__codelineno-43-10"></a><span class="w">    </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">child</span><span class="p">);</span>
+<a id="__codelineno-43-11" name="__codelineno-43-11" href="#__codelineno-43-11"></a><span class="w">    </span><span class="c1">// 回転後の部分木のルートを返す</span>
+<a id="__codelineno-43-12" name="__codelineno-43-12" href="#__codelineno-43-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
+<a id="__codelineno-43-13" name="__codelineno-43-13" href="#__codelineno-43-13"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.java</span><pre><span></span><code><a id="__codelineno-44-1" name="__codelineno-44-1" href="#__codelineno-44-1"></a><span class="cm">/* 右回転操作 */</span>
+<a id="__codelineno-44-2" name="__codelineno-44-2" href="#__codelineno-44-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="nf">rightRotate</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-44-3" name="__codelineno-44-3" href="#__codelineno-44-3"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="p">;</span>
+<a id="__codelineno-44-4" name="__codelineno-44-4" href="#__codelineno-44-4"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">grandChild</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">.</span><span class="na">right</span><span class="p">;</span>
+<a id="__codelineno-44-5" name="__codelineno-44-5" href="#__codelineno-44-5"></a><span class="w">    </span><span class="c1">// child を軸として node を右に回転</span>
+<a id="__codelineno-44-6" name="__codelineno-44-6" href="#__codelineno-44-6"></a><span class="w">    </span><span class="n">child</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-44-7" name="__codelineno-44-7" href="#__codelineno-44-7"></a><span class="w">    </span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grandChild</span><span class="p">;</span>
+<a id="__codelineno-44-8" name="__codelineno-44-8" href="#__codelineno-44-8"></a><span class="w">    </span><span class="c1">// ノードの高さを更新</span>
+<a id="__codelineno-44-9" name="__codelineno-44-9" href="#__codelineno-44-9"></a><span class="w">    </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-44-10" name="__codelineno-44-10" href="#__codelineno-44-10"></a><span class="w">    </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">child</span><span class="p">);</span>
+<a id="__codelineno-44-11" name="__codelineno-44-11" href="#__codelineno-44-11"></a><span class="w">    </span><span class="c1">// 回転後の部分木の根を返す</span>
+<a id="__codelineno-44-12" name="__codelineno-44-12" href="#__codelineno-44-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
+<a id="__codelineno-44-13" name="__codelineno-44-13" href="#__codelineno-44-13"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.cs</span><pre><span></span><code><a id="__codelineno-45-1" name="__codelineno-45-1" href="#__codelineno-45-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">RightRotate</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.go</span><pre><span></span><code><a id="__codelineno-46-1" name="__codelineno-46-1" href="#__codelineno-46-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">aVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">rightRotate</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.swift</span><pre><span></span><code><a id="__codelineno-47-1" name="__codelineno-47-1" href="#__codelineno-47-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">rightRotate</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.js</span><pre><span></span><code><a id="__codelineno-48-1" name="__codelineno-48-1" href="#__codelineno-48-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">rightRotate</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.ts</span><pre><span></span><code><a id="__codelineno-49-1" name="__codelineno-49-1" href="#__codelineno-49-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">rightRotate</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.dart</span><pre><span></span><code><a id="__codelineno-50-1" name="__codelineno-50-1" href="#__codelineno-50-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">rightRotate</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.rs</span><pre><span></span><code><a id="__codelineno-51-1" name="__codelineno-51-1" href="#__codelineno-51-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">right_rotate</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.c</span><pre><span></span><code><a id="__codelineno-52-1" name="__codelineno-52-1" href="#__codelineno-52-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">rightRotate</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.kt</span><pre><span></span><code><a id="__codelineno-53-1" name="__codelineno-53-1" href="#__codelineno-53-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">rightRotate</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-54-1" name="__codelineno-54-1" href="#__codelineno-54-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">right_rotate</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.zig</span><pre><span></span><code><a id="__codelineno-55-1" name="__codelineno-55-1" href="#__codelineno-55-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">rightRotate</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h3 id="2_1">2. &nbsp; 左回転<a class="headerlink" href="#2_1" title="Permanent link">&para;</a></h3>
+<p>対応して、上記の不平衡二分木の「鏡像」を考慮すると、下図に示す「左回転」操作を実行する必要があります。</p>
+<p><a class="glightbox" href="../avl_tree.assets/avltree_left_rotate.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="左回転操作" class="animation-figure" src="../avl_tree.assets/avltree_left_rotate.png" /></a></p>
+<p align="center"> 図 7-28 &nbsp; 左回転操作 </p>
+
+<p>同様に、下図に示すように、<code>child</code>ノードに左の子（<code>grand_child</code>と表記）がある場合、左回転で手順を追加する必要があります：<code>grand_child</code>を<code>node</code>の右の子に設定します。</p>
+<p><a class="glightbox" href="../avl_tree.assets/avltree_left_rotate_with_grandchild.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="grand_childがある左回転" class="animation-figure" src="../avl_tree.assets/avltree_left_rotate_with_grandchild.png" /></a></p>
+<p align="center"> 図 7-29 &nbsp; grand_childがある左回転 </p>
+
+<p>**右回転と左回転の操作は論理的に対称であり、2つの対称的な不平衡タイプを解決します**ことが観察できます。対称性に基づいて、右回転の実装コードですべての<code>left</code>を<code>right</code>に、すべての<code>right</code>を<code>left</code>に置き換えることで、左回転の実装コードを得ることができます：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="6:14"><input checked="checked" id="__tabbed_6_1" name="__tabbed_6" type="radio" /><input id="__tabbed_6_2" name="__tabbed_6" type="radio" /><input id="__tabbed_6_3" name="__tabbed_6" type="radio" /><input id="__tabbed_6_4" name="__tabbed_6" type="radio" /><input id="__tabbed_6_5" name="__tabbed_6" type="radio" /><input id="__tabbed_6_6" name="__tabbed_6" type="radio" /><input id="__tabbed_6_7" name="__tabbed_6" type="radio" /><input id="__tabbed_6_8" name="__tabbed_6" type="radio" /><input id="__tabbed_6_9" name="__tabbed_6" type="radio" /><input id="__tabbed_6_10" name="__tabbed_6" type="radio" /><input id="__tabbed_6_11" name="__tabbed_6" type="radio" /><input id="__tabbed_6_12" name="__tabbed_6" type="radio" /><input id="__tabbed_6_13" name="__tabbed_6" type="radio" /><input id="__tabbed_6_14" name="__tabbed_6" type="radio" /><div class="tabbed-labels"><label for="__tabbed_6_1">Python</label><label for="__tabbed_6_2">C++</label><label for="__tabbed_6_3">Java</label><label for="__tabbed_6_4">C#</label><label for="__tabbed_6_5">Go</label><label for="__tabbed_6_6">Swift</label><label for="__tabbed_6_7">JS</label><label for="__tabbed_6_8">TS</label><label for="__tabbed_6_9">Dart</label><label for="__tabbed_6_10">Rust</label><label for="__tabbed_6_11">C</label><label for="__tabbed_6_12">Kotlin</label><label for="__tabbed_6_13">Ruby</label><label for="__tabbed_6_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.py</span><pre><span></span><code><a id="__codelineno-56-1" name="__codelineno-56-1" href="#__codelineno-56-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">left_rotate</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">node</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-56-2" name="__codelineno-56-2" href="#__codelineno-56-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;左回転操作&quot;&quot;&quot;</span>
+<a id="__codelineno-56-3" name="__codelineno-56-3" href="#__codelineno-56-3"></a>    <span class="n">child</span> <span class="o">=</span> <span class="n">node</span><span class="o">.</span><span class="n">right</span>
+<a id="__codelineno-56-4" name="__codelineno-56-4" href="#__codelineno-56-4"></a>    <span class="n">grand_child</span> <span class="o">=</span> <span class="n">child</span><span class="o">.</span><span class="n">left</span>
+<a id="__codelineno-56-5" name="__codelineno-56-5" href="#__codelineno-56-5"></a>    <span class="c1"># childを中心にnodeを左に回転</span>
+<a id="__codelineno-56-6" name="__codelineno-56-6" href="#__codelineno-56-6"></a>    <span class="n">child</span><span class="o">.</span><span class="n">left</span> <span class="o">=</span> <span class="n">node</span>
+<a id="__codelineno-56-7" name="__codelineno-56-7" href="#__codelineno-56-7"></a>    <span class="n">node</span><span class="o">.</span><span class="n">right</span> <span class="o">=</span> <span class="n">grand_child</span>
+<a id="__codelineno-56-8" name="__codelineno-56-8" href="#__codelineno-56-8"></a>    <span class="c1"># ノードの高さを更新</span>
+<a id="__codelineno-56-9" name="__codelineno-56-9" href="#__codelineno-56-9"></a>    <span class="bp">self</span><span class="o">.</span><span class="n">update_height</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
+<a id="__codelineno-56-10" name="__codelineno-56-10" href="#__codelineno-56-10"></a>    <span class="bp">self</span><span class="o">.</span><span class="n">update_height</span><span class="p">(</span><span class="n">child</span><span class="p">)</span>
+<a id="__codelineno-56-11" name="__codelineno-56-11" href="#__codelineno-56-11"></a>    <span class="c1"># 回転後の部分木のルートを返す</span>
+<a id="__codelineno-56-12" name="__codelineno-56-12" href="#__codelineno-56-12"></a>    <span class="k">return</span> <span class="n">child</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.cpp</span><pre><span></span><code><a id="__codelineno-57-1" name="__codelineno-57-1" href="#__codelineno-57-1"></a><span class="cm">/* 左回転操作 */</span>
+<a id="__codelineno-57-2" name="__codelineno-57-2" href="#__codelineno-57-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">leftRotate</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-57-3" name="__codelineno-57-3" href="#__codelineno-57-3"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-57-4" name="__codelineno-57-4" href="#__codelineno-57-4"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">grandChild</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">;</span>
+<a id="__codelineno-57-5" name="__codelineno-57-5" href="#__codelineno-57-5"></a><span class="w">    </span><span class="c1">// childを中心にnodeを左に回転</span>
+<a id="__codelineno-57-6" name="__codelineno-57-6" href="#__codelineno-57-6"></a><span class="w">    </span><span class="n">child</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-57-7" name="__codelineno-57-7" href="#__codelineno-57-7"></a><span class="w">    </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grandChild</span><span class="p">;</span>
+<a id="__codelineno-57-8" name="__codelineno-57-8" href="#__codelineno-57-8"></a><span class="w">    </span><span class="c1">// ノードの高さを更新</span>
+<a id="__codelineno-57-9" name="__codelineno-57-9" href="#__codelineno-57-9"></a><span class="w">    </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-57-10" name="__codelineno-57-10" href="#__codelineno-57-10"></a><span class="w">    </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">child</span><span class="p">);</span>
+<a id="__codelineno-57-11" name="__codelineno-57-11" href="#__codelineno-57-11"></a><span class="w">    </span><span class="c1">// 回転後の部分木のルートを返す</span>
+<a id="__codelineno-57-12" name="__codelineno-57-12" href="#__codelineno-57-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
+<a id="__codelineno-57-13" name="__codelineno-57-13" href="#__codelineno-57-13"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.java</span><pre><span></span><code><a id="__codelineno-58-1" name="__codelineno-58-1" href="#__codelineno-58-1"></a><span class="cm">/* 左回転操作 */</span>
+<a id="__codelineno-58-2" name="__codelineno-58-2" href="#__codelineno-58-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="nf">leftRotate</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-58-3" name="__codelineno-58-3" href="#__codelineno-58-3"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="p">;</span>
+<a id="__codelineno-58-4" name="__codelineno-58-4" href="#__codelineno-58-4"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">grandChild</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">.</span><span class="na">left</span><span class="p">;</span>
+<a id="__codelineno-58-5" name="__codelineno-58-5" href="#__codelineno-58-5"></a><span class="w">    </span><span class="c1">// child を軸として node を左に回転</span>
+<a id="__codelineno-58-6" name="__codelineno-58-6" href="#__codelineno-58-6"></a><span class="w">    </span><span class="n">child</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-58-7" name="__codelineno-58-7" href="#__codelineno-58-7"></a><span class="w">    </span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">grandChild</span><span class="p">;</span>
+<a id="__codelineno-58-8" name="__codelineno-58-8" href="#__codelineno-58-8"></a><span class="w">    </span><span class="c1">// ノードの高さを更新</span>
+<a id="__codelineno-58-9" name="__codelineno-58-9" href="#__codelineno-58-9"></a><span class="w">    </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-58-10" name="__codelineno-58-10" href="#__codelineno-58-10"></a><span class="w">    </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">child</span><span class="p">);</span>
+<a id="__codelineno-58-11" name="__codelineno-58-11" href="#__codelineno-58-11"></a><span class="w">    </span><span class="c1">// 回転後の部分木の根を返す</span>
+<a id="__codelineno-58-12" name="__codelineno-58-12" href="#__codelineno-58-12"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
+<a id="__codelineno-58-13" name="__codelineno-58-13" href="#__codelineno-58-13"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.cs</span><pre><span></span><code><a id="__codelineno-59-1" name="__codelineno-59-1" href="#__codelineno-59-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">LeftRotate</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.go</span><pre><span></span><code><a id="__codelineno-60-1" name="__codelineno-60-1" href="#__codelineno-60-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">aVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">leftRotate</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.swift</span><pre><span></span><code><a id="__codelineno-61-1" name="__codelineno-61-1" href="#__codelineno-61-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">leftRotate</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.js</span><pre><span></span><code><a id="__codelineno-62-1" name="__codelineno-62-1" href="#__codelineno-62-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">leftRotate</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.ts</span><pre><span></span><code><a id="__codelineno-63-1" name="__codelineno-63-1" href="#__codelineno-63-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">leftRotate</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.dart</span><pre><span></span><code><a id="__codelineno-64-1" name="__codelineno-64-1" href="#__codelineno-64-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">leftRotate</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.rs</span><pre><span></span><code><a id="__codelineno-65-1" name="__codelineno-65-1" href="#__codelineno-65-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">left_rotate</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.c</span><pre><span></span><code><a id="__codelineno-66-1" name="__codelineno-66-1" href="#__codelineno-66-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">leftRotate</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.kt</span><pre><span></span><code><a id="__codelineno-67-1" name="__codelineno-67-1" href="#__codelineno-67-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">leftRotate</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-68-1" name="__codelineno-68-1" href="#__codelineno-68-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">left_rotate</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.zig</span><pre><span></span><code><a id="__codelineno-69-1" name="__codelineno-69-1" href="#__codelineno-69-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">leftRotate</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h3 id="3">3. &nbsp; 左右回転<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
+<p>下図に示す不平衡ノード3の場合、左回転または右回転のいずれかだけでは部分木のバランスを回復できません。この場合、まず<code>child</code>に対して「左回転」を実行し、次に<code>node</code>に対して「右回転」を実行する必要があります。</p>
+<p><a class="glightbox" href="../avl_tree.assets/avltree_left_right_rotate.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="左右回転" class="animation-figure" src="../avl_tree.assets/avltree_left_right_rotate.png" /></a></p>
+<p align="center"> 図 7-30 &nbsp; 左右回転 </p>
+
+<h3 id="4">4. &nbsp; 右左回転<a class="headerlink" href="#4" title="Permanent link">&para;</a></h3>
+<p>下図に示すように、上記の不平衡二分木の鏡像ケースでは、まず<code>child</code>に対して「右回転」を実行し、次に<code>node</code>に対して「左回転」を実行する必要があります。</p>
+<p><a class="glightbox" href="../avl_tree.assets/avltree_right_left_rotate.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="右左回転" class="animation-figure" src="../avl_tree.assets/avltree_right_left_rotate.png" /></a></p>
+<p align="center"> 図 7-31 &nbsp; 右左回転 </p>
+
+<h3 id="5">5. &nbsp; 回転の選択<a class="headerlink" href="#5" title="Permanent link">&para;</a></h3>
+<p>下図に示す4種類の不平衡は、それぞれ上記で説明したケースに対応し、右回転、左右回転、右左回転、左回転が必要です。</p>
+<p><a class="glightbox" href="../avl_tree.assets/avltree_rotation_cases.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="AVL木の4つの回転ケース" class="animation-figure" src="../avl_tree.assets/avltree_rotation_cases.png" /></a></p>
+<p align="center"> 図 7-32 &nbsp; AVL木の4つの回転ケース </p>
+
+<p>下表に示すように、不平衡ノードの平衡因子とその高い側の子の平衡因子の符号を判断することで、不平衡ノードが上記のどのケースに属するかを決定します。</p>
+<p align="center"> 表 7-3 &nbsp; 4つの回転ケースの選択条件 </p>
+
+<div class="center-table">
+<table>
+<thead>
+<tr>
+<th>不平衡ノードの平衡因子</th>
+<th>子ノードの平衡因子</th>
+<th>使用する回転方法</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td><span class="arithmatex">\(&gt; 1\)</span>（左に傾いた木）</td>
+<td><span class="arithmatex">\(\geq 0\)</span></td>
+<td>右回転</td>
+</tr>
+<tr>
+<td><span class="arithmatex">\(&gt; 1\)</span>（左に傾いた木）</td>
+<td><span class="arithmatex">\(&lt;0\)</span></td>
+<td>左回転してから右回転</td>
+</tr>
+<tr>
+<td><span class="arithmatex">\(&lt; -1\)</span>（右に傾いた木）</td>
+<td><span class="arithmatex">\(\leq 0\)</span></td>
+<td>左回転</td>
+</tr>
+<tr>
+<td><span class="arithmatex">\(&lt; -1\)</span>（右に傾いた木）</td>
+<td><span class="arithmatex">\(&gt;0\)</span></td>
+<td>右回転してから左回転</td>
+</tr>
+</tbody>
+</table>
+</div>
+<p>便宜上、回転操作を関数にカプセル化します。<strong>この関数により、さまざまな種類の不平衡に対して回転を実行し、不平衡ノードのバランスを回復できます</strong>。コードは以下の通りです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="7:14"><input checked="checked" id="__tabbed_7_1" name="__tabbed_7" type="radio" /><input id="__tabbed_7_2" name="__tabbed_7" type="radio" /><input id="__tabbed_7_3" name="__tabbed_7" type="radio" /><input id="__tabbed_7_4" name="__tabbed_7" type="radio" /><input id="__tabbed_7_5" name="__tabbed_7" type="radio" /><input id="__tabbed_7_6" name="__tabbed_7" type="radio" /><input id="__tabbed_7_7" name="__tabbed_7" type="radio" /><input id="__tabbed_7_8" name="__tabbed_7" type="radio" /><input id="__tabbed_7_9" name="__tabbed_7" type="radio" /><input id="__tabbed_7_10" name="__tabbed_7" type="radio" /><input id="__tabbed_7_11" name="__tabbed_7" type="radio" /><input id="__tabbed_7_12" name="__tabbed_7" type="radio" /><input id="__tabbed_7_13" name="__tabbed_7" type="radio" /><input id="__tabbed_7_14" name="__tabbed_7" type="radio" /><div class="tabbed-labels"><label for="__tabbed_7_1">Python</label><label for="__tabbed_7_2">C++</label><label for="__tabbed_7_3">Java</label><label for="__tabbed_7_4">C#</label><label for="__tabbed_7_5">Go</label><label for="__tabbed_7_6">Swift</label><label for="__tabbed_7_7">JS</label><label for="__tabbed_7_8">TS</label><label for="__tabbed_7_9">Dart</label><label for="__tabbed_7_10">Rust</label><label for="__tabbed_7_11">C</label><label for="__tabbed_7_12">Kotlin</label><label for="__tabbed_7_13">Ruby</label><label for="__tabbed_7_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.py</span><pre><span></span><code><a id="__codelineno-70-1" name="__codelineno-70-1" href="#__codelineno-70-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">rotate</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">node</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-70-2" name="__codelineno-70-2" href="#__codelineno-70-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;回転操作を実行して部分木のバランスを復元&quot;&quot;&quot;</span>
+<a id="__codelineno-70-3" name="__codelineno-70-3" href="#__codelineno-70-3"></a>    <span class="c1"># nodeのバランス因子を取得</span>
+<a id="__codelineno-70-4" name="__codelineno-70-4" href="#__codelineno-70-4"></a>    <span class="n">balance_factor</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">balance_factor</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
+<a id="__codelineno-70-5" name="__codelineno-70-5" href="#__codelineno-70-5"></a>    <span class="c1"># 左偏り木</span>
+<a id="__codelineno-70-6" name="__codelineno-70-6" href="#__codelineno-70-6"></a>    <span class="k">if</span> <span class="n">balance_factor</span> <span class="o">&gt;</span> <span class="mi">1</span><span class="p">:</span>
+<a id="__codelineno-70-7" name="__codelineno-70-7" href="#__codelineno-70-7"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">balance_factor</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="p">)</span> <span class="o">&gt;=</span> <span class="mi">0</span><span class="p">:</span>
+<a id="__codelineno-70-8" name="__codelineno-70-8" href="#__codelineno-70-8"></a>            <span class="c1"># 右回転</span>
+<a id="__codelineno-70-9" name="__codelineno-70-9" href="#__codelineno-70-9"></a>            <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">right_rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
+<a id="__codelineno-70-10" name="__codelineno-70-10" href="#__codelineno-70-10"></a>        <span class="k">else</span><span class="p">:</span>
+<a id="__codelineno-70-11" name="__codelineno-70-11" href="#__codelineno-70-11"></a>            <span class="c1"># 左回転してから右回転</span>
+<a id="__codelineno-70-12" name="__codelineno-70-12" href="#__codelineno-70-12"></a>            <span class="n">node</span><span class="o">.</span><span class="n">left</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">left_rotate</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="p">)</span>
+<a id="__codelineno-70-13" name="__codelineno-70-13" href="#__codelineno-70-13"></a>            <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">right_rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
+<a id="__codelineno-70-14" name="__codelineno-70-14" href="#__codelineno-70-14"></a>    <span class="c1"># 右偏り木</span>
+<a id="__codelineno-70-15" name="__codelineno-70-15" href="#__codelineno-70-15"></a>    <span class="k">elif</span> <span class="n">balance_factor</span> <span class="o">&lt;</span> <span class="o">-</span><span class="mi">1</span><span class="p">:</span>
+<a id="__codelineno-70-16" name="__codelineno-70-16" href="#__codelineno-70-16"></a>        <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">balance_factor</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">)</span> <span class="o">&lt;=</span> <span class="mi">0</span><span class="p">:</span>
+<a id="__codelineno-70-17" name="__codelineno-70-17" href="#__codelineno-70-17"></a>            <span class="c1"># 左回転</span>
+<a id="__codelineno-70-18" name="__codelineno-70-18" href="#__codelineno-70-18"></a>            <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">left_rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
+<a id="__codelineno-70-19" name="__codelineno-70-19" href="#__codelineno-70-19"></a>        <span class="k">else</span><span class="p">:</span>
+<a id="__codelineno-70-20" name="__codelineno-70-20" href="#__codelineno-70-20"></a>            <span class="c1"># 右回転してから左回転</span>
+<a id="__codelineno-70-21" name="__codelineno-70-21" href="#__codelineno-70-21"></a>            <span class="n">node</span><span class="o">.</span><span class="n">right</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">right_rotate</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>
+<a id="__codelineno-70-22" name="__codelineno-70-22" href="#__codelineno-70-22"></a>            <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">left_rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
+<a id="__codelineno-70-23" name="__codelineno-70-23" href="#__codelineno-70-23"></a>    <span class="c1"># バランスの取れた木、回転不要、戻る</span>
+<a id="__codelineno-70-24" name="__codelineno-70-24" href="#__codelineno-70-24"></a>    <span class="k">return</span> <span class="n">node</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.cpp</span><pre><span></span><code><a id="__codelineno-71-1" name="__codelineno-71-1" href="#__codelineno-71-1"></a><span class="cm">/* 回転操作を実行して部分木の平衡を回復 */</span>
+<a id="__codelineno-71-2" name="__codelineno-71-2" href="#__codelineno-71-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">rotate</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-71-3" name="__codelineno-71-3" href="#__codelineno-71-3"></a><span class="w">    </span><span class="c1">// nodeの平衡因子を取得</span>
+<a id="__codelineno-71-4" name="__codelineno-71-4" href="#__codelineno-71-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">_balanceFactor</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">balanceFactor</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-71-5" name="__codelineno-71-5" href="#__codelineno-71-5"></a><span class="w">    </span><span class="c1">// 左に傾いた木</span>
+<a id="__codelineno-71-6" name="__codelineno-71-6" href="#__codelineno-71-6"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">_balanceFactor</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-71-7" name="__codelineno-71-7" href="#__codelineno-71-7"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">balanceFactor</span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">)</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-71-8" name="__codelineno-71-8" href="#__codelineno-71-8"></a><span class="w">            </span><span class="c1">// 右回転</span>
+<a id="__codelineno-71-9" name="__codelineno-71-9" href="#__codelineno-71-9"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">rightRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-71-10" name="__codelineno-71-10" href="#__codelineno-71-10"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-71-11" name="__codelineno-71-11" href="#__codelineno-71-11"></a><span class="w">            </span><span class="c1">// 先に左回転、その後右回転</span>
+<a id="__codelineno-71-12" name="__codelineno-71-12" href="#__codelineno-71-12"></a><span class="w">            </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">leftRotate</span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">);</span>
+<a id="__codelineno-71-13" name="__codelineno-71-13" href="#__codelineno-71-13"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">rightRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-71-14" name="__codelineno-71-14" href="#__codelineno-71-14"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-71-15" name="__codelineno-71-15" href="#__codelineno-71-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-71-16" name="__codelineno-71-16" href="#__codelineno-71-16"></a><span class="w">    </span><span class="c1">// 右に傾いた木</span>
+<a id="__codelineno-71-17" name="__codelineno-71-17" href="#__codelineno-71-17"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">_balanceFactor</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="mi">-1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-71-18" name="__codelineno-71-18" href="#__codelineno-71-18"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">balanceFactor</span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">)</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-71-19" name="__codelineno-71-19" href="#__codelineno-71-19"></a><span class="w">            </span><span class="c1">// 左回転</span>
+<a id="__codelineno-71-20" name="__codelineno-71-20" href="#__codelineno-71-20"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">leftRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-71-21" name="__codelineno-71-21" href="#__codelineno-71-21"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-71-22" name="__codelineno-71-22" href="#__codelineno-71-22"></a><span class="w">            </span><span class="c1">// 先に右回転、その後左回転</span>
+<a id="__codelineno-71-23" name="__codelineno-71-23" href="#__codelineno-71-23"></a><span class="w">            </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rightRotate</span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-71-24" name="__codelineno-71-24" href="#__codelineno-71-24"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">leftRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-71-25" name="__codelineno-71-25" href="#__codelineno-71-25"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-71-26" name="__codelineno-71-26" href="#__codelineno-71-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-71-27" name="__codelineno-71-27" href="#__codelineno-71-27"></a><span class="w">    </span><span class="c1">// 平衡な木、回転不要、そのまま戻る</span>
+<a id="__codelineno-71-28" name="__codelineno-71-28" href="#__codelineno-71-28"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-71-29" name="__codelineno-71-29" href="#__codelineno-71-29"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.java</span><pre><span></span><code><a id="__codelineno-72-1" name="__codelineno-72-1" href="#__codelineno-72-1"></a><span class="cm">/* 回転操作を実行して部分木の平衡を回復 */</span>
+<a id="__codelineno-72-2" name="__codelineno-72-2" href="#__codelineno-72-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="nf">rotate</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">node</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-72-3" name="__codelineno-72-3" href="#__codelineno-72-3"></a><span class="w">    </span><span class="c1">// node の平衡因子を取得</span>
+<a id="__codelineno-72-4" name="__codelineno-72-4" href="#__codelineno-72-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">balanceFactor</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">balanceFactor</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-72-5" name="__codelineno-72-5" href="#__codelineno-72-5"></a><span class="w">    </span><span class="c1">// 左傾斜の木</span>
+<a id="__codelineno-72-6" name="__codelineno-72-6" href="#__codelineno-72-6"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">balanceFactor</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-72-7" name="__codelineno-72-7" href="#__codelineno-72-7"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">balanceFactor</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="p">)</span><span class="w"> </span><span class="o">&gt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-72-8" name="__codelineno-72-8" href="#__codelineno-72-8"></a><span class="w">            </span><span class="c1">// 右回転</span>
+<a id="__codelineno-72-9" name="__codelineno-72-9" href="#__codelineno-72-9"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">rightRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-72-10" name="__codelineno-72-10" href="#__codelineno-72-10"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-72-11" name="__codelineno-72-11" href="#__codelineno-72-11"></a><span class="w">            </span><span class="c1">// 先に左回転、その後右回転</span>
+<a id="__codelineno-72-12" name="__codelineno-72-12" href="#__codelineno-72-12"></a><span class="w">            </span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">leftRotate</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="p">);</span>
+<a id="__codelineno-72-13" name="__codelineno-72-13" href="#__codelineno-72-13"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">rightRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-72-14" name="__codelineno-72-14" href="#__codelineno-72-14"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-72-15" name="__codelineno-72-15" href="#__codelineno-72-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-72-16" name="__codelineno-72-16" href="#__codelineno-72-16"></a><span class="w">    </span><span class="c1">// 右傾斜の木</span>
+<a id="__codelineno-72-17" name="__codelineno-72-17" href="#__codelineno-72-17"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">balanceFactor</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-72-18" name="__codelineno-72-18" href="#__codelineno-72-18"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">balanceFactor</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="p">)</span><span class="w"> </span><span class="o">&lt;=</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-72-19" name="__codelineno-72-19" href="#__codelineno-72-19"></a><span class="w">            </span><span class="c1">// 左回転</span>
+<a id="__codelineno-72-20" name="__codelineno-72-20" href="#__codelineno-72-20"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">leftRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-72-21" name="__codelineno-72-21" href="#__codelineno-72-21"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-72-22" name="__codelineno-72-22" href="#__codelineno-72-22"></a><span class="w">            </span><span class="c1">// 先に右回転、その後左回転</span>
+<a id="__codelineno-72-23" name="__codelineno-72-23" href="#__codelineno-72-23"></a><span class="w">            </span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rightRotate</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="p">);</span>
+<a id="__codelineno-72-24" name="__codelineno-72-24" href="#__codelineno-72-24"></a><span class="w">            </span><span class="k">return</span><span class="w"> </span><span class="n">leftRotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-72-25" name="__codelineno-72-25" href="#__codelineno-72-25"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-72-26" name="__codelineno-72-26" href="#__codelineno-72-26"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-72-27" name="__codelineno-72-27" href="#__codelineno-72-27"></a><span class="w">    </span><span class="c1">// 平衡木、回転は不要、戻る</span>
+<a id="__codelineno-72-28" name="__codelineno-72-28" href="#__codelineno-72-28"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-72-29" name="__codelineno-72-29" href="#__codelineno-72-29"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.cs</span><pre><span></span><code><a id="__codelineno-73-1" name="__codelineno-73-1" href="#__codelineno-73-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Rotate</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.go</span><pre><span></span><code><a id="__codelineno-74-1" name="__codelineno-74-1" href="#__codelineno-74-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">aVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">rotate</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.swift</span><pre><span></span><code><a id="__codelineno-75-1" name="__codelineno-75-1" href="#__codelineno-75-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">rotate</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.js</span><pre><span></span><code><a id="__codelineno-76-1" name="__codelineno-76-1" href="#__codelineno-76-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">rotate</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.ts</span><pre><span></span><code><a id="__codelineno-77-1" name="__codelineno-77-1" href="#__codelineno-77-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">rotate</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.dart</span><pre><span></span><code><a id="__codelineno-78-1" name="__codelineno-78-1" href="#__codelineno-78-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">rotate</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.rs</span><pre><span></span><code><a id="__codelineno-79-1" name="__codelineno-79-1" href="#__codelineno-79-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">rotate</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.c</span><pre><span></span><code><a id="__codelineno-80-1" name="__codelineno-80-1" href="#__codelineno-80-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">rotate</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.kt</span><pre><span></span><code><a id="__codelineno-81-1" name="__codelineno-81-1" href="#__codelineno-81-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">rotate</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-82-1" name="__codelineno-82-1" href="#__codelineno-82-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">rotate</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.zig</span><pre><span></span><code><a id="__codelineno-83-1" name="__codelineno-83-1" href="#__codelineno-83-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">rotate</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h2 id="753-avl">7.5.3 &nbsp; AVL木の一般的な操作<a class="headerlink" href="#753-avl" title="Permanent link">&para;</a></h2>
+<h3 id="1_2">1. &nbsp; ノードの挿入<a class="headerlink" href="#1_2" title="Permanent link">&para;</a></h3>
+<p>AVL木のノード挿入操作は二分探索木のそれと似ています。唯一の違いは、AVL木でノードを挿入した後、そのノードから根ノードまでのパス上に一連の不平衡ノードが現れる可能性があることです。したがって、<strong>このノードから始めて上向きに回転操作を実行し、すべての不平衡ノードのバランスを回復する必要があります</strong>。コードは以下の通りです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="8:14"><input checked="checked" id="__tabbed_8_1" name="__tabbed_8" type="radio" /><input id="__tabbed_8_2" name="__tabbed_8" type="radio" /><input id="__tabbed_8_3" name="__tabbed_8" type="radio" /><input id="__tabbed_8_4" name="__tabbed_8" type="radio" /><input id="__tabbed_8_5" name="__tabbed_8" type="radio" /><input id="__tabbed_8_6" name="__tabbed_8" type="radio" /><input id="__tabbed_8_7" name="__tabbed_8" type="radio" /><input id="__tabbed_8_8" name="__tabbed_8" type="radio" /><input id="__tabbed_8_9" name="__tabbed_8" type="radio" /><input id="__tabbed_8_10" name="__tabbed_8" type="radio" /><input id="__tabbed_8_11" name="__tabbed_8" type="radio" /><input id="__tabbed_8_12" name="__tabbed_8" type="radio" /><input id="__tabbed_8_13" name="__tabbed_8" type="radio" /><input id="__tabbed_8_14" name="__tabbed_8" type="radio" /><div class="tabbed-labels"><label for="__tabbed_8_1">Python</label><label for="__tabbed_8_2">C++</label><label for="__tabbed_8_3">Java</label><label for="__tabbed_8_4">C#</label><label for="__tabbed_8_5">Go</label><label for="__tabbed_8_6">Swift</label><label for="__tabbed_8_7">JS</label><label for="__tabbed_8_8">TS</label><label for="__tabbed_8_9">Dart</label><label for="__tabbed_8_10">Rust</label><label for="__tabbed_8_11">C</label><label for="__tabbed_8_12">Kotlin</label><label for="__tabbed_8_13">Ruby</label><label for="__tabbed_8_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.py</span><pre><span></span><code><a id="__codelineno-84-1" name="__codelineno-84-1" href="#__codelineno-84-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">val</span><span class="p">):</span>
+<a id="__codelineno-84-2" name="__codelineno-84-2" href="#__codelineno-84-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;ノードを挿入&quot;&quot;&quot;</span>
+<a id="__codelineno-84-3" name="__codelineno-84-3" href="#__codelineno-84-3"></a>    <span class="bp">self</span><span class="o">.</span><span class="n">_root</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">insert_helper</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_root</span><span class="p">,</span> <span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-84-4" name="__codelineno-84-4" href="#__codelineno-84-4"></a>
+<a id="__codelineno-84-5" name="__codelineno-84-5" href="#__codelineno-84-5"></a><span class="k">def</span><span class="w"> </span><span class="nf">insert_helper</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">node</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">TreeNode</span><span class="p">:</span>
+<a id="__codelineno-84-6" name="__codelineno-84-6" href="#__codelineno-84-6"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;再帰的にノードを挿入（ヘルパーメソッド）&quot;&quot;&quot;</span>
+<a id="__codelineno-84-7" name="__codelineno-84-7" href="#__codelineno-84-7"></a>    <span class="k">if</span> <span class="n">node</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-84-8" name="__codelineno-84-8" href="#__codelineno-84-8"></a>        <span class="k">return</span> <span class="n">TreeNode</span><span class="p">(</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-84-9" name="__codelineno-84-9" href="#__codelineno-84-9"></a>    <span class="c1"># 1. 挿入位置を見つけてノードを挿入</span>
+<a id="__codelineno-84-10" name="__codelineno-84-10" href="#__codelineno-84-10"></a>    <span class="k">if</span> <span class="n">val</span> <span class="o">&lt;</span> <span class="n">node</span><span class="o">.</span><span class="n">val</span><span class="p">:</span>
+<a id="__codelineno-84-11" name="__codelineno-84-11" href="#__codelineno-84-11"></a>        <span class="n">node</span><span class="o">.</span><span class="n">left</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">insert_helper</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="p">,</span> <span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-84-12" name="__codelineno-84-12" href="#__codelineno-84-12"></a>    <span class="k">elif</span> <span class="n">val</span> <span class="o">&gt;</span> <span class="n">node</span><span class="o">.</span><span class="n">val</span><span class="p">:</span>
+<a id="__codelineno-84-13" name="__codelineno-84-13" href="#__codelineno-84-13"></a>        <span class="n">node</span><span class="o">.</span><span class="n">right</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">insert_helper</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">,</span> <span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-84-14" name="__codelineno-84-14" href="#__codelineno-84-14"></a>    <span class="k">else</span><span class="p">:</span>
+<a id="__codelineno-84-15" name="__codelineno-84-15" href="#__codelineno-84-15"></a>        <span class="c1"># 重複ノードは挿入しない、戻る</span>
+<a id="__codelineno-84-16" name="__codelineno-84-16" href="#__codelineno-84-16"></a>        <span class="k">return</span> <span class="n">node</span>
+<a id="__codelineno-84-17" name="__codelineno-84-17" href="#__codelineno-84-17"></a>    <span class="c1"># ノードの高さを更新</span>
+<a id="__codelineno-84-18" name="__codelineno-84-18" href="#__codelineno-84-18"></a>    <span class="bp">self</span><span class="o">.</span><span class="n">update_height</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
+<a id="__codelineno-84-19" name="__codelineno-84-19" href="#__codelineno-84-19"></a>    <span class="c1"># 2. 回転操作を実行して部分木のバランスを復元</span>
+<a id="__codelineno-84-20" name="__codelineno-84-20" href="#__codelineno-84-20"></a>    <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.cpp</span><pre><span></span><code><a id="__codelineno-85-1" name="__codelineno-85-1" href="#__codelineno-85-1"></a><span class="cm">/* ノードを挿入 */</span>
+<a id="__codelineno-85-2" name="__codelineno-85-2" href="#__codelineno-85-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-85-3" name="__codelineno-85-3" href="#__codelineno-85-3"></a><span class="w">    </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">insertHelper</span><span class="p">(</span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-85-4" name="__codelineno-85-4" href="#__codelineno-85-4"></a><span class="p">}</span>
+<a id="__codelineno-85-5" name="__codelineno-85-5" href="#__codelineno-85-5"></a>
+<a id="__codelineno-85-6" name="__codelineno-85-6" href="#__codelineno-85-6"></a><span class="cm">/* ノードを再帰的に挿入（ヘルパーメソッド） */</span>
+<a id="__codelineno-85-7" name="__codelineno-85-7" href="#__codelineno-85-7"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">insertHelper</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-85-8" name="__codelineno-85-8" href="#__codelineno-85-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span>
+<a id="__codelineno-85-9" name="__codelineno-85-9" href="#__codelineno-85-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-85-10" name="__codelineno-85-10" href="#__codelineno-85-10"></a><span class="w">    </span><span class="cm">/* 1. 挿入位置を見つけてノードを挿入 */</span>
+<a id="__codelineno-85-11" name="__codelineno-85-11" href="#__codelineno-85-11"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-85-12" name="__codelineno-85-12" href="#__codelineno-85-12"></a><span class="w">        </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">insertHelper</span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-85-13" name="__codelineno-85-13" href="#__codelineno-85-13"></a><span class="w">    </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-85-14" name="__codelineno-85-14" href="#__codelineno-85-14"></a><span class="w">        </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">insertHelper</span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-85-15" name="__codelineno-85-15" href="#__codelineno-85-15"></a><span class="w">    </span><span class="k">else</span>
+<a id="__codelineno-85-16" name="__codelineno-85-16" href="#__codelineno-85-16"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span><span class="w">    </span><span class="c1">// 重複ノードは挿入しない、そのまま戻る</span>
+<a id="__codelineno-85-17" name="__codelineno-85-17" href="#__codelineno-85-17"></a><span class="w">    </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span><span class="w"> </span><span class="c1">// ノードの高さを更新</span>
+<a id="__codelineno-85-18" name="__codelineno-85-18" href="#__codelineno-85-18"></a><span class="w">    </span><span class="cm">/* 2. 回転操作を実行して部分木の平衡を回復 */</span>
+<a id="__codelineno-85-19" name="__codelineno-85-19" href="#__codelineno-85-19"></a><span class="w">    </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-85-20" name="__codelineno-85-20" href="#__codelineno-85-20"></a><span class="w">    </span><span class="c1">// 部分木のルートノードを返す</span>
+<a id="__codelineno-85-21" name="__codelineno-85-21" href="#__codelineno-85-21"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-85-22" name="__codelineno-85-22" href="#__codelineno-85-22"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.java</span><pre><span></span><code><a id="__codelineno-86-1" name="__codelineno-86-1" href="#__codelineno-86-1"></a><span class="cm">/* ノードを挿入 */</span>
+<a id="__codelineno-86-2" name="__codelineno-86-2" href="#__codelineno-86-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-86-3" name="__codelineno-86-3" href="#__codelineno-86-3"></a><span class="w">    </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">insertHelper</span><span class="p">(</span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-86-4" name="__codelineno-86-4" href="#__codelineno-86-4"></a><span class="p">}</span>
+<a id="__codelineno-86-5" name="__codelineno-86-5" href="#__codelineno-86-5"></a>
+<a id="__codelineno-86-6" name="__codelineno-86-6" href="#__codelineno-86-6"></a><span class="cm">/* 再帰的にノードを挿入（補助メソッド） */</span>
+<a id="__codelineno-86-7" name="__codelineno-86-7" href="#__codelineno-86-7"></a><span class="n">TreeNode</span><span class="w"> </span><span class="nf">insertHelper</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">node</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-86-8" name="__codelineno-86-8" href="#__codelineno-86-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
+<a id="__codelineno-86-9" name="__codelineno-86-9" href="#__codelineno-86-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-86-10" name="__codelineno-86-10" href="#__codelineno-86-10"></a><span class="w">    </span><span class="cm">/* 1. 挿入位置を見つけてノードを挿入 */</span>
+<a id="__codelineno-86-11" name="__codelineno-86-11" href="#__codelineno-86-11"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">val</span><span class="p">)</span>
+<a id="__codelineno-86-12" name="__codelineno-86-12" href="#__codelineno-86-12"></a><span class="w">        </span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">insertHelper</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-86-13" name="__codelineno-86-13" href="#__codelineno-86-13"></a><span class="w">    </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">val</span><span class="p">)</span>
+<a id="__codelineno-86-14" name="__codelineno-86-14" href="#__codelineno-86-14"></a><span class="w">        </span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">insertHelper</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-86-15" name="__codelineno-86-15" href="#__codelineno-86-15"></a><span class="w">    </span><span class="k">else</span>
+<a id="__codelineno-86-16" name="__codelineno-86-16" href="#__codelineno-86-16"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span><span class="w"> </span><span class="c1">// 重複ノードは挿入しない、戻る</span>
+<a id="__codelineno-86-17" name="__codelineno-86-17" href="#__codelineno-86-17"></a><span class="w">    </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span><span class="w"> </span><span class="c1">// ノードの高さを更新</span>
+<a id="__codelineno-86-18" name="__codelineno-86-18" href="#__codelineno-86-18"></a><span class="w">    </span><span class="cm">/* 2. 回転操作を実行して部分木の平衡を回復 */</span>
+<a id="__codelineno-86-19" name="__codelineno-86-19" href="#__codelineno-86-19"></a><span class="w">    </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-86-20" name="__codelineno-86-20" href="#__codelineno-86-20"></a><span class="w">    </span><span class="c1">// 部分木の根ノードを返す</span>
+<a id="__codelineno-86-21" name="__codelineno-86-21" href="#__codelineno-86-21"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-86-22" name="__codelineno-86-22" href="#__codelineno-86-22"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.cs</span><pre><span></span><code><a id="__codelineno-87-1" name="__codelineno-87-1" href="#__codelineno-87-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Insert</span><span class="p">}</span>
+<a id="__codelineno-87-2" name="__codelineno-87-2" href="#__codelineno-87-2"></a>
+<a id="__codelineno-87-3" name="__codelineno-87-3" href="#__codelineno-87-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">InsertHelper</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.go</span><pre><span></span><code><a id="__codelineno-88-1" name="__codelineno-88-1" href="#__codelineno-88-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">aVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">insert</span><span class="p">}</span>
+<a id="__codelineno-88-2" name="__codelineno-88-2" href="#__codelineno-88-2"></a>
+<a id="__codelineno-88-3" name="__codelineno-88-3" href="#__codelineno-88-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">aVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">insertHelper</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.swift</span><pre><span></span><code><a id="__codelineno-89-1" name="__codelineno-89-1" href="#__codelineno-89-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="bp">insert</span><span class="p">}</span>
+<a id="__codelineno-89-2" name="__codelineno-89-2" href="#__codelineno-89-2"></a>
+<a id="__codelineno-89-3" name="__codelineno-89-3" href="#__codelineno-89-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">insertHelper</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.js</span><pre><span></span><code><a id="__codelineno-90-1" name="__codelineno-90-1" href="#__codelineno-90-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">insert</span><span class="p">}</span>
+<a id="__codelineno-90-2" name="__codelineno-90-2" href="#__codelineno-90-2"></a>
+<a id="__codelineno-90-3" name="__codelineno-90-3" href="#__codelineno-90-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">insertHelper</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.ts</span><pre><span></span><code><a id="__codelineno-91-1" name="__codelineno-91-1" href="#__codelineno-91-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">insert</span><span class="p">}</span>
+<a id="__codelineno-91-2" name="__codelineno-91-2" href="#__codelineno-91-2"></a>
+<a id="__codelineno-91-3" name="__codelineno-91-3" href="#__codelineno-91-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">insertHelper</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.dart</span><pre><span></span><code><a id="__codelineno-92-1" name="__codelineno-92-1" href="#__codelineno-92-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">insert</span><span class="p">}</span>
+<a id="__codelineno-92-2" name="__codelineno-92-2" href="#__codelineno-92-2"></a>
+<a id="__codelineno-92-3" name="__codelineno-92-3" href="#__codelineno-92-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">insertHelper</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.rs</span><pre><span></span><code><a id="__codelineno-93-1" name="__codelineno-93-1" href="#__codelineno-93-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">insert</span><span class="p">}</span>
+<a id="__codelineno-93-2" name="__codelineno-93-2" href="#__codelineno-93-2"></a>
+<a id="__codelineno-93-3" name="__codelineno-93-3" href="#__codelineno-93-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">insert_helper</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.c</span><pre><span></span><code><a id="__codelineno-94-1" name="__codelineno-94-1" href="#__codelineno-94-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">insert</span><span class="p">}</span>
+<a id="__codelineno-94-2" name="__codelineno-94-2" href="#__codelineno-94-2"></a>
+<a id="__codelineno-94-3" name="__codelineno-94-3" href="#__codelineno-94-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">insertHelper</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.kt</span><pre><span></span><code><a id="__codelineno-95-1" name="__codelineno-95-1" href="#__codelineno-95-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">insert</span><span class="p">}</span>
+<a id="__codelineno-95-2" name="__codelineno-95-2" href="#__codelineno-95-2"></a>
+<a id="__codelineno-95-3" name="__codelineno-95-3" href="#__codelineno-95-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">insertHelper</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-96-1" name="__codelineno-96-1" href="#__codelineno-96-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">insert</span><span class="p">}</span>
+<a id="__codelineno-96-2" name="__codelineno-96-2" href="#__codelineno-96-2"></a>
+<a id="__codelineno-96-3" name="__codelineno-96-3" href="#__codelineno-96-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">insert_helper</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.zig</span><pre><span></span><code><a id="__codelineno-97-1" name="__codelineno-97-1" href="#__codelineno-97-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">insert</span><span class="p">}</span>
+<a id="__codelineno-97-2" name="__codelineno-97-2" href="#__codelineno-97-2"></a>
+<a id="__codelineno-97-3" name="__codelineno-97-3" href="#__codelineno-97-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">insertHelper</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h3 id="2_2">2. &nbsp; ノードの削除<a class="headerlink" href="#2_2" title="Permanent link">&para;</a></h3>
+<p>同様に、二分探索木でのノード削除方法に基づいて、下から上へ回転操作を実行してすべての不平衡ノードのバランスを回復する必要があります。コードは以下の通りです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="9:14"><input checked="checked" id="__tabbed_9_1" name="__tabbed_9" type="radio" /><input id="__tabbed_9_2" name="__tabbed_9" type="radio" /><input id="__tabbed_9_3" name="__tabbed_9" type="radio" /><input id="__tabbed_9_4" name="__tabbed_9" type="radio" /><input id="__tabbed_9_5" name="__tabbed_9" type="radio" /><input id="__tabbed_9_6" name="__tabbed_9" type="radio" /><input id="__tabbed_9_7" name="__tabbed_9" type="radio" /><input id="__tabbed_9_8" name="__tabbed_9" type="radio" /><input id="__tabbed_9_9" name="__tabbed_9" type="radio" /><input id="__tabbed_9_10" name="__tabbed_9" type="radio" /><input id="__tabbed_9_11" name="__tabbed_9" type="radio" /><input id="__tabbed_9_12" name="__tabbed_9" type="radio" /><input id="__tabbed_9_13" name="__tabbed_9" type="radio" /><input id="__tabbed_9_14" name="__tabbed_9" type="radio" /><div class="tabbed-labels"><label for="__tabbed_9_1">Python</label><label for="__tabbed_9_2">C++</label><label for="__tabbed_9_3">Java</label><label for="__tabbed_9_4">C#</label><label for="__tabbed_9_5">Go</label><label for="__tabbed_9_6">Swift</label><label for="__tabbed_9_7">JS</label><label for="__tabbed_9_8">TS</label><label for="__tabbed_9_9">Dart</label><label for="__tabbed_9_10">Rust</label><label for="__tabbed_9_11">C</label><label for="__tabbed_9_12">Kotlin</label><label for="__tabbed_9_13">Ruby</label><label for="__tabbed_9_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.py</span><pre><span></span><code><a id="__codelineno-98-1" name="__codelineno-98-1" href="#__codelineno-98-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-98-2" name="__codelineno-98-2" href="#__codelineno-98-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;ノードを削除&quot;&quot;&quot;</span>
+<a id="__codelineno-98-3" name="__codelineno-98-3" href="#__codelineno-98-3"></a>    <span class="bp">self</span><span class="o">.</span><span class="n">_root</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">remove_helper</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_root</span><span class="p">,</span> <span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-98-4" name="__codelineno-98-4" href="#__codelineno-98-4"></a>
+<a id="__codelineno-98-5" name="__codelineno-98-5" href="#__codelineno-98-5"></a><span class="k">def</span><span class="w"> </span><span class="nf">remove_helper</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">node</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-98-6" name="__codelineno-98-6" href="#__codelineno-98-6"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;再帰的にノードを削除（ヘルパーメソッド）&quot;&quot;&quot;</span>
+<a id="__codelineno-98-7" name="__codelineno-98-7" href="#__codelineno-98-7"></a>    <span class="k">if</span> <span class="n">node</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-98-8" name="__codelineno-98-8" href="#__codelineno-98-8"></a>        <span class="k">return</span> <span class="kc">None</span>
+<a id="__codelineno-98-9" name="__codelineno-98-9" href="#__codelineno-98-9"></a>    <span class="c1"># 1. ノードを見つけて削除</span>
+<a id="__codelineno-98-10" name="__codelineno-98-10" href="#__codelineno-98-10"></a>    <span class="k">if</span> <span class="n">val</span> <span class="o">&lt;</span> <span class="n">node</span><span class="o">.</span><span class="n">val</span><span class="p">:</span>
+<a id="__codelineno-98-11" name="__codelineno-98-11" href="#__codelineno-98-11"></a>        <span class="n">node</span><span class="o">.</span><span class="n">left</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">remove_helper</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="p">,</span> <span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-98-12" name="__codelineno-98-12" href="#__codelineno-98-12"></a>    <span class="k">elif</span> <span class="n">val</span> <span class="o">&gt;</span> <span class="n">node</span><span class="o">.</span><span class="n">val</span><span class="p">:</span>
+<a id="__codelineno-98-13" name="__codelineno-98-13" href="#__codelineno-98-13"></a>        <span class="n">node</span><span class="o">.</span><span class="n">right</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">remove_helper</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">,</span> <span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-98-14" name="__codelineno-98-14" href="#__codelineno-98-14"></a>    <span class="k">else</span><span class="p">:</span>
+<a id="__codelineno-98-15" name="__codelineno-98-15" href="#__codelineno-98-15"></a>        <span class="k">if</span> <span class="n">node</span><span class="o">.</span><span class="n">left</span> <span class="ow">is</span> <span class="kc">None</span> <span class="ow">or</span> <span class="n">node</span><span class="o">.</span><span class="n">right</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-98-16" name="__codelineno-98-16" href="#__codelineno-98-16"></a>            <span class="n">child</span> <span class="o">=</span> <span class="n">node</span><span class="o">.</span><span class="n">left</span> <span class="ow">or</span> <span class="n">node</span><span class="o">.</span><span class="n">right</span>
+<a id="__codelineno-98-17" name="__codelineno-98-17" href="#__codelineno-98-17"></a>            <span class="c1"># 子ノード数 = 0、ノードを削除して戻る</span>
+<a id="__codelineno-98-18" name="__codelineno-98-18" href="#__codelineno-98-18"></a>            <span class="k">if</span> <span class="n">child</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-98-19" name="__codelineno-98-19" href="#__codelineno-98-19"></a>                <span class="k">return</span> <span class="kc">None</span>
+<a id="__codelineno-98-20" name="__codelineno-98-20" href="#__codelineno-98-20"></a>            <span class="c1"># 子ノード数 = 1、ノードを削除</span>
+<a id="__codelineno-98-21" name="__codelineno-98-21" href="#__codelineno-98-21"></a>            <span class="k">else</span><span class="p">:</span>
+<a id="__codelineno-98-22" name="__codelineno-98-22" href="#__codelineno-98-22"></a>                <span class="n">node</span> <span class="o">=</span> <span class="n">child</span>
+<a id="__codelineno-98-23" name="__codelineno-98-23" href="#__codelineno-98-23"></a>        <span class="k">else</span><span class="p">:</span>
+<a id="__codelineno-98-24" name="__codelineno-98-24" href="#__codelineno-98-24"></a>            <span class="c1"># 子ノード数 = 2、中順走査の次のノードを削除し、それで現在のノードを置き換え</span>
+<a id="__codelineno-98-25" name="__codelineno-98-25" href="#__codelineno-98-25"></a>            <span class="n">temp</span> <span class="o">=</span> <span class="n">node</span><span class="o">.</span><span class="n">right</span>
+<a id="__codelineno-98-26" name="__codelineno-98-26" href="#__codelineno-98-26"></a>            <span class="k">while</span> <span class="n">temp</span><span class="o">.</span><span class="n">left</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-98-27" name="__codelineno-98-27" href="#__codelineno-98-27"></a>                <span class="n">temp</span> <span class="o">=</span> <span class="n">temp</span><span class="o">.</span><span class="n">left</span>
+<a id="__codelineno-98-28" name="__codelineno-98-28" href="#__codelineno-98-28"></a>            <span class="n">node</span><span class="o">.</span><span class="n">right</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">remove_helper</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">,</span> <span class="n">temp</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-98-29" name="__codelineno-98-29" href="#__codelineno-98-29"></a>            <span class="n">node</span><span class="o">.</span><span class="n">val</span> <span class="o">=</span> <span class="n">temp</span><span class="o">.</span><span class="n">val</span>
+<a id="__codelineno-98-30" name="__codelineno-98-30" href="#__codelineno-98-30"></a>    <span class="c1"># ノードの高さを更新</span>
+<a id="__codelineno-98-31" name="__codelineno-98-31" href="#__codelineno-98-31"></a>    <span class="bp">self</span><span class="o">.</span><span class="n">update_height</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
+<a id="__codelineno-98-32" name="__codelineno-98-32" href="#__codelineno-98-32"></a>    <span class="c1"># 2. 回転操作を実行して部分木のバランスを復元</span>
+<a id="__codelineno-98-33" name="__codelineno-98-33" href="#__codelineno-98-33"></a>    <span class="k">return</span> <span class="bp">self</span><span class="o">.</span><span class="n">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">)</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.cpp</span><pre><span></span><code><a id="__codelineno-99-1" name="__codelineno-99-1" href="#__codelineno-99-1"></a><span class="cm">/* ノードを削除 */</span>
+<a id="__codelineno-99-2" name="__codelineno-99-2" href="#__codelineno-99-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-99-3" name="__codelineno-99-3" href="#__codelineno-99-3"></a><span class="w">    </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-99-4" name="__codelineno-99-4" href="#__codelineno-99-4"></a><span class="p">}</span>
+<a id="__codelineno-99-5" name="__codelineno-99-5" href="#__codelineno-99-5"></a>
+<a id="__codelineno-99-6" name="__codelineno-99-6" href="#__codelineno-99-6"></a><span class="cm">/* ノードを再帰的に削除（ヘルパーメソッド） */</span>
+<a id="__codelineno-99-7" name="__codelineno-99-7" href="#__codelineno-99-7"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">removeHelper</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-99-8" name="__codelineno-99-8" href="#__codelineno-99-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span>
+<a id="__codelineno-99-9" name="__codelineno-99-9" href="#__codelineno-99-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="k">nullptr</span><span class="p">;</span>
+<a id="__codelineno-99-10" name="__codelineno-99-10" href="#__codelineno-99-10"></a><span class="w">    </span><span class="cm">/* 1. ノードを見つけて削除 */</span>
+<a id="__codelineno-99-11" name="__codelineno-99-11" href="#__codelineno-99-11"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-99-12" name="__codelineno-99-12" href="#__codelineno-99-12"></a><span class="w">        </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-99-13" name="__codelineno-99-13" href="#__codelineno-99-13"></a><span class="w">    </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-99-14" name="__codelineno-99-14" href="#__codelineno-99-14"></a><span class="w">        </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-99-15" name="__codelineno-99-15" href="#__codelineno-99-15"></a><span class="w">    </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-99-16" name="__codelineno-99-16" href="#__codelineno-99-16"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-99-17" name="__codelineno-99-17" href="#__codelineno-99-17"></a><span class="w">            </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-99-18" name="__codelineno-99-18" href="#__codelineno-99-18"></a><span class="w">            </span><span class="c1">// 子ノード数 = 0、ノードを削除して戻る</span>
+<a id="__codelineno-99-19" name="__codelineno-99-19" href="#__codelineno-99-19"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">child</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-99-20" name="__codelineno-99-20" href="#__codelineno-99-20"></a><span class="w">                </span><span class="k">delete</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-99-21" name="__codelineno-99-21" href="#__codelineno-99-21"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="k">nullptr</span><span class="p">;</span>
+<a id="__codelineno-99-22" name="__codelineno-99-22" href="#__codelineno-99-22"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-99-23" name="__codelineno-99-23" href="#__codelineno-99-23"></a><span class="w">            </span><span class="c1">// 子ノード数 = 1、ノードを削除</span>
+<a id="__codelineno-99-24" name="__codelineno-99-24" href="#__codelineno-99-24"></a><span class="w">            </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-99-25" name="__codelineno-99-25" href="#__codelineno-99-25"></a><span class="w">                </span><span class="k">delete</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-99-26" name="__codelineno-99-26" href="#__codelineno-99-26"></a><span class="w">                </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
+<a id="__codelineno-99-27" name="__codelineno-99-27" href="#__codelineno-99-27"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-99-28" name="__codelineno-99-28" href="#__codelineno-99-28"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-99-29" name="__codelineno-99-29" href="#__codelineno-99-29"></a><span class="w">            </span><span class="c1">// 子ノード数 = 2、中順走査の次のノードを削除し、現在のノードと置き換える</span>
+<a id="__codelineno-99-30" name="__codelineno-99-30" href="#__codelineno-99-30"></a><span class="w">            </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-99-31" name="__codelineno-99-31" href="#__codelineno-99-31"></a><span class="w">            </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">temp</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-99-32" name="__codelineno-99-32" href="#__codelineno-99-32"></a><span class="w">                </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">;</span>
+<a id="__codelineno-99-33" name="__codelineno-99-33" href="#__codelineno-99-33"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-99-34" name="__codelineno-99-34" href="#__codelineno-99-34"></a><span class="w">            </span><span class="kt">int</span><span class="w"> </span><span class="n">tempVal</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-99-35" name="__codelineno-99-35" href="#__codelineno-99-35"></a><span class="w">            </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">,</span><span class="w"> </span><span class="n">temp</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-99-36" name="__codelineno-99-36" href="#__codelineno-99-36"></a><span class="w">            </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tempVal</span><span class="p">;</span>
+<a id="__codelineno-99-37" name="__codelineno-99-37" href="#__codelineno-99-37"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-99-38" name="__codelineno-99-38" href="#__codelineno-99-38"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-99-39" name="__codelineno-99-39" href="#__codelineno-99-39"></a><span class="w">    </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span><span class="w"> </span><span class="c1">// ノードの高さを更新</span>
+<a id="__codelineno-99-40" name="__codelineno-99-40" href="#__codelineno-99-40"></a><span class="w">    </span><span class="cm">/* 2. 回転操作を実行して部分木の平衡を回復 */</span>
+<a id="__codelineno-99-41" name="__codelineno-99-41" href="#__codelineno-99-41"></a><span class="w">    </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-99-42" name="__codelineno-99-42" href="#__codelineno-99-42"></a><span class="w">    </span><span class="c1">// 部分木のルートノードを返す</span>
+<a id="__codelineno-99-43" name="__codelineno-99-43" href="#__codelineno-99-43"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-99-44" name="__codelineno-99-44" href="#__codelineno-99-44"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.java</span><pre><span></span><code><a id="__codelineno-100-1" name="__codelineno-100-1" href="#__codelineno-100-1"></a><span class="cm">/* ノードを削除 */</span>
+<a id="__codelineno-100-2" name="__codelineno-100-2" href="#__codelineno-100-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-100-3" name="__codelineno-100-3" href="#__codelineno-100-3"></a><span class="w">    </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-100-4" name="__codelineno-100-4" href="#__codelineno-100-4"></a><span class="p">}</span>
+<a id="__codelineno-100-5" name="__codelineno-100-5" href="#__codelineno-100-5"></a>
+<a id="__codelineno-100-6" name="__codelineno-100-6" href="#__codelineno-100-6"></a><span class="cm">/* 再帰的にノードを削除（補助メソッド） */</span>
+<a id="__codelineno-100-7" name="__codelineno-100-7" href="#__codelineno-100-7"></a><span class="n">TreeNode</span><span class="w"> </span><span class="nf">removeHelper</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">node</span><span class="p">,</span><span class="w"> </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-100-8" name="__codelineno-100-8" href="#__codelineno-100-8"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
+<a id="__codelineno-100-9" name="__codelineno-100-9" href="#__codelineno-100-9"></a><span class="w">        </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-100-10" name="__codelineno-100-10" href="#__codelineno-100-10"></a><span class="w">    </span><span class="cm">/* 1. ノードを見つけて削除 */</span>
+<a id="__codelineno-100-11" name="__codelineno-100-11" href="#__codelineno-100-11"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">val</span><span class="p">)</span>
+<a id="__codelineno-100-12" name="__codelineno-100-12" href="#__codelineno-100-12"></a><span class="w">        </span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-100-13" name="__codelineno-100-13" href="#__codelineno-100-13"></a><span class="w">    </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">val</span><span class="p">)</span>
+<a id="__codelineno-100-14" name="__codelineno-100-14" href="#__codelineno-100-14"></a><span class="w">        </span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="p">,</span><span class="w"> </span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-100-15" name="__codelineno-100-15" href="#__codelineno-100-15"></a><span class="w">    </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-100-16" name="__codelineno-100-16" href="#__codelineno-100-16"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-100-17" name="__codelineno-100-17" href="#__codelineno-100-17"></a><span class="w">            </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="p">;</span>
+<a id="__codelineno-100-18" name="__codelineno-100-18" href="#__codelineno-100-18"></a><span class="w">            </span><span class="c1">// 子ノード数 = 0、ノードを削除して戻る</span>
+<a id="__codelineno-100-19" name="__codelineno-100-19" href="#__codelineno-100-19"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">child</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
+<a id="__codelineno-100-20" name="__codelineno-100-20" href="#__codelineno-100-20"></a><span class="w">                </span><span class="k">return</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-100-21" name="__codelineno-100-21" href="#__codelineno-100-21"></a><span class="w">            </span><span class="c1">// 子ノード数 = 1、ノードを削除</span>
+<a id="__codelineno-100-22" name="__codelineno-100-22" href="#__codelineno-100-22"></a><span class="w">            </span><span class="k">else</span>
+<a id="__codelineno-100-23" name="__codelineno-100-23" href="#__codelineno-100-23"></a><span class="w">                </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
+<a id="__codelineno-100-24" name="__codelineno-100-24" href="#__codelineno-100-24"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-100-25" name="__codelineno-100-25" href="#__codelineno-100-25"></a><span class="w">            </span><span class="c1">// 子ノード数 = 2、中順走査の次のノードを削除し、現在のノードをそれで置き換える</span>
+<a id="__codelineno-100-26" name="__codelineno-100-26" href="#__codelineno-100-26"></a><span class="w">            </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="p">;</span>
+<a id="__codelineno-100-27" name="__codelineno-100-27" href="#__codelineno-100-27"></a><span class="w">            </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">temp</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-100-28" name="__codelineno-100-28" href="#__codelineno-100-28"></a><span class="w">                </span><span class="n">temp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="p">.</span><span class="na">left</span><span class="p">;</span>
+<a id="__codelineno-100-29" name="__codelineno-100-29" href="#__codelineno-100-29"></a><span class="w">            </span><span class="p">}</span>
+<a id="__codelineno-100-30" name="__codelineno-100-30" href="#__codelineno-100-30"></a><span class="w">            </span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">removeHelper</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="p">,</span><span class="w"> </span><span class="n">temp</span><span class="p">.</span><span class="na">val</span><span class="p">);</span>
+<a id="__codelineno-100-31" name="__codelineno-100-31" href="#__codelineno-100-31"></a><span class="w">            </span><span class="n">node</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">temp</span><span class="p">.</span><span class="na">val</span><span class="p">;</span>
+<a id="__codelineno-100-32" name="__codelineno-100-32" href="#__codelineno-100-32"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-100-33" name="__codelineno-100-33" href="#__codelineno-100-33"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-100-34" name="__codelineno-100-34" href="#__codelineno-100-34"></a><span class="w">    </span><span class="n">updateHeight</span><span class="p">(</span><span class="n">node</span><span class="p">);</span><span class="w"> </span><span class="c1">// ノードの高さを更新</span>
+<a id="__codelineno-100-35" name="__codelineno-100-35" href="#__codelineno-100-35"></a><span class="w">    </span><span class="cm">/* 2. 回転操作を実行して部分木の平衡を回復 */</span>
+<a id="__codelineno-100-36" name="__codelineno-100-36" href="#__codelineno-100-36"></a><span class="w">    </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">rotate</span><span class="p">(</span><span class="n">node</span><span class="p">);</span>
+<a id="__codelineno-100-37" name="__codelineno-100-37" href="#__codelineno-100-37"></a><span class="w">    </span><span class="c1">// 部分木の根ノードを返す</span>
+<a id="__codelineno-100-38" name="__codelineno-100-38" href="#__codelineno-100-38"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-100-39" name="__codelineno-100-39" href="#__codelineno-100-39"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.cs</span><pre><span></span><code><a id="__codelineno-101-1" name="__codelineno-101-1" href="#__codelineno-101-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Remove</span><span class="p">}</span>
+<a id="__codelineno-101-2" name="__codelineno-101-2" href="#__codelineno-101-2"></a>
+<a id="__codelineno-101-3" name="__codelineno-101-3" href="#__codelineno-101-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">RemoveHelper</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.go</span><pre><span></span><code><a id="__codelineno-102-1" name="__codelineno-102-1" href="#__codelineno-102-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">aVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">remove</span><span class="p">}</span>
+<a id="__codelineno-102-2" name="__codelineno-102-2" href="#__codelineno-102-2"></a>
+<a id="__codelineno-102-3" name="__codelineno-102-3" href="#__codelineno-102-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">aVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">removeHelper</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.swift</span><pre><span></span><code><a id="__codelineno-103-1" name="__codelineno-103-1" href="#__codelineno-103-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">remove</span><span class="p">}</span>
+<a id="__codelineno-103-2" name="__codelineno-103-2" href="#__codelineno-103-2"></a>
+<a id="__codelineno-103-3" name="__codelineno-103-3" href="#__codelineno-103-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">removeHelper</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.js</span><pre><span></span><code><a id="__codelineno-104-1" name="__codelineno-104-1" href="#__codelineno-104-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">remove</span><span class="p">}</span>
+<a id="__codelineno-104-2" name="__codelineno-104-2" href="#__codelineno-104-2"></a>
+<a id="__codelineno-104-3" name="__codelineno-104-3" href="#__codelineno-104-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">removeHelper</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.ts</span><pre><span></span><code><a id="__codelineno-105-1" name="__codelineno-105-1" href="#__codelineno-105-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">remove</span><span class="p">}</span>
+<a id="__codelineno-105-2" name="__codelineno-105-2" href="#__codelineno-105-2"></a>
+<a id="__codelineno-105-3" name="__codelineno-105-3" href="#__codelineno-105-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">removeHelper</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.dart</span><pre><span></span><code><a id="__codelineno-106-1" name="__codelineno-106-1" href="#__codelineno-106-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">remove</span><span class="p">}</span>
+<a id="__codelineno-106-2" name="__codelineno-106-2" href="#__codelineno-106-2"></a>
+<a id="__codelineno-106-3" name="__codelineno-106-3" href="#__codelineno-106-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">removeHelper</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.rs</span><pre><span></span><code><a id="__codelineno-107-1" name="__codelineno-107-1" href="#__codelineno-107-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">remove</span><span class="p">}</span>
+<a id="__codelineno-107-2" name="__codelineno-107-2" href="#__codelineno-107-2"></a>
+<a id="__codelineno-107-3" name="__codelineno-107-3" href="#__codelineno-107-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">remove_helper</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.c</span><pre><span></span><code><a id="__codelineno-108-1" name="__codelineno-108-1" href="#__codelineno-108-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">removeItem</span><span class="p">}</span>
+<a id="__codelineno-108-2" name="__codelineno-108-2" href="#__codelineno-108-2"></a>
+<a id="__codelineno-108-3" name="__codelineno-108-3" href="#__codelineno-108-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">removeHelper</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.kt</span><pre><span></span><code><a id="__codelineno-109-1" name="__codelineno-109-1" href="#__codelineno-109-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">remove</span><span class="p">}</span>
+<a id="__codelineno-109-2" name="__codelineno-109-2" href="#__codelineno-109-2"></a>
+<a id="__codelineno-109-3" name="__codelineno-109-3" href="#__codelineno-109-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">removeHelper</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.rb</span><pre><span></span><code><a id="__codelineno-110-1" name="__codelineno-110-1" href="#__codelineno-110-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">remove</span><span class="p">}</span>
+<a id="__codelineno-110-2" name="__codelineno-110-2" href="#__codelineno-110-2"></a>
+<a id="__codelineno-110-3" name="__codelineno-110-3" href="#__codelineno-110-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">AVLTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">remove_helper</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">avl_tree.zig</span><pre><span></span><code><a id="__codelineno-111-1" name="__codelineno-111-1" href="#__codelineno-111-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">remove</span><span class="p">}</span>
+<a id="__codelineno-111-2" name="__codelineno-111-2" href="#__codelineno-111-2"></a>
+<a id="__codelineno-111-3" name="__codelineno-111-3" href="#__codelineno-111-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">AVLTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">removeHelper</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h3 id="3_1">3. &nbsp; ノードの検索<a class="headerlink" href="#3_1" title="Permanent link">&para;</a></h3>
+<p>AVL木でのノード検索操作は二分探索木のそれと一致しており、ここでは詳述しません。</p>
+<h2 id="754-avl">7.5.4 &nbsp; AVL木の典型的な応用<a class="headerlink" href="#754-avl" title="Permanent link">&para;</a></h2>
+<ul>
+<li>大量のデータの整理と格納に使用され、検索頻度が高く、挿入と削除の頻度が低いシナリオに適しています。</li>
+<li>データベースのインデックスシステムの構築に使用されます。</li>
+<li>赤黒木も一般的な平衡二分探索木の一種です。AVL木と比較して、赤黒木はより緩い平衡条件を持ち、ノードの挿入と削除にかかる回転数が少なく、ノードの追加と削除操作の平均効率が高くなります。</li>
+</ul>
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diff --git a/ja/chapter_tree/binary_search_tree.assets/bst_remove_case2.png b/ja/chapter_tree/binary_search_tree.assets/bst_remove_case2.png
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diff --git a/ja/chapter_tree/binary_search_tree.assets/bst_remove_case3_step2.png b/ja/chapter_tree/binary_search_tree.assets/bst_remove_case3_step2.png
new file mode 100644
index 0000000000000000000000000000000000000000..0efa18000da314a42af5e2afc9fd5cab292fccbd
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+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#741" class="md-nav__link">
+    <span class="md-ellipsis">
+      7.4.1 &nbsp; 二分探索木の操作
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="7.4.1   二分探索木の操作">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; ノードの検索
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; ノードの挿入
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#3" class="md-nav__link">
+    <span class="md-ellipsis">
+      3. &nbsp; ノードの削除
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#4" class="md-nav__link">
+    <span class="md-ellipsis">
+      4. &nbsp; 中順走査は順序付けされている
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#742" class="md-nav__link">
+    <span class="md-ellipsis">
+      7.4.2 &nbsp; 二分探索木の効率
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#743" class="md-nav__link">
+    <span class="md-ellipsis">
+      7.4.3 &nbsp; 二分探索木の一般的な応用
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
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+              
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
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+    
+      
+      
+  
+  
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+          
+        
+      
+    
+    
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+    <li class="md-nav__item md-nav__item--nested">
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+  
+  <span class="md-ellipsis">
+    参考文献
+  </span>
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+            参考文献
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+            
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+        </nav>
+      
+    </li>
+  
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+  </ul>
+</nav>
+                  </div>
+                </div>
+              </div>
+            
+            
+              
+              <div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
+                <div class="md-sidebar__scrollwrap">
+                  <div class="md-sidebar__inner">
+                    
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#741" class="md-nav__link">
+    <span class="md-ellipsis">
+      7.4.1 &nbsp; 二分探索木の操作
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="7.4.1   二分探索木の操作">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; ノードの検索
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; ノードの挿入
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#3" class="md-nav__link">
+    <span class="md-ellipsis">
+      3. &nbsp; ノードの削除
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#4" class="md-nav__link">
+    <span class="md-ellipsis">
+      4. &nbsp; 中順走査は順序付けされている
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#742" class="md-nav__link">
+    <span class="md-ellipsis">
+      7.4.2 &nbsp; 二分探索木の効率
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#743" class="md-nav__link">
+    <span class="md-ellipsis">
+      7.4.3 &nbsp; 二分探索木の一般的な応用
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+                  </div>
+                </div>
+              </div>
+            
+          
+          
+            <div class="md-content" data-md-component="content">
+              <article class="md-content__inner md-typeset">
+                
+                  <!-- Tags -->
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+  <!-- Edit button -->
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+    <a
+      href="https://github.com/krahets/hello-algo/tree/main/ja/docs/chapter_tree/binary_search_tree.md"
+      title="編集"
+      class="md-content__button md-icon"
+    >
+      
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
+    </a>
+  
+
+  <!-- View button -->
+  
+
+
+<!-- Page content -->
+<h1 id="74">7.4 &nbsp; 二分探索木<a class="headerlink" href="#74" title="Permanent link">&para;</a></h1>
+<p>下図に示すように、<u>二分探索木</u>は以下の条件を満たします。</p>
+<ol>
+<li>根ノードについて、左部分木のすべてのノードの値 <span class="arithmatex">\(&lt;\)</span> 根ノードの値 <span class="arithmatex">\(&lt;\)</span> 右部分木のすべてのノードの値。</li>
+<li>任意のノードの左と右の部分木も二分探索木です。つまり、条件<code>1.</code>も満たします。</li>
+</ol>
+<p><a class="glightbox" href="../binary_search_tree.assets/binary_search_tree.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="二分探索木" class="animation-figure" src="../binary_search_tree.assets/binary_search_tree.png" /></a></p>
+<p align="center"> 図 7-16 &nbsp; 二分探索木 </p>
+
+<h2 id="741">7.4.1 &nbsp; 二分探索木の操作<a class="headerlink" href="#741" title="Permanent link">&para;</a></h2>
+<p>二分探索木をクラス<code>BinarySearchTree</code>としてカプセル化し、木の根ノードを指すメンバー変数<code>root</code>を宣言します。</p>
+<h3 id="1">1. &nbsp; ノードの検索<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<p>ターゲットノード値<code>num</code>が与えられた場合、二分探索木の性質に従って検索できます。下図に示すように、ノード<code>cur</code>を宣言し、二分木の根ノード<code>root</code>から開始し、ノード値<code>cur.val</code>と<code>num</code>のサイズを比較するループを行います。</p>
+<ul>
+<li><code>cur.val &lt; num</code>の場合、ターゲットノードは<code>cur</code>の右部分木にあることを意味するため、<code>cur = cur.right</code>を実行します。</li>
+<li><code>cur.val &gt; num</code>の場合、ターゲットノードは<code>cur</code>の左部分木にあることを意味するため、<code>cur = cur.left</code>を実行します。</li>
+<li><code>cur.val = num</code>の場合、ターゲットノードが見つかったことを意味するため、ループを終了してノードを返します。</li>
+</ul>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:4"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">&lt;1&gt;</label><label for="__tabbed_1_2">&lt;2&gt;</label><label for="__tabbed_1_3">&lt;3&gt;</label><label for="__tabbed_1_4">&lt;4&gt;</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<p><a class="glightbox" href="../binary_search_tree.assets/bst_search_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="二分探索木でのノード検索例" class="animation-figure" src="../binary_search_tree.assets/bst_search_step1.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../binary_search_tree.assets/bst_search_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="bst_search_step2" class="animation-figure" src="../binary_search_tree.assets/bst_search_step2.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../binary_search_tree.assets/bst_search_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="bst_search_step3" class="animation-figure" src="../binary_search_tree.assets/bst_search_step3.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../binary_search_tree.assets/bst_search_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="bst_search_step4" class="animation-figure" src="../binary_search_tree.assets/bst_search_step4.png" /></a></p>
+</div>
+</div>
+</div>
+<p align="center"> 図 7-17 &nbsp; 二分探索木でのノード検索例 </p>
+
+<p>二分探索木での検索操作は二分探索アルゴリズムと同じ原理で動作し、各ラウンドでケースの半分を排除します。ループ数は最大で二分木の高さです。二分木が平衡している場合、<span class="arithmatex">\(O(\log n)\)</span>の時間を使用します。コード例は以下の通りです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:14"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><input id="__tabbed_2_14" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label><label for="__tabbed_2_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_tree.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">search</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">num</span><span class="p">:</span> <span class="nb">int</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;ノードを探索&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="n">cur</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_root</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="c1"># ループで探索、葉ノードを通過した後にブレーク</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="k">while</span> <span class="n">cur</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>        <span class="c1"># ターゲットノードはcurの右部分木にある</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>        <span class="k">if</span> <span class="n">cur</span><span class="o">.</span><span class="n">val</span> <span class="o">&lt;</span> <span class="n">num</span><span class="p">:</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>            <span class="n">cur</span> <span class="o">=</span> <span class="n">cur</span><span class="o">.</span><span class="n">right</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>        <span class="c1"># ターゲットノードはcurの左部分木にある</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>        <span class="k">elif</span> <span class="n">cur</span><span class="o">.</span><span class="n">val</span> <span class="o">&gt;</span> <span class="n">num</span><span class="p">:</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>            <span class="n">cur</span> <span class="o">=</span> <span class="n">cur</span><span class="o">.</span><span class="n">left</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>        <span class="c1"># ターゲットノードを発見、ループをブレーク</span>
+<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>        <span class="k">else</span><span class="p">:</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>            <span class="k">break</span>
+<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>    <span class="k">return</span> <span class="n">cur</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_tree.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* ノードを検索 */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">search</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="c1">// ループで検索、葉ノードを通り過ぎたら終了</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">        </span><span class="c1">// 目標ノードはcurの右部分木にある</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">            </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">        </span><span class="c1">// 目標ノードはcurの左部分木にある</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">            </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">;</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">        </span><span class="c1">// 目標ノードを見つけた、ループを抜ける</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">        </span><span class="k">else</span>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">    </span><span class="c1">// 目標ノードを返す</span>
+<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">cur</span><span class="p">;</span>
+<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_tree.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* ノードを検索 */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="nf">search</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</span><span class="p">;</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="c1">// ループで検索、葉ノードを通過後に終了</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">        </span><span class="c1">// 対象ノードは cur の右部分木にある</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">            </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="na">right</span><span class="p">;</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">        </span><span class="c1">// 対象ノードは cur の左部分木にある</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">        </span><span class="k">else</span><span class="w"> </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">&gt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">            </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="na">left</span><span class="p">;</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">        </span><span class="c1">// 対象ノードを見つけた、ループを終了</span>
+<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">        </span><span class="k">else</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">    </span><span class="c1">// 対象ノードを返す</span>
+<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">cur</span><span class="p">;</span>
+<a id="__codelineno-2-18" name="__codelineno-2-18" href="#__codelineno-2-18"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_tree.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">BinarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Search</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_tree.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">binarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">search</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_tree.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">BinarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">search</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_tree.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">BinarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">search</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_tree.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">BinarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">search</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_tree.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">BinarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">search</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_tree.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">BinarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">search</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_tree.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">BinarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">search</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_tree.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">BinarySearchTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">search</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_tree.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">BinarySearchTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">search</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_tree.zig</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">BinarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">search</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h3 id="2">2. &nbsp; ノードの挿入<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
+<p>挿入する要素<code>num</code>が与えられた場合、二分探索木の性質「左部分木 &lt; 根ノード &lt; 右部分木」を維持するため、挿入操作は下図に示すように進行します。</p>
+<ol>
+<li><strong>挿入位置を見つける</strong>: 検索操作と同様に、根ノードから開始し、現在のノード値と<code>num</code>のサイズ関係に従って下向きにループし、葉ノードを通過（<code>None</code>に走査）するまで、ループを終了します。</li>
+<li><strong>この位置にノードを挿入</strong>: ノード<code>num</code>を初期化し、<code>None</code>があった場所に配置します。</li>
+</ol>
+<p><a class="glightbox" href="../binary_search_tree.assets/bst_insert.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="二分探索木へのノード挿入" class="animation-figure" src="../binary_search_tree.assets/bst_insert.png" /></a></p>
+<p align="center"> 図 7-18 &nbsp; 二分探索木へのノード挿入 </p>
+
+<p>コード実装では、以下の2点に注意してください。</p>
+<ul>
+<li>二分探索木は重複ノードの存在を許可しません。そうでなければ、その定義に違反します。したがって、挿入するノードが既に木に存在する場合、挿入は実行されず、ノードは直接戻ります。</li>
+<li>挿入操作を実行するには、前のループからのノードを保存するためにノード<code>pre</code>を使用する必要があります。このようにして、<code>None</code>に走査したときに、その親ノードを取得でき、ノード挿入操作を完了できます。</li>
+</ul>
+<div class="tabbed-set tabbed-alternate" data-tabs="3:14"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><input id="__tabbed_3_14" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label><label for="__tabbed_3_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_tree.py</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">num</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;ノードを挿入&quot;&quot;&quot;</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a>    <span class="c1"># 木が空の場合、ルートノードを初期化</span>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a>    <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">_root</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">_root</span> <span class="o">=</span> <span class="n">TreeNode</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a>        <span class="k">return</span>
+<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a>    <span class="c1"># ループで探索、葉ノードを通過した後にブレーク</span>
+<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a>    <span class="n">cur</span><span class="p">,</span> <span class="n">pre</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_root</span><span class="p">,</span> <span class="kc">None</span>
+<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a>    <span class="k">while</span> <span class="n">cur</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a>        <span class="c1"># 重複ノードを発見したため、戻る</span>
+<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a>        <span class="k">if</span> <span class="n">cur</span><span class="o">.</span><span class="n">val</span> <span class="o">==</span> <span class="n">num</span><span class="p">:</span>
+<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a>            <span class="k">return</span>
+<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a>        <span class="n">pre</span> <span class="o">=</span> <span class="n">cur</span>
+<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a>        <span class="c1"># 挿入位置はcurの右部分木にある</span>
+<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a>        <span class="k">if</span> <span class="n">cur</span><span class="o">.</span><span class="n">val</span> <span class="o">&lt;</span> <span class="n">num</span><span class="p">:</span>
+<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a>            <span class="n">cur</span> <span class="o">=</span> <span class="n">cur</span><span class="o">.</span><span class="n">right</span>
+<a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a>        <span class="c1"># 挿入位置はcurの左部分木にある</span>
+<a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a>        <span class="k">else</span><span class="p">:</span>
+<a id="__codelineno-14-19" name="__codelineno-14-19" href="#__codelineno-14-19"></a>            <span class="n">cur</span> <span class="o">=</span> <span class="n">cur</span><span class="o">.</span><span class="n">left</span>
+<a id="__codelineno-14-20" name="__codelineno-14-20" href="#__codelineno-14-20"></a>    <span class="c1"># ノードを挿入</span>
+<a id="__codelineno-14-21" name="__codelineno-14-21" href="#__codelineno-14-21"></a>    <span class="n">node</span> <span class="o">=</span> <span class="n">TreeNode</span><span class="p">(</span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-14-22" name="__codelineno-14-22" href="#__codelineno-14-22"></a>    <span class="k">if</span> <span class="n">pre</span><span class="o">.</span><span class="n">val</span> <span class="o">&lt;</span> <span class="n">num</span><span class="p">:</span>
+<a id="__codelineno-14-23" name="__codelineno-14-23" href="#__codelineno-14-23"></a>        <span class="n">pre</span><span class="o">.</span><span class="n">right</span> <span class="o">=</span> <span class="n">node</span>
+<a id="__codelineno-14-24" name="__codelineno-14-24" href="#__codelineno-14-24"></a>    <span class="k">else</span><span class="p">:</span>
+<a id="__codelineno-14-25" name="__codelineno-14-25" href="#__codelineno-14-25"></a>        <span class="n">pre</span><span class="o">.</span><span class="n">left</span> <span class="o">=</span> <span class="n">node</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_tree.cpp</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* ノードを挿入 */</span>
+<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="c1">// 木が空の場合、ルートノードを初期化</span>
+<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">        </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="o">*</span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">;</span>
+<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="w">    </span><span class="c1">// ループで検索、葉ノードを通り過ぎたら終了</span>
+<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="w">        </span><span class="c1">// 重複ノードを見つけた場合、戻る</span>
+<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="w">        </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">;</span>
+<a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="w">        </span><span class="c1">// 挿入位置はcurの右部分木にある</span>
+<a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-15-17" name="__codelineno-15-17" href="#__codelineno-15-17"></a><span class="w">            </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-15-18" name="__codelineno-15-18" href="#__codelineno-15-18"></a><span class="w">        </span><span class="c1">// 挿入位置はcurの左部分木にある</span>
+<a id="__codelineno-15-19" name="__codelineno-15-19" href="#__codelineno-15-19"></a><span class="w">        </span><span class="k">else</span>
+<a id="__codelineno-15-20" name="__codelineno-15-20" href="#__codelineno-15-20"></a><span class="w">            </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">;</span>
+<a id="__codelineno-15-21" name="__codelineno-15-21" href="#__codelineno-15-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-15-22" name="__codelineno-15-22" href="#__codelineno-15-22"></a><span class="w">    </span><span class="c1">// ノードを挿入</span>
+<a id="__codelineno-15-23" name="__codelineno-15-23" href="#__codelineno-15-23"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-15-24" name="__codelineno-15-24" href="#__codelineno-15-24"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pre</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-15-25" name="__codelineno-15-25" href="#__codelineno-15-25"></a><span class="w">        </span><span class="n">pre</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-15-26" name="__codelineno-15-26" href="#__codelineno-15-26"></a><span class="w">    </span><span class="k">else</span>
+<a id="__codelineno-15-27" name="__codelineno-15-27" href="#__codelineno-15-27"></a><span class="w">        </span><span class="n">pre</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-15-28" name="__codelineno-15-28" href="#__codelineno-15-28"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_tree.java</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* ノードを挿入 */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">insert</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="c1">// 木が空の場合、根ノードを初期化</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">        </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="w">    </span><span class="c1">// ループで検索、葉ノードを通過後に終了</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="w">        </span><span class="c1">// 重複ノードを見つけた場合、戻る</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w">            </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="w">        </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">;</span>
+<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="w">        </span><span class="c1">// 挿入位置は cur の右部分木にある</span>
+<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-16-17" name="__codelineno-16-17" href="#__codelineno-16-17"></a><span class="w">            </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="na">right</span><span class="p">;</span>
+<a id="__codelineno-16-18" name="__codelineno-16-18" href="#__codelineno-16-18"></a><span class="w">        </span><span class="c1">// 挿入位置は cur の左部分木にある</span>
+<a id="__codelineno-16-19" name="__codelineno-16-19" href="#__codelineno-16-19"></a><span class="w">        </span><span class="k">else</span>
+<a id="__codelineno-16-20" name="__codelineno-16-20" href="#__codelineno-16-20"></a><span class="w">            </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="na">left</span><span class="p">;</span>
+<a id="__codelineno-16-21" name="__codelineno-16-21" href="#__codelineno-16-21"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-16-22" name="__codelineno-16-22" href="#__codelineno-16-22"></a><span class="w">    </span><span class="c1">// ノードを挿入</span>
+<a id="__codelineno-16-23" name="__codelineno-16-23" href="#__codelineno-16-23"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">num</span><span class="p">);</span>
+<a id="__codelineno-16-24" name="__codelineno-16-24" href="#__codelineno-16-24"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pre</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-16-25" name="__codelineno-16-25" href="#__codelineno-16-25"></a><span class="w">        </span><span class="n">pre</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-16-26" name="__codelineno-16-26" href="#__codelineno-16-26"></a><span class="w">    </span><span class="k">else</span>
+<a id="__codelineno-16-27" name="__codelineno-16-27" href="#__codelineno-16-27"></a><span class="w">        </span><span class="n">pre</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-16-28" name="__codelineno-16-28" href="#__codelineno-16-28"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_tree.cs</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">BinarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Insert</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_tree.go</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">binarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">insert</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_tree.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">BinarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="bp">insert</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_tree.js</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">BinarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">insert</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_tree.ts</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">BinarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">insert</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_tree.dart</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">BinarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">insert</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_tree.rs</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">BinarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">insert</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_tree.c</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">BinarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">insert</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_tree.kt</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">BinarySearchTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">insert</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_tree.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">BinarySearchTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">insert</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_tree.zig</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">BinarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">insert</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>ノードの検索と同様に、ノードの挿入には<span class="arithmatex">\(O(\log n)\)</span>の時間を使用します。</p>
+<h3 id="3">3. &nbsp; ノードの削除<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
+<p>まず、二分木でターゲットノードを見つけ、それを削除します。ノードの挿入と同様に、削除操作が完了した後も、二分探索木の性質「左部分木 &lt; 根ノード &lt; 右部分木」が満たされることを保証する必要があります。したがって、ターゲットノードの子ノード数に基づいて、0、1、2の3つのケースに分け、対応するノード削除操作を実行します。</p>
+<p>下図に示すように、削除するノードの次数が<span class="arithmatex">\(0\)</span>の場合、そのノードは葉ノードであることを意味し、直接削除できます。</p>
+<p><a class="glightbox" href="../binary_search_tree.assets/bst_remove_case1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="二分探索木でのノード削除（次数0）" class="animation-figure" src="../binary_search_tree.assets/bst_remove_case1.png" /></a></p>
+<p align="center"> 図 7-19 &nbsp; 二分探索木でのノード削除（次数0） </p>
+
+<p>下図に示すように、削除するノードの次数が<span class="arithmatex">\(1\)</span>の場合、削除するノードをその子ノードで置き換えるだけで十分です。</p>
+<p><a class="glightbox" href="../binary_search_tree.assets/bst_remove_case2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="二分探索木でのノード削除（次数1）" class="animation-figure" src="../binary_search_tree.assets/bst_remove_case2.png" /></a></p>
+<p align="center"> 図 7-20 &nbsp; 二分探索木でのノード削除（次数1） </p>
+
+<p>削除するノードの次数が<span class="arithmatex">\(2\)</span>の場合、直接削除することはできませんが、ノードを使用して置き換える必要があります。二分探索木の性質「左部分木 <span class="arithmatex">\(&lt;\)</span> 根ノード <span class="arithmatex">\(&lt;\)</span> 右部分木」を維持するため、<strong>このノードは右部分木の最小ノードまたは左部分木の最大ノードのいずれかです</strong>。</p>
+<p>右部分木の最小ノード（中順走査での次のノード）を選択すると仮定すると、削除操作は下図に示すように進行します。</p>
+<ol>
+<li>削除するノードの「中順走査シーケンス」での次のノードを見つけ、<code>tmp</code>として示します。</li>
+<li>削除するノードの値を<code>tmp</code>の値で置き換え、木内でノード<code>tmp</code>を再帰的に削除します。</li>
+</ol>
+<div class="tabbed-set tabbed-alternate" data-tabs="4:4"><input checked="checked" id="__tabbed_4_1" name="__tabbed_4" type="radio" /><input id="__tabbed_4_2" name="__tabbed_4" type="radio" /><input id="__tabbed_4_3" name="__tabbed_4" type="radio" /><input id="__tabbed_4_4" name="__tabbed_4" type="radio" /><div class="tabbed-labels"><label for="__tabbed_4_1">&lt;1&gt;</label><label for="__tabbed_4_2">&lt;2&gt;</label><label for="__tabbed_4_3">&lt;3&gt;</label><label for="__tabbed_4_4">&lt;4&gt;</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<p><a class="glightbox" href="../binary_search_tree.assets/bst_remove_case3_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="二分探索木でのノード削除（次数2）" class="animation-figure" src="../binary_search_tree.assets/bst_remove_case3_step1.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../binary_search_tree.assets/bst_remove_case3_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="bst_remove_case3_step2" class="animation-figure" src="../binary_search_tree.assets/bst_remove_case3_step2.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../binary_search_tree.assets/bst_remove_case3_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="bst_remove_case3_step3" class="animation-figure" src="../binary_search_tree.assets/bst_remove_case3_step3.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../binary_search_tree.assets/bst_remove_case3_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="bst_remove_case3_step4" class="animation-figure" src="../binary_search_tree.assets/bst_remove_case3_step4.png" /></a></p>
+</div>
+</div>
+</div>
+<p align="center"> 図 7-21 &nbsp; 二分探索木でのノード削除（次数2） </p>
+
+<p>ノードを削除する操作も<span class="arithmatex">\(O(\log n)\)</span>の時間を使用します。削除するノードを見つけるのに<span class="arithmatex">\(O(\log n)\)</span>の時間が必要で、中順走査の後継ノードを取得するのに<span class="arithmatex">\(O(\log n)\)</span>の時間が必要です。コード例は以下の通りです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="5:14"><input checked="checked" id="__tabbed_5_1" name="__tabbed_5" type="radio" /><input id="__tabbed_5_2" name="__tabbed_5" type="radio" /><input id="__tabbed_5_3" name="__tabbed_5" type="radio" /><input id="__tabbed_5_4" name="__tabbed_5" type="radio" /><input id="__tabbed_5_5" name="__tabbed_5" type="radio" /><input id="__tabbed_5_6" name="__tabbed_5" type="radio" /><input id="__tabbed_5_7" name="__tabbed_5" type="radio" /><input id="__tabbed_5_8" name="__tabbed_5" type="radio" /><input id="__tabbed_5_9" name="__tabbed_5" type="radio" /><input id="__tabbed_5_10" name="__tabbed_5" type="radio" /><input id="__tabbed_5_11" name="__tabbed_5" type="radio" /><input id="__tabbed_5_12" name="__tabbed_5" type="radio" /><input id="__tabbed_5_13" name="__tabbed_5" type="radio" /><input id="__tabbed_5_14" name="__tabbed_5" type="radio" /><div class="tabbed-labels"><label for="__tabbed_5_1">Python</label><label for="__tabbed_5_2">C++</label><label for="__tabbed_5_3">Java</label><label for="__tabbed_5_4">C#</label><label for="__tabbed_5_5">Go</label><label for="__tabbed_5_6">Swift</label><label for="__tabbed_5_7">JS</label><label for="__tabbed_5_8">TS</label><label for="__tabbed_5_9">Dart</label><label for="__tabbed_5_10">Rust</label><label for="__tabbed_5_11">C</label><label for="__tabbed_5_12">Kotlin</label><label for="__tabbed_5_13">Ruby</label><label for="__tabbed_5_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_tree.py</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">num</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;ノードを削除&quot;&quot;&quot;</span>
+<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a>    <span class="c1"># 木が空の場合、戻る</span>
+<a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a>    <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">_root</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a>        <span class="k">return</span>
+<a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a>    <span class="c1"># ループで探索、葉ノードを通過した後にブレーク</span>
+<a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a>    <span class="n">cur</span><span class="p">,</span> <span class="n">pre</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_root</span><span class="p">,</span> <span class="kc">None</span>
+<a id="__codelineno-28-8" name="__codelineno-28-8" href="#__codelineno-28-8"></a>    <span class="k">while</span> <span class="n">cur</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-28-9" name="__codelineno-28-9" href="#__codelineno-28-9"></a>        <span class="c1"># 削除するノードを発見、ループをブレーク</span>
+<a id="__codelineno-28-10" name="__codelineno-28-10" href="#__codelineno-28-10"></a>        <span class="k">if</span> <span class="n">cur</span><span class="o">.</span><span class="n">val</span> <span class="o">==</span> <span class="n">num</span><span class="p">:</span>
+<a id="__codelineno-28-11" name="__codelineno-28-11" href="#__codelineno-28-11"></a>            <span class="k">break</span>
+<a id="__codelineno-28-12" name="__codelineno-28-12" href="#__codelineno-28-12"></a>        <span class="n">pre</span> <span class="o">=</span> <span class="n">cur</span>
+<a id="__codelineno-28-13" name="__codelineno-28-13" href="#__codelineno-28-13"></a>        <span class="c1"># 削除するノードはcurの右部分木にある</span>
+<a id="__codelineno-28-14" name="__codelineno-28-14" href="#__codelineno-28-14"></a>        <span class="k">if</span> <span class="n">cur</span><span class="o">.</span><span class="n">val</span> <span class="o">&lt;</span> <span class="n">num</span><span class="p">:</span>
+<a id="__codelineno-28-15" name="__codelineno-28-15" href="#__codelineno-28-15"></a>            <span class="n">cur</span> <span class="o">=</span> <span class="n">cur</span><span class="o">.</span><span class="n">right</span>
+<a id="__codelineno-28-16" name="__codelineno-28-16" href="#__codelineno-28-16"></a>        <span class="c1"># 削除するノードはcurの左部分木にある</span>
+<a id="__codelineno-28-17" name="__codelineno-28-17" href="#__codelineno-28-17"></a>        <span class="k">else</span><span class="p">:</span>
+<a id="__codelineno-28-18" name="__codelineno-28-18" href="#__codelineno-28-18"></a>            <span class="n">cur</span> <span class="o">=</span> <span class="n">cur</span><span class="o">.</span><span class="n">left</span>
+<a id="__codelineno-28-19" name="__codelineno-28-19" href="#__codelineno-28-19"></a>    <span class="c1"># 削除するノードが存在しない場合、戻る</span>
+<a id="__codelineno-28-20" name="__codelineno-28-20" href="#__codelineno-28-20"></a>    <span class="k">if</span> <span class="n">cur</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-28-21" name="__codelineno-28-21" href="#__codelineno-28-21"></a>        <span class="k">return</span>
+<a id="__codelineno-28-22" name="__codelineno-28-22" href="#__codelineno-28-22"></a>
+<a id="__codelineno-28-23" name="__codelineno-28-23" href="#__codelineno-28-23"></a>    <span class="c1"># 子ノード数 = 0 または 1</span>
+<a id="__codelineno-28-24" name="__codelineno-28-24" href="#__codelineno-28-24"></a>    <span class="k">if</span> <span class="n">cur</span><span class="o">.</span><span class="n">left</span> <span class="ow">is</span> <span class="kc">None</span> <span class="ow">or</span> <span class="n">cur</span><span class="o">.</span><span class="n">right</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-28-25" name="__codelineno-28-25" href="#__codelineno-28-25"></a>        <span class="c1"># 子ノード数 = 0/1の場合、child = null/その子ノード</span>
+<a id="__codelineno-28-26" name="__codelineno-28-26" href="#__codelineno-28-26"></a>        <span class="n">child</span> <span class="o">=</span> <span class="n">cur</span><span class="o">.</span><span class="n">left</span> <span class="ow">or</span> <span class="n">cur</span><span class="o">.</span><span class="n">right</span>
+<a id="__codelineno-28-27" name="__codelineno-28-27" href="#__codelineno-28-27"></a>        <span class="c1"># ノードcurを削除</span>
+<a id="__codelineno-28-28" name="__codelineno-28-28" href="#__codelineno-28-28"></a>        <span class="k">if</span> <span class="n">cur</span> <span class="o">!=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_root</span><span class="p">:</span>
+<a id="__codelineno-28-29" name="__codelineno-28-29" href="#__codelineno-28-29"></a>            <span class="k">if</span> <span class="n">pre</span><span class="o">.</span><span class="n">left</span> <span class="o">==</span> <span class="n">cur</span><span class="p">:</span>
+<a id="__codelineno-28-30" name="__codelineno-28-30" href="#__codelineno-28-30"></a>                <span class="n">pre</span><span class="o">.</span><span class="n">left</span> <span class="o">=</span> <span class="n">child</span>
+<a id="__codelineno-28-31" name="__codelineno-28-31" href="#__codelineno-28-31"></a>            <span class="k">else</span><span class="p">:</span>
+<a id="__codelineno-28-32" name="__codelineno-28-32" href="#__codelineno-28-32"></a>                <span class="n">pre</span><span class="o">.</span><span class="n">right</span> <span class="o">=</span> <span class="n">child</span>
+<a id="__codelineno-28-33" name="__codelineno-28-33" href="#__codelineno-28-33"></a>        <span class="k">else</span><span class="p">:</span>
+<a id="__codelineno-28-34" name="__codelineno-28-34" href="#__codelineno-28-34"></a>            <span class="c1"># 削除されるノードがルートの場合、ルートを再割り当て</span>
+<a id="__codelineno-28-35" name="__codelineno-28-35" href="#__codelineno-28-35"></a>            <span class="bp">self</span><span class="o">.</span><span class="n">_root</span> <span class="o">=</span> <span class="n">child</span>
+<a id="__codelineno-28-36" name="__codelineno-28-36" href="#__codelineno-28-36"></a>    <span class="c1"># 子ノード数 = 2</span>
+<a id="__codelineno-28-37" name="__codelineno-28-37" href="#__codelineno-28-37"></a>    <span class="k">else</span><span class="p">:</span>
+<a id="__codelineno-28-38" name="__codelineno-28-38" href="#__codelineno-28-38"></a>        <span class="c1"># curの中順走査の次のノードを取得</span>
+<a id="__codelineno-28-39" name="__codelineno-28-39" href="#__codelineno-28-39"></a>        <span class="n">tmp</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">=</span> <span class="n">cur</span><span class="o">.</span><span class="n">right</span>
+<a id="__codelineno-28-40" name="__codelineno-28-40" href="#__codelineno-28-40"></a>        <span class="k">while</span> <span class="n">tmp</span><span class="o">.</span><span class="n">left</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-28-41" name="__codelineno-28-41" href="#__codelineno-28-41"></a>            <span class="n">tmp</span> <span class="o">=</span> <span class="n">tmp</span><span class="o">.</span><span class="n">left</span>
+<a id="__codelineno-28-42" name="__codelineno-28-42" href="#__codelineno-28-42"></a>        <span class="c1"># 再帰的にノードtmpを削除</span>
+<a id="__codelineno-28-43" name="__codelineno-28-43" href="#__codelineno-28-43"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">remove</span><span class="p">(</span><span class="n">tmp</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-28-44" name="__codelineno-28-44" href="#__codelineno-28-44"></a>        <span class="c1"># curをtmpで置き換え</span>
+<a id="__codelineno-28-45" name="__codelineno-28-45" href="#__codelineno-28-45"></a>        <span class="n">cur</span><span class="o">.</span><span class="n">val</span> <span class="o">=</span> <span class="n">tmp</span><span class="o">.</span><span class="n">val</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_tree.cpp</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="cm">/* ノードを削除 */</span>
+<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="w">    </span><span class="c1">// 木が空の場合、戻る</span>
+<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span>
+<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="o">*</span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">;</span>
+<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="w">    </span><span class="c1">// ループで検索、葉ノードを通り過ぎたら終了</span>
+<a id="__codelineno-29-8" name="__codelineno-29-8" href="#__codelineno-29-8"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-9" name="__codelineno-29-9" href="#__codelineno-29-9"></a><span class="w">        </span><span class="c1">// 削除するノードを見つけた、ループを抜ける</span>
+<a id="__codelineno-29-10" name="__codelineno-29-10" href="#__codelineno-29-10"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-29-11" name="__codelineno-29-11" href="#__codelineno-29-11"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-29-12" name="__codelineno-29-12" href="#__codelineno-29-12"></a><span class="w">        </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">;</span>
+<a id="__codelineno-29-13" name="__codelineno-29-13" href="#__codelineno-29-13"></a><span class="w">        </span><span class="c1">// 削除するノードはcurの右部分木にある</span>
+<a id="__codelineno-29-14" name="__codelineno-29-14" href="#__codelineno-29-14"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-29-15" name="__codelineno-29-15" href="#__codelineno-29-15"></a><span class="w">            </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-29-16" name="__codelineno-29-16" href="#__codelineno-29-16"></a><span class="w">        </span><span class="c1">// 削除するノードはcurの左部分木にある</span>
+<a id="__codelineno-29-17" name="__codelineno-29-17" href="#__codelineno-29-17"></a><span class="w">        </span><span class="k">else</span>
+<a id="__codelineno-29-18" name="__codelineno-29-18" href="#__codelineno-29-18"></a><span class="w">            </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">;</span>
+<a id="__codelineno-29-19" name="__codelineno-29-19" href="#__codelineno-29-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-20" name="__codelineno-29-20" href="#__codelineno-29-20"></a><span class="w">    </span><span class="c1">// 削除するノードがない場合、戻る</span>
+<a id="__codelineno-29-21" name="__codelineno-29-21" href="#__codelineno-29-21"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span>
+<a id="__codelineno-29-22" name="__codelineno-29-22" href="#__codelineno-29-22"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-29-23" name="__codelineno-29-23" href="#__codelineno-29-23"></a><span class="w">    </span><span class="c1">// 子ノード数 = 0 または 1</span>
+<a id="__codelineno-29-24" name="__codelineno-29-24" href="#__codelineno-29-24"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-25" name="__codelineno-29-25" href="#__codelineno-29-25"></a><span class="w">        </span><span class="c1">// 子ノード数 = 0 / 1の場合、child = nullptr / その子ノード</span>
+<a id="__codelineno-29-26" name="__codelineno-29-26" href="#__codelineno-29-26"></a><span class="w">        </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-29-27" name="__codelineno-29-27" href="#__codelineno-29-27"></a><span class="w">        </span><span class="c1">// ノードcurを削除</span>
+<a id="__codelineno-29-28" name="__codelineno-29-28" href="#__codelineno-29-28"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-29" name="__codelineno-29-29" href="#__codelineno-29-29"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pre</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">cur</span><span class="p">)</span>
+<a id="__codelineno-29-30" name="__codelineno-29-30" href="#__codelineno-29-30"></a><span class="w">                </span><span class="n">pre</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
+<a id="__codelineno-29-31" name="__codelineno-29-31" href="#__codelineno-29-31"></a><span class="w">            </span><span class="k">else</span>
+<a id="__codelineno-29-32" name="__codelineno-29-32" href="#__codelineno-29-32"></a><span class="w">                </span><span class="n">pre</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
+<a id="__codelineno-29-33" name="__codelineno-29-33" href="#__codelineno-29-33"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-34" name="__codelineno-29-34" href="#__codelineno-29-34"></a><span class="w">            </span><span class="c1">// 削除されるノードがルートの場合、ルートを再割り当て</span>
+<a id="__codelineno-29-35" name="__codelineno-29-35" href="#__codelineno-29-35"></a><span class="w">            </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
+<a id="__codelineno-29-36" name="__codelineno-29-36" href="#__codelineno-29-36"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-29-37" name="__codelineno-29-37" href="#__codelineno-29-37"></a><span class="w">        </span><span class="c1">// メモリを解放</span>
+<a id="__codelineno-29-38" name="__codelineno-29-38" href="#__codelineno-29-38"></a><span class="w">        </span><span class="k">delete</span><span class="w"> </span><span class="n">cur</span><span class="p">;</span>
+<a id="__codelineno-29-39" name="__codelineno-29-39" href="#__codelineno-29-39"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-40" name="__codelineno-29-40" href="#__codelineno-29-40"></a><span class="w">    </span><span class="c1">// 子ノード数 = 2</span>
+<a id="__codelineno-29-41" name="__codelineno-29-41" href="#__codelineno-29-41"></a><span class="w">    </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-42" name="__codelineno-29-42" href="#__codelineno-29-42"></a><span class="w">        </span><span class="c1">// curの中順走査の次のノードを取得</span>
+<a id="__codelineno-29-43" name="__codelineno-29-43" href="#__codelineno-29-43"></a><span class="w">        </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">;</span>
+<a id="__codelineno-29-44" name="__codelineno-29-44" href="#__codelineno-29-44"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">tmp</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-29-45" name="__codelineno-29-45" href="#__codelineno-29-45"></a><span class="w">            </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">;</span>
+<a id="__codelineno-29-46" name="__codelineno-29-46" href="#__codelineno-29-46"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-29-47" name="__codelineno-29-47" href="#__codelineno-29-47"></a><span class="w">        </span><span class="kt">int</span><span class="w"> </span><span class="n">tmpVal</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-29-48" name="__codelineno-29-48" href="#__codelineno-29-48"></a><span class="w">        </span><span class="c1">// ノードtmpを再帰的に削除</span>
+<a id="__codelineno-29-49" name="__codelineno-29-49" href="#__codelineno-29-49"></a><span class="w">        </span><span class="n">remove</span><span class="p">(</span><span class="n">tmp</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-29-50" name="__codelineno-29-50" href="#__codelineno-29-50"></a><span class="w">        </span><span class="c1">// curをtmpで置き換え</span>
+<a id="__codelineno-29-51" name="__codelineno-29-51" href="#__codelineno-29-51"></a><span class="w">        </span><span class="n">cur</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmpVal</span><span class="p">;</span>
+<a id="__codelineno-29-52" name="__codelineno-29-52" href="#__codelineno-29-52"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-29-53" name="__codelineno-29-53" href="#__codelineno-29-53"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_tree.java</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="cm">/* ノードを削除 */</span>
+<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">remove</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">num</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="w">    </span><span class="c1">// 木が空の場合、戻る</span>
+<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
+<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">root</span><span class="p">,</span><span class="w"> </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-30-7" name="__codelineno-30-7" href="#__codelineno-30-7"></a><span class="w">    </span><span class="c1">// ループで検索、葉ノードを通過後に終了</span>
+<a id="__codelineno-30-8" name="__codelineno-30-8" href="#__codelineno-30-8"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-9" name="__codelineno-30-9" href="#__codelineno-30-9"></a><span class="w">        </span><span class="c1">// 削除するノードを見つけた、ループを終了</span>
+<a id="__codelineno-30-10" name="__codelineno-30-10" href="#__codelineno-30-10"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-30-11" name="__codelineno-30-11" href="#__codelineno-30-11"></a><span class="w">            </span><span class="k">break</span><span class="p">;</span>
+<a id="__codelineno-30-12" name="__codelineno-30-12" href="#__codelineno-30-12"></a><span class="w">        </span><span class="n">pre</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">;</span>
+<a id="__codelineno-30-13" name="__codelineno-30-13" href="#__codelineno-30-13"></a><span class="w">        </span><span class="c1">// 削除するノードは cur の右部分木にある</span>
+<a id="__codelineno-30-14" name="__codelineno-30-14" href="#__codelineno-30-14"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">&lt;</span><span class="w"> </span><span class="n">num</span><span class="p">)</span>
+<a id="__codelineno-30-15" name="__codelineno-30-15" href="#__codelineno-30-15"></a><span class="w">            </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="na">right</span><span class="p">;</span>
+<a id="__codelineno-30-16" name="__codelineno-30-16" href="#__codelineno-30-16"></a><span class="w">        </span><span class="c1">// 削除するノードは cur の左部分木にある</span>
+<a id="__codelineno-30-17" name="__codelineno-30-17" href="#__codelineno-30-17"></a><span class="w">        </span><span class="k">else</span>
+<a id="__codelineno-30-18" name="__codelineno-30-18" href="#__codelineno-30-18"></a><span class="w">            </span><span class="n">cur</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="na">left</span><span class="p">;</span>
+<a id="__codelineno-30-19" name="__codelineno-30-19" href="#__codelineno-30-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-20" name="__codelineno-30-20" href="#__codelineno-30-20"></a><span class="w">    </span><span class="c1">// 削除するノードがない場合、戻る</span>
+<a id="__codelineno-30-21" name="__codelineno-30-21" href="#__codelineno-30-21"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
+<a id="__codelineno-30-22" name="__codelineno-30-22" href="#__codelineno-30-22"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-30-23" name="__codelineno-30-23" href="#__codelineno-30-23"></a><span class="w">    </span><span class="c1">// 子ノード数 = 0 または 1</span>
+<a id="__codelineno-30-24" name="__codelineno-30-24" href="#__codelineno-30-24"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">||</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-25" name="__codelineno-30-25" href="#__codelineno-30-25"></a><span class="w">        </span><span class="c1">// 子ノード数 = 0/1 の場合、child = null/その子ノード</span>
+<a id="__codelineno-30-26" name="__codelineno-30-26" href="#__codelineno-30-26"></a><span class="w">        </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">child</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="p">:</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="na">right</span><span class="p">;</span>
+<a id="__codelineno-30-27" name="__codelineno-30-27" href="#__codelineno-30-27"></a><span class="w">        </span><span class="c1">// ノード cur を削除</span>
+<a id="__codelineno-30-28" name="__codelineno-30-28" href="#__codelineno-30-28"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">cur</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-29" name="__codelineno-30-29" href="#__codelineno-30-29"></a><span class="w">            </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">pre</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="n">cur</span><span class="p">)</span>
+<a id="__codelineno-30-30" name="__codelineno-30-30" href="#__codelineno-30-30"></a><span class="w">                </span><span class="n">pre</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
+<a id="__codelineno-30-31" name="__codelineno-30-31" href="#__codelineno-30-31"></a><span class="w">            </span><span class="k">else</span>
+<a id="__codelineno-30-32" name="__codelineno-30-32" href="#__codelineno-30-32"></a><span class="w">                </span><span class="n">pre</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
+<a id="__codelineno-30-33" name="__codelineno-30-33" href="#__codelineno-30-33"></a><span class="w">        </span><span class="p">}</span><span class="w"> </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-34" name="__codelineno-30-34" href="#__codelineno-30-34"></a><span class="w">            </span><span class="c1">// 削除されるノードが根の場合、根を再割り当て</span>
+<a id="__codelineno-30-35" name="__codelineno-30-35" href="#__codelineno-30-35"></a><span class="w">            </span><span class="n">root</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">child</span><span class="p">;</span>
+<a id="__codelineno-30-36" name="__codelineno-30-36" href="#__codelineno-30-36"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-30-37" name="__codelineno-30-37" href="#__codelineno-30-37"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-38" name="__codelineno-30-38" href="#__codelineno-30-38"></a><span class="w">    </span><span class="c1">// 子ノード数 = 2</span>
+<a id="__codelineno-30-39" name="__codelineno-30-39" href="#__codelineno-30-39"></a><span class="w">    </span><span class="k">else</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-40" name="__codelineno-30-40" href="#__codelineno-30-40"></a><span class="w">        </span><span class="c1">// cur の中順走査の次のノードを取得</span>
+<a id="__codelineno-30-41" name="__codelineno-30-41" href="#__codelineno-30-41"></a><span class="w">        </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">cur</span><span class="p">.</span><span class="na">right</span><span class="p">;</span>
+<a id="__codelineno-30-42" name="__codelineno-30-42" href="#__codelineno-30-42"></a><span class="w">        </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="n">tmp</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-30-43" name="__codelineno-30-43" href="#__codelineno-30-43"></a><span class="w">            </span><span class="n">tmp</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">.</span><span class="na">left</span><span class="p">;</span>
+<a id="__codelineno-30-44" name="__codelineno-30-44" href="#__codelineno-30-44"></a><span class="w">        </span><span class="p">}</span>
+<a id="__codelineno-30-45" name="__codelineno-30-45" href="#__codelineno-30-45"></a><span class="w">        </span><span class="c1">// 再帰的にノード tmp を削除</span>
+<a id="__codelineno-30-46" name="__codelineno-30-46" href="#__codelineno-30-46"></a><span class="w">        </span><span class="n">remove</span><span class="p">(</span><span class="n">tmp</span><span class="p">.</span><span class="na">val</span><span class="p">);</span>
+<a id="__codelineno-30-47" name="__codelineno-30-47" href="#__codelineno-30-47"></a><span class="w">        </span><span class="c1">// cur を tmp で置き換える</span>
+<a id="__codelineno-30-48" name="__codelineno-30-48" href="#__codelineno-30-48"></a><span class="w">        </span><span class="n">cur</span><span class="p">.</span><span class="na">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">tmp</span><span class="p">.</span><span class="na">val</span><span class="p">;</span>
+<a id="__codelineno-30-49" name="__codelineno-30-49" href="#__codelineno-30-49"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-30-50" name="__codelineno-30-50" href="#__codelineno-30-50"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_tree.cs</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">BinarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">Remove</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_tree.go</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{</span><span class="nx">binarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">remove</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_tree.swift</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="n">BinarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">remove</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_tree.js</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">BinarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">remove</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_tree.ts</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{</span><span class="nx">BinarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">remove</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_tree.dart</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">BinarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">remove</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_tree.rs</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">BinarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">remove</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_tree.c</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">BinarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">removeItem</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_tree.kt</span><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="n">BinarySearchTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">remove</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_tree.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{</span><span class="no">BinarySearchTree</span><span class="p">}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">remove</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_search_tree.zig</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{</span><span class="n">BinarySearchTree</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">remove</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h3 id="4">4. &nbsp; 中順走査は順序付けされている<a class="headerlink" href="#4" title="Permanent link">&para;</a></h3>
+<p>下図に示すように、二分木の中順走査は「左 <span class="arithmatex">\(\rightarrow\)</span> 根 <span class="arithmatex">\(\rightarrow\)</span> 右」の走査順序に従い、二分探索木は「左子ノード <span class="arithmatex">\(&lt;\)</span> 根ノード <span class="arithmatex">\(&lt;\)</span> 右子ノード」のサイズ関係を満たします。</p>
+<p>これは、二分探索木で中順走査を実行するときに、常に次に小さいノードが最初に走査されることを意味し、重要な性質につながります：<strong>二分探索木の中順走査のシーケンスは昇順です</strong>。</p>
+<p>中順走査の昇順性質を使用して、二分探索木で順序付けされたデータを取得するには<span class="arithmatex">\(O(n)\)</span>の時間のみが必要で、追加のソート操作は不要であり、非常に効率的です。</p>
+<p><a class="glightbox" href="../binary_search_tree.assets/bst_inorder_traversal.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="二分探索木の中順走査シーケンス" class="animation-figure" src="../binary_search_tree.assets/bst_inorder_traversal.png" /></a></p>
+<p align="center"> 図 7-22 &nbsp; 二分探索木の中順走査シーケンス </p>
+
+<h2 id="742">7.4.2 &nbsp; 二分探索木の効率<a class="headerlink" href="#742" title="Permanent link">&para;</a></h2>
+<p>データのセットが与えられた場合、配列または二分探索木を使用して格納することを検討します。下の表を観察すると、二分探索木のすべての操作は対数時間計算量を持ち、安定して効率的です。配列は、頻繁な追加と検索や削除の頻度が少ないシナリオでのみ、二分探索木よりも効率的です。</p>
+<p align="center"> 表 7-2 &nbsp; 配列と探索木の効率比較 </p>
+
+<div class="center-table">
+<table>
+<thead>
+<tr>
+<th></th>
+<th>未ソート配列</th>
+<th>二分探索木</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td>要素の検索</td>
+<td><span class="arithmatex">\(O(n)\)</span></td>
+<td><span class="arithmatex">\(O(\log n)\)</span></td>
+</tr>
+<tr>
+<td>要素の挿入</td>
+<td><span class="arithmatex">\(O(1)\)</span></td>
+<td><span class="arithmatex">\(O(\log n)\)</span></td>
+</tr>
+<tr>
+<td>要素の削除</td>
+<td><span class="arithmatex">\(O(n)\)</span></td>
+<td><span class="arithmatex">\(O(\log n)\)</span></td>
+</tr>
+</tbody>
+</table>
+</div>
+<p>理想的には、二分探索木は「平衡」しており、任意のノードを<span class="arithmatex">\(\log n\)</span>ループ内で見つけることができます。</p>
+<p>しかし、二分探索木で継続的にノードを挿入および削除すると、下図に示すように連結リストに退化する可能性があり、さまざまな操作の時間計算量も<span class="arithmatex">\(O(n)\)</span>に悪化します。</p>
+<p><a class="glightbox" href="../binary_search_tree.assets/bst_degradation.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="二分探索木の退化" class="animation-figure" src="../binary_search_tree.assets/bst_degradation.png" /></a></p>
+<p align="center"> 図 7-23 &nbsp; 二分探索木の退化 </p>
+
+<h2 id="743">7.4.3 &nbsp; 二分探索木の一般的な応用<a class="headerlink" href="#743" title="Permanent link">&para;</a></h2>
+<ul>
+<li>システムでの多レベルインデックスとして使用され、効率的な検索、挿入、削除操作を実装します。</li>
+<li>特定の検索アルゴリズムの基盤となるデータ構造として機能します。</li>
+<li>データストリームを格納して、その順序付けされた状態を維持するために使用されます。</li>
+</ul>
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+    html.glightbox-open { overflow: initial; height: 100%; }
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+    .gslide-image img { background: white; }
+    .gscrollbar-fixer { padding-right: 15px; }
+    .gdesc-inner { font-size: 0.75rem; }
+    body[data-md-color-scheme="slate"] .gdesc-inner { background: var(--md-default-bg-color);}
+    body[data-md-color-scheme="slate"] .gslide-title { color: var(--md-default-fg-color);}
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+    <input class="md-toggle" data-md-toggle="search" type="checkbox" id="__search" autocomplete="off">
+    <label class="md-overlay" for="__drawer"></label>
+    <div data-md-component="skip">
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+        
+        <a href="#71" class="md-skip">
+          コンテンツにスキップ
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+      
+    </div>
+    <div data-md-component="announce">
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+        <aside class="md-banner">
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+            
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+        </aside>
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+  <nav class="md-header__inner md-grid" aria-label="ヘッダー">
+    <a href="../.." title="Hello アルゴリズム" class="md-header__button md-logo" aria-label="Hello アルゴリズム" data-md-component="logo">
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+  <img src="../../assets/images/logo.svg" alt="logo">
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+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 6h18v2H3V6m0 5h18v2H3v-2m0 5h18v2H3v-2Z"/></svg>
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+    <div class="md-header__title" data-md-component="header-title">
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+        <div class="md-header__topic" data-md-component="header-topic">
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+        <form class="md-header__option" data-md-component="palette">
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+    <input class="md-option" data-md-color-media="" data-md-color-scheme="default" data-md-color-primary="white" data-md-color-accent="teal"  aria-label="ダークモード"  type="radio" name="__palette" id="__palette_0">
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+        <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07 19.07 3.5m-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13.51 1.67m-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87.4 1.31M19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35-2.53-2.2m4.33-2.7 1.15-2.77 2.2 2.54-3.35.23m1.15-4.96-1.14-2.78 3.34.24-2.2 2.54M9.63 18.93l2.77 1.15-2.53 2.19-.24-3.34Z"/></svg>
+      </label>
+    
+  
+    
+    
+    
+    <input class="md-option" data-md-color-media="" data-md-color-scheme="slate" data-md-color-primary="black" data-md-color-accent="teal"  aria-label="ライトモード"  type="radio" name="__palette" id="__palette_1">
+    
+      <label class="md-header__button md-icon" title="ライトモード" for="__palette_0" hidden>
+        <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M7.5 2c-1.79 1.15-3 3.18-3 5.5s1.21 4.35 3.03 5.5C4.46 13 2 10.54 2 7.5A5.5 5.5 0 0 1 7.5 2m11.57 1.5 1.43 1.43L4.93 20.5 3.5 19.07 19.07 3.5m-6.18 2.43L11.41 5 9.97 6l.42-1.7L9 3.24l1.75-.12.58-1.65L12 3.1l1.73.03-1.35 1.13.51 1.67m-3.3 3.61-1.16-.73-1.12.78.34-1.32-1.09-.83 1.36-.09.45-1.29.51 1.27 1.36.03-1.05.87.4 1.31M19 13.5a5.5 5.5 0 0 1-5.5 5.5c-1.22 0-2.35-.4-3.26-1.07l7.69-7.69c.67.91 1.07 2.04 1.07 3.26m-4.4 6.58 2.77-1.15-.24 3.35-2.53-2.2m4.33-2.7 1.15-2.77 2.2 2.54-3.35.23m1.15-4.96-1.14-2.78 3.34.24-2.2 2.54M9.63 18.93l2.77 1.15-2.53 2.19-.24-3.34Z"/></svg>
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+    
+  
+</form>
+      
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+    
+      <script>var media,input,key,value,palette=__md_get("__palette");if(palette&&palette.color){"(prefers-color-scheme)"===palette.color.media&&(media=matchMedia("(prefers-color-scheme: light)"),input=document.querySelector(media.matches?"[data-md-color-media='(prefers-color-scheme: light)']":"[data-md-color-media='(prefers-color-scheme: dark)']"),palette.color.media=input.getAttribute("data-md-color-media"),palette.color.scheme=input.getAttribute("data-md-color-scheme"),palette.color.primary=input.getAttribute("data-md-color-primary"),palette.color.accent=input.getAttribute("data-md-color-accent"));for([key,value]of Object.entries(palette.color))document.body.setAttribute("data-md-color-"+key,value)}</script>
+    
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+      <div class="md-header__option">
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+    </button>
+    <div class="md-select__inner">
+      <ul class="md-select__list">
+        
+          <li class="md-select__item">
+            <a href="/chapter_tree/binary_tree/" hreflang="zh" class="md-select__link">
+              简体中文
+            </a>
+          </li>
+        
+          <li class="md-select__item">
+            <a href="/zh-hant/chapter_tree/binary_tree/" hreflang="zh-Hant" class="md-select__link">
+              繁體中文
+            </a>
+          </li>
+        
+          <li class="md-select__item">
+            <a href="/en/chapter_tree/binary_tree/" hreflang="en" class="md-select__link">
+              English
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+          </li>
+        
+          <li class="md-select__item">
+            <a href="/ja/chapter_tree/binary_tree/" hreflang="ja" class="md-select__link">
+              日本語
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+      <label class="md-header__button md-icon" for="__search">
+        
+        <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9.5 3A6.5 6.5 0 0 1 16 9.5c0 1.61-.59 3.09-1.56 4.23l.27.27h.79l5 5-1.5 1.5-5-5v-.79l-.27-.27A6.516 6.516 0 0 1 9.5 16 6.5 6.5 0 0 1 3 9.5 6.5 6.5 0 0 1 9.5 3m0 2C7 5 5 7 5 9.5S7 14 9.5 14 14 12 14 9.5 12 5 9.5 5Z"/></svg>
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+  <label class="md-search__overlay" for="__search"></label>
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+        <button type="reset" class="md-search__icon md-icon" title="クリア" aria-label="クリア" tabindex="-1">
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+        </button>
+      </nav>
+      
+        <div class="md-search__suggest" data-md-component="search-suggest"></div>
+      
+    </form>
+    <div class="md-search__output">
+      <div class="md-search__scrollwrap" data-md-scrollfix>
+        <div class="md-search-result" data-md-component="search-result">
+          <div class="md-search-result__meta">
+            検索を初期化
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+          <ol class="md-search-result__list" role="presentation"></ol>
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+    
+    
+      <div class="md-header__source">
+        <a href="https://github.com/krahets/hello-algo" title="リポジトリへ" class="md-source" data-md-component="source">
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+    
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 496 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"/></svg>
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+  <div class="md-source__repository">
+    krahets/hello-algo
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+      <main class="md-main" data-md-component="main">
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+              
+              <div class="md-sidebar md-sidebar--primary" data-md-component="sidebar" data-md-type="navigation" >
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+                  <div class="md-sidebar__inner">
+                    
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+<nav class="md-nav md-nav--primary" aria-label="ナビゲーション" data-md-level="0">
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+    
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 496 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z"/></svg>
+  </div>
+  <div class="md-source__repository">
+    krahets/hello-algo
+  </div>
+</a>
+    </div>
+  
+  <ul class="md-nav__list" data-md-scrollfix>
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
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+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_1" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hello_algo/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m13.13 22.19-1.63-3.83c1.57-.58 3.04-1.36 4.4-2.27l-2.77 6.1M5.64 12.5l-3.83-1.63 6.1-2.77C7 9.46 6.22 10.93 5.64 12.5M19.22 4c.28 0 .53 0 .74.05.17 1.39-.02 4.25-3.3 7.53-1.7 1.71-3.73 3.02-6.01 3.89l-2.15-2.1c.92-2.31 2.23-4.34 3.92-6.03C15.18 4.58 17.64 4 19.22 4m0-2c-1.98 0-4.98.69-8.22 3.93-2.19 2.19-3.5 4.6-4.35 6.71-.28.75-.09 1.57.46 2.13l2.13 2.12c.38.38.89.61 1.42.61.23 0 .47-.06.7-.15A19.1 19.1 0 0 0 18.07 13c5.66-5.66 3.54-10.61 3.54-10.61S20.7 2 19.22 2m-4.68 7.46c-.78-.78-.78-2.05 0-2.83s2.05-.78 2.83 0c.77.78.78 2.05 0 2.83-.78.78-2.05.78-2.83 0m-5.66 7.07-1.41-1.41 1.41 1.41M6.24 22l3.64-3.64c-.34-.09-.67-.24-.97-.45L4.83 22h1.41M2 22h1.41l4.77-4.76-1.42-1.41L2 20.59V22m0-2.83 4.09-4.08c-.21-.3-.36-.62-.45-.97L2 17.76v1.41Z"/></svg>
+  
+  <span class="md-ellipsis">
+    はじめに
+  </span>
+  
+
+            </a>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_1_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_1">
+            <span class="md-nav__icon md-icon"></span>
+            はじめに
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
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+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
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+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
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+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_2" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_preface/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M21 4H3a2 2 0 0 0-2 2v13a2 2 0 0 0 2 2h18a2 2 0 0 0 2-2V6a2 2 0 0 0-2-2M3 19V6h8v13H3m18 0h-8V6h8v13m-7-9.5h6V11h-6V9.5m0 2.5h6v1.5h-6V12m0 2.5h6V16h-6v-1.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 0 章 &nbsp; 前書き
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_2" id="__nav_2_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_2_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_2">
+            <span class="md-nav__icon md-icon"></span>
+            第 0 章 &nbsp; 前書き
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/about_the_book/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.1 &nbsp; この本について
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/suggestions/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.2 &nbsp; 本書の使い方
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_preface/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
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+      
+      
+  
+  
+  
+  
+    
+    
+      
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+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_introduction/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#711" class="md-nav__link">
+    <span class="md-ellipsis">
+      7.1.1 &nbsp; 二分木の一般的な用語
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#712" class="md-nav__link">
+    <span class="md-ellipsis">
+      7.1.2 &nbsp; 二分木の基本操作
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="7.1.2   二分木の基本操作">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 二分木の初期化
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; ノードの挿入と削除
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#713" class="md-nav__link">
+    <span class="md-ellipsis">
+      7.1.3 &nbsp; 二分木の一般的な種類
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="7.1.3   二分木の一般的な種類">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1_1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 完全二分木
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2_1" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; 完備二分木
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#3" class="md-nav__link">
+    <span class="md-ellipsis">
+      3. &nbsp; 満二分木
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#4" class="md-nav__link">
+    <span class="md-ellipsis">
+      4. &nbsp; 平衡二分木
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#714" class="md-nav__link">
+    <span class="md-ellipsis">
+      7.1.4 &nbsp; 二分木の退化
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
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+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
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+            
+              
+            
+              
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
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+            
+              
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+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
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+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
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+      
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+          
+        
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+    
+    
+    
+    
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+      
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+            <a href="../../chapter_reference/" class="md-nav__link ">
+              
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9 3v15h3V3H9m3 2 4 13 3-1-4-13-3 1M5 5v13h3V5H5M3 19v2h18v-2H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    参考文献
+  </span>
+  
+
+            </a>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_19_label" aria-expanded="false">
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+            参考文献
+          </label>
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+            
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+      
+    </li>
+  
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+    
+  </ul>
+</nav>
+                  </div>
+                </div>
+              </div>
+            
+            
+              
+              <div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
+                <div class="md-sidebar__scrollwrap">
+                  <div class="md-sidebar__inner">
+                    
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#711" class="md-nav__link">
+    <span class="md-ellipsis">
+      7.1.1 &nbsp; 二分木の一般的な用語
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#712" class="md-nav__link">
+    <span class="md-ellipsis">
+      7.1.2 &nbsp; 二分木の基本操作
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="7.1.2   二分木の基本操作">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 二分木の初期化
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; ノードの挿入と削除
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#713" class="md-nav__link">
+    <span class="md-ellipsis">
+      7.1.3 &nbsp; 二分木の一般的な種類
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="7.1.3   二分木の一般的な種類">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1_1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 完全二分木
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2_1" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; 完備二分木
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#3" class="md-nav__link">
+    <span class="md-ellipsis">
+      3. &nbsp; 満二分木
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#4" class="md-nav__link">
+    <span class="md-ellipsis">
+      4. &nbsp; 平衡二分木
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#714" class="md-nav__link">
+    <span class="md-ellipsis">
+      7.1.4 &nbsp; 二分木の退化
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+                  </div>
+                </div>
+              </div>
+            
+          
+          
+            <div class="md-content" data-md-component="content">
+              <article class="md-content__inner md-typeset">
+                
+                  <!-- Tags -->
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+
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+<!-- Actions -->
+
+
+  <!-- Edit button -->
+  
+    <a
+      href="https://github.com/krahets/hello-algo/tree/main/ja/docs/chapter_tree/binary_tree.md"
+      title="編集"
+      class="md-content__button md-icon"
+    >
+      
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
+    </a>
+  
+
+  <!-- View button -->
+  
+
+
+<!-- Page content -->
+<h1 id="71">7.1 &nbsp; 二分木<a class="headerlink" href="#71" title="Permanent link">&para;</a></h1>
+<p><u>二分木</u>は、祖先と子孫の間の階層関係を表現し、「二つに分割する」分割統治法の論理を体現する非線形データ構造です。連結リストと同様に、二分木の基本単位はノードであり、各ノードは値、左の子ノードへの参照、右の子ノードへの参照を含みます。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:14"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><input id="__tabbed_1_14" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label><label for="__tabbed_1_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">class</span><span class="w"> </span><span class="nc">TreeNode</span><span class="p">:</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;二分木ノード&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="k">def</span><span class="w"> </span><span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">val</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">val</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="n">val</span>                <span class="c1"># ノード値</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">left</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span>  <span class="c1"># 左の子ノードへの参照</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>        <span class="bp">self</span><span class="o">.</span><span class="n">right</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span> <span class="o">=</span> <span class="kc">None</span> <span class="c1"># 右の子ノードへの参照</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* 二分木ノード */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="k">struct</span><span class="w"> </span><span class="nc">TreeNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w">          </span><span class="c1">// ノード値</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">left</span><span class="p">;</span><span class="w">   </span><span class="c1">// 左の子ノードへのポインタ</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">right</span><span class="p">;</span><span class="w">  </span><span class="c1">// 右の子ノードへのポインタ</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="n">TreeNode</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">x</span><span class="p">)</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="n">val</span><span class="p">(</span><span class="n">x</span><span class="p">),</span><span class="w"> </span><span class="n">left</span><span class="p">(</span><span class="k">nullptr</span><span class="p">),</span><span class="w"> </span><span class="n">right</span><span class="p">(</span><span class="k">nullptr</span><span class="p">)</span><span class="w"> </span><span class="p">{}</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="p">};</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* 二分木ノード */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="kd">class</span> <span class="nc">TreeNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w">         </span><span class="c1">// ノード値</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">left</span><span class="p">;</span><span class="w">   </span><span class="c1">// 左の子ノードへの参照</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">right</span><span class="p">;</span><span class="w">  </span><span class="c1">// 右の子ノードへの参照</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="n">TreeNode</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">x</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">x</span><span class="p">;</span><span class="w"> </span><span class="p">}</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="cm">/* 二分木ノード */</span>
+<a id="__codelineno-3-2" name="__codelineno-3-2" href="#__codelineno-3-2"></a><span class="k">class</span><span class="w"> </span><span class="nf">TreeNode</span><span class="p">(</span><span class="kt">int?</span><span class="w"> </span><span class="n">x</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-3-3" name="__codelineno-3-3" href="#__codelineno-3-3"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="kt">int?</span><span class="w"> </span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">x</span><span class="p">;</span><span class="w">    </span><span class="c1">// ノード値</span>
+<a id="__codelineno-3-4" name="__codelineno-3-4" href="#__codelineno-3-4"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">left</span><span class="p">;</span><span class="w">  </span><span class="c1">// 左の子ノードへの参照</span>
+<a id="__codelineno-3-5" name="__codelineno-3-5" href="#__codelineno-3-5"></a><span class="w">    </span><span class="k">public</span><span class="w"> </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">right</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右の子ノードへの参照</span>
+<a id="__codelineno-3-6" name="__codelineno-3-6" href="#__codelineno-3-6"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="cm">/* 二分木ノード */</span>
+<a id="__codelineno-4-2" name="__codelineno-4-2" href="#__codelineno-4-2"></a><span class="kd">type</span><span class="w"> </span><span class="nx">TreeNode</span><span class="w"> </span><span class="kd">struct</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-3" name="__codelineno-4-3" href="#__codelineno-4-3"></a><span class="w">    </span><span class="nx">Val</span><span class="w">   </span><span class="kt">int</span>
+<a id="__codelineno-4-4" name="__codelineno-4-4" href="#__codelineno-4-4"></a><span class="w">    </span><span class="nx">Left</span><span class="w">  </span><span class="o">*</span><span class="nx">TreeNode</span>
+<a id="__codelineno-4-5" name="__codelineno-4-5" href="#__codelineno-4-5"></a><span class="w">    </span><span class="nx">Right</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span>
+<a id="__codelineno-4-6" name="__codelineno-4-6" href="#__codelineno-4-6"></a><span class="p">}</span>
+<a id="__codelineno-4-7" name="__codelineno-4-7" href="#__codelineno-4-7"></a><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-4-8" name="__codelineno-4-8" href="#__codelineno-4-8"></a><span class="kd">func</span><span class="w"> </span><span class="nx">NewTreeNode</span><span class="p">(</span><span class="nx">v</span><span class="w"> </span><span class="kt">int</span><span class="p">)</span><span class="w"> </span><span class="o">*</span><span class="nx">TreeNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-4-9" name="__codelineno-4-9" href="#__codelineno-4-9"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="o">&amp;</span><span class="nx">TreeNode</span><span class="p">{</span>
+<a id="__codelineno-4-10" name="__codelineno-4-10" href="#__codelineno-4-10"></a><span class="w">        </span><span class="nx">Left</span><span class="p">:</span><span class="w">  </span><span class="kc">nil</span><span class="p">,</span><span class="w"> </span><span class="c1">// 左の子ノードへのポインタ</span>
+<a id="__codelineno-4-11" name="__codelineno-4-11" href="#__codelineno-4-11"></a><span class="w">        </span><span class="nx">Right</span><span class="p">:</span><span class="w"> </span><span class="kc">nil</span><span class="p">,</span><span class="w"> </span><span class="c1">// 右の子ノードへのポインタ</span>
+<a id="__codelineno-4-12" name="__codelineno-4-12" href="#__codelineno-4-12"></a><span class="w">        </span><span class="nx">Val</span><span class="p">:</span><span class="w">   </span><span class="nx">v</span><span class="p">,</span><span class="w">   </span><span class="c1">// ノード値</span>
+<a id="__codelineno-4-13" name="__codelineno-4-13" href="#__codelineno-4-13"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-4-14" name="__codelineno-4-14" href="#__codelineno-4-14"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="cm">/* 二分木ノード */</span>
+<a id="__codelineno-5-2" name="__codelineno-5-2" href="#__codelineno-5-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">TreeNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-3" name="__codelineno-5-3" href="#__codelineno-5-3"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">val</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="w"> </span><span class="c1">// ノード値</span>
+<a id="__codelineno-5-4" name="__codelineno-5-4" href="#__codelineno-5-4"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">left</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">?</span><span class="w"> </span><span class="c1">// 左の子ノードへの参照</span>
+<a id="__codelineno-5-5" name="__codelineno-5-5" href="#__codelineno-5-5"></a><span class="w">    </span><span class="kd">var</span><span class="w"> </span><span class="nv">right</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">?</span><span class="w"> </span><span class="c1">// 右の子ノードへの参照</span>
+<a id="__codelineno-5-6" name="__codelineno-5-6" href="#__codelineno-5-6"></a>
+<a id="__codelineno-5-7" name="__codelineno-5-7" href="#__codelineno-5-7"></a><span class="w">    </span><span class="kd">init</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="nb">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-5-8" name="__codelineno-5-8" href="#__codelineno-5-8"></a><span class="w">        </span><span class="n">val</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">x</span>
+<a id="__codelineno-5-9" name="__codelineno-5-9" href="#__codelineno-5-9"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-5-10" name="__codelineno-5-10" href="#__codelineno-5-10"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="cm">/* 二分木ノード */</span>
+<a id="__codelineno-6-2" name="__codelineno-6-2" href="#__codelineno-6-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">TreeNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-3" name="__codelineno-6-3" href="#__codelineno-6-3"></a><span class="w">    </span><span class="nx">val</span><span class="p">;</span><span class="w"> </span><span class="c1">// ノード値</span>
+<a id="__codelineno-6-4" name="__codelineno-6-4" href="#__codelineno-6-4"></a><span class="w">    </span><span class="nx">left</span><span class="p">;</span><span class="w"> </span><span class="c1">// 左の子ノードへのポインタ</span>
+<a id="__codelineno-6-5" name="__codelineno-6-5" href="#__codelineno-6-5"></a><span class="w">    </span><span class="nx">right</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右の子ノードへのポインタ</span>
+<a id="__codelineno-6-6" name="__codelineno-6-6" href="#__codelineno-6-6"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">(</span><span class="nx">val</span><span class="p">,</span><span class="w"> </span><span class="nx">left</span><span class="p">,</span><span class="w"> </span><span class="nx">right</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-6-7" name="__codelineno-6-7" href="#__codelineno-6-7"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="mf">0</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="nx">val</span><span class="p">;</span>
+<a id="__codelineno-6-8" name="__codelineno-6-8" href="#__codelineno-6-8"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">left</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="nx">left</span><span class="p">;</span>
+<a id="__codelineno-6-9" name="__codelineno-6-9" href="#__codelineno-6-9"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">right</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="kc">null</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="nx">right</span><span class="p">;</span>
+<a id="__codelineno-6-10" name="__codelineno-6-10" href="#__codelineno-6-10"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-6-11" name="__codelineno-6-11" href="#__codelineno-6-11"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="cm">/* 二分木ノード */</span>
+<a id="__codelineno-7-2" name="__codelineno-7-2" href="#__codelineno-7-2"></a><span class="kd">class</span><span class="w"> </span><span class="nx">TreeNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-3" name="__codelineno-7-3" href="#__codelineno-7-3"></a><span class="w">    </span><span class="nx">val</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">;</span>
+<a id="__codelineno-7-4" name="__codelineno-7-4" href="#__codelineno-7-4"></a><span class="w">    </span><span class="nx">left</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-7-5" name="__codelineno-7-5" href="#__codelineno-7-5"></a><span class="w">    </span><span class="nx">right</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">;</span>
+<a id="__codelineno-7-6" name="__codelineno-7-6" href="#__codelineno-7-6"></a>
+<a id="__codelineno-7-7" name="__codelineno-7-7" href="#__codelineno-7-7"></a><span class="w">    </span><span class="kr">constructor</span><span class="p">(</span><span class="nx">val?</span><span class="o">:</span><span class="w"> </span><span class="kt">number</span><span class="p">,</span><span class="w"> </span><span class="nx">left?</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">,</span><span class="w"> </span><span class="nx">right?</span><span class="o">:</span><span class="w"> </span><span class="kt">TreeNode</span><span class="w"> </span><span class="o">|</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-7-8" name="__codelineno-7-8" href="#__codelineno-7-8"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">val</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">0</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">val</span><span class="p">;</span><span class="w"> </span><span class="c1">// ノード値</span>
+<a id="__codelineno-7-9" name="__codelineno-7-9" href="#__codelineno-7-9"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">left</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">null</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">left</span><span class="p">;</span><span class="w"> </span><span class="c1">// 左の子ノードへの参照</span>
+<a id="__codelineno-7-10" name="__codelineno-7-10" href="#__codelineno-7-10"></a><span class="w">        </span><span class="k">this</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">right</span><span class="w"> </span><span class="o">===</span><span class="w"> </span><span class="kc">undefined</span><span class="w"> </span><span class="o">?</span><span class="w"> </span><span class="nx">null</span><span class="w"> </span><span class="o">:</span><span class="w"> </span><span class="kt">right</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右の子ノードへの参照</span>
+<a id="__codelineno-7-11" name="__codelineno-7-11" href="#__codelineno-7-11"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-7-12" name="__codelineno-7-12" href="#__codelineno-7-12"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="cm">/* 二分木ノード */</span>
+<a id="__codelineno-8-2" name="__codelineno-8-2" href="#__codelineno-8-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">TreeNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-8-3" name="__codelineno-8-3" href="#__codelineno-8-3"></a><span class="w">  </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w">         </span><span class="c1">// ノード値</span>
+<a id="__codelineno-8-4" name="__codelineno-8-4" href="#__codelineno-8-4"></a><span class="w">  </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">left</span><span class="p">;</span><span class="w">  </span><span class="c1">// 左の子ノードへの参照</span>
+<a id="__codelineno-8-5" name="__codelineno-8-5" href="#__codelineno-8-5"></a><span class="w">  </span><span class="n">TreeNode</span><span class="o">?</span><span class="w"> </span><span class="n">right</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右の子ノードへの参照</span>
+<a id="__codelineno-8-6" name="__codelineno-8-6" href="#__codelineno-8-6"></a><span class="w">  </span><span class="n">TreeNode</span><span class="p">(</span><span class="k">this</span><span class="p">.</span><span class="n">val</span><span class="p">,</span><span class="w"> </span><span class="p">[</span><span class="k">this</span><span class="p">.</span><span class="n">left</span><span class="p">,</span><span class="w"> </span><span class="k">this</span><span class="p">.</span><span class="n">right</span><span class="p">]);</span>
+<a id="__codelineno-8-7" name="__codelineno-8-7" href="#__codelineno-8-7"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="k">use</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">rc</span><span class="p">::</span><span class="n">Rc</span><span class="p">;</span>
+<a id="__codelineno-9-2" name="__codelineno-9-2" href="#__codelineno-9-2"></a><span class="k">use</span><span class="w"> </span><span class="n">std</span><span class="p">::</span><span class="n">cell</span><span class="p">::</span><span class="n">RefCell</span><span class="p">;</span>
+<a id="__codelineno-9-3" name="__codelineno-9-3" href="#__codelineno-9-3"></a>
+<a id="__codelineno-9-4" name="__codelineno-9-4" href="#__codelineno-9-4"></a><span class="cm">/* 二分木ノード */</span>
+<a id="__codelineno-9-5" name="__codelineno-9-5" href="#__codelineno-9-5"></a><span class="k">struct</span><span class="w"> </span><span class="nc">TreeNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-6" name="__codelineno-9-6" href="#__codelineno-9-6"></a><span class="w">    </span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">,</span><span class="w">                               </span><span class="c1">// ノード値</span>
+<a id="__codelineno-9-7" name="__codelineno-9-7" href="#__codelineno-9-7"></a><span class="w">    </span><span class="n">left</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;</span><span class="p">,</span><span class="w">    </span><span class="c1">// 左の子ノードへの参照</span>
+<a id="__codelineno-9-8" name="__codelineno-9-8" href="#__codelineno-9-8"></a><span class="w">    </span><span class="n">right</span><span class="p">:</span><span class="w"> </span><span class="nb">Option</span><span class="o">&lt;</span><span class="n">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;&gt;&gt;</span><span class="p">,</span><span class="w">   </span><span class="c1">// 右の子ノードへの参照</span>
+<a id="__codelineno-9-9" name="__codelineno-9-9" href="#__codelineno-9-9"></a><span class="p">}</span>
+<a id="__codelineno-9-10" name="__codelineno-9-10" href="#__codelineno-9-10"></a>
+<a id="__codelineno-9-11" name="__codelineno-9-11" href="#__codelineno-9-11"></a><span class="k">impl</span><span class="w"> </span><span class="n">TreeNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-12" name="__codelineno-9-12" href="#__codelineno-9-12"></a><span class="w">    </span><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-9-13" name="__codelineno-9-13" href="#__codelineno-9-13"></a><span class="w">    </span><span class="k">fn</span><span class="w"> </span><span class="nf">new</span><span class="p">(</span><span class="n">val</span><span class="p">:</span><span class="w"> </span><span class="kt">i32</span><span class="p">)</span><span class="w"> </span><span class="p">-&gt;</span><span class="w"> </span><span class="nc">Rc</span><span class="o">&lt;</span><span class="n">RefCell</span><span class="o">&lt;</span><span class="bp">Self</span><span class="o">&gt;&gt;</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-14" name="__codelineno-9-14" href="#__codelineno-9-14"></a><span class="w">        </span><span class="n">Rc</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="n">RefCell</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="bp">Self</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-9-15" name="__codelineno-9-15" href="#__codelineno-9-15"></a><span class="w">            </span><span class="n">val</span><span class="p">,</span>
+<a id="__codelineno-9-16" name="__codelineno-9-16" href="#__codelineno-9-16"></a><span class="w">            </span><span class="n">left</span><span class="p">:</span><span class="w"> </span><span class="nb">None</span><span class="p">,</span>
+<a id="__codelineno-9-17" name="__codelineno-9-17" href="#__codelineno-9-17"></a><span class="w">            </span><span class="n">right</span><span class="p">:</span><span class="w"> </span><span class="nb">None</span>
+<a id="__codelineno-9-18" name="__codelineno-9-18" href="#__codelineno-9-18"></a><span class="w">        </span><span class="p">}))</span>
+<a id="__codelineno-9-19" name="__codelineno-9-19" href="#__codelineno-9-19"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-9-20" name="__codelineno-9-20" href="#__codelineno-9-20"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="cm">/* 二分木ノード */</span>
+<a id="__codelineno-10-2" name="__codelineno-10-2" href="#__codelineno-10-2"></a><span class="k">typedef</span><span class="w"> </span><span class="k">struct</span><span class="w"> </span><span class="nc">TreeNode</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-3" name="__codelineno-10-3" href="#__codelineno-10-3"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">;</span><span class="w">                </span><span class="c1">// ノード値</span>
+<a id="__codelineno-10-4" name="__codelineno-10-4" href="#__codelineno-10-4"></a><span class="w">    </span><span class="kt">int</span><span class="w"> </span><span class="n">height</span><span class="p">;</span><span class="w">             </span><span class="c1">// ノードの高さ</span>
+<a id="__codelineno-10-5" name="__codelineno-10-5" href="#__codelineno-10-5"></a><span class="w">    </span><span class="k">struct</span><span class="w"> </span><span class="nc">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">left</span><span class="p">;</span><span class="w">  </span><span class="c1">// 左の子ノードへのポインタ</span>
+<a id="__codelineno-10-6" name="__codelineno-10-6" href="#__codelineno-10-6"></a><span class="w">    </span><span class="k">struct</span><span class="w"> </span><span class="nc">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">right</span><span class="p">;</span><span class="w"> </span><span class="c1">// 右の子ノードへのポインタ</span>
+<a id="__codelineno-10-7" name="__codelineno-10-7" href="#__codelineno-10-7"></a><span class="p">}</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">;</span>
+<a id="__codelineno-10-8" name="__codelineno-10-8" href="#__codelineno-10-8"></a>
+<a id="__codelineno-10-9" name="__codelineno-10-9" href="#__codelineno-10-9"></a><span class="cm">/* コンストラクタ */</span>
+<a id="__codelineno-10-10" name="__codelineno-10-10" href="#__codelineno-10-10"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="nf">newTreeNode</span><span class="p">(</span><span class="kt">int</span><span class="w"> </span><span class="n">val</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-10-11" name="__codelineno-10-11" href="#__codelineno-10-11"></a><span class="w">    </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-10-12" name="__codelineno-10-12" href="#__codelineno-10-12"></a>
+<a id="__codelineno-10-13" name="__codelineno-10-13" href="#__codelineno-10-13"></a><span class="w">    </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="p">)</span><span class="n">malloc</span><span class="p">(</span><span class="k">sizeof</span><span class="p">(</span><span class="n">TreeNode</span><span class="p">));</span>
+<a id="__codelineno-10-14" name="__codelineno-10-14" href="#__codelineno-10-14"></a><span class="w">    </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">val</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">val</span><span class="p">;</span>
+<a id="__codelineno-10-15" name="__codelineno-10-15" href="#__codelineno-10-15"></a><span class="w">    </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">height</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="mi">0</span><span class="p">;</span>
+<a id="__codelineno-10-16" name="__codelineno-10-16" href="#__codelineno-10-16"></a><span class="w">    </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
+<a id="__codelineno-10-17" name="__codelineno-10-17" href="#__codelineno-10-17"></a><span class="w">    </span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">NULL</span><span class="p">;</span>
+<a id="__codelineno-10-18" name="__codelineno-10-18" href="#__codelineno-10-18"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">node</span><span class="p">;</span>
+<a id="__codelineno-10-19" name="__codelineno-10-19" href="#__codelineno-10-19"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="cm">/* 二分木ノード */</span>
+<a id="__codelineno-11-2" name="__codelineno-11-2" href="#__codelineno-11-2"></a><span class="kd">class</span><span class="w"> </span><span class="nc">TreeNode</span><span class="p">(</span><span class="kd">val</span><span class="w"> </span><span class="nv">_val</span><span class="p">:</span><span class="w"> </span><span class="kt">Int</span><span class="p">)</span><span class="w"> </span><span class="p">{</span><span class="w">  </span><span class="c1">// ノード値</span>
+<a id="__codelineno-11-3" name="__codelineno-11-3" href="#__codelineno-11-3"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">left</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode? </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="w">   </span><span class="c1">// 左の子ノードへの参照</span>
+<a id="__codelineno-11-4" name="__codelineno-11-4" href="#__codelineno-11-4"></a><span class="w">    </span><span class="kd">val</span><span class="w"> </span><span class="nv">right</span><span class="p">:</span><span class="w"> </span><span class="n">TreeNode? </span><span class="o">=</span><span class="w"> </span><span class="kc">null</span><span class="w">  </span><span class="c1">// 右の子ノードへの参照</span>
+<a id="__codelineno-11-5" name="__codelineno-11-5" href="#__codelineno-11-5"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a>
+</code></pre></div>
+</div>
+</div>
+</div>
+<p>各ノードは2つの参照（ポインタ）を持ち、それぞれ<u>左の子ノード</u>と<u>右の子ノード</u>を指しています。このノードは、これら2つの子ノードの<u>親ノード</u>と呼ばれます。二分木のノードが与えられたとき、このノードの左の子とその下にあるすべてのノードで形成される木を、このノードの<u>左部分木</u>と呼びます。同様に、<u>右部分木</u>も定義できます。</p>
+<p><strong>二分木では、葉ノードを除いて、他のすべてのノードは子ノードと空でない部分木を含みます。</strong> 下図に示すように、「ノード2」を親ノードとして見ると、その左と右の子ノードはそれぞれ「ノード4」と「ノード5」です。左部分木は「ノード4」とその下にあるすべてのノードで形成され、右部分木は「ノード5」とその下にあるすべてのノードで形成されます。</p>
+<p><a class="glightbox" href="../binary_tree.assets/binary_tree_definition.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="親ノード、子ノード、部分木" class="animation-figure" src="../binary_tree.assets/binary_tree_definition.png" /></a></p>
+<p align="center"> 図 7-1 &nbsp; 親ノード、子ノード、部分木 </p>
+
+<h2 id="711">7.1.1 &nbsp; 二分木の一般的な用語<a class="headerlink" href="#711" title="Permanent link">&para;</a></h2>
+<p>二分木でよく使用される用語を下図に示します。</p>
+<ul>
+<li><u>根ノード</u>：二分木の最上位レベルにあるノードで、親ノードを持ちません。</li>
+<li><u>葉ノード</u>：子ノードを持たないノードで、両方のポインタが<code>None</code>を指しています。</li>
+<li><u>辺</u>：2つのノードを結ぶ線分で、ノード間の参照（ポインタ）を表現します。</li>
+<li>ノードの<u>レベル</u>：上から下に向かって増加し、根ノードがレベル1です。</li>
+<li>ノードの<u>次数</u>：ノードが持つ子ノードの数です。二分木では、次数は0、1、または2になります。</li>
+<li>二分木の<u>高さ</u>：根ノードから最も遠い葉ノードまでの辺の数です。</li>
+<li>ノードの<u>深さ</u>：根ノードからそのノードまでの辺の数です。</li>
+<li>ノードの<u>高さ</u>：最も遠い葉ノードからそのノードまでの辺の数です。</li>
+</ul>
+<p><a class="glightbox" href="../binary_tree.assets/binary_tree_terminology.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="二分木の一般的な用語" class="animation-figure" src="../binary_tree.assets/binary_tree_terminology.png" /></a></p>
+<p align="center"> 図 7-2 &nbsp; 二分木の一般的な用語 </p>
+
+<div class="admonition tip">
+<p class="admonition-title">Tip</p>
+<p>「高さ」と「深さ」は通常「通過する辺の数」として定義しますが、一部の問題や教科書では「通過するノードの数」として定義されることがあります。この場合、高さと深さの両方を1だけ増やす必要があります。</p>
+</div>
+<h2 id="712">7.1.2 &nbsp; 二分木の基本操作<a class="headerlink" href="#712" title="Permanent link">&para;</a></h2>
+<h3 id="1">1. &nbsp; 二分木の初期化<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<p>連結リストと同様に、二分木の初期化では、まずノードを作成し、次にそれらの間の参照（ポインタ）を確立します。</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:14"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><input id="__tabbed_2_14" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label><label for="__tabbed_2_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree.py</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="c1"># 二分木の初期化</span>
+<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="c1"># ノードの初期化</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a><span class="n">n1</span> <span class="o">=</span> <span class="n">TreeNode</span><span class="p">(</span><span class="n">val</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a><span class="n">n2</span> <span class="o">=</span> <span class="n">TreeNode</span><span class="p">(</span><span class="n">val</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a><span class="n">n3</span> <span class="o">=</span> <span class="n">TreeNode</span><span class="p">(</span><span class="n">val</span><span class="o">=</span><span class="mi">3</span><span class="p">)</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a><span class="n">n4</span> <span class="o">=</span> <span class="n">TreeNode</span><span class="p">(</span><span class="n">val</span><span class="o">=</span><span class="mi">4</span><span class="p">)</span>
+<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a><span class="n">n5</span> <span class="o">=</span> <span class="n">TreeNode</span><span class="p">(</span><span class="n">val</span><span class="o">=</span><span class="mi">5</span><span class="p">)</span>
+<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a><span class="c1"># ノード間の参照（ポインタ）を結ぶ</span>
+<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a><span class="n">n1</span><span class="o">.</span><span class="n">left</span> <span class="o">=</span> <span class="n">n2</span>
+<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="n">n1</span><span class="o">.</span><span class="n">right</span> <span class="o">=</span> <span class="n">n3</span>
+<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="n">n2</span><span class="o">.</span><span class="n">left</span> <span class="o">=</span> <span class="n">n4</span>
+<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a><span class="n">n2</span><span class="o">.</span><span class="n">right</span> <span class="o">=</span> <span class="n">n5</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree.cpp</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 二分木の初期化 */</span>
+<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="c1">// ノードの初期化</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="n">TreeNode</span><span class="o">*</span><span class="w"> </span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="n">TreeNode</span><span class="o">*</span><span class="w"> </span><span class="n">n2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="n">TreeNode</span><span class="o">*</span><span class="w"> </span><span class="n">n3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
+<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="n">TreeNode</span><span class="o">*</span><span class="w"> </span><span class="n">n4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
+<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="n">TreeNode</span><span class="o">*</span><span class="w"> </span><span class="n">n5</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
+<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="c1">// ノード間の参照（ポインタ）を結ぶ</span>
+<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="n">n1</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span><span class="p">;</span>
+<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a><span class="n">n1</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n3</span><span class="p">;</span>
+<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="n">n2</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n4</span><span class="p">;</span>
+<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="n">n2</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n5</span><span class="p">;</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree.java</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="c1">// ノードの初期化</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="n">TreeNode</span><span class="w"> </span><span class="n">n2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="n">TreeNode</span><span class="w"> </span><span class="n">n3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="n">TreeNode</span><span class="w"> </span><span class="n">n4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="n">TreeNode</span><span class="w"> </span><span class="n">n5</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="c1">// ノード間の参照（ポインタ）を結ぶ</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="n">n1</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span><span class="p">;</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="n">n1</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n3</span><span class="p">;</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a><span class="n">n2</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n4</span><span class="p">;</span>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="n">n2</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n5</span><span class="p">;</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree.cs</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="cm">/* 二分木の初期化 */</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a><span class="c1">// ノードの初期化</span>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="n">TreeNode</span><span class="w"> </span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a><span class="n">TreeNode</span><span class="w"> </span><span class="n">n2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="n">TreeNode</span><span class="w"> </span><span class="n">n3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
+<a id="__codelineno-17-6" name="__codelineno-17-6" href="#__codelineno-17-6"></a><span class="n">TreeNode</span><span class="w"> </span><span class="n">n4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
+<a id="__codelineno-17-7" name="__codelineno-17-7" href="#__codelineno-17-7"></a><span class="n">TreeNode</span><span class="w"> </span><span class="n">n5</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
+<a id="__codelineno-17-8" name="__codelineno-17-8" href="#__codelineno-17-8"></a><span class="c1">// ノード間の参照（ポインタ）を結ぶ</span>
+<a id="__codelineno-17-9" name="__codelineno-17-9" href="#__codelineno-17-9"></a><span class="n">n1</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span><span class="p">;</span>
+<a id="__codelineno-17-10" name="__codelineno-17-10" href="#__codelineno-17-10"></a><span class="n">n1</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n3</span><span class="p">;</span>
+<a id="__codelineno-17-11" name="__codelineno-17-11" href="#__codelineno-17-11"></a><span class="n">n2</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n4</span><span class="p">;</span>
+<a id="__codelineno-17-12" name="__codelineno-17-12" href="#__codelineno-17-12"></a><span class="n">n2</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n5</span><span class="p">;</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree.go</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="cm">/* 二分木の初期化 */</span>
+<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a><span class="c1">// ノードの初期化</span>
+<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="nx">n1</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">NewTreeNode</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a><span class="nx">n2</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">NewTreeNode</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="nx">n3</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">NewTreeNode</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
+<a id="__codelineno-18-6" name="__codelineno-18-6" href="#__codelineno-18-6"></a><span class="nx">n4</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">NewTreeNode</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
+<a id="__codelineno-18-7" name="__codelineno-18-7" href="#__codelineno-18-7"></a><span class="nx">n5</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">NewTreeNode</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
+<a id="__codelineno-18-8" name="__codelineno-18-8" href="#__codelineno-18-8"></a><span class="c1">// ノード間の参照（ポインタ）を結ぶ</span>
+<a id="__codelineno-18-9" name="__codelineno-18-9" href="#__codelineno-18-9"></a><span class="nx">n1</span><span class="p">.</span><span class="nx">Left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">n2</span>
+<a id="__codelineno-18-10" name="__codelineno-18-10" href="#__codelineno-18-10"></a><span class="nx">n1</span><span class="p">.</span><span class="nx">Right</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">n3</span>
+<a id="__codelineno-18-11" name="__codelineno-18-11" href="#__codelineno-18-11"></a><span class="nx">n2</span><span class="p">.</span><span class="nx">Left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">n4</span>
+<a id="__codelineno-18-12" name="__codelineno-18-12" href="#__codelineno-18-12"></a><span class="nx">n2</span><span class="p">.</span><span class="nx">Right</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">n5</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="c1">// ノードの初期化</span>
+<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a><span class="kd">let</span><span class="w"> </span><span class="nv">n1</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="mi">1</span><span class="p">)</span>
+<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="kd">let</span><span class="w"> </span><span class="nv">n2</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="mi">2</span><span class="p">)</span>
+<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a><span class="kd">let</span><span class="w"> </span><span class="nv">n3</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="mi">3</span><span class="p">)</span>
+<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="kd">let</span><span class="w"> </span><span class="nv">n4</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="mi">4</span><span class="p">)</span>
+<a id="__codelineno-19-6" name="__codelineno-19-6" href="#__codelineno-19-6"></a><span class="kd">let</span><span class="w"> </span><span class="nv">n5</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="mi">5</span><span class="p">)</span>
+<a id="__codelineno-19-7" name="__codelineno-19-7" href="#__codelineno-19-7"></a><span class="c1">// ノード間の参照（ポインタ）を結ぶ</span>
+<a id="__codelineno-19-8" name="__codelineno-19-8" href="#__codelineno-19-8"></a><span class="n">n1</span><span class="p">.</span><span class="kr">left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">n2</span>
+<a id="__codelineno-19-9" name="__codelineno-19-9" href="#__codelineno-19-9"></a><span class="n">n1</span><span class="p">.</span><span class="kr">right</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">n3</span>
+<a id="__codelineno-19-10" name="__codelineno-19-10" href="#__codelineno-19-10"></a><span class="n">n2</span><span class="p">.</span><span class="kr">left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">n4</span>
+<a id="__codelineno-19-11" name="__codelineno-19-11" href="#__codelineno-19-11"></a><span class="n">n2</span><span class="p">.</span><span class="kr">right</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">n5</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree.js</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="cm">/* 二分木の初期化 */</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a><span class="c1">// ノードの初期化</span>
+<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="kd">let</span><span class="w"> </span><span class="nx">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">TreeNode</span><span class="p">(</span><span class="mf">1</span><span class="p">),</span>
+<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a><span class="w">    </span><span class="nx">n2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">TreeNode</span><span class="p">(</span><span class="mf">2</span><span class="p">),</span>
+<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="w">    </span><span class="nx">n3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">TreeNode</span><span class="p">(</span><span class="mf">3</span><span class="p">),</span>
+<a id="__codelineno-20-6" name="__codelineno-20-6" href="#__codelineno-20-6"></a><span class="w">    </span><span class="nx">n4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">TreeNode</span><span class="p">(</span><span class="mf">4</span><span class="p">),</span>
+<a id="__codelineno-20-7" name="__codelineno-20-7" href="#__codelineno-20-7"></a><span class="w">    </span><span class="nx">n5</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">TreeNode</span><span class="p">(</span><span class="mf">5</span><span class="p">);</span>
+<a id="__codelineno-20-8" name="__codelineno-20-8" href="#__codelineno-20-8"></a><span class="c1">// ノード間の参照（ポインタ）を結ぶ</span>
+<a id="__codelineno-20-9" name="__codelineno-20-9" href="#__codelineno-20-9"></a><span class="nx">n1</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n2</span><span class="p">;</span>
+<a id="__codelineno-20-10" name="__codelineno-20-10" href="#__codelineno-20-10"></a><span class="nx">n1</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n3</span><span class="p">;</span>
+<a id="__codelineno-20-11" name="__codelineno-20-11" href="#__codelineno-20-11"></a><span class="nx">n2</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n4</span><span class="p">;</span>
+<a id="__codelineno-20-12" name="__codelineno-20-12" href="#__codelineno-20-12"></a><span class="nx">n2</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n5</span><span class="p">;</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree.ts</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="cm">/* 二分木の初期化 */</span>
+<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a><span class="c1">// ノードの初期化</span>
+<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="kd">let</span><span class="w"> </span><span class="nx">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">TreeNode</span><span class="p">(</span><span class="mf">1</span><span class="p">),</span>
+<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a><span class="w">    </span><span class="nx">n2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">TreeNode</span><span class="p">(</span><span class="mf">2</span><span class="p">),</span>
+<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="w">    </span><span class="nx">n3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">TreeNode</span><span class="p">(</span><span class="mf">3</span><span class="p">),</span>
+<a id="__codelineno-21-6" name="__codelineno-21-6" href="#__codelineno-21-6"></a><span class="w">    </span><span class="nx">n4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">TreeNode</span><span class="p">(</span><span class="mf">4</span><span class="p">),</span>
+<a id="__codelineno-21-7" name="__codelineno-21-7" href="#__codelineno-21-7"></a><span class="w">    </span><span class="nx">n5</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">TreeNode</span><span class="p">(</span><span class="mf">5</span><span class="p">);</span>
+<a id="__codelineno-21-8" name="__codelineno-21-8" href="#__codelineno-21-8"></a><span class="c1">// ノード間の参照（ポインタ）を結ぶ</span>
+<a id="__codelineno-21-9" name="__codelineno-21-9" href="#__codelineno-21-9"></a><span class="nx">n1</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n2</span><span class="p">;</span>
+<a id="__codelineno-21-10" name="__codelineno-21-10" href="#__codelineno-21-10"></a><span class="nx">n1</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n3</span><span class="p">;</span>
+<a id="__codelineno-21-11" name="__codelineno-21-11" href="#__codelineno-21-11"></a><span class="nx">n2</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n4</span><span class="p">;</span>
+<a id="__codelineno-21-12" name="__codelineno-21-12" href="#__codelineno-21-12"></a><span class="nx">n2</span><span class="p">.</span><span class="nx">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n5</span><span class="p">;</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree.dart</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="cm">/* 二分木の初期化 */</span>
+<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a><span class="c1">// ノードの初期化</span>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="n">TreeNode</span><span class="w"> </span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="m">1</span><span class="p">);</span>
+<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a><span class="n">TreeNode</span><span class="w"> </span><span class="n">n2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="m">2</span><span class="p">);</span>
+<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="n">TreeNode</span><span class="w"> </span><span class="n">n3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="m">3</span><span class="p">);</span>
+<a id="__codelineno-22-6" name="__codelineno-22-6" href="#__codelineno-22-6"></a><span class="n">TreeNode</span><span class="w"> </span><span class="n">n4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="m">4</span><span class="p">);</span>
+<a id="__codelineno-22-7" name="__codelineno-22-7" href="#__codelineno-22-7"></a><span class="n">TreeNode</span><span class="w"> </span><span class="n">n5</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="m">5</span><span class="p">);</span>
+<a id="__codelineno-22-8" name="__codelineno-22-8" href="#__codelineno-22-8"></a><span class="c1">// ノード間の参照（ポインタ）を結ぶ</span>
+<a id="__codelineno-22-9" name="__codelineno-22-9" href="#__codelineno-22-9"></a><span class="n">n1</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span><span class="p">;</span>
+<a id="__codelineno-22-10" name="__codelineno-22-10" href="#__codelineno-22-10"></a><span class="n">n1</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n3</span><span class="p">;</span>
+<a id="__codelineno-22-11" name="__codelineno-22-11" href="#__codelineno-22-11"></a><span class="n">n2</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n4</span><span class="p">;</span>
+<a id="__codelineno-22-12" name="__codelineno-22-12" href="#__codelineno-22-12"></a><span class="n">n2</span><span class="p">.</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n5</span><span class="p">;</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree.rs</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="c1">// ノードの初期化</span>
+<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a><span class="kd">let</span><span class="w"> </span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="kd">let</span><span class="w"> </span><span class="n">n2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a><span class="kd">let</span><span class="w"> </span><span class="n">n3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
+<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="kd">let</span><span class="w"> </span><span class="n">n4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
+<a id="__codelineno-23-6" name="__codelineno-23-6" href="#__codelineno-23-6"></a><span class="kd">let</span><span class="w"> </span><span class="n">n5</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
+<a id="__codelineno-23-7" name="__codelineno-23-7" href="#__codelineno-23-7"></a><span class="c1">// ノード間の参照（ポインタ）を結ぶ</span>
+<a id="__codelineno-23-8" name="__codelineno-23-8" href="#__codelineno-23-8"></a><span class="n">n1</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">n2</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
+<a id="__codelineno-23-9" name="__codelineno-23-9" href="#__codelineno-23-9"></a><span class="n">n1</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">n3</span><span class="p">);</span>
+<a id="__codelineno-23-10" name="__codelineno-23-10" href="#__codelineno-23-10"></a><span class="n">n2</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">n4</span><span class="p">);</span>
+<a id="__codelineno-23-11" name="__codelineno-23-11" href="#__codelineno-23-11"></a><span class="n">n2</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">n5</span><span class="p">);</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree.c</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="cm">/* 二分木の初期化 */</span>
+<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a><span class="c1">// ノードの初期化</span>
+<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newTreeNode</span><span class="p">(</span><span class="mi">1</span><span class="p">);</span>
+<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">n2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newTreeNode</span><span class="p">(</span><span class="mi">2</span><span class="p">);</span>
+<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">n3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newTreeNode</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
+<a id="__codelineno-24-6" name="__codelineno-24-6" href="#__codelineno-24-6"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">n4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newTreeNode</span><span class="p">(</span><span class="mi">4</span><span class="p">);</span>
+<a id="__codelineno-24-7" name="__codelineno-24-7" href="#__codelineno-24-7"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">n5</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newTreeNode</span><span class="p">(</span><span class="mi">5</span><span class="p">);</span>
+<a id="__codelineno-24-8" name="__codelineno-24-8" href="#__codelineno-24-8"></a><span class="c1">// ノード間の参照（ポインタ）を結ぶ</span>
+<a id="__codelineno-24-9" name="__codelineno-24-9" href="#__codelineno-24-9"></a><span class="n">n1</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span><span class="p">;</span>
+<a id="__codelineno-24-10" name="__codelineno-24-10" href="#__codelineno-24-10"></a><span class="n">n1</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n3</span><span class="p">;</span>
+<a id="__codelineno-24-11" name="__codelineno-24-11" href="#__codelineno-24-11"></a><span class="n">n2</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n4</span><span class="p">;</span>
+<a id="__codelineno-24-12" name="__codelineno-24-12" href="#__codelineno-24-12"></a><span class="n">n2</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n5</span><span class="p">;</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree.kt</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="c1">// ノードの初期化</span>
+<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a><span class="kd">val</span><span class="w"> </span><span class="nv">n1</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="m">1</span><span class="p">)</span>
+<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="kd">val</span><span class="w"> </span><span class="nv">n2</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="m">2</span><span class="p">)</span>
+<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a><span class="kd">val</span><span class="w"> </span><span class="nv">n3</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="m">3</span><span class="p">)</span>
+<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="kd">val</span><span class="w"> </span><span class="nv">n4</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="m">4</span><span class="p">)</span>
+<a id="__codelineno-25-6" name="__codelineno-25-6" href="#__codelineno-25-6"></a><span class="kd">val</span><span class="w"> </span><span class="nv">n5</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="m">5</span><span class="p">)</span>
+<a id="__codelineno-25-7" name="__codelineno-25-7" href="#__codelineno-25-7"></a><span class="c1">// ノード間の参照（ポインタ）を結ぶ</span>
+<a id="__codelineno-25-8" name="__codelineno-25-8" href="#__codelineno-25-8"></a><span class="n">n1</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span>
+<a id="__codelineno-25-9" name="__codelineno-25-9" href="#__codelineno-25-9"></a><span class="n">n1</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n3</span>
+<a id="__codelineno-25-10" name="__codelineno-25-10" href="#__codelineno-25-10"></a><span class="n">n2</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n4</span>
+<a id="__codelineno-25-11" name="__codelineno-25-11" href="#__codelineno-25-11"></a><span class="n">n2</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n5</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree.zig</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h3 id="2">2. &nbsp; ノードの挿入と削除<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
+<p>連結リストと同様に、二分木でのノードの挿入と削除はポインタを変更することで実現できます。下図に例を示します。</p>
+<p><a class="glightbox" href="../binary_tree.assets/binary_tree_add_remove.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="二分木でのノードの挿入と削除" class="animation-figure" src="../binary_tree.assets/binary_tree_add_remove.png" /></a></p>
+<p align="center"> 図 7-3 &nbsp; 二分木でのノードの挿入と削除 </p>
+
+<div class="tabbed-set tabbed-alternate" data-tabs="3:14"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><input id="__tabbed_3_12" name="__tabbed_3" type="radio" /><input id="__tabbed_3_13" name="__tabbed_3" type="radio" /><input id="__tabbed_3_14" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">Python</label><label for="__tabbed_3_2">C++</label><label for="__tabbed_3_3">Java</label><label for="__tabbed_3_4">C#</label><label for="__tabbed_3_5">Go</label><label for="__tabbed_3_6">Swift</label><label for="__tabbed_3_7">JS</label><label for="__tabbed_3_8">TS</label><label for="__tabbed_3_9">Dart</label><label for="__tabbed_3_10">Rust</label><label for="__tabbed_3_11">C</label><label for="__tabbed_3_12">Kotlin</label><label for="__tabbed_3_13">Ruby</label><label for="__tabbed_3_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree.py</span><pre><span></span><code><a id="__codelineno-28-1" name="__codelineno-28-1" href="#__codelineno-28-1"></a><span class="c1"># ノードの挿入と削除</span>
+<a id="__codelineno-28-2" name="__codelineno-28-2" href="#__codelineno-28-2"></a><span class="n">p</span> <span class="o">=</span> <span class="n">TreeNode</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-28-3" name="__codelineno-28-3" href="#__codelineno-28-3"></a><span class="c1"># n1 -&gt; n2の間にノードPを挿入</span>
+<a id="__codelineno-28-4" name="__codelineno-28-4" href="#__codelineno-28-4"></a><span class="n">n1</span><span class="o">.</span><span class="n">left</span> <span class="o">=</span> <span class="n">p</span>
+<a id="__codelineno-28-5" name="__codelineno-28-5" href="#__codelineno-28-5"></a><span class="n">p</span><span class="o">.</span><span class="n">left</span> <span class="o">=</span> <span class="n">n2</span>
+<a id="__codelineno-28-6" name="__codelineno-28-6" href="#__codelineno-28-6"></a><span class="c1"># ノードPを削除</span>
+<a id="__codelineno-28-7" name="__codelineno-28-7" href="#__codelineno-28-7"></a><span class="n">n1</span><span class="o">.</span><span class="n">left</span> <span class="o">=</span> <span class="n">n2</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree.cpp</span><pre><span></span><code><a id="__codelineno-29-1" name="__codelineno-29-1" href="#__codelineno-29-1"></a><span class="cm">/* ノードの挿入と削除 */</span>
+<a id="__codelineno-29-2" name="__codelineno-29-2" href="#__codelineno-29-2"></a><span class="n">TreeNode</span><span class="o">*</span><span class="w"> </span><span class="n">P</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-29-3" name="__codelineno-29-3" href="#__codelineno-29-3"></a><span class="c1">// n1とn2の間にノードPを挿入</span>
+<a id="__codelineno-29-4" name="__codelineno-29-4" href="#__codelineno-29-4"></a><span class="n">n1</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">P</span><span class="p">;</span>
+<a id="__codelineno-29-5" name="__codelineno-29-5" href="#__codelineno-29-5"></a><span class="n">P</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span><span class="p">;</span>
+<a id="__codelineno-29-6" name="__codelineno-29-6" href="#__codelineno-29-6"></a><span class="c1">// ノードPを削除</span>
+<a id="__codelineno-29-7" name="__codelineno-29-7" href="#__codelineno-29-7"></a><span class="n">n1</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span><span class="p">;</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree.java</span><pre><span></span><code><a id="__codelineno-30-1" name="__codelineno-30-1" href="#__codelineno-30-1"></a><span class="n">TreeNode</span><span class="w"> </span><span class="n">P</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-30-2" name="__codelineno-30-2" href="#__codelineno-30-2"></a><span class="c1">// n1とn2の間にノードPを挿入</span>
+<a id="__codelineno-30-3" name="__codelineno-30-3" href="#__codelineno-30-3"></a><span class="n">n1</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">P</span><span class="p">;</span>
+<a id="__codelineno-30-4" name="__codelineno-30-4" href="#__codelineno-30-4"></a><span class="n">P</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span><span class="p">;</span>
+<a id="__codelineno-30-5" name="__codelineno-30-5" href="#__codelineno-30-5"></a><span class="c1">// ノードPを削除</span>
+<a id="__codelineno-30-6" name="__codelineno-30-6" href="#__codelineno-30-6"></a><span class="n">n1</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span><span class="p">;</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree.cs</span><pre><span></span><code><a id="__codelineno-31-1" name="__codelineno-31-1" href="#__codelineno-31-1"></a><span class="cm">/* ノードの挿入と削除 */</span>
+<a id="__codelineno-31-2" name="__codelineno-31-2" href="#__codelineno-31-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="n">P</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-31-3" name="__codelineno-31-3" href="#__codelineno-31-3"></a><span class="c1">// n1とn2の間にノードPを挿入</span>
+<a id="__codelineno-31-4" name="__codelineno-31-4" href="#__codelineno-31-4"></a><span class="n">n1</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">P</span><span class="p">;</span>
+<a id="__codelineno-31-5" name="__codelineno-31-5" href="#__codelineno-31-5"></a><span class="n">P</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span><span class="p">;</span>
+<a id="__codelineno-31-6" name="__codelineno-31-6" href="#__codelineno-31-6"></a><span class="c1">// ノードPを削除</span>
+<a id="__codelineno-31-7" name="__codelineno-31-7" href="#__codelineno-31-7"></a><span class="n">n1</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span><span class="p">;</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree.go</span><pre><span></span><code><a id="__codelineno-32-1" name="__codelineno-32-1" href="#__codelineno-32-1"></a><span class="cm">/* ノードの挿入と削除 */</span>
+<a id="__codelineno-32-2" name="__codelineno-32-2" href="#__codelineno-32-2"></a><span class="c1">// n1とn2の間にノードPを挿入</span>
+<a id="__codelineno-32-3" name="__codelineno-32-3" href="#__codelineno-32-3"></a><span class="nx">p</span><span class="w"> </span><span class="o">:=</span><span class="w"> </span><span class="nx">NewTreeNode</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-32-4" name="__codelineno-32-4" href="#__codelineno-32-4"></a><span class="nx">n1</span><span class="p">.</span><span class="nx">Left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">p</span>
+<a id="__codelineno-32-5" name="__codelineno-32-5" href="#__codelineno-32-5"></a><span class="nx">p</span><span class="p">.</span><span class="nx">Left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">n2</span>
+<a id="__codelineno-32-6" name="__codelineno-32-6" href="#__codelineno-32-6"></a><span class="c1">// ノードPを削除</span>
+<a id="__codelineno-32-7" name="__codelineno-32-7" href="#__codelineno-32-7"></a><span class="nx">n1</span><span class="p">.</span><span class="nx">Left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="nx">n2</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree.swift</span><pre><span></span><code><a id="__codelineno-33-1" name="__codelineno-33-1" href="#__codelineno-33-1"></a><span class="kd">let</span><span class="w"> </span><span class="nv">P</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="n">x</span><span class="p">:</span><span class="w"> </span><span class="mi">0</span><span class="p">)</span>
+<a id="__codelineno-33-2" name="__codelineno-33-2" href="#__codelineno-33-2"></a><span class="c1">// n1とn2の間にノードPを挿入</span>
+<a id="__codelineno-33-3" name="__codelineno-33-3" href="#__codelineno-33-3"></a><span class="n">n1</span><span class="p">.</span><span class="kr">left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">P</span>
+<a id="__codelineno-33-4" name="__codelineno-33-4" href="#__codelineno-33-4"></a><span class="n">P</span><span class="p">.</span><span class="kr">left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">n2</span>
+<a id="__codelineno-33-5" name="__codelineno-33-5" href="#__codelineno-33-5"></a><span class="c1">// ノードPを削除</span>
+<a id="__codelineno-33-6" name="__codelineno-33-6" href="#__codelineno-33-6"></a><span class="n">n1</span><span class="p">.</span><span class="kr">left</span><span class="w"> </span><span class="p">=</span><span class="w"> </span><span class="n">n2</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree.js</span><pre><span></span><code><a id="__codelineno-34-1" name="__codelineno-34-1" href="#__codelineno-34-1"></a><span class="cm">/* ノードの挿入と削除 */</span>
+<a id="__codelineno-34-2" name="__codelineno-34-2" href="#__codelineno-34-2"></a><span class="kd">let</span><span class="w"> </span><span class="nx">P</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">TreeNode</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-34-3" name="__codelineno-34-3" href="#__codelineno-34-3"></a><span class="c1">// n1とn2の間にノードPを挿入</span>
+<a id="__codelineno-34-4" name="__codelineno-34-4" href="#__codelineno-34-4"></a><span class="nx">n1</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">P</span><span class="p">;</span>
+<a id="__codelineno-34-5" name="__codelineno-34-5" href="#__codelineno-34-5"></a><span class="nx">P</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n2</span><span class="p">;</span>
+<a id="__codelineno-34-6" name="__codelineno-34-6" href="#__codelineno-34-6"></a><span class="c1">// ノードPを削除</span>
+<a id="__codelineno-34-7" name="__codelineno-34-7" href="#__codelineno-34-7"></a><span class="nx">n1</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n2</span><span class="p">;</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree.ts</span><pre><span></span><code><a id="__codelineno-35-1" name="__codelineno-35-1" href="#__codelineno-35-1"></a><span class="cm">/* ノードの挿入と削除 */</span>
+<a id="__codelineno-35-2" name="__codelineno-35-2" href="#__codelineno-35-2"></a><span class="kd">const</span><span class="w"> </span><span class="nx">P</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="ow">new</span><span class="w"> </span><span class="nx">TreeNode</span><span class="p">(</span><span class="mf">0</span><span class="p">);</span>
+<a id="__codelineno-35-3" name="__codelineno-35-3" href="#__codelineno-35-3"></a><span class="c1">// n1とn2の間にノードPを挿入</span>
+<a id="__codelineno-35-4" name="__codelineno-35-4" href="#__codelineno-35-4"></a><span class="nx">n1</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">P</span><span class="p">;</span>
+<a id="__codelineno-35-5" name="__codelineno-35-5" href="#__codelineno-35-5"></a><span class="nx">P</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n2</span><span class="p">;</span>
+<a id="__codelineno-35-6" name="__codelineno-35-6" href="#__codelineno-35-6"></a><span class="c1">// ノードPを削除</span>
+<a id="__codelineno-35-7" name="__codelineno-35-7" href="#__codelineno-35-7"></a><span class="nx">n1</span><span class="p">.</span><span class="nx">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nx">n2</span><span class="p">;</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree.dart</span><pre><span></span><code><a id="__codelineno-36-1" name="__codelineno-36-1" href="#__codelineno-36-1"></a><span class="cm">/* ノードの挿入と削除 */</span>
+<a id="__codelineno-36-2" name="__codelineno-36-2" href="#__codelineno-36-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="n">P</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="m">0</span><span class="p">);</span>
+<a id="__codelineno-36-3" name="__codelineno-36-3" href="#__codelineno-36-3"></a><span class="c1">// n1とn2の間にノードPを挿入</span>
+<a id="__codelineno-36-4" name="__codelineno-36-4" href="#__codelineno-36-4"></a><span class="n">n1</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">P</span><span class="p">;</span>
+<a id="__codelineno-36-5" name="__codelineno-36-5" href="#__codelineno-36-5"></a><span class="n">P</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span><span class="p">;</span>
+<a id="__codelineno-36-6" name="__codelineno-36-6" href="#__codelineno-36-6"></a><span class="c1">// ノードPを削除</span>
+<a id="__codelineno-36-7" name="__codelineno-36-7" href="#__codelineno-36-7"></a><span class="n">n1</span><span class="p">.</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span><span class="p">;</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree.rs</span><pre><span></span><code><a id="__codelineno-37-1" name="__codelineno-37-1" href="#__codelineno-37-1"></a><span class="kd">let</span><span class="w"> </span><span class="n">p</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">::</span><span class="n">new</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-37-2" name="__codelineno-37-2" href="#__codelineno-37-2"></a><span class="c1">// n1とn2の間にノードPを挿入</span>
+<a id="__codelineno-37-3" name="__codelineno-37-3" href="#__codelineno-37-3"></a><span class="n">n1</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">p</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
+<a id="__codelineno-37-4" name="__codelineno-37-4" href="#__codelineno-37-4"></a><span class="n">p</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">n2</span><span class="p">.</span><span class="n">clone</span><span class="p">());</span>
+<a id="__codelineno-37-5" name="__codelineno-37-5" href="#__codelineno-37-5"></a><span class="c1">// ノードPを削除</span>
+<a id="__codelineno-37-6" name="__codelineno-37-6" href="#__codelineno-37-6"></a><span class="n">n1</span><span class="p">.</span><span class="n">borrow_mut</span><span class="p">().</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="nb">Some</span><span class="p">(</span><span class="n">n2</span><span class="p">);</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree.c</span><pre><span></span><code><a id="__codelineno-38-1" name="__codelineno-38-1" href="#__codelineno-38-1"></a><span class="cm">/* ノードの挿入と削除 */</span>
+<a id="__codelineno-38-2" name="__codelineno-38-2" href="#__codelineno-38-2"></a><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">P</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">newTreeNode</span><span class="p">(</span><span class="mi">0</span><span class="p">);</span>
+<a id="__codelineno-38-3" name="__codelineno-38-3" href="#__codelineno-38-3"></a><span class="c1">// n1とn2の間にノードPを挿入</span>
+<a id="__codelineno-38-4" name="__codelineno-38-4" href="#__codelineno-38-4"></a><span class="n">n1</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">P</span><span class="p">;</span>
+<a id="__codelineno-38-5" name="__codelineno-38-5" href="#__codelineno-38-5"></a><span class="n">P</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span><span class="p">;</span>
+<a id="__codelineno-38-6" name="__codelineno-38-6" href="#__codelineno-38-6"></a><span class="c1">// ノードPを削除</span>
+<a id="__codelineno-38-7" name="__codelineno-38-7" href="#__codelineno-38-7"></a><span class="n">n1</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span><span class="p">;</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree.kt</span><pre><span></span><code><a id="__codelineno-39-1" name="__codelineno-39-1" href="#__codelineno-39-1"></a><span class="kd">val</span><span class="w"> </span><span class="nv">P</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">TreeNode</span><span class="p">(</span><span class="m">0</span><span class="p">)</span>
+<a id="__codelineno-39-2" name="__codelineno-39-2" href="#__codelineno-39-2"></a><span class="c1">// n1とn2の間にノードPを挿入</span>
+<a id="__codelineno-39-3" name="__codelineno-39-3" href="#__codelineno-39-3"></a><span class="n">n1</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">P</span>
+<a id="__codelineno-39-4" name="__codelineno-39-4" href="#__codelineno-39-4"></a><span class="n">P</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span>
+<a id="__codelineno-39-5" name="__codelineno-39-5" href="#__codelineno-39-5"></a><span class="c1">// ノードPを削除</span>
+<a id="__codelineno-39-6" name="__codelineno-39-6" href="#__codelineno-39-6"></a><span class="n">n1</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">n2</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree.rb</span><pre><span></span><code><a id="__codelineno-40-1" name="__codelineno-40-1" href="#__codelineno-40-1"></a>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree.zig</span><pre><span></span><code><a id="__codelineno-41-1" name="__codelineno-41-1" href="#__codelineno-41-1"></a>
+</code></pre></div>
+</div>
+</div>
+</div>
+<div class="admonition tip">
+<p class="admonition-title">Tip</p>
+<p>ノードの挿入は二分木の元の論理構造を変更する可能性があり、ノードの削除は通常そのノードとそのすべての部分木を削除することになることに注意してください。したがって、二分木では、挿入と削除は通常一連の操作を通じて実行され、意味のある結果を得ます。</p>
+</div>
+<h2 id="713">7.1.3 &nbsp; 二分木の一般的な種類<a class="headerlink" href="#713" title="Permanent link">&para;</a></h2>
+<h3 id="1_1">1. &nbsp; 完全二分木<a class="headerlink" href="#1_1" title="Permanent link">&para;</a></h3>
+<p>下図に示すように、<u>完全二分木</u>では、すべてのレベルがノードで完全に埋められています。完全二分木では、葉ノードの次数は<span class="arithmatex">\(0\)</span>で、他のすべてのノードの次数は<span class="arithmatex">\(2\)</span>です。ノードの総数は<span class="arithmatex">\(2^{h+1} - 1\)</span>として計算でき、ここで<span class="arithmatex">\(h\)</span>は木の高さです。これは標準的な指数関係を示し、自然界の細胞分裂の一般的な現象を反映しています。</p>
+<div class="admonition tip">
+<p class="admonition-title">Tip</p>
+<p>中国語圏では、完全二分木はしばしば<u>満二分木</u>と呼ばれることに注意してください。</p>
+</div>
+<p><a class="glightbox" href="../binary_tree.assets/perfect_binary_tree.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="完全二分木" class="animation-figure" src="../binary_tree.assets/perfect_binary_tree.png" /></a></p>
+<p align="center"> 図 7-4 &nbsp; 完全二分木 </p>
+
+<h3 id="2_1">2. &nbsp; 完備二分木<a class="headerlink" href="#2_1" title="Permanent link">&para;</a></h3>
+<p>下図に示すように、<u>完備二分木</u>は、最下位レベルのみが完全に埋められていない可能性がある二分木で、最下位レベルのノードは左から右に連続して埋められる必要があります。完全二分木は完備二分木でもあることに注意してください。</p>
+<p><a class="glightbox" href="../binary_tree.assets/complete_binary_tree.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="完備二分木" class="animation-figure" src="../binary_tree.assets/complete_binary_tree.png" /></a></p>
+<p align="center"> 図 7-5 &nbsp; 完備二分木 </p>
+
+<h3 id="3">3. &nbsp; 満二分木<a class="headerlink" href="#3" title="Permanent link">&para;</a></h3>
+<p>下図に示すように、<u>満二分木</u>では、葉ノードを除いて、他のすべてのノードが2つの子ノードを持ちます。</p>
+<p><a class="glightbox" href="../binary_tree.assets/full_binary_tree.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="満二分木" class="animation-figure" src="../binary_tree.assets/full_binary_tree.png" /></a></p>
+<p align="center"> 図 7-6 &nbsp; 満二分木 </p>
+
+<h3 id="4">4. &nbsp; 平衡二分木<a class="headerlink" href="#4" title="Permanent link">&para;</a></h3>
+<p>下図に示すように、<u>平衡二分木</u>では、任意のノードの左と右の部分木の高さの絶対差が1を超えません。</p>
+<p><a class="glightbox" href="../binary_tree.assets/balanced_binary_tree.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="平衡二分木" class="animation-figure" src="../binary_tree.assets/balanced_binary_tree.png" /></a></p>
+<p align="center"> 図 7-7 &nbsp; 平衡二分木 </p>
+
+<h2 id="714">7.1.4 &nbsp; 二分木の退化<a class="headerlink" href="#714" title="Permanent link">&para;</a></h2>
+<p>下図は、二分木の理想的な構造と退化した構造を示しています。二分木は、すべてのレベルが埋められているときに「完全二分木」になり、すべてのノードが一方に偏っているときに「連結リスト」に退化します。</p>
+<ul>
+<li>完全二分木は、二分木の「分割統治法」の利点を十分に活用できる理想的なシナリオです。</li>
+<li>一方、連結リストは別の極端を表し、すべての操作が線形になり、時間計算量が<span class="arithmatex">\(O(n)\)</span>になります。</li>
+</ul>
+<p><a class="glightbox" href="../binary_tree.assets/binary_tree_best_worst_cases.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="二分木の最良と最悪の構造" class="animation-figure" src="../binary_tree.assets/binary_tree_best_worst_cases.png" /></a></p>
+<p align="center"> 図 7-8 &nbsp; 二分木の最良と最悪の構造 </p>
+
+<p>下表に示すように、最良と最悪の構造では、二分木は葉ノード数、総ノード数、高さの最大値または最小値を達成します。</p>
+<p align="center"> 表 7-1 &nbsp; 二分木の最良と最悪の構造 </p>
+
+<div class="center-table">
+<table>
+<thead>
+<tr>
+<th></th>
+<th>完全二分木</th>
+<th>連結リスト</th>
+</tr>
+</thead>
+<tbody>
+<tr>
+<td>レベル<span class="arithmatex">\(i\)</span>のノード数</td>
+<td><span class="arithmatex">\(2^{i-1}\)</span></td>
+<td><span class="arithmatex">\(1\)</span></td>
+</tr>
+<tr>
+<td>高さ<span class="arithmatex">\(h\)</span>の木の葉ノード数</td>
+<td><span class="arithmatex">\(2^h\)</span></td>
+<td><span class="arithmatex">\(1\)</span></td>
+</tr>
+<tr>
+<td>高さ<span class="arithmatex">\(h\)</span>の木の総ノード数</td>
+<td><span class="arithmatex">\(2^{h+1} - 1\)</span></td>
+<td><span class="arithmatex">\(h + 1\)</span></td>
+</tr>
+<tr>
+<td>総ノード数<span class="arithmatex">\(n\)</span>の木の高さ</td>
+<td><span class="arithmatex">\(\log_2 (n+1) - 1\)</span></td>
+<td><span class="arithmatex">\(n - 1\)</span></td>
+</tr>
+</tbody>
+</table>
+</div>
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+        
+  
+  <span class="md-ellipsis">
+    0.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_introduction/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#721" class="md-nav__link">
+    <span class="md-ellipsis">
+      7.2.1 &nbsp; レベル順走査
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="7.2.1   レベル順走査">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; コード実装
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; 計算量分析
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#722" class="md-nav__link">
+    <span class="md-ellipsis">
+      7.2.2 &nbsp; 前順、中順、後順走査
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="7.2.2   前順、中順、後順走査">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1_1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; コード実装
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2_1" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; 計算量分析
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
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+    15.1 &nbsp; 貪欲アルゴリズム
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+    15.2 &nbsp; 分数ナップサック問題
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+  
+
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+
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+  
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+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
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+
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+
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+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
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+    15.4 &nbsp; 最大積切断問題
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+  
+
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+
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+  
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+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
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+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
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+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
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+
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+  
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+  
+
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+
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+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
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+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#721" class="md-nav__link">
+    <span class="md-ellipsis">
+      7.2.1 &nbsp; レベル順走査
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="7.2.1   レベル順走査">
+      <ul class="md-nav__list">
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+    </span>
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+  
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+        
+          <li class="md-nav__item">
+  <a href="#2" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; 計算量分析
+    </span>
+  </a>
+  
+</li>
+        
+      </ul>
+    </nav>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#722" class="md-nav__link">
+    <span class="md-ellipsis">
+      7.2.2 &nbsp; 前順、中順、後順走査
+    </span>
+  </a>
+  
+    <nav class="md-nav" aria-label="7.2.2   前順、中順、後順走査">
+      <ul class="md-nav__list">
+        
+          <li class="md-nav__item">
+  <a href="#1_1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; コード実装
+    </span>
+  </a>
+  
+</li>
+        
+          <li class="md-nav__item">
+  <a href="#2_1" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; 計算量分析
+    </span>
+  </a>
+  
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+    </nav>
+  
+</li>
+      
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+      
+      <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.--><path d="M441 58.9 453.1 71c9.4 9.4 9.4 24.6 0 33.9L424 134.1 377.9 88 407 58.9c9.4-9.4 24.6-9.4 33.9 0zM209.8 256.2 344 121.9l46.1 46.1-134.3 134.2c-2.9 2.9-6.5 5-10.4 6.1L186.9 325l16.7-58.5c1.1-3.9 3.2-7.5 6.1-10.4zM373.1 25 175.8 222.2c-8.7 8.7-15 19.4-18.3 31.1l-28.6 100c-2.4 8.4-.1 17.4 6.1 23.6s15.2 8.5 23.6 6.1l100-28.6c11.8-3.4 22.5-9.7 31.1-18.3L487 138.9c28.1-28.1 28.1-73.7 0-101.8L474.9 25c-28.1-28.1-73.7-28.1-101.8 0zM88 64c-48.6 0-88 39.4-88 88v272c0 48.6 39.4 88 88 88h272c48.6 0 88-39.4 88-88V312c0-13.3-10.7-24-24-24s-24 10.7-24 24v112c0 22.1-17.9 40-40 40H88c-22.1 0-40-17.9-40-40V152c0-22.1 17.9-40 40-40h112c13.3 0 24-10.7 24-24s-10.7-24-24-24H88z"/></svg>
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+<!-- Page content -->
+<h1 id="72">7.2 &nbsp; 二分木の走査<a class="headerlink" href="#72" title="Permanent link">&para;</a></h1>
+<p>物理的構造の観点から見ると、木は連結リストに基づくデータ構造です。したがって、その走査方法はポインタを通してノードに一つずつアクセスすることを含みます。しかし、木は非線形データ構造であるため、木の走査は連結リストの走査よりも複雑で、検索アルゴリズムの支援が必要です。</p>
+<p>二分木の一般的な走査方法には、レベル順走査、前順走査、中順走査、後順走査があります。</p>
+<h2 id="721">7.2.1 &nbsp; レベル順走査<a class="headerlink" href="#721" title="Permanent link">&para;</a></h2>
+<p>下図に示すように、<u>レベル順走査</u>は二分木を上から下へ、層ごとに走査します。各レベル内では、左から右へノードを訪問します。</p>
+<p>レベル順走査は本質的に<u>幅優先走査</u>の一種で、<u>幅優先探索（BFS）</u>とも呼ばれ、「周囲に向かって外向きに拡張する」層ごとの走査方法を体現しています。</p>
+<p><a class="glightbox" href="../binary_tree_traversal.assets/binary_tree_bfs.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="二分木のレベル順走査" class="animation-figure" src="../binary_tree_traversal.assets/binary_tree_bfs.png" /></a></p>
+<p align="center"> 図 7-9 &nbsp; 二分木のレベル順走査 </p>
+
+<h3 id="1">1. &nbsp; コード実装<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<p>幅優先走査は通常「キュー」の助けを借りて実装されます。キューは「先入れ先出し」の規則に従い、幅優先走査は「層ごとの進行」規則に従います。両者の基本的な考え方は一致しています。実装コードは以下の通りです：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="1:14"><input checked="checked" id="__tabbed_1_1" name="__tabbed_1" type="radio" /><input id="__tabbed_1_2" name="__tabbed_1" type="radio" /><input id="__tabbed_1_3" name="__tabbed_1" type="radio" /><input id="__tabbed_1_4" name="__tabbed_1" type="radio" /><input id="__tabbed_1_5" name="__tabbed_1" type="radio" /><input id="__tabbed_1_6" name="__tabbed_1" type="radio" /><input id="__tabbed_1_7" name="__tabbed_1" type="radio" /><input id="__tabbed_1_8" name="__tabbed_1" type="radio" /><input id="__tabbed_1_9" name="__tabbed_1" type="radio" /><input id="__tabbed_1_10" name="__tabbed_1" type="radio" /><input id="__tabbed_1_11" name="__tabbed_1" type="radio" /><input id="__tabbed_1_12" name="__tabbed_1" type="radio" /><input id="__tabbed_1_13" name="__tabbed_1" type="radio" /><input id="__tabbed_1_14" name="__tabbed_1" type="radio" /><div class="tabbed-labels"><label for="__tabbed_1_1">Python</label><label for="__tabbed_1_2">C++</label><label for="__tabbed_1_3">Java</label><label for="__tabbed_1_4">C#</label><label for="__tabbed_1_5">Go</label><label for="__tabbed_1_6">Swift</label><label for="__tabbed_1_7">JS</label><label for="__tabbed_1_8">TS</label><label for="__tabbed_1_9">Dart</label><label for="__tabbed_1_10">Rust</label><label for="__tabbed_1_11">C</label><label for="__tabbed_1_12">Kotlin</label><label for="__tabbed_1_13">Ruby</label><label for="__tabbed_1_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree_bfs.py</span><pre><span></span><code><a id="__codelineno-0-1" name="__codelineno-0-1" href="#__codelineno-0-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">level_order</span><span class="p">(</span><span class="n">root</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">)</span> <span class="o">-&gt;</span> <span class="nb">list</span><span class="p">[</span><span class="nb">int</span><span class="p">]:</span>
+<a id="__codelineno-0-2" name="__codelineno-0-2" href="#__codelineno-0-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;レベル順走査&quot;&quot;&quot;</span>
+<a id="__codelineno-0-3" name="__codelineno-0-3" href="#__codelineno-0-3"></a>    <span class="c1"># キューを初期化し、ルートノードを追加</span>
+<a id="__codelineno-0-4" name="__codelineno-0-4" href="#__codelineno-0-4"></a>    <span class="n">queue</span><span class="p">:</span> <span class="n">deque</span><span class="p">[</span><span class="n">TreeNode</span><span class="p">]</span> <span class="o">=</span> <span class="n">deque</span><span class="p">()</span>
+<a id="__codelineno-0-5" name="__codelineno-0-5" href="#__codelineno-0-5"></a>    <span class="n">queue</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">root</span><span class="p">)</span>
+<a id="__codelineno-0-6" name="__codelineno-0-6" href="#__codelineno-0-6"></a>    <span class="c1"># 走査シーケンスを格納するリストを初期化</span>
+<a id="__codelineno-0-7" name="__codelineno-0-7" href="#__codelineno-0-7"></a>    <span class="n">res</span> <span class="o">=</span> <span class="p">[]</span>
+<a id="__codelineno-0-8" name="__codelineno-0-8" href="#__codelineno-0-8"></a>    <span class="k">while</span> <span class="n">queue</span><span class="p">:</span>
+<a id="__codelineno-0-9" name="__codelineno-0-9" href="#__codelineno-0-9"></a>        <span class="n">node</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">=</span> <span class="n">queue</span><span class="o">.</span><span class="n">popleft</span><span class="p">()</span>  <span class="c1"># キューからデキュー</span>
+<a id="__codelineno-0-10" name="__codelineno-0-10" href="#__codelineno-0-10"></a>        <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>  <span class="c1"># ノードの値を保存</span>
+<a id="__codelineno-0-11" name="__codelineno-0-11" href="#__codelineno-0-11"></a>        <span class="k">if</span> <span class="n">node</span><span class="o">.</span><span class="n">left</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-0-12" name="__codelineno-0-12" href="#__codelineno-0-12"></a>            <span class="n">queue</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">left</span><span class="p">)</span>  <span class="c1"># 左の子ノードをエンキュー</span>
+<a id="__codelineno-0-13" name="__codelineno-0-13" href="#__codelineno-0-13"></a>        <span class="k">if</span> <span class="n">node</span><span class="o">.</span><span class="n">right</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-0-14" name="__codelineno-0-14" href="#__codelineno-0-14"></a>            <span class="n">queue</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">node</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>  <span class="c1"># 右の子ノードをエンキュー</span>
+<a id="__codelineno-0-15" name="__codelineno-0-15" href="#__codelineno-0-15"></a>    <span class="k">return</span> <span class="n">res</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree_bfs.cpp</span><pre><span></span><code><a id="__codelineno-1-1" name="__codelineno-1-1" href="#__codelineno-1-1"></a><span class="cm">/* レベル順走査 */</span>
+<a id="__codelineno-1-2" name="__codelineno-1-2" href="#__codelineno-1-2"></a><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">levelOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-3" name="__codelineno-1-3" href="#__codelineno-1-3"></a><span class="w">    </span><span class="c1">// キューを初期化、ルートノードを追加</span>
+<a id="__codelineno-1-4" name="__codelineno-1-4" href="#__codelineno-1-4"></a><span class="w">    </span><span class="n">queue</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*&gt;</span><span class="w"> </span><span class="n">queue</span><span class="p">;</span>
+<a id="__codelineno-1-5" name="__codelineno-1-5" href="#__codelineno-1-5"></a><span class="w">    </span><span class="n">queue</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">root</span><span class="p">);</span>
+<a id="__codelineno-1-6" name="__codelineno-1-6" href="#__codelineno-1-6"></a><span class="w">    </span><span class="c1">// 走査順序を保存するリストを初期化</span>
+<a id="__codelineno-1-7" name="__codelineno-1-7" href="#__codelineno-1-7"></a><span class="w">    </span><span class="n">vector</span><span class="o">&lt;</span><span class="kt">int</span><span class="o">&gt;</span><span class="w"> </span><span class="n">vec</span><span class="p">;</span>
+<a id="__codelineno-1-8" name="__codelineno-1-8" href="#__codelineno-1-8"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">queue</span><span class="p">.</span><span class="n">empty</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-1-9" name="__codelineno-1-9" href="#__codelineno-1-9"></a><span class="w">        </span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="n">front</span><span class="p">();</span>
+<a id="__codelineno-1-10" name="__codelineno-1-10" href="#__codelineno-1-10"></a><span class="w">        </span><span class="n">queue</span><span class="p">.</span><span class="n">pop</span><span class="p">();</span><span class="w">              </span><span class="c1">// キューからデキュー</span>
+<a id="__codelineno-1-11" name="__codelineno-1-11" href="#__codelineno-1-11"></a><span class="w">        </span><span class="n">vec</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">);</span><span class="w"> </span><span class="c1">// ノード値を保存</span>
+<a id="__codelineno-1-12" name="__codelineno-1-12" href="#__codelineno-1-12"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span>
+<a id="__codelineno-1-13" name="__codelineno-1-13" href="#__codelineno-1-13"></a><span class="w">            </span><span class="n">queue</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">);</span><span class="w"> </span><span class="c1">// 左の子ノードをエンキュー</span>
+<a id="__codelineno-1-14" name="__codelineno-1-14" href="#__codelineno-1-14"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span>
+<a id="__codelineno-1-15" name="__codelineno-1-15" href="#__codelineno-1-15"></a><span class="w">            </span><span class="n">queue</span><span class="p">.</span><span class="n">push</span><span class="p">(</span><span class="n">node</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">);</span><span class="w"> </span><span class="c1">// 右の子ノードをエンキュー</span>
+<a id="__codelineno-1-16" name="__codelineno-1-16" href="#__codelineno-1-16"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-1-17" name="__codelineno-1-17" href="#__codelineno-1-17"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">vec</span><span class="p">;</span>
+<a id="__codelineno-1-18" name="__codelineno-1-18" href="#__codelineno-1-18"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree_bfs.java</span><pre><span></span><code><a id="__codelineno-2-1" name="__codelineno-2-1" href="#__codelineno-2-1"></a><span class="cm">/* レベル順走査 */</span>
+<a id="__codelineno-2-2" name="__codelineno-2-2" href="#__codelineno-2-2"></a><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="nf">levelOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-3" name="__codelineno-2-3" href="#__codelineno-2-3"></a><span class="w">    </span><span class="c1">// キューを初期化し、根ノードを追加</span>
+<a id="__codelineno-2-4" name="__codelineno-2-4" href="#__codelineno-2-4"></a><span class="w">    </span><span class="n">Queue</span><span class="o">&lt;</span><span class="n">TreeNode</span><span class="o">&gt;</span><span class="w"> </span><span class="n">queue</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">LinkedList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-2-5" name="__codelineno-2-5" href="#__codelineno-2-5"></a><span class="w">    </span><span class="n">queue</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">root</span><span class="p">);</span>
+<a id="__codelineno-2-6" name="__codelineno-2-6" href="#__codelineno-2-6"></a><span class="w">    </span><span class="c1">// 走査順序を格納するリストを初期化</span>
+<a id="__codelineno-2-7" name="__codelineno-2-7" href="#__codelineno-2-7"></a><span class="w">    </span><span class="n">List</span><span class="o">&lt;</span><span class="n">Integer</span><span class="o">&gt;</span><span class="w"> </span><span class="n">list</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="k">new</span><span class="w"> </span><span class="n">ArrayList</span><span class="o">&lt;&gt;</span><span class="p">();</span>
+<a id="__codelineno-2-8" name="__codelineno-2-8" href="#__codelineno-2-8"></a><span class="w">    </span><span class="k">while</span><span class="w"> </span><span class="p">(</span><span class="o">!</span><span class="n">queue</span><span class="p">.</span><span class="na">isEmpty</span><span class="p">())</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-2-9" name="__codelineno-2-9" href="#__codelineno-2-9"></a><span class="w">        </span><span class="n">TreeNode</span><span class="w"> </span><span class="n">node</span><span class="w"> </span><span class="o">=</span><span class="w"> </span><span class="n">queue</span><span class="p">.</span><span class="na">poll</span><span class="p">();</span><span class="w"> </span><span class="c1">// キューのデキュー</span>
+<a id="__codelineno-2-10" name="__codelineno-2-10" href="#__codelineno-2-10"></a><span class="w">        </span><span class="n">list</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">val</span><span class="p">);</span><span class="w">           </span><span class="c1">// ノードの値を保存</span>
+<a id="__codelineno-2-11" name="__codelineno-2-11" href="#__codelineno-2-11"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
+<a id="__codelineno-2-12" name="__codelineno-2-12" href="#__codelineno-2-12"></a><span class="w">            </span><span class="n">queue</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">left</span><span class="p">);</span><span class="w">   </span><span class="c1">// 左の子ノードをエンキュー</span>
+<a id="__codelineno-2-13" name="__codelineno-2-13" href="#__codelineno-2-13"></a><span class="w">        </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="w"> </span><span class="o">!=</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
+<a id="__codelineno-2-14" name="__codelineno-2-14" href="#__codelineno-2-14"></a><span class="w">            </span><span class="n">queue</span><span class="p">.</span><span class="na">offer</span><span class="p">(</span><span class="n">node</span><span class="p">.</span><span class="na">right</span><span class="p">);</span><span class="w">  </span><span class="c1">// 右の子ノードをエンキュー</span>
+<a id="__codelineno-2-15" name="__codelineno-2-15" href="#__codelineno-2-15"></a><span class="w">    </span><span class="p">}</span>
+<a id="__codelineno-2-16" name="__codelineno-2-16" href="#__codelineno-2-16"></a><span class="w">    </span><span class="k">return</span><span class="w"> </span><span class="n">list</span><span class="p">;</span>
+<a id="__codelineno-2-17" name="__codelineno-2-17" href="#__codelineno-2-17"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree_bfs.cs</span><pre><span></span><code><a id="__codelineno-3-1" name="__codelineno-3-1" href="#__codelineno-3-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">binary_tree_bfs</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">LevelOrder</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree_bfs.go</span><pre><span></span><code><a id="__codelineno-4-1" name="__codelineno-4-1" href="#__codelineno-4-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">levelOrder</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree_bfs.swift</span><pre><span></span><code><a id="__codelineno-5-1" name="__codelineno-5-1" href="#__codelineno-5-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">levelOrder</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree_bfs.js</span><pre><span></span><code><a id="__codelineno-6-1" name="__codelineno-6-1" href="#__codelineno-6-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">levelOrder</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree_bfs.ts</span><pre><span></span><code><a id="__codelineno-7-1" name="__codelineno-7-1" href="#__codelineno-7-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">levelOrder</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree_bfs.dart</span><pre><span></span><code><a id="__codelineno-8-1" name="__codelineno-8-1" href="#__codelineno-8-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">levelOrder</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree_bfs.rs</span><pre><span></span><code><a id="__codelineno-9-1" name="__codelineno-9-1" href="#__codelineno-9-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">level_order</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree_bfs.c</span><pre><span></span><code><a id="__codelineno-10-1" name="__codelineno-10-1" href="#__codelineno-10-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">levelOrder</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree_bfs.kt</span><pre><span></span><code><a id="__codelineno-11-1" name="__codelineno-11-1" href="#__codelineno-11-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">levelOrder</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree_bfs.rb</span><pre><span></span><code><a id="__codelineno-12-1" name="__codelineno-12-1" href="#__codelineno-12-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">level_order</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree_bfs.zig</span><pre><span></span><code><a id="__codelineno-13-1" name="__codelineno-13-1" href="#__codelineno-13-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">levelOrder</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<h3 id="2">2. &nbsp; 計算量分析<a class="headerlink" href="#2" title="Permanent link">&para;</a></h3>
+<ul>
+<li><strong>時間計算量は<span class="arithmatex">\(O(n)\)</span></strong>: すべてのノードが一度ずつ訪問され、<span class="arithmatex">\(O(n)\)</span>の時間がかかります。ここで<span class="arithmatex">\(n\)</span>はノード数です。</li>
+<li><strong>空間計算量は<span class="arithmatex">\(O(n)\)</span></strong>: 最悪の場合、つまり完全二分木の場合、最下位レベルに走査する前に、キューは最大<span class="arithmatex">\((n + 1) / 2\)</span>個のノードを同時に含むことができ、<span class="arithmatex">\(O(n)\)</span>の空間を占有します。</li>
+</ul>
+<h2 id="722">7.2.2 &nbsp; 前順、中順、後順走査<a class="headerlink" href="#722" title="Permanent link">&para;</a></h2>
+<p>対応して、前順、中順、後順走査はすべて<u>深度優先走査</u>に属し、<u>深度優先探索（DFS）</u>とも呼ばれ、「まず最後まで進み、その後バックトラックして続行する」走査方法を体現しています。</p>
+<p>下図は二分木に対して深度優先走査を実行する動作原理を示しています。<strong>深度優先走査は二分木全体を「歩き回る」ようなもので</strong>、各ノードで3つの位置に遭遇し、それらは前順、中順、後順走査に対応しています。</p>
+<p><a class="glightbox" href="../binary_tree_traversal.assets/binary_tree_dfs.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="二分探索木の前順、中順、後順走査" class="animation-figure" src="../binary_tree_traversal.assets/binary_tree_dfs.png" /></a></p>
+<p align="center"> 図 7-10 &nbsp; 二分探索木の前順、中順、後順走査 </p>
+
+<h3 id="1_1">1. &nbsp; コード実装<a class="headerlink" href="#1_1" title="Permanent link">&para;</a></h3>
+<p>深度優先探索は通常再帰に基づいて実装されます：</p>
+<div class="tabbed-set tabbed-alternate" data-tabs="2:14"><input checked="checked" id="__tabbed_2_1" name="__tabbed_2" type="radio" /><input id="__tabbed_2_2" name="__tabbed_2" type="radio" /><input id="__tabbed_2_3" name="__tabbed_2" type="radio" /><input id="__tabbed_2_4" name="__tabbed_2" type="radio" /><input id="__tabbed_2_5" name="__tabbed_2" type="radio" /><input id="__tabbed_2_6" name="__tabbed_2" type="radio" /><input id="__tabbed_2_7" name="__tabbed_2" type="radio" /><input id="__tabbed_2_8" name="__tabbed_2" type="radio" /><input id="__tabbed_2_9" name="__tabbed_2" type="radio" /><input id="__tabbed_2_10" name="__tabbed_2" type="radio" /><input id="__tabbed_2_11" name="__tabbed_2" type="radio" /><input id="__tabbed_2_12" name="__tabbed_2" type="radio" /><input id="__tabbed_2_13" name="__tabbed_2" type="radio" /><input id="__tabbed_2_14" name="__tabbed_2" type="radio" /><div class="tabbed-labels"><label for="__tabbed_2_1">Python</label><label for="__tabbed_2_2">C++</label><label for="__tabbed_2_3">Java</label><label for="__tabbed_2_4">C#</label><label for="__tabbed_2_5">Go</label><label for="__tabbed_2_6">Swift</label><label for="__tabbed_2_7">JS</label><label for="__tabbed_2_8">TS</label><label for="__tabbed_2_9">Dart</label><label for="__tabbed_2_10">Rust</label><label for="__tabbed_2_11">C</label><label for="__tabbed_2_12">Kotlin</label><label for="__tabbed_2_13">Ruby</label><label for="__tabbed_2_14">Zig</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree_dfs.py</span><pre><span></span><code><a id="__codelineno-14-1" name="__codelineno-14-1" href="#__codelineno-14-1"></a><span class="k">def</span><span class="w"> </span><span class="nf">pre_order</span><span class="p">(</span><span class="n">root</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">):</span>
+<a id="__codelineno-14-2" name="__codelineno-14-2" href="#__codelineno-14-2"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;前順走査&quot;&quot;&quot;</span>
+<a id="__codelineno-14-3" name="__codelineno-14-3" href="#__codelineno-14-3"></a>    <span class="k">if</span> <span class="n">root</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-14-4" name="__codelineno-14-4" href="#__codelineno-14-4"></a>        <span class="k">return</span>
+<a id="__codelineno-14-5" name="__codelineno-14-5" href="#__codelineno-14-5"></a>    <span class="c1"># 訪問順序: ルートノード -&gt; 左部分木 -&gt; 右部分木</span>
+<a id="__codelineno-14-6" name="__codelineno-14-6" href="#__codelineno-14-6"></a>    <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-14-7" name="__codelineno-14-7" href="#__codelineno-14-7"></a>    <span class="n">pre_order</span><span class="p">(</span><span class="n">root</span><span class="o">=</span><span class="n">root</span><span class="o">.</span><span class="n">left</span><span class="p">)</span>
+<a id="__codelineno-14-8" name="__codelineno-14-8" href="#__codelineno-14-8"></a>    <span class="n">pre_order</span><span class="p">(</span><span class="n">root</span><span class="o">=</span><span class="n">root</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>
+<a id="__codelineno-14-9" name="__codelineno-14-9" href="#__codelineno-14-9"></a>
+<a id="__codelineno-14-10" name="__codelineno-14-10" href="#__codelineno-14-10"></a><span class="k">def</span><span class="w"> </span><span class="nf">in_order</span><span class="p">(</span><span class="n">root</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">):</span>
+<a id="__codelineno-14-11" name="__codelineno-14-11" href="#__codelineno-14-11"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;中順走査&quot;&quot;&quot;</span>
+<a id="__codelineno-14-12" name="__codelineno-14-12" href="#__codelineno-14-12"></a>    <span class="k">if</span> <span class="n">root</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-14-13" name="__codelineno-14-13" href="#__codelineno-14-13"></a>        <span class="k">return</span>
+<a id="__codelineno-14-14" name="__codelineno-14-14" href="#__codelineno-14-14"></a>    <span class="c1"># 訪問順序: 左部分木 -&gt; ルートノード -&gt; 右部分木</span>
+<a id="__codelineno-14-15" name="__codelineno-14-15" href="#__codelineno-14-15"></a>    <span class="n">in_order</span><span class="p">(</span><span class="n">root</span><span class="o">=</span><span class="n">root</span><span class="o">.</span><span class="n">left</span><span class="p">)</span>
+<a id="__codelineno-14-16" name="__codelineno-14-16" href="#__codelineno-14-16"></a>    <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>
+<a id="__codelineno-14-17" name="__codelineno-14-17" href="#__codelineno-14-17"></a>    <span class="n">in_order</span><span class="p">(</span><span class="n">root</span><span class="o">=</span><span class="n">root</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>
+<a id="__codelineno-14-18" name="__codelineno-14-18" href="#__codelineno-14-18"></a>
+<a id="__codelineno-14-19" name="__codelineno-14-19" href="#__codelineno-14-19"></a><span class="k">def</span><span class="w"> </span><span class="nf">post_order</span><span class="p">(</span><span class="n">root</span><span class="p">:</span> <span class="n">TreeNode</span> <span class="o">|</span> <span class="kc">None</span><span class="p">):</span>
+<a id="__codelineno-14-20" name="__codelineno-14-20" href="#__codelineno-14-20"></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;後順走査&quot;&quot;&quot;</span>
+<a id="__codelineno-14-21" name="__codelineno-14-21" href="#__codelineno-14-21"></a>    <span class="k">if</span> <span class="n">root</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+<a id="__codelineno-14-22" name="__codelineno-14-22" href="#__codelineno-14-22"></a>        <span class="k">return</span>
+<a id="__codelineno-14-23" name="__codelineno-14-23" href="#__codelineno-14-23"></a>    <span class="c1"># 訪問順序: 左部分木 -&gt; 右部分木 -&gt; ルートノード</span>
+<a id="__codelineno-14-24" name="__codelineno-14-24" href="#__codelineno-14-24"></a>    <span class="n">post_order</span><span class="p">(</span><span class="n">root</span><span class="o">=</span><span class="n">root</span><span class="o">.</span><span class="n">left</span><span class="p">)</span>
+<a id="__codelineno-14-25" name="__codelineno-14-25" href="#__codelineno-14-25"></a>    <span class="n">post_order</span><span class="p">(</span><span class="n">root</span><span class="o">=</span><span class="n">root</span><span class="o">.</span><span class="n">right</span><span class="p">)</span>
+<a id="__codelineno-14-26" name="__codelineno-14-26" href="#__codelineno-14-26"></a>    <span class="n">res</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">root</span><span class="o">.</span><span class="n">val</span><span class="p">)</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree_dfs.cpp</span><pre><span></span><code><a id="__codelineno-15-1" name="__codelineno-15-1" href="#__codelineno-15-1"></a><span class="cm">/* 前順走査 */</span>
+<a id="__codelineno-15-2" name="__codelineno-15-2" href="#__codelineno-15-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-3" name="__codelineno-15-3" href="#__codelineno-15-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span>
+<a id="__codelineno-15-4" name="__codelineno-15-4" href="#__codelineno-15-4"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-15-5" name="__codelineno-15-5" href="#__codelineno-15-5"></a><span class="w">    </span><span class="c1">// 訪問優先度：ルートノード -&gt; 左部分木 -&gt; 右部分木</span>
+<a id="__codelineno-15-6" name="__codelineno-15-6" href="#__codelineno-15-6"></a><span class="w">    </span><span class="n">vec</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-15-7" name="__codelineno-15-7" href="#__codelineno-15-7"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">);</span>
+<a id="__codelineno-15-8" name="__codelineno-15-8" href="#__codelineno-15-8"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-15-9" name="__codelineno-15-9" href="#__codelineno-15-9"></a><span class="p">}</span>
+<a id="__codelineno-15-10" name="__codelineno-15-10" href="#__codelineno-15-10"></a>
+<a id="__codelineno-15-11" name="__codelineno-15-11" href="#__codelineno-15-11"></a><span class="cm">/* 中順走査 */</span>
+<a id="__codelineno-15-12" name="__codelineno-15-12" href="#__codelineno-15-12"></a><span class="kt">void</span><span class="w"> </span><span class="nf">inOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-13" name="__codelineno-15-13" href="#__codelineno-15-13"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span>
+<a id="__codelineno-15-14" name="__codelineno-15-14" href="#__codelineno-15-14"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-15-15" name="__codelineno-15-15" href="#__codelineno-15-15"></a><span class="w">    </span><span class="c1">// 訪問優先度：左部分木 -&gt; ルートノード -&gt; 右部分木</span>
+<a id="__codelineno-15-16" name="__codelineno-15-16" href="#__codelineno-15-16"></a><span class="w">    </span><span class="n">inOrder</span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">);</span>
+<a id="__codelineno-15-17" name="__codelineno-15-17" href="#__codelineno-15-17"></a><span class="w">    </span><span class="n">vec</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-15-18" name="__codelineno-15-18" href="#__codelineno-15-18"></a><span class="w">    </span><span class="n">inOrder</span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-15-19" name="__codelineno-15-19" href="#__codelineno-15-19"></a><span class="p">}</span>
+<a id="__codelineno-15-20" name="__codelineno-15-20" href="#__codelineno-15-20"></a>
+<a id="__codelineno-15-21" name="__codelineno-15-21" href="#__codelineno-15-21"></a><span class="cm">/* 後順走査 */</span>
+<a id="__codelineno-15-22" name="__codelineno-15-22" href="#__codelineno-15-22"></a><span class="kt">void</span><span class="w"> </span><span class="nf">postOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="o">*</span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-15-23" name="__codelineno-15-23" href="#__codelineno-15-23"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="k">nullptr</span><span class="p">)</span>
+<a id="__codelineno-15-24" name="__codelineno-15-24" href="#__codelineno-15-24"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-15-25" name="__codelineno-15-25" href="#__codelineno-15-25"></a><span class="w">    </span><span class="c1">// 訪問優先度：左部分木 -&gt; 右部分木 -&gt; ルートノード</span>
+<a id="__codelineno-15-26" name="__codelineno-15-26" href="#__codelineno-15-26"></a><span class="w">    </span><span class="n">postOrder</span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">left</span><span class="p">);</span>
+<a id="__codelineno-15-27" name="__codelineno-15-27" href="#__codelineno-15-27"></a><span class="w">    </span><span class="n">postOrder</span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">right</span><span class="p">);</span>
+<a id="__codelineno-15-28" name="__codelineno-15-28" href="#__codelineno-15-28"></a><span class="w">    </span><span class="n">vec</span><span class="p">.</span><span class="n">push_back</span><span class="p">(</span><span class="n">root</span><span class="o">-&gt;</span><span class="n">val</span><span class="p">);</span>
+<a id="__codelineno-15-29" name="__codelineno-15-29" href="#__codelineno-15-29"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree_dfs.java</span><pre><span></span><code><a id="__codelineno-16-1" name="__codelineno-16-1" href="#__codelineno-16-1"></a><span class="cm">/* 前順走査 */</span>
+<a id="__codelineno-16-2" name="__codelineno-16-2" href="#__codelineno-16-2"></a><span class="kt">void</span><span class="w"> </span><span class="nf">preOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-3" name="__codelineno-16-3" href="#__codelineno-16-3"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
+<a id="__codelineno-16-4" name="__codelineno-16-4" href="#__codelineno-16-4"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-16-5" name="__codelineno-16-5" href="#__codelineno-16-5"></a><span class="w">    </span><span class="c1">// 訪問優先度: 根ノード -&gt; 左部分木 -&gt; 右部分木</span>
+<a id="__codelineno-16-6" name="__codelineno-16-6" href="#__codelineno-16-6"></a><span class="w">    </span><span class="n">list</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">val</span><span class="p">);</span>
+<a id="__codelineno-16-7" name="__codelineno-16-7" href="#__codelineno-16-7"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">left</span><span class="p">);</span>
+<a id="__codelineno-16-8" name="__codelineno-16-8" href="#__codelineno-16-8"></a><span class="w">    </span><span class="n">preOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">right</span><span class="p">);</span>
+<a id="__codelineno-16-9" name="__codelineno-16-9" href="#__codelineno-16-9"></a><span class="p">}</span>
+<a id="__codelineno-16-10" name="__codelineno-16-10" href="#__codelineno-16-10"></a>
+<a id="__codelineno-16-11" name="__codelineno-16-11" href="#__codelineno-16-11"></a><span class="cm">/* 中順走査 */</span>
+<a id="__codelineno-16-12" name="__codelineno-16-12" href="#__codelineno-16-12"></a><span class="kt">void</span><span class="w"> </span><span class="nf">inOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-13" name="__codelineno-16-13" href="#__codelineno-16-13"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
+<a id="__codelineno-16-14" name="__codelineno-16-14" href="#__codelineno-16-14"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-16-15" name="__codelineno-16-15" href="#__codelineno-16-15"></a><span class="w">    </span><span class="c1">// 訪問優先度: 左部分木 -&gt; 根ノード -&gt; 右部分木</span>
+<a id="__codelineno-16-16" name="__codelineno-16-16" href="#__codelineno-16-16"></a><span class="w">    </span><span class="n">inOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">left</span><span class="p">);</span>
+<a id="__codelineno-16-17" name="__codelineno-16-17" href="#__codelineno-16-17"></a><span class="w">    </span><span class="n">list</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">val</span><span class="p">);</span>
+<a id="__codelineno-16-18" name="__codelineno-16-18" href="#__codelineno-16-18"></a><span class="w">    </span><span class="n">inOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">right</span><span class="p">);</span>
+<a id="__codelineno-16-19" name="__codelineno-16-19" href="#__codelineno-16-19"></a><span class="p">}</span>
+<a id="__codelineno-16-20" name="__codelineno-16-20" href="#__codelineno-16-20"></a>
+<a id="__codelineno-16-21" name="__codelineno-16-21" href="#__codelineno-16-21"></a><span class="cm">/* 後順走査 */</span>
+<a id="__codelineno-16-22" name="__codelineno-16-22" href="#__codelineno-16-22"></a><span class="kt">void</span><span class="w"> </span><span class="nf">postOrder</span><span class="p">(</span><span class="n">TreeNode</span><span class="w"> </span><span class="n">root</span><span class="p">)</span><span class="w"> </span><span class="p">{</span>
+<a id="__codelineno-16-23" name="__codelineno-16-23" href="#__codelineno-16-23"></a><span class="w">    </span><span class="k">if</span><span class="w"> </span><span class="p">(</span><span class="n">root</span><span class="w"> </span><span class="o">==</span><span class="w"> </span><span class="kc">null</span><span class="p">)</span>
+<a id="__codelineno-16-24" name="__codelineno-16-24" href="#__codelineno-16-24"></a><span class="w">        </span><span class="k">return</span><span class="p">;</span>
+<a id="__codelineno-16-25" name="__codelineno-16-25" href="#__codelineno-16-25"></a><span class="w">    </span><span class="c1">// 訪問優先度: 左部分木 -&gt; 右部分木 -&gt; 根ノード</span>
+<a id="__codelineno-16-26" name="__codelineno-16-26" href="#__codelineno-16-26"></a><span class="w">    </span><span class="n">postOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">left</span><span class="p">);</span>
+<a id="__codelineno-16-27" name="__codelineno-16-27" href="#__codelineno-16-27"></a><span class="w">    </span><span class="n">postOrder</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">right</span><span class="p">);</span>
+<a id="__codelineno-16-28" name="__codelineno-16-28" href="#__codelineno-16-28"></a><span class="w">    </span><span class="n">list</span><span class="p">.</span><span class="na">add</span><span class="p">(</span><span class="n">root</span><span class="p">.</span><span class="na">val</span><span class="p">);</span>
+<a id="__codelineno-16-29" name="__codelineno-16-29" href="#__codelineno-16-29"></a><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree_dfs.cs</span><pre><span></span><code><a id="__codelineno-17-1" name="__codelineno-17-1" href="#__codelineno-17-1"></a><span class="na">[class]</span><span class="p">{</span><span class="n">binary_tree_dfs</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">PreOrder</span><span class="p">}</span>
+<a id="__codelineno-17-2" name="__codelineno-17-2" href="#__codelineno-17-2"></a>
+<a id="__codelineno-17-3" name="__codelineno-17-3" href="#__codelineno-17-3"></a><span class="na">[class]</span><span class="p">{</span><span class="n">binary_tree_dfs</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">InOrder</span><span class="p">}</span>
+<a id="__codelineno-17-4" name="__codelineno-17-4" href="#__codelineno-17-4"></a>
+<a id="__codelineno-17-5" name="__codelineno-17-5" href="#__codelineno-17-5"></a><span class="na">[class]</span><span class="p">{</span><span class="n">binary_tree_dfs</span><span class="p">}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">PostOrder</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree_dfs.go</span><pre><span></span><code><a id="__codelineno-18-1" name="__codelineno-18-1" href="#__codelineno-18-1"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">preOrder</span><span class="p">}</span>
+<a id="__codelineno-18-2" name="__codelineno-18-2" href="#__codelineno-18-2"></a>
+<a id="__codelineno-18-3" name="__codelineno-18-3" href="#__codelineno-18-3"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">inOrder</span><span class="p">}</span>
+<a id="__codelineno-18-4" name="__codelineno-18-4" href="#__codelineno-18-4"></a>
+<a id="__codelineno-18-5" name="__codelineno-18-5" href="#__codelineno-18-5"></a><span class="p">[</span><span class="nx">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="nx">postOrder</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree_dfs.swift</span><pre><span></span><code><a id="__codelineno-19-1" name="__codelineno-19-1" href="#__codelineno-19-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">preOrder</span><span class="p">}</span>
+<a id="__codelineno-19-2" name="__codelineno-19-2" href="#__codelineno-19-2"></a>
+<a id="__codelineno-19-3" name="__codelineno-19-3" href="#__codelineno-19-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">inOrder</span><span class="p">}</span>
+<a id="__codelineno-19-4" name="__codelineno-19-4" href="#__codelineno-19-4"></a>
+<a id="__codelineno-19-5" name="__codelineno-19-5" href="#__codelineno-19-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="kd">func</span><span class="p">]{</span><span class="n">postOrder</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree_dfs.js</span><pre><span></span><code><a id="__codelineno-20-1" name="__codelineno-20-1" href="#__codelineno-20-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">preOrder</span><span class="p">}</span>
+<a id="__codelineno-20-2" name="__codelineno-20-2" href="#__codelineno-20-2"></a>
+<a id="__codelineno-20-3" name="__codelineno-20-3" href="#__codelineno-20-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">inOrder</span><span class="p">}</span>
+<a id="__codelineno-20-4" name="__codelineno-20-4" href="#__codelineno-20-4"></a>
+<a id="__codelineno-20-5" name="__codelineno-20-5" href="#__codelineno-20-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">postOrder</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree_dfs.ts</span><pre><span></span><code><a id="__codelineno-21-1" name="__codelineno-21-1" href="#__codelineno-21-1"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">preOrder</span><span class="p">}</span>
+<a id="__codelineno-21-2" name="__codelineno-21-2" href="#__codelineno-21-2"></a>
+<a id="__codelineno-21-3" name="__codelineno-21-3" href="#__codelineno-21-3"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">inOrder</span><span class="p">}</span>
+<a id="__codelineno-21-4" name="__codelineno-21-4" href="#__codelineno-21-4"></a>
+<a id="__codelineno-21-5" name="__codelineno-21-5" href="#__codelineno-21-5"></a><span class="p">[</span><span class="kd">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="nx">func</span><span class="p">]{</span><span class="nx">postOrder</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree_dfs.dart</span><pre><span></span><code><a id="__codelineno-22-1" name="__codelineno-22-1" href="#__codelineno-22-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">preOrder</span><span class="p">}</span>
+<a id="__codelineno-22-2" name="__codelineno-22-2" href="#__codelineno-22-2"></a>
+<a id="__codelineno-22-3" name="__codelineno-22-3" href="#__codelineno-22-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">inOrder</span><span class="p">}</span>
+<a id="__codelineno-22-4" name="__codelineno-22-4" href="#__codelineno-22-4"></a>
+<a id="__codelineno-22-5" name="__codelineno-22-5" href="#__codelineno-22-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">postOrder</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree_dfs.rs</span><pre><span></span><code><a id="__codelineno-23-1" name="__codelineno-23-1" href="#__codelineno-23-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">pre_order</span><span class="p">}</span>
+<a id="__codelineno-23-2" name="__codelineno-23-2" href="#__codelineno-23-2"></a>
+<a id="__codelineno-23-3" name="__codelineno-23-3" href="#__codelineno-23-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">in_order</span><span class="p">}</span>
+<a id="__codelineno-23-4" name="__codelineno-23-4" href="#__codelineno-23-4"></a>
+<a id="__codelineno-23-5" name="__codelineno-23-5" href="#__codelineno-23-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">post_order</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree_dfs.c</span><pre><span></span><code><a id="__codelineno-24-1" name="__codelineno-24-1" href="#__codelineno-24-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">preOrder</span><span class="p">}</span>
+<a id="__codelineno-24-2" name="__codelineno-24-2" href="#__codelineno-24-2"></a>
+<a id="__codelineno-24-3" name="__codelineno-24-3" href="#__codelineno-24-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">inOrder</span><span class="p">}</span>
+<a id="__codelineno-24-4" name="__codelineno-24-4" href="#__codelineno-24-4"></a>
+<a id="__codelineno-24-5" name="__codelineno-24-5" href="#__codelineno-24-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">postOrder</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree_dfs.kt</span><pre><span></span><code><a id="__codelineno-25-1" name="__codelineno-25-1" href="#__codelineno-25-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">preOrder</span><span class="p">}</span>
+<a id="__codelineno-25-2" name="__codelineno-25-2" href="#__codelineno-25-2"></a>
+<a id="__codelineno-25-3" name="__codelineno-25-3" href="#__codelineno-25-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">inOrder</span><span class="p">}</span>
+<a id="__codelineno-25-4" name="__codelineno-25-4" href="#__codelineno-25-4"></a>
+<a id="__codelineno-25-5" name="__codelineno-25-5" href="#__codelineno-25-5"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">postOrder</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree_dfs.rb</span><pre><span></span><code><a id="__codelineno-26-1" name="__codelineno-26-1" href="#__codelineno-26-1"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">pre_order</span><span class="p">}</span>
+<a id="__codelineno-26-2" name="__codelineno-26-2" href="#__codelineno-26-2"></a>
+<a id="__codelineno-26-3" name="__codelineno-26-3" href="#__codelineno-26-3"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">in_order</span><span class="p">}</span>
+<a id="__codelineno-26-4" name="__codelineno-26-4" href="#__codelineno-26-4"></a>
+<a id="__codelineno-26-5" name="__codelineno-26-5" href="#__codelineno-26-5"></a><span class="o">[</span><span class="n">class</span><span class="o">]</span><span class="p">{}</span><span class="o">-[</span><span class="n">func</span><span class="o">]</span><span class="p">{</span><span class="n">post_order</span><span class="p">}</span>
+</code></pre></div>
+</div>
+<div class="tabbed-block">
+<div class="highlight"><span class="filename">binary_tree_dfs.zig</span><pre><span></span><code><a id="__codelineno-27-1" name="__codelineno-27-1" href="#__codelineno-27-1"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">preOrder</span><span class="p">}</span>
+<a id="__codelineno-27-2" name="__codelineno-27-2" href="#__codelineno-27-2"></a>
+<a id="__codelineno-27-3" name="__codelineno-27-3" href="#__codelineno-27-3"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">inOrder</span><span class="p">}</span>
+<a id="__codelineno-27-4" name="__codelineno-27-4" href="#__codelineno-27-4"></a>
+<a id="__codelineno-27-5" name="__codelineno-27-5" href="#__codelineno-27-5"></a><span class="p">[</span><span class="n">class</span><span class="p">]{}</span><span class="o">-</span><span class="p">[</span><span class="n">func</span><span class="p">]{</span><span class="n">postOrder</span><span class="p">}</span>
+</code></pre></div>
+</div>
+</div>
+</div>
+<div class="admonition tip">
+<p class="admonition-title">Tip</p>
+<p>深度優先探索は反復に基づいても実装できます。興味のある読者は自分で学習してください。</p>
+</div>
+<p>下図は二分木の前順走査の再帰プロセスを示しており、これは「再帰」と「復帰」という2つの反対の部分に分けることができます。</p>
+<ol>
+<li>「再帰」は新しいメソッドを開始することを意味し、プログラムはこのプロセスで次のノードにアクセスします。</li>
+<li>「復帰」は関数が戻ることを意味し、現在のノードが完全にアクセスされたことを示します。</li>
+</ol>
+<div class="tabbed-set tabbed-alternate" data-tabs="3:11"><input checked="checked" id="__tabbed_3_1" name="__tabbed_3" type="radio" /><input id="__tabbed_3_2" name="__tabbed_3" type="radio" /><input id="__tabbed_3_3" name="__tabbed_3" type="radio" /><input id="__tabbed_3_4" name="__tabbed_3" type="radio" /><input id="__tabbed_3_5" name="__tabbed_3" type="radio" /><input id="__tabbed_3_6" name="__tabbed_3" type="radio" /><input id="__tabbed_3_7" name="__tabbed_3" type="radio" /><input id="__tabbed_3_8" name="__tabbed_3" type="radio" /><input id="__tabbed_3_9" name="__tabbed_3" type="radio" /><input id="__tabbed_3_10" name="__tabbed_3" type="radio" /><input id="__tabbed_3_11" name="__tabbed_3" type="radio" /><div class="tabbed-labels"><label for="__tabbed_3_1">&lt;1&gt;</label><label for="__tabbed_3_2">&lt;2&gt;</label><label for="__tabbed_3_3">&lt;3&gt;</label><label for="__tabbed_3_4">&lt;4&gt;</label><label for="__tabbed_3_5">&lt;5&gt;</label><label for="__tabbed_3_6">&lt;6&gt;</label><label for="__tabbed_3_7">&lt;7&gt;</label><label for="__tabbed_3_8">&lt;8&gt;</label><label for="__tabbed_3_9">&lt;9&gt;</label><label for="__tabbed_3_10">&lt;10&gt;</label><label for="__tabbed_3_11">&lt;11&gt;</label></div>
+<div class="tabbed-content">
+<div class="tabbed-block">
+<p><a class="glightbox" href="../binary_tree_traversal.assets/preorder_step1.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="前順走査の再帰プロセス" class="animation-figure" src="../binary_tree_traversal.assets/preorder_step1.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../binary_tree_traversal.assets/preorder_step2.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="preorder_step2" class="animation-figure" src="../binary_tree_traversal.assets/preorder_step2.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../binary_tree_traversal.assets/preorder_step3.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="preorder_step3" class="animation-figure" src="../binary_tree_traversal.assets/preorder_step3.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../binary_tree_traversal.assets/preorder_step4.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="preorder_step4" class="animation-figure" src="../binary_tree_traversal.assets/preorder_step4.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../binary_tree_traversal.assets/preorder_step5.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="preorder_step5" class="animation-figure" src="../binary_tree_traversal.assets/preorder_step5.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../binary_tree_traversal.assets/preorder_step6.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="preorder_step6" class="animation-figure" src="../binary_tree_traversal.assets/preorder_step6.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../binary_tree_traversal.assets/preorder_step7.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="preorder_step7" class="animation-figure" src="../binary_tree_traversal.assets/preorder_step7.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../binary_tree_traversal.assets/preorder_step8.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="preorder_step8" class="animation-figure" src="../binary_tree_traversal.assets/preorder_step8.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../binary_tree_traversal.assets/preorder_step9.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="preorder_step9" class="animation-figure" src="../binary_tree_traversal.assets/preorder_step9.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../binary_tree_traversal.assets/preorder_step10.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="preorder_step10" class="animation-figure" src="../binary_tree_traversal.assets/preorder_step10.png" /></a></p>
+</div>
+<div class="tabbed-block">
+<p><a class="glightbox" href="../binary_tree_traversal.assets/preorder_step11.png" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="preorder_step11" class="animation-figure" src="../binary_tree_traversal.assets/preorder_step11.png" /></a></p>
+</div>
+</div>
+</div>
+<p align="center"> 図 7-11 &nbsp; 前順走査の再帰プロセス </p>
+
+<h3 id="2_1">2. &nbsp; 計算量分析<a class="headerlink" href="#2_1" title="Permanent link">&para;</a></h3>
+<ul>
+<li><strong>時間計算量は<span class="arithmatex">\(O(n)\)</span></strong>: すべてのノードが一度ずつ訪問され、<span class="arithmatex">\(O(n)\)</span>の時間を使用します。</li>
+<li><strong>空間計算量は<span class="arithmatex">\(O(n)\)</span></strong>: 最悪の場合、つまり木が連結リストに退化した場合、再帰の深さは<span class="arithmatex">\(n\)</span>に達し、システムは<span class="arithmatex">\(O(n)\)</span>のスタックフレーム空間を占有します。</li>
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+  
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+    はじめに
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+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M21 4H3a2 2 0 0 0-2 2v13a2 2 0 0 0 2 2h18a2 2 0 0 0 2-2V6a2 2 0 0 0-2-2M3 19V6h8v13H3m18 0h-8V6h8v13m-7-9.5h6V11h-6V9.5m0 2.5h6v1.5h-6V12m0 2.5h6V16h-6v-1.5Z"/></svg>
+  
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+    第 0 章 &nbsp; 前書き
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+      <a href="../chapter_preface/about_the_book/" class="md-nav__link">
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+    0.1 &nbsp; この本について
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+    0.2 &nbsp; 本書の使い方
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+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_preface/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    0.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_3" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_introduction/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 1 章 &nbsp; アルゴリズムとの出会い
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_3" id="__nav_3_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_3_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_3">
+            <span class="md-nav__icon md-icon"></span>
+            第 1 章 &nbsp; アルゴリズムとの出会い
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_introduction/algorithms_are_everywhere/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.1 &nbsp; アルゴリズムはどこにでもある
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_introduction/what_is_dsa/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.2 &nbsp; アルゴリズムとは何か
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_introduction/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    1.3 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_4" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_computational_complexity/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_4" id="__nav_4_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_4_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_4">
+            <span class="md-nav__icon md-icon"></span>
+            第 2 章 &nbsp; 計算量解析
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/performance_evaluation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.1 &nbsp; アルゴリズム効率評価
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/iteration_and_recursion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.2 &nbsp; 反復と再帰
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_computational_complexity/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    2.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_5" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_data_structure/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 3 章 &nbsp; データ構造
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_5" id="__nav_5_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="./" class="md-nav__link md-nav__link--active">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link md-nav__link--active" for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
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+
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+<h1 id="7">第 7 章 &nbsp; 木<a class="headerlink" href="#7" title="Permanent link">&para;</a></h1>
+<p><a class="glightbox" href="../assets/covers/chapter_tree.jpg" data-type="image" data-width="100%" data-height="auto" data-desc-position="bottom"><img alt="木" class="cover-image" src="../assets/covers/chapter_tree.jpg" /></a></p>
+<div class="admonition abstract">
+<p class="admonition-title">Abstract</p>
+<p>そびえ立つ木は活力に満ちた本質を放ち、深い根と豊かな葉を誇りながらも、その枝は疎らに散らばり、幽玄な雰囲気を醸し出しています。</p>
+<p>それはデータにおける分割統治の鮮やかな形を私たちに示しています。</p>
+</div>
+<h2 id="_1">章の内容<a class="headerlink" href="#_1" title="Permanent link">&para;</a></h2>
+<ul>
+<li><a href="binary_tree/">7.1 &nbsp; 二分木</a></li>
+<li><a href="binary_tree_traversal/">7.2 &nbsp; 二分木の走査</a></li>
+<li><a href="array_representation_of_tree/">7.3 &nbsp; 木の配列表現</a></li>
+<li><a href="binary_search_tree/">7.4 &nbsp; 二分探索木</a></li>
+<li><a href="avl_tree/">7.5 &nbsp; AVL木 *</a></li>
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+      <a href="../../chapter_preface/summary/" class="md-nav__link">
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+  
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+    第 1 章 &nbsp; アルゴリズムとの出会い
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+  
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+      <a href="../../chapter_introduction/summary/" class="md-nav__link">
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+    1.3 &nbsp; まとめ
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+        
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+  
+  <span class="md-ellipsis">
+    第 2 章 &nbsp; 計算量解析
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+            第 2 章 &nbsp; 計算量解析
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+    2.1 &nbsp; アルゴリズム効率評価
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+    2.2 &nbsp; 反復と再帰
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+  
+
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+      <a href="../../chapter_computational_complexity/time_complexity/" class="md-nav__link">
+        
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+    2.3 &nbsp; 時間計算量
+  </span>
+  
+
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+      <a href="../../chapter_computational_complexity/space_complexity/" class="md-nav__link">
+        
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+  <span class="md-ellipsis">
+    2.4 &nbsp; 空間計算量
+  </span>
+  
+
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+    </li>
+  
+
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+  
+  
+  
+  
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+      <a href="../../chapter_computational_complexity/summary/" class="md-nav__link">
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+  
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+    第 3 章 &nbsp; データ構造
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+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_5_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_5">
+            <span class="md-nav__icon md-icon"></span>
+            第 3 章 &nbsp; データ構造
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/classification_of_data_structure/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.1 &nbsp; データ構造の分類
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/basic_data_types/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.2 &nbsp; 基本データ型
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/number_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.3 &nbsp; 数値エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/character_encoding/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.4 &nbsp; 文字エンコーディング *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_data_structure/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    3.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_6" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_array_and_linkedlist/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 4 章 &nbsp; 配列と連結リスト
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_6" id="__nav_6_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_6_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_6">
+            <span class="md-nav__icon md-icon"></span>
+            第 4 章 &nbsp; 配列と連結リスト
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/array/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.1 &nbsp; 配列
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/linked_list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.2 &nbsp; 連結リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/list/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.3 &nbsp; リスト
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/ram_and_cache/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.4 &nbsp; メモリとキャッシュ *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_array_and_linkedlist/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    4.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_7" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_stack_and_queue/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 5 章 &nbsp; スタックとキュー
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_7" id="__nav_7_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_7_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_7">
+            <span class="md-nav__icon md-icon"></span>
+            第 5 章 &nbsp; スタックとキュー
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/stack/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.1 &nbsp; スタック
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/queue/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.2 &nbsp; キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/deque/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.3 &nbsp; 両端キュー
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_stack_and_queue/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    5.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_8" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_hashing/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 6 章 &nbsp; ハッシュ表
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_8" id="__nav_8_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_8_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_8">
+            <span class="md-nav__icon md-icon"></span>
+            第 6 章 &nbsp; ハッシュ表
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_map/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.1 &nbsp; ハッシュ表
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_collision/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.2 &nbsp; ハッシュ衝突
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/hash_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.3 &nbsp; ハッシュアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_hashing/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    6.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+    
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--active md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_9" checked>
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 7 章 &nbsp; 木
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_9" id="__nav_9_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_9_label" aria-expanded="true">
+          <label class="md-nav__title" for="__nav_9">
+            <span class="md-nav__icon md-icon"></span>
+            第 7 章 &nbsp; 木
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../binary_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.1 &nbsp; 二分木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../binary_tree_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.2 &nbsp; 二分木の走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../array_representation_of_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.3 &nbsp; 木の配列表現
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../binary_search_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.4 &nbsp; 二分探索木
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../avl_tree/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    7.5 &nbsp; AVL木 *
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+    
+  
+  
+  
+    <li class="md-nav__item md-nav__item--active">
+      
+      <input class="md-nav__toggle md-toggle" type="checkbox" id="__toc">
+      
+      
+        
+      
+      
+        <label class="md-nav__link md-nav__link--active" for="__toc">
+          
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+          <span class="md-nav__icon md-icon"></span>
+        </label>
+      
+      <a href="./" class="md-nav__link md-nav__link--active">
+        
+  
+  <span class="md-ellipsis">
+    7.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+      
+        
+
+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 重要なポイント
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#2-q-a" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; Q &amp; A
+    </span>
+  </a>
+  
+</li>
+      
+    </ul>
+  
+</nav>
+      
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_10" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_heap/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 8 章 &nbsp; ヒープ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_10" id="__nav_10_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_10_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_10">
+            <span class="md-nav__icon md-icon"></span>
+            第 8 章 &nbsp; ヒープ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.1 &nbsp; ヒープ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/build_heap/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.2 &nbsp; ヒープの構築
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/top_k/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.3 &nbsp; Top-k問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_heap/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    8.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_11" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_graph/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 9 章 &nbsp; グラフ
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_11" id="__nav_11_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_11_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_11">
+            <span class="md-nav__icon md-icon"></span>
+            第 9 章 &nbsp; グラフ
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.1 &nbsp; グラフ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_operations/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.2 &nbsp; グラフの基本操作
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/graph_traversal/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.3 &nbsp; グラフの走査
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_graph/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    9.4 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_12" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_searching/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 10 章 &nbsp; 探索
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_12" id="__nav_12_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_12_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_12">
+            <span class="md-nav__icon md-icon"></span>
+            第 10 章 &nbsp; 探索
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.1 &nbsp; 二分探索
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_insertion/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.2 &nbsp; 二分探索挿入点
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/binary_search_edge/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.3 &nbsp; 二分探索の境界
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/replace_linear_by_hashing/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.4 &nbsp; ハッシュ最適化戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/searching_algorithm_revisited/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.5 &nbsp; 探索アルゴリズム再考
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_searching/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    10.6 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_13" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_sorting/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 11 章 &nbsp; ソート
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_13" id="__nav_13_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_13_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_13">
+            <span class="md-nav__icon md-icon"></span>
+            第 11 章 &nbsp; ソート
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/sorting_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.1 &nbsp; ソートアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/selection_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.2 &nbsp; 選択ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bubble_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.3 &nbsp; バブルソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/insertion_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.4 &nbsp; 挿入ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/quick_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.5 &nbsp; クイックソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/merge_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.6 &nbsp; マージソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/heap_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.7 &nbsp; ヒープソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/bucket_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.8 &nbsp; バケットソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/counting_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.9 &nbsp; 計数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/radix_sort/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.10 &nbsp; 基数ソート
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_sorting/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    11.11 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_14" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_divide_and_conquer/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 12 章 &nbsp; 分割統治
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_14" id="__nav_14_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_14_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_14">
+            <span class="md-nav__icon md-icon"></span>
+            第 12 章 &nbsp; 分割統治
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/divide_and_conquer/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.1 &nbsp; 分割統治アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/binary_search_recur/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.2 &nbsp; 分割統治探索戦略
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/build_binary_tree_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.3 &nbsp; 二分木構築問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/hanota_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.4 &nbsp; ハノイの塔問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_divide_and_conquer/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    12.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_15" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_backtracking/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 13 章 &nbsp; バックトラッキング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_15" id="__nav_15_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_15_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_15">
+            <span class="md-nav__icon md-icon"></span>
+            第 13 章 &nbsp; バックトラッキング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/backtracking_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.1 &nbsp; バックトラッキングアルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/permutations_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.2 &nbsp; 順列問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/subset_sum_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.3 &nbsp; 部分集合和問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/n_queens_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.4 &nbsp; Nクイーン問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_backtracking/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    13.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_16" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_dynamic_programming/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 14 章 &nbsp; 動的プログラミング
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_16" id="__nav_16_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_16_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_16">
+            <span class="md-nav__icon md-icon"></span>
+            第 14 章 &nbsp; 動的プログラミング
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/intro_to_dynamic_programming/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.1 &nbsp; 動的プログラミング入門
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_problem_features/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.2 &nbsp; DP問題の特性
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/dp_solution_pipeline/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.3 &nbsp; DP問題解決アプローチ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.4 &nbsp; 0-1ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/unbounded_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.5 &nbsp; 無制限ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/edit_distance_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.6 &nbsp; 編集距離問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_dynamic_programming/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    14.7 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_17" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_greedy/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 15 章 &nbsp; 貪欲法
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_17" id="__nav_17_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_17_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_17">
+            <span class="md-nav__icon md-icon"></span>
+            第 15 章 &nbsp; 貪欲法
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/greedy_algorithm/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.1 &nbsp; 貪欲アルゴリズム
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/fractional_knapsack_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.2 &nbsp; 分数ナップサック問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_capacity_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.3 &nbsp; 最大容量問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/max_product_cutting_problem/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.4 &nbsp; 最大積切断問題
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_greedy/summary/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    15.5 &nbsp; まとめ
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
+  
+  
+    
+    
+      
+        
+          
+        
+      
+        
+      
+        
+      
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_18" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_appendix/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z"/></svg>
+  
+  <span class="md-ellipsis">
+    第 16 章 &nbsp; 付録
+  </span>
+  
+
+            </a>
+            
+              
+              <label class="md-nav__link " for="__nav_18" id="__nav_18_label" tabindex="0">
+                <span class="md-nav__icon md-icon"></span>
+              </label>
+            
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+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_18_label" aria-expanded="false">
+          <label class="md-nav__title" for="__nav_18">
+            <span class="md-nav__icon md-icon"></span>
+            第 16 章 &nbsp; 付録
+          </label>
+          <ul class="md-nav__list" data-md-scrollfix>
+            
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/installation/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.1 &nbsp; プログラミング環境のインストール
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/contribution/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.2 &nbsp; 一緒に創作に参加
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+              
+                
+  
+  
+  
+  
+    <li class="md-nav__item">
+      <a href="../../chapter_appendix/terminology/" class="md-nav__link">
+        
+  
+  <span class="md-ellipsis">
+    16.3 &nbsp; 用語集
+  </span>
+  
+
+      </a>
+    </li>
+  
+
+              
+            
+          </ul>
+        </nav>
+      
+    </li>
+  
+
+    
+      
+      
+  
+  
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+  
+    
+    
+      
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+          
+        
+      
+    
+    
+    
+    
+    <li class="md-nav__item md-nav__item--nested">
+      
+        
+        
+        
+        <input class="md-nav__toggle md-toggle " type="checkbox" id="__nav_19" >
+        
+          
+          
+          <div class="md-nav__link md-nav__container">
+            <a href="../../chapter_reference/" class="md-nav__link ">
+              
+  
+    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 24 24"><path d="M9 3v15h3V3H9m3 2 4 13 3-1-4-13-3 1M5 5v13h3V5H5M3 19v2h18v-2H3Z"/></svg>
+  
+  <span class="md-ellipsis">
+    参考文献
+  </span>
+  
+
+            </a>
+            
+          </div>
+        
+        <nav class="md-nav" data-md-level="1" aria-labelledby="__nav_19_label" aria-expanded="false">
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+            参考文献
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+                  </div>
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+            
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+              <div class="md-sidebar md-sidebar--secondary" data-md-component="sidebar" data-md-type="toc" >
+                <div class="md-sidebar__scrollwrap">
+                  <div class="md-sidebar__inner">
+                    
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+<nav class="md-nav md-nav--secondary" aria-label="目次">
+  
+  
+  
+    
+  
+  
+    <label class="md-nav__title" for="__toc">
+      <span class="md-nav__icon md-icon"></span>
+      目次
+    </label>
+    <ul class="md-nav__list" data-md-component="toc" data-md-scrollfix>
+      
+        <li class="md-nav__item">
+  <a href="#1" class="md-nav__link">
+    <span class="md-ellipsis">
+      1. &nbsp; 重要なポイント
+    </span>
+  </a>
+  
+</li>
+      
+        <li class="md-nav__item">
+  <a href="#2-q-a" class="md-nav__link">
+    <span class="md-ellipsis">
+      2. &nbsp; Q &amp; A
+    </span>
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+  
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+      
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+  
+</nav>
+                  </div>
+                </div>
+              </div>
+            
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+            <div class="md-content" data-md-component="content">
+              <article class="md-content__inner md-typeset">
+                
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+<h1 id="76">7.6 &nbsp; まとめ<a class="headerlink" href="#76" title="Permanent link">&para;</a></h1>
+<h3 id="1">1. &nbsp; 重要なポイント<a class="headerlink" href="#1" title="Permanent link">&para;</a></h3>
+<ul>
+<li>二分木は非線形データ構造で、「一つを二つに分ける」分割統治のロジックを反映しています。各二分木ノードには値と2つのポインタが含まれ、それぞれ左と右の子ノードを指します。</li>
+<li>二分木のノードについて、その左（右）子ノードとその下に形成される木は、まとめてそのノードの左（右）部分木と呼ばれます。</li>
+<li>二分木に関連する用語には、根ノード、葉ノード、レベル、次数、エッジ、高さ、深さがあります。</li>
+<li>二分木の初期化、ノードの挿入、ノードの削除の操作は、連結リストの操作と似ています。</li>
+<li>一般的な二分木の種類には、完全二分木、完備二分木、満二分木、平衡二分木があります。完全二分木は理想的な状態を表し、連結リストは退化後の最悪の状態です。</li>
+<li>二分木は、ノード値と空きスロットをレベル順走査シーケンスで配置し、親ノードと子ノード間のインデックスマッピング関係に基づいてポインタを実装することで、配列を使用して表現できます。</li>
+<li>二分木のレベル順走査は幅優先探索手法で、「円を拡大しながら」の層ごとの走査方式を反映しています。通常はキューを使用して実装されます。</li>
+<li>前順、中順、後順走査はすべて深度優先探索手法で、「まず最後まで行き、その後バックトラックして続行する」走査方式を反映しています。通常は再帰を使用して実装されます。</li>
+<li>二分探索木は要素検索のための効率的なデータ構造で、検索、挿入、削除操作の時間計算量はすべて<span class="arithmatex">\(O(\log n)\)</span>です。二分探索木が連結リストに退化すると、これらの時間計算量は<span class="arithmatex">\(O(n)\)</span>に悪化します。</li>
+<li>AVL木は平衡二分探索木とも呼ばれ、回転操作を通して継続的なノード挿入と削除後も木が平衡を保つことを保証します。</li>
+<li>AVL木の回転操作には、右回転、左回転、右左回転、左右回転があります。ノードの挿入または削除後、AVL木はボトムアップ方式でこれらの回転を実行して自己平衡を取ります。</li>
+</ul>
+<h3 id="2-q-a">2. &nbsp; Q &amp; A<a class="headerlink" href="#2-q-a" title="Permanent link">&para;</a></h3>
+<p><strong>Q</strong>: 一つのノードのみを持つ二分木について、木の高さと根ノードの深さの両方が<span class="arithmatex">\(0\)</span>ですか？</p>
+<p>はい、高さと深さは通常「通過したエッジの数」として定義されるためです。</p>
+<p><strong>Q</strong>: 二分木における挿入と削除は一般的に一連の操作によって達成されます。ここでの「一連の操作」とは何を指しますか？子ノードのリソースを解放することを意味しますか？</p>
+<p>二分探索木を例に取ると、ノードを削除する操作は3つの異なるシナリオで処理する必要があり、それぞれ複数ステップのノード操作が必要です。</p>
+<p><strong>Q</strong>: 二分木のDFS走査で前順、中順、後順の3つのシーケンスがあるのはなぜですか？その用途は何ですか？</p>
+<p>配列の順次および逆順走査と同様に、前順、中順、後順走査は二分木を走査する3つの方法であり、特定の順序で走査結果を取得できます。例えば、二分探索木では、ノードサイズが「左子ノード値 &lt; 根ノード値 &lt; 右子ノード値」を満たすため、「左 <span class="arithmatex">\(\rightarrow\)</span> 根 <span class="arithmatex">\(\rightarrow\)</span> 右」の優先順位で木を走査することで、順序付けられたノードシーケンスを取得できます。</p>
+<p><strong>Q</strong>: 不平衡ノード<code>node</code>、<code>child</code>、<code>grand_child</code>間の関係を処理する右回転操作において、右回転後に<code>node</code>とその親ノード間の接続と<code>node</code>の元のリンクが失われるのではありませんか？</p>
+<p>この問題を再帰的な観点から見る必要があります。<code>right_rotate(root)</code>操作は部分木の根ノードを渡し、最終的に<code>return child</code>で回転された部分木の根ノードを返します。部分木の根ノードとその親ノード間の接続は、この関数が戻った後に確立され、これは右回転操作の保守範囲外です。</p>
+<p><strong>Q</strong>: C++では、関数は<code>private</code>と<code>public</code>セクションに分かれています。これにはどのような考慮事項がありますか？なぜ<code>height()</code>関数と<code>updateHeight()</code>関数がそれぞれ<code>public</code>と<code>private</code>に配置されているのですか？</p>
+<p>これはメソッドの使用範囲によります。メソッドがクラス内でのみ使用される場合、<code>private</code>に設計されます。例えば、ユーザーが独自に<code>updateHeight()</code>を呼び出すことは意味がありません。これは挿入または削除操作の一ステップに過ぎないからです。しかし、<code>height()</code>はノードの高さにアクセスするためのもので、<code>vector.size()</code>と同様であるため、使用のために<code>public</code>に設定されています。</p>
+<p><strong>Q</strong>: 入力データのセットから二分探索木をどのように構築しますか？根ノードの選択は非常に重要ですか？</p>
+<p>はい、木を構築する方法は二分探索木コードの<code>build_tree()</code>メソッドで提供されています。根ノードの選択については、通常入力データをソートし、中央の要素を根ノードとして選択し、再帰的に左と右の部分木を構築します。このアプローチは木の平衡を最大化します。</p>
+<p><strong>Q</strong>: Javaでは、文字列比較に常に<code>equals()</code>メソッドを使用する必要がありますか？</p>
+<p>Javaでは、プリミティブデータ型の場合、<code>==</code>は2つの変数の値が等しいかどうかを比較するために使用されます。参照型の場合、2つのシンボルの動作原理は異なります。</p>
+<ul>
+<li><code>==</code>: 2つの変数が同じオブジェクトを指しているかどうか、つまりメモリ内の位置が同じかどうかを比較するために使用されます。</li>
+<li><code>equals()</code>: 2つのオブジェクトの値が等しいかどうかを比較するために使用されます。</li>
+</ul>
+<p>したがって、値を比較するには<code>equals()</code>を使用すべきです。ただし、<code>String a = "hi"; String b = "hi";</code>で初期化された文字列は文字列定数プールに格納され、同じオブジェクトを指すため、<code>a == b</code>も2つの文字列の内容を比較するために使用できます。</p>
+<p><strong>Q</strong>: 最下位レベルに到達する前に、幅優先走査でキュー内のノード数は<span class="arithmatex">\(2^h\)</span>ですか？</p>
+<p>はい、例えば高さ<span class="arithmatex">\(h = 2\)</span>の満二分木は合計<span class="arithmatex">\(n = 7\)</span>個のノードを持ち、最下位レベルには<span class="arithmatex">\(4 = 2^h = (n + 1) / 2\)</span>個のノードがあります。</p>
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diff --git a/ja/index.html b/ja/index.html
new file mode 100644
index 000000000..359112f3d
--- /dev/null
+++ b/ja/index.html
@@ -0,0 +1,1842 @@
+<!DOCTYPE html>
+<html class="no-js" lang="ja">
+  <head>
+    <meta charset="utf-8"/>
+    <meta content="width=device-width,initial-scale=1" name="viewport"/>
+    <meta content="アニメーションで図解、ワンクリック実行のデータ構造とアルゴリズムチュートリアル" name="description"/>
+    <meta content="krahets" name="author"/>
+    <link href="https://www.hello-algo.com/ja/" rel="canonical"/>
+    <link href="assets/images/favicon.png" rel="icon"/>
+    <meta content="mkdocs-1.5.3, mkdocs-material-9.5.5" name="generator"/>
+    <title>
+      Hello アルゴリズム
+    </title>
+    <link href="assets/stylesheets/main.50c56a3b.min.css" rel="stylesheet"/>
+    <link href="assets/stylesheets/palette.06af60db.min.css" rel="stylesheet"/>
+    <link crossorigin="" href="https://fonts.gstatic.com" rel="preconnect"/>
+    <link href="https://fonts.googleapis.com/css?family=Noto+Sans+JP:300,300i,400,400i,700,700i%7CFira+Code:400,400i,700,700i&amp;display=fallback" rel="stylesheet"/>
+    <style>
+      :root{--md-text-font:"Noto Sans JP";--md-code-font:"Fira Code"}
+    </style>
+    <link href="stylesheets/extra.css" rel="stylesheet"/>
+    <script>
+      __md_scope=new URL(".",location),__md_hash=e=>[...e].reduce((e,_)=>(e<<5)-e+_.charCodeAt(0),0),__md_get=(e,_=localStorage,t=__md_scope)=>JSON.parse(_.getItem(t.pathname+"."+e)),__md_set=(e,_,t=localStorage,a=__md_scope)=>{try{t.setItem(a.pathname+"."+e,JSON.stringify(_))}catch(e){}}
+    </script>
+  </head>
+  <body data-md-color-accent="teal" data-md-color-primary="white" data-md-color-scheme="default" dir="ltr" style="background-color: var(--md-body-bg-color);">
+    <input autocomplete="off" class="md-toggle" data-md-toggle="drawer" id="__drawer" type="checkbox"/>
+    <input autocomplete="off" class="md-toggle" data-md-toggle="search" id="__search" type="checkbox"/>
+    <label class="md-overlay" for="__drawer">
+    </label>
+    <div data-md-component="skip">
+    </div>
+    <div data-md-color-primary="black" data-md-color-scheme="slate" data-md-component="announce">
+    </div>
+    <header class="md-header md-header--landing" data-md-color-primary="black" data-md-color-scheme="slate" data-md-component="header">
+      <nav aria-label="ヘッダー" class="md-header__inner md-grid">
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+              配列と連結リスト
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+            <span style="left: 31.42%; top: 8.679%;">
+              分割統治法
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+          </a>
+          <a href="chapter_backtracking/">
+            <img alt="" src="../assets/hero/chapter_backtracking.png" style="height: 17.338%; left: 4.875%; top: 32.925%;"/>
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+              動的計画法
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+          </a>
+          <a href="chapter_greedy/">
+            <img alt="" src="../assets/hero/chapter_greedy.png" style="height: 14.127%; left: 23.132%; top: 75.803%;"/>
+            <span style="left: 21.619%; top: 86.85%;">
+              貪欲法
+            </span>
+          </a>
+        </div>
+        <div class="heading-div">
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+          <div style="pointer-events: auto;">
+            <p style="margin-top: max(-1vh, -2vw); margin-bottom: min(2vh, 3.5vw);">
+              アニメーション解説とワンクリック実行ができるデータ構造とアルゴリズムのチュートリアル
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+          <img alt="Preview" src="index.assets/hello_algo_header.png" style="width: 100%; max-width: 41.5em;"/>
+          <div class="code-badge">
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+            <img alt="" src="https://img.shields.io/badge/JS-snow?logo=javascript&amp;logoColor=E9CE30"/>
+            <img alt="" src="https://img.shields.io/badge/Go-snow?logo=go&amp;logoColor=00ADD8"/>
+            <img alt="" src="https://img.shields.io/badge/Swift-snow?logo=swift&amp;logoColor=F05138"/>
+            <img alt="" src="https://img.shields.io/badge/Rust-snow?logo=rust&amp;logoColor=000000"/>
+            <img alt="" src="https://img.shields.io/badge/Ruby-snow?logo=ruby&amp;logoColor=CC342D"/>
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+            <img alt="" src="https://img.shields.io/badge/TS-snow?logo=typescript&amp;logoColor=3178C6"/>
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+          <p style="margin-top: 2em;">
+            500 枚のアニメーション図解、14 類のプログラミング言語のコード、3000 件のコミュニティQ&amp;Aで，データ構造とアルゴリズムをすばやく習得しよう
+          </p>
+        </div>
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+            推薦文
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+            <div class="intro-text endor-text">
+              <p style="margin-bottom: 0;">
+                「わかりやすいデータ構造とアルゴリズムの入門書で、読者が手と頭を使って学べるよう導いてくれます。アルゴリズム初心者に強くおすすめします。」
+              </p>
+              <p style="font-weight: bold;">
+                —— 邓俊辉，清華大学コンピュータ系教授
+              </p>
+            </div>
+            <div class="intro-text endor-text">
+              <p style="margin-bottom: 0;">
+                「もし私が当時データ構造とアルゴリズムを学んでいたときに『Hello アルゴリズム』があったなら、学習は10倍も簡単だったはずだ！」
+              </p>
+              <p style="font-weight: bold;">
+                —— 李沐，アマゾンのシニアプリンシパルサイエンティスト
+              </p>
+            </div>
+          </div>
+        </div>
+      </section>
+      <section class="home-div" data-md-color-primary="white" data-md-color-scheme="default">
+        <div class="section-content">
+          <div class="intro-container">
+            <div class="intro-text">
+              <div>
+                <div style="display: flex; align-items: center;">
+                  <svg height="1.5em" viewbox="0 0 640 512" width="1.5em" xmlns="http://www.w3.org/2000/svg">
+                    <path d="M256 0H576c35.3 0 64 28.7 64 64V288c0 35.3-28.7 64-64 64H256c-35.3 0-64-28.7-64-64V64c0-35.3 28.7-64 64-64zM476 106.7C471.5 100 464 96 456 96s-15.5 4-20 10.7l-56 84L362.7 169c-4.6-5.7-11.5-9-18.7-9s-14.2 3.3-18.7 9l-64 80c-5.8 7.2-6.9 17.1-2.9 25.4s12.4 13.6 21.6 13.6h80 48H552c8.9 0 17-4.9 21.2-12.7s3.7-17.3-1.2-24.6l-96-144zM336 96a32 32 0 1 0 -64 0 32 32 0 1 0 64 0zM64 128h96V384v32c0 17.7 14.3 32 32 32H320c17.7 0 32-14.3 32-32V384H512v64c0 35.3-28.7 64-64 64H64c-35.3 0-64-28.7-64-64V192c0-35.3 28.7-64 64-64zm8 64c-8.8 0-16 7.2-16 16v16c0 8.8 7.2 16 16 16H88c8.8 0 16-7.2 16-16V208c0-8.8-7.2-16-16-16H72zm0 104c-8.8 0-16 7.2-16 16v16c0 8.8 7.2 16 16 16H88c8.8 0 16-7.2 16-16V312c0-8.8-7.2-16-16-16H72zm0 104c-8.8 0-16 7.2-16 16v16c0 8.8 7.2 16 16 16H88c8.8 0 16-7.2 16-16V416c0-8.8-7.2-16-16-16H72zm336 16v16c0 8.8 7.2 16 16 16h16c8.8 0 16-7.2 16-16V416c0-8.8-7.2-16-16-16H424c-8.8 0-16 7.2-16 16z" fill="var(--md-primary-bg-color)">
+                    </path>
+                  </svg>
+                  <h3 style="margin-left: 0.5em;">
+                    アニメーション図解
+                  </h3>
+                </div>
+                <p style="margin: 0;">
+                  内容は明快で理解しやすく、学習曲線は緩やか
+                </p>
+                <p class="intro-quote">
+                  "A picture is worth a thousand words."
+                  <br/>
+                  「一枚の絵は千の言葉に値する」
+                </p>
+              </div>
+            </div>
+            <img alt="Animation example" class="intro-image" src="index.assets/animation.gif"/>
+          </div>
+          <div class="intro-container">
+            <img alt="Running code example" class="intro-image" src="index.assets/running_code.gif"/>
+            <div class="intro-text">
+              <div>
+                <div style="display: flex; align-items: center;">
+                  <svg height="1.5em" viewbox="0 0 640 512" width="1.5em" xmlns="http://www.w3.org/2000/svg">
+                    <path d="M392.8 1.2c-17-4.9-34.7 5-39.6 22l-128 448c-4.9 17 5 34.7 22 39.6s34.7-5 39.6-22l128-448c4.9-17-5-34.7-22-39.6zm80.6 120.1c-12.5 12.5-12.5 32.8 0 45.3L562.7 256l-89.4 89.4c-12.5 12.5-12.5 32.8 0 45.3s32.8 12.5 45.3 0l112-112c12.5-12.5 12.5-32.8 0-45.3l-112-112c-12.5-12.5-32.8-12.5-45.3 0zm-306.7 0c-12.5-12.5-32.8-12.5-45.3 0l-112 112c-12.5 12.5-12.5 32.8 0 45.3l112 112c12.5 12.5 32.8 12.5 45.3 0s12.5-32.8 0-45.3L77.3 256l89.4-89.4c12.5-12.5 32.8-12.5 45.3 0z" fill="var(--md-primary-bg-color)">
+                    </path>
+                  </svg>
+                  <h3 style="margin-left: 0.5em;">
+                    ワンクリック実行
+                  </h3>
+                </div>
+                <p style="margin: 0;">
+                  10種類以上のプログラミング言語で、コードを可視化して実行
+                </p>
+                <p class="intro-quote">
+                  "Talk is cheap. Show me the code."
+                  <br/>
+                  「口で言うよりコードを見せよ」
+                </p>
+              </div>
+            </div>
+          </div>
+          <div class="intro-container">
+            <div class="intro-text">
+              <div>
+                <div style="display: flex; align-items: center;">
+                  <svg height="1.5em" viewbox="0 0 640 512" width="1.5em" xmlns="http://www.w3.org/2000/svg">
+                    <path d="M88.2 309.1c9.8-18.3 6.8-40.8-7.5-55.8C59.4 230.9 48 204 48 176c0-63.5 63.8-128 160-128s160 64.5 160 128s-63.8 128-160 128c-13.1 0-25.8-1.3-37.8-3.6c-10.4-2-21.2-.6-30.7 4.2c-4.1 2.1-8.3 4.1-12.6 6c-16 7.2-32.9 13.5-49.9 18c2.8-4.6 5.4-9.1 7.9-13.6c1.1-1.9 2.2-3.9 3.2-5.9zM0 176c0 41.8 17.2 80.1 45.9 110.3c-.9 1.7-1.9 3.5-2.8 5.1c-10.3 18.4-22.3 36.5-36.6 52.1c-6.6 7-8.3 17.2-4.6 25.9C5.8 378.3 14.4 384 24 384c43 0 86.5-13.3 122.7-29.7c4.8-2.2 9.6-4.5 14.2-6.8c15.1 3 30.9 4.5 47.1 4.5c114.9 0 208-78.8 208-176S322.9 0 208 0S0 78.8 0 176zM432 480c16.2 0 31.9-1.6 47.1-4.5c4.6 2.3 9.4 4.6 14.2 6.8C529.5 498.7 573 512 616 512c9.6 0 18.2-5.7 22-14.5c3.8-8.8 2-19-4.6-25.9c-14.2-15.6-26.2-33.7-36.6-52.1c-.9-1.7-1.9-3.4-2.8-5.1C622.8 384.1 640 345.8 640 304c0-94.4-87.9-171.5-198.2-175.8c4.1 15.2 6.2 31.2 6.2 47.8l0 .6c87.2 6.7 144 67.5 144 127.4c0 28-11.4 54.9-32.7 77.2c-14.3 15-17.3 37.6-7.5 55.8c1.1 2 2.2 4 3.2 5.9c2.5 4.5 5.2 9 7.9 13.6c-17-4.5-33.9-10.7-49.9-18c-4.3-1.9-8.5-3.9-12.6-6c-9.5-4.8-20.3-6.2-30.7-4.2c-12.1 2.4-24.7 3.6-37.8 3.6c-61.7 0-110-26.5-136.8-62.3c-16 5.4-32.8 9.4-50 11.8C279 439.8 350 480 432 480z" fill="var(--md-primary-bg-color)">
+                    </path>
+                  </svg>
+                  <h3 style="margin-left: 0.5em;">
+                    相互学習
+                  </h3>
+                </div>
+                <p style="margin: 0;">
+                  議論や質問を歓迎し、読者同士でともに前進
+                </p>
+                <p class="intro-quote">
+                  "Learning by teaching."
+                  <br/>
+                  「教えることで学ぶ」
+                </p>
+              </div>
+            </div>
+            <img alt="Comments example" class="intro-image" src="index.assets/comment.gif"/>
+          </div>
+        </div>
+      </section>
+      <section class="home-div" data-md-color-primary="grey" data-md-color-scheme="slate">
+        <div class="section-content" style="max-width: 90vw;">
+          <div style="margin: 2em auto;">
+            <h3>
+              著者
+            </h3>
+            <div class="profile-div">
+              <div class="profile-cell">
+                <a href="https://github.com/krahets">
+                  <img alt="Author: yudongjin" class="profile-img" src="../assets/avatar/avatar_yudongjin.jpg"/>
+                  <br/>
+                  <b>
+                    靳宇栋（@krahets）
+                  </b>
+                </a>
+              </div>
+            </div>
+          </div>
+          <div style="margin: 2em auto;">
+            <h3>
+              コードレビュー担当者
+            </h3>
+            <div class="profile-div">
+              <div class="profile-cell">
+                <a href="https://github.com/coderonion">
+                  <img alt="Reviewer: coderonion" class="profile-img" src="../assets/avatar/avatar_coderonion.jpg"/>
+                  <br/>
+                  <b>
+                    coderonion
+                  </b>
+                  <br/>
+                  <sub>
+                    Zig, Rust
+                  </sub>
+                </a>
+              </div>
+              <div class="profile-cell">
+                <a href="https://github.com/curtishd">
+                  <img alt="Reviewer: curtishd" class="profile-img" src="../assets/avatar/avatar_curtishd.jpg"/>
+                  <br/>
+                  <b>
+                    curtishd
+                  </b>
+                  <br/>
+                  <sub>
+                    Kotlin
+                  </sub>
+                </a>
+              </div>
+              <div class="profile-cell">
+                <a href="https://github.com/Gonglja">
+                  <img alt="Reviewer: Gonglja" class="profile-img" src="../assets/avatar/avatar_Gonglja.jpg"/>
+                  <br/>
+                  <b>
+                    Gonglja
+                  </b>
+                  <br/>
+                  <sub>
+                    C, C++
+                  </sub>
+                </a>
+              </div>
+              <div class="profile-cell">
+                <a href="https://github.com/gvenusleo">
+                  <img alt="Reviewer: gvenusleo" class="profile-img" src="../assets/avatar/avatar_gvenusleo.jpg"/>
+                  <br/>
+                  <b>
+                    gvenusleo
+                  </b>
+                  <br/>
+                  <sub>
+                    Dart
+                  </sub>
+                </a>
+              </div>
+              <div class="profile-cell">
+                <a href="https://github.com/hpstory">
+                  <img alt="Reviewer: hpstory" class="profile-img" src="../assets/avatar/avatar_hpstory.jpg"/>
+                  <br/>
+                  <b>
+                    hpstory
+                  </b>
+                  <br/>
+                  <sub>
+                    C#
+                  </sub>
+                </a>
+              </div>
+              <div class="profile-cell">
+                <a href="https://github.com/justin-tse">
+                  <img alt="Reviewer: justin-tse" class="profile-img" src="../assets/avatar/avatar_justin-tse.jpg"/>
+                  <br/>
+                  <b>
+                    justin-tse
+                  </b>
+                  <br/>
+                  <sub>
+                    JS, TS
+                  </sub>
+                </a>
+              </div>
+              <div class="profile-cell">
+                <a href="https://github.com/khoaxuantu">
+                  <img alt="Reviewer: khoaxuantu" class="profile-img" src="../assets/avatar/avatar_khoaxuantu.jpg"/>
+                  <br/>
+                  <b>
+                    khoaxuantu
+                  </b>
+                  <br/>
+                  <sub>
+                    Ruby
+                  </sub>
+                </a>
+              </div>
+              <div class="profile-cell">
+                <a href="https://github.com/krahets">
+                  <img alt="Reviewer: krahets" class="profile-img" src="../assets/avatar/avatar_krahets.jpg"/>
+                  <br/>
+                  <b>
+                    krahets
+                  </b>
+                  <br/>
+                  <sub>
+                    Python, Java
+                  </sub>
+                </a>
+              </div>
+              <div class="profile-cell">
+                <a href="https://github.com/night-cruise">
+                  <img alt="Reviewer: night-cruise" class="profile-img" src="../assets/avatar/avatar_night-cruise.jpg"/>
+                  <br/>
+                  <b>
+                    night-cruise
+                  </b>
+                  <br/>
+                  <sub>
+                    Rust
+                  </sub>
+                </a>
+              </div>
+              <div class="profile-cell">
+                <a href="https://github.com/nuomi1">
+                  <img alt="Reviewer: nuomi1" class="profile-img" src="../assets/avatar/avatar_nuomi1.jpg"/>
+                  <br/>
+                  <b>
+                    nuomi1
+                  </b>
+                  <br/>
+                  <sub>
+                    Swift
+                  </sub>
+                </a>
+              </div>
+              <div class="profile-cell">
+                <a href="https://github.com/Reanon">
+                  <img alt="Reviewer: Reanon" class="profile-img" src="../assets/avatar/avatar_Reanon.jpg"/>
+                  <br/>
+                  <b>
+                    Reanon
+                  </b>
+                  <br/>
+                  <sub>
+                    Go, C
+                  </sub>
+                </a>
+              </div>
+              <div class="profile-cell">
+                <a href="https://github.com/rongyi">
+                  <img alt="Reviewer: rongyi" class="profile-img" src="../assets/avatar/avatar_rongyi.jpg"/>
+                  <br/>
+                  <b>
+                    rongyi
+                  </b>
+                  <br/>
+                  <sub>
+                    Rust
+                  </sub>
+                </a>
+              </div>
+            </div>
+          </div>
+          <div style="margin: 2em auto;">
+            <h3>
+              日本語版審閱者
+            </h3>
+            <div class="profile-div">
+              <div class="profile-cell">
+                <a href="https://github.com/eltociear">
+                  <img alt="Reviewer: eltociear" class="profile-img" src="../assets/avatar/avatar_eltociear.jpg"/>
+                  <br/>
+                  <b>
+                    eltociear
+                  </b>
+                </a>
+              </div>
+            </div>
+          </div>
+          <div style="margin: 2em auto;">
+            <h3>
+              貢献者
+            </h3>
+            <p>
+              本書はオープンソースコミュニティの200名を超える貢献者の皆さんの共同の努力によって継続的に改善されています。時間と労力に感謝します！
+            </p>
+            <a href="https://github.com/krahets/hello-algo/graphs/contributors">
+              <img alt="Contributors" src="https://contrib.rocks/image?repo=krahets/hello-algo&amp;max=300&amp;columns=12" style="width: 100%; max-width: 38.5em;"/>
+            </a>
+          </div>
+        </div>
+      </section>
+      <main class="md-main" data-md-component="main" style="height: 0;">
+        <div class="md-main__inner md-grid">
+          <div class="md-sidebar md-sidebar--primary" data-md-component="sidebar" data-md-type="navigation" hidden="">
+            <div class="md-sidebar__scrollwrap">
+              <div class="md-sidebar__inner">
+                <nav aria-label="ナビゲーション" class="md-nav md-nav--primary" data-md-level="0">
+                  <label class="md-nav__title" for="__drawer">
+                    <a aria-label="Hello アルゴリズム" class="md-nav__button md-logo" data-md-component="logo" href="." title="Hello アルゴリズム">
+                      <img alt="logo" src="assets/images/logo.svg"/>
+                    </a>
+                    Hello アルゴリズム
+                  </label>
+                  <div class="md-nav__source">
+                    <a class="md-source" data-md-component="source" href="https://github.com/krahets/hello-algo" title="リポジトリへ">
+                      <div class="md-source__icon md-icon">
+                        <svg viewbox="0 0 496 512" xmlns="http://www.w3.org/2000/svg">
+                          <!--! Font Awesome Free 6.5.1 by @fontawesome - https://fontawesome.com License - https://fontawesome.com/license/free (Icons: CC BY 4.0, Fonts: SIL OFL 1.1, Code: MIT License) Copyright 2023 Fonticons, Inc.-->
+                          <path d="M165.9 397.4c0 2-2.3 3.6-5.2 3.6-3.3.3-5.6-1.3-5.6-3.6 0-2 2.3-3.6 5.2-3.6 3-.3 5.6 1.3 5.6 3.6zm-31.1-4.5c-.7 2 1.3 4.3 4.3 4.9 2.6 1 5.6 0 6.2-2s-1.3-4.3-4.3-5.2c-2.6-.7-5.5.3-6.2 2.3zm44.2-1.7c-2.9.7-4.9 2.6-4.6 4.9.3 2 2.9 3.3 5.9 2.6 2.9-.7 4.9-2.6 4.6-4.6-.3-1.9-3-3.2-5.9-2.9zM244.8 8C106.1 8 0 113.3 0 252c0 110.9 69.8 205.8 169.5 239.2 12.8 2.3 17.3-5.6 17.3-12.1 0-6.2-.3-40.4-.3-61.4 0 0-70 15-84.7-29.8 0 0-11.4-29.1-27.8-36.6 0 0-22.9-15.7 1.6-15.4 0 0 24.9 2 38.6 25.8 21.9 38.6 58.6 27.5 72.9 20.9 2.3-16 8.8-27.1 16-33.7-55.9-6.2-112.3-14.3-112.3-110.5 0-27.5 7.6-41.3 23.6-58.9-2.6-6.5-11.1-33.3 2.6-67.9 20.9-6.5 69 27 69 27 20-5.6 41.5-8.5 62.8-8.5s42.8 2.9 62.8 8.5c0 0 48.1-33.6 69-27 13.7 34.7 5.2 61.4 2.6 67.9 16 17.7 25.8 31.5 25.8 58.9 0 96.5-58.9 104.2-114.8 110.5 9.2 7.9 17 22.9 17 46.4 0 33.7-.3 75.4-.3 83.6 0 6.5 4.6 14.4 17.3 12.1C428.2 457.8 496 362.9 496 252 496 113.3 383.5 8 244.8 8zM97.2 352.9c-1.3 1-1 3.3.7 5.2 1.6 1.6 3.9 2.3 5.2 1 1.3-1 1-3.3-.7-5.2-1.6-1.6-3.9-2.3-5.2-1zm-10.8-8.1c-.7 1.3.3 2.9 2.3 3.9 1.6 1 3.6.7 4.3-.7.7-1.3-.3-2.9-2.3-3.9-2-.6-3.6-.3-4.3.7zm32.4 35.6c-1.6 1.3-1 4.3 1.3 6.2 2.3 2.3 5.2 2.6 6.5 1 1.3-1.3.7-4.3-1.3-6.2-2.2-2.3-5.2-2.6-6.5-1zm-11.4-14.7c-1.6 1-1.6 3.6 0 5.9 1.6 2.3 4.3 3.3 5.6 2.3 1.6-1.3 1.6-3.9 0-6.2-1.4-2.3-4-3.3-5.6-2z">
+                          </path>
+                        </svg>
+                      </div>
+                      <div class="md-source__repository">
+                        krahets/hello-algo
+                      </div>
+                    </a>
+                  </div>
+                  <ul class="md-nav__list" data-md-scrollfix="">
+                    <li class="md-nav__item md-nav__item--nested">
+                      <input class="md-nav__toggle md-toggle" id="__nav_1" type="checkbox"/>
+                      <div class="md-nav__link md-nav__container">
+                        <a class="md-nav__link" href="chapter_hello_algo/">
+                          <svg viewbox="0 0 24 24" xmlns="http://www.w3.org/2000/svg">
+                            <path d="m13.13 22.19-1.63-3.83c1.57-.58 3.04-1.36 4.4-2.27l-2.77 6.1M5.64 12.5l-3.83-1.63 6.1-2.77C7 9.46 6.22 10.93 5.64 12.5M19.22 4c.28 0 .53 0 .74.05.17 1.39-.02 4.25-3.3 7.53-1.7 1.71-3.73 3.02-6.01 3.89l-2.15-2.1c.92-2.31 2.23-4.34 3.92-6.03C15.18 4.58 17.64 4 19.22 4m0-2c-1.98 0-4.98.69-8.22 3.93-2.19 2.19-3.5 4.6-4.35 6.71-.28.75-.09 1.57.46 2.13l2.13 2.12c.38.38.89.61 1.42.61.23 0 .47-.06.7-.15A19.1 19.1 0 0 0 18.07 13c5.66-5.66 3.54-10.61 3.54-10.61S20.7 2 19.22 2m-4.68 7.46c-.78-.78-.78-2.05 0-2.83s2.05-.78 2.83 0c.77.78.78 2.05 0 2.83-.78.78-2.05.78-2.83 0m-5.66 7.07-1.41-1.41 1.41 1.41M6.24 22l3.64-3.64c-.34-.09-.67-.24-.97-.45L4.83 22h1.41M2 22h1.41l4.77-4.76-1.42-1.41L2 20.59V22m0-2.83 4.09-4.08c-.21-.3-.36-.62-.45-.97L2 17.76v1.41Z">
+                            </path>
+                          </svg>
+                          <span class="md-ellipsis">
+                            はじめに
+                          </span>
+                        </a>
+                      </div>
+                      <nav aria-expanded="false" aria-labelledby="__nav_1_label" class="md-nav" data-md-level="1">
+                        <label class="md-nav__title" for="__nav_1">
+                          <span class="md-nav__icon md-icon">
+                          </span>
+                          はじめに
+                        </label>
+                        <ul class="md-nav__list" data-md-scrollfix="">
+                        </ul>
+                      </nav>
+                    </li>
+                    <li class="md-nav__item md-nav__item--nested">
+                      <input class="md-nav__toggle md-toggle" id="__nav_2" type="checkbox"/>
+                      <div class="md-nav__link md-nav__container">
+                        <a class="md-nav__link" href="chapter_preface/">
+                          <svg viewbox="0 0 24 24" xmlns="http://www.w3.org/2000/svg">
+                            <path d="M21 4H3a2 2 0 0 0-2 2v13a2 2 0 0 0 2 2h18a2 2 0 0 0 2-2V6a2 2 0 0 0-2-2M3 19V6h8v13H3m18 0h-8V6h8v13m-7-9.5h6V11h-6V9.5m0 2.5h6v1.5h-6V12m0 2.5h6V16h-6v-1.5Z">
+                            </path>
+                          </svg>
+                          <span class="md-ellipsis">
+                            第 0 章   前書き
+                          </span>
+                        </a>
+                        <label class="md-nav__link" for="__nav_2" id="__nav_2_label" tabindex="0">
+                          <span class="md-nav__icon md-icon">
+                          </span>
+                        </label>
+                      </div>
+                      <nav aria-expanded="false" aria-labelledby="__nav_2_label" class="md-nav" data-md-level="1">
+                        <label class="md-nav__title" for="__nav_2">
+                          <span class="md-nav__icon md-icon">
+                          </span>
+                          第 0 章   前書き
+                        </label>
+                        <ul class="md-nav__list" data-md-scrollfix="">
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_preface/about_the_book/">
+                              <span class="md-ellipsis">
+                                0.1   この本について
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_preface/suggestions/">
+                              <span class="md-ellipsis">
+                                0.2   本書の使い方
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_preface/summary/">
+                              <span class="md-ellipsis">
+                                0.3   まとめ
+                              </span>
+                            </a>
+                          </li>
+                        </ul>
+                      </nav>
+                    </li>
+                    <li class="md-nav__item md-nav__item--nested">
+                      <input class="md-nav__toggle md-toggle" id="__nav_3" type="checkbox"/>
+                      <div class="md-nav__link md-nav__container">
+                        <a class="md-nav__link" href="chapter_introduction/">
+                          <svg viewbox="0 0 24 24" xmlns="http://www.w3.org/2000/svg">
+                            <path d="M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2m0 16H5V5h14v14M6.2 7.7h5v1.5h-5V7.7m6.8 8.1h5v1.5h-5v-1.5m0-2.6h5v1.5h-5v-1.5M8 18h1.5v-2h2v-1.5h-2v-2H8v2H6V16h2v2m6.1-7.1 1.4-1.4 1.4 1.4 1.1-1-1.4-1.4L18 7.1 16.9 6l-1.4 1.4L14.1 6 13 7.1l1.4 1.4L13 9.9l1.1 1Z">
+                            </path>
+                          </svg>
+                          <span class="md-ellipsis">
+                            第 1 章   アルゴリズムとの出会い
+                          </span>
+                        </a>
+                        <label class="md-nav__link" for="__nav_3" id="__nav_3_label" tabindex="0">
+                          <span class="md-nav__icon md-icon">
+                          </span>
+                        </label>
+                      </div>
+                      <nav aria-expanded="false" aria-labelledby="__nav_3_label" class="md-nav" data-md-level="1">
+                        <label class="md-nav__title" for="__nav_3">
+                          <span class="md-nav__icon md-icon">
+                          </span>
+                          第 1 章   アルゴリズムとの出会い
+                        </label>
+                        <ul class="md-nav__list" data-md-scrollfix="">
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_introduction/algorithms_are_everywhere/">
+                              <span class="md-ellipsis">
+                                1.1   アルゴリズムはどこにでもある
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_introduction/what_is_dsa/">
+                              <span class="md-ellipsis">
+                                1.2   アルゴリズムとは何か
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_introduction/summary/">
+                              <span class="md-ellipsis">
+                                1.3   まとめ
+                              </span>
+                            </a>
+                          </li>
+                        </ul>
+                      </nav>
+                    </li>
+                    <li class="md-nav__item md-nav__item--nested">
+                      <input class="md-nav__toggle md-toggle" id="__nav_4" type="checkbox"/>
+                      <div class="md-nav__link md-nav__container">
+                        <a class="md-nav__link" href="chapter_computational_complexity/">
+                          <svg viewbox="0 0 24 24" xmlns="http://www.w3.org/2000/svg">
+                            <path d="M6 2h12v6l-4 4 4 4v6H6v-6l4-4-4-4V2m10 14.5-4-4-4 4V20h8v-3.5m-4-5 4-4V4H8v3.5l4 4M10 6h4v.75l-2 2-2-2V6Z">
+                            </path>
+                          </svg>
+                          <span class="md-ellipsis">
+                            第 2 章   計算量解析
+                          </span>
+                        </a>
+                        <label class="md-nav__link" for="__nav_4" id="__nav_4_label" tabindex="0">
+                          <span class="md-nav__icon md-icon">
+                          </span>
+                        </label>
+                      </div>
+                      <nav aria-expanded="false" aria-labelledby="__nav_4_label" class="md-nav" data-md-level="1">
+                        <label class="md-nav__title" for="__nav_4">
+                          <span class="md-nav__icon md-icon">
+                          </span>
+                          第 2 章   計算量解析
+                        </label>
+                        <ul class="md-nav__list" data-md-scrollfix="">
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_computational_complexity/performance_evaluation/">
+                              <span class="md-ellipsis">
+                                2.1   アルゴリズム効率評価
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_computational_complexity/iteration_and_recursion/">
+                              <span class="md-ellipsis">
+                                2.2   反復と再帰
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_computational_complexity/time_complexity/">
+                              <span class="md-ellipsis">
+                                2.3   時間計算量
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_computational_complexity/space_complexity/">
+                              <span class="md-ellipsis">
+                                2.4   空間計算量
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_computational_complexity/summary/">
+                              <span class="md-ellipsis">
+                                2.5   まとめ
+                              </span>
+                            </a>
+                          </li>
+                        </ul>
+                      </nav>
+                    </li>
+                    <li class="md-nav__item md-nav__item--nested">
+                      <input class="md-nav__toggle md-toggle" id="__nav_5" type="checkbox"/>
+                      <div class="md-nav__link md-nav__container">
+                        <a class="md-nav__link" href="chapter_data_structure/">
+                          <svg viewbox="0 0 24 24" xmlns="http://www.w3.org/2000/svg">
+                            <path d="M11 13.5v8H3v-8h8m-2 2H5v4h4v-4M12 2l5.5 9h-11L12 2m0 3.86L10.08 9h3.84L12 5.86M17.5 13c2.5 0 4.5 2 4.5 4.5S20 22 17.5 22 13 20 13 17.5s2-4.5 4.5-4.5m0 2a2.5 2.5 0 0 0-2.5 2.5 2.5 2.5 0 0 0 2.5 2.5 2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-2.5-2.5Z">
+                            </path>
+                          </svg>
+                          <span class="md-ellipsis">
+                            第 3 章   データ構造
+                          </span>
+                        </a>
+                        <label class="md-nav__link" for="__nav_5" id="__nav_5_label" tabindex="0">
+                          <span class="md-nav__icon md-icon">
+                          </span>
+                        </label>
+                      </div>
+                      <nav aria-expanded="false" aria-labelledby="__nav_5_label" class="md-nav" data-md-level="1">
+                        <label class="md-nav__title" for="__nav_5">
+                          <span class="md-nav__icon md-icon">
+                          </span>
+                          第 3 章   データ構造
+                        </label>
+                        <ul class="md-nav__list" data-md-scrollfix="">
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_data_structure/classification_of_data_structure/">
+                              <span class="md-ellipsis">
+                                3.1   データ構造の分類
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_data_structure/basic_data_types/">
+                              <span class="md-ellipsis">
+                                3.2   基本データ型
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_data_structure/number_encoding/">
+                              <span class="md-ellipsis">
+                                3.3   数値エンコーディング *
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_data_structure/character_encoding/">
+                              <span class="md-ellipsis">
+                                3.4   文字エンコーディング *
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_data_structure/summary/">
+                              <span class="md-ellipsis">
+                                3.5   まとめ
+                              </span>
+                            </a>
+                          </li>
+                        </ul>
+                      </nav>
+                    </li>
+                    <li class="md-nav__item md-nav__item--nested">
+                      <input class="md-nav__toggle md-toggle" id="__nav_6" type="checkbox"/>
+                      <div class="md-nav__link md-nav__container">
+                        <a class="md-nav__link" href="chapter_array_and_linkedlist/">
+                          <svg viewbox="0 0 24 24" xmlns="http://www.w3.org/2000/svg">
+                            <path d="M3 5v14h17V5H3m4 2v2H5V7h2m-2 6v-2h2v2H5m0 2h2v2H5v-2m13 2H9v-2h9v2m0-4H9v-2h9v2m0-4H9V7h9v2Z">
+                            </path>
+                          </svg>
+                          <span class="md-ellipsis">
+                            第 4 章   配列と連結リスト
+                          </span>
+                        </a>
+                        <label class="md-nav__link" for="__nav_6" id="__nav_6_label" tabindex="0">
+                          <span class="md-nav__icon md-icon">
+                          </span>
+                        </label>
+                      </div>
+                      <nav aria-expanded="false" aria-labelledby="__nav_6_label" class="md-nav" data-md-level="1">
+                        <label class="md-nav__title" for="__nav_6">
+                          <span class="md-nav__icon md-icon">
+                          </span>
+                          第 4 章   配列と連結リスト
+                        </label>
+                        <ul class="md-nav__list" data-md-scrollfix="">
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_array_and_linkedlist/array/">
+                              <span class="md-ellipsis">
+                                4.1   配列
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_array_and_linkedlist/linked_list/">
+                              <span class="md-ellipsis">
+                                4.2   連結リスト
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_array_and_linkedlist/list/">
+                              <span class="md-ellipsis">
+                                4.3   リスト
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_array_and_linkedlist/ram_and_cache/">
+                              <span class="md-ellipsis">
+                                4.4   メモリとキャッシュ *
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_array_and_linkedlist/summary/">
+                              <span class="md-ellipsis">
+                                4.5   まとめ
+                              </span>
+                            </a>
+                          </li>
+                        </ul>
+                      </nav>
+                    </li>
+                    <li class="md-nav__item md-nav__item--nested">
+                      <input class="md-nav__toggle md-toggle" id="__nav_7" type="checkbox"/>
+                      <div class="md-nav__link md-nav__container">
+                        <a class="md-nav__link" href="chapter_stack_and_queue/">
+                          <svg viewbox="0 0 24 24" xmlns="http://www.w3.org/2000/svg">
+                            <path d="M17.36 20.2v-5.38h1.79V22H3v-7.18h1.8v5.38h12.56M6.77 14.32l.37-1.76 8.79 1.85-.37 1.76-8.79-1.85m1.16-4.21.76-1.61 8.14 3.78-.76 1.62-8.14-3.79m2.26-3.99 1.15-1.38 6.9 5.76-1.15 1.37-6.9-5.75m4.45-4.25L20 9.08l-1.44 1.07-5.36-7.21 1.44-1.07M6.59 18.41v-1.8h8.98v1.8H6.59Z">
+                            </path>
+                          </svg>
+                          <span class="md-ellipsis">
+                            第 5 章   スタックとキュー
+                          </span>
+                        </a>
+                        <label class="md-nav__link" for="__nav_7" id="__nav_7_label" tabindex="0">
+                          <span class="md-nav__icon md-icon">
+                          </span>
+                        </label>
+                      </div>
+                      <nav aria-expanded="false" aria-labelledby="__nav_7_label" class="md-nav" data-md-level="1">
+                        <label class="md-nav__title" for="__nav_7">
+                          <span class="md-nav__icon md-icon">
+                          </span>
+                          第 5 章   スタックとキュー
+                        </label>
+                        <ul class="md-nav__list" data-md-scrollfix="">
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_stack_and_queue/stack/">
+                              <span class="md-ellipsis">
+                                5.1   スタック
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_stack_and_queue/queue/">
+                              <span class="md-ellipsis">
+                                5.2   キュー
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_stack_and_queue/deque/">
+                              <span class="md-ellipsis">
+                                5.3   両端キュー
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_stack_and_queue/summary/">
+                              <span class="md-ellipsis">
+                                5.4   まとめ
+                              </span>
+                            </a>
+                          </li>
+                        </ul>
+                      </nav>
+                    </li>
+                    <li class="md-nav__item md-nav__item--nested">
+                      <input class="md-nav__toggle md-toggle" id="__nav_8" type="checkbox"/>
+                      <div class="md-nav__link md-nav__container">
+                        <a class="md-nav__link" href="chapter_hashing/">
+                          <svg viewbox="0 0 24 24" xmlns="http://www.w3.org/2000/svg">
+                            <path d="M19.3 17.89c1.32-2.1.7-4.89-1.41-6.21a4.52 4.52 0 0 0-6.21 1.41C10.36 15.2 11 18 13.09 19.3c1.47.92 3.33.92 4.8 0L21 22.39 22.39 21l-3.09-3.11m-2-.62c-.98.98-2.56.97-3.54 0-.97-.98-.97-2.56.01-3.54.97-.97 2.55-.97 3.53 0 .96.99.95 2.57-.03 3.54h.03M19 4H5a2 2 0 0 0-2 2v12a2 2 0 0 0 2 2h5.81a6.3 6.3 0 0 1-1.31-2H5v-4h4.18c.16-.71.43-1.39.82-2H5V8h6v2.81a6.3 6.3 0 0 1 2-1.31V8h6v2a6.499 6.499 0 0 1 2 2V6a2 2 0 0 0-2-2Z">
+                            </path>
+                          </svg>
+                          <span class="md-ellipsis">
+                            第 6 章   ハッシュ表
+                          </span>
+                        </a>
+                        <label class="md-nav__link" for="__nav_8" id="__nav_8_label" tabindex="0">
+                          <span class="md-nav__icon md-icon">
+                          </span>
+                        </label>
+                      </div>
+                      <nav aria-expanded="false" aria-labelledby="__nav_8_label" class="md-nav" data-md-level="1">
+                        <label class="md-nav__title" for="__nav_8">
+                          <span class="md-nav__icon md-icon">
+                          </span>
+                          第 6 章   ハッシュ表
+                        </label>
+                        <ul class="md-nav__list" data-md-scrollfix="">
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_hashing/hash_map/">
+                              <span class="md-ellipsis">
+                                6.1   ハッシュ表
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_hashing/hash_collision/">
+                              <span class="md-ellipsis">
+                                6.2   ハッシュ衝突
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_hashing/hash_algorithm/">
+                              <span class="md-ellipsis">
+                                6.3   ハッシュアルゴリズム
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_hashing/summary/">
+                              <span class="md-ellipsis">
+                                6.4   まとめ
+                              </span>
+                            </a>
+                          </li>
+                        </ul>
+                      </nav>
+                    </li>
+                    <li class="md-nav__item md-nav__item--nested">
+                      <input class="md-nav__toggle md-toggle" id="__nav_9" type="checkbox"/>
+                      <div class="md-nav__link md-nav__container">
+                        <a class="md-nav__link" href="chapter_tree/">
+                          <svg viewbox="0 0 24 24" xmlns="http://www.w3.org/2000/svg">
+                            <path d="M19.5 17c-.14 0-.26 0-.39.04L17.5 13.8c.45-.45.75-1.09.75-1.8a2.5 2.5 0 0 0-2.5-2.5c-.14 0-.25 0-.4.04L13.74 6.3c.47-.46.76-1.09.76-1.8a2.5 2.5 0 0 0-5 0c0 .7.29 1.34.76 1.79L8.65 9.54c-.15-.04-.26-.04-.4-.04a2.5 2.5 0 0 0-2.5 2.5c0 .71.29 1.34.75 1.79l-1.61 3.25C4.76 17 4.64 17 4.5 17a2.5 2.5 0 0 0 0 5A2.5 2.5 0 0 0 7 19.5c0-.7-.29-1.34-.76-1.79l1.62-3.25c.14.04.26.04.39.04s.25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0A2.5 2.5 0 0 0 12 17c-.13 0-.26 0-.39.04L10 13.8c.45-.45.75-1.09.75-1.8 0-.7-.29-1.33-.75-1.79l1.61-3.25c.13.04.26.04.39.04s.26 0 .39-.04L14 10.21a2.5 2.5 0 0 0 1.75 4.29c.13 0 .25 0 .38-.04l1.63 3.25c-.47.45-.76 1.09-.76 1.79a2.5 2.5 0 0 0 5 0 2.5 2.5 0 0 0-2.5-2.5m-15 3.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1m8.5-1c0 .55-.45 1-1 1s-1-.45-1-1 .45-1 1-1 1 .45 1 1M7.25 12c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1M11 4.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m3.75 7.5c0-.55.45-1 1-1s1 .45 1 1-.45 1-1 1-1-.45-1-1m4.75 8.5c-.55 0-1-.45-1-1s.45-1 1-1 1 .45 1 1-.45 1-1 1Z">
+                            </path>
+                          </svg>
+                          <span class="md-ellipsis">
+                            第 7 章   木
+                          </span>
+                        </a>
+                        <label class="md-nav__link" for="__nav_9" id="__nav_9_label" tabindex="0">
+                          <span class="md-nav__icon md-icon">
+                          </span>
+                        </label>
+                      </div>
+                      <nav aria-expanded="false" aria-labelledby="__nav_9_label" class="md-nav" data-md-level="1">
+                        <label class="md-nav__title" for="__nav_9">
+                          <span class="md-nav__icon md-icon">
+                          </span>
+                          第 7 章   木
+                        </label>
+                        <ul class="md-nav__list" data-md-scrollfix="">
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_tree/binary_tree/">
+                              <span class="md-ellipsis">
+                                7.1   二分木
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_tree/binary_tree_traversal/">
+                              <span class="md-ellipsis">
+                                7.2   二分木の走査
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_tree/array_representation_of_tree/">
+                              <span class="md-ellipsis">
+                                7.3   木の配列表現
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_tree/binary_search_tree/">
+                              <span class="md-ellipsis">
+                                7.4   二分探索木
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_tree/avl_tree/">
+                              <span class="md-ellipsis">
+                                7.5   AVL木 *
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_tree/summary/">
+                              <span class="md-ellipsis">
+                                7.6   まとめ
+                              </span>
+                            </a>
+                          </li>
+                        </ul>
+                      </nav>
+                    </li>
+                    <li class="md-nav__item md-nav__item--nested">
+                      <input class="md-nav__toggle md-toggle" id="__nav_10" type="checkbox"/>
+                      <div class="md-nav__link md-nav__container">
+                        <a class="md-nav__link" href="chapter_heap/">
+                          <svg viewbox="0 0 24 24" xmlns="http://www.w3.org/2000/svg">
+                            <path d="M12 1a2.5 2.5 0 0 0-2.5 2.5A2.5 2.5 0 0 0 11 5.79V7H7a2 2 0 0 0-2 2v.71A2.5 2.5 0 0 0 3.5 12 2.5 2.5 0 0 0 5 14.29V15H4a2 2 0 0 0-2 2v1.21A2.5 2.5 0 0 0 .5 20.5 2.5 2.5 0 0 0 3 23a2.5 2.5 0 0 0 2.5-2.5A2.5 2.5 0 0 0 4 18.21V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 9 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2H7v-.71A2.5 2.5 0 0 0 8.5 12 2.5 2.5 0 0 0 7 9.71V9h10v.71A2.5 2.5 0 0 0 15.5 12a2.5 2.5 0 0 0 1.5 2.29V15h-1a2 2 0 0 0-2 2v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 15 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17h4v1.21a2.5 2.5 0 0 0-1.5 2.29A2.5 2.5 0 0 0 21 23a2.5 2.5 0 0 0 2.5-2.5 2.5 2.5 0 0 0-1.5-2.29V17a2 2 0 0 0-2-2h-1v-.71A2.5 2.5 0 0 0 20.5 12 2.5 2.5 0 0 0 19 9.71V9a2 2 0 0 0-2-2h-4V5.79a2.5 2.5 0 0 0 1.5-2.29A2.5 2.5 0 0 0 12 1m0 1.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M6 11a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m12 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1M3 19.5a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1m6 0a1 1 0 0 1 1 1 1 1 0 0 1-1 1 1 1 0 0 1-1-1 1 1 0 0 1 1-1Z">
+                            </path>
+                          </svg>
+                          <span class="md-ellipsis">
+                            第 8 章   ヒープ
+                          </span>
+                        </a>
+                        <label class="md-nav__link" for="__nav_10" id="__nav_10_label" tabindex="0">
+                          <span class="md-nav__icon md-icon">
+                          </span>
+                        </label>
+                      </div>
+                      <nav aria-expanded="false" aria-labelledby="__nav_10_label" class="md-nav" data-md-level="1">
+                        <label class="md-nav__title" for="__nav_10">
+                          <span class="md-nav__icon md-icon">
+                          </span>
+                          第 8 章   ヒープ
+                        </label>
+                        <ul class="md-nav__list" data-md-scrollfix="">
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_heap/heap/">
+                              <span class="md-ellipsis">
+                                8.1   ヒープ
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_heap/build_heap/">
+                              <span class="md-ellipsis">
+                                8.2   ヒープの構築
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_heap/top_k/">
+                              <span class="md-ellipsis">
+                                8.3   Top-k問題
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_heap/summary/">
+                              <span class="md-ellipsis">
+                                8.4   まとめ
+                              </span>
+                            </a>
+                          </li>
+                        </ul>
+                      </nav>
+                    </li>
+                    <li class="md-nav__item md-nav__item--nested">
+                      <input class="md-nav__toggle md-toggle" id="__nav_11" type="checkbox"/>
+                      <div class="md-nav__link md-nav__container">
+                        <a class="md-nav__link" href="chapter_graph/">
+                          <svg viewbox="0 0 24 24" xmlns="http://www.w3.org/2000/svg">
+                            <path d="m12 5.37-.44-.06L6 14.9c.24.21.4.48.47.78h11.06c.07-.3.23-.57.47-.78l-5.56-9.59-.44.06M6.6 16.53l4.28 2.53c.29-.27.69-.43 1.12-.43.43 0 .83.16 1.12.43l4.28-2.53H6.6M12 22a1.68 1.68 0 0 1-1.68-1.68l.09-.56-4.3-2.55c-.31.36-.76.58-1.27.58a1.68 1.68 0 0 1-1.68-1.68c0-.79.53-1.45 1.26-1.64V9.36c-.83-.11-1.47-.82-1.47-1.68A1.68 1.68 0 0 1 4.63 6c.55 0 1.03.26 1.34.66l4.41-2.53-.06-.45c0-.93.75-1.68 1.68-1.68.93 0 1.68.75 1.68 1.68l-.06.45 4.41 2.53c.31-.4.79-.66 1.34-.66a1.68 1.68 0 0 1 1.68 1.68c0 .86-.64 1.57-1.47 1.68v5.11c.73.19 1.26.85 1.26 1.64a1.68 1.68 0 0 1-1.68 1.68c-.51 0-.96-.22-1.27-.58l-4.3 2.55.09.56A1.68 1.68 0 0 1 12 22M10.8 4.86 6.3 7.44l.02.24c0 .71-.44 1.32-1.06 1.57l.03 5.25 5.51-9.64m2.4 0 5.51 9.64.03-5.25c-.62-.25-1.06-.86-1.06-1.57l.02-.24-4.5-2.58Z">
+                            </path>
+                          </svg>
+                          <span class="md-ellipsis">
+                            第 9 章   グラフ
+                          </span>
+                        </a>
+                        <label class="md-nav__link" for="__nav_11" id="__nav_11_label" tabindex="0">
+                          <span class="md-nav__icon md-icon">
+                          </span>
+                        </label>
+                      </div>
+                      <nav aria-expanded="false" aria-labelledby="__nav_11_label" class="md-nav" data-md-level="1">
+                        <label class="md-nav__title" for="__nav_11">
+                          <span class="md-nav__icon md-icon">
+                          </span>
+                          第 9 章   グラフ
+                        </label>
+                        <ul class="md-nav__list" data-md-scrollfix="">
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_graph/graph/">
+                              <span class="md-ellipsis">
+                                9.1   グラフ
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_graph/graph_operations/">
+                              <span class="md-ellipsis">
+                                9.2   グラフの基本操作
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_graph/graph_traversal/">
+                              <span class="md-ellipsis">
+                                9.3   グラフの走査
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_graph/summary/">
+                              <span class="md-ellipsis">
+                                9.4   まとめ
+                              </span>
+                            </a>
+                          </li>
+                        </ul>
+                      </nav>
+                    </li>
+                    <li class="md-nav__item md-nav__item--nested">
+                      <input class="md-nav__toggle md-toggle" id="__nav_12" type="checkbox"/>
+                      <div class="md-nav__link md-nav__container">
+                        <a class="md-nav__link" href="chapter_searching/">
+                          <svg viewbox="0 0 24 24" xmlns="http://www.w3.org/2000/svg">
+                            <path d="m19.31 18.9 3.08 3.1L21 23.39l-3.12-3.07c-.69.43-1.51.68-2.38.68-2.5 0-4.5-2-4.5-4.5s2-4.5 4.5-4.5 4.5 2 4.5 4.5c0 .88-.25 1.71-.69 2.4m-3.81.1a2.5 2.5 0 0 0 0-5 2.5 2.5 0 0 0 0 5M21 4v2H3V4h18M3 16v-2h6v2H3m0-5V9h18v2h-2.03c-1.01-.63-2.2-1-3.47-1s-2.46.37-3.47 1H3Z">
+                            </path>
+                          </svg>
+                          <span class="md-ellipsis">
+                            第 10 章   探索
+                          </span>
+                        </a>
+                        <label class="md-nav__link" for="__nav_12" id="__nav_12_label" tabindex="0">
+                          <span class="md-nav__icon md-icon">
+                          </span>
+                        </label>
+                      </div>
+                      <nav aria-expanded="false" aria-labelledby="__nav_12_label" class="md-nav" data-md-level="1">
+                        <label class="md-nav__title" for="__nav_12">
+                          <span class="md-nav__icon md-icon">
+                          </span>
+                          第 10 章   探索
+                        </label>
+                        <ul class="md-nav__list" data-md-scrollfix="">
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_searching/binary_search/">
+                              <span class="md-ellipsis">
+                                10.1   二分探索
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_searching/binary_search_insertion/">
+                              <span class="md-ellipsis">
+                                10.2   二分探索挿入点
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_searching/binary_search_edge/">
+                              <span class="md-ellipsis">
+                                10.3   二分探索の境界
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_searching/replace_linear_by_hashing/">
+                              <span class="md-ellipsis">
+                                10.4   ハッシュ最適化戦略
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_searching/searching_algorithm_revisited/">
+                              <span class="md-ellipsis">
+                                10.5   探索アルゴリズム再考
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_searching/summary/">
+                              <span class="md-ellipsis">
+                                10.6   まとめ
+                              </span>
+                            </a>
+                          </li>
+                        </ul>
+                      </nav>
+                    </li>
+                    <li class="md-nav__item md-nav__item--nested">
+                      <input class="md-nav__toggle md-toggle" id="__nav_13" type="checkbox"/>
+                      <div class="md-nav__link md-nav__container">
+                        <a class="md-nav__link" href="chapter_sorting/">
+                          <svg viewbox="0 0 24 24" xmlns="http://www.w3.org/2000/svg">
+                            <path d="M19 17h3l-4 4-4-4h3V3h2M2 17h10v2H2M6 5v2H2V5m0 6h7v2H2v-2Z">
+                            </path>
+                          </svg>
+                          <span class="md-ellipsis">
+                            第 11 章   ソート
+                          </span>
+                        </a>
+                        <label class="md-nav__link" for="__nav_13" id="__nav_13_label" tabindex="0">
+                          <span class="md-nav__icon md-icon">
+                          </span>
+                        </label>
+                      </div>
+                      <nav aria-expanded="false" aria-labelledby="__nav_13_label" class="md-nav" data-md-level="1">
+                        <label class="md-nav__title" for="__nav_13">
+                          <span class="md-nav__icon md-icon">
+                          </span>
+                          第 11 章   ソート
+                        </label>
+                        <ul class="md-nav__list" data-md-scrollfix="">
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_sorting/sorting_algorithm/">
+                              <span class="md-ellipsis">
+                                11.1   ソートアルゴリズム
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_sorting/selection_sort/">
+                              <span class="md-ellipsis">
+                                11.2   選択ソート
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_sorting/bubble_sort/">
+                              <span class="md-ellipsis">
+                                11.3   バブルソート
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_sorting/insertion_sort/">
+                              <span class="md-ellipsis">
+                                11.4   挿入ソート
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_sorting/quick_sort/">
+                              <span class="md-ellipsis">
+                                11.5   クイックソート
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_sorting/merge_sort/">
+                              <span class="md-ellipsis">
+                                11.6   マージソート
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_sorting/heap_sort/">
+                              <span class="md-ellipsis">
+                                11.7   ヒープソート
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_sorting/bucket_sort/">
+                              <span class="md-ellipsis">
+                                11.8   バケットソート
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_sorting/counting_sort/">
+                              <span class="md-ellipsis">
+                                11.9   計数ソート
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_sorting/radix_sort/">
+                              <span class="md-ellipsis">
+                                11.10   基数ソート
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_sorting/summary/">
+                              <span class="md-ellipsis">
+                                11.11   まとめ
+                              </span>
+                            </a>
+                          </li>
+                        </ul>
+                      </nav>
+                    </li>
+                    <li class="md-nav__item md-nav__item--nested">
+                      <input class="md-nav__toggle md-toggle" id="__nav_14" type="checkbox"/>
+                      <div class="md-nav__link md-nav__container">
+                        <a class="md-nav__link" href="chapter_divide_and_conquer/">
+                          <svg viewbox="0 0 24 24" xmlns="http://www.w3.org/2000/svg">
+                            <path d="M17 7v2h5V7h-5M2 9v6h5V9H2m10 0v2H9v2h3v2l3-3-3-3m5 2v2h5v-2h-5m0 4v2h5v-2h-5Z">
+                            </path>
+                          </svg>
+                          <span class="md-ellipsis">
+                            第 12 章   分割統治
+                          </span>
+                        </a>
+                        <label class="md-nav__link" for="__nav_14" id="__nav_14_label" tabindex="0">
+                          <span class="md-nav__icon md-icon">
+                          </span>
+                        </label>
+                      </div>
+                      <nav aria-expanded="false" aria-labelledby="__nav_14_label" class="md-nav" data-md-level="1">
+                        <label class="md-nav__title" for="__nav_14">
+                          <span class="md-nav__icon md-icon">
+                          </span>
+                          第 12 章   分割統治
+                        </label>
+                        <ul class="md-nav__list" data-md-scrollfix="">
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_divide_and_conquer/divide_and_conquer/">
+                              <span class="md-ellipsis">
+                                12.1   分割統治アルゴリズム
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_divide_and_conquer/binary_search_recur/">
+                              <span class="md-ellipsis">
+                                12.2   分割統治探索戦略
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_divide_and_conquer/build_binary_tree_problem/">
+                              <span class="md-ellipsis">
+                                12.3   二分木構築問題
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_divide_and_conquer/hanota_problem/">
+                              <span class="md-ellipsis">
+                                12.4   ハノイの塔問題
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_divide_and_conquer/summary/">
+                              <span class="md-ellipsis">
+                                12.5   まとめ
+                              </span>
+                            </a>
+                          </li>
+                        </ul>
+                      </nav>
+                    </li>
+                    <li class="md-nav__item md-nav__item--nested">
+                      <input class="md-nav__toggle md-toggle" id="__nav_15" type="checkbox"/>
+                      <div class="md-nav__link md-nav__container">
+                        <a class="md-nav__link" href="chapter_backtracking/">
+                          <svg viewbox="0 0 24 24" xmlns="http://www.w3.org/2000/svg">
+                            <path d="M18 15a3 3 0 0 1 3 3 3 3 0 0 1-3 3 2.99 2.99 0 0 1-2.83-2H14v-2h1.17c.41-1.17 1.52-2 2.83-2m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m0-9a1.43 1.43 0 0 0 1.43-1.43 1.43 1.43 0 1 0-2.86 0A1.43 1.43 0 0 0 18 8m0-5.43a4 4 0 0 1 4 4C22 9.56 18 14 18 14s-4-4.44-4-7.43a4 4 0 0 1 4-4M8.83 17H10v2H8.83A2.99 2.99 0 0 1 6 21a3 3 0 0 1-3-3c0-1.31.83-2.42 2-2.83V14h2v1.17c.85.3 1.53.98 1.83 1.83M6 17a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1M6 3a3 3 0 0 1 3 3c0 1.31-.83 2.42-2 2.83V10H5V8.83A2.99 2.99 0 0 1 3 6a3 3 0 0 1 3-3m0 2a1 1 0 0 0-1 1 1 1 0 0 0 1 1 1 1 0 0 0 1-1 1 1 0 0 0-1-1m5 14v-2h2v2h-2m-4-6H5v-2h2v2Z">
+                            </path>
+                          </svg>
+                          <span class="md-ellipsis">
+                            第 13 章   バックトラッキング
+                          </span>
+                        </a>
+                        <label class="md-nav__link" for="__nav_15" id="__nav_15_label" tabindex="0">
+                          <span class="md-nav__icon md-icon">
+                          </span>
+                        </label>
+                      </div>
+                      <nav aria-expanded="false" aria-labelledby="__nav_15_label" class="md-nav" data-md-level="1">
+                        <label class="md-nav__title" for="__nav_15">
+                          <span class="md-nav__icon md-icon">
+                          </span>
+                          第 13 章   バックトラッキング
+                        </label>
+                        <ul class="md-nav__list" data-md-scrollfix="">
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_backtracking/backtracking_algorithm/">
+                              <span class="md-ellipsis">
+                                13.1   バックトラッキングアルゴリズム
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_backtracking/permutations_problem/">
+                              <span class="md-ellipsis">
+                                13.2   順列問題
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_backtracking/subset_sum_problem/">
+                              <span class="md-ellipsis">
+                                13.3   部分集合和問題
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_backtracking/n_queens_problem/">
+                              <span class="md-ellipsis">
+                                13.4   Nクイーン問題
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_backtracking/summary/">
+                              <span class="md-ellipsis">
+                                13.5   まとめ
+                              </span>
+                            </a>
+                          </li>
+                        </ul>
+                      </nav>
+                    </li>
+                    <li class="md-nav__item md-nav__item--nested">
+                      <input class="md-nav__toggle md-toggle" id="__nav_16" type="checkbox"/>
+                      <div class="md-nav__link md-nav__container">
+                        <a class="md-nav__link" href="chapter_dynamic_programming/">
+                          <svg viewbox="0 0 24 24" xmlns="http://www.w3.org/2000/svg">
+                            <path d="M22 15h-2v3c0 1.11-.89 2-2 2h-3v2l-3-3 3-3v2h3v-3h-2l3-3 3 3m0-11v4c0 1.1-.9 2-2 2H10v10c0 1.1-.9 2-2 2H4c-1.1 0-2-.9-2-2V4c0-1.1.9-2 2-2h16c1.1 0 2 .9 2 2M4 8h4V4H4v4m0 2v4h4v-4H4m4 10v-4H4v4h4m6-12V4h-4v4h4m6-4h-4v4h4V4Z">
+                            </path>
+                          </svg>
+                          <span class="md-ellipsis">
+                            第 14 章   動的プログラミング
+                          </span>
+                        </a>
+                        <label class="md-nav__link" for="__nav_16" id="__nav_16_label" tabindex="0">
+                          <span class="md-nav__icon md-icon">
+                          </span>
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+                      </div>
+                      <nav aria-expanded="false" aria-labelledby="__nav_16_label" class="md-nav" data-md-level="1">
+                        <label class="md-nav__title" for="__nav_16">
+                          <span class="md-nav__icon md-icon">
+                          </span>
+                          第 14 章   動的プログラミング
+                        </label>
+                        <ul class="md-nav__list" data-md-scrollfix="">
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_dynamic_programming/intro_to_dynamic_programming/">
+                              <span class="md-ellipsis">
+                                14.1   動的プログラミング入門
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_dynamic_programming/dp_problem_features/">
+                              <span class="md-ellipsis">
+                                14.2   DP問題の特性
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_dynamic_programming/dp_solution_pipeline/">
+                              <span class="md-ellipsis">
+                                14.3   DP問題解決アプローチ
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_dynamic_programming/knapsack_problem/">
+                              <span class="md-ellipsis">
+                                14.4   0-1ナップサック問題
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_dynamic_programming/unbounded_knapsack_problem/">
+                              <span class="md-ellipsis">
+                                14.5   無制限ナップサック問題
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_dynamic_programming/edit_distance_problem/">
+                              <span class="md-ellipsis">
+                                14.6   編集距離問題
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_dynamic_programming/summary/">
+                              <span class="md-ellipsis">
+                                14.7   まとめ
+                              </span>
+                            </a>
+                          </li>
+                        </ul>
+                      </nav>
+                    </li>
+                    <li class="md-nav__item md-nav__item--nested">
+                      <input class="md-nav__toggle md-toggle" id="__nav_17" type="checkbox"/>
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+                            <path d="M13 3c3.88 0 7 3.14 7 7 0 2.8-1.63 5.19-4 6.31V21H9v-3H8c-1.11 0-2-.89-2-2v-3H4.5c-.42 0-.66-.5-.42-.81L6 9.66A7.003 7.003 0 0 1 13 3m0-2C8.41 1 4.61 4.42 4.06 8.9L2.5 11h-.03l-.02.03c-.55.76-.62 1.76-.19 2.59.36.69 1 1.17 1.74 1.32V16c0 1.85 1.28 3.42 3 3.87V23h11v-5.5c2.5-1.67 4-4.44 4-7.5 0-4.97-4.04-9-9-9m4 7.83c0 1.54-1.36 2.77-3.42 4.64L13 14l-.58-.53C10.36 11.6 9 10.37 9 8.83c0-1.2.96-2.19 2.16-2.2h.04c.69 0 1.35.31 1.8.83.45-.52 1.11-.83 1.8-.83 1.2-.01 2.2.96 2.2 2.16v.04Z">
+                            </path>
+                          </svg>
+                          <span class="md-ellipsis">
+                            第 15 章   貪欲法
+                          </span>
+                        </a>
+                        <label class="md-nav__link" for="__nav_17" id="__nav_17_label" tabindex="0">
+                          <span class="md-nav__icon md-icon">
+                          </span>
+                        </label>
+                      </div>
+                      <nav aria-expanded="false" aria-labelledby="__nav_17_label" class="md-nav" data-md-level="1">
+                        <label class="md-nav__title" for="__nav_17">
+                          <span class="md-nav__icon md-icon">
+                          </span>
+                          第 15 章   貪欲法
+                        </label>
+                        <ul class="md-nav__list" data-md-scrollfix="">
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_greedy/greedy_algorithm/">
+                              <span class="md-ellipsis">
+                                15.1   貪欲アルゴリズム
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_greedy/fractional_knapsack_problem/">
+                              <span class="md-ellipsis">
+                                15.2   分数ナップサック問題
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_greedy/max_capacity_problem/">
+                              <span class="md-ellipsis">
+                                15.3   最大容量問題
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_greedy/max_product_cutting_problem/">
+                              <span class="md-ellipsis">
+                                15.4   最大積切断問題
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_greedy/summary/">
+                              <span class="md-ellipsis">
+                                15.5   まとめ
+                              </span>
+                            </a>
+                          </li>
+                        </ul>
+                      </nav>
+                    </li>
+                    <li class="md-nav__item md-nav__item--nested">
+                      <input class="md-nav__toggle md-toggle" id="__nav_18" type="checkbox"/>
+                      <div class="md-nav__link md-nav__container">
+                        <a class="md-nav__link" href="chapter_appendix/">
+                          <svg viewbox="0 0 24 24" xmlns="http://www.w3.org/2000/svg">
+                            <path d="M11 18h2v-2h-2v2m1-16A10 10 0 0 0 2 12a10 10 0 0 0 10 10 10 10 0 0 0 10-10A10 10 0 0 0 12 2m0 18c-4.41 0-8-3.59-8-8s3.59-8 8-8 8 3.59 8 8-3.59 8-8 8m0-14a4 4 0 0 0-4 4h2a2 2 0 0 1 2-2 2 2 0 0 1 2 2c0 2-3 1.75-3 5h2c0-2.25 3-2.5 3-5a4 4 0 0 0-4-4Z">
+                            </path>
+                          </svg>
+                          <span class="md-ellipsis">
+                            第 16 章   付録
+                          </span>
+                        </a>
+                        <label class="md-nav__link" for="__nav_18" id="__nav_18_label" tabindex="0">
+                          <span class="md-nav__icon md-icon">
+                          </span>
+                        </label>
+                      </div>
+                      <nav aria-expanded="false" aria-labelledby="__nav_18_label" class="md-nav" data-md-level="1">
+                        <label class="md-nav__title" for="__nav_18">
+                          <span class="md-nav__icon md-icon">
+                          </span>
+                          第 16 章   付録
+                        </label>
+                        <ul class="md-nav__list" data-md-scrollfix="">
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_appendix/installation/">
+                              <span class="md-ellipsis">
+                                16.1   プログラミング環境のインストール
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_appendix/contribution/">
+                              <span class="md-ellipsis">
+                                16.2   一緒に創作に参加
+                              </span>
+                            </a>
+                          </li>
+                          <li class="md-nav__item">
+                            <a class="md-nav__link" href="chapter_appendix/terminology/">
+                              <span class="md-ellipsis">
+                                16.3   用語集
+                              </span>
+                            </a>
+                          </li>
+                        </ul>
+                      </nav>
+                    </li>
+                    <li class="md-nav__item md-nav__item--nested">
+                      <input class="md-nav__toggle md-toggle" id="__nav_19" type="checkbox"/>
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+                            <path d="M9 3v15h3V3H9m3 2 4 13 3-1-4-13-3 1M5 5v13h3V5H5M3 19v2h18v-2H3Z">
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+                          </svg>
+                          <span class="md-ellipsis">
+                            参考文献
+                          </span>
+                        </a>
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+                        <label class="md-nav__title" for="__nav_19">
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+                          </span>
+                          参考文献
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+      <div class="md-dialog__inner md-typeset">
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+    </div>
+    <script id="__config" type="application/json">
+      {"base": ".", "features": ["content.action.edit", "content.code.annotate", "content.code.copy", "content.tabs.link", "content.tooltips", "navigation.indexes", "navigation.top", "navigation.footer", "navigation.tracking", "search.highlight", "search.share", "search.suggest", "toc.follow"], "search": "assets/javascripts/workers/search.b8dbb3d2.min.js", "translations": {"clipboard.copied": "\u30b3\u30d4\u30fc\u3057\u307e\u3057\u305f", "clipboard.copy": "\u30af\u30ea\u30c3\u30d7\u30dc\u30fc\u30c9\u3078\u30b3\u30d4\u30fc", "search.result.more.one": "\u3053\u306e\u30da\u30fc\u30b8\u5185\u306b\u3082\u30461\u4ef6\u898b\u3064\u304b\u308a\u307e\u3057\u305f", "search.result.more.other": "\u3053\u306e\u30da\u30fc\u30b8\u5185\u306b\u3042\u3068#\u4ef6\u898b\u3064\u304b\u308a\u307e\u3057\u305f", "search.result.none": "\u4f55\u3082\u898b\u3064\u304b\u308a\u307e\u305b\u3093\u3067\u3057\u305f", "search.result.one": "1\u4ef6\u898b\u3064\u304b\u308a\u307e\u3057\u305f", "search.result.other": "#\u4ef6\u898b\u3064\u304b\u308a\u307e\u3057\u305f", "search.result.placeholder": "\u691c\u7d22\u30ad\u30fc\u30ef\u30fc\u30c9\u3092\u5165\u529b\u3057\u3066\u304f\u3060\u3055\u3044", "search.result.term.missing": "\u691c\u7d22\u306b\u542b\u307e\u308c\u306a\u3044", "select.version": "\u30d0\u30fc\u30b8\u30e7\u30f3\u5207\u308a\u66ff\u3048"}}
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+    <script src="javascripts/mathjax.js">
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+    <script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/3.2.2/es5/tex-mml-chtml.min.js">
+    </script>
+  </body>
+</html>
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diff --git a/ja/javascripts/katex.js b/ja/javascripts/katex.js
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--- /dev/null
+++ b/ja/javascripts/katex.js
@@ -0,0 +1,11 @@
+document$.subscribe(({ body }) => {
+  renderMathInElement(body, {
+    delimiters: [
+      { left: "$$", right: "$$", display: true },
+      { left: "$", right: "$", display: false },
+      { left: "\\(", right: "\\)", display: false },
+      { left: "\\[", right: "\\]", display: true },
+    ],
+  });
+});
+/*! update cache: 20251017053011 */
diff --git a/ja/javascripts/mathjax.js b/ja/javascripts/mathjax.js
new file mode 100644
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+++ b/ja/javascripts/mathjax.js
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+window.MathJax = {
+  tex: {
+    inlineMath: [["\\(", "\\)"]],
+    displayMath: [["\\[", "\\]"]],
+    processEscapes: true,
+    processEnvironments: true,
+  },
+  options: {
+    ignoreHtmlClass: ".*|",
+    processHtmlClass: "arithmatex",
+    enableMenu: false,
+  },
+};
+
+document$.subscribe(() => {
+  MathJax.typesetPromise();
+});
+/*! update cache: 20251017053011 */
diff --git a/ja/partials/LICENSE b/ja/partials/LICENSE
new file mode 100644
index 000000000..98d7a71b5
--- /dev/null
+++ b/ja/partials/LICENSE
@@ -0,0 +1,19 @@
+Copyright (c) 2016-2023 Martin Donath <martin.donath@squidfunk.com>
+
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to
+deal in the Software without restriction, including without limitation the
+rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
+sell copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in
+all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
+FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
+IN THE SOFTWARE.
\ No newline at end of file
diff --git a/ja/search/search_index.json b/ja/search/search_index.json
new file mode 100644
index 000000000..054985356
--- /dev/null
+++ b/ja/search/search_index.json
@@ -0,0 +1 @@
+{"config":{"lang":["ja"],"separator":"[\\s\\-\u3000\u3001\u3002\uff0c\uff0e]+","pipeline":["stemmer"]},"docs":[{"location":"chapter_appendix/","title":"\u7b2c 16 \u7ae0 \u00a0 \u4ed8\u9332","text":""},{"location":"chapter_appendix/#_1","title":"\u7ae0\u306e\u5185\u5bb9","text":"<ul> <li>16.1 \u00a0 \u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u74b0\u5883\u306e\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb</li> <li>16.2 \u00a0 \u4e00\u7dd2\u306b\u5275\u4f5c\u306b\u53c2\u52a0</li> <li>16.3 \u00a0 \u7528\u8a9e\u96c6</li> </ul>"},{"location":"chapter_appendix/contribution/","title":"16.2 \u00a0 \u30b3\u30f3\u30c8\u30ea\u30d3\u30e5\u30fc\u30b7\u30e7\u30f3","text":"<p>\u8457\u8005\u306e\u80fd\u529b\u306b\u9650\u308a\u304c\u3042\u308b\u305f\u3081\u3001\u672c\u66f8\u306b\u306f\u3044\u304f\u3064\u304b\u306e\u7701\u7565\u3084\u8aa4\u308a\u304c\u907f\u3051\u3089\u308c\u307e\u305b\u3093\u3002\u3054\u7406\u89e3\u3092\u304a\u9858\u3044\u3057\u307e\u3059\u3002\u8aa4\u5b57\u3001\u30ea\u30f3\u30af\u5207\u308c\u3001\u5185\u5bb9\u306e\u6b20\u843d\u3001\u6587\u7ae0\u306e\u66d6\u6627\u3055\u3001\u8aac\u660e\u306e\u4e0d\u660e\u78ba\u3055\u3001\u307e\u305f\u306f\u4e0d\u5408\u7406\u306a\u6587\u7ae0\u69cb\u9020\u3092\u767a\u898b\u3055\u308c\u305f\u5834\u5408\u306f\u3001\u8aad\u8005\u306b\u3088\u308a\u826f\u8cea\u306a\u5b66\u7fd2\u30ea\u30bd\u30fc\u30b9\u3092\u63d0\u4f9b\u3059\u308b\u305f\u3081\u3001\u4fee\u6b63\u306b\u3054\u5354\u529b\u304f\u3060\u3055\u3044\u3002</p> <p>\u3059\u3079\u3066\u306e\u30b3\u30f3\u30c8\u30ea\u30d3\u30e5\u30fc\u30bf\u30fc\u306eGitHub ID\u306f\u3001\u672c\u66f8\u306e\u30ea\u30dd\u30b8\u30c8\u30ea\u3001\u30a6\u30a7\u30d6\u3001PDF\u30d0\u30fc\u30b8\u30e7\u30f3\u306e\u30db\u30fc\u30e0\u30da\u30fc\u30b8\u306b\u8868\u793a\u3055\u308c\u3001\u30aa\u30fc\u30d7\u30f3\u30bd\u30fc\u30b9\u30b3\u30df\u30e5\u30cb\u30c6\u30a3\u3078\u306e\u7121\u79c1\u306e\u8ca2\u732e\u306b\u611f\u8b1d\u3044\u305f\u3057\u307e\u3059\u3002</p> <p>\u30aa\u30fc\u30d7\u30f3\u30bd\u30fc\u30b9\u306e\u9b45\u529b</p> <p>\u7d19\u306e\u672c\u306e2\u3064\u306e\u5370\u5237\u7248\u306e\u9593\u9694\u306f\u3057\u3070\u3057\u3070\u9577\u304f\u3001\u5185\u5bb9\u306e\u66f4\u65b0\u304c\u975e\u5e38\u306b\u4e0d\u4fbf\u3067\u3059\u3002</p> <p>\u3057\u304b\u3057\u3001\u3053\u306e\u30aa\u30fc\u30d7\u30f3\u30bd\u30fc\u30b9\u306e\u672c\u3067\u306f\u3001\u5185\u5bb9\u306e\u66f4\u65b0\u30b5\u30a4\u30af\u30eb\u306f\u6570\u65e5\u3001\u3055\u3089\u306b\u306f\u6570\u6642\u9593\u306b\u77ed\u7e2e\u3055\u308c\u307e\u3059\u3002</p>"},{"location":"chapter_appendix/contribution/#1","title":"1. \u00a0 \u5185\u5bb9\u306e\u5fae\u8abf\u6574","text":"<p>\u4e0b\u306e\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u5404\u30da\u30fc\u30b8\u306e\u53f3\u4e0a\u89d2\u306b\u300c\u7de8\u96c6\u30a2\u30a4\u30b3\u30f3\u300d\u304c\u3042\u308a\u307e\u3059\u3002\u4ee5\u4e0b\u306e\u624b\u9806\u306b\u5f93\u3063\u3066\u30c6\u30ad\u30b9\u30c8\u3084\u30b3\u30fc\u30c9\u3092\u4fee\u6b63\u3067\u304d\u307e\u3059\u3002</p> <ol> <li>\u300c\u7de8\u96c6\u30a2\u30a4\u30b3\u30f3\u300d\u3092\u30af\u30ea\u30c3\u30af\u3057\u307e\u3059\u3002\u300c\u3053\u306e\u30ea\u30dd\u30b8\u30c8\u30ea\u3092\u30d5\u30a9\u30fc\u30af\u3057\u307e\u3059\u304b\u300d\u3068\u4fc3\u3055\u308c\u305f\u5834\u5408\u306f\u3001\u540c\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002</li> <li>Markdown\u30bd\u30fc\u30b9\u30d5\u30a1\u30a4\u30eb\u306e\u5185\u5bb9\u3092\u4fee\u6b63\u3057\u3001\u5185\u5bb9\u306e\u6b63\u78ba\u6027\u3092\u78ba\u8a8d\u3057\u3001\u30d5\u30a9\u30fc\u30de\u30c3\u30c8\u306e\u4e00\u8cab\u6027\u3092\u4fdd\u3064\u3088\u3046\u306b\u3057\u3066\u304f\u3060\u3055\u3044\u3002</li> <li>\u30da\u30fc\u30b8\u306e\u4e0b\u90e8\u3067\u4fee\u6b63\u8aac\u660e\u3092\u8a18\u5165\u3057\u3001\u300cPropose file change\u300d\u30dc\u30bf\u30f3\u3092\u30af\u30ea\u30c3\u30af\u3057\u307e\u3059\u3002\u30da\u30fc\u30b8\u304c\u30ea\u30c0\u30a4\u30ec\u30af\u30c8\u3055\u308c\u305f\u5f8c\u3001\u300cCreate pull request\u300d\u30dc\u30bf\u30f3\u3092\u30af\u30ea\u30c3\u30af\u3057\u3066\u30d7\u30eb\u30ea\u30af\u30a8\u30b9\u30c8\u3092\u958b\u59cb\u3057\u307e\u3059\u3002</li> </ol> <p></p> <p> \u56f3 16-3 \u00a0 \u30da\u30fc\u30b8\u7de8\u96c6\u30dc\u30bf\u30f3 </p> <p>\u56f3\u306f\u76f4\u63a5\u4fee\u6b63\u3067\u304d\u306a\u3044\u305f\u3081\u3001\u65b0\u3057\u3044Issue\u3092\u4f5c\u6210\u3059\u308b\u304b\u3001\u554f\u984c\u3092\u8aac\u660e\u3059\u308b\u30b3\u30e1\u30f3\u30c8\u304c\u5fc5\u8981\u3067\u3059\u3002\u3067\u304d\u308b\u3060\u3051\u65e9\u304f\u56f3\u3092\u518d\u63cf\u753b\u3057\u3066\u7f6e\u304d\u63db\u3048\u307e\u3059\u3002</p>"},{"location":"chapter_appendix/contribution/#2","title":"2. \u00a0 \u5185\u5bb9\u306e\u4f5c\u6210","text":"<p>\u3053\u306e\u30aa\u30fc\u30d7\u30f3\u30bd\u30fc\u30b9\u30d7\u30ed\u30b8\u30a7\u30af\u30c8\u3078\u306e\u53c2\u52a0\u306b\u8208\u5473\u304c\u3042\u308b\u5834\u5408\u3001\u30b3\u30fc\u30c9\u3092\u4ed6\u306e\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u306b\u7ffb\u8a33\u3057\u305f\u308a\u3001\u8a18\u4e8b\u306e\u5185\u5bb9\u3092\u62e1\u5f35\u3057\u305f\u308a\u3059\u308b\u3053\u3068\u3092\u542b\u3081\u3066\u3001\u4ee5\u4e0b\u306e\u30d7\u30eb\u30ea\u30af\u30a8\u30b9\u30c8\u30ef\u30fc\u30af\u30d5\u30ed\u30fc\u3092\u5b9f\u88c5\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002</p> <ol> <li>GitHub\u306b\u30ed\u30b0\u30a4\u30f3\u3057\u3001\u672c\u66f8\u306e\u30b3\u30fc\u30c9\u30ea\u30dd\u30b8\u30c8\u30ea\u3092\u500b\u4eba\u30a2\u30ab\u30a6\u30f3\u30c8\u306b\u30d5\u30a9\u30fc\u30af\u3057\u307e\u3059\u3002</li> <li>\u30d5\u30a9\u30fc\u30af\u3057\u305f\u30ea\u30dd\u30b8\u30c8\u30ea\u306e\u30a6\u30a7\u30d6\u30da\u30fc\u30b8\u306b\u79fb\u52d5\u3057\u3001<code>git clone</code>\u30b3\u30de\u30f3\u30c9\u3092\u4f7f\u7528\u3057\u3066\u30ea\u30dd\u30b8\u30c8\u30ea\u3092\u30ed\u30fc\u30ab\u30eb\u30de\u30b7\u30f3\u306b\u30af\u30ed\u30fc\u30f3\u3057\u307e\u3059\u3002</li> <li>\u30ed\u30fc\u30ab\u30eb\u3067\u5185\u5bb9\u3092\u4f5c\u6210\u3057\u3001\u5b8c\u5168\u306a\u30c6\u30b9\u30c8\u3092\u5b9f\u884c\u3057\u3066\u30b3\u30fc\u30c9\u306e\u6b63\u78ba\u6027\u3092\u691c\u8a3c\u3057\u307e\u3059\u3002</li> <li>\u30ed\u30fc\u30ab\u30eb\u3067\u884c\u3063\u305f\u5909\u66f4\u3092\u30b3\u30df\u30c3\u30c8\u3057\u3001\u30ea\u30e2\u30fc\u30c8\u30ea\u30dd\u30b8\u30c8\u30ea\u306b\u30d7\u30c3\u30b7\u30e5\u3057\u307e\u3059\u3002</li> <li>\u30ea\u30dd\u30b8\u30c8\u30ea\u306e\u30a6\u30a7\u30d6\u30da\u30fc\u30b8\u3092\u66f4\u65b0\u3057\u3001\u300cCreate pull request\u300d\u30dc\u30bf\u30f3\u3092\u30af\u30ea\u30c3\u30af\u3057\u3066\u30d7\u30eb\u30ea\u30af\u30a8\u30b9\u30c8\u3092\u958b\u59cb\u3057\u307e\u3059\u3002</li> </ol>"},{"location":"chapter_appendix/contribution/#3-docker","title":"3. \u00a0 Docker\u30c7\u30d7\u30ed\u30a4\u30e1\u30f3\u30c8","text":"<p><code>hello-algo</code>\u30eb\u30fc\u30c8\u30c7\u30a3\u30ec\u30af\u30c8\u30ea\u3067\u3001\u4ee5\u4e0b\u306eDocker\u30b9\u30af\u30ea\u30d7\u30c8\u3092\u5b9f\u884c\u3057\u3066<code>http://localhost:8000</code>\u3067\u30d7\u30ed\u30b8\u30a7\u30af\u30c8\u306b\u30a2\u30af\u30bb\u30b9\u3057\u307e\u3059\uff1a</p> <pre><code>docker-compose up -d\n</code></pre> <p>\u4ee5\u4e0b\u306e\u30b3\u30de\u30f3\u30c9\u3092\u4f7f\u7528\u3057\u3066\u30c7\u30d7\u30ed\u30a4\u30e1\u30f3\u30c8\u3092\u524a\u9664\u3057\u307e\u3059\uff1a</p> <pre><code>docker-compose down\n</code></pre>"},{"location":"chapter_appendix/installation/","title":"16.1 \u00a0 \u30a4\u30f3\u30b9\u30c8\u30fc\u30eb","text":""},{"location":"chapter_appendix/installation/#1611-ide","title":"16.1.1 \u00a0 IDE\u306e\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb","text":"<p>\u30ed\u30fc\u30ab\u30eb\u306e\u7d71\u5408\u958b\u767a\u74b0\u5883\uff08IDE\uff09\u3068\u3057\u3066\u3001\u30aa\u30fc\u30d7\u30f3\u30bd\u30fc\u30b9\u3067\u8efd\u91cf\u306aVS Code\u3092\u4f7f\u7528\u3059\u308b\u3053\u3068\u3092\u304a\u52e7\u3081\u3057\u307e\u3059\u3002VS Code\u516c\u5f0f\u30a6\u30a7\u30d6\u30b5\u30a4\u30c8\u306b\u30a2\u30af\u30bb\u30b9\u3057\u3001\u304a\u4f7f\u3044\u306e\u30aa\u30da\u30ec\u30fc\u30c6\u30a3\u30f3\u30b0\u30b7\u30b9\u30c6\u30e0\u306b\u9069\u3057\u305fVS Code\u306e\u30d0\u30fc\u30b8\u30e7\u30f3\u3092\u9078\u629e\u3057\u3066\u30c0\u30a6\u30f3\u30ed\u30fc\u30c9\u3057\u3001\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3057\u3066\u304f\u3060\u3055\u3044\u3002</p> <p></p> <p> \u56f3 16-1 \u00a0 \u516c\u5f0f\u30a6\u30a7\u30d6\u30b5\u30a4\u30c8\u304b\u3089VS Code\u3092\u30c0\u30a6\u30f3\u30ed\u30fc\u30c9 </p> <p>VS Code\u306b\u306f\u5f37\u529b\u306a\u62e1\u5f35\u6a5f\u80fd\u30a8\u30b3\u30b7\u30b9\u30c6\u30e0\u304c\u3042\u308a\u3001\u307b\u3068\u3093\u3069\u306e\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u306e\u5b9f\u884c\u3068\u30c7\u30d0\u30c3\u30b0\u3092\u30b5\u30dd\u30fc\u30c8\u3057\u3066\u3044\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u300cPython Extension Pack\u300d\u3092\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3057\u305f\u5f8c\u3001Python\u30b3\u30fc\u30c9\u3092\u30c7\u30d0\u30c3\u30b0\u3067\u304d\u307e\u3059\u3002\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u624b\u9806\u3092\u4e0b\u306e\u56f3\u306b\u793a\u3057\u307e\u3059\u3002</p> <p></p> <p> \u56f3 16-2 \u00a0 VS Code\u62e1\u5f35\u6a5f\u80fd\u30d1\u30c3\u30af\u306e\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb </p>"},{"location":"chapter_appendix/installation/#1612","title":"16.1.2 \u00a0 \u8a00\u8a9e\u74b0\u5883\u306e\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb","text":""},{"location":"chapter_appendix/installation/#1-python","title":"1. \u00a0 Python\u74b0\u5883","text":"<ol> <li>Miniconda3\u3092\u30c0\u30a6\u30f3\u30ed\u30fc\u30c9\u3057\u3066\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3057\u307e\u3059\u3002Python 3.10\u4ee5\u964d\u304c\u5fc5\u8981\u3067\u3059\u3002</li> <li>VS Code\u62e1\u5f35\u6a5f\u80fd\u30de\u30fc\u30b1\u30c3\u30c8\u30d7\u30ec\u30a4\u30b9\u3067<code>python</code>\u3092\u691c\u7d22\u3057\u3001Python Extension Pack\u3092\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3057\u307e\u3059\u3002</li> <li>\uff08\u30aa\u30d7\u30b7\u30e7\u30f3\uff09\u30b3\u30de\u30f3\u30c9\u30e9\u30a4\u30f3\u3067<code>pip install black</code>\u3092\u5165\u529b\u3057\u3066\u3001\u30b3\u30fc\u30c9\u30d5\u30a9\u30fc\u30de\u30c3\u30c6\u30a3\u30f3\u30b0\u30c4\u30fc\u30eb\u3092\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3057\u307e\u3059\u3002</li> </ol>"},{"location":"chapter_appendix/installation/#2-cc","title":"2. \u00a0 C/C++\u74b0\u5883","text":"<ol> <li>Windows\u30b7\u30b9\u30c6\u30e0\u3067\u306fMinGW\u3092\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\uff08\u8a2d\u5b9a\u30c1\u30e5\u30fc\u30c8\u30ea\u30a2\u30eb\uff09\u3002MacOS\u306b\u306fClang\u304c\u4ed8\u5c5e\u3057\u3066\u3044\u308b\u305f\u3081\u3001\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u306f\u4e0d\u8981\u3067\u3059\u3002</li> <li>VS Code\u62e1\u5f35\u6a5f\u80fd\u30de\u30fc\u30b1\u30c3\u30c8\u30d7\u30ec\u30a4\u30b9\u3067<code>c++</code>\u3092\u691c\u7d22\u3057\u3001C/C++ Extension Pack\u3092\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3057\u307e\u3059\u3002</li> <li>\uff08\u30aa\u30d7\u30b7\u30e7\u30f3\uff09\u8a2d\u5b9a\u30da\u30fc\u30b8\u3092\u958b\u304d\u3001<code>Clang_format_fallback Style</code>\u30b3\u30fc\u30c9\u30d5\u30a9\u30fc\u30de\u30c3\u30c6\u30a3\u30f3\u30b0\u30aa\u30d7\u30b7\u30e7\u30f3\u3092\u691c\u7d22\u3057\u3001<code>{ BasedOnStyle: Microsoft, BreakBeforeBraces: Attach }</code>\u306b\u8a2d\u5b9a\u3057\u307e\u3059\u3002</li> </ol>"},{"location":"chapter_appendix/installation/#3-java","title":"3. \u00a0 Java\u74b0\u5883","text":"<ol> <li>OpenJDK\u3092\u30c0\u30a6\u30f3\u30ed\u30fc\u30c9\u3057\u3066\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3057\u307e\u3059\uff08\u30d0\u30fc\u30b8\u30e7\u30f3\u306fJDK 9\u3088\u308a\u65b0\u3057\u3044\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\uff09\u3002</li> <li>VS Code\u62e1\u5f35\u6a5f\u80fd\u30de\u30fc\u30b1\u30c3\u30c8\u30d7\u30ec\u30a4\u30b9\u3067<code>java</code>\u3092\u691c\u7d22\u3057\u3001Extension Pack for Java\u3092\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3057\u307e\u3059\u3002</li> </ol>"},{"location":"chapter_appendix/installation/#4-c","title":"4. \u00a0 C#\u74b0\u5883","text":"<ol> <li>.Net 8.0\u3092\u30c0\u30a6\u30f3\u30ed\u30fc\u30c9\u3057\u3066\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3057\u307e\u3059\u3002</li> <li>VS Code\u62e1\u5f35\u6a5f\u80fd\u30de\u30fc\u30b1\u30c3\u30c8\u30d7\u30ec\u30a4\u30b9\u3067<code>C# Dev Kit</code>\u3092\u691c\u7d22\u3057\u3001C# Dev Kit\u3092\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3057\u307e\u3059\uff08\u8a2d\u5b9a\u30c1\u30e5\u30fc\u30c8\u30ea\u30a2\u30eb\uff09\u3002</li> <li>Visual Studio\u3092\u4f7f\u7528\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\uff08\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u30c1\u30e5\u30fc\u30c8\u30ea\u30a2\u30eb\uff09\u3002</li> </ol>"},{"location":"chapter_appendix/installation/#5-go","title":"5. \u00a0 Go\u74b0\u5883","text":"<ol> <li>go\u3092\u30c0\u30a6\u30f3\u30ed\u30fc\u30c9\u3057\u3066\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3057\u307e\u3059\u3002</li> <li>VS Code\u62e1\u5f35\u6a5f\u80fd\u30de\u30fc\u30b1\u30c3\u30c8\u30d7\u30ec\u30a4\u30b9\u3067<code>go</code>\u3092\u691c\u7d22\u3057\u3001Go\u3092\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3057\u307e\u3059\u3002</li> <li><code>Ctrl + Shift + P</code>\u3092\u62bc\u3057\u3066\u30b3\u30de\u30f3\u30c9\u30d0\u30fc\u3092\u547c\u3073\u51fa\u3057\u3001go\u3068\u5165\u529b\u3057\u3001<code>Go: Install/Update Tools</code>\u3092\u9078\u629e\u3057\u3001\u3059\u3079\u3066\u3092\u9078\u629e\u3057\u3066\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3057\u307e\u3059\u3002</li> </ol>"},{"location":"chapter_appendix/installation/#6-swift","title":"6. \u00a0 Swift\u74b0\u5883","text":"<ol> <li>Swift\u3092\u30c0\u30a6\u30f3\u30ed\u30fc\u30c9\u3057\u3066\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3057\u307e\u3059\u3002</li> <li>VS Code\u62e1\u5f35\u6a5f\u80fd\u30de\u30fc\u30b1\u30c3\u30c8\u30d7\u30ec\u30a4\u30b9\u3067<code>swift</code>\u3092\u691c\u7d22\u3057\u3001Swift for Visual Studio Code\u3092\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3057\u307e\u3059\u3002</li> </ol>"},{"location":"chapter_appendix/installation/#7-javascript","title":"7. \u00a0 JavaScript\u74b0\u5883","text":"<ol> <li>Node.js\u3092\u30c0\u30a6\u30f3\u30ed\u30fc\u30c9\u3057\u3066\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3057\u307e\u3059\u3002</li> <li>\uff08\u30aa\u30d7\u30b7\u30e7\u30f3\uff09VS Code\u62e1\u5f35\u6a5f\u80fd\u30de\u30fc\u30b1\u30c3\u30c8\u30d7\u30ec\u30a4\u30b9\u3067<code>Prettier</code>\u3092\u691c\u7d22\u3057\u3001\u30b3\u30fc\u30c9\u30d5\u30a9\u30fc\u30de\u30c3\u30c6\u30a3\u30f3\u30b0\u30c4\u30fc\u30eb\u3092\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3057\u307e\u3059\u3002</li> </ol>"},{"location":"chapter_appendix/installation/#8-typescript","title":"8. \u00a0 TypeScript\u74b0\u5883","text":"<ol> <li>JavaScript\u74b0\u5883\u3068\u540c\u3058\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u624b\u9806\u306b\u5f93\u3044\u307e\u3059\u3002</li> <li>TypeScript Execute (tsx)\u3092\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3057\u307e\u3059\u3002</li> <li>VS Code\u62e1\u5f35\u6a5f\u80fd\u30de\u30fc\u30b1\u30c3\u30c8\u30d7\u30ec\u30a4\u30b9\u3067<code>typescript</code>\u3092\u691c\u7d22\u3057\u3001Pretty TypeScript Errors\u3092\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3057\u307e\u3059\u3002</li> </ol>"},{"location":"chapter_appendix/installation/#9-dart","title":"9. \u00a0 Dart\u74b0\u5883","text":"<ol> <li>Dart\u3092\u30c0\u30a6\u30f3\u30ed\u30fc\u30c9\u3057\u3066\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3057\u307e\u3059\u3002</li> <li>VS Code\u62e1\u5f35\u6a5f\u80fd\u30de\u30fc\u30b1\u30c3\u30c8\u30d7\u30ec\u30a4\u30b9\u3067<code>dart</code>\u3092\u691c\u7d22\u3057\u3001Dart\u3092\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3057\u307e\u3059\u3002</li> </ol>"},{"location":"chapter_appendix/installation/#10-rust","title":"10. \u00a0 Rust\u74b0\u5883","text":"<ol> <li>Rust\u3092\u30c0\u30a6\u30f3\u30ed\u30fc\u30c9\u3057\u3066\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3057\u307e\u3059\u3002</li> <li>VS Code\u62e1\u5f35\u6a5f\u80fd\u30de\u30fc\u30b1\u30c3\u30c8\u30d7\u30ec\u30a4\u30b9\u3067<code>rust</code>\u3092\u691c\u7d22\u3057\u3001rust-analyzer\u3092\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3057\u307e\u3059\u3002</li> </ol>"},{"location":"chapter_appendix/terminology/","title":"16.3 \u00a0 \u7528\u8a9e\u96c6","text":"<p>\u4e0b\u306e\u8868\u306f\u672c\u66f8\u306b\u767b\u5834\u3059\u308b\u91cd\u8981\u306a\u7528\u8a9e\u3092\u30ea\u30b9\u30c8\u30a2\u30c3\u30d7\u3057\u3066\u304a\u308a\u3001\u4ee5\u4e0b\u306e\u70b9\u306b\u6ce8\u610f\u3059\u308b\u4fa1\u5024\u304c\u3042\u308a\u307e\u3059\u3002</p> <ul> <li>\u82f1\u8a9e\u6587\u732e\u3092\u8aad\u307f\u3084\u3059\u304f\u3059\u308b\u305f\u3081\u3001\u7528\u8a9e\u306e\u82f1\u8a9e\u540d\u3092\u899a\u3048\u308b\u3053\u3068\u3092\u304a\u52e7\u3081\u3057\u307e\u3059\u3002</li> <li>\u4e00\u90e8\u306e\u7528\u8a9e\u306f\u7c21\u4f53\u5b57\u4e2d\u56fd\u8a9e\u3068\u7e41\u4f53\u5b57\u4e2d\u56fd\u8a9e\u3067\u7570\u306a\u308b\u540d\u524d\u3092\u6301\u3061\u307e\u3059\u3002</li> </ul> <p> \u8868 16-1 \u00a0 \u30c7\u30fc\u30bf\u69cb\u9020\u3068\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u91cd\u8981\u7528\u8a9e </p> English \u65e5\u672c\u8a9e \u7b80\u4f53\u4e2d\u6587 \u7e41\u4f53\u4e2d\u6587 algorithm \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0 \u7b97\u6cd5 \u6f14\u7b97\u6cd5 data structure \u30c7\u30fc\u30bf\u69cb\u9020 \u6570\u636e\u7ed3\u6784 \u8cc7\u6599\u7d50\u69cb code \u30b3\u30fc\u30c9 \u4ee3\u7801 \u7a0b\u5f0f\u78bc file \u30d5\u30a1\u30a4\u30eb \u6587\u4ef6 \u6a94\u6848 function \u95a2\u6570 \u51fd\u6570 \u51fd\u5f0f method \u30e1\u30bd\u30c3\u30c9 \u65b9\u6cd5 \u65b9\u6cd5 variable \u5909\u6570 \u53d8\u91cf \u8b8a\u6578 asymptotic complexity analysis \u6f38\u8fd1\u8a08\u7b97\u91cf\u89e3\u6790 \u6e10\u8fd1\u590d\u6742\u5ea6\u5206\u6790 \u6f38\u8fd1\u8907\u96dc\u5ea6\u5206\u6790 time complexity \u6642\u9593\u8a08\u7b97\u91cf \u65f6\u95f4\u590d\u6742\u5ea6 \u6642\u9593\u8907\u96dc\u5ea6 space complexity \u7a7a\u9593\u8a08\u7b97\u91cf \u7a7a\u95f4\u590d\u6742\u5ea6 \u7a7a\u9593\u8907\u96dc\u5ea6 loop \u30eb\u30fc\u30d7 \u5faa\u73af \u8ff4\u5708 iteration \u53cd\u5fa9 \u8fed\u4ee3 \u8fed\u4ee3 recursion \u518d\u5e30 \u9012\u5f52 \u905e\u8ff4 tail recursion \u672b\u5c3e\u518d\u5e30 \u5c3e\u9012\u5f52 \u5c3e\u905e\u8ff4 recursion tree \u518d\u5e30\u6728 \u9012\u5f52\u6811 \u905e\u8ff4\u6a39 big-\\(O\\) notation \u30d3\u30c3\u30b0O\u8a18\u6cd5 \u5927 \\(O\\) \u8bb0\u53f7 \u5927 \\(O\\) \u8a18\u865f asymptotic upper bound \u6f38\u8fd1\u4e0a\u754c \u6e10\u8fd1\u4e0a\u754c \u6f38\u8fd1\u4e0a\u754c sign-magnitude \u7b26\u53f7\u3068\u7d76\u5bfe\u5024 \u539f\u7801 \u539f\u78bc 1's complement 1\u306e\u88dc\u6570 \u53cd\u7801 \u4e00\u88dc\u6578 2's complement 2\u306e\u88dc\u6570 \u8865\u7801 \u4e8c\u88dc\u6578 array \u914d\u5217 \u6570\u7ec4 \u9663\u5217 index \u30a4\u30f3\u30c7\u30c3\u30af\u30b9 \u7d22\u5f15 \u7d22\u5f15 linked list \u9023\u7d50\u30ea\u30b9\u30c8 \u94fe\u8868 \u93c8\u7d50\u4e32\u5217 linked list node, list node \u9023\u7d50\u30ea\u30b9\u30c8\u30ce\u30fc\u30c9 \u94fe\u8868\u8282\u70b9 \u93c8\u7d50\u4e32\u5217\u7bc0\u9ede head node \u5148\u982d\u30ce\u30fc\u30c9 \u5934\u8282\u70b9 \u982d\u7bc0\u9ede tail node \u672b\u5c3e\u30ce\u30fc\u30c9 \u5c3e\u8282\u70b9 \u5c3e\u7bc0\u9ede list \u30ea\u30b9\u30c8 \u5217\u8868 \u4e32\u5217 dynamic array \u52d5\u7684\u914d\u5217 \u52a8\u6001\u6570\u7ec4 \u52d5\u614b\u9663\u5217 hard disk \u30cf\u30fc\u30c9\u30c7\u30a3\u30b9\u30af \u786c\u76d8 \u786c\u789f random-access memory (RAM) \u30e1\u30e2\u30ea \u5185\u5b58 \u8a18\u61b6\u9ad4 cache memory \u30ad\u30e3\u30c3\u30b7\u30e5\u30e1\u30e2\u30ea \u7f13\u5b58 \u5feb\u53d6 cache miss \u30ad\u30e3\u30c3\u30b7\u30e5\u30df\u30b9 \u7f13\u5b58\u672a\u547d\u4e2d \u5feb\u53d6\u672a\u547d\u4e2d cache hit rate \u30ad\u30e3\u30c3\u30b7\u30e5\u30d2\u30c3\u30c8\u7387 \u7f13\u5b58\u547d\u4e2d\u7387 \u5feb\u53d6\u547d\u4e2d\u7387 stack \u30b9\u30bf\u30c3\u30af \u6808 \u5806\u758a top of the stack \u30b9\u30bf\u30c3\u30af\u30c8\u30c3\u30d7 \u6808\u9876 \u5806\u758a\u9802 bottom of the stack \u30b9\u30bf\u30c3\u30af\u30dc\u30c8\u30e0 \u6808\u5e95 \u5806\u758a\u5e95 queue \u30ad\u30e5\u30fc \u961f\u5217 \u4f47\u5217 double-ended queue \u4e21\u7aef\u30ad\u30e5\u30fc \u53cc\u5411\u961f\u5217 \u96d9\u5411\u4f47\u5217 front of the queue \u30ad\u30e5\u30fc\u306e\u5148\u982d \u961f\u9996 \u4f47\u5217\u9996 rear of the queue \u30ad\u30e5\u30fc\u306e\u672b\u5c3e \u961f\u5c3e \u4f47\u5217\u5c3e hash table \u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb \u54c8\u5e0c\u8868 \u96dc\u6e4a\u8868 hash set \u30cf\u30c3\u30b7\u30e5\u30bb\u30c3\u30c8 \u54c8\u5e0c\u96c6\u5408 \u96dc\u6e4a\u96c6\u5408 bucket \u30d0\u30b1\u30c3\u30c8 \u6876 \u6876 hash function \u30cf\u30c3\u30b7\u30e5\u95a2\u6570 \u54c8\u5e0c\u51fd\u6570 \u96dc\u6e4a\u51fd\u5f0f hash collision \u30cf\u30c3\u30b7\u30e5\u885d\u7a81 \u54c8\u5e0c\u51b2\u7a81 \u96dc\u6e4a\u885d\u7a81 load factor \u8ca0\u8377\u7387 \u8d1f\u8f7d\u56e0\u5b50 \u8ca0\u8f09\u56e0\u5b50 separate chaining \u30c1\u30a7\u30a4\u30f3\u6cd5 \u94fe\u5f0f\u5730\u5740 \u93c8\u7d50\u4f4d\u5740 open addressing \u30aa\u30fc\u30d7\u30f3\u30a2\u30c9\u30ec\u30b9\u6cd5 \u5f00\u653e\u5bfb\u5740 \u958b\u653e\u5b9a\u5740 linear probing \u7dda\u5f62\u30d7\u30ed\u30fc\u30d6\u6cd5 \u7ebf\u6027\u63a2\u6d4b \u7dda\u6027\u63a2\u67e5 lazy deletion \u9045\u5ef6\u524a\u9664 \u61d2\u5220\u9664 \u61f6\u522a\u9664 binary tree \u4e8c\u5206\u6728 \u4e8c\u53c9\u6811 \u4e8c\u5143\u6a39 tree node \u6728\u306e\u30ce\u30fc\u30c9 \u6811\u8282\u70b9 \u6a39\u7bc0\u9ede left-child node \u5de6\u306e\u5b50\u30ce\u30fc\u30c9 \u5de6\u5b50\u8282\u70b9 \u5de6\u5b50\u7bc0\u9ede right-child node \u53f3\u306e\u5b50\u30ce\u30fc\u30c9 \u53f3\u5b50\u8282\u70b9 \u53f3\u5b50\u7bc0\u9ede parent node \u89aa\u30ce\u30fc\u30c9 \u7236\u8282\u70b9 \u7236\u7bc0\u9ede left subtree \u5de6\u306e\u90e8\u5206\u6728 \u5de6\u5b50\u6811 \u5de6\u5b50\u6a39 right subtree \u53f3\u306e\u90e8\u5206\u6728 \u53f3\u5b50\u6811 \u53f3\u5b50\u6a39 root node \u30eb\u30fc\u30c8\u30ce\u30fc\u30c9 \u6839\u8282\u70b9 \u6839\u7bc0\u9ede leaf node \u8449\u30ce\u30fc\u30c9 \u53f6\u8282\u70b9 \u8449\u7bc0\u9ede edge \u30a8\u30c3\u30b8 \u8fb9 \u908a level \u30ec\u30d9\u30eb \u5c42 \u5c64 degree \u6b21\u6570 \u5ea6 \u5ea6 height \u9ad8\u3055 \u9ad8\u5ea6 \u9ad8\u5ea6 depth \u6df1\u3055 \u6df1\u5ea6 \u6df1\u5ea6 perfect binary tree \u5b8c\u5168\u4e8c\u5206\u6728 \u5b8c\u7f8e\u4e8c\u53c9\u6811 \u5b8c\u7f8e\u4e8c\u5143\u6a39 complete binary tree \u5b8c\u5168\u4e8c\u5206\u6728 \u5b8c\u5168\u4e8c\u53c9\u6811 \u5b8c\u5168\u4e8c\u5143\u6a39 full binary tree \u6e80\u4e8c\u5206\u6728 \u5b8c\u6ee1\u4e8c\u53c9\u6811 \u5b8c\u6eff\u4e8c\u5143\u6a39 balanced binary tree \u5e73\u8861\u4e8c\u5206\u6728 \u5e73\u8861\u4e8c\u53c9\u6811 \u5e73\u8861\u4e8c\u5143\u6a39 binary search tree \u4e8c\u5206\u63a2\u7d22\u6728 \u4e8c\u53c9\u641c\u7d22\u6811 \u4e8c\u5143\u641c\u5c0b\u6a39 AVL tree AVL\u6728 AVL \u6811 AVL \u6a39 red-black tree \u8d64\u9ed2\u6728 \u7ea2\u9ed1\u6811 \u7d05\u9ed1\u6a39 level-order traversal \u30ec\u30d9\u30eb\u9806\u8d70\u67fb \u5c42\u5e8f\u904d\u5386 \u5c64\u5e8f\u8d70\u8a2a breadth-first traversal \u5e45\u512a\u5148\u8d70\u67fb \u5e7f\u5ea6\u4f18\u5148\u904d\u5386 \u5ee3\u5ea6\u512a\u5148\u8d70\u8a2a depth-first traversal \u6df1\u3055\u512a\u5148\u8d70\u67fb \u6df1\u5ea6\u4f18\u5148\u904d\u5386 \u6df1\u5ea6\u512a\u5148\u8d70\u8a2a binary search tree \u4e8c\u5206\u63a2\u7d22\u6728 \u4e8c\u53c9\u641c\u7d22\u6811 \u4e8c\u5143\u641c\u5c0b\u6a39 balanced binary search tree \u5e73\u8861\u4e8c\u5206\u63a2\u7d22\u6728 \u5e73\u8861\u4e8c\u53c9\u641c\u7d22\u6811 \u5e73\u8861\u4e8c\u5143\u641c\u5c0b\u6a39 balance factor \u5e73\u8861\u56e0\u5b50 \u5e73\u8861\u56e0\u5b50 \u5e73\u8861\u56e0\u5b50 heap \u30d2\u30fc\u30d7 \u5806 \u5806\u7a4d max heap \u6700\u5927\u30d2\u30fc\u30d7 \u5927\u9876\u5806 \u5927\u9802\u5806\u7a4d min heap \u6700\u5c0f\u30d2\u30fc\u30d7 \u5c0f\u9876\u5806 \u5c0f\u9802\u5806\u7a4d priority queue \u512a\u5148\u5ea6\u30ad\u30e5\u30fc \u4f18\u5148\u961f\u5217 \u512a\u5148\u4f47\u5217 heapify \u30d2\u30fc\u30d7\u5316 \u5806\u5316 \u5806\u7a4d\u5316 top-\\(k\\) problem Top-\\(k\\) \u554f\u984c Top-\\(k\\) \u95ee\u9898 Top-\\(k\\) \u554f\u984c graph \u30b0\u30e9\u30d5 \u56fe \u5716 vertex \u9802\u70b9 \u9876\u70b9 \u9802\u9ede undirected graph \u7121\u5411\u30b0\u30e9\u30d5 \u65e0\u5411\u56fe \u7121\u5411\u5716 directed graph \u6709\u5411\u30b0\u30e9\u30d5 \u6709\u5411\u56fe \u6709\u5411\u5716 connected graph \u9023\u7d50\u30b0\u30e9\u30d5 \u8fde\u901a\u56fe \u9023\u901a\u5716 disconnected graph \u975e\u9023\u7d50\u30b0\u30e9\u30d5 \u975e\u8fde\u901a\u56fe \u975e\u9023\u901a\u5716 weighted graph \u91cd\u307f\u4ed8\u304d\u30b0\u30e9\u30d5 \u6709\u6743\u56fe \u6709\u6b0a\u5716 adjacency \u96a3\u63a5 \u90bb\u63a5 \u9130\u63a5 path \u30d1\u30b9 \u8def\u5f84 \u8def\u5f91 in-degree \u5165\u6b21\u6570 \u5165\u5ea6 \u5165\u5ea6 out-degree \u51fa\u6b21\u6570 \u51fa\u5ea6 \u51fa\u5ea6 adjacency matrix \u96a3\u63a5\u884c\u5217 \u90bb\u63a5\u77e9\u9635 \u9130\u63a5\u77e9\u9663 adjacency list \u96a3\u63a5\u30ea\u30b9\u30c8 \u90bb\u63a5\u8868 \u9130\u63a5\u8868 breadth-first search \u5e45\u512a\u5148\u63a2\u7d22 \u5e7f\u5ea6\u4f18\u5148\u641c\u7d22 \u5ee3\u5ea6\u512a\u5148\u641c\u5c0b depth-first search \u6df1\u3055\u512a\u5148\u63a2\u7d22 \u6df1\u5ea6\u4f18\u5148\u641c\u7d22 \u6df1\u5ea6\u512a\u5148\u641c\u5c0b binary search \u4e8c\u5206\u63a2\u7d22 \u4e8c\u5206\u67e5\u627e \u4e8c\u5206\u641c\u5c0b searching algorithm \u63a2\u7d22\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0 \u641c\u7d22\u7b97\u6cd5 \u641c\u5c0b\u6f14\u7b97\u6cd5 sorting algorithm \u30bd\u30fc\u30c8\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0 \u6392\u5e8f\u7b97\u6cd5 \u6392\u5e8f\u6f14\u7b97\u6cd5 selection sort \u9078\u629e\u30bd\u30fc\u30c8 \u9009\u62e9\u6392\u5e8f \u9078\u64c7\u6392\u5e8f bubble sort \u30d0\u30d6\u30eb\u30bd\u30fc\u30c8 \u5192\u6ce1\u6392\u5e8f \u6ce1\u6cab\u6392\u5e8f insertion sort \u633f\u5165\u30bd\u30fc\u30c8 \u63d2\u5165\u6392\u5e8f \u63d2\u5165\u6392\u5e8f quick sort \u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8 \u5feb\u901f\u6392\u5e8f \u5feb\u901f\u6392\u5e8f merge sort \u30de\u30fc\u30b8\u30bd\u30fc\u30c8 \u5f52\u5e76\u6392\u5e8f \u5408\u4f75\u6392\u5e8f heap sort \u30d2\u30fc\u30d7\u30bd\u30fc\u30c8 \u5806\u6392\u5e8f \u5806\u7a4d\u6392\u5e8f bucket sort \u30d0\u30b1\u30c3\u30c8\u30bd\u30fc\u30c8 \u6876\u6392\u5e8f \u6876\u6392\u5e8f counting sort \u8a08\u6570\u30bd\u30fc\u30c8 \u8ba1\u6570\u6392\u5e8f \u8a08\u6578\u6392\u5e8f radix sort \u57fa\u6570\u30bd\u30fc\u30c8 \u57fa\u6570\u6392\u5e8f \u57fa\u6578\u6392\u5e8f divide and conquer \u5206\u5272\u7d71\u6cbb\u6cd5 \u5206\u6cbb \u5206\u6cbb hanota problem \u30cf\u30ce\u30a4\u306e\u5854\u554f\u984c \u6c49\u8bfa\u5854\u95ee\u9898 \u6cb3\u5167\u5854\u554f\u984c backtracking algorithm \u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0 \u56de\u6eaf\u7b97\u6cd5 \u56de\u6eaf\u6f14\u7b97\u6cd5 constraint \u5236\u7d04 \u7ea6\u675f \u7d04\u675f solution \u89e3 \u89e3 \u89e3 state \u72b6\u614b \u72b6\u6001 \u72c0\u614b pruning \u679d\u5208\u308a \u526a\u679d \u526a\u679d permutations problem \u9806\u5217\u554f\u984c \u5168\u6392\u5217\u95ee\u9898 \u5168\u6392\u5217\u554f\u984c subset-sum problem \u90e8\u5206\u96c6\u5408\u548c\u554f\u984c \u5b50\u96c6\u548c\u95ee\u9898 \u5b50\u96c6\u5408\u554f\u984c \\(n\\)-queens problem \\(n\\) \u30af\u30a4\u30fc\u30f3\u554f\u984c \\(n\\) \u7687\u540e\u95ee\u9898 \\(n\\) \u7687\u540e\u554f\u984c dynamic programming \u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0 \u52a8\u6001\u89c4\u5212 \u52d5\u614b\u898f\u5283 initial state \u521d\u671f\u72b6\u614b \u521d\u59cb\u72b6\u6001 \u521d\u59cb\u72c0\u614b state-transition equation \u72b6\u614b\u9077\u79fb\u65b9\u7a0b\u5f0f \u72b6\u6001\u8f6c\u79fb\u65b9\u7a0b \u72c0\u614b\u8f49\u79fb\u65b9\u7a0b knapsack problem \u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c \u80cc\u5305\u95ee\u9898 \u80cc\u5305\u554f\u984c edit distance problem \u7de8\u96c6\u8ddd\u96e2\u554f\u984c \u7f16\u8f91\u8ddd\u79bb\u95ee\u9898 \u7de8\u8f2f\u8ddd\u96e2\u554f\u984c greedy algorithm \u8caa\u6b32\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0 \u8d2a\u5fc3\u7b97\u6cd5 \u8caa\u5a6a\u6f14\u7b97\u6cd5"},{"location":"chapter_array_and_linkedlist/","title":"\u7b2c 4 \u7ae0 \u00a0 \u914d\u5217\u3068\u9023\u7d50\u30ea\u30b9\u30c8","text":"<p>Abstract</p> <p>\u30c7\u30fc\u30bf\u69cb\u9020\u306e\u4e16\u754c\u306f\u9811\u4e08\u306a\u30ec\u30f3\u30ac\u306e\u58c1\u306b\u4f3c\u3066\u3044\u307e\u3059\u3002</p> <p>\u914d\u5217\u3067\u306f\u3001\u30ec\u30f3\u30ac\u304c\u3074\u3063\u305f\u308a\u3068\u6574\u5217\u3057\u3001\u305d\u308c\u305e\u308c\u304c\u6b21\u306e\u3082\u306e\u3068\u7d99\u304e\u76ee\u306a\u304f\u96a3\u308a\u5408\u3063\u3066\u3001\u7d71\u4e00\u3055\u308c\u305f\u5f62\u6210\u3092\u4f5c\u3063\u3066\u3044\u308b\u59ff\u3092\u60f3\u50cf\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u4e00\u65b9\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u3067\u306f\u3001\u3053\u308c\u3089\u306e\u30ec\u30f3\u30ac\u304c\u81ea\u7531\u306b\u6563\u3089\u3070\u308a\u3001\u305d\u308c\u3089\u306e\u9593\u3092\u512a\u96c5\u306b\u7de8\u307f\u8fbc\u3080\u8526\u306b\u62b1\u304b\u308c\u3066\u3044\u307e\u3059\u3002</p>"},{"location":"chapter_array_and_linkedlist/#_1","title":"\u7ae0\u306e\u5185\u5bb9","text":"<ul> <li>4.1 \u00a0 \u914d\u5217</li> <li>4.2 \u00a0 \u9023\u7d50\u30ea\u30b9\u30c8</li> <li>4.3 \u00a0 \u30ea\u30b9\u30c8</li> <li>4.4 \u00a0 \u30e1\u30e2\u30ea\u3068\u30ad\u30e3\u30c3\u30b7\u30e5 *</li> <li>4.5 \u00a0 \u307e\u3068\u3081</li> </ul>"},{"location":"chapter_array_and_linkedlist/array/","title":"4.1 \u00a0 \u914d\u5217","text":"<p>\u914d\u5217\u306f\u7dda\u5f62\u30c7\u30fc\u30bf\u69cb\u9020\u3067\u3001\u540c\u3058\u3088\u3046\u306a\u9805\u76ee\u304c\u4e26\u3093\u3067\u3044\u308b\u3088\u3046\u306a\u3082\u306e\u3067\u3001\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u306e\u30e1\u30e2\u30ea\u5185\u306e\u9023\u7d9a\u3057\u305f\u7a7a\u9593\u306b\u4e00\u7dd2\u306b\u683c\u7d0d\u3055\u308c\u307e\u3059\u3002\u3053\u308c\u306f\u6574\u7406\u3055\u308c\u305f\u683c\u7d0d\u3092\u7dad\u6301\u3059\u308b\u30b7\u30fc\u30b1\u30f3\u30b9\u306e\u3088\u3046\u306a\u3082\u306e\u3067\u3059\u3002\u3053\u306e\u4e26\u3073\u306e\u5404\u9805\u76ee\u306b\u306f\u3001\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3068\u3057\u3066\u77e5\u3089\u308c\u308b\u72ec\u81ea\u306e\u300c\u4f4d\u7f6e\u300d\u304c\u3042\u308a\u307e\u3059\u3002\u4ee5\u4e0b\u306e\u56f3\u3092\u53c2\u7167\u3057\u3066\u3001\u914d\u5217\u306e\u52d5\u4f5c\u3092\u89b3\u5bdf\u3057\u3001\u3053\u308c\u3089\u306e\u91cd\u8981\u306a\u7528\u8a9e\u3092\u7406\u89e3\u3057\u3066\u304f\u3060\u3055\u3044\u3002</p> <p></p> <p> \u56f3 4-1 \u00a0 \u914d\u5217\u306e\u5b9a\u7fa9\u3068\u683c\u7d0d\u65b9\u6cd5 </p>"},{"location":"chapter_array_and_linkedlist/array/#411","title":"4.1.1 \u00a0 \u914d\u5217\u306e\u4e00\u822c\u7684\u306a\u64cd\u4f5c","text":""},{"location":"chapter_array_and_linkedlist/array/#1","title":"1. \u00a0 \u914d\u5217\u306e\u521d\u671f\u5316","text":"<p>\u914d\u5217\u306f\u5fc5\u8981\u306b\u5fdc\u3058\u30662\u3064\u306e\u65b9\u6cd5\u3067\u521d\u671f\u5316\u3067\u304d\u307e\u3059\uff1a\u521d\u671f\u5024\u306a\u3057\u307e\u305f\u306f\u6307\u5b9a\u3055\u308c\u305f\u521d\u671f\u5024\u4ed8\u304d\u3067\u3059\u3002\u521d\u671f\u5024\u304c\u6307\u5b9a\u3055\u308c\u3066\u3044\u306a\u3044\u5834\u5408\u3001\u307b\u3068\u3093\u3069\u306e\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u306f\u914d\u5217\u8981\u7d20\u3092\\(0\\)\u306b\u8a2d\u5b9a\u3057\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinZig array.py<pre><code># \u914d\u5217\u3092\u521d\u671f\u5316\narr: list[int] = [0] * 5  # [ 0, 0, 0, 0, 0 ]\nnums: list[int] = [1, 3, 2, 5, 4]\n</code></pre> array.cpp<pre><code>/* \u914d\u5217\u3092\u521d\u671f\u5316 */\n// \u30b9\u30bf\u30c3\u30af\u306b\u683c\u7d0d\nint arr[5];\nint nums[5] = { 1, 3, 2, 5, 4 };\n// \u30d2\u30fc\u30d7\u306b\u683c\u7d0d\uff08\u624b\u52d5\u3067\u306e\u30e1\u30e2\u30ea\u89e3\u653e\u304c\u5fc5\u8981\uff09\nint* arr1 = new int[5];\nint* nums1 = new int[5] { 1, 3, 2, 5, 4 };\n</code></pre> array.java<pre><code>/* \u914d\u5217\u3092\u521d\u671f\u5316 */\nint[] arr = new int[5]; // { 0, 0, 0, 0, 0 }\nint[] nums = { 1, 3, 2, 5, 4 };\n</code></pre> array.cs<pre><code>/* \u914d\u5217\u3092\u521d\u671f\u5316 */\nint[] arr = new int[5]; // [ 0, 0, 0, 0, 0 ]\nint[] nums = [1, 3, 2, 5, 4];\n</code></pre> array.go<pre><code>/* \u914d\u5217\u3092\u521d\u671f\u5316 */\nvar arr [5]int\n// Go\u3067\u306f\u3001\u9577\u3055\u3092\u6307\u5b9a\uff08[5]int\uff09\u3059\u308b\u3068\u914d\u5217\u3092\u793a\u3057\u3001\u6307\u5b9a\u3057\u306a\u3044\uff08[]int\uff09\u3068\u30b9\u30e9\u30a4\u30b9\u3092\u793a\u3057\u307e\u3059\u3002\n// Go\u306e\u914d\u5217\u306f\u30b3\u30f3\u30d1\u30a4\u30eb\u6642\u306b\u56fa\u5b9a\u9577\u3092\u6301\u3064\u3088\u3046\u8a2d\u8a08\u3055\u308c\u3066\u3044\u308b\u305f\u3081\u3001\u9577\u3055\u306e\u6307\u5b9a\u306b\u306f\u5b9a\u6570\u306e\u307f\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002\n// extend()\u30e1\u30bd\u30c3\u30c9\u306e\u5b9f\u88c5\u306e\u4fbf\u5b9c\u4e0a\u3001\u3053\u3053\u3067\u306fSlice\u3092\u914d\u5217\u3068\u3057\u3066\u6271\u3044\u307e\u3059\u3002\nnums := []int{1, 3, 2, 5, 4}\n</code></pre> array.swift<pre><code>/* \u914d\u5217\u3092\u521d\u671f\u5316 */\nlet arr = Array(repeating: 0, count: 5) // [0, 0, 0, 0, 0]\nlet nums = [1, 3, 2, 5, 4]\n</code></pre> array.js<pre><code>/* \u914d\u5217\u3092\u521d\u671f\u5316 */\nvar arr = new Array(5).fill(0);\nvar nums = [1, 3, 2, 5, 4];\n</code></pre> array.ts<pre><code>/* \u914d\u5217\u3092\u521d\u671f\u5316 */\nlet arr: number[] = new Array(5).fill(0);\nlet nums: number[] = [1, 3, 2, 5, 4];\n</code></pre> array.dart<pre><code>/* \u914d\u5217\u3092\u521d\u671f\u5316 */\nList&lt;int&gt; arr = List.filled(5, 0); // [0, 0, 0, 0, 0]\nList&lt;int&gt; nums = [1, 3, 2, 5, 4];\n</code></pre> array.rs<pre><code>/* \u914d\u5217\u3092\u521d\u671f\u5316 */\nlet arr: [i32; 5] = [0; 5]; // [0, 0, 0, 0, 0]\nlet slice: &amp;[i32] = &amp;[0; 5];\n// Rust\u3067\u306f\u3001\u9577\u3055\u3092\u6307\u5b9a\uff08[i32; 5]\uff09\u3059\u308b\u3068\u914d\u5217\u3092\u793a\u3057\u3001\u6307\u5b9a\u3057\u306a\u3044\uff08&amp;[i32]\uff09\u3068\u30b9\u30e9\u30a4\u30b9\u3092\u793a\u3057\u307e\u3059\u3002\n// Rust\u306e\u914d\u5217\u306f\u30b3\u30f3\u30d1\u30a4\u30eb\u6642\u306b\u56fa\u5b9a\u9577\u3092\u6301\u3064\u3088\u3046\u8a2d\u8a08\u3055\u308c\u3066\u3044\u308b\u305f\u3081\u3001\u9577\u3055\u306e\u6307\u5b9a\u306b\u306f\u5b9a\u6570\u306e\u307f\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002\n// \u4e00\u822c\u7684\u306bRust\u3067\u306f\u52d5\u7684\u914d\u5217\u3068\u3057\u3066Vector\u304c\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\n// extend()\u30e1\u30bd\u30c3\u30c9\u306e\u5b9f\u88c5\u306e\u4fbf\u5b9c\u4e0a\u3001\u3053\u3053\u3067\u306f\u30d9\u30af\u30bf\u30fc\u3092\u914d\u5217\u3068\u3057\u3066\u6271\u3044\u307e\u3059\u3002\nlet nums: Vec&lt;i32&gt; = vec![1, 3, 2, 5, 4];\n</code></pre> array.c<pre><code>/* \u914d\u5217\u3092\u521d\u671f\u5316 */\nint arr[5] = { 0 }; // { 0, 0, 0, 0, 0 }\nint nums[5] = { 1, 3, 2, 5, 4 };\n</code></pre> array.kt<pre><code>\n</code></pre> array.zig<pre><code>// \u914d\u5217\u3092\u521d\u671f\u5316\nvar arr = [_]i32{0} ** 5; // { 0, 0, 0, 0, 0 }\nvar nums = [_]i32{ 1, 3, 2, 5, 4 };\n</code></pre>"},{"location":"chapter_array_and_linkedlist/array/#2","title":"2. \u00a0 \u8981\u7d20\u3078\u306e\u30a2\u30af\u30bb\u30b9","text":"<p>\u914d\u5217\u5185\u306e\u8981\u7d20\u306f\u9023\u7d9a\u3057\u305f\u30e1\u30e2\u30ea\u7a7a\u9593\u306b\u683c\u7d0d\u3055\u308c\u308b\u305f\u3081\u3001\u5404\u8981\u7d20\u306e\u30e1\u30e2\u30ea\u30a2\u30c9\u30ec\u30b9\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u304c\u7c21\u5358\u306b\u306a\u308a\u307e\u3059\u3002\u4ee5\u4e0b\u306e\u56f3\u306b\u793a\u3055\u308c\u3066\u3044\u308b\u516c\u5f0f\u306f\u3001\u914d\u5217\u306e\u30e1\u30e2\u30ea\u30a2\u30c9\u30ec\u30b9\uff08\u7279\u306b\u3001\u6700\u521d\u306e\u8981\u7d20\u306e\u30a2\u30c9\u30ec\u30b9\uff09\u3068\u8981\u7d20\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u5229\u7528\u3057\u3066\u3001\u8981\u7d20\u306e\u30e1\u30e2\u30ea\u30a2\u30c9\u30ec\u30b9\u3092\u6c7a\u5b9a\u3059\u308b\u306e\u306b\u5f79\u7acb\u3061\u307e\u3059\u3002\u3053\u306e\u8a08\u7b97\u306b\u3088\u308a\u3001\u76ee\u7684\u306e\u8981\u7d20\u3078\u306e\u76f4\u63a5\u30a2\u30af\u30bb\u30b9\u304c\u5408\u7406\u5316\u3055\u308c\u307e\u3059\u3002</p> <p></p> <p> \u56f3 4-2 \u00a0 \u914d\u5217\u8981\u7d20\u306e\u30e1\u30e2\u30ea\u30a2\u30c9\u30ec\u30b9\u8a08\u7b97 </p> <p>\u4e0a\u306e\u56f3\u3067\u89b3\u5bdf\u3055\u308c\u308b\u3088\u3046\u306b\u3001\u914d\u5217\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306f\u6163\u4f8b\u7684\u306b\\(0\\)\u304b\u3089\u59cb\u307e\u308a\u307e\u3059\u3002\u3053\u308c\u306f\u76f4\u611f\u306b\u53cd\u3059\u308b\u3088\u3046\u306b\u898b\u3048\u308b\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u3002\u6570\u3092\u6570\u3048\u308b\u306e\u306f\u901a\u5e38\\(1\\)\u304b\u3089\u59cb\u307e\u308b\u305f\u3081\u3067\u3059\u304c\u3001\u30a2\u30c9\u30ec\u30b9\u8a08\u7b97\u516c\u5f0f\u5185\u3067\u306f\u3001**\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306f\u672c\u8cea\u7684\u306b\u30e1\u30e2\u30ea\u30a2\u30c9\u30ec\u30b9\u304b\u3089\u306e\u30aa\u30d5\u30bb\u30c3\u30c8**\u3067\u3059\u3002\u6700\u521d\u306e\u8981\u7d20\u306e\u30a2\u30c9\u30ec\u30b9\u3067\u306f\u3001\u3053\u306e\u30aa\u30d5\u30bb\u30c3\u30c8\u306f\\(0\\)\u3067\u3001\u305d\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u304c\\(0\\)\u3067\u3042\u308b\u3053\u3068\u3092\u691c\u8a3c\u3057\u3066\u3044\u307e\u3059\u3002</p> <p>\u914d\u5217\u5185\u306e\u8981\u7d20\u3078\u306e\u30a2\u30af\u30bb\u30b9\u306f\u975e\u5e38\u306b\u52b9\u7387\u7684\u3067\u3001\\(O(1)\\)\u6642\u9593\u3067\u4efb\u610f\u306e\u8981\u7d20\u306b\u30e9\u30f3\u30c0\u30e0\u30a2\u30af\u30bb\u30b9\u3067\u304d\u307e\u3059\u3002</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig array.py<pre><code>def random_access(nums: list[int]) -&gt; int:\n    \"\"\"\u8981\u7d20\u3078\u306e\u30e9\u30f3\u30c0\u30e0\u30a2\u30af\u30bb\u30b9\"\"\"\n    # \u533a\u9593 [0, len(nums)-1] \u304b\u3089\u6570\u5024\u3092\u30e9\u30f3\u30c0\u30e0\u306b\u9078\u629e\n    random_index = random.randint(0, len(nums) - 1)\n    # \u30e9\u30f3\u30c0\u30e0\u306a\u8981\u7d20\u3092\u53d6\u5f97\u3057\u3066\u8fd4\u3059\n    random_num = nums[random_index]\n    return random_num\n</code></pre> array.cpp<pre><code>/* \u8981\u7d20\u3078\u306e\u4e71\u6570\u30a2\u30af\u30bb\u30b9 */\nint randomAccess(int *nums, int size) {\n    // [0, size)\u306e\u7bc4\u56f2\u3067\u4e71\u6570\u3092\u9078\u629e\n    int randomIndex = rand() % size;\n    // \u4e71\u6570\u8981\u7d20\u3092\u53d6\u5f97\u3057\u3066\u8fd4\u5374\n    int randomNum = nums[randomIndex];\n    return randomNum;\n}\n</code></pre> array.java<pre><code>/* \u8981\u7d20\u3078\u306e\u30e9\u30f3\u30c0\u30e0\u30a2\u30af\u30bb\u30b9 */\nint randomAccess(int[] nums) {\n    // \u533a\u9593 [0, nums.length) \u304b\u3089\u30e9\u30f3\u30c0\u30e0\u306b\u6570\u3092\u9078\u629e\n    int randomIndex = ThreadLocalRandom.current().nextInt(0, nums.length);\n    // \u30e9\u30f3\u30c0\u30e0\u8981\u7d20\u3092\u53d6\u5f97\u3057\u3066\u8fd4\u3059\n    int randomNum = nums[randomIndex];\n    return randomNum;\n}\n</code></pre> array.cs<pre><code>[class]{array}-[func]{RandomAccess}\n</code></pre> array.go<pre><code>[class]{}-[func]{randomAccess}\n</code></pre> array.swift<pre><code>[class]{}-[func]{randomAccess}\n</code></pre> array.js<pre><code>[class]{}-[func]{randomAccess}\n</code></pre> array.ts<pre><code>[class]{}-[func]{randomAccess}\n</code></pre> array.dart<pre><code>[class]{}-[func]{randomAccess}\n</code></pre> array.rs<pre><code>[class]{}-[func]{random_access}\n</code></pre> array.c<pre><code>[class]{}-[func]{randomAccess}\n</code></pre> array.kt<pre><code>[class]{}-[func]{randomAccess}\n</code></pre> array.rb<pre><code>[class]{}-[func]{random_access}\n</code></pre> array.zig<pre><code>[class]{}-[func]{randomAccess}\n</code></pre>"},{"location":"chapter_array_and_linkedlist/array/#3","title":"3. \u00a0 \u8981\u7d20\u306e\u633f\u5165","text":"<p>\u914d\u5217\u8981\u7d20\u306f\u30e1\u30e2\u30ea\u5185\u3067\u5bc6\u306b\u8a70\u307e\u3063\u3066\u304a\u308a\u3001\u305d\u308c\u3089\u306e\u9593\u306b\u8ffd\u52a0\u30c7\u30fc\u30bf\u3092\u53ce\u5bb9\u3059\u308b\u305f\u3081\u306e\u7a7a\u9593\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u4ee5\u4e0b\u306e\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u914d\u5217\u306e\u4e2d\u592e\u306b\u8981\u7d20\u3092\u633f\u5165\u3059\u308b\u306b\u306f\u3001\u5f8c\u7d9a\u306e\u3059\u3079\u3066\u306e\u8981\u7d20\u30921\u3064\u305a\u3064\u5f8c\u308d\u306b\u30b7\u30d5\u30c8\u3057\u3066\u3001\u65b0\u3057\u3044\u8981\u7d20\u306e\u305f\u3081\u306e\u7a7a\u9593\u3092\u4f5c\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002</p> <p></p> <p> \u56f3 4-3 \u00a0 \u914d\u5217\u8981\u7d20\u633f\u5165\u306e\u4f8b </p> <p>\u914d\u5217\u306e\u9577\u3055\u304c\u56fa\u5b9a\u3055\u308c\u3066\u3044\u308b\u305f\u3081\u3001\u8981\u7d20\u3092\u633f\u5165\u3059\u308b\u3068\u5fc5\u7136\u7684\u306b\u914d\u5217\u306e\u6700\u5f8c\u306e\u8981\u7d20\u304c\u5931\u308f\u308c\u308b\u3053\u3068\u306b\u6ce8\u610f\u3059\u308b\u3053\u3068\u304c\u91cd\u8981\u3067\u3059\u3002\u3053\u306e\u554f\u984c\u3092\u89e3\u6c7a\u3059\u308b\u65b9\u6cd5\u306f\u300c\u30ea\u30b9\u30c8\u300d\u306e\u7ae0\u3067\u63a2\u6c42\u3055\u308c\u307e\u3059\u3002</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig array.py<pre><code>def insert(nums: list[int], num: int, index: int):\n    \"\"\"\u30a4\u30f3\u30c7\u30c3\u30af\u30b9 index \u306b\u8981\u7d20 num \u3092\u633f\u5165\"\"\"\n    # \u30a4\u30f3\u30c7\u30c3\u30af\u30b9 index \u3088\u308a\u5f8c\u306e\u3059\u3079\u3066\u306e\u8981\u7d20\u30921\u3064\u5f8c\u308d\u306b\u79fb\u52d5\n    for i in range(len(nums) - 1, index, -1):\n        nums[i] = nums[i - 1]\n    # num \u3092 index \u306e\u4f4d\u7f6e\u306e\u8981\u7d20\u306b\u4ee3\u5165\n    nums[index] = num\n</code></pre> array.cpp<pre><code>/* `index`\u306b\u8981\u7d20num\u3092\u633f\u5165 */\nvoid insert(int *nums, int size, int num, int index) {\n    // `index`\u3088\u308a\u5f8c\u306e\u3059\u3079\u3066\u306e\u8981\u7d20\u30921\u3064\u5f8c\u308d\u306b\u79fb\u52d5\n    for (int i = size - 1; i &gt; index; i--) {\n        nums[i] = nums[i - 1];\n    }\n    // index\u306e\u4f4d\u7f6e\u306bnum\u3092\u4ee3\u5165\n    nums[index] = num;\n}\n</code></pre> array.java<pre><code>/* `index` \u306b\u8981\u7d20 num \u3092\u633f\u5165 */\nvoid insert(int[] nums, int num, int index) {\n    // `index` \u3088\u308a\u5f8c\u306e\u3059\u3079\u3066\u306e\u8981\u7d20\u30921\u3064\u5f8c\u308d\u306b\u79fb\u52d5\n    for (int i = nums.length - 1; i &gt; index; i--) {\n        nums[i] = nums[i - 1];\n    }\n    // index \u306e\u8981\u7d20\u306b num \u3092\u4ee3\u5165\n    nums[index] = num;\n}\n</code></pre> array.cs<pre><code>[class]{array}-[func]{Insert}\n</code></pre> array.go<pre><code>[class]{}-[func]{insert}\n</code></pre> array.swift<pre><code>[class]{}-[func]{insert}\n</code></pre> array.js<pre><code>[class]{}-[func]{insert}\n</code></pre> array.ts<pre><code>[class]{}-[func]{insert}\n</code></pre> array.dart<pre><code>[class]{}-[func]{insert}\n</code></pre> array.rs<pre><code>[class]{}-[func]{insert}\n</code></pre> array.c<pre><code>[class]{}-[func]{insert}\n</code></pre> array.kt<pre><code>[class]{}-[func]{insert}\n</code></pre> array.rb<pre><code>[class]{}-[func]{insert}\n</code></pre> array.zig<pre><code>[class]{}-[func]{insert}\n</code></pre>"},{"location":"chapter_array_and_linkedlist/array/#4","title":"4. \u00a0 \u8981\u7d20\u306e\u524a\u9664","text":"<p>\u540c\u69d8\u306b\u3001\u4ee5\u4e0b\u306e\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\\(i\\)\u306e\u8981\u7d20\u3092\u524a\u9664\u3059\u308b\u306b\u306f\u3001\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\\(i\\)\u306b\u7d9a\u304f\u3059\u3079\u3066\u306e\u8981\u7d20\u30921\u3064\u305a\u3064\u524d\u306b\u79fb\u52d5\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002</p> <p></p> <p> \u56f3 4-4 \u00a0 \u914d\u5217\u8981\u7d20\u524a\u9664\u306e\u4f8b </p> <p>\u524a\u9664\u5f8c\u3001\u5143\u306e\u6700\u5f8c\u306e\u8981\u7d20\u306f\u300c\u610f\u5473\u304c\u306a\u3044\u300d\u3082\u306e\u306b\u306a\u308b\u305f\u3081\u3001\u7279\u5b9a\u306e\u4fee\u6b63\u306f\u5fc5\u8981\u306a\u3044\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig array.py<pre><code>def remove(nums: list[int], index: int):\n    \"\"\"\u30a4\u30f3\u30c7\u30c3\u30af\u30b9 index \u306e\u8981\u7d20\u3092\u524a\u9664\"\"\"\n    # \u30a4\u30f3\u30c7\u30c3\u30af\u30b9 index \u3088\u308a\u5f8c\u306e\u3059\u3079\u3066\u306e\u8981\u7d20\u30921\u3064\u524d\u306b\u79fb\u52d5\n    for i in range(index, len(nums) - 1):\n        nums[i] = nums[i + 1]\n</code></pre> array.cpp<pre><code>/* `index`\u306e\u8981\u7d20\u3092\u524a\u9664 */\nvoid remove(int *nums, int size, int index) {\n    // `index`\u3088\u308a\u5f8c\u306e\u3059\u3079\u3066\u306e\u8981\u7d20\u30921\u3064\u524d\u306b\u79fb\u52d5\n    for (int i = index; i &lt; size - 1; i++) {\n        nums[i] = nums[i + 1];\n    }\n}\n</code></pre> array.java<pre><code>/* `index` \u306e\u8981\u7d20\u3092\u524a\u9664 */\nvoid remove(int[] nums, int index) {\n    // `index` \u3088\u308a\u5f8c\u306e\u3059\u3079\u3066\u306e\u8981\u7d20\u30921\u3064\u524d\u306b\u79fb\u52d5\n    for (int i = index; i &lt; nums.length - 1; i++) {\n        nums[i] = nums[i + 1];\n    }\n}\n</code></pre> array.cs<pre><code>[class]{array}-[func]{Remove}\n</code></pre> array.go<pre><code>[class]{}-[func]{remove}\n</code></pre> array.swift<pre><code>[class]{}-[func]{remove}\n</code></pre> array.js<pre><code>[class]{}-[func]{remove}\n</code></pre> array.ts<pre><code>[class]{}-[func]{remove}\n</code></pre> array.dart<pre><code>[class]{}-[func]{remove}\n</code></pre> array.rs<pre><code>[class]{}-[func]{remove}\n</code></pre> array.c<pre><code>[class]{}-[func]{removeItem}\n</code></pre> array.kt<pre><code>[class]{}-[func]{remove}\n</code></pre> array.rb<pre><code>[class]{}-[func]{remove}\n</code></pre> array.zig<pre><code>[class]{}-[func]{remove}\n</code></pre> <p>\u8981\u7d04\u3059\u308b\u3068\u3001\u914d\u5217\u306e\u633f\u5165\u3068\u524a\u9664\u64cd\u4f5c\u306b\u306f\u4ee5\u4e0b\u306e\u6b20\u70b9\u304c\u3042\u308a\u307e\u3059\uff1a</p> <ul> <li>\u9ad8\u3044\u6642\u9593\u8a08\u7b97\u91cf\uff1a\u914d\u5217\u306e\u633f\u5165\u3068\u524a\u9664\u306e\u4e21\u65b9\u306e\u5e73\u5747\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O(n)\\)\u3067\u3001\u3053\u3053\u3067\\(n\\)\u306f\u914d\u5217\u306e\u9577\u3055\u3067\u3059\u3002</li> <li>\u8981\u7d20\u306e\u640d\u5931\uff1a\u914d\u5217\u306e\u9577\u3055\u304c\u56fa\u5b9a\u3055\u308c\u3066\u3044\u308b\u305f\u3081\u3001\u633f\u5165\u6642\u306b\u914d\u5217\u306e\u5bb9\u91cf\u3092\u8d85\u3048\u308b\u8981\u7d20\u306f\u5931\u308f\u308c\u307e\u3059\u3002</li> <li>\u30e1\u30e2\u30ea\u306e\u7121\u99c4\uff1a\u3088\u308a\u9577\u3044\u914d\u5217\u3092\u521d\u671f\u5316\u3057\u3066\u524d\u90e8\u5206\u306e\u307f\u3092\u5229\u7528\u3059\u308b\u3068\u3001\u633f\u5165\u6642\u306b\u300c\u610f\u5473\u306e\u306a\u3044\u300d\u672b\u5c3e\u8981\u7d20\u304c\u751f\u3058\u3001\u30e1\u30e2\u30ea\u7a7a\u9593\u306e\u7121\u99c4\u306b\u3064\u306a\u304c\u308a\u307e\u3059\u3002</li> </ul>"},{"location":"chapter_array_and_linkedlist/array/#5","title":"5. \u00a0 \u914d\u5217\u306e\u8d70\u67fb","text":"<p>\u307b\u3068\u3093\u3069\u306e\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u3067\u306f\u3001\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u4f7f\u7528\u3059\u308b\u304b\u3001\u5404\u8981\u7d20\u3092\u76f4\u63a5\u53cd\u5fa9\u3059\u308b\u3053\u3068\u3067\u914d\u5217\u3092\u8d70\u67fb\u3067\u304d\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig array.py<pre><code>def traverse(nums: list[int]):\n    \"\"\"\u914d\u5217\u306e\u8d70\u67fb\"\"\"\n    count = 0\n    # \u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306b\u3088\u308b\u914d\u5217\u306e\u8d70\u67fb\n    for i in range(len(nums)):\n        count += nums[i]\n    # \u914d\u5217\u8981\u7d20\u306e\u8d70\u67fb\n    for num in nums:\n        count += num\n    # \u30c7\u30fc\u30bf\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3068\u8981\u7d20\u306e\u4e21\u65b9\u3092\u8d70\u67fb\n    for i, num in enumerate(nums):\n        count += nums[i]\n        count += num\n</code></pre> array.cpp<pre><code>/* \u914d\u5217\u306e\u8d70\u67fb */\nvoid traverse(int *nums, int size) {\n    int count = 0;\n    // \u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306b\u3088\u308b\u914d\u5217\u306e\u8d70\u67fb\n    for (int i = 0; i &lt; size; i++) {\n        count += nums[i];\n    }\n}\n</code></pre> array.java<pre><code>/* \u914d\u5217\u3092\u8d70\u67fb */\nvoid traverse(int[] nums) {\n    int count = 0;\n    // \u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306b\u3088\u308b\u914d\u5217\u306e\u8d70\u67fb\n    for (int i = 0; i &lt; nums.length; i++) {\n        count += nums[i];\n    }\n    // \u914d\u5217\u8981\u7d20\u306e\u8d70\u67fb\n    for (int num : nums) {\n        count += num;\n    }\n}\n</code></pre> array.cs<pre><code>[class]{array}-[func]{Traverse}\n</code></pre> array.go<pre><code>[class]{}-[func]{traverse}\n</code></pre> array.swift<pre><code>[class]{}-[func]{traverse}\n</code></pre> array.js<pre><code>[class]{}-[func]{traverse}\n</code></pre> array.ts<pre><code>[class]{}-[func]{traverse}\n</code></pre> array.dart<pre><code>[class]{}-[func]{traverse}\n</code></pre> array.rs<pre><code>[class]{}-[func]{traverse}\n</code></pre> array.c<pre><code>[class]{}-[func]{traverse}\n</code></pre> array.kt<pre><code>[class]{}-[func]{traverse}\n</code></pre> array.rb<pre><code>[class]{}-[func]{traverse}\n</code></pre> array.zig<pre><code>[class]{}-[func]{traverse}\n</code></pre>"},{"location":"chapter_array_and_linkedlist/array/#6","title":"6. \u00a0 \u8981\u7d20\u306e\u691c\u7d22","text":"<p>\u914d\u5217\u5185\u306e\u7279\u5b9a\u306e\u8981\u7d20\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u306f\u3001\u914d\u5217\u3092\u53cd\u5fa9\u3057\u3001\u5404\u8981\u7d20\u3092\u30c1\u30a7\u30c3\u30af\u3057\u3066\u76ee\u7684\u306e\u5024\u3068\u4e00\u81f4\u3059\u308b\u304b\u3069\u3046\u304b\u3092\u6c7a\u5b9a\u3059\u308b\u3053\u3068\u3092\u542b\u307f\u307e\u3059\u3002</p> <p>\u914d\u5217\u306f\u7dda\u5f62\u30c7\u30fc\u30bf\u69cb\u9020\u3067\u3042\u308b\u305f\u3081\u3001\u3053\u306e\u64cd\u4f5c\u306f\u4e00\u822c\u7684\u306b\u300c\u7dda\u5f62\u63a2\u7d22\u300d\u3068\u547c\u3070\u308c\u307e\u3059\u3002</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig array.py<pre><code>def find(nums: list[int], target: int) -&gt; int:\n    \"\"\"\u914d\u5217\u5185\u306e\u6307\u5b9a\u3055\u308c\u305f\u8981\u7d20\u3092\u691c\u7d22\"\"\"\n    for i in range(len(nums)):\n        if nums[i] == target:\n            return i\n    return -1\n</code></pre> array.cpp<pre><code>/* \u914d\u5217\u5185\u306e\u6307\u5b9a\u8981\u7d20\u3092\u691c\u7d22 */\nint find(int *nums, int size, int target) {\n    for (int i = 0; i &lt; size; i++) {\n        if (nums[i] == target)\n            return i;\n    }\n    return -1;\n}\n</code></pre> array.java<pre><code>/* \u914d\u5217\u5185\u3067\u6307\u5b9a\u3055\u308c\u305f\u8981\u7d20\u3092\u691c\u7d22 */\nint find(int[] nums, int target) {\n    for (int i = 0; i &lt; nums.length; i++) {\n        if (nums[i] == target)\n            return i;\n    }\n    return -1;\n}\n</code></pre> array.cs<pre><code>[class]{array}-[func]{Find}\n</code></pre> array.go<pre><code>[class]{}-[func]{find}\n</code></pre> array.swift<pre><code>[class]{}-[func]{find}\n</code></pre> array.js<pre><code>[class]{}-[func]{find}\n</code></pre> array.ts<pre><code>[class]{}-[func]{find}\n</code></pre> array.dart<pre><code>[class]{}-[func]{find}\n</code></pre> array.rs<pre><code>[class]{}-[func]{find}\n</code></pre> array.c<pre><code>[class]{}-[func]{find}\n</code></pre> array.kt<pre><code>[class]{}-[func]{find}\n</code></pre> array.rb<pre><code>[class]{}-[func]{find}\n</code></pre> array.zig<pre><code>[class]{}-[func]{find}\n</code></pre>"},{"location":"chapter_array_and_linkedlist/array/#7","title":"7. \u00a0 \u914d\u5217\u306e\u62e1\u5f35","text":"<p>\u8907\u96d1\u306a\u30b7\u30b9\u30c6\u30e0\u74b0\u5883\u3067\u306f\u3001\u5b89\u5168\u306a\u5bb9\u91cf\u62e1\u5f35\u306e\u305f\u3081\u306b\u914d\u5217\u306e\u5f8c\u306b\u30e1\u30e2\u30ea\u7a7a\u9593\u306e\u53ef\u7528\u6027\u3092\u78ba\u4fdd\u3059\u308b\u3053\u3068\u304c\u56f0\u96e3\u306b\u306a\u308a\u307e\u3059\u3002\u305d\u306e\u7d50\u679c\u3001\u307b\u3068\u3093\u3069\u306e\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u3067\u306f\u3001**\u914d\u5217\u306e\u9577\u3055\u306f\u4e0d\u5909**\u3067\u3059\u3002</p> <p>\u914d\u5217\u3092\u62e1\u5f35\u3059\u308b\u306b\u306f\u3001\u3088\u308a\u5927\u304d\u306a\u914d\u5217\u3092\u4f5c\u6210\u3057\u3001\u5143\u306e\u914d\u5217\u304b\u3089\u8981\u7d20\u3092\u30b3\u30d4\u30fc\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u64cd\u4f5c\u306e\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O(n)\\)\u3067\u3001\u5927\u304d\u306a\u914d\u5217\u3067\u306f\u6642\u9593\u304c\u304b\u304b\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002\u30b3\u30fc\u30c9\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig array.py<pre><code>def extend(nums: list[int], enlarge: int) -&gt; list[int]:\n    \"\"\"\u914d\u5217\u306e\u9577\u3055\u3092\u62e1\u5f35\"\"\"\n    # \u62e1\u5f35\u3055\u308c\u305f\u9577\u3055\u306e\u914d\u5217\u3092\u521d\u671f\u5316\n    res = [0] * (len(nums) + enlarge)\n    # \u5143\u306e\u914d\u5217\u306e\u3059\u3079\u3066\u306e\u8981\u7d20\u3092\u65b0\u3057\u3044\u914d\u5217\u306b\u30b3\u30d4\u30fc\n    for i in range(len(nums)):\n        res[i] = nums[i]\n    # \u62e1\u5f35\u5f8c\u306e\u65b0\u3057\u3044\u914d\u5217\u3092\u8fd4\u3059\n    return res\n</code></pre> array.cpp<pre><code>/* \u914d\u5217\u9577\u306e\u62e1\u5f35 */\nint *extend(int *nums, int size, int enlarge) {\n    // \u62e1\u5f35\u3055\u308c\u305f\u9577\u3055\u306e\u914d\u5217\u3092\u521d\u671f\u5316\n    int *res = new int[size + enlarge];\n    // \u5143\u306e\u914d\u5217\u306e\u5168\u8981\u7d20\u3092\u65b0\u3057\u3044\u914d\u5217\u306b\u30b3\u30d4\u30fc\n    for (int i = 0; i &lt; size; i++) {\n        res[i] = nums[i];\n    }\n    // \u30e1\u30e2\u30ea\u3092\u89e3\u653e\n    delete[] nums;\n    // \u62e1\u5f35\u5f8c\u306e\u65b0\u3057\u3044\u914d\u5217\u3092\u8fd4\u5374\n    return res;\n}\n</code></pre> array.java<pre><code>/* \u914d\u5217\u9577\u306e\u62e1\u5f35 */\nint[] extend(int[] nums, int enlarge) {\n    // \u62e1\u5f35\u3055\u308c\u305f\u9577\u3055\u306e\u914d\u5217\u3092\u521d\u671f\u5316\n    int[] res = new int[nums.length + enlarge];\n    // \u5143\u306e\u914d\u5217\u306e\u3059\u3079\u3066\u306e\u8981\u7d20\u3092\u65b0\u3057\u3044\u914d\u5217\u306b\u30b3\u30d4\u30fc\n    for (int i = 0; i &lt; nums.length; i++) {\n        res[i] = nums[i];\n    }\n    // \u62e1\u5f35\u5f8c\u306e\u65b0\u3057\u3044\u914d\u5217\u3092\u8fd4\u3059\n    return res;\n}\n</code></pre> array.cs<pre><code>[class]{array}-[func]{Extend}\n</code></pre> array.go<pre><code>[class]{}-[func]{extend}\n</code></pre> array.swift<pre><code>[class]{}-[func]{extend}\n</code></pre> array.js<pre><code>[class]{}-[func]{extend}\n</code></pre> array.ts<pre><code>[class]{}-[func]{extend}\n</code></pre> array.dart<pre><code>[class]{}-[func]{extend}\n</code></pre> array.rs<pre><code>[class]{}-[func]{extend}\n</code></pre> array.c<pre><code>[class]{}-[func]{extend}\n</code></pre> array.kt<pre><code>[class]{}-[func]{extend}\n</code></pre> array.rb<pre><code>[class]{}-[func]{extend}\n</code></pre> array.zig<pre><code>[class]{}-[func]{extend}\n</code></pre>"},{"location":"chapter_array_and_linkedlist/array/#412","title":"4.1.2 \u00a0 \u914d\u5217\u306e\u5229\u70b9\u3068\u5236\u9650","text":"<p>\u914d\u5217\u306f\u9023\u7d9a\u3057\u305f\u30e1\u30e2\u30ea\u7a7a\u9593\u306b\u683c\u7d0d\u3055\u308c\u3001\u540c\u3058\u578b\u306e\u8981\u7d20\u3067\u69cb\u6210\u3055\u308c\u307e\u3059\u3002\u3053\u306e\u30a2\u30d7\u30ed\u30fc\u30c1\u306f\u3001\u30b7\u30b9\u30c6\u30e0\u304c\u30c7\u30fc\u30bf\u69cb\u9020\u64cd\u4f5c\u306e\u52b9\u7387\u3092\u6700\u9069\u5316\u3059\u308b\u305f\u3081\u306b\u6d3b\u7528\u3067\u304d\u308b\u5b9f\u8cea\u7684\u306a\u4e8b\u524d\u60c5\u5831\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002</p> <ul> <li>\u9ad8\u3044\u7a7a\u9593\u52b9\u7387\uff1a\u914d\u5217\u306f\u30c7\u30fc\u30bf\u306e\u305f\u3081\u306e\u9023\u7d9a\u3057\u305f\u30e1\u30e2\u30ea\u30d6\u30ed\u30c3\u30af\u3092\u5272\u308a\u5f53\u3066\u3001\u8ffd\u52a0\u306e\u69cb\u9020\u7684\u30aa\u30fc\u30d0\u30fc\u30d8\u30c3\u30c9\u306e\u5fc5\u8981\u6027\u3092\u6392\u9664\u3057\u307e\u3059\u3002</li> <li>\u30e9\u30f3\u30c0\u30e0\u30a2\u30af\u30bb\u30b9\u306e\u30b5\u30dd\u30fc\u30c8\uff1a\u914d\u5217\u306f\u4efb\u610f\u306e\u8981\u7d20\u3078\u306e\\(O(1)\\)\u6642\u9593\u30a2\u30af\u30bb\u30b9\u3092\u53ef\u80fd\u306b\u3057\u307e\u3059\u3002</li> <li>\u30ad\u30e3\u30c3\u30b7\u30e5\u5c40\u6240\u6027\uff1a\u914d\u5217\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9\u3059\u308b\u3068\u304d\u3001\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u306f\u305d\u308c\u3089\u3092\u8aad\u307f\u8fbc\u3080\u3060\u3051\u3067\u306a\u304f\u3001\u5468\u56f2\u306e\u30c7\u30fc\u30bf\u3082\u30ad\u30e3\u30c3\u30b7\u30e5\u3057\u3001\u9ad8\u901f\u30ad\u30e3\u30c3\u30b7\u30e5\u3092\u5229\u7528\u3057\u3066\u5f8c\u7d9a\u306e\u64cd\u4f5c\u901f\u5ea6\u3092\u5411\u4e0a\u3055\u305b\u307e\u3059\u3002</li> </ul> <p>\u3057\u304b\u3057\u3001\u9023\u7d9a\u7a7a\u9593\u683c\u7d0d\u306f\u8af8\u5203\u306e\u5263\u3067\u3001\u4ee5\u4e0b\u306e\u5236\u9650\u304c\u3042\u308a\u307e\u3059\uff1a</p> <ul> <li>\u633f\u5165\u3068\u524a\u9664\u306e\u52b9\u7387\u304c\u4f4e\u3044\uff1a\u914d\u5217\u306b\u591a\u304f\u306e\u8981\u7d20\u304c\u84c4\u7a4d\u3055\u308c\u308b\u3068\u3001\u8981\u7d20\u306e\u633f\u5165\u3084\u524a\u9664\u306b\u306f\u5927\u91cf\u306e\u8981\u7d20\u3092\u30b7\u30d5\u30c8\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002</li> <li>\u56fa\u5b9a\u9577\uff1a\u914d\u5217\u306e\u9577\u3055\u306f\u521d\u671f\u5316\u5f8c\u306b\u56fa\u5b9a\u3055\u308c\u307e\u3059\u3002\u914d\u5217\u3092\u62e1\u5f35\u3059\u308b\u306b\u306f\u3001\u3059\u3079\u3066\u306e\u30c7\u30fc\u30bf\u3092\u65b0\u3057\u3044\u914d\u5217\u306b\u30b3\u30d4\u30fc\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u3001\u5927\u304d\u306a\u30b3\u30b9\u30c8\u304c\u304b\u304b\u308a\u307e\u3059\u3002</li> <li>\u7a7a\u9593\u306e\u7121\u99c4\uff1a\u5272\u308a\u5f53\u3066\u3089\u308c\u305f\u914d\u5217\u30b5\u30a4\u30ba\u304c\u5fc5\u8981\u4ee5\u4e0a\u306b\u5927\u304d\u3044\u5834\u5408\u3001\u4f59\u5206\u306a\u7a7a\u9593\u304c\u7121\u99c4\u306b\u306a\u308a\u307e\u3059\u3002</li> </ul>"},{"location":"chapter_array_and_linkedlist/array/#413","title":"4.1.3 \u00a0 \u914d\u5217\u306e\u5178\u578b\u7684\u306a\u5fdc\u7528","text":"<p>\u914d\u5217\u306f\u57fa\u672c\u7684\u3067\u5e83\u304f\u4f7f\u7528\u3055\u308c\u308b\u30c7\u30fc\u30bf\u69cb\u9020\u3067\u3059\u3002\u69d8\u3005\u306a\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u983b\u7e41\u306b\u5fdc\u7528\u3055\u308c\u3001\u8907\u96d1\u306a\u30c7\u30fc\u30bf\u69cb\u9020\u306e\u5b9f\u88c5\u306b\u5f79\u7acb\u3061\u307e\u3059\u3002</p> <ul> <li>\u30e9\u30f3\u30c0\u30e0\u30a2\u30af\u30bb\u30b9\uff1a\u914d\u5217\u306f\u30e9\u30f3\u30c0\u30e0\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u304c\u5fc5\u8981\u306a\u3068\u304d\u306e\u30c7\u30fc\u30bf\u683c\u7d0d\u306b\u7406\u60f3\u7684\u3067\u3059\u3002\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306b\u57fa\u3065\u3044\u3066\u30e9\u30f3\u30c0\u30e0\u30b7\u30fc\u30b1\u30f3\u30b9\u3092\u751f\u6210\u3059\u308b\u3053\u3068\u3067\u3001\u52b9\u7387\u7684\u306b\u30e9\u30f3\u30c0\u30e0\u30b5\u30f3\u30d7\u30ea\u30f3\u30b0\u3092\u5b9f\u73fe\u3067\u304d\u307e\u3059\u3002</li> <li>\u30bd\u30fc\u30c8\u3068\u691c\u7d22\uff1a\u914d\u5217\u306f\u30bd\u30fc\u30c8\u3068\u691c\u7d22\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u6700\u3082\u4e00\u822c\u7684\u306b\u4f7f\u7528\u3055\u308c\u308b\u30c7\u30fc\u30bf\u69cb\u9020\u3067\u3059\u3002\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u3001\u30de\u30fc\u30b8\u30bd\u30fc\u30c8\u3001\u4e8c\u5206\u63a2\u7d22\u306a\u3069\u306e\u6280\u8853\u306f\u4e3b\u306b\u914d\u5217\u3067\u52d5\u4f5c\u3057\u307e\u3059\u3002</li> <li>\u30eb\u30c3\u30af\u30a2\u30c3\u30d7\u30c6\u30fc\u30d6\u30eb\uff1a\u914d\u5217\u306f\u8fc5\u901f\u306a\u8981\u7d20\u3084\u95a2\u4fc2\u306e\u53d6\u5f97\u306e\u305f\u3081\u306e\u52b9\u7387\u7684\u306a\u30eb\u30c3\u30af\u30a2\u30c3\u30d7\u30c6\u30fc\u30d6\u30eb\u3068\u3057\u3066\u6a5f\u80fd\u3057\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u6587\u5b57\u3092ASCII\u30b3\u30fc\u30c9\u306b\u30de\u30c3\u30d4\u30f3\u30b0\u3059\u308b\u3053\u3068\u306f\u3001ASCII\u30b3\u30fc\u30c9\u5024\u3092\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3068\u3057\u3066\u4f7f\u7528\u3057\u3001\u5bfe\u5fdc\u3059\u308b\u8981\u7d20\u3092\u914d\u5217\u306b\u683c\u7d0d\u3059\u308b\u3053\u3068\u3067\u7c21\u5358\u306b\u306a\u308a\u307e\u3059\u3002</li> <li>\u6a5f\u68b0\u5b66\u7fd2\uff1a\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u306e\u9818\u57df\u3067\u306f\u3001\u914d\u5217\u306f\u30d9\u30af\u30c8\u30eb\u3001\u884c\u5217\u3001\u30c6\u30f3\u30bd\u30eb\u3092\u542b\u3080\u91cd\u8981\u306a\u7dda\u5f62\u4ee3\u6570\u6f14\u7b97\u306e\u5b9f\u884c\u306b\u304a\u3044\u3066\u91cd\u8981\u306a\u5f79\u5272\u3092\u679c\u305f\u3057\u307e\u3059\u3002\u914d\u5217\u306f\u30cb\u30e5\u30fc\u30e9\u30eb\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u306b\u304a\u3044\u3066\u4e3b\u8981\u304b\u3064\u6700\u3082\u5e83\u7bc4\u56f2\u306b\u4f7f\u7528\u3055\u308c\u308b\u30c7\u30fc\u30bf\u69cb\u9020\u3068\u3057\u3066\u6a5f\u80fd\u3057\u307e\u3059\u3002</li> <li>\u30c7\u30fc\u30bf\u69cb\u9020\u306e\u5b9f\u88c5\uff1a\u914d\u5217\u306f\u3001\u30b9\u30bf\u30c3\u30af\u3001\u30ad\u30e5\u30fc\u3001\u30cf\u30c3\u30b7\u30e5\u8868\u3001\u30d2\u30fc\u30d7\u3001\u30b0\u30e9\u30d5\u306a\u3069\u3001\u69d8\u3005\u306a\u30c7\u30fc\u30bf\u69cb\u9020\u3092\u5b9f\u88c5\u3059\u308b\u305f\u3081\u306e\u69cb\u6210\u8981\u7d20\u3068\u3057\u3066\u6a5f\u80fd\u3057\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u30b0\u30e9\u30d5\u306e\u96a3\u63a5\u884c\u5217\u8868\u73fe\u306f\u672c\u8cea\u7684\u306b\u4e8c\u6b21\u5143\u914d\u5217\u3067\u3059\u3002</li> </ul>"},{"location":"chapter_array_and_linkedlist/linked_list/","title":"4.2 \u00a0 \u9023\u7d50\u30ea\u30b9\u30c8","text":"<p>\u30e1\u30e2\u30ea\u7a7a\u9593\u306f\u3001\u3059\u3079\u3066\u306e\u30d7\u30ed\u30b0\u30e9\u30e0\u9593\u3067\u5171\u6709\u3055\u308c\u308b\u30ea\u30bd\u30fc\u30b9\u3067\u3059\u3002\u8907\u96d1\u306a\u30b7\u30b9\u30c6\u30e0\u74b0\u5883\u3067\u306f\u3001\u4f7f\u7528\u53ef\u80fd\u306a\u30e1\u30e2\u30ea\u304c\u30e1\u30e2\u30ea\u7a7a\u9593\u5168\u4f53\u306b\u5206\u6563\u3057\u3066\u3044\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002\u914d\u5217\u306b\u5272\u308a\u5f53\u3066\u3089\u308c\u308b\u30e1\u30e2\u30ea\u306f\u9023\u7d9a\u3057\u3066\u3044\u308b\u5fc5\u8981\u304c\u3042\u308b\u3053\u3068\u3092\u7406\u89e3\u3057\u3066\u3044\u307e\u3059\u304c\u3001\u975e\u5e38\u306b\u5927\u304d\u306a\u914d\u5217\u306e\u5834\u5408\u3001\u5341\u5206\u306a\u5927\u304d\u3055\u306e\u9023\u7d9a\u30e1\u30e2\u30ea\u7a7a\u9593\u3092\u898b\u3064\u3051\u308b\u306e\u306f\u56f0\u96e3\u306a\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u3053\u3067\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u306e\u67d4\u8edf\u306a\u5229\u70b9\u304c\u660e\u3089\u304b\u306b\u306a\u308a\u307e\u3059\u3002</p> <p>\u9023\u7d50\u30ea\u30b9\u30c8\u306f\u7dda\u5f62\u30c7\u30fc\u30bf\u69cb\u9020\u3067\u3042\u308a\u3001\u5404\u8981\u7d20\u306f\u30ce\u30fc\u30c9\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u3067\u3001\u30ce\u30fc\u30c9\u306f\u300c\u53c2\u7167\u300d\u3092\u901a\u3058\u3066\u76f8\u4e92\u63a5\u7d9a\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u53c2\u7167\u306f\u5f8c\u7d9a\u30ce\u30fc\u30c9\u306e\u30e1\u30e2\u30ea\u30a2\u30c9\u30ec\u30b9\u3092\u4fdd\u6301\u3057\u30011\u3064\u306e\u30ce\u30fc\u30c9\u304b\u3089\u6b21\u306e\u30ce\u30fc\u30c9\u3078\u306e\u30ca\u30d3\u30b2\u30fc\u30b7\u30e7\u30f3\u3092\u53ef\u80fd\u306b\u3057\u307e\u3059\u3002</p> <p>\u9023\u7d50\u30ea\u30b9\u30c8\u306e\u8a2d\u8a08\u3067\u306f\u3001\u30ce\u30fc\u30c9\u3092\u9023\u7d9a\u3059\u308b\u30e1\u30e2\u30ea\u30a2\u30c9\u30ec\u30b9\u3092\u5fc5\u8981\u3068\u305b\u305a\u306b\u3001\u30e1\u30e2\u30ea\u4f4d\u7f6e\u5168\u4f53\u306b\u5206\u6563\u914d\u7f6e\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002</p> <p></p> <p> \u56f3 4-5 \u00a0 \u9023\u7d50\u30ea\u30b9\u30c8\u306e\u5b9a\u7fa9\u3068\u683c\u7d0d\u65b9\u6cd5 </p> <p>\u4e0a\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u306e\u57fa\u672c\u7684\u306a\u69cb\u6210\u8981\u7d20\u306f\u30ce\u30fc\u30c9\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u3067\u3059\u3002\u5404\u30ce\u30fc\u30c9\u306f2\u3064\u306e\u4e3b\u8981\u306a\u30b3\u30f3\u30dd\u30fc\u30cd\u30f3\u30c8\u3067\u69cb\u6210\u3055\u308c\u3066\u3044\u307e\u3059\uff1a\u30ce\u30fc\u30c9\u306e\u300c\u5024\u300d\u3068\u6b21\u306e\u30ce\u30fc\u30c9\u3078\u306e\u300c\u53c2\u7167\u300d\u3067\u3059\u3002</p> <ul> <li>\u9023\u7d50\u30ea\u30b9\u30c8\u306e\u6700\u521d\u306e\u30ce\u30fc\u30c9\u306f\u300c\u30d8\u30c3\u30c9\u30ce\u30fc\u30c9\u300d\u3001\u6700\u5f8c\u306e\u30ce\u30fc\u30c9\u306f\u300c\u30c6\u30fc\u30eb\u30ce\u30fc\u30c9\u300d\u3067\u3059\u3002</li> <li>\u30c6\u30fc\u30eb\u30ce\u30fc\u30c9\u306f\u300cnull\u300d\u3092\u6307\u3057\u3001Java\u3067\u306f<code>null</code>\u3001C++\u3067\u306f<code>nullptr</code>\u3001Python\u3067\u306f<code>None</code>\u3068\u3057\u3066\u6307\u5b9a\u3055\u308c\u307e\u3059\u3002</li> <li>C\u3001C++\u3001Go\u3001Rust\u306a\u3069\u306e\u30dd\u30a4\u30f3\u30bf\u3092\u30b5\u30dd\u30fc\u30c8\u3059\u308b\u8a00\u8a9e\u3067\u306f\u3001\u3053\u306e\u300c\u53c2\u7167\u300d\u306f\u901a\u5e38\u300c\u30dd\u30a4\u30f3\u30bf\u300d\u3068\u3057\u3066\u5b9f\u88c5\u3055\u308c\u307e\u3059\u3002</li> </ul> <p>\u4ee5\u4e0b\u306e\u30b3\u30fc\u30c9\u304c\u793a\u3059\u3088\u3046\u306b\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u306e<code>ListNode</code>\u306f\u5024\u3092\u4fdd\u6301\u3059\u308b\u3060\u3051\u3067\u306a\u304f\u3001\u8ffd\u52a0\u306e\u53c2\u7167\uff08\u307e\u305f\u306f\u30dd\u30a4\u30f3\u30bf\uff09\u3082\u7dad\u6301\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u306f\u540c\u3058\u91cf\u306e\u30c7\u30fc\u30bf\u3092\u683c\u7d0d\u3059\u308b\u5834\u5408\u3001\u914d\u5217\u3088\u308a\u3082\u591a\u304f\u306e\u30e1\u30e2\u30ea\u7a7a\u9593\u3092\u5360\u6709\u3057\u307e\u3059\u3002</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinZig <pre><code>class ListNode:\n    \"\"\"\u9023\u7d50\u30ea\u30b9\u30c8\u30ce\u30fc\u30c9\u30af\u30e9\u30b9\"\"\"\n    def __init__(self, val: int):\n        self.val: int = val               # \u30ce\u30fc\u30c9\u5024\n        self.next: ListNode | None = None # \u6b21\u306e\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\n</code></pre> <pre><code>/* \u9023\u7d50\u30ea\u30b9\u30c8\u30ce\u30fc\u30c9\u69cb\u9020\u4f53 */\nstruct ListNode {\n    int val;         // \u30ce\u30fc\u30c9\u5024\n    ListNode *next;  // \u6b21\u306e\u30ce\u30fc\u30c9\u3078\u306e\u30dd\u30a4\u30f3\u30bf\n    ListNode(int x) : val(x), next(nullptr) {}  // \u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf\n};\n</code></pre> <pre><code>/* \u9023\u7d50\u30ea\u30b9\u30c8\u30ce\u30fc\u30c9\u30af\u30e9\u30b9 */\nclass ListNode {\n    int val;        // \u30ce\u30fc\u30c9\u5024\n    ListNode next;  // \u6b21\u306e\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\n    ListNode(int x) { val = x; }  // \u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf\n}\n</code></pre> <pre><code>/* \u9023\u7d50\u30ea\u30b9\u30c8\u30ce\u30fc\u30c9\u30af\u30e9\u30b9 */\nclass ListNode(int x) {  // \u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf\n    int val = x;         // \u30ce\u30fc\u30c9\u5024\n    ListNode? next;      // \u6b21\u306e\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\n}\n</code></pre> <pre><code>/* \u9023\u7d50\u30ea\u30b9\u30c8\u30ce\u30fc\u30c9\u69cb\u9020\u4f53 */\ntype ListNode struct {\n    Val  int       // \u30ce\u30fc\u30c9\u5024\n    Next *ListNode // \u6b21\u306e\u30ce\u30fc\u30c9\u3078\u306e\u30dd\u30a4\u30f3\u30bf\n}\n\n// NewListNode \u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf\u3001\u65b0\u3057\u3044\u9023\u7d50\u30ea\u30b9\u30c8\u3092\u4f5c\u6210\nfunc NewListNode(val int) *ListNode {\n    return &amp;ListNode{\n        Val:  val,\n        Next: nil,\n    }\n}\n</code></pre> <pre><code>/* \u9023\u7d50\u30ea\u30b9\u30c8\u30ce\u30fc\u30c9\u30af\u30e9\u30b9 */\nclass ListNode {\n    var val: Int // \u30ce\u30fc\u30c9\u5024\n    var next: ListNode? // \u6b21\u306e\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\n\n    init(x: Int) { // \u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf\n        val = x\n    }\n}\n</code></pre> <pre><code>/* \u9023\u7d50\u30ea\u30b9\u30c8\u30ce\u30fc\u30c9\u30af\u30e9\u30b9 */\nclass ListNode {\n    constructor(val, next) {\n        this.val = (val === undefined ? 0 : val);       // \u30ce\u30fc\u30c9\u5024\n        this.next = (next === undefined ? null : next); // \u6b21\u306e\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\n    }\n}\n</code></pre> <pre><code>/* \u9023\u7d50\u30ea\u30b9\u30c8\u30ce\u30fc\u30c9\u30af\u30e9\u30b9 */\nclass ListNode {\n    val: number;\n    next: ListNode | null;\n    constructor(val?: number, next?: ListNode | null) {\n        this.val = val === undefined ? 0 : val;        // \u30ce\u30fc\u30c9\u5024\n        this.next = next === undefined ? null : next;  // \u6b21\u306e\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\n    }\n}\n</code></pre> <pre><code>/* \u9023\u7d50\u30ea\u30b9\u30c8\u30ce\u30fc\u30c9\u30af\u30e9\u30b9 */\nclass ListNode {\n  int val; // \u30ce\u30fc\u30c9\u5024\n  ListNode? next; // \u6b21\u306e\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\n  ListNode(this.val, [this.next]); // \u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf\n}\n</code></pre> <pre><code>use std::rc::Rc;\nuse std::cell::RefCell;\n/* \u9023\u7d50\u30ea\u30b9\u30c8\u30ce\u30fc\u30c9\u30af\u30e9\u30b9 */\n#[derive(Debug)]\nstruct ListNode {\n    val: i32, // \u30ce\u30fc\u30c9\u5024\n    next: Option&lt;Rc&lt;RefCell&lt;ListNode&gt;&gt;&gt;, // \u6b21\u306e\u30ce\u30fc\u30c9\u3078\u306e\u30dd\u30a4\u30f3\u30bf\n}\n</code></pre> <pre><code>/* \u9023\u7d50\u30ea\u30b9\u30c8\u30ce\u30fc\u30c9\u69cb\u9020\u4f53 */\ntypedef struct ListNode {\n    int val;               // \u30ce\u30fc\u30c9\u5024\n    struct ListNode *next; // \u6b21\u306e\u30ce\u30fc\u30c9\u3078\u306e\u30dd\u30a4\u30f3\u30bf\n} ListNode;\n\n/* \u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf */\nListNode *newListNode(int val) {\n    ListNode *node;\n    node = (ListNode *) malloc(sizeof(ListNode));\n    node-&gt;val = val;\n    node-&gt;next = NULL;\n    return node;\n}\n</code></pre> <pre><code>\n</code></pre> <pre><code>// \u9023\u7d50\u30ea\u30b9\u30c8\u30ce\u30fc\u30c9\u30af\u30e9\u30b9\npub fn ListNode(comptime T: type) type {\n    return struct {\n        const Self = @This();\n\n        val: T = 0, // \u30ce\u30fc\u30c9\u5024\n        next: ?*Self = null, // \u6b21\u306e\u30ce\u30fc\u30c9\u3078\u306e\u30dd\u30a4\u30f3\u30bf\n\n        // \u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf\n        pub fn init(self: *Self, x: i32) void {\n            self.val = x;\n            self.next = null;\n        }\n    };\n}\n</code></pre>"},{"location":"chapter_array_and_linkedlist/linked_list/#421","title":"4.2.1 \u00a0 \u9023\u7d50\u30ea\u30b9\u30c8\u306e\u4e00\u822c\u7684\u306a\u64cd\u4f5c","text":""},{"location":"chapter_array_and_linkedlist/linked_list/#1","title":"1. \u00a0 \u9023\u7d50\u30ea\u30b9\u30c8\u306e\u521d\u671f\u5316","text":"<p>\u9023\u7d50\u30ea\u30b9\u30c8\u306e\u69cb\u7bc9\u306f2\u6bb5\u968e\u306e\u30d7\u30ed\u30bb\u30b9\u3067\u3059\uff1a\u307e\u305a\u5404\u30ce\u30fc\u30c9\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u3092\u521d\u671f\u5316\u3057\u3001\u6b21\u306b\u30ce\u30fc\u30c9\u9593\u306e\u53c2\u7167\u30ea\u30f3\u30af\u3092\u5f62\u6210\u3057\u307e\u3059\u3002\u521d\u671f\u5316\u5f8c\u3001\u30d8\u30c3\u30c9\u30ce\u30fc\u30c9\u304b\u3089<code>next</code>\u53c2\u7167\u3092\u305f\u3069\u3063\u3066\u3059\u3079\u3066\u306e\u30ce\u30fc\u30c9\u3092\u9806\u6b21\u5de1\u56de\u3067\u304d\u307e\u3059\u3002</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinZig linked_list.py<pre><code># \u9023\u7d50\u30ea\u30b9\u30c8\u3092\u521d\u671f\u5316: 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4\n# \u5404\u30ce\u30fc\u30c9\u3092\u521d\u671f\u5316\nn0 = ListNode(1)\nn1 = ListNode(3)\nn2 = ListNode(2)\nn3 = ListNode(5)\nn4 = ListNode(4)\n# \u30ce\u30fc\u30c9\u9593\u306e\u53c2\u7167\u3092\u69cb\u7bc9\nn0.next = n1\nn1.next = n2\nn2.next = n3\nn3.next = n4\n</code></pre> linked_list.cpp<pre><code>/* \u9023\u7d50\u30ea\u30b9\u30c8\u3092\u521d\u671f\u5316: 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// \u5404\u30ce\u30fc\u30c9\u3092\u521d\u671f\u5316\nListNode* n0 = new ListNode(1);\nListNode* n1 = new ListNode(3);\nListNode* n2 = new ListNode(2);\nListNode* n3 = new ListNode(5);\nListNode* n4 = new ListNode(4);\n// \u30ce\u30fc\u30c9\u9593\u306e\u53c2\u7167\u3092\u69cb\u7bc9\nn0-&gt;next = n1;\nn1-&gt;next = n2;\nn2-&gt;next = n3;\nn3-&gt;next = n4;\n</code></pre> linked_list.java<pre><code>/* \u9023\u7d50\u30ea\u30b9\u30c8\u3092\u521d\u671f\u5316: 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// \u5404\u30ce\u30fc\u30c9\u3092\u521d\u671f\u5316\nListNode n0 = new ListNode(1);\nListNode n1 = new ListNode(3);\nListNode n2 = new ListNode(2);\nListNode n3 = new ListNode(5);\nListNode n4 = new ListNode(4);\n// \u30ce\u30fc\u30c9\u9593\u306e\u53c2\u7167\u3092\u69cb\u7bc9\nn0.next = n1;\nn1.next = n2;\nn2.next = n3;\nn3.next = n4;\n</code></pre> linked_list.cs<pre><code>/* \u9023\u7d50\u30ea\u30b9\u30c8\u3092\u521d\u671f\u5316: 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// \u5404\u30ce\u30fc\u30c9\u3092\u521d\u671f\u5316\nListNode n0 = new(1);\nListNode n1 = new(3);\nListNode n2 = new(2);\nListNode n3 = new(5);\nListNode n4 = new(4);\n// \u30ce\u30fc\u30c9\u9593\u306e\u53c2\u7167\u3092\u69cb\u7bc9\nn0.next = n1;\nn1.next = n2;\nn2.next = n3;\nn3.next = n4;\n</code></pre> linked_list.go<pre><code>/* \u9023\u7d50\u30ea\u30b9\u30c8\u3092\u521d\u671f\u5316: 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// \u5404\u30ce\u30fc\u30c9\u3092\u521d\u671f\u5316\nn0 := NewListNode(1)\nn1 := NewListNode(3)\nn2 := NewListNode(2)\nn3 := NewListNode(5)\nn4 := NewListNode(4)\n// \u30ce\u30fc\u30c9\u9593\u306e\u53c2\u7167\u3092\u69cb\u7bc9\nn0.Next = n1\nn1.Next = n2\nn2.Next = n3\nn3.Next = n4\n</code></pre> linked_list.swift<pre><code>/* \u9023\u7d50\u30ea\u30b9\u30c8\u3092\u521d\u671f\u5316: 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// \u5404\u30ce\u30fc\u30c9\u3092\u521d\u671f\u5316\nlet n0 = ListNode(x: 1)\nlet n1 = ListNode(x: 3)\nlet n2 = ListNode(x: 2)\nlet n3 = ListNode(x: 5)\nlet n4 = ListNode(x: 4)\n// \u30ce\u30fc\u30c9\u9593\u306e\u53c2\u7167\u3092\u69cb\u7bc9\nn0.next = n1\nn1.next = n2\nn2.next = n3\nn3.next = n4\n</code></pre> linked_list.js<pre><code>/* \u9023\u7d50\u30ea\u30b9\u30c8\u3092\u521d\u671f\u5316: 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// \u5404\u30ce\u30fc\u30c9\u3092\u521d\u671f\u5316\nconst n0 = new ListNode(1);\nconst n1 = new ListNode(3);\nconst n2 = new ListNode(2);\nconst n3 = new ListNode(5);\nconst n4 = new ListNode(4);\n// \u30ce\u30fc\u30c9\u9593\u306e\u53c2\u7167\u3092\u69cb\u7bc9\nn0.next = n1;\nn1.next = n2;\nn2.next = n3;\nn3.next = n4;\n</code></pre> linked_list.ts<pre><code>/* \u9023\u7d50\u30ea\u30b9\u30c8\u3092\u521d\u671f\u5316: 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// \u5404\u30ce\u30fc\u30c9\u3092\u521d\u671f\u5316\nconst n0 = new ListNode(1);\nconst n1 = new ListNode(3);\nconst n2 = new ListNode(2);\nconst n3 = new ListNode(5);\nconst n4 = new ListNode(4);\n// \u30ce\u30fc\u30c9\u9593\u306e\u53c2\u7167\u3092\u69cb\u7bc9\nn0.next = n1;\nn1.next = n2;\nn2.next = n3;\nn3.next = n4;\n</code></pre> linked_list.dart<pre><code>/* \u9023\u7d50\u30ea\u30b9\u30c8\u3092\u521d\u671f\u5316: 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// \u5404\u30ce\u30fc\u30c9\u3092\u521d\u671f\u5316\nListNode n0 = ListNode(1);\nListNode n1 = ListNode(3);\nListNode n2 = ListNode(2);\nListNode n3 = ListNode(5);\nListNode n4 = ListNode(4);\n// \u30ce\u30fc\u30c9\u9593\u306e\u53c2\u7167\u3092\u69cb\u7bc9\nn0.next = n1;\nn1.next = n2;\nn2.next = n3;\nn3.next = n4;\n</code></pre> linked_list.rs<pre><code>/* \u9023\u7d50\u30ea\u30b9\u30c8\u3092\u521d\u671f\u5316: 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// \u5404\u30ce\u30fc\u30c9\u3092\u521d\u671f\u5316\nlet n0 = Rc::new(RefCell::new(ListNode { val: 1, next: None }));\nlet n1 = Rc::new(RefCell::new(ListNode { val: 3, next: None }));\nlet n2 = Rc::new(RefCell::new(ListNode { val: 2, next: None }));\nlet n3 = Rc::new(RefCell::new(ListNode { val: 5, next: None }));\nlet n4 = Rc::new(RefCell::new(ListNode { val: 4, next: None }));\n\n// \u30ce\u30fc\u30c9\u9593\u306e\u53c2\u7167\u3092\u69cb\u7bc9\nn0.borrow_mut().next = Some(n1.clone());\nn1.borrow_mut().next = Some(n2.clone());\nn2.borrow_mut().next = Some(n3.clone());\nn3.borrow_mut().next = Some(n4.clone());\n</code></pre> linked_list.c<pre><code>/* \u9023\u7d50\u30ea\u30b9\u30c8\u3092\u521d\u671f\u5316: 1 -&gt; 3 -&gt; 2 -&gt; 5 -&gt; 4 */\n// \u5404\u30ce\u30fc\u30c9\u3092\u521d\u671f\u5316\nListNode* n0 = newListNode(1);\nListNode* n1 = newListNode(3);\nListNode* n2 = newListNode(2);\nListNode* n3 = newListNode(5);\nListNode* n4 = newListNode(4);\n// \u30ce\u30fc\u30c9\u9593\u306e\u53c2\u7167\u3092\u69cb\u7bc9\nn0-&gt;next = n1;\nn1-&gt;next = n2;\nn2-&gt;next = n3;\nn3-&gt;next = n4;\n</code></pre> linked_list.kt<pre><code>\n</code></pre> linked_list.zig<pre><code>// \u9023\u7d50\u30ea\u30b9\u30c8\u3092\u521d\u671f\u5316\n// \u5404\u30ce\u30fc\u30c9\u3092\u521d\u671f\u5316\nvar n0 = inc.ListNode(i32){.val = 1};\nvar n1 = inc.ListNode(i32){.val = 3};\nvar n2 = inc.ListNode(i32){.val = 2};\nvar n3 = inc.ListNode(i32){.val = 5};\nvar n4 = inc.ListNode(i32){.val = 4};\n// \u30ce\u30fc\u30c9\u9593\u306e\u53c2\u7167\u3092\u69cb\u7bc9\nn0.next = &amp;n1;\nn1.next = &amp;n2;\nn2.next = &amp;n3;\nn3.next = &amp;n4;\n</code></pre> <p>\u914d\u5217\u5168\u4f53\u306f1\u3064\u306e\u5909\u6570\u3067\u3059\u3002\u4f8b\u3048\u3070\u3001\u914d\u5217<code>nums</code>\u306b\u306f<code>nums[0]</code>\u3001<code>nums[1]</code>\u306a\u3069\u306e\u8981\u7d20\u304c\u542b\u307e\u308c\u307e\u3059\u304c\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u306f\u8907\u6570\u306e\u7570\u306a\u308b\u30ce\u30fc\u30c9\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u3067\u69cb\u6210\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u901a\u5e38\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u306f\u305d\u306e\u30d8\u30c3\u30c9\u30ce\u30fc\u30c9\u3067\u53c2\u7167\u3055\u308c\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u524d\u306e\u30b3\u30fc\u30c9\u30b9\u30cb\u30da\u30c3\u30c8\u306e\u9023\u7d50\u30ea\u30b9\u30c8\u306f<code>n0</code>\u3068\u3057\u3066\u53c2\u7167\u3055\u308c\u307e\u3059\u3002</p>"},{"location":"chapter_array_and_linkedlist/linked_list/#2","title":"2. \u00a0 \u30ce\u30fc\u30c9\u306e\u633f\u5165","text":"<p>\u9023\u7d50\u30ea\u30b9\u30c8\u306b\u30ce\u30fc\u30c9\u3092\u633f\u5165\u3059\u308b\u306e\u306f\u975e\u5e38\u306b\u7c21\u5358\u3067\u3059\u3002\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u96a3\u63a5\u3059\u308b2\u3064\u306e\u30ce\u30fc\u30c9<code>n0</code>\u3068<code>n1</code>\u306e\u9593\u306b\u65b0\u3057\u3044\u30ce\u30fc\u30c9<code>P</code>\u3092\u633f\u5165\u3059\u308b\u3053\u3068\u3092\u76ee\u6307\u3059\u3068\u3057\u307e\u3059\u3002\u3053\u308c\u306f2\u3064\u306e\u30ce\u30fc\u30c9\u53c2\u7167\uff08\u30dd\u30a4\u30f3\u30bf\uff09\u3092\u5909\u66f4\u3059\u308b\u3060\u3051\u3067\u5b9f\u73fe\u3067\u304d\u3001\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O(1)\\)\u3067\u3059\u3002</p> <p>\u6bd4\u8f03\u3059\u308b\u3068\u3001\u914d\u5217\u306b\u8981\u7d20\u3092\u633f\u5165\u3059\u308b\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O(n)\\)\u3067\u3042\u308a\u3001\u5927\u91cf\u306e\u30c7\u30fc\u30bf\u3092\u6271\u3046\u5834\u5408\u306b\u306f\u52b9\u7387\u304c\u60aa\u304f\u306a\u308a\u307e\u3059\u3002</p> <p></p> <p> \u56f3 4-6 \u00a0 \u9023\u7d50\u30ea\u30b9\u30c8\u30ce\u30fc\u30c9\u633f\u5165\u306e\u4f8b </p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig linked_list.py<pre><code>def insert(n0: ListNode, P: ListNode):\n    \"\"\"\u9023\u7d50\u30ea\u30b9\u30c8\u306e\u30ce\u30fc\u30c9 n0 \u306e\u5f8c\u306b\u30ce\u30fc\u30c9 P \u3092\u633f\u5165\"\"\"\n    n1 = n0.next\n    P.next = n1\n    n0.next = P\n</code></pre> linked_list.cpp<pre><code>/* \u9023\u7d50\u30ea\u30b9\u30c8\u306e\u30ce\u30fc\u30c9n0\u306e\u5f8c\u306b\u30ce\u30fc\u30c9P\u3092\u633f\u5165 */\nvoid insert(ListNode *n0, ListNode *P) {\n    ListNode *n1 = n0-&gt;next;\n    P-&gt;next = n1;\n    n0-&gt;next = P;\n}\n</code></pre> linked_list.java<pre><code>/* \u9023\u7d50\u30ea\u30b9\u30c8\u3067\u30ce\u30fc\u30c9 n0 \u306e\u5f8c\u306b\u30ce\u30fc\u30c9 P \u3092\u633f\u5165 */\nvoid insert(ListNode n0, ListNode P) {\n    ListNode n1 = n0.next;\n    P.next = n1;\n    n0.next = P;\n}\n</code></pre> linked_list.cs<pre><code>[class]{linked_list}-[func]{Insert}\n</code></pre> linked_list.go<pre><code>[class]{}-[func]{insertNode}\n</code></pre> linked_list.swift<pre><code>[class]{}-[func]{insert}\n</code></pre> linked_list.js<pre><code>[class]{}-[func]{insert}\n</code></pre> linked_list.ts<pre><code>[class]{}-[func]{insert}\n</code></pre> linked_list.dart<pre><code>[class]{}-[func]{insert}\n</code></pre> linked_list.rs<pre><code>[class]{}-[func]{insert}\n</code></pre> linked_list.c<pre><code>[class]{}-[func]{insert}\n</code></pre> linked_list.kt<pre><code>[class]{}-[func]{insert}\n</code></pre> linked_list.rb<pre><code>[class]{}-[func]{insert}\n</code></pre> linked_list.zig<pre><code>[class]{}-[func]{insert}\n</code></pre>"},{"location":"chapter_array_and_linkedlist/linked_list/#3","title":"3. \u00a0 \u30ce\u30fc\u30c9\u306e\u524a\u9664","text":"<p>\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u304b\u3089\u30ce\u30fc\u30c9\u3092\u524a\u9664\u3059\u308b\u3053\u3068\u3082\u975e\u5e38\u306b\u7c21\u5358\u3067\u30011\u3064\u306e\u30ce\u30fc\u30c9\u306e\u53c2\u7167\uff08\u30dd\u30a4\u30f3\u30bf\uff09\u3092\u5909\u66f4\u3059\u308b\u3060\u3051\u3067\u3059\u3002</p> <p>\u91cd\u8981\u306a\u70b9\u306f\u3001\u30ce\u30fc\u30c9<code>P</code>\u304c\u524a\u9664\u3055\u308c\u305f\u5f8c\u3082<code>n1</code>\u3092\u6307\u3057\u7d9a\u3051\u3066\u3044\u308b\u3053\u3068\u3067\u3059\u304c\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u306e\u5de1\u56de\u4e2d\u306b\u306f\u30a2\u30af\u30bb\u30b9\u3067\u304d\u306a\u304f\u306a\u308b\u3053\u3068\u3067\u3059\u3002\u3053\u308c\u306f\u4e8b\u5b9f\u4e0a\u3001<code>P</code>\u304c\u9023\u7d50\u30ea\u30b9\u30c8\u306e\u4e00\u90e8\u3067\u306f\u306a\u304f\u306a\u3063\u305f\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002</p> <p></p> <p> \u56f3 4-7 \u00a0 \u9023\u7d50\u30ea\u30b9\u30c8\u30ce\u30fc\u30c9\u306e\u524a\u9664 </p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig linked_list.py<pre><code>def remove(n0: ListNode):\n    \"\"\"\u9023\u7d50\u30ea\u30b9\u30c8\u306e\u30ce\u30fc\u30c9 n0 \u306e\u5f8c\u306e\u6700\u521d\u306e\u30ce\u30fc\u30c9\u3092\u524a\u9664\"\"\"\n    if not n0.next:\n        return\n    # n0 -&gt; P -&gt; n1\n    P = n0.next\n    n1 = P.next\n    n0.next = n1\n</code></pre> linked_list.cpp<pre><code>/* \u9023\u7d50\u30ea\u30b9\u30c8\u306e\u30ce\u30fc\u30c9n0\u306e\u5f8c\u306e\u6700\u521d\u306e\u30ce\u30fc\u30c9\u3092\u524a\u9664 */\nvoid remove(ListNode *n0) {\n    if (n0-&gt;next == nullptr)\n        return;\n    // n0 -&gt; P -&gt; n1\n    ListNode *P = n0-&gt;next;\n    ListNode *n1 = P-&gt;next;\n    n0-&gt;next = n1;\n    // \u30e1\u30e2\u30ea\u3092\u89e3\u653e\n    delete P;\n}\n</code></pre> linked_list.java<pre><code>/* \u9023\u7d50\u30ea\u30b9\u30c8\u3067\u30ce\u30fc\u30c9 n0 \u306e\u5f8c\u306e\u6700\u521d\u306e\u30ce\u30fc\u30c9\u3092\u524a\u9664 */\nvoid remove(ListNode n0) {\n    if (n0.next == null)\n        return;\n    // n0 -&gt; P -&gt; n1\n    ListNode P = n0.next;\n    ListNode n1 = P.next;\n    n0.next = n1;\n}\n</code></pre> linked_list.cs<pre><code>[class]{linked_list}-[func]{Remove}\n</code></pre> linked_list.go<pre><code>[class]{}-[func]{removeItem}\n</code></pre> linked_list.swift<pre><code>[class]{}-[func]{remove}\n</code></pre> linked_list.js<pre><code>[class]{}-[func]{remove}\n</code></pre> linked_list.ts<pre><code>[class]{}-[func]{remove}\n</code></pre> linked_list.dart<pre><code>[class]{}-[func]{remove}\n</code></pre> linked_list.rs<pre><code>[class]{}-[func]{remove}\n</code></pre> linked_list.c<pre><code>[class]{}-[func]{removeItem}\n</code></pre> linked_list.kt<pre><code>[class]{}-[func]{remove}\n</code></pre> linked_list.rb<pre><code>[class]{}-[func]{remove}\n</code></pre> linked_list.zig<pre><code>[class]{}-[func]{remove}\n</code></pre>"},{"location":"chapter_array_and_linkedlist/linked_list/#4","title":"4. \u00a0 \u30ce\u30fc\u30c9\u3078\u306e\u30a2\u30af\u30bb\u30b9","text":"<p>\u9023\u7d50\u30ea\u30b9\u30c8\u3067\u306e\u30ce\u30fc\u30c9\u3078\u306e\u30a2\u30af\u30bb\u30b9\u306f\u52b9\u7387\u304c\u60aa\u3044\u3067\u3059\u3002\u524d\u8ff0\u3057\u305f\u3088\u3046\u306b\u3001\u914d\u5217\u306e\u4efb\u610f\u306e\u8981\u7d20\u306b\u306f\\(O(1)\\)\u6642\u9593\u3067\u30a2\u30af\u30bb\u30b9\u3067\u304d\u307e\u3059\u3002\u5bfe\u7167\u7684\u306b\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u3067\u306f\u3001\u30d7\u30ed\u30b0\u30e9\u30e0\u306f\u30d8\u30c3\u30c9\u30ce\u30fc\u30c9\u304b\u3089\u958b\u59cb\u3057\u3066\u76ee\u7684\u306e\u30ce\u30fc\u30c9\u304c\u898b\u3064\u304b\u308b\u307e\u3067\u9806\u6b21\u30ce\u30fc\u30c9\u3092\u5de1\u56de\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u306e\\(i\\)\u756a\u76ee\u306e\u30ce\u30fc\u30c9\u306b\u30a2\u30af\u30bb\u30b9\u3059\u308b\u306b\u306f\u3001\u30d7\u30ed\u30b0\u30e9\u30e0\u306f\\(i - 1\\)\u500b\u306e\u30ce\u30fc\u30c9\u3092\u53cd\u5fa9\u51e6\u7406\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u3001\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O(n)\\)\u306b\u306a\u308a\u307e\u3059\u3002</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig linked_list.py<pre><code>def access(head: ListNode, index: int) -&gt; ListNode | None:\n    \"\"\"\u9023\u7d50\u30ea\u30b9\u30c8\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9 index \u306e\u30ce\u30fc\u30c9\u306b\u30a2\u30af\u30bb\u30b9\"\"\"\n    for _ in range(index):\n        if not head:\n            return None\n        head = head.next\n    return head\n</code></pre> linked_list.cpp<pre><code>/* \u9023\u7d50\u30ea\u30b9\u30c8\u306e`index`\u756a\u76ee\u306e\u30ce\u30fc\u30c9\u306b\u30a2\u30af\u30bb\u30b9 */\nListNode *access(ListNode *head, int index) {\n    for (int i = 0; i &lt; index; i++) {\n        if (head == nullptr)\n            return nullptr;\n        head = head-&gt;next;\n    }\n    return head;\n}\n</code></pre> linked_list.java<pre><code>/* \u9023\u7d50\u30ea\u30b9\u30c8\u306e `index` \u306e\u30ce\u30fc\u30c9\u306b\u30a2\u30af\u30bb\u30b9 */\nListNode access(ListNode head, int index) {\n    for (int i = 0; i &lt; index; i++) {\n        if (head == null)\n            return null;\n        head = head.next;\n    }\n    return head;\n}\n</code></pre> linked_list.cs<pre><code>[class]{linked_list}-[func]{Access}\n</code></pre> linked_list.go<pre><code>[class]{}-[func]{access}\n</code></pre> linked_list.swift<pre><code>[class]{}-[func]{access}\n</code></pre> linked_list.js<pre><code>[class]{}-[func]{access}\n</code></pre> linked_list.ts<pre><code>[class]{}-[func]{access}\n</code></pre> linked_list.dart<pre><code>[class]{}-[func]{access}\n</code></pre> linked_list.rs<pre><code>[class]{}-[func]{access}\n</code></pre> linked_list.c<pre><code>[class]{}-[func]{access}\n</code></pre> linked_list.kt<pre><code>[class]{}-[func]{access}\n</code></pre> linked_list.rb<pre><code>[class]{}-[func]{access}\n</code></pre> linked_list.zig<pre><code>[class]{}-[func]{access}\n</code></pre>"},{"location":"chapter_array_and_linkedlist/linked_list/#5","title":"5. \u00a0 \u30ce\u30fc\u30c9\u306e\u691c\u7d22","text":"<p>\u9023\u7d50\u30ea\u30b9\u30c8\u3092\u5de1\u56de\u3057\u3066\u3001\u5024\u304c<code>target</code>\u306b\u4e00\u81f4\u3059\u308b\u30ce\u30fc\u30c9\u3092\u898b\u3064\u3051\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u5185\u3067\u306e\u305d\u306e\u30ce\u30fc\u30c9\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u51fa\u529b\u3057\u307e\u3059\u3002\u3053\u306e\u624b\u9806\u3082\u7dda\u5f62\u691c\u7d22\u306e\u4f8b\u3067\u3059\u3002\u5bfe\u5fdc\u3059\u308b\u30b3\u30fc\u30c9\u306f\u4ee5\u4e0b\u306e\u3068\u304a\u308a\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig linked_list.py<pre><code>def find(head: ListNode, target: int) -&gt; int:\n    \"\"\"\u9023\u7d50\u30ea\u30b9\u30c8\u3067\u5024 target \u3092\u6301\u3064\u6700\u521d\u306e\u30ce\u30fc\u30c9\u3092\u691c\u7d22\"\"\"\n    index = 0\n    while head:\n        if head.val == target:\n            return index\n        head = head.next\n        index += 1\n    return -1\n</code></pre> linked_list.cpp<pre><code>/* \u9023\u7d50\u30ea\u30b9\u30c8\u3067\u5024\u304ctarget\u306e\u6700\u521d\u306e\u30ce\u30fc\u30c9\u3092\u691c\u7d22 */\nint find(ListNode *head, int target) {\n    int index = 0;\n    while (head != nullptr) {\n        if (head-&gt;val == target)\n            return index;\n        head = head-&gt;next;\n        index++;\n    }\n    return -1;\n}\n</code></pre> linked_list.java<pre><code>/* \u9023\u7d50\u30ea\u30b9\u30c8\u3067\u5024 target \u3092\u6301\u3064\u6700\u521d\u306e\u30ce\u30fc\u30c9\u3092\u691c\u7d22 */\nint find(ListNode head, int target) {\n    int index = 0;\n    while (head != null) {\n        if (head.val == target)\n            return index;\n        head = head.next;\n        index++;\n    }\n    return -1;\n}\n</code></pre> linked_list.cs<pre><code>[class]{linked_list}-[func]{Find}\n</code></pre> linked_list.go<pre><code>[class]{}-[func]{findNode}\n</code></pre> linked_list.swift<pre><code>[class]{}-[func]{find}\n</code></pre> linked_list.js<pre><code>[class]{}-[func]{find}\n</code></pre> linked_list.ts<pre><code>[class]{}-[func]{find}\n</code></pre> linked_list.dart<pre><code>[class]{}-[func]{find}\n</code></pre> linked_list.rs<pre><code>[class]{}-[func]{find}\n</code></pre> linked_list.c<pre><code>[class]{}-[func]{find}\n</code></pre> linked_list.kt<pre><code>[class]{}-[func]{find}\n</code></pre> linked_list.rb<pre><code>[class]{}-[func]{find}\n</code></pre> linked_list.zig<pre><code>[class]{}-[func]{find}\n</code></pre>"},{"location":"chapter_array_and_linkedlist/linked_list/#422-vs","title":"4.2.2 \u00a0 \u914d\u5217 vs. \u9023\u7d50\u30ea\u30b9\u30c8","text":"<p>\u4e0b\u8868\u306f\u914d\u5217\u3068\u9023\u7d50\u30ea\u30b9\u30c8\u306e\u7279\u6027\u3092\u307e\u3068\u3081\u3001\u69d8\u3005\u306a\u64cd\u4f5c\u306b\u304a\u3051\u308b\u52b9\u7387\u3082\u6bd4\u8f03\u3057\u3066\u3044\u307e\u3059\u3002\u305d\u308c\u305e\u308c\u304c\u5bfe\u7167\u7684\u306a\u683c\u7d0d\u6226\u7565\u3092\u4f7f\u7528\u3059\u308b\u305f\u3081\u3001\u305d\u308c\u305e\u308c\u306e\u7279\u6027\u3068\u64cd\u4f5c\u52b9\u7387\u306f\u660e\u78ba\u306b\u5bfe\u6bd4\u3055\u308c\u3066\u3044\u307e\u3059\u3002</p> <p> \u8868 4-1 \u00a0 \u914d\u5217\u3068\u9023\u7d50\u30ea\u30b9\u30c8\u306e\u52b9\u7387\u6bd4\u8f03 </p> \u914d\u5217 \u9023\u7d50\u30ea\u30b9\u30c8 \u683c\u7d0d\u65b9\u5f0f \u9023\u7d9a\u30e1\u30e2\u30ea\u7a7a\u9593 \u5206\u6563\u30e1\u30e2\u30ea\u7a7a\u9593 \u5bb9\u91cf\u62e1\u5f35 \u56fa\u5b9a\u9577 \u67d4\u8edf\u306a\u62e1\u5f35 \u30e1\u30e2\u30ea\u52b9\u7387 \u8981\u7d20\u3042\u305f\u308a\u306e\u30e1\u30e2\u30ea\u5c11\u3001\u6f5c\u5728\u7684\u306a\u7a7a\u9593\u306e\u7121\u99c4 \u8981\u7d20\u3042\u305f\u308a\u306e\u30e1\u30e2\u30ea\u591a \u8981\u7d20\u3078\u306e\u30a2\u30af\u30bb\u30b9 \\(O(1)\\) \\(O(n)\\) \u8981\u7d20\u306e\u8ffd\u52a0 \\(O(n)\\) \\(O(1)\\) \u8981\u7d20\u306e\u524a\u9664 \\(O(n)\\) \\(O(1)\\)"},{"location":"chapter_array_and_linkedlist/linked_list/#423","title":"4.2.3 \u00a0 \u9023\u7d50\u30ea\u30b9\u30c8\u306e\u4e00\u822c\u7684\u306a\u7a2e\u985e","text":"<p>\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u306b\u306f3\u3064\u306e\u4e00\u822c\u7684\u306a\u7a2e\u985e\u304c\u3042\u308a\u307e\u3059\u3002</p> <ul> <li>\u5358\u65b9\u5411\u9023\u7d50\u30ea\u30b9\u30c8\uff1a\u3053\u308c\u306f\u524d\u8ff0\u3057\u305f\u6a19\u6e96\u7684\u306a\u9023\u7d50\u30ea\u30b9\u30c8\u3067\u3059\u3002\u5358\u65b9\u5411\u9023\u7d50\u30ea\u30b9\u30c8\u306e\u30ce\u30fc\u30c9\u306b\u306f\u5024\u3068\u6b21\u306e\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\u304c\u542b\u307e\u308c\u307e\u3059\u3002\u6700\u521d\u306e\u30ce\u30fc\u30c9\u306f\u30d8\u30c3\u30c9\u30ce\u30fc\u30c9\u3068\u547c\u3070\u308c\u3001null\uff08<code>None</code>\uff09\u3092\u6307\u3059\u6700\u5f8c\u306e\u30ce\u30fc\u30c9\u306f\u30c6\u30fc\u30eb\u30ce\u30fc\u30c9\u3067\u3059\u3002</li> <li>\u5faa\u74b0\u9023\u7d50\u30ea\u30b9\u30c8\uff1a\u3053\u308c\u306f\u5358\u65b9\u5411\u9023\u7d50\u30ea\u30b9\u30c8\u306e\u30c6\u30fc\u30eb\u30ce\u30fc\u30c9\u304c\u30d8\u30c3\u30c9\u30ce\u30fc\u30c9\u3092\u6307\u3057\u3066\u30eb\u30fc\u30d7\u3092\u4f5c\u308b\u3053\u3068\u3067\u5f62\u6210\u3055\u308c\u307e\u3059\u3002\u5faa\u74b0\u9023\u7d50\u30ea\u30b9\u30c8\u3067\u306f\u3001\u4efb\u610f\u306e\u30ce\u30fc\u30c9\u304c\u30d8\u30c3\u30c9\u30ce\u30fc\u30c9\u3068\u3057\u3066\u6a5f\u80fd\u3067\u304d\u307e\u3059\u3002</li> <li>\u53cc\u65b9\u5411\u9023\u7d50\u30ea\u30b9\u30c8\uff1a\u5358\u65b9\u5411\u9023\u7d50\u30ea\u30b9\u30c8\u3068\u306f\u5bfe\u7167\u7684\u306b\u3001\u53cc\u65b9\u5411\u9023\u7d50\u30ea\u30b9\u30c8\u306f2\u3064\u306e\u65b9\u5411\u3067\u53c2\u7167\u3092\u7dad\u6301\u3057\u307e\u3059\u3002\u5404\u30ce\u30fc\u30c9\u306b\u306f\u5f8c\u7d9a\u8005\uff08\u6b21\u306e\u30ce\u30fc\u30c9\uff09\u3068\u524d\u4efb\u8005\uff08\u524d\u306e\u30ce\u30fc\u30c9\uff09\u306e\u4e21\u65b9\u3078\u306e\u53c2\u7167\uff08\u30dd\u30a4\u30f3\u30bf\uff09\u304c\u542b\u307e\u308c\u307e\u3059\u3002\u53cc\u65b9\u5411\u9023\u7d50\u30ea\u30b9\u30c8\u306f\u3069\u3061\u3089\u306e\u65b9\u5411\u306b\u3082\u5de1\u56de\u3067\u304d\u308b\u3088\u308a\u591a\u304f\u306e\u67d4\u8edf\u6027\u3092\u63d0\u4f9b\u3057\u307e\u3059\u304c\u3001\u3088\u308a\u591a\u304f\u306e\u30e1\u30e2\u30ea\u7a7a\u9593\u3082\u6d88\u8cbb\u3057\u307e\u3059\u3002</li> </ul> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinZig <pre><code>class ListNode:\n    \"\"\"\u53cc\u65b9\u5411\u9023\u7d50\u30ea\u30b9\u30c8\u30ce\u30fc\u30c9\u30af\u30e9\u30b9\"\"\"\n    def __init__(self, val: int):\n        self.val: int = val                # \u30ce\u30fc\u30c9\u5024\n        self.next: ListNode | None = None  # \u5f8c\u7d9a\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\n        self.prev: ListNode | None = None  # \u524d\u4efb\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\n</code></pre> <pre><code>/* \u53cc\u65b9\u5411\u9023\u7d50\u30ea\u30b9\u30c8\u30ce\u30fc\u30c9\u69cb\u9020\u4f53 */\nstruct ListNode {\n    int val;         // \u30ce\u30fc\u30c9\u5024\n    ListNode *next;  // \u5f8c\u7d9a\u30ce\u30fc\u30c9\u3078\u306e\u30dd\u30a4\u30f3\u30bf\n    ListNode *prev;  // \u524d\u4efb\u30ce\u30fc\u30c9\u3078\u306e\u30dd\u30a4\u30f3\u30bf\n    ListNode(int x) : val(x), next(nullptr), prev(nullptr) {}  // \u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf\n};\n</code></pre> <pre><code>/* \u53cc\u65b9\u5411\u9023\u7d50\u30ea\u30b9\u30c8\u30ce\u30fc\u30c9\u30af\u30e9\u30b9 */\nclass ListNode {\n    int val;        // \u30ce\u30fc\u30c9\u5024\n    ListNode next;  // \u6b21\u306e\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\n    ListNode prev;  // \u524d\u4efb\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\n    ListNode(int x) { val = x; }  // \u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf\n}\n</code></pre> <pre><code>/* \u53cc\u65b9\u5411\u9023\u7d50\u30ea\u30b9\u30c8\u30ce\u30fc\u30c9\u30af\u30e9\u30b9 */\nclass ListNode(int x) {  // \u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf\n    int val = x;    // \u30ce\u30fc\u30c9\u5024\n    ListNode next;  // \u6b21\u306e\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\n    ListNode prev;  // \u524d\u4efb\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\n}\n</code></pre> <pre><code>/* \u53cc\u65b9\u5411\u9023\u7d50\u30ea\u30b9\u30c8\u30ce\u30fc\u30c9\u69cb\u9020\u4f53 */\ntype DoublyListNode struct {\n    Val  int             // \u30ce\u30fc\u30c9\u5024\n    Next *DoublyListNode // \u5f8c\u7d9a\u30ce\u30fc\u30c9\u3078\u306e\u30dd\u30a4\u30f3\u30bf\n    Prev *DoublyListNode // \u524d\u4efb\u30ce\u30fc\u30c9\u3078\u306e\u30dd\u30a4\u30f3\u30bf\n}\n\n// NewDoublyListNode \u521d\u671f\u5316\nfunc NewDoublyListNode(val int) *DoublyListNode {\n    return &amp;DoublyListNode{\n        Val:  val,\n        Next: nil,\n        Prev: nil,\n    }\n}\n</code></pre> <pre><code>/* \u53cc\u65b9\u5411\u9023\u7d50\u30ea\u30b9\u30c8\u30ce\u30fc\u30c9\u30af\u30e9\u30b9 */\nclass ListNode {\n    var val: Int // \u30ce\u30fc\u30c9\u5024\n    var next: ListNode? // \u6b21\u306e\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\n    var prev: ListNode? // \u524d\u4efb\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\n\n    init(x: Int) { // \u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf\n        val = x\n    }\n}\n</code></pre> <pre><code>/* \u53cc\u65b9\u5411\u9023\u7d50\u30ea\u30b9\u30c8\u30ce\u30fc\u30c9\u30af\u30e9\u30b9 */\nclass ListNode {\n    constructor(val, next, prev) {\n        this.val = val  ===  undefined ? 0 : val;        // \u30ce\u30fc\u30c9\u5024\n        this.next = next  ===  undefined ? null : next;  // \u5f8c\u7d9a\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\n        this.prev = prev  ===  undefined ? null : prev;  // \u524d\u4efb\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\n    }\n}\n</code></pre> <pre><code>/* \u53cc\u65b9\u5411\u9023\u7d50\u30ea\u30b9\u30c8\u30ce\u30fc\u30c9\u30af\u30e9\u30b9 */\nclass ListNode {\n    val: number;\n    next: ListNode | null;\n    prev: ListNode | null;\n    constructor(val?: number, next?: ListNode | null, prev?: ListNode | null) {\n        this.val = val  ===  undefined ? 0 : val;        // \u30ce\u30fc\u30c9\u5024\n        this.next = next  ===  undefined ? null : next;  // \u5f8c\u7d9a\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\n        this.prev = prev  ===  undefined ? null : prev;  // \u524d\u4efb\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\n    }\n}\n</code></pre> <pre><code>/* \u53cc\u65b9\u5411\u9023\u7d50\u30ea\u30b9\u30c8\u30ce\u30fc\u30c9\u30af\u30e9\u30b9 */\nclass ListNode {\n    int val;        // \u30ce\u30fc\u30c9\u5024\n    ListNode next;  // \u6b21\u306e\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\n    ListNode prev;  // \u524d\u4efb\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\n    ListNode(this.val, [this.next, this.prev]);  // \u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf\n}\n</code></pre> <pre><code>use std::rc::Rc;\nuse std::cell::RefCell;\n\n/* \u53cc\u65b9\u5411\u9023\u7d50\u30ea\u30b9\u30c8\u30ce\u30fc\u30c9\u578b */\n#[derive(Debug)]\nstruct ListNode {\n    val: i32, // \u30ce\u30fc\u30c9\u5024\n    next: Option&lt;Rc&lt;RefCell&lt;ListNode&gt;&gt;&gt;, // \u5f8c\u7d9a\u30ce\u30fc\u30c9\u3078\u306e\u30dd\u30a4\u30f3\u30bf\n    prev: Option&lt;Rc&lt;RefCell&lt;ListNode&gt;&gt;&gt;, // \u524d\u4efb\u30ce\u30fc\u30c9\u3078\u306e\u30dd\u30a4\u30f3\u30bf\n}\n\n/* \u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf */\nimpl ListNode {\n    fn new(val: i32) -&gt; Self {\n        ListNode {\n            val,\n            next: None,\n            prev: None,\n        }\n    }\n}\n</code></pre> <pre><code>/* \u53cc\u65b9\u5411\u9023\u7d50\u30ea\u30b9\u30c8\u30ce\u30fc\u30c9\u69cb\u9020\u4f53 */\ntypedef struct ListNode {\n    int val;               // \u30ce\u30fc\u30c9\u5024\n    struct ListNode *next; // \u5f8c\u7d9a\u30ce\u30fc\u30c9\u3078\u306e\u30dd\u30a4\u30f3\u30bf\n    struct ListNode *prev; // \u524d\u4efb\u30ce\u30fc\u30c9\u3078\u306e\u30dd\u30a4\u30f3\u30bf\n} ListNode;\n\n/* \u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf */\nListNode *newListNode(int val) {\n    ListNode *node, *next;\n    node = (ListNode *) malloc(sizeof(ListNode));\n    node-&gt;val = val;\n    node-&gt;next = NULL;\n    node-&gt;prev = NULL;\n    return node;\n}\n</code></pre> <pre><code>\n</code></pre> <pre><code>// \u53cc\u65b9\u5411\u9023\u7d50\u30ea\u30b9\u30c8\u30ce\u30fc\u30c9\u30af\u30e9\u30b9\npub fn ListNode(comptime T: type) type {\n    return struct {\n        const Self = @This();\n\n        val: T = 0, // \u30ce\u30fc\u30c9\u5024\n        next: ?*Self = null, // \u5f8c\u7d9a\u30ce\u30fc\u30c9\u3078\u306e\u30dd\u30a4\u30f3\u30bf\n        prev: ?*Self = null, // \u524d\u4efb\u30ce\u30fc\u30c9\u3078\u306e\u30dd\u30a4\u30f3\u30bf\n\n        // \u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf\n        pub fn init(self: *Self, x: i32) void {\n            self.val = x;\n            self.next = null;\n            self.prev = null;\n        }\n    };\n}\n</code></pre> <p></p> <p> \u56f3 4-8 \u00a0 \u9023\u7d50\u30ea\u30b9\u30c8\u306e\u4e00\u822c\u7684\u306a\u7a2e\u985e </p>"},{"location":"chapter_array_and_linkedlist/linked_list/#424","title":"4.2.4 \u00a0 \u9023\u7d50\u30ea\u30b9\u30c8\u306e\u5178\u578b\u7684\u306a\u5fdc\u7528","text":"<p>\u5358\u65b9\u5411\u9023\u7d50\u30ea\u30b9\u30c8\u306f\u3001\u30b9\u30bf\u30c3\u30af\u3001\u30ad\u30e5\u30fc\u3001\u30cf\u30c3\u30b7\u30e5\u8868\u3001\u30b0\u30e9\u30d5\u306e\u5b9f\u88c5\u306b\u3088\u304f\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002</p> <ul> <li>\u30b9\u30bf\u30c3\u30af\u3068\u30ad\u30e5\u30fc\uff1a\u5358\u65b9\u5411\u9023\u7d50\u30ea\u30b9\u30c8\u3067\u3001\u633f\u5165\u3068\u524a\u9664\u304c\u540c\u3058\u7aef\u3067\u884c\u308f\u308c\u308b\u5834\u5408\u3001\u30b9\u30bf\u30c3\u30af\uff08\u5f8c\u5165\u5148\u51fa\uff09\u306e\u3088\u3046\u306b\u52d5\u4f5c\u3057\u307e\u3059\u3002\u9006\u306b\u3001\u633f\u5165\u304c\u4e00\u65b9\u306e\u7aef\u3067\u3001\u524a\u9664\u304c\u3082\u3046\u4e00\u65b9\u306e\u7aef\u3067\u884c\u308f\u308c\u308b\u5834\u5408\u3001\u30ad\u30e5\u30fc\uff08\u5148\u5165\u5148\u51fa\uff09\u306e\u3088\u3046\u306b\u6a5f\u80fd\u3057\u307e\u3059\u3002</li> <li>\u30cf\u30c3\u30b7\u30e5\u8868\uff1a\u9023\u7d50\u30ea\u30b9\u30c8\u306f\u3001\u30cf\u30c3\u30b7\u30e5\u885d\u7a81\u3092\u89e3\u6c7a\u3059\u308b\u4eba\u6c17\u306e\u65b9\u6cd5\u3067\u3042\u308b\u9023\u9396\u6cd5\u3067\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u3053\u3053\u3067\u306f\u3001\u3059\u3079\u3066\u306e\u885d\u7a81\u3057\u305f\u8981\u7d20\u304c\u9023\u7d50\u30ea\u30b9\u30c8\u306b\u30b0\u30eb\u30fc\u30d7\u5316\u3055\u308c\u307e\u3059\u3002</li> <li>\u30b0\u30e9\u30d5\uff1a\u30b0\u30e9\u30d5\u8868\u73fe\u306e\u6a19\u6e96\u7684\u306a\u65b9\u6cd5\u3067\u3042\u308b\u96a3\u63a5\u30ea\u30b9\u30c8\u306f\u3001\u5404\u30b0\u30e9\u30d5\u9802\u70b9\u3092\u9023\u7d50\u30ea\u30b9\u30c8\u306b\u95a2\u9023\u4ed8\u3051\u307e\u3059\u3002\u3053\u306e\u30ea\u30b9\u30c8\u306b\u306f\u3001\u5bfe\u5fdc\u3059\u308b\u9802\u70b9\u306b\u63a5\u7d9a\u3055\u308c\u305f\u9802\u70b9\u3092\u8868\u3059\u8981\u7d20\u304c\u542b\u307e\u308c\u307e\u3059\u3002</li> </ul> <p>\u53cc\u65b9\u5411\u9023\u7d50\u30ea\u30b9\u30c8\u306f\u3001\u524d\u5f8c\u306e\u8981\u7d20\u3078\u306e\u9ad8\u901f\u30a2\u30af\u30bb\u30b9\u304c\u5fc5\u8981\u306a\u30b7\u30ca\u30ea\u30aa\u306b\u6700\u9069\u3067\u3059\u3002</p> <ul> <li>\u9ad8\u5ea6\u306a\u30c7\u30fc\u30bf\u69cb\u9020\uff1a\u8d64\u9ed2\u6728\u3084B\u6728\u306a\u3069\u306e\u69cb\u9020\u3067\u306f\u3001\u30ce\u30fc\u30c9\u306e\u89aa\u3078\u306e\u30a2\u30af\u30bb\u30b9\u304c\u91cd\u8981\u3067\u3059\u3002\u3053\u308c\u306f\u5404\u30ce\u30fc\u30c9\u306b\u89aa\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\u3092\u7d44\u307f\u8fbc\u3080\u3053\u3068\u3067\u5b9f\u73fe\u3055\u308c\u3001\u53cc\u65b9\u5411\u9023\u7d50\u30ea\u30b9\u30c8\u306b\u4f3c\u3066\u3044\u307e\u3059\u3002</li> <li>\u30d6\u30e9\u30a6\u30b6\u5c65\u6b74\uff1aWeb\u30d6\u30e9\u30a6\u30b6\u3067\u306f\u3001\u53cc\u65b9\u5411\u9023\u7d50\u30ea\u30b9\u30c8\u306b\u3088\u308a\u3001\u30e6\u30fc\u30b6\u30fc\u304c\u524d\u9032\u307e\u305f\u306f\u5f8c\u9000\u30dc\u30bf\u30f3\u3092\u30af\u30ea\u30c3\u30af\u3057\u305f\u3068\u304d\u306e\u8a2a\u554f\u30da\u30fc\u30b8\u306e\u5c65\u6b74\u30ca\u30d3\u30b2\u30fc\u30b7\u30e7\u30f3\u304c\u5bb9\u6613\u306b\u306a\u308a\u307e\u3059\u3002</li> <li>LRU\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\uff1a\u53cc\u65b9\u5411\u9023\u7d50\u30ea\u30b9\u30c8\u306f\u3001\u6700\u8fd1\u6700\u5c11\u4f7f\u7528\uff08LRU\uff09\u30ad\u30e3\u30c3\u30b7\u30e5\u524a\u9664\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306b\u9069\u3057\u3066\u304a\u308a\u3001\u6700\u8fd1\u6700\u5c11\u4f7f\u7528\u30c7\u30fc\u30bf\u306e\u8fc5\u901f\u306a\u8b58\u5225\u3068\u3001\u9ad8\u901f\u306a\u30ce\u30fc\u30c9\u8ffd\u52a0\u30fb\u524a\u9664\u3092\u53ef\u80fd\u306b\u3057\u307e\u3059\u3002</li> </ul> <p>\u5faa\u74b0\u9023\u7d50\u30ea\u30b9\u30c8\u306f\u3001\u30aa\u30da\u30ec\u30fc\u30c6\u30a3\u30f3\u30b0\u30b7\u30b9\u30c6\u30e0\u3067\u306e\u30ea\u30bd\u30fc\u30b9\u30b9\u30b1\u30b8\u30e5\u30fc\u30ea\u30f3\u30b0\u306a\u3069\u3001\u5468\u671f\u7684\u306a\u64cd\u4f5c\u304c\u5fc5\u8981\u306a\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u306b\u6700\u9069\u3067\u3059\u3002</p> <ul> <li>\u30e9\u30a6\u30f3\u30c9\u30ed\u30d3\u30f3\u30b9\u30b1\u30b8\u30e5\u30fc\u30ea\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\uff1a\u30aa\u30da\u30ec\u30fc\u30c6\u30a3\u30f3\u30b0\u30b7\u30b9\u30c6\u30e0\u3067\u306f\u3001\u30e9\u30a6\u30f3\u30c9\u30ed\u30d3\u30f3\u30b9\u30b1\u30b8\u30e5\u30fc\u30ea\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u4e00\u822c\u7684\u306aCPU\u30b9\u30b1\u30b8\u30e5\u30fc\u30ea\u30f3\u30b0\u65b9\u6cd5\u3067\u3042\u308a\u3001\u30d7\u30ed\u30bb\u30b9\u306e\u30b0\u30eb\u30fc\u30d7\u3092\u5faa\u74b0\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u5404\u30d7\u30ed\u30bb\u30b9\u306b\u306f\u30bf\u30a4\u30e0\u30b9\u30e9\u30a4\u30b9\u304c\u5272\u308a\u5f53\u3066\u3089\u308c\u3001\u671f\u9650\u5207\u308c\u306b\u306a\u308b\u3068CPU\u306f\u6b21\u306e\u30d7\u30ed\u30bb\u30b9\u306b\u56de\u8ee2\u3057\u307e\u3059\u3002\u3053\u306e\u5faa\u74b0\u64cd\u4f5c\u306f\u5faa\u74b0\u9023\u7d50\u30ea\u30b9\u30c8\u3092\u4f7f\u7528\u3057\u3066\u52b9\u7387\u7684\u306b\u5b9f\u73fe\u3067\u304d\u3001\u3059\u3079\u3066\u306e\u30d7\u30ed\u30bb\u30b9\u9593\u3067\u516c\u5e73\u304b\u3064\u6642\u5206\u5272\u30b7\u30b9\u30c6\u30e0\u3092\u53ef\u80fd\u306b\u3057\u307e\u3059\u3002</li> <li>\u30c7\u30fc\u30bf\u30d0\u30c3\u30d5\u30a1\uff1a\u5faa\u74b0\u9023\u7d50\u30ea\u30b9\u30c8\u306f\u3001\u30aa\u30fc\u30c7\u30a3\u30aa\u3084\u30d3\u30c7\u30aa\u30d7\u30ec\u30fc\u30e4\u30fc\u306a\u3069\u306e\u30c7\u30fc\u30bf\u30d0\u30c3\u30d5\u30a1\u3067\u3082\u4f7f\u7528\u3055\u308c\u3001\u30c7\u30fc\u30bf\u30b9\u30c8\u30ea\u30fc\u30e0\u304c\u8907\u6570\u306e\u30d0\u30c3\u30d5\u30a1\u30d6\u30ed\u30c3\u30af\u306b\u5206\u5272\u3055\u308c\u3001\u30b7\u30fc\u30e0\u30ec\u30b9\u306a\u518d\u751f\u306e\u305f\u3081\u306b\u5faa\u74b0\u65b9\u5f0f\u3067\u914d\u7f6e\u3055\u308c\u307e\u3059\u3002</li> </ul>"},{"location":"chapter_array_and_linkedlist/list/","title":"4.3 \u00a0 \u30ea\u30b9\u30c8","text":"<p>\u30ea\u30b9\u30c8\u306f\u3001\u8981\u7d20\u3078\u306e\u30a2\u30af\u30bb\u30b9\u3001\u5909\u66f4\u3001\u8ffd\u52a0\u3001\u524a\u9664\u3001\u8d70\u67fb\u306a\u3069\u306e\u64cd\u4f5c\u3092\u30b5\u30dd\u30fc\u30c8\u3059\u308b\u3001\u9806\u5e8f\u4ed8\u3051\u3089\u308c\u305f\u8981\u7d20\u306e\u30b3\u30ec\u30af\u30b7\u30e7\u30f3\u3092\u8868\u3059\u62bd\u8c61\u7684\u306a\u30c7\u30fc\u30bf\u69cb\u9020\u306e\u6982\u5ff5\u3067\u3042\u308a\u3001\u30e6\u30fc\u30b6\u30fc\u304c\u5bb9\u91cf\u5236\u9650\u3092\u8003\u616e\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u305b\u3093\u3002\u30ea\u30b9\u30c8\u306f\u9023\u7d50\u30ea\u30b9\u30c8\u307e\u305f\u306f\u914d\u5217\u306b\u57fa\u3065\u3044\u3066\u5b9f\u88c5\u3067\u304d\u307e\u3059\u3002</p> <ul> <li>\u9023\u7d50\u30ea\u30b9\u30c8\u306f\u672c\u8cea\u7684\u306b\u30ea\u30b9\u30c8\u3068\u3057\u3066\u6a5f\u80fd\u3057\u3001\u8981\u7d20\u306e\u8ffd\u52a0\u3001\u524a\u9664\u3001\u691c\u7d22\u3001\u5909\u66f4\u306e\u64cd\u4f5c\u3092\u30b5\u30dd\u30fc\u30c8\u3057\u3001\u30b5\u30a4\u30ba\u3092\u52d5\u7684\u306b\u8abf\u6574\u3059\u308b\u67d4\u8edf\u6027\u304c\u3042\u308a\u307e\u3059\u3002</li> <li>\u914d\u5217\u3082\u3053\u308c\u3089\u306e\u64cd\u4f5c\u3092\u30b5\u30dd\u30fc\u30c8\u3057\u307e\u3059\u304c\u3001\u9577\u3055\u304c\u4e0d\u5909\u3067\u3042\u308b\u305f\u3081\u3001\u9577\u3055\u5236\u9650\u306e\u3042\u308b\u30ea\u30b9\u30c8\u3068\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002</li> </ul> <p>\u914d\u5217\u3092\u4f7f\u7528\u3057\u3066\u30ea\u30b9\u30c8\u3092\u5b9f\u88c5\u3059\u308b\u5834\u5408\u3001\u9577\u3055\u306e\u4e0d\u5909\u6027\u306b\u3088\u308a\u30ea\u30b9\u30c8\u306e\u5b9f\u7528\u6027\u304c\u4f4e\u4e0b\u3057\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u4e8b\u524d\u306b\u683c\u7d0d\u3059\u308b\u30c7\u30fc\u30bf\u91cf\u3092\u4e88\u6e2c\u3059\u308b\u3053\u3068\u304c\u56f0\u96e3\u306a\u5834\u5408\u304c\u591a\u304f\u3001\u9069\u5207\u306a\u30ea\u30b9\u30c8\u9577\u3092\u9078\u629e\u3059\u308b\u3053\u3068\u304c\u56f0\u96e3\u3067\u3042\u308b\u305f\u3081\u3067\u3059\u3002\u9577\u3055\u304c\u5c0f\u3055\u3059\u304e\u308b\u3068\u8981\u4ef6\u3092\u6e80\u305f\u3055\u306a\u3044\u53ef\u80fd\u6027\u304c\u3042\u308a\u3001\u5927\u304d\u3059\u304e\u308b\u3068\u30e1\u30e2\u30ea\u7a7a\u9593\u3092\u7121\u99c4\u306b\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002</p> <p>\u3053\u306e\u554f\u984c\u3092\u89e3\u6c7a\u3059\u308b\u305f\u3081\u306b\u3001\u52d5\u7684\u914d\u5217\u3092\u4f7f\u7528\u3057\u3066\u30ea\u30b9\u30c8\u3092\u5b9f\u88c5\u3067\u304d\u307e\u3059\u3002\u3053\u308c\u306f\u914d\u5217\u306e\u5229\u70b9\u3092\u7d99\u627f\u3057\u3001\u30d7\u30ed\u30b0\u30e9\u30e0\u5b9f\u884c\u4e2d\u306b\u52d5\u7684\u306b\u62e1\u5f35\u3067\u304d\u307e\u3059\u3002</p> <p>\u5b9f\u969b\u3001\u591a\u304f\u306e\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u306e\u6a19\u6e96\u30e9\u30a4\u30d6\u30e9\u30ea\u306f\u52d5\u7684\u914d\u5217\u3092\u4f7f\u7528\u3057\u3066\u30ea\u30b9\u30c8\u3092\u5b9f\u88c5\u3057\u3066\u3044\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001Python\u306e<code>list</code>\u3001Java\u306e<code>ArrayList</code>\u3001C++\u306e<code>vector</code>\u3001C#\u306e<code>List</code>\u306a\u3069\u3067\u3059\u3002\u4ee5\u4e0b\u306e\u8b70\u8ad6\u3067\u306f\u3001\u300c\u30ea\u30b9\u30c8\u300d\u3068\u300c\u52d5\u7684\u914d\u5217\u300d\u3092\u540c\u7fa9\u306e\u6982\u5ff5\u3068\u3057\u3066\u6271\u3044\u307e\u3059\u3002</p>"},{"location":"chapter_array_and_linkedlist/list/#431","title":"4.3.1 \u00a0 \u30ea\u30b9\u30c8\u306e\u4e00\u822c\u7684\u306a\u64cd\u4f5c","text":""},{"location":"chapter_array_and_linkedlist/list/#1","title":"1. \u00a0 \u30ea\u30b9\u30c8\u306e\u521d\u671f\u5316","text":"<p>\u901a\u5e38\u3001\u300c\u521d\u671f\u5024\u306a\u3057\u300d\u3068\u300c\u521d\u671f\u5024\u3042\u308a\u300d\u306e2\u3064\u306e\u521d\u671f\u5316\u65b9\u6cd5\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinZig list.py<pre><code># \u30ea\u30b9\u30c8\u3092\u521d\u671f\u5316\n# \u521d\u671f\u5024\u306a\u3057\nnums1: list[int] = []\n# \u521d\u671f\u5024\u3042\u308a\nnums: list[int] = [1, 3, 2, 5, 4]\n</code></pre> list.cpp<pre><code>/* \u30ea\u30b9\u30c8\u3092\u521d\u671f\u5316 */\n// \u6ce8\u610f: C++\u3067\u306f\u3001vector\u304c\u3053\u3053\u3067\u8aac\u660e\u3055\u308c\u3066\u3044\u308bnums\u306b\u76f8\u5f53\u3057\u307e\u3059\n// \u521d\u671f\u5024\u306a\u3057\nvector&lt;int&gt; nums1;\n// \u521d\u671f\u5024\u3042\u308a\nvector&lt;int&gt; nums = { 1, 3, 2, 5, 4 };\n</code></pre> list.java<pre><code>/* \u30ea\u30b9\u30c8\u3092\u521d\u671f\u5316 */\n// \u521d\u671f\u5024\u306a\u3057\nList&lt;Integer&gt; nums1 = new ArrayList&lt;&gt;();\n// \u521d\u671f\u5024\u3042\u308a\uff08\u8981\u7d20\u578b\u306fint[]\u306e\u30e9\u30c3\u30d1\u30fc\u30af\u30e9\u30b9Integer[]\u3067\u3042\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\uff09\nInteger[] numbers = new Integer[] { 1, 3, 2, 5, 4 };\nList&lt;Integer&gt; nums = new ArrayList&lt;&gt;(Arrays.asList(numbers));\n</code></pre> list.cs<pre><code>/* \u30ea\u30b9\u30c8\u3092\u521d\u671f\u5316 */\n// \u521d\u671f\u5024\u306a\u3057\nList&lt;int&gt; nums1 = [];\n// \u521d\u671f\u5024\u3042\u308a\nint[] numbers = [1, 3, 2, 5, 4];\nList&lt;int&gt; nums = [.. numbers];\n</code></pre> list_test.go<pre><code>/* \u30ea\u30b9\u30c8\u3092\u521d\u671f\u5316 */\n// \u521d\u671f\u5024\u306a\u3057\nnums1 := []int{}\n// \u521d\u671f\u5024\u3042\u308a\nnums := []int{1, 3, 2, 5, 4}\n</code></pre> list.swift<pre><code>/* \u30ea\u30b9\u30c8\u3092\u521d\u671f\u5316 */\n// \u521d\u671f\u5024\u306a\u3057\nlet nums1: [Int] = []\n// \u521d\u671f\u5024\u3042\u308a\nvar nums = [1, 3, 2, 5, 4]\n</code></pre> list.js<pre><code>/* \u30ea\u30b9\u30c8\u3092\u521d\u671f\u5316 */\n// \u521d\u671f\u5024\u306a\u3057\nconst nums1 = [];\n// \u521d\u671f\u5024\u3042\u308a\nconst nums = [1, 3, 2, 5, 4];\n</code></pre> list.ts<pre><code>/* \u30ea\u30b9\u30c8\u3092\u521d\u671f\u5316 */\n// \u521d\u671f\u5024\u306a\u3057\nconst nums1: number[] = [];\n// \u521d\u671f\u5024\u3042\u308a\nconst nums: number[] = [1, 3, 2, 5, 4];\n</code></pre> list.dart<pre><code>/* \u30ea\u30b9\u30c8\u3092\u521d\u671f\u5316 */\n// \u521d\u671f\u5024\u306a\u3057\nList&lt;int&gt; nums1 = [];\n// \u521d\u671f\u5024\u3042\u308a\nList&lt;int&gt; nums = [1, 3, 2, 5, 4];\n</code></pre> list.rs<pre><code>/* \u30ea\u30b9\u30c8\u3092\u521d\u671f\u5316 */\n// \u521d\u671f\u5024\u306a\u3057\nlet nums1: Vec&lt;i32&gt; = Vec::new();\n// \u521d\u671f\u5024\u3042\u308a\nlet nums: Vec&lt;i32&gt; = vec![1, 3, 2, 5, 4];\n</code></pre> list.c<pre><code>// C\u306f\u7d44\u307f\u8fbc\u307f\u306e\u52d5\u7684\u914d\u5217\u3092\u63d0\u4f9b\u3057\u3066\u3044\u307e\u305b\u3093\n</code></pre> list.kt<pre><code>\n</code></pre> list.zig<pre><code>// \u30ea\u30b9\u30c8\u3092\u521d\u671f\u5316\nvar nums = std.ArrayList(i32).init(std.heap.page_allocator);\ndefer nums.deinit();\ntry nums.appendSlice(&amp;[_]i32{ 1, 3, 2, 5, 4 });\n</code></pre>"},{"location":"chapter_array_and_linkedlist/list/#2","title":"2. \u00a0 \u8981\u7d20\u3078\u306e\u30a2\u30af\u30bb\u30b9","text":"<p>\u30ea\u30b9\u30c8\u306f\u672c\u8cea\u7684\u306b\u914d\u5217\u3067\u3042\u308b\u305f\u3081\u3001\\(O(1)\\)\u6642\u9593\u3067\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9\u3057\u66f4\u65b0\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u3001\u975e\u5e38\u306b\u52b9\u7387\u7684\u3067\u3059\u3002</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinZig list.py<pre><code># \u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9\nnum: int = nums[1]  # \u30a4\u30f3\u30c7\u30c3\u30af\u30b91\u306e\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9\n\n# \u8981\u7d20\u3092\u66f4\u65b0\nnums[1] = 0    # \u30a4\u30f3\u30c7\u30c3\u30af\u30b91\u306e\u8981\u7d20\u30920\u306b\u66f4\u65b0\n</code></pre> list.cpp<pre><code>/* \u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\nint num = nums[1];  // \u30a4\u30f3\u30c7\u30c3\u30af\u30b91\u306e\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9\n\n/* \u8981\u7d20\u3092\u66f4\u65b0 */\nnums[1] = 0;  // \u30a4\u30f3\u30c7\u30c3\u30af\u30b91\u306e\u8981\u7d20\u30920\u306b\u66f4\u65b0\n</code></pre> list.java<pre><code>/* \u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\nint num = nums.get(1);  // \u30a4\u30f3\u30c7\u30c3\u30af\u30b91\u306e\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9\n\n/* \u8981\u7d20\u3092\u66f4\u65b0 */\nnums.set(1, 0);  // \u30a4\u30f3\u30c7\u30c3\u30af\u30b91\u306e\u8981\u7d20\u30920\u306b\u66f4\u65b0\n</code></pre> list.cs<pre><code>/* \u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\nint num = nums[1];  // \u30a4\u30f3\u30c7\u30c3\u30af\u30b91\u306e\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9\n\n/* \u8981\u7d20\u3092\u66f4\u65b0 */\nnums[1] = 0;  // \u30a4\u30f3\u30c7\u30c3\u30af\u30b91\u306e\u8981\u7d20\u30920\u306b\u66f4\u65b0\n</code></pre> list_test.go<pre><code>/* \u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\nnum := nums[1]  // \u30a4\u30f3\u30c7\u30c3\u30af\u30b91\u306e\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9\n\n/* \u8981\u7d20\u3092\u66f4\u65b0 */\nnums[1] = 0     // \u30a4\u30f3\u30c7\u30c3\u30af\u30b91\u306e\u8981\u7d20\u30920\u306b\u66f4\u65b0\n</code></pre> list.swift<pre><code>/* \u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\nlet num = nums[1] // \u30a4\u30f3\u30c7\u30c3\u30af\u30b91\u306e\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9\n\n/* \u8981\u7d20\u3092\u66f4\u65b0 */\nnums[1] = 0 // \u30a4\u30f3\u30c7\u30c3\u30af\u30b91\u306e\u8981\u7d20\u30920\u306b\u66f4\u65b0\n</code></pre> list.js<pre><code>/* \u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\nconst num = nums[1];  // \u30a4\u30f3\u30c7\u30c3\u30af\u30b91\u306e\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9\n\n/* \u8981\u7d20\u3092\u66f4\u65b0 */\nnums[1] = 0;  // \u30a4\u30f3\u30c7\u30c3\u30af\u30b91\u306e\u8981\u7d20\u30920\u306b\u66f4\u65b0\n</code></pre> list.ts<pre><code>/* \u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\nconst num: number = nums[1];  // \u30a4\u30f3\u30c7\u30c3\u30af\u30b91\u306e\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9\n\n/* \u8981\u7d20\u3092\u66f4\u65b0 */\nnums[1] = 0;  // \u30a4\u30f3\u30c7\u30c3\u30af\u30b91\u306e\u8981\u7d20\u30920\u306b\u66f4\u65b0\n</code></pre> list.dart<pre><code>/* \u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\nint num = nums[1];  // \u30a4\u30f3\u30c7\u30c3\u30af\u30b91\u306e\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9\n\n/* \u8981\u7d20\u3092\u66f4\u65b0 */\nnums[1] = 0;  // \u30a4\u30f3\u30c7\u30c3\u30af\u30b91\u306e\u8981\u7d20\u30920\u306b\u66f4\u65b0\n</code></pre> list.rs<pre><code>/* \u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\nlet num: i32 = nums[1];  // \u30a4\u30f3\u30c7\u30c3\u30af\u30b91\u306e\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9\n/* \u8981\u7d20\u3092\u66f4\u65b0 */\nnums[1] = 0;             // \u30a4\u30f3\u30c7\u30c3\u30af\u30b91\u306e\u8981\u7d20\u30920\u306b\u66f4\u65b0\n</code></pre> list.c<pre><code>// C\u306f\u7d44\u307f\u8fbc\u307f\u306e\u52d5\u7684\u914d\u5217\u3092\u63d0\u4f9b\u3057\u3066\u3044\u307e\u305b\u3093\n</code></pre> list.kt<pre><code>\n</code></pre> list.zig<pre><code>// \u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9\nvar num = nums.items[1]; // \u30a4\u30f3\u30c7\u30c3\u30af\u30b91\u306e\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9\n\n// \u8981\u7d20\u3092\u66f4\u65b0\nnums.items[1] = 0; // \u30a4\u30f3\u30c7\u30c3\u30af\u30b91\u306e\u8981\u7d20\u30920\u306b\u66f4\u65b0\n</code></pre>"},{"location":"chapter_array_and_linkedlist/list/#3","title":"3. \u00a0 \u8981\u7d20\u306e\u633f\u5165\u3068\u524a\u9664","text":"<p>\u914d\u5217\u3068\u6bd4\u8f03\u3057\u3066\u3001\u30ea\u30b9\u30c8\u306f\u8981\u7d20\u306e\u8ffd\u52a0\u3068\u524a\u9664\u306b\u304a\u3044\u3066\u3088\u308a\u67d4\u8edf\u6027\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u30ea\u30b9\u30c8\u306e\u672b\u5c3e\u3078\u306e\u8981\u7d20\u8ffd\u52a0\u306f\\(O(1)\\)\u64cd\u4f5c\u3067\u3059\u304c\u3001\u30ea\u30b9\u30c8\u306e\u4ed6\u306e\u5834\u6240\u3067\u306e\u8981\u7d20\u306e\u633f\u5165\u3068\u524a\u9664\u306e\u52b9\u7387\u306f\u914d\u5217\u3068\u540c\u3058\u307e\u307e\u3067\u3001\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O(n)\\)\u3067\u3059\u3002</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinZig list.py<pre><code># \u30ea\u30b9\u30c8\u3092\u30af\u30ea\u30a2\nnums.clear()\n\n# \u672b\u5c3e\u306b\u8981\u7d20\u3092\u8ffd\u52a0\nnums.append(1)\nnums.append(3)\nnums.append(2)\nnums.append(5)\nnums.append(4)\n\n# \u4e2d\u9593\u306b\u8981\u7d20\u3092\u633f\u5165\nnums.insert(3, 6)  # \u30a4\u30f3\u30c7\u30c3\u30af\u30b93\u306b\u6570\u50246\u3092\u633f\u5165\n\n# \u8981\u7d20\u3092\u524a\u9664\nnums.pop(3)        # \u30a4\u30f3\u30c7\u30c3\u30af\u30b93\u306e\u8981\u7d20\u3092\u524a\u9664\n</code></pre> list.cpp<pre><code>/* \u30ea\u30b9\u30c8\u3092\u30af\u30ea\u30a2 */\nnums.clear();\n\n/* \u672b\u5c3e\u306b\u8981\u7d20\u3092\u8ffd\u52a0 */\nnums.push_back(1);\nnums.push_back(3);\nnums.push_back(2);\nnums.push_back(5);\nnums.push_back(4);\n\n/* \u4e2d\u9593\u306b\u8981\u7d20\u3092\u633f\u5165 */\nnums.insert(nums.begin() + 3, 6);  // \u30a4\u30f3\u30c7\u30c3\u30af\u30b93\u306b\u6570\u50246\u3092\u633f\u5165\n\n/* \u8981\u7d20\u3092\u524a\u9664 */\nnums.erase(nums.begin() + 3);      // \u30a4\u30f3\u30c7\u30c3\u30af\u30b93\u306e\u8981\u7d20\u3092\u524a\u9664\n</code></pre> list.java<pre><code>/* \u30ea\u30b9\u30c8\u3092\u30af\u30ea\u30a2 */\nnums.clear();\n\n/* \u672b\u5c3e\u306b\u8981\u7d20\u3092\u8ffd\u52a0 */\nnums.add(1);\nnums.add(3);\nnums.add(2);\nnums.add(5);\nnums.add(4);\n\n/* \u4e2d\u9593\u306b\u8981\u7d20\u3092\u633f\u5165 */\nnums.add(3, 6);  // \u30a4\u30f3\u30c7\u30c3\u30af\u30b93\u306b\u6570\u50246\u3092\u633f\u5165\n\n/* \u8981\u7d20\u3092\u524a\u9664 */\nnums.remove(3);  // \u30a4\u30f3\u30c7\u30c3\u30af\u30b93\u306e\u8981\u7d20\u3092\u524a\u9664\n</code></pre> list.cs<pre><code>/* \u30ea\u30b9\u30c8\u3092\u30af\u30ea\u30a2 */\nnums.Clear();\n\n/* \u672b\u5c3e\u306b\u8981\u7d20\u3092\u8ffd\u52a0 */\nnums.Add(1);\nnums.Add(3);\nnums.Add(2);\nnums.Add(5);\nnums.Add(4);\n\n/* \u4e2d\u9593\u306b\u8981\u7d20\u3092\u633f\u5165 */\nnums.Insert(3, 6);\n\n/* \u8981\u7d20\u3092\u524a\u9664 */\nnums.RemoveAt(3);\n</code></pre> list_test.go<pre><code>/* \u30ea\u30b9\u30c8\u3092\u30af\u30ea\u30a2 */\nnums = nil\n\n/* \u672b\u5c3e\u306b\u8981\u7d20\u3092\u8ffd\u52a0 */\nnums = append(nums, 1)\nnums = append(nums, 3)\nnums = append(nums, 2)\nnums = append(nums, 5)\nnums = append(nums, 4)\n\n/* \u4e2d\u9593\u306b\u8981\u7d20\u3092\u633f\u5165 */\nnums = append(nums[:3], append([]int{6}, nums[3:]...)...) // \u30a4\u30f3\u30c7\u30c3\u30af\u30b93\u306b\u6570\u50246\u3092\u633f\u5165\n\n/* \u8981\u7d20\u3092\u524a\u9664 */\nnums = append(nums[:3], nums[4:]...) // \u30a4\u30f3\u30c7\u30c3\u30af\u30b93\u306e\u8981\u7d20\u3092\u524a\u9664\n</code></pre> list.swift<pre><code>/* \u30ea\u30b9\u30c8\u3092\u30af\u30ea\u30a2 */\nnums.removeAll()\n\n/* \u672b\u5c3e\u306b\u8981\u7d20\u3092\u8ffd\u52a0 */\nnums.append(1)\nnums.append(3)\nnums.append(2)\nnums.append(5)\nnums.append(4)\n\n/* \u4e2d\u9593\u306b\u8981\u7d20\u3092\u633f\u5165 */\nnums.insert(6, at: 3) // \u30a4\u30f3\u30c7\u30c3\u30af\u30b93\u306b\u6570\u50246\u3092\u633f\u5165\n\n/* \u8981\u7d20\u3092\u524a\u9664 */\nnums.remove(at: 3) // \u30a4\u30f3\u30c7\u30c3\u30af\u30b93\u306e\u8981\u7d20\u3092\u524a\u9664\n</code></pre> list.js<pre><code>/* \u30ea\u30b9\u30c8\u3092\u30af\u30ea\u30a2 */\nnums.length = 0;\n\n/* \u672b\u5c3e\u306b\u8981\u7d20\u3092\u8ffd\u52a0 */\nnums.push(1);\nnums.push(3);\nnums.push(2);\nnums.push(5);\nnums.push(4);\n\n/* \u4e2d\u9593\u306b\u8981\u7d20\u3092\u633f\u5165 */\nnums.splice(3, 0, 6);\n\n/* \u8981\u7d20\u3092\u524a\u9664 */\nnums.splice(3, 1);\n</code></pre> list.ts<pre><code>/* \u30ea\u30b9\u30c8\u3092\u30af\u30ea\u30a2 */\nnums.length = 0;\n\n/* \u672b\u5c3e\u306b\u8981\u7d20\u3092\u8ffd\u52a0 */\nnums.push(1);\nnums.push(3);\nnums.push(2);\nnums.push(5);\nnums.push(4);\n\n/* \u4e2d\u9593\u306b\u8981\u7d20\u3092\u633f\u5165 */\nnums.splice(3, 0, 6);\n\n/* \u8981\u7d20\u3092\u524a\u9664 */\nnums.splice(3, 1);\n</code></pre> list.dart<pre><code>/* \u30ea\u30b9\u30c8\u3092\u30af\u30ea\u30a2 */\nnums.clear();\n\n/* \u672b\u5c3e\u306b\u8981\u7d20\u3092\u8ffd\u52a0 */\nnums.add(1);\nnums.add(3);\nnums.add(2);\nnums.add(5);\nnums.add(4);\n\n/* \u4e2d\u9593\u306b\u8981\u7d20\u3092\u633f\u5165 */\nnums.insert(3, 6); // \u30a4\u30f3\u30c7\u30c3\u30af\u30b93\u306b\u6570\u50246\u3092\u633f\u5165\n\n/* \u8981\u7d20\u3092\u524a\u9664 */\nnums.removeAt(3); // \u30a4\u30f3\u30c7\u30c3\u30af\u30b93\u306e\u8981\u7d20\u3092\u524a\u9664\n</code></pre> list.rs<pre><code>/* \u30ea\u30b9\u30c8\u3092\u30af\u30ea\u30a2 */\nnums.clear();\n\n/* \u672b\u5c3e\u306b\u8981\u7d20\u3092\u8ffd\u52a0 */\nnums.push(1);\nnums.push(3);\nnums.push(2);\nnums.push(5);\nnums.push(4);\n\n/* \u4e2d\u9593\u306b\u8981\u7d20\u3092\u633f\u5165 */\nnums.insert(3, 6);  // \u30a4\u30f3\u30c7\u30c3\u30af\u30b93\u306b\u6570\u50246\u3092\u633f\u5165\n\n/* \u8981\u7d20\u3092\u524a\u9664 */\nnums.remove(3);    // \u30a4\u30f3\u30c7\u30c3\u30af\u30b93\u306e\u8981\u7d20\u3092\u524a\u9664\n</code></pre> list.c<pre><code>// C\u306f\u7d44\u307f\u8fbc\u307f\u306e\u52d5\u7684\u914d\u5217\u3092\u63d0\u4f9b\u3057\u3066\u3044\u307e\u305b\u3093\n</code></pre> list.kt<pre><code>\n</code></pre> list.zig<pre><code>// \u30ea\u30b9\u30c8\u3092\u30af\u30ea\u30a2\nnums.clearRetainingCapacity();\n\n// \u672b\u5c3e\u306b\u8981\u7d20\u3092\u8ffd\u52a0\ntry nums.append(1);\ntry nums.append(3);\ntry nums.append(2);\ntry nums.append(5);\ntry nums.append(4);\n\n// \u4e2d\u9593\u306b\u8981\u7d20\u3092\u633f\u5165\ntry nums.insert(3, 6); // \u30a4\u30f3\u30c7\u30c3\u30af\u30b93\u306b\u6570\u50246\u3092\u633f\u5165\n\n// \u8981\u7d20\u3092\u524a\u9664\n_ = nums.orderedRemove(3); // \u30a4\u30f3\u30c7\u30c3\u30af\u30b93\u306e\u8981\u7d20\u3092\u524a\u9664\n</code></pre>"},{"location":"chapter_array_and_linkedlist/list/#4","title":"4. \u00a0 \u30ea\u30b9\u30c8\u306e\u53cd\u5fa9","text":"<p>\u914d\u5217\u3068\u540c\u69d8\u306b\u3001\u30ea\u30b9\u30c8\u306f\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u4f7f\u7528\u3057\u3066\u53cd\u5fa9\u3059\u308b\u3053\u3068\u3082\u3001\u5404\u8981\u7d20\u3092\u76f4\u63a5\u53cd\u5fa9\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinZig list.py<pre><code># \u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3067\u30ea\u30b9\u30c8\u3092\u53cd\u5fa9\ncount = 0\nfor i in range(len(nums)):\n    count += nums[i]\n\n# \u30ea\u30b9\u30c8\u8981\u7d20\u3092\u76f4\u63a5\u53cd\u5fa9\nfor num in nums:\n    count += num\n</code></pre> list.cpp<pre><code>/* \u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3067\u30ea\u30b9\u30c8\u3092\u53cd\u5fa9 */\nint count = 0;\nfor (int i = 0; i &lt; nums.size(); i++) {\n    count += nums[i];\n}\n\n/* \u30ea\u30b9\u30c8\u8981\u7d20\u3092\u76f4\u63a5\u53cd\u5fa9 */\ncount = 0;\nfor (int num : nums) {\n    count += num;\n}\n</code></pre> list.java<pre><code>/* \u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3067\u30ea\u30b9\u30c8\u3092\u53cd\u5fa9 */\nint count = 0;\nfor (int i = 0; i &lt; nums.size(); i++) {\n    count += nums.get(i);\n}\n\n/* \u30ea\u30b9\u30c8\u8981\u7d20\u3092\u76f4\u63a5\u53cd\u5fa9 */\nfor (int num : nums) {\n    count += num;\n}\n</code></pre> list.cs<pre><code>/* \u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3067\u30ea\u30b9\u30c8\u3092\u53cd\u5fa9 */\nint count = 0;\nfor (int i = 0; i &lt; nums.Count; i++) {\n    count += nums[i];\n}\n\n/* \u30ea\u30b9\u30c8\u8981\u7d20\u3092\u76f4\u63a5\u53cd\u5fa9 */\ncount = 0;\nforeach (int num in nums) {\n    count += num;\n}\n</code></pre> list_test.go<pre><code>/* \u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3067\u30ea\u30b9\u30c8\u3092\u53cd\u5fa9 */\ncount := 0\nfor i := 0; i &lt; len(nums); i++ {\n    count += nums[i]\n}\n\n/* \u30ea\u30b9\u30c8\u8981\u7d20\u3092\u76f4\u63a5\u53cd\u5fa9 */\ncount = 0\nfor _, num := range nums {\n    count += num\n}\n</code></pre> list.swift<pre><code>/* \u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3067\u30ea\u30b9\u30c8\u3092\u53cd\u5fa9 */\nvar count = 0\nfor i in nums.indices {\n    count += nums[i]\n}\n\n/* \u30ea\u30b9\u30c8\u8981\u7d20\u3092\u76f4\u63a5\u53cd\u5fa9 */\ncount = 0\nfor num in nums {\n    count += num\n}\n</code></pre> list.js<pre><code>/* \u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3067\u30ea\u30b9\u30c8\u3092\u53cd\u5fa9 */\nlet count = 0;\nfor (let i = 0; i &lt; nums.length; i++) {\n    count += nums[i];\n}\n\n/* \u30ea\u30b9\u30c8\u8981\u7d20\u3092\u76f4\u63a5\u53cd\u5fa9 */\ncount = 0;\nfor (const num of nums) {\n    count += num;\n}\n</code></pre> list.ts<pre><code>/* \u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3067\u30ea\u30b9\u30c8\u3092\u53cd\u5fa9 */\nlet count = 0;\nfor (let i = 0; i &lt; nums.length; i++) {\n    count += nums[i];\n}\n\n/* \u30ea\u30b9\u30c8\u8981\u7d20\u3092\u76f4\u63a5\u53cd\u5fa9 */\ncount = 0;\nfor (const num of nums) {\n    count += num;\n}\n</code></pre> list.dart<pre><code>/* \u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3067\u30ea\u30b9\u30c8\u3092\u53cd\u5fa9 */\nint count = 0;\nfor (var i = 0; i &lt; nums.length; i++) {\n    count += nums[i];\n}\n\n/* \u30ea\u30b9\u30c8\u8981\u7d20\u3092\u76f4\u63a5\u53cd\u5fa9 */\ncount = 0;\nfor (var num in nums) {\n    count += num;\n}\n</code></pre> list.rs<pre><code>// \u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3067\u30ea\u30b9\u30c8\u3092\u53cd\u5fa9\nlet mut _count = 0;\nfor i in 0..nums.len() {\n    _count += nums[i];\n}\n\n// \u30ea\u30b9\u30c8\u8981\u7d20\u3092\u76f4\u63a5\u53cd\u5fa9\n_count = 0;\nfor num in &amp;nums {\n    _count += num;\n}\n</code></pre> list.c<pre><code>// C\u306f\u7d44\u307f\u8fbc\u307f\u306e\u52d5\u7684\u914d\u5217\u3092\u63d0\u4f9b\u3057\u3066\u3044\u307e\u305b\u3093\n</code></pre> list.kt<pre><code>\n</code></pre> list.zig<pre><code>// \u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3067\u30ea\u30b9\u30c8\u3092\u53cd\u5fa9\nvar count: i32 = 0;\nvar i: i32 = 0;\nwhile (i &lt; nums.items.len) : (i += 1) {\n    count += nums[i];\n}\n\n// \u30ea\u30b9\u30c8\u8981\u7d20\u3092\u76f4\u63a5\u53cd\u5fa9\ncount = 0;\nfor (nums.items) |num| {\n    count += num;\n}\n</code></pre>"},{"location":"chapter_array_and_linkedlist/list/#5","title":"5. \u00a0 \u30ea\u30b9\u30c8\u306e\u9023\u7d50","text":"<p>\u65b0\u3057\u3044\u30ea\u30b9\u30c8<code>nums1</code>\u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u304d\u3001\u305d\u308c\u3092\u5143\u306e\u30ea\u30b9\u30c8\u306e\u672b\u5c3e\u306b\u8ffd\u52a0\u3067\u304d\u307e\u3059\u3002</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinZig list.py<pre><code># 2\u3064\u306e\u30ea\u30b9\u30c8\u3092\u9023\u7d50\nnums1: list[int] = [6, 8, 7, 10, 9]\nnums += nums1  # nums1\u3092nums\u306e\u672b\u5c3e\u306b\u9023\u7d50\n</code></pre> list.cpp<pre><code>/* 2\u3064\u306e\u30ea\u30b9\u30c8\u3092\u9023\u7d50 */\nvector&lt;int&gt; nums1 = { 6, 8, 7, 10, 9 };\n// nums1\u3092nums\u306e\u672b\u5c3e\u306b\u9023\u7d50\nnums.insert(nums.end(), nums1.begin(), nums1.end());\n</code></pre> list.java<pre><code>/* 2\u3064\u306e\u30ea\u30b9\u30c8\u3092\u9023\u7d50 */\nList&lt;Integer&gt; nums1 = new ArrayList&lt;&gt;(Arrays.asList(new Integer[] { 6, 8, 7, 10, 9 }));\nnums.addAll(nums1);  // nums1\u3092nums\u306e\u672b\u5c3e\u306b\u9023\u7d50\n</code></pre> list.cs<pre><code>/* 2\u3064\u306e\u30ea\u30b9\u30c8\u3092\u9023\u7d50 */\nList&lt;int&gt; nums1 = [6, 8, 7, 10, 9];\nnums.AddRange(nums1);  // nums1\u3092nums\u306e\u672b\u5c3e\u306b\u9023\u7d50\n</code></pre> list_test.go<pre><code>/* 2\u3064\u306e\u30ea\u30b9\u30c8\u3092\u9023\u7d50 */\nnums1 := []int{6, 8, 7, 10, 9}\nnums = append(nums, nums1...)  // nums1\u3092nums\u306e\u672b\u5c3e\u306b\u9023\u7d50\n</code></pre> list.swift<pre><code>/* 2\u3064\u306e\u30ea\u30b9\u30c8\u3092\u9023\u7d50 */\nlet nums1 = [6, 8, 7, 10, 9]\nnums.append(contentsOf: nums1) // nums1\u3092nums\u306e\u672b\u5c3e\u306b\u9023\u7d50\n</code></pre> list.js<pre><code>/* 2\u3064\u306e\u30ea\u30b9\u30c8\u3092\u9023\u7d50 */\nconst nums1 = [6, 8, 7, 10, 9];\nnums.push(...nums1);  // nums1\u3092nums\u306e\u672b\u5c3e\u306b\u9023\u7d50\n</code></pre> list.ts<pre><code>/* 2\u3064\u306e\u30ea\u30b9\u30c8\u3092\u9023\u7d50 */\nconst nums1: number[] = [6, 8, 7, 10, 9];\nnums.push(...nums1);  // nums1\u3092nums\u306e\u672b\u5c3e\u306b\u9023\u7d50\n</code></pre> list.dart<pre><code>/* 2\u3064\u306e\u30ea\u30b9\u30c8\u3092\u9023\u7d50 */\nList&lt;int&gt; nums1 = [6, 8, 7, 10, 9];\nnums.addAll(nums1);  // nums1\u3092nums\u306e\u672b\u5c3e\u306b\u9023\u7d50\n</code></pre> list.rs<pre><code>/* 2\u3064\u306e\u30ea\u30b9\u30c8\u3092\u9023\u7d50 */\nlet nums1: Vec&lt;i32&gt; = vec![6, 8, 7, 10, 9];\nnums.extend(nums1);\n</code></pre> list.c<pre><code>// C\u306f\u7d44\u307f\u8fbc\u307f\u306e\u52d5\u7684\u914d\u5217\u3092\u63d0\u4f9b\u3057\u3066\u3044\u307e\u305b\u3093\n</code></pre> list.kt<pre><code>\n</code></pre> list.zig<pre><code>// 2\u3064\u306e\u30ea\u30b9\u30c8\u3092\u9023\u7d50\nvar nums1 = std.ArrayList(i32).init(std.heap.page_allocator);\ndefer nums1.deinit();\ntry nums1.appendSlice(&amp;[_]i32{ 6, 8, 7, 10, 9 });\ntry nums.insertSlice(nums.items.len, nums1.items); // nums1\u3092nums\u306e\u672b\u5c3e\u306b\u9023\u7d50\n</code></pre>"},{"location":"chapter_array_and_linkedlist/list/#6","title":"6. \u00a0 \u30ea\u30b9\u30c8\u306e\u30bd\u30fc\u30c8","text":"<p>\u30ea\u30b9\u30c8\u304c\u30bd\u30fc\u30c8\u3055\u308c\u308b\u3068\u3001\u300c\u4e8c\u5206\u63a2\u7d22\u300d\u3084\u300c\u53cc\u30dd\u30a4\u30f3\u30bf\u300d\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306a\u3069\u3001\u914d\u5217\u95a2\u9023\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u554f\u984c\u3067\u3088\u304f\u4f7f\u7528\u3055\u308c\u308b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinZig list.py<pre><code># \u30ea\u30b9\u30c8\u3092\u30bd\u30fc\u30c8\nnums.sort()  # \u30bd\u30fc\u30c8\u5f8c\u3001\u30ea\u30b9\u30c8\u8981\u7d20\u306f\u6607\u9806\u306b\u306a\u308a\u307e\u3059\n</code></pre> list.cpp<pre><code>/* \u30ea\u30b9\u30c8\u3092\u30bd\u30fc\u30c8 */\nsort(nums.begin(), nums.end());  // \u30bd\u30fc\u30c8\u5f8c\u3001\u30ea\u30b9\u30c8\u8981\u7d20\u306f\u6607\u9806\u306b\u306a\u308a\u307e\u3059\n</code></pre> list.java<pre><code>/* \u30ea\u30b9\u30c8\u3092\u30bd\u30fc\u30c8 */\nCollections.sort(nums);  // \u30bd\u30fc\u30c8\u5f8c\u3001\u30ea\u30b9\u30c8\u8981\u7d20\u306f\u6607\u9806\u306b\u306a\u308a\u307e\u3059\n</code></pre> list.cs<pre><code>/* \u30ea\u30b9\u30c8\u3092\u30bd\u30fc\u30c8 */\nnums.Sort(); // \u30bd\u30fc\u30c8\u5f8c\u3001\u30ea\u30b9\u30c8\u8981\u7d20\u306f\u6607\u9806\u306b\u306a\u308a\u307e\u3059\n</code></pre> list_test.go<pre><code>/* \u30ea\u30b9\u30c8\u3092\u30bd\u30fc\u30c8 */\nsort.Ints(nums)  // \u30bd\u30fc\u30c8\u5f8c\u3001\u30ea\u30b9\u30c8\u8981\u7d20\u306f\u6607\u9806\u306b\u306a\u308a\u307e\u3059\n</code></pre> list.swift<pre><code>/* \u30ea\u30b9\u30c8\u3092\u30bd\u30fc\u30c8 */\nnums.sort() // \u30bd\u30fc\u30c8\u5f8c\u3001\u30ea\u30b9\u30c8\u8981\u7d20\u306f\u6607\u9806\u306b\u306a\u308a\u307e\u3059\n</code></pre> list.js<pre><code>/* \u30ea\u30b9\u30c8\u3092\u30bd\u30fc\u30c8 */\nnums.sort((a, b) =&gt; a - b);  // \u30bd\u30fc\u30c8\u5f8c\u3001\u30ea\u30b9\u30c8\u8981\u7d20\u306f\u6607\u9806\u306b\u306a\u308a\u307e\u3059\n</code></pre> list.ts<pre><code>/* \u30ea\u30b9\u30c8\u3092\u30bd\u30fc\u30c8 */\nnums.sort((a, b) =&gt; a - b);  // \u30bd\u30fc\u30c8\u5f8c\u3001\u30ea\u30b9\u30c8\u8981\u7d20\u306f\u6607\u9806\u306b\u306a\u308a\u307e\u3059\n</code></pre> list.dart<pre><code>/* \u30ea\u30b9\u30c8\u3092\u30bd\u30fc\u30c8 */\nnums.sort(); // \u30bd\u30fc\u30c8\u5f8c\u3001\u30ea\u30b9\u30c8\u8981\u7d20\u306f\u6607\u9806\u306b\u306a\u308a\u307e\u3059\n</code></pre> list.rs<pre><code>/* \u30ea\u30b9\u30c8\u3092\u30bd\u30fc\u30c8 */\nnums.sort(); // \u30bd\u30fc\u30c8\u5f8c\u3001\u30ea\u30b9\u30c8\u8981\u7d20\u306f\u6607\u9806\u306b\u306a\u308a\u307e\u3059\n</code></pre> list.c<pre><code>// C\u306f\u7d44\u307f\u8fbc\u307f\u306e\u52d5\u7684\u914d\u5217\u3092\u63d0\u4f9b\u3057\u3066\u3044\u307e\u305b\u3093\n</code></pre> list.kt<pre><code>\n</code></pre> list.zig<pre><code>// \u30ea\u30b9\u30c8\u3092\u30bd\u30fc\u30c8\nstd.sort.sort(i32, nums.items, {}, comptime std.sort.asc(i32));\n</code></pre>"},{"location":"chapter_array_and_linkedlist/list/#432","title":"4.3.2 \u00a0 \u30ea\u30b9\u30c8\u306e\u5b9f\u88c5","text":"<p>\u591a\u304f\u306e\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u306b\u306f\u3001Java\u3001C++\u3001Python\u306a\u3069\u3092\u542b\u3080\u7d44\u307f\u8fbc\u307f\u30ea\u30b9\u30c8\u304c\u4ed8\u5c5e\u3057\u3066\u3044\u307e\u3059\u3002\u305d\u308c\u3089\u306e\u5b9f\u88c5\u306f\u3001\u521d\u671f\u5bb9\u91cf\u3084\u62e1\u5f35\u4fc2\u6570\u306a\u3069\u306e\u69d8\u3005\u306a\u30d1\u30e9\u30e1\u30fc\u30bf\u3092\u614e\u91cd\u306b\u8003\u616e\u3057\u305f\u8a2d\u5b9a\u3067\u3001\u8907\u96d1\u306b\u306a\u308a\u304c\u3061\u3067\u3059\u3002\u8208\u5473\u306e\u3042\u308b\u8aad\u8005\u306f\u3001\u3055\u3089\u306a\u308b\u5b66\u7fd2\u306e\u305f\u3081\u306b\u30bd\u30fc\u30b9\u30b3\u30fc\u30c9\u3092\u8abf\u3079\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002</p> <p>\u30ea\u30b9\u30c8\u304c\u3069\u306e\u3088\u3046\u306b\u52d5\u4f5c\u3059\u308b\u304b\u306e\u7406\u89e3\u3092\u6df1\u3081\u308b\u305f\u3081\u306b\u30013\u3064\u306e\u91cd\u8981\u306a\u8a2d\u8a08\u5074\u9762\u306b\u7126\u70b9\u3092\u5f53\u3066\u3066\u3001\u7c21\u7565\u5316\u3055\u308c\u305f\u30ea\u30b9\u30c8\u306e\u5b9f\u88c5\u3092\u8a66\u307f\u307e\u3059\uff1a</p> <ul> <li>\u521d\u671f\u5bb9\u91cf\uff1a\u914d\u5217\u306b\u5408\u7406\u7684\u306a\u521d\u671f\u5bb9\u91cf\u3092\u9078\u629e\u3057\u307e\u3059\u3002\u3053\u306e\u4f8b\u3067\u306f\u3001\u521d\u671f\u5bb9\u91cf\u3068\u3057\u306610\u3092\u9078\u629e\u3057\u307e\u3059\u3002</li> <li>\u30b5\u30a4\u30ba\u8a18\u9332\uff1a\u30ea\u30b9\u30c8\u5185\u306e\u73fe\u5728\u306e\u8981\u7d20\u6570\u3092\u8a18\u9332\u3059\u308b\u5909\u6570<code>size</code>\u3092\u5ba3\u8a00\u3057\u3001\u8981\u7d20\u306e\u633f\u5165\u3068\u524a\u9664\u3067\u30ea\u30a2\u30eb\u30bf\u30a4\u30e0\u306b\u66f4\u65b0\u3057\u307e\u3059\u3002\u3053\u306e\u5909\u6570\u306b\u3088\u308a\u3001\u30ea\u30b9\u30c8\u306e\u672b\u5c3e\u3092\u7279\u5b9a\u3057\u3001\u62e1\u5f35\u304c\u5fc5\u8981\u304b\u3069\u3046\u304b\u3092\u5224\u65ad\u3067\u304d\u307e\u3059\u3002</li> <li>\u62e1\u5f35\u30e1\u30ab\u30cb\u30ba\u30e0\uff1a\u8981\u7d20\u633f\u5165\u6642\u306b\u30ea\u30b9\u30c8\u304c\u6e80\u676f\u306b\u9054\u3057\u305f\u5834\u5408\u3001\u62e1\u5f35\u30d7\u30ed\u30bb\u30b9\u304c\u5fc5\u8981\u3067\u3059\u3002\u3053\u308c\u306b\u306f\u62e1\u5f35\u4fc2\u6570\u306b\u57fa\u3065\u3044\u3066\u3088\u308a\u5927\u304d\u306a\u914d\u5217\u3092\u4f5c\u6210\u3057\u3001\u73fe\u5728\u306e\u914d\u5217\u304b\u3089\u3059\u3079\u3066\u306e\u8981\u7d20\u3092\u65b0\u3057\u3044\u914d\u5217\u306b\u8ee2\u9001\u3059\u308b\u3053\u3068\u304c\u542b\u307e\u308c\u307e\u3059\u3002\u3053\u306e\u4f8b\u3067\u306f\u3001\u62e1\u5f35\u306e\u305f\u3073\u306b\u914d\u5217\u30b5\u30a4\u30ba\u30922\u500d\u306b\u3059\u308b\u3053\u3068\u3092\u898f\u5b9a\u3057\u307e\u3059\u3002</li> </ul> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig my_list.py<pre><code>class MyList:\n    \"\"\"\u30ea\u30b9\u30c8\u30af\u30e9\u30b9\"\"\"\n\n    def __init__(self):\n        \"\"\"\u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf\"\"\"\n        self._capacity: int = 10  # \u30ea\u30b9\u30c8\u306e\u5bb9\u91cf\n        self._arr: list[int] = [0] * self._capacity  # \u914d\u5217\uff08\u30ea\u30b9\u30c8\u8981\u7d20\u3092\u683c\u7d0d\uff09\n        self._size: int = 0  # \u30ea\u30b9\u30c8\u306e\u9577\u3055\uff08\u73fe\u5728\u306e\u8981\u7d20\u6570\uff09\n        self._extend_ratio: int = 2  # \u5404\u30ea\u30b9\u30c8\u62e1\u5f35\u306e\u500d\u6570\n\n    def size(self) -&gt; int:\n        \"\"\"\u30ea\u30b9\u30c8\u306e\u9577\u3055\uff08\u73fe\u5728\u306e\u8981\u7d20\u6570\uff09\u3092\u53d6\u5f97\"\"\"\n        return self._size\n\n    def capacity(self) -&gt; int:\n        \"\"\"\u30ea\u30b9\u30c8\u306e\u5bb9\u91cf\u3092\u53d6\u5f97\"\"\"\n        return self._capacity\n\n    def get(self, index: int) -&gt; int:\n        \"\"\"\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9\"\"\"\n        # \u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u304c\u7bc4\u56f2\u5916\u306e\u5834\u5408\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u4f8b\u5916\u3092\u30b9\u30ed\u30fc\n        if index &lt; 0 or index &gt;= self._size:\n            raise IndexError(\"Index out of bounds\")\n        return self._arr[index]\n\n    def set(self, num: int, index: int):\n        \"\"\"\u8981\u7d20\u3092\u66f4\u65b0\"\"\"\n        if index &lt; 0 or index &gt;= self._size:\n            raise IndexError(\"Index out of bounds\")\n        self._arr[index] = num\n\n    def add(self, num: int):\n        \"\"\"\u672b\u5c3e\u306b\u8981\u7d20\u3092\u8ffd\u52a0\"\"\"\n        # \u8981\u7d20\u6570\u304c\u5bb9\u91cf\u3092\u8d85\u3048\u308b\u5834\u5408\u3001\u62e1\u5f35\u30e1\u30ab\u30cb\u30ba\u30e0\u3092\u30c8\u30ea\u30ac\u30fc\n        if self.size() == self.capacity():\n            self.extend_capacity()\n        self._arr[self._size] = num\n        self._size += 1\n\n    def insert(self, num: int, index: int):\n        \"\"\"\u4e2d\u9593\u306b\u8981\u7d20\u3092\u633f\u5165\"\"\"\n        if index &lt; 0 or index &gt;= self._size:\n            raise IndexError(\"Index out of bounds\")\n        # \u8981\u7d20\u6570\u304c\u5bb9\u91cf\u3092\u8d85\u3048\u308b\u5834\u5408\u3001\u62e1\u5f35\u30e1\u30ab\u30cb\u30ba\u30e0\u3092\u30c8\u30ea\u30ac\u30fc\n        if self._size == self.capacity():\n            self.extend_capacity()\n        # \u30a4\u30f3\u30c7\u30c3\u30af\u30b9 index \u3088\u308a\u5f8c\u306e\u3059\u3079\u3066\u306e\u8981\u7d20\u30921\u3064\u5f8c\u308d\u306b\u79fb\u52d5\n        for j in range(self._size - 1, index - 1, -1):\n            self._arr[j + 1] = self._arr[j]\n        self._arr[index] = num\n        # \u8981\u7d20\u6570\u3092\u66f4\u65b0\n        self._size += 1\n\n    def remove(self, index: int) -&gt; int:\n        \"\"\"\u8981\u7d20\u3092\u524a\u9664\"\"\"\n        if index &lt; 0 or index &gt;= self._size:\n            raise IndexError(\"Index out of bounds\")\n        num = self._arr[index]\n        # \u30a4\u30f3\u30c7\u30c3\u30af\u30b9 index \u3088\u308a\u5f8c\u306e\u3059\u3079\u3066\u306e\u8981\u7d20\u30921\u3064\u524d\u306b\u79fb\u52d5\n        for j in range(index, self._size - 1):\n            self._arr[j] = self._arr[j + 1]\n        # \u8981\u7d20\u6570\u3092\u66f4\u65b0\n        self._size -= 1\n        # \u524a\u9664\u3055\u308c\u305f\u8981\u7d20\u3092\u8fd4\u3059\n        return num\n\n    def extend_capacity(self):\n        \"\"\"\u30ea\u30b9\u30c8\u3092\u62e1\u5f35\"\"\"\n        # \u5143\u306e\u914d\u5217\u306e _extend_ratio \u500d\u306e\u9577\u3055\u306e\u65b0\u3057\u3044\u914d\u5217\u3092\u4f5c\u6210\u3057\u3001\u5143\u306e\u914d\u5217\u3092\u65b0\u3057\u3044\u914d\u5217\u306b\u30b3\u30d4\u30fc\n        self._arr = self._arr + [0] * self.capacity() * (self._extend_ratio - 1)\n        # \u30ea\u30b9\u30c8\u306e\u5bb9\u91cf\u3092\u66f4\u65b0\n        self._capacity = len(self._arr)\n\n    def to_array(self) -&gt; list[int]:\n        \"\"\"\u6709\u52b9\u306a\u9577\u3055\u306e\u30ea\u30b9\u30c8\u3092\u8fd4\u3059\"\"\"\n        return self._arr[: self._size]\n</code></pre> my_list.cpp<pre><code>/* \u30ea\u30b9\u30c8\u30af\u30e9\u30b9 */\nclass MyList {\n  private:\n    int *arr;             // \u914d\u5217\uff08\u30ea\u30b9\u30c8\u8981\u7d20\u3092\u683c\u7d0d\uff09\n    int arrCapacity = 10; // \u30ea\u30b9\u30c8\u306e\u5bb9\u91cf\n    int arrSize = 0;      // \u30ea\u30b9\u30c8\u306e\u9577\u3055\uff08\u73fe\u5728\u306e\u8981\u7d20\u6570\uff09\n    int extendRatio = 2;   // \u30ea\u30b9\u30c8\u62e1\u5f35\u6642\u306e\u500d\u7387\n\n  public:\n    /* \u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf */\n    MyList() {\n        arr = new int[arrCapacity];\n    }\n\n    /* \u30c7\u30b9\u30c8\u30e9\u30af\u30bf */\n    ~MyList() {\n        delete[] arr;\n    }\n\n    /* \u30ea\u30b9\u30c8\u306e\u9577\u3055\u3092\u53d6\u5f97\uff08\u73fe\u5728\u306e\u8981\u7d20\u6570\uff09*/\n    int size() {\n        return arrSize;\n    }\n\n    /* \u30ea\u30b9\u30c8\u306e\u5bb9\u91cf\u3092\u53d6\u5f97 */\n    int capacity() {\n        return arrCapacity;\n    }\n\n    /* \u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\n    int get(int index) {\n        // \u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u304c\u7bc4\u56f2\u5916\u306e\u5834\u5408\u3001\u4f8b\u5916\u3092\u30b9\u30ed\u30fc\uff08\u4ee5\u4e0b\u540c\u69d8\uff09\n        if (index &lt; 0 || index &gt;= size())\n            throw out_of_range(\"Index out of bounds\");\n        return arr[index];\n    }\n\n    /* \u8981\u7d20\u3092\u66f4\u65b0 */\n    void set(int index, int num) {\n        if (index &lt; 0 || index &gt;= size())\n            throw out_of_range(\"Index out of bounds\");\n        arr[index] = num;\n    }\n\n    /* \u672b\u5c3e\u306b\u8981\u7d20\u3092\u8ffd\u52a0 */\n    void add(int num) {\n        // \u8981\u7d20\u6570\u304c\u5bb9\u91cf\u3092\u8d85\u3048\u305f\u5834\u5408\u3001\u62e1\u5f35\u30e1\u30ab\u30cb\u30ba\u30e0\u3092\u30c8\u30ea\u30ac\u30fc\n        if (size() == capacity())\n            extendCapacity();\n        arr[size()] = num;\n        // \u8981\u7d20\u6570\u3092\u66f4\u65b0\n        arrSize++;\n    }\n\n    /* \u4e2d\u9593\u306b\u8981\u7d20\u3092\u633f\u5165 */\n    void insert(int index, int num) {\n        if (index &lt; 0 || index &gt;= size())\n            throw out_of_range(\"Index out of bounds\");\n        // \u8981\u7d20\u6570\u304c\u5bb9\u91cf\u3092\u8d85\u3048\u305f\u5834\u5408\u3001\u62e1\u5f35\u30e1\u30ab\u30cb\u30ba\u30e0\u3092\u30c8\u30ea\u30ac\u30fc\n        if (size() == capacity())\n            extendCapacity();\n        // `index`\u3088\u308a\u5f8c\u306e\u3059\u3079\u3066\u306e\u8981\u7d20\u30921\u3064\u5f8c\u308d\u306b\u79fb\u52d5\n        for (int j = size() - 1; j &gt;= index; j--) {\n            arr[j + 1] = arr[j];\n        }\n        arr[index] = num;\n        // \u8981\u7d20\u6570\u3092\u66f4\u65b0\n        arrSize++;\n    }\n\n    /* \u8981\u7d20\u3092\u524a\u9664 */\n    int remove(int index) {\n        if (index &lt; 0 || index &gt;= size())\n            throw out_of_range(\"Index out of bounds\");\n        int num = arr[index];\n        // `index`\u3088\u308a\u5f8c\u306e\u3059\u3079\u3066\u306e\u8981\u7d20\u30921\u3064\u524d\u306b\u79fb\u52d5\n        for (int j = index; j &lt; size() - 1; j++) {\n            arr[j] = arr[j + 1];\n        }\n        // \u8981\u7d20\u6570\u3092\u66f4\u65b0\n        arrSize--;\n        // \u524a\u9664\u3055\u308c\u305f\u8981\u7d20\u3092\u8fd4\u5374\n        return num;\n    }\n\n    /* \u30ea\u30b9\u30c8\u3092\u62e1\u5f35 */\n    void extendCapacity() {\n        // \u5143\u306e\u914d\u5217\u306eextendRatio\u500d\u306e\u9577\u3055\u3067\u65b0\u3057\u3044\u914d\u5217\u3092\u4f5c\u6210\n        int newCapacity = capacity() * extendRatio;\n        int *tmp = arr;\n        arr = new int[newCapacity];\n        // \u5143\u306e\u914d\u5217\u306e\u3059\u3079\u3066\u306e\u8981\u7d20\u3092\u65b0\u3057\u3044\u914d\u5217\u306b\u30b3\u30d4\u30fc\n        for (int i = 0; i &lt; size(); i++) {\n            arr[i] = tmp[i];\n        }\n        // \u30e1\u30e2\u30ea\u3092\u89e3\u653e\n        delete[] tmp;\n        arrCapacity = newCapacity;\n    }\n\n    /* \u30ea\u30b9\u30c8\u3092Vector\u306b\u5909\u63db\u3057\u3066\u5370\u5237\u7528\u306b\u4f7f\u7528 */\n    vector&lt;int&gt; toVector() {\n        // \u6709\u52b9\u306a\u9577\u3055\u7bc4\u56f2\u5185\u306e\u8981\u7d20\u306e\u307f\u3092\u5909\u63db\n        vector&lt;int&gt; vec(size());\n        for (int i = 0; i &lt; size(); i++) {\n            vec[i] = arr[i];\n        }\n        return vec;\n    }\n};\n</code></pre> my_list.java<pre><code>/* \u30ea\u30b9\u30c8\u30af\u30e9\u30b9 */\nclass MyList {\n    private int[] arr; // \u914d\u5217\uff08\u30ea\u30b9\u30c8\u8981\u7d20\u3092\u683c\u7d0d\uff09\n    private int capacity = 10; // \u30ea\u30b9\u30c8\u5bb9\u91cf\n    private int size = 0; // \u30ea\u30b9\u30c8\u9577\uff08\u73fe\u5728\u306e\u8981\u7d20\u6570\uff09\n    private int extendRatio = 2; // \u30ea\u30b9\u30c8\u306e\u5404\u62e1\u5f35\u500d\u7387\n\n    /* \u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf */\n    public MyList() {\n        arr = new int[capacity];\n    }\n\n    /* \u30ea\u30b9\u30c8\u9577\u3092\u53d6\u5f97\uff08\u73fe\u5728\u306e\u8981\u7d20\u6570\uff09 */\n    public int size() {\n        return size;\n    }\n\n    /* \u30ea\u30b9\u30c8\u5bb9\u91cf\u3092\u53d6\u5f97 */\n    public int capacity() {\n        return capacity;\n    }\n\n    /* \u8981\u7d20\u3078\u306e\u30a2\u30af\u30bb\u30b9 */\n    public int get(int index) {\n        // \u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u304c\u7bc4\u56f2\u5916\u306e\u5834\u5408\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u4f8b\u5916\u3092\u30b9\u30ed\u30fc\n        if (index &lt; 0 || index &gt;= size)\n            throw new IndexOutOfBoundsException(\"\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u304c\u7bc4\u56f2\u5916\u3067\u3059\");\n        return arr[index];\n    }\n\n    /* \u8981\u7d20\u306e\u66f4\u65b0 */\n    public void set(int index, int num) {\n        if (index &lt; 0 || index &gt;= size)\n            throw new IndexOutOfBoundsException(\"\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u304c\u7bc4\u56f2\u5916\u3067\u3059\");\n        arr[index] = num;\n    }\n\n    /* \u672b\u5c3e\u306b\u8981\u7d20\u3092\u8ffd\u52a0 */\n    public void add(int num) {\n        // \u8981\u7d20\u6570\u304c\u5bb9\u91cf\u3092\u8d85\u3048\u308b\u5834\u5408\u3001\u62e1\u5f35\u30e1\u30ab\u30cb\u30ba\u30e0\u3092\u5b9f\u884c\n        if (size == capacity())\n            extendCapacity();\n        arr[size] = num;\n        // \u8981\u7d20\u6570\u3092\u66f4\u65b0\n        size++;\n    }\n\n    /* \u4e2d\u9593\u306b\u8981\u7d20\u3092\u633f\u5165 */\n    public void insert(int index, int num) {\n        if (index &lt; 0 || index &gt;= size)\n            throw new IndexOutOfBoundsException(\"\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u304c\u7bc4\u56f2\u5916\u3067\u3059\");\n        // \u8981\u7d20\u6570\u304c\u5bb9\u91cf\u3092\u8d85\u3048\u308b\u5834\u5408\u3001\u62e1\u5f35\u30e1\u30ab\u30cb\u30ba\u30e0\u3092\u5b9f\u884c\n        if (size == capacity())\n            extendCapacity();\n        // `index` \u3088\u308a\u5f8c\u306e\u3059\u3079\u3066\u306e\u8981\u7d20\u30921\u3064\u5f8c\u308d\u306b\u79fb\u52d5\n        for (int j = size - 1; j &gt;= index; j--) {\n            arr[j + 1] = arr[j];\n        }\n        arr[index] = num;\n        // \u8981\u7d20\u6570\u3092\u66f4\u65b0\n        size++;\n    }\n\n    /* \u8981\u7d20\u306e\u524a\u9664 */\n    public int remove(int index) {\n        if (index &lt; 0 || index &gt;= size)\n            throw new IndexOutOfBoundsException(\"\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u304c\u7bc4\u56f2\u5916\u3067\u3059\");\n        int num = arr[index];\n        // `index` \u3088\u308a\u5f8c\u306e\u3059\u3079\u3066\u306e\u8981\u7d20\u30921\u3064\u524d\u306b\u79fb\u52d5\n        for (int j = index; j &lt; size - 1; j++) {\n            arr[j] = arr[j + 1];\n        }\n        // \u8981\u7d20\u6570\u3092\u66f4\u65b0\n        size--;\n        // \u524a\u9664\u3055\u308c\u305f\u8981\u7d20\u3092\u8fd4\u3059\n        return num;\n    }\n\n    /* \u30ea\u30b9\u30c8\u3092\u62e1\u5f35 */\n    public void extendCapacity() {\n        // \u5143\u306e\u914d\u5217\u306e\u9577\u3055\u3092 extendRatio \u500d\u3057\u305f\u65b0\u3057\u3044\u914d\u5217\u3092\u4f5c\u6210\u3057\u3001\u5143\u306e\u914d\u5217\u3092\u65b0\u3057\u3044\u914d\u5217\u306b\u30b3\u30d4\u30fc\n        arr = Arrays.copyOf(arr, capacity() * extendRatio);\n        // \u30ea\u30b9\u30c8\u5bb9\u91cf\u3092\u66f4\u65b0\n        capacity = arr.length;\n    }\n\n    /* \u30ea\u30b9\u30c8\u3092\u914d\u5217\u306b\u5909\u63db */\n    public int[] toArray() {\n        int size = size();\n        // \u6709\u52b9\u306a\u9577\u3055\u7bc4\u56f2\u5185\u306e\u8981\u7d20\u306e\u307f\u3092\u5909\u63db\n        int[] arr = new int[size];\n        for (int i = 0; i &lt; size; i++) {\n            arr[i] = get(i);\n        }\n        return arr;\n    }\n}\n</code></pre> my_list.cs<pre><code>[class]{MyList}-[func]{}\n</code></pre> my_list.go<pre><code>[class]{myList}-[func]{}\n</code></pre> my_list.swift<pre><code>[class]{MyList}-[func]{}\n</code></pre> my_list.js<pre><code>[class]{MyList}-[func]{}\n</code></pre> my_list.ts<pre><code>[class]{MyList}-[func]{}\n</code></pre> my_list.dart<pre><code>[class]{MyList}-[func]{}\n</code></pre> my_list.rs<pre><code>[class]{MyList}-[func]{}\n</code></pre> my_list.c<pre><code>[class]{MyList}-[func]{}\n</code></pre> my_list.kt<pre><code>[class]{MyList}-[func]{}\n</code></pre> my_list.rb<pre><code>[class]{MyList}-[func]{}\n</code></pre> my_list.zig<pre><code>[class]{MyList}-[func]{}\n</code></pre>"},{"location":"chapter_array_and_linkedlist/ram_and_cache/","title":"4.4 \u00a0 \u30e1\u30e2\u30ea\u3068\u30ad\u30e3\u30c3\u30b7\u30e5 *","text":"<p>\u3053\u306e\u7ae0\u306e\u6700\u521d\u306e2\u3064\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u3067\u306f\u3001\u300c\u9023\u7d9a\u683c\u7d0d\u300d\u3068\u300c\u5206\u6563\u683c\u7d0d\u300d\u3092\u305d\u308c\u305e\u308c\u8868\u73fe\u3059\u308b2\u3064\u306e\u57fa\u672c\u7684\u306a\u30c7\u30fc\u30bf\u69cb\u9020\u3067\u3042\u308b\u914d\u5217\u3068\u9023\u7d50\u30ea\u30b9\u30c8\u3092\u63a2\u7a76\u3057\u307e\u3057\u305f\u3002</p> <p>\u5b9f\u969b\u3001\u7269\u7406\u69cb\u9020\u306f\u30d7\u30ed\u30b0\u30e9\u30e0\u304c\u30e1\u30e2\u30ea\u3068\u30ad\u30e3\u30c3\u30b7\u30e5\u3092\u3069\u306e\u7a0b\u5ea6\u52b9\u7387\u7684\u306b\u5229\u7528\u3059\u308b\u304b\u3092\u5927\u304d\u304f\u6c7a\u5b9a\u3057\u3001\u3053\u308c\u304c\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5168\u4f53\u7684\u306a\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u306b\u5f71\u97ff\u3092\u4e0e\u3048\u307e\u3059\u3002</p>"},{"location":"chapter_array_and_linkedlist/ram_and_cache/#441","title":"4.4.1 \u00a0 \u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u8a18\u61b6\u88c5\u7f6e","text":"<p>\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u306b\u306f3\u7a2e\u985e\u306e\u8a18\u61b6\u88c5\u7f6e\u304c\u3042\u308a\u307e\u3059\uff1a\u30cf\u30fc\u30c9\u30c7\u30a3\u30b9\u30af\u3001\u30e9\u30f3\u30c0\u30e0\u30a2\u30af\u30bb\u30b9\u30e1\u30e2\u30ea\uff08RAM\uff09\u3001\u304a\u3088\u3073\u30ad\u30e3\u30c3\u30b7\u30e5\u30e1\u30e2\u30ea\u3067\u3059\u3002\u4ee5\u4e0b\u306e\u8868\u306f\u3001\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u30b7\u30b9\u30c6\u30e0\u306b\u304a\u3051\u308b\u305d\u308c\u305e\u308c\u306e\u5f79\u5272\u3068\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u7279\u6027\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002</p> <p> \u8868 4-2 \u00a0 \u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u8a18\u61b6\u88c5\u7f6e </p> \u30cf\u30fc\u30c9\u30c7\u30a3\u30b9\u30af \u30e1\u30e2\u30ea \u30ad\u30e3\u30c3\u30b7\u30e5 \u7528\u9014 OS\u3001\u30d7\u30ed\u30b0\u30e9\u30e0\u3001\u30d5\u30a1\u30a4\u30eb\u306a\u3069\u306e\u30c7\u30fc\u30bf\u306e\u9577\u671f\u4fdd\u5b58 \u73fe\u5728\u5b9f\u884c\u4e2d\u306e\u30d7\u30ed\u30b0\u30e9\u30e0\u3068\u51e6\u7406\u4e2d\u306e\u30c7\u30fc\u30bf\u306e\u4e00\u6642\u4fdd\u5b58 \u983b\u7e41\u306b\u30a2\u30af\u30bb\u30b9\u3055\u308c\u308b\u30c7\u30fc\u30bf\u3068\u547d\u4ee4\u3092\u4fdd\u5b58\u3057\u3001CPU\u306e\u30e1\u30e2\u30ea\u3078\u306e\u30a2\u30af\u30bb\u30b9\u6570\u3092\u524a\u6e1b \u63ee\u767a\u6027 \u96fb\u6e90\u30aa\u30d5\u5f8c\u3082\u30c7\u30fc\u30bf\u306f\u5931\u308f\u308c\u306a\u3044 \u96fb\u6e90\u30aa\u30d5\u5f8c\u306b\u30c7\u30fc\u30bf\u306f\u5931\u308f\u308c\u308b \u96fb\u6e90\u30aa\u30d5\u5f8c\u306b\u30c7\u30fc\u30bf\u306f\u5931\u308f\u308c\u308b \u5bb9\u91cf \u3088\u308a\u5927\u304d\u3044\u3001TB\u30ec\u30d9\u30eb \u3088\u308a\u5c0f\u3055\u3044\u3001GB\u30ec\u30d9\u30eb \u975e\u5e38\u306b\u5c0f\u3055\u3044\u3001MB\u30ec\u30d9\u30eb \u901f\u5ea6 \u3088\u308a\u9045\u3044\u3001\u6570\u767e\u304b\u3089\u6570\u5343MB/s \u3088\u308a\u9ad8\u901f\u3001\u6570\u5341GB/s \u975e\u5e38\u306b\u9ad8\u901f\u3001\u6570\u5341\u304b\u3089\u6570\u767eGB/s \u4fa1\u683c\uff08USD\uff09 \u3088\u308a\u5b89\u4fa1\u3001\u6570\u30bb\u30f3\u30c8/GB \u3088\u308a\u9ad8\u4fa1\u3001\u6570\u30c9\u30eb/GB \u975e\u5e38\u306b\u9ad8\u4fa1\u3001CPU\u3068\u4e00\u7dd2\u306b\u4fa1\u683c\u8a2d\u5b9a <p>\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u8a18\u61b6\u30b7\u30b9\u30c6\u30e0\u306f\u3001\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u30d4\u30e9\u30df\u30c3\u30c9\u3068\u3057\u3066\u8996\u899a\u5316\u3067\u304d\u307e\u3059\u3002\u30d4\u30e9\u30df\u30c3\u30c9\u306e\u4e0a\u90e8\u306b\u3042\u308b\u8a18\u61b6\u88c5\u7f6e\u307b\u3069\u9ad8\u901f\u3067\u3001\u5bb9\u91cf\u304c\u5c0f\u3055\u304f\u3001\u3088\u308a\u9ad8\u4fa1\u3067\u3059\u3002\u3053\u306e\u30de\u30eb\u30c1\u30ec\u30d9\u30eb\u8a2d\u8a08\u306f\u5076\u7136\u3067\u306f\u306a\u304f\u3001\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u79d1\u5b66\u8005\u3068\u30a8\u30f3\u30b8\u30cb\u30a2\u306b\u3088\u308b\u614e\u91cd\u306a\u691c\u8a0e\u306e\u7d50\u679c\u3067\u3059\u3002</p> <ul> <li>\u30cf\u30fc\u30c9\u30c7\u30a3\u30b9\u30af\u3092\u30e1\u30e2\u30ea\u306b\u7f6e\u304d\u63db\u3048\u308b\u306e\u306f\u56f0\u96e3\u3067\u3059\u3002\u7b2c\u4e00\u306b\u3001\u30e1\u30e2\u30ea\u5185\u306e\u30c7\u30fc\u30bf\u306f\u96fb\u6e90\u30aa\u30d5\u5f8c\u306b\u5931\u308f\u308c\u308b\u305f\u3081\u3001\u9577\u671f\u30c7\u30fc\u30bf\u4fdd\u5b58\u306b\u306f\u9069\u3057\u3066\u3044\u307e\u305b\u3093\u3002\u7b2c\u4e8c\u306b\u3001\u30e1\u30e2\u30ea\u306f\u30cf\u30fc\u30c9\u30c7\u30a3\u30b9\u30af\u3088\u308a\u3082\u5927\u5e45\u306b\u9ad8\u4fa1\u3067\u3001\u6d88\u8cbb\u8005\u5e02\u5834\u3067\u306e\u5e83\u7bc4\u56f2\u306a\u4f7f\u7528\u306e\u5b9f\u73fe\u53ef\u80fd\u6027\u3092\u5236\u9650\u3057\u3066\u3044\u307e\u3059\u3002</li> <li>\u30ad\u30e3\u30c3\u30b7\u30e5\u306f\u5927\u5bb9\u91cf\u3068\u9ad8\u901f\u306e\u30c8\u30ec\u30fc\u30c9\u30aa\u30d5\u306b\u76f4\u9762\u3057\u3066\u3044\u307e\u3059\u3002L1\u3001L2\u3001L3\u30ad\u30e3\u30c3\u30b7\u30e5\u306e\u5bb9\u91cf\u304c\u5897\u52a0\u3059\u308b\u306b\u3064\u308c\u3066\u3001\u305d\u306e\u7269\u7406\u30b5\u30a4\u30ba\u304c\u5927\u304d\u304f\u306a\u308a\u3001CPU\u30b3\u30a2\u304b\u3089\u306e\u8ddd\u96e2\u304c\u5897\u52a0\u3057\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u30c7\u30fc\u30bf\u8ee2\u9001\u6642\u9593\u304c\u9577\u304f\u306a\u308a\u3001\u30a2\u30af\u30bb\u30b9\u9045\u5ef6\u304c\u9ad8\u304f\u306a\u308a\u307e\u3059\u3002\u73fe\u5728\u306e\u6280\u8853\u3067\u306f\u3001\u30de\u30eb\u30c1\u30ec\u30d9\u30eb\u30ad\u30e3\u30c3\u30b7\u30e5\u69cb\u9020\u304c\u5bb9\u91cf\u3001\u901f\u5ea6\u3001\u30b3\u30b9\u30c8\u306e\u9593\u306e\u6700\u9069\u306a\u30d0\u30e9\u30f3\u30b9\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002</li> </ul> <p></p> <p> \u56f3 4-9 \u00a0 \u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u8a18\u61b6\u30b7\u30b9\u30c6\u30e0 </p> <p>Tip</p> <p>\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u306e\u8a18\u61b6\u968e\u5c64\u306f\u3001\u901f\u5ea6\u3001\u5bb9\u91cf\u3001\u30b3\u30b9\u30c8\u306e\u9593\u306e\u614e\u91cd\u306a\u30d0\u30e9\u30f3\u30b9\u3092\u53cd\u6620\u3057\u3066\u3044\u307e\u3059\u3002\u3053\u306e\u30bf\u30a4\u30d7\u306e\u30c8\u30ec\u30fc\u30c9\u30aa\u30d5\u306f\u69d8\u3005\u306a\u696d\u754c\u3067\u4e00\u822c\u7684\u3067\u3042\u308a\u3001\u5229\u76ca\u3068\u5236\u9650\u306e\u9593\u306e\u6700\u9069\u306a\u30d0\u30e9\u30f3\u30b9\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u91cd\u8981\u3067\u3059\u3002</p> <p>\u5168\u4f53\u7684\u306b\u3001\u30cf\u30fc\u30c9\u30c7\u30a3\u30b9\u30af\u306f\u5927\u91cf\u306e\u30c7\u30fc\u30bf\u306e\u9577\u671f\u4fdd\u5b58\u3092\u63d0\u4f9b\u3057\u3001\u30e1\u30e2\u30ea\u306f\u30d7\u30ed\u30b0\u30e9\u30e0\u5b9f\u884c\u4e2d\u306b\u51e6\u7406\u3055\u308c\u308b\u30c7\u30fc\u30bf\u306e\u4e00\u6642\u4fdd\u5b58\u3068\u3057\u3066\u6a5f\u80fd\u3057\u3001\u30ad\u30e3\u30c3\u30b7\u30e5\u306f\u983b\u7e41\u306b\u30a2\u30af\u30bb\u30b9\u3055\u308c\u308b\u30c7\u30fc\u30bf\u3068\u547d\u4ee4\u3092\u4fdd\u5b58\u3057\u3066\u5b9f\u884c\u52b9\u7387\u3092\u5411\u4e0a\u3055\u305b\u307e\u3059\u3002\u305d\u308c\u3089\u306f\u4e00\u7dd2\u306b\u306a\u3063\u3066\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u30b7\u30b9\u30c6\u30e0\u306e\u52b9\u7387\u7684\u306a\u52d5\u4f5c\u3092\u4fdd\u8a3c\u3057\u307e\u3059\u3002</p> <p>\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u30d7\u30ed\u30b0\u30e9\u30e0\u5b9f\u884c\u4e2d\u3001\u30c7\u30fc\u30bf\u306f\u30cf\u30fc\u30c9\u30c7\u30a3\u30b9\u30af\u304b\u3089\u30e1\u30e2\u30ea\u306b\u8aad\u307f\u8fbc\u307e\u308c\u3001CPU\u8a08\u7b97\u304c\u884c\u308f\u308c\u307e\u3059\u3002CPU\u306e\u62e1\u5f35\u3068\u3057\u3066\u6a5f\u80fd\u3059\u308b\u30ad\u30e3\u30c3\u30b7\u30e5\u306f\u3001**\u30e1\u30e2\u30ea\u304b\u3089\u30a4\u30f3\u30c6\u30ea\u30b8\u30a7\u30f3\u30c8\u306b\u30c7\u30fc\u30bf\u3092\u5148\u8aad\u307f**\u3057\u3001CPU\u306e\u3088\u308a\u9ad8\u901f\u306a\u30c7\u30fc\u30bf\u30a2\u30af\u30bb\u30b9\u3092\u53ef\u80fd\u306b\u3057\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u30d7\u30ed\u30b0\u30e9\u30e0\u5b9f\u884c\u52b9\u7387\u304c\u5927\u5e45\u306b\u5411\u4e0a\u3057\u3001\u4f4e\u901f\u306a\u30e1\u30e2\u30ea\u3078\u306e\u4f9d\u5b58\u304c\u6e1b\u5c11\u3057\u307e\u3059\u3002</p> <p></p> <p> \u56f3 4-10 \u00a0 \u30cf\u30fc\u30c9\u30c7\u30a3\u30b9\u30af\u3001\u30e1\u30e2\u30ea\u3001\u30ad\u30e3\u30c3\u30b7\u30e5\u9593\u306e\u30c7\u30fc\u30bf\u30d5\u30ed\u30fc </p>"},{"location":"chapter_array_and_linkedlist/ram_and_cache/#442","title":"4.4.2 \u00a0 \u30c7\u30fc\u30bf\u69cb\u9020\u306e\u30e1\u30e2\u30ea\u52b9\u7387","text":"<p>\u30e1\u30e2\u30ea\u7a7a\u9593\u5229\u7528\u306e\u89b3\u70b9\u304b\u3089\u3001\u914d\u5217\u3068\u9023\u7d50\u30ea\u30b9\u30c8\u306b\u306f\u305d\u308c\u305e\u308c\u5229\u70b9\u3068\u5236\u9650\u304c\u3042\u308a\u307e\u3059\u3002</p> <p>\u4e00\u65b9\u3067\u3001**\u30e1\u30e2\u30ea\u306f\u9650\u3089\u308c\u3066\u304a\u308a\u3001\u8907\u6570\u306e\u30d7\u30ed\u30b0\u30e9\u30e0\u9593\u3067\u5171\u6709\u3067\u304d\u306a\u3044**\u305f\u3081\u3001\u30c7\u30fc\u30bf\u69cb\u9020\u3067\u306e\u7a7a\u9593\u4f7f\u7528\u306e\u6700\u9069\u5316\u306f\u91cd\u8981\u3067\u3059\u3002\u914d\u5217\u306f\u8981\u7d20\u304c\u5bc6\u63a5\u306b\u30d1\u30c3\u30af\u3055\u308c\u3066\u304a\u308a\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u306e\u3088\u3046\u306b\u53c2\u7167\uff08\u30dd\u30a4\u30f3\u30bf\uff09\u306e\u305f\u3081\u306e\u8ffd\u52a0\u30e1\u30e2\u30ea\u3092\u5fc5\u8981\u3068\u3057\u306a\u3044\u305f\u3081\u3001\u7a7a\u9593\u52b9\u7387\u7684\u3067\u3059\u3002\u3057\u304b\u3057\u3001\u914d\u5217\u306f\u9023\u7d9a\u3057\u305f\u30e1\u30e2\u30ea\u30d6\u30ed\u30c3\u30af\u3092\u4e8b\u524d\u306b\u5272\u308a\u5f53\u3066\u308b\u5fc5\u8981\u304c\u3042\u308a\u3001\u5272\u308a\u5f53\u3066\u3089\u308c\u305f\u7a7a\u9593\u304c\u5b9f\u969b\u306e\u5fc5\u8981\u91cf\u3092\u8d85\u3048\u308b\u5834\u5408\u3001\u7121\u99c4\u306b\u3064\u306a\u304c\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002\u914d\u5217\u306e\u62e1\u5f35\u3082\u8ffd\u52a0\u306e\u6642\u9593\u3068\u7a7a\u9593\u306e\u30aa\u30fc\u30d0\u30fc\u30d8\u30c3\u30c9\u3092\u4f34\u3044\u307e\u3059\u3002\u5bfe\u7167\u7684\u306b\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u306f\u5404\u30ce\u30fc\u30c9\u306b\u5bfe\u3057\u3066\u30e1\u30e2\u30ea\u3092\u52d5\u7684\u306b\u5272\u308a\u5f53\u3066\u30fb\u89e3\u653e\u3057\u3001\u30dd\u30a4\u30f3\u30bf\u306e\u305f\u3081\u306e\u8ffd\u52a0\u30e1\u30e2\u30ea\u306e\u30b3\u30b9\u30c8\u3067\u3088\u308a\u5927\u304d\u306a\u67d4\u8edf\u6027\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002</p> <p>\u4e00\u65b9\u3067\u3001\u30d7\u30ed\u30b0\u30e9\u30e0\u5b9f\u884c\u4e2d\u3001\u7e70\u308a\u8fd4\u3055\u308c\u308b\u30e1\u30e2\u30ea\u306e\u5272\u308a\u5f53\u3066\u3068\u89e3\u653e\u306f\u30e1\u30e2\u30ea\u306e\u65ad\u7247\u5316\u3092\u5897\u52a0\u3055\u305b\u3001\u30e1\u30e2\u30ea\u5229\u7528\u52b9\u7387\u3092\u4f4e\u4e0b\u3055\u305b\u307e\u3059\u3002\u914d\u5217\u306f\u9023\u7d9a\u8a18\u61b6\u65b9\u5f0f\u306b\u3088\u308a\u3001\u30e1\u30e2\u30ea\u65ad\u7247\u5316\u3092\u5f15\u304d\u8d77\u3053\u3059\u53ef\u80fd\u6027\u304c\u6bd4\u8f03\u7684\u4f4e\u3044\u3067\u3059\u3002\u5bfe\u7167\u7684\u306b\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u306f\u8981\u7d20\u3092\u975e\u9023\u7d9a\u306e\u5834\u6240\u306b\u4fdd\u5b58\u3057\u3001\u983b\u7e41\u306a\u633f\u5165\u3068\u524a\u9664\u306f\u30e1\u30e2\u30ea\u65ad\u7247\u5316\u3092\u60aa\u5316\u3055\u305b\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002</p>"},{"location":"chapter_array_and_linkedlist/ram_and_cache/#443","title":"4.4.3 \u00a0 \u30c7\u30fc\u30bf\u69cb\u9020\u306e\u30ad\u30e3\u30c3\u30b7\u30e5\u52b9\u7387","text":"<p>\u30ad\u30e3\u30c3\u30b7\u30e5\u306f\u30e1\u30e2\u30ea\u3088\u308a\u3082\u7a7a\u9593\u5bb9\u91cf\u304c\u306f\u308b\u304b\u306b\u5c0f\u3055\u3044\u3067\u3059\u304c\u3001\u306f\u308b\u304b\u306b\u9ad8\u901f\u3067\u3001\u30d7\u30ed\u30b0\u30e9\u30e0\u5b9f\u884c\u901f\u5ea6\u306b\u304a\u3044\u3066\u91cd\u8981\u306a\u5f79\u5272\u3092\u679c\u305f\u3057\u307e\u3059\u3002\u9650\u3089\u308c\u305f\u5bb9\u91cf\u306e\u305f\u3081\u3001\u30ad\u30e3\u30c3\u30b7\u30e5\u306f\u983b\u7e41\u306b\u30a2\u30af\u30bb\u30b9\u3055\u308c\u308b\u30c7\u30fc\u30bf\u306e\u30b5\u30d6\u30bb\u30c3\u30c8\u306e\u307f\u3092\u4fdd\u5b58\u3067\u304d\u307e\u3059\u3002CPU\u304c\u30ad\u30e3\u30c3\u30b7\u30e5\u306b\u5b58\u5728\u3057\u306a\u3044\u30c7\u30fc\u30bf\u306b\u30a2\u30af\u30bb\u30b9\u3057\u3088\u3046\u3068\u3059\u308b\u3068\u3001\u30ad\u30e3\u30c3\u30b7\u30e5\u30df\u30b9\u304c\u767a\u751f\u3057\u3001CPU\u306f\u4f4e\u901f\u306a\u30e1\u30e2\u30ea\u304b\u3089\u5fc5\u8981\u306a\u30c7\u30fc\u30bf\u3092\u53d6\u5f97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u3001\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u306b\u5f71\u97ff\u3092\u4e0e\u3048\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002</p> <p>\u660e\u3089\u304b\u306b\u3001\u30ad\u30e3\u30c3\u30b7\u30e5\u30df\u30b9\u304c\u5c11\u306a\u3044\u307b\u3069\u3001CPU\u306e\u30c7\u30fc\u30bf\u8aad\u307f\u66f8\u304d\u52b9\u7387\u304c\u9ad8\u304f\u3001\u30d7\u30ed\u30b0\u30e9\u30e0\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u304c\u5411\u4e0a\u3057\u307e\u3059\u3002CPU\u304c\u30ad\u30e3\u30c3\u30b7\u30e5\u304b\u3089\u30c7\u30fc\u30bf\u3092\u6b63\u5e38\u306b\u53d6\u5f97\u3059\u308b\u5272\u5408\u306f\u30ad\u30e3\u30c3\u30b7\u30e5\u30d2\u30c3\u30c8\u7387\u3068\u547c\u3070\u308c\u3001\u30ad\u30e3\u30c3\u30b7\u30e5\u52b9\u7387\u3092\u6e2c\u5b9a\u3059\u308b\u305f\u3081\u306b\u3088\u304f\u4f7f\u7528\u3055\u308c\u308b\u6307\u6a19\u3067\u3059\u3002</p> <p>\u3088\u308a\u9ad8\u3044\u52b9\u7387\u3092\u9054\u6210\u3059\u308b\u305f\u3081\u306b\u3001\u30ad\u30e3\u30c3\u30b7\u30e5\u306f\u4ee5\u4e0b\u306e\u30c7\u30fc\u30bf\u30ed\u30fc\u30c9\u30e1\u30ab\u30cb\u30ba\u30e0\u3092\u63a1\u7528\u3057\u307e\u3059\u3002</p> <ul> <li>\u30ad\u30e3\u30c3\u30b7\u30e5\u30e9\u30a4\u30f3\uff1a\u30ad\u30e3\u30c3\u30b7\u30e5\u306f\u500b\u3005\u306e\u30d0\u30a4\u30c8\u3067\u306f\u306a\u304f\u3001\u30ad\u30e3\u30c3\u30b7\u30e5\u30e9\u30a4\u30f3\u3068\u547c\u3070\u308c\u308b\u5358\u4f4d\u3067\u30c7\u30fc\u30bf\u3092\u4fdd\u5b58\u30fb\u30ed\u30fc\u30c9\u3057\u3066\u52d5\u4f5c\u3057\u307e\u3059\u3002\u3053\u306e\u30a2\u30d7\u30ed\u30fc\u30c1\u306f\u3001\u4e00\u5ea6\u306b\u3088\u308a\u5927\u304d\u306a\u30c7\u30fc\u30bf\u30d6\u30ed\u30c3\u30af\u3092\u8ee2\u9001\u3059\u308b\u3053\u3068\u3067\u52b9\u7387\u3092\u5411\u4e0a\u3055\u305b\u307e\u3059\u3002</li> <li>\u5148\u8aad\u307f\u30e1\u30ab\u30cb\u30ba\u30e0\uff1a\u30d7\u30ed\u30bb\u30c3\u30b5\u306f\u30c7\u30fc\u30bf\u30a2\u30af\u30bb\u30b9\u30d1\u30bf\u30fc\u30f3\uff08\u4f8b\uff1a\u9023\u7d9a\u307e\u305f\u306f\u56fa\u5b9a\u30b9\u30c8\u30e9\u30a4\u30c9\u30a2\u30af\u30bb\u30b9\uff09\u3092\u4e88\u6e2c\u3057\u3001\u3053\u308c\u3089\u306e\u30d1\u30bf\u30fc\u30f3\u306b\u57fa\u3065\u3044\u3066\u30c7\u30fc\u30bf\u3092\u30ad\u30e3\u30c3\u30b7\u30e5\u306b\u5148\u8aad\u307f\u3057\u3066\u3001\u30ad\u30e3\u30c3\u30b7\u30e5\u30d2\u30c3\u30c8\u7387\u3092\u5411\u4e0a\u3055\u305b\u307e\u3059\u3002</li> <li>\u7a7a\u9593\u7684\u5c40\u6240\u6027\uff1a\u7279\u5b9a\u306e\u30c7\u30fc\u30bf\u304c\u30a2\u30af\u30bb\u30b9\u3055\u308c\u308b\u3068\u3001\u8fd1\u304f\u306e\u30c7\u30fc\u30bf\u3082\u307e\u3082\u306a\u304f\u30a2\u30af\u30bb\u30b9\u3055\u308c\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u308c\u3092\u6d3b\u7528\u3059\u308b\u305f\u3081\u306b\u3001\u30ad\u30e3\u30c3\u30b7\u30e5\u306f\u8981\u6c42\u3055\u308c\u305f\u30c7\u30fc\u30bf\u3068\u4e00\u7dd2\u306b\u96a3\u63a5\u3059\u308b\u30c7\u30fc\u30bf\u3092\u30ed\u30fc\u30c9\u3057\u3001\u30d2\u30c3\u30c8\u7387\u3092\u5411\u4e0a\u3055\u305b\u307e\u3059\u3002</li> <li>\u6642\u9593\u7684\u5c40\u6240\u6027\uff1a\u30c7\u30fc\u30bf\u304c\u30a2\u30af\u30bb\u30b9\u3055\u308c\u305f\u5834\u5408\u3001\u8fd1\u3044\u5c06\u6765\u306b\u518d\u3073\u30a2\u30af\u30bb\u30b9\u3055\u308c\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002\u30ad\u30e3\u30c3\u30b7\u30e5\u306f\u3053\u306e\u539f\u7406\u3092\u4f7f\u7528\u3057\u3066\u3001\u6700\u8fd1\u30a2\u30af\u30bb\u30b9\u3055\u308c\u305f\u30c7\u30fc\u30bf\u3092\u4fdd\u6301\u3057\u3066\u30d2\u30c3\u30c8\u7387\u3092\u5411\u4e0a\u3055\u305b\u307e\u3059\u3002</li> </ul> <p>\u5b9f\u969b\u3001\u914d\u5217\u3068\u9023\u7d50\u30ea\u30b9\u30c8\u306f\u7570\u306a\u308b\u30ad\u30e3\u30c3\u30b7\u30e5\u5229\u7528\u52b9\u7387\u3092\u6301\u3061\u3001\u3053\u308c\u306f\u4e3b\u306b\u4ee5\u4e0b\u306e\u5074\u9762\u306b\u53cd\u6620\u3055\u308c\u307e\u3059\u3002</p> <ul> <li>\u5360\u6709\u7a7a\u9593\uff1a\u9023\u7d50\u30ea\u30b9\u30c8\u8981\u7d20\u306f\u914d\u5217\u8981\u7d20\u3088\u308a\u3082\u591a\u304f\u306e\u7a7a\u9593\u3092\u5360\u6709\u3059\u308b\u305f\u3081\u3001\u30ad\u30e3\u30c3\u30b7\u30e5\u306b\u4fdd\u6301\u3055\u308c\u308b\u6709\u52b9\u30c7\u30fc\u30bf\u304c\u5c11\u306a\u304f\u306a\u308a\u307e\u3059\u3002</li> <li>\u30ad\u30e3\u30c3\u30b7\u30e5\u30e9\u30a4\u30f3\uff1a\u9023\u7d50\u30ea\u30b9\u30c8\u30c7\u30fc\u30bf\u306f\u30e1\u30e2\u30ea\u5168\u4f53\u306b\u6563\u5728\u3057\u3001\u30ad\u30e3\u30c3\u30b7\u30e5\u306f\u300c\u884c\u5358\u4f4d\u3067\u30ed\u30fc\u30c9\u300d\u3055\u308c\u308b\u305f\u3081\u3001\u30ed\u30fc\u30c9\u3055\u308c\u308b\u7121\u52b9\u30c7\u30fc\u30bf\u306e\u5272\u5408\u304c\u9ad8\u304f\u306a\u308a\u307e\u3059\u3002</li> <li>\u5148\u8aad\u307f\u30e1\u30ab\u30cb\u30ba\u30e0\uff1a\u914d\u5217\u306e\u30c7\u30fc\u30bf\u30a2\u30af\u30bb\u30b9\u30d1\u30bf\u30fc\u30f3\u306f\u9023\u7d50\u30ea\u30b9\u30c8\u3088\u308a\u3082\u300c\u4e88\u6e2c\u53ef\u80fd\u300d\u3067\u3001\u3064\u307e\u308a\u30b7\u30b9\u30c6\u30e0\u304c\u3053\u308c\u304b\u3089\u30ed\u30fc\u30c9\u3055\u308c\u308b\u30c7\u30fc\u30bf\u3092\u63a8\u6e2c\u3057\u3084\u3059\u3044\u3067\u3059\u3002</li> <li>\u7a7a\u9593\u7684\u5c40\u6240\u6027\uff1a\u914d\u5217\u306f\u9023\u7d9a\u3057\u305f\u30e1\u30e2\u30ea\u7a7a\u9593\u306b\u4fdd\u5b58\u3055\u308c\u308b\u305f\u3081\u3001\u30ed\u30fc\u30c9\u3055\u308c\u3066\u3044\u308b\u30c7\u30fc\u30bf\u306e\u8fd1\u304f\u306e\u30c7\u30fc\u30bf\u304c\u307e\u3082\u306a\u304f\u30a2\u30af\u30bb\u30b9\u3055\u308c\u308b\u53ef\u80fd\u6027\u304c\u9ad8\u304f\u306a\u308a\u307e\u3059\u3002</li> </ul> <p>\u5168\u4f53\u7684\u306b\u3001\u914d\u5217\u306f\u3088\u308a\u9ad8\u3044\u30ad\u30e3\u30c3\u30b7\u30e5\u30d2\u30c3\u30c8\u7387\u3092\u6301\u3061\u3001\u4e00\u822c\u7684\u306b\u9023\u7d50\u30ea\u30b9\u30c8\u3088\u308a\u3082\u64cd\u4f5c\u52b9\u7387\u304c\u9ad8\u3044\u3067\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u914d\u5217\u306b\u57fa\u3065\u304f\u30c7\u30fc\u30bf\u69cb\u9020\u306f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u554f\u984c\u306e\u89e3\u6c7a\u306b\u304a\u3044\u3066\u4eba\u6c17\u304c\u3042\u308a\u307e\u3059\u3002</p> <p>**\u9ad8\u3044\u30ad\u30e3\u30c3\u30b7\u30e5\u52b9\u7387\u304c\u914d\u5217\u304c\u5e38\u306b\u9023\u7d50\u30ea\u30b9\u30c8\u3088\u308a\u512a\u308c\u3066\u3044\u308b\u3068\u3044\u3046\u610f\u5473\u3067\u306f\u306a\u3044**\u3053\u3068\u306b\u6ce8\u610f\u3059\u3079\u304d\u3067\u3059\u3002\u30c7\u30fc\u30bf\u69cb\u9020\u306e\u9078\u629e\u306f\u7279\u5b9a\u306e\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u8981\u4ef6\u306b\u4f9d\u5b58\u3059\u3079\u304d\u3067\u3059\u3002\u4f8b\u3048\u3070\u3001\u914d\u5217\u3068\u9023\u7d50\u30ea\u30b9\u30c8\u306e\u4e21\u65b9\u304c\u300c\u30b9\u30bf\u30c3\u30af\u300d\u30c7\u30fc\u30bf\u69cb\u9020\u3092\u5b9f\u88c5\u3067\u304d\u307e\u3059\u304c\uff08\u6b21\u7ae0\u3067\u8a73\u7d30\u8aac\u660e\uff09\u3001\u305d\u308c\u3089\u306f\u7570\u306a\u308b\u30b7\u30ca\u30ea\u30aa\u306b\u9069\u3057\u3066\u3044\u307e\u3059\u3002</p> <ul> <li>\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u554f\u984c\u3067\u306f\u3001\u3088\u308a\u9ad8\u3044\u64cd\u4f5c\u52b9\u7387\u3068\u30e9\u30f3\u30c0\u30e0\u30a2\u30af\u30bb\u30b9\u6a5f\u80fd\u3092\u63d0\u4f9b\u3059\u308b\u305f\u3081\u3001\u914d\u5217\u306b\u57fa\u3065\u304f\u30b9\u30bf\u30c3\u30af\u3092\u9078\u629e\u3059\u308b\u50be\u5411\u304c\u3042\u308a\u307e\u3059\u3002\u552f\u4e00\u306e\u30b3\u30b9\u30c8\u306f\u914d\u5217\u306b\u5bfe\u3057\u3066\u4e00\u5b9a\u91cf\u306e\u30e1\u30e2\u30ea\u7a7a\u9593\u3092\u4e8b\u524d\u306b\u5272\u308a\u5f53\u3066\u308b\u5fc5\u8981\u304c\u3042\u308b\u3053\u3068\u3067\u3059\u3002</li> <li>\u30c7\u30fc\u30bf\u91cf\u304c\u975e\u5e38\u306b\u5927\u304d\u304f\u3001\u9ad8\u5ea6\u306b\u52d5\u7684\u3067\u3001\u30b9\u30bf\u30c3\u30af\u306e\u4e88\u60f3\u30b5\u30a4\u30ba\u3092\u63a8\u5b9a\u3059\u308b\u306e\u304c\u56f0\u96e3\u306a\u5834\u5408\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u306b\u57fa\u3065\u304f\u30b9\u30bf\u30c3\u30af\u304c\u3088\u308a\u826f\u3044\u9078\u629e\u3067\u3059\u3002\u9023\u7d50\u30ea\u30b9\u30c8\u306f\u5927\u91cf\u306e\u30c7\u30fc\u30bf\u3092\u30e1\u30e2\u30ea\u306e\u7570\u306a\u308b\u90e8\u5206\u306b\u5206\u6563\u3067\u304d\u3001\u914d\u5217\u62e1\u5f35\u306e\u8ffd\u52a0\u30aa\u30fc\u30d0\u30fc\u30d8\u30c3\u30c9\u3092\u56de\u907f\u3067\u304d\u307e\u3059\u3002</li> </ul>"},{"location":"chapter_array_and_linkedlist/summary/","title":"4.5 \u00a0 \u307e\u3068\u3081","text":""},{"location":"chapter_array_and_linkedlist/summary/#1","title":"1. \u00a0 \u91cd\u8981\u306a\u5fa9\u7fd2","text":"<ul> <li>\u914d\u5217\u3068\u9023\u7d50\u30ea\u30b9\u30c8\u306f2\u3064\u306e\u57fa\u672c\u7684\u306a\u30c7\u30fc\u30bf\u69cb\u9020\u3067\u3042\u308a\u3001\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u30e1\u30e2\u30ea\u306b\u304a\u3051\u308b2\u3064\u306e\u683c\u7d0d\u65b9\u6cd5\u3092\u8868\u3057\u3066\u3044\u307e\u3059\uff1a\u9023\u7d9a\u7a7a\u9593\u683c\u7d0d\u3068\u975e\u9023\u7d9a\u7a7a\u9593\u683c\u7d0d\u3067\u3059\u3002\u305d\u308c\u3089\u306e\u7279\u6027\u306f\u4e92\u3044\u306b\u88dc\u5b8c\u3057\u5408\u3044\u307e\u3059\u3002</li> <li>\u914d\u5217\u306f\u30e9\u30f3\u30c0\u30e0\u30a2\u30af\u30bb\u30b9\u3092\u30b5\u30dd\u30fc\u30c8\u3057\u3001\u4f7f\u7528\u3059\u308b\u30e1\u30e2\u30ea\u304c\u5c11\u306a\u3044\u4e00\u65b9\u3067\u3001\u8981\u7d20\u306e\u633f\u5165\u3068\u524a\u9664\u306f\u975e\u52b9\u7387\u7684\u3067\u3001\u521d\u671f\u5316\u5f8c\u306e\u9577\u3055\u304c\u56fa\u5b9a\u3055\u308c\u3066\u3044\u307e\u3059\u3002</li> <li>\u9023\u7d50\u30ea\u30b9\u30c8\u306f\u53c2\u7167\uff08\u30dd\u30a4\u30f3\u30bf\uff09\u306e\u5909\u66f4\u306b\u3088\u3063\u3066\u52b9\u7387\u7684\u306a\u30ce\u30fc\u30c9\u306e\u633f\u5165\u3068\u524a\u9664\u3092\u5b9f\u88c5\u3057\u3001\u9577\u3055\u3092\u67d4\u8edf\u306b\u8abf\u6574\u3067\u304d\u307e\u3059\u304c\u3001\u30ce\u30fc\u30c9\u30a2\u30af\u30bb\u30b9\u52b9\u7387\u304c\u4f4e\u304f\u3001\u3088\u308a\u591a\u304f\u306e\u30e1\u30e2\u30ea\u3092\u6d88\u8cbb\u3057\u307e\u3059\u3002</li> <li>\u9023\u7d50\u30ea\u30b9\u30c8\u306e\u4e00\u822c\u7684\u306a\u7a2e\u985e\u306b\u306f\u3001\u5358\u65b9\u5411\u9023\u7d50\u30ea\u30b9\u30c8\u3001\u5faa\u74b0\u9023\u7d50\u30ea\u30b9\u30c8\u3001\u53cc\u65b9\u5411\u9023\u7d50\u30ea\u30b9\u30c8\u304c\u3042\u308a\u3001\u305d\u308c\u305e\u308c\u306b\u72ec\u81ea\u306e\u5fdc\u7528\u30b7\u30ca\u30ea\u30aa\u304c\u3042\u308a\u307e\u3059\u3002</li> <li>\u30ea\u30b9\u30c8\u306f\u8981\u7d20\u306e\u9806\u5e8f\u4ed8\u3051\u3089\u308c\u305f\u30b3\u30ec\u30af\u30b7\u30e7\u30f3\u3067\u3001\u8ffd\u52a0\u3001\u524a\u9664\u3001\u5909\u66f4\u3092\u30b5\u30dd\u30fc\u30c8\u3057\u3001\u901a\u5e38\u306f\u52d5\u7684\u914d\u5217\u306b\u57fa\u3065\u3044\u3066\u5b9f\u88c5\u3055\u308c\u3001\u914d\u5217\u306e\u5229\u70b9\u3092\u4fdd\u6301\u3057\u306a\u304c\u3089\u67d4\u8edf\u306a\u9577\u3055\u8abf\u6574\u3092\u53ef\u80fd\u306b\u3057\u307e\u3059\u3002</li> <li>\u30ea\u30b9\u30c8\u306e\u51fa\u73fe\u306b\u3088\u308a\u914d\u5217\u306e\u5b9f\u7528\u6027\u304c\u5927\u5e45\u306b\u5411\u4e0a\u3057\u307e\u3057\u305f\u304c\u3001\u4e00\u90e8\u306e\u30e1\u30e2\u30ea\u7a7a\u9593\u306e\u7121\u99c4\u306b\u3064\u306a\u304c\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002</li> <li>\u30d7\u30ed\u30b0\u30e9\u30e0\u5b9f\u884c\u4e2d\u3001\u30c7\u30fc\u30bf\u306f\u4e3b\u306b\u30e1\u30e2\u30ea\u306b\u683c\u7d0d\u3055\u308c\u307e\u3059\u3002\u914d\u5217\u306f\u3088\u308a\u9ad8\u3044\u30e1\u30e2\u30ea\u7a7a\u9593\u52b9\u7387\u3092\u63d0\u4f9b\u3057\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u306f\u30e1\u30e2\u30ea\u4f7f\u7528\u306b\u304a\u3044\u3066\u3088\u308a\u67d4\u8edf\u3067\u3059\u3002</li> <li>\u30ad\u30e3\u30c3\u30b7\u30e5\u306f\u3001\u30ad\u30e3\u30c3\u30b7\u30e5\u30e9\u30a4\u30f3\u3001\u5148\u8aad\u307f\u3001\u7a7a\u9593\u7684\u5c40\u6240\u6027\u3001\u6642\u9593\u7684\u5c40\u6240\u6027\u306a\u3069\u306e\u30e1\u30ab\u30cb\u30ba\u30e0\u3092\u901a\u3058\u3066CPU\u306b\u9ad8\u901f\u30c7\u30fc\u30bf\u30a2\u30af\u30bb\u30b9\u3092\u63d0\u4f9b\u3057\u3001\u30d7\u30ed\u30b0\u30e9\u30e0\u5b9f\u884c\u52b9\u7387\u3092\u5927\u5e45\u306b\u5411\u4e0a\u3055\u305b\u307e\u3059\u3002</li> <li>\u3088\u308a\u9ad8\u3044\u30ad\u30e3\u30c3\u30b7\u30e5\u30d2\u30c3\u30c8\u7387\u306b\u3088\u308a\u3001\u914d\u5217\u306f\u4e00\u822c\u7684\u306b\u9023\u7d50\u30ea\u30b9\u30c8\u3088\u308a\u3082\u52b9\u7387\u7684\u3067\u3059\u3002\u30c7\u30fc\u30bf\u69cb\u9020\u3092\u9078\u629e\u3059\u308b\u969b\u306f\u3001\u7279\u5b9a\u306e\u30cb\u30fc\u30ba\u3068\u30b7\u30ca\u30ea\u30aa\u306b\u57fa\u3065\u3044\u3066\u9069\u5207\u306a\u9078\u629e\u3092\u3059\u3079\u304d\u3067\u3059\u3002</li> </ul>"},{"location":"chapter_array_and_linkedlist/summary/#2-q-a","title":"2. \u00a0 Q &amp; A","text":"<p>Q\uff1a\u914d\u5217\u3092\u30b9\u30bf\u30c3\u30af\u306b\u683c\u7d0d\u3059\u308b\u304b\u30d2\u30fc\u30d7\u306b\u683c\u7d0d\u3059\u308b\u304b\u306f\u3001\u6642\u9593\u3068\u7a7a\u9593\u52b9\u7387\u306b\u5f71\u97ff\u3057\u307e\u3059\u304b\uff1f</p> <p>\u30b9\u30bf\u30c3\u30af\u3068\u30d2\u30fc\u30d7\u306e\u4e21\u65b9\u306b\u683c\u7d0d\u3055\u308c\u308b\u914d\u5217\u306f\u9023\u7d9a\u3057\u305f\u30e1\u30e2\u30ea\u7a7a\u9593\u306b\u683c\u7d0d\u3055\u308c\u3001\u30c7\u30fc\u30bf\u64cd\u4f5c\u52b9\u7387\u306f\u672c\u8cea\u7684\u306b\u540c\u3058\u3067\u3059\u3002\u3057\u304b\u3057\u3001\u30b9\u30bf\u30c3\u30af\u3068\u30d2\u30fc\u30d7\u306b\u306f\u72ec\u81ea\u306e\u7279\u6027\u304c\u3042\u308a\u3001\u4ee5\u4e0b\u306e\u9055\u3044\u304c\u751f\u3058\u307e\u3059\u3002</p> <ol> <li>\u5272\u308a\u5f53\u3066\u3068\u89e3\u653e\u52b9\u7387\uff1a\u30b9\u30bf\u30c3\u30af\u306f\u3088\u308a\u5c0f\u3055\u306a\u30e1\u30e2\u30ea\u30d6\u30ed\u30c3\u30af\u3067\u3001\u30b3\u30f3\u30d1\u30a4\u30e9\u306b\u3088\u3063\u3066\u81ea\u52d5\u7684\u306b\u5272\u308a\u5f53\u3066\u3089\u308c\u307e\u3059\u3002\u30d2\u30fc\u30d7\u30e1\u30e2\u30ea\u306f\u6bd4\u8f03\u7684\u5927\u304d\u304f\u3001\u30b3\u30fc\u30c9\u3067\u52d5\u7684\u306b\u5272\u308a\u5f53\u3066\u308b\u3053\u3068\u304c\u3067\u304d\u3001\u65ad\u7247\u5316\u3057\u3084\u3059\u3044\u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u30d2\u30fc\u30d7\u3067\u306e\u5272\u308a\u5f53\u3066\u3068\u89e3\u653e\u64cd\u4f5c\u306f\u4e00\u822c\u7684\u306b\u30b9\u30bf\u30c3\u30af\u3088\u308a\u3082\u9045\u304f\u306a\u308a\u307e\u3059\u3002</li> <li>\u30b5\u30a4\u30ba\u5236\u9650\uff1a\u30b9\u30bf\u30c3\u30af\u30e1\u30e2\u30ea\u306f\u6bd4\u8f03\u7684\u5c0f\u3055\u304f\u3001\u30d2\u30fc\u30d7\u30b5\u30a4\u30ba\u306f\u4e00\u822c\u7684\u306b\u5229\u7528\u53ef\u80fd\u306a\u30e1\u30e2\u30ea\u306b\u3088\u3063\u3066\u5236\u9650\u3055\u308c\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u30d2\u30fc\u30d7\u306f\u5927\u304d\u306a\u914d\u5217\u306e\u683c\u7d0d\u306b\u3088\u308a\u9069\u3057\u3066\u3044\u307e\u3059\u3002</li> <li>\u67d4\u8edf\u6027\uff1a\u30b9\u30bf\u30c3\u30af\u4e0a\u306e\u914d\u5217\u306e\u30b5\u30a4\u30ba\u306f\u30b3\u30f3\u30d1\u30a4\u30eb\u6642\u306b\u6c7a\u5b9a\u3055\u308c\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u304c\u3001\u30d2\u30fc\u30d7\u4e0a\u306e\u914d\u5217\u306e\u30b5\u30a4\u30ba\u306f\u5b9f\u884c\u6642\u306b\u52d5\u7684\u306b\u6c7a\u5b9a\u3067\u304d\u307e\u3059\u3002</li> </ol> <p>Q\uff1a\u306a\u305c\u914d\u5217\u306f\u540c\u3058\u578b\u306e\u8981\u7d20\u3092\u5fc5\u8981\u3068\u3057\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u306f\u540c\u3058\u578b\u306e\u8981\u7d20\u3092\u5f37\u8abf\u3057\u306a\u3044\u306e\u3067\u3059\u304b\uff1f</p> <p>\u9023\u7d50\u30ea\u30b9\u30c8\u306f\u53c2\u7167\uff08\u30dd\u30a4\u30f3\u30bf\uff09\u306b\u3088\u3063\u3066\u63a5\u7d9a\u3055\u308c\u305f\u30ce\u30fc\u30c9\u3067\u69cb\u6210\u3055\u308c\u3001\u5404\u30ce\u30fc\u30c9\u306fint\u3001double\u3001string\u3001object\u306a\u3069\u3001\u7570\u306a\u308b\u578b\u306e\u30c7\u30fc\u30bf\u3092\u683c\u7d0d\u3067\u304d\u307e\u3059\u3002</p> <p>\u5bfe\u7167\u7684\u306b\u3001\u914d\u5217\u8981\u7d20\u306f\u540c\u3058\u578b\u3067\u3042\u308b\u5fc5\u8981\u304c\u3042\u308a\u3001\u3053\u308c\u306b\u3088\u308a\u5bfe\u5fdc\u3059\u308b\u8981\u7d20\u4f4d\u7f6e\u306b\u30a2\u30af\u30bb\u30b9\u3059\u308b\u305f\u3081\u306e\u30aa\u30d5\u30bb\u30c3\u30c8\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001int\u3068long\u578b\u306e\u4e21\u65b9\u3092\u542b\u3080\u914d\u5217\u3067\u3001\u5358\u4e00\u8981\u7d20\u304c\u305d\u308c\u305e\u308c4\u30d0\u30a4\u30c8\u30688\u30d0\u30a4\u30c8\u3092\u5360\u6709\u3059\u308b\u5834\u5408\u3001\u914d\u5217\u306b2\u3064\u306e\u7570\u306a\u308b\u9577\u3055\u306e\u8981\u7d20\u304c\u542b\u307e\u308c\u3066\u3044\u308b\u305f\u3081\u3001\u4ee5\u4e0b\u306e\u5f0f\u3092\u4f7f\u7528\u3057\u3066\u30aa\u30d5\u30bb\u30c3\u30c8\u3092\u8a08\u7b97\u3067\u304d\u307e\u305b\u3093\u3002</p> <pre><code># \u8981\u7d20\u30e1\u30e2\u30ea\u30a2\u30c9\u30ec\u30b9 = \u914d\u5217\u30e1\u30e2\u30ea\u30a2\u30c9\u30ec\u30b9 + \u8981\u7d20\u9577 * \u8981\u7d20\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\n</code></pre> <p>Q\uff1a\u30ce\u30fc\u30c9\u3092\u524a\u9664\u3057\u305f\u5f8c\u3001<code>P.next</code>\u3092<code>None</code>\u306b\u8a2d\u5b9a\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u304b\uff1f</p> <p><code>P.next</code>\u3092\u5909\u66f4\u3057\u306a\u304f\u3066\u3082\u554f\u984c\u3042\u308a\u307e\u305b\u3093\u3002\u9023\u7d50\u30ea\u30b9\u30c8\u306e\u89b3\u70b9\u304b\u3089\u3001\u30d8\u30c3\u30c9\u30ce\u30fc\u30c9\u304b\u3089\u30c6\u30fc\u30eb\u30ce\u30fc\u30c9\u307e\u3067\u306e\u5de1\u56de\u3067<code>P</code>\u306b\u906d\u9047\u3059\u308b\u3053\u3068\u306f\u3082\u3046\u3042\u308a\u307e\u305b\u3093\u3002\u3053\u308c\u306f\u3001\u30ce\u30fc\u30c9<code>P</code>\u304c\u30ea\u30b9\u30c8\u304b\u3089\u52b9\u679c\u7684\u306b\u524a\u9664\u3055\u308c\u305f\u3053\u3068\u3092\u610f\u5473\u3057\u3001<code>P</code>\u304c\u6307\u3059\u5834\u6240\u306f\u3082\u306f\u3084\u30ea\u30b9\u30c8\u306b\u5f71\u97ff\u3057\u307e\u305b\u3093\u3002</p> <p>\u30ac\u30d9\u30fc\u30b8\u30b3\u30ec\u30af\u30b7\u30e7\u30f3\u306e\u89b3\u70b9\u304b\u3089\u3001Java\u3001Python\u3001Go\u306a\u3069\u306e\u81ea\u52d5\u30ac\u30d9\u30fc\u30b8\u30b3\u30ec\u30af\u30b7\u30e7\u30f3\u30e1\u30ab\u30cb\u30ba\u30e0\u3092\u6301\u3064\u8a00\u8a9e\u3067\u306f\u3001\u30ce\u30fc\u30c9<code>P</code>\u304c\u53ce\u96c6\u3055\u308c\u308b\u304b\u3069\u3046\u304b\u306f\u3001\u305d\u308c\u3092\u6307\u3059\u53c2\u7167\u304c\u307e\u3060\u3042\u308b\u304b\u3069\u3046\u304b\u306b\u4f9d\u5b58\u3057\u3001<code>P.next</code>\u306e\u5024\u306b\u306f\u4f9d\u5b58\u3057\u307e\u305b\u3093\u3002C\u3084C++\u306a\u3069\u306e\u8a00\u8a9e\u3067\u306f\u3001\u30ce\u30fc\u30c9\u306e\u30e1\u30e2\u30ea\u3092\u624b\u52d5\u3067\u89e3\u653e\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002</p> <p>Q\uff1a\u9023\u7d50\u30ea\u30b9\u30c8\u3067\u306f\u3001\u633f\u5165\u3068\u524a\u9664\u64cd\u4f5c\u306e\u6642\u9593\u8a08\u7b97\u91cf\u306f<code>O(1)</code>\u3067\u3059\u3002\u3057\u304b\u3057\u3001\u633f\u5165\u3084\u524a\u9664\u524d\u306e\u8981\u7d20\u691c\u7d22\u306b\u306f<code>O(n)</code>\u6642\u9593\u304c\u304b\u304b\u308b\u306e\u3067\u3001\u306a\u305c\u6642\u9593\u8a08\u7b97\u91cf\u306f<code>O(n)</code>\u3067\u306f\u306a\u3044\u306e\u3067\u3059\u304b\uff1f</p> <p>\u8981\u7d20\u3092\u6700\u521d\u306b\u691c\u7d22\u3057\u3066\u304b\u3089\u524a\u9664\u3059\u308b\u5834\u5408\u3001\u6642\u9593\u8a08\u7b97\u91cf\u306f\u78ba\u304b\u306b<code>O(n)</code>\u3067\u3059\u3002\u3057\u304b\u3057\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u306e\u633f\u5165\u3068\u524a\u9664\u306b\u304a\u3051\u308b<code>O(1)</code>\u306e\u5229\u70b9\u306f\u4ed6\u306e\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u3067\u5b9f\u73fe\u3067\u304d\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u3092\u4f7f\u7528\u3057\u305f\u4e21\u7aef\u30ad\u30e5\u30fc\u306e\u5b9f\u88c5\u3067\u306f\u3001\u5e38\u306b\u30d8\u30c3\u30c9\u3068\u30c6\u30fc\u30eb\u30ce\u30fc\u30c9\u3092\u6307\u3059\u30dd\u30a4\u30f3\u30bf\u3092\u7dad\u6301\u3057\u3001\u5404\u633f\u5165\u3068\u524a\u9664\u64cd\u4f5c\u3092<code>O(1)</code>\u306b\u3057\u307e\u3059\u3002</p> <p>Q\uff1a\u300c\u9023\u7d50\u30ea\u30b9\u30c8\u306e\u5b9a\u7fa9\u3068\u683c\u7d0d\u65b9\u6cd5\u300d\u306e\u56f3\u3067\u3001\u8584\u9752\u8272\u306e\u683c\u7d0d\u30ce\u30fc\u30c9\u306f\u5358\u4e00\u306e\u30e1\u30e2\u30ea\u30a2\u30c9\u30ec\u30b9\u3092\u5360\u6709\u3057\u307e\u3059\u304b\u3001\u305d\u308c\u3068\u3082\u30ce\u30fc\u30c9\u5024\u3068\u534a\u5206\u3092\u5171\u6709\u3057\u307e\u3059\u304b\uff1f</p> <p>\u56f3\u306f\u5358\u306a\u308b\u5b9a\u6027\u7684\u306a\u8868\u73fe\u3067\u3042\u308a\u3001\u5b9a\u91cf\u7684\u5206\u6790\u306f\u7279\u5b9a\u306e\u72b6\u6cc1\u306b\u4f9d\u5b58\u3057\u307e\u3059\u3002</p> <ul> <li>\u7570\u306a\u308b\u578b\u306e\u30ce\u30fc\u30c9\u5024\u306f\u7570\u306a\u308b\u91cf\u306e\u7a7a\u9593\u3092\u5360\u6709\u3057\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001int\u3001long\u3001double\u3001\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u3067\u3059\u3002</li> <li>\u30dd\u30a4\u30f3\u30bf\u5909\u6570\u306b\u3088\u3063\u3066\u5360\u6709\u3055\u308c\u308b\u30e1\u30e2\u30ea\u7a7a\u9593\u306f\u3001\u4f7f\u7528\u3055\u308c\u308b\u30aa\u30da\u30ec\u30fc\u30c6\u30a3\u30f3\u30b0\u30b7\u30b9\u30c6\u30e0\u3068\u30b3\u30f3\u30d1\u30a4\u30eb\u74b0\u5883\u306b\u4f9d\u5b58\u3057\u3001\u901a\u5e388\u30d0\u30a4\u30c8\u307e\u305f\u306f4\u30d0\u30a4\u30c8\u3067\u3059\u3002</li> </ul> <p>Q\uff1a\u30ea\u30b9\u30c8\u306e\u672b\u5c3e\u3078\u306e\u8981\u7d20\u8ffd\u52a0\u306f\u5e38\u306b<code>O(1)</code>\u3067\u3059\u304b\uff1f</p> <p>\u8981\u7d20\u3092\u8ffd\u52a0\u3059\u308b\u3053\u3068\u3067\u30ea\u30b9\u30c8\u9577\u3092\u8d85\u3048\u308b\u5834\u5408\u3001\u30ea\u30b9\u30c8\u306f\u6700\u521d\u306b\u62e1\u5f35\u3055\u308c\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u30b7\u30b9\u30c6\u30e0\u306f\u65b0\u3057\u3044\u30e1\u30e2\u30ea\u30d6\u30ed\u30c3\u30af\u3092\u8981\u6c42\u3057\u3001\u5143\u306e\u30ea\u30b9\u30c8\u306e\u3059\u3079\u3066\u306e\u8981\u7d20\u3092\u79fb\u52d5\u3059\u308b\u305f\u3081\u3001\u3053\u306e\u5834\u5408\u306e\u6642\u9593\u8a08\u7b97\u91cf\u306f<code>O(n)</code>\u306b\u306a\u308a\u307e\u3059\u3002</p> <p>Q\uff1a\u300c\u30ea\u30b9\u30c8\u306e\u51fa\u73fe\u306b\u3088\u308a\u914d\u5217\u306e\u5b9f\u7528\u6027\u304c\u5927\u5e45\u306b\u5411\u4e0a\u3057\u307e\u3057\u305f\u304c\u3001\u4e00\u90e8\u306e\u30e1\u30e2\u30ea\u7a7a\u9593\u306e\u7121\u99c4\u306b\u3064\u306a\u304c\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u300d\u3068\u3044\u3046\u6587\u306f\u3001\u5bb9\u91cf\u3001\u9577\u3055\u3001\u62e1\u5f35\u4fc2\u6570\u306a\u3069\u306e\u8ffd\u52a0\u5909\u6570\u306b\u3088\u3063\u3066\u5360\u6709\u3055\u308c\u308b\u30e1\u30e2\u30ea\u3092\u6307\u3057\u3066\u3044\u307e\u3059\u304b\uff1f</p> <p>\u3053\u3053\u3067\u306e\u7a7a\u9593\u306e\u7121\u99c4\u306f\u4e3b\u306b2\u3064\u306e\u5074\u9762\u3092\u6307\u3057\u307e\u3059\uff1a\u4e00\u65b9\u3067\u3001\u30ea\u30b9\u30c8\u306f\u521d\u671f\u9577\u3067\u8a2d\u5b9a\u3055\u308c\u307e\u3059\u304c\u3001\u5e38\u306b\u5fc5\u8981\u3068\u306f\u9650\u308a\u307e\u305b\u3093\u3002\u4ed6\u65b9\u3067\u3001\u983b\u7e41\u306a\u62e1\u5f35\u3092\u9632\u3050\u305f\u3081\u3001\u62e1\u5f35\u306f\u901a\u5e38\\(\\times 1.5\\)\u306a\u3069\u306e\u4fc2\u6570\u3067\u4e57\u7b97\u3055\u308c\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u591a\u304f\u306e\u7a7a\u304d\u30b9\u30ed\u30c3\u30c8\u304c\u751f\u307e\u308c\u3001\u901a\u5e38\u306f\u5b8c\u5168\u306b\u57cb\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u305b\u3093\u3002</p> <p>Q\uff1aPython\u3067<code>n = [1, 2, 3]</code>\u3092\u521d\u671f\u5316\u3057\u305f\u5f8c\u3001\u3053\u308c\u30893\u3064\u306e\u8981\u7d20\u306e\u30a2\u30c9\u30ec\u30b9\u306f\u9023\u7d9a\u3057\u3066\u3044\u307e\u3059\u304c\u3001<code>m = [2, 1, 3]</code>\u3092\u521d\u671f\u5316\u3059\u308b\u3068\u3001\u5404\u8981\u7d20\u306e<code>id</code>\u306f\u9023\u7d9a\u3057\u3066\u3044\u306a\u3044\u304c<code>n</code>\u306e\u3082\u306e\u3068\u540c\u4e00\u3067\u3059\u3002\u3053\u308c\u3089\u306e\u8981\u7d20\u306e\u30a2\u30c9\u30ec\u30b9\u304c\u9023\u7d9a\u3057\u3066\u3044\u306a\u3044\u5834\u5408\u3001<code>m</code>\u306f\u307e\u3060\u914d\u5217\u3067\u3059\u304b\uff1f</p> <p>\u30ea\u30b9\u30c8\u8981\u7d20\u3092\u9023\u7d50\u30ea\u30b9\u30c8\u30ce\u30fc\u30c9<code>n = [n1, n2, n3, n4, n5]</code>\u306b\u7f6e\u304d\u63db\u3048\u308b\u5834\u5408\u3001\u3053\u308c\u30895\u3064\u306e\u30ce\u30fc\u30c9\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u3082\u901a\u5e38\u30e1\u30e2\u30ea\u5168\u4f53\u306b\u5206\u6563\u3057\u3066\u3044\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u30ea\u30b9\u30c8\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u304c\u4e0e\u3048\u3089\u308c\u308c\u3070\u3001<code>O(1)</code>\u6642\u9593\u3067\u30ce\u30fc\u30c9\u306e\u30e1\u30e2\u30ea\u30a2\u30c9\u30ec\u30b9\u306b\u30a2\u30af\u30bb\u30b9\u3067\u304d\u3001\u5bfe\u5fdc\u3059\u308b\u30ce\u30fc\u30c9\u306b\u30a2\u30af\u30bb\u30b9\u3067\u304d\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u914d\u5217\u304c\u30ce\u30fc\u30c9\u81ea\u4f53\u3067\u306f\u306a\u304f\u3001\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\u3092\u683c\u7d0d\u3059\u308b\u305f\u3081\u3067\u3059\u3002</p> <p>\u591a\u304f\u306e\u8a00\u8a9e\u3068\u306f\u7570\u306a\u308a\u3001Python\u3067\u306f\u6570\u5024\u3082\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u3068\u3057\u3066\u30e9\u30c3\u30d7\u3055\u308c\u3001\u30ea\u30b9\u30c8\u306f\u6570\u5024\u81ea\u4f53\u3067\u306f\u306a\u304f\u3001\u3053\u308c\u3089\u306e\u6570\u5024\u3078\u306e\u53c2\u7167\u3092\u683c\u7d0d\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u30012\u3064\u306e\u914d\u5217\u306e\u540c\u3058\u6570\u5024\u304c\u540c\u3058<code>id</code>\u3092\u6301\u3061\u3001\u3053\u308c\u3089\u306e\u6570\u5024\u306e\u30e1\u30e2\u30ea\u30a2\u30c9\u30ec\u30b9\u306f\u9023\u7d9a\u3067\u3042\u308b\u5fc5\u8981\u304c\u306a\u3044\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002</p> <p>Q\uff1aC++ STL\u306e<code>std::list</code>\u306f\u3059\u3067\u306b\u53cc\u65b9\u5411\u9023\u7d50\u30ea\u30b9\u30c8\u3092\u5b9f\u88c5\u3057\u3066\u3044\u307e\u3059\u304c\u3001\u4e00\u90e8\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u66f8\u7c4d\u3067\u306f\u76f4\u63a5\u4f7f\u7528\u3057\u3066\u3044\u306a\u3044\u3088\u3046\u3067\u3059\u3002\u4f55\u304b\u5236\u9650\u304c\u3042\u308a\u307e\u3059\u304b\uff1f</p> <p>\u4e00\u65b9\u3067\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u5b9f\u88c5\u3059\u308b\u969b\u306f\u914d\u5217\u3092\u4f7f\u7528\u3059\u308b\u3053\u3068\u3092\u597d\u307f\u3001\u5fc5\u8981\u306a\u5834\u5408\u306e\u307f\u9023\u7d50\u30ea\u30b9\u30c8\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002\u4e3b\u306b2\u3064\u306e\u7406\u7531\u304c\u3042\u308a\u307e\u3059\u3002</p> <ul> <li>\u7a7a\u9593\u30aa\u30fc\u30d0\u30fc\u30d8\u30c3\u30c9\uff1a\u5404\u8981\u7d20\u306b2\u3064\u306e\u8ffd\u52a0\u30dd\u30a4\u30f3\u30bf\uff08\u524d\u306e\u8981\u7d20\u7528\u3068\u6b21\u306e\u8981\u7d20\u7528\uff09\u304c\u5fc5\u8981\u306a\u305f\u3081\u3001<code>std::list</code>\u306f\u901a\u5e38<code>std::vector</code>\u3088\u308a\u3082\u591a\u304f\u306e\u7a7a\u9593\u3092\u5360\u6709\u3057\u307e\u3059\u3002</li> <li>\u30ad\u30e3\u30c3\u30b7\u30e5\u975e\u53cb\u597d\u7684\uff1a\u30c7\u30fc\u30bf\u304c\u9023\u7d9a\u3057\u3066\u683c\u7d0d\u3055\u308c\u3066\u3044\u306a\u3044\u305f\u3081\u3001<code>std::list</code>\u306f\u30ad\u30e3\u30c3\u30b7\u30e5\u5229\u7528\u7387\u304c\u4f4e\u304f\u306a\u308a\u307e\u3059\u3002\u4e00\u822c\u7684\u306b\u3001<code>std::vector</code>\u306e\u65b9\u304c\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u304c\u512a\u308c\u3066\u3044\u307e\u3059\u3002</li> </ul> <p>\u4ed6\u65b9\u3067\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u306f\u4e3b\u306b\u4e8c\u5206\u6728\u3068\u30b0\u30e9\u30d5\u306b\u5fc5\u8981\u3067\u3059\u3002\u30b9\u30bf\u30c3\u30af\u3068\u30ad\u30e5\u30fc\u306f\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u3067\u306f\u306a\u304f\u3001\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u306e<code>stack</code>\u3068<code>queue</code>\u30af\u30e9\u30b9\u3092\u4f7f\u7528\u3057\u3066\u5b9f\u88c5\u3055\u308c\u308b\u3053\u3068\u304c\u591a\u3044\u3067\u3059\u3002</p> <p>Q\uff1a\u30ea\u30b9\u30c8<code>res = [0] * self.size()</code>\u3092\u521d\u671f\u5316\u3059\u308b\u3068\u3001<code>res</code>\u306e\u5404\u8981\u7d20\u306f\u540c\u3058\u30a2\u30c9\u30ec\u30b9\u3092\u53c2\u7167\u3057\u307e\u3059\u304b\uff1f</p> <p>\u3044\u3044\u3048\u3002\u3057\u304b\u3057\u3001\u3053\u306e\u554f\u984c\u306f\u4e8c\u6b21\u5143\u914d\u5217\u3067\u767a\u751f\u3057\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u4e8c\u6b21\u5143\u30ea\u30b9\u30c8<code>res = [[0]] * self.size()</code>\u3092\u521d\u671f\u5316\u3059\u308b\u3068\u3001\u540c\u3058\u30ea\u30b9\u30c8<code>[0]</code>\u3092\u8907\u6570\u56de\u53c2\u7167\u3059\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002</p> <p>Q\uff1a\u30ce\u30fc\u30c9\u3092\u524a\u9664\u3059\u308b\u969b\u3001\u305d\u306e\u5f8c\u7d9a\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\u3092\u65ad\u3064\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u304b\uff1f</p> <p>\u30c7\u30fc\u30bf\u69cb\u9020\u3068\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\uff08\u554f\u984c\u89e3\u6c7a\uff09\u306e\u89b3\u70b9\u304b\u3089\u3001\u30d7\u30ed\u30b0\u30e9\u30e0\u306e\u30ed\u30b8\u30c3\u30af\u304c\u6b63\u3057\u3044\u9650\u308a\u3001\u30ea\u30f3\u30af\u3092\u65ad\u305f\u306a\u304f\u3066\u3082\u554f\u984c\u3042\u308a\u307e\u305b\u3093\u3002\u6a19\u6e96\u30e9\u30a4\u30d6\u30e9\u30ea\u306e\u89b3\u70b9\u304b\u3089\u3001\u30ea\u30f3\u30af\u3092\u65ad\u3064\u65b9\u304c\u5b89\u5168\u3067\u8ad6\u7406\u7684\u306b\u660e\u78ba\u3067\u3059\u3002\u30ea\u30f3\u30af\u3092\u65ad\u305f\u305a\u3001\u524a\u9664\u3055\u308c\u305f\u30ce\u30fc\u30c9\u304c\u9069\u5207\u306b\u30ea\u30b5\u30a4\u30af\u30eb\u3055\u308c\u306a\u3044\u5834\u5408\u3001\u5f8c\u7d9a\u30ce\u30fc\u30c9\u306e\u30e1\u30e2\u30ea\u306e\u30ea\u30b5\u30a4\u30af\u30eb\u306b\u5f71\u97ff\u3092\u4e0e\u3048\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002</p>"},{"location":"chapter_backtracking/","title":"\u7b2c 13 \u7ae0 \u00a0 \u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0","text":"<p>Abstract</p> <p>\u8ff7\u8def\u306e\u63a2\u691c\u5bb6\u306e\u3088\u3046\u306b\u3001\u79c1\u305f\u3061\u306f\u524d\u9032\u3059\u308b\u9053\u3067\u969c\u5bb3\u306b\u906d\u9047\u3059\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002</p> <p>\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u306e\u529b\u306f\u3001\u79c1\u305f\u3061\u306b\u65b0\u3057\u304f\u59cb\u3081\u308b\u3053\u3068\u3001\u8a66\u3057\u7d9a\u3051\u308b\u3053\u3068\u3001\u305d\u3057\u3066\u6700\u7d42\u7684\u306b\u5149\u3078\u306e\u51fa\u53e3\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u3092\u53ef\u80fd\u306b\u3057\u307e\u3059\u3002</p>"},{"location":"chapter_backtracking/#_1","title":"\u7ae0\u306e\u5185\u5bb9","text":"<ul> <li>13.1 \u00a0 \u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0</li> <li>13.2 \u00a0 \u9806\u5217\u554f\u984c</li> <li>13.3 \u00a0 \u90e8\u5206\u96c6\u5408\u548c\u554f\u984c</li> <li>13.4 \u00a0 N\u30af\u30a4\u30fc\u30f3\u554f\u984c</li> <li>13.5 \u00a0 \u307e\u3068\u3081</li> </ul>"},{"location":"chapter_backtracking/backtracking_algorithm/","title":"13.1 \u00a0 \u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0","text":"<p>\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u5168\u6570\u63a2\u7d22\u306b\u3088\u3063\u3066\u554f\u984c\u3092\u89e3\u6c7a\u3059\u308b\u65b9\u6cd5\u3067\u3059\u3002\u305d\u306e\u6838\u5fc3\u6982\u5ff5\u306f\u3001\u521d\u671f\u72b6\u614b\u304b\u3089\u958b\u59cb\u3057\u3066\u3059\u3079\u3066\u306e\u53ef\u80fd\u306a\u89e3\u3092\u7dcf\u5f53\u305f\u308a\u3067\u63a2\u7d22\u3059\u308b\u3053\u3068\u3067\u3059\u3002\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u6b63\u3057\u3044\u3082\u306e\u3092\u8a18\u9332\u3057\u3001\u89e3\u304c\u898b\u3064\u304b\u308b\u304b\u3001\u3059\u3079\u3066\u306e\u53ef\u80fd\u306a\u89e3\u304c\u8a66\u3055\u308c\u305f\u304c\u89e3\u304c\u898b\u3064\u304b\u3089\u306a\u3044\u307e\u3067\u7d9a\u3051\u307e\u3059\u3002</p> <p>\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u306f\u901a\u5e38\u300c\u6df1\u3055\u512a\u5148\u63a2\u7d22\u300d\u3092\u4f7f\u7528\u3057\u3066\u89e3\u7a7a\u9593\u3092\u8d70\u67fb\u3057\u307e\u3059\u3002\u300c\u4e8c\u5206\u6728\u300d\u306e\u7ae0\u3067\u3001\u524d\u9806\u3001\u4e2d\u9806\u3001\u5f8c\u9806\u8d70\u67fb\u306f\u3059\u3079\u3066\u6df1\u3055\u512a\u5148\u63a2\u7d22\u3067\u3042\u308b\u3053\u3068\u3092\u8ff0\u3079\u307e\u3057\u305f\u3002\u6b21\u306b\u3001\u524d\u9806\u8d70\u67fb\u3092\u4f7f\u7528\u3057\u3066\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u554f\u984c\u3092\u89e3\u6c7a\u3057\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u52d5\u4f5c\u3092\u6bb5\u968e\u7684\u306b\u7406\u89e3\u3057\u3066\u3044\u304d\u307e\u3059\u3002</p> <p>\u4f8b1</p> <p>\u4e8c\u5206\u6728\u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408\u3001\u5024\u304c \\(7\\) \u306e\u3059\u3079\u3066\u306e\u30ce\u30fc\u30c9\u3092\u691c\u7d22\u3057\u3066\u8a18\u9332\u3057\u3001\u30ea\u30b9\u30c8\u3067\u8fd4\u3057\u3066\u304f\u3060\u3055\u3044\u3002</p> <p>\u3053\u306e\u554f\u984c\u3092\u89e3\u6c7a\u3059\u308b\u305f\u3081\u306b\u3001\u3053\u306e\u6728\u3092\u524d\u9806\u3067\u8d70\u67fb\u3057\u3001\u73fe\u5728\u306e\u30ce\u30fc\u30c9\u306e\u5024\u304c \\(7\\) \u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\u3057\u307e\u3059\u3002\u305d\u3046\u3067\u3042\u308c\u3070\u3001\u30ce\u30fc\u30c9\u306e\u5024\u3092\u7d50\u679c\u30ea\u30b9\u30c8 <code>res</code> \u306b\u8ffd\u52a0\u3057\u307e\u3059\u3002\u30d7\u30ed\u30bb\u30b9\u306f\u4ee5\u4e0b\u306e\u56f3\u306b\u793a\u3055\u308c\u3066\u3044\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig preorder_traversal_i_compact.py<pre><code>def pre_order(root: TreeNode):\n    \"\"\"\u524d\u9806\u8d70\u67fb\uff1a\u4f8b\u4e00\"\"\"\n    if root is None:\n        return\n    if root.val == 7:\n        # \u89e3\u3092\u8a18\u9332\n        res.append(root)\n    pre_order(root.left)\n    pre_order(root.right)\n</code></pre> preorder_traversal_i_compact.cpp<pre><code>/* \u524d\u9806\u8d70\u67fb\uff1a\u4f8b\uff11 */\nvoid preOrder(TreeNode *root) {\n    if (root == nullptr) {\n        return;\n    }\n    if (root-&gt;val == 7) {\n        // \u89e3\u3092\u8a18\u9332\n        res.push_back(root);\n    }\n    preOrder(root-&gt;left);\n    preOrder(root-&gt;right);\n}\n</code></pre> preorder_traversal_i_compact.java<pre><code>/* \u524d\u9806\u8d70\u67fb\uff1a\u4f8b\uff11 */\nvoid preOrder(TreeNode root) {\n    if (root == null) {\n        return;\n    }\n    if (root.val == 7) {\n        // \u89e3\u3092\u8a18\u9332\n        res.add(root);\n    }\n    preOrder(root.left);\n    preOrder(root.right);\n}\n</code></pre> preorder_traversal_i_compact.cs<pre><code>[class]{preorder_traversal_i_compact}-[func]{PreOrder}\n</code></pre> preorder_traversal_i_compact.go<pre><code>[class]{}-[func]{preOrderI}\n</code></pre> preorder_traversal_i_compact.swift<pre><code>[class]{}-[func]{preOrder}\n</code></pre> preorder_traversal_i_compact.js<pre><code>[class]{}-[func]{preOrder}\n</code></pre> preorder_traversal_i_compact.ts<pre><code>[class]{}-[func]{preOrder}\n</code></pre> preorder_traversal_i_compact.dart<pre><code>[class]{}-[func]{preOrder}\n</code></pre> preorder_traversal_i_compact.rs<pre><code>[class]{}-[func]{pre_order}\n</code></pre> preorder_traversal_i_compact.c<pre><code>[class]{}-[func]{preOrder}\n</code></pre> preorder_traversal_i_compact.kt<pre><code>[class]{}-[func]{preOrder}\n</code></pre> preorder_traversal_i_compact.rb<pre><code>[class]{}-[func]{pre_order}\n</code></pre> preorder_traversal_i_compact.zig<pre><code>[class]{}-[func]{preOrder}\n</code></pre> <p></p> <p> \u56f3 13-1 \u00a0 \u524d\u9806\u8d70\u67fb\u3067\u306e\u30ce\u30fc\u30c9\u691c\u7d22 </p>"},{"location":"chapter_backtracking/backtracking_algorithm/#1311","title":"13.1.1 \u00a0 \u8a66\u884c\u3068\u5f8c\u9000","text":"<p>\u89e3\u7a7a\u9593\u3092\u63a2\u7d22\u3059\u308b\u969b\u306b\u300c\u8a66\u884c\u300d\u3068\u300c\u5f8c\u9000\u300d\u6226\u7565\u3092\u4f7f\u7528\u3059\u308b\u305f\u3081\u3001\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3068\u547c\u3070\u308c\u307e\u3059\u3002\u63a2\u7d22\u4e2d\u3001\u6e80\u8db3\u306e\u3044\u304f\u89e3\u3092\u5f97\u308b\u305f\u3081\u306b\u3082\u306f\u3084\u9032\u3081\u306a\u3044\u72b6\u614b\u306b\u906d\u9047\u3059\u308b\u305f\u3073\u306b\u3001\u524d\u306e\u9078\u629e\u3092\u53d6\u308a\u6d88\u3057\u3066\u524d\u306e\u72b6\u614b\u306b\u623b\u308a\u3001\u6b21\u306e\u8a66\u884c\u306e\u305f\u3081\u306b\u4ed6\u306e\u53ef\u80fd\u306a\u9078\u629e\u3092\u9078\u629e\u3067\u304d\u308b\u3088\u3046\u306b\u3057\u307e\u3059\u3002</p> <p>\u4f8b1\u3067\u306f\u3001\u5404\u30ce\u30fc\u30c9\u306e\u8a2a\u554f\u304c\u300c\u8a66\u884c\u300d\u3092\u958b\u59cb\u3057\u307e\u3059\u3002\u305d\u3057\u3066\u8449\u30ce\u30fc\u30c9\u3092\u901a\u904e\u3059\u308b\u304b\u3001<code>return</code> \u6587\u3067\u89aa\u30ce\u30fc\u30c9\u306b\u623b\u308b\u3053\u3068\u304c\u300c\u5f8c\u9000\u300d\u3092\u793a\u5506\u3057\u307e\u3059\u3002</p> <p>\u5f8c\u9000\u306f\u5358\u306b\u95a2\u6570\u306e\u623b\u308a\u5024\u3067\u306f\u306a\u3044\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u4f8b1\u306e\u554f\u984c\u3092\u5c11\u3057\u62e1\u5f35\u3057\u3066\u3001\u305d\u308c\u304c\u4f55\u3092\u610f\u5473\u3059\u308b\u304b\u3092\u8aac\u660e\u3057\u307e\u3059\u3002</p> <p>\u4f8b2</p> <p>\u4e8c\u5206\u6728\u3067\u3001\u5024\u304c \\(7\\) \u306e\u3059\u3079\u3066\u306e\u30ce\u30fc\u30c9\u3092\u691c\u7d22\u3057\u3001\u3059\u3079\u3066\u306e\u30de\u30c3\u30c1\u30f3\u30b0\u30ce\u30fc\u30c9\u306b\u3064\u3044\u3066\u3001\u30eb\u30fc\u30c8\u30ce\u30fc\u30c9\u304b\u3089\u305d\u306e\u30ce\u30fc\u30c9\u307e\u3067\u306e\u30d1\u30b9\u3092\u8fd4\u3057\u3066\u304f\u3060\u3055\u3044\u3002</p> <p>\u4f8b1\u306e\u30b3\u30fc\u30c9\u306b\u57fa\u3065\u3044\u3066\u3001\u8a2a\u554f\u3057\u305f\u30ce\u30fc\u30c9\u30d1\u30b9\u3092\u8a18\u9332\u3059\u308b\u305f\u3081\u306b <code>path</code> \u3068\u3044\u3046\u30ea\u30b9\u30c8\u3092\u4f7f\u7528\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u5024\u304c \\(7\\) \u306e\u30ce\u30fc\u30c9\u306b\u5230\u9054\u3059\u308b\u3068\u3001<code>path</code> \u3092\u30b3\u30d4\u30fc\u3057\u3066\u7d50\u679c\u30ea\u30b9\u30c8 <code>res</code> \u306b\u8ffd\u52a0\u3057\u307e\u3059\u3002\u8d70\u67fb\u5f8c\u3001<code>res</code> \u306b\u306f\u3059\u3079\u3066\u306e\u89e3\u304c\u4fdd\u6301\u3055\u308c\u307e\u3059\u3002\u30b3\u30fc\u30c9\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig preorder_traversal_ii_compact.py<pre><code>def pre_order(root: TreeNode):\n    \"\"\"\u524d\u9806\u8d70\u67fb\uff1a\u4f8b\u4e8c\"\"\"\n    if root is None:\n        return\n    # \u8a66\u884c\n    path.append(root)\n    if root.val == 7:\n        # \u89e3\u3092\u8a18\u9332\n        res.append(list(path))\n    pre_order(root.left)\n    pre_order(root.right)\n    # \u64a4\u56de\n    path.pop()\n</code></pre> preorder_traversal_ii_compact.cpp<pre><code>/* \u524d\u9806\u8d70\u67fb\uff1a\u4f8b\uff12 */\nvoid preOrder(TreeNode *root) {\n    if (root == nullptr) {\n        return;\n    }\n    // \u8a66\u884c\n    path.push_back(root);\n    if (root-&gt;val == 7) {\n        // \u89e3\u3092\u8a18\u9332\n        res.push_back(path);\n    }\n    preOrder(root-&gt;left);\n    preOrder(root-&gt;right);\n    // \u56de\u9000\n    path.pop_back();\n}\n</code></pre> preorder_traversal_ii_compact.java<pre><code>/* \u524d\u9806\u8d70\u67fb\uff1a\u4f8b\uff12 */\nvoid preOrder(TreeNode root) {\n    if (root == null) {\n        return;\n    }\n    // \u8a66\u884c\n    path.add(root);\n    if (root.val == 7) {\n        // \u89e3\u3092\u8a18\u9332\n        res.add(new ArrayList&lt;&gt;(path));\n    }\n    preOrder(root.left);\n    preOrder(root.right);\n    // \u56de\u9000\n    path.remove(path.size() - 1);\n}\n</code></pre> preorder_traversal_ii_compact.cs<pre><code>[class]{preorder_traversal_ii_compact}-[func]{PreOrder}\n</code></pre> preorder_traversal_ii_compact.go<pre><code>[class]{}-[func]{preOrderII}\n</code></pre> preorder_traversal_ii_compact.swift<pre><code>[class]{}-[func]{preOrder}\n</code></pre> preorder_traversal_ii_compact.js<pre><code>[class]{}-[func]{preOrder}\n</code></pre> preorder_traversal_ii_compact.ts<pre><code>[class]{}-[func]{preOrder}\n</code></pre> preorder_traversal_ii_compact.dart<pre><code>[class]{}-[func]{preOrder}\n</code></pre> preorder_traversal_ii_compact.rs<pre><code>[class]{}-[func]{pre_order}\n</code></pre> preorder_traversal_ii_compact.c<pre><code>[class]{}-[func]{preOrder}\n</code></pre> preorder_traversal_ii_compact.kt<pre><code>[class]{}-[func]{preOrder}\n</code></pre> preorder_traversal_ii_compact.rb<pre><code>[class]{}-[func]{pre_order}\n</code></pre> preorder_traversal_ii_compact.zig<pre><code>[class]{}-[func]{preOrder}\n</code></pre> <p>\u5404\u300c\u8a66\u884c\u300d\u3067\u3001\u73fe\u5728\u306e\u30ce\u30fc\u30c9\u3092 <code>path</code> \u306b\u8ffd\u52a0\u3059\u308b\u3053\u3068\u3067\u30d1\u30b9\u3092\u8a18\u9332\u3057\u307e\u3059\u3002\u300c\u5f8c\u9000\u300d\u304c\u5fc5\u8981\u306a\u3068\u304d\u306f\u3044\u3064\u3067\u3082\u3001<code>path</code> \u304b\u3089\u30ce\u30fc\u30c9\u3092\u30dd\u30c3\u30d7\u3057\u3066**\u3053\u306e\u5931\u6557\u3057\u305f\u8a66\u884c\u524d\u306e\u72b6\u614b\u3092\u5fa9\u5143\u3057\u307e\u3059**\u3002</p> <p>\u4ee5\u4e0b\u306e\u56f3\u306b\u793a\u3059\u30d7\u30ed\u30bb\u30b9\u3092\u89b3\u5bdf\u3059\u308b\u3053\u3068\u3067\u3001\u8a66\u884c\u306f\u300c\u524d\u9032\u300d\u306e\u3088\u3046\u3067\u3001\u5f8c\u9000\u306f\u300c\u5143\u306b\u623b\u3059\u300d\u306e\u3088\u3046\u3067\u3059\u3002\u5f8c\u8005\u306e\u30da\u30a2\u306f\u3001\u5bfe\u5fdc\u3059\u308b\u3082\u306e\u306b\u5bfe\u3059\u308b\u9006\u64cd\u4f5c\u3068\u898b\u306a\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> \u56f3 13-2 \u00a0 \u8a66\u884c\u3068\u5f8c\u9000 </p>"},{"location":"chapter_backtracking/backtracking_algorithm/#1312","title":"13.1.2 \u00a0 \u526a\u5b9a","text":"<p>\u8907\u96d1\u306a\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u554f\u984c\u306f\u901a\u5e381\u3064\u4ee5\u4e0a\u306e\u5236\u7d04\u3092\u542b\u307f\u3001\u3053\u308c\u3089\u306f\u300c\u526a\u5b9a\u300d\u306b\u3088\u304f\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002</p> <p>\u4f8b3</p> <p>\u4e8c\u5206\u6728\u3067\u3001\u5024\u304c \\(7\\) \u306e\u3059\u3079\u3066\u306e\u30ce\u30fc\u30c9\u3092\u691c\u7d22\u3057\u3001\u30eb\u30fc\u30c8\u304b\u3089\u3053\u308c\u3089\u306e\u30ce\u30fc\u30c9\u307e\u3067\u306e\u30d1\u30b9\u3092\u8fd4\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u305f\u3060\u3057\u3001\u30d1\u30b9\u306b\u306f\u5024\u304c \\(3\\) \u306e\u30ce\u30fc\u30c9\u3092\u542b\u307e\u306a\u3044\u3068\u3044\u3046\u5236\u9650\u304c\u3042\u308a\u307e\u3059\u3002</p> <p>\u4e0a\u8a18\u306e\u5236\u7d04\u3092\u6e80\u305f\u3059\u305f\u3081\u306b\u3001\u526a\u5b9a\u64cd\u4f5c\u3092\u8ffd\u52a0\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\uff1a\u691c\u7d22\u30d7\u30ed\u30bb\u30b9\u4e2d\u306b\u3001\u5024\u304c \\(3\\) \u306e\u30ce\u30fc\u30c9\u306b\u906d\u9047\u3057\u305f\u5834\u5408\u3001\u305d\u306e\u30d1\u30b9\u3092\u901a\u3058\u3066\u3055\u3089\u306b\u691c\u7d22\u3059\u308b\u3053\u3068\u3092\u5373\u5ea7\u306b\u4e2d\u6b62\u3057\u307e\u3059\u3002\u30b3\u30fc\u30c9\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig preorder_traversal_iii_compact.py<pre><code>def pre_order(root: TreeNode):\n    \"\"\"\u524d\u9806\u8d70\u67fb\uff1a\u4f8b\u4e09\"\"\"\n    # \u679d\u5208\u308a\n    if root is None or root.val == 3:\n        return\n    # \u8a66\u884c\n    path.append(root)\n    if root.val == 7:\n        # \u89e3\u3092\u8a18\u9332\n        res.append(list(path))\n    pre_order(root.left)\n    pre_order(root.right)\n    # \u64a4\u56de\n    path.pop()\n</code></pre> preorder_traversal_iii_compact.cpp<pre><code>/* \u524d\u9806\u8d70\u67fb\uff1a\u4f8b\uff13 */\nvoid preOrder(TreeNode *root) {\n    // \u526a\u5b9a\n    if (root == nullptr || root-&gt;val == 3) {\n        return;\n    }\n    // \u8a66\u884c\n    path.push_back(root);\n    if (root-&gt;val == 7) {\n        // \u89e3\u3092\u8a18\u9332\n        res.push_back(path);\n    }\n    preOrder(root-&gt;left);\n    preOrder(root-&gt;right);\n    // \u56de\u9000\n    path.pop_back();\n}\n</code></pre> preorder_traversal_iii_compact.java<pre><code>/* \u524d\u9806\u8d70\u67fb\uff1a\u4f8b\uff13 */\nvoid preOrder(TreeNode root) {\n    // \u526a\u5b9a\n    if (root == null || root.val == 3) {\n        return;\n    }\n    // \u8a66\u884c\n    path.add(root);\n    if (root.val == 7) {\n        // \u89e3\u3092\u8a18\u9332\n        res.add(new ArrayList&lt;&gt;(path));\n    }\n    preOrder(root.left);\n    preOrder(root.right);\n    // \u56de\u9000\n    path.remove(path.size() - 1);\n}\n</code></pre> preorder_traversal_iii_compact.cs<pre><code>[class]{preorder_traversal_iii_compact}-[func]{PreOrder}\n</code></pre> preorder_traversal_iii_compact.go<pre><code>[class]{}-[func]{preOrderIII}\n</code></pre> preorder_traversal_iii_compact.swift<pre><code>[class]{}-[func]{preOrder}\n</code></pre> preorder_traversal_iii_compact.js<pre><code>[class]{}-[func]{preOrder}\n</code></pre> preorder_traversal_iii_compact.ts<pre><code>[class]{}-[func]{preOrder}\n</code></pre> preorder_traversal_iii_compact.dart<pre><code>[class]{}-[func]{preOrder}\n</code></pre> preorder_traversal_iii_compact.rs<pre><code>[class]{}-[func]{pre_order}\n</code></pre> preorder_traversal_iii_compact.c<pre><code>[class]{}-[func]{preOrder}\n</code></pre> preorder_traversal_iii_compact.kt<pre><code>[class]{}-[func]{preOrder}\n</code></pre> preorder_traversal_iii_compact.rb<pre><code>[class]{}-[func]{pre_order}\n</code></pre> preorder_traversal_iii_compact.zig<pre><code>[class]{}-[func]{preOrder}\n</code></pre> <p>\u300c\u526a\u5b9a\u300d\u306f\u975e\u5e38\u306b\u751f\u304d\u751f\u304d\u3068\u3057\u305f\u540d\u8a5e\u3067\u3059\u3002\u4ee5\u4e0b\u306e\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u691c\u7d22\u30d7\u30ed\u30bb\u30b9\u3067\u3001\u5236\u7d04\u3092\u6e80\u305f\u3055\u306a\u3044\u691c\u7d22\u5206\u5c90\u3092\u300c\u5207\u308a\u53d6\u308a\u300d\u307e\u3059\u3002\u3055\u3089\u306a\u308b\u4e0d\u8981\u306a\u8a66\u884c\u3092\u907f\u3051\u3001\u691c\u7d22\u52b9\u7387\u3092\u5411\u4e0a\u3055\u305b\u307e\u3059\u3002</p> <p></p> <p> \u56f3 13-3 \u00a0 \u5236\u7d04\u306b\u57fa\u3065\u304f\u526a\u5b9a </p>"},{"location":"chapter_backtracking/backtracking_algorithm/#1313","title":"13.1.3 \u00a0 \u30d5\u30ec\u30fc\u30e0\u30ef\u30fc\u30af\u30b3\u30fc\u30c9","text":"<p>\u4eca\u5ea6\u306f\u3001\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u304b\u3089\u300c\u8a66\u884c\u3001\u5f8c\u9000\u3001\u526a\u5b9a\u300d\u306e\u4e3b\u8981\u306a\u30d5\u30ec\u30fc\u30e0\u30ef\u30fc\u30af\u3092\u62bd\u51fa\u3057\u3066\u3001\u30b3\u30fc\u30c9\u306e\u6c4e\u7528\u6027\u3092\u5411\u4e0a\u3055\u305b\u3066\u307f\u307e\u3057\u3087\u3046\u3002</p> <p>\u4ee5\u4e0b\u306e\u30d5\u30ec\u30fc\u30e0\u30ef\u30fc\u30af\u30b3\u30fc\u30c9\u3067\u306f\u3001<code>state</code> \u306f\u554f\u984c\u306e\u73fe\u5728\u306e\u72b6\u614b\u3092\u8868\u3057\u3001<code>choices</code> \u306f\u73fe\u5728\u306e\u72b6\u614b\u3067\u5229\u7528\u53ef\u80fd\u306a\u9078\u629e\u80a2\u3092\u8868\u3057\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig <pre><code>def backtrack(state: State, choices: list[choice], res: list[state]):\n    \"\"\"\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u30d5\u30ec\u30fc\u30e0\u30ef\u30fc\u30af\"\"\"\n    # \u89e3\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\n    if is_solution(state):\n        # \u89e3\u3092\u8a18\u9332\n        record_solution(state, res)\n        # \u691c\u7d22\u3092\u505c\u6b62\n        return\n    # \u3059\u3079\u3066\u306e\u9078\u629e\u80a2\u3092\u53cd\u5fa9\n    for choice in choices:\n        # \u526a\u5b9a\uff1a\u9078\u629e\u80a2\u304c\u6709\u52b9\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\n        if is_valid(state, choice):\n            # \u8a66\u884c\uff1a\u9078\u629e\u3092\u884c\u3044\u3001\u72b6\u614b\u3092\u66f4\u65b0\n            make_choice(state, choice)\n            backtrack(state, choices, res)\n            # \u5f8c\u9000\uff1a\u9078\u629e\u3092\u53d6\u308a\u6d88\u3057\u3001\u524d\u306e\u72b6\u614b\u306b\u623b\u3059\n            undo_choice(state, choice)\n</code></pre> <pre><code>/* \u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u30d5\u30ec\u30fc\u30e0\u30ef\u30fc\u30af */\nvoid backtrack(State *state, vector&lt;Choice *&gt; &amp;choices, vector&lt;State *&gt; &amp;res) {\n    // \u89e3\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\n    if (isSolution(state)) {\n        // \u89e3\u3092\u8a18\u9332\n        recordSolution(state, res);\n        // \u691c\u7d22\u3092\u505c\u6b62\n        return;\n    }\n    // \u3059\u3079\u3066\u306e\u9078\u629e\u80a2\u3092\u53cd\u5fa9\n    for (Choice choice : choices) {\n        // \u526a\u5b9a\uff1a\u9078\u629e\u80a2\u304c\u6709\u52b9\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\n        if (isValid(state, choice)) {\n            // \u8a66\u884c\uff1a\u9078\u629e\u3092\u884c\u3044\u3001\u72b6\u614b\u3092\u66f4\u65b0\n            makeChoice(state, choice);\n            backtrack(state, choices, res);\n            // \u5f8c\u9000\uff1a\u9078\u629e\u3092\u53d6\u308a\u6d88\u3057\u3001\u524d\u306e\u72b6\u614b\u306b\u623b\u3059\n            undoChoice(state, choice);\n        }\n    }\n}\n</code></pre> <pre><code>/* \u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u30d5\u30ec\u30fc\u30e0\u30ef\u30fc\u30af */\nvoid backtrack(State state, List&lt;Choice&gt; choices, List&lt;State&gt; res) {\n    // \u89e3\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\n    if (isSolution(state)) {\n        // \u89e3\u3092\u8a18\u9332\n        recordSolution(state, res);\n        // \u691c\u7d22\u3092\u505c\u6b62\n        return;\n    }\n    // \u3059\u3079\u3066\u306e\u9078\u629e\u80a2\u3092\u53cd\u5fa9\n    for (Choice choice : choices) {\n        // \u526a\u5b9a\uff1a\u9078\u629e\u80a2\u304c\u6709\u52b9\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\n        if (isValid(state, choice)) {\n            // \u8a66\u884c\uff1a\u9078\u629e\u3092\u884c\u3044\u3001\u72b6\u614b\u3092\u66f4\u65b0\n            makeChoice(state, choice);\n            backtrack(state, choices, res);\n            // \u5f8c\u9000\uff1a\u9078\u629e\u3092\u53d6\u308a\u6d88\u3057\u3001\u524d\u306e\u72b6\u614b\u306b\u623b\u3059\n            undoChoice(state, choice);\n        }\n    }\n}\n</code></pre> <pre><code>/* \u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u30d5\u30ec\u30fc\u30e0\u30ef\u30fc\u30af */\nvoid Backtrack(State state, List&lt;Choice&gt; choices, List&lt;State&gt; res) {\n    // \u89e3\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\n    if (IsSolution(state)) {\n        // \u89e3\u3092\u8a18\u9332\n        RecordSolution(state, res);\n        // \u691c\u7d22\u3092\u505c\u6b62\n        return;\n    }\n    // \u3059\u3079\u3066\u306e\u9078\u629e\u80a2\u3092\u53cd\u5fa9\n    foreach (Choice choice in choices) {\n        // \u526a\u5b9a\uff1a\u9078\u629e\u80a2\u304c\u6709\u52b9\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\n        if (IsValid(state, choice)) {\n            // \u8a66\u884c\uff1a\u9078\u629e\u3092\u884c\u3044\u3001\u72b6\u614b\u3092\u66f4\u65b0\n            MakeChoice(state, choice);\n            Backtrack(state, choices, res);\n            // \u5f8c\u9000\uff1a\u9078\u629e\u3092\u53d6\u308a\u6d88\u3057\u3001\u524d\u306e\u72b6\u614b\u306b\u623b\u3059\n            UndoChoice(state, choice);\n        }\n    }\n}\n</code></pre> <pre><code>/* \u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u30d5\u30ec\u30fc\u30e0\u30ef\u30fc\u30af */\nfunc backtrack(state *State, choices []Choice, res *[]State) {\n    // \u89e3\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\n    if isSolution(state) {\n        // \u89e3\u3092\u8a18\u9332\n        recordSolution(state, res)\n        // \u691c\u7d22\u3092\u505c\u6b62\n        return\n    }\n    // \u3059\u3079\u3066\u306e\u9078\u629e\u80a2\u3092\u53cd\u5fa9\n    for _, choice := range choices {\n        // \u526a\u5b9a\uff1a\u9078\u629e\u80a2\u304c\u6709\u52b9\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\n        if isValid(state, choice) {\n            // \u8a66\u884c\uff1a\u9078\u629e\u3092\u884c\u3044\u3001\u72b6\u614b\u3092\u66f4\u65b0\n            makeChoice(state, choice)\n            backtrack(state, choices, res)\n            // \u5f8c\u9000\uff1a\u9078\u629e\u3092\u53d6\u308a\u6d88\u3057\u3001\u524d\u306e\u72b6\u614b\u306b\u623b\u3059\n            undoChoice(state, choice)\n        }\n    }\n}\n</code></pre> <pre><code>/* \u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u30d5\u30ec\u30fc\u30e0\u30ef\u30fc\u30af */\nfunc backtrack(state: inout State, choices: [Choice], res: inout [State]) {\n    // \u89e3\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\n    if isSolution(state: state) {\n        // \u89e3\u3092\u8a18\u9332\n        recordSolution(state: state, res: &amp;res)\n        // \u691c\u7d22\u3092\u505c\u6b62\n        return\n    }\n    // \u3059\u3079\u3066\u306e\u9078\u629e\u80a2\u3092\u53cd\u5fa9\n    for choice in choices {\n        // \u526a\u5b9a\uff1a\u9078\u629e\u80a2\u304c\u6709\u52b9\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\n        if isValid(state: state, choice: choice) {\n            // \u8a66\u884c\uff1a\u9078\u629e\u3092\u884c\u3044\u3001\u72b6\u614b\u3092\u66f4\u65b0\n            makeChoice(state: &amp;state, choice: choice)\n            backtrack(state: &amp;state, choices: choices, res: &amp;res)\n            // \u5f8c\u9000\uff1a\u9078\u629e\u3092\u53d6\u308a\u6d88\u3057\u3001\u524d\u306e\u72b6\u614b\u306b\u623b\u3059\n            undoChoice(state: &amp;state, choice: choice)\n        }\n    }\n}\n</code></pre> <pre><code>/* \u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u30d5\u30ec\u30fc\u30e0\u30ef\u30fc\u30af */\nfunction backtrack(state, choices, res) {\n    // \u89e3\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\n    if (isSolution(state)) {\n        // \u89e3\u3092\u8a18\u9332\n        recordSolution(state, res);\n        // \u691c\u7d22\u3092\u505c\u6b62\n        return;\n    }\n    // \u3059\u3079\u3066\u306e\u9078\u629e\u80a2\u3092\u53cd\u5fa9\n    for (let choice of choices) {\n        // \u526a\u5b9a\uff1a\u9078\u629e\u80a2\u304c\u6709\u52b9\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\n        if (isValid(state, choice)) {\n            // \u8a66\u884c\uff1a\u9078\u629e\u3092\u884c\u3044\u3001\u72b6\u614b\u3092\u66f4\u65b0\n            makeChoice(state, choice);\n            backtrack(state, choices, res);\n            // \u5f8c\u9000\uff1a\u9078\u629e\u3092\u53d6\u308a\u6d88\u3057\u3001\u524d\u306e\u72b6\u614b\u306b\u623b\u3059\n            undoChoice(state, choice);\n        }\n    }\n}\n</code></pre> <pre><code>/* \u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u30d5\u30ec\u30fc\u30e0\u30ef\u30fc\u30af */\nfunction backtrack(state: State, choices: Choice[], res: State[]): void {\n    // \u89e3\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\n    if (isSolution(state)) {\n        // \u89e3\u3092\u8a18\u9332\n        recordSolution(state, res);\n        // \u691c\u7d22\u3092\u505c\u6b62\n        return;\n    }\n    // \u3059\u3079\u3066\u306e\u9078\u629e\u80a2\u3092\u53cd\u5fa9\n    for (let choice of choices) {\n        // \u526a\u5b9a\uff1a\u9078\u629e\u80a2\u304c\u6709\u52b9\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\n        if (isValid(state, choice)) {\n            // \u8a66\u884c\uff1a\u9078\u629e\u3092\u884c\u3044\u3001\u72b6\u614b\u3092\u66f4\u65b0\n            makeChoice(state, choice);\n            backtrack(state, choices, res);\n            // \u5f8c\u9000\uff1a\u9078\u629e\u3092\u53d6\u308a\u6d88\u3057\u3001\u524d\u306e\u72b6\u614b\u306b\u623b\u3059\n            undoChoice(state, choice);\n        }\n    }\n}\n</code></pre> <pre><code>/* \u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u30d5\u30ec\u30fc\u30e0\u30ef\u30fc\u30af */\nvoid backtrack(State state, List&lt;Choice&gt;, List&lt;State&gt; res) {\n  // \u89e3\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\n  if (isSolution(state)) {\n    // \u89e3\u3092\u8a18\u9332\n    recordSolution(state, res);\n    // \u691c\u7d22\u3092\u505c\u6b62\n    return;\n  }\n  // \u3059\u3079\u3066\u306e\u9078\u629e\u80a2\u3092\u53cd\u5fa9\n  for (Choice choice in choices) {\n    // \u526a\u5b9a\uff1a\u9078\u629e\u80a2\u304c\u6709\u52b9\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\n    if (isValid(state, choice)) {\n      // \u8a66\u884c\uff1a\u9078\u629e\u3092\u884c\u3044\u3001\u72b6\u614b\u3092\u66f4\u65b0\n      makeChoice(state, choice);\n      backtrack(state, choices, res);\n      // \u5f8c\u9000\uff1a\u9078\u629e\u3092\u53d6\u308a\u6d88\u3057\u3001\u524d\u306e\u72b6\u614b\u306b\u623b\u3059\n      undoChoice(state, choice);\n    }\n  }\n}\n</code></pre> <pre><code>/* \u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u30d5\u30ec\u30fc\u30e0\u30ef\u30fc\u30af */\nfn backtrack(state: &amp;mut State, choices: &amp;Vec&lt;Choice&gt;, res: &amp;mut Vec&lt;State&gt;) {\n    // \u89e3\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\n    if is_solution(state) {\n        // \u89e3\u3092\u8a18\u9332\n        record_solution(state, res);\n        // \u691c\u7d22\u3092\u505c\u6b62\n        return;\n    }\n    // \u3059\u3079\u3066\u306e\u9078\u629e\u80a2\u3092\u53cd\u5fa9\n    for choice in choices {\n        // \u526a\u5b9a\uff1a\u9078\u629e\u80a2\u304c\u6709\u52b9\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\n        if is_valid(state, choice) {\n            // \u8a66\u884c\uff1a\u9078\u629e\u3092\u884c\u3044\u3001\u72b6\u614b\u3092\u66f4\u65b0\n            make_choice(state, choice);\n            backtrack(state, choices, res);\n            // \u5f8c\u9000\uff1a\u9078\u629e\u3092\u53d6\u308a\u6d88\u3057\u3001\u524d\u306e\u72b6\u614b\u306b\u623b\u3059\n            undo_choice(state, choice);\n        }\n    }\n}\n</code></pre> <pre><code>/* \u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u30d5\u30ec\u30fc\u30e0\u30ef\u30fc\u30af */\nvoid backtrack(State *state, Choice *choices, int numChoices, State *res, int numRes) {\n    // \u89e3\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\n    if (isSolution(state)) {\n        // \u89e3\u3092\u8a18\u9332\n        recordSolution(state, res, numRes);\n        // \u691c\u7d22\u3092\u505c\u6b62\n        return;\n    }\n    // \u3059\u3079\u3066\u306e\u9078\u629e\u80a2\u3092\u53cd\u5fa9\n    for (int i = 0; i &lt; numChoices; i++) {\n        // \u526a\u5b9a\uff1a\u9078\u629e\u80a2\u304c\u6709\u52b9\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\n        if (isValid(state, &amp;choices[i])) {\n            // \u8a66\u884c\uff1a\u9078\u629e\u3092\u884c\u3044\u3001\u72b6\u614b\u3092\u66f4\u65b0\n            makeChoice(state, &amp;choices[i]);\n            backtrack(state, choices, numChoices, res, numRes);\n            // \u5f8c\u9000\uff1a\u9078\u629e\u3092\u53d6\u308a\u6d88\u3057\u3001\u524d\u306e\u72b6\u614b\u306b\u623b\u3059\n            undoChoice(state, &amp;choices[i]);\n        }\n    }\n}\n</code></pre> <pre><code>/* \u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u30d5\u30ec\u30fc\u30e0\u30ef\u30fc\u30af */\nfun backtrack(state: State?, choices: List&lt;Choice?&gt;, res: List&lt;State?&gt;?) {\n    // \u89e3\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\n    if (isSolution(state)) {\n        // \u89e3\u3092\u8a18\u9332\n        recordSolution(state, res)\n        // \u691c\u7d22\u3092\u505c\u6b62\n        return\n    }\n    // \u3059\u3079\u3066\u306e\u9078\u629e\u80a2\u3092\u53cd\u5fa9\n    for (choice in choices) {\n        // \u526a\u5b9a\uff1a\u9078\u629e\u80a2\u304c\u6709\u52b9\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\n        if (isValid(state, choice)) {\n            // \u8a66\u884c\uff1a\u9078\u629e\u3092\u884c\u3044\u3001\u72b6\u614b\u3092\u66f4\u65b0\n            makeChoice(state, choice)\n            backtrack(state, choices, res)\n            // \u5f8c\u9000\uff1a\u9078\u629e\u3092\u53d6\u308a\u6d88\u3057\u3001\u524d\u306e\u72b6\u614b\u306b\u623b\u3059\n            undoChoice(state, choice)\n        }\n    }\n}\n</code></pre> <pre><code>### \u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u30d5\u30ec\u30fc\u30e0\u30ef\u30fc\u30af ###\ndef backtrack(state, choices, res)\n    # \u89e3\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\n    if is_solution?(state)\n        # \u89e3\u3092\u8a18\u9332\n        record_solution(state, res)\n        return\n    end\n\n    # \u3059\u3079\u3066\u306e\u9078\u629e\u80a2\u3092\u53cd\u5fa9\n    for choice in choices\n        # \u526a\u5b9a\uff1a\u9078\u629e\u80a2\u304c\u6709\u52b9\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\n        if is_valid?(state, choice)\n            # \u8a66\u884c\uff1a\u9078\u629e\u3092\u884c\u3044\u3001\u72b6\u614b\u3092\u66f4\u65b0\n            make_choice(state, choice)\n            backtrack(state, choices, res)\n            # \u5f8c\u9000\uff1a\u9078\u629e\u3092\u53d6\u308a\u6d88\u3057\u3001\u524d\u306e\u72b6\u614b\u306b\u623b\u3059\n            undo_choice(state, choice)\n        end\n    end\nend\n</code></pre> <pre><code>\n</code></pre> <p>\u6b21\u306b\u3001\u30d5\u30ec\u30fc\u30e0\u30ef\u30fc\u30af\u30b3\u30fc\u30c9\u306b\u57fa\u3065\u3044\u3066\u4f8b\u984c 3 \u3092\u89e3\u304d\u307e\u3059\u3002\u72b6\u614b <code>state</code> \u306f\u30ce\u30fc\u30c9\u306e\u8d70\u67fb\u7d4c\u8def\u3092\u8868\u3057\u3001\u9078\u629e\u80a2 <code>choices</code> \u306f\u73fe\u5728\u30ce\u30fc\u30c9\u306e\u5de6\u5b50\u30ce\u30fc\u30c9\u3068\u53f3\u5b50\u30ce\u30fc\u30c9\u3001\u7d50\u679c <code>res</code> \u306f\u7d4c\u8def\u30ea\u30b9\u30c8\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig preorder_traversal_iii_template.py<pre><code>def is_solution(state: list[TreeNode]) -&gt; bool:\n    \"\"\"\u73fe\u5728\u306e\u72b6\u614b\u304c\u89e3\u304b\u3069\u3046\u304b\u3092\u5224\u5b9a\"\"\"\n    return state and state[-1].val == 7\n\ndef record_solution(state: list[TreeNode], res: list[list[TreeNode]]):\n    \"\"\"\u89e3\u3092\u8a18\u9332\"\"\"\n    res.append(list(state))\n\ndef is_valid(state: list[TreeNode], choice: TreeNode) -&gt; bool:\n    \"\"\"\u73fe\u5728\u306e\u72b6\u614b\u4e0b\u3067\u9078\u629e\u304c\u5408\u6cd5\u304b\u3069\u3046\u304b\u3092\u5224\u5b9a\"\"\"\n    return choice is not None and choice.val != 3\n\ndef make_choice(state: list[TreeNode], choice: TreeNode):\n    \"\"\"\u72b6\u614b\u3092\u66f4\u65b0\"\"\"\n    state.append(choice)\n\ndef undo_choice(state: list[TreeNode], choice: TreeNode):\n    \"\"\"\u72b6\u614b\u3092\u5fa9\u5143\"\"\"\n    state.pop()\n\ndef backtrack(\n    state: list[TreeNode], choices: list[TreeNode], res: list[list[TreeNode]]\n):\n    \"\"\"\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\uff1a\u4f8b\u4e09\"\"\"\n    # \u89e3\u304b\u3069\u3046\u304b\u3092\u30c1\u30a7\u30c3\u30af\n    if is_solution(state):\n        # \u89e3\u3092\u8a18\u9332\n        record_solution(state, res)\n    # \u3059\u3079\u3066\u306e\u9078\u629e\u80a2\u3092\u8d70\u67fb\n    for choice in choices:\n        # \u679d\u5208\u308a\uff1a\u9078\u629e\u304c\u5408\u6cd5\u304b\u3069\u3046\u304b\u3092\u30c1\u30a7\u30c3\u30af\n        if is_valid(state, choice):\n            # \u8a66\u884c\uff1a\u9078\u629e\u3092\u884c\u3044\u3001\u72b6\u614b\u3092\u66f4\u65b0\n            make_choice(state, choice)\n            # \u6b21\u306e\u9078\u629e\u30e9\u30a6\u30f3\u30c9\u306b\u9032\u3080\n            backtrack(state, [choice.left, choice.right], res)\n            # \u64a4\u56de\uff1a\u9078\u629e\u3092\u53d6\u308a\u6d88\u3057\u3001\u524d\u306e\u72b6\u614b\u306b\u5fa9\u5143\n            undo_choice(state, choice)\n</code></pre> preorder_traversal_iii_template.cpp<pre><code>/* \u73fe\u5728\u306e\u72b6\u614b\u304c\u89e3\u304b\u3069\u3046\u304b\u3092\u5224\u5b9a */\nbool isSolution(vector&lt;TreeNode *&gt; &amp;state) {\n    return !state.empty() &amp;&amp; state.back()-&gt;val == 7;\n}\n\n/* \u89e3\u3092\u8a18\u9332 */\nvoid recordSolution(vector&lt;TreeNode *&gt; &amp;state, vector&lt;vector&lt;TreeNode *&gt;&gt; &amp;res) {\n    res.push_back(state);\n}\n\n/* \u73fe\u5728\u306e\u72b6\u614b\u4e0b\u3067\u9078\u629e\u304c\u5408\u6cd5\u304b\u3069\u3046\u304b\u3092\u5224\u5b9a */\nbool isValid(vector&lt;TreeNode *&gt; &amp;state, TreeNode *choice) {\n    return choice != nullptr &amp;&amp; choice-&gt;val != 3;\n}\n\n/* \u72b6\u614b\u3092\u66f4\u65b0 */\nvoid makeChoice(vector&lt;TreeNode *&gt; &amp;state, TreeNode *choice) {\n    state.push_back(choice);\n}\n\n/* \u72b6\u614b\u3092\u5fa9\u5143 */\nvoid undoChoice(vector&lt;TreeNode *&gt; &amp;state, TreeNode *choice) {\n    state.pop_back();\n}\n\n/* \u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\uff1a\u4f8b\uff13 */\nvoid backtrack(vector&lt;TreeNode *&gt; &amp;state, vector&lt;TreeNode *&gt; &amp;choices, vector&lt;vector&lt;TreeNode *&gt;&gt; &amp;res) {\n    // \u89e3\u304b\u3069\u3046\u304b\u3092\u30c1\u30a7\u30c3\u30af\n    if (isSolution(state)) {\n        // \u89e3\u3092\u8a18\u9332\n        recordSolution(state, res);\n    }\n    // \u3059\u3079\u3066\u306e\u9078\u629e\u80a2\u3092\u8d70\u67fb\n    for (TreeNode *choice : choices) {\n        // \u526a\u5b9a\uff1a\u9078\u629e\u304c\u5408\u6cd5\u304b\u3069\u3046\u304b\u3092\u30c1\u30a7\u30c3\u30af\n        if (isValid(state, choice)) {\n            // \u8a66\u884c\uff1a\u9078\u629e\u3092\u884c\u3044\u3001\u72b6\u614b\u3092\u66f4\u65b0\n            makeChoice(state, choice);\n            // \u6b21\u306e\u30e9\u30a6\u30f3\u30c9\u306e\u9078\u629e\u306b\u9032\u3080\n            vector&lt;TreeNode *&gt; nextChoices{choice-&gt;left, choice-&gt;right};\n            backtrack(state, nextChoices, res);\n            // \u56de\u9000\uff1a\u9078\u629e\u3092\u53d6\u308a\u6d88\u3057\u3001\u524d\u306e\u72b6\u614b\u306b\u5fa9\u5143\n            undoChoice(state, choice);\n        }\n    }\n}\n</code></pre> preorder_traversal_iii_template.java<pre><code>/* \u73fe\u5728\u306e\u72b6\u614b\u304c\u89e3\u304b\u3069\u3046\u304b\u3092\u5224\u5b9a */\nboolean isSolution(List&lt;TreeNode&gt; state) {\n    return !state.isEmpty() &amp;&amp; state.get(state.size() - 1).val == 7;\n}\n\n/* \u89e3\u3092\u8a18\u9332 */\nvoid recordSolution(List&lt;TreeNode&gt; state, List&lt;List&lt;TreeNode&gt;&gt; res) {\n    res.add(new ArrayList&lt;&gt;(state));\n}\n\n/* \u73fe\u5728\u306e\u72b6\u614b\u4e0b\u3067\u9078\u629e\u304c\u5408\u6cd5\u304b\u3069\u3046\u304b\u3092\u5224\u5b9a */\nboolean isValid(List&lt;TreeNode&gt; state, TreeNode choice) {\n    return choice != null &amp;&amp; choice.val != 3;\n}\n\n/* \u72b6\u614b\u3092\u66f4\u65b0 */\nvoid makeChoice(List&lt;TreeNode&gt; state, TreeNode choice) {\n    state.add(choice);\n}\n\n/* \u72b6\u614b\u3092\u5fa9\u5143 */\nvoid undoChoice(List&lt;TreeNode&gt; state, TreeNode choice) {\n    state.remove(state.size() - 1);\n}\n\n/* \u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\uff1a\u4f8b\uff13 */\nvoid backtrack(List&lt;TreeNode&gt; state, List&lt;TreeNode&gt; choices, List&lt;List&lt;TreeNode&gt;&gt; res) {\n    // \u89e3\u304b\u3069\u3046\u304b\u3092\u30c1\u30a7\u30c3\u30af\n    if (isSolution(state)) {\n        // \u89e3\u3092\u8a18\u9332\n        recordSolution(state, res);\n    }\n    // \u3059\u3079\u3066\u306e\u9078\u629e\u80a2\u3092\u8d70\u67fb\n    for (TreeNode choice : choices) {\n        // \u526a\u5b9a\uff1a\u9078\u629e\u304c\u5408\u6cd5\u304b\u3069\u3046\u304b\u3092\u30c1\u30a7\u30c3\u30af\n        if (isValid(state, choice)) {\n            // \u8a66\u884c\uff1a\u9078\u629e\u3092\u884c\u3044\u3001\u72b6\u614b\u3092\u66f4\u65b0\n            makeChoice(state, choice);\n            // \u6b21\u306e\u30e9\u30a6\u30f3\u30c9\u306e\u9078\u629e\u306b\u9032\u3080\n            backtrack(state, Arrays.asList(choice.left, choice.right), res);\n            // \u56de\u9000\uff1a\u9078\u629e\u3092\u53d6\u308a\u6d88\u3057\u3001\u524d\u306e\u72b6\u614b\u306b\u5fa9\u5143\n            undoChoice(state, choice);\n        }\n    }\n}\n</code></pre> preorder_traversal_iii_template.cs<pre><code>[class]{preorder_traversal_iii_template}-[func]{IsSolution}\n\n[class]{preorder_traversal_iii_template}-[func]{RecordSolution}\n\n[class]{preorder_traversal_iii_template}-[func]{IsValid}\n\n[class]{preorder_traversal_iii_template}-[func]{MakeChoice}\n\n[class]{preorder_traversal_iii_template}-[func]{UndoChoice}\n\n[class]{preorder_traversal_iii_template}-[func]{Backtrack}\n</code></pre> preorder_traversal_iii_template.go<pre><code>[class]{}-[func]{isSolution}\n\n[class]{}-[func]{recordSolution}\n\n[class]{}-[func]{isValid}\n\n[class]{}-[func]{makeChoice}\n\n[class]{}-[func]{undoChoice}\n\n[class]{}-[func]{backtrackIII}\n</code></pre> preorder_traversal_iii_template.swift<pre><code>[class]{}-[func]{isSolution}\n\n[class]{}-[func]{recordSolution}\n\n[class]{}-[func]{isValid}\n\n[class]{}-[func]{makeChoice}\n\n[class]{}-[func]{undoChoice}\n\n[class]{}-[func]{backtrack}\n</code></pre> preorder_traversal_iii_template.js<pre><code>[class]{}-[func]{isSolution}\n\n[class]{}-[func]{recordSolution}\n\n[class]{}-[func]{isValid}\n\n[class]{}-[func]{makeChoice}\n\n[class]{}-[func]{undoChoice}\n\n[class]{}-[func]{backtrack}\n</code></pre> preorder_traversal_iii_template.ts<pre><code>[class]{}-[func]{isSolution}\n\n[class]{}-[func]{recordSolution}\n\n[class]{}-[func]{isValid}\n\n[class]{}-[func]{makeChoice}\n\n[class]{}-[func]{undoChoice}\n\n[class]{}-[func]{backtrack}\n</code></pre> preorder_traversal_iii_template.dart<pre><code>[class]{}-[func]{isSolution}\n\n[class]{}-[func]{recordSolution}\n\n[class]{}-[func]{isValid}\n\n[class]{}-[func]{makeChoice}\n\n[class]{}-[func]{undoChoice}\n\n[class]{}-[func]{backtrack}\n</code></pre> preorder_traversal_iii_template.rs<pre><code>[class]{}-[func]{is_solution}\n\n[class]{}-[func]{record_solution}\n\n[class]{}-[func]{is_valid}\n\n[class]{}-[func]{make_choice}\n\n[class]{}-[func]{undo_choice}\n\n[class]{}-[func]{backtrack}\n</code></pre> preorder_traversal_iii_template.c<pre><code>[class]{}-[func]{isSolution}\n\n[class]{}-[func]{recordSolution}\n\n[class]{}-[func]{isValid}\n\n[class]{}-[func]{makeChoice}\n\n[class]{}-[func]{undoChoice}\n\n[class]{}-[func]{backtrack}\n</code></pre> preorder_traversal_iii_template.kt<pre><code>[class]{}-[func]{isSolution}\n\n[class]{}-[func]{recordSolution}\n\n[class]{}-[func]{isValid}\n\n[class]{}-[func]{makeChoice}\n\n[class]{}-[func]{undoChoice}\n\n[class]{}-[func]{backtrack}\n</code></pre> preorder_traversal_iii_template.rb<pre><code>[class]{}-[func]{is_solution}\n\n[class]{}-[func]{record_solution}\n\n[class]{}-[func]{is_valid}\n\n[class]{}-[func]{make_choice}\n\n[class]{}-[func]{undo_choice}\n\n[class]{}-[func]{backtrack}\n</code></pre> preorder_traversal_iii_template.zig<pre><code>[class]{}-[func]{isSolution}\n\n[class]{}-[func]{recordSolution}\n\n[class]{}-[func]{isValid}\n\n[class]{}-[func]{makeChoice}\n\n[class]{}-[func]{undoChoice}\n\n[class]{}-[func]{backtrack}\n</code></pre> <p>\u554f\u984c\u6587\u306e\u610f\u5473\u306b\u5f93\u3044\u3001\u5024\u304c \\(7\\) \u306e\u30ce\u30fc\u30c9\u3092\u898b\u3064\u3051\u305f\u5f8c\u3082\u63a2\u7d22\u3092\u7d9a\u3051\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u89e3\u3092\u8a18\u9332\u3057\u305f\u5f8c\u306e <code>return</code> \u6587\u3092\u524a\u9664\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u6b21\u306e\u56f3\u306f\u3001<code>return</code> \u6587\u3092\u4fdd\u6301\u3059\u308b\u5834\u5408\u3068\u524a\u9664\u3059\u308b\u5834\u5408\u306e\u63a2\u7d22\u904e\u7a0b\u306e\u6bd4\u8f03\u3067\u3059\u3002</p> <p></p> <p> \u56f3 13-4 \u00a0 return\u3092\u4fdd\u6301\u3059\u308b\u5834\u5408\u3068\u524a\u9664\u3059\u308b\u5834\u5408\u306e\u63a2\u7d22\u904e\u7a0b\u306e\u6bd4\u8f03 </p> <p>\u524d\u9806\u8d70\u67fb\u306b\u57fa\u3065\u304f\u30b3\u30fc\u30c9\u5b9f\u88c5\u3068\u6bd4\u3079\u308b\u3068\u3001\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u30d5\u30ec\u30fc\u30e0\u30ef\u30fc\u30af\u306b\u57fa\u3065\u304f\u5b9f\u88c5\u306f\u3084\u3084\u5197\u9577\u306b\u898b\u3048\u307e\u3059\u304c\u3001\u6c4e\u7528\u6027\u306f\u3088\u308a\u9ad8\u3044\u3067\u3059\u3002\u5b9f\u969b\u3001\u591a\u304f\u306e\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u554f\u984c\u306f\u3053\u306e\u30d5\u30ec\u30fc\u30e0\u30ef\u30fc\u30af\u306e\u4e0b\u3067\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u5177\u4f53\u7684\u306a\u554f\u984c\u306b\u5fdc\u3058\u3066 <code>state</code> \u3068 <code>choices</code> \u3092\u5b9a\u7fa9\u3057\u3001\u30d5\u30ec\u30fc\u30e0\u30ef\u30fc\u30af\u5185\u306e\u5404\u30e1\u30bd\u30c3\u30c9\u3092\u5b9f\u88c5\u3059\u308c\u3070\u3088\u3044\u306e\u3067\u3059\u3002</p>"},{"location":"chapter_backtracking/backtracking_algorithm/#1314","title":"13.1.4 \u00a0 \u3088\u304f\u4f7f\u308f\u308c\u308b\u7528\u8a9e","text":"<p>\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u554f\u984c\u3092\u3088\u308a\u660e\u78ba\u306b\u5206\u6790\u3059\u308b\u305f\u3081\u306b\u3001\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u3088\u304f\u4f7f\u308f\u308c\u308b\u7528\u8a9e\u306e\u610f\u5473\u3092\u307e\u3068\u3081\u3001\u4f8b\u984c 3 \u306e\u5bfe\u5fdc\u4f8b\u3092\u4ee5\u4e0b\u306e\u8868\u306b\u793a\u3057\u307e\u3059\u3002</p> <p> \u8868 13-1 \u00a0 \u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u3088\u304f\u4f7f\u308f\u308c\u308b\u7528\u8a9e </p> \u540d\u79f0 \u5b9a\u7fa9 \u4f8b\u984c 3 \u89e3\uff08solution\uff09 \u89e3\u306f\u554f\u984c\u306e\u7279\u5b9a\u6761\u4ef6\u3092\u6e80\u305f\u3059\u7b54\u3048\u3067\u3042\u308a\u30011 \u3064\u307e\u305f\u306f\u8907\u6570\u5b58\u5728\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308b \u6839\u30ce\u30fc\u30c9\u304b\u3089\u30ce\u30fc\u30c9 \\(7\\) \u307e\u3067\u306e\u5236\u7d04\u6761\u4ef6\u3092\u6e80\u305f\u3059\u3059\u3079\u3066\u306e\u7d4c\u8def \u5236\u7d04\u6761\u4ef6\uff08constraint\uff09 \u5236\u7d04\u6761\u4ef6\u306f\u3001\u89e3\u306e\u5b9f\u73fe\u53ef\u80fd\u6027\u3092\u5236\u9650\u3059\u308b\u6761\u4ef6\u3067\u3042\u308a\u3001\u901a\u5e38\u306f\u679d\u5208\u308a\u306b\u4f7f\u7528\u3055\u308c\u308b \u7d4c\u8def\u306b\u30ce\u30fc\u30c9 \\(3\\) \u3092\u542b\u307e\u306a\u3044 \u72b6\u614b\uff08state\uff09 \u72b6\u614b\u306f\u3001\u3042\u308b\u6642\u70b9\u3067\u306e\u554f\u984c\u306e\u72b6\u6cc1\u3092\u8868\u3057\u3001\u3053\u308c\u307e\u3067\u306b\u884c\u3063\u305f\u9078\u629e\u3092\u542b\u3080 \u73fe\u5728\u8a2a\u554f\u3057\u305f\u30ce\u30fc\u30c9\u7d4c\u8def\u3001\u3059\u306a\u308f\u3061 <code>path</code> \u30ce\u30fc\u30c9\u30ea\u30b9\u30c8 \u8a66\u884c\uff08attempt\uff09 \u8a66\u884c\u306f\u3001\u5229\u7528\u53ef\u80fd\u306a\u9078\u629e\u80a2\u306b\u57fa\u3065\u3044\u3066\u89e3\u7a7a\u9593\u3092\u63a2\u7d22\u3059\u308b\u904e\u7a0b\u3067\u3042\u308a\u3001\u9078\u629e\u3092\u884c\u3044\u3001\u72b6\u614b\u3092\u66f4\u65b0\u3057\u3001\u89e3\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\u3059\u308b \u5de6\uff08\u53f3\uff09\u5b50\u30ce\u30fc\u30c9\u3092\u518d\u5e30\u7684\u306b\u8a2a\u554f\u3057\u3001\u30ce\u30fc\u30c9\u3092 <code>path</code> \u306b\u8ffd\u52a0\u3057\u3001\u30ce\u30fc\u30c9\u306e\u5024\u304c \\(7\\) \u304b\u3092\u78ba\u8a8d\u3059\u308b \u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30af\uff08backtracking\uff09 \u5236\u7d04\u6761\u4ef6\u3092\u6e80\u305f\u3055\u306a\u3044\u72b6\u614b\u306b\u906d\u9047\u3057\u305f\u5834\u5408\u3001\u4ee5\u524d\u306e\u9078\u629e\u3092\u53d6\u308a\u6d88\u3057\u3066\u524d\u306e\u72b6\u614b\u306b\u623b\u308b\u3053\u3068 \u8449\u30ce\u30fc\u30c9\u3092\u8d8a\u3048\u305f\u3068\u304d\u3001\u63a2\u7d22\u7d42\u4e86\u3001\u5024\u304c \\(3\\) \u306e\u30ce\u30fc\u30c9\u306b\u906d\u9047\u3057\u305f\u3068\u304d\u63a2\u7d22\u3092\u7d42\u4e86\u3057\u3001\u95a2\u6570\u304c\u623b\u308b \u679d\u5208\u308a\uff08pruning\uff09 \u554f\u984c\u306e\u7279\u6027\u3084\u5236\u7d04\u6761\u4ef6\u306b\u57fa\u3065\u304d\u3001\u7121\u610f\u5473\u306a\u63a2\u7d22\u7d4c\u8def\u3092\u907f\u3051\u308b\u65b9\u6cd5\u3067\u3042\u308a\u3001\u63a2\u7d22\u52b9\u7387\u3092\u5411\u4e0a\u3055\u305b\u308b \u5024\u304c \\(3\\) \u306e\u30ce\u30fc\u30c9\u306b\u906d\u9047\u3057\u305f\u5834\u5408\u3001\u305d\u308c\u4ee5\u4e0a\u63a2\u7d22\u3057\u306a\u3044 <p>Tip</p> <p>\u554f\u984c\u3001\u89e3\u3001\u72b6\u614b\u306a\u3069\u306e\u6982\u5ff5\u306f\u4e00\u822c\u7684\u306a\u3082\u306e\u3067\u3042\u308a\u3001\u5206\u5272\u7d71\u6cbb\u3001\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u3001\u52d5\u7684\u8a08\u753b\u6cd5\u3001\u8caa\u6b32\u6cd5\u306a\u3069\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306b\u3082\u95a2\u4fc2\u3057\u307e\u3059\u3002</p>"},{"location":"chapter_backtracking/backtracking_algorithm/#1315","title":"13.1.5 \u00a0 \u9577\u6240\u3068\u9650\u754c","text":"<p>\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u672c\u8cea\u7684\u306b\u6df1\u3055\u512a\u5148\u63a2\u7d22\uff08DFS\uff09\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u4e00\u7a2e\u3067\u3042\u308a\u3001\u6761\u4ef6\u3092\u6e80\u305f\u3059\u89e3\u3092\u898b\u3064\u3051\u308b\u307e\u3067\u3042\u3089\u3086\u308b\u53ef\u80fd\u306a\u89e3\u3092\u8a66\u307f\u307e\u3059\u3002\u3053\u306e\u65b9\u6cd5\u306e\u5229\u70b9\u306f\u3001\u3059\u3079\u3066\u306e\u53ef\u80fd\u306a\u89e3\u3092\u898b\u3064\u3051\u3089\u308c\u308b\u70b9\u3067\u3042\u308a\u3001\u9069\u5207\u306a\u679d\u5208\u308a\u3092\u884c\u3048\u3070\u52b9\u7387\u304c\u9ad8\u3044\u3053\u3068\u3067\u3059\u3002</p> <p>\u3057\u304b\u3057\u3001\u5927\u898f\u6a21\u307e\u305f\u306f\u8907\u96d1\u306a\u554f\u984c\u3092\u6271\u3046\u5834\u5408\u3001\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5b9f\u884c\u52b9\u7387\u306f\u8a31\u5bb9\u3067\u304d\u306a\u3044\u307b\u3069\u4f4e\u4e0b\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002</p> <ul> <li>\u6642\u9593\uff1a\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u901a\u5e38\u3001\u72b6\u614b\u7a7a\u9593\u306e\u3059\u3079\u3066\u306e\u53ef\u80fd\u6027\u3092\u63a2\u7d22\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u3001\u6642\u9593\u8a08\u7b97\u91cf\u306f\u6307\u6570\u30aa\u30fc\u30c0\u30fc\u307e\u305f\u306f\u968e\u4e57\u30aa\u30fc\u30c0\u30fc\u306b\u9054\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002</li> <li>\u7a7a\u9593\uff1a\u518d\u5e30\u547c\u3073\u51fa\u3057\u4e2d\u306b\u73fe\u5728\u306e\u72b6\u614b\uff08\u4f8b\uff1a\u7d4c\u8def\u3001\u679d\u5208\u308a\u7528\u306e\u88dc\u52a9\u5909\u6570\u306a\u3069\uff09\u3092\u4fdd\u5b58\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u3001\u6df1\u3055\u304c\u5927\u304d\u3044\u5834\u5408\u3001\u7a7a\u9593\u306e\u4f7f\u7528\u91cf\u304c\u5897\u52a0\u3057\u307e\u3059\u3002</li> </ul> <p>\u305d\u308c\u3067\u3082\u306a\u304a\u3001\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u7279\u5b9a\u306e\u63a2\u7d22\u554f\u984c\u3084\u5236\u7d04\u6e80\u8db3\u554f\u984c\u306e\u6700\u826f\u306e\u89e3\u6cd5\u3067\u3042\u308b\u3053\u3068\u304c\u591a\u3044\u3067\u3059\u3002\u3053\u308c\u3089\u306e\u554f\u984c\u3067\u306f\u3001\u3069\u306e\u9078\u629e\u304c\u6709\u52b9\u306a\u89e3\u3092\u751f\u6210\u3059\u308b\u304b\u3092\u4e88\u6e2c\u3067\u304d\u306a\u3044\u305f\u3081\u3001\u3059\u3079\u3066\u306e\u53ef\u80fd\u306a\u9078\u629e\u3092\u8a66\u3059\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306a\u5834\u5408\u3001**\u52b9\u7387\u306e\u6700\u9069\u5316\u304c\u9375**\u3068\u306a\u308a\u307e\u3059\u3002\u4e00\u822c\u7684\u306a\u6700\u9069\u5316\u624b\u6cd5\u306f\u6b21\u306e 2 \u3064\u3067\u3059\u3002</p> <ul> <li>\u679d\u5208\u308a\uff1a\u89e3\u3092\u751f\u6210\u3057\u306a\u3044\u3053\u3068\u304c\u78ba\u5b9f\u306a\u7d4c\u8def\u3092\u907f\u3051\u308b\u3053\u3068\u3067\u3001\u6642\u9593\u3068\u7a7a\u9593\u3092\u7bc0\u7d04\u3057\u307e\u3059\u3002</li> <li>\u30d2\u30e5\u30fc\u30ea\u30b9\u30c6\u30a3\u30c3\u30af\u63a2\u7d22\uff1a\u63a2\u7d22\u4e2d\u306b\u6226\u7565\u3084\u8a55\u4fa1\u5024\u3092\u5c0e\u5165\u3057\u3001\u6709\u52b9\u306a\u89e3\u3092\u751f\u6210\u3059\u308b\u53ef\u80fd\u6027\u304c\u9ad8\u3044\u7d4c\u8def\u3092\u512a\u5148\u7684\u306b\u63a2\u7d22\u3057\u307e\u3059\u3002</li> </ul>"},{"location":"chapter_backtracking/backtracking_algorithm/#1316","title":"13.1.6 \u00a0 \u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u306e\u5178\u578b\u7684\u306a\u4f8b\u984c","text":"<p>\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u3001\u591a\u304f\u306e\u63a2\u7d22\u554f\u984c\u3001\u5236\u7d04\u6e80\u8db3\u554f\u984c\u3001\u7d44\u5408\u305b\u6700\u9069\u5316\u554f\u984c\u3092\u89e3\u304f\u306e\u306b\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002</p> <p>\u63a2\u7d22\u554f\u984c\uff1a\u3053\u306e\u7a2e\u306e\u554f\u984c\u306e\u76ee\u6a19\u306f\u3001\u7279\u5b9a\u306e\u6761\u4ef6\u3092\u6e80\u305f\u3059\u89e3\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u3067\u3059\u3002</p> <ul> <li>\u5168\u9806\u5217\u554f\u984c\uff1a\u4e0e\u3048\u3089\u308c\u305f\u96c6\u5408\u306e\u3059\u3079\u3066\u306e\u53ef\u80fd\u306a\u9806\u5217\u3092\u6c42\u3081\u308b\u3002</li> <li>\u90e8\u5206\u548c\u554f\u984c\uff1a\u4e0e\u3048\u3089\u308c\u305f\u96c6\u5408\u3068\u76ee\u6a19\u548c\u306b\u5bfe\u3057\u3066\u3001\u548c\u304c\u76ee\u6a19\u5024\u306b\u306a\u308b\u3059\u3079\u3066\u306e\u90e8\u5206\u96c6\u5408\u3092\u6c42\u3081\u308b\u3002</li> <li>\u30cf\u30ce\u30a4\u306e\u5854\uff1a3 \u672c\u306e\u67f1\u3068\u7570\u306a\u308b\u30b5\u30a4\u30ba\u306e\u5186\u76e4\u304c\u3042\u308a\u3001\u3059\u3079\u3066\u306e\u5186\u76e4\u3092 1 \u672c\u306e\u67f1\u304b\u3089\u5225\u306e\u67f1\u306b\u79fb\u3059\u30021 \u56de\u306b 1 \u679a\u3057\u304b\u52d5\u304b\u305b\u305a\u3001\u5927\u304d\u306a\u5186\u76e4\u3092\u5c0f\u3055\u3044\u5186\u76e4\u306e\u4e0a\u306b\u7f6e\u304f\u3053\u3068\u306f\u3067\u304d\u306a\u3044\u3002</li> </ul> <p>\u5236\u7d04\u6e80\u8db3\u554f\u984c\uff1a\u3053\u306e\u7a2e\u306e\u554f\u984c\u306e\u76ee\u6a19\u306f\u3001\u3059\u3079\u3066\u306e\u5236\u7d04\u6761\u4ef6\u3092\u6e80\u305f\u3059\u89e3\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u3067\u3059\u3002</p> <ul> <li>\\(n\\) \u30af\u30a4\u30fc\u30f3\u554f\u984c\uff1a\\(n imes n\\) \u306e\u30c1\u30a7\u30b9\u76e4\u306b \\(n\\) \u500b\u306e\u30af\u30a4\u30fc\u30f3\u3092\u914d\u7f6e\u3057\u3001\u4e92\u3044\u306b\u653b\u6483\u3057\u306a\u3044\u3088\u3046\u306b\u3059\u308b\u3002</li> <li>\u6570\u72ec\uff1a\\(9 imes 9\\) \u306e\u30b0\u30ea\u30c3\u30c9\u306b\u6570\u5b57 \\(1\\) ~ \\(9\\) \u3092\u5165\u529b\u3057\u3001\u5404\u884c\u3001\u5217\u3001\\(3 imes 3\\) \u306e\u30b5\u30d6\u30b0\u30ea\u30c3\u30c9\u306b\u91cd\u8907\u304c\u306a\u3044\u3088\u3046\u306b\u3059\u308b\u3002</li> <li>\u30b0\u30e9\u30d5\u5f69\u8272\u554f\u984c\uff1a\u4e0e\u3048\u3089\u308c\u305f\u7121\u5411\u30b0\u30e9\u30d5\u306b\u5bfe\u3057\u3001\u96a3\u63a5\u9802\u70b9\u304c\u7570\u306a\u308b\u8272\u306b\u306a\u308b\u3088\u3046\u306b\u6700\u5c0f\u9650\u306e\u8272\u3067\u5f69\u8272\u3059\u308b\u3002</li> </ul> <p>\u7d44\u5408\u305b\u6700\u9069\u5316\u554f\u984c\uff1a\u3053\u306e\u7a2e\u306e\u554f\u984c\u306e\u76ee\u6a19\u306f\u3001\u7d44\u5408\u305b\u7a7a\u9593\u5185\u3067\u7279\u5b9a\u306e\u6761\u4ef6\u3092\u6e80\u305f\u3059\u6700\u9069\u89e3\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u3067\u3059\u3002</p> <ul> <li>0-1 \u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c\uff1a\u4e0e\u3048\u3089\u308c\u305f\u7269\u54c1\u7fa4\u3068\u30d0\u30c3\u30af\u30d1\u30c3\u30af\u304c\u3042\u308a\u3001\u5404\u7269\u54c1\u306b\u306f\u4fa1\u5024\u3068\u91cd\u3055\u304c\u8a2d\u5b9a\u3055\u308c\u3066\u3044\u308b\u3002\u30d0\u30c3\u30af\u30d1\u30c3\u30af\u306e\u5bb9\u91cf\u5236\u9650\u5185\u3067\u3001\u7dcf\u4fa1\u5024\u3092\u6700\u5927\u5316\u3059\u308b\u7269\u54c1\u306e\u9078\u629e\u3092\u6c42\u3081\u308b\u3002</li> <li>\u65c5\u884c\u30bb\u30fc\u30eb\u30b9\u30de\u30f3\u554f\u984c\uff1a\u30b0\u30e9\u30d5\u4e0a\u3067\u30011 \u3064\u306e\u70b9\u304b\u3089\u51fa\u767a\u3057\u3001\u3059\u3079\u3066\u306e\u4ed6\u306e\u70b9\u3092 1 \u56de\u305a\u3064\u8a2a\u554f\u3057\u3066\u51fa\u767a\u70b9\u306b\u623b\u308b\u6700\u77ed\u7d4c\u8def\u3092\u6c42\u3081\u308b\u3002</li> <li>\u6700\u5927\u30af\u30ea\u30fc\u30af\u554f\u984c\uff1a\u4e0e\u3048\u3089\u308c\u305f\u7121\u5411\u30b0\u30e9\u30d5\u306e\u4e2d\u3067\u3001\u4efb\u610f\u306e 2 \u9802\u70b9\u9593\u306b\u8fba\u304c\u5b58\u5728\u3059\u308b\u6700\u5927\u306e\u5b8c\u5168\u90e8\u5206\u30b0\u30e9\u30d5\u3092\u898b\u3064\u3051\u308b\u3002</li> </ul> <p>\u6ce8\u610f\u3059\u3079\u304d\u306f\u3001\u591a\u304f\u306e\u7d44\u5408\u305b\u6700\u9069\u5316\u554f\u984c\u306b\u5bfe\u3057\u3066\u3001\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u304c\u6700\u9069\u89e3\u6cd5\u3067\u306f\u306a\u3044\u3068\u3044\u3046\u3053\u3068\u3067\u3059\u3002</p> <ul> <li>0-1 \u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c\u306f\u3001\u6642\u9593\u52b9\u7387\u3092\u9ad8\u3081\u308b\u305f\u3081\u306b\u52d5\u7684\u8a08\u753b\u6cd5\u304c\u3088\u304f\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002</li> <li>\u65c5\u884c\u30bb\u30fc\u30eb\u30b9\u30de\u30f3\u554f\u984c\u306f\u6709\u540d\u306a NP-Hard \u554f\u984c\u3067\u3042\u308a\u3001\u907a\u4f1d\u7684\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3084\u30a2\u30f3\u30c8\u30b3\u30ed\u30cb\u30fc\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306a\u3069\u306e\u624b\u6cd5\u304c\u3088\u304f\u4f7f\u308f\u308c\u307e\u3059\u3002</li> <li>\u6700\u5927\u30af\u30ea\u30fc\u30af\u554f\u984c\u306f\u30b0\u30e9\u30d5\u7406\u8ad6\u306e\u53e4\u5178\u7684\u306a\u554f\u984c\u3067\u3042\u308a\u3001\u8caa\u6b32\u6cd5\u306a\u3069\u306e\u30d2\u30e5\u30fc\u30ea\u30b9\u30c6\u30a3\u30c3\u30af\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002</li> </ul>"},{"location":"chapter_backtracking/n_queens_problem/","title":"13.4 \u00a0 N\u30af\u30a4\u30fc\u30f3\u554f\u984c","text":"<p>Question</p> <p>\u30c1\u30a7\u30b9\u306e\u30eb\u30fc\u30eb\u306b\u3088\u308b\u3068\u3001\u30af\u30a4\u30fc\u30f3\u306f\u540c\u3058\u884c\u3001\u5217\u3001\u307e\u305f\u306f\u5bfe\u89d2\u7dda\u4e0a\u306e\u99d2\u3092\u653b\u6483\u3067\u304d\u307e\u3059\u3002\\(n\\) \u500b\u306e\u30af\u30a4\u30fc\u30f3\u3068 \\(n \\times n\\) \u306e\u30c1\u30a7\u30b9\u30dc\u30fc\u30c9\u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408\u30012\u3064\u306e\u30af\u30a4\u30fc\u30f3\u304c\u4e92\u3044\u306b\u653b\u6483\u3067\u304d\u306a\u3044\u914d\u7f6e\u3092\u898b\u3064\u3051\u3066\u304f\u3060\u3055\u3044\u3002</p> <p>\u4ee5\u4e0b\u306e\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\\(n = 4\\) \u306e\u5834\u5408\u30012\u3064\u306e\u89e3\u304c\u3042\u308a\u307e\u3059\u3002\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u89b3\u70b9\u304b\u3089\u3001\\(n \\times n\\) \u306e\u30c1\u30a7\u30b9\u30dc\u30fc\u30c9\u306b\u306f \\(n^2\\) \u500b\u306e\u30de\u30b9\u304c\u3042\u308a\u3001\u3059\u3079\u3066\u306e\u53ef\u80fd\u306a\u9078\u629e\u80a2 <code>choices</code> \u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002\u30c1\u30a7\u30b9\u30dc\u30fc\u30c9\u306e\u72b6\u614b <code>state</code> \u306f\u3001\u5404\u30af\u30a4\u30fc\u30f3\u304c\u914d\u7f6e\u3055\u308c\u308b\u306b\u3064\u308c\u3066\u7d99\u7d9a\u7684\u306b\u5909\u5316\u3057\u307e\u3059\u3002</p> <p></p> <p> \u56f3 13-15 \u00a0 4\u30af\u30a4\u30fc\u30f3\u554f\u984c\u306e\u89e3 </p> <p>\u4ee5\u4e0b\u306e\u56f3\u306f\u3001\u3053\u306e\u554f\u984c\u306e3\u3064\u306e\u5236\u7d04\u3092\u793a\u3057\u3066\u3044\u307e\u3059\uff1a\u8907\u6570\u306e\u30af\u30a4\u30fc\u30f3\u306f\u540c\u3058\u884c\u3001\u5217\u3001\u307e\u305f\u306f\u5bfe\u89d2\u7dda\u3092\u5360\u6709\u3067\u304d\u307e\u305b\u3093\u3002\u5bfe\u89d2\u7dda\u306f\u4e3b\u5bfe\u89d2\u7dda <code>\\</code> \u3068\u526f\u5bfe\u89d2\u7dda <code>/</code> \u306b\u5206\u304b\u308c\u308b\u3053\u3068\u306b\u6ce8\u610f\u3059\u308b\u3053\u3068\u304c\u91cd\u8981\u3067\u3059\u3002</p> <p></p> <p> \u56f3 13-16 \u00a0 N\u30af\u30a4\u30fc\u30f3\u554f\u984c\u306e\u5236\u7d04 </p>"},{"location":"chapter_backtracking/n_queens_problem/#1","title":"1. \u00a0 \u884c\u3054\u3068\u306e\u914d\u7f6e\u6226\u7565","text":"<p>\u30af\u30a4\u30fc\u30f3\u306e\u6570\u304c\u30c1\u30a7\u30b9\u30dc\u30fc\u30c9\u306e\u884c\u6570\u3068\u7b49\u3057\u304f\u3001\u3069\u3061\u3089\u3082 \\(n\\) \u3067\u3042\u308b\u305f\u3081\u3001**\u30c1\u30a7\u30b9\u30dc\u30fc\u30c9\u306e\u5404\u884c\u306b\u306f1\u3064\u306e\u30af\u30a4\u30fc\u30f3\u306e\u307f\u304c\u914d\u7f6e\u3067\u304d\u308b\u3053\u3068\u304c**\u5bb9\u6613\u306b\u7d50\u8ad6\u4ed8\u3051\u3089\u308c\u307e\u3059\u3002</p> <p>\u3053\u308c\u306f\u3001\u884c\u3054\u3068\u306e\u914d\u7f6e\u6226\u7565\u3092\u63a1\u7528\u3067\u304d\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\uff1a\u6700\u521d\u306e\u884c\u304b\u3089\u958b\u59cb\u3057\u3066\u3001\u6700\u5f8c\u306e\u884c\u306b\u5230\u9054\u3059\u308b\u307e\u3067\u884c\u3054\u3068\u306b1\u3064\u306e\u30af\u30a4\u30fc\u30f3\u3092\u914d\u7f6e\u3057\u307e\u3059\u3002</p> <p>\u4ee5\u4e0b\u306e\u56f3\u306f\u30014\u30af\u30a4\u30fc\u30f3\u554f\u984c\u306e\u884c\u3054\u3068\u306e\u914d\u7f6e\u30d7\u30ed\u30bb\u30b9\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002\u30b9\u30da\u30fc\u30b9\u306e\u5236\u9650\u306b\u3088\u308a\u3001\u56f3\u306f\u6700\u521d\u306e\u884c\u306e1\u3064\u306e\u691c\u7d22\u5206\u5c90\u306e\u307f\u3092\u5c55\u958b\u3057\u3001\u5217\u3068\u5bfe\u89d2\u7dda\u306e\u5236\u7d04\u3092\u6e80\u305f\u3055\u306a\u3044\u914d\u7f6e\u3092\u526a\u5b9a\u3057\u307e\u3059\u3002</p> <p></p> <p> \u56f3 13-17 \u00a0 \u884c\u3054\u3068\u306e\u914d\u7f6e\u6226\u7565 </p> <p>\u672c\u8cea\u7684\u306b\u3001\u884c\u3054\u3068\u306e\u914d\u7f6e\u6226\u7565\u306f\u526a\u5b9a\u95a2\u6570\u3068\u3057\u3066\u6a5f\u80fd\u3057\u3001\u540c\u3058\u884c\u306b\u8907\u6570\u306e\u30af\u30a4\u30fc\u30f3\u3092\u914d\u7f6e\u3059\u308b\u3059\u3079\u3066\u306e\u691c\u7d22\u5206\u5c90\u3092\u9664\u53bb\u3057\u307e\u3059\u3002</p>"},{"location":"chapter_backtracking/n_queens_problem/#2","title":"2. \u00a0 \u5217\u3068\u5bfe\u89d2\u7dda\u306e\u526a\u5b9a","text":"<p>\u5217\u306e\u5236\u7d04\u3092\u6e80\u305f\u3059\u305f\u3081\u306b\u3001\u9577\u3055 \\(n\\) \u306e\u30d6\u30fc\u30eb\u914d\u5217 <code>cols</code> \u3092\u4f7f\u7528\u3057\u3066\u3001\u5404\u5217\u306b\u30af\u30a4\u30fc\u30f3\u304c\u5360\u6709\u3055\u308c\u3066\u3044\u308b\u304b\u3069\u3046\u304b\u3092\u8ffd\u8de1\u3067\u304d\u307e\u3059\u3002\u5404\u914d\u7f6e\u6c7a\u5b9a\u306e\u524d\u306b\u3001<code>cols</code> \u3092\u4f7f\u7528\u3057\u3066\u3059\u3067\u306b\u30af\u30a4\u30fc\u30f3\u304c\u3042\u308b\u5217\u3092\u526a\u5b9a\u3057\u3001\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u4e2d\u306b\u52d5\u7684\u306b\u66f4\u65b0\u3055\u308c\u307e\u3059\u3002</p> <p>Tip</p> <p>\u884c\u5217\u306e\u539f\u70b9\u306f\u5de6\u4e0a\u9685\u306b\u3042\u308a\u3001\u884c\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306f\u4e0a\u304b\u3089\u4e0b\u306b\u5897\u52a0\u3057\u3001\u5217\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306f\u5de6\u304b\u3089\u53f3\u306b\u5897\u52a0\u3059\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002</p> <p>\u5bfe\u89d2\u7dda\u306e\u5236\u7d04\u306f\u3069\u3046\u3067\u3057\u3087\u3046\u304b\uff1f\u30c1\u30a7\u30b9\u30dc\u30fc\u30c9\u4e0a\u306e\u7279\u5b9a\u306e\u30bb\u30eb\u306e\u884c\u3068\u5217\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092 \\((row, col)\\) \u3068\u3057\u307e\u3059\u3002\u7279\u5b9a\u306e\u4e3b\u5bfe\u89d2\u7dda\u3092\u9078\u629e\u3059\u308b\u3053\u3068\u3067\u3001\u305d\u306e\u5bfe\u89d2\u7dda\u4e0a\u306e\u3059\u3079\u3066\u306e\u30bb\u30eb\u3067\u5dee \\(row - col\\) \u304c\u540c\u3058\u3067\u3042\u308b\u3053\u3068\u306b\u6c17\u4ed8\u304d\u307e\u3059\u3002\u3064\u307e\u308a\u3001\\(row - col\\) \u306f\u4e3b\u5bfe\u89d2\u7dda\u4e0a\u3067\u5b9a\u6570\u5024\u3067\u3059\u3002</p> <p>\u8a00\u3044\u63db\u3048\u308b\u3068\u30012\u3064\u306e\u30bb\u30eb\u304c \\(row_1 - col_1 = row_2 - col_2\\) \u3092\u6e80\u305f\u3059\u5834\u5408\u3001\u305d\u308c\u3089\u306f\u78ba\u5b9f\u306b\u540c\u3058\u4e3b\u5bfe\u89d2\u7dda\u4e0a\u306b\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u30d1\u30bf\u30fc\u30f3\u3092\u4f7f\u7528\u3057\u3066\u3001\u4ee5\u4e0b\u306e\u56f3\u306b\u793a\u3059\u914d\u5217 <code>diags1</code> \u3092\u5229\u7528\u3057\u3066\u3001\u30af\u30a4\u30fc\u30f3\u304c\u4e3b\u5bfe\u89d2\u7dda\u4e0a\u306b\u3042\u308b\u304b\u3069\u3046\u304b\u3092\u8ffd\u8de1\u3067\u304d\u307e\u3059\u3002</p> <p>\u540c\u69d8\u306b\u3001\\(row + col\\) \u306e\u548c\u306f\u526f\u5bfe\u89d2\u7dda\u4e0a\u306e\u3059\u3079\u3066\u306e\u30bb\u30eb\u3067\u5b9a\u6570\u5024\u3067\u3059\u3002\u914d\u5217 <code>diags2</code> \u3092\u4f7f\u7528\u3057\u3066\u526f\u5bfe\u89d2\u7dda\u306e\u5236\u7d04\u3082\u51e6\u7406\u3067\u304d\u307e\u3059\u3002</p> <p></p> <p> \u56f3 13-18 \u00a0 \u5217\u3068\u5bfe\u89d2\u7dda\u306e\u5236\u7d04\u306e\u51e6\u7406 </p>"},{"location":"chapter_backtracking/n_queens_problem/#3","title":"3. \u00a0 \u30b3\u30fc\u30c9\u5b9f\u88c5","text":"<p>\\(n\\) \u6b21\u5143\u306e\u6b63\u65b9\u884c\u5217\u3067\u306f\u3001\\(row - col\\) \u306e\u7bc4\u56f2\u306f \\([-n + 1, n - 1]\\) \u3067\u3001\\(row + col\\) \u306e\u7bc4\u56f2\u306f \\([0, 2n - 2]\\) \u3067\u3042\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u4e3b\u5bfe\u89d2\u7dda\u3068\u526f\u5bfe\u89d2\u7dda\u306e\u6570\u306f\u3069\u3061\u3089\u3082 \\(2n - 1\\) \u3067\u3001\u914d\u5217 <code>diags1</code> \u3068 <code>diags2</code> \u306e\u9577\u3055\u306f \\(2n - 1\\) \u3067\u3059\u3002</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig n_queens.py<pre><code>def backtrack(\n    row: int,\n    n: int,\n    state: list[list[str]],\n    res: list[list[list[str]]],\n    cols: list[bool],\n    diags1: list[bool],\n    diags2: list[bool],\n):\n    \"\"\"\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\uff1an \u30af\u30a4\u30fc\u30f3\"\"\"\n    # \u3059\u3079\u3066\u306e\u884c\u304c\u914d\u7f6e\u3055\u308c\u305f\u3089\u3001\u89e3\u3092\u8a18\u9332\n    if row == n:\n        res.append([list(row) for row in state])\n        return\n    # \u3059\u3079\u3066\u306e\u5217\u3092\u8d70\u67fb\n    for col in range(n):\n        # \u30bb\u30eb\u306b\u5bfe\u5fdc\u3059\u308b\u4e3b\u5bfe\u89d2\u7dda\u3068\u526f\u5bfe\u89d2\u7dda\u3092\u8a08\u7b97\n        diag1 = row - col + n - 1\n        diag2 = row + col\n        # \u679d\u5208\u308a\uff1a\u30bb\u30eb\u306e\u5217\u3001\u4e3b\u5bfe\u89d2\u7dda\u3001\u526f\u5bfe\u89d2\u7dda\u306b\u30af\u30a4\u30fc\u30f3\u3092\u914d\u7f6e\u3057\u306a\u3044\n        if not cols[col] and not diags1[diag1] and not diags2[diag2]:\n            # \u8a66\u884c\uff1a\u30bb\u30eb\u306b\u30af\u30a4\u30fc\u30f3\u3092\u914d\u7f6e\n            state[row][col] = \"Q\"\n            cols[col] = diags1[diag1] = diags2[diag2] = True\n            # \u6b21\u306e\u884c\u3092\u914d\u7f6e\n            backtrack(row + 1, n, state, res, cols, diags1, diags2)\n            # \u64a4\u56de\uff1a\u30bb\u30eb\u3092\u7a7a\u306e\u30b9\u30dd\u30c3\u30c8\u306b\u5fa9\u5143\n            state[row][col] = \"#\"\n            cols[col] = diags1[diag1] = diags2[diag2] = False\n\ndef n_queens(n: int) -&gt; list[list[list[str]]]:\n    \"\"\"n \u30af\u30a4\u30fc\u30f3\u3092\u89e3\u304f\"\"\"\n    # n*n \u30b5\u30a4\u30ba\u306e\u30c1\u30a7\u30b9\u30dc\u30fc\u30c9\u3092\u521d\u671f\u5316\u3001'Q' \u306f\u30af\u30a4\u30fc\u30f3\u3092\u8868\u3057\u3001'#' \u306f\u7a7a\u306e\u30b9\u30dd\u30c3\u30c8\u3092\u8868\u3059\n    state = [[\"#\" for _ in range(n)] for _ in range(n)]\n    cols = [False] * n  # \u30af\u30a4\u30fc\u30f3\u304c\u3042\u308b\u5217\u3092\u8a18\u9332\n    diags1 = [False] * (2 * n - 1)  # \u30af\u30a4\u30fc\u30f3\u304c\u3042\u308b\u4e3b\u5bfe\u89d2\u7dda\u3092\u8a18\u9332\n    diags2 = [False] * (2 * n - 1)  # \u30af\u30a4\u30fc\u30f3\u304c\u3042\u308b\u526f\u5bfe\u89d2\u7dda\u3092\u8a18\u9332\n    res = []\n    backtrack(0, n, state, res, cols, diags1, diags2)\n\n    return res\n</code></pre> n_queens.cpp<pre><code>/* \u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\uff1an \u30af\u30a4\u30fc\u30f3 */\nvoid backtrack(int row, int n, vector&lt;vector&lt;string&gt;&gt; &amp;state, vector&lt;vector&lt;vector&lt;string&gt;&gt;&gt; &amp;res, vector&lt;bool&gt; &amp;cols,\n               vector&lt;bool&gt; &amp;diags1, vector&lt;bool&gt; &amp;diags2) {\n    // \u3059\u3079\u3066\u306e\u884c\u304c\u914d\u7f6e\u3055\u308c\u305f\u3089\u3001\u89e3\u3092\u8a18\u9332\n    if (row == n) {\n        res.push_back(state);\n        return;\n    }\n    // \u3059\u3079\u3066\u306e\u5217\u3092\u8d70\u67fb\n    for (int col = 0; col &lt; n; col++) {\n        // \u30bb\u30eb\u306b\u5bfe\u5fdc\u3059\u308b\u4e3b\u5bfe\u89d2\u7dda\u3068\u526f\u5bfe\u89d2\u7dda\u3092\u8a08\u7b97\n        int diag1 = row - col + n - 1;\n        int diag2 = row + col;\n        // \u526a\u5b9a\uff1a\u30bb\u30eb\u306e\u5217\u3001\u4e3b\u5bfe\u89d2\u7dda\u3001\u526f\u5bfe\u89d2\u7dda\u306b\u30af\u30a4\u30fc\u30f3\u3092\u914d\u7f6e\u3059\u308b\u3053\u3068\u3092\u8a31\u53ef\u3057\u306a\u3044\n        if (!cols[col] &amp;&amp; !diags1[diag1] &amp;&amp; !diags2[diag2]) {\n            // \u8a66\u884c\uff1a\u30bb\u30eb\u306b\u30af\u30a4\u30fc\u30f3\u3092\u914d\u7f6e\n            state[row][col] = \"Q\";\n            cols[col] = diags1[diag1] = diags2[diag2] = true;\n            // \u6b21\u306e\u884c\u3092\u914d\u7f6e\n            backtrack(row + 1, n, state, res, cols, diags1, diags2);\n            // \u56de\u9000\uff1a\u30bb\u30eb\u3092\u7a7a\u306e\u30b9\u30dd\u30c3\u30c8\u306b\u5fa9\u5143\n            state[row][col] = \"#\";\n            cols[col] = diags1[diag1] = diags2[diag2] = false;\n        }\n    }\n}\n\n/* n \u30af\u30a4\u30fc\u30f3\u3092\u89e3\u304f */\nvector&lt;vector&lt;vector&lt;string&gt;&gt;&gt; nQueens(int n) {\n    // n*n \u30b5\u30a4\u30ba\u306e\u30c1\u30a7\u30b9\u30dc\u30fc\u30c9\u3092\u521d\u671f\u5316\u3001'Q' \u306f\u30af\u30a4\u30fc\u30f3\u3092\u8868\u3057\u3001'#' \u306f\u7a7a\u306e\u30b9\u30dd\u30c3\u30c8\u3092\u8868\u3059\n    vector&lt;vector&lt;string&gt;&gt; state(n, vector&lt;string&gt;(n, \"#\"));\n    vector&lt;bool&gt; cols(n, false);           // \u30af\u30a4\u30fc\u30f3\u306e\u3042\u308b\u5217\u3092\u8a18\u9332\n    vector&lt;bool&gt; diags1(2 * n - 1, false); // \u30af\u30a4\u30fc\u30f3\u306e\u3042\u308b\u4e3b\u5bfe\u89d2\u7dda\u3092\u8a18\u9332\n    vector&lt;bool&gt; diags2(2 * n - 1, false); // \u30af\u30a4\u30fc\u30f3\u306e\u3042\u308b\u526f\u5bfe\u89d2\u7dda\u3092\u8a18\u9332\n    vector&lt;vector&lt;vector&lt;string&gt;&gt;&gt; res;\n\n    backtrack(0, n, state, res, cols, diags1, diags2);\n\n    return res;\n}\n</code></pre> n_queens.java<pre><code>/* \u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\uff1an \u30af\u30a4\u30fc\u30f3 */\nvoid backtrack(int row, int n, List&lt;List&lt;String&gt;&gt; state, List&lt;List&lt;List&lt;String&gt;&gt;&gt; res,\n        boolean[] cols, boolean[] diags1, boolean[] diags2) {\n    // \u3059\u3079\u3066\u306e\u884c\u304c\u914d\u7f6e\u3055\u308c\u305f\u3089\u3001\u89e3\u3092\u8a18\u9332\n    if (row == n) {\n        List&lt;List&lt;String&gt;&gt; copyState = new ArrayList&lt;&gt;();\n        for (List&lt;String&gt; sRow : state) {\n            copyState.add(new ArrayList&lt;&gt;(sRow));\n        }\n        res.add(copyState);\n        return;\n    }\n    // \u3059\u3079\u3066\u306e\u5217\u3092\u8d70\u67fb\n    for (int col = 0; col &lt; n; col++) {\n        // \u30bb\u30eb\u306b\u5bfe\u5fdc\u3059\u308b\u4e3b\u5bfe\u89d2\u7dda\u3068\u526f\u5bfe\u89d2\u7dda\u3092\u8a08\u7b97\n        int diag1 = row - col + n - 1;\n        int diag2 = row + col;\n        // \u526a\u5b9a\uff1a\u30bb\u30eb\u306e\u5217\u3001\u4e3b\u5bfe\u89d2\u7dda\u3001\u526f\u5bfe\u89d2\u7dda\u306b\u30af\u30a4\u30fc\u30f3\u3092\u914d\u7f6e\u3059\u308b\u3053\u3068\u3092\u8a31\u53ef\u3057\u306a\u3044\n        if (!cols[col] &amp;&amp; !diags1[diag1] &amp;&amp; !diags2[diag2]) {\n            // \u8a66\u884c\uff1a\u30bb\u30eb\u306b\u30af\u30a4\u30fc\u30f3\u3092\u914d\u7f6e\n            state.get(row).set(col, \"Q\");\n            cols[col] = diags1[diag1] = diags2[diag2] = true;\n            // \u6b21\u306e\u884c\u3092\u914d\u7f6e\n            backtrack(row + 1, n, state, res, cols, diags1, diags2);\n            // \u56de\u9000\uff1a\u30bb\u30eb\u3092\u7a7a\u306e\u30b9\u30dd\u30c3\u30c8\u306b\u5fa9\u5143\n            state.get(row).set(col, \"#\");\n            cols[col] = diags1[diag1] = diags2[diag2] = false;\n        }\n    }\n}\n\n/* n \u30af\u30a4\u30fc\u30f3\u3092\u89e3\u304f */\nList&lt;List&lt;List&lt;String&gt;&gt;&gt; nQueens(int n) {\n    // n*n \u30b5\u30a4\u30ba\u306e\u30c1\u30a7\u30b9\u30dc\u30fc\u30c9\u3092\u521d\u671f\u5316\u3001'Q' \u306f\u30af\u30a4\u30fc\u30f3\u3092\u8868\u3057\u3001'#' \u306f\u7a7a\u306e\u30b9\u30dd\u30c3\u30c8\u3092\u8868\u3059\n    List&lt;List&lt;String&gt;&gt; state = new ArrayList&lt;&gt;();\n    for (int i = 0; i &lt; n; i++) {\n        List&lt;String&gt; row = new ArrayList&lt;&gt;();\n        for (int j = 0; j &lt; n; j++) {\n            row.add(\"#\");\n        }\n        state.add(row);\n    }\n    boolean[] cols = new boolean[n]; // \u30af\u30a4\u30fc\u30f3\u306e\u3042\u308b\u5217\u3092\u8a18\u9332\n    boolean[] diags1 = new boolean[2 * n - 1]; // \u30af\u30a4\u30fc\u30f3\u306e\u3042\u308b\u4e3b\u5bfe\u89d2\u7dda\u3092\u8a18\u9332\n    boolean[] diags2 = new boolean[2 * n - 1]; // \u30af\u30a4\u30fc\u30f3\u306e\u3042\u308b\u526f\u5bfe\u89d2\u7dda\u3092\u8a18\u9332\n    List&lt;List&lt;List&lt;String&gt;&gt;&gt; res = new ArrayList&lt;&gt;();\n\n    backtrack(0, n, state, res, cols, diags1, diags2);\n\n    return res;\n}\n</code></pre> n_queens.cs<pre><code>[class]{n_queens}-[func]{Backtrack}\n\n[class]{n_queens}-[func]{NQueens}\n</code></pre> n_queens.go<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{nQueens}\n</code></pre> n_queens.swift<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{nQueens}\n</code></pre> n_queens.js<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{nQueens}\n</code></pre> n_queens.ts<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{nQueens}\n</code></pre> n_queens.dart<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{nQueens}\n</code></pre> n_queens.rs<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{n_queens}\n</code></pre> n_queens.c<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{nQueens}\n</code></pre> n_queens.kt<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{nQueens}\n</code></pre> n_queens.rb<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{n_queens}\n</code></pre> n_queens.zig<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{nQueens}\n</code></pre> <p>\\(n\\) \u500b\u306e\u30af\u30a4\u30fc\u30f3\u3092\u884c\u3054\u3068\u306b\u914d\u7f6e\u3057\u3001\u5217\u306e\u5236\u7d04\u3092\u8003\u616e\u3057\u3066\u3001\u6700\u521d\u306e\u884c\u304b\u3089\u6700\u5f8c\u306e\u884c\u307e\u3067\u3001\\(n\\)\u3001\\(n-1\\)\u3001\\(\\dots\\)\u3001\\(2\\)\u3001\\(1\\) \u306e\u9078\u629e\u80a2\u304c\u3042\u308a\u3001\\(O(n!)\\) \u6642\u9593\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002\u89e3\u3092\u8a18\u9332\u3059\u308b\u969b\u3001\u884c\u5217 <code>state</code> \u3092\u30b3\u30d4\u30fc\u3057\u3066 <code>res</code> \u306b\u8ffd\u52a0\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u3001\u30b3\u30d4\u30fc\u64cd\u4f5c\u306f \\(O(n^2)\\) \u6642\u9593\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u5168\u4f53\u306e\u6642\u9593\u8a08\u7b97\u91cf\u306f \\(O(n! \\cdot n^2)\\) \u3067\u3059\u3002\u5b9f\u969b\u306b\u306f\u3001\u5bfe\u89d2\u7dda\u5236\u7d04\u306b\u57fa\u3065\u304f\u526a\u5b9a\u306b\u3088\u308a\u691c\u7d22\u7a7a\u9593\u3092\u5927\u5e45\u306b\u524a\u6e1b\u3067\u304d\u308b\u305f\u3081\u3001\u591a\u304f\u306e\u5834\u5408\u3001\u691c\u7d22\u52b9\u7387\u306f\u4e0a\u8a18\u306e\u6642\u9593\u8a08\u7b97\u91cf\u3088\u308a\u3082\u512a\u308c\u3066\u3044\u307e\u3059\u3002</p> <p>\u914d\u5217 <code>state</code> \u306f \\(O(n^2)\\) \u7a7a\u9593\u3092\u4f7f\u7528\u3057\u3001\u914d\u5217 <code>cols</code>\u3001<code>diags1</code>\u3001<code>diags2</code> \u306f\u305d\u308c\u305e\u308c \\(O(n)\\) \u7a7a\u9593\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002\u6700\u5927\u518d\u5e30\u6df1\u5ea6\u306f \\(n\\) \u3067\u3001\\(O(n)\\) \u306e\u30b9\u30bf\u30c3\u30af\u30d5\u30ec\u30fc\u30e0\u7a7a\u9593\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u7a7a\u9593\u8a08\u7b97\u91cf\u306f \\(O(n^2)\\) \u3067\u3059\u3002</p>"},{"location":"chapter_backtracking/permutations_problem/","title":"13.2 \u00a0 \u9806\u5217\u554f\u984c","text":"<p>\u9806\u5217\u554f\u984c\u306f\u3001\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5178\u578b\u7684\u306a\u5fdc\u7528\u3067\u3059\u3002\u3053\u308c\u306f\u3001\u914d\u5217\u3084\u6587\u5b57\u5217\u306a\u3069\u306e\u4e0e\u3048\u3089\u308c\u305f\u96c6\u5408\u304b\u3089\u8981\u7d20\u306e\u3059\u3079\u3066\u306e\u53ef\u80fd\u306a\u914d\u7f6e\uff08\u9806\u5217\uff09\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u3092\u542b\u307f\u307e\u3059\u3002</p> <p>\u4ee5\u4e0b\u306e\u8868\u306f\u3001\u5165\u529b\u914d\u5217\u3068\u305d\u306e\u5bfe\u5fdc\u3059\u308b\u9806\u5217\u3092\u542b\u3080\u3044\u304f\u3064\u304b\u306e\u4f8b\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002</p> <p> \u8868 13-2 \u00a0 \u9806\u5217\u306e\u4f8b </p> \u5165\u529b\u914d\u5217 \u9806\u5217 \\([1]\\) \\([1]\\) \\([1, 2]\\) \\([1, 2], [2, 1]\\) \\([1, 2, 3]\\) \\([1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]\\)"},{"location":"chapter_backtracking/permutations_problem/#1321","title":"13.2.1 \u00a0 \u91cd\u8907\u8981\u7d20\u304c\u306a\u3044\u5834\u5408","text":"<p>Question</p> <p>\u91cd\u8907\u8981\u7d20\u306e\u306a\u3044\u6574\u6570\u914d\u5217\u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408\u3001\u3059\u3079\u3066\u306e\u53ef\u80fd\u306a\u9806\u5217\u3092\u8fd4\u3057\u3066\u304f\u3060\u3055\u3044\u3002</p> <p>\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u306e\u89b3\u70b9\u304b\u3089\u3001\u9806\u5217\u3092\u751f\u6210\u3059\u308b\u30d7\u30ed\u30bb\u30b9\u3092\u4e00\u9023\u306e\u9078\u629e\u3068\u3057\u3066\u898b\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002 \u5165\u529b\u914d\u5217\u304c \\([1, 2, 3]\\) \u3060\u3068\u3057\u307e\u3059\u3002\u6700\u521d\u306b \\(1\\) \u3092\u9078\u629e\u3057\u3001\u6b21\u306b \\(3\\)\u3001\u6700\u5f8c\u306b \\(2\\) \u3092\u9078\u629e\u3059\u308b\u3068\u3001\u9806\u5217 \\([1, 3, 2]\\) \u304c\u5f97\u3089\u308c\u307e\u3059\u3002\u300c\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u300d\u306f\u524d\u306e\u9078\u629e\u3092\u53d6\u308a\u6d88\u3057\u3066\u3001\u4ee3\u66ff\u30aa\u30d7\u30b7\u30e7\u30f3\u3092\u63a2\u7d22\u3059\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002</p> <p>\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u306e\u89b3\u70b9\u304b\u3089\u3001\u5019\u88dc\u96c6\u5408 <code>choices</code> \u306f\u5165\u529b\u914d\u5217\u306e\u3059\u3079\u3066\u306e\u8981\u7d20\u3067\u69cb\u6210\u3055\u308c\u3001<code>state</code> \u306f\u3053\u308c\u307e\u3067\u306b\u9078\u629e\u3055\u308c\u305f\u8981\u7d20\u3092\u4fdd\u6301\u3057\u307e\u3059\u3002\u5404\u8981\u7d20\u306f\u4e00\u5ea6\u3060\u3051\u9078\u629e\u3067\u304d\u308b\u305f\u3081\u3001<code>state</code> \u306e\u3059\u3079\u3066\u306e\u8981\u7d20\u306f\u4e00\u610f\u3067\u3042\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002</p> <p>\u4ee5\u4e0b\u306e\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u691c\u7d22\u30d7\u30ed\u30bb\u30b9\u3092\u518d\u5e30\u6728\u306b\u5c55\u958b\u3067\u304d\u307e\u3059\u3002\u5404\u30ce\u30fc\u30c9\u306f\u73fe\u5728\u306e <code>state</code> \u3092\u8868\u3057\u307e\u3059\u3002\u30eb\u30fc\u30c8\u30ce\u30fc\u30c9\u304b\u3089\u958b\u59cb\u3057\u3066\u30013\u56de\u306e\u9078\u629e\u306e\u5f8c\u3001\u8449\u30ce\u30fc\u30c9\u306b\u5230\u9054\u3057\u307e\u3059\u2014\u305d\u308c\u305e\u308c\u304c\u9806\u5217\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002</p> <p></p> <p> \u56f3 13-5 \u00a0 \u9806\u5217\u306e\u518d\u5e30\u6728 </p>"},{"location":"chapter_backtracking/permutations_problem/#1","title":"1. \u00a0 \u91cd\u8907\u9078\u629e\u306e\u526a\u5b9a","text":"<p>\u5404\u8981\u7d20\u304c\u4e00\u5ea6\u3060\u3051\u9078\u629e\u3055\u308c\u308b\u3053\u3068\u3092\u4fdd\u8a3c\u3059\u308b\u305f\u3081\u306b\u3001\u30d6\u30fc\u30eb\u914d\u5217 <code>selected</code> \u3092\u5c0e\u5165\u3057\u307e\u3059\u3002\u3053\u3053\u3067 <code>selected[i]</code> \u306f <code>choices[i]</code> \u304c\u9078\u629e\u3055\u308c\u305f\u304b\u3069\u3046\u304b\u3092\u793a\u3057\u307e\u3059\u3002\u6b21\u306b\u3001\u3053\u306e\u914d\u5217\u306b\u57fa\u3065\u3044\u3066\u526a\u5b9a\u30b9\u30c6\u30c3\u30d7\u3092\u5b9f\u884c\u3057\u307e\u3059\uff1a</p> <ul> <li><code>choice[i]</code> \u3092\u9078\u629e\u3057\u305f\u5f8c\u3001<code>selected[i]</code> \u3092 \\(\\text{True}\\) \u306b\u8a2d\u5b9a\u3057\u3066\u9078\u629e\u3055\u308c\u305f\u3068\u30de\u30fc\u30af\u3057\u307e\u3059\u3002</li> <li><code>choices</code> \u3092\u53cd\u5fa9\u51e6\u7406\u3059\u308b\u969b\u3001\u9078\u629e\u3055\u308c\u305f\u3068\u30de\u30fc\u30af\u3055\u308c\u305f\u3059\u3079\u3066\u306e\u8981\u7d20\u3092\u30b9\u30ad\u30c3\u30d7\u3057\u307e\u3059\uff08\u3064\u307e\u308a\u3001\u305d\u308c\u3089\u306e\u5206\u5c90\u3092\u526a\u5b9a\u3057\u307e\u3059\uff09\u3002</li> </ul> <p>\u4ee5\u4e0b\u306e\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u6700\u521d\u306e\u30e9\u30a6\u30f3\u30c9\u30671\u3092\u9078\u629e\u3057\u30012\u756a\u76ee\u306e\u30e9\u30a6\u30f3\u30c9\u30673\u3092\u9078\u629e\u3057\u3001\u6700\u5f8c\u306e\u30e9\u30a6\u30f3\u30c9\u30672\u3092\u9078\u629e\u3059\u308b\u3068\u3057\u307e\u3059\u30022\u756a\u76ee\u306e\u30e9\u30a6\u30f3\u30c9\u3067\u8981\u7d201\u306e\u5206\u5c90\u3068\u30013\u756a\u76ee\u306e\u30e9\u30a6\u30f3\u30c9\u3067\u8981\u7d201\u30683\u306e\u5206\u5c90\u3092\u526a\u5b9a\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002</p> <p></p> <p> \u56f3 13-6 \u00a0 \u9806\u5217\u306e\u526a\u5b9a\u4f8b </p> <p>\u56f3\u304b\u3089\u3001\u3053\u306e\u526a\u5b9a\u30d7\u30ed\u30bb\u30b9\u304c\u691c\u7d22\u7a7a\u9593\u3092 \\(O(n^n)\\) \u304b\u3089 \\(O(n!)\\) \u306b\u524a\u6e1b\u3059\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002</p>"},{"location":"chapter_backtracking/permutations_problem/#2","title":"2. \u00a0 \u30b3\u30fc\u30c9\u5b9f\u88c5","text":"<p>\u3053\u306e\u7406\u89e3\u306b\u3088\u308a\u3001\u30d5\u30ec\u30fc\u30e0\u30ef\u30fc\u30af\u30b3\u30fc\u30c9\u306e\u300c\u7a7a\u6b04\u3092\u57cb\u3081\u308b\u300d\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u5168\u4f53\u306e\u30b3\u30fc\u30c9\u3092\u7c21\u6f54\u306b\u4fdd\u3064\u305f\u3081\u3001\u30d5\u30ec\u30fc\u30e0\u30ef\u30fc\u30af\u306e\u5404\u90e8\u5206\u3092\u500b\u5225\u306b\u5b9f\u88c5\u305b\u305a\u3001\u4ee3\u308f\u308a\u306b <code>backtrack()</code> \u95a2\u6570\u3067\u3059\u3079\u3066\u3092\u5c55\u958b\u3057\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig permutations_i.py<pre><code>def backtrack(\n    state: list[int], choices: list[int], selected: list[bool], res: list[list[int]]\n):\n    \"\"\"\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\uff1a\u9806\u5217 I\"\"\"\n    # \u72b6\u614b\u306e\u9577\u3055\u304c\u8981\u7d20\u6570\u3068\u7b49\u3057\u3044\u3068\u304d\u3001\u89e3\u3092\u8a18\u9332\n    if len(state) == len(choices):\n        res.append(list(state))\n        return\n    # \u3059\u3079\u3066\u306e\u9078\u629e\u80a2\u3092\u8d70\u67fb\n    for i, choice in enumerate(choices):\n        # \u679d\u5208\u308a\uff1a\u8981\u7d20\u306e\u91cd\u8907\u9078\u629e\u3092\u8a31\u53ef\u3057\u306a\u3044\n        if not selected[i]:\n            # \u8a66\u884c\uff1a\u9078\u629e\u3092\u884c\u3044\u3001\u72b6\u614b\u3092\u66f4\u65b0\n            selected[i] = True\n            state.append(choice)\n            # \u6b21\u306e\u9078\u629e\u30e9\u30a6\u30f3\u30c9\u306b\u9032\u3080\n            backtrack(state, choices, selected, res)\n            # \u64a4\u56de\uff1a\u9078\u629e\u3092\u53d6\u308a\u6d88\u3057\u3001\u524d\u306e\u72b6\u614b\u306b\u5fa9\u5143\n            selected[i] = False\n            state.pop()\n\ndef permutations_i(nums: list[int]) -&gt; list[list[int]]:\n    \"\"\"\u9806\u5217 I\"\"\"\n    res = []\n    backtrack(state=[], choices=nums, selected=[False] * len(nums), res=res)\n    return res\n</code></pre> permutations_i.cpp<pre><code>/* \u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\uff1a\u9806\u5217 I */\nvoid backtrack(vector&lt;int&gt; &amp;state, const vector&lt;int&gt; &amp;choices, vector&lt;bool&gt; &amp;selected, vector&lt;vector&lt;int&gt;&gt; &amp;res) {\n    // \u72b6\u614b\u306e\u9577\u3055\u304c\u8981\u7d20\u6570\u3068\u7b49\u3057\u304f\u306a\u3063\u305f\u3089\u3001\u89e3\u3092\u8a18\u9332\n    if (state.size() == choices.size()) {\n        res.push_back(state);\n        return;\n    }\n    // \u3059\u3079\u3066\u306e\u9078\u629e\u80a2\u3092\u8d70\u67fb\n    for (int i = 0; i &lt; choices.size(); i++) {\n        int choice = choices[i];\n        // \u526a\u5b9a\uff1a\u8981\u7d20\u306e\u91cd\u8907\u9078\u629e\u3092\u8a31\u53ef\u3057\u306a\u3044\n        if (!selected[i]) {\n            // \u8a66\u884c\uff1a\u9078\u629e\u3092\u884c\u3044\u3001\u72b6\u614b\u3092\u66f4\u65b0\n            selected[i] = true;\n            state.push_back(choice);\n            // \u6b21\u306e\u30e9\u30a6\u30f3\u30c9\u306e\u9078\u629e\u306b\u9032\u3080\n            backtrack(state, choices, selected, res);\n            // \u56de\u9000\uff1a\u9078\u629e\u3092\u53d6\u308a\u6d88\u3057\u3001\u524d\u306e\u72b6\u614b\u306b\u5fa9\u5143\n            selected[i] = false;\n            state.pop_back();\n        }\n    }\n}\n\n/* \u9806\u5217 I */\nvector&lt;vector&lt;int&gt;&gt; permutationsI(vector&lt;int&gt; nums) {\n    vector&lt;int&gt; state;\n    vector&lt;bool&gt; selected(nums.size(), false);\n    vector&lt;vector&lt;int&gt;&gt; res;\n    backtrack(state, nums, selected, res);\n    return res;\n}\n</code></pre> permutations_i.java<pre><code>/* \u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\uff1a\u9806\u5217 I */\nvoid backtrack(List&lt;Integer&gt; state, int[] choices, boolean[] selected, List&lt;List&lt;Integer&gt;&gt; res) {\n    // \u72b6\u614b\u306e\u9577\u3055\u304c\u8981\u7d20\u6570\u3068\u7b49\u3057\u304f\u306a\u3063\u305f\u3089\u3001\u89e3\u3092\u8a18\u9332\n    if (state.size() == choices.length) {\n        res.add(new ArrayList&lt;Integer&gt;(state));\n        return;\n    }\n    // \u3059\u3079\u3066\u306e\u9078\u629e\u80a2\u3092\u8d70\u67fb\n    for (int i = 0; i &lt; choices.length; i++) {\n        int choice = choices[i];\n        // \u526a\u5b9a\uff1a\u8981\u7d20\u306e\u91cd\u8907\u9078\u629e\u3092\u8a31\u53ef\u3057\u306a\u3044\n        if (!selected[i]) {\n            // \u8a66\u884c\uff1a\u9078\u629e\u3092\u884c\u3044\u3001\u72b6\u614b\u3092\u66f4\u65b0\n            selected[i] = true;\n            state.add(choice);\n            // \u6b21\u306e\u30e9\u30a6\u30f3\u30c9\u306e\u9078\u629e\u306b\u9032\u3080\n            backtrack(state, choices, selected, res);\n            // \u56de\u9000\uff1a\u9078\u629e\u3092\u53d6\u308a\u6d88\u3057\u3001\u524d\u306e\u72b6\u614b\u306b\u5fa9\u5143\n            selected[i] = false;\n            state.remove(state.size() - 1);\n        }\n    }\n}\n\n/* \u9806\u5217 I */\nList&lt;List&lt;Integer&gt;&gt; permutationsI(int[] nums) {\n    List&lt;List&lt;Integer&gt;&gt; res = new ArrayList&lt;List&lt;Integer&gt;&gt;();\n    backtrack(new ArrayList&lt;Integer&gt;(), nums, new boolean[nums.length], res);\n    return res;\n}\n</code></pre> permutations_i.cs<pre><code>[class]{permutations_i}-[func]{Backtrack}\n\n[class]{permutations_i}-[func]{PermutationsI}\n</code></pre> permutations_i.go<pre><code>[class]{}-[func]{backtrackI}\n\n[class]{}-[func]{permutationsI}\n</code></pre> permutations_i.swift<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{permutationsI}\n</code></pre> permutations_i.js<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{permutationsI}\n</code></pre> permutations_i.ts<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{permutationsI}\n</code></pre> permutations_i.dart<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{permutationsI}\n</code></pre> permutations_i.rs<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{permutations_i}\n</code></pre> permutations_i.c<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{permutationsI}\n</code></pre> permutations_i.kt<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{permutationsI}\n</code></pre> permutations_i.rb<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{permutations_i}\n</code></pre> permutations_i.zig<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{permutationsI}\n</code></pre>"},{"location":"chapter_backtracking/permutations_problem/#1322","title":"13.2.2 \u00a0 \u91cd\u8907\u8981\u7d20\u3092\u8003\u616e\u3059\u308b\u5834\u5408","text":"<p>Question</p> <p>**\u91cd\u8907\u8981\u7d20\u3092\u542b\u3080\u53ef\u80fd\u6027\u306e\u3042\u308b**\u6574\u6570\u914d\u5217\u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408\u3001\u3059\u3079\u3066\u306e\u4e00\u610f\u306e\u9806\u5217\u3092\u8fd4\u3057\u3066\u304f\u3060\u3055\u3044\u3002</p> <p>\u5165\u529b\u914d\u5217\u304c \\([1, 1, 2]\\) \u3060\u3068\u3057\u307e\u3059\u30022\u3064\u306e\u540c\u4e00\u8981\u7d20 \\(1\\) \u3092\u533a\u5225\u3059\u308b\u305f\u3081\u306b\u30012\u756a\u76ee\u3092 \\(\\hat{1}\\) \u3068\u30e9\u30d9\u30eb\u4ed8\u3051\u3057\u307e\u3059\u3002</p> <p>\u4ee5\u4e0b\u306e\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u3053\u306e\u65b9\u6cd5\u3067\u751f\u6210\u3055\u308c\u308b\u9806\u5217\u306e\u534a\u5206\u306f\u91cd\u8907\u3067\u3059\uff1a</p> <p></p> <p> \u56f3 13-7 \u00a0 \u91cd\u8907\u9806\u5217 </p> <p>\u3067\u306f\u3001\u3053\u308c\u3089\u306e\u91cd\u8907\u9806\u5217\u3092\u3069\u306e\u3088\u3046\u306b\u9664\u53bb\u3067\u304d\u308b\u3067\u3057\u3087\u3046\u304b\uff1f\u4e00\u3064\u306e\u76f4\u63a5\u7684\u306a\u30a2\u30d7\u30ed\u30fc\u30c1\u306f\u3001\u3059\u3079\u3066\u306e\u9806\u5217\u3092\u751f\u6210\u3057\u305f\u5f8c\u306b\u30cf\u30c3\u30b7\u30e5\u30bb\u30c3\u30c8\u3092\u4f7f\u7528\u3057\u3066\u91cd\u8907\u3092\u9664\u53bb\u3059\u308b\u3053\u3068\u3067\u3059\u3002\u3057\u304b\u3057\u3001\u3053\u308c\u306f\u3042\u307e\u308a\u512a\u96c5\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u91cd\u8907\u3092\u751f\u6210\u3059\u308b\u5206\u5c90\u306f\u672c\u6765\u4e0d\u8981\u3067\u3042\u308a\u3001\u4e8b\u524d\u306b\u526a\u5b9a\u3055\u308c\u308b\u3079\u304d\u3060\u304b\u3089\u3067\u3059\u3001\u3053\u308c\u306b\u3088\u308a\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u52b9\u7387\u304c\u5411\u4e0a\u3057\u307e\u3059\u3002</p>"},{"location":"chapter_backtracking/permutations_problem/#1_1","title":"1. \u00a0 \u7b49\u5024\u8981\u7d20\u306e\u526a\u5b9a","text":"<p>\u4ee5\u4e0b\u306e\u56f3\u3092\u898b\u308b\u3068\u3001\u6700\u521d\u306e\u30e9\u30a6\u30f3\u30c9\u3067 \\(1\\) \u307e\u305f\u306f \\(\\hat{1}\\) \u3092\u9078\u629e\u3059\u308b\u3068\u540c\u3058\u9806\u5217\u306b\u3064\u306a\u304c\u308b\u305f\u3081\u3001\\(\\hat{1}\\) \u3092\u526a\u5b9a\u3057\u307e\u3059\u3002</p> <p>\u540c\u69d8\u306b\u3001\u6700\u521d\u306e\u30e9\u30a6\u30f3\u30c9\u3067 \\(2\\) \u3092\u9078\u629e\u3057\u305f\u5f8c\u30012\u756a\u76ee\u306e\u30e9\u30a6\u30f3\u30c9\u3067 \\(1\\) \u307e\u305f\u306f \\(\\hat{1}\\) \u3092\u9078\u629e\u3057\u3066\u3082\u91cd\u8907\u5206\u5c90\u306b\u3064\u306a\u304c\u308b\u305f\u3081\u3001\u305d\u306e\u6642\u3082 \\(\\hat{1}\\) \u3092\u526a\u5b9a\u3057\u307e\u3059\u3002</p> <p>\u672c\u8cea\u7684\u306b\u3001\u79c1\u305f\u3061\u306e\u76ee\u6a19\u306f\u3001\u8907\u6570\u306e\u540c\u4e00\u8981\u7d20\u304c\u9078\u629e\u306e\u5404\u30e9\u30a6\u30f3\u30c9\u3067\u4e00\u5ea6\u3060\u3051\u9078\u629e\u3055\u308c\u308b\u3053\u3068\u3092\u4fdd\u8a3c\u3059\u308b\u3053\u3068\u3067\u3059\u3002</p> <p></p> <p> \u56f3 13-8 \u00a0 \u91cd\u8907\u9806\u5217\u306e\u526a\u5b9a </p>"},{"location":"chapter_backtracking/permutations_problem/#2_1","title":"2. \u00a0 \u30b3\u30fc\u30c9\u5b9f\u88c5","text":"<p>\u524d\u306e\u554f\u984c\u306e\u30b3\u30fc\u30c9\u306b\u57fa\u3065\u3044\u3066\u3001\u5404\u30e9\u30a6\u30f3\u30c9\u3067\u30cf\u30c3\u30b7\u30e5\u30bb\u30c3\u30c8 <code>duplicated</code> \u3092\u5c0e\u5165\u3057\u307e\u3059\u3002\u3053\u306e\u30bb\u30c3\u30c8\u306f\u3001\u3059\u3067\u306b\u8a66\u884c\u3057\u305f\u8981\u7d20\u3092\u8ffd\u8de1\u3057\u3001\u91cd\u8907\u3092\u526a\u5b9a\u3067\u304d\u308b\u3088\u3046\u306b\u3057\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig permutations_ii.py<pre><code>def backtrack(\n    state: list[int], choices: list[int], selected: list[bool], res: list[list[int]]\n):\n    \"\"\"\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\uff1a\u9806\u5217 II\"\"\"\n    # \u72b6\u614b\u306e\u9577\u3055\u304c\u8981\u7d20\u6570\u3068\u7b49\u3057\u3044\u3068\u304d\u3001\u89e3\u3092\u8a18\u9332\n    if len(state) == len(choices):\n        res.append(list(state))\n        return\n    # \u3059\u3079\u3066\u306e\u9078\u629e\u80a2\u3092\u8d70\u67fb\n    duplicated = set[int]()\n    for i, choice in enumerate(choices):\n        # \u679d\u5208\u308a\uff1a\u8981\u7d20\u306e\u91cd\u8907\u9078\u629e\u3092\u8a31\u53ef\u305b\u305a\u3001\u7b49\u3057\u3044\u8981\u7d20\u306e\u91cd\u8907\u9078\u629e\u3082\u8a31\u53ef\u3057\u306a\u3044\n        if not selected[i] and choice not in duplicated:\n            # \u8a66\u884c\uff1a\u9078\u629e\u3092\u884c\u3044\u3001\u72b6\u614b\u3092\u66f4\u65b0\n            duplicated.add(choice)  # \u9078\u629e\u3055\u308c\u305f\u8981\u7d20\u5024\u3092\u8a18\u9332\n            selected[i] = True\n            state.append(choice)\n            # \u6b21\u306e\u9078\u629e\u30e9\u30a6\u30f3\u30c9\u306b\u9032\u3080\n            backtrack(state, choices, selected, res)\n            # \u64a4\u56de\uff1a\u9078\u629e\u3092\u53d6\u308a\u6d88\u3057\u3001\u524d\u306e\u72b6\u614b\u306b\u5fa9\u5143\n            selected[i] = False\n            state.pop()\n\ndef permutations_ii(nums: list[int]) -&gt; list[list[int]]:\n    \"\"\"\u9806\u5217 II\"\"\"\n    res = []\n    backtrack(state=[], choices=nums, selected=[False] * len(nums), res=res)\n    return res\n</code></pre> permutations_ii.cpp<pre><code>/* \u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\uff1a\u9806\u5217 II */\nvoid backtrack(vector&lt;int&gt; &amp;state, const vector&lt;int&gt; &amp;choices, vector&lt;bool&gt; &amp;selected, vector&lt;vector&lt;int&gt;&gt; &amp;res) {\n    // \u72b6\u614b\u306e\u9577\u3055\u304c\u8981\u7d20\u6570\u3068\u7b49\u3057\u304f\u306a\u3063\u305f\u3089\u3001\u89e3\u3092\u8a18\u9332\n    if (state.size() == choices.size()) {\n        res.push_back(state);\n        return;\n    }\n    // \u3059\u3079\u3066\u306e\u9078\u629e\u80a2\u3092\u8d70\u67fb\n    unordered_set&lt;int&gt; duplicated;\n    for (int i = 0; i &lt; choices.size(); i++) {\n        int choice = choices[i];\n        // \u526a\u5b9a\uff1a\u8981\u7d20\u306e\u91cd\u8907\u9078\u629e\u3092\u8a31\u53ef\u305b\u305a\u3001\u7b49\u3057\u3044\u8981\u7d20\u306e\u91cd\u8907\u9078\u629e\u3082\u8a31\u53ef\u3057\u306a\u3044\n        if (!selected[i] &amp;&amp; duplicated.find(choice) == duplicated.end()) {\n            // \u8a66\u884c\uff1a\u9078\u629e\u3092\u884c\u3044\u3001\u72b6\u614b\u3092\u66f4\u65b0\n            duplicated.emplace(choice); // \u9078\u629e\u3055\u308c\u305f\u8981\u7d20\u5024\u3092\u8a18\u9332\n            selected[i] = true;\n            state.push_back(choice);\n            // \u6b21\u306e\u30e9\u30a6\u30f3\u30c9\u306e\u9078\u629e\u306b\u9032\u3080\n            backtrack(state, choices, selected, res);\n            // \u56de\u9000\uff1a\u9078\u629e\u3092\u53d6\u308a\u6d88\u3057\u3001\u524d\u306e\u72b6\u614b\u306b\u5fa9\u5143\n            selected[i] = false;\n            state.pop_back();\n        }\n    }\n}\n\n/* \u9806\u5217 II */\nvector&lt;vector&lt;int&gt;&gt; permutationsII(vector&lt;int&gt; nums) {\n    vector&lt;int&gt; state;\n    vector&lt;bool&gt; selected(nums.size(), false);\n    vector&lt;vector&lt;int&gt;&gt; res;\n    backtrack(state, nums, selected, res);\n    return res;\n}\n</code></pre> permutations_ii.java<pre><code>/* \u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\uff1a\u9806\u5217 II */\nvoid backtrack(List&lt;Integer&gt; state, int[] choices, boolean[] selected, List&lt;List&lt;Integer&gt;&gt; res) {\n    // \u72b6\u614b\u306e\u9577\u3055\u304c\u8981\u7d20\u6570\u3068\u7b49\u3057\u304f\u306a\u3063\u305f\u3089\u3001\u89e3\u3092\u8a18\u9332\n    if (state.size() == choices.length) {\n        res.add(new ArrayList&lt;Integer&gt;(state));\n        return;\n    }\n    // \u3059\u3079\u3066\u306e\u9078\u629e\u80a2\u3092\u8d70\u67fb\n    Set&lt;Integer&gt; duplicated = new HashSet&lt;Integer&gt;();\n    for (int i = 0; i &lt; choices.length; i++) {\n        int choice = choices[i];\n        // \u526a\u5b9a\uff1a\u8981\u7d20\u306e\u91cd\u8907\u9078\u629e\u3092\u8a31\u53ef\u305b\u305a\u3001\u7b49\u3057\u3044\u8981\u7d20\u306e\u91cd\u8907\u9078\u629e\u3082\u8a31\u53ef\u3057\u306a\u3044\n        if (!selected[i] &amp;&amp; !duplicated.contains(choice)) {\n            // \u8a66\u884c\uff1a\u9078\u629e\u3092\u884c\u3044\u3001\u72b6\u614b\u3092\u66f4\u65b0\n            duplicated.add(choice); // \u9078\u629e\u3055\u308c\u305f\u8981\u7d20\u5024\u3092\u8a18\u9332\n            selected[i] = true;\n            state.add(choice);\n            // \u6b21\u306e\u30e9\u30a6\u30f3\u30c9\u306e\u9078\u629e\u306b\u9032\u3080\n            backtrack(state, choices, selected, res);\n            // \u56de\u9000\uff1a\u9078\u629e\u3092\u53d6\u308a\u6d88\u3057\u3001\u524d\u306e\u72b6\u614b\u306b\u5fa9\u5143\n            selected[i] = false;\n            state.remove(state.size() - 1);\n        }\n    }\n}\n\n/* \u9806\u5217 II */\nList&lt;List&lt;Integer&gt;&gt; permutationsII(int[] nums) {\n    List&lt;List&lt;Integer&gt;&gt; res = new ArrayList&lt;List&lt;Integer&gt;&gt;();\n    backtrack(new ArrayList&lt;Integer&gt;(), nums, new boolean[nums.length], res);\n    return res;\n}\n</code></pre> permutations_ii.cs<pre><code>[class]{permutations_ii}-[func]{Backtrack}\n\n[class]{permutations_ii}-[func]{PermutationsII}\n</code></pre> permutations_ii.go<pre><code>[class]{}-[func]{backtrackII}\n\n[class]{}-[func]{permutationsII}\n</code></pre> permutations_ii.swift<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{permutationsII}\n</code></pre> permutations_ii.js<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{permutationsII}\n</code></pre> permutations_ii.ts<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{permutationsII}\n</code></pre> permutations_ii.dart<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{permutationsII}\n</code></pre> permutations_ii.rs<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{permutations_ii}\n</code></pre> permutations_ii.c<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{permutationsII}\n</code></pre> permutations_ii.kt<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{permutationsII}\n</code></pre> permutations_ii.rb<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{permutations_ii}\n</code></pre> permutations_ii.zig<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{permutationsII}\n</code></pre> <p>\u3059\u3079\u3066\u306e\u8981\u7d20\u304c\u7570\u306a\u308b\u3068\u4eee\u5b9a\u3059\u308b\u3068\u3001\\(n\\) \u500b\u306e\u8981\u7d20\u306e\u9806\u5217\u306f \\(n!\\) \uff08\u968e\u4e57\uff09\u500b\u3042\u308a\u307e\u3059\u3002\u5404\u7d50\u679c\u3092\u8a18\u9332\u3059\u308b\u306b\u306f\u9577\u3055 \\(n\\) \u306e\u30ea\u30b9\u30c8\u3092\u30b3\u30d4\u30fc\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u3001\u3053\u308c\u306b\u306f \\(O(n)\\) \u6642\u9593\u304c\u304b\u304b\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u7dcf\u6642\u9593\u8a08\u7b97\u91cf\u306f \\(O(n!n)\\) \u3067\u3059\u3002</p> <p>\u6700\u5927\u518d\u5e30\u6df1\u5ea6\u306f \\(n\\) \u3067\u3001\\(O(n)\\) \u306e\u30b9\u30bf\u30c3\u30af\u7a7a\u9593\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002<code>selected</code> \u914d\u5217\u3082 \\(O(n)\\) \u7a7a\u9593\u304c\u5fc5\u8981\u3067\u3059\u3002\u4e00\u5ea6\u306b\u6700\u5927 \\(n\\) \u500b\u306e\u500b\u5225\u306e <code>duplicated</code> \u30bb\u30c3\u30c8\u304c\u5b58\u5728\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308b\u305f\u3081\u3001\u305d\u308c\u3089\u306f\u96c6\u5408\u7684\u306b \\(O(n^2)\\) \u7a7a\u9593\u3092\u5360\u6709\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u7a7a\u9593\u8a08\u7b97\u91cf\u306f \\(O(n^2)\\) \u3067\u3059\u3002</p>"},{"location":"chapter_backtracking/permutations_problem/#3-2","title":"3. \u00a0 2\u3064\u306e\u526a\u5b9a\u65b9\u6cd5\u306e\u6bd4\u8f03","text":"<p><code>selected</code> \u3068 <code>duplicated</code> \u306f\u3069\u3061\u3089\u3082\u526a\u5b9a\u30e1\u30ab\u30cb\u30ba\u30e0\u3068\u3057\u3066\u6a5f\u80fd\u3057\u307e\u3059\u304c\u3001\u7570\u306a\u308b\u554f\u984c\u3092\u30bf\u30fc\u30b2\u30c3\u30c8\u306b\u3057\u3066\u3044\u307e\u3059\uff1a</p> <ul> <li>\u91cd\u8907\u9078\u629e\u306e\u526a\u5b9a\uff08<code>selected</code> \u7d4c\u7531\uff09\uff1a\u691c\u7d22\u5168\u4f53\u306b\u5358\u4e00\u306e <code>selected</code> \u914d\u5217\u304c\u3042\u308a\u3001\u73fe\u5728\u306e\u72b6\u614b\u306b\u3059\u3067\u306b\u3042\u308b\u8981\u7d20\u3092\u793a\u3057\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u540c\u3058\u8981\u7d20\u304c <code>state</code> \u306b\u8907\u6570\u56de\u73fe\u308c\u308b\u3053\u3068\u3092\u9632\u304e\u307e\u3059\u3002</li> <li>\u7b49\u5024\u8981\u7d20\u306e\u526a\u5b9a\uff08<code>duplicated</code> \u7d4c\u7531\uff09\uff1a<code>backtrack</code> \u95a2\u6570\u306e\u5404\u547c\u3073\u51fa\u3057\u306f\u72ec\u81ea\u306e <code>duplicated</code> \u30bb\u30c3\u30c8\u3092\u4f7f\u7528\u3057\u3001\u305d\u306e\u7279\u5b9a\u306e\u53cd\u5fa9\uff08<code>for</code> \u30eb\u30fc\u30d7\uff09\u3067\u3059\u3067\u306b\u9078\u629e\u3055\u308c\u305f\u8981\u7d20\u3092\u8a18\u9332\u3057\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u7b49\u3057\u3044\u8981\u7d20\u304c\u9078\u629e\u306e\u5404\u30e9\u30a6\u30f3\u30c9\u3067\u4e00\u5ea6\u3060\u3051\u9078\u629e\u3055\u308c\u308b\u3053\u3068\u3092\u4fdd\u8a3c\u3057\u307e\u3059\u3002</li> </ul> <p>\u4ee5\u4e0b\u306e\u56f3\u306f\u3001\u3053\u308c\u30892\u3064\u306e\u526a\u5b9a\u6226\u7565\u306e\u7bc4\u56f2\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002\u6728\u306e\u5404\u30ce\u30fc\u30c9\u306f\u9078\u629e\u3092\u8868\u3057\u307e\u3059\u3002\u30eb\u30fc\u30c8\u304b\u3089\u4efb\u610f\u306e\u8449\u3078\u306e\u7d4c\u8def\u306f\u30011\u3064\u306e\u5b8c\u5168\u306a\u9806\u5217\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002</p> <p></p> <p> \u56f3 13-9 \u00a0 2\u3064\u306e\u526a\u5b9a\u6761\u4ef6\u306e\u7bc4\u56f2 </p>"},{"location":"chapter_backtracking/subset_sum_problem/","title":"13.3 \u00a0 \u90e8\u5206\u96c6\u5408\u548c\u554f\u984c","text":""},{"location":"chapter_backtracking/subset_sum_problem/#1331","title":"13.3.1 \u00a0 \u91cd\u8907\u8981\u7d20\u304c\u306a\u3044\u5834\u5408","text":"<p>Question</p> <p>\u6b63\u306e\u6574\u6570\u306e\u914d\u5217 <code>nums</code> \u3068\u30bf\u30fc\u30b2\u30c3\u30c8\u6b63\u6574\u6570 <code>target</code> \u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408\u3001\u7d44\u307f\u5408\u308f\u305b\u5185\u306e\u8981\u7d20\u306e\u548c\u304c <code>target</code> \u306b\u7b49\u3057\u304f\u306a\u308b\u3088\u3046\u306a\u3059\u3079\u3066\u306e\u53ef\u80fd\u306a\u7d44\u307f\u5408\u308f\u305b\u3092\u898b\u3064\u3051\u3066\u304f\u3060\u3055\u3044\u3002\u4e0e\u3048\u3089\u308c\u305f\u914d\u5217\u306b\u306f\u91cd\u8907\u8981\u7d20\u304c\u306a\u304f\u3001\u5404\u8981\u7d20\u306f\u8907\u6570\u56de\u9078\u629e\u3067\u304d\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u7d44\u307f\u5408\u308f\u305b\u3092\u91cd\u8907\u3059\u308b\u7d44\u307f\u5408\u308f\u305b\u3092\u542b\u307e\u306a\u3044\u30ea\u30b9\u30c8\u3068\u3057\u3066\u8fd4\u3057\u3066\u304f\u3060\u3055\u3044\u3002</p> <p>\u4f8b\u3048\u3070\u3001\u5165\u529b\u96c6\u5408 \\(\\{3, 4, 5\\}\\) \u3068\u30bf\u30fc\u30b2\u30c3\u30c8\u6574\u6570 \\(9\\) \u306e\u5834\u5408\u3001\u89e3\u306f \\(\\{3, 3, 3\\}, \\{4, 5\\}\\) \u3067\u3059\u3002\u4ee5\u4e0b\u306e2\u70b9\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002</p> <ul> <li>\u5165\u529b\u96c6\u5408\u306e\u8981\u7d20\u306f\u7121\u5236\u9650\u306b\u9078\u629e\u3067\u304d\u307e\u3059\u3002</li> <li>\u90e8\u5206\u96c6\u5408\u306f\u8981\u7d20\u306e\u9806\u5e8f\u3092\u533a\u5225\u3057\u307e\u305b\u3093\u3002\u4f8b\u3048\u3070 \\(\\{4, 5\\}\\) \u3068 \\(\\{5, 4\\}\\) \u306f\u540c\u3058\u90e8\u5206\u96c6\u5408\u3067\u3059\u3002</li> </ul>"},{"location":"chapter_backtracking/subset_sum_problem/#1","title":"1. \u00a0 \u9806\u5217\u89e3\u6cd5\u306e\u53c2\u8003","text":"<p>\u9806\u5217\u554f\u984c\u3068\u540c\u69d8\u306b\u3001\u90e8\u5206\u96c6\u5408\u306e\u751f\u6210\u3092\u4e00\u9023\u306e\u9078\u629e\u3068\u3057\u3066\u60f3\u50cf\u3067\u304d\u3001\u9078\u629e\u30d7\u30ed\u30bb\u30b9\u4e2d\u306b\u300c\u8981\u7d20\u548c\u300d\u3092\u30ea\u30a2\u30eb\u30bf\u30a4\u30e0\u3067\u66f4\u65b0\u3067\u304d\u307e\u3059\u3002\u8981\u7d20\u548c\u304c <code>target</code> \u306b\u7b49\u3057\u304f\u306a\u3063\u305f\u3068\u304d\u3001\u90e8\u5206\u96c6\u5408\u3092\u7d50\u679c\u30ea\u30b9\u30c8\u306b\u8a18\u9332\u3057\u307e\u3059\u3002</p> <p>\u9806\u5217\u554f\u984c\u3068\u306f\u7570\u306a\u308a\u3001\u3053\u306e\u554f\u984c\u3067\u306f\u8981\u7d20\u306f\u7121\u5236\u9650\u306b\u9078\u629e\u3067\u304d\u308b\u305f\u3081\u3001\u8981\u7d20\u304c\u9078\u629e\u3055\u308c\u305f\u304b\u3069\u3046\u304b\u3092\u8a18\u9332\u3059\u308b\u305f\u3081\u306e <code>selected</code> \u30d6\u30fc\u30eb\u914d\u5217\u3092\u4f7f\u7528\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u305b\u3093\u3002\u9806\u5217\u30b3\u30fc\u30c9\u306b\u8efd\u5fae\u306a\u4fee\u6b63\u3092\u52a0\u3048\u3066\u3001\u6700\u521d\u306b\u554f\u984c\u3092\u89e3\u6c7a\u3067\u304d\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig subset_sum_i_naive.py<pre><code>def backtrack(\n    state: list[int],\n    target: int,\n    total: int,\n    choices: list[int],\n    res: list[list[int]],\n):\n    \"\"\"\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\uff1a\u90e8\u5206\u96c6\u5408\u306e\u548c I\"\"\"\n    # \u90e8\u5206\u96c6\u5408\u306e\u548c\u304c target \u3068\u7b49\u3057\u3044\u3068\u304d\u3001\u89e3\u3092\u8a18\u9332\n    if total == target:\n        res.append(list(state))\n        return\n    # \u3059\u3079\u3066\u306e\u9078\u629e\u80a2\u3092\u8d70\u67fb\n    for i in range(len(choices)):\n        # \u679d\u5208\u308a\uff1a\u90e8\u5206\u96c6\u5408\u306e\u548c\u304c target \u3092\u8d85\u3048\u308b\u5834\u5408\u3001\u305d\u306e\u9078\u629e\u3092\u30b9\u30ad\u30c3\u30d7\n        if total + choices[i] &gt; target:\n            continue\n        # \u8a66\u884c\uff1a\u9078\u629e\u3092\u884c\u3044\u3001\u8981\u7d20\u3068 total \u3092\u66f4\u65b0\n        state.append(choices[i])\n        # \u6b21\u306e\u9078\u629e\u30e9\u30a6\u30f3\u30c9\u306b\u9032\u3080\n        backtrack(state, target, total + choices[i], choices, res)\n        # \u64a4\u56de\uff1a\u9078\u629e\u3092\u53d6\u308a\u6d88\u3057\u3001\u524d\u306e\u72b6\u614b\u306b\u5fa9\u5143\n        state.pop()\n\ndef subset_sum_i_naive(nums: list[int], target: int) -&gt; list[list[int]]:\n    \"\"\"\u90e8\u5206\u96c6\u5408\u306e\u548c I \u3092\u89e3\u304f\uff08\u91cd\u8907\u3059\u308b\u90e8\u5206\u96c6\u5408\u3092\u542b\u3080\uff09\"\"\"\n    state = []  # \u72b6\u614b\uff08\u90e8\u5206\u96c6\u5408\uff09\n    total = 0  # \u90e8\u5206\u96c6\u5408\u306e\u548c\n    res = []  # \u7d50\u679c\u30ea\u30b9\u30c8\uff08\u90e8\u5206\u96c6\u5408\u30ea\u30b9\u30c8\uff09\n    backtrack(state, target, total, nums, res)\n    return res\n</code></pre> subset_sum_i_naive.cpp<pre><code>/* \u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\uff1a\u90e8\u5206\u96c6\u5408\u548c I */\nvoid backtrack(vector&lt;int&gt; &amp;state, int target, int total, vector&lt;int&gt; &amp;choices, vector&lt;vector&lt;int&gt;&gt; &amp;res) {\n    // \u90e8\u5206\u96c6\u5408\u306e\u548c\u304ctarget\u3068\u7b49\u3057\u3044\u3068\u304d\u3001\u89e3\u3092\u8a18\u9332\n    if (total == target) {\n        res.push_back(state);\n        return;\n    }\n    // \u3059\u3079\u3066\u306e\u9078\u629e\u80a2\u3092\u8d70\u67fb\n    for (int i = 0; i &lt; choices.size(); i++) {\n        // \u526a\u5b9a\uff1a\u90e8\u5206\u96c6\u5408\u306e\u548c\u304ctarget\u3092\u8d85\u3048\u305f\u5834\u5408\u3001\u305d\u306e\u9078\u629e\u3092\u30b9\u30ad\u30c3\u30d7\n        if (total + choices[i] &gt; target) {\n            continue;\n        }\n        // \u8a66\u884c\uff1a\u9078\u629e\u3092\u884c\u3044\u3001\u8981\u7d20\u3068total\u3092\u66f4\u65b0\n        state.push_back(choices[i]);\n        // \u6b21\u306e\u30e9\u30a6\u30f3\u30c9\u306e\u9078\u629e\u306b\u9032\u3080\n        backtrack(state, target, total + choices[i], choices, res);\n        // \u56de\u9000\uff1a\u9078\u629e\u3092\u53d6\u308a\u6d88\u3057\u3001\u524d\u306e\u72b6\u614b\u306b\u5fa9\u5143\n        state.pop_back();\n    }\n}\n\n/* \u90e8\u5206\u96c6\u5408\u548c I \u3092\u89e3\u304f\uff08\u91cd\u8907\u3059\u308b\u90e8\u5206\u96c6\u5408\u3092\u542b\u3080\uff09 */\nvector&lt;vector&lt;int&gt;&gt; subsetSumINaive(vector&lt;int&gt; nums, int target) {\n    vector&lt;int&gt; state;       // \u72b6\u614b\uff08\u90e8\u5206\u96c6\u5408\uff09\n    int total = 0;           // \u90e8\u5206\u96c6\u5408\u306e\u548c\n    vector&lt;vector&lt;int&gt;&gt; res; // \u7d50\u679c\u30ea\u30b9\u30c8\uff08\u90e8\u5206\u96c6\u5408\u30ea\u30b9\u30c8\uff09\n    backtrack(state, target, total, nums, res);\n    return res;\n}\n</code></pre> subset_sum_i_naive.java<pre><code>/* \u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\uff1a\u90e8\u5206\u96c6\u5408\u548c I */\nvoid backtrack(List&lt;Integer&gt; state, int target, int total, int[] choices, List&lt;List&lt;Integer&gt;&gt; res) {\n    // \u90e8\u5206\u96c6\u5408\u306e\u548c\u304ctarget\u3068\u7b49\u3057\u3044\u3068\u304d\u3001\u89e3\u3092\u8a18\u9332\n    if (total == target) {\n        res.add(new ArrayList&lt;&gt;(state));\n        return;\n    }\n    // \u3059\u3079\u3066\u306e\u9078\u629e\u80a2\u3092\u8d70\u67fb\n    for (int i = 0; i &lt; choices.length; i++) {\n        // \u526a\u5b9a\uff1a\u90e8\u5206\u96c6\u5408\u306e\u548c\u304ctarget\u3092\u8d85\u3048\u305f\u5834\u5408\u3001\u305d\u306e\u9078\u629e\u3092\u30b9\u30ad\u30c3\u30d7\n        if (total + choices[i] &gt; target) {\n            continue;\n        }\n        // \u8a66\u884c\uff1a\u9078\u629e\u3092\u884c\u3044\u3001\u8981\u7d20\u3068total\u3092\u66f4\u65b0\n        state.add(choices[i]);\n        // \u6b21\u306e\u30e9\u30a6\u30f3\u30c9\u306e\u9078\u629e\u306b\u9032\u3080\n        backtrack(state, target, total + choices[i], choices, res);\n        // \u56de\u9000\uff1a\u9078\u629e\u3092\u53d6\u308a\u6d88\u3057\u3001\u524d\u306e\u72b6\u614b\u306b\u5fa9\u5143\n        state.remove(state.size() - 1);\n    }\n}\n\n/* \u90e8\u5206\u96c6\u5408\u548c I \u3092\u89e3\u304f\uff08\u91cd\u8907\u3059\u308b\u90e8\u5206\u96c6\u5408\u3092\u542b\u3080\uff09 */\nList&lt;List&lt;Integer&gt;&gt; subsetSumINaive(int[] nums, int target) {\n    List&lt;Integer&gt; state = new ArrayList&lt;&gt;(); // \u72b6\u614b\uff08\u90e8\u5206\u96c6\u5408\uff09\n    int total = 0; // \u90e8\u5206\u96c6\u5408\u306e\u548c\n    List&lt;List&lt;Integer&gt;&gt; res = new ArrayList&lt;&gt;(); // \u7d50\u679c\u30ea\u30b9\u30c8\uff08\u90e8\u5206\u96c6\u5408\u30ea\u30b9\u30c8\uff09\n    backtrack(state, target, total, nums, res);\n    return res;\n}\n</code></pre> subset_sum_i_naive.cs<pre><code>[class]{subset_sum_i_naive}-[func]{Backtrack}\n\n[class]{subset_sum_i_naive}-[func]{SubsetSumINaive}\n</code></pre> subset_sum_i_naive.go<pre><code>[class]{}-[func]{backtrackSubsetSumINaive}\n\n[class]{}-[func]{subsetSumINaive}\n</code></pre> subset_sum_i_naive.swift<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subsetSumINaive}\n</code></pre> subset_sum_i_naive.js<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subsetSumINaive}\n</code></pre> subset_sum_i_naive.ts<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subsetSumINaive}\n</code></pre> subset_sum_i_naive.dart<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subsetSumINaive}\n</code></pre> subset_sum_i_naive.rs<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subset_sum_i_naive}\n</code></pre> subset_sum_i_naive.c<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subsetSumINaive}\n</code></pre> subset_sum_i_naive.kt<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subsetSumINaive}\n</code></pre> subset_sum_i_naive.rb<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subset_sum_i_naive}\n</code></pre> subset_sum_i_naive.zig<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subsetSumINaive}\n</code></pre> <p>\u914d\u5217 \\([3, 4, 5]\\) \u3068\u30bf\u30fc\u30b2\u30c3\u30c8\u8981\u7d20 \\(9\\) \u3092\u4e0a\u8a18\u306e\u30b3\u30fc\u30c9\u306b\u5165\u529b\u3059\u308b\u3068\u3001\u7d50\u679c \\([3, 3, 3], [4, 5], [5, 4]\\) \u304c\u5f97\u3089\u308c\u307e\u3059\u3002\u548c\u304c \\(9\\) \u306e\u3059\u3079\u3066\u306e\u90e8\u5206\u96c6\u5408\u3092\u6b63\u5e38\u306b\u898b\u3064\u3051\u307e\u3057\u305f\u304c\u3001\u91cd\u8907\u3059\u308b\u90e8\u5206\u96c6\u5408 \\([4, 5]\\) \u3068 \\([5, 4]\\) \u304c\u542b\u307e\u308c\u3066\u3044\u307e\u3059\u3002</p> <p>\u3053\u308c\u306f\u3001\u691c\u7d22\u30d7\u30ed\u30bb\u30b9\u304c\u9078\u629e\u306e\u9806\u5e8f\u3092\u533a\u5225\u3059\u308b\u305f\u3081\u3067\u3059\u304c\u3001\u90e8\u5206\u96c6\u5408\u306f\u9078\u629e\u9806\u5e8f\u3092\u533a\u5225\u3057\u307e\u305b\u3093\u3002\u4ee5\u4e0b\u306e\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\\(5\\) \u306e\u524d\u306b \\(4\\) \u3092\u9078\u629e\u3059\u308b\u3053\u3068\u3068 \\(4\\) \u306e\u524d\u306b \\(5\\) \u3092\u9078\u629e\u3059\u308b\u3053\u3068\u306f\u7570\u306a\u308b\u5206\u5c90\u3067\u3059\u304c\u3001\u540c\u3058\u90e8\u5206\u96c6\u5408\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002</p> <p></p> <p> \u56f3 13-10 \u00a0 \u90e8\u5206\u96c6\u5408\u306e\u691c\u7d22\u3068\u5883\u754c\u5916\u306e\u526a\u5b9a </p> <p>\u91cd\u8907\u3059\u308b\u90e8\u5206\u96c6\u5408\u3092\u9664\u53bb\u3059\u308b\u305f\u3081\u306b\u3001\u76f4\u63a5\u7684\u306a\u30a2\u30a4\u30c7\u30a2\u306f\u7d50\u679c\u30ea\u30b9\u30c8\u3092\u91cd\u8907\u9664\u53bb\u3059\u308b\u3053\u3068\u3067\u3059\u3002\u3057\u304b\u3057\u3001\u3053\u306e\u65b9\u6cd5\u306f2\u3064\u306e\u7406\u7531\u3067\u975e\u5e38\u306b\u975e\u52b9\u7387\u7684\u3067\u3059\u3002</p> <ul> <li>\u914d\u5217\u8981\u7d20\u304c\u591a\u3044\u5834\u5408\u3001\u7279\u306b <code>target</code> \u304c\u5927\u304d\u3044\u5834\u5408\u3001\u691c\u7d22\u30d7\u30ed\u30bb\u30b9\u3067\u5927\u91cf\u306e\u91cd\u8907\u3059\u308b\u90e8\u5206\u96c6\u5408\u304c\u751f\u6210\u3055\u308c\u307e\u3059\u3002</li> <li>\u90e8\u5206\u96c6\u5408\uff08\u914d\u5217\uff09\u306e\u5dee\u7570\u3092\u6bd4\u8f03\u3059\u308b\u3053\u3068\u306f\u975e\u5e38\u306b\u6642\u9593\u304c\u304b\u304b\u308a\u3001\u307e\u305a\u914d\u5217\u3092\u30bd\u30fc\u30c8\u3057\u3001\u6b21\u306b\u914d\u5217\u306e\u5404\u8981\u7d20\u306e\u5dee\u7570\u3092\u6bd4\u8f03\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002</li> </ul>"},{"location":"chapter_backtracking/subset_sum_problem/#2","title":"2. \u00a0 \u91cd\u8907\u90e8\u5206\u96c6\u5408\u306e\u526a\u5b9a","text":"<p>\u526a\u5b9a\u3092\u901a\u3058\u3066\u691c\u7d22\u30d7\u30ed\u30bb\u30b9\u4e2d\u306b\u91cd\u8907\u9664\u53bb\u3092\u691c\u8a0e\u3057\u307e\u3059\u3002\u4ee5\u4e0b\u306e\u56f3\u3092\u89b3\u5bdf\u3059\u308b\u3068\u3001\u7570\u306a\u308b\u9806\u5e8f\u3067\u914d\u5217\u8981\u7d20\u3092\u9078\u629e\u3059\u308b\u3068\u304d\u306b\u91cd\u8907\u3059\u308b\u90e8\u5206\u96c6\u5408\u304c\u751f\u6210\u3055\u308c\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u4ee5\u4e0b\u306e\u72b6\u6cc1\u3067\u3059\u3002</p> <ol> <li>\u6700\u521d\u306e\u30e9\u30a6\u30f3\u30c9\u3067 \\(3\\) \u3092\u9078\u629e\u3057\u30012\u756a\u76ee\u306e\u30e9\u30a6\u30f3\u30c9\u3067 \\(4\\) \u3092\u9078\u629e\u3059\u308b\u3068\u3001\u3053\u308c\u30892\u3064\u306e\u8981\u7d20\u3092\u542b\u3080\u3059\u3079\u3066\u306e\u90e8\u5206\u96c6\u5408\u304c\u751f\u6210\u3055\u308c\u3001\\([3, 4, \\dots]\\) \u3068\u8868\u8a18\u3055\u308c\u307e\u3059\u3002</li> <li>\u5f8c\u3067\u3001\u6700\u521d\u306e\u30e9\u30a6\u30f3\u30c9\u3067 \\(4\\) \u304c\u9078\u629e\u3055\u308c\u305f\u3068\u304d\u30012\u756a\u76ee\u306e\u30e9\u30a6\u30f3\u30c9\u306f \\(3\\) \u3092\u30b9\u30ad\u30c3\u30d7\u3059\u3079\u304d\u3067\u3059\u3002\u3053\u306e\u9078\u629e\u306b\u3088\u3063\u3066\u751f\u6210\u3055\u308c\u308b\u90e8\u5206\u96c6\u5408 \\([4, 3, \\dots]\\) \u306f\u30b9\u30c6\u30c3\u30d7 <code>1.</code> \u306e\u90e8\u5206\u96c6\u5408\u3068\u5b8c\u5168\u306b\u91cd\u8907\u3059\u308b\u304b\u3089\u3067\u3059\u3002</li> </ol> <p>\u691c\u7d22\u30d7\u30ed\u30bb\u30b9\u3067\u306f\u3001\u5404\u5c64\u306e\u9078\u629e\u304c\u5de6\u304b\u3089\u53f3\u306b\u4e00\u3064\u305a\u3064\u8a66\u884c\u3055\u308c\u308b\u305f\u3081\u3001\u53f3\u5074\u306e\u5206\u5c90\u307b\u3069\u3088\u308a\u591a\u304f\u526a\u5b9a\u3055\u308c\u307e\u3059\u3002</p> <ol> <li>\u6700\u521d\u306e2\u30e9\u30a6\u30f3\u30c9\u3067 \\(3\\) \u3068 \\(5\\) \u3092\u9078\u629e\u3057\u3001\u90e8\u5206\u96c6\u5408 \\([3, 5, \\dots]\\) \u3092\u751f\u6210\u3057\u307e\u3059\u3002</li> <li>\u6700\u521d\u306e2\u30e9\u30a6\u30f3\u30c9\u3067 \\(4\\) \u3068 \\(5\\) \u3092\u9078\u629e\u3057\u3001\u90e8\u5206\u96c6\u5408 \\([4, 5, \\dots]\\) \u3092\u751f\u6210\u3057\u307e\u3059\u3002</li> <li>\u6700\u521d\u306e\u30e9\u30a6\u30f3\u30c9\u3067 \\(5\\) \u304c\u9078\u629e\u3055\u308c\u305f\u5834\u5408\u30012\u756a\u76ee\u306e\u30e9\u30a6\u30f3\u30c9\u306f \\(3\\) \u3068 \\(4\\) \u3092\u30b9\u30ad\u30c3\u30d7\u3059\u3079\u304d\u3067\u3059\u3002\u90e8\u5206\u96c6\u5408 \\([5, 3, \\dots]\\) \u3068 \\([5, 4, \\dots]\\) \u306f\u30b9\u30c6\u30c3\u30d7 <code>1.</code> \u3068 <code>2.</code> \u3067\u8a18\u8ff0\u3055\u308c\u305f\u90e8\u5206\u96c6\u5408\u3068\u5b8c\u5168\u306b\u91cd\u8907\u3059\u308b\u304b\u3089\u3067\u3059\u3002</li> </ol> <p></p> <p> \u56f3 13-11 \u00a0 \u7570\u306a\u308b\u9078\u629e\u9806\u5e8f\u306b\u3088\u308b\u91cd\u8907\u90e8\u5206\u96c6\u5408 </p> <p>\u8981\u7d04\u3059\u308b\u3068\u3001\u5165\u529b\u914d\u5217 \\([x_1, x_2, \\dots, x_n]\\) \u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408\u3001\u691c\u7d22\u30d7\u30ed\u30bb\u30b9\u3067\u306e\u9078\u629e\u30b7\u30fc\u30b1\u30f3\u30b9\u306f \\([x_{i_1}, x_{i_2}, \\dots, x_{i_m}]\\) \u3067\u3042\u308b\u3079\u304d\u3067\u3001\\(i_1 \\leq i_2 \\leq \\dots \\leq i_m\\) \u3092\u6e80\u305f\u3059\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u6761\u4ef6\u3092\u6e80\u305f\u3055\u306a\u3044\u9078\u629e\u30b7\u30fc\u30b1\u30f3\u30b9\u306f\u91cd\u8907\u3092\u5f15\u304d\u8d77\u3053\u3057\u3001\u526a\u5b9a\u3055\u308c\u308b\u3079\u304d\u3067\u3059\u3002</p>"},{"location":"chapter_backtracking/subset_sum_problem/#3","title":"3. \u00a0 \u30b3\u30fc\u30c9\u5b9f\u88c5","text":"<p>\u3053\u306e\u526a\u5b9a\u3092\u5b9f\u88c5\u3059\u308b\u305f\u3081\u306b\u3001\u5909\u6570 <code>start</code> \u3092\u521d\u671f\u5316\u3057\u3001\u3053\u308c\u306f\u8d70\u67fb\u306e\u958b\u59cb\u70b9\u3092\u793a\u3057\u307e\u3059\u3002\u9078\u629e \\(x_{i}\\) \u3092\u884c\u3063\u305f\u5f8c\u3001\u6b21\u306e\u30e9\u30a6\u30f3\u30c9\u3092\u30a4\u30f3\u30c7\u30c3\u30af\u30b9 \\(i\\) \u304b\u3089\u958b\u59cb\u3059\u308b\u3088\u3046\u306b\u8a2d\u5b9a\u3057\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u9078\u629e\u30b7\u30fc\u30b1\u30f3\u30b9\u304c \\(i_1 \\leq i_2 \\leq \\dots \\leq i_m\\) \u3092\u6e80\u305f\u3059\u3053\u3068\u304c\u4fdd\u8a3c\u3055\u308c\u3001\u90e8\u5206\u96c6\u5408\u306e\u4e00\u610f\u6027\u304c\u4fdd\u8a3c\u3055\u308c\u307e\u3059\u3002</p> <p>\u3055\u3089\u306b\u3001\u30b3\u30fc\u30c9\u306b\u4ee5\u4e0b\u306e2\u3064\u306e\u6700\u9069\u5316\u3092\u884c\u3044\u307e\u3057\u305f\u3002</p> <ul> <li>\u691c\u7d22\u3092\u958b\u59cb\u3059\u308b\u524d\u306b\u3001\u914d\u5217 <code>nums</code> \u3092\u30bd\u30fc\u30c8\u3057\u307e\u3059\u3002\u3059\u3079\u3066\u306e\u9078\u629e\u306e\u8d70\u67fb\u3067\u3001\u90e8\u5206\u96c6\u5408\u548c\u304c <code>target</code> \u3092\u8d85\u3048\u305f\u3068\u304d\u306b\u30eb\u30fc\u30d7\u3092\u76f4\u63a5\u7d42\u4e86\u3057\u307e\u3059\u3002\u5f8c\u7d9a\u306e\u8981\u7d20\u306f\u3088\u308a\u5927\u304d\u304f\u3001\u305d\u308c\u3089\u306e\u90e8\u5206\u96c6\u5408\u548c\u306f\u78ba\u5b9f\u306b <code>target</code> \u3092\u8d85\u3048\u308b\u304b\u3089\u3067\u3059\u3002</li> <li>\u8981\u7d20\u548c\u5909\u6570 <code>total</code> \u3092\u9664\u53bb\u3057\u3001<code>target</code> \u306b\u5bfe\u3057\u3066\u6e1b\u7b97\u3092\u5b9f\u884c\u3057\u3066\u8981\u7d20\u548c\u3092\u30ab\u30a6\u30f3\u30c8\u3057\u307e\u3059\u3002<code>target</code> \u304c \\(0\\) \u306b\u7b49\u3057\u304f\u306a\u3063\u305f\u3068\u304d\u3001\u89e3\u3092\u8a18\u9332\u3057\u307e\u3059\u3002</li> </ul> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig subset_sum_i.py<pre><code>def backtrack(\n    state: list[int], target: int, choices: list[int], start: int, res: list[list[int]]\n):\n    \"\"\"\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\uff1a\u90e8\u5206\u96c6\u5408\u306e\u548c I\"\"\"\n    # \u90e8\u5206\u96c6\u5408\u306e\u548c\u304c target \u3068\u7b49\u3057\u3044\u3068\u304d\u3001\u89e3\u3092\u8a18\u9332\n    if target == 0:\n        res.append(list(state))\n        return\n    # \u3059\u3079\u3066\u306e\u9078\u629e\u80a2\u3092\u8d70\u67fb\n    # \u679d\u5208\u308a\u4e8c\uff1astart \u304b\u3089\u8d70\u67fb\u3092\u958b\u59cb\u3057\u3066\u91cd\u8907\u3059\u308b\u90e8\u5206\u96c6\u5408\u306e\u751f\u6210\u3092\u907f\u3051\u308b\n    for i in range(start, len(choices)):\n        # \u679d\u5208\u308a\u4e00\uff1a\u90e8\u5206\u96c6\u5408\u306e\u548c\u304c target \u3092\u8d85\u3048\u308b\u5834\u5408\u3001\u76f4\u3061\u306b\u30eb\u30fc\u30d7\u3092\u7d42\u4e86\n        # \u3053\u308c\u306f\u914d\u5217\u304c\u30bd\u30fc\u30c8\u3055\u308c\u3066\u304a\u308a\u3001\u5f8c\u306e\u8981\u7d20\u304c\u3088\u308a\u5927\u304d\u3044\u305f\u3081\u3001\u90e8\u5206\u96c6\u5408\u306e\u548c\u306f\u5fc5\u305a target \u3092\u8d85\u3048\u308b\u305f\u3081\n        if target - choices[i] &lt; 0:\n            break\n        # \u8a66\u884c\uff1a\u9078\u629e\u3092\u884c\u3044\u3001target\u3001start \u3092\u66f4\u65b0\n        state.append(choices[i])\n        # \u6b21\u306e\u9078\u629e\u30e9\u30a6\u30f3\u30c9\u306b\u9032\u3080\n        backtrack(state, target - choices[i], choices, i, res)\n        # \u64a4\u56de\uff1a\u9078\u629e\u3092\u53d6\u308a\u6d88\u3057\u3001\u524d\u306e\u72b6\u614b\u306b\u5fa9\u5143\n        state.pop()\n\ndef subset_sum_i(nums: list[int], target: int) -&gt; list[list[int]]:\n    \"\"\"\u90e8\u5206\u96c6\u5408\u306e\u548c I \u3092\u89e3\u304f\"\"\"\n    state = []  # \u72b6\u614b\uff08\u90e8\u5206\u96c6\u5408\uff09\n    nums.sort()  # nums \u3092\u30bd\u30fc\u30c8\n    start = 0  # \u8d70\u67fb\u306e\u958b\u59cb\u70b9\n    res = []  # \u7d50\u679c\u30ea\u30b9\u30c8\uff08\u90e8\u5206\u96c6\u5408\u30ea\u30b9\u30c8\uff09\n    backtrack(state, target, nums, start, res)\n    return res\n</code></pre> subset_sum_i.cpp<pre><code>/* \u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\uff1a\u90e8\u5206\u96c6\u5408\u548c I */\nvoid backtrack(vector&lt;int&gt; &amp;state, int target, vector&lt;int&gt; &amp;choices, int start, vector&lt;vector&lt;int&gt;&gt; &amp;res) {\n    // \u90e8\u5206\u96c6\u5408\u306e\u548c\u304ctarget\u3068\u7b49\u3057\u3044\u3068\u304d\u3001\u89e3\u3092\u8a18\u9332\n    if (target == 0) {\n        res.push_back(state);\n        return;\n    }\n    // \u3059\u3079\u3066\u306e\u9078\u629e\u80a2\u3092\u8d70\u67fb\n    // \u526a\u5b9a\u4e8c\uff1astart\u304b\u3089\u8d70\u67fb\u3092\u958b\u59cb\u3057\u3001\u91cd\u8907\u3059\u308b\u90e8\u5206\u96c6\u5408\u306e\u751f\u6210\u3092\u56de\u907f\n    for (int i = start; i &lt; choices.size(); i++) {\n        // \u526a\u5b9a\u4e00\uff1a\u90e8\u5206\u96c6\u5408\u306e\u548c\u304ctarget\u3092\u8d85\u3048\u305f\u5834\u5408\u3001\u5373\u5ea7\u306b\u30eb\u30fc\u30d7\u3092\u7d42\u4e86\n        // \u914d\u5217\u304c\u30bd\u30fc\u30c8\u3055\u308c\u3066\u3044\u308b\u305f\u3081\u3001\u5f8c\u306e\u8981\u7d20\u306f\u3055\u3089\u306b\u5927\u304d\u304f\u3001\u90e8\u5206\u96c6\u5408\u306e\u548c\u306f\u5fc5\u305atarget\u3092\u8d85\u3048\u308b\n        if (target - choices[i] &lt; 0) {\n            break;\n        }\n        // \u8a66\u884c\uff1a\u9078\u629e\u3092\u884c\u3044\u3001target\u3001start\u3092\u66f4\u65b0\n        state.push_back(choices[i]);\n        // \u6b21\u306e\u30e9\u30a6\u30f3\u30c9\u306e\u9078\u629e\u306b\u9032\u3080\n        backtrack(state, target - choices[i], choices, i, res);\n        // \u56de\u9000\uff1a\u9078\u629e\u3092\u53d6\u308a\u6d88\u3057\u3001\u524d\u306e\u72b6\u614b\u306b\u5fa9\u5143\n        state.pop_back();\n    }\n}\n\n/* \u90e8\u5206\u96c6\u5408\u548c I \u3092\u89e3\u304f */\nvector&lt;vector&lt;int&gt;&gt; subsetSumI(vector&lt;int&gt; nums, int target) {\n    vector&lt;int&gt; state;              // \u72b6\u614b\uff08\u90e8\u5206\u96c6\u5408\uff09\n    sort(nums.begin(), nums.end()); // nums \u3092\u30bd\u30fc\u30c8\n    int start = 0;                  // \u8d70\u67fb\u306e\u958b\u59cb\u70b9\n    vector&lt;vector&lt;int&gt;&gt; res;        // \u7d50\u679c\u30ea\u30b9\u30c8\uff08\u90e8\u5206\u96c6\u5408\u30ea\u30b9\u30c8\uff09\n    backtrack(state, target, nums, start, res);\n    return res;\n}\n</code></pre> subset_sum_i.java<pre><code>/* \u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\uff1a\u90e8\u5206\u96c6\u5408\u548c I */\nvoid backtrack(List&lt;Integer&gt; state, int target, int[] choices, int start, List&lt;List&lt;Integer&gt;&gt; res) {\n    // \u90e8\u5206\u96c6\u5408\u306e\u548c\u304ctarget\u3068\u7b49\u3057\u3044\u3068\u304d\u3001\u89e3\u3092\u8a18\u9332\n    if (target == 0) {\n        res.add(new ArrayList&lt;&gt;(state));\n        return;\n    }\n    // \u3059\u3079\u3066\u306e\u9078\u629e\u80a2\u3092\u8d70\u67fb\n    // \u526a\u5b9a\u4e8c\uff1astart\u304b\u3089\u8d70\u67fb\u3092\u958b\u59cb\u3057\u3001\u91cd\u8907\u3059\u308b\u90e8\u5206\u96c6\u5408\u306e\u751f\u6210\u3092\u56de\u907f\n    for (int i = start; i &lt; choices.length; i++) {\n        // \u526a\u5b9a\u4e00\uff1a\u90e8\u5206\u96c6\u5408\u306e\u548c\u304ctarget\u3092\u8d85\u3048\u305f\u5834\u5408\u3001\u5373\u5ea7\u306b\u30eb\u30fc\u30d7\u3092\u7d42\u4e86\n        // \u914d\u5217\u304c\u30bd\u30fc\u30c8\u3055\u308c\u3066\u3044\u308b\u305f\u3081\u3001\u5f8c\u306e\u8981\u7d20\u306f\u3055\u3089\u306b\u5927\u304d\u304f\u3001\u90e8\u5206\u96c6\u5408\u306e\u548c\u306f\u5fc5\u305atarget\u3092\u8d85\u3048\u308b\n        if (target - choices[i] &lt; 0) {\n            break;\n        }\n        // \u8a66\u884c\uff1a\u9078\u629e\u3092\u884c\u3044\u3001target\u3001start\u3092\u66f4\u65b0\n        state.add(choices[i]);\n        // \u6b21\u306e\u30e9\u30a6\u30f3\u30c9\u306e\u9078\u629e\u306b\u9032\u3080\n        backtrack(state, target - choices[i], choices, i, res);\n        // \u56de\u9000\uff1a\u9078\u629e\u3092\u53d6\u308a\u6d88\u3057\u3001\u524d\u306e\u72b6\u614b\u306b\u5fa9\u5143\n        state.remove(state.size() - 1);\n    }\n}\n\n/* \u90e8\u5206\u96c6\u5408\u548c I \u3092\u89e3\u304f */\nList&lt;List&lt;Integer&gt;&gt; subsetSumI(int[] nums, int target) {\n    List&lt;Integer&gt; state = new ArrayList&lt;&gt;(); // \u72b6\u614b\uff08\u90e8\u5206\u96c6\u5408\uff09\n    Arrays.sort(nums); // nums \u3092\u30bd\u30fc\u30c8\n    int start = 0; // \u8d70\u67fb\u306e\u958b\u59cb\u70b9\n    List&lt;List&lt;Integer&gt;&gt; res = new ArrayList&lt;&gt;(); // \u7d50\u679c\u30ea\u30b9\u30c8\uff08\u90e8\u5206\u96c6\u5408\u30ea\u30b9\u30c8\uff09\n    backtrack(state, target, nums, start, res);\n    return res;\n}\n</code></pre> subset_sum_i.cs<pre><code>[class]{subset_sum_i}-[func]{Backtrack}\n\n[class]{subset_sum_i}-[func]{SubsetSumI}\n</code></pre> subset_sum_i.go<pre><code>[class]{}-[func]{backtrackSubsetSumI}\n\n[class]{}-[func]{subsetSumI}\n</code></pre> subset_sum_i.swift<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subsetSumI}\n</code></pre> subset_sum_i.js<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subsetSumI}\n</code></pre> subset_sum_i.ts<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subsetSumI}\n</code></pre> subset_sum_i.dart<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subsetSumI}\n</code></pre> subset_sum_i.rs<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subset_sum_i}\n</code></pre> subset_sum_i.c<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subsetSumI}\n</code></pre> subset_sum_i.kt<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subsetSumI}\n</code></pre> subset_sum_i.rb<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subset_sum_i}\n</code></pre> subset_sum_i.zig<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subsetSumI}\n</code></pre> <p>\u4ee5\u4e0b\u306e\u56f3\u306f\u3001\u914d\u5217 \\([3, 4, 5]\\) \u3068\u30bf\u30fc\u30b2\u30c3\u30c8\u8981\u7d20 \\(9\\) \u3092\u4e0a\u8a18\u306e\u30b3\u30fc\u30c9\u306b\u5165\u529b\u3057\u305f\u5f8c\u306e\u5168\u4f53\u7684\u306a\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30d7\u30ed\u30bb\u30b9\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002</p> <p></p> <p> \u56f3 13-12 \u00a0 \u90e8\u5206\u96c6\u5408\u548c I \u306e\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30d7\u30ed\u30bb\u30b9 </p>"},{"location":"chapter_backtracking/subset_sum_problem/#1332","title":"13.3.2 \u00a0 \u91cd\u8907\u8981\u7d20\u304c\u3042\u308b\u5834\u5408\u3092\u8003\u616e","text":"<p>Question</p> <p>\u6b63\u306e\u6574\u6570\u306e\u914d\u5217 <code>nums</code> \u3068\u30bf\u30fc\u30b2\u30c3\u30c8\u6b63\u6574\u6570 <code>target</code> \u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408\u3001\u7d44\u307f\u5408\u308f\u305b\u5185\u306e\u8981\u7d20\u306e\u548c\u304c <code>target</code> \u306b\u7b49\u3057\u304f\u306a\u308b\u3088\u3046\u306a\u3059\u3079\u3066\u306e\u53ef\u80fd\u306a\u7d44\u307f\u5408\u308f\u305b\u3092\u898b\u3064\u3051\u3066\u304f\u3060\u3055\u3044\u3002\u4e0e\u3048\u3089\u308c\u305f\u914d\u5217\u306b\u306f\u91cd\u8907\u8981\u7d20\u304c\u542b\u307e\u308c\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u3001\u5404\u8981\u7d20\u306f\u4e00\u5ea6\u3060\u3051\u9078\u629e\u3067\u304d\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u7d44\u307f\u5408\u308f\u305b\u3092\u91cd\u8907\u3059\u308b\u7d44\u307f\u5408\u308f\u305b\u3092\u542b\u307e\u306a\u3044\u30ea\u30b9\u30c8\u3068\u3057\u3066\u8fd4\u3057\u3066\u304f\u3060\u3055\u3044\u3002</p> <p>\u524d\u306e\u554f\u984c\u3068\u6bd4\u8f03\u3057\u3066\u3001\u3053\u306e\u554f\u984c\u306e\u5165\u529b\u914d\u5217\u306b\u306f\u91cd\u8907\u8981\u7d20\u304c\u542b\u307e\u308c\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u3001\u65b0\u3057\u3044\u554f\u984c\u304c\u5c0e\u5165\u3055\u308c\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u914d\u5217 \\([4, \\hat{4}, 5]\\) \u3068\u30bf\u30fc\u30b2\u30c3\u30c8\u8981\u7d20 \\(9\\) \u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408\u3001\u65e2\u5b58\u306e\u30b3\u30fc\u30c9\u306e\u51fa\u529b\u7d50\u679c\u306f \\([4, 5], [\\hat{4}, 5]\\) \u3068\u306a\u308a\u3001\u91cd\u8907\u3059\u308b\u90e8\u5206\u96c6\u5408\u304c\u751f\u6210\u3055\u308c\u307e\u3059\u3002</p> <p>\u3053\u306e\u91cd\u8907\u306e\u7406\u7531\u306f\u3001\u7279\u5b9a\u306e\u30e9\u30a6\u30f3\u30c9\u3067\u7b49\u3057\u3044\u8981\u7d20\u304c\u8907\u6570\u56de\u9078\u629e\u3055\u308c\u308b\u3053\u3068\u3067\u3059\u3002\u4ee5\u4e0b\u306e\u56f3\u3067\u306f\u3001\u6700\u521d\u306e\u30e9\u30a6\u30f3\u30c9\u306b3\u3064\u306e\u9078\u629e\u80a2\u304c\u3042\u308a\u3001\u305d\u306e\u3046\u30612\u3064\u304c \\(4\\) \u3067\u3042\u308a\u30012\u3064\u306e\u91cd\u8907\u3059\u308b\u691c\u7d22\u5206\u5c90\u3092\u751f\u6210\u3057\u3001\u91cd\u8907\u3059\u308b\u90e8\u5206\u96c6\u5408\u3092\u51fa\u529b\u3057\u307e\u3059\u3002\u540c\u69d8\u306b\u30012\u756a\u76ee\u306e\u30e9\u30a6\u30f3\u30c9\u306e2\u3064\u306e \\(4\\) \u3082\u91cd\u8907\u3059\u308b\u90e8\u5206\u96c6\u5408\u3092\u751f\u6210\u3057\u307e\u3059\u3002</p> <p></p> <p> \u56f3 13-13 \u00a0 \u7b49\u3057\u3044\u8981\u7d20\u306b\u3088\u308b\u91cd\u8907\u90e8\u5206\u96c6\u5408 </p>"},{"location":"chapter_backtracking/subset_sum_problem/#1_1","title":"1. \u00a0 \u7b49\u5024\u8981\u7d20\u306e\u526a\u5b9a","text":"<p>\u3053\u306e\u554f\u984c\u3092\u89e3\u6c7a\u3059\u308b\u305f\u3081\u306b\u3001\u7b49\u3057\u3044\u8981\u7d20\u304c\u30e9\u30a6\u30f3\u30c9\u3054\u3068\u306b\u4e00\u5ea6\u3060\u3051\u9078\u629e\u3055\u308c\u308b\u3088\u3046\u306b\u5236\u9650\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u5b9f\u88c5\u306f\u975e\u5e38\u306b\u5de7\u5999\u3067\u3059\uff1a\u914d\u5217\u304c\u30bd\u30fc\u30c8\u3055\u308c\u3066\u3044\u308b\u305f\u3081\u3001\u7b49\u3057\u3044\u8981\u7d20\u306f\u96a3\u63a5\u3057\u3066\u3044\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u7279\u5b9a\u306e\u30e9\u30a6\u30f3\u30c9\u306e\u9078\u629e\u3067\u3001\u73fe\u5728\u306e\u8981\u7d20\u304c\u305d\u306e\u5de6\u5074\u306e\u8981\u7d20\u3068\u7b49\u3057\u3044\u5834\u5408\u3001\u305d\u308c\u306f\u3059\u3067\u306b\u9078\u629e\u3055\u308c\u3066\u3044\u308b\u3053\u3068\u3092\u610f\u5473\u3059\u308b\u305f\u3081\u3001\u73fe\u5728\u306e\u8981\u7d20\u3092\u76f4\u63a5\u30b9\u30ad\u30c3\u30d7\u3057\u307e\u3059\u3002</p> <p>\u540c\u6642\u306b\u3001\u3053\u306e\u554f\u984c\u3067\u306f\u5404\u914d\u5217\u8981\u7d20\u306f\u4e00\u5ea6\u3060\u3051\u9078\u629e\u3067\u304d\u308b\u3068\u898f\u5b9a\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u5e78\u3044\u3001\u5909\u6570 <code>start</code> \u3092\u4f7f\u7528\u3057\u3066\u3053\u306e\u5236\u7d04\u3082\u6e80\u305f\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\uff1a\u9078\u629e \\(x_{i}\\) \u3092\u884c\u3063\u305f\u5f8c\u3001\u6b21\u306e\u30e9\u30a6\u30f3\u30c9\u3092\u30a4\u30f3\u30c7\u30c3\u30af\u30b9 \\(i + 1\\) \u304b\u3089\u524d\u65b9\u306b\u958b\u59cb\u3059\u308b\u3088\u3046\u306b\u8a2d\u5b9a\u3057\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u91cd\u8907\u3059\u308b\u90e8\u5206\u96c6\u5408\u304c\u9664\u53bb\u3055\u308c\u308b\u3060\u3051\u3067\u306a\u304f\u3001\u8981\u7d20\u306e\u91cd\u8907\u9078\u629e\u3082\u56de\u907f\u3055\u308c\u307e\u3059\u3002</p>"},{"location":"chapter_backtracking/subset_sum_problem/#2_1","title":"2. \u00a0 \u30b3\u30fc\u30c9\u5b9f\u88c5","text":"PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig subset_sum_ii.py<pre><code>def backtrack(\n    state: list[int], target: int, choices: list[int], start: int, res: list[list[int]]\n):\n    \"\"\"\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\uff1a\u90e8\u5206\u96c6\u5408\u306e\u548c II\"\"\"\n    # \u90e8\u5206\u96c6\u5408\u306e\u548c\u304c target \u3068\u7b49\u3057\u3044\u3068\u304d\u3001\u89e3\u3092\u8a18\u9332\n    if target == 0:\n        res.append(list(state))\n        return\n    # \u3059\u3079\u3066\u306e\u9078\u629e\u80a2\u3092\u8d70\u67fb\n    # \u679d\u5208\u308a\u4e8c\uff1astart \u304b\u3089\u8d70\u67fb\u3092\u958b\u59cb\u3057\u3066\u91cd\u8907\u3059\u308b\u90e8\u5206\u96c6\u5408\u306e\u751f\u6210\u3092\u907f\u3051\u308b\n    # \u679d\u5208\u308a\u4e09\uff1astart \u304b\u3089\u8d70\u67fb\u3092\u958b\u59cb\u3057\u3066\u540c\u3058\u8981\u7d20\u306e\u91cd\u8907\u9078\u629e\u3092\u907f\u3051\u308b\n    for i in range(start, len(choices)):\n        # \u679d\u5208\u308a\u4e00\uff1a\u90e8\u5206\u96c6\u5408\u306e\u548c\u304c target \u3092\u8d85\u3048\u308b\u5834\u5408\u3001\u76f4\u3061\u306b\u30eb\u30fc\u30d7\u3092\u7d42\u4e86\n        # \u3053\u308c\u306f\u914d\u5217\u304c\u30bd\u30fc\u30c8\u3055\u308c\u3066\u304a\u308a\u3001\u5f8c\u306e\u8981\u7d20\u304c\u3088\u308a\u5927\u304d\u3044\u305f\u3081\u3001\u90e8\u5206\u96c6\u5408\u306e\u548c\u306f\u5fc5\u305a target \u3092\u8d85\u3048\u308b\u305f\u3081\n        if target - choices[i] &lt; 0:\n            break\n        # \u679d\u5208\u308a\u56db\uff1a\u8981\u7d20\u304c\u5de6\u306e\u8981\u7d20\u3068\u7b49\u3057\u3044\u5834\u5408\u3001\u691c\u7d22\u5206\u5c90\u304c\u91cd\u8907\u3057\u3066\u3044\u308b\u3053\u3068\u3092\u793a\u3059\u305f\u3081\u3001\u30b9\u30ad\u30c3\u30d7\n        if i &gt; start and choices[i] == choices[i - 1]:\n            continue\n        # \u8a66\u884c\uff1a\u9078\u629e\u3092\u884c\u3044\u3001target\u3001start \u3092\u66f4\u65b0\n        state.append(choices[i])\n        # \u6b21\u306e\u9078\u629e\u30e9\u30a6\u30f3\u30c9\u306b\u9032\u3080\n        backtrack(state, target - choices[i], choices, i + 1, res)\n        # \u64a4\u56de\uff1a\u9078\u629e\u3092\u53d6\u308a\u6d88\u3057\u3001\u524d\u306e\u72b6\u614b\u306b\u5fa9\u5143\n        state.pop()\n\ndef subset_sum_ii(nums: list[int], target: int) -&gt; list[list[int]]:\n    \"\"\"\u90e8\u5206\u96c6\u5408\u306e\u548c II \u3092\u89e3\u304f\"\"\"\n    state = []  # \u72b6\u614b\uff08\u90e8\u5206\u96c6\u5408\uff09\n    nums.sort()  # nums \u3092\u30bd\u30fc\u30c8\n    start = 0  # \u8d70\u67fb\u306e\u958b\u59cb\u70b9\n    res = []  # \u7d50\u679c\u30ea\u30b9\u30c8\uff08\u90e8\u5206\u96c6\u5408\u30ea\u30b9\u30c8\uff09\n    backtrack(state, target, nums, start, res)\n    return res\n</code></pre> subset_sum_ii.cpp<pre><code>/* \u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\uff1a\u90e8\u5206\u96c6\u5408\u548c II */\nvoid backtrack(vector&lt;int&gt; &amp;state, int target, vector&lt;int&gt; &amp;choices, int start, vector&lt;vector&lt;int&gt;&gt; &amp;res) {\n    // \u90e8\u5206\u96c6\u5408\u306e\u548c\u304ctarget\u3068\u7b49\u3057\u3044\u3068\u304d\u3001\u89e3\u3092\u8a18\u9332\n    if (target == 0) {\n        res.push_back(state);\n        return;\n    }\n    // \u3059\u3079\u3066\u306e\u9078\u629e\u80a2\u3092\u8d70\u67fb\n    // \u526a\u5b9a\u4e8c\uff1astart\u304b\u3089\u8d70\u67fb\u3092\u958b\u59cb\u3057\u3001\u91cd\u8907\u3059\u308b\u90e8\u5206\u96c6\u5408\u306e\u751f\u6210\u3092\u56de\u907f\n    // \u526a\u5b9a\u4e09\uff1astart\u304b\u3089\u8d70\u67fb\u3092\u958b\u59cb\u3057\u3001\u540c\u3058\u8981\u7d20\u306e\u7e70\u308a\u8fd4\u3057\u9078\u629e\u3092\u56de\u907f\n    for (int i = start; i &lt; choices.size(); i++) {\n        // \u526a\u5b9a\u4e00\uff1a\u90e8\u5206\u96c6\u5408\u306e\u548c\u304ctarget\u3092\u8d85\u3048\u305f\u5834\u5408\u3001\u5373\u5ea7\u306b\u30eb\u30fc\u30d7\u3092\u7d42\u4e86\n        // \u914d\u5217\u304c\u30bd\u30fc\u30c8\u3055\u308c\u3066\u3044\u308b\u305f\u3081\u3001\u5f8c\u306e\u8981\u7d20\u306f\u3055\u3089\u306b\u5927\u304d\u304f\u3001\u90e8\u5206\u96c6\u5408\u306e\u548c\u306f\u5fc5\u305atarget\u3092\u8d85\u3048\u308b\n        if (target - choices[i] &lt; 0) {\n            break;\n        }\n        // \u526a\u5b9a\u56db\uff1a\u8981\u7d20\u304c\u5de6\u306e\u8981\u7d20\u3068\u7b49\u3057\u3044\u5834\u5408\u3001\u691c\u7d22\u30d6\u30e9\u30f3\u30c1\u306e\u91cd\u8907\u3092\u793a\u3059\u306e\u3067\u30b9\u30ad\u30c3\u30d7\n        if (i &gt; start &amp;&amp; choices[i] == choices[i - 1]) {\n            continue;\n        }\n        // \u8a66\u884c\uff1a\u9078\u629e\u3092\u884c\u3044\u3001target\u3001start\u3092\u66f4\u65b0\n        state.push_back(choices[i]);\n        // \u6b21\u306e\u30e9\u30a6\u30f3\u30c9\u306e\u9078\u629e\u306b\u9032\u3080\n        backtrack(state, target - choices[i], choices, i + 1, res);\n        // \u56de\u9000\uff1a\u9078\u629e\u3092\u53d6\u308a\u6d88\u3057\u3001\u524d\u306e\u72b6\u614b\u306b\u5fa9\u5143\n        state.pop_back();\n    }\n}\n\n/* \u90e8\u5206\u96c6\u5408\u548c II \u3092\u89e3\u304f */\nvector&lt;vector&lt;int&gt;&gt; subsetSumII(vector&lt;int&gt; nums, int target) {\n    vector&lt;int&gt; state;              // \u72b6\u614b\uff08\u90e8\u5206\u96c6\u5408\uff09\n    sort(nums.begin(), nums.end()); // nums \u3092\u30bd\u30fc\u30c8\n    int start = 0;                  // \u8d70\u67fb\u306e\u958b\u59cb\u70b9\n    vector&lt;vector&lt;int&gt;&gt; res;        // \u7d50\u679c\u30ea\u30b9\u30c8\uff08\u90e8\u5206\u96c6\u5408\u30ea\u30b9\u30c8\uff09\n    backtrack(state, target, nums, start, res);\n    return res;\n}\n</code></pre> subset_sum_ii.java<pre><code>/* \u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\uff1a\u90e8\u5206\u96c6\u5408\u548c II */\nvoid backtrack(List&lt;Integer&gt; state, int target, int[] choices, int start, List&lt;List&lt;Integer&gt;&gt; res) {\n    // \u90e8\u5206\u96c6\u5408\u306e\u548c\u304ctarget\u3068\u7b49\u3057\u3044\u3068\u304d\u3001\u89e3\u3092\u8a18\u9332\n    if (target == 0) {\n        res.add(new ArrayList&lt;&gt;(state));\n        return;\n    }\n    // \u3059\u3079\u3066\u306e\u9078\u629e\u80a2\u3092\u8d70\u67fb\n    // \u526a\u5b9a\u4e8c\uff1astart\u304b\u3089\u8d70\u67fb\u3092\u958b\u59cb\u3057\u3001\u91cd\u8907\u3059\u308b\u90e8\u5206\u96c6\u5408\u306e\u751f\u6210\u3092\u56de\u907f\n    // \u526a\u5b9a\u4e09\uff1astart\u304b\u3089\u8d70\u67fb\u3092\u958b\u59cb\u3057\u3001\u540c\u3058\u8981\u7d20\u306e\u7e70\u308a\u8fd4\u3057\u9078\u629e\u3092\u56de\u907f\n    for (int i = start; i &lt; choices.length; i++) {\n        // \u526a\u5b9a\u4e00\uff1a\u90e8\u5206\u96c6\u5408\u306e\u548c\u304ctarget\u3092\u8d85\u3048\u305f\u5834\u5408\u3001\u5373\u5ea7\u306b\u30eb\u30fc\u30d7\u3092\u7d42\u4e86\n        // \u914d\u5217\u304c\u30bd\u30fc\u30c8\u3055\u308c\u3066\u3044\u308b\u305f\u3081\u3001\u5f8c\u306e\u8981\u7d20\u306f\u3055\u3089\u306b\u5927\u304d\u304f\u3001\u90e8\u5206\u96c6\u5408\u306e\u548c\u306f\u5fc5\u305atarget\u3092\u8d85\u3048\u308b\n        if (target - choices[i] &lt; 0) {\n            break;\n        }\n        // \u526a\u5b9a\u56db\uff1a\u8981\u7d20\u304c\u5de6\u306e\u8981\u7d20\u3068\u7b49\u3057\u3044\u5834\u5408\u3001\u691c\u7d22\u30d6\u30e9\u30f3\u30c1\u306e\u91cd\u8907\u3092\u793a\u3059\u306e\u3067\u30b9\u30ad\u30c3\u30d7\n        if (i &gt; start &amp;&amp; choices[i] == choices[i - 1]) {\n            continue;\n        }\n        // \u8a66\u884c\uff1a\u9078\u629e\u3092\u884c\u3044\u3001target\u3001start\u3092\u66f4\u65b0\n        state.add(choices[i]);\n        // \u6b21\u306e\u30e9\u30a6\u30f3\u30c9\u306e\u9078\u629e\u306b\u9032\u3080\n        backtrack(state, target - choices[i], choices, i + 1, res);\n        // \u56de\u9000\uff1a\u9078\u629e\u3092\u53d6\u308a\u6d88\u3057\u3001\u524d\u306e\u72b6\u614b\u306b\u5fa9\u5143\n        state.remove(state.size() - 1);\n    }\n}\n\n/* \u90e8\u5206\u96c6\u5408\u548c II \u3092\u89e3\u304f */\nList&lt;List&lt;Integer&gt;&gt; subsetSumII(int[] nums, int target) {\n    List&lt;Integer&gt; state = new ArrayList&lt;&gt;(); // \u72b6\u614b\uff08\u90e8\u5206\u96c6\u5408\uff09\n    Arrays.sort(nums); // nums \u3092\u30bd\u30fc\u30c8\n    int start = 0; // \u8d70\u67fb\u306e\u958b\u59cb\u70b9\n    List&lt;List&lt;Integer&gt;&gt; res = new ArrayList&lt;&gt;(); // \u7d50\u679c\u30ea\u30b9\u30c8\uff08\u90e8\u5206\u96c6\u5408\u30ea\u30b9\u30c8\uff09\n    backtrack(state, target, nums, start, res);\n    return res;\n}\n</code></pre> subset_sum_ii.cs<pre><code>[class]{subset_sum_ii}-[func]{Backtrack}\n\n[class]{subset_sum_ii}-[func]{SubsetSumII}\n</code></pre> subset_sum_ii.go<pre><code>[class]{}-[func]{backtrackSubsetSumII}\n\n[class]{}-[func]{subsetSumII}\n</code></pre> subset_sum_ii.swift<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subsetSumII}\n</code></pre> subset_sum_ii.js<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subsetSumII}\n</code></pre> subset_sum_ii.ts<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subsetSumII}\n</code></pre> subset_sum_ii.dart<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subsetSumII}\n</code></pre> subset_sum_ii.rs<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subset_sum_ii}\n</code></pre> subset_sum_ii.c<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subsetSumII}\n</code></pre> subset_sum_ii.kt<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subsetSumII}\n</code></pre> subset_sum_ii.rb<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subset_sum_ii}\n</code></pre> subset_sum_ii.zig<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{subsetSumII}\n</code></pre> <p>\u4ee5\u4e0b\u306e\u56f3\u306f\u3001\u914d\u5217 \\([4, 4, 5]\\) \u3068\u30bf\u30fc\u30b2\u30c3\u30c8\u8981\u7d20 \\(9\\) \u306e\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30d7\u30ed\u30bb\u30b9\u3092\u793a\u3057\u30014\u7a2e\u985e\u306e\u526a\u5b9a\u64cd\u4f5c\u304c\u542b\u307e\u308c\u3066\u3044\u307e\u3059\u3002\u56f3\u3068\u30b3\u30fc\u30c9\u306e\u30b3\u30e1\u30f3\u30c8\u3092\u7d44\u307f\u5408\u308f\u305b\u3066\u3001\u691c\u7d22\u30d7\u30ed\u30bb\u30b9\u5168\u4f53\u3068\u5404\u7a2e\u985e\u306e\u526a\u5b9a\u64cd\u4f5c\u306e\u52d5\u4f5c\u3092\u7406\u89e3\u3057\u3066\u304f\u3060\u3055\u3044\u3002</p> <p></p> <p> \u56f3 13-14 \u00a0 \u90e8\u5206\u96c6\u5408\u548c II \u306e\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30d7\u30ed\u30bb\u30b9 </p>"},{"location":"chapter_backtracking/summary/","title":"13.5 \u00a0 \u307e\u3068\u3081","text":""},{"location":"chapter_backtracking/summary/#1","title":"1. \u00a0 \u91cd\u8981\u306a\u5fa9\u7fd2","text":"<ul> <li>\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u672c\u8cea\u306f\u5168\u6570\u63a2\u7d22\u3067\u3059\u3002\u89e3\u7a7a\u9593\u306e\u6df1\u3055\u512a\u5148\u8d70\u67fb\u3092\u5b9f\u884c\u3059\u308b\u3053\u3068\u3067\u6761\u4ef6\u3092\u6e80\u305f\u3059\u89e3\u3092\u6c42\u3081\u307e\u3059\u3002\u691c\u7d22\u4e2d\u306b\u6e80\u8db3\u306e\u3044\u304f\u89e3\u304c\u898b\u3064\u304b\u3063\u305f\u5834\u5408\u3001\u305d\u308c\u3092\u8a18\u9332\u3057\u3001\u3059\u3079\u3066\u306e\u89e3\u304c\u898b\u3064\u304b\u308b\u304b\u8d70\u67fb\u304c\u5b8c\u4e86\u3059\u308b\u307e\u3067\u7d9a\u3051\u307e\u3059\u3002</li> <li>\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u691c\u7d22\u30d7\u30ed\u30bb\u30b9\u306b\u306f\u8a66\u884c\u3068\u5f8c\u9000\u304c\u542b\u307e\u308c\u307e\u3059\u3002\u6df1\u3055\u512a\u5148\u63a2\u7d22\u3092\u4f7f\u7528\u3057\u3066\u69d8\u3005\u306a\u9078\u629e\u3092\u63a2\u7d22\u3057\u3001\u9078\u629e\u304c\u5236\u7d04\u3092\u6e80\u305f\u3055\u306a\u3044\u5834\u5408\u3001\u524d\u306e\u9078\u629e\u3092\u53d6\u308a\u6d88\u3057\u307e\u3059\u3002\u305d\u3057\u3066\u524d\u306e\u72b6\u614b\u306b\u623b\u3063\u3066\u4ed6\u306e\u30aa\u30d7\u30b7\u30e7\u30f3\u3092\u8a66\u3057\u7d9a\u3051\u307e\u3059\u3002\u8a66\u884c\u3068\u5f8c\u9000\u306f\u53cd\u5bfe\u65b9\u5411\u306e\u64cd\u4f5c\u3067\u3059\u3002</li> <li>\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u554f\u984c\u306b\u306f\u901a\u5e38\u8907\u6570\u306e\u5236\u7d04\u304c\u542b\u307e\u308c\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u5236\u7d04\u306f\u526a\u5b9a\u64cd\u4f5c\u3092\u5b9f\u884c\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002\u526a\u5b9a\u306f\u4e0d\u8981\u306a\u691c\u7d22\u5206\u5c90\u3092\u4e8b\u524d\u306b\u7d42\u4e86\u3057\u3001\u691c\u7d22\u52b9\u7387\u3092\u5927\u5e45\u306b\u5411\u4e0a\u3055\u305b\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002</li> <li>\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u4e3b\u306b\u691c\u7d22\u554f\u984c\u3068\u5236\u7d04\u6e80\u8db3\u554f\u984c\u3092\u89e3\u6c7a\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u7d44\u307f\u5408\u308f\u305b\u6700\u9069\u5316\u554f\u984c\u306f\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u3092\u4f7f\u7528\u3057\u3066\u89e3\u6c7a\u3067\u304d\u307e\u3059\u304c\u3001\u591a\u304f\u306e\u5834\u5408\u3001\u3088\u308a\u52b9\u7387\u7684\u307e\u305f\u306f\u52b9\u679c\u7684\u306a\u89e3\u6c7a\u65b9\u6cd5\u304c\u5229\u7528\u53ef\u80fd\u3067\u3059\u3002</li> <li>\u9806\u5217\u554f\u984c\u306f\u3001\u4e0e\u3048\u3089\u308c\u305f\u96c6\u5408\u306e\u8981\u7d20\u306e\u3059\u3079\u3066\u306e\u53ef\u80fd\u306a\u9806\u5217\u3092\u691c\u7d22\u3059\u308b\u3053\u3068\u3092\u76ee\u7684\u3068\u3057\u307e\u3059\u3002\u5404\u8981\u7d20\u304c\u9078\u629e\u3055\u308c\u305f\u304b\u3069\u3046\u304b\u3092\u8a18\u9332\u3059\u308b\u305f\u3081\u306b\u914d\u5217\u3092\u4f7f\u7528\u3057\u3001\u540c\u3058\u8981\u7d20\u306e\u91cd\u8907\u9078\u629e\u3092\u907f\u3051\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u5404\u8981\u7d20\u304c\u4e00\u5ea6\u3060\u3051\u9078\u629e\u3055\u308c\u308b\u3053\u3068\u304c\u4fdd\u8a3c\u3055\u308c\u307e\u3059\u3002</li> <li>\u9806\u5217\u554f\u984c\u3067\u306f\u3001\u96c6\u5408\u306b\u91cd\u8907\u8981\u7d20\u304c\u542b\u307e\u308c\u3066\u3044\u308b\u5834\u5408\u3001\u6700\u7d42\u7d50\u679c\u306b\u91cd\u8907\u9806\u5217\u304c\u542b\u307e\u308c\u307e\u3059\u3002\u540c\u4e00\u8981\u7d20\u304c\u5404\u30e9\u30a6\u30f3\u30c9\u3067\u4e00\u5ea6\u3060\u3051\u9078\u629e\u3067\u304d\u308b\u3088\u3046\u306b\u5236\u9650\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u3001\u3053\u308c\u306f\u901a\u5e38\u30cf\u30c3\u30b7\u30e5\u30bb\u30c3\u30c8\u3092\u4f7f\u7528\u3057\u3066\u5b9f\u88c5\u3055\u308c\u307e\u3059\u3002</li> <li>\u90e8\u5206\u96c6\u5408\u548c\u554f\u984c\u306f\u3001\u4e0e\u3048\u3089\u308c\u305f\u96c6\u5408\u3067\u30bf\u30fc\u30b2\u30c3\u30c8\u5024\u306b\u5408\u8a08\u3059\u308b\u5168\u3066\u306e\u90e8\u5206\u96c6\u5408\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u3092\u76ee\u7684\u3068\u3057\u307e\u3059\u3002\u96c6\u5408\u306f\u8981\u7d20\u306e\u9806\u5e8f\u3092\u533a\u5225\u3057\u307e\u305b\u3093\u304c\u3001\u691c\u7d22\u30d7\u30ed\u30bb\u30b9\u3067\u306f\u91cd\u8907\u3059\u308b\u90e8\u5206\u96c6\u5408\u304c\u751f\u6210\u3055\u308c\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u304c\u7570\u306a\u308b\u8981\u7d20\u9806\u5e8f\u3092\u72ec\u7279\u306e\u30d1\u30b9\u3068\u3057\u3066\u63a2\u7d22\u3059\u308b\u305f\u3081\u306b\u767a\u751f\u3057\u307e\u3059\u3002\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u306e\u524d\u306b\u3001\u30c7\u30fc\u30bf\u3092\u30bd\u30fc\u30c8\u3057\u3001\u5404\u30e9\u30a6\u30f3\u30c9\u306e\u8d70\u67fb\u306e\u958b\u59cb\u70b9\u3092\u793a\u3059\u5909\u6570\u3092\u8a2d\u5b9a\u3057\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u91cd\u8907\u3059\u308b\u90e8\u5206\u96c6\u5408\u3092\u751f\u6210\u3059\u308b\u691c\u7d22\u5206\u5c90\u3092\u526a\u5b9a\u3067\u304d\u307e\u3059\u3002</li> <li>\u90e8\u5206\u96c6\u5408\u548c\u554f\u984c\u3067\u306f\u3001\u914d\u5217\u5185\u306e\u7b49\u3057\u3044\u8981\u7d20\u306f\u91cd\u8907\u96c6\u5408\u3092\u751f\u6210\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002\u914d\u5217\u304c\u3059\u3067\u306b\u30bd\u30fc\u30c8\u3055\u308c\u3066\u3044\u308b\u3068\u3044\u3046\u524d\u63d0\u6761\u4ef6\u3092\u4f7f\u7528\u3057\u3066\u3001\u96a3\u63a5\u3059\u308b\u8981\u7d20\u304c\u7b49\u3057\u3044\u304b\u3069\u3046\u304b\u3092\u5224\u5b9a\u3059\u308b\u3053\u3068\u3067\u526a\u5b9a\u3092\u884c\u3044\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u7b49\u3057\u3044\u8981\u7d20\u304c\u30e9\u30a6\u30f3\u30c9\u3054\u3068\u306b\u4e00\u5ea6\u3060\u3051\u9078\u629e\u3055\u308c\u308b\u3053\u3068\u304c\u4fdd\u8a3c\u3055\u308c\u307e\u3059\u3002</li> <li>\\(n\\) \u30af\u30a4\u30fc\u30f3\u554f\u984c\u306f\u30012\u3064\u306e\u30af\u30a4\u30fc\u30f3\u304c\u4e92\u3044\u306b\u653b\u6483\u3067\u304d\u306a\u3044\u3088\u3046\u306b \\(n \\times n\\) \u306e\u30c1\u30a7\u30b9\u30dc\u30fc\u30c9\u306b \\(n\\) \u500b\u306e\u30af\u30a4\u30fc\u30f3\u3092\u914d\u7f6e\u3059\u308b\u65b9\u6848\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u3092\u76ee\u7684\u3068\u3057\u307e\u3059\u3002\u554f\u984c\u306e\u5236\u7d04\u306b\u306f\u884c\u5236\u7d04\u3001\u5217\u5236\u7d04\u3001\u304a\u3088\u3073\u4e3b\u5bfe\u89d2\u7dda\u3068\u526f\u5bfe\u89d2\u7dda\u306e\u5236\u7d04\u304c\u542b\u307e\u308c\u307e\u3059\u3002\u884c\u5236\u7d04\u3092\u6e80\u305f\u3059\u305f\u3081\u306b\u3001\u884c\u3054\u3068\u306b1\u3064\u306e\u30af\u30a4\u30fc\u30f3\u3092\u914d\u7f6e\u3059\u308b\u6226\u7565\u3092\u63a1\u7528\u3057\u3001\u5404\u884c\u306b1\u3064\u306e\u30af\u30a4\u30fc\u30f3\u304c\u914d\u7f6e\u3055\u308c\u308b\u3053\u3068\u3092\u4fdd\u8a3c\u3057\u307e\u3059\u3002</li> <li>\u5217\u5236\u7d04\u3068\u5bfe\u89d2\u7dda\u5236\u7d04\u306e\u51e6\u7406\u306f\u4f3c\u3066\u3044\u307e\u3059\u3002\u5217\u5236\u7d04\u306b\u3064\u3044\u3066\u306f\u3001\u5404\u5217\u306b\u30af\u30a4\u30fc\u30f3\u304c\u3042\u308b\u304b\u3069\u3046\u304b\u3092\u8a18\u9332\u3059\u308b\u914d\u5217\u3092\u4f7f\u7528\u3057\u3001\u9078\u629e\u3055\u308c\u305f\u30bb\u30eb\u304c\u5408\u6cd5\u304b\u3069\u3046\u304b\u3092\u793a\u3057\u307e\u3059\u3002\u5bfe\u89d2\u7dda\u5236\u7d04\u306b\u3064\u3044\u3066\u306f\u30012\u3064\u306e\u914d\u5217\u3092\u4f7f\u7528\u3057\u3066\u4e3b\u5bfe\u89d2\u7dda\u3068\u526f\u5bfe\u89d2\u7dda\u306b\u305d\u308c\u305e\u308c\u30af\u30a4\u30fc\u30f3\u306e\u5b58\u5728\u3092\u8a18\u9332\u3057\u307e\u3059\u3002\u8ab2\u984c\u306f\u3001\u540c\u3058\u4e3b\u5bfe\u89d2\u7dda\u307e\u305f\u306f\u526f\u5bfe\u89d2\u7dda\u4e0a\u306e\u30bb\u30eb\u306e\u884c\u3068\u5217\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u9593\u306e\u95a2\u4fc2\u3092\u6c7a\u5b9a\u3059\u308b\u3053\u3068\u3067\u3059\u3002</li> </ul>"},{"location":"chapter_backtracking/summary/#2-q-a","title":"2. \u00a0 Q &amp; A","text":"<p>Q: \u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u3068\u518d\u5e30\u306e\u95a2\u4fc2\u3092\u3069\u306e\u3088\u3046\u306b\u7406\u89e3\u3059\u308c\u3070\u3088\u3044\u3067\u3059\u304b\uff1f</p> <p>\u5168\u4f53\u7684\u306b\u3001\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u306f\u300c\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u6226\u7565\u300d\u3067\u3042\u308a\u3001\u518d\u5e30\u306f\u3088\u308a\u300c\u30c4\u30fc\u30eb\u300d\u3067\u3059\u3002</p> <ul> <li>\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u901a\u5e38\u518d\u5e30\u306b\u57fa\u3065\u3044\u3066\u3044\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u306f\u518d\u5e30\u306e\u5fdc\u7528\u30b7\u30ca\u30ea\u30aa\u306e\u4e00\u3064\u3067\u3042\u308a\u3001\u7279\u306b\u691c\u7d22\u554f\u984c\u306b\u304a\u3044\u3066\u3067\u3059\u3002</li> <li>\u518d\u5e30\u306e\u69cb\u9020\u306f\u300c\u90e8\u5206\u554f\u984c\u5206\u89e3\u300d\u306e\u554f\u984c\u89e3\u6c7a\u30d1\u30e9\u30c0\u30a4\u30e0\u3092\u53cd\u6620\u3057\u307e\u3059\u3002\u5206\u5272\u7d71\u6cbb\u3001\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u3001\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\uff08\u30e1\u30e2\u5316\u518d\u5e30\uff09\u3092\u542b\u3080\u554f\u984c\u306e\u89e3\u6c7a\u3067\u3088\u304f\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002</li> </ul>"},{"location":"chapter_computational_complexity/","title":"\u7b2c 2 \u7ae0 \u00a0 \u8907\u96d1\u5ea6\u89e3\u6790","text":"<p>Abstract</p> <p>\u8907\u96d1\u5ea6\u89e3\u6790\u306f\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5e83\u5927\u306a\u5b87\u5b99\u306b\u304a\u3051\u308b\u6642\u7a7a\u306e\u30ca\u30d3\u30b2\u30fc\u30bf\u30fc\u306e\u3088\u3046\u306a\u3082\u306e\u3067\u3059\u3002</p> <p>\u6642\u9593\u3068\u7a7a\u9593\u306e\u6b21\u5143\u3092\u3088\u308a\u6df1\u304f\u63a2\u6c42\u3057\u3001\u3088\u308a\u512a\u96c5\u306a\u89e3\u6c7a\u7b56\u3092\u6c42\u3081\u308b\u305f\u3081\u306e\u30ac\u30a4\u30c9\u3068\u306a\u308a\u307e\u3059\u3002</p>"},{"location":"chapter_computational_complexity/#_1","title":"\u7ae0\u306e\u5185\u5bb9","text":"<ul> <li>2.1 \u00a0 \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u52b9\u7387\u8a55\u4fa1</li> <li>2.2 \u00a0 \u53cd\u5fa9\u3068\u518d\u5e30</li> <li>2.3 \u00a0 \u6642\u9593\u8a08\u7b97\u91cf</li> <li>2.4 \u00a0 \u7a7a\u9593\u8a08\u7b97\u91cf</li> <li>2.5 \u00a0 \u307e\u3068\u3081</li> </ul>"},{"location":"chapter_computational_complexity/iteration_and_recursion/","title":"2.2 \u00a0 \u53cd\u5fa9\u3068\u518d\u5e30","text":"<p>\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306b\u304a\u3044\u3066\u3001\u30bf\u30b9\u30af\u306e\u7e70\u308a\u8fd4\u3057\u5b9f\u884c\u306f\u975e\u5e38\u306b\u4e00\u822c\u7684\u3067\u3042\u308a\u3001\u8907\u96d1\u5ea6\u306e\u5206\u6790\u3068\u5bc6\u63a5\u306b\u95a2\u4fc2\u3057\u3066\u3044\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u6642\u9593\u8a08\u7b97\u91cf\u3068\u7a7a\u9593\u8a08\u7b97\u91cf\u306e\u6982\u5ff5\u3092\u8a73\u3057\u304f\u5b66\u3076\u524d\u306b\u3001\u307e\u305a\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u3067\u7e70\u308a\u8fd4\u3057\u30bf\u30b9\u30af\u3092\u5b9f\u88c5\u3059\u308b\u65b9\u6cd5\u3092\u63a2\u7a76\u3057\u307e\u3057\u3087\u3046\u3002\u3053\u308c\u306b\u306f\u30012\u3064\u306e\u57fa\u672c\u7684\u306a\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u5236\u5fa1\u69cb\u9020\u3067\u3042\u308b\u53cd\u5fa9\u3068\u518d\u5e30\u306e\u7406\u89e3\u304c\u542b\u307e\u308c\u307e\u3059\u3002</p>"},{"location":"chapter_computational_complexity/iteration_and_recursion/#221","title":"2.2.1 \u00a0 \u53cd\u5fa9","text":"<p>\u53cd\u5fa9\u306f\u3001\u30bf\u30b9\u30af\u3092\u7e70\u308a\u8fd4\u3057\u5b9f\u884c\u3059\u308b\u305f\u3081\u306e\u5236\u5fa1\u69cb\u9020\u3067\u3059\u3002\u53cd\u5fa9\u3067\u306f\u3001\u30d7\u30ed\u30b0\u30e9\u30e0\u306f\u7279\u5b9a\u306e\u6761\u4ef6\u304c\u6e80\u305f\u3055\u308c\u3066\u3044\u308b\u9650\u308a\u30b3\u30fc\u30c9\u30d6\u30ed\u30c3\u30af\u3092\u7e70\u308a\u8fd4\u3057\u5b9f\u884c\u3057\u3001\u3053\u306e\u6761\u4ef6\u304c\u6e80\u305f\u3055\u308c\u306a\u304f\u306a\u308b\u307e\u3067\u7d9a\u3051\u307e\u3059\u3002</p>"},{"location":"chapter_computational_complexity/iteration_and_recursion/#1-for","title":"1. \u00a0 for\u30eb\u30fc\u30d7","text":"<p><code>for</code>\u30eb\u30fc\u30d7\u306f\u53cd\u5fa9\u306e\u6700\u3082\u4e00\u822c\u7684\u306a\u5f62\u5f0f\u306e1\u3064\u3067\u3042\u308a\u3001\u53cd\u5fa9\u56de\u6570\u304c\u4e8b\u524d\u306b\u5206\u304b\u3063\u3066\u3044\u308b\u5834\u5408\u306b\u7279\u306b\u9069\u3057\u3066\u3044\u307e\u3059\u3002</p> <p>\u4ee5\u4e0b\u306e\u95a2\u6570\u306f<code>for</code>\u30eb\u30fc\u30d7\u3092\u4f7f\u7528\u3057\u3066\\(1 + 2 + \\dots + n\\)\u306e\u5408\u8a08\u3092\u5b9f\u884c\u3057\u3001\u5408\u8a08\u3092\u5909\u6570<code>res</code>\u306b\u683c\u7d0d\u3057\u307e\u3059\u3002Python\u3067\u306f\u3001<code>range(a, b)</code>\u306f<code>a</code>\u3092\u542b\u307f<code>b</code>\u3092\u9664\u304f\u533a\u9593\u3092\u4f5c\u6210\u3059\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u3064\u307e\u308a\u3001\\(a\\)\u304b\u3089\\(b\u22121\\)\u307e\u3067\u306e\u7bc4\u56f2\u3067\u53cd\u5fa9\u3057\u307e\u3059\u3002</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig iteration.py<pre><code>def for_loop(n: int) -&gt; int:\n    \"\"\"for\u30eb\u30fc\u30d7\"\"\"\n    res = 0\n    # 1, 2, ..., n-1, n \u306e\u5408\u8a08\u3092\u30eb\u30fc\u30d7\n    for i in range(1, n + 1):\n        res += i\n    return res\n</code></pre> iteration.cpp<pre><code>/* for \u30eb\u30fc\u30d7 */\nint forLoop(int n) {\n    int res = 0;\n    // 1, 2, ..., n-1, n \u306e\u5408\u8a08\u3092\u30eb\u30fc\u30d7\u8a08\u7b97\n    for (int i = 1; i &lt;= n; ++i) {\n        res += i;\n    }\n    return res;\n}\n</code></pre> iteration.java<pre><code>/* for \u30eb\u30fc\u30d7 */\nint forLoop(int n) {\n    int res = 0;\n    // 1, 2, ..., n-1, n \u306e\u5408\u8a08\u3092\u30eb\u30fc\u30d7\u8a08\u7b97\n    for (int i = 1; i &lt;= n; i++) {\n        res += i;\n    }\n    return res;\n}\n</code></pre> iteration.cs<pre><code>[class]{iteration}-[func]{ForLoop}\n</code></pre> iteration.go<pre><code>[class]{}-[func]{forLoop}\n</code></pre> iteration.swift<pre><code>[class]{}-[func]{forLoop}\n</code></pre> iteration.js<pre><code>[class]{}-[func]{forLoop}\n</code></pre> iteration.ts<pre><code>[class]{}-[func]{forLoop}\n</code></pre> iteration.dart<pre><code>[class]{}-[func]{forLoop}\n</code></pre> iteration.rs<pre><code>[class]{}-[func]{for_loop}\n</code></pre> iteration.c<pre><code>[class]{}-[func]{forLoop}\n</code></pre> iteration.kt<pre><code>[class]{}-[func]{forLoop}\n</code></pre> iteration.rb<pre><code>[class]{}-[func]{for_loop}\n</code></pre> iteration.zig<pre><code>[class]{}-[func]{forLoop}\n</code></pre> <p>\u4ee5\u4e0b\u306e\u56f3\u306f\u3053\u306e\u5408\u8a08\u95a2\u6570\u3092\u8868\u3057\u3066\u3044\u307e\u3059\u3002</p> <p></p> <p> \u56f3 2-1 \u00a0 Flowchart of the sum function </p> <p>\u3053\u306e\u5408\u8a08\u95a2\u6570\u3067\u306e\u64cd\u4f5c\u6570\u306f\u5165\u529b\u30c7\u30fc\u30bf\u306e\u30b5\u30a4\u30ba\\(n\\)\u306b\u6bd4\u4f8b\u3059\u308b\u3001\u3064\u307e\u308a\u7dda\u5f62\u95a2\u4fc2\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u300c\u7dda\u5f62\u95a2\u4fc2\u300d\u3053\u305d\u304c\u6642\u9593\u8a08\u7b97\u91cf\u304c\u8a18\u8ff0\u3059\u308b\u3082\u306e\u3067\u3059\u3002\u3053\u306e\u30c8\u30d4\u30c3\u30af\u306b\u3064\u3044\u3066\u306f\u6b21\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u3067\u8a73\u3057\u304f\u8aac\u660e\u3057\u307e\u3059\u3002</p>"},{"location":"chapter_computational_complexity/iteration_and_recursion/#2-while","title":"2. \u00a0 while\u30eb\u30fc\u30d7","text":"<p><code>for</code>\u30eb\u30fc\u30d7\u3068\u540c\u69d8\u306b\u3001<code>while</code>\u30eb\u30fc\u30d7\u306f\u53cd\u5fa9\u3092\u5b9f\u88c5\u3059\u308b\u305f\u3081\u306e\u3082\u30461\u3064\u306e\u30a2\u30d7\u30ed\u30fc\u30c1\u3067\u3059\u3002<code>while</code>\u30eb\u30fc\u30d7\u3067\u306f\u3001\u30d7\u30ed\u30b0\u30e9\u30e0\u306f\u5404\u53cd\u5fa9\u306e\u958b\u59cb\u6642\u306b\u6761\u4ef6\u3092\u30c1\u30a7\u30c3\u30af\u3057\u3001\u6761\u4ef6\u304c\u771f\u306e\u5834\u5408\u306f\u5b9f\u884c\u3092\u7d99\u7d9a\u3057\u3001\u305d\u3046\u3067\u306a\u3051\u308c\u3070\u30eb\u30fc\u30d7\u3092\u7d42\u4e86\u3057\u307e\u3059\u3002</p> <p>\u4ee5\u4e0b\u3067\u306f<code>while</code>\u30eb\u30fc\u30d7\u3092\u4f7f\u7528\u3057\u3066\u5408\u8a08\\(1 + 2 + \\dots + n\\)\u3092\u5b9f\u88c5\u3057\u307e\u3059\u3002</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig iteration.py<pre><code>def while_loop(n: int) -&gt; int:\n    \"\"\"while\u30eb\u30fc\u30d7\"\"\"\n    res = 0\n    i = 1  # \u6761\u4ef6\u5909\u6570\u3092\u521d\u671f\u5316\n    # 1, 2, ..., n-1, n \u306e\u5408\u8a08\u3092\u30eb\u30fc\u30d7\n    while i &lt;= n:\n        res += i\n        i += 1  # \u6761\u4ef6\u5909\u6570\u3092\u66f4\u65b0\n    return res\n</code></pre> iteration.cpp<pre><code>/* while \u30eb\u30fc\u30d7 */\nint whileLoop(int n) {\n    int res = 0;\n    int i = 1; // \u6761\u4ef6\u5909\u6570\u3092\u521d\u671f\u5316\n    // 1, 2, ..., n-1, n \u306e\u5408\u8a08\u3092\u30eb\u30fc\u30d7\u8a08\u7b97\n    while (i &lt;= n) {\n        res += i;\n        i++; // \u6761\u4ef6\u5909\u6570\u3092\u66f4\u65b0\n    }\n    return res;\n}\n</code></pre> iteration.java<pre><code>/* while \u30eb\u30fc\u30d7 */\nint whileLoop(int n) {\n    int res = 0;\n    int i = 1; // \u6761\u4ef6\u5909\u6570\u3092\u521d\u671f\u5316\n    // 1, 2, ..., n-1, n \u306e\u5408\u8a08\u3092\u30eb\u30fc\u30d7\u8a08\u7b97\n    while (i &lt;= n) {\n        res += i;\n        i++; // \u6761\u4ef6\u5909\u6570\u3092\u66f4\u65b0\n    }\n    return res;\n}\n</code></pre> iteration.cs<pre><code>[class]{iteration}-[func]{WhileLoop}\n</code></pre> iteration.go<pre><code>[class]{}-[func]{whileLoop}\n</code></pre> iteration.swift<pre><code>[class]{}-[func]{whileLoop}\n</code></pre> iteration.js<pre><code>[class]{}-[func]{whileLoop}\n</code></pre> iteration.ts<pre><code>[class]{}-[func]{whileLoop}\n</code></pre> iteration.dart<pre><code>[class]{}-[func]{whileLoop}\n</code></pre> iteration.rs<pre><code>[class]{}-[func]{while_loop}\n</code></pre> iteration.c<pre><code>[class]{}-[func]{whileLoop}\n</code></pre> iteration.kt<pre><code>[class]{}-[func]{whileLoop}\n</code></pre> iteration.rb<pre><code>[class]{}-[func]{while_loop}\n</code></pre> iteration.zig<pre><code>[class]{}-[func]{whileLoop}\n</code></pre> <p><code>while</code>\u30eb\u30fc\u30d7\u306f<code>for</code>\u30eb\u30fc\u30d7\u3088\u308a\u3082\u67d4\u8edf\u6027\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u7279\u306b\u3001\u6761\u4ef6\u5909\u6570\u306e\u30ab\u30b9\u30bf\u30e0\u521d\u671f\u5316\u3068\u5404\u30b9\u30c6\u30c3\u30d7\u3067\u306e\u5909\u66f4\u304c\u53ef\u80fd\u3067\u3059\u3002</p> <p>\u4f8b\u3048\u3070\u3001\u4ee5\u4e0b\u306e\u30b3\u30fc\u30c9\u3067\u306f\u3001\u6761\u4ef6\u5909\u6570\\(i\\)\u304c\u5404\u30e9\u30a6\u30f3\u30c9\u30672\u56de\u66f4\u65b0\u3055\u308c\u307e\u3059\u304c\u3001\u3053\u308c\u306f<code>for</code>\u30eb\u30fc\u30d7\u3067\u306f\u5b9f\u88c5\u304c\u4e0d\u4fbf\u3067\u3059\u3002</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig iteration.py<pre><code>def while_loop_ii(n: int) -&gt; int:\n    \"\"\"while\u30eb\u30fc\u30d7\uff082\u3064\u306e\u66f4\u65b0\uff09\"\"\"\n    res = 0\n    i = 1  # \u6761\u4ef6\u5909\u6570\u3092\u521d\u671f\u5316\n    # 1, 4, 10, ... \u306e\u5408\u8a08\u3092\u30eb\u30fc\u30d7\n    while i &lt;= n:\n        res += i\n        # \u6761\u4ef6\u5909\u6570\u3092\u66f4\u65b0\n        i += 1\n        i *= 2\n    return res\n</code></pre> iteration.cpp<pre><code>/* while \u30eb\u30fc\u30d7\uff082\u3064\u306e\u66f4\u65b0\uff09 */\nint whileLoopII(int n) {\n    int res = 0;\n    int i = 1; // \u6761\u4ef6\u5909\u6570\u3092\u521d\u671f\u5316\n    // 1, 4, 10, ... \u306e\u5408\u8a08\u3092\u30eb\u30fc\u30d7\u8a08\u7b97\n    while (i &lt;= n) {\n        res += i;\n        // \u6761\u4ef6\u5909\u6570\u3092\u66f4\u65b0\n        i++;\n        i *= 2;\n    }\n    return res;\n}\n</code></pre> iteration.java<pre><code>/* while \u30eb\u30fc\u30d7\uff082\u3064\u306e\u66f4\u65b0\uff09 */\nint whileLoopII(int n) {\n    int res = 0;\n    int i = 1; // \u6761\u4ef6\u5909\u6570\u3092\u521d\u671f\u5316\n    // 1, 4, 10, ... \u306e\u5408\u8a08\u3092\u30eb\u30fc\u30d7\u8a08\u7b97\n    while (i &lt;= n) {\n        res += i;\n        // \u6761\u4ef6\u5909\u6570\u3092\u66f4\u65b0\n        i++;\n        i *= 2;\n    }\n    return res;\n}\n</code></pre> iteration.cs<pre><code>[class]{iteration}-[func]{WhileLoopII}\n</code></pre> iteration.go<pre><code>[class]{}-[func]{whileLoopII}\n</code></pre> iteration.swift<pre><code>[class]{}-[func]{whileLoopII}\n</code></pre> iteration.js<pre><code>[class]{}-[func]{whileLoopII}\n</code></pre> iteration.ts<pre><code>[class]{}-[func]{whileLoopII}\n</code></pre> iteration.dart<pre><code>[class]{}-[func]{whileLoopII}\n</code></pre> iteration.rs<pre><code>[class]{}-[func]{while_loop_ii}\n</code></pre> iteration.c<pre><code>[class]{}-[func]{whileLoopII}\n</code></pre> iteration.kt<pre><code>[class]{}-[func]{whileLoopII}\n</code></pre> iteration.rb<pre><code>[class]{}-[func]{while_loop_ii}\n</code></pre> iteration.zig<pre><code>[class]{}-[func]{whileLoopII}\n</code></pre> <p>\u5168\u4f53\u7684\u306b\u3001<code>for</code>\u30eb\u30fc\u30d7\u306f\u3088\u308a\u7c21\u6f54\u3067\u3001<code>while</code>\u30eb\u30fc\u30d7\u306f\u3088\u308a\u67d4\u8edf\u3067\u3059\u3002\u3069\u3061\u3089\u3082\u53cd\u5fa9\u69cb\u9020\u3092\u5b9f\u88c5\u3067\u304d\u307e\u3059\u3002\u3069\u3061\u3089\u3092\u4f7f\u7528\u3059\u308b\u304b\u306f\u3001\u554f\u984c\u306e\u5177\u4f53\u7684\u306a\u8981\u4ef6\u306b\u57fa\u3065\u3044\u3066\u6c7a\u5b9a\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002</p>"},{"location":"chapter_computational_complexity/iteration_and_recursion/#3","title":"3. \u00a0 \u30cd\u30b9\u30c8\u3057\u305f\u30eb\u30fc\u30d7","text":"<p>1\u3064\u306e\u30eb\u30fc\u30d7\u69cb\u9020\u3092\u5225\u306e\u30eb\u30fc\u30d7\u69cb\u9020\u5185\u306b\u30cd\u30b9\u30c8\u3067\u304d\u307e\u3059\u3002\u4ee5\u4e0b\u306f<code>for</code>\u30eb\u30fc\u30d7\u3092\u4f7f\u7528\u3057\u305f\u4f8b\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig iteration.py<pre><code>def nested_for_loop(n: int) -&gt; str:\n    \"\"\"\u4e8c\u91cdfor\u30eb\u30fc\u30d7\"\"\"\n    res = \"\"\n    # i = 1, 2, ..., n-1, n \u3092\u30eb\u30fc\u30d7\n    for i in range(1, n + 1):\n        # j = 1, 2, ..., n-1, n \u3092\u30eb\u30fc\u30d7\n        for j in range(1, n + 1):\n            res += f\"({i}, {j}), \"\n    return res\n</code></pre> iteration.cpp<pre><code>/* 2\u91cd for \u30eb\u30fc\u30d7 */\nstring nestedForLoop(int n) {\n    ostringstream res;\n    // \u30eb\u30fc\u30d7 i = 1, 2, ..., n-1, n\n    for (int i = 1; i &lt;= n; ++i) {\n        // \u30eb\u30fc\u30d7 j = 1, 2, ..., n-1, n\n        for (int j = 1; j &lt;= n; ++j) {\n            res &lt;&lt; \"(\" &lt;&lt; i &lt;&lt; \", \" &lt;&lt; j &lt;&lt; \"), \";\n        }\n    }\n    return res.str();\n}\n</code></pre> iteration.java<pre><code>/* 2\u91cd for \u30eb\u30fc\u30d7 */\nString nestedForLoop(int n) {\n    StringBuilder res = new StringBuilder();\n    // \u30eb\u30fc\u30d7 i = 1, 2, ..., n-1, n\n    for (int i = 1; i &lt;= n; i++) {\n        // \u30eb\u30fc\u30d7 j = 1, 2, ..., n-1, n\n        for (int j = 1; j &lt;= n; j++) {\n            res.append(\"(\" + i + \", \" + j + \"), \");\n        }\n    }\n    return res.toString();\n}\n</code></pre> iteration.cs<pre><code>[class]{iteration}-[func]{NestedForLoop}\n</code></pre> iteration.go<pre><code>[class]{}-[func]{nestedForLoop}\n</code></pre> iteration.swift<pre><code>[class]{}-[func]{nestedForLoop}\n</code></pre> iteration.js<pre><code>[class]{}-[func]{nestedForLoop}\n</code></pre> iteration.ts<pre><code>[class]{}-[func]{nestedForLoop}\n</code></pre> iteration.dart<pre><code>[class]{}-[func]{nestedForLoop}\n</code></pre> iteration.rs<pre><code>[class]{}-[func]{nested_for_loop}\n</code></pre> iteration.c<pre><code>[class]{}-[func]{nestedForLoop}\n</code></pre> iteration.kt<pre><code>[class]{}-[func]{nestedForLoop}\n</code></pre> iteration.rb<pre><code>[class]{}-[func]{nested_for_loop}\n</code></pre> iteration.zig<pre><code>[class]{}-[func]{nestedForLoop}\n</code></pre> <p>\u4ee5\u4e0b\u306e\u56f3\u306f\u3053\u306e\u30cd\u30b9\u30c8\u3057\u305f\u30eb\u30fc\u30d7\u3092\u8868\u3057\u3066\u3044\u307e\u3059\u3002</p> <p></p> <p> \u56f3 2-2 \u00a0 Flowchart of the nested loop </p> <p>\u3053\u306e\u3088\u3046\u306a\u5834\u5408\u3001\u95a2\u6570\u306e\u64cd\u4f5c\u6570\u306f\\(n^2\\)\u306b\u6bd4\u4f8b\u3057\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5b9f\u884c\u6642\u9593\u3068\u5165\u529b\u30c7\u30fc\u30bf\u306e\u30b5\u30a4\u30ba\\(n\\)\u306b\u306f\u300c\u4e8c\u6b21\u95a2\u4fc2\u300d\u304c\u3042\u308a\u307e\u3059\u3002</p> <p>\u3055\u3089\u306b\u30cd\u30b9\u30c8\u3057\u305f\u30eb\u30fc\u30d7\u3092\u8ffd\u52a0\u3059\u308b\u3053\u3068\u3067\u8907\u96d1\u5ea6\u3092\u9ad8\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u3001\u5404\u30ec\u30d9\u30eb\u306e\u30cd\u30b9\u30c8\u306f\u4e8b\u5b9f\u4e0a\u300c\u6b21\u5143\u3092\u5897\u52a0\u300d\u3055\u305b\u3001\u6642\u9593\u8a08\u7b97\u91cf\u3092\u300c\u4e09\u6b21\u300d\u3001\u300c\u56db\u6b21\u300d\u306a\u3069\u306b\u5f15\u304d\u4e0a\u3052\u307e\u3059\u3002</p>"},{"location":"chapter_computational_complexity/iteration_and_recursion/#222","title":"2.2.2 \u00a0 \u518d\u5e30","text":"<p>\u518d\u5e30\u306f\u3001\u95a2\u6570\u304c\u81ea\u5206\u81ea\u8eab\u3092\u547c\u3073\u51fa\u3059\u3053\u3068\u3067\u554f\u984c\u3092\u89e3\u6c7a\u3059\u308b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u6226\u7565\u3067\u3059\u3002\u4e3b\u306b2\u3064\u306e\u30d5\u30a7\u30fc\u30ba\u304c\u542b\u307e\u308c\u307e\u3059\uff1a</p> <ol> <li>\u547c\u3073\u51fa\u3057: \u30d7\u30ed\u30b0\u30e9\u30e0\u304c\u81ea\u5206\u81ea\u8eab\u3092\u7e70\u308a\u8fd4\u3057\u547c\u3073\u51fa\u3057\u3001\u3057\u3070\u3057\u3070\u3088\u308a\u5c0f\u3055\u3044\u307e\u305f\u306f\u3088\u308a\u5358\u7d14\u306a\u5f15\u6570\u3067\u3001\u300c\u7d42\u4e86\u6761\u4ef6\u300d\u306b\u5411\u304b\u3063\u3066\u9032\u307f\u307e\u3059\u3002</li> <li>\u8fd4\u5374: \u300c\u7d42\u4e86\u6761\u4ef6\u300d\u304c\u30c8\u30ea\u30ac\u30fc\u3055\u308c\u308b\u3068\u3001\u30d7\u30ed\u30b0\u30e9\u30e0\u306f\u6700\u3082\u6df1\u3044\u518d\u5e30\u95a2\u6570\u304b\u3089\u8fd4\u308a\u59cb\u3081\u3001\u5404\u30ec\u30a4\u30e4\u30fc\u306e\u7d50\u679c\u3092\u96c6\u7d04\u3057\u307e\u3059\u3002</li> </ol> <p>\u5b9f\u88c5\u306e\u89b3\u70b9\u304b\u3089\u3001\u518d\u5e30\u30b3\u30fc\u30c9\u306f\u4e3b\u306b3\u3064\u306e\u8981\u7d20\u3092\u542b\u307f\u307e\u3059\u3002</p> <ol> <li>\u7d42\u4e86\u6761\u4ef6: \u300c\u547c\u3073\u51fa\u3057\u300d\u304b\u3089\u300c\u8fd4\u5374\u300d\u306b\u3044\u3064\u5207\u308a\u66ff\u3048\u308b\u304b\u3092\u6c7a\u5b9a\u3057\u307e\u3059\u3002</li> <li>\u518d\u5e30\u547c\u3073\u51fa\u3057: \u300c\u547c\u3073\u51fa\u3057\u300d\u306b\u5bfe\u5fdc\u3057\u3001\u95a2\u6570\u304c\u81ea\u5206\u81ea\u8eab\u3092\u547c\u3073\u51fa\u3057\u3001\u901a\u5e38\u306f\u3088\u308a\u5c0f\u3055\u3044\u307e\u305f\u306f\u3088\u308a\u5358\u7d14\u5316\u3055\u308c\u305f\u30d1\u30e9\u30e1\u30fc\u30bf\u3067\u884c\u3044\u307e\u3059\u3002</li> <li>\u7d50\u679c\u306e\u8fd4\u5374: \u300c\u8fd4\u5374\u300d\u306b\u5bfe\u5fdc\u3057\u3001\u73fe\u5728\u306e\u518d\u5e30\u30ec\u30d9\u30eb\u306e\u7d50\u679c\u304c\u524d\u306e\u30ec\u30a4\u30e4\u30fc\u306b\u8fd4\u3055\u308c\u307e\u3059\u3002</li> </ol> <p>\u4ee5\u4e0b\u306e\u30b3\u30fc\u30c9\u3092\u89b3\u5bdf\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u5358\u7d14\u306b\u95a2\u6570<code>recur(n)</code>\u3092\u547c\u3073\u51fa\u3059\u3060\u3051\u3067\\(1 + 2 + \\dots + n\\)\u306e\u5408\u8a08\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig recursion.py<pre><code>def recur(n: int) -&gt; int:\n    \"\"\"\u518d\u5e30\"\"\"\n    # \u7d42\u4e86\u6761\u4ef6\n    if n == 1:\n        return 1\n    # \u518d\u5e30\uff1a\u518d\u5e30\u547c\u3073\u51fa\u3057\n    res = recur(n - 1)\n    # \u5fa9\u5e30\uff1a\u7d50\u679c\u3092\u8fd4\u3059\n    return n + res\n</code></pre> recursion.cpp<pre><code>/* \u518d\u5e30 */\nint recur(int n) {\n    // \u7d42\u4e86\u6761\u4ef6\n    if (n == 1)\n        return 1;\n    // \u518d\u5e30\uff1a\u518d\u5e30\u547c\u3073\u51fa\u3057\n    int res = recur(n - 1);\n    // \u623b\u308a\u5024\uff1a\u7d50\u679c\u3092\u8fd4\u3059\n    return n + res;\n}\n</code></pre> recursion.java<pre><code>/* \u518d\u5e30 */\nint recur(int n) {\n    // \u7d42\u4e86\u6761\u4ef6\n    if (n == 1)\n        return 1;\n    // \u518d\u5e30\uff1a\u518d\u5e30\u547c\u3073\u51fa\u3057\n    int res = recur(n - 1);\n    // \u623b\u308a\u5024\uff1a\u7d50\u679c\u3092\u8fd4\u3059\n    return n + res;\n}\n</code></pre> recursion.cs<pre><code>[class]{recursion}-[func]{Recur}\n</code></pre> recursion.go<pre><code>[class]{}-[func]{recur}\n</code></pre> recursion.swift<pre><code>[class]{}-[func]{recur}\n</code></pre> recursion.js<pre><code>[class]{}-[func]{recur}\n</code></pre> recursion.ts<pre><code>[class]{}-[func]{recur}\n</code></pre> recursion.dart<pre><code>[class]{}-[func]{recur}\n</code></pre> recursion.rs<pre><code>[class]{}-[func]{recur}\n</code></pre> recursion.c<pre><code>[class]{}-[func]{recur}\n</code></pre> recursion.kt<pre><code>[class]{}-[func]{recur}\n</code></pre> recursion.rb<pre><code>[class]{}-[func]{recur}\n</code></pre> recursion.zig<pre><code>[class]{}-[func]{recur}\n</code></pre> <p>\u4ee5\u4e0b\u306e\u56f3\u306f\u3053\u306e\u95a2\u6570\u306e\u518d\u5e30\u30d7\u30ed\u30bb\u30b9\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002</p> <p></p> <p> \u56f3 2-3 \u00a0 Recursive process of the sum function </p> <p>\u53cd\u5fa9\u3068\u518d\u5e30\u306f\u8a08\u7b97\u306e\u89b3\u70b9\u304b\u3089\u540c\u3058\u7d50\u679c\u3092\u9054\u6210\u3067\u304d\u307e\u3059\u304c\u3001\u305d\u308c\u3089\u306f\u601d\u8003\u3068\u554f\u984c\u89e3\u6c7a\u306e\u5168\u304f\u7570\u306a\u308b\u30d1\u30e9\u30c0\u30a4\u30e0\u3092\u8868\u3057\u307e\u3059\u3002</p> <ul> <li>\u53cd\u5fa9: \u300c\u30dc\u30c8\u30e0\u30a2\u30c3\u30d7\u300d\u3067\u554f\u984c\u3092\u89e3\u6c7a\u3057\u307e\u3059\u3002\u6700\u3082\u57fa\u672c\u7684\u306a\u30b9\u30c6\u30c3\u30d7\u304b\u3089\u59cb\u307e\u308a\u3001\u30bf\u30b9\u30af\u304c\u5b8c\u4e86\u3059\u308b\u307e\u3067\u3053\u308c\u3089\u306e\u30b9\u30c6\u30c3\u30d7\u3092\u7e70\u308a\u8fd4\u3057\u8ffd\u52a0\u307e\u305f\u306f\u7d2f\u7a4d\u3057\u307e\u3059\u3002</li> <li>\u518d\u5e30: \u300c\u30c8\u30c3\u30d7\u30c0\u30a6\u30f3\u300d\u3067\u554f\u984c\u3092\u89e3\u6c7a\u3057\u307e\u3059\u3002\u5143\u306e\u554f\u984c\u3092\u3088\u308a\u5c0f\u3055\u306a\u30b5\u30d6\u554f\u984c\u306b\u5206\u89e3\u3057\u3001\u5404\u30b5\u30d6\u554f\u984c\u306f\u5143\u306e\u554f\u984c\u3068\u540c\u3058\u5f62\u5f0f\u3092\u6301\u3061\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u30b5\u30d6\u554f\u984c\u306f\u3001\u89e3\u304c\u5206\u304b\u3063\u3066\u3044\u308b\u30d9\u30fc\u30b9\u30b1\u30fc\u30b9\u3067\u505c\u6b62\u3059\u308b\u307e\u3067\u3001\u3055\u3089\u306b\u5c0f\u3055\u306a\u30b5\u30d6\u554f\u984c\u306b\u5206\u89e3\u3055\u308c\u307e\u3059\u3002</li> </ul> <p>\u5148\u307b\u3069\u306e\u5408\u8a08\u95a2\u6570\u306e\u4f8b\u3092\u53d6\u3063\u3066\u307f\u307e\u3057\u3087\u3046\u3002\\(f(n) = 1 + 2 + \\dots + n\\)\u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002</p> <ul> <li>\u53cd\u5fa9: \u3053\u306e\u30a2\u30d7\u30ed\u30fc\u30c1\u3067\u306f\u3001\u30eb\u30fc\u30d7\u5185\u3067\u5408\u8a08\u30d7\u30ed\u30bb\u30b9\u3092\u30b7\u30df\u30e5\u30ec\u30fc\u30c8\u3057\u307e\u3059\u3002\\(1\\)\u304b\u3089\u59cb\u307e\u308a\\(n\\)\u307e\u3067\u6a2a\u65ad\u3057\u3001\u5404\u53cd\u5fa9\u3067\u5408\u8a08\u64cd\u4f5c\u3092\u5b9f\u884c\u3057\u3066\u6700\u7d42\u7684\u306b\\(f(n)\\)\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002</li> <li>\u518d\u5e30: \u3053\u3053\u3067\u306f\u3001\u554f\u984c\u306f\u30b5\u30d6\u554f\u984c\u306b\u5206\u89e3\u3055\u308c\u307e\u3059\uff1a\\(f(n) = n + f(n-1)\\)\u3002\u3053\u306e\u5206\u89e3\u306f\u3001\u30d9\u30fc\u30b9\u30b1\u30fc\u30b9\u306e\\(f(1) = 1\\)\u306b\u5230\u9054\u3059\u308b\u307e\u3067\u518d\u5e30\u7684\u306b\u7d9a\u304d\u3001\u305d\u3053\u3067\u518d\u5e30\u304c\u7d42\u4e86\u3057\u307e\u3059\u3002</li> </ul>"},{"location":"chapter_computational_complexity/iteration_and_recursion/#1","title":"1. \u00a0 \u547c\u3073\u51fa\u3057\u30b9\u30bf\u30c3\u30af","text":"<p>\u518d\u5e30\u95a2\u6570\u304c\u81ea\u5206\u81ea\u8eab\u3092\u547c\u3073\u51fa\u3059\u305f\u3073\u306b\u3001\u30b7\u30b9\u30c6\u30e0\u306f\u65b0\u3057\u304f\u958b\u59cb\u3055\u308c\u305f\u95a2\u6570\u306b\u30e1\u30e2\u30ea\u3092\u5272\u308a\u5f53\u3066\u3066\u3001\u30ed\u30fc\u30ab\u30eb\u5909\u6570\u3001\u623b\u308a\u30a2\u30c9\u30ec\u30b9\u3001\u305d\u306e\u4ed6\u306e\u95a2\u9023\u60c5\u5831\u3092\u683c\u7d0d\u3057\u307e\u3059\u3002\u3053\u308c\u306f2\u3064\u306e\u4e3b\u8981\u306a\u7d50\u679c\u3092\u3082\u305f\u3089\u3057\u307e\u3059\u3002</p> <ul> <li>\u95a2\u6570\u306e\u30b3\u30f3\u30c6\u30ad\u30b9\u30c8\u30c7\u30fc\u30bf\u306f\u300c\u30b9\u30bf\u30c3\u30af\u30d5\u30ec\u30fc\u30e0\u7a7a\u9593\u300d\u3068\u547c\u3070\u308c\u308b\u30e1\u30e2\u30ea\u9818\u57df\u306b\u683c\u7d0d\u3055\u308c\u3001\u95a2\u6570\u304c\u8fd4\u3055\u308c\u305f\u5f8c\u306b\u306e\u307f\u89e3\u653e\u3055\u308c\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u518d\u5e30\u306f\u4e00\u822c\u7684\u306b\u53cd\u5fa9\u3088\u308a\u3082\u591a\u304f\u306e\u30e1\u30e2\u30ea\u7a7a\u9593\u3092\u6d88\u8cbb\u3057\u307e\u3059\u3002</li> <li>\u518d\u5e30\u547c\u3073\u51fa\u3057\u306f\u8ffd\u52a0\u306e\u30aa\u30fc\u30d0\u30fc\u30d8\u30c3\u30c9\u3092\u5c0e\u5165\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u518d\u5e30\u306f\u901a\u5e38\u30eb\u30fc\u30d7\u3088\u308a\u3082\u6642\u9593\u52b9\u7387\u304c\u52a3\u308a\u307e\u3059\u3002</li> </ul> <p>\u4ee5\u4e0b\u306e\u56f3\u306b\u793a\u3055\u308c\u3066\u3044\u308b\u3088\u3046\u306b\u3001\u7d42\u4e86\u6761\u4ef6\u304c\u30c8\u30ea\u30ac\u30fc\u3055\u308c\u308b\u524d\u306b\\(n\\)\u500b\u306e\u672a\u8fd4\u5374\u306e\u518d\u5e30\u95a2\u6570\u304c\u3042\u308a\u3001\u518d\u5e30\u306e\u6df1\u3055\u304c\\(n\\)\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002</p> <p></p> <p> \u56f3 2-4 \u00a0 Recursion call depth </p> <p>\u5b9f\u969b\u306b\u306f\u3001\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u3067\u8a31\u53ef\u3055\u308c\u308b\u518d\u5e30\u306e\u6df1\u3055\u306f\u901a\u5e38\u5236\u9650\u3055\u308c\u3066\u304a\u308a\u3001\u904e\u5ea6\u306b\u6df1\u3044\u518d\u5e30\u306f\u30b9\u30bf\u30c3\u30af\u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u30a8\u30e9\u30fc\u3092\u5f15\u304d\u8d77\u3053\u3059\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002</p>"},{"location":"chapter_computational_complexity/iteration_and_recursion/#2","title":"2. \u00a0 \u672b\u5c3e\u518d\u5e30","text":"<p>\u8208\u5473\u6df1\u3044\u3053\u3068\u306b\u3001\u95a2\u6570\u304c\u8fd4\u3059\u76f4\u524d\u306e\u6700\u5f8c\u306e\u30b9\u30c6\u30c3\u30d7\u3068\u3057\u3066\u518d\u5e30\u547c\u3073\u51fa\u3057\u3092\u5b9f\u884c\u3059\u308b\u5834\u5408\u3001\u30b3\u30f3\u30d1\u30a4\u30e9\u307e\u305f\u306f\u30a4\u30f3\u30bf\u30fc\u30d7\u30ea\u30bf\u30fc\u306b\u3088\u3063\u3066\u53cd\u5fa9\u3068\u540c\u3058\u7a7a\u9593\u52b9\u7387\u306b\u306a\u308b\u3088\u3046\u306b\u6700\u9069\u5316\u3067\u304d\u307e\u3059\u3002\u3053\u306e\u30b7\u30ca\u30ea\u30aa\u306f\u672b\u5c3e\u518d\u5e30\u3068\u3057\u3066\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\u3002</p> <ul> <li>\u901a\u5e38\u306e\u518d\u5e30: \u6a19\u6e96\u7684\u306a\u518d\u5e30\u3067\u306f\u3001\u95a2\u6570\u304c\u524d\u306e\u30ec\u30d9\u30eb\u306b\u623b\u3063\u305f\u3068\u304d\u3001\u3055\u3089\u306b\u30b3\u30fc\u30c9\u3092\u5b9f\u884c\u3057\u7d9a\u3051\u308b\u305f\u3081\u3001\u30b7\u30b9\u30c6\u30e0\u306f\u524d\u306e\u547c\u3073\u51fa\u3057\u306e\u30b3\u30f3\u30c6\u30ad\u30b9\u30c8\u3092\u4fdd\u5b58\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002</li> <li>\u672b\u5c3e\u518d\u5e30: \u3053\u3053\u3067\u306f\u3001\u518d\u5e30\u547c\u3073\u51fa\u3057\u306f\u95a2\u6570\u304c\u8fd4\u3059\u524d\u306e\u6700\u7d42\u64cd\u4f5c\u3067\u3059\u3002\u3053\u308c\u306f\u3001\u524d\u306e\u30ec\u30d9\u30eb\u306b\u623b\u3063\u305f\u969b\u306b\u3001\u3055\u3089\u306a\u308b\u30a2\u30af\u30b7\u30e7\u30f3\u304c\u5fc5\u8981\u306a\u3044\u3053\u3068\u3092\u610f\u5473\u3059\u308b\u305f\u3081\u3001\u30b7\u30b9\u30c6\u30e0\u306f\u524d\u306e\u30ec\u30d9\u30eb\u306e\u30b3\u30f3\u30c6\u30ad\u30b9\u30c8\u3092\u4fdd\u5b58\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u305b\u3093\u3002</li> </ul> <p>\u4f8b\u3048\u3070\u3001\\(1 + 2 + \\dots + n\\)\u306e\u8a08\u7b97\u3067\u306f\u3001\u7d50\u679c\u5909\u6570<code>res</code>\u3092\u95a2\u6570\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u306b\u3059\u308b\u3053\u3068\u3067\u3001\u672b\u5c3e\u518d\u5e30\u3092\u5b9f\u73fe\u3067\u304d\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig recursion.py<pre><code>def tail_recur(n, res):\n    \"\"\"\u672b\u5c3e\u518d\u5e30\"\"\"\n    # \u7d42\u4e86\u6761\u4ef6\n    if n == 0:\n        return res\n    # \u672b\u5c3e\u518d\u5e30\u547c\u3073\u51fa\u3057\n    return tail_recur(n - 1, res + n)\n</code></pre> recursion.cpp<pre><code>/* \u672b\u5c3e\u518d\u5e30 */\nint tailRecur(int n, int res) {\n    // \u7d42\u4e86\u6761\u4ef6\n    if (n == 0)\n        return res;\n    // \u672b\u5c3e\u518d\u5e30\u547c\u3073\u51fa\u3057\n    return tailRecur(n - 1, res + n);\n}\n</code></pre> recursion.java<pre><code>/* \u672b\u5c3e\u518d\u5e30 */\nint tailRecur(int n, int res) {\n    // \u7d42\u4e86\u6761\u4ef6\n    if (n == 0)\n        return res;\n    // \u672b\u5c3e\u518d\u5e30\u547c\u3073\u51fa\u3057\n    return tailRecur(n - 1, res + n);\n}\n</code></pre> recursion.cs<pre><code>[class]{recursion}-[func]{TailRecur}\n</code></pre> recursion.go<pre><code>[class]{}-[func]{tailRecur}\n</code></pre> recursion.swift<pre><code>[class]{}-[func]{tailRecur}\n</code></pre> recursion.js<pre><code>[class]{}-[func]{tailRecur}\n</code></pre> recursion.ts<pre><code>[class]{}-[func]{tailRecur}\n</code></pre> recursion.dart<pre><code>[class]{}-[func]{tailRecur}\n</code></pre> recursion.rs<pre><code>[class]{}-[func]{tail_recur}\n</code></pre> recursion.c<pre><code>[class]{}-[func]{tailRecur}\n</code></pre> recursion.kt<pre><code>[class]{}-[func]{tailRecur}\n</code></pre> recursion.rb<pre><code>[class]{}-[func]{tail_recur}\n</code></pre> recursion.zig<pre><code>[class]{}-[func]{tailRecur}\n</code></pre> <p>\u672b\u5c3e\u518d\u5e30\u306e\u5b9f\u884c\u30d7\u30ed\u30bb\u30b9\u306f\u4ee5\u4e0b\u306e\u56f3\u306b\u793a\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u901a\u5e38\u306e\u518d\u5e30\u3068\u672b\u5c3e\u518d\u5e30\u3092\u6bd4\u8f03\u3059\u308b\u3068\u3001\u5408\u8a08\u64cd\u4f5c\u306e\u30dd\u30a4\u30f3\u30c8\u304c\u7570\u306a\u308a\u307e\u3059\u3002</p> <ul> <li>\u901a\u5e38\u306e\u518d\u5e30: \u5408\u8a08\u64cd\u4f5c\u306f\u300c\u8fd4\u5374\u300d\u30d5\u30a7\u30fc\u30ba\u3067\u767a\u751f\u3057\u3001\u5404\u30ec\u30a4\u30e4\u30fc\u304c\u8fd4\u3063\u305f\u5f8c\u306b\u3082\u3046\u4e00\u5ea6\u5408\u8a08\u304c\u5fc5\u8981\u3067\u3059\u3002</li> <li>\u672b\u5c3e\u518d\u5e30: \u5408\u8a08\u64cd\u4f5c\u306f\u300c\u547c\u3073\u51fa\u3057\u300d\u30d5\u30a7\u30fc\u30ba\u3067\u767a\u751f\u3057\u3001\u300c\u8fd4\u5374\u300d\u30d5\u30a7\u30fc\u30ba\u306f\u5404\u30ec\u30a4\u30e4\u30fc\u3092\u901a\u3058\u3066\u8fd4\u3059\u3060\u3051\u3067\u3059\u3002</li> </ul> <p></p> <p> \u56f3 2-5 \u00a0 Tail recursion process </p> <p>Tip</p> <p>\u591a\u304f\u306e\u30b3\u30f3\u30d1\u30a4\u30e9\u3084\u30a4\u30f3\u30bf\u30fc\u30d7\u30ea\u30bf\u30fc\u306f\u672b\u5c3e\u518d\u5e30\u6700\u9069\u5316\u3092\u30b5\u30dd\u30fc\u30c8\u3057\u3066\u3044\u306a\u3044\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u4f8b\u3048\u3070\u3001Python\u306f\u30c7\u30d5\u30a9\u30eb\u30c8\u3067\u672b\u5c3e\u518d\u5e30\u6700\u9069\u5316\u3092\u30b5\u30dd\u30fc\u30c8\u3057\u3066\u3044\u306a\u3044\u305f\u3081\u3001\u95a2\u6570\u304c\u672b\u5c3e\u518d\u5e30\u306e\u5f62\u5f0f\u3067\u3042\u3063\u3066\u3082\u3001\u30b9\u30bf\u30c3\u30af\u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u306e\u554f\u984c\u306b\u906d\u9047\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002</p>"},{"location":"chapter_computational_complexity/iteration_and_recursion/#3_1","title":"3. \u00a0 \u518d\u5e30\u6728","text":"<p>\u300c\u5206\u5272\u7d71\u6cbb\u300d\u306b\u95a2\u9023\u3059\u308b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u6271\u3046\u969b\u3001\u518d\u5e30\u306f\u53cd\u5fa9\u3088\u308a\u3082\u3057\u3070\u3057\u3070\u3088\u308a\u76f4\u611f\u7684\u306a\u30a2\u30d7\u30ed\u30fc\u30c1\u3068\u3088\u308a\u8aad\u307f\u3084\u3059\u3044\u30b3\u30fc\u30c9\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u300c\u30d5\u30a3\u30dc\u30ca\u30c3\u30c1\u6570\u5217\u300d\u3092\u4f8b\u306b\u53d6\u3063\u3066\u307f\u307e\u3057\u3087\u3046\u3002</p> <p>Question</p> <p>\u30d5\u30a3\u30dc\u30ca\u30c3\u30c1\u6570\u5217\\(0, 1, 1, 2, 3, 5, 8, 13, \\dots\\)\u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408\u3001\u6570\u5217\u306e\\(n\\)\u756a\u76ee\u306e\u6570\u3092\u6c42\u3081\u306a\u3055\u3044\u3002</p> <p>\u30d5\u30a3\u30dc\u30ca\u30c3\u30c1\u6570\u5217\u306e\\(n\\)\u756a\u76ee\u306e\u6570\u3092\\(f(n)\\)\u3068\u3059\u308b\u3068\u30012\u3064\u306e\u7d50\u8ad6\u3092\u7c21\u5358\u306b\u5c0e\u304d\u51fa\u305b\u307e\u3059\uff1a</p> <ul> <li>\u6570\u5217\u306e\u6700\u521d\u306e2\u3064\u306e\u6570\u306f\\(f(1) = 0\\)\u3068\\(f(2) = 1\\)\u3067\u3059\u3002</li> <li>\u6570\u5217\u306e\u5404\u6570\u306f\u524d\u306e2\u3064\u306e\u6570\u306e\u5408\u8a08\u3067\u3059\u3002\u3064\u307e\u308a\u3001\\(f(n) = f(n - 1) + f(n - 2)\\)\u3067\u3059\u3002</li> </ul> <p>\u518d\u5e30\u95a2\u4fc2\u3092\u4f7f\u7528\u3057\u3001\u6700\u521d\u306e2\u3064\u306e\u6570\u3092\u7d42\u4e86\u6761\u4ef6\u3068\u3057\u3066\u8003\u616e\u3059\u308b\u3068\u3001\u518d\u5e30\u30b3\u30fc\u30c9\u3092\u66f8\u3051\u307e\u3059\u3002<code>fib(n)</code>\u3092\u547c\u3073\u51fa\u3059\u3068\u30d5\u30a3\u30dc\u30ca\u30c3\u30c1\u6570\u5217\u306e\\(n\\)\u756a\u76ee\u306e\u6570\u304c\u5f97\u3089\u308c\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig recursion.py<pre><code>def fib(n: int) -&gt; int:\n    \"\"\"\u30d5\u30a3\u30dc\u30ca\u30c3\u30c1\u6570\u5217\uff1a\u518d\u5e30\"\"\"\n    # \u7d42\u4e86\u6761\u4ef6 f(1) = 0, f(2) = 1\n    if n == 1 or n == 2:\n        return n - 1\n    # \u518d\u5e30\u547c\u3073\u51fa\u3057 f(n) = f(n-1) + f(n-2)\n    res = fib(n - 1) + fib(n - 2)\n    # \u7d50\u679c f(n) \u3092\u8fd4\u3059\n    return res\n</code></pre> recursion.cpp<pre><code>/* \u30d5\u30a3\u30dc\u30ca\u30c3\u30c1\u6570\u5217\uff1a\u518d\u5e30 */\nint fib(int n) {\n    // \u7d42\u4e86\u6761\u4ef6 f(1) = 0, f(2) = 1\n    if (n == 1 || n == 2)\n        return n - 1;\n    // \u518d\u5e30\u547c\u3073\u51fa\u3057 f(n) = f(n-1) + f(n-2)\n    int res = fib(n - 1) + fib(n - 2);\n    // \u7d50\u679c f(n) \u3092\u8fd4\u3059\n    return res;\n}\n</code></pre> recursion.java<pre><code>/* \u30d5\u30a3\u30dc\u30ca\u30c3\u30c1\u6570\u5217\uff1a\u518d\u5e30 */\nint fib(int n) {\n    // \u7d42\u4e86\u6761\u4ef6 f(1) = 0, f(2) = 1\n    if (n == 1 || n == 2)\n        return n - 1;\n    // \u518d\u5e30\u547c\u3073\u51fa\u3057 f(n) = f(n-1) + f(n-2)\n    int res = fib(n - 1) + fib(n - 2);\n    // \u7d50\u679c f(n) \u3092\u8fd4\u3059\n    return res;\n}\n</code></pre> recursion.cs<pre><code>[class]{recursion}-[func]{Fib}\n</code></pre> recursion.go<pre><code>[class]{}-[func]{fib}\n</code></pre> recursion.swift<pre><code>[class]{}-[func]{fib}\n</code></pre> recursion.js<pre><code>[class]{}-[func]{fib}\n</code></pre> recursion.ts<pre><code>[class]{}-[func]{fib}\n</code></pre> recursion.dart<pre><code>[class]{}-[func]{fib}\n</code></pre> recursion.rs<pre><code>[class]{}-[func]{fib}\n</code></pre> recursion.c<pre><code>[class]{}-[func]{fib}\n</code></pre> recursion.kt<pre><code>[class]{}-[func]{fib}\n</code></pre> recursion.rb<pre><code>[class]{}-[func]{fib}\n</code></pre> recursion.zig<pre><code>[class]{}-[func]{fib}\n</code></pre> <p>\u4e0a\u8a18\u306e\u30b3\u30fc\u30c9\u3092\u89b3\u5bdf\u3059\u308b\u3068\u3001\u305d\u308c\u81ea\u4f53\u306e\u4e2d\u30672\u3064\u306e\u95a2\u6570\u3092\u518d\u5e30\u7684\u306b\u547c\u3073\u51fa\u3057\u3066\u3044\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002\u3064\u307e\u308a\u30011\u56de\u306e\u547c\u3073\u51fa\u3057\u30672\u3064\u306e\u5206\u5c90\u547c\u3073\u51fa\u3057\u304c\u751f\u6210\u3055\u308c\u307e\u3059\u3002\u4ee5\u4e0b\u306e\u56f3\u306b\u793a\u3055\u308c\u3066\u3044\u308b\u3088\u3046\u306b\u3001\u3053\u306e\u7d99\u7d9a\u7684\u306a\u518d\u5e30\u547c\u3073\u51fa\u3057\u306f\u6700\u7d42\u7684\u306b\u6df1\u3055\\(n\\)\u306e\u518d\u5e30\u6728\u3092\u4f5c\u6210\u3057\u307e\u3059\u3002</p> <p></p> <p> \u56f3 2-6 \u00a0 Fibonacci sequence recursion tree </p> <p>\u57fa\u672c\u7684\u306b\u3001\u518d\u5e30\u306f\u300c\u554f\u984c\u3092\u3088\u308a\u5c0f\u3055\u306a\u30b5\u30d6\u554f\u984c\u306b\u5206\u89e3\u3059\u308b\u300d\u30d1\u30e9\u30c0\u30a4\u30e0\u3092\u4f53\u73fe\u3057\u3066\u3044\u307e\u3059\u3002\u3053\u306e\u5206\u5272\u7d71\u6cbb\u6226\u7565\u306f\u91cd\u8981\u3067\u3059\u3002</p> <ul> <li>\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u89b3\u70b9\u304b\u3089\u3001\u63a2\u7d22\u3001\u30bd\u30fc\u30c8\u3001\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u3001\u5206\u5272\u7d71\u6cbb\u3001\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u306a\u3069\u306e\u591a\u304f\u306e\u91cd\u8981\u306a\u6226\u7565\u306f\u3001\u76f4\u63a5\u7684\u307e\u305f\u306f\u9593\u63a5\u7684\u306b\u3053\u306e\u601d\u8003\u65b9\u6cd5\u3092\u4f7f\u7528\u3057\u3066\u3044\u307e\u3059\u3002</li> <li>\u30c7\u30fc\u30bf\u69cb\u9020\u306e\u89b3\u70b9\u304b\u3089\u3001\u518d\u5e30\u306f\u9023\u7d50\u30ea\u30b9\u30c8\u3001\u6728\u3001\u30b0\u30e9\u30d5\u3092\u6271\u3046\u306e\u306b\u81ea\u7136\u306b\u9069\u3057\u3066\u304a\u308a\u3001\u3053\u308c\u3089\u306f\u5206\u5272\u7d71\u6cbb\u30a2\u30d7\u30ed\u30fc\u30c1\u3092\u4f7f\u7528\u3057\u305f\u5206\u6790\u306b\u9069\u3057\u3066\u3044\u308b\u305f\u3081\u3067\u3059\u3002</li> </ul>"},{"location":"chapter_computational_complexity/iteration_and_recursion/#223","title":"2.2.3 \u00a0 \u6bd4\u8f03","text":"<p>\u4e0a\u8a18\u306e\u5185\u5bb9\u3092\u307e\u3068\u3081\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u8868\u306f\u5b9f\u88c5\u3001\u6027\u80fd\u3001\u9069\u7528\u6027\u306e\u89b3\u70b9\u304b\u3089\u53cd\u5fa9\u3068\u518d\u5e30\u306e\u9055\u3044\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002</p> <p> \u8868: \u53cd\u5fa9\u3068\u518d\u5e30\u306e\u7279\u6027\u306e\u6bd4\u8f03 </p> \u53cd\u5fa9 \u518d\u5e30 \u30a2\u30d7\u30ed\u30fc\u30c1 \u30eb\u30fc\u30d7\u69cb\u9020 \u95a2\u6570\u304c\u81ea\u5206\u81ea\u8eab\u3092\u547c\u3073\u51fa\u3059 \u6642\u9593\u52b9\u7387 \u4e00\u822c\u7684\u306b\u3088\u308a\u9ad8\u3044\u52b9\u7387\u3001\u95a2\u6570\u547c\u3073\u51fa\u3057\u306e\u30aa\u30fc\u30d0\u30fc\u30d8\u30c3\u30c9\u306a\u3057 \u5404\u95a2\u6570\u547c\u3073\u51fa\u3057\u304c\u30aa\u30fc\u30d0\u30fc\u30d8\u30c3\u30c9\u3092\u751f\u6210 \u30e1\u30e2\u30ea\u4f7f\u7528\u91cf \u901a\u5e38\u306f\u56fa\u5b9a\u30b5\u30a4\u30ba\u306e\u30e1\u30e2\u30ea\u7a7a\u9593\u3092\u4f7f\u7528 \u7d2f\u7a4d\u7684\u306a\u95a2\u6570\u547c\u3073\u51fa\u3057\u304c\u5927\u91cf\u306e\u30b9\u30bf\u30c3\u30af\u30d5\u30ec\u30fc\u30e0\u7a7a\u9593\u3092\u4f7f\u7528\u3059\u308b\u53ef\u80fd\u6027 \u9069\u7528\u53ef\u80fd\u306a\u554f\u984c \u5358\u7d14\u306a\u30eb\u30fc\u30d7\u30bf\u30b9\u30af\u306b\u9069\u3057\u3066\u3044\u308b\u3001\u76f4\u611f\u7684\u3067\u8aad\u307f\u3084\u3059\u3044\u30b3\u30fc\u30c9 \u554f\u984c\u306e\u5206\u89e3\u306b\u9069\u3057\u3066\u3044\u308b\uff08\u6728\u3001\u30b0\u30e9\u30d5\u3001\u5206\u5272\u7d71\u6cbb\u3001\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u306a\u3069\uff09\u3001\u7c21\u6f54\u3067\u660e\u78ba\u306a\u30b3\u30fc\u30c9\u69cb\u9020 <p>Tip</p> <p>\u4ee5\u4e0b\u306e\u5185\u5bb9\u304c\u7406\u89e3\u3057\u306b\u304f\u3044\u5834\u5408\u306f\u3001\u300c\u30b9\u30bf\u30c3\u30af\u300d\u306e\u7ae0\u3092\u8aad\u3093\u3060\u5f8c\u306b\u518d\u3073\u8a2a\u308c\u308b\u3053\u3068\u3092\u691c\u8a0e\u3057\u3066\u304f\u3060\u3055\u3044\u3002</p> <p>\u305d\u308c\u3067\u306f\u3001\u53cd\u5fa9\u3068\u518d\u5e30\u306e\u672c\u8cea\u7684\u306a\u95a2\u9023\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\uff1f\u4e0a\u8a18\u306e\u518d\u5e30\u95a2\u6570\u3092\u4f8b\u306b\u53d6\u308b\u3068\u3001\u5408\u8a08\u64cd\u4f5c\u306f\u518d\u5e30\u306e\u300c\u8fd4\u5374\u300d\u30d5\u30a7\u30fc\u30ba\u3067\u767a\u751f\u3057\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u6700\u521d\u306b\u547c\u3073\u51fa\u3055\u308c\u305f\u95a2\u6570\u304c\u6700\u5f8c\u306b\u5408\u8a08\u64cd\u4f5c\u3092\u5b8c\u4e86\u3059\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u3001\u30b9\u30bf\u30c3\u30af\u306e\u300c\u5f8c\u5165\u308c\u5148\u51fa\u3057\u300d\u539f\u7406\u3092\u53cd\u6620\u3057\u3066\u3044\u307e\u3059\u3002</p> <p>\u300c\u547c\u3073\u51fa\u3057\u30b9\u30bf\u30c3\u30af\u300d\u3084\u300c\u30b9\u30bf\u30c3\u30af\u30d5\u30ec\u30fc\u30e0\u7a7a\u9593\u300d\u306a\u3069\u306e\u518d\u5e30\u7528\u8a9e\u306f\u3001\u518d\u5e30\u3068\u30b9\u30bf\u30c3\u30af\u306e\u5bc6\u63a5\u306a\u95a2\u4fc2\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002</p> <ol> <li>\u547c\u3073\u51fa\u3057: \u95a2\u6570\u304c\u547c\u3073\u51fa\u3055\u308c\u308b\u3068\u3001\u30b7\u30b9\u30c6\u30e0\u306f\u300c\u547c\u3073\u51fa\u3057\u30b9\u30bf\u30c3\u30af\u300d\u4e0a\u306b\u305d\u306e\u95a2\u6570\u7528\u306e\u65b0\u3057\u3044\u30b9\u30bf\u30c3\u30af\u30d5\u30ec\u30fc\u30e0\u3092\u5272\u308a\u5f53\u3066\u3001\u30ed\u30fc\u30ab\u30eb\u5909\u6570\u3001\u30d1\u30e9\u30e1\u30fc\u30bf\u3001\u623b\u308a\u30a2\u30c9\u30ec\u30b9\u3001\u305d\u306e\u4ed6\u306e\u30c7\u30fc\u30bf\u3092\u683c\u7d0d\u3057\u307e\u3059\u3002</li> <li>\u8fd4\u5374: \u95a2\u6570\u304c\u5b9f\u884c\u3092\u5b8c\u4e86\u3057\u3066\u8fd4\u308b\u3068\u3001\u5bfe\u5fdc\u3059\u308b\u30b9\u30bf\u30c3\u30af\u30d5\u30ec\u30fc\u30e0\u304c\u300c\u547c\u3073\u51fa\u3057\u30b9\u30bf\u30c3\u30af\u300d\u304b\u3089\u524a\u9664\u3055\u308c\u3001\u524d\u306e\u95a2\u6570\u306e\u5b9f\u884c\u74b0\u5883\u304c\u5fa9\u5143\u3055\u308c\u307e\u3059\u3002</li> </ol> <p>\u3057\u305f\u304c\u3063\u3066\u3001\u660e\u793a\u7684\u306a\u30b9\u30bf\u30c3\u30af\u3092\u4f7f\u7528\u3057\u3066\u547c\u3073\u51fa\u3057\u30b9\u30bf\u30c3\u30af\u306e\u52d5\u4f5c\u3092\u30b7\u30df\u30e5\u30ec\u30fc\u30c8\u3067\u304d\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u518d\u5e30\u3092\u53cd\u5fa9\u5f62\u5f0f\u306b\u5909\u63db\u3067\u304d\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig recursion.py<pre><code>def for_loop_recur(n: int) -&gt; int:\n    \"\"\"\u53cd\u5fa9\u3067\u518d\u5e30\u3092\u30b7\u30df\u30e5\u30ec\u30fc\u30c8\"\"\"\n    # \u660e\u793a\u7684\u306a\u30b9\u30bf\u30c3\u30af\u3092\u4f7f\u7528\u3057\u3066\u30b7\u30b9\u30c6\u30e0\u30b3\u30fc\u30eb\u30b9\u30bf\u30c3\u30af\u3092\u30b7\u30df\u30e5\u30ec\u30fc\u30c8\n    stack = []\n    res = 0\n    # \u518d\u5e30\uff1a\u518d\u5e30\u547c\u3073\u51fa\u3057\n    for i in range(n, 0, -1):\n        # \u300c\u30b9\u30bf\u30c3\u30af\u3078\u306e\u30d7\u30c3\u30b7\u30e5\u300d\u3067\u300c\u518d\u5e30\u300d\u3092\u30b7\u30df\u30e5\u30ec\u30fc\u30c8\n        stack.append(i)\n    # \u5fa9\u5e30\uff1a\u7d50\u679c\u3092\u8fd4\u3059\n    while stack:\n        # \u300c\u30b9\u30bf\u30c3\u30af\u304b\u3089\u306e\u30dd\u30c3\u30d7\u300d\u3067\u300c\u5fa9\u5e30\u300d\u3092\u30b7\u30df\u30e5\u30ec\u30fc\u30c8\n        res += stack.pop()\n    # res = 1+2+3+...+n\n    return res\n</code></pre> recursion.cpp<pre><code>/* \u53cd\u5fa9\u3067\u518d\u5e30\u3092\u30b7\u30df\u30e5\u30ec\u30fc\u30c8 */\nint forLoopRecur(int n) {\n    // \u660e\u793a\u7684\u306a\u30b9\u30bf\u30c3\u30af\u3092\u4f7f\u7528\u3057\u3066\u30b7\u30b9\u30c6\u30e0\u30b3\u30fc\u30eb\u30b9\u30bf\u30c3\u30af\u3092\u30b7\u30df\u30e5\u30ec\u30fc\u30c8\n    stack&lt;int&gt; stack;\n    int res = 0;\n    // \u518d\u5e30\uff1a\u518d\u5e30\u547c\u3073\u51fa\u3057\n    for (int i = n; i &gt; 0; i--) {\n        // \u300c\u30b9\u30bf\u30c3\u30af\u3078\u306e\u30d7\u30c3\u30b7\u30e5\u300d\u3067\u300c\u518d\u5e30\u300d\u3092\u30b7\u30df\u30e5\u30ec\u30fc\u30c8\n        stack.push(i);\n    }\n    // \u623b\u308a\u5024\uff1a\u7d50\u679c\u3092\u8fd4\u3059\n    while (!stack.empty()) {\n        // \u300c\u30b9\u30bf\u30c3\u30af\u304b\u3089\u306e\u30dd\u30c3\u30d7\u300d\u3067\u300c\u623b\u308a\u5024\u300d\u3092\u30b7\u30df\u30e5\u30ec\u30fc\u30c8\n        res += stack.top();\n        stack.pop();\n    }\n    // res = 1+2+3+...+n\n    return res;\n}\n</code></pre> recursion.java<pre><code>/* \u53cd\u5fa9\u3067\u518d\u5e30\u3092\u30b7\u30df\u30e5\u30ec\u30fc\u30c8 */\nint forLoopRecur(int n) {\n    // \u660e\u793a\u7684\u306a\u30b9\u30bf\u30c3\u30af\u3092\u4f7f\u7528\u3057\u3066\u30b7\u30b9\u30c6\u30e0\u30b3\u30fc\u30eb\u30b9\u30bf\u30c3\u30af\u3092\u30b7\u30df\u30e5\u30ec\u30fc\u30c8\n    Stack&lt;Integer&gt; stack = new Stack&lt;&gt;();\n    int res = 0;\n    // \u518d\u5e30\uff1a\u518d\u5e30\u547c\u3073\u51fa\u3057\n    for (int i = n; i &gt; 0; i--) {\n        // \u300c\u30b9\u30bf\u30c3\u30af\u3078\u306e\u30d7\u30c3\u30b7\u30e5\u300d\u3067\u300c\u518d\u5e30\u300d\u3092\u30b7\u30df\u30e5\u30ec\u30fc\u30c8\n        stack.push(i);\n    }\n    // \u623b\u308a\u5024\uff1a\u7d50\u679c\u3092\u8fd4\u3059\n    while (!stack.isEmpty()) {\n        // \u300c\u30b9\u30bf\u30c3\u30af\u304b\u3089\u306e\u30dd\u30c3\u30d7\u300d\u3067\u300c\u623b\u308a\u5024\u300d\u3092\u30b7\u30df\u30e5\u30ec\u30fc\u30c8\n        res += stack.pop();\n    }\n    // res = 1+2+3+...+n\n    return res;\n}\n</code></pre> recursion.cs<pre><code>[class]{recursion}-[func]{ForLoopRecur}\n</code></pre> recursion.go<pre><code>[class]{}-[func]{forLoopRecur}\n</code></pre> recursion.swift<pre><code>[class]{}-[func]{forLoopRecur}\n</code></pre> recursion.js<pre><code>[class]{}-[func]{forLoopRecur}\n</code></pre> recursion.ts<pre><code>[class]{}-[func]{forLoopRecur}\n</code></pre> recursion.dart<pre><code>[class]{}-[func]{forLoopRecur}\n</code></pre> recursion.rs<pre><code>[class]{}-[func]{for_loop_recur}\n</code></pre> recursion.c<pre><code>[class]{}-[func]{forLoopRecur}\n</code></pre> recursion.kt<pre><code>[class]{}-[func]{forLoopRecur}\n</code></pre> recursion.rb<pre><code>[class]{}-[func]{for_loop_recur}\n</code></pre> recursion.zig<pre><code>[class]{}-[func]{forLoopRecur}\n</code></pre> <p>\u4e0a\u8a18\u306e\u30b3\u30fc\u30c9\u3092\u89b3\u5bdf\u3059\u308b\u3068\u3001\u518d\u5e30\u304c\u53cd\u5fa9\u306b\u5909\u63db\u3055\u308c\u305f\u3068\u304d\u3001\u30b3\u30fc\u30c9\u306f\u3088\u308a\u8907\u96d1\u306b\u306a\u308a\u307e\u3059\u3002\u53cd\u5fa9\u3068\u518d\u5e30\u306f\u3057\u3070\u3057\u3070\u76f8\u4e92\u306b\u5909\u63db\u3067\u304d\u307e\u3059\u304c\u30012\u3064\u306e\u7406\u7531\u3067\u305d\u3046\u3059\u308b\u3053\u3068\u304c\u5e38\u306b\u63a8\u5968\u3055\u308c\u308b\u308f\u3051\u3067\u306f\u3042\u308a\u307e\u305b\u3093\uff1a</p> <ul> <li>\u5909\u63db\u3055\u308c\u305f\u30b3\u30fc\u30c9\u306f\u7406\u89e3\u304c\u3088\u308a\u56f0\u96e3\u306b\u306a\u308a\u3001\u8aad\u307f\u306b\u304f\u304f\u306a\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002</li> <li>\u4e00\u90e8\u306e\u8907\u96d1\u306a\u554f\u984c\u3067\u306f\u3001\u30b7\u30b9\u30c6\u30e0\u306e\u547c\u3073\u51fa\u3057\u30b9\u30bf\u30c3\u30af\u306e\u52d5\u4f5c\u3092\u30b7\u30df\u30e5\u30ec\u30fc\u30c8\u3059\u308b\u3053\u3068\u306f\u975e\u5e38\u306b\u56f0\u96e3\u3067\u3059\u3002</li> </ul> <p>\u7d50\u8ad6\u3068\u3057\u3066\u3001\u53cd\u5fa9\u307e\u305f\u306f\u518d\u5e30\u3092\u9078\u629e\u3059\u308b\u304b\u306f\u554f\u984c\u306e\u5177\u4f53\u7684\u306a\u6027\u8cea\u306b\u3088\u308a\u307e\u3059\u3002\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u306e\u5b9f\u8df5\u3067\u306f\u3001\u4e21\u65b9\u306e\u9577\u6240\u3068\u77ed\u6240\u3092\u6bd4\u8f03\u691c\u8a0e\u3057\u3001\u624b\u5143\u306e\u72b6\u6cc1\u306b\u6700\u3082\u9069\u3057\u305f\u30a2\u30d7\u30ed\u30fc\u30c1\u3092\u9078\u629e\u3059\u308b\u3053\u3068\u304c\u91cd\u8981\u3067\u3059\u3002</p>"},{"location":"chapter_computational_complexity/performance_evaluation/","title":"2.1 \u00a0 \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u52b9\u7387\u8a55\u4fa1","text":"<p>\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u8a2d\u8a08\u306b\u304a\u3044\u3066\u3001\u79c1\u305f\u3061\u306f\u9806\u5e8f\u306b\u5f93\u3063\u3066\u4ee5\u4e0b\u306e2\u3064\u306e\u76ee\u6a19\u3092\u8ffd\u6c42\u3057\u307e\u3059\u3002</p> <ol> <li>\u554f\u984c\u306e\u89e3\u6c7a\u7b56\u3092\u898b\u3064\u3051\u308b: \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u3001\u6307\u5b9a\u3055\u308c\u305f\u5165\u529b\u7bc4\u56f2\u5185\u3067\u78ba\u5b9f\u306b\u6b63\u3057\u3044\u89e3\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3079\u304d\u3067\u3059\u3002</li> <li>\u6700\u9069\u89e3\u3092\u6c42\u3081\u308b: \u540c\u3058\u554f\u984c\u306b\u5bfe\u3057\u3066\u8907\u6570\u306e\u89e3\u6c7a\u7b56\u304c\u5b58\u5728\u3059\u308b\u5834\u5408\u304c\u3042\u308a\u3001\u79c1\u305f\u3061\u306f\u53ef\u80fd\u306a\u9650\u308a\u6700\u3082\u52b9\u7387\u7684\u306a\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u3092\u76ee\u6307\u3057\u307e\u3059\u3002</li> </ol> <p>\u3064\u307e\u308a\u3001\u554f\u984c\u3092\u89e3\u6c7a\u3067\u304d\u308b\u3053\u3068\u3092\u524d\u63d0\u3068\u3057\u3066\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u52b9\u7387\u304c\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u8a55\u4fa1\u3059\u308b\u4e3b\u8981\u306a\u57fa\u6e96\u3068\u306a\u3063\u3066\u304a\u308a\u3001\u3053\u308c\u306b\u306f\u4ee5\u4e0b\u306e2\u3064\u306e\u6b21\u5143\u304c\u542b\u307e\u308c\u307e\u3059\u3002</p> <ul> <li>\u6642\u9593\u52b9\u7387: \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u304c\u5b9f\u884c\u3055\u308c\u308b\u901f\u5ea6\u3002</li> <li>\u7a7a\u9593\u52b9\u7387: \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u304c\u5360\u6709\u3059\u308b\u30e1\u30e2\u30ea\u7a7a\u9593\u306e\u30b5\u30a4\u30ba\u3002</li> </ul> <p>\u8981\u3059\u308b\u306b\u3001\u79c1\u305f\u3061\u306e\u76ee\u6a19\u306f\u3001\u9ad8\u901f\u3067\u30e1\u30e2\u30ea\u52b9\u7387\u306e\u826f\u3044\u30c7\u30fc\u30bf\u69cb\u9020\u3068\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u8a2d\u8a08\u3059\u308b\u3053\u3068\u3067\u3059\u3002\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u52b9\u7387\u3092\u52b9\u679c\u7684\u306b\u8a55\u4fa1\u3059\u308b\u3053\u3068\u306f\u91cd\u8981\u3067\u3059\u3002\u306a\u305c\u306a\u3089\u3001\u305d\u3046\u3059\u308b\u3053\u3068\u3067\u521d\u3081\u3066\u69d8\u3005\u306a\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u6bd4\u8f03\u3057\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u8a2d\u8a08\u3068\u6700\u9069\u5316\u30d7\u30ed\u30bb\u30b9\u3092\u5c0e\u304f\u3053\u3068\u304c\u3067\u304d\u308b\u304b\u3089\u3067\u3059\u3002</p> <p>\u52b9\u7387\u8a55\u4fa1\u306b\u306f\u4e3b\u306b2\u3064\u306e\u65b9\u6cd5\u304c\u3042\u308a\u307e\u3059\uff1a\u5b9f\u969b\u306e\u30c6\u30b9\u30c8\u3068\u7406\u8ad6\u7684\u63a8\u5b9a\u3067\u3059\u3002</p>"},{"location":"chapter_computational_complexity/performance_evaluation/#211","title":"2.1.1 \u00a0 \u5b9f\u969b\u306e\u30c6\u30b9\u30c8","text":"<p>\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0<code>A</code>\u3068<code>B</code>\u304c\u3042\u308a\u3001\u3069\u3061\u3089\u3082\u540c\u3058\u554f\u984c\u3092\u89e3\u6c7a\u3067\u304d\u3001\u305d\u308c\u3089\u306e\u52b9\u7387\u3092\u6bd4\u8f03\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u3068\u3057\u307e\u3059\u3002\u6700\u3082\u76f4\u63a5\u7684\u306a\u65b9\u6cd5\u306f\u3001\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u3092\u4f7f\u7528\u3057\u3066\u3053\u308c\u30892\u3064\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u5b9f\u884c\u3057\u3001\u5b9f\u884c\u6642\u9593\u3068\u30e1\u30e2\u30ea\u4f7f\u7528\u91cf\u3092\u76e3\u8996\u30fb\u8a18\u9332\u3059\u308b\u3053\u3068\u3067\u3059\u3002\u3053\u306e\u8a55\u4fa1\u65b9\u6cd5\u306f\u5b9f\u969b\u306e\u72b6\u6cc1\u3092\u53cd\u6620\u3057\u307e\u3059\u304c\u3001\u5927\u304d\u306a\u5236\u9650\u304c\u3042\u308a\u307e\u3059\u3002</p> <p>\u4e00\u65b9\u3067\u3001\u30c6\u30b9\u30c8\u74b0\u5883\u304b\u3089\u306e\u5e72\u6e09\u3092\u6392\u9664\u3059\u308b\u3053\u3068\u306f\u56f0\u96e3\u3067\u3059\u3002\u30cf\u30fc\u30c9\u30a6\u30a7\u30a2\u69cb\u6210\u306f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u6027\u80fd\u306b\u5f71\u97ff\u3092\u4e0e\u3048\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u4e26\u5217\u5ea6\u306e\u9ad8\u3044\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u30de\u30eb\u30c1\u30b3\u30a2CPU\u3067\u306e\u5b9f\u884c\u306b\u3088\u308a\u9069\u3057\u3066\u3044\u307e\u3059\u3057\u3001\u96c6\u7d04\u7684\u306a\u30e1\u30e2\u30ea\u64cd\u4f5c\u3092\u542b\u3080\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u9ad8\u6027\u80fd\u30e1\u30e2\u30ea\u3067\u3088\u308a\u826f\u3044\u6027\u80fd\u3092\u767a\u63ee\u3057\u307e\u3059\u3002\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u30c6\u30b9\u30c8\u7d50\u679c\u306f\u3001\u7570\u306a\u308b\u30de\u30b7\u30f3\u9593\u3067\u5909\u308f\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u5e73\u5747\u52b9\u7387\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u306b\u8907\u6570\u306e\u30de\u30b7\u30f3\u3067\u30c6\u30b9\u30c8\u3059\u308b\u3053\u3068\u304c\u5b9f\u7528\u7684\u3067\u306a\u3044\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002</p> <p>\u4e00\u65b9\u3067\u3001\u5b8c\u5168\u306a\u30c6\u30b9\u30c8\u3092\u5b9f\u65bd\u3059\u308b\u3053\u3068\u306f\u975e\u5e38\u306b\u30ea\u30bd\u30fc\u30b9\u96c6\u7d04\u7684\u3067\u3059\u3002\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u52b9\u7387\u306f\u5165\u529b\u30c7\u30fc\u30bf\u30b5\u30a4\u30ba\u306b\u3088\u3063\u3066\u5909\u308f\u308a\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u30c7\u30fc\u30bf\u91cf\u304c\u5c11\u306a\u3044\u5834\u5408\u306f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0<code>A</code>\u304c<code>B</code>\u3088\u308a\u901f\u304f\u5b9f\u884c\u3055\u308c\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u304c\u3001\u30c7\u30fc\u30bf\u91cf\u304c\u591a\u3044\u5834\u5408\u306f\u30c6\u30b9\u30c8\u7d50\u679c\u304c\u9006\u306b\u306a\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u8aac\u5f97\u529b\u306e\u3042\u308b\u7d50\u8ad6\u3092\u5c0e\u304f\u305f\u3081\u306b\u306f\u3001\u5e45\u5e83\u3044\u5165\u529b\u30c7\u30fc\u30bf\u30b5\u30a4\u30ba\u3092\u30c6\u30b9\u30c8\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u3001\u3053\u308c\u306b\u306f\u904e\u5ea6\u306a\u8a08\u7b97\u30ea\u30bd\u30fc\u30b9\u304c\u5fc5\u8981\u306b\u306a\u308a\u307e\u3059\u3002</p>"},{"location":"chapter_computational_complexity/performance_evaluation/#212","title":"2.1.2 \u00a0 \u7406\u8ad6\u7684\u63a8\u5b9a","text":"<p>\u5b9f\u969b\u306e\u30c6\u30b9\u30c8\u306e\u5927\u304d\u306a\u5236\u9650\u306b\u3088\u308a\u3001\u8a08\u7b97\u306e\u307f\u3067\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u52b9\u7387\u3092\u8a55\u4fa1\u3059\u308b\u3053\u3068\u3092\u691c\u8a0e\u3067\u304d\u307e\u3059\u3002\u3053\u306e\u63a8\u5b9a\u65b9\u6cd5\u306f\u6f38\u8fd1\u7684\u8907\u96d1\u5ea6\u89e3\u6790\u3001\u307e\u305f\u306f\u5358\u306b\u8907\u96d1\u5ea6\u89e3\u6790\u3068\u3057\u3066\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\u3002</p> <p>\u8907\u96d1\u5ea6\u89e3\u6790\u306f\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5b9f\u884c\u306b\u5fc5\u8981\u306a\u6642\u9593\u3068\u7a7a\u9593\u30ea\u30bd\u30fc\u30b9\u3068\u5165\u529b\u30c7\u30fc\u30bf\u306e\u30b5\u30a4\u30ba\u3068\u306e\u95a2\u4fc2\u3092\u53cd\u6620\u3057\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u5165\u529b\u30c7\u30fc\u30bf\u306e\u30b5\u30a4\u30ba\u304c\u5897\u52a0\u3059\u308b\u306b\u3064\u308c\u3066\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306b\u5fc5\u8981\u306a\u6642\u9593\u3068\u7a7a\u9593\u306e\u5897\u52a0\u50be\u5411\u3092\u8a18\u8ff0\u3057\u307e\u3059\u3002\u3053\u306e\u5b9a\u7fa9\u306f\u8907\u96d1\u306b\u805e\u3053\u3048\u308b\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u304c\u3001\u3088\u308a\u826f\u304f\u7406\u89e3\u3059\u308b\u305f\u3081\u306b3\u3064\u306e\u91cd\u8981\u306a\u30dd\u30a4\u30f3\u30c8\u306b\u5206\u89e3\u3067\u304d\u307e\u3059\u3002</p> <ul> <li>\u300c\u6642\u9593\u3068\u7a7a\u9593\u30ea\u30bd\u30fc\u30b9\u300d\u306f\u3001\u305d\u308c\u305e\u308c\u6642\u9593\u8a08\u7b97\u91cf\u3068\u7a7a\u9593\u8a08\u7b97\u91cf\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002</li> <li>\u300c\u5165\u529b\u30c7\u30fc\u30bf\u306e\u30b5\u30a4\u30ba\u304c\u5897\u52a0\u3059\u308b\u306b\u3064\u308c\u3066\u300d\u306f\u3001\u8907\u96d1\u5ea6\u304c\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u52b9\u7387\u3068\u5165\u529b\u30c7\u30fc\u30bf\u91cf\u3068\u306e\u95a2\u4fc2\u3092\u53cd\u6620\u3059\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002</li> <li>\u300c\u6642\u9593\u3068\u7a7a\u9593\u306e\u5897\u52a0\u50be\u5411\u300d\u306f\u3001\u8907\u96d1\u5ea6\u89e3\u6790\u304c\u5b9f\u884c\u6642\u9593\u3084\u5360\u6709\u7a7a\u9593\u306e\u5177\u4f53\u7684\u306a\u5024\u3067\u306f\u306a\u304f\u3001\u6642\u9593\u3084\u7a7a\u9593\u304c\u5897\u52a0\u3059\u308b\u300c\u7387\u300d\u306b\u7126\u70b9\u3092\u5f53\u3066\u308b\u3053\u3068\u3092\u793a\u3057\u307e\u3059\u3002</li> </ul> <p>\u8907\u96d1\u5ea6\u89e3\u6790\u306f\u5b9f\u969b\u306e\u30c6\u30b9\u30c8\u65b9\u6cd5\u306e\u6b20\u70b9\u3092\u514b\u670d\u3057\u307e\u3059\u3002\u3053\u308c\u306f\u4ee5\u4e0b\u306e\u5074\u9762\u3067\u53cd\u6620\u3055\u308c\u307e\u3059\uff1a</p> <ul> <li>\u5b9f\u969b\u306b\u30b3\u30fc\u30c9\u3092\u5b9f\u884c\u3059\u308b\u5fc5\u8981\u304c\u306a\u3044\u305f\u3081\u3001\u3088\u308a\u74b0\u5883\u306b\u512a\u3057\u304f\u3001\u30a8\u30cd\u30eb\u30ae\u30fc\u52b9\u7387\u304c\u826f\u3044\u3067\u3059\u3002</li> <li>\u30c6\u30b9\u30c8\u74b0\u5883\u306b\u4f9d\u5b58\u305b\u305a\u3001\u3059\u3079\u3066\u306e\u52d5\u4f5c\u30d7\u30e9\u30c3\u30c8\u30d5\u30a9\u30fc\u30e0\u306b\u9069\u7528\u3067\u304d\u307e\u3059\u3002</li> <li>\u7570\u306a\u308b\u30c7\u30fc\u30bf\u91cf\u3067\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u52b9\u7387\u3092\u53cd\u6620\u3067\u304d\u3001\u7279\u306b\u5927\u91cf\u30c7\u30fc\u30bf\u3067\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u6027\u80fd\u3092\u793a\u3057\u307e\u3059\u3002</li> </ul> <p>Tip</p> <p>\u8907\u96d1\u5ea6\u306e\u6982\u5ff5\u306b\u3064\u3044\u3066\u307e\u3060\u6df7\u4e71\u3057\u3066\u3044\u308b\u5834\u5408\u3067\u3082\u3001\u5fc3\u914d\u3057\u306a\u3044\u3067\u304f\u3060\u3055\u3044\u3002\u4ee5\u964d\u306e\u7ae0\u3067\u8a73\u3057\u304f\u53d6\u308a\u4e0a\u3052\u307e\u3059\u3002</p> <p>\u8907\u96d1\u5ea6\u89e3\u6790\u306f\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u52b9\u7387\u3092\u8a55\u4fa1\u3059\u308b\u300c\u3082\u306e\u3055\u3057\u300d\u3092\u63d0\u4f9b\u3057\u3001\u5b9f\u884c\u306b\u5fc5\u8981\u306a\u6642\u9593\u3068\u7a7a\u9593\u30ea\u30bd\u30fc\u30b9\u3092\u6e2c\u5b9a\u3057\u3001\u7570\u306a\u308b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u52b9\u7387\u3092\u6bd4\u8f03\u3059\u308b\u3053\u3068\u3092\u53ef\u80fd\u306b\u3057\u307e\u3059\u3002</p> <p>\u8907\u96d1\u5ea6\u306f\u6570\u5b66\u7684\u6982\u5ff5\u3067\u3042\u308a\u3001\u521d\u5fc3\u8005\u306b\u306f\u62bd\u8c61\u7684\u3067\u56f0\u96e3\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u3002\u3053\u306e\u89b3\u70b9\u304b\u3089\u3001\u8907\u96d1\u5ea6\u89e3\u6790\u306f\u6700\u521d\u306b\u7d39\u4ecb\u3059\u308b\u306e\u306b\u6700\u3082\u9069\u3057\u305f\u30c8\u30d4\u30c3\u30af\u3067\u306f\u306a\u3044\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u3002\u3057\u304b\u3057\u3001\u7279\u5b9a\u306e\u30c7\u30fc\u30bf\u69cb\u9020\u3084\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u7279\u6027\u306b\u3064\u3044\u3066\u8b70\u8ad6\u3059\u308b\u3068\u304d\u3001\u305d\u306e\u901f\u5ea6\u3068\u7a7a\u9593\u4f7f\u7528\u91cf\u3092\u5206\u6790\u3059\u308b\u3053\u3068\u3092\u907f\u3051\u308b\u306e\u306f\u56f0\u96e3\u3067\u3059\u3002</p> <p>\u8981\u7d04\u3059\u308b\u3068\u3001\u30c7\u30fc\u30bf\u69cb\u9020\u3068\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306b\u6df1\u304f\u5165\u308b\u524d\u306b\u8907\u96d1\u5ea6\u89e3\u6790\u306e\u57fa\u672c\u7684\u306a\u7406\u89e3\u3092\u8eab\u306b\u3064\u3051\u308b\u3053\u3068\u3092\u304a\u52e7\u3081\u3057\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u7c21\u5358\u306a\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u8907\u96d1\u5ea6\u89e3\u6790\u3092\u5b9f\u884c\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002</p>"},{"location":"chapter_computational_complexity/space_complexity/","title":"2.4 \u00a0 \u7a7a\u9593\u8a08\u7b97\u91cf","text":"<p>\u7a7a\u9593\u8a08\u7b97\u91cf\u306f\u3001\u30c7\u30fc\u30bf\u91cf\u304c\u5897\u52a0\u3059\u308b\u306b\u3064\u308c\u3066\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u304c\u5360\u6709\u3059\u308b\u30e1\u30e2\u30ea\u7a7a\u9593\u306e\u5897\u52a0\u50be\u5411\u3092\u6e2c\u5b9a\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u3053\u306e\u6982\u5ff5\u306f\u6642\u9593\u8a08\u7b97\u91cf\u3068\u975e\u5e38\u306b\u4f3c\u3066\u3044\u307e\u3059\u304c\u3001\u300c\u5b9f\u884c\u6642\u9593\u300d\u304c\u300c\u5360\u6709\u30e1\u30e2\u30ea\u7a7a\u9593\u300d\u306b\u7f6e\u304d\u63db\u3048\u3089\u308c\u3066\u3044\u307e\u3059\u3002</p>"},{"location":"chapter_computational_complexity/space_complexity/#241","title":"2.4.1 \u00a0 \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306b\u95a2\u9023\u3059\u308b\u7a7a\u9593","text":"<p>\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u304c\u5b9f\u884c\u4e2d\u306b\u4f7f\u7528\u3059\u308b\u30e1\u30e2\u30ea\u7a7a\u9593\u306b\u306f\u3001\u4e3b\u306b\u4ee5\u4e0b\u306e\u7a2e\u985e\u304c\u3042\u308a\u307e\u3059\u3002</p> <ul> <li>\u5165\u529b\u7a7a\u9593: \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5165\u529b\u30c7\u30fc\u30bf\u3092\u683c\u7d0d\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002</li> <li>\u4e00\u6642\u7a7a\u9593: \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5b9f\u884c\u4e2d\u306b\u5909\u6570\u3001\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u3001\u95a2\u6570\u30b3\u30f3\u30c6\u30ad\u30b9\u30c8\u3001\u305d\u306e\u4ed6\u306e\u30c7\u30fc\u30bf\u3092\u683c\u7d0d\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002</li> <li>\u51fa\u529b\u7a7a\u9593: \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u51fa\u529b\u30c7\u30fc\u30bf\u3092\u683c\u7d0d\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002</li> </ul> <p>\u4e00\u822c\u7684\u306b\u3001\u7a7a\u9593\u8a08\u7b97\u91cf\u306e\u7d71\u8a08\u7bc4\u56f2\u306b\u306f\u300c\u4e00\u6642\u7a7a\u9593\u300d\u3068\u300c\u51fa\u529b\u7a7a\u9593\u300d\u306e\u4e21\u65b9\u304c\u542b\u307e\u308c\u307e\u3059\u3002</p> <p>\u4e00\u6642\u7a7a\u9593\u306f\u3055\u3089\u306b3\u3064\u306e\u90e8\u5206\u306b\u5206\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002</p> <ul> <li>\u4e00\u6642\u30c7\u30fc\u30bf: \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5b9f\u884c\u4e2d\u306b\u69d8\u3005\u306a\u5b9a\u6570\u3001\u5909\u6570\u3001\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u306a\u3069\u3092\u4fdd\u5b58\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002</li> <li>\u30b9\u30bf\u30c3\u30af\u30d5\u30ec\u30fc\u30e0\u7a7a\u9593: \u547c\u3073\u51fa\u3055\u308c\u305f\u95a2\u6570\u306e\u30b3\u30f3\u30c6\u30ad\u30b9\u30c8\u30c7\u30fc\u30bf\u3092\u4fdd\u5b58\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u30b7\u30b9\u30c6\u30e0\u306f\u95a2\u6570\u304c\u547c\u3073\u51fa\u3055\u308c\u308b\u305f\u3073\u306b\u30b9\u30bf\u30c3\u30af\u306e\u9802\u4e0a\u306b\u30b9\u30bf\u30c3\u30af\u30d5\u30ec\u30fc\u30e0\u3092\u4f5c\u6210\u3057\u3001\u95a2\u6570\u304c\u8fd4\u3055\u308c\u305f\u5f8c\u306b\u30b9\u30bf\u30c3\u30af\u30d5\u30ec\u30fc\u30e0\u7a7a\u9593\u3092\u89e3\u653e\u3057\u307e\u3059\u3002</li> <li>\u547d\u4ee4\u7a7a\u9593: \u30b3\u30f3\u30d1\u30a4\u30eb\u6e08\u307f\u30d7\u30ed\u30b0\u30e9\u30e0\u547d\u4ee4\u3092\u683c\u7d0d\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u3001\u5b9f\u969b\u306e\u7d71\u8a08\u3067\u306f\u901a\u5e38\u7121\u8996\u3067\u304d\u307e\u3059\u3002</li> </ul> <p>\u30d7\u30ed\u30b0\u30e9\u30e0\u306e\u7a7a\u9593\u8a08\u7b97\u91cf\u3092\u5206\u6790\u3059\u308b\u969b\u3001\u901a\u5e38\u306f\u4e00\u6642\u30c7\u30fc\u30bf\u3001\u30b9\u30bf\u30c3\u30af\u30d5\u30ec\u30fc\u30e0\u7a7a\u9593\u3001\u51fa\u529b\u30c7\u30fc\u30bf\u3092\u30ab\u30a6\u30f3\u30c8\u3057\u307e\u3059\u3002\u4ee5\u4e0b\u306e\u56f3\u306b\u793a\u3055\u308c\u3066\u3044\u307e\u3059\u3002</p> <p></p> <p> \u56f3 2-15 \u00a0 Space types used in algorithms </p> <p>\u95a2\u9023\u3059\u308b\u30b3\u30fc\u30c9\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinZig <pre><code>class Node:\n    \"\"\"\u30af\u30e9\u30b9\"\"\"\n    def __init__(self, x: int):\n        self.val: int = x               # \u30ce\u30fc\u30c9\u5024\n        self.next: Node | None = None   # \u6b21\u306e\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\n\ndef function() -&gt; int:\n    \"\"\"\u95a2\u6570\"\"\"\n    # \u7279\u5b9a\u306e\u64cd\u4f5c\u3092\u5b9f\u884c...\n    return 0\n\ndef algorithm(n) -&gt; int:    # \u5165\u529b\u30c7\u30fc\u30bf\n    A = 0                   # \u4e00\u6642\u30c7\u30fc\u30bf\uff08\u5b9a\u6570\u3001\u901a\u5e38\u5927\u6587\u5b57\uff09\n    b = 0                   # \u4e00\u6642\u30c7\u30fc\u30bf\uff08\u5909\u6570\uff09\n    node = Node(0)          # \u4e00\u6642\u30c7\u30fc\u30bf\uff08\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\uff09\n    c = function()          # \u30b9\u30bf\u30c3\u30af\u30d5\u30ec\u30fc\u30e0\u7a7a\u9593\uff08\u95a2\u6570\u547c\u3073\u51fa\u3057\uff09\n    return A + b + c        # \u51fa\u529b\u30c7\u30fc\u30bf\n</code></pre> <pre><code>/* \u69cb\u9020\u4f53 */\nstruct Node {\n    int val;\n    Node *next;\n    Node(int x) : val(x), next(nullptr) {}\n};\n\n/* \u95a2\u6570 */\nint func() {\n    // \u7279\u5b9a\u306e\u64cd\u4f5c\u3092\u5b9f\u884c...\n    return 0;\n}\n\nint algorithm(int n) {          // \u5165\u529b\u30c7\u30fc\u30bf\n    const int a = 0;            // \u4e00\u6642\u30c7\u30fc\u30bf\uff08\u5b9a\u6570\uff09\n    int b = 0;                  // \u4e00\u6642\u30c7\u30fc\u30bf\uff08\u5909\u6570\uff09\n    Node* node = new Node(0);   // \u4e00\u6642\u30c7\u30fc\u30bf\uff08\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\uff09\n    int c = func();             // \u30b9\u30bf\u30c3\u30af\u30d5\u30ec\u30fc\u30e0\u7a7a\u9593\uff08\u95a2\u6570\u547c\u3073\u51fa\u3057\uff09\n    return a + b + c;           // \u51fa\u529b\u30c7\u30fc\u30bf\n}\n</code></pre> <pre><code>/* \u30af\u30e9\u30b9 */\nclass Node {\n    int val;\n    Node next;\n    Node(int x) { val = x; }\n}\n\n/* \u95a2\u6570 */\nint function() {\n    // \u7279\u5b9a\u306e\u64cd\u4f5c\u3092\u5b9f\u884c...\n    return 0;\n}\n\nint algorithm(int n) {          // \u5165\u529b\u30c7\u30fc\u30bf\n    final int a = 0;            // \u4e00\u6642\u30c7\u30fc\u30bf\uff08\u5b9a\u6570\uff09\n    int b = 0;                  // \u4e00\u6642\u30c7\u30fc\u30bf\uff08\u5909\u6570\uff09\n    Node node = new Node(0);    // \u4e00\u6642\u30c7\u30fc\u30bf\uff08\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\uff09\n    int c = function();         // \u30b9\u30bf\u30c3\u30af\u30d5\u30ec\u30fc\u30e0\u7a7a\u9593\uff08\u95a2\u6570\u547c\u3073\u51fa\u3057\uff09\n    return a + b + c;           // \u51fa\u529b\u30c7\u30fc\u30bf\n}\n</code></pre> <pre><code>/* \u30af\u30e9\u30b9 */\nclass Node {\n    int val;\n    Node next;\n    Node(int x) { val = x; }\n}\n\n/* \u95a2\u6570 */\nint Function() {\n    // \u7279\u5b9a\u306e\u64cd\u4f5c\u3092\u5b9f\u884c...\n    return 0;\n}\n\nint Algorithm(int n) {  // \u5165\u529b\u30c7\u30fc\u30bf\n    const int a = 0;    // \u4e00\u6642\u30c7\u30fc\u30bf\uff08\u5b9a\u6570\uff09\n    int b = 0;          // \u4e00\u6642\u30c7\u30fc\u30bf\uff08\u5909\u6570\uff09\n    Node node = new(0); // \u4e00\u6642\u30c7\u30fc\u30bf\uff08\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\uff09\n    int c = Function(); // \u30b9\u30bf\u30c3\u30af\u30d5\u30ec\u30fc\u30e0\u7a7a\u9593\uff08\u95a2\u6570\u547c\u3073\u51fa\u3057\uff09\n    return a + b + c;   // \u51fa\u529b\u30c7\u30fc\u30bf\n}\n</code></pre> <pre><code>/* \u69cb\u9020\u4f53 */\ntype node struct {\n    val  int\n    next *node\n}\n\n/* \u30ce\u30fc\u30c9\u69cb\u9020\u4f53\u3092\u4f5c\u6210 */\nfunc newNode(val int) *node {\n    return &amp;node{val: val}\n}\n\n/* \u95a2\u6570 */\nfunc function() int {\n    // \u7279\u5b9a\u306e\u64cd\u4f5c\u3092\u5b9f\u884c...\n    return 0\n}\n\nfunc algorithm(n int) int { // \u5165\u529b\u30c7\u30fc\u30bf\n    const a = 0             // \u4e00\u6642\u30c7\u30fc\u30bf\uff08\u5b9a\u6570\uff09\n    b := 0                  // \u4e00\u6642\u30c7\u30fc\u30bf\uff08\u5909\u6570\uff09\n    newNode(0)              // \u4e00\u6642\u30c7\u30fc\u30bf\uff08\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\uff09\n    c := function()         // \u30b9\u30bf\u30c3\u30af\u30d5\u30ec\u30fc\u30e0\u7a7a\u9593\uff08\u95a2\u6570\u547c\u3073\u51fa\u3057\uff09\n    return a + b + c        // \u51fa\u529b\u30c7\u30fc\u30bf\n}\n</code></pre> <pre><code>/* \u30af\u30e9\u30b9 */\nclass Node {\n    var val: Int\n    var next: Node?\n\n    init(x: Int) {\n        val = x\n    }\n}\n\n/* \u95a2\u6570 */\nfunc function() -&gt; Int {\n    // \u7279\u5b9a\u306e\u64cd\u4f5c\u3092\u5b9f\u884c...\n    return 0\n}\n\nfunc algorithm(n: Int) -&gt; Int { // \u5165\u529b\u30c7\u30fc\u30bf\n    let a = 0                   // \u4e00\u6642\u30c7\u30fc\u30bf\uff08\u5b9a\u6570\uff09\n    var b = 0                   // \u4e00\u6642\u30c7\u30fc\u30bf\uff08\u5909\u6570\uff09\n    let node = Node(x: 0)       // \u4e00\u6642\u30c7\u30fc\u30bf\uff08\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\uff09\n    let c = function()          // \u30b9\u30bf\u30c3\u30af\u30d5\u30ec\u30fc\u30e0\u7a7a\u9593\uff08\u95a2\u6570\u547c\u3073\u51fa\u3057\uff09\n    return a + b + c            // \u51fa\u529b\u30c7\u30fc\u30bf\n}\n</code></pre> <pre><code>/* \u30af\u30e9\u30b9 */\nclass Node {\n    val;\n    next;\n    constructor(val) {\n        this.val = val === undefined ? 0 : val; // \u30ce\u30fc\u30c9\u5024\n        this.next = null;                       // \u6b21\u306e\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\n    }\n}\n\n/* \u95a2\u6570 */\nfunction constFunc() {\n    // \u7279\u5b9a\u306e\u64cd\u4f5c\u3092\u5b9f\u884c\n    return 0;\n}\n\nfunction algorithm(n) {         // \u5165\u529b\u30c7\u30fc\u30bf\n    const a = 0;                // \u4e00\u6642\u30c7\u30fc\u30bf\uff08\u5b9a\u6570\uff09\n    let b = 0;                  // \u4e00\u6642\u30c7\u30fc\u30bf\uff08\u5909\u6570\uff09\n    const node = new Node(0);   // \u4e00\u6642\u30c7\u30fc\u30bf\uff08\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\uff09\n    const c = constFunc();      // \u30b9\u30bf\u30c3\u30af\u30d5\u30ec\u30fc\u30e0\u7a7a\u9593\uff08\u95a2\u6570\u547c\u3073\u51fa\u3057\uff09\n    return a + b + c;           // \u51fa\u529b\u30c7\u30fc\u30bf\n}\n</code></pre> <pre><code>/* \u30af\u30e9\u30b9 */\nclass Node {\n    val: number;\n    next: Node | null;\n    constructor(val?: number) {\n        this.val = val === undefined ? 0 : val; // \u30ce\u30fc\u30c9\u5024\n        this.next = null;                       // \u6b21\u306e\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\n    }\n}\n\n/* \u95a2\u6570 */\nfunction constFunc(): number {\n    // \u7279\u5b9a\u306e\u64cd\u4f5c\u3092\u5b9f\u884c\n    return 0;\n}\n\nfunction algorithm(n: number): number { // \u5165\u529b\u30c7\u30fc\u30bf\n    const a = 0;                        // \u4e00\u6642\u30c7\u30fc\u30bf\uff08\u5b9a\u6570\uff09\n    let b = 0;                          // \u4e00\u6642\u30c7\u30fc\u30bf\uff08\u5909\u6570\uff09\n    const node = new Node(0);           // \u4e00\u6642\u30c7\u30fc\u30bf\uff08\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\uff09\n    const c = constFunc();              // \u30b9\u30bf\u30c3\u30af\u30d5\u30ec\u30fc\u30e0\u7a7a\u9593\uff08\u95a2\u6570\u547c\u3073\u51fa\u3057\uff09\n    return a + b + c;                   // \u51fa\u529b\u30c7\u30fc\u30bf\n}\n</code></pre> <pre><code>/* \u30af\u30e9\u30b9 */\nclass Node {\n  int val;\n  Node next;\n  Node(this.val, [this.next]);\n}\n\n/* \u95a2\u6570 */\nint function() {\n  // \u7279\u5b9a\u306e\u64cd\u4f5c\u3092\u5b9f\u884c...\n  return 0;\n}\n\nint algorithm(int n) {  // \u5165\u529b\u30c7\u30fc\u30bf\n  const int a = 0;      // \u4e00\u6642\u30c7\u30fc\u30bf\uff08\u5b9a\u6570\uff09\n  int b = 0;            // \u4e00\u6642\u30c7\u30fc\u30bf\uff08\u5909\u6570\uff09\n  Node node = Node(0);  // \u4e00\u6642\u30c7\u30fc\u30bf\uff08\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\uff09\n  int c = function();   // \u30b9\u30bf\u30c3\u30af\u30d5\u30ec\u30fc\u30e0\u7a7a\u9593\uff08\u95a2\u6570\u547c\u3073\u51fa\u3057\uff09\n  return a + b + c;     // \u51fa\u529b\u30c7\u30fc\u30bf\n}\n</code></pre> <pre><code>use std::rc::Rc;\nuse std::cell::RefCell;\n\n/* \u69cb\u9020\u4f53 */\nstruct Node {\n    val: i32,\n    next: Option&lt;Rc&lt;RefCell&lt;Node&gt;&gt;&gt;,\n}\n\n/* \u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf */\nimpl Node {\n    fn new(val: i32) -&gt; Self {\n        Self { val: val, next: None }\n    }\n}\n\n/* \u95a2\u6570 */\nfn function() -&gt; i32 {\n    // \u7279\u5b9a\u306e\u64cd\u4f5c\u3092\u5b9f\u884c...\n    return 0;\n}\n\nfn algorithm(n: i32) -&gt; i32 {   // \u5165\u529b\u30c7\u30fc\u30bf\n    const a: i32 = 0;           // \u4e00\u6642\u30c7\u30fc\u30bf\uff08\u5b9a\u6570\uff09\n    let mut b = 0;              // \u4e00\u6642\u30c7\u30fc\u30bf\uff08\u5909\u6570\uff09\n    let node = Node::new(0);    // \u4e00\u6642\u30c7\u30fc\u30bf\uff08\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\uff09\n    let c = function();         // \u30b9\u30bf\u30c3\u30af\u30d5\u30ec\u30fc\u30e0\u7a7a\u9593\uff08\u95a2\u6570\u547c\u3073\u51fa\u3057\uff09\n    return a + b + c;           // \u51fa\u529b\u30c7\u30fc\u30bf\n}\n</code></pre> <pre><code>/* \u95a2\u6570 */\nint func() {\n    // \u7279\u5b9a\u306e\u64cd\u4f5c\u3092\u5b9f\u884c...\n    return 0;\n}\n\nint algorithm(int n) {  // \u5165\u529b\u30c7\u30fc\u30bf\n    const int a = 0;    // \u4e00\u6642\u30c7\u30fc\u30bf\uff08\u5b9a\u6570\uff09\n    int b = 0;          // \u4e00\u6642\u30c7\u30fc\u30bf\uff08\u5909\u6570\uff09\n    int c = func();     // \u30b9\u30bf\u30c3\u30af\u30d5\u30ec\u30fc\u30e0\u7a7a\u9593\uff08\u95a2\u6570\u547c\u3073\u51fa\u3057\uff09\n    return a + b + c;   // \u51fa\u529b\u30c7\u30fc\u30bf\n}\n</code></pre> <pre><code>\n</code></pre> <pre><code>\n</code></pre>"},{"location":"chapter_computational_complexity/space_complexity/#242","title":"2.4.2 \u00a0 \u8a08\u7b97\u65b9\u6cd5","text":"<p>\u7a7a\u9593\u8a08\u7b97\u91cf\u3092\u8a08\u7b97\u3059\u308b\u65b9\u6cd5\u306f\u6642\u9593\u8a08\u7b97\u91cf\u3068\u307b\u307c\u540c\u69d8\u3067\u3001\u7d71\u8a08\u5bfe\u8c61\u3092\u300c\u64cd\u4f5c\u6570\u300d\u304b\u3089\u300c\u4f7f\u7528\u7a7a\u9593\u306e\u30b5\u30a4\u30ba\u300d\u306b\u5909\u66f4\u3059\u308b\u3060\u3051\u3067\u3059\u3002</p> <p>\u3057\u304b\u3057\u3001\u6642\u9593\u8a08\u7b97\u91cf\u3068\u306f\u7570\u306a\u308a\u3001\u901a\u5e38\u306f\u6700\u60aa\u30b1\u30fc\u30b9\u7a7a\u9593\u8a08\u7b97\u91cf\u306e\u307f\u306b\u7126\u70b9\u3092\u5f53\u3066\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u30e1\u30e2\u30ea\u7a7a\u9593\u304c\u30cf\u30fc\u30c9\u8981\u4ef6\u3067\u3042\u308a\u3001\u3059\u3079\u3066\u306e\u5165\u529b\u30c7\u30fc\u30bf\u306e\u4e0b\u3067\u5341\u5206\u306a\u30e1\u30e2\u30ea\u7a7a\u9593\u304c\u78ba\u4fdd\u3055\u308c\u3066\u3044\u308b\u3053\u3068\u3092\u4fdd\u8a3c\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u305f\u3081\u3067\u3059\u3002</p> <p>\u4ee5\u4e0b\u306e\u30b3\u30fc\u30c9\u3092\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u6700\u60aa\u30b1\u30fc\u30b9\u7a7a\u9593\u8a08\u7b97\u91cf\u306e\u300c\u6700\u60aa\u30b1\u30fc\u30b9\u300d\u3068\u3044\u3046\u7528\u8a9e\u306b\u306f2\u3064\u306e\u610f\u5473\u304c\u3042\u308a\u307e\u3059\u3002</p> <ol> <li>\u6700\u60aa\u306e\u5165\u529b\u30c7\u30fc\u30bf\u306b\u57fa\u3065\u304f: \\(n &lt; 10\\)\u306e\u5834\u5408\u3001\u7a7a\u9593\u8a08\u7b97\u91cf\u306f\\(O(1)\\)\u3067\u3059\u304c\u3001\\(n &gt; 10\\)\u306e\u5834\u5408\u3001\u521d\u671f\u5316\u3055\u308c\u305f\u914d\u5217<code>nums</code>\u304c\\(O(n)\\)\u306e\u7a7a\u9593\u3092\u5360\u6709\u3059\u308b\u305f\u3081\u3001\u6700\u60aa\u30b1\u30fc\u30b9\u7a7a\u9593\u8a08\u7b97\u91cf\u306f\\(O(n)\\)\u3067\u3059\u3002</li> <li>\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5b9f\u884c\u4e2d\u306b\u4f7f\u7528\u3055\u308c\u308b\u30d4\u30fc\u30af\u30e1\u30e2\u30ea\u306b\u57fa\u3065\u304f: \u4f8b\u3048\u3070\u3001\u6700\u5f8c\u306e\u884c\u3092\u5b9f\u884c\u3059\u308b\u524d\u3001\u30d7\u30ed\u30b0\u30e9\u30e0\u306f\\(O(1)\\)\u306e\u7a7a\u9593\u3092\u5360\u6709\u3057\u307e\u3059\u3002\u914d\u5217<code>nums</code>\u3092\u521d\u671f\u5316\u3059\u308b\u969b\u3001\u30d7\u30ed\u30b0\u30e9\u30e0\u306f\\(O(n)\\)\u306e\u7a7a\u9593\u3092\u5360\u6709\u3059\u308b\u305f\u3081\u3001\u6700\u60aa\u30b1\u30fc\u30b9\u7a7a\u9593\u8a08\u7b97\u91cf\u306f\\(O(n)\\)\u3067\u3059\u3002</li> </ol> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinZig <pre><code>def algorithm(n: int):\n    a = 0               # O(1)\n    b = [0] * 10000     # O(1)\n    if n &gt; 10:\n        nums = [0] * n  # O(n)\n</code></pre> <pre><code>void algorithm(int n) {\n    int a = 0;               // O(1)\n    vector&lt;int&gt; b(10000);    // O(1)\n    if (n &gt; 10)\n        vector&lt;int&gt; nums(n); // O(n)\n}\n</code></pre> <pre><code>void algorithm(int n) {\n    int a = 0;                   // O(1)\n    int[] b = new int[10000];    // O(1)\n    if (n &gt; 10)\n        int[] nums = new int[n]; // O(n)\n}\n</code></pre> <pre><code>void Algorithm(int n) {\n    int a = 0;                   // O(1)\n    int[] b = new int[10000];    // O(1)\n    if (n &gt; 10) {\n        int[] nums = new int[n]; // O(n)\n    }\n}\n</code></pre> <pre><code>func algorithm(n int) {\n    a := 0                      // O(1)\n    b := make([]int, 10000)     // O(1)\n    var nums []int\n    if n &gt; 10 {\n        nums := make([]int, n)  // O(n)\n    }\n    fmt.Println(a, b, nums)\n}\n</code></pre> <pre><code>func algorithm(n: Int) {\n    let a = 0 // O(1)\n    let b = Array(repeating: 0, count: 10000) // O(1)\n    if n &gt; 10 {\n        let nums = Array(repeating: 0, count: n) // O(n)\n    }\n}\n</code></pre> <pre><code>function algorithm(n) {\n    const a = 0;                   // O(1)\n    const b = new Array(10000);    // O(1)\n    if (n &gt; 10) {\n        const nums = new Array(n); // O(n)\n    }\n}\n</code></pre> <pre><code>function algorithm(n: number): void {\n    const a = 0;                   // O(1)\n    const b = new Array(10000);    // O(1)\n    if (n &gt; 10) {\n        const nums = new Array(n); // O(n)\n    }\n}\n</code></pre> <pre><code>void algorithm(int n) {\n  int a = 0;                            // O(1)\n  List&lt;int&gt; b = List.filled(10000, 0);  // O(1)\n  if (n &gt; 10) {\n    List&lt;int&gt; nums = List.filled(n, 0); // O(n)\n  }\n}\n</code></pre> <pre><code>fn algorithm(n: i32) {\n    let a = 0;                           // O(1)\n    let b = [0; 10000];                  // O(1)\n    if n &gt; 10 {\n        let nums = vec![0; n as usize];  // O(n)\n    }\n}\n</code></pre> <pre><code>void algorithm(int n) {\n    int a = 0;               // O(1)\n    int b[10000];            // O(1)\n    if (n &gt; 10)\n        int nums[n] = {0};   // O(n)\n}\n</code></pre> <pre><code>\n</code></pre> <pre><code>\n</code></pre> <p>\u518d\u5e30\u95a2\u6570\u3067\u306f\u3001\u30b9\u30bf\u30c3\u30af\u30d5\u30ec\u30fc\u30e0\u7a7a\u9593\u3092\u8003\u616e\u306b\u5165\u308c\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u4ee5\u4e0b\u306e\u30b3\u30fc\u30c9\u3092\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinZig <pre><code>def function() -&gt; int:\n    # \u7279\u5b9a\u306e\u64cd\u4f5c\u3092\u5b9f\u884c\n    return 0\n\ndef loop(n: int):\n    \"\"\"\u30eb\u30fc\u30d7 O(1)\"\"\"\n    for _ in range(n):\n        function()\n\ndef recur(n: int):\n    \"\"\"\u518d\u5e30 O(n)\"\"\"\n    if n == 1:\n        return\n    return recur(n - 1)\n</code></pre> <pre><code>int func() {\n    // \u7279\u5b9a\u306e\u64cd\u4f5c\u3092\u5b9f\u884c\n    return 0;\n}\n/* \u30b5\u30a4\u30af\u30eb O(1) */\nvoid loop(int n) {\n    for (int i = 0; i &lt; n; i++) {\n        func();\n    }\n}\n/* \u518d\u5e30 O(n) */\nvoid recur(int n) {\n    if (n == 1) return;\n    recur(n - 1);\n}\n</code></pre> <pre><code>int function() {\n    // \u7279\u5b9a\u306e\u64cd\u4f5c\u3092\u5b9f\u884c\n    return 0;\n}\n/* \u30b5\u30a4\u30af\u30eb O(1) */\nvoid loop(int n) {\n    for (int i = 0; i &lt; n; i++) {\n        function();\n    }\n}\n/* \u518d\u5e30 O(n) */\nvoid recur(int n) {\n    if (n == 1) return;\n    recur(n - 1);\n}\n</code></pre> <pre><code>int Function() {\n    // \u7279\u5b9a\u306e\u64cd\u4f5c\u3092\u5b9f\u884c\n    return 0;\n}\n/* \u30b5\u30a4\u30af\u30eb O(1) */\nvoid Loop(int n) {\n    for (int i = 0; i &lt; n; i++) {\n        Function();\n    }\n}\n/* \u518d\u5e30 O(n) */\nint Recur(int n) {\n    if (n == 1) return 1;\n    return Recur(n - 1);\n}\n</code></pre> <pre><code>func function() int {\n    // \u7279\u5b9a\u306e\u64cd\u4f5c\u3092\u5b9f\u884c\n    return 0\n}\n\n/* \u30b5\u30a4\u30af\u30eb O(1) */\nfunc loop(n int) {\n    for i := 0; i &lt; n; i++ {\n        function()\n    }\n}\n\n/* \u518d\u5e30 O(n) */\nfunc recur(n int) {\n    if n == 1 {\n        return\n    }\n    recur(n - 1)\n}\n</code></pre> <pre><code>@discardableResult\nfunc function() -&gt; Int {\n    // \u7279\u5b9a\u306e\u64cd\u4f5c\u3092\u5b9f\u884c\n    return 0\n}\n\n/* \u30b5\u30a4\u30af\u30eb O(1) */\nfunc loop(n: Int) {\n    for _ in 0 ..&lt; n {\n        function()\n    }\n}\n\n/* \u518d\u5e30 O(n) */\nfunc recur(n: Int) {\n    if n == 1 {\n        return\n    }\n    recur(n: n - 1)\n}\n</code></pre> <pre><code>function constFunc() {\n    // \u7279\u5b9a\u306e\u64cd\u4f5c\u3092\u5b9f\u884c\n    return 0;\n}\n/* \u30b5\u30a4\u30af\u30eb O(1) */\nfunction loop(n) {\n    for (let i = 0; i &lt; n; i++) {\n        constFunc();\n    }\n}\n/* \u518d\u5e30 O(n) */\nfunction recur(n) {\n    if (n === 1) return;\n    return recur(n - 1);\n}\n</code></pre> <pre><code>function constFunc(): number {\n    // \u7279\u5b9a\u306e\u64cd\u4f5c\u3092\u5b9f\u884c\n    return 0;\n}\n/* \u30b5\u30a4\u30af\u30eb O(1) */\nfunction loop(n: number): void {\n    for (let i = 0; i &lt; n; i++) {\n        constFunc();\n    }\n}\n/* \u518d\u5e30 O(n) */\nfunction recur(n: number): void {\n    if (n === 1) return;\n    return recur(n - 1);\n}\n</code></pre> <pre><code>int function() {\n  // \u7279\u5b9a\u306e\u64cd\u4f5c\u3092\u5b9f\u884c\n  return 0;\n}\n/* \u30b5\u30a4\u30af\u30eb O(1) */\nvoid loop(int n) {\n  for (int i = 0; i &lt; n; i++) {\n    function();\n  }\n}\n/* \u518d\u5e30 O(n) */\nvoid recur(int n) {\n  if (n == 1) return;\n  recur(n - 1);\n}\n</code></pre> <pre><code>fn function() -&gt; i32 {\n    // \u7279\u5b9a\u306e\u64cd\u4f5c\u3092\u5b9f\u884c\n    return 0;\n}\n/* \u30b5\u30a4\u30af\u30eb O(1) */\nfn loop(n: i32) {\n    for i in 0..n {\n        function();\n    }\n}\n/* \u518d\u5e30 O(n) */\nvoid recur(n: i32) {\n    if n == 1 {\n        return;\n    }\n    recur(n - 1);\n}\n</code></pre> <pre><code>int func() {\n    // \u7279\u5b9a\u306e\u64cd\u4f5c\u3092\u5b9f\u884c\n    return 0;\n}\n/* \u30b5\u30a4\u30af\u30eb O(1) */\nvoid loop(int n) {\n    for (int i = 0; i &lt; n; i++) {\n        func();\n    }\n}\n/* \u518d\u5e30 O(n) */\nvoid recur(int n) {\n    if (n == 1) return;\n    recur(n - 1);\n}\n</code></pre> <pre><code>\n</code></pre> <pre><code>\n</code></pre> <p><code>loop()</code>\u95a2\u6570\u3068<code>recur()</code>\u95a2\u6570\u306e\u6642\u9593\u8a08\u7b97\u91cf\u306f\u4e21\u65b9\u3068\u3082\\(O(n)\\)\u3067\u3059\u304c\u3001\u305d\u308c\u3089\u306e\u7a7a\u9593\u8a08\u7b97\u91cf\u306f\u7570\u306a\u308a\u307e\u3059\u3002</p> <ul> <li><code>loop()</code>\u95a2\u6570\u306f\u30eb\u30fc\u30d7\u5185\u3067<code>function()</code>\u3092\\(n\\)\u56de\u547c\u3073\u51fa\u3057\u3001\u5404\u53cd\u5fa9\u306e<code>function()</code>\u306f\u8fd4\u3063\u3066\u305d\u306e\u30b9\u30bf\u30c3\u30af\u30d5\u30ec\u30fc\u30e0\u7a7a\u9593\u3092\u89e3\u653e\u3059\u308b\u305f\u3081\u3001\u7a7a\u9593\u8a08\u7b97\u91cf\u306f\\(O(1)\\)\u306e\u307e\u307e\u3067\u3059\u3002</li> <li>\u518d\u5e30\u95a2\u6570<code>recur()</code>\u306f\u5b9f\u884c\u4e2d\u306b\\(n\\)\u500b\u306e\u672a\u8fd4\u5374\u306e<code>recur()</code>\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u304c\u540c\u6642\u306b\u5b58\u5728\u3059\u308b\u305f\u3081\u3001\\(O(n)\\)\u306e\u30b9\u30bf\u30c3\u30af\u30d5\u30ec\u30fc\u30e0\u7a7a\u9593\u3092\u5360\u6709\u3057\u307e\u3059\u3002</li> </ul>"},{"location":"chapter_computational_complexity/space_complexity/#243","title":"2.4.3 \u00a0 \u4e00\u822c\u7684\u306a\u7a2e\u985e","text":"<p>\u5165\u529b\u30c7\u30fc\u30bf\u306e\u30b5\u30a4\u30ba\u3092\\(n\\)\u3068\u3059\u308b\u3068\u3001\u4e0b\u56f3\u306f\u4e00\u822c\u7684\u306a\u7a7a\u9593\u8a08\u7b97\u91cf\u306e\u7a2e\u985e\u3092\u793a\u3057\u3066\u3044\u307e\u3059\uff08\u4f4e\u3044\u3082\u306e\u304b\u3089\u9ad8\u3044\u3082\u306e\u3078\u3068\u4e26\u3079\u3089\u308c\u3066\u3044\u307e\u3059\uff09\u3002</p> \\[ \\begin{aligned} &amp; O(1) &lt; O(\\log n) &lt; O(n) &lt; O(n^2) &lt; O(2^n) \\newline &amp; \\text{\u5b9a\u6570} &lt; \\text{\u5bfe\u6570} &lt; \\text{\u7dda\u5f62} &lt; \\text{\u4e8c\u6b21} &lt; \\text{\u6307\u6570} \\end{aligned} \\] <p></p> <p> \u56f3 2-16 \u00a0 Common types of space complexity </p>"},{"location":"chapter_computational_complexity/space_complexity/#1-o1","title":"1. \u00a0 \u5b9a\u6570\u30aa\u30fc\u30c0\u30fc \\(O(1)\\)","text":"<p>\u5b9a\u6570\u30aa\u30fc\u30c0\u30fc\u306f\u3001\u5165\u529b\u30c7\u30fc\u30bf\u30b5\u30a4\u30ba\\(n\\)\u3068\u306f\u7121\u95a2\u4fc2\u306a\u5b9a\u6570\u3001\u5909\u6570\u3001\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u3067\u4e00\u822c\u7684\u3067\u3059\u3002</p> <p>\u30eb\u30fc\u30d7\u3067\u5909\u6570\u3092\u521d\u671f\u5316\u3057\u305f\u308a\u95a2\u6570\u3092\u547c\u3073\u51fa\u3057\u305f\u308a\u3059\u308b\u305f\u3081\u306b\u5360\u6709\u3055\u308c\u308b\u30e1\u30e2\u30ea\u306f\u3001\u6b21\u306e\u30b5\u30a4\u30af\u30eb\u306b\u5165\u308b\u969b\u306b\u89e3\u653e\u3055\u308c\u3001\u7a7a\u9593\u4e0a\u3067\u7d2f\u7a4d\u3055\u308c\u306a\u3044\u305f\u3081\u3001\u7a7a\u9593\u8a08\u7b97\u91cf\u306f\\(O(1)\\)\u306e\u307e\u307e\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig space_complexity.py<pre><code>def function() -&gt; int:\n    \"\"\"\u95a2\u6570\"\"\"\n    # \u4f55\u3089\u304b\u306e\u64cd\u4f5c\u3092\u5b9f\u884c\n    return 0\n\ndef constant(n: int):\n    \"\"\"\u5b9a\u6570\u8907\u96d1\u5ea6\"\"\"\n    # \u5b9a\u6570\u3001\u5909\u6570\u3001\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u306f O(1) \u306e\u30b9\u30da\u30fc\u30b9\u3092\u5360\u6709\n    a = 0\n    nums = [0] * 10000\n    node = ListNode(0)\n    # \u30eb\u30fc\u30d7\u5185\u306e\u5909\u6570\u306f O(1) \u306e\u30b9\u30da\u30fc\u30b9\u3092\u5360\u6709\n    for _ in range(n):\n        c = 0\n    # \u30eb\u30fc\u30d7\u5185\u306e\u95a2\u6570\u306f O(1) \u306e\u30b9\u30da\u30fc\u30b9\u3092\u5360\u6709\n    for _ in range(n):\n        function()\n</code></pre> space_complexity.cpp<pre><code>/* \u95a2\u6570 */\nint func() {\n    // \u4f55\u3089\u304b\u306e\u64cd\u4f5c\u3092\u5b9f\u884c\n    return 0;\n}\n\n/* \u5b9a\u6570\u8a08\u7b97\u91cf */\nvoid constant(int n) {\n    // \u5b9a\u6570\u3001\u5909\u6570\u3001\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u306f O(1) \u7a7a\u9593\u3092\u5360\u3081\u308b\n    const int a = 0;\n    int b = 0;\n    vector&lt;int&gt; nums(10000);\n    ListNode node(0);\n    // \u30eb\u30fc\u30d7\u5185\u306e\u5909\u6570\u306f O(1) \u7a7a\u9593\u3092\u5360\u3081\u308b\n    for (int i = 0; i &lt; n; i++) {\n        int c = 0;\n    }\n    // \u30eb\u30fc\u30d7\u5185\u306e\u95a2\u6570\u306f O(1) \u7a7a\u9593\u3092\u5360\u3081\u308b\n    for (int i = 0; i &lt; n; i++) {\n        func();\n    }\n}\n</code></pre> space_complexity.java<pre><code>/* \u95a2\u6570 */\nint function() {\n    // \u4f55\u3089\u304b\u306e\u64cd\u4f5c\u3092\u5b9f\u884c\n    return 0;\n}\n\n/* \u5b9a\u6570\u8a08\u7b97\u91cf */\nvoid constant(int n) {\n    // \u5b9a\u6570\u3001\u5909\u6570\u3001\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u306f O(1) \u7a7a\u9593\u3092\u5360\u3081\u308b\n    final int a = 0;\n    int b = 0;\n    int[] nums = new int[10000];\n    ListNode node = new ListNode(0);\n    // \u30eb\u30fc\u30d7\u5185\u306e\u5909\u6570\u306f O(1) \u7a7a\u9593\u3092\u5360\u3081\u308b\n    for (int i = 0; i &lt; n; i++) {\n        int c = 0;\n    }\n    // \u30eb\u30fc\u30d7\u5185\u306e\u95a2\u6570\u306f O(1) \u7a7a\u9593\u3092\u5360\u3081\u308b\n    for (int i = 0; i &lt; n; i++) {\n        function();\n    }\n}\n</code></pre> space_complexity.cs<pre><code>[class]{space_complexity}-[func]{Function}\n\n[class]{space_complexity}-[func]{Constant}\n</code></pre> space_complexity.go<pre><code>[class]{}-[func]{function}\n\n[class]{}-[func]{spaceConstant}\n</code></pre> space_complexity.swift<pre><code>[class]{}-[func]{function}\n\n[class]{}-[func]{constant}\n</code></pre> space_complexity.js<pre><code>[class]{}-[func]{constFunc}\n\n[class]{}-[func]{constant}\n</code></pre> space_complexity.ts<pre><code>[class]{}-[func]{constFunc}\n\n[class]{}-[func]{constant}\n</code></pre> space_complexity.dart<pre><code>[class]{}-[func]{function}\n\n[class]{}-[func]{constant}\n</code></pre> space_complexity.rs<pre><code>[class]{}-[func]{function}\n\n[class]{}-[func]{constant}\n</code></pre> space_complexity.c<pre><code>[class]{}-[func]{func}\n\n[class]{}-[func]{constant}\n</code></pre> space_complexity.kt<pre><code>[class]{}-[func]{function}\n\n[class]{}-[func]{constant}\n</code></pre> space_complexity.rb<pre><code>[class]{}-[func]{function}\n\n[class]{}-[func]{constant}\n</code></pre> space_complexity.zig<pre><code>[class]{}-[func]{function}\n\n[class]{}-[func]{constant}\n</code></pre>"},{"location":"chapter_computational_complexity/space_complexity/#2-on","title":"2. \u00a0 \u7dda\u5f62\u30aa\u30fc\u30c0\u30fc \\(O(n)\\)","text":"<p>\u7dda\u5f62\u30aa\u30fc\u30c0\u30fc\u306f\u914d\u5217\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u3001\u30b9\u30bf\u30c3\u30af\u3001\u30ad\u30e5\u30fc\u306a\u3069\u3067\u4e00\u822c\u7684\u3067\u3001\u8981\u7d20\u6570\u306f\\(n\\)\u306b\u6bd4\u4f8b\u3057\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig space_complexity.py<pre><code>def linear(n: int):\n    \"\"\"\u7dda\u5f62\u8907\u96d1\u5ea6\"\"\"\n    # \u9577\u3055 n \u306e\u30ea\u30b9\u30c8\u306f O(n) \u306e\u30b9\u30da\u30fc\u30b9\u3092\u5360\u6709\n    nums = [0] * n\n    # \u9577\u3055 n \u306e\u30cf\u30c3\u30b7\u30e5\u30de\u30c3\u30d7\u306f O(n) \u306e\u30b9\u30da\u30fc\u30b9\u3092\u5360\u6709\n    hmap = dict[int, str]()\n    for i in range(n):\n        hmap[i] = str(i)\n</code></pre> space_complexity.cpp<pre><code>/* \u7dda\u5f62\u8a08\u7b97\u91cf */\nvoid linear(int n) {\n    // \u9577\u3055 n \u306e\u914d\u5217\u306f O(n) \u7a7a\u9593\u3092\u5360\u3081\u308b\n    vector&lt;int&gt; nums(n);\n    // \u9577\u3055 n \u306e\u30ea\u30b9\u30c8\u306f O(n) \u7a7a\u9593\u3092\u5360\u3081\u308b\n    vector&lt;ListNode&gt; nodes;\n    for (int i = 0; i &lt; n; i++) {\n        nodes.push_back(ListNode(i));\n    }\n    // \u9577\u3055 n \u306e\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u306f O(n) \u7a7a\u9593\u3092\u5360\u3081\u308b\n    unordered_map&lt;int, string&gt; map;\n    for (int i = 0; i &lt; n; i++) {\n        map[i] = to_string(i);\n    }\n}\n</code></pre> space_complexity.java<pre><code>/* \u7dda\u5f62\u8a08\u7b97\u91cf */\nvoid linear(int n) {\n    // \u9577\u3055 n \u306e\u914d\u5217\u306f O(n) \u7a7a\u9593\u3092\u5360\u3081\u308b\n    int[] nums = new int[n];\n    // \u9577\u3055 n \u306e\u30ea\u30b9\u30c8\u306f O(n) \u7a7a\u9593\u3092\u5360\u3081\u308b\n    List&lt;ListNode&gt; nodes = new ArrayList&lt;&gt;();\n    for (int i = 0; i &lt; n; i++) {\n        nodes.add(new ListNode(i));\n    }\n    // \u9577\u3055 n \u306e\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u306f O(n) \u7a7a\u9593\u3092\u5360\u3081\u308b\n    Map&lt;Integer, String&gt; map = new HashMap&lt;&gt;();\n    for (int i = 0; i &lt; n; i++) {\n        map.put(i, String.valueOf(i));\n    }\n}\n</code></pre> space_complexity.cs<pre><code>[class]{space_complexity}-[func]{Linear}\n</code></pre> space_complexity.go<pre><code>[class]{}-[func]{spaceLinear}\n</code></pre> space_complexity.swift<pre><code>[class]{}-[func]{linear}\n</code></pre> space_complexity.js<pre><code>[class]{}-[func]{linear}\n</code></pre> space_complexity.ts<pre><code>[class]{}-[func]{linear}\n</code></pre> space_complexity.dart<pre><code>[class]{}-[func]{linear}\n</code></pre> space_complexity.rs<pre><code>[class]{}-[func]{linear}\n</code></pre> space_complexity.c<pre><code>[class]{HashTable}-[func]{}\n\n[class]{}-[func]{linear}\n</code></pre> space_complexity.kt<pre><code>[class]{}-[func]{linear}\n</code></pre> space_complexity.rb<pre><code>[class]{}-[func]{linear}\n</code></pre> space_complexity.zig<pre><code>[class]{}-[func]{linear}\n</code></pre> <p>\u4e0b\u56f3\u306b\u793a\u3055\u308c\u3066\u3044\u308b\u3088\u3046\u306b\u3001\u3053\u306e\u95a2\u6570\u306e\u518d\u5e30\u6df1\u5ea6\u306f\\(n\\)\u3067\u3001\\(n\\)\u500b\u306e\u672a\u8fd4\u5374\u306e<code>linear_recur()</code>\u95a2\u6570\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u304c\u3042\u308a\u3001\\(O(n)\\)\u30b5\u30a4\u30ba\u306e\u30b9\u30bf\u30c3\u30af\u30d5\u30ec\u30fc\u30e0\u7a7a\u9593\u3092\u4f7f\u7528\u3057\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig space_complexity.py<pre><code>def linear_recur(n: int):\n    \"\"\"\u7dda\u5f62\u8907\u96d1\u5ea6\uff08\u518d\u5e30\u5b9f\u88c5\uff09\"\"\"\n    print(\"\u518d\u5e30 n =\", n)\n    if n == 1:\n        return\n    linear_recur(n - 1)\n</code></pre> space_complexity.cpp<pre><code>/* \u7dda\u5f62\u8a08\u7b97\u91cf\uff08\u518d\u5e30\u5b9f\u88c5\uff09 */\nvoid linearRecur(int n) {\n    cout &lt;&lt; \"\u518d\u5e30 n = \" &lt;&lt; n &lt;&lt; endl;\n    if (n == 1)\n        return;\n    linearRecur(n - 1);\n}\n</code></pre> space_complexity.java<pre><code>/* \u7dda\u5f62\u8a08\u7b97\u91cf\uff08\u518d\u5e30\u5b9f\u88c5\uff09 */\nvoid linearRecur(int n) {\n    System.out.println(\"\u518d\u5e30 n = \" + n);\n    if (n == 1)\n        return;\n    linearRecur(n - 1);\n}\n</code></pre> space_complexity.cs<pre><code>[class]{space_complexity}-[func]{LinearRecur}\n</code></pre> space_complexity.go<pre><code>[class]{}-[func]{spaceLinearRecur}\n</code></pre> space_complexity.swift<pre><code>[class]{}-[func]{linearRecur}\n</code></pre> space_complexity.js<pre><code>[class]{}-[func]{linearRecur}\n</code></pre> space_complexity.ts<pre><code>[class]{}-[func]{linearRecur}\n</code></pre> space_complexity.dart<pre><code>[class]{}-[func]{linearRecur}\n</code></pre> space_complexity.rs<pre><code>[class]{}-[func]{linear_recur}\n</code></pre> space_complexity.c<pre><code>[class]{}-[func]{linearRecur}\n</code></pre> space_complexity.kt<pre><code>[class]{}-[func]{linearRecur}\n</code></pre> space_complexity.rb<pre><code>[class]{}-[func]{linear_recur}\n</code></pre> space_complexity.zig<pre><code>[class]{}-[func]{linearRecur}\n</code></pre> <p></p> <p> \u56f3 2-17 \u00a0 Recursive function generating linear order space complexity </p>"},{"location":"chapter_computational_complexity/space_complexity/#3-on2","title":"3. \u00a0 \u4e8c\u6b21\u30aa\u30fc\u30c0\u30fc \\(O(n^2)\\)","text":"<p>\u4e8c\u6b21\u30aa\u30fc\u30c0\u30fc\u306f\u884c\u5217\u3084\u30b0\u30e9\u30d5\u3067\u4e00\u822c\u7684\u3067\u3001\u8981\u7d20\u6570\u306f\\(n\\)\u306e\u4e8c\u4e57\u306b\u6bd4\u4f8b\u3057\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig space_complexity.py<pre><code>def quadratic(n: int):\n    \"\"\"\u5e73\u65b9\u8907\u96d1\u5ea6\"\"\"\n    # \u4e8c\u6b21\u5143\u30ea\u30b9\u30c8\u306f O(n^2) \u306e\u30b9\u30da\u30fc\u30b9\u3092\u5360\u6709\n    num_matrix = [[0] * n for _ in range(n)]\n</code></pre> space_complexity.cpp<pre><code>/* \u4e8c\u6b21\u8a08\u7b97\u91cf */\nvoid quadratic(int n) {\n    // \u4e8c\u6b21\u5143\u30ea\u30b9\u30c8\u306f O(n^2) \u7a7a\u9593\u3092\u5360\u3081\u308b\n    vector&lt;vector&lt;int&gt;&gt; numMatrix;\n    for (int i = 0; i &lt; n; i++) {\n        vector&lt;int&gt; tmp;\n        for (int j = 0; j &lt; n; j++) {\n            tmp.push_back(0);\n        }\n        numMatrix.push_back(tmp);\n    }\n}\n</code></pre> space_complexity.java<pre><code>/* \u4e8c\u6b21\u8a08\u7b97\u91cf */\nvoid quadratic(int n) {\n    // \u884c\u5217\u306f O(n^2) \u7a7a\u9593\u3092\u5360\u3081\u308b\n    int[][] numMatrix = new int[n][n];\n    // \u4e8c\u6b21\u5143\u30ea\u30b9\u30c8\u306f O(n^2) \u7a7a\u9593\u3092\u5360\u3081\u308b\n    List&lt;List&lt;Integer&gt;&gt; numList = new ArrayList&lt;&gt;();\n    for (int i = 0; i &lt; n; i++) {\n        List&lt;Integer&gt; tmp = new ArrayList&lt;&gt;();\n        for (int j = 0; j &lt; n; j++) {\n            tmp.add(0);\n        }\n        numList.add(tmp);\n    }\n}\n</code></pre> space_complexity.cs<pre><code>[class]{space_complexity}-[func]{Quadratic}\n</code></pre> space_complexity.go<pre><code>[class]{}-[func]{spaceQuadratic}\n</code></pre> space_complexity.swift<pre><code>[class]{}-[func]{quadratic}\n</code></pre> space_complexity.js<pre><code>[class]{}-[func]{quadratic}\n</code></pre> space_complexity.ts<pre><code>[class]{}-[func]{quadratic}\n</code></pre> space_complexity.dart<pre><code>[class]{}-[func]{quadratic}\n</code></pre> space_complexity.rs<pre><code>[class]{}-[func]{quadratic}\n</code></pre> space_complexity.c<pre><code>[class]{}-[func]{quadratic}\n</code></pre> space_complexity.kt<pre><code>[class]{}-[func]{quadratic}\n</code></pre> space_complexity.rb<pre><code>[class]{}-[func]{quadratic}\n</code></pre> space_complexity.zig<pre><code>[class]{}-[func]{quadratic}\n</code></pre> <p>\u4e0b\u56f3\u306b\u793a\u3055\u308c\u3066\u3044\u308b\u3088\u3046\u306b\u3001\u3053\u306e\u95a2\u6570\u306e\u518d\u5e30\u6df1\u5ea6\u306f\\(n\\)\u3067\u3001\u5404\u518d\u5e30\u547c\u3073\u51fa\u3057\u3067\u9577\u3055\\(n\\)\u3001\\(n-1\\)\u3001\\(\\dots\\)\u3001\\(2\\)\u3001\\(1\\)\u306e\u914d\u5217\u304c\u521d\u671f\u5316\u3055\u308c\u3001\u5e73\u5747\\(n/2\\)\u3068\u306a\u308a\u3001\u5168\u4f53\u3068\u3057\u3066\\(O(n^2)\\)\u306e\u7a7a\u9593\u3092\u5360\u6709\u3057\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig space_complexity.py<pre><code>def quadratic_recur(n: int) -&gt; int:\n    \"\"\"\u5e73\u65b9\u8907\u96d1\u5ea6\uff08\u518d\u5e30\u5b9f\u88c5\uff09\"\"\"\n    if n &lt;= 0:\n        return 0\n    nums = [0] * n\n    print(f\"\u518d\u5e30 n = {n} \u306e\u4e2d\u3067\u914d\u5217\u306e\u9577\u3055 = {len(nums)}\")\n    return quadratic_recur(n - 1)\n</code></pre> space_complexity.cpp<pre><code>/* \u4e8c\u6b21\u8a08\u7b97\u91cf\uff08\u518d\u5e30\u5b9f\u88c5\uff09 */\nint quadraticRecur(int n) {\n    if (n &lt;= 0)\n        return 0;\n    vector&lt;int&gt; nums(n);\n    cout &lt;&lt; \"\u518d\u5e30 n = \" &lt;&lt; n &lt;&lt; \", nums \u306e\u9577\u3055 = \" &lt;&lt; nums.size() &lt;&lt; endl;\n    return quadraticRecur(n - 1);\n}\n</code></pre> space_complexity.java<pre><code>/* \u4e8c\u6b21\u8a08\u7b97\u91cf\uff08\u518d\u5e30\u5b9f\u88c5\uff09 */\nint quadraticRecur(int n) {\n    if (n &lt;= 0)\n        return 0;\n    // \u914d\u5217 nums \u306e\u9577\u3055 = n, n-1, ..., 2, 1\n    int[] nums = new int[n];\n    System.out.println(\"\u518d\u5e30 n = \" + n + \" \u306e nums \u306e\u9577\u3055 = \" + nums.length);\n    return quadraticRecur(n - 1);\n}\n</code></pre> space_complexity.cs<pre><code>[class]{space_complexity}-[func]{QuadraticRecur}\n</code></pre> space_complexity.go<pre><code>[class]{}-[func]{spaceQuadraticRecur}\n</code></pre> space_complexity.swift<pre><code>[class]{}-[func]{quadraticRecur}\n</code></pre> space_complexity.js<pre><code>[class]{}-[func]{quadraticRecur}\n</code></pre> space_complexity.ts<pre><code>[class]{}-[func]{quadraticRecur}\n</code></pre> space_complexity.dart<pre><code>[class]{}-[func]{quadraticRecur}\n</code></pre> space_complexity.rs<pre><code>[class]{}-[func]{quadratic_recur}\n</code></pre> space_complexity.c<pre><code>[class]{}-[func]{quadraticRecur}\n</code></pre> space_complexity.kt<pre><code>[class]{}-[func]{quadraticRecur}\n</code></pre> space_complexity.rb<pre><code>[class]{}-[func]{quadratic_recur}\n</code></pre> space_complexity.zig<pre><code>[class]{}-[func]{quadraticRecur}\n</code></pre> <p></p> <p> \u56f3 2-18 \u00a0 Recursive function generating quadratic order space complexity </p>"},{"location":"chapter_computational_complexity/space_complexity/#4-o2n","title":"4. \u00a0 \u6307\u6570\u30aa\u30fc\u30c0\u30fc \\(O(2^n)\\)","text":"<p>\u6307\u6570\u30aa\u30fc\u30c0\u30fc\u306f\u4e8c\u5206\u6728\u3067\u4e00\u822c\u7684\u3067\u3059\u3002\u4e0b\u56f3\u3092\u89b3\u5bdf\u3059\u308b\u3068\u3001\\(n\\)\u30ec\u30d9\u30eb\u306e\u300c\u5b8c\u5168\u4e8c\u5206\u6728\u300d\u306f\\(2^n - 1\\)\u500b\u306e\u30ce\u30fc\u30c9\u3092\u6301\u3061\u3001\\(O(2^n)\\)\u306e\u7a7a\u9593\u3092\u5360\u6709\u3057\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig space_complexity.py<pre><code>def build_tree(n: int) -&gt; TreeNode | None:\n    \"\"\"\u6307\u6570\u8907\u96d1\u5ea6\uff08\u5b8c\u5168\u4e8c\u5206\u6728\u306e\u69cb\u7bc9\uff09\"\"\"\n    if n == 0:\n        return None\n    root = TreeNode(0)\n    root.left = build_tree(n - 1)\n    root.right = build_tree(n - 1)\n    return root\n</code></pre> space_complexity.cpp<pre><code>/* \u6307\u6570\u8a08\u7b97\u91cf\uff08\u5b8c\u5168\u4e8c\u5206\u6728\u306e\u69cb\u7bc9\uff09 */\nTreeNode *buildTree(int n) {\n    if (n == 0)\n        return nullptr;\n    TreeNode *root = new TreeNode(0);\n    root-&gt;left = buildTree(n - 1);\n    root-&gt;right = buildTree(n - 1);\n    return root;\n}\n</code></pre> space_complexity.java<pre><code>/* \u6307\u6570\u8a08\u7b97\u91cf\uff08\u5b8c\u5168\u4e8c\u5206\u6728\u306e\u69cb\u7bc9\uff09 */\nTreeNode buildTree(int n) {\n    if (n == 0)\n        return null;\n    TreeNode root = new TreeNode(0);\n    root.left = buildTree(n - 1);\n    root.right = buildTree(n - 1);\n    return root;\n}\n</code></pre> space_complexity.cs<pre><code>[class]{space_complexity}-[func]{BuildTree}\n</code></pre> space_complexity.go<pre><code>[class]{}-[func]{buildTree}\n</code></pre> space_complexity.swift<pre><code>[class]{}-[func]{buildTree}\n</code></pre> space_complexity.js<pre><code>[class]{}-[func]{buildTree}\n</code></pre> space_complexity.ts<pre><code>[class]{}-[func]{buildTree}\n</code></pre> space_complexity.dart<pre><code>[class]{}-[func]{buildTree}\n</code></pre> space_complexity.rs<pre><code>[class]{}-[func]{build_tree}\n</code></pre> space_complexity.c<pre><code>[class]{}-[func]{buildTree}\n</code></pre> space_complexity.kt<pre><code>[class]{}-[func]{buildTree}\n</code></pre> space_complexity.rb<pre><code>[class]{}-[func]{build_tree}\n</code></pre> space_complexity.zig<pre><code>[class]{}-[func]{buildTree}\n</code></pre> <p></p> <p> \u56f3 2-19 \u00a0 Full binary tree generating exponential order space complexity </p>"},{"location":"chapter_computational_complexity/space_complexity/#5-olog-n","title":"5. \u00a0 \u5bfe\u6570\u30aa\u30fc\u30c0\u30fc \\(O(\\log n)\\)","text":"<p>\u5bfe\u6570\u30aa\u30fc\u30c0\u30fc\u306f\u5206\u5272\u7d71\u6cbb\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u4e00\u822c\u7684\u3067\u3059\u3002\u4f8b\u3048\u3070\u3001\u30de\u30fc\u30b8\u30bd\u30fc\u30c8\u3067\u306f\u3001\u9577\u3055\\(n\\)\u306e\u914d\u5217\u304c\u5404\u30e9\u30a6\u30f3\u30c9\u3067\u518d\u5e30\u7684\u306b\u534a\u5206\u306b\u5206\u5272\u3055\u308c\u3001\u9ad8\u3055\\(\\log n\\)\u306e\u518d\u5e30\u6728\u3092\u5f62\u6210\u3057\u3001\\(O(\\log n)\\)\u306e\u30b9\u30bf\u30c3\u30af\u30d5\u30ec\u30fc\u30e0\u7a7a\u9593\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002</p> <p>\u5225\u306e\u4f8b\u306f\u3001\u6570\u5024\u3092\u6587\u5b57\u5217\u306b\u5909\u63db\u3059\u308b\u3053\u3068\u3067\u3059\u3002\u6b63\u306e\u6574\u6570\\(n\\)\u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408\u3001\u305d\u306e\u6841\u6570\u306f\\(\\log_{10} n + 1\\)\u3067\u3001\u6587\u5b57\u5217\u306e\u9577\u3055\u306b\u5bfe\u5fdc\u3059\u308b\u305f\u3081\u3001\u7a7a\u9593\u8a08\u7b97\u91cf\u306f\\(O(\\log_{10} n + 1) = O(\\log n)\\)\u3067\u3059\u3002</p>"},{"location":"chapter_computational_complexity/space_complexity/#244","title":"2.4.4 \u00a0 \u6642\u9593\u3068\u7a7a\u9593\u306e\u30d0\u30e9\u30f3\u30b9","text":"<p>\u7406\u60f3\u7684\u306b\u306f\u3001\u6642\u9593\u8a08\u7b97\u91cf\u3068\u7a7a\u9593\u8a08\u7b97\u91cf\u306e\u4e21\u65b9\u304c\u6700\u9069\u3067\u3042\u308b\u3053\u3068\u3092\u76ee\u6307\u3057\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u5b9f\u969b\u306b\u306f\u4e21\u65b9\u3092\u540c\u6642\u306b\u6700\u9069\u5316\u3059\u308b\u3053\u3068\u306f\u3057\u3070\u3057\u3070\u56f0\u96e3\u3067\u3059\u3002</p> <p>\u6642\u9593\u8a08\u7b97\u91cf\u3092\u4e0b\u3052\u308b\u3053\u3068\u306f\u901a\u5e38\u3001\u7a7a\u9593\u8a08\u7b97\u91cf\u306e\u5897\u52a0\u3092\u4ee3\u511f\u3068\u3057\u3001\u305d\u306e\u9006\u3082\u540c\u69d8\u3067\u3059\u3002\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u901f\u5ea6\u3092\u5411\u4e0a\u3055\u305b\u308b\u305f\u3081\u306b\u30e1\u30e2\u30ea\u7a7a\u9593\u3092\u72a0\u7272\u306b\u3059\u308b\u30a2\u30d7\u30ed\u30fc\u30c1\u306f\u300c\u6642\u7a7a\u30c8\u30ec\u30fc\u30c9\u30aa\u30d5\u300d\u3068\u3057\u3066\u77e5\u3089\u308c\u3001\u305d\u306e\u9006\u306f\u300c\u7a7a\u6642\u30c8\u30ec\u30fc\u30c9\u30aa\u30d5\u300d\u3068\u3057\u3066\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\u3002</p> <p>\u9078\u629e\u306f\u3001\u3069\u3061\u3089\u306e\u5074\u9762\u3092\u3088\u308a\u91cd\u8996\u3059\u308b\u304b\u306b\u4f9d\u5b58\u3057\u307e\u3059\u3002\u307b\u3068\u3093\u3069\u306e\u5834\u5408\u3001\u6642\u9593\u306f\u7a7a\u9593\u3088\u308a\u3082\u8cb4\u91cd\u3067\u3042\u308b\u305f\u3081\u3001\u300c\u6642\u7a7a\u30c8\u30ec\u30fc\u30c9\u30aa\u30d5\u300d\u304c\u3088\u308a\u4e00\u822c\u7684\u306a\u6226\u7565\u3067\u3059\u3002\u3082\u3061\u308d\u3093\u3001\u5927\u91cf\u306e\u30c7\u30fc\u30bf\u3092\u6271\u3046\u969b\u306f\u7a7a\u9593\u8a08\u7b97\u91cf\u3092\u5236\u5fa1\u3059\u308b\u3053\u3068\u3082\u975e\u5e38\u306b\u91cd\u8981\u3067\u3059\u3002</p>"},{"location":"chapter_computational_complexity/summary/","title":"2.5 \u00a0 \u307e\u3068\u3081","text":""},{"location":"chapter_computational_complexity/summary/#1","title":"1. \u00a0 \u91cd\u8981\u306a\u30ec\u30d3\u30e5\u30fc","text":"<p>\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u52b9\u7387\u8a55\u4fa1</p> <ul> <li>\u6642\u9593\u52b9\u7387\u3068\u7a7a\u9593\u52b9\u7387\u306f\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u512a\u52a3\u3092\u8a55\u4fa1\u3059\u308b2\u3064\u306e\u4e3b\u8981\u306a\u57fa\u6e96\u3067\u3059\u3002</li> <li>\u5b9f\u969b\u306e\u30c6\u30b9\u30c8\u306b\u3088\u3063\u3066\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u52b9\u7387\u3092\u8a55\u4fa1\u3067\u304d\u307e\u3059\u304c\u3001\u30c6\u30b9\u30c8\u74b0\u5883\u306e\u5f71\u97ff\u3092\u6392\u9664\u3059\u308b\u3053\u3068\u306f\u56f0\u96e3\u3067\u3001\u5927\u91cf\u306e\u8a08\u7b97\u30ea\u30bd\u30fc\u30b9\u3092\u6d88\u8cbb\u3057\u307e\u3059\u3002</li> <li>\u8907\u96d1\u5ea6\u5206\u6790\u306f\u5b9f\u969b\u306e\u30c6\u30b9\u30c8\u306e\u6b20\u70b9\u3092\u514b\u670d\u3067\u304d\u307e\u3059\u3002\u305d\u306e\u7d50\u679c\u306f\u3059\u3079\u3066\u306e\u52d5\u4f5c\u30d7\u30e9\u30c3\u30c8\u30d5\u30a9\u30fc\u30e0\u306b\u9069\u7528\u3067\u304d\u3001\u7570\u306a\u308b\u30c7\u30fc\u30bf\u30b9\u30b1\u30fc\u30eb\u3067\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u52b9\u7387\u3092\u660e\u3089\u304b\u306b\u3067\u304d\u307e\u3059\u3002</li> </ul> <p>\u6642\u9593\u8a08\u7b97\u91cf</p> <ul> <li>\u6642\u9593\u8a08\u7b97\u91cf\u306f\u3001\u30c7\u30fc\u30bf\u91cf\u306e\u5897\u52a0\u306b\u4f34\u3046\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5b9f\u884c\u6642\u9593\u306e\u50be\u5411\u3092\u6e2c\u5b9a\u3057\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u52b9\u7387\u3092\u52b9\u679c\u7684\u306b\u8a55\u4fa1\u3057\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u5165\u529b\u30c7\u30fc\u30bf\u91cf\u304c\u5c11\u306a\u3044\u5834\u5408\u3084\u6642\u9593\u8a08\u7b97\u91cf\u304c\u540c\u3058\u5834\u5408\u306a\u3069\u3001\u7279\u5b9a\u306e\u30b1\u30fc\u30b9\u3067\u306f\u5931\u6557\u3059\u308b\u3053\u3068\u304c\u3042\u308a\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u52b9\u7387\u3092\u6b63\u78ba\u306b\u6bd4\u8f03\u3059\u308b\u3053\u3068\u304c\u56f0\u96e3\u306b\u306a\u308a\u307e\u3059\u3002</li> <li>\u6700\u60aa\u30b1\u30fc\u30b9\u6642\u9593\u8a08\u7b97\u91cf\u306f\u30d3\u30c3\u30b0\\(O\\)\u8a18\u6cd5\u3092\u4f7f\u7528\u3057\u3066\u8868\u8a18\u3055\u308c\u3001\u6f38\u8fd1\u4e0a\u9650\u3092\u8868\u3057\u3001\\(n\\)\u304c\u7121\u9650\u5927\u306b\u8fd1\u3065\u304f\u306b\u3064\u308c\u3066\u306e\u64cd\u4f5c\u6570\\(T(n)\\)\u306e\u5897\u52a0\u30ec\u30d9\u30eb\u3092\u53cd\u6620\u3057\u307e\u3059\u3002</li> <li>\u6642\u9593\u8a08\u7b97\u91cf\u306e\u8a08\u7b97\u306b\u306f2\u3064\u306e\u30b9\u30c6\u30c3\u30d7\u304c\u542b\u307e\u308c\u307e\u3059\uff1a\u307e\u305a\u64cd\u4f5c\u6570\u3092\u30ab\u30a6\u30f3\u30c8\u3057\u3001\u6b21\u306b\u6f38\u8fd1\u4e0a\u9650\u3092\u6c7a\u5b9a\u3057\u307e\u3059\u3002</li> <li>\u4e00\u822c\u7684\u306a\u6642\u9593\u8a08\u7b97\u91cf\u306f\u3001\u4f4e\u3044\u3082\u306e\u304b\u3089\u9ad8\u3044\u3082\u306e\u3078\u3068\u4e26\u3079\u308b\u3068\u3001\\(O(1)\\)\u3001\\(O(\\log n)\\)\u3001\\(O(n)\\)\u3001\\(O(n \\log n)\\)\u3001\\(O(n^2)\\)\u3001\\(O(2^n)\\)\u3001\\(O(n!)\\)\u306a\u3069\u304c\u542b\u307e\u308c\u307e\u3059\u3002</li> <li>\u4e00\u90e8\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u6642\u9593\u8a08\u7b97\u91cf\u306f\u56fa\u5b9a\u3055\u308c\u3066\u304a\u3089\u305a\u3001\u5165\u529b\u30c7\u30fc\u30bf\u306e\u5206\u5e03\u306b\u4f9d\u5b58\u3057\u307e\u3059\u3002\u6642\u9593\u8a08\u7b97\u91cf\u306f\u6700\u60aa\u3001\u6700\u826f\u3001\u5e73\u5747\u306e\u30b1\u30fc\u30b9\u306b\u5206\u3051\u3089\u308c\u307e\u3059\u3002\u6700\u826f\u30b1\u30fc\u30b9\u306f\u3001\u5165\u529b\u30c7\u30fc\u30bf\u304c\u6700\u826f\u30b1\u30fc\u30b9\u3092\u9054\u6210\u3059\u308b\u305f\u3081\u306b\u53b3\u683c\u306a\u6761\u4ef6\u3092\u6e80\u305f\u3059\u5fc5\u8981\u304c\u3042\u308b\u305f\u3081\u3001\u307b\u3068\u3093\u3069\u4f7f\u7528\u3055\u308c\u307e\u305b\u3093\u3002</li> <li>\u5e73\u5747\u6642\u9593\u8a08\u7b97\u91cf\u306f\u3001\u30e9\u30f3\u30c0\u30e0\u30c7\u30fc\u30bf\u5165\u529b\u4e0b\u3067\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u52b9\u7387\u3092\u53cd\u6620\u3057\u3001\u5b9f\u969b\u306e\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u3067\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u6027\u80fd\u306b\u5bc6\u63a5\u306b\u985e\u4f3c\u3057\u3066\u3044\u307e\u3059\u3002\u5e73\u5747\u6642\u9593\u8a08\u7b97\u91cf\u306e\u8a08\u7b97\u306b\u306f\u3001\u5165\u529b\u30c7\u30fc\u30bf\u306e\u5206\u5e03\u3068\u305d\u306e\u5f8c\u306e\u6570\u5b66\u7684\u671f\u5f85\u5024\u3092\u8003\u616e\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002</li> </ul> <p>\u7a7a\u9593\u8a08\u7b97\u91cf</p> <ul> <li>\u7a7a\u9593\u8a08\u7b97\u91cf\u306f\u3001\u6642\u9593\u8a08\u7b97\u91cf\u3068\u540c\u69d8\u306b\u3001\u30c7\u30fc\u30bf\u91cf\u306e\u5897\u52a0\u306b\u4f34\u3046\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u304c\u5360\u6709\u3059\u308b\u30e1\u30e2\u30ea\u7a7a\u9593\u306e\u50be\u5411\u3092\u6e2c\u5b9a\u3057\u307e\u3059\u3002</li> <li>\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5b9f\u884c\u4e2d\u306b\u4f7f\u7528\u3055\u308c\u308b\u95a2\u9023\u30e1\u30e2\u30ea\u7a7a\u9593\u306f\u3001\u5165\u529b\u7a7a\u9593\u3001\u4e00\u6642\u7a7a\u9593\u3001\u51fa\u529b\u7a7a\u9593\u306b\u5206\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u4e00\u822c\u7684\u306b\u3001\u5165\u529b\u7a7a\u9593\u306f\u7a7a\u9593\u8a08\u7b97\u91cf\u306e\u8a08\u7b97\u306b\u542b\u307e\u308c\u307e\u305b\u3093\u3002\u4e00\u6642\u7a7a\u9593\u306f\u4e00\u6642\u30c7\u30fc\u30bf\u3001\u30b9\u30bf\u30c3\u30af\u30d5\u30ec\u30fc\u30e0\u7a7a\u9593\u3001\u547d\u4ee4\u7a7a\u9593\u306b\u5206\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u3001\u30b9\u30bf\u30c3\u30af\u30d5\u30ec\u30fc\u30e0\u7a7a\u9593\u306f\u901a\u5e38\u3001\u518d\u5e30\u95a2\u6570\u3067\u306e\u307f\u7a7a\u9593\u8a08\u7b97\u91cf\u306b\u5f71\u97ff\u3057\u307e\u3059\u3002</li> <li>\u901a\u5e38\u306f\u6700\u60aa\u30b1\u30fc\u30b9\u7a7a\u9593\u8a08\u7b97\u91cf\u306e\u307f\u306b\u7126\u70b9\u3092\u5f53\u3066\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u6700\u60aa\u306e\u5165\u529b\u30c7\u30fc\u30bf\u3068\u64cd\u4f5c\u306e\u6700\u60aa\u306e\u77ac\u9593\u3067\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u7a7a\u9593\u8a08\u7b97\u91cf\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002</li> <li>\u4e00\u822c\u7684\u306a\u7a7a\u9593\u8a08\u7b97\u91cf\u306f\u3001\u4f4e\u3044\u3082\u306e\u304b\u3089\u9ad8\u3044\u3082\u306e\u3078\u3068\u4e26\u3079\u308b\u3068\u3001\\(O(1)\\)\u3001\\(O(\\log n)\\)\u3001\\(O(n)\\)\u3001\\(O(n^2)\\)\u3001\\(O(2^n)\\)\u306a\u3069\u304c\u542b\u307e\u308c\u307e\u3059\u3002</li> </ul>"},{"location":"chapter_computational_complexity/summary/#2-q-a","title":"2. \u00a0 Q &amp; A","text":"<p>Q: \u672b\u5c3e\u518d\u5e30\u306e\u7a7a\u9593\u8a08\u7b97\u91cf\u306f\\(O(1)\\)\u3067\u3059\u304b\uff1f</p> <p>\u7406\u8ad6\u7684\u306b\u306f\u3001\u672b\u5c3e\u518d\u5e30\u95a2\u6570\u306e\u7a7a\u9593\u8a08\u7b97\u91cf\u306f\\(O(1)\\)\u306b\u6700\u9069\u5316\u3067\u304d\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u307b\u3068\u3093\u3069\u306e\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\uff08Java\u3001Python\u3001C++\u3001Go\u3001C#\u306a\u3069\uff09\u306f\u672b\u5c3e\u518d\u5e30\u306e\u81ea\u52d5\u6700\u9069\u5316\u3092\u30b5\u30dd\u30fc\u30c8\u3057\u3066\u3044\u306a\u3044\u305f\u3081\u3001\u4e00\u822c\u7684\u306b\u7a7a\u9593\u8a08\u7b97\u91cf\u306f\\(O(n)\\)\u3068\u8003\u3048\u3089\u308c\u3066\u3044\u307e\u3059\u3002</p> <p>Q: \u300c\u95a2\u6570\u300d\u3068\u300c\u30e1\u30bd\u30c3\u30c9\u300d\u3068\u3044\u3046\u7528\u8a9e\u306e\u9055\u3044\u306f\u4f55\u3067\u3059\u304b\uff1f</p> <p>\u95a2\u6570\u306f\u72ec\u7acb\u3057\u3066\u5b9f\u884c\u3067\u304d\u3001\u3059\u3079\u3066\u306e\u30d1\u30e9\u30e1\u30fc\u30bf\u304c\u660e\u793a\u7684\u306b\u6e21\u3055\u308c\u307e\u3059\u3002\u30e1\u30bd\u30c3\u30c9\u306f\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u306b\u95a2\u9023\u4ed8\u3051\u3089\u308c\u3001\u305d\u308c\u3092\u547c\u3073\u51fa\u3059\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u306b\u6697\u9ed9\u7684\u306b\u6e21\u3055\u308c\u3001\u30af\u30e9\u30b9\u306e\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u5185\u306b\u542b\u307e\u308c\u308b\u30c7\u30fc\u30bf\u3092\u64cd\u4f5c\u3067\u304d\u307e\u3059\u3002</p> <p>\u4e00\u822c\u7684\u306a\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u304b\u3089\u306e\u4f8b\u3092\u3044\u304f\u3064\u304b\u793a\u3057\u307e\u3059\uff1a</p> <ul> <li>C\u306f\u624b\u7d9a\u304d\u578b\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u3067\u3001\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u6307\u5411\u306e\u6982\u5ff5\u304c\u306a\u3044\u305f\u3081\u3001\u95a2\u6570\u306e\u307f\u304c\u3042\u308a\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u69cb\u9020\u4f53\uff08struct\uff09\u3092\u4f5c\u6210\u3059\u308b\u3053\u3068\u3067\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u6307\u5411\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u3092\u30b7\u30df\u30e5\u30ec\u30fc\u30c8\u3067\u304d\u3001\u3053\u308c\u3089\u306e\u69cb\u9020\u4f53\u306b\u95a2\u9023\u4ed8\u3051\u3089\u308c\u305f\u95a2\u6570\u306f\u4ed6\u306e\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u306e\u30e1\u30bd\u30c3\u30c9\u3068\u540c\u7b49\u3067\u3059\u3002</li> <li>Java\u3068C#\u306f\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u6307\u5411\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u3067\u3001\u30b3\u30fc\u30c9\u30d6\u30ed\u30c3\u30af\uff08\u30e1\u30bd\u30c3\u30c9\uff09\u306f\u901a\u5e38\u30af\u30e9\u30b9\u306e\u4e00\u90e8\u3067\u3059\u3002\u9759\u7684\u30e1\u30bd\u30c3\u30c9\u306f\u30af\u30e9\u30b9\u306b\u30d0\u30a4\u30f3\u30c9\u3055\u308c\u3001\u7279\u5b9a\u306e\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u5909\u6570\u306b\u30a2\u30af\u30bb\u30b9\u3067\u304d\u306a\u3044\u305f\u3081\u3001\u95a2\u6570\u306e\u3088\u3046\u306b\u52d5\u4f5c\u3057\u307e\u3059\u3002</li> <li>C++\u3068Python\u306f\u624b\u7d9a\u304d\u578b\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\uff08\u95a2\u6570\uff09\u3068\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u6307\u5411\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\uff08\u30e1\u30bd\u30c3\u30c9\uff09\u306e\u4e21\u65b9\u3092\u30b5\u30dd\u30fc\u30c8\u3057\u3066\u3044\u307e\u3059\u3002</li> </ul> <p>Q: \u300c\u7a7a\u9593\u8a08\u7b97\u91cf\u306e\u4e00\u822c\u7684\u306a\u7a2e\u985e\u300d\u306e\u56f3\u306f\u3001\u5360\u6709\u7a7a\u9593\u306e\u7d76\u5bfe\u30b5\u30a4\u30ba\u3092\u53cd\u6620\u3057\u3066\u3044\u307e\u3059\u304b\uff1f</p> <p>\u3044\u3044\u3048\u3001\u56f3\u306f\u7a7a\u9593\u8a08\u7b97\u91cf\u3092\u793a\u3057\u3066\u304a\u308a\u3001\u3053\u308c\u306f\u5897\u52a0\u50be\u5411\u3092\u53cd\u6620\u3059\u308b\u3082\u306e\u3067\u3042\u308a\u3001\u5360\u6709\u7a7a\u9593\u306e\u7d76\u5bfe\u30b5\u30a4\u30ba\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002</p> <p>\\(n = 8\\)\u3092\u53d6\u308b\u3068\u3001\u5404\u66f2\u7dda\u306e\u5024\u304c\u305d\u306e\u95a2\u6570\u306b\u5bfe\u5fdc\u3057\u3066\u3044\u306a\u3044\u3053\u3068\u306b\u6c17\u3065\u304f\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u3002\u3053\u308c\u306f\u3001\u5404\u66f2\u7dda\u306b\u5b9a\u6570\u9805\u304c\u542b\u307e\u308c\u3066\u3044\u308b\u305f\u3081\u3067\u3001\u5024\u306e\u7bc4\u56f2\u3092\u8996\u899a\u7684\u306b\u5feb\u9069\u306a\u7bc4\u56f2\u306b\u5727\u7e2e\u3059\u308b\u3053\u3068\u3092\u610f\u56f3\u3057\u3066\u3044\u307e\u3059\u3002</p> <p>\u5b9f\u969b\u306b\u306f\u3001\u901a\u5e38\u306f\u5404\u30e1\u30bd\u30c3\u30c9\u306e\u300c\u5b9a\u6570\u9805\u300d\u8907\u96d1\u5ea6\u3092\u77e5\u3089\u306a\u3044\u305f\u3081\u3001\u8907\u96d1\u5ea6\u306e\u307f\u306b\u57fa\u3065\u3044\u3066\\(n = 8\\)\u306e\u6700\u826f\u30bd\u30ea\u30e5\u30fc\u30b7\u30e7\u30f3\u3092\u9078\u629e\u3059\u308b\u3053\u3068\u306f\u4e00\u822c\u7684\u306b\u4e0d\u53ef\u80fd\u3067\u3059\u3002\u3057\u304b\u3057\u3001\\(n = 8^5\\)\u306e\u5834\u5408\u3001\u5897\u52a0\u50be\u5411\u304c\u652f\u914d\u7684\u306b\u306a\u308b\u305f\u3081\u3001\u9078\u629e\u304c\u306f\u308b\u304b\u306b\u5bb9\u6613\u306b\u306a\u308a\u307e\u3059\u3002</p>"},{"location":"chapter_computational_complexity/time_complexity/","title":"2.3 \u00a0 \u6642\u9593\u8a08\u7b97\u91cf","text":"<p>\u5b9f\u884c\u6642\u9593\u306f\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u52b9\u7387\u3092\u76f4\u611f\u7684\u306b\u8a55\u4fa1\u3067\u304d\u307e\u3059\u3002\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5b9f\u884c\u6642\u9593\u3092\u6b63\u78ba\u306b\u63a8\u5b9a\u3059\u308b\u306b\u306f\u3069\u3046\u3059\u308c\u3070\u3088\u3044\u3067\u3057\u3087\u3046\u304b\uff1f</p> <ol> <li>\u5b9f\u884c\u30d7\u30e9\u30c3\u30c8\u30d5\u30a9\u30fc\u30e0\u306e\u6c7a\u5b9a: \u3053\u308c\u306b\u306f\u3001\u30cf\u30fc\u30c9\u30a6\u30a7\u30a2\u69cb\u6210\u3001\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u3001\u30b7\u30b9\u30c6\u30e0\u74b0\u5883\u306a\u3069\u304c\u542b\u307e\u308c\u3001\u3053\u308c\u3089\u3059\u3079\u3066\u304c\u30b3\u30fc\u30c9\u306e\u5b9f\u884c\u52b9\u7387\u306b\u5f71\u97ff\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002</li> <li>\u69d8\u3005\u306a\u8a08\u7b97\u64cd\u4f5c\u306e\u5b9f\u884c\u6642\u9593\u306e\u8a55\u4fa1: \u4f8b\u3048\u3070\u3001\u52a0\u7b97\u64cd\u4f5c<code>+</code>\u306f1 ns\u3001\u4e57\u7b97\u64cd\u4f5c<code>*</code>\u306f10 ns\u3001\u5370\u5237\u64cd\u4f5c<code>print()</code>\u306f5 ns\u306a\u3069\u304b\u304b\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002</li> <li>\u30b3\u30fc\u30c9\u5185\u306e\u3059\u3079\u3066\u306e\u8a08\u7b97\u64cd\u4f5c\u3092\u30ab\u30a6\u30f3\u30c8: \u3053\u308c\u3089\u3059\u3079\u3066\u306e\u64cd\u4f5c\u306e\u5b9f\u884c\u6642\u9593\u3092\u5408\u8a08\u3059\u308b\u3068\u3001\u7dcf\u5b9f\u884c\u6642\u9593\u304c\u5f97\u3089\u308c\u307e\u3059\u3002</li> </ol> <p>\u4f8b\u3048\u3070\u3001\u5165\u529b\u30b5\u30a4\u30ba\u304c\\(n\\)\u306e\u4ee5\u4e0b\u306e\u30b3\u30fc\u30c9\u3092\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinZig <pre><code># \u7279\u5b9a\u306e\u64cd\u4f5c\u30d7\u30e9\u30c3\u30c8\u30d5\u30a9\u30fc\u30e0\u4e0b\u3067\ndef algorithm(n: int):\n    a = 2      # 1 ns\n    a = a + 1  # 1 ns\n    a = a * 2  # 10 ns\n    # n\u56de\u30eb\u30fc\u30d7\n    for _ in range(n):  # 1 ns\n        print(0)        # 5 ns\n</code></pre> <pre><code>// \u7279\u5b9a\u306e\u64cd\u4f5c\u30d7\u30e9\u30c3\u30c8\u30d5\u30a9\u30fc\u30e0\u4e0b\u3067\nvoid algorithm(int n) {\n    int a = 2;  // 1 ns\n    a = a + 1;  // 1 ns\n    a = a * 2;  // 10 ns\n    // n\u56de\u30eb\u30fc\u30d7\n    for (int i = 0; i &lt; n; i++) {  // 1 ns, \u6bce\u56dei++\u304c\u5b9f\u884c\u3055\u308c\u308b\n        cout &lt;&lt; 0 &lt;&lt; endl;         // 5 ns\n    }\n}\n</code></pre> <pre><code>// \u7279\u5b9a\u306e\u64cd\u4f5c\u30d7\u30e9\u30c3\u30c8\u30d5\u30a9\u30fc\u30e0\u4e0b\u3067\nvoid algorithm(int n) {\n    int a = 2;  // 1 ns\n    a = a + 1;  // 1 ns\n    a = a * 2;  // 10 ns\n    // n\u56de\u30eb\u30fc\u30d7\n    for (int i = 0; i &lt; n; i++) {  // 1 ns, \u6bce\u56dei++\u304c\u5b9f\u884c\u3055\u308c\u308b\n        System.out.println(0);     // 5 ns\n    }\n}\n</code></pre> <pre><code>// \u7279\u5b9a\u306e\u64cd\u4f5c\u30d7\u30e9\u30c3\u30c8\u30d5\u30a9\u30fc\u30e0\u4e0b\u3067\nvoid Algorithm(int n) {\n    int a = 2;  // 1 ns\n    a = a + 1;  // 1 ns\n    a = a * 2;  // 10 ns\n    // n\u56de\u30eb\u30fc\u30d7\n    for (int i = 0; i &lt; n; i++) {  // 1 ns, \u6bce\u56dei++\u304c\u5b9f\u884c\u3055\u308c\u308b\n        Console.WriteLine(0);      // 5 ns\n    }\n}\n</code></pre> <pre><code>// \u7279\u5b9a\u306e\u64cd\u4f5c\u30d7\u30e9\u30c3\u30c8\u30d5\u30a9\u30fc\u30e0\u4e0b\u3067\nfunc algorithm(n int) {\n    a := 2     // 1 ns\n    a = a + 1  // 1 ns\n    a = a * 2  // 10 ns\n    // n\u56de\u30eb\u30fc\u30d7\n    for i := 0; i &lt; n; i++ {  // 1 ns\n        fmt.Println(a)        // 5 ns\n    }\n}\n</code></pre> <pre><code>// \u7279\u5b9a\u306e\u64cd\u4f5c\u30d7\u30e9\u30c3\u30c8\u30d5\u30a9\u30fc\u30e0\u4e0b\u3067\nfunc algorithm(n: Int) {\n    var a = 2 // 1 ns\n    a = a + 1 // 1 ns\n    a = a * 2 // 10 ns\n    // n\u56de\u30eb\u30fc\u30d7\n    for _ in 0 ..&lt; n { // 1 ns\n        print(0) // 5 ns\n    }\n}\n</code></pre> <pre><code>// \u7279\u5b9a\u306e\u64cd\u4f5c\u30d7\u30e9\u30c3\u30c8\u30d5\u30a9\u30fc\u30e0\u4e0b\u3067\nfunction algorithm(n) {\n    var a = 2; // 1 ns\n    a = a + 1; // 1 ns\n    a = a * 2; // 10 ns\n    // n\u56de\u30eb\u30fc\u30d7\n    for(let i = 0; i &lt; n; i++) { // 1 ns, \u6bce\u56dei++\u304c\u5b9f\u884c\u3055\u308c\u308b\n        console.log(0); // 5 ns\n    }\n}\n</code></pre> <pre><code>// \u7279\u5b9a\u306e\u64cd\u4f5c\u30d7\u30e9\u30c3\u30c8\u30d5\u30a9\u30fc\u30e0\u4e0b\u3067\nfunction algorithm(n: number): void {\n    var a: number = 2; // 1 ns\n    a = a + 1; // 1 ns\n    a = a * 2; // 10 ns\n    // n\u56de\u30eb\u30fc\u30d7\n    for(let i = 0; i &lt; n; i++) { // 1 ns, \u6bce\u56dei++\u304c\u5b9f\u884c\u3055\u308c\u308b\n        console.log(0); // 5 ns\n    }\n}\n</code></pre> <pre><code>// \u7279\u5b9a\u306e\u64cd\u4f5c\u30d7\u30e9\u30c3\u30c8\u30d5\u30a9\u30fc\u30e0\u4e0b\u3067\nvoid algorithm(int n) {\n  int a = 2; // 1 ns\n  a = a + 1; // 1 ns\n  a = a * 2; // 10 ns\n  // n\u56de\u30eb\u30fc\u30d7\n  for (int i = 0; i &lt; n; i++) { // 1 ns, \u6bce\u56dei++\u304c\u5b9f\u884c\u3055\u308c\u308b\n    print(0); // 5 ns\n  }\n}\n</code></pre> <pre><code>// \u7279\u5b9a\u306e\u64cd\u4f5c\u30d7\u30e9\u30c3\u30c8\u30d5\u30a9\u30fc\u30e0\u4e0b\u3067\nfn algorithm(n: i32) {\n    let mut a = 2;      // 1 ns\n    a = a + 1;          // 1 ns\n    a = a * 2;          // 10 ns\n    // n\u56de\u30eb\u30fc\u30d7\n    for _ in 0..n {     // \u6bce\u56dei++\u30671 ns\n        println!(\"{}\", 0);  // 5 ns\n    }\n}\n</code></pre> <pre><code>// \u7279\u5b9a\u306e\u64cd\u4f5c\u30d7\u30e9\u30c3\u30c8\u30d5\u30a9\u30fc\u30e0\u4e0b\u3067\nvoid algorithm(int n) {\n    int a = 2;  // 1 ns\n    a = a + 1;  // 1 ns\n    a = a * 2;  // 10 ns\n    // n\u56de\u30eb\u30fc\u30d7\n    for (int i = 0; i &lt; n; i++) {   // 1 ns, \u6bce\u56dei++\u304c\u5b9f\u884c\u3055\u308c\u308b\n        printf(\"%d\", 0);            // 5 ns\n    }\n}\n</code></pre> <pre><code>\n</code></pre> <pre><code>// \u7279\u5b9a\u306e\u64cd\u4f5c\u30d7\u30e9\u30c3\u30c8\u30d5\u30a9\u30fc\u30e0\u4e0b\u3067\nfn algorithm(n: usize) void {\n    var a: i32 = 2; // 1 ns\n    a += 1; // 1 ns\n    a *= 2; // 10 ns\n    // n\u56de\u30eb\u30fc\u30d7\n    for (0..n) |_| { // 1 ns\n        std.debug.print(\"{}\\n\", .{0}); // 5 ns\n    }\n}\n</code></pre> <p>\u4e0a\u8a18\u306e\u65b9\u6cd5\u3092\u4f7f\u7528\u3059\u308b\u3068\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5b9f\u884c\u6642\u9593\u306f\\((6n + 12)\\) ns\u3068\u3057\u3066\u8a08\u7b97\u3067\u304d\u307e\u3059\uff1a</p> \\[ 1 + 1 + 10 + (1 + 5) \\times n = 6n + 12 \\] <p>\u3057\u304b\u3057\u3001\u5b9f\u969b\u306b\u306f\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5b9f\u884c\u6642\u9593\u3092\u30ab\u30a6\u30f3\u30c8\u3059\u308b\u3053\u3068\u306f\u5b9f\u7528\u7684\u3067\u3082\u5408\u7406\u7684\u3067\u3082\u3042\u308a\u307e\u305b\u3093\u3002\u7b2c\u4e00\u306b\u3001\u63a8\u5b9a\u6642\u9593\u3092\u5b9f\u884c\u30d7\u30e9\u30c3\u30c8\u30d5\u30a9\u30fc\u30e0\u306b\u7d50\u3073\u4ed8\u3051\u305f\u304f\u3042\u308a\u307e\u305b\u3093\u3002\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u69d8\u3005\u306a\u30d7\u30e9\u30c3\u30c8\u30d5\u30a9\u30fc\u30e0\u3067\u5b9f\u884c\u3055\u308c\u308b\u5fc5\u8981\u304c\u3042\u308b\u304b\u3089\u3067\u3059\u3002\u7b2c\u4e8c\u306b\u3001\u5404\u7a2e\u64cd\u4f5c\u306e\u5b9f\u884c\u6642\u9593\u3092\u77e5\u308b\u3053\u3068\u306f\u56f0\u96e3\u3067\u3042\u308a\u3001\u63a8\u5b9a\u30d7\u30ed\u30bb\u30b9\u3092\u96e3\u3057\u304f\u3057\u307e\u3059\u3002</p>"},{"location":"chapter_computational_complexity/time_complexity/#231","title":"2.3.1 \u00a0 \u6642\u9593\u5897\u52a0\u50be\u5411\u306e\u8a55\u4fa1","text":"<p>\u6642\u9593\u8a08\u7b97\u91cf\u5206\u6790\u306f\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5b9f\u884c\u6642\u9593\u3092\u30ab\u30a6\u30f3\u30c8\u3059\u308b\u306e\u3067\u306f\u306a\u304f\u3001**\u30c7\u30fc\u30bf\u91cf\u304c\u5897\u52a0\u3059\u308b\u306b\u3064\u308c\u3066\u306e\u5b9f\u884c\u6642\u9593\u306e\u5897\u52a0\u50be\u5411**\u3092\u5206\u6790\u3057\u307e\u3059\u3002</p> <p>\u3053\u306e\u300c\u6642\u9593\u5897\u52a0\u50be\u5411\u300d\u306e\u6982\u5ff5\u3092\u4f8b\u3067\u7406\u89e3\u3057\u307e\u3057\u3087\u3046\u3002\u5165\u529b\u30c7\u30fc\u30bf\u30b5\u30a4\u30ba\u3092\\(n\\)\u3068\u3057\u30013\u3064\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0<code>A</code>\u3001<code>B</code>\u3001<code>C</code>\u3092\u8003\u3048\u3066\u307f\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinZig <pre><code># \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0A\u306e\u6642\u9593\u8a08\u7b97\u91cf\uff1a\u5b9a\u6570\u30aa\u30fc\u30c0\u30fc\ndef algorithm_A(n: int):\n    print(0)\n# \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0B\u306e\u6642\u9593\u8a08\u7b97\u91cf\uff1a\u7dda\u5f62\u30aa\u30fc\u30c0\u30fc\ndef algorithm_B(n: int):\n    for _ in range(n):\n        print(0)\n# \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0C\u306e\u6642\u9593\u8a08\u7b97\u91cf\uff1a\u5b9a\u6570\u30aa\u30fc\u30c0\u30fc\ndef algorithm_C(n: int):\n    for _ in range(1000000):\n        print(0)\n</code></pre> <pre><code>// \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0A\u306e\u6642\u9593\u8a08\u7b97\u91cf\uff1a\u5b9a\u6570\u30aa\u30fc\u30c0\u30fc\nvoid algorithm_A(int n) {\n    cout &lt;&lt; 0 &lt;&lt; endl;\n}\n// \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0B\u306e\u6642\u9593\u8a08\u7b97\u91cf\uff1a\u7dda\u5f62\u30aa\u30fc\u30c0\u30fc\nvoid algorithm_B(int n) {\n    for (int i = 0; i &lt; n; i++) {\n        cout &lt;&lt; 0 &lt;&lt; endl;\n    }\n}\n// \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0C\u306e\u6642\u9593\u8a08\u7b97\u91cf\uff1a\u5b9a\u6570\u30aa\u30fc\u30c0\u30fc\nvoid algorithm_C(int n) {\n    for (int i = 0; i &lt; 1000000; i++) {\n        cout &lt;&lt; 0 &lt;&lt; endl;\n    }\n}\n</code></pre> <pre><code>// \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0A\u306e\u6642\u9593\u8a08\u7b97\u91cf\uff1a\u5b9a\u6570\u30aa\u30fc\u30c0\u30fc\nvoid algorithm_A(int n) {\n    System.out.println(0);\n}\n// \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0B\u306e\u6642\u9593\u8a08\u7b97\u91cf\uff1a\u7dda\u5f62\u30aa\u30fc\u30c0\u30fc\nvoid algorithm_B(int n) {\n    for (int i = 0; i &lt; n; i++) {\n        System.out.println(0);\n    }\n}\n// \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0C\u306e\u6642\u9593\u8a08\u7b97\u91cf\uff1a\u5b9a\u6570\u30aa\u30fc\u30c0\u30fc\nvoid algorithm_C(int n) {\n    for (int i = 0; i &lt; 1000000; i++) {\n        System.out.println(0);\n    }\n}\n</code></pre> <pre><code>// \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0A\u306e\u6642\u9593\u8a08\u7b97\u91cf\uff1a\u5b9a\u6570\u30aa\u30fc\u30c0\u30fc\nvoid AlgorithmA(int n) {\n    Console.WriteLine(0);\n}\n// \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0B\u306e\u6642\u9593\u8a08\u7b97\u91cf\uff1a\u7dda\u5f62\u30aa\u30fc\u30c0\u30fc\nvoid AlgorithmB(int n) {\n    for (int i = 0; i &lt; n; i++) {\n        Console.WriteLine(0);\n    }\n}\n// \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0C\u306e\u6642\u9593\u8a08\u7b97\u91cf\uff1a\u5b9a\u6570\u30aa\u30fc\u30c0\u30fc\nvoid AlgorithmC(int n) {\n    for (int i = 0; i &lt; 1000000; i++) {\n        Console.WriteLine(0);\n    }\n}\n</code></pre> <pre><code>// \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0A\u306e\u6642\u9593\u8a08\u7b97\u91cf\uff1a\u5b9a\u6570\u30aa\u30fc\u30c0\u30fc\nfunc algorithm_A(n int) {\n    fmt.Println(0)\n}\n// \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0B\u306e\u6642\u9593\u8a08\u7b97\u91cf\uff1a\u7dda\u5f62\u30aa\u30fc\u30c0\u30fc\nfunc algorithm_B(n int) {\n    for i := 0; i &lt; n; i++ {\n        fmt.Println(0)\n    }\n}\n// \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0C\u306e\u6642\u9593\u8a08\u7b97\u91cf\uff1a\u5b9a\u6570\u30aa\u30fc\u30c0\u30fc\nfunc algorithm_C(n int) {\n    for i := 0; i &lt; 1000000; i++ {\n        fmt.Println(0)\n    }\n}\n</code></pre> <pre><code>// \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0A\u306e\u6642\u9593\u8a08\u7b97\u91cf\uff1a\u5b9a\u6570\u30aa\u30fc\u30c0\u30fc\nfunc algorithmA(n: Int) {\n    print(0)\n}\n\n// \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0B\u306e\u6642\u9593\u8a08\u7b97\u91cf\uff1a\u7dda\u5f62\u30aa\u30fc\u30c0\u30fc\nfunc algorithmB(n: Int) {\n    for _ in 0 ..&lt; n {\n        print(0)\n    }\n}\n\n// \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0C\u306e\u6642\u9593\u8a08\u7b97\u91cf\uff1a\u5b9a\u6570\u30aa\u30fc\u30c0\u30fc\nfunc algorithmC(n: Int) {\n    for _ in 0 ..&lt; 1_000_000 {\n        print(0)\n    }\n}\n</code></pre> <pre><code>// \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0A\u306e\u6642\u9593\u8a08\u7b97\u91cf\uff1a\u5b9a\u6570\u30aa\u30fc\u30c0\u30fc\nfunction algorithm_A(n) {\n    console.log(0);\n}\n// \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0B\u306e\u6642\u9593\u8a08\u7b97\u91cf\uff1a\u7dda\u5f62\u30aa\u30fc\u30c0\u30fc\nfunction algorithm_B(n) {\n    for (let i = 0; i &lt; n; i++) {\n        console.log(0);\n    }\n}\n// \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0C\u306e\u6642\u9593\u8a08\u7b97\u91cf\uff1a\u5b9a\u6570\u30aa\u30fc\u30c0\u30fc\nfunction algorithm_C(n) {\n    for (let i = 0; i &lt; 1000000; i++) {\n        console.log(0);\n    }\n}\n</code></pre> <pre><code>// \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0A\u306e\u6642\u9593\u8a08\u7b97\u91cf\uff1a\u5b9a\u6570\u30aa\u30fc\u30c0\u30fc\nfunction algorithm_A(n: number): void {\n    console.log(0);\n}\n// \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0B\u306e\u6642\u9593\u8a08\u7b97\u91cf\uff1a\u7dda\u5f62\u30aa\u30fc\u30c0\u30fc\nfunction algorithm_B(n: number): void {\n    for (let i = 0; i &lt; n; i++) {\n        console.log(0);\n    }\n}\n// \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0C\u306e\u6642\u9593\u8a08\u7b97\u91cf\uff1a\u5b9a\u6570\u30aa\u30fc\u30c0\u30fc\nfunction algorithm_C(n: number): void {\n    for (let i = 0; i &lt; 1000000; i++) {\n        console.log(0);\n    }\n}\n</code></pre> <pre><code>// \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0A\u306e\u6642\u9593\u8a08\u7b97\u91cf\uff1a\u5b9a\u6570\u30aa\u30fc\u30c0\u30fc\nvoid algorithmA(int n) {\n  print(0);\n}\n// \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0B\u306e\u6642\u9593\u8a08\u7b97\u91cf\uff1a\u7dda\u5f62\u30aa\u30fc\u30c0\u30fc\nvoid algorithmB(int n) {\n  for (int i = 0; i &lt; n; i++) {\n    print(0);\n  }\n}\n// \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0C\u306e\u6642\u9593\u8a08\u7b97\u91cf\uff1a\u5b9a\u6570\u30aa\u30fc\u30c0\u30fc\nvoid algorithmC(int n) {\n  for (int i = 0; i &lt; 1000000; i++) {\n    print(0);\n  }\n}\n</code></pre> <pre><code>// \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0A\u306e\u6642\u9593\u8a08\u7b97\u91cf\uff1a\u5b9a\u6570\u30aa\u30fc\u30c0\u30fc\nfn algorithm_A(n: i32) {\n    println!(\"{}\", 0);\n}\n// \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0B\u306e\u6642\u9593\u8a08\u7b97\u91cf\uff1a\u7dda\u5f62\u30aa\u30fc\u30c0\u30fc\nfn algorithm_B(n: i32) {\n    for _ in 0..n {\n        println!(\"{}\", 0);\n    }\n}\n// \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0C\u306e\u6642\u9593\u8a08\u7b97\u91cf\uff1a\u5b9a\u6570\u30aa\u30fc\u30c0\u30fc\nfn algorithm_C(n: i32) {\n    for _ in 0..1000000 {\n        println!(\"{}\", 0);\n    }\n}\n</code></pre> <pre><code>// \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0A\u306e\u6642\u9593\u8a08\u7b97\u91cf\uff1a\u5b9a\u6570\u30aa\u30fc\u30c0\u30fc\nvoid algorithm_A(int n) {\n    printf(\"%d\", 0);\n}\n// \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0B\u306e\u6642\u9593\u8a08\u7b97\u91cf\uff1a\u7dda\u5f62\u30aa\u30fc\u30c0\u30fc\nvoid algorithm_B(int n) {\n    for (int i = 0; i &lt; n; i++) {\n        printf(\"%d\", 0);\n    }\n}\n// \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0C\u306e\u6642\u9593\u8a08\u7b97\u91cf\uff1a\u5b9a\u6570\u30aa\u30fc\u30c0\u30fc\nvoid algorithm_C(int n) {\n    for (int i = 0; i &lt; 1000000; i++) {\n        printf(\"%d\", 0);\n    }\n}\n</code></pre> <pre><code>\n</code></pre> <pre><code>// \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0A\u306e\u6642\u9593\u8a08\u7b97\u91cf\uff1a\u5b9a\u6570\u30aa\u30fc\u30c0\u30fc\nfn algorithm_A(n: usize) void {\n    _ = n;\n    std.debug.print(\"{}\\n\", .{0});\n}\n// \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0B\u306e\u6642\u9593\u8a08\u7b97\u91cf\uff1a\u7dda\u5f62\u30aa\u30fc\u30c0\u30fc\nfn algorithm_B(n: i32) void {\n    for (0..n) |_| {\n        std.debug.print(\"{}\\n\", .{0});\n    }\n}\n// \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0C\u306e\u6642\u9593\u8a08\u7b97\u91cf\uff1a\u5b9a\u6570\u30aa\u30fc\u30c0\u30fc\nfn algorithm_C(n: i32) void {\n    _ = n;\n    for (0..1000000) |_| {\n        std.debug.print(\"{}\\n\", .{0});\n    }\n}\n</code></pre> <p>\u4e0b\u56f3\u306f\u3053\u308c\u30893\u3064\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u6642\u9593\u8a08\u7b97\u91cf\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002</p> <ul> <li>\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0<code>A</code>\u306b\u306f1\u3064\u306e\u5370\u5237\u64cd\u4f5c\u306e\u307f\u304c\u3042\u308a\u3001\u305d\u306e\u5b9f\u884c\u6642\u9593\u306f\\(n\\)\u3068\u3068\u3082\u306b\u5897\u52a0\u3057\u307e\u305b\u3093\u3002\u305d\u306e\u6642\u9593\u8a08\u7b97\u91cf\u306f\u300c\u5b9a\u6570\u30aa\u30fc\u30c0\u30fc\u300d\u3068\u8003\u3048\u3089\u308c\u307e\u3059\u3002</li> <li>\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0<code>B</code>\u306b\u306f\\(n\\)\u56de\u30eb\u30fc\u30d7\u3059\u308b\u5370\u5237\u64cd\u4f5c\u304c\u3042\u308a\u3001\u305d\u306e\u5b9f\u884c\u6642\u9593\u306f\\(n\\)\u3068\u7dda\u5f62\u306b\u5897\u52a0\u3057\u307e\u3059\u3002\u305d\u306e\u6642\u9593\u8a08\u7b97\u91cf\u306f\u300c\u7dda\u5f62\u30aa\u30fc\u30c0\u30fc\u300d\u3067\u3059\u3002</li> <li>\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0<code>C</code>\u306b\u306f1,000,000\u56de\u30eb\u30fc\u30d7\u3059\u308b\u5370\u5237\u64cd\u4f5c\u304c\u3042\u308a\u307e\u3059\u3002\u6642\u9593\u306f\u304b\u304b\u308a\u307e\u3059\u304c\u3001\u5165\u529b\u30c7\u30fc\u30bf\u30b5\u30a4\u30ba\\(n\\)\u3068\u306f\u7121\u95a2\u4fc2\u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001<code>C</code>\u306e\u6642\u9593\u8a08\u7b97\u91cf\u306f<code>A</code>\u3068\u540c\u3058\u300c\u5b9a\u6570\u30aa\u30fc\u30c0\u30fc\u300d\u3067\u3059\u3002</li> </ul> <p></p> <p> \u56f3 2-7 \u00a0 Time growth trend of algorithms a, b, and c </p> <p>\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5b9f\u884c\u6642\u9593\u3092\u76f4\u63a5\u30ab\u30a6\u30f3\u30c8\u3059\u308b\u3053\u3068\u3068\u6bd4\u8f03\u3057\u3066\u3001\u6642\u9593\u8a08\u7b97\u91cf\u5206\u6790\u306e\u7279\u5fb4\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\uff1f</p> <ul> <li>\u6642\u9593\u8a08\u7b97\u91cf\u306f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u52b9\u7387\u3092\u52b9\u679c\u7684\u306b\u8a55\u4fa1\u3057\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0<code>B</code>\u306f\u7dda\u5f62\u306b\u5897\u52a0\u3059\u308b\u5b9f\u884c\u6642\u9593\u3092\u6301\u3061\u3001\\(n &gt; 1\\)\u306e\u6642\u306f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0<code>A</code>\u3088\u308a\u9045\u304f\u3001\\(n &gt; 1,000,000\\)\u306e\u6642\u306f<code>C</code>\u3088\u308a\u9045\u304f\u306a\u308a\u307e\u3059\u3002\u5b9f\u969b\u3001\u5165\u529b\u30c7\u30fc\u30bf\u30b5\u30a4\u30ba\\(n\\)\u304c\u5341\u5206\u306b\u5927\u304d\u3044\u9650\u308a\u3001\u300c\u5b9a\u6570\u30aa\u30fc\u30c0\u30fc\u300d\u8907\u96d1\u5ea6\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u5e38\u306b\u300c\u7dda\u5f62\u30aa\u30fc\u30c0\u30fc\u300d\u3088\u308a\u3082\u512a\u308c\u3066\u304a\u308a\u3001\u6642\u9593\u5897\u52a0\u50be\u5411\u306e\u672c\u8cea\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002</li> <li>\u6642\u9593\u8a08\u7b97\u91cf\u5206\u6790\u306f\u3088\u308a\u76f4\u611f\u7684\u3067\u3059\u3002\u660e\u3089\u304b\u306b\u3001\u5b9f\u884c\u30d7\u30e9\u30c3\u30c8\u30d5\u30a9\u30fc\u30e0\u3068\u8a08\u7b97\u64cd\u4f5c\u306e\u7a2e\u985e\u306f\u5b9f\u884c\u6642\u9593\u5897\u52a0\u306e\u50be\u5411\u3068\u306f\u7121\u95a2\u4fc2\u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u6642\u9593\u8a08\u7b97\u91cf\u5206\u6790\u3067\u306f\u3001\u3059\u3079\u3066\u306e\u8a08\u7b97\u64cd\u4f5c\u306e\u5b9f\u884c\u6642\u9593\u3092\u540c\u3058\u300c\u5358\u4f4d\u6642\u9593\u300d\u3068\u3057\u3066\u6271\u3046\u3053\u3068\u304c\u3067\u304d\u3001\u300c\u8a08\u7b97\u64cd\u4f5c\u5b9f\u884c\u6642\u9593\u30ab\u30a6\u30f3\u30c8\u300d\u3092\u300c\u8a08\u7b97\u64cd\u4f5c\u30ab\u30a6\u30f3\u30c8\u300d\u306b\u5358\u7d14\u5316\u3067\u304d\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u63a8\u5b9a\u306e\u8907\u96d1\u3055\u304c\u5927\u5e45\u306b\u8efd\u6e1b\u3055\u308c\u307e\u3059\u3002</li> <li>\u6642\u9593\u8a08\u7b97\u91cf\u306b\u306f\u5236\u9650\u304c\u3042\u308a\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0<code>A</code>\u3068<code>C</code>\u306f\u540c\u3058\u6642\u9593\u8a08\u7b97\u91cf\u3092\u6301\u3061\u307e\u3059\u304c\u3001\u5b9f\u969b\u306e\u5b9f\u884c\u6642\u9593\u306f\u5927\u304d\u304f\u7570\u306a\u308b\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002\u540c\u69d8\u306b\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0<code>B</code>\u306f<code>C</code>\u3088\u308a\u3082\u9ad8\u3044\u6642\u9593\u8a08\u7b97\u91cf\u3092\u6301\u3061\u307e\u3059\u304c\u3001\u5165\u529b\u30c7\u30fc\u30bf\u30b5\u30a4\u30ba\\(n\\)\u304c\u5c0f\u3055\u3044\u5834\u5408\u306f\u660e\u3089\u304b\u306b\u512a\u308c\u3066\u3044\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u5834\u5408\u3001\u6642\u9593\u8a08\u7b97\u91cf\u306e\u307f\u306b\u57fa\u3065\u3044\u3066\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u52b9\u7387\u3092\u5224\u65ad\u3059\u308b\u3053\u3068\u306f\u56f0\u96e3\u3067\u3059\u3002\u3057\u304b\u3057\u3001\u3053\u308c\u3089\u306e\u554f\u984c\u306b\u3082\u304b\u304b\u308f\u3089\u305a\u3001\u8907\u96d1\u5ea6\u5206\u6790\u306f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u52b9\u7387\u3092\u8a55\u4fa1\u3059\u308b\u305f\u3081\u306e\u6700\u3082\u52b9\u679c\u7684\u3067\u4e00\u822c\u7684\u306b\u4f7f\u7528\u3055\u308c\u308b\u65b9\u6cd5\u3067\u3059\u3002</li> </ul>"},{"location":"chapter_computational_complexity/time_complexity/#232","title":"2.3.2 \u00a0 \u6f38\u8fd1\u4e0a\u9650","text":"<p>\u5165\u529b\u30b5\u30a4\u30ba\u304c\\(n\\)\u306e\u95a2\u6570\u3092\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinZig <pre><code>def algorithm(n: int):\n    a = 1      # +1\n    a = a + 1  # +1\n    a = a * 2  # +1\n    # n\u56de\u30eb\u30fc\u30d7\n    for i in range(n):  # +1\n        print(0)        # +1\n</code></pre> <pre><code>void algorithm(int n) {\n    int a = 1;  // +1\n    a = a + 1;  // +1\n    a = a * 2;  // +1\n    // n\u56de\u30eb\u30fc\u30d7\n    for (int i = 0; i &lt; n; i++) { // +1 (\u6bce\u56dei++\u304c\u5b9f\u884c\u3055\u308c\u308b)\n        cout &lt;&lt; 0 &lt;&lt; endl;    // +1\n    }\n}\n</code></pre> <pre><code>void algorithm(int n) {\n    int a = 1;  // +1\n    a = a + 1;  // +1\n    a = a * 2;  // +1\n    // n\u56de\u30eb\u30fc\u30d7\n    for (int i = 0; i &lt; n; i++) { // +1 (\u6bce\u56dei++\u304c\u5b9f\u884c\u3055\u308c\u308b)\n        System.out.println(0);    // +1\n    }\n}\n</code></pre> <pre><code>void Algorithm(int n) {\n    int a = 1;  // +1\n    a = a + 1;  // +1\n    a = a * 2;  // +1\n    // n\u56de\u30eb\u30fc\u30d7\n    for (int i = 0; i &lt; n; i++) {   // +1 (\u6bce\u56dei++\u304c\u5b9f\u884c\u3055\u308c\u308b)\n        Console.WriteLine(0);   // +1\n    }\n}\n</code></pre> <pre><code>func algorithm(n int) {\n    a := 1      // +1\n    a = a + 1   // +1\n    a = a * 2   // +1\n    // n\u56de\u30eb\u30fc\u30d7\n    for i := 0; i &lt; n; i++ {   // +1\n        fmt.Println(a)         // +1\n    }\n}\n</code></pre> <pre><code>func algorithm(n: Int) {\n    var a = 1 // +1\n    a = a + 1 // +1\n    a = a * 2 // +1\n    // n\u56de\u30eb\u30fc\u30d7\n    for _ in 0 ..&lt; n { // +1\n        print(0) // +1\n    }\n}\n</code></pre> <pre><code>function algorithm(n) {\n    var a = 1; // +1\n    a += 1; // +1\n    a *= 2; // +1\n    // n\u56de\u30eb\u30fc\u30d7\n    for(let i = 0; i &lt; n; i++){ // +1 (\u6bce\u56dei++\u304c\u5b9f\u884c\u3055\u308c\u308b)\n        console.log(0); // +1\n    }\n}\n</code></pre> <pre><code>function algorithm(n: number): void{\n    var a: number = 1; // +1\n    a += 1; // +1\n    a *= 2; // +1\n    // n\u56de\u30eb\u30fc\u30d7\n    for(let i = 0; i &lt; n; i++){ // +1 (\u6bce\u56dei++\u304c\u5b9f\u884c\u3055\u308c\u308b)\n        console.log(0); // +1\n    }\n}\n</code></pre> <pre><code>void algorithm(int n) {\n  int a = 1; // +1\n  a = a + 1; // +1\n  a = a * 2; // +1\n  // n\u56de\u30eb\u30fc\u30d7\n  for (int i = 0; i &lt; n; i++) { // +1 (\u6bce\u56dei++\u304c\u5b9f\u884c\u3055\u308c\u308b)\n    print(0); // +1\n  }\n}\n</code></pre> <pre><code>fn algorithm(n: i32) {\n    let mut a = 1;   // +1\n    a = a + 1;      // +1\n    a = a * 2;      // +1\n\n    // n\u56de\u30eb\u30fc\u30d7\n    for _ in 0..n { // +1 (\u6bce\u56dei++\u304c\u5b9f\u884c\u3055\u308c\u308b)\n        println!(\"{}\", 0); // +1\n    }\n}\n</code></pre> <pre><code>void algorithm(int n) {\n    int a = 1;  // +1\n    a = a + 1;  // +1\n    a = a * 2;  // +1\n    // n\u56de\u30eb\u30fc\u30d7\n    for (int i = 0; i &lt; n; i++) {   // +1 (\u6bce\u56dei++\u304c\u5b9f\u884c\u3055\u308c\u308b)\n        printf(\"%d\", 0);            // +1\n    }\n}\n</code></pre> <pre><code>\n</code></pre> <pre><code>fn algorithm(n: usize) void {\n    var a: i32 = 1; // +1\n    a += 1; // +1\n    a *= 2; // +1\n    // n\u56de\u30eb\u30fc\u30d7\n    for (0..n) |_| { // +1 (\u6bce\u56dei++\u304c\u5b9f\u884c\u3055\u308c\u308b)\n        std.debug.print(\"{}\\n\", .{0}); // +1\n    }\n}\n</code></pre> <p>\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u64cd\u4f5c\u6570\u3092\u5165\u529b\u30b5\u30a4\u30ba\\(n\\)\u306e\u95a2\u6570\u3068\u3057\u3066\u8868\u3059\u95a2\u6570\u3092\\(T(n)\\)\u3068\u3059\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u4f8b\u3092\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\uff1a</p> \\[ T(n) = 3 + 2n \\] <p>\\(T(n)\\)\u306f\u7dda\u5f62\u95a2\u6570\u3067\u3042\u308b\u305f\u3081\u3001\u305d\u306e\u5897\u52a0\u50be\u5411\u306f\u7dda\u5f62\u3067\u3042\u308a\u3001\u3057\u305f\u304c\u3063\u3066\u3001\u305d\u306e\u6642\u9593\u8a08\u7b97\u91cf\u306f\u7dda\u5f62\u30aa\u30fc\u30c0\u30fc\u3067\u3001\\(O(n)\\)\u3068\u8868\u8a18\u3055\u308c\u307e\u3059\u3002\u3053\u306e\u6570\u5b66\u8a18\u6cd5\u306f\u30d3\u30c3\u30b0O\u8a18\u6cd5\u3068\u3057\u3066\u77e5\u3089\u308c\u3001\u95a2\u6570\\(T(n)\\)\u306e\u6f38\u8fd1\u4e0a\u9650\u3092\u8868\u3057\u307e\u3059\u3002</p> <p>\u672c\u8cea\u7684\u306b\u3001\u6642\u9593\u8a08\u7b97\u91cf\u5206\u6790\u306f\u300c\u64cd\u4f5c\u6570\\(T(n)\\)\u300d\u306e\u6f38\u8fd1\u4e0a\u9650\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u3067\u3059\u3002\u305d\u308c\u306b\u306f\u6b63\u78ba\u306a\u6570\u5b66\u7684\u5b9a\u7fa9\u304c\u3042\u308a\u307e\u3059\u3002</p> <p>\u6f38\u8fd1\u4e0a\u9650</p> <p>\u3059\u3079\u3066\u306e\\(n &gt; n_0\\)\u306b\u5bfe\u3057\u3066\\(T(n) \\leq c \\cdot f(n)\\)\u3068\u306a\u308b\u3088\u3046\u306a\u6b63\u306e\u5b9f\u6570\\(c\\)\u3068\\(n_0\\)\u304c\u5b58\u5728\u3059\u308b\u5834\u5408\u3001\\(f(n)\\)\u306f\\(T(n)\\)\u306e\u6f38\u8fd1\u4e0a\u9650\u3068\u307f\u306a\u3055\u308c\u3001\\(T(n) = O(f(n))\\)\u3068\u8868\u8a18\u3055\u308c\u307e\u3059\u3002</p> <p>\u4e0b\u56f3\u306b\u793a\u3055\u308c\u3066\u3044\u308b\u3088\u3046\u306b\u3001\u6f38\u8fd1\u4e0a\u9650\u306e\u8a08\u7b97\u3067\u306f\u3001\\(n\\)\u304c\u7121\u9650\u5927\u306b\u8fd1\u3065\u304f\u306b\u3064\u308c\u3066\u3001\\(T(n)\\)\u3068\\(f(n)\\)\u304c\u540c\u3058\u5897\u52a0\u30aa\u30fc\u30c0\u30fc\u3092\u6301\u3061\u3001\u5b9a\u6570\u56e0\u5b50\\(c\\)\u306e\u307f\u304c\u7570\u306a\u308b\u3088\u3046\u306a\u95a2\u6570\\(f(n)\\)\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u542b\u307e\u308c\u307e\u3059\u3002</p> <p></p> <p> \u56f3 2-8 \u00a0 Asymptotic upper bound of a function </p>"},{"location":"chapter_computational_complexity/time_complexity/#233","title":"2.3.3 \u00a0 \u8a08\u7b97\u65b9\u6cd5","text":"<p>\u6f38\u8fd1\u4e0a\u9650\u306e\u6982\u5ff5\u306f\u6570\u5b66\u7684\u306b\u6fc3\u5bc6\u306b\u898b\u3048\u308b\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u304c\u3001\u4eca\u3059\u3050\u5b8c\u5168\u306b\u7406\u89e3\u3059\u308b\u5fc5\u8981\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u307e\u305a\u8a08\u7b97\u65b9\u6cd5\u3092\u7406\u89e3\u3057\u3001\u6642\u9593\u3092\u304b\u3051\u3066\u7df4\u7fd2\u3057\u7406\u89e3\u3057\u307e\u3057\u3087\u3046\u3002</p> <p>\\(f(n)\\)\u304c\u6c7a\u307e\u308c\u3070\u3001\u6642\u9593\u8a08\u7b97\u91cf\\(O(f(n))\\)\u304c\u5f97\u3089\u308c\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u6f38\u8fd1\u4e0a\u9650\\(f(n)\\)\u3092\u3069\u306e\u3088\u3046\u306b\u6c7a\u5b9a\u3059\u308b\u306e\u3067\u3057\u3087\u3046\u304b\uff1f\u3053\u306e\u30d7\u30ed\u30bb\u30b9\u306b\u306f\u4e00\u822c\u7684\u306b2\u3064\u306e\u30b9\u30c6\u30c3\u30d7\u304c\u542b\u307e\u308c\u307e\u3059\uff1a\u64cd\u4f5c\u6570\u306e\u30ab\u30a6\u30f3\u30c8\u3068\u6f38\u8fd1\u4e0a\u9650\u306e\u6c7a\u5b9a\u3067\u3059\u3002</p>"},{"location":"chapter_computational_complexity/time_complexity/#1-1","title":"1. \u00a0 \u30b9\u30c6\u30c3\u30d71: \u64cd\u4f5c\u6570\u306e\u30ab\u30a6\u30f3\u30c8","text":"<p>\u3053\u306e\u30b9\u30c6\u30c3\u30d7\u3067\u306f\u3001\u30b3\u30fc\u30c9\u3092\u884c\u3054\u3068\u306b\u78ba\u8a8d\u3057\u307e\u3059\u3002\u3057\u304b\u3057\u3001\\(c \\cdot f(n)\\)\u306e\u5b9a\u6570\\(c\\)\u306e\u5b58\u5728\u306b\u3088\u308a\u3001\\(T(n)\\)\u306e\u3059\u3079\u3066\u306e\u4fc2\u6570\u3068\u5b9a\u6570\u9805\u306f\u7121\u8996\u3067\u304d\u307e\u3059\u3002\u3053\u306e\u539f\u7406\u306b\u3088\u308a\u3001\u64cd\u4f5c\u3092\u30ab\u30a6\u30f3\u30c8\u3059\u308b\u969b\u306e\u7c21\u7565\u5316\u6280\u6cd5\u304c\u53ef\u80fd\u306b\u306a\u308a\u307e\u3059\u3002</p> <ol> <li>\\(T(n)\\)\u306e\u5b9a\u6570\u9805\u3092\u7121\u8996\u3057\u307e\u3059\u3002\u3053\u308c\u3089\u306f\\(n\\)\u3068\u306f\u7121\u95a2\u4fc2\u3067\u3042\u308b\u305f\u3081\u3001\u6642\u9593\u8a08\u7b97\u91cf\u306b\u5f71\u97ff\u3057\u307e\u305b\u3093\u3002</li> <li>\u3059\u3079\u3066\u306e\u4fc2\u6570\u3092\u7701\u7565\u3057\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\\(2n\\)\u3001\\(5n + 1\\)\u56de\u306a\u3069\u306e\u30eb\u30fc\u30d7\u306f\u3001\\(n\\)\u306e\u524d\u306e\u4fc2\u6570\u304c\u6642\u9593\u8a08\u7b97\u91cf\u306b\u5f71\u97ff\u3057\u306a\u3044\u305f\u3081\u3001\\(n\\)\u56de\u306b\u7c21\u7565\u5316\u3067\u304d\u307e\u3059\u3002</li> <li>\u30cd\u30b9\u30c8\u3057\u305f\u30eb\u30fc\u30d7\u306b\u306f\u4e57\u7b97\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002\u7dcf\u64cd\u4f5c\u6570\u306f\u5404\u30eb\u30fc\u30d7\u306e\u64cd\u4f5c\u6570\u306e\u7a4d\u3067\u3042\u308a\u3001\u30dd\u30a4\u30f3\u30c81\u30682\u306e\u7c21\u7565\u5316\u6280\u6cd5\u3092\u5404\u30eb\u30fc\u30d7\u30ec\u30d9\u30eb\u306b\u9069\u7528\u3057\u307e\u3059\u3002</li> </ol> <p>\u95a2\u6570\u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408\u3001\u3053\u308c\u3089\u306e\u6280\u6cd5\u3092\u4f7f\u7528\u3057\u3066\u64cd\u4f5c\u3092\u30ab\u30a6\u30f3\u30c8\u3067\u304d\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinZig <pre><code>def algorithm(n: int):\n    a = 1      # +0 (\u6280\u6cd51)\n    a = a + n  # +0 (\u6280\u6cd51)\n    # +n (\u6280\u6cd52)\n    for i in range(5 * n + 1):\n        print(0)\n    # +n*n (\u6280\u6cd53)\n    for i in range(2 * n):\n        for j in range(n + 1):\n            print(0)\n</code></pre> <pre><code>void algorithm(int n) {\n    int a = 1;  // +0 (\u6280\u6cd51)\n    a = a + n;  // +0 (\u6280\u6cd51)\n    // +n (\u6280\u6cd52)\n    for (int i = 0; i &lt; 5 * n + 1; i++) {\n        cout &lt;&lt; 0 &lt;&lt; endl;\n    }\n    // +n*n (\u6280\u6cd53)\n    for (int i = 0; i &lt; 2 * n; i++) {\n        for (int j = 0; j &lt; n + 1; j++) {\n            cout &lt;&lt; 0 &lt;&lt; endl;\n        }\n    }\n}\n</code></pre> <pre><code>void algorithm(int n) {\n    int a = 1;  // +0 (\u6280\u6cd51)\n    a = a + n;  // +0 (\u6280\u6cd51)\n    // +n (\u6280\u6cd52)\n    for (int i = 0; i &lt; 5 * n + 1; i++) {\n        System.out.println(0);\n    }\n    // +n*n (\u6280\u6cd53)\n    for (int i = 0; i &lt; 2 * n; i++) {\n        for (int j = 0; j &lt; n + 1; j++) {\n            System.out.println(0);\n        }\n    }\n}\n</code></pre> <pre><code>void Algorithm(int n) {\n    int a = 1;  // +0 (\u6280\u6cd51)\n    a = a + n;  // +0 (\u6280\u6cd51)\n    // +n (\u6280\u6cd52)\n    for (int i = 0; i &lt; 5 * n + 1; i++) {\n        Console.WriteLine(0);\n    }\n    // +n*n (\u6280\u6cd53)\n    for (int i = 0; i &lt; 2 * n; i++) {\n        for (int j = 0; j &lt; n + 1; j++) {\n            Console.WriteLine(0);\n        }\n    }\n}\n</code></pre> <pre><code>func algorithm(n int) {\n    a := 1     // +0 (\u6280\u6cd51)\n    a = a + n  // +0 (\u6280\u6cd51)\n    // +n (\u6280\u6cd52)\n    for i := 0; i &lt; 5 * n + 1; i++ {\n        fmt.Println(0)\n    }\n    // +n*n (\u6280\u6cd53)\n    for i := 0; i &lt; 2 * n; i++ {\n        for j := 0; j &lt; n + 1; j++ {\n            fmt.Println(0)\n        }\n    }\n}\n</code></pre> <pre><code>func algorithm(n: Int) {\n    var a = 1 // +0 (\u6280\u6cd51)\n    a = a + n // +0 (\u6280\u6cd51)\n    // +n (\u6280\u6cd52)\n    for _ in 0 ..&lt; (5 * n + 1) {\n        print(0)\n    }\n    // +n*n (\u6280\u6cd53)\n    for _ in 0 ..&lt; (2 * n) {\n        for _ in 0 ..&lt; (n + 1) {\n            print(0)\n        }\n    }\n}\n</code></pre> <pre><code>function algorithm(n) {\n    let a = 1;  // +0 (\u6280\u6cd51)\n    a = a + n;  // +0 (\u6280\u6cd51)\n    // +n (\u6280\u6cd52)\n    for (let i = 0; i &lt; 5 * n + 1; i++) {\n        console.log(0);\n    }\n    // +n*n (\u6280\u6cd53)\n    for (let i = 0; i &lt; 2 * n; i++) {\n        for (let j = 0; j &lt; n + 1; j++) {\n            console.log(0);\n        }\n    }\n}\n</code></pre> <pre><code>function algorithm(n: number): void {\n    let a = 1;  // +0 (\u6280\u6cd51)\n    a = a + n;  // +0 (\u6280\u6cd51)\n    // +n (\u6280\u6cd52)\n    for (let i = 0; i &lt; 5 * n + 1; i++) {\n        console.log(0);\n    }\n    // +n*n (\u6280\u6cd53)\n    for (let i = 0; i &lt; 2 * n; i++) {\n        for (let j = 0; j &lt; n + 1; j++) {\n            console.log(0);\n        }\n    }\n}\n</code></pre> <pre><code>void algorithm(int n) {\n  int a = 1; // +0 (\u6280\u6cd51)\n  a = a + n; // +0 (\u6280\u6cd51)\n  // +n (\u6280\u6cd52)\n  for (int i = 0; i &lt; 5 * n + 1; i++) {\n    print(0);\n  }\n  // +n*n (\u6280\u6cd53)\n  for (int i = 0; i &lt; 2 * n; i++) {\n    for (int j = 0; j &lt; n + 1; j++) {\n      print(0);\n    }\n  }\n}\n</code></pre> <pre><code>fn algorithm(n: i32) {\n    let mut a = 1;     // +0 (\u6280\u6cd51)\n    a = a + n;        // +0 (\u6280\u6cd51)\n\n    // +n (\u6280\u6cd52)\n    for i in 0..(5 * n + 1) {\n        println!(\"{}\", 0);\n    }\n\n    // +n*n (\u6280\u6cd53)\n    for i in 0..(2 * n) {\n        for j in 0..(n + 1) {\n            println!(\"{}\", 0);\n        }\n    }\n}\n</code></pre> <pre><code>void algorithm(int n) {\n    int a = 1;  // +0 (\u6280\u6cd51)\n    a = a + n;  // +0 (\u6280\u6cd51)\n    // +n (\u6280\u6cd52)\n    for (int i = 0; i &lt; 5 * n + 1; i++) {\n        printf(\"%d\", 0);\n    }\n    // +n*n (\u6280\u6cd53)\n    for (int i = 0; i &lt; 2 * n; i++) {\n        for (int j = 0; j &lt; n + 1; j++) {\n            printf(\"%d\", 0);\n        }\n    }\n}\n</code></pre> <pre><code>\n</code></pre> <pre><code>fn algorithm(n: usize) void {\n    var a: i32 = 1;     // +0 (\u6280\u6cd51)\n    a = a + @as(i32, @intCast(n));        // +0 (\u6280\u6cd51)\n\n    // +n (\u6280\u6cd52)\n    for(0..(5 * n + 1)) |_| {\n        std.debug.print(\"{}\\n\", .{0});\n    }\n\n    // +n*n (\u6280\u6cd53)\n    for(0..(2 * n)) |_| {\n        for(0..(n + 1)) |_| {\n            std.debug.print(\"{}\\n\", .{0});\n        }\n    }\n}\n</code></pre> <p>\u4ee5\u4e0b\u306e\u5f0f\u306f\u3001\u7c21\u7565\u5316\u524d\u5f8c\u306e\u30ab\u30a6\u30f3\u30c8\u7d50\u679c\u3092\u793a\u3057\u3066\u304a\u308a\u3001\u3069\u3061\u3089\u3082\\(O(n^2)\\)\u306e\u6642\u9593\u8a08\u7b97\u91cf\u306b\u5c0e\u304d\u307e\u3059\uff1a</p> \\[ \\begin{aligned} T(n) &amp; = 2n(n + 1) + (5n + 1) + 2 &amp; \\text{\u5b8c\u5168\u30ab\u30a6\u30f3\u30c8 (-.-|||)} \\newline &amp; = 2n^2 + 7n + 3 \\newline T(n) &amp; = n^2 + n &amp; \\text{\u7c21\u7565\u5316\u30ab\u30a6\u30f3\u30c8 (o.O)} \\end{aligned} \\]"},{"location":"chapter_computational_complexity/time_complexity/#2-2","title":"2. \u00a0 \u30b9\u30c6\u30c3\u30d72: \u6f38\u8fd1\u4e0a\u9650\u306e\u6c7a\u5b9a","text":"<p>\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(T(n)\\)\u306e\u6700\u9ad8\u6b21\u9805\u306b\u3088\u3063\u3066\u6c7a\u5b9a\u3055\u308c\u307e\u3059\u3002\u3053\u308c\u306f\u3001\\(n\\)\u304c\u7121\u9650\u5927\u306b\u8fd1\u3065\u304f\u306b\u3064\u308c\u3066\u3001\u6700\u9ad8\u6b21\u9805\u304c\u652f\u914d\u7684\u306b\u306a\u308a\u3001\u4ed6\u306e\u9805\u306e\u5f71\u97ff\u306f\u7121\u8996\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308b\u305f\u3081\u3067\u3059\u3002</p> <p>\u4ee5\u4e0b\u306e\u8868\u306f\u3001\u7570\u306a\u308b\u64cd\u4f5c\u30ab\u30a6\u30f3\u30c8\u3068\u305d\u308c\u306b\u5bfe\u5fdc\u3059\u308b\u6642\u9593\u8a08\u7b97\u91cf\u306e\u4f8b\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002\u4fc2\u6570\u304c\u5897\u52a0\u30aa\u30fc\u30c0\u30fc\u3092\u5909\u66f4\u3067\u304d\u306a\u3044\u3053\u3068\u3092\u5f37\u8abf\u3059\u308b\u305f\u3081\u306b\u3001\u8a87\u5f35\u3055\u308c\u305f\u5024\u304c\u4f7f\u7528\u3055\u308c\u3066\u3044\u307e\u3059\u3002\\(n\\)\u304c\u975e\u5e38\u306b\u5927\u304d\u304f\u306a\u308b\u3068\u3001\u3053\u308c\u3089\u306e\u5b9a\u6570\u306f\u91cd\u8981\u3067\u306a\u304f\u306a\u308a\u307e\u3059\u3002</p> <p> \u8868: \u7570\u306a\u308b\u64cd\u4f5c\u30ab\u30a6\u30f3\u30c8\u306b\u5bfe\u3059\u308b\u6642\u9593\u8a08\u7b97\u91cf </p> \u64cd\u4f5c\u30ab\u30a6\u30f3\u30c8 \\(T(n)\\) \u6642\u9593\u8a08\u7b97\u91cf \\(O(f(n))\\) \\(100000\\) \\(O(1)\\) \\(3n + 2\\) \\(O(n)\\) \\(2n^2 + 3n + 2\\) \\(O(n^2)\\) \\(n^3 + 10000n^2\\) \\(O(n^3)\\) \\(2^n + 10000n^{10000}\\) \\(O(2^n)\\)"},{"location":"chapter_computational_complexity/time_complexity/#234","title":"2.3.4 \u00a0 \u4e00\u822c\u7684\u306a\u6642\u9593\u8a08\u7b97\u91cf\u306e\u7a2e\u985e","text":"<p>\u5165\u529b\u30c7\u30fc\u30bf\u30b5\u30a4\u30ba\u3092\\(n\\)\u3068\u3057\u307e\u3057\u3087\u3046\u3002\u4e00\u822c\u7684\u306a\u6642\u9593\u8a08\u7b97\u91cf\u306e\u7a2e\u985e\u3092\u4e0b\u56f3\u306b\u793a\u3057\u3001\u4f4e\u3044\u3082\u306e\u304b\u3089\u9ad8\u3044\u3082\u306e\u3078\u3068\u4e26\u3079\u3066\u3044\u307e\u3059\uff1a</p> \\[ \\begin{aligned} &amp; O(1) &lt; O(\\log n) &lt; O(n) &lt; O(n \\log n) &lt; O(n^2) &lt; O(2^n) &lt; O(n!) \\newline &amp; \\text{\u5b9a\u6570} &lt; \\text{\u5bfe\u6570} &lt; \\text{\u7dda\u5f62} &lt; \\text{\u7dda\u5f62\u5bfe\u6570} &lt; \\text{\u4e8c\u6b21} &lt; \\text{\u6307\u6570} &lt; \\text{\u968e\u4e57} \\end{aligned} \\] <p></p> <p> \u56f3 2-9 \u00a0 Common types of time complexity </p>"},{"location":"chapter_computational_complexity/time_complexity/#1-o1","title":"1. \u00a0 \u5b9a\u6570\u30aa\u30fc\u30c0\u30fc \\(O(1)\\)","text":"<p>\u5b9a\u6570\u30aa\u30fc\u30c0\u30fc\u306f\u3001\u64cd\u4f5c\u6570\u304c\u5165\u529b\u30c7\u30fc\u30bf\u30b5\u30a4\u30ba\\(n\\)\u3068\u306f\u7121\u95a2\u4fc2\u3067\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002\u4ee5\u4e0b\u306e\u95a2\u6570\u3067\u306f\u3001\u64cd\u4f5c\u6570<code>size</code>\u304c\u5927\u304d\u3044\u5834\u5408\u3067\u3082\u3001\\(n\\)\u3068\u306f\u7121\u95a2\u4fc2\u3067\u3042\u308b\u305f\u3081\u3001\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O(1)\\)\u306e\u307e\u307e\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig time_complexity.py<pre><code>def constant(n: int) -&gt; int:\n    \"\"\"\u5b9a\u6570\u8907\u96d1\u5ea6\"\"\"\n    count = 0\n    size = 100000\n    for _ in range(size):\n        count += 1\n    return count\n</code></pre> time_complexity.cpp<pre><code>/* \u5b9a\u6570\u8a08\u7b97\u91cf */\nint constant(int n) {\n    int count = 0;\n    int size = 100000;\n    for (int i = 0; i &lt; size; i++)\n        count++;\n    return count;\n}\n</code></pre> time_complexity.java<pre><code>/* \u5b9a\u6570\u8a08\u7b97\u91cf */\nint constant(int n) {\n    int count = 0;\n    int size = 100000;\n    for (int i = 0; i &lt; size; i++)\n        count++;\n    return count;\n}\n</code></pre> time_complexity.cs<pre><code>[class]{time_complexity}-[func]{Constant}\n</code></pre> time_complexity.go<pre><code>[class]{}-[func]{constant}\n</code></pre> time_complexity.swift<pre><code>[class]{}-[func]{constant}\n</code></pre> time_complexity.js<pre><code>[class]{}-[func]{constant}\n</code></pre> time_complexity.ts<pre><code>[class]{}-[func]{constant}\n</code></pre> time_complexity.dart<pre><code>[class]{}-[func]{constant}\n</code></pre> time_complexity.rs<pre><code>[class]{}-[func]{constant}\n</code></pre> time_complexity.c<pre><code>[class]{}-[func]{constant}\n</code></pre> time_complexity.kt<pre><code>[class]{}-[func]{constant}\n</code></pre> time_complexity.rb<pre><code>[class]{}-[func]{constant}\n</code></pre> time_complexity.zig<pre><code>[class]{}-[func]{constant}\n</code></pre>"},{"location":"chapter_computational_complexity/time_complexity/#2-on","title":"2. \u00a0 \u7dda\u5f62\u30aa\u30fc\u30c0\u30fc \\(O(n)\\)","text":"<p>\u7dda\u5f62\u30aa\u30fc\u30c0\u30fc\u306f\u3001\u64cd\u4f5c\u6570\u304c\u5165\u529b\u30c7\u30fc\u30bf\u30b5\u30a4\u30ba\\(n\\)\u3068\u7dda\u5f62\u306b\u5897\u52a0\u3059\u308b\u3053\u3068\u3092\u793a\u3057\u307e\u3059\u3002\u7dda\u5f62\u30aa\u30fc\u30c0\u30fc\u306f\u4e00\u822c\u7684\u306b\u5358\u4e00\u30eb\u30fc\u30d7\u69cb\u9020\u3067\u73fe\u308c\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig time_complexity.py<pre><code>def linear(n: int) -&gt; int:\n    \"\"\"\u7dda\u5f62\u8907\u96d1\u5ea6\"\"\"\n    count = 0\n    for _ in range(n):\n        count += 1\n    return count\n</code></pre> time_complexity.cpp<pre><code>/* \u7dda\u5f62\u8a08\u7b97\u91cf */\nint linear(int n) {\n    int count = 0;\n    for (int i = 0; i &lt; n; i++)\n        count++;\n    return count;\n}\n</code></pre> time_complexity.java<pre><code>/* \u7dda\u5f62\u8a08\u7b97\u91cf */\nint linear(int n) {\n    int count = 0;\n    for (int i = 0; i &lt; n; i++)\n        count++;\n    return count;\n}\n</code></pre> time_complexity.cs<pre><code>[class]{time_complexity}-[func]{Linear}\n</code></pre> time_complexity.go<pre><code>[class]{}-[func]{linear}\n</code></pre> time_complexity.swift<pre><code>[class]{}-[func]{linear}\n</code></pre> time_complexity.js<pre><code>[class]{}-[func]{linear}\n</code></pre> time_complexity.ts<pre><code>[class]{}-[func]{linear}\n</code></pre> time_complexity.dart<pre><code>[class]{}-[func]{linear}\n</code></pre> time_complexity.rs<pre><code>[class]{}-[func]{linear}\n</code></pre> time_complexity.c<pre><code>[class]{}-[func]{linear}\n</code></pre> time_complexity.kt<pre><code>[class]{}-[func]{linear}\n</code></pre> time_complexity.rb<pre><code>[class]{}-[func]{linear}\n</code></pre> time_complexity.zig<pre><code>[class]{}-[func]{linear}\n</code></pre> <p>\u914d\u5217\u306e\u8d70\u67fb\u3084\u9023\u7d50\u30ea\u30b9\u30c8\u306e\u8d70\u67fb\u306a\u3069\u306e\u64cd\u4f5c\u306f\u6642\u9593\u8a08\u7b97\u91cf\u304c\\(O(n)\\)\u3067\u3001\\(n\\)\u306f\u914d\u5217\u307e\u305f\u306f\u30ea\u30b9\u30c8\u306e\u9577\u3055\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig time_complexity.py<pre><code>def array_traversal(nums: list[int]) -&gt; int:\n    \"\"\"\u7dda\u5f62\u8907\u96d1\u5ea6\uff08\u914d\u5217\u306e\u8d70\u67fb\uff09\"\"\"\n    count = 0\n    # \u30eb\u30fc\u30d7\u56de\u6570\u306f\u914d\u5217\u306e\u9577\u3055\u306b\u6bd4\u4f8b\u3059\u308b\n    for num in nums:\n        count += 1\n    return count\n</code></pre> time_complexity.cpp<pre><code>/* \u7dda\u5f62\u8a08\u7b97\u91cf\uff08\u914d\u5217\u306e\u8d70\u67fb\uff09 */\nint arrayTraversal(vector&lt;int&gt; &amp;nums) {\n    int count = 0;\n    // \u30eb\u30fc\u30d7\u56de\u6570\u306f\u914d\u5217\u306e\u9577\u3055\u306b\u6bd4\u4f8b\n    for (int num : nums) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.java<pre><code>/* \u7dda\u5f62\u8a08\u7b97\u91cf\uff08\u914d\u5217\u306e\u8d70\u67fb\uff09 */\nint arrayTraversal(int[] nums) {\n    int count = 0;\n    // \u30eb\u30fc\u30d7\u56de\u6570\u306f\u914d\u5217\u306e\u9577\u3055\u306b\u6bd4\u4f8b\n    for (int num : nums) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.cs<pre><code>[class]{time_complexity}-[func]{ArrayTraversal}\n</code></pre> time_complexity.go<pre><code>[class]{}-[func]{arrayTraversal}\n</code></pre> time_complexity.swift<pre><code>[class]{}-[func]{arrayTraversal}\n</code></pre> time_complexity.js<pre><code>[class]{}-[func]{arrayTraversal}\n</code></pre> time_complexity.ts<pre><code>[class]{}-[func]{arrayTraversal}\n</code></pre> time_complexity.dart<pre><code>[class]{}-[func]{arrayTraversal}\n</code></pre> time_complexity.rs<pre><code>[class]{}-[func]{array_traversal}\n</code></pre> time_complexity.c<pre><code>[class]{}-[func]{arrayTraversal}\n</code></pre> time_complexity.kt<pre><code>[class]{}-[func]{arrayTraversal}\n</code></pre> time_complexity.rb<pre><code>[class]{}-[func]{array_traversal}\n</code></pre> time_complexity.zig<pre><code>[class]{}-[func]{arrayTraversal}\n</code></pre> <p>\u5165\u529b\u30c7\u30fc\u30bf\u30b5\u30a4\u30ba\\(n\\)\u306f\u5165\u529b\u30c7\u30fc\u30bf\u306e\u7a2e\u985e\u306b\u57fa\u3065\u3044\u3066\u6c7a\u5b9a\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u6700\u521d\u306e\u4f8b\u3067\u306f\u3001\\(n\\)\u306f\u5165\u529b\u30c7\u30fc\u30bf\u30b5\u30a4\u30ba\u3092\u8868\u3057\u30012\u756a\u76ee\u306e\u4f8b\u3067\u306f\u3001\u914d\u5217\u306e\u9577\u3055\\(n\\)\u304c\u30c7\u30fc\u30bf\u30b5\u30a4\u30ba\u3067\u3059\u3002</p>"},{"location":"chapter_computational_complexity/time_complexity/#3-on2","title":"3. \u00a0 \u4e8c\u6b21\u30aa\u30fc\u30c0\u30fc \\(O(n^2)\\)","text":"<p>\u4e8c\u6b21\u30aa\u30fc\u30c0\u30fc\u306f\u3001\u64cd\u4f5c\u6570\u304c\u5165\u529b\u30c7\u30fc\u30bf\u30b5\u30a4\u30ba\\(n\\)\u306e\u4e8c\u4e57\u306b\u6bd4\u4f8b\u3057\u3066\u5897\u52a0\u3059\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002\u4e8c\u6b21\u30aa\u30fc\u30c0\u30fc\u306f\u901a\u5e38\u30cd\u30b9\u30c8\u3057\u305f\u30eb\u30fc\u30d7\u3067\u73fe\u308c\u3001\u5916\u5074\u3068\u5185\u5074\u306e\u30eb\u30fc\u30d7\u306e\u4e21\u65b9\u304c\u6642\u9593\u8a08\u7b97\u91cf\\(O(n)\\)\u3092\u6301\u3061\u3001\u5168\u4f53\u306e\u8907\u96d1\u5ea6\u306f\\(O(n^2)\\)\u306b\u306a\u308a\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig time_complexity.py<pre><code>def quadratic(n: int) -&gt; int:\n    \"\"\"\u4e8c\u6b21\u8907\u96d1\u5ea6\"\"\"\n    count = 0\n    # \u30eb\u30fc\u30d7\u56de\u6570\u306f\u30c7\u30fc\u30bf\u30b5\u30a4\u30ban\u306e\u4e8c\u4e57\u306b\u6bd4\u4f8b\u3059\u308b\n    for i in range(n):\n        for j in range(n):\n            count += 1\n    return count\n</code></pre> time_complexity.cpp<pre><code>/* \u4e8c\u6b21\u8a08\u7b97\u91cf */\nint quadratic(int n) {\n    int count = 0;\n    // \u30eb\u30fc\u30d7\u56de\u6570\u306f\u30c7\u30fc\u30bf\u30b5\u30a4\u30ba n \u306e\u4e8c\u4e57\u306b\u6bd4\u4f8b\n    for (int i = 0; i &lt; n; i++) {\n        for (int j = 0; j &lt; n; j++) {\n            count++;\n        }\n    }\n    return count;\n}\n</code></pre> time_complexity.java<pre><code>/* \u4e8c\u6b21\u8a08\u7b97\u91cf */\nint quadratic(int n) {\n    int count = 0;\n    // \u30eb\u30fc\u30d7\u56de\u6570\u306f\u30c7\u30fc\u30bf\u30b5\u30a4\u30ba n \u306e\u4e8c\u4e57\u306b\u6bd4\u4f8b\n    for (int i = 0; i &lt; n; i++) {\n        for (int j = 0; j &lt; n; j++) {\n            count++;\n        }\n    }\n    return count;\n}\n</code></pre> time_complexity.cs<pre><code>[class]{time_complexity}-[func]{Quadratic}\n</code></pre> time_complexity.go<pre><code>[class]{}-[func]{quadratic}\n</code></pre> time_complexity.swift<pre><code>[class]{}-[func]{quadratic}\n</code></pre> time_complexity.js<pre><code>[class]{}-[func]{quadratic}\n</code></pre> time_complexity.ts<pre><code>[class]{}-[func]{quadratic}\n</code></pre> time_complexity.dart<pre><code>[class]{}-[func]{quadratic}\n</code></pre> time_complexity.rs<pre><code>[class]{}-[func]{quadratic}\n</code></pre> time_complexity.c<pre><code>[class]{}-[func]{quadratic}\n</code></pre> time_complexity.kt<pre><code>[class]{}-[func]{quadratic}\n</code></pre> time_complexity.rb<pre><code>[class]{}-[func]{quadratic}\n</code></pre> time_complexity.zig<pre><code>[class]{}-[func]{quadratic}\n</code></pre> <p>\u4e0b\u56f3\u306f\u5b9a\u6570\u30aa\u30fc\u30c0\u30fc\u3001\u7dda\u5f62\u30aa\u30fc\u30c0\u30fc\u3001\u4e8c\u6b21\u30aa\u30fc\u30c0\u30fc\u306e\u6642\u9593\u8a08\u7b97\u91cf\u3092\u6bd4\u8f03\u3057\u3066\u3044\u307e\u3059\u3002</p> <p></p> <p> \u56f3 2-10 \u00a0 Constant, linear, and quadratic order time complexities </p> <p>\u4f8b\u3048\u3070\u3001\u30d0\u30d6\u30eb\u30bd\u30fc\u30c8\u3067\u306f\u3001\u5916\u5074\u306e\u30eb\u30fc\u30d7\u304c\\(n - 1\\)\u56de\u5b9f\u884c\u3055\u308c\u3001\u5185\u5074\u306e\u30eb\u30fc\u30d7\u304c\\(n-1\\)\u3001\\(n-2\\)\u3001...\u3001\\(2\\)\u3001\\(1\\)\u56de\u5b9f\u884c\u3055\u308c\u3001\u5e73\u5747\\(n / 2\\)\u56de\u3068\u306a\u308a\u3001\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O((n - 1) n / 2) = O(n^2)\\)\u306b\u306a\u308a\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig time_complexity.py<pre><code>def bubble_sort(nums: list[int]) -&gt; int:\n    \"\"\"\u4e8c\u6b21\u8907\u96d1\u5ea6\uff08\u30d0\u30d6\u30eb\u30bd\u30fc\u30c8\uff09\"\"\"\n    count = 0  # \u30ab\u30a6\u30f3\u30bf\n    # \u5916\u5074\u306e\u30eb\u30fc\u30d7: \u672a\u30bd\u30fc\u30c8\u7bc4\u56f2\u306f [0, i]\n    for i in range(len(nums) - 1, 0, -1):\n        # \u5185\u5074\u306e\u30eb\u30fc\u30d7: \u672a\u30bd\u30fc\u30c8\u7bc4\u56f2 [0, i] \u306e\u6700\u5927\u8981\u7d20\u3092\u53f3\u7aef\u306b\u30b9\u30ef\u30c3\u30d7\n        for j in range(i):\n            if nums[j] &gt; nums[j + 1]:\n                # nums[j] \u3068 nums[j + 1] \u3092\u30b9\u30ef\u30c3\u30d7\n                tmp: int = nums[j]\n                nums[j] = nums[j + 1]\n                nums[j + 1] = tmp\n                count += 3  # \u8981\u7d20\u306e\u30b9\u30ef\u30c3\u30d7\u306f3\u3064\u306e\u500b\u5225\u64cd\u4f5c\u3092\u542b\u3080\n    return count\n</code></pre> time_complexity.cpp<pre><code>/* \u4e8c\u6b21\u8a08\u7b97\u91cf\uff08\u30d0\u30d6\u30eb\u30bd\u30fc\u30c8\uff09 */\nint bubbleSort(vector&lt;int&gt; &amp;nums) {\n    int count = 0; // \u30ab\u30a6\u30f3\u30bf\u30fc\n    // \u5916\u5074\u30eb\u30fc\u30d7\uff1a\u672a\u30bd\u30fc\u30c8\u7bc4\u56f2\u306f [0, i]\n    for (int i = nums.size() - 1; i &gt; 0; i--) {\n        // \u5185\u5074\u30eb\u30fc\u30d7\uff1a\u672a\u30bd\u30fc\u30c8\u7bc4\u56f2 [0, i] \u306e\u6700\u5927\u8981\u7d20\u3092\u7bc4\u56f2\u306e\u53f3\u7aef\u306b\u30b9\u30ef\u30c3\u30d7\n        for (int j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // nums[j] \u3068 nums[j + 1] \u3092\u30b9\u30ef\u30c3\u30d7\n                int tmp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = tmp;\n                count += 3; // \u8981\u7d20\u306e\u30b9\u30ef\u30c3\u30d7\u306b\u306f3\u3064\u306e\u500b\u5225\u64cd\u4f5c\u304c\u542b\u307e\u308c\u308b\n            }\n        }\n    }\n    return count;\n}\n</code></pre> time_complexity.java<pre><code>/* \u4e8c\u6b21\u8a08\u7b97\u91cf\uff08\u30d0\u30d6\u30eb\u30bd\u30fc\u30c8\uff09 */\nint bubbleSort(int[] nums) {\n    int count = 0; // \u30ab\u30a6\u30f3\u30bf\u30fc\n    // \u5916\u5074\u30eb\u30fc\u30d7\uff1a\u672a\u30bd\u30fc\u30c8\u7bc4\u56f2\u306f [0, i]\n    for (int i = nums.length - 1; i &gt; 0; i--) {\n        // \u5185\u5074\u30eb\u30fc\u30d7\uff1a\u672a\u30bd\u30fc\u30c8\u7bc4\u56f2 [0, i] \u306e\u6700\u5927\u8981\u7d20\u3092\u7bc4\u56f2\u306e\u53f3\u7aef\u306b\u30b9\u30ef\u30c3\u30d7\n        for (int j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // nums[j] \u3068 nums[j + 1] \u3092\u30b9\u30ef\u30c3\u30d7\n                int tmp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = tmp;\n                count += 3; // \u8981\u7d20\u306e\u30b9\u30ef\u30c3\u30d7\u306b\u306f3\u3064\u306e\u500b\u5225\u64cd\u4f5c\u304c\u542b\u307e\u308c\u308b\n            }\n        }\n    }\n    return count;\n}\n</code></pre> time_complexity.cs<pre><code>[class]{time_complexity}-[func]{BubbleSort}\n</code></pre> time_complexity.go<pre><code>[class]{}-[func]{bubbleSort}\n</code></pre> time_complexity.swift<pre><code>[class]{}-[func]{bubbleSort}\n</code></pre> time_complexity.js<pre><code>[class]{}-[func]{bubbleSort}\n</code></pre> time_complexity.ts<pre><code>[class]{}-[func]{bubbleSort}\n</code></pre> time_complexity.dart<pre><code>[class]{}-[func]{bubbleSort}\n</code></pre> time_complexity.rs<pre><code>[class]{}-[func]{bubble_sort}\n</code></pre> time_complexity.c<pre><code>[class]{}-[func]{bubbleSort}\n</code></pre> time_complexity.kt<pre><code>[class]{}-[func]{bubbleSort}\n</code></pre> time_complexity.rb<pre><code>[class]{}-[func]{bubble_sort}\n</code></pre> time_complexity.zig<pre><code>[class]{}-[func]{bubbleSort}\n</code></pre>"},{"location":"chapter_computational_complexity/time_complexity/#4-o2n","title":"4. \u00a0 \u6307\u6570\u30aa\u30fc\u30c0\u30fc \\(O(2^n)\\)","text":"<p>\u751f\u7269\u5b66\u7684\u300c\u7d30\u80de\u5206\u88c2\u300d\u306f\u6307\u6570\u30aa\u30fc\u30c0\u30fc\u5897\u52a0\u306e\u5178\u578b\u4f8b\u3067\u3059\uff1a1\u3064\u306e\u7d30\u80de\u304b\u3089\u59cb\u307e\u308a\u30011\u56de\u306e\u5206\u88c2\u5f8c\u306b2\u3064\u30012\u56de\u306e\u5206\u88c2\u5f8c\u306b4\u3064\u3068\u306a\u308a\u3001\\(n\\)\u56de\u306e\u5206\u88c2\u5f8c\u306b\\(2^n\\)\u500b\u306e\u7d30\u80de\u306b\u306a\u308a\u307e\u3059\u3002</p> <p>\u4e0b\u56f3\u3068\u30b3\u30fc\u30c9\u306f\u7d30\u80de\u5206\u88c2\u30d7\u30ed\u30bb\u30b9\u3092\u30b7\u30df\u30e5\u30ec\u30fc\u30c8\u3057\u3001\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O(2^n)\\)\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig time_complexity.py<pre><code>def exponential(n: int) -&gt; int:\n    \"\"\"\u6307\u6570\u8907\u96d1\u5ea6\uff08\u30eb\u30fc\u30d7\u5b9f\u88c5\uff09\"\"\"\n    count = 0\n    base = 1\n    # \u30bb\u30eb\u306f\u6bce\u56de2\u3064\u306b\u5206\u88c2\u3057\u30011, 2, 4, 8, ..., 2^(n-1) \u306e\u6570\u5217\u3092\u5f62\u6210\u3059\u308b\n    for _ in range(n):\n        for _ in range(base):\n            count += 1\n        base *= 2\n    # count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n    return count\n</code></pre> time_complexity.cpp<pre><code>/* \u6307\u6570\u8a08\u7b97\u91cf\uff08\u30eb\u30fc\u30d7\u5b9f\u88c5\uff09 */\nint exponential(int n) {\n    int count = 0, base = 1;\n    // \u30bb\u30eb\u306f\u6bce\u30e9\u30a6\u30f3\u30c92\u3064\u306b\u5206\u88c2\u3057\u3001\u6570\u5217 1, 2, 4, 8, ..., 2^(n-1) \u3092\u5f62\u6210\n    for (int i = 0; i &lt; n; i++) {\n        for (int j = 0; j &lt; base; j++) {\n            count++;\n        }\n        base *= 2;\n    }\n    // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n    return count;\n}\n</code></pre> time_complexity.java<pre><code>/* \u6307\u6570\u8a08\u7b97\u91cf\uff08\u30eb\u30fc\u30d7\u5b9f\u88c5\uff09 */\nint exponential(int n) {\n    int count = 0, base = 1;\n    // \u30bb\u30eb\u306f\u6bce\u30e9\u30a6\u30f3\u30c92\u3064\u306b\u5206\u88c2\u3057\u3001\u6570\u5217 1, 2, 4, 8, ..., 2^(n-1) \u3092\u5f62\u6210\n    for (int i = 0; i &lt; n; i++) {\n        for (int j = 0; j &lt; base; j++) {\n            count++;\n        }\n        base *= 2;\n    }\n    // count = 1 + 2 + 4 + 8 + .. + 2^(n-1) = 2^n - 1\n    return count;\n}\n</code></pre> time_complexity.cs<pre><code>[class]{time_complexity}-[func]{Exponential}\n</code></pre> time_complexity.go<pre><code>[class]{}-[func]{exponential}\n</code></pre> time_complexity.swift<pre><code>[class]{}-[func]{exponential}\n</code></pre> time_complexity.js<pre><code>[class]{}-[func]{exponential}\n</code></pre> time_complexity.ts<pre><code>[class]{}-[func]{exponential}\n</code></pre> time_complexity.dart<pre><code>[class]{}-[func]{exponential}\n</code></pre> time_complexity.rs<pre><code>[class]{}-[func]{exponential}\n</code></pre> time_complexity.c<pre><code>[class]{}-[func]{exponential}\n</code></pre> time_complexity.kt<pre><code>[class]{}-[func]{exponential}\n</code></pre> time_complexity.rb<pre><code>[class]{}-[func]{exponential}\n</code></pre> time_complexity.zig<pre><code>[class]{}-[func]{exponential}\n</code></pre> <p></p> <p> \u56f3 2-11 \u00a0 Exponential order time complexity </p> <p>\u5b9f\u969b\u306b\u306f\u3001\u6307\u6570\u30aa\u30fc\u30c0\u30fc\u306f\u518d\u5e30\u95a2\u6570\u3067\u3088\u304f\u73fe\u308c\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u4ee5\u4e0b\u306e\u30b3\u30fc\u30c9\u3067\u306f\u3001\u518d\u5e30\u7684\u306b2\u3064\u306e\u534a\u5206\u306b\u5206\u5272\u3057\u3001\\(n\\)\u56de\u306e\u5206\u5272\u5f8c\u306b\u505c\u6b62\u3057\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig time_complexity.py<pre><code>def exp_recur(n: int) -&gt; int:\n    \"\"\"\u6307\u6570\u8907\u96d1\u5ea6\uff08\u518d\u5e30\u5b9f\u88c5\uff09\"\"\"\n    if n == 1:\n        return 1\n    return exp_recur(n - 1) + exp_recur(n - 1) + 1\n</code></pre> time_complexity.cpp<pre><code>/* \u6307\u6570\u8a08\u7b97\u91cf\uff08\u518d\u5e30\u5b9f\u88c5\uff09 */\nint expRecur(int n) {\n    if (n == 1)\n        return 1;\n    return expRecur(n - 1) + expRecur(n - 1) + 1;\n}\n</code></pre> time_complexity.java<pre><code>/* \u6307\u6570\u8a08\u7b97\u91cf\uff08\u518d\u5e30\u5b9f\u88c5\uff09 */\nint expRecur(int n) {\n    if (n == 1)\n        return 1;\n    return expRecur(n - 1) + expRecur(n - 1) + 1;\n}\n</code></pre> time_complexity.cs<pre><code>[class]{time_complexity}-[func]{ExpRecur}\n</code></pre> time_complexity.go<pre><code>[class]{}-[func]{expRecur}\n</code></pre> time_complexity.swift<pre><code>[class]{}-[func]{expRecur}\n</code></pre> time_complexity.js<pre><code>[class]{}-[func]{expRecur}\n</code></pre> time_complexity.ts<pre><code>[class]{}-[func]{expRecur}\n</code></pre> time_complexity.dart<pre><code>[class]{}-[func]{expRecur}\n</code></pre> time_complexity.rs<pre><code>[class]{}-[func]{exp_recur}\n</code></pre> time_complexity.c<pre><code>[class]{}-[func]{expRecur}\n</code></pre> time_complexity.kt<pre><code>[class]{}-[func]{expRecur}\n</code></pre> time_complexity.rb<pre><code>[class]{}-[func]{exp_recur}\n</code></pre> time_complexity.zig<pre><code>[class]{}-[func]{expRecur}\n</code></pre> <p>\u6307\u6570\u30aa\u30fc\u30c0\u30fc\u306e\u5897\u52a0\u306f\u6975\u3081\u3066\u6025\u901f\u3067\u3001\u5168\u6570\u63a2\u7d22\u6cd5\uff08\u30d6\u30eb\u30fc\u30c8\u30d5\u30a9\u30fc\u30b9\u3001\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u306a\u3069\uff09\u3067\u3088\u304f\u898b\u3089\u308c\u307e\u3059\u3002\u5927\u898f\u6a21\u554f\u984c\u3067\u306f\u3001\u6307\u6570\u30aa\u30fc\u30c0\u30fc\u306f\u53d7\u3051\u5165\u308c\u3089\u308c\u305a\u3001\u3057\u3070\u3057\u3070\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u3084\u8caa\u6b32\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u304c\u89e3\u6c7a\u7b56\u3068\u3057\u3066\u5fc5\u8981\u306b\u306a\u308a\u307e\u3059\u3002</p>"},{"location":"chapter_computational_complexity/time_complexity/#5-olog-n","title":"5. \u00a0 \u5bfe\u6570\u30aa\u30fc\u30c0\u30fc \\(O(\\log n)\\)","text":"<p>\u6307\u6570\u30aa\u30fc\u30c0\u30fc\u3068\u306f\u5bfe\u7167\u7684\u306b\u3001\u5bfe\u6570\u30aa\u30fc\u30c0\u30fc\u306f\u300c\u5404\u30e9\u30a6\u30f3\u30c9\u3067\u30b5\u30a4\u30ba\u304c\u534a\u5206\u306b\u306a\u308b\u300d\u72b6\u6cc1\u3092\u53cd\u6620\u3057\u307e\u3059\u3002\u5165\u529b\u30c7\u30fc\u30bf\u30b5\u30a4\u30ba\u304c\\(n\\)\u306e\u5834\u5408\u3001\u5404\u30e9\u30a6\u30f3\u30c9\u3067\u30b5\u30a4\u30ba\u304c\u534a\u5206\u306b\u306a\u308b\u305f\u3081\u3001\u53cd\u5fa9\u56de\u6570\u306f\\(\\log_2 n\\)\u3067\u3001\u3053\u308c\u306f\\(2^n\\)\u306e\u9006\u95a2\u6570\u3067\u3059\u3002</p> <p>\u4e0b\u56f3\u3068\u30b3\u30fc\u30c9\u306f\u300c\u5404\u30e9\u30a6\u30f3\u30c9\u3067\u534a\u5206\u306b\u3059\u308b\u300d\u30d7\u30ed\u30bb\u30b9\u3092\u30b7\u30df\u30e5\u30ec\u30fc\u30c8\u3057\u3001\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O(\\log_2 n)\\)\u3067\u3001\u4e00\u822c\u7684\u306b\\(O(\\log n)\\)\u3068\u7701\u7565\u3055\u308c\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig time_complexity.py<pre><code>def logarithmic(n: int) -&gt; int:\n    \"\"\"\u5bfe\u6570\u8907\u96d1\u5ea6\uff08\u30eb\u30fc\u30d7\u5b9f\u88c5\uff09\"\"\"\n    count = 0\n    while n &gt; 1:\n        n = n / 2\n        count += 1\n    return count\n</code></pre> time_complexity.cpp<pre><code>/* \u5bfe\u6570\u8a08\u7b97\u91cf\uff08\u30eb\u30fc\u30d7\u5b9f\u88c5\uff09 */\nint logarithmic(int n) {\n    int count = 0;\n    while (n &gt; 1) {\n        n = n / 2;\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.java<pre><code>/* \u5bfe\u6570\u8a08\u7b97\u91cf\uff08\u30eb\u30fc\u30d7\u5b9f\u88c5\uff09 */\nint logarithmic(int n) {\n    int count = 0;\n    while (n &gt; 1) {\n        n = n / 2;\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.cs<pre><code>[class]{time_complexity}-[func]{Logarithmic}\n</code></pre> time_complexity.go<pre><code>[class]{}-[func]{logarithmic}\n</code></pre> time_complexity.swift<pre><code>[class]{}-[func]{logarithmic}\n</code></pre> time_complexity.js<pre><code>[class]{}-[func]{logarithmic}\n</code></pre> time_complexity.ts<pre><code>[class]{}-[func]{logarithmic}\n</code></pre> time_complexity.dart<pre><code>[class]{}-[func]{logarithmic}\n</code></pre> time_complexity.rs<pre><code>[class]{}-[func]{logarithmic}\n</code></pre> time_complexity.c<pre><code>[class]{}-[func]{logarithmic}\n</code></pre> time_complexity.kt<pre><code>[class]{}-[func]{logarithmic}\n</code></pre> time_complexity.rb<pre><code>[class]{}-[func]{logarithmic}\n</code></pre> time_complexity.zig<pre><code>[class]{}-[func]{logarithmic}\n</code></pre> <p></p> <p> \u56f3 2-12 \u00a0 Logarithmic order time complexity </p> <p>\u6307\u6570\u30aa\u30fc\u30c0\u30fc\u3068\u540c\u69d8\u306b\u3001\u5bfe\u6570\u30aa\u30fc\u30c0\u30fc\u3082\u518d\u5e30\u95a2\u6570\u3067\u983b\u7e41\u306b\u73fe\u308c\u307e\u3059\u3002\u4ee5\u4e0b\u306e\u30b3\u30fc\u30c9\u306f\u9ad8\u3055\\(\\log_2 n\\)\u306e\u518d\u5e30\u6728\u3092\u5f62\u6210\u3057\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig time_complexity.py<pre><code>def log_recur(n: int) -&gt; int:\n    \"\"\"\u5bfe\u6570\u8907\u96d1\u5ea6\uff08\u518d\u5e30\u5b9f\u88c5\uff09\"\"\"\n    if n &lt;= 1:\n        return 0\n    return log_recur(n / 2) + 1\n</code></pre> time_complexity.cpp<pre><code>/* \u5bfe\u6570\u8a08\u7b97\u91cf\uff08\u518d\u5e30\u5b9f\u88c5\uff09 */\nint logRecur(int n) {\n    if (n &lt;= 1)\n        return 0;\n    return logRecur(n / 2) + 1;\n}\n</code></pre> time_complexity.java<pre><code>/* \u5bfe\u6570\u8a08\u7b97\u91cf\uff08\u518d\u5e30\u5b9f\u88c5\uff09 */\nint logRecur(int n) {\n    if (n &lt;= 1)\n        return 0;\n    return logRecur(n / 2) + 1;\n}\n</code></pre> time_complexity.cs<pre><code>[class]{time_complexity}-[func]{LogRecur}\n</code></pre> time_complexity.go<pre><code>[class]{}-[func]{logRecur}\n</code></pre> time_complexity.swift<pre><code>[class]{}-[func]{logRecur}\n</code></pre> time_complexity.js<pre><code>[class]{}-[func]{logRecur}\n</code></pre> time_complexity.ts<pre><code>[class]{}-[func]{logRecur}\n</code></pre> time_complexity.dart<pre><code>[class]{}-[func]{logRecur}\n</code></pre> time_complexity.rs<pre><code>[class]{}-[func]{log_recur}\n</code></pre> time_complexity.c<pre><code>[class]{}-[func]{logRecur}\n</code></pre> time_complexity.kt<pre><code>[class]{}-[func]{logRecur}\n</code></pre> time_complexity.rb<pre><code>[class]{}-[func]{log_recur}\n</code></pre> time_complexity.zig<pre><code>[class]{}-[func]{logRecur}\n</code></pre> <p>\u5bfe\u6570\u30aa\u30fc\u30c0\u30fc\u306f\u5206\u5272\u7d71\u6cbb\u6226\u7565\u306b\u57fa\u3065\u304f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5178\u578b\u3067\u3001\u300c\u591a\u304f\u306b\u5206\u5272\u300d\u3068\u300c\u8907\u96d1\u306a\u554f\u984c\u3092\u5358\u7d14\u5316\u300d\u3059\u308b\u30a2\u30d7\u30ed\u30fc\u30c1\u3092\u4f53\u73fe\u3057\u3066\u3044\u307e\u3059\u3002\u5897\u52a0\u304c\u9045\u304f\u3001\u5b9a\u6570\u30aa\u30fc\u30c0\u30fc\u306e\u6b21\u306b\u6700\u3082\u7406\u60f3\u7684\u306a\u6642\u9593\u8a08\u7b97\u91cf\u3067\u3059\u3002</p> <p>\\(O(\\log n)\\)\u306e\u5e95\u306f\u4f55\u3067\u3059\u304b\uff1f</p> <p>\u6280\u8853\u7684\u306b\u306f\u3001\u300c\\(m\\)\u306b\u5206\u5272\u300d\u306f\u6642\u9593\u8a08\u7b97\u91cf\\(O(\\log_m n)\\)\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002\u5bfe\u6570\u306e\u5e95\u5909\u66f4\u516c\u5f0f\u3092\u4f7f\u7528\u3059\u308b\u3068\u3001\u7570\u306a\u308b\u5bfe\u6570\u8907\u96d1\u5ea6\u3092\u7b49\u4fa1\u306b\u3067\u304d\u307e\u3059\uff1a</p> \\[ O(\\log_m n) = O(\\log_k n / \\log_k m) = O(\\log_k n) \\] <p>\u3053\u308c\u306f\u3001\u5e95\\(m\\)\u3092\u8907\u96d1\u5ea6\u306b\u5f71\u97ff\u3092\u4e0e\u3048\u308b\u3053\u3068\u306a\u304f\u5909\u66f4\u3067\u304d\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u3057\u3070\u3057\u3070\u5e95\\(m\\)\u3092\u7701\u7565\u3057\u3001\u5358\u306b\u5bfe\u6570\u30aa\u30fc\u30c0\u30fc\u3092\\(O(\\log n)\\)\u3068\u8868\u8a18\u3057\u307e\u3059\u3002</p>"},{"location":"chapter_computational_complexity/time_complexity/#6-on-log-n","title":"6. \u00a0 \u7dda\u5f62\u5bfe\u6570\u30aa\u30fc\u30c0\u30fc \\(O(n \\log n)\\)","text":"<p>\u7dda\u5f62\u5bfe\u6570\u30aa\u30fc\u30c0\u30fc\u306f\u30cd\u30b9\u30c8\u3057\u305f\u30eb\u30fc\u30d7\u3067\u3088\u304f\u73fe\u308c\u30012\u3064\u306e\u30eb\u30fc\u30d7\u306e\u8907\u96d1\u5ea6\u304c\u305d\u308c\u305e\u308c\\(O(\\log n)\\)\u3068\\(O(n)\\)\u3067\u3059\u3002\u95a2\u9023\u3059\u308b\u30b3\u30fc\u30c9\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig time_complexity.py<pre><code>def linear_log_recur(n: int) -&gt; int:\n    \"\"\"\u7dda\u5f62\u5bfe\u6570\u8907\u96d1\u5ea6\"\"\"\n    if n &lt;= 1:\n        return 1\n    count: int = linear_log_recur(n // 2) + linear_log_recur(n // 2)\n    for _ in range(n):\n        count += 1\n    return count\n</code></pre> time_complexity.cpp<pre><code>/* \u7dda\u5f62\u5bfe\u6570\u8a08\u7b97\u91cf */\nint linearLogRecur(int n) {\n    if (n &lt;= 1)\n        return 1;\n    int count = linearLogRecur(n / 2) + linearLogRecur(n / 2);\n    for (int i = 0; i &lt; n; i++) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.java<pre><code>/* \u7dda\u5f62\u5bfe\u6570\u8a08\u7b97\u91cf */\nint linearLogRecur(int n) {\n    if (n &lt;= 1)\n        return 1;\n    int count = linearLogRecur(n / 2) + linearLogRecur(n / 2);\n    for (int i = 0; i &lt; n; i++) {\n        count++;\n    }\n    return count;\n}\n</code></pre> time_complexity.cs<pre><code>[class]{time_complexity}-[func]{LinearLogRecur}\n</code></pre> time_complexity.go<pre><code>[class]{}-[func]{linearLogRecur}\n</code></pre> time_complexity.swift<pre><code>[class]{}-[func]{linearLogRecur}\n</code></pre> time_complexity.js<pre><code>[class]{}-[func]{linearLogRecur}\n</code></pre> time_complexity.ts<pre><code>[class]{}-[func]{linearLogRecur}\n</code></pre> time_complexity.dart<pre><code>[class]{}-[func]{linearLogRecur}\n</code></pre> time_complexity.rs<pre><code>[class]{}-[func]{linear_log_recur}\n</code></pre> time_complexity.c<pre><code>[class]{}-[func]{linearLogRecur}\n</code></pre> time_complexity.kt<pre><code>[class]{}-[func]{linearLogRecur}\n</code></pre> time_complexity.rb<pre><code>[class]{}-[func]{linear_log_recur}\n</code></pre> time_complexity.zig<pre><code>[class]{}-[func]{linearLogRecur}\n</code></pre> <p>\u4e0b\u56f3\u306f\u7dda\u5f62\u5bfe\u6570\u30aa\u30fc\u30c0\u30fc\u304c\u3069\u306e\u3088\u3046\u306b\u751f\u6210\u3055\u308c\u308b\u304b\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002\u4e8c\u5206\u6728\u306e\u5404\u30ec\u30d9\u30eb\u306b\u306f\\(n\\)\u500b\u306e\u64cd\u4f5c\u304c\u3042\u308a\u3001\u6728\u306b\u306f\\(\\log_2 n + 1\\)\u30ec\u30d9\u30eb\u304c\u3042\u308a\u3001\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O(n \\log n)\\)\u306b\u306a\u308a\u307e\u3059\u3002</p> <p></p> <p> \u56f3 2-13 \u00a0 Linear-logarithmic order time complexity </p> <p>\u4e3b\u6d41\u306e\u30bd\u30fc\u30c8\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u901a\u5e38\\(O(n \\log n)\\)\u306e\u6642\u9593\u8a08\u7b97\u91cf\u3092\u6301\u3061\u3001\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u3001\u30de\u30fc\u30b8\u30bd\u30fc\u30c8\u3001\u30d2\u30fc\u30d7\u30bd\u30fc\u30c8\u306a\u3069\u304c\u3042\u308a\u307e\u3059\u3002</p>"},{"location":"chapter_computational_complexity/time_complexity/#7-on","title":"7. \u00a0 \u968e\u4e57\u30aa\u30fc\u30c0\u30fc \\(O(n!)\\)","text":"<p>\u968e\u4e57\u30aa\u30fc\u30c0\u30fc\u306f\u300c\u5168\u9806\u5217\u300d\u306e\u6570\u5b66\u554f\u984c\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002\\(n\\)\u500b\u306e\u7570\u306a\u308b\u8981\u7d20\u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408\u3001\u53ef\u80fd\u306a\u9806\u5217\u306e\u7dcf\u6570\u306f\uff1a</p> \\[ n! = n \\times (n - 1) \\times (n - 2) \\times \\dots \\times 2 \\times 1 \\] <p>\u968e\u4e57\u306f\u901a\u5e38\u518d\u5e30\u3092\u4f7f\u7528\u3057\u3066\u5b9f\u88c5\u3055\u308c\u307e\u3059\u3002\u4ee5\u4e0b\u306e\u30b3\u30fc\u30c9\u3068\u56f3\u306b\u793a\u3055\u308c\u3066\u3044\u308b\u3088\u3046\u306b\u3001\u7b2c1\u30ec\u30d9\u30eb\u306f\\(n\\)\u500b\u306e\u5206\u5c90\u306b\u5206\u5272\u3055\u308c\u3001\u7b2c2\u30ec\u30d9\u30eb\u306f\\(n - 1\\)\u500b\u306e\u5206\u5c90\u306b\u5206\u5272\u3055\u308c\u3001\u7b2c\\(n\\)\u30ec\u30d9\u30eb\u5f8c\u306b\u505c\u6b62\u3057\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig time_complexity.py<pre><code>def factorial_recur(n: int) -&gt; int:\n    \"\"\"\u968e\u4e57\u8907\u96d1\u5ea6\uff08\u518d\u5e30\u5b9f\u88c5\uff09\"\"\"\n    if n == 0:\n        return 1\n    count = 0\n    # 1\u3064\u304b\u3089n\u306b\u5206\u5c90\n    for _ in range(n):\n        count += factorial_recur(n - 1)\n    return count\n</code></pre> time_complexity.cpp<pre><code>/* \u968e\u4e57\u8a08\u7b97\u91cf\uff08\u518d\u5e30\u5b9f\u88c5\uff09 */\nint factorialRecur(int n) {\n    if (n == 0)\n        return 1;\n    int count = 0;\n    // 1\u304b\u3089 n \u306b\u5206\u88c2\n    for (int i = 0; i &lt; n; i++) {\n        count += factorialRecur(n - 1);\n    }\n    return count;\n}\n</code></pre> time_complexity.java<pre><code>/* \u968e\u4e57\u8a08\u7b97\u91cf\uff08\u518d\u5e30\u5b9f\u88c5\uff09 */\nint factorialRecur(int n) {\n    if (n == 0)\n        return 1;\n    int count = 0;\n    // 1\u304b\u3089 n \u306b\u5206\u88c2\n    for (int i = 0; i &lt; n; i++) {\n        count += factorialRecur(n - 1);\n    }\n    return count;\n}\n</code></pre> time_complexity.cs<pre><code>[class]{time_complexity}-[func]{FactorialRecur}\n</code></pre> time_complexity.go<pre><code>[class]{}-[func]{factorialRecur}\n</code></pre> time_complexity.swift<pre><code>[class]{}-[func]{factorialRecur}\n</code></pre> time_complexity.js<pre><code>[class]{}-[func]{factorialRecur}\n</code></pre> time_complexity.ts<pre><code>[class]{}-[func]{factorialRecur}\n</code></pre> time_complexity.dart<pre><code>[class]{}-[func]{factorialRecur}\n</code></pre> time_complexity.rs<pre><code>[class]{}-[func]{factorial_recur}\n</code></pre> time_complexity.c<pre><code>[class]{}-[func]{factorialRecur}\n</code></pre> time_complexity.kt<pre><code>[class]{}-[func]{factorialRecur}\n</code></pre> time_complexity.rb<pre><code>[class]{}-[func]{factorial_recur}\n</code></pre> time_complexity.zig<pre><code>[class]{}-[func]{factorialRecur}\n</code></pre> <p></p> <p> \u56f3 2-14 \u00a0 Factorial order time complexity </p> <p>\u968e\u4e57\u30aa\u30fc\u30c0\u30fc\u306f\u6307\u6570\u30aa\u30fc\u30c0\u30fc\u3088\u308a\u3082\u3055\u3089\u306b\u901f\u304f\u5897\u52a0\u3059\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u3088\u308a\u5927\u304d\u306a\\(n\\)\u5024\u3067\u306f\u53d7\u3051\u5165\u308c\u3089\u308c\u307e\u305b\u3093\u3002</p>"},{"location":"chapter_computational_complexity/time_complexity/#235","title":"2.3.5 \u00a0 \u6700\u60aa\u3001\u6700\u826f\u3001\u5e73\u5747\u6642\u9593\u8a08\u7b97\u91cf","text":"<p>\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u6642\u9593\u52b9\u7387\u306f\u56fa\u5b9a\u3055\u308c\u3066\u3044\u306a\u3044\u3053\u3068\u304c\u591a\u304f\u3001\u5165\u529b\u30c7\u30fc\u30bf\u306e\u5206\u5e03\u306b\u4f9d\u5b58\u3057\u307e\u3059\u3002\u9577\u3055\\(n\\)\u306e\u914d\u5217<code>nums</code>\u304c\u3042\u308a\u3001\\(1\\)\u304b\u3089\\(n\\)\u307e\u3067\u306e\u6570\u3067\u69cb\u6210\u3055\u308c\u3001\u305d\u308c\u305e\u308c\u304c\u4e00\u5ea6\u3060\u3051\u73fe\u308c\u307e\u3059\u304c\u3001\u30e9\u30f3\u30c0\u30e0\u306b\u30b7\u30e3\u30c3\u30d5\u30eb\u3055\u308c\u305f\u9806\u5e8f\u3067\u3042\u308b\u3068\u3057\u307e\u3059\u3002\u30bf\u30b9\u30af\u306f\u8981\u7d20\\(1\\)\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8fd4\u3059\u3053\u3068\u3067\u3059\u3002\u4ee5\u4e0b\u306e\u7d50\u8ad6\u3092\u5c0e\u3051\u307e\u3059\uff1a</p> <ul> <li><code>nums = [?, ?, ..., 1]</code>\u306e\u5834\u5408\u3001\u3064\u307e\u308a\u6700\u5f8c\u306e\u8981\u7d20\u304c\\(1\\)\u306e\u5834\u5408\u3001\u914d\u5217\u306e\u5b8c\u5168\u306a\u8d70\u67fb\u304c\u5fc5\u8981\u3067\u3001\u6700\u60aa\u30b1\u30fc\u30b9\u6642\u9593\u8a08\u7b97\u91cf\\(O(n)\\)\u3092\u9054\u6210\u3057\u307e\u3059\u3002</li> <li><code>nums = [1, ?, ?, ...]</code>\u306e\u5834\u5408\u3001\u3064\u307e\u308a\u6700\u521d\u306e\u8981\u7d20\u304c\\(1\\)\u306e\u5834\u5408\u3001\u914d\u5217\u306e\u9577\u3055\u306b\u95a2\u4fc2\u306a\u304f\u3001\u3055\u3089\u306a\u308b\u8d70\u67fb\u306f\u4e0d\u8981\u3067\u3001\u6700\u826f\u30b1\u30fc\u30b9\u6642\u9593\u8a08\u7b97\u91cf\\(\\Omega(1)\\)\u3092\u9054\u6210\u3057\u307e\u3059\u3002</li> </ul> <p>\u300c\u6700\u60aa\u30b1\u30fc\u30b9\u6642\u9593\u8a08\u7b97\u91cf\u300d\u306f\u6f38\u8fd1\u4e0a\u9650\u306b\u5bfe\u5fdc\u3057\u3001\u5927\u304d\u306a\\(O\\)\u8a18\u6cd5\u3067\u8868\u3055\u308c\u307e\u3059\u3002\u5bfe\u5fdc\u3057\u3066\u3001\u300c\u6700\u826f\u30b1\u30fc\u30b9\u6642\u9593\u8a08\u7b97\u91cf\u300d\u306f\u6f38\u8fd1\u4e0b\u9650\u306b\u5bfe\u5fdc\u3057\u3001\\(\\Omega\\)\u3067\u8868\u3055\u308c\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig worst_best_time_complexity.py<pre><code>def random_numbers(n: int) -&gt; list[int]:\n    \"\"\"\u8981\u7d20 1, 2, ..., n \u3092\u542b\u3080\u914d\u5217\u3092\u751f\u6210\u3001\u9806\u5e8f\u306f\u30b7\u30e3\u30c3\u30d5\u30eb\"\"\"\n    # \u914d\u5217 nums = 1, 2, 3, ..., n \u3092\u751f\u6210\n    nums = [i for i in range(1, n + 1)]\n    # \u914d\u5217\u8981\u7d20\u3092\u30e9\u30f3\u30c0\u30e0\u306b\u30b7\u30e3\u30c3\u30d5\u30eb\n    random.shuffle(nums)\n    return nums\n\ndef find_one(nums: list[int]) -&gt; int:\n    \"\"\"\u914d\u5217 nums \u3067\u6570\u5024 1 \u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u691c\u7d22\"\"\"\n    for i in range(len(nums)):\n        # \u8981\u7d20 1 \u304c\u914d\u5217\u306e\u6700\u521d\u306b\u3042\u308b\u5834\u5408\u3001\u6700\u826f\u6642\u9593\u8a08\u7b97\u91cf O(1) \u3092\u9054\u6210\n        # \u8981\u7d20 1 \u304c\u914d\u5217\u306e\u6700\u5f8c\u306b\u3042\u308b\u5834\u5408\u3001\u6700\u60aa\u6642\u9593\u8a08\u7b97\u91cf O(n) \u3092\u9054\u6210\n        if nums[i] == 1:\n            return i\n    return -1\n</code></pre> worst_best_time_complexity.cpp<pre><code>/* \u8981\u7d20 {1, 2, ..., n} \u3092\u30e9\u30f3\u30c0\u30e0\u306b\u30b7\u30e3\u30c3\u30d5\u30eb\u3057\u305f\u914d\u5217\u3092\u751f\u6210 */\nvector&lt;int&gt; randomNumbers(int n) {\n    vector&lt;int&gt; nums(n);\n    // \u914d\u5217 nums = { 1, 2, 3, ..., n } \u3092\u751f\u6210\n    for (int i = 0; i &lt; n; i++) {\n        nums[i] = i + 1;\n    }\n    // \u30b7\u30b9\u30c6\u30e0\u6642\u523b\u3092\u4f7f\u7528\u3057\u3066\u30e9\u30f3\u30c0\u30e0\u30b7\u30fc\u30c9\u3092\u751f\u6210\n    unsigned seed = chrono::system_clock::now().time_since_epoch().count();\n    // \u914d\u5217\u8981\u7d20\u3092\u30e9\u30f3\u30c0\u30e0\u306b\u30b7\u30e3\u30c3\u30d5\u30eb\n    shuffle(nums.begin(), nums.end(), default_random_engine(seed));\n    return nums;\n}\n\n/* \u914d\u5217 nums \u3067\u6570\u50241\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u898b\u3064\u3051\u308b */\nint findOne(vector&lt;int&gt; &amp;nums) {\n    for (int i = 0; i &lt; nums.size(); i++) {\n        // \u8981\u7d201\u304c\u914d\u5217\u306e\u5148\u982d\u306b\u3042\u308b\u5834\u5408\u3001\u6700\u826f\u6642\u9593\u8a08\u7b97\u91cf O(1) \u3092\u9054\u6210\n        // \u8981\u7d201\u304c\u914d\u5217\u306e\u672b\u5c3e\u306b\u3042\u308b\u5834\u5408\u3001\u6700\u60aa\u6642\u9593\u8a08\u7b97\u91cf O(n) \u3092\u9054\u6210\n        if (nums[i] == 1)\n            return i;\n    }\n    return -1;\n}\n</code></pre> worst_best_time_complexity.java<pre><code>/* \u8981\u7d20 {1, 2, ..., n} \u3092\u30e9\u30f3\u30c0\u30e0\u306b\u30b7\u30e3\u30c3\u30d5\u30eb\u3057\u305f\u914d\u5217\u3092\u751f\u6210 */\nint[] randomNumbers(int n) {\n    Integer[] nums = new Integer[n];\n    // \u914d\u5217 nums = { 1, 2, 3, ..., n } \u3092\u751f\u6210\n    for (int i = 0; i &lt; n; i++) {\n        nums[i] = i + 1;\n    }\n    // \u914d\u5217\u8981\u7d20\u3092\u30e9\u30f3\u30c0\u30e0\u306b\u30b7\u30e3\u30c3\u30d5\u30eb\n    Collections.shuffle(Arrays.asList(nums));\n    // Integer[] -&gt; int[]\n    int[] res = new int[n];\n    for (int i = 0; i &lt; n; i++) {\n        res[i] = nums[i];\n    }\n    return res;\n}\n\n/* \u914d\u5217 nums \u3067\u6570\u50241\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u898b\u3064\u3051\u308b */\nint findOne(int[] nums) {\n    for (int i = 0; i &lt; nums.length; i++) {\n        // \u8981\u7d201\u304c\u914d\u5217\u306e\u5148\u982d\u306b\u3042\u308b\u5834\u5408\u3001\u6700\u826f\u6642\u9593\u8a08\u7b97\u91cf O(1) \u3092\u9054\u6210\n        // \u8981\u7d201\u304c\u914d\u5217\u306e\u672b\u5c3e\u306b\u3042\u308b\u5834\u5408\u3001\u6700\u60aa\u6642\u9593\u8a08\u7b97\u91cf O(n) \u3092\u9054\u6210\n        if (nums[i] == 1)\n            return i;\n    }\n    return -1;\n}\n</code></pre> worst_best_time_complexity.cs<pre><code>[class]{worst_best_time_complexity}-[func]{RandomNumbers}\n\n[class]{worst_best_time_complexity}-[func]{FindOne}\n</code></pre> worst_best_time_complexity.go<pre><code>[class]{}-[func]{randomNumbers}\n\n[class]{}-[func]{findOne}\n</code></pre> worst_best_time_complexity.swift<pre><code>[class]{}-[func]{randomNumbers}\n\n[class]{}-[func]{findOne}\n</code></pre> worst_best_time_complexity.js<pre><code>[class]{}-[func]{randomNumbers}\n\n[class]{}-[func]{findOne}\n</code></pre> worst_best_time_complexity.ts<pre><code>[class]{}-[func]{randomNumbers}\n\n[class]{}-[func]{findOne}\n</code></pre> worst_best_time_complexity.dart<pre><code>[class]{}-[func]{randomNumbers}\n\n[class]{}-[func]{findOne}\n</code></pre> worst_best_time_complexity.rs<pre><code>[class]{}-[func]{random_numbers}\n\n[class]{}-[func]{find_one}\n</code></pre> worst_best_time_complexity.c<pre><code>[class]{}-[func]{randomNumbers}\n\n[class]{}-[func]{findOne}\n</code></pre> worst_best_time_complexity.kt<pre><code>[class]{}-[func]{randomNumbers}\n\n[class]{}-[func]{findOne}\n</code></pre> worst_best_time_complexity.rb<pre><code>[class]{}-[func]{random_numbers}\n\n[class]{}-[func]{find_one}\n</code></pre> worst_best_time_complexity.zig<pre><code>[class]{}-[func]{randomNumbers}\n\n[class]{}-[func]{findOne}\n</code></pre> <p>\u6700\u826f\u30b1\u30fc\u30b9\u6642\u9593\u8a08\u7b97\u91cf\u306f\u5b9f\u969b\u306b\u306f\u307b\u3068\u3093\u3069\u4f7f\u7528\u3055\u308c\u306a\u3044\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u901a\u5e38\u306f\u975e\u5e38\u306b\u4f4e\u3044\u78ba\u7387\u3067\u306e\u307f\u9054\u6210\u53ef\u80fd\u3067\u3001\u8aa4\u89e3\u3092\u62db\u304f\u53ef\u80fd\u6027\u304c\u3042\u308b\u304b\u3089\u3067\u3059\u3002\u6700\u60aa\u30b1\u30fc\u30b9\u6642\u9593\u8a08\u7b97\u91cf\u306f\u3088\u308a\u5b9f\u7528\u7684\u3067\u3001\u52b9\u7387\u306e\u5b89\u5168\u5024\u3092\u63d0\u4f9b\u3057\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u81ea\u4fe1\u3092\u6301\u3063\u3066\u4f7f\u7528\u3067\u304d\u308b\u3088\u3046\u306b\u3057\u307e\u3059\u3002</p> <p>\u4e0a\u8a18\u306e\u4f8b\u304b\u3089\u3001\u6700\u60aa\u30b1\u30fc\u30b9\u3068\u6700\u826f\u30b1\u30fc\u30b9\u306e\u6642\u9593\u8a08\u7b97\u91cf\u306f\u4e21\u65b9\u3068\u3082\u300c\u7279\u6b8a\u306a\u30c7\u30fc\u30bf\u5206\u5e03\u300d\u4e0b\u3067\u306e\u307f\u767a\u751f\u3057\u3001\u767a\u751f\u78ba\u7387\u304c\u5c0f\u3055\u304f\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5b9f\u884c\u52b9\u7387\u3092\u6b63\u78ba\u306b\u53cd\u6620\u3057\u306a\u3044\u53ef\u80fd\u6027\u304c\u3042\u308b\u3053\u3068\u304c\u660e\u3089\u304b\u3067\u3059\u3002\u5bfe\u7167\u7684\u306b\u3001\u5e73\u5747\u6642\u9593\u8a08\u7b97\u91cf\u306f\u30e9\u30f3\u30c0\u30e0\u5165\u529b\u30c7\u30fc\u30bf\u4e0b\u3067\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u52b9\u7387\u3092\u53cd\u6620\u3067\u304d\u3001\\(\\Theta\\)\u8a18\u6cd5\u3067\u8868\u3055\u308c\u307e\u3059\u3002</p> <p>\u4e00\u90e8\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u306f\u3001\u30e9\u30f3\u30c0\u30e0\u30c7\u30fc\u30bf\u5206\u5e03\u4e0b\u3067\u306e\u5e73\u5747\u30b1\u30fc\u30b9\u3092\u7c21\u5358\u306b\u63a8\u5b9a\u3067\u304d\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u524d\u8ff0\u306e\u4f8b\u3067\u306f\u3001\u5165\u529b\u914d\u5217\u304c\u30b7\u30e3\u30c3\u30d5\u30eb\u3055\u308c\u3066\u3044\u308b\u305f\u3081\u3001\u8981\u7d20\\(1\\)\u304c\u4efb\u610f\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306b\u73fe\u308c\u308b\u78ba\u7387\u306f\u7b49\u3057\u3044\u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5e73\u5747\u30eb\u30fc\u30d7\u6570\u306f\u914d\u5217\u9577\u3055\u306e\u534a\u5206\\(n / 2\\)\u3067\u3001\u5e73\u5747\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(\\Theta(n / 2) = \\Theta(n)\\)\u3067\u3059\u3002</p> <p>\u3057\u304b\u3057\u3001\u3088\u308a\u8907\u96d1\u306a\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5e73\u5747\u6642\u9593\u8a08\u7b97\u91cf\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u306f\u975e\u5e38\u306b\u56f0\u96e3\u3067\u3059\u3002\u30c7\u30fc\u30bf\u5206\u5e03\u4e0b\u3067\u306e\u5168\u4f53\u7684\u306a\u6570\u5b66\u7684\u671f\u5f85\u5024\u3092\u5206\u6790\u3059\u308b\u3053\u3068\u304c\u56f0\u96e3\u3060\u304b\u3089\u3067\u3059\u3002\u305d\u306e\u3088\u3046\u306a\u5834\u5408\u3001\u901a\u5e38\u306f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u52b9\u7387\u3092\u5224\u65ad\u3059\u308b\u57fa\u6e96\u3068\u3057\u3066\u6700\u60aa\u30b1\u30fc\u30b9\u6642\u9593\u8a08\u7b97\u91cf\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002</p> <p>\\(\\Theta\\)\u8a18\u53f7\u306f\u306a\u305c\u307b\u3068\u3093\u3069\u898b\u3089\u308c\u306a\u3044\u306e\u3067\u3059\u304b\uff1f</p> <p>\u304a\u305d\u3089\u304f\\(O\\)\u8a18\u6cd5\u304c\u3088\u308a\u4e00\u822c\u7684\u306b\u8a71\u3055\u308c\u308b\u305f\u3081\u3001\u5e73\u5747\u6642\u9593\u8a08\u7b97\u91cf\u3092\u8868\u3059\u305f\u3081\u306b\u3088\u304f\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u53b3\u5bc6\u306b\u8a00\u3048\u3070\u3001\u3053\u306e\u5b9f\u8df5\u306f\u6b63\u78ba\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u3053\u306e\u672c\u3084\u4ed6\u306e\u8cc7\u6599\u3067\u300c\u5e73\u5747\u6642\u9593\u8a08\u7b97\u91cf\\(O(n)\\)\u300d\u306e\u3088\u3046\u306a\u8868\u73fe\u306b\u906d\u9047\u3057\u305f\u5834\u5408\u306f\u3001\u76f4\u63a5\\(\\Theta(n)\\)\u3068\u3057\u3066\u7406\u89e3\u3057\u3066\u304f\u3060\u3055\u3044\u3002</p>"},{"location":"chapter_data_structure/","title":"\u7b2c 3 \u7ae0 \u00a0 \u30c7\u30fc\u30bf\u69cb\u9020","text":"<p>Abstract</p> <p>\u30c7\u30fc\u30bf\u69cb\u9020\u306f\u5805\u7262\u3067\u591a\u69d8\u306a\u30d5\u30ec\u30fc\u30e0\u30ef\u30fc\u30af\u3068\u3057\u3066\u6a5f\u80fd\u3057\u307e\u3059\u3002</p> <p>\u30c7\u30fc\u30bf\u306e\u6574\u7136\u3068\u3057\u305f\u7d44\u7e54\u5316\u306e\u305f\u3081\u306e\u8a2d\u8a08\u56f3\u3092\u63d0\u4f9b\u3057\u3001\u305d\u306e\u4e0a\u3067\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u304c\u751f\u304d\u751f\u304d\u3068\u52d5\u304d\u51fa\u3057\u307e\u3059\u3002</p>"},{"location":"chapter_data_structure/#_1","title":"\u7ae0\u306e\u5185\u5bb9","text":"<ul> <li>3.1 \u00a0 \u30c7\u30fc\u30bf\u69cb\u9020\u306e\u5206\u985e</li> <li>3.2 \u00a0 \u57fa\u672c\u30c7\u30fc\u30bf\u578b</li> <li>3.3 \u00a0 \u6570\u5024\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0 *</li> <li>3.4 \u00a0 \u6587\u5b57\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0 *</li> <li>3.5 \u00a0 \u307e\u3068\u3081</li> </ul>"},{"location":"chapter_data_structure/basic_data_types/","title":"3.2 \u00a0 \u57fa\u672c\u30c7\u30fc\u30bf\u578b","text":"<p>\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u5185\u306e\u30c7\u30fc\u30bf\u306b\u3064\u3044\u3066\u8003\u3048\u308b\u969b\u3001\u30c6\u30ad\u30b9\u30c8\u3001\u753b\u50cf\u3001\u52d5\u753b\u3001\u97f3\u58f0\u30013D\u30e2\u30c7\u30eb\u306a\u3069\u3001\u69d8\u3005\u306a\u5f62\u5f0f\u304c\u601d\u3044\u6d6e\u304b\u3073\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u7d44\u7e54\u7684\u306a\u5f62\u5f0f\u306f\u7570\u306a\u308a\u307e\u3059\u304c\u3001\u3059\u3079\u3066\u69d8\u3005\u306a\u57fa\u672c\u30c7\u30fc\u30bf\u578b\u304b\u3089\u69cb\u6210\u3055\u308c\u3066\u3044\u307e\u3059\u3002</p> <p>**\u57fa\u672c\u30c7\u30fc\u30bf\u578b\u3068\u306f\u3001CPU\u304c\u76f4\u63a5\u64cd\u4f5c\u3067\u304d\u308b\u3082\u306e**\u3067\u3042\u308a\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u76f4\u63a5\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u4e3b\u306b\u4ee5\u4e0b\u304c\u542b\u307e\u308c\u307e\u3059\u3002</p> <ul> <li>\u6574\u6570\u578b\uff1a<code>byte</code>\u3001<code>short</code>\u3001<code>int</code>\u3001<code>long</code></li> <li>\u6d6e\u52d5\u5c0f\u6570\u70b9\u578b\uff1a<code>float</code>\u3001<code>double</code>\u3001\u5c0f\u6570\u3092\u8868\u73fe\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528</li> <li>\u6587\u5b57\u578b\uff1a<code>char</code>\u3001\u69d8\u3005\u306a\u8a00\u8a9e\u306e\u6587\u5b57\u3001\u53e5\u8aad\u70b9\u3001\u3055\u3089\u306b\u306f\u7d75\u6587\u5b57\u3092\u8868\u73fe\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528</li> <li>\u30d6\u30fc\u30eb\u578b\uff1a<code>bool</code>\u3001\u300c\u306f\u3044\u300d\u307e\u305f\u306f\u300c\u3044\u3044\u3048\u300d\u306e\u5224\u65ad\u3092\u8868\u73fe\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528</li> </ul> <p>\u57fa\u672c\u30c7\u30fc\u30bf\u578b\u306f\u3001\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u5185\u3067\u4e8c\u9032\u5f62\u5f0f\u3067\u683c\u7d0d\u3055\u308c\u307e\u3059\u30021\u3064\u306e\u4e8c\u9032\u6841\u306f1\u30d3\u30c3\u30c8\u3067\u3059\u3002\u307b\u3068\u3093\u3069\u306e\u73fe\u4ee3\u7684\u306a\u30aa\u30da\u30ec\u30fc\u30c6\u30a3\u30f3\u30b0\u30b7\u30b9\u30c6\u30e0\u3067\u306f\u30011\u30d0\u30a4\u30c8\u306f8\u30d3\u30c3\u30c8\u3067\u69cb\u6210\u3055\u308c\u3066\u3044\u307e\u3059\u3002</p> <p>\u57fa\u672c\u30c7\u30fc\u30bf\u578b\u306e\u5024\u306e\u7bc4\u56f2\u306f\u3001\u305d\u308c\u3089\u304c\u5360\u3081\u308b\u7a7a\u9593\u306e\u30b5\u30a4\u30ba\u306b\u4f9d\u5b58\u3057\u307e\u3059\u3002\u4ee5\u4e0b\u3067\u306f\u3001Java\u3092\u4f8b\u306b\u8aac\u660e\u3057\u307e\u3059\u3002</p> <ul> <li>\u6574\u6570\u578b<code>byte</code>\u306f1\u30d0\u30a4\u30c8 = 8\u30d3\u30c3\u30c8\u3092\u5360\u3081\u3001\\(2^8\\)\u500b\u306e\u6570\u5024\u3092\u8868\u73fe\u3067\u304d\u307e\u3059\u3002</li> <li>\u6574\u6570\u578b<code>int</code>\u306f4\u30d0\u30a4\u30c8 = 32\u30d3\u30c3\u30c8\u3092\u5360\u3081\u3001\\(2^{32}\\)\u500b\u306e\u6570\u5024\u3092\u8868\u73fe\u3067\u304d\u307e\u3059\u3002</li> </ul> <p>\u4ee5\u4e0b\u306e\u8868\u306f\u3001Java\u306b\u304a\u3051\u308b\u69d8\u3005\u306a\u57fa\u672c\u30c7\u30fc\u30bf\u578b\u304c\u5360\u3081\u308b\u7a7a\u9593\u3001\u5024\u306e\u7bc4\u56f2\u3001\u30c7\u30d5\u30a9\u30eb\u30c8\u5024\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002\u3053\u306e\u8868\u3092\u6697\u8a18\u3059\u308b\u5fc5\u8981\u306f\u3042\u308a\u307e\u305b\u3093\u304c\u3001\u4e00\u822c\u7684\u306a\u7406\u89e3\u3092\u6301\u3061\u3001\u5fc5\u8981\u6642\u306b\u53c2\u7167\u3059\u308b\u3053\u3068\u3092\u304a\u52e7\u3081\u3057\u307e\u3059\u3002</p> <p> \u8868 3-1 \u00a0 \u57fa\u672c\u30c7\u30fc\u30bf\u578b\u304c\u5360\u3081\u308b\u7a7a\u9593\u3068\u5024\u306e\u7bc4\u56f2 </p> \u578b \u30b7\u30f3\u30dc\u30eb \u5360\u6709\u7a7a\u9593 \u6700\u5c0f\u5024 \u6700\u5927\u5024 \u30c7\u30d5\u30a9\u30eb\u30c8\u5024 \u6574\u6570 <code>byte</code> 1\u30d0\u30a4\u30c8 \\(-2^7\\) (\\(-128\\)) \\(2^7 - 1\\) (\\(127\\)) 0 <code>short</code> 2\u30d0\u30a4\u30c8 \\(-2^{15}\\) \\(2^{15} - 1\\) 0 <code>int</code> 4\u30d0\u30a4\u30c8 \\(-2^{31}\\) \\(2^{31} - 1\\) 0 <code>long</code> 8\u30d0\u30a4\u30c8 \\(-2^{63}\\) \\(2^{63} - 1\\) 0 \u6d6e\u52d5\u5c0f\u6570\u70b9 <code>float</code> 4\u30d0\u30a4\u30c8 \\(1.175 \\times 10^{-38}\\) \\(3.403 \\times 10^{38}\\) \\(0.0\\text{f}\\) <code>double</code> 8\u30d0\u30a4\u30c8 \\(2.225 \\times 10^{-308}\\) \\(1.798 \\times 10^{308}\\) 0.0 \u6587\u5b57 <code>char</code> 2\u30d0\u30a4\u30c8 0 \\(2^{16} - 1\\) 0 \u30d6\u30fc\u30eb <code>bool</code> 1\u30d0\u30a4\u30c8 \\(\\text{false}\\) \\(\\text{true}\\) \\(\\text{false}\\) <p>\u4e0a\u8a18\u306e\u8868\u306fJava\u306e\u57fa\u672c\u30c7\u30fc\u30bf\u578b\u306b\u7279\u6709\u3067\u3042\u308b\u3053\u3068\u306b\u3054\u6ce8\u610f\u304f\u3060\u3055\u3044\u3002\u3059\u3079\u3066\u306e\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u306b\u306f\u72ec\u81ea\u306e\u30c7\u30fc\u30bf\u578b\u5b9a\u7fa9\u304c\u3042\u308a\u3001\u5360\u6709\u7a7a\u9593\u3001\u5024\u306e\u7bc4\u56f2\u3001\u30c7\u30d5\u30a9\u30eb\u30c8\u5024\u304c\u7570\u306a\u308b\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002</p> <ul> <li>Python\u3067\u306f\u3001\u6574\u6570\u578b<code>int</code>\u306f\u4efb\u610f\u306e\u30b5\u30a4\u30ba\u306b\u306a\u308b\u3053\u3068\u304c\u3067\u304d\u3001\u5229\u7528\u53ef\u80fd\u306a\u30e1\u30e2\u30ea\u306b\u3088\u3063\u3066\u306e\u307f\u5236\u9650\u3055\u308c\u307e\u3059\u3002\u6d6e\u52d5\u5c0f\u6570\u70b9<code>float</code>\u306f\u500d\u7cbe\u5ea664\u30d3\u30c3\u30c8\u3067\u3059\u3002<code>char</code>\u578b\u306f\u5b58\u5728\u305b\u305a\u3001\u5358\u4e00\u6587\u5b57\u306f\u5b9f\u969b\u306b\u306f\u9577\u30551\u306e\u6587\u5b57\u5217<code>str</code>\u3067\u3059\u3002</li> <li>C\u304a\u3088\u3073C++\u3067\u306f\u57fa\u672c\u30c7\u30fc\u30bf\u578b\u306e\u30b5\u30a4\u30ba\u304c\u6307\u5b9a\u3055\u308c\u3066\u304a\u3089\u305a\u3001\u5b9f\u88c5\u3068\u30d7\u30e9\u30c3\u30c8\u30d5\u30a9\u30fc\u30e0\u306b\u3088\u3063\u3066\u7570\u306a\u308a\u307e\u3059\u3002\u4e0a\u8a18\u306e\u8868\u306fLP64\u30c7\u30fc\u30bf\u30e2\u30c7\u30eb\u306b\u5f93\u3063\u3066\u304a\u308a\u3001Linux\u3084macOS\u3092\u542b\u3080Unix 64\u30d3\u30c3\u30c8\u30aa\u30da\u30ec\u30fc\u30c6\u30a3\u30f3\u30b0\u30b7\u30b9\u30c6\u30e0\u3067\u4f7f\u7528\u3055\u308c\u3066\u3044\u307e\u3059\u3002</li> <li>C\u304a\u3088\u3073C++\u306b\u304a\u3051\u308b<code>char</code>\u306e\u30b5\u30a4\u30ba\u306f1\u30d0\u30a4\u30c8\u3067\u3059\u304c\u3001\u307b\u3068\u3093\u3069\u306e\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u3067\u306f\u3001\u7279\u5b9a\u306e\u6587\u5b57\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u65b9\u6cd5\u306b\u4f9d\u5b58\u3057\u3001\u8a73\u7d30\u306f\u300c\u6587\u5b57\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u300d\u306e\u7ae0\u3067\u8aac\u660e\u3055\u308c\u3066\u3044\u307e\u3059\u3002</li> <li>\u30d6\u30fc\u30eb\u5024\u306e\u8868\u73fe\u306b\u306f1\u30d3\u30c3\u30c8\uff080\u307e\u305f\u306f1\uff09\u306e\u307f\u304c\u5fc5\u8981\u3067\u3059\u304c\u3001\u901a\u5e38\u306f\u30e1\u30e2\u30ea\u5185\u306b1\u30d0\u30a4\u30c8\u3068\u3057\u3066\u683c\u7d0d\u3055\u308c\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u73fe\u4ee3\u306e\u30b3\u30f3\u30d4\u30e5\u30fc\u30bfCPU\u304c\u901a\u5e381\u30d0\u30a4\u30c8\u3092\u6700\u5c0f\u306e\u30a2\u30c9\u30ec\u30b9\u53ef\u80fd\u306a\u30e1\u30e2\u30ea\u5358\u4f4d\u3068\u3057\u3066\u4f7f\u7528\u3059\u308b\u305f\u3081\u3067\u3059\u3002</li> </ul> <p>\u3067\u306f\u3001\u57fa\u672c\u30c7\u30fc\u30bf\u578b\u3068\u30c7\u30fc\u30bf\u69cb\u9020\u306e\u95a2\u4fc2\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\uff1f\u30c7\u30fc\u30bf\u69cb\u9020\u3068\u306f\u3001\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u5185\u3067\u30c7\u30fc\u30bf\u3092\u7d44\u7e54\u5316\u3057\u683c\u7d0d\u3059\u308b\u65b9\u6cd5\u3067\u3042\u308b\u3053\u3068\u3092\u77e5\u3063\u3066\u3044\u307e\u3059\u3002\u3053\u3053\u3067\u306e\u7126\u70b9\u306f\u300c\u30c7\u30fc\u30bf\u300d\u3067\u306f\u306a\u304f\u300c\u69cb\u9020\u300d\u3067\u3059\u3002</p> <p>\u300c\u6570\u5024\u306e\u5217\u300d\u3092\u8868\u73fe\u3057\u305f\u3044\u5834\u5408\u3001\u81ea\u7136\u306b\u914d\u5217\u306e\u4f7f\u7528\u3092\u8003\u3048\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u914d\u5217\u306e\u7dda\u5f62\u69cb\u9020\u304c\u6570\u5024\u306e\u96a3\u63a5\u6027\u3068\u9806\u5e8f\u6027\u3092\u8868\u73fe\u3067\u304d\u308b\u305f\u3081\u3067\u3059\u304c\u3001\u683c\u7d0d\u3055\u308c\u308b\u5185\u5bb9\u304c\u6574\u6570<code>int</code>\u3001\u5c0f\u6570<code>float</code>\u3001\u6587\u5b57<code>char</code>\u306e\u3044\u305a\u308c\u3067\u3042\u3063\u3066\u3082\u3001\u300c\u30c7\u30fc\u30bf\u69cb\u9020\u300d\u3068\u306f\u7121\u95a2\u4fc2\u3067\u3059\u3002</p> <p>\u8a00\u3044\u63db\u3048\u308b\u3068\u3001\u57fa\u672c\u30c7\u30fc\u30bf\u578b\u306f\u30c7\u30fc\u30bf\u306e\u300c\u5185\u5bb9\u578b\u300d\u3092\u63d0\u4f9b\u3057\u3001\u30c7\u30fc\u30bf\u69cb\u9020\u306f\u30c7\u30fc\u30bf\u306e\u300c\u7d44\u7e54\u5316\u65b9\u6cd5\u300d\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u4ee5\u4e0b\u306e\u30b3\u30fc\u30c9\u3067\u306f\u3001\u540c\u3058\u30c7\u30fc\u30bf\u69cb\u9020\uff08\u914d\u5217\uff09\u3092\u4f7f\u7528\u3057\u3066\u3001<code>int</code>\u3001<code>float</code>\u3001<code>char</code>\u3001<code>bool</code>\u306a\u3069\u306e\u7570\u306a\u308b\u57fa\u672c\u30c7\u30fc\u30bf\u578b\u3092\u683c\u7d0d\u3057\u8868\u73fe\u3057\u3066\u3044\u307e\u3059\u3002</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinZig <pre><code># \u69d8\u3005\u306a\u57fa\u672c\u30c7\u30fc\u30bf\u578b\u3092\u4f7f\u7528\u3057\u3066\u914d\u5217\u3092\u521d\u671f\u5316\nnumbers: list[int] = [0] * 5\ndecimals: list[float] = [0.0] * 5\n# Python\u306e\u6587\u5b57\u306f\u5b9f\u969b\u306b\u306f\u9577\u30551\u306e\u6587\u5b57\u5217\ncharacters: list[str] = ['0'] * 5\nbools: list[bool] = [False] * 5\n# Python\u306e\u30ea\u30b9\u30c8\u306f\u69d8\u3005\u306a\u57fa\u672c\u30c7\u30fc\u30bf\u578b\u3068\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u53c2\u7167\u3092\u81ea\u7531\u306b\u683c\u7d0d\u53ef\u80fd\ndata = [0, 0.0, 'a', False, ListNode(0)]\n</code></pre> <pre><code>// \u69d8\u3005\u306a\u57fa\u672c\u30c7\u30fc\u30bf\u578b\u3092\u4f7f\u7528\u3057\u3066\u914d\u5217\u3092\u521d\u671f\u5316\nint numbers[5];\nfloat decimals[5];\nchar characters[5];\nbool bools[5];\n</code></pre> <pre><code>// \u69d8\u3005\u306a\u57fa\u672c\u30c7\u30fc\u30bf\u578b\u3092\u4f7f\u7528\u3057\u3066\u914d\u5217\u3092\u521d\u671f\u5316\nint[] numbers = new int[5];\nfloat[] decimals = new float[5];\nchar[] characters = new char[5];\nboolean[] bools = new boolean[5];\n</code></pre> <pre><code>// \u69d8\u3005\u306a\u57fa\u672c\u30c7\u30fc\u30bf\u578b\u3092\u4f7f\u7528\u3057\u3066\u914d\u5217\u3092\u521d\u671f\u5316\nint[] numbers = new int[5];\nfloat[] decimals = new float[5];\nchar[] characters = new char[5];\nbool[] bools = new bool[5];\n</code></pre> <pre><code>// \u69d8\u3005\u306a\u57fa\u672c\u30c7\u30fc\u30bf\u578b\u3092\u4f7f\u7528\u3057\u3066\u914d\u5217\u3092\u521d\u671f\u5316\nvar numbers = [5]int{}\nvar decimals = [5]float64{}\nvar characters = [5]byte{}\nvar bools = [5]bool{}\n</code></pre> <pre><code>// \u69d8\u3005\u306a\u57fa\u672c\u30c7\u30fc\u30bf\u578b\u3092\u4f7f\u7528\u3057\u3066\u914d\u5217\u3092\u521d\u671f\u5316\nlet numbers = Array(repeating: 0, count: 5)\nlet decimals = Array(repeating: 0.0, count: 5)\nlet characters: [Character] = Array(repeating: \"a\", count: 5)\nlet bools = Array(repeating: false, count: 5)\n</code></pre> <pre><code>// JavaScript\u306e\u914d\u5217\u306f\u69d8\u3005\u306a\u57fa\u672c\u30c7\u30fc\u30bf\u578b\u3068\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u3092\u81ea\u7531\u306b\u683c\u7d0d\u53ef\u80fd\nconst array = [0, 0.0, 'a', false];\n</code></pre> <pre><code>// \u69d8\u3005\u306a\u57fa\u672c\u30c7\u30fc\u30bf\u578b\u3092\u4f7f\u7528\u3057\u3066\u914d\u5217\u3092\u521d\u671f\u5316\nconst numbers: number[] = [];\nconst characters: string[] = [];\nconst bools: boolean[] = [];\n</code></pre> <pre><code>// \u69d8\u3005\u306a\u57fa\u672c\u30c7\u30fc\u30bf\u578b\u3092\u4f7f\u7528\u3057\u3066\u914d\u5217\u3092\u521d\u671f\u5316\nList&lt;int&gt; numbers = List.filled(5, 0);\nList&lt;double&gt; decimals = List.filled(5, 0.0);\nList&lt;String&gt; characters = List.filled(5, 'a');\nList&lt;bool&gt; bools = List.filled(5, false);\n</code></pre> <pre><code>// \u69d8\u3005\u306a\u57fa\u672c\u30c7\u30fc\u30bf\u578b\u3092\u4f7f\u7528\u3057\u3066\u914d\u5217\u3092\u521d\u671f\u5316\nlet numbers: Vec&lt;i32&gt; = vec![0; 5];\nlet decimals: Vec&lt;f32&gt; = vec![0.0, 5];\nlet characters: Vec&lt;char&gt; = vec!['0'; 5];\nlet bools: Vec&lt;bool&gt; = vec![false; 5];\n</code></pre> <pre><code>// \u69d8\u3005\u306a\u57fa\u672c\u30c7\u30fc\u30bf\u578b\u3092\u4f7f\u7528\u3057\u3066\u914d\u5217\u3092\u521d\u671f\u5316\nint numbers[10];\nfloat decimals[10];\nchar characters[10];\nbool bools[10];\n</code></pre> <pre><code>\n</code></pre> <pre><code>// \u69d8\u3005\u306a\u57fa\u672c\u30c7\u30fc\u30bf\u578b\u3092\u4f7f\u7528\u3057\u3066\u914d\u5217\u3092\u521d\u671f\u5316\nvar numbers: [5]i32 = undefined;\nvar decimals: [5]f32 = undefined;\nvar characters: [5]u8 = undefined;\nvar bools: [5]bool = undefined;\n</code></pre>"},{"location":"chapter_data_structure/character_encoding/","title":"3.4 \u00a0 \u6587\u5b57\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0 *","text":"<p>\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u30b7\u30b9\u30c6\u30e0\u3067\u306f\u3001\u3059\u3079\u3066\u306e\u30c7\u30fc\u30bf\u304c\u4e8c\u9032\u5f62\u5f0f\u3067\u683c\u7d0d\u3055\u308c\u3001<code>char</code>\u3082\u4f8b\u5916\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u6587\u5b57\u3092\u8868\u73fe\u3059\u308b\u305f\u3081\u306b\u3001\u5404\u6587\u5b57\u3068\u4e8c\u9032\u6570\u306e\u4e00\u5bfe\u4e00\u306e\u30de\u30c3\u30d4\u30f3\u30b0\u3092\u5b9a\u7fa9\u3059\u308b\u300c\u6587\u5b57\u30bb\u30c3\u30c8\u300d\u3092\u958b\u767a\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u6587\u5b57\u30bb\u30c3\u30c8\u304c\u3042\u308c\u3070\u3001\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u306f\u8868\u3092\u53c2\u7167\u3057\u3066\u4e8c\u9032\u6570\u3092\u6587\u5b57\u306b\u5909\u63db\u3067\u304d\u307e\u3059\u3002</p>"},{"location":"chapter_data_structure/character_encoding/#341-ascii","title":"3.4.1 \u00a0 ASCII\u6587\u5b57\u30bb\u30c3\u30c8","text":"<p>ASCII\u30b3\u30fc\u30c9\u306f\u6700\u3082\u521d\u671f\u306e\u6587\u5b57\u30bb\u30c3\u30c8\u306e\u4e00\u3064\u3067\u3001\u6b63\u5f0f\u306b\u306fAmerican Standard Code for Information Interchange\u3068\u3057\u3066\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\u30027\u3064\u306e\u4e8c\u9032\u6841\uff081\u30d0\u30a4\u30c8\u306e\u4e0b\u4f4d7\u30d3\u30c3\u30c8\uff09\u3092\u4f7f\u7528\u3057\u3066\u6587\u5b57\u3092\u8868\u73fe\u3057\u3001\u6700\u5927128\u7a2e\u985e\u306e\u7570\u306a\u308b\u6587\u5b57\u3092\u8868\u73fe\u3067\u304d\u307e\u3059\u3002\u4ee5\u4e0b\u306e\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001ASCII\u306b\u306f\u82f1\u8a9e\u306e\u5927\u6587\u5b57\u3068\u5c0f\u6587\u5b57\u30010\u301c9\u306e\u6570\u5b57\u3001\u69d8\u3005\u306a\u53e5\u8aad\u70b9\u3001\u7279\u5b9a\u306e\u5236\u5fa1\u6587\u5b57\uff08\u6539\u884c\u3084\u30bf\u30d6\u306a\u3069\uff09\u304c\u542b\u307e\u308c\u3066\u3044\u307e\u3059\u3002</p> <p></p> <p> \u56f3 3-6 \u00a0 ASCII\u30b3\u30fc\u30c9 </p> <p>\u3057\u304b\u3057\u3001ASCII\u306f\u82f1\u8a9e\u306e\u6587\u5b57\u306e\u307f\u3092\u8868\u73fe\u3067\u304d\u307e\u3059\u3002\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u306e\u30b0\u30ed\u30fc\u30d0\u30eb\u5316\u306b\u4f34\u3044\u3001\u3088\u308a\u591a\u304f\u306e\u8a00\u8a9e\u3092\u8868\u73fe\u3059\u308b\u305f\u3081\u306bEASCII\u3068\u547c\u3070\u308c\u308b\u6587\u5b57\u30bb\u30c3\u30c8\u304c\u958b\u767a\u3055\u308c\u307e\u3057\u305f\u3002ASCII\u306e7\u30d3\u30c3\u30c8\u69cb\u9020\u304b\u30898\u30d3\u30c3\u30c8\u306b\u62e1\u5f35\u3057\u3001256\u6587\u5b57\u306e\u8868\u73fe\u3092\u53ef\u80fd\u306b\u3057\u307e\u3057\u305f\u3002</p> <p>\u4e16\u754c\u7684\u306b\u3001\u69d8\u3005\u306a\u5730\u57df\u56fa\u6709\u306eEASCII\u6587\u5b57\u30bb\u30c3\u30c8\u304c\u5c0e\u5165\u3055\u308c\u307e\u3057\u305f\u3002\u3053\u308c\u3089\u306e\u30bb\u30c3\u30c8\u306e\u6700\u521d\u306e128\u6587\u5b57\u306fASCII\u3068\u4e00\u81f4\u3057\u3066\u3044\u307e\u3059\u304c\u3001\u6b8b\u308a\u306e128\u6587\u5b57\u306f\u7570\u306a\u308b\u8a00\u8a9e\u306e\u8981\u4ef6\u306b\u5bfe\u5fdc\u3059\u308b\u305f\u3081\u306b\u7570\u306a\u3063\u3066\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u307e\u3059\u3002</p>"},{"location":"chapter_data_structure/character_encoding/#342-gbk","title":"3.4.2 \u00a0 GBK\u6587\u5b57\u30bb\u30c3\u30c8","text":"<p>\u5f8c\u306b\u3001**EASCII\u3067\u3082\u591a\u304f\u306e\u8a00\u8a9e\u306e\u6587\u5b57\u8981\u4ef6\u3092\u6e80\u305f\u3059\u3053\u3068\u304c\u3067\u304d\u306a\u3044**\u3053\u3068\u304c\u5224\u660e\u3057\u307e\u3057\u305f\u3002\u4f8b\u3048\u3070\u3001\u4e2d\u56fd\u8a9e\u306b\u306f\u7d0410\u4e07\u306e\u6f22\u5b57\u304c\u3042\u308a\u3001\u305d\u306e\u3046\u3061\u6570\u5343\u304c\u5b9a\u671f\u7684\u306b\u4f7f\u7528\u3055\u308c\u3066\u3044\u307e\u3059\u30021980\u5e74\u3001\u4e2d\u56fd\u6a19\u6e96\u5316\u59d4\u54e1\u4f1a\u306f6763\u306e\u4e2d\u56fd\u8a9e\u6587\u5b57\u3092\u542b\u3080GB2312\u6587\u5b57\u30bb\u30c3\u30c8\u3092\u767a\u8868\u3057\u3001\u4e2d\u56fd\u8a9e\u306e\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u51e6\u7406\u30cb\u30fc\u30ba\u3092\u672c\u8cea\u7684\u306b\u6e80\u305f\u3057\u307e\u3057\u305f\u3002</p> <p>\u3057\u304b\u3057\u3001GB2312\u306f\u4e00\u90e8\u306e\u7a00\u5c11\u6587\u5b57\u3084\u7e41\u4f53\u5b57\u3092\u51e6\u7406\u3067\u304d\u307e\u305b\u3093\u3067\u3057\u305f\u3002GBK\u6587\u5b57\u30bb\u30c3\u30c8\u306fGB2312\u3092\u62e1\u5f35\u3057\u300121886\u306e\u4e2d\u56fd\u8a9e\u6587\u5b57\u3092\u542b\u3093\u3067\u3044\u307e\u3059\u3002GBK\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u30b9\u30ad\u30fc\u30e0\u3067\u306f\u3001ASCII\u6587\u5b57\u306f1\u30d0\u30a4\u30c8\u3067\u8868\u73fe\u3055\u308c\u3001\u4e2d\u56fd\u8a9e\u6587\u5b57\u306f2\u30d0\u30a4\u30c8\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002</p>"},{"location":"chapter_data_structure/character_encoding/#343-unicode","title":"3.4.3 \u00a0 Unicode\u6587\u5b57\u30bb\u30c3\u30c8","text":"<p>\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u6280\u8853\u306e\u6025\u901f\u306a\u767a\u5c55\u3068\u591a\u6570\u306e\u6587\u5b57\u30bb\u30c3\u30c8\u304a\u3088\u3073\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u6a19\u6e96\u306b\u3088\u308a\u3001\u6570\u591a\u304f\u306e\u554f\u984c\u304c\u767a\u751f\u3057\u307e\u3057\u305f\u3002\u4e00\u65b9\u3067\u306f\u3001\u3053\u308c\u3089\u306e\u6587\u5b57\u30bb\u30c3\u30c8\u306f\u4e00\u822c\u7684\u306b\u7279\u5b9a\u306e\u8a00\u8a9e\u306e\u6587\u5b57\u306e\u307f\u3092\u5b9a\u7fa9\u3057\u3001\u591a\u8a00\u8a9e\u74b0\u5883\u3067\u306f\u9069\u5207\u306b\u6a5f\u80fd\u3067\u304d\u307e\u305b\u3093\u3067\u3057\u305f\u3002\u4ed6\u65b9\u3067\u306f\u3001\u540c\u3058\u8a00\u8a9e\u306b\u5bfe\u3059\u308b\u8907\u6570\u306e\u6587\u5b57\u30bb\u30c3\u30c8\u6a19\u6e96\u306e\u5b58\u5728\u306b\u3088\u308a\u3001\u7570\u306a\u308b\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u6a19\u6e96\u3092\u4f7f\u7528\u3059\u308b\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u9593\u3067\u60c5\u5831\u4ea4\u63db\u3092\u884c\u3046\u969b\u306b\u6587\u5b57\u5316\u3051\u304c\u767a\u751f\u3057\u307e\u3057\u305f\u3002</p> <p>\u5f53\u6642\u306e\u7814\u7a76\u8005\u305f\u3061\u306f\u8003\u3048\u307e\u3057\u305f\uff1a\u4e16\u754c\u306e\u3059\u3079\u3066\u306e\u8a00\u8a9e\u3068\u8a18\u53f7\u3092\u542b\u3080\u5305\u62ec\u7684\u306a\u6587\u5b57\u30bb\u30c3\u30c8\u304c\u958b\u767a\u3055\u308c\u308c\u3070\u3001\u8a00\u8a9e\u6a2a\u65ad\u74b0\u5883\u3068\u6587\u5b57\u5316\u3051\u306b\u95a2\u9023\u3059\u308b\u554f\u984c\u3092\u89e3\u6c7a\u3067\u304d\u308b\u306e\u3067\u306f\u306a\u3044\u3067\u3057\u3087\u3046\u304b\uff1f \u3053\u306e\u30a2\u30a4\u30c7\u30a2\u306b\u30a4\u30f3\u30b9\u30d1\u30a4\u30a2\u3055\u308c\u3066\u3001\u5e83\u7bc4\u56f2\u306a\u6587\u5b57\u30bb\u30c3\u30c8\u3067\u3042\u308bUnicode\u304c\u8a95\u751f\u3057\u307e\u3057\u305f\u3002</p> <p>Unicode\u306f\u4e2d\u56fd\u8a9e\u3067\u300c\u7edf\u4e00\u7801\u300d\uff08\u7d71\u4e00\u30b3\u30fc\u30c9\uff09\u3068\u547c\u3070\u308c\u3001\u7406\u8ad6\u7684\u306b100\u4e07\u6587\u5b57\u4ee5\u4e0a\u3092\u53ce\u5bb9\u3067\u304d\u307e\u3059\u3002\u4e16\u754c\u4e2d\u306e\u3059\u3079\u3066\u306e\u6587\u5b57\u3092\u5358\u4e00\u306e\u30bb\u30c3\u30c8\u306b\u7d44\u307f\u8fbc\u307f\u3001\u69d8\u3005\u306a\u8a00\u8a9e\u306e\u51e6\u7406\u3068\u8868\u793a\u306e\u305f\u3081\u306e\u6c4e\u7528\u6587\u5b57\u30bb\u30c3\u30c8\u3092\u63d0\u4f9b\u3057\u3001\u7570\u306a\u308b\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u6a19\u6e96\u306b\u3088\u308b\u6587\u5b57\u5316\u3051\u306e\u554f\u984c\u3092\u6e1b\u3089\u3059\u3053\u3068\u3092\u76ee\u6307\u3057\u3066\u3044\u307e\u3059\u3002</p> <p>1991\u5e74\u306e\u30ea\u30ea\u30fc\u30b9\u4ee5\u6765\u3001Unicode\u306f\u65b0\u3057\u3044\u8a00\u8a9e\u3068\u6587\u5b57\u3092\u542b\u3080\u3088\u3046\u7d99\u7d9a\u7684\u306b\u62e1\u5f35\u3055\u308c\u3066\u3044\u307e\u3059\u30022022\u5e749\u6708\u73fe\u5728\u3001Unicode\u306b\u306f149,186\u6587\u5b57\u304c\u542b\u307e\u308c\u3066\u304a\u308a\u3001\u69d8\u3005\u306a\u8a00\u8a9e\u306e\u6587\u5b57\u3001\u8a18\u53f7\u3001\u3055\u3089\u306b\u306f\u7d75\u6587\u5b57\u3082\u542b\u307e\u308c\u3066\u3044\u307e\u3059\u3002\u5e83\u5927\u306aUnicode\u6587\u5b57\u30bb\u30c3\u30c8\u3067\u306f\u3001\u4e00\u822c\u7684\u306b\u4f7f\u7528\u3055\u308c\u308b\u6587\u5b57\u306f2\u30d0\u30a4\u30c8\u3092\u5360\u6709\u3057\u3001\u4e00\u90e8\u306e\u7a00\u5c11\u306a\u6587\u5b57\u306f3\u30d0\u30a4\u30c8\u307e\u305f\u306f4\u30d0\u30a4\u30c8\u3092\u5360\u6709\u3059\u308b\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002</p> <p>Unicode\u306f\u5404\u6587\u5b57\u306b\u6570\u5024\uff08\u300c\u30b3\u30fc\u30c9\u30dd\u30a4\u30f3\u30c8\u300d\u3068\u547c\u3070\u308c\u308b\uff09\u3092\u5272\u308a\u5f53\u3066\u308b\u6c4e\u7528\u6587\u5b57\u30bb\u30c3\u30c8\u3067\u3059\u304c\u3001\u3053\u308c\u3089\u306e\u6587\u5b57\u30b3\u30fc\u30c9\u30dd\u30a4\u30f3\u30c8\u304c\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u30b7\u30b9\u30c6\u30e0\u306b\u3069\u306e\u3088\u3046\u306b\u683c\u7d0d\u3055\u308c\u308b\u3079\u304d\u304b\u306f\u6307\u5b9a\u3057\u3066\u3044\u307e\u305b\u3093\u3002\u7591\u554f\u304c\u751f\u3058\u308b\u304b\u3082\u3057\u308c\u307e\u305b\u3093\uff1a\u30b7\u30b9\u30c6\u30e0\u306f\u30c6\u30ad\u30b9\u30c8\u5185\u306e\u7570\u306a\u308b\u9577\u3055\u306eUnicode\u30b3\u30fc\u30c9\u30dd\u30a4\u30f3\u30c8\u3092\u3069\u306e\u3088\u3046\u306b\u89e3\u91c8\u3059\u308b\u306e\u3067\u3057\u3087\u3046\u304b\uff1f\u4f8b\u3048\u3070\u30012\u30d0\u30a4\u30c8\u306e\u30b3\u30fc\u30c9\u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408\u3001\u30b7\u30b9\u30c6\u30e0\u306f\u305d\u308c\u304c\u5358\u4e00\u306e2\u30d0\u30a4\u30c8\u6587\u5b57\u3092\u8868\u3059\u306e\u304b\u30012\u3064\u306e1\u30d0\u30a4\u30c8\u6587\u5b57\u3092\u8868\u3059\u306e\u304b\u3092\u3069\u306e\u3088\u3046\u306b\u5224\u65ad\u3059\u308b\u306e\u3067\u3057\u3087\u3046\u304b\uff1f</p> <p>\u3053\u306e\u554f\u984c\u306b\u5bfe\u3059\u308b\u7c21\u5358\u306a\u89e3\u6c7a\u7b56\u306f\u3001\u3059\u3079\u3066\u306e\u6587\u5b57\u3092\u7b49\u9577\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u3068\u3057\u3066\u683c\u7d0d\u3059\u308b\u3053\u3068\u3067\u3059\u3002\u4ee5\u4e0b\u306e\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u300cHello\u300d\u306e\u5404\u6587\u5b57\u306f1\u30d0\u30a4\u30c8\u3092\u5360\u6709\u3057\u3001\u300c\u7b97\u6cd5\u300d\uff08\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\uff09\u306e\u5404\u6587\u5b57\u306f2\u30d0\u30a4\u30c8\u3092\u5360\u6709\u3057\u307e\u3059\u3002\u4e0a\u4f4d\u30d3\u30c3\u30c8\u3092\u30bc\u30ed\u3067\u57cb\u3081\u308b\u3053\u3068\u3067\u3001\u300cHello \u7b97\u6cd5\u300d\u306e\u3059\u3079\u3066\u306e\u6587\u5b57\u30922\u30d0\u30a4\u30c8\u3068\u3057\u3066\u30a8\u30f3\u30b3\u30fc\u30c9\u3067\u304d\u307e\u3059\u3002\u3053\u306e\u65b9\u6cd5\u306b\u3088\u308a\u3001\u30b7\u30b9\u30c6\u30e0\u306f2\u30d0\u30a4\u30c8\u3054\u3068\u306b\u6587\u5b57\u3092\u89e3\u91c8\u3057\u3001\u30d5\u30ec\u30fc\u30ba\u306e\u5185\u5bb9\u3092\u5fa9\u5143\u3067\u304d\u307e\u3059\u3002</p> <p></p> <p> \u56f3 3-7 \u00a0 Unicode\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u4f8b </p> <p>\u3057\u304b\u3057\u3001ASCII\u304c\u793a\u3057\u305f\u3088\u3046\u306b\u3001\u82f1\u8a9e\u306e\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u306b\u306f1\u30d0\u30a4\u30c8\u306e\u307f\u304c\u5fc5\u8981\u3067\u3059\u3002\u4e0a\u8a18\u306e\u30a2\u30d7\u30ed\u30fc\u30c1\u3092\u4f7f\u7528\u3059\u308b\u3068\u3001\u82f1\u8a9e\u30c6\u30ad\u30b9\u30c8\u304c\u5360\u6709\u3059\u308b\u7a7a\u9593\u304cASCII\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u3068\u6bd4\u8f03\u3057\u30662\u500d\u306b\u306a\u308a\u3001\u30e1\u30e2\u30ea\u7a7a\u9593\u306e\u7121\u99c4\u306b\u306a\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u3088\u308a\u52b9\u7387\u7684\u306aUnicode\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u65b9\u6cd5\u304c\u5fc5\u8981\u3067\u3059\u3002</p>"},{"location":"chapter_data_structure/character_encoding/#344-utf-8","title":"3.4.4 \u00a0 UTF-8\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0","text":"<p>\u73fe\u5728\u3001UTF-8\u306f\u56fd\u969b\u7684\u306b\u6700\u3082\u5e83\u304f\u4f7f\u7528\u3055\u308c\u3066\u3044\u308bUnicode\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u65b9\u6cd5\u306b\u306a\u3063\u3066\u3044\u307e\u3059\u3002**\u3053\u308c\u306f\u53ef\u5909\u9577\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0**\u3067\u3001\u6587\u5b57\u306e\u8907\u96d1\u3055\u306b\u5fdc\u3058\u30661\u301c4\u30d0\u30a4\u30c8\u3092\u4f7f\u7528\u3057\u3066\u6587\u5b57\u3092\u8868\u73fe\u3057\u307e\u3059\u3002ASCII\u6587\u5b57\u306f1\u30d0\u30a4\u30c8\u306e\u307f\u304c\u5fc5\u8981\u3067\u3001\u30e9\u30c6\u30f3\u6587\u5b57\u3068\u30ae\u30ea\u30b7\u30e3\u6587\u5b57\u306f2\u30d0\u30a4\u30c8\u3001\u4e00\u822c\u7684\u306b\u4f7f\u7528\u3055\u308c\u308b\u4e2d\u56fd\u8a9e\u6587\u5b57\u306f3\u30d0\u30a4\u30c8\u3001\u305d\u306e\u4ed6\u306e\u7a00\u5c11\u306a\u6587\u5b57\u306f4\u30d0\u30a4\u30c8\u304c\u5fc5\u8981\u3067\u3059\u3002</p> <p>UTF-8\u306e\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u898f\u5247\u306f\u8907\u96d1\u3067\u306f\u306a\u304f\u30012\u3064\u306e\u30b1\u30fc\u30b9\u306b\u5206\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\uff1a</p> <ul> <li>1\u30d0\u30a4\u30c8\u6587\u5b57\u306e\u5834\u5408\u3001\u6700\u4e0a\u4f4d\u30d3\u30c3\u30c8\u3092\\(0\\)\u306b\u8a2d\u5b9a\u3057\u3001\u6b8b\u308a\u306e7\u30d3\u30c3\u30c8\u3092Unicode\u30b3\u30fc\u30c9\u30dd\u30a4\u30f3\u30c8\u306b\u8a2d\u5b9a\u3057\u307e\u3059\u3002\u6ce8\u76ee\u3059\u3079\u304d\u306f\u3001ASCII\u6587\u5b57\u304cUnicode\u30bb\u30c3\u30c8\u306e\u6700\u521d\u306e128\u30b3\u30fc\u30c9\u30dd\u30a4\u30f3\u30c8\u3092\u5360\u6709\u3059\u308b\u3053\u3068\u3067\u3059\u3002\u3053\u308c\u306f**UTF-8\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u304cASCII\u3068\u5f8c\u65b9\u4e92\u63db\u6027\u304c\u3042\u308b**\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002\u3053\u308c\u306f\u3001UTF-8\u3092\u4f7f\u7528\u3057\u3066\u53e4\u3044ASCII\u30c6\u30ad\u30b9\u30c8\u3092\u89e3\u6790\u3067\u304d\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002</li> <li>\u9577\u3055\\(n\\)\u30d0\u30a4\u30c8\u306e\u6587\u5b57\uff08\\(n &gt; 1\\)\uff09\u306e\u5834\u5408\u3001\u6700\u521d\u306e\u30d0\u30a4\u30c8\u306e\u6700\u4e0a\u4f4d\\(n\\)\u30d3\u30c3\u30c8\u3092\\(1\\)\u306b\u8a2d\u5b9a\u3057\u3001\\((n + 1)^{\\text{th}}\\)\u30d3\u30c3\u30c8\u3092\\(0\\)\u306b\u8a2d\u5b9a\u3057\u307e\u3059\u30022\u756a\u76ee\u306e\u30d0\u30a4\u30c8\u304b\u3089\u3001\u5404\u30d0\u30a4\u30c8\u306e\u6700\u4e0a\u4f4d2\u30d3\u30c3\u30c8\u3092\\(10\\)\u306b\u8a2d\u5b9a\u3057\u307e\u3059\u3002\u6b8b\u308a\u306e\u30d3\u30c3\u30c8\u306fUnicode\u30b3\u30fc\u30c9\u30dd\u30a4\u30f3\u30c8\u3092\u57cb\u3081\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002</li> </ul> <p>\u4ee5\u4e0b\u306e\u56f3\u306f\u300cHello\u7b97\u6cd5\u300d\u306eUTF-8\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002\u6700\u4e0a\u4f4d\\(n\\)\u30d3\u30c3\u30c8\u304c\\(1\\)\u306b\u8a2d\u5b9a\u3055\u308c\u3066\u3044\u308b\u305f\u3081\u3001\u30b7\u30b9\u30c6\u30e0\u306f\u6700\u4e0a\u4f4d\u30d3\u30c3\u30c8\u3067\\(1\\)\u306b\u8a2d\u5b9a\u3055\u308c\u305f\u30d3\u30c3\u30c8\u6570\u3092\u6570\u3048\u308b\u3053\u3068\u3067\u6587\u5b57\u306e\u9577\u3055\u3092\\(n\\)\u3068\u3057\u3066\u6c7a\u5b9a\u3067\u304d\u308b\u3053\u3068\u304c\u89b3\u5bdf\u3067\u304d\u307e\u3059\u3002</p> <p>\u3057\u304b\u3057\u3001\u306a\u305c\u6b8b\u308a\u306e\u30d0\u30a4\u30c8\u306e\u6700\u4e0a\u4f4d2\u30d3\u30c3\u30c8\u3092\\(10\\)\u306b\u8a2d\u5b9a\u3059\u308b\u306e\u3067\u3057\u3087\u3046\u304b\uff1f\u5b9f\u969b\u3001\u3053\u306e\\(10\\)\u306f\u4e00\u7a2e\u306e\u30c1\u30a7\u30c3\u30af\u30b5\u30e0\u3068\u3057\u3066\u6a5f\u80fd\u3057\u307e\u3059\u3002\u30b7\u30b9\u30c6\u30e0\u304c\u9593\u9055\u3063\u305f\u30d0\u30a4\u30c8\u304b\u3089\u30c6\u30ad\u30b9\u30c8\u306e\u89e3\u6790\u3092\u958b\u59cb\u3057\u305f\u5834\u5408\u3001\u30d0\u30a4\u30c8\u306e\u5148\u982d\u306e\\(10\\)\u306b\u3088\u308a\u30b7\u30b9\u30c6\u30e0\u306f\u7570\u5e38\u3092\u8fc5\u901f\u306b\u691c\u51fa\u3067\u304d\u307e\u3059\u3002</p> <p>\\(10\\)\u3092\u30c1\u30a7\u30c3\u30af\u30b5\u30e0\u3068\u3057\u3066\u4f7f\u7528\u3059\u308b\u7406\u7531\u306f\u3001UTF-8\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u898f\u5247\u306e\u4e0b\u3067\u306f\u3001\u6587\u5b57\u306e\u6700\u4e0a\u4f4d2\u30d3\u30c3\u30c8\u304c\\(10\\)\u306b\u306a\u308b\u3053\u3068\u306f\u4e0d\u53ef\u80fd\u3060\u304b\u3089\u3067\u3059\u3002\u3053\u308c\u306f\u77db\u76fe\u306b\u3088\u308a\u8a3c\u660e\u3067\u304d\u307e\u3059\uff1a\u6587\u5b57\u306e\u6700\u4e0a\u4f4d2\u30d3\u30c3\u30c8\u304c\\(10\\)\u306e\u5834\u5408\u3001\u6587\u5b57\u306e\u9577\u3055\u304c\\(1\\)\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u3057\u3001\u3053\u308c\u306fASCII\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002\u3057\u304b\u3057\u3001ASCII\u6587\u5b57\u306e\u6700\u4e0a\u4f4d\u30d3\u30c3\u30c8\u306f\\(0\\)\u3067\u3042\u308b\u3079\u304d\u3067\u3001\u3053\u308c\u306f\u4eee\u5b9a\u3068\u77db\u76fe\u3057\u307e\u3059\u3002</p> <p></p> <p> \u56f3 3-8 \u00a0 UTF-8\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u4f8b </p> <p>UTF-8\u4ee5\u5916\u306b\u3082\u3001\u4ed6\u306e\u4e00\u822c\u7684\u306a\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u65b9\u6cd5\u306b\u306f\u4ee5\u4e0b\u304c\u3042\u308a\u307e\u3059\uff1a</p> <ul> <li>UTF-16\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\uff1a2\u307e\u305f\u306f4\u30d0\u30a4\u30c8\u3092\u4f7f\u7528\u3057\u3066\u6587\u5b57\u3092\u8868\u73fe\u3057\u307e\u3059\u3002\u3059\u3079\u3066\u306eASCII\u6587\u5b57\u3068\u4e00\u822c\u7684\u306b\u4f7f\u7528\u3055\u308c\u308b\u975e\u82f1\u8a9e\u6587\u5b57\u306f2\u30d0\u30a4\u30c8\u3067\u8868\u73fe\u3055\u308c\u3001\u5c11\u6570\u306e\u6587\u5b57\u306f4\u30d0\u30a4\u30c8\u304c\u5fc5\u8981\u3067\u3059\u30022\u30d0\u30a4\u30c8\u6587\u5b57\u306e\u5834\u5408\u3001UTF-16\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u306fUnicode\u30b3\u30fc\u30c9\u30dd\u30a4\u30f3\u30c8\u3068\u7b49\u3057\u304f\u306a\u308a\u307e\u3059\u3002</li> <li>UTF-32\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\uff1a\u3059\u3079\u3066\u306e\u6587\u5b57\u304c4\u30d0\u30a4\u30c8\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002\u3053\u308c\u306f\u3001UTF-32\u304cUTF-8\u3084UTF-16\u3088\u308a\u3082\u591a\u304f\u306e\u7a7a\u9593\u3092\u5360\u6709\u3059\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u3001\u7279\u306bASCII\u6587\u5b57\u306e\u5272\u5408\u304c\u9ad8\u3044\u30c6\u30ad\u30b9\u30c8\u3067\u306f\u9855\u8457\u3067\u3059\u3002</li> </ul> <p>\u30b9\u30c8\u30ec\u30fc\u30b8\u7a7a\u9593\u306e\u89b3\u70b9\u304b\u3089\u3001UTF-8\u3092\u4f7f\u7528\u3057\u3066\u82f1\u8a9e\u6587\u5b57\u3092\u8868\u73fe\u3059\u308b\u3053\u3068\u306f1\u30d0\u30a4\u30c8\u306e\u307f\u304c\u5fc5\u8981\u306a\u305f\u3081\u975e\u5e38\u306b\u52b9\u7387\u7684\u3067\u3059\u3002UTF-16\u3092\u4f7f\u7528\u3057\u3066\u4e00\u90e8\u306e\u975e\u82f1\u8a9e\u6587\u5b57\uff08\u4e2d\u56fd\u8a9e\u306a\u3069\uff09\u3092\u30a8\u30f3\u30b3\u30fc\u30c9\u3059\u308b\u3053\u3068\u306f\u30012\u30d0\u30a4\u30c8\u306e\u307f\u304c\u5fc5\u8981\u306a\u305f\u3081\u3088\u308a\u52b9\u7387\u7684\u306b\u306a\u308b\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002\u4e00\u65b9\u3001UTF-8\u3067\u306f3\u30d0\u30a4\u30c8\u304c\u5fc5\u8981\u306b\u306a\u308b\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002</p> <p>\u4e92\u63db\u6027\u306e\u89b3\u70b9\u304b\u3089\u3001UTF-8\u306f\u6700\u3082\u6c4e\u7528\u6027\u304c\u3042\u308a\u3001\u591a\u304f\u306e\u30c4\u30fc\u30eb\u3068\u30e9\u30a4\u30d6\u30e9\u30ea\u304cUTF-8\u3092\u512a\u5148\u7684\u306b\u30b5\u30dd\u30fc\u30c8\u3057\u3066\u3044\u307e\u3059\u3002</p>"},{"location":"chapter_data_structure/character_encoding/#345","title":"3.4.5 \u00a0 \u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u306b\u304a\u3051\u308b\u6587\u5b57\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0","text":"<p>\u6b74\u53f2\u7684\u306b\u3001\u591a\u304f\u306e\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u306f\u30d7\u30ed\u30b0\u30e9\u30e0\u5b9f\u884c\u4e2d\u306e\u6587\u5b57\u5217\u51e6\u7406\u306bUTF-16\u3084UTF-32\u306a\u3069\u306e\u56fa\u5b9a\u9577\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u3092\u5229\u7528\u3057\u3066\u3044\u307e\u3057\u305f\u3002\u3053\u308c\u306b\u3088\u308a\u6587\u5b57\u5217\u3092\u914d\u5217\u3068\u3057\u3066\u51e6\u7406\u3067\u304d\u3001\u3044\u304f\u3064\u304b\u306e\u5229\u70b9\u304c\u3042\u308a\u307e\u3059\uff1a</p> <ul> <li>\u30e9\u30f3\u30c0\u30e0\u30a2\u30af\u30bb\u30b9\uff1aUTF-16\u3067\u30a8\u30f3\u30b3\u30fc\u30c9\u3055\u308c\u305f\u6587\u5b57\u5217\u306f\u7c21\u5358\u306b\u30e9\u30f3\u30c0\u30e0\u30a2\u30af\u30bb\u30b9\u3067\u304d\u307e\u3059\u3002\u53ef\u5909\u9577\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u3067\u3042\u308bUTF-8\u306e\u5834\u5408\u3001\\(i^{th}\\)\u6587\u5b57\u306e\u4f4d\u7f6e\u3092\u7279\u5b9a\u3059\u308b\u306b\u306f\u6587\u5b57\u5217\u306e\u958b\u59cb\u304b\u3089\\(i^{th}\\)\u4f4d\u7f6e\u307e\u3067\u8d70\u67fb\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u3001\\(O(n)\\)\u6642\u9593\u304c\u304b\u304b\u308a\u307e\u3059\u3002</li> <li>\u6587\u5b57\u6570\u30ab\u30a6\u30f3\u30c8\uff1a\u30e9\u30f3\u30c0\u30e0\u30a2\u30af\u30bb\u30b9\u3068\u540c\u69d8\u306b\u3001UTF-16\u3067\u30a8\u30f3\u30b3\u30fc\u30c9\u3055\u308c\u305f\u6587\u5b57\u5217\u306e\u6587\u5b57\u6570\u3092\u30ab\u30a6\u30f3\u30c8\u3059\u308b\u3053\u3068\u306f\\(O(1)\\)\u64cd\u4f5c\u3067\u3059\u3002\u3057\u304b\u3057\u3001UTF-8\u3067\u30a8\u30f3\u30b3\u30fc\u30c9\u3055\u308c\u305f\u6587\u5b57\u5217\u306e\u6587\u5b57\u6570\u3092\u30ab\u30a6\u30f3\u30c8\u3059\u308b\u306b\u306f\u6587\u5b57\u5217\u5168\u4f53\u3092\u8d70\u67fb\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002</li> <li>\u6587\u5b57\u5217\u64cd\u4f5c\uff1a\u5206\u5272\u3001\u9023\u7d50\u3001\u633f\u5165\u3001\u524a\u9664\u306a\u3069\u306e\u591a\u304f\u306e\u6587\u5b57\u5217\u64cd\u4f5c\u306f\u3001UTF-16\u3067\u30a8\u30f3\u30b3\u30fc\u30c9\u3055\u308c\u305f\u6587\u5b57\u5217\u3067\u7c21\u5358\u3067\u3059\u3002\u3053\u308c\u3089\u306e\u64cd\u4f5c\u306f\u4e00\u822c\u7684\u306b\u3001UTF-8\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u306e\u6709\u52b9\u6027\u3092\u78ba\u4fdd\u3059\u308b\u305f\u3081\u306bUTF-8\u3067\u30a8\u30f3\u30b3\u30fc\u30c9\u3055\u308c\u305f\u6587\u5b57\u5217\u3067\u8ffd\u52a0\u306e\u8a08\u7b97\u304c\u5fc5\u8981\u3067\u3059\u3002</li> </ul> <p>\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u306b\u304a\u3051\u308b\u6587\u5b57\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u30b9\u30ad\u30fc\u30e0\u306e\u8a2d\u8a08\u306f\u3001\u69d8\u3005\u306a\u8981\u56e0\u3092\u542b\u3080\u8208\u5473\u6df1\u3044\u30c8\u30d4\u30c3\u30af\u3067\u3059\uff1a</p> <ul> <li>Java\u306e<code>String</code>\u578b\u306fUTF-16\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u3092\u4f7f\u7528\u3057\u3001\u5404\u6587\u5b57\u304c2\u30d0\u30a4\u30c8\u3092\u5360\u6709\u3057\u307e\u3059\u3002\u3053\u308c\u306f\u300116\u30d3\u30c3\u30c8\u304c\u3059\u3079\u3066\u306e\u53ef\u80fd\u306a\u6587\u5b57\u3092\u8868\u73fe\u3059\u308b\u306e\u306b\u5341\u5206\u3067\u3042\u308b\u3068\u3044\u3046\u521d\u671f\u306e\u4fe1\u5ff5\u306b\u57fa\u3065\u3044\u3066\u304a\u308a\u3001\u5f8c\u306b\u9593\u9055\u3044\u3067\u3042\u308b\u3053\u3068\u304c\u8a3c\u660e\u3055\u308c\u307e\u3057\u305f\u3002Unicode\u6a19\u6e96\u304c16\u30d3\u30c3\u30c8\u3092\u8d85\u3048\u3066\u62e1\u5f35\u3055\u308c\u308b\u3068\u3001Java\u306e\u6587\u5b57\u306f\u300c\u30b5\u30ed\u30b2\u30fc\u30c8\u30da\u30a2\u300d\u3068\u3057\u3066\u77e5\u3089\u308c\u308b16\u30d3\u30c3\u30c8\u5024\u306e\u30da\u30a2\u3067\u8868\u73fe\u3055\u308c\u308b\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002</li> <li>JavaScript\u3068TypeScript\u306f\u3001Java\u3068\u540c\u69d8\u306e\u7406\u7531\u3067UTF-16\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002JavaScript\u304c1995\u5e74\u306bNetscape\u306b\u3088\u3063\u3066\u6700\u521d\u306b\u5c0e\u5165\u3055\u308c\u305f\u3068\u304d\u3001Unicode\u306f\u307e\u3060\u521d\u671f\u6bb5\u968e\u306b\u3042\u308a\u300116\u30d3\u30c3\u30c8\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u306f\u3059\u3079\u3066\u306eUnicode\u6587\u5b57\u3092\u8868\u73fe\u3059\u308b\u306e\u306b\u5341\u5206\u3067\u3057\u305f\u3002</li> <li>C#\u306fUTF-16\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u3092\u4f7f\u7528\u3057\u3001\u3053\u308c\u306f\u4e3b\u306bMicrosoft\u306b\u3088\u3063\u3066\u8a2d\u8a08\u3055\u308c\u305f.NET\u30d7\u30e9\u30c3\u30c8\u30d5\u30a9\u30fc\u30e0\u3001\u304a\u3088\u3073\u591a\u304f\u306eMicrosoft\u6280\u8853\uff08Windows\u30aa\u30da\u30ec\u30fc\u30c6\u30a3\u30f3\u30b0\u30b7\u30b9\u30c6\u30e0\u3092\u542b\u3080\uff09\u304cUTF-16\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u3092\u5e83\u7bc4\u56f2\u306b\u4f7f\u7528\u3057\u3066\u3044\u308b\u305f\u3081\u3067\u3059\u3002</li> </ul> <p>\u6587\u5b57\u6570\u306e\u904e\u5c0f\u8a55\u4fa1\u306b\u3088\u308a\u3001\u3053\u308c\u3089\u306e\u8a00\u8a9e\u306f16\u30d3\u30c3\u30c8\u3092\u8d85\u3048\u308bUnicode\u6587\u5b57\u3092\u8868\u73fe\u3059\u308b\u305f\u3081\u306b\u300c\u30b5\u30ed\u30b2\u30fc\u30c8\u30da\u30a2\u300d\u3092\u4f7f\u7528\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3057\u305f\u3002\u3053\u306e\u30a2\u30d7\u30ed\u30fc\u30c1\u306b\u306f\u6b20\u70b9\u304c\u3042\u308a\u307e\u3059\uff1a\u30b5\u30ed\u30b2\u30fc\u30c8\u30da\u30a2\u3092\u542b\u3080\u6587\u5b57\u5217\u306f2\u30d0\u30a4\u30c8\u307e\u305f\u306f4\u30d0\u30a4\u30c8\u3092\u5360\u6709\u3059\u308b\u6587\u5b57\u3092\u6301\u3064\u5834\u5408\u304c\u3042\u308a\u3001\u56fa\u5b9a\u9577\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u306e\u5229\u70b9\u3092\u5931\u3044\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u30b5\u30ed\u30b2\u30fc\u30c8\u30da\u30a2\u306e\u51e6\u7406\u306f\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u306b\u8907\u96d1\u3055\u3068\u30c7\u30d0\u30c3\u30b0\u306e\u56f0\u96e3\u3055\u3092\u8ffd\u52a0\u3057\u307e\u3059\u3002</p> <p>\u3053\u308c\u3089\u306e\u8ab2\u984c\u306b\u5bfe\u51e6\u3059\u308b\u305f\u3081\u3001\u4e00\u90e8\u306e\u8a00\u8a9e\u306f\u4ee3\u66ff\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u6226\u7565\u3092\u63a1\u7528\u3057\u3066\u3044\u307e\u3059\uff1a</p> <ul> <li>Python\u306e<code>str</code>\u578b\u306f\u3001\u6587\u5b57\u306e\u30b9\u30c8\u30ec\u30fc\u30b8\u9577\u304c\u6587\u5b57\u5217\u5185\u306e\u6700\u5927\u306eUnicode\u30b3\u30fc\u30c9\u30dd\u30a4\u30f3\u30c8\u306b\u4f9d\u5b58\u3059\u308b\u67d4\u8edf\u306a\u8868\u73fe\u3067Unicode\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002\u3059\u3079\u3066\u306e\u6587\u5b57\u304cASCII\u306e\u5834\u5408\u3001\u5404\u6587\u5b57\u306f1\u30d0\u30a4\u30c8\u3092\u5360\u6709\u3057\u3001\u57fa\u672c\u591a\u8a00\u8a9e\u9762\uff08BMP\uff09\u5185\u306e\u6587\u5b57\u306f2\u30d0\u30a4\u30c8\u3001BMP\u3092\u8d85\u3048\u308b\u6587\u5b57\u306f4\u30d0\u30a4\u30c8\u3092\u5360\u6709\u3057\u307e\u3059\u3002</li> <li>Go\u306e<code>string</code>\u578b\u306f\u5185\u90e8\u7684\u306bUTF-8\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002Go\u306f\u500b\u5225\u306eUnicode\u30b3\u30fc\u30c9\u30dd\u30a4\u30f3\u30c8\u3092\u8868\u73fe\u3059\u308b\u305f\u3081\u306e<code>rune</code>\u578b\u3082\u63d0\u4f9b\u3057\u307e\u3059\u3002</li> <li>Rust\u306e<code>str</code>\u3068<code>String</code>\u578b\u306f\u5185\u90e8\u7684\u306bUTF-8\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002Rust\u306f\u500b\u5225\u306eUnicode\u30b3\u30fc\u30c9\u30dd\u30a4\u30f3\u30c8\u7528\u306e<code>char</code>\u578b\u3082\u63d0\u4f9b\u3057\u307e\u3059\u3002</li> </ul> <p>\u4e0a\u8a18\u306e\u8b70\u8ad6\u306f\u3001\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u3067\u306e\u6587\u5b57\u5217\u306e\u683c\u7d0d\u65b9\u6cd5\u306b\u95a2\u3059\u308b\u3082\u306e\u3067\u3042\u308a\u3001**\u30d5\u30a1\u30a4\u30eb\u3067\u306e\u6587\u5b57\u5217\u306e\u683c\u7d0d\u65b9\u6cd5\u3084\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u4e0a\u3067\u306e\u9001\u4fe1\u65b9\u6cd5\u3068\u306f\u7570\u306a\u308b**\u3053\u3068\u306b\u6ce8\u610f\u3059\u308b\u3053\u3068\u304c\u91cd\u8981\u3067\u3059\u3002\u30d5\u30a1\u30a4\u30eb\u30b9\u30c8\u30ec\u30fc\u30b8\u3084\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u9001\u4fe1\u3067\u306f\u3001\u6587\u5b57\u5217\u306f\u901a\u5e38\u3001\u6700\u9069\u306a\u4e92\u63db\u6027\u3068\u7a7a\u9593\u52b9\u7387\u306e\u305f\u3081\u306bUTF-8\u5f62\u5f0f\u3067\u30a8\u30f3\u30b3\u30fc\u30c9\u3055\u308c\u307e\u3059\u3002</p>"},{"location":"chapter_data_structure/classification_of_data_structure/","title":"3.1 \u00a0 \u30c7\u30fc\u30bf\u69cb\u9020\u306e\u5206\u985e","text":"<p>\u4e00\u822c\u7684\u306a\u30c7\u30fc\u30bf\u69cb\u9020\u306b\u306f\u3001\u914d\u5217\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u3001\u30b9\u30bf\u30c3\u30af\u3001\u30ad\u30e5\u30fc\u3001\u30cf\u30c3\u30b7\u30e5\u8868\u3001\u6728\u3001\u30d2\u30fc\u30d7\u3001\u30b0\u30e9\u30d5\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u308c\u3089\u306f\u300c\u8ad6\u7406\u69cb\u9020\u300d\u3068\u300c\u7269\u7406\u69cb\u9020\u300d\u306b\u5206\u985e\u3067\u304d\u307e\u3059\u3002</p>"},{"location":"chapter_data_structure/classification_of_data_structure/#311","title":"3.1.1 \u00a0 \u8ad6\u7406\u69cb\u9020\uff1a\u7dda\u5f62\u3068\u975e\u7dda\u5f62","text":"<p>\u8ad6\u7406\u69cb\u9020\u306f\u30c7\u30fc\u30bf\u8981\u7d20\u9593\u306e\u8ad6\u7406\u7684\u95a2\u4fc2\u3092\u660e\u3089\u304b\u306b\u3057\u307e\u3059\u3002\u914d\u5217\u3068\u9023\u7d50\u30ea\u30b9\u30c8\u3067\u306f\u3001\u30c7\u30fc\u30bf\u306f\u7279\u5b9a\u306e\u9806\u5e8f\u3067\u914d\u7f6e\u3055\u308c\u3001\u30c7\u30fc\u30bf\u9593\u306e\u7dda\u5f62\u95a2\u4fc2\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002\u4e00\u65b9\u3001\u6728\u3067\u306f\u3001\u30c7\u30fc\u30bf\u306f\u4e0a\u304b\u3089\u4e0b\u3078\u968e\u5c64\u7684\u306b\u914d\u7f6e\u3055\u308c\u3001\u300c\u7956\u5148\u300d\u3068\u300c\u5b50\u5b6b\u300d\u9593\u306e\u6d3e\u751f\u95a2\u4fc2\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002\u305d\u3057\u3066\u3001\u30b0\u30e9\u30d5\u306f\u30ce\u30fc\u30c9\u3068\u30a8\u30c3\u30b8\u304b\u3089\u69cb\u6210\u3055\u308c\u3001\u8907\u96d1\u306a\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u95a2\u4fc2\u3092\u53cd\u6620\u3057\u3066\u3044\u307e\u3059\u3002</p> <p>\u4e0b\u56f3\u306b\u793a\u3055\u308c\u3066\u3044\u308b\u3088\u3046\u306b\u3001\u8ad6\u7406\u69cb\u9020\u306f\u300c\u7dda\u5f62\u300d\u3068\u300c\u975e\u7dda\u5f62\u300d\u306e2\u3064\u306e\u4e3b\u8981\u30ab\u30c6\u30b4\u30ea\u306b\u5206\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u7dda\u5f62\u69cb\u9020\u306f\u3088\u308a\u76f4\u611f\u7684\u3067\u3001\u30c7\u30fc\u30bf\u304c\u8ad6\u7406\u95a2\u4fc2\u306b\u304a\u3044\u3066\u7dda\u5f62\u306b\u914d\u7f6e\u3055\u308c\u3066\u3044\u308b\u3053\u3068\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002\u975e\u7dda\u5f62\u69cb\u9020\u306f\u3001\u9006\u306b\u975e\u7dda\u5f62\u306b\u914d\u7f6e\u3055\u308c\u3066\u3044\u307e\u3059\u3002</p> <ul> <li>\u7dda\u5f62\u30c7\u30fc\u30bf\u69cb\u9020\uff1a\u914d\u5217\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u3001\u30b9\u30bf\u30c3\u30af\u3001\u30ad\u30e5\u30fc\u3001\u30cf\u30c3\u30b7\u30e5\u8868\u3002\u8981\u7d20\u304c\u4e00\u5bfe\u4e00\u306e\u9806\u6b21\u95a2\u4fc2\u3092\u6301\u3061\u307e\u3059\u3002</li> <li>\u975e\u7dda\u5f62\u30c7\u30fc\u30bf\u69cb\u9020\uff1a\u6728\u3001\u30d2\u30fc\u30d7\u3001\u30b0\u30e9\u30d5\u3001\u30cf\u30c3\u30b7\u30e5\u8868\u3002</li> </ul> <p>\u975e\u7dda\u5f62\u30c7\u30fc\u30bf\u69cb\u9020\u306f\u3001\u3055\u3089\u306b\u6728\u69cb\u9020\u3068\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u69cb\u9020\u306b\u5206\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002</p> <ul> <li>\u6728\u69cb\u9020\uff1a\u6728\u3001\u30d2\u30fc\u30d7\u3001\u30cf\u30c3\u30b7\u30e5\u8868\u3002\u8981\u7d20\u304c\u4e00\u5bfe\u591a\u306e\u95a2\u4fc2\u3092\u6301\u3061\u307e\u3059\u3002</li> <li>\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u69cb\u9020\uff1a\u30b0\u30e9\u30d5\u3002\u8981\u7d20\u304c\u591a\u5bfe\u591a\u306e\u95a2\u4fc2\u3092\u6301\u3061\u307e\u3059\u3002</li> </ul> <p></p> <p> \u56f3 3-1 \u00a0 Linear and non-linear data structures </p>"},{"location":"chapter_data_structure/classification_of_data_structure/#312","title":"3.1.2 \u00a0 \u7269\u7406\u69cb\u9020\uff1a\u9023\u7d9a\u3068\u5206\u6563","text":"<p>\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5b9f\u884c\u4e2d\u3001\u51e6\u7406\u3055\u308c\u308b\u30c7\u30fc\u30bf\u306f\u30e1\u30e2\u30ea\u306b\u683c\u7d0d\u3055\u308c\u307e\u3059\u3002\u4e0b\u56f3\u306f\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u306e\u30e1\u30e2\u30ea\u30b9\u30c6\u30a3\u30c3\u30af\u3092\u793a\u3057\u3066\u304a\u308a\u3001\u5404\u9ed2\u3044\u6b63\u65b9\u5f62\u306f\u7269\u7406\u30e1\u30e2\u30ea\u7a7a\u9593\u3067\u3059\u3002\u30e1\u30e2\u30ea\u3092\u5de8\u5927\u306aExcel\u30b9\u30d7\u30ec\u30c3\u30c9\u30b7\u30fc\u30c8\u3068\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u3001\u5404\u30bb\u30eb\u306f\u4e00\u5b9a\u91cf\u306e\u30c7\u30fc\u30bf\u3092\u683c\u7d0d\u3067\u304d\u307e\u3059\u3002</p> <p>\u30b7\u30b9\u30c6\u30e0\u306f\u30e1\u30e2\u30ea\u30a2\u30c9\u30ec\u30b9\u306b\u3088\u3063\u3066\u76ee\u6a19\u4f4d\u7f6e\u306e\u30c7\u30fc\u30bf\u306b\u30a2\u30af\u30bb\u30b9\u3057\u307e\u3059\u3002\u4e0b\u56f3\u306b\u793a\u3055\u308c\u3066\u3044\u308b\u3088\u3046\u306b\u3001\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u306f\u7279\u5b9a\u306e\u30eb\u30fc\u30eb\u306b\u5f93\u3063\u3066\u8868\u306e\u5404\u30bb\u30eb\u306b\u4e00\u610f\u306e\u8b58\u5225\u5b50\u3092\u5272\u308a\u5f53\u3066\u3001\u5404\u30e1\u30e2\u30ea\u7a7a\u9593\u304c\u4e00\u610f\u306e\u30e1\u30e2\u30ea\u30a2\u30c9\u30ec\u30b9\u3092\u6301\u3064\u3053\u3068\u3092\u4fdd\u8a3c\u3057\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u30a2\u30c9\u30ec\u30b9\u306b\u3088\u308a\u3001\u30d7\u30ed\u30b0\u30e9\u30e0\u306f\u30e1\u30e2\u30ea\u306b\u683c\u7d0d\u3055\u308c\u305f\u30c7\u30fc\u30bf\u306b\u30a2\u30af\u30bb\u30b9\u3067\u304d\u307e\u3059\u3002</p> <p></p> <p> \u56f3 3-2 \u00a0 Memory stick, memory spaces, memory addresses </p> <p>Tip</p> <p>\u30e1\u30e2\u30ea\u3092Excel\u30b9\u30d7\u30ec\u30c3\u30c9\u30b7\u30fc\u30c8\u306b\u6bd4\u8f03\u3059\u308b\u3053\u3068\u306f\u7c21\u7565\u5316\u3055\u308c\u305f\u985e\u63a8\u3067\u3042\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u30e1\u30e2\u30ea\u306e\u5b9f\u969b\u306e\u52d5\u4f5c\u30e1\u30ab\u30cb\u30ba\u30e0\u306f\u3088\u308a\u8907\u96d1\u3067\u3001\u30a2\u30c9\u30ec\u30b9\u7a7a\u9593\u3001\u30e1\u30e2\u30ea\u7ba1\u7406\u3001\u30ad\u30e3\u30c3\u30b7\u30e5\u30e1\u30ab\u30cb\u30ba\u30e0\u3001\u4eee\u60f3\u30e1\u30e2\u30ea\u3001\u7269\u7406\u30e1\u30e2\u30ea\u306a\u3069\u306e\u6982\u5ff5\u304c\u95a2\u4fc2\u3057\u3066\u3044\u307e\u3059\u3002</p> <p>\u30e1\u30e2\u30ea\u306f\u3059\u3079\u3066\u306e\u30d7\u30ed\u30b0\u30e9\u30e0\u306e\u5171\u6709\u30ea\u30bd\u30fc\u30b9\u3067\u3059\u3002\u3042\u308b\u30e1\u30e2\u30ea\u30d6\u30ed\u30c3\u30af\u304c1\u3064\u306e\u30d7\u30ed\u30b0\u30e9\u30e0\u306b\u3088\u3063\u3066\u5360\u6709\u3055\u308c\u308b\u3068\u3001\u4ed6\u306e\u30d7\u30ed\u30b0\u30e9\u30e0\u304c\u540c\u6642\u306b\u4f7f\u7528\u3059\u308b\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u30e1\u30e2\u30ea\u30ea\u30bd\u30fc\u30b9\u306f\u30c7\u30fc\u30bf\u69cb\u9020\u3068\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u8a2d\u8a08\u306b\u304a\u3051\u308b\u91cd\u8981\u306a\u8003\u616e\u4e8b\u9805\u3067\u3059\u3002\u4f8b\u3048\u3070\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u30d4\u30fc\u30af\u30e1\u30e2\u30ea\u4f7f\u7528\u91cf\u306f\u3001\u30b7\u30b9\u30c6\u30e0\u306e\u6b8b\u308a\u7a7a\u304d\u30e1\u30e2\u30ea\u3092\u8d85\u3048\u3066\u306f\u3044\u3051\u307e\u305b\u3093\u3002\u9023\u7d9a\u3057\u305f\u30e1\u30e2\u30ea\u30d6\u30ed\u30c3\u30af\u304c\u4e0d\u8db3\u3057\u3066\u3044\u308b\u5834\u5408\u306f\u3001\u975e\u9023\u7d9a\u30e1\u30e2\u30ea\u30d6\u30ed\u30c3\u30af\u306b\u683c\u7d0d\u3067\u304d\u308b\u30c7\u30fc\u30bf\u69cb\u9020\u3092\u9078\u629e\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002</p> <p>\u4e0b\u56f3\u306b\u793a\u3055\u308c\u3066\u3044\u308b\u3088\u3046\u306b\u3001\u7269\u7406\u69cb\u9020\u306f\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u30e1\u30e2\u30ea\u306b\u304a\u3051\u308b\u30c7\u30fc\u30bf\u306e\u683c\u7d0d\u65b9\u6cd5\u3092\u53cd\u6620\u3057\u3001\u9023\u7d9a\u7a7a\u9593\u683c\u7d0d\uff08\u914d\u5217\uff09\u3068\u975e\u9023\u7d9a\u7a7a\u9593\u683c\u7d0d\uff08\u9023\u7d50\u30ea\u30b9\u30c8\uff09\u306b\u5206\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u30022\u3064\u306e\u30bf\u30a4\u30d7\u306e\u7269\u7406\u69cb\u9020\u306f\u3001\u6642\u9593\u52b9\u7387\u3068\u7a7a\u9593\u52b9\u7387\u306e\u89b3\u70b9\u3067\u88dc\u5b8c\u7684\u306a\u7279\u6027\u3092\u793a\u3057\u307e\u3059\u3002</p> <p></p> <p> \u56f3 3-3 \u00a0 Contiguous space storage and dispersed space storage </p> <p>\u3059\u3079\u3066\u306e\u30c7\u30fc\u30bf\u69cb\u9020\u306f\u914d\u5217\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u3001\u307e\u305f\u306f\u305d\u306e\u7d44\u307f\u5408\u308f\u305b\u306b\u57fa\u3065\u3044\u3066\u5b9f\u88c5\u3055\u308c\u3066\u3044\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u4f8b\u3048\u3070\u3001\u30b9\u30bf\u30c3\u30af\u3068\u30ad\u30e5\u30fc\u306f\u914d\u5217\u307e\u305f\u306f\u9023\u7d50\u30ea\u30b9\u30c8\u306e\u3069\u3061\u3089\u3067\u3082\u5b9f\u88c5\u3067\u304d\u307e\u3059\u3002\u30cf\u30c3\u30b7\u30e5\u8868\u306e\u5b9f\u88c5\u306b\u306f\u914d\u5217\u3068\u9023\u7d50\u30ea\u30b9\u30c8\u306e\u4e21\u65b9\u304c\u95a2\u4fc2\u3059\u308b\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002</p> <ul> <li>\u914d\u5217\u30d9\u30fc\u30b9\u306e\u5b9f\u88c5\uff1a\u30b9\u30bf\u30c3\u30af\u3001\u30ad\u30e5\u30fc\u3001\u30cf\u30c3\u30b7\u30e5\u8868\u3001\u6728\u3001\u30d2\u30fc\u30d7\u3001\u30b0\u30e9\u30d5\u3001\u884c\u5217\u3001\u30c6\u30f3\u30bd\u30eb\uff08\u6b21\u5143\\(\\geq 3\\)\u306e\u914d\u5217\uff09\u3002</li> <li>\u9023\u7d50\u30ea\u30b9\u30c8\u30d9\u30fc\u30b9\u306e\u5b9f\u88c5\uff1a\u30b9\u30bf\u30c3\u30af\u3001\u30ad\u30e5\u30fc\u3001\u30cf\u30c3\u30b7\u30e5\u8868\u3001\u6728\u3001\u30d2\u30fc\u30d7\u3001\u30b0\u30e9\u30d5\u306a\u3069\u3002</li> </ul> <p>\u914d\u5217\u306b\u57fa\u3065\u3044\u3066\u5b9f\u88c5\u3055\u308c\u305f\u30c7\u30fc\u30bf\u69cb\u9020\u306f\u300c\u9759\u7684\u30c7\u30fc\u30bf\u69cb\u9020\u300d\u3068\u3082\u547c\u3070\u308c\u3001\u521d\u671f\u5316\u5f8c\u306b\u9577\u3055\u3092\u5909\u66f4\u3067\u304d\u306a\u3044\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002\u9006\u306b\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u306b\u57fa\u3065\u3044\u305f\u3082\u306e\u306f\u300c\u52d5\u7684\u30c7\u30fc\u30bf\u69cb\u9020\u300d\u3068\u547c\u3070\u308c\u3001\u30d7\u30ed\u30b0\u30e9\u30e0\u5b9f\u884c\u4e2d\u306b\u30b5\u30a4\u30ba\u3092\u8abf\u6574\u3067\u304d\u307e\u3059\u3002</p> <p>Tip</p> <p>\u7269\u7406\u69cb\u9020\u3092\u7406\u89e3\u3059\u308b\u306e\u304c\u56f0\u96e3\u306a\u5834\u5408\u306f\u3001\u6b21\u306e\u7ae0\u300c\u914d\u5217\u3068\u9023\u7d50\u30ea\u30b9\u30c8\u300d\u3092\u8aad\u3093\u3067\u304b\u3089\u3001\u3053\u306e\u7bc0\u306b\u623b\u308b\u3053\u3068\u3092\u304a\u52e7\u3081\u3057\u307e\u3059\u3002</p>"},{"location":"chapter_data_structure/number_encoding/","title":"3.3 \u00a0 \u6570\u5024\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0 *","text":"<p>Tip</p> <p>\u672c\u66f8\u3067\u306f\u3001\u30a2\u30b9\u30bf\u30ea\u30b9\u30af\u300c*\u300d\u304c\u4ed8\u3044\u305f\u7ae0\u306f\u4efb\u610f\u8aad\u66f8\u3067\u3059\u3002\u6642\u9593\u304c\u4e0d\u8db3\u3057\u3066\u3044\u308b\u5834\u5408\u3084\u96e3\u3057\u3044\u3068\u611f\u3058\u308b\u5834\u5408\u306f\u3001\u6700\u521d\u306f\u3053\u308c\u3089\u3092\u30b9\u30ad\u30c3\u30d7\u3057\u3066\u3001\u5fc5\u9808\u306e\u7ae0\u3092\u5b8c\u4e86\u3057\u305f\u5f8c\u306b\u623b\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002</p>"},{"location":"chapter_data_structure/number_encoding/#331","title":"3.3.1 \u00a0 \u6574\u6570\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0","text":"<p>\u524d\u306e\u7bc0\u306e\u8868\u3067\u3001\u3059\u3079\u3066\u306e\u6574\u6570\u578b\u306f\u6b63\u306e\u6570\u3088\u308a\u30821\u3064\u591a\u3044\u8ca0\u306e\u6570\u3092\u8868\u73fe\u3067\u304d\u308b\u3053\u3068\u3092\u89b3\u5bdf\u3057\u307e\u3057\u305f\u3002\u4f8b\u3048\u3070\u3001<code>byte</code>\u306e\u7bc4\u56f2\u306f\\([-128, 127]\\)\u3067\u3059\u3002\u3053\u306e\u73fe\u8c61\u306f\u76f4\u611f\u306b\u53cd\u3059\u308b\u3088\u3046\u306b\u898b\u3048\u3001\u305d\u306e\u6839\u672c\u7684\u306a\u7406\u7531\u306b\u306f\u7b26\u53f7\u7d76\u5bfe\u5024\u30011\u306e\u88dc\u6570\u30012\u306e\u88dc\u6570\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u306e\u77e5\u8b58\u304c\u95a2\u4e0e\u3057\u3066\u3044\u307e\u3059\u3002</p> <p>\u307e\u305a\u91cd\u8981\u306a\u3053\u3068\u306f\u3001**\u6570\u5024\u306f\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u5185\u30672\u306e\u88dc\u6570\u5f62\u5f0f\u3067\u683c\u7d0d\u3055\u308c\u308b**\u3068\u3044\u3046\u3053\u3068\u3067\u3059\u3002\u306a\u305c\u305d\u3046\u306a\u306e\u304b\u3092\u5206\u6790\u3059\u308b\u524d\u306b\u3001\u3053\u308c\u30893\u3064\u306e\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u65b9\u6cd5\u3092\u5b9a\u7fa9\u3057\u307e\u3057\u3087\u3046\uff1a</p> <ul> <li>\u7b26\u53f7\u7d76\u5bfe\u5024\uff1a\u6570\u5024\u306e\u4e8c\u9032\u8868\u73fe\u306e\u6700\u4e0a\u4f4d\u30d3\u30c3\u30c8\u3092\u7b26\u53f7\u30d3\u30c3\u30c8\u3068\u3057\u3001\\(0\\)\u306f\u6b63\u306e\u6570\u3001\\(1\\)\u306f\u8ca0\u306e\u6570\u3092\u8868\u3057\u307e\u3059\u3002\u6b8b\u308a\u306e\u30d3\u30c3\u30c8\u306f\u6570\u5024\u306e\u5024\u3092\u8868\u3057\u307e\u3059\u3002</li> <li>1\u306e\u88dc\u6570\uff1a\u6b63\u306e\u6570\u306e1\u306e\u88dc\u6570\u306f\u7b26\u53f7\u7d76\u5bfe\u5024\u3068\u540c\u3058\u3067\u3059\u3002\u8ca0\u306e\u6570\u306e\u5834\u5408\u3001\u7b26\u53f7\u30d3\u30c3\u30c8\u4ee5\u5916\u306e\u3059\u3079\u3066\u306e\u30d3\u30c3\u30c8\u3092\u53cd\u8ee2\u3057\u3066\u5f97\u3089\u308c\u307e\u3059\u3002</li> <li>2\u306e\u88dc\u6570\uff1a\u6b63\u306e\u6570\u306e2\u306e\u88dc\u6570\u306f\u7b26\u53f7\u7d76\u5bfe\u5024\u3068\u540c\u3058\u3067\u3059\u3002\u8ca0\u306e\u6570\u306e\u5834\u5408\u3001\u305d\u306e1\u306e\u88dc\u6570\u306b\\(1\\)\u3092\u52a0\u3048\u3066\u5f97\u3089\u308c\u307e\u3059\u3002</li> </ul> <p>\u4ee5\u4e0b\u306e\u56f3\u306f\u3001\u7b26\u53f7\u7d76\u5bfe\u5024\u30011\u306e\u88dc\u6570\u30012\u306e\u88dc\u6570\u9593\u306e\u5909\u63db\u3092\u793a\u3057\u3066\u3044\u307e\u3059\uff1a</p> <p></p> <p> \u56f3 3-4 \u00a0 \u7b26\u53f7\u7d76\u5bfe\u5024\u30011\u306e\u88dc\u6570\u30012\u306e\u88dc\u6570\u9593\u306e\u5909\u63db </p> <p>\u7b26\u53f7\u7d76\u5bfe\u5024\u306f\u6700\u3082\u76f4\u611f\u7684\u3067\u3059\u304c\u3001\u5236\u9650\u304c\u3042\u308a\u307e\u3059\u3002\u4e00\u3064\u306b\u306f\u3001\u7b26\u53f7\u7d76\u5bfe\u5024\u306e\u8ca0\u306e\u6570\u306f\u8a08\u7b97\u3067\u76f4\u63a5\u4f7f\u7528\u3067\u304d\u307e\u305b\u3093\u3002\u4f8b\u3048\u3070\u3001\u7b26\u53f7\u7d76\u5bfe\u5024\u3067\\(1 + (-2)\\)\u3092\u8a08\u7b97\u3059\u308b\u3068\\(-3\\)\u306b\u306a\u308a\u3001\u3053\u308c\u306f\u6b63\u3057\u304f\u3042\u308a\u307e\u305b\u3093\u3002</p> \\[ \\begin{aligned} &amp; 1 + (-2) \\newline &amp; \\rightarrow 0000 \\; 0001 + 1000 \\; 0010 \\newline &amp; = 1000 \\; 0011 \\newline &amp; \\rightarrow -3 \\end{aligned} \\] <p>\u3053\u306e\u554f\u984c\u306b\u5bfe\u51e6\u3059\u308b\u305f\u3081\u3001\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u306f1\u306e\u88dc\u6570\u3092\u5c0e\u5165\u3057\u307e\u3057\u305f\u30021\u306e\u88dc\u6570\u306b\u5909\u63db\u3057\u3066\\(1 + (-2)\\)\u3092\u8a08\u7b97\u3057\u3001\u7d50\u679c\u3092\u7b26\u53f7\u7d76\u5bfe\u5024\u306b\u623b\u3059\u3068\u3001\u6b63\u3057\u3044\u7d50\u679c\\(-1\\)\u304c\u5f97\u3089\u308c\u307e\u3059\u3002</p> \\[ \\begin{aligned} &amp; 1 + (-2) \\newline &amp; \\rightarrow 0000 \\; 0001 \\; \\text{(\u7b26\u53f7\u7d76\u5bfe\u5024)} + 1000 \\; 0010 \\; \\text{(\u7b26\u53f7\u7d76\u5bfe\u5024)} \\newline &amp; = 0000 \\; 0001 \\; \\text{(1\u306e\u88dc\u6570)} + 1111 \\; 1101 \\; \\text{(1\u306e\u88dc\u6570)} \\newline &amp; = 1111 \\; 1110 \\; \\text{(1\u306e\u88dc\u6570)} \\newline &amp; = 1000 \\; 0001 \\; \\text{(\u7b26\u53f7\u7d76\u5bfe\u5024)} \\newline &amp; \\rightarrow -1 \\end{aligned} \\] <p>\u307e\u305f\u3001\u7b26\u53f7\u7d76\u5bfe\u5024\u3067\u306f0\u306b2\u3064\u306e\u8868\u73fe\u304c\u3042\u308a\u307e\u3059\uff1a\\(+0\\)\u3068\\(-0\\)\u3067\u3059\u3002\u3053\u308c\u306f0\u306b\u5bfe\u3057\u30662\u3064\u306e\u7570\u306a\u308b\u4e8c\u9032\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u304c\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u3001\u66d6\u6627\u3055\u3092\u5f15\u304d\u8d77\u3053\u3059\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u6761\u4ef6\u30c1\u30a7\u30c3\u30af\u3067\u6b63\u3068\u8ca0\u306e0\u3092\u533a\u5225\u3057\u306a\u3044\u3068\u3001\u6b63\u3057\u304f\u306a\u3044\u7d50\u679c\u306b\u306a\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u66d6\u6627\u3055\u306b\u5bfe\u51e6\u3059\u308b\u306b\u306f\u8ffd\u52a0\u306e\u30c1\u30a7\u30c3\u30af\u304c\u5fc5\u8981\u3067\u3001\u8a08\u7b97\u52b9\u7387\u304c\u4f4e\u4e0b\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002</p> \\[ \\begin{aligned} +0 &amp; \\rightarrow 0000 \\; 0000 \\newline -0 &amp; \\rightarrow 1000 \\; 0000 \\end{aligned} \\] <p>\u7b26\u53f7\u7d76\u5bfe\u5024\u3068\u540c\u69d8\u306b\u30011\u306e\u88dc\u6570\u3082\u6b63\u3068\u8ca0\u306e0\u306e\u66d6\u6627\u3055\u306b\u60a9\u307e\u3055\u308c\u307e\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u306f\u3055\u3089\u306b2\u306e\u88dc\u6570\u3092\u5c0e\u5165\u3057\u307e\u3057\u305f\u3002\u7b26\u53f7\u7d76\u5bfe\u5024\u30011\u306e\u88dc\u6570\u30012\u306e\u88dc\u6570\u306b\u304a\u3051\u308b\u8ca0\u306e0\u306e\u5909\u63db\u904e\u7a0b\u3092\u89b3\u5bdf\u3057\u3066\u307f\u307e\u3057\u3087\u3046\uff1a</p> \\[ \\begin{aligned} -0 \\rightarrow \\; &amp; 1000 \\; 0000 \\; \\text{(\u7b26\u53f7\u7d76\u5bfe\u5024)} \\newline = \\; &amp; 1111 \\; 1111 \\; \\text{(1\u306e\u88dc\u6570)} \\newline = 1 \\; &amp; 0000 \\; 0000 \\; \\text{(2\u306e\u88dc\u6570)} \\newline \\end{aligned} \\] <p>\u8ca0\u306e0\u306e1\u306e\u88dc\u6570\u306b\\(1\\)\u3092\u52a0\u3048\u308b\u3068\u6841\u4e0a\u304c\u308a\u304c\u767a\u751f\u3057\u307e\u3059\u304c\u3001<code>byte</code>\u306e\u9577\u3055\u306f8\u30d3\u30c3\u30c8\u306e\u307f\u306e\u305f\u3081\u30019\u756a\u76ee\u306e\u30d3\u30c3\u30c8\u3078\u306e\u6841\u4e0a\u304c\u308a\\(1\\)\u306f\u7834\u68c4\u3055\u308c\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001**\u8ca0\u306e0\u306e2\u306e\u88dc\u6570\u306f\\(0000 \\; 0000\\)**\u3067\u3001\u6b63\u306e0\u3068\u540c\u3058\u306b\u306a\u308a\u3001\u66d6\u6627\u3055\u304c\u89e3\u6c7a\u3055\u308c\u307e\u3059\u3002</p> <p>\u6700\u5f8c\u306e\u8b0e\u306f\u3001<code>byte</code>\u306e\\([-128, 127]\\)\u306e\u7bc4\u56f2\u3067\u3001\u8ffd\u52a0\u306e\u8ca0\u306e\u6570\\(-128\\)\u304c\u3042\u308b\u3053\u3068\u3067\u3059\u3002\\([-127, +127]\\)\u306e\u533a\u9593\u3067\u306f\u3001\u3059\u3079\u3066\u306e\u6574\u6570\u306b\u5bfe\u5fdc\u3059\u308b\u7b26\u53f7\u7d76\u5bfe\u5024\u30011\u306e\u88dc\u6570\u30012\u306e\u88dc\u6570\u304c\u3042\u308a\u3001\u76f8\u4e92\u5909\u63db\u304c\u53ef\u80fd\u3067\u3042\u308b\u3053\u3068\u3092\u89b3\u5bdf\u3057\u307e\u3059\u3002</p> <p>\u3057\u304b\u3057\u30012\u306e\u88dc\u6570\\(1000 \\; 0000\\)\u306f\u5bfe\u5fdc\u3059\u308b\u7b26\u53f7\u7d76\u5bfe\u5024\u3092\u6301\u305f\u306a\u3044\u4f8b\u5916\u3067\u3059\u3002\u5909\u63db\u65b9\u6cd5\u306b\u3088\u308b\u3068\u3001\u305d\u306e\u7b26\u53f7\u7d76\u5bfe\u5024\u306f\\(0000 \\; 0000\\)\u3067\u30010\u3092\u793a\u3057\u307e\u3059\u3002\u3053\u308c\u306f\u77db\u76fe\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002\u306a\u305c\u306a\u3089\u3001\u305d\u306e2\u306e\u88dc\u6570\u306f\u81ea\u5206\u81ea\u8eab\u3092\u8868\u3059\u3079\u304d\u3060\u304b\u3089\u3067\u3059\u3002\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u306f\u3001\u3053\u306e\u7279\u5225\u306a2\u306e\u88dc\u6570\\(1000 \\; 0000\\)\u3092\\(-128\\)\u3092\u8868\u3059\u3082\u306e\u3068\u3057\u3066\u6307\u5b9a\u3057\u3066\u3044\u307e\u3059\u3002\u5b9f\u969b\u30012\u306e\u88dc\u6570\u3067\u306e\\((-1) + (-127)\\)\u306e\u8a08\u7b97\u7d50\u679c\u306f\\(-128\\)\u306b\u306a\u308a\u307e\u3059\u3002</p> \\[ \\begin{aligned} &amp; (-127) + (-1) \\newline &amp; \\rightarrow 1111 \\; 1111 \\; \\text{(\u7b26\u53f7\u7d76\u5bfe\u5024)} + 1000 \\; 0001 \\; \\text{(\u7b26\u53f7\u7d76\u5bfe\u5024)} \\newline &amp; = 1000 \\; 0000 \\; \\text{(1\u306e\u88dc\u6570)} + 1111 \\; 1110 \\; \\text{(1\u306e\u88dc\u6570)} \\newline &amp; = 1000 \\; 0001 \\; \\text{(2\u306e\u88dc\u6570)} + 1111 \\; 1111 \\; \\text{(2\u306e\u88dc\u6570)} \\newline &amp; = 1000 \\; 0000 \\; \\text{(2\u306e\u88dc\u6570)} \\newline &amp; \\rightarrow -128 \\end{aligned} \\] <p>\u304a\u6c17\u3065\u304d\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u304c\u3001\u3053\u308c\u3089\u306e\u8a08\u7b97\u306f\u3059\u3079\u3066\u52a0\u7b97\u3067\u3042\u308a\u3001\u91cd\u8981\u306a\u4e8b\u5b9f\u3092\u793a\u5506\u3057\u3066\u3044\u307e\u3059\uff1a\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u306e\u5185\u90e8\u30cf\u30fc\u30c9\u30a6\u30a7\u30a2\u56de\u8def\u306f\u4e3b\u306b\u52a0\u7b97\u6f14\u7b97\u3092\u4e2d\u5fc3\u306b\u8a2d\u8a08\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u52a0\u7b97\u304c\u4e57\u7b97\u3001\u9664\u7b97\u3001\u6e1b\u7b97\u306a\u3069\u306e\u4ed6\u306e\u6f14\u7b97\u3068\u6bd4\u8f03\u3057\u3066\u30cf\u30fc\u30c9\u30a6\u30a7\u30a2\u3067\u5b9f\u88c5\u3057\u3084\u3059\u304f\u3001\u4e26\u5217\u5316\u304c\u5bb9\u6613\u3067\u9ad8\u901f\u8a08\u7b97\u304c\u53ef\u80fd\u3060\u304b\u3089\u3067\u3059\u3002</p> <p>\u3053\u308c\u306f\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u304c\u52a0\u7b97\u306e\u307f\u3092\u5b9f\u884c\u3067\u304d\u308b\u3053\u3068\u3092\u610f\u5473\u3059\u308b\u3082\u306e\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u52a0\u7b97\u3068\u57fa\u672c\u7684\u306a\u8ad6\u7406\u6f14\u7b97\u3092\u7d44\u307f\u5408\u308f\u305b\u308b\u3053\u3068\u3067\u3001\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u306f\u69d8\u3005\u306a\u4ed6\u306e\u6570\u5b66\u6f14\u7b97\u3092\u5b9f\u884c\u3067\u304d\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u6e1b\u7b97\\(a - b\\)\u306f\\(a + (-b)\\)\u306b\u5909\u63db\u3067\u304d\u3001\u4e57\u7b97\u3068\u9664\u7b97\u306f\u8907\u6570\u306e\u52a0\u7b97\u307e\u305f\u306f\u6e1b\u7b97\u306b\u5909\u63db\u3067\u304d\u307e\u3059\u3002</p> <p>\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u30672\u306e\u88dc\u6570\u3092\u4f7f\u7528\u3059\u308b\u7406\u7531\u3092\u307e\u3068\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\uff1a2\u306e\u88dc\u6570\u8868\u73fe\u306b\u3088\u308a\u3001\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u306f\u540c\u3058\u56de\u8def\u3068\u6f14\u7b97\u3092\u4f7f\u7528\u3057\u3066\u6b63\u3068\u8ca0\u306e\u6570\u306e\u52a0\u7b97\u3092\u51e6\u7406\u3067\u304d\u3001\u6e1b\u7b97\u7528\u306e\u7279\u5225\u306a\u30cf\u30fc\u30c9\u30a6\u30a7\u30a2\u56de\u8def\u306e\u5fc5\u8981\u6027\u3092\u6392\u9664\u3057\u3001\u6b63\u3068\u8ca0\u306e0\u306e\u66d6\u6627\u3055\u3092\u56de\u907f\u3067\u304d\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u30cf\u30fc\u30c9\u30a6\u30a7\u30a2\u8a2d\u8a08\u304c\u5927\u5e45\u306b\u7c21\u7d20\u5316\u3055\u308c\u3001\u8a08\u7b97\u52b9\u7387\u304c\u5411\u4e0a\u3057\u307e\u3059\u3002</p> <p>2\u306e\u88dc\u6570\u306e\u8a2d\u8a08\u306f\u975e\u5e38\u306b\u5de7\u5999\u3067\u3001\u30b9\u30da\u30fc\u30b9\u306e\u5236\u7d04\u306b\u3088\u308a\u3001\u3053\u3053\u3067\u505c\u6b62\u3057\u307e\u3059\u3002\u8208\u5473\u306e\u3042\u308b\u8aad\u8005\u306f\u3055\u3089\u306b\u63a2\u6c42\u3059\u308b\u3053\u3068\u3092\u5968\u52b1\u3057\u307e\u3059\u3002</p>"},{"location":"chapter_data_structure/number_encoding/#332","title":"3.3.2 \u00a0 \u6d6e\u52d5\u5c0f\u6570\u70b9\u6570\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0","text":"<p>\u8208\u5473\u6df1\u3044\u3053\u3068\u306b\u6c17\u3065\u3044\u305f\u304b\u3082\u3057\u308c\u307e\u305b\u3093\uff1a\u540c\u30584\u30d0\u30a4\u30c8\u306e\u9577\u3055\u306b\u3082\u304b\u304b\u308f\u3089\u305a\u3001\u306a\u305c<code>float</code>\u306f<code>int</code>\u3068\u6bd4\u8f03\u3057\u3066\u306f\u308b\u304b\u306b\u5927\u304d\u3044\u5024\u306e\u7bc4\u56f2\u3092\u6301\u3064\u306e\u3067\u3057\u3087\u3046\u304b\uff1f\u3053\u308c\u306f\u76f4\u611f\u306b\u53cd\u3059\u308b\u3088\u3046\u306b\u898b\u3048\u307e\u3059\u3002<code>float</code>\u306f\u5206\u6570\u3092\u8868\u73fe\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u305f\u3081\u3001\u7bc4\u56f2\u304c\u7e2e\u5c0f\u3059\u308b\u3068\u4e88\u60f3\u3055\u308c\u308b\u304b\u3089\u3067\u3059\u3002</p> <p>\u5b9f\u969b\u3001\u3053\u308c\u306f\u6d6e\u52d5\u5c0f\u6570\u70b9\u6570\uff08<code>float</code>\uff09\u3067\u4f7f\u7528\u3055\u308c\u308b\u7570\u306a\u308b\u8868\u73fe\u65b9\u6cd5\u306b\u3088\u308b\u3082\u306e\u3067\u3059\u300232\u30d3\u30c3\u30c8\u306e\u4e8c\u9032\u6570\u3092\u6b21\u306e\u3088\u3046\u306b\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\uff1a</p> \\[ b_{31} b_{30} b_{29} \\ldots b_2 b_1 b_0 \\] <p>IEEE 754\u6a19\u6e96\u306b\u3088\u308b\u3068\u300132\u30d3\u30c3\u30c8\u306e<code>float</code>\u306f\u6b21\u306e3\u3064\u306e\u90e8\u5206\u3067\u69cb\u6210\u3055\u308c\u307e\u3059\uff1a</p> <ul> <li>\u7b26\u53f7\u30d3\u30c3\u30c8\\(\\mathrm{S}\\)\uff1a1\u30d3\u30c3\u30c8\u3092\u5360\u6709\u3057\u3001\\(b_{31}\\)\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002</li> <li>\u6307\u6570\u30d3\u30c3\u30c8\\(\\mathrm{E}\\)\uff1a8\u30d3\u30c3\u30c8\u3092\u5360\u6709\u3057\u3001\\(b_{30} b_{29} \\ldots b_{23}\\)\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002</li> <li>\u4eee\u6570\u30d3\u30c3\u30c8\\(\\mathrm{N}\\)\uff1a23\u30d3\u30c3\u30c8\u3092\u5360\u6709\u3057\u3001\\(b_{22} b_{21} \\ldots b_0\\)\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002</li> </ul> <p>\u4e8c\u9032<code>float</code>\u6570\u306e\u5024\u306f\u6b21\u306e\u3088\u3046\u306b\u8a08\u7b97\u3055\u308c\u307e\u3059\uff1a</p> \\[ \\text{val} = (-1)^{b_{31}} \\times 2^{\\left(b_{30} b_{29} \\ldots b_{23}\\right)_2 - 127} \\times \\left(1 . b_{22} b_{21} \\ldots b_0\\right)_2 \\] <p>\u5341\u9032\u516c\u5f0f\u306b\u5909\u63db\u3059\u308b\u3068\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff1a</p> \\[ \\text{val} = (-1)^{\\mathrm{S}} \\times 2^{\\mathrm{E} - 127} \\times (1 + \\mathrm{N}) \\] <p>\u5404\u6210\u5206\u306e\u7bc4\u56f2\u306f\uff1a</p> \\[ \\begin{aligned} \\mathrm{S} \\in &amp; \\{ 0, 1\\}, \\quad \\mathrm{E} \\in \\{ 1, 2, \\dots, 254 \\} \\newline (1 + \\mathrm{N}) = &amp; (1 + \\sum_{i=1}^{23} b_{23-i} \\times 2^{-i}) \\subset [1, 2 - 2^{-23}] \\end{aligned} \\] <p></p> <p> \u56f3 3-5 \u00a0 IEEE 754\u6a19\u6e96\u3067\u306e\u6d6e\u52d5\u5c0f\u6570\u70b9\u6570\u306e\u8a08\u7b97\u4f8b </p> <p>\u4e0a\u306e\u56f3\u3092\u89b3\u5bdf\u3059\u308b\u3068\u3001\u4f8b\u306e\u30c7\u30fc\u30bf\\(\\mathrm{S} = 0\\)\u3001\\(\\mathrm{E} = 124\\)\u3001\\(\\mathrm{N} = 2^{-2} + 2^{-3} = 0.375\\)\u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408\uff1a</p> \\[ \\text{val} = (-1)^0 \\times 2^{124 - 127} \\times (1 + 0.375) = 0.171875 \\] <p>\u3053\u308c\u3067\u6700\u521d\u306e\u8cea\u554f\u306b\u7b54\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\uff1a<code>float</code>\u306e\u8868\u73fe\u306b\u306f\u6307\u6570\u30d3\u30c3\u30c8\u304c\u542b\u307e\u308c\u3066\u3044\u308b\u305f\u3081\u3001<code>int</code>\u3088\u308a\u3082\u306f\u308b\u304b\u306b\u5927\u304d\u3044\u7bc4\u56f2\u3092\u6301\u3061\u307e\u3059\u3002\u4e0a\u8a18\u306e\u8a08\u7b97\u306b\u57fa\u3065\u304f\u3068\u3001<code>float</code>\u3067\u8868\u73fe\u53ef\u80fd\u306a\u6700\u5927\u6b63\u306e\u6570\u306f\u7d04\\(2^{254 - 127} \\times (2 - 2^{-23}) \\approx 3.4 \\times 10^{38}\\)\u3067\u3001\u6700\u5c0f\u8ca0\u306e\u6570\u306f\u7b26\u53f7\u30d3\u30c3\u30c8\u3092\u5207\u308a\u66ff\u3048\u308b\u3053\u3068\u3067\u5f97\u3089\u308c\u307e\u3059\u3002</p> <p>\u3057\u304b\u3057\u3001<code>float</code>\u306e\u62e1\u5f35\u3055\u308c\u305f\u7bc4\u56f2\u306e\u30c8\u30ec\u30fc\u30c9\u30aa\u30d5\u306f\u7cbe\u5ea6\u306e\u72a0\u7272\u3067\u3059\u3002\u6574\u6570\u578b<code>int</code>\u306f32\u30d3\u30c3\u30c8\u3059\u3079\u3066\u3092\u6570\u5024\u8868\u73fe\u306b\u4f7f\u7528\u3057\u3001\u5024\u306f\u5747\u7b49\u306b\u5206\u5e03\u3057\u3066\u3044\u307e\u3059\u304c\u3001\u6307\u6570\u30d3\u30c3\u30c8\u306e\u305f\u3081\u3001<code>float</code>\u306e\u5024\u304c\u5927\u304d\u3044\u307b\u3069\u3001\u96a3\u63a5\u3059\u308b\u6570\u5024\u9593\u306e\u5dee\u304c\u5927\u304d\u304f\u306a\u308a\u307e\u3059\u3002</p> <p>\u4ee5\u4e0b\u306e\u8868\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u6307\u6570\u30d3\u30c3\u30c8\\(\\mathrm{E} = 0\\)\u3068\\(\\mathrm{E} = 255\\)\u306f\u7279\u5225\u306a\u610f\u5473\u3092\u6301\u3061\u30010\u3001\u7121\u9650\u5927\u3001\\(\\mathrm{NaN}\\)\u306a\u3069\u3092\u8868\u73fe\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002</p> <p> \u8868 3-2 \u00a0 \u6307\u6570\u30d3\u30c3\u30c8\u306e\u610f\u5473 </p> \u6307\u6570\u30d3\u30c3\u30c8E \u4eee\u6570\u30d3\u30c3\u30c8\\(\\mathrm{N} = 0\\) \u4eee\u6570\u30d3\u30c3\u30c8\\(\\mathrm{N} \\ne 0\\) \u8a08\u7b97\u516c\u5f0f \\(0\\) \\(\\pm 0\\) \u975e\u6b63\u898f\u5316\u6570 \\((-1)^{\\mathrm{S}} \\times 2^{-126} \\times (0.\\mathrm{N})\\) \\(1, 2, \\dots, 254\\) \u6b63\u898f\u5316\u6570 \u6b63\u898f\u5316\u6570 \\((-1)^{\\mathrm{S}} \\times 2^{(\\mathrm{E} -127)} \\times (1.\\mathrm{N})\\) \\(255\\) \\(\\pm \\infty\\) \\(\\mathrm{NaN}\\) <p>\u975e\u6b63\u898f\u5316\u6570\u306f\u6d6e\u52d5\u5c0f\u6570\u70b9\u6570\u306e\u7cbe\u5ea6\u3092\u5927\u5e45\u306b\u5411\u4e0a\u3055\u305b\u308b\u3053\u3068\u306f\u6ce8\u76ee\u306b\u5024\u3057\u307e\u3059\u3002\u6700\u5c0f\u306e\u6b63\u306e\u6b63\u898f\u5316\u6570\u306f\\(2^{-126}\\)\u3067\u3001\u6700\u5c0f\u306e\u6b63\u306e\u975e\u6b63\u898f\u5316\u6570\u306f\\(2^{-126} \\times 2^{-23}\\)\u3067\u3059\u3002</p> <p>\u500d\u7cbe\u5ea6<code>double</code>\u3082<code>float</code>\u3068\u540c\u69d8\u306e\u8868\u73fe\u65b9\u6cd5\u3092\u4f7f\u7528\u3057\u307e\u3059\u304c\u3001\u7c21\u6f54\u3055\u306e\u305f\u3081\u3053\u3053\u3067\u306f\u8a73\u8ff0\u3057\u307e\u305b\u3093\u3002</p>"},{"location":"chapter_data_structure/summary/","title":"3.5 \u00a0 \u307e\u3068\u3081","text":""},{"location":"chapter_data_structure/summary/#1","title":"1. \u00a0 \u91cd\u8981\u306a\u30dd\u30a4\u30f3\u30c8","text":"<ul> <li>\u30c7\u30fc\u30bf\u69cb\u9020\u306f\u8ad6\u7406\u69cb\u9020\u3068\u7269\u7406\u69cb\u9020\u306e2\u3064\u306e\u89b3\u70b9\u304b\u3089\u5206\u985e\u3067\u304d\u307e\u3059\u3002\u8ad6\u7406\u69cb\u9020\u306f\u30c7\u30fc\u30bf\u9593\u306e\u8ad6\u7406\u7684\u95a2\u4fc2\u3092\u8a18\u8ff0\u3057\u3001\u7269\u7406\u69cb\u9020\u306f\u30c7\u30fc\u30bf\u304c\u30e1\u30e2\u30ea\u306b\u3069\u306e\u3088\u3046\u306b\u683c\u7d0d\u3055\u308c\u308b\u304b\u3092\u8a18\u8ff0\u3057\u307e\u3059\u3002</li> <li>\u3088\u304f\u4f7f\u7528\u3055\u308c\u308b\u8ad6\u7406\u69cb\u9020\u306b\u306f\u3001\u7dda\u5f62\u69cb\u9020\u3001\u6728\u3001\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u304c\u3042\u308a\u307e\u3059\u3002\u901a\u5e38\u3001\u8ad6\u7406\u69cb\u9020\u306b\u57fa\u3065\u3044\u3066\u30c7\u30fc\u30bf\u69cb\u9020\u3092\u7dda\u5f62\uff08\u914d\u5217\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u3001\u30b9\u30bf\u30c3\u30af\u3001\u30ad\u30e5\u30fc\uff09\u3068\u975e\u7dda\u5f62\uff08\u6728\u3001\u30b0\u30e9\u30d5\u3001\u30d2\u30fc\u30d7\uff09\u306b\u5206\u3051\u307e\u3059\u3002\u30cf\u30c3\u30b7\u30e5\u8868\u306e\u5b9f\u88c5\u306f\u7dda\u5f62\u3068\u975e\u7dda\u5f62\u306e\u4e21\u65b9\u306e\u30c7\u30fc\u30bf\u69cb\u9020\u3092\u542b\u3080\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002</li> <li>\u30d7\u30ed\u30b0\u30e9\u30e0\u304c\u5b9f\u884c\u4e2d\u306e\u969b\u3001\u30c7\u30fc\u30bf\u306f\u30e1\u30e2\u30ea\u306b\u683c\u7d0d\u3055\u308c\u307e\u3059\u3002\u5404\u30e1\u30e2\u30ea\u7a7a\u9593\u306b\u306f\u5bfe\u5fdc\u3059\u308b\u30a2\u30c9\u30ec\u30b9\u304c\u3042\u308a\u3001\u30d7\u30ed\u30b0\u30e9\u30e0\u306f\u3053\u308c\u3089\u306e\u30a2\u30c9\u30ec\u30b9\u3092\u901a\u3058\u3066\u30c7\u30fc\u30bf\u306b\u30a2\u30af\u30bb\u30b9\u3057\u307e\u3059\u3002</li> <li>\u7269\u7406\u69cb\u9020\u306f\u9023\u7d9a\u7a7a\u9593\u683c\u7d0d\uff08\u914d\u5217\uff09\u3068\u96e2\u6563\u7a7a\u9593\u683c\u7d0d\uff08\u9023\u7d50\u30ea\u30b9\u30c8\uff09\u306b\u5206\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3059\u3079\u3066\u306e\u30c7\u30fc\u30bf\u69cb\u9020\u306f\u914d\u5217\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u3001\u307e\u305f\u306f\u305d\u306e\u4e21\u65b9\u306e\u7d44\u307f\u5408\u308f\u305b\u3092\u4f7f\u7528\u3057\u3066\u5b9f\u88c5\u3055\u308c\u307e\u3059\u3002</li> <li>\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u306e\u57fa\u672c\u30c7\u30fc\u30bf\u578b\u306b\u306f\u3001\u6574\u6570\uff08<code>byte</code>\u3001<code>short</code>\u3001<code>int</code>\u3001<code>long</code>\uff09\u3001\u6d6e\u52d5\u5c0f\u6570\u70b9\u6570\uff08<code>float</code>\u3001<code>double</code>\uff09\u3001\u6587\u5b57\uff08<code>char</code>\uff09\u3001\u30d6\u30fc\u30eb\u5024\uff08<code>bool</code>\uff09\u304c\u542b\u307e\u308c\u307e\u3059\u3002\u30c7\u30fc\u30bf\u578b\u306e\u5024\u306e\u7bc4\u56f2\u306f\u3001\u305d\u306e\u30b5\u30a4\u30ba\u3068\u8868\u73fe\u306b\u4f9d\u5b58\u3057\u307e\u3059\u3002</li> <li>\u7b26\u53f7\u7d76\u5bfe\u5024\u30011\u306e\u88dc\u6570\u30012\u306e\u88dc\u6570\u306f\u3001\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u3067\u6574\u6570\u3092\u30a8\u30f3\u30b3\u30fc\u30c9\u3059\u308b3\u3064\u306e\u65b9\u6cd5\u3067\u3042\u308a\u3001\u76f8\u4e92\u306b\u5909\u63db\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u7b26\u53f7\u7d76\u5bfe\u5024\u306e\u6700\u4e0a\u4f4d\u30d3\u30c3\u30c8\u306f\u7b26\u53f7\u30d3\u30c3\u30c8\u3067\u3001\u6b8b\u308a\u306e\u30d3\u30c3\u30c8\u306f\u6570\u5024\u306e\u5024\u3092\u8868\u3057\u307e\u3059\u3002</li> <li>\u6574\u6570\u306f\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u30672\u306e\u88dc\u6570\u306b\u3088\u3063\u3066\u30a8\u30f3\u30b3\u30fc\u30c9\u3055\u308c\u307e\u3059\u3002\u3053\u306e\u8868\u73fe\u306e\u5229\u70b9\u306b\u306f\u3001(i)\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u304c\u6b63\u3068\u8ca0\u306e\u6574\u6570\u306e\u52a0\u7b97\u3092\u7d71\u4e00\u3067\u304d\u308b\u3001(ii)\u6e1b\u7b97\u7528\u306e\u7279\u5225\u306a\u30cf\u30fc\u30c9\u30a6\u30a7\u30a2\u56de\u8def\u3092\u8a2d\u8a08\u3059\u308b\u5fc5\u8981\u304c\u306a\u3044\u3001(iii)\u6b63\u3068\u8ca0\u306e0\u306e\u66d6\u6627\u3055\u304c\u306a\u3044\u3001\u304c\u3042\u308a\u307e\u3059\u3002</li> <li>\u6d6e\u52d5\u5c0f\u6570\u70b9\u6570\u306e\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u306f\u30011\u3064\u306e\u7b26\u53f7\u30d3\u30c3\u30c8\u30018\u3064\u306e\u6307\u6570\u30d3\u30c3\u30c8\u300123\u306e\u4eee\u6570\u30d3\u30c3\u30c8\u3067\u69cb\u6210\u3055\u308c\u307e\u3059\u3002\u6307\u6570\u30d3\u30c3\u30c8\u306e\u305f\u3081\u3001\u6d6e\u52d5\u5c0f\u6570\u70b9\u6570\u306e\u7bc4\u56f2\u306f\u6574\u6570\u3088\u308a\u3082\u306f\u308b\u304b\u306b\u5927\u304d\u304f\u306a\u308a\u307e\u3059\u304c\u3001\u7cbe\u5ea6\u3092\u72a0\u7272\u306b\u3057\u307e\u3059\u3002</li> <li>ASCII\u306f\u6700\u521d\u671f\u306e\u82f1\u8a9e\u6587\u5b57\u30bb\u30c3\u30c8\u3067\u30011\u30d0\u30a4\u30c8\u306e\u9577\u3055\u3067\u8a08127\u6587\u5b57\u3067\u3059\u3002GBK\u306f\u4eba\u6c17\u306e\u3042\u308b\u4e2d\u56fd\u8a9e\u6587\u5b57\u30bb\u30c3\u30c8\u3067\u30012\u4e07\u6587\u5b57\u4ee5\u4e0a\u306e\u4e2d\u56fd\u8a9e\u6587\u5b57\u3092\u542b\u307f\u307e\u3059\u3002Unicode\u306f\u4e16\u754c\u306e\u69d8\u3005\u306a\u8a00\u8a9e\u306e\u6587\u5b57\u3092\u542b\u3080\u5b8c\u5168\u306a\u6587\u5b57\u30bb\u30c3\u30c8\u6a19\u6e96\u3092\u63d0\u4f9b\u3059\u308b\u3053\u3068\u3092\u76ee\u7684\u3068\u3057\u3001\u6587\u5b57\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u65b9\u6cd5\u306e\u4e0d\u4e00\u81f4\u306b\u3088\u308b\u6587\u5b57\u5316\u3051\u554f\u984c\u3092\u89e3\u6c7a\u3057\u307e\u3059\u3002</li> <li>UTF-8\u306f\u6700\u3082\u4eba\u6c17\u304c\u3042\u308a\u4e00\u822c\u7684\u306aUnicode\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u65b9\u6cd5\u3067\u3059\u3002\u3053\u308c\u306f\u53ef\u5909\u9577\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u65b9\u6cd5\u3067\u3001\u512a\u308c\u305f\u62e1\u5f35\u6027\u3068\u7a7a\u9593\u52b9\u7387\u3092\u6301\u3061\u307e\u3059\u3002UTF-16\u3068UTF-32\u306f\u56fa\u5b9a\u9577\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u65b9\u6cd5\u3067\u3059\u3002\u4e2d\u56fd\u8a9e\u6587\u5b57\u3092\u30a8\u30f3\u30b3\u30fc\u30c9\u3059\u308b\u969b\u3001UTF-16\u306fUTF-8\u3088\u308a\u3082\u5c11\u306a\u3044\u7a7a\u9593\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002Java\u3084C#\u306a\u3069\u306e\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u306f\u30c7\u30d5\u30a9\u30eb\u30c8\u3067UTF-16\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002</li> </ul>"},{"location":"chapter_data_structure/summary/#2-q-a","title":"2. \u00a0 Q &amp; A","text":"<p>Q: \u306a\u305c\u30cf\u30c3\u30b7\u30e5\u8868\u306f\u7dda\u5f62\u3068\u975e\u7dda\u5f62\u306e\u4e21\u65b9\u306e\u30c7\u30fc\u30bf\u69cb\u9020\u3092\u542b\u3080\u306e\u3067\u3059\u304b\uff1f</p> <p>\u30cf\u30c3\u30b7\u30e5\u8868\u306e\u57fa\u790e\u69cb\u9020\u306f\u914d\u5217\u3067\u3059\u3002\u30cf\u30c3\u30b7\u30e5\u885d\u7a81\u3092\u89e3\u6c7a\u3059\u308b\u305f\u3081\u306b\u3001\u300c\u30c1\u30a7\u30a4\u30f3\u6cd5\u300d\u3092\u4f7f\u7528\u3059\u308b\u5834\u5408\u304c\u3042\u308a\u307e\u3059\uff08\u5f8c\u306e\u7bc0\u300c\u30cf\u30c3\u30b7\u30e5\u885d\u7a81\u300d\u3067\u8aac\u660e\uff09\uff1a\u914d\u5217\u306e\u5404\u30d0\u30b1\u30c3\u30c8\u306f\u9023\u7d50\u30ea\u30b9\u30c8\u3092\u6307\u3057\u3001\u305d\u306e\u9577\u3055\u304c\u7279\u5b9a\u306e\u95be\u5024\u3088\u308a\u5927\u304d\u304f\u306a\u308b\u3068\u6728\uff08\u901a\u5e38\u306f\u8d64\u9ed2\u6728\uff09\u306b\u5909\u63db\u3055\u308c\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002 \u683c\u7d0d\u306e\u89b3\u70b9\u304b\u3089\u3001\u30cf\u30c3\u30b7\u30e5\u8868\u306e\u57fa\u790e\u69cb\u9020\u306f\u914d\u5217\u3067\u3001\u5404\u30d0\u30b1\u30c3\u30c8\u306b\u306f\u5024\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u3001\u307e\u305f\u306f\u6728\u304c\u542b\u307e\u308c\u308b\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u30cf\u30c3\u30b7\u30e5\u8868\u306f\u7dda\u5f62\u30c7\u30fc\u30bf\u69cb\u9020\uff08\u914d\u5217\u3001\u9023\u7d50\u30ea\u30b9\u30c8\uff09\u3068\u975e\u7dda\u5f62\u30c7\u30fc\u30bf\u69cb\u9020\uff08\u6728\uff09\u306e\u4e21\u65b9\u3092\u542b\u3080\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002</p> <p>Q: <code>char</code>\u578b\u306e\u9577\u3055\u306f1\u30d0\u30a4\u30c8\u3067\u3059\u304b\uff1f</p> <p><code>char</code>\u578b\u306e\u9577\u3055\u306f\u3001\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u306e\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u65b9\u6cd5\u306b\u3088\u3063\u3066\u6c7a\u307e\u308a\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001Java\u3001JavaScript\u3001TypeScript\u3001C#\u306f\u3059\u3079\u3066UTF-16\u30a8\u30f3\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\uff08Unicode\u30b3\u30fc\u30c9\u30dd\u30a4\u30f3\u30c8\u3092\u4fdd\u5b58\u3059\u308b\u305f\u3081\uff09\u3092\u4f7f\u7528\u3059\u308b\u305f\u3081\u3001<code>char</code>\u578b\u306e\u9577\u3055\u306f2\u30d0\u30a4\u30c8\u3067\u3059\u3002</p> <p>Q: \u914d\u5217\u30d9\u30fc\u30b9\u306e\u30c7\u30fc\u30bf\u69cb\u9020\u3092\u300c\u9759\u7684\u30c7\u30fc\u30bf\u69cb\u9020\u300d\u3068\u547c\u3076\u3053\u3068\u306b\u66d6\u6627\u3055\u306f\u3042\u308a\u307e\u305b\u3093\u304b\uff1f\u30b9\u30bf\u30c3\u30af\u3082\u30d7\u30c3\u30b7\u30e5\u3084\u30dd\u30c3\u30d7\u306a\u3069\u306e\u300c\u52d5\u7684\u300d\u64cd\u4f5c\u3092\u5b9f\u884c\u3067\u304d\u307e\u3059\u3002</p> <p>\u30b9\u30bf\u30c3\u30af\u306f\u52d5\u7684\u306a\u30c7\u30fc\u30bf\u64cd\u4f5c\u3092\u5b9f\u88c5\u3067\u304d\u307e\u3059\u304c\u3001\u30c7\u30fc\u30bf\u69cb\u9020\u306f\u4f9d\u7136\u3068\u3057\u3066\u300c\u9759\u7684\u300d\u3067\u3059\uff08\u9577\u3055\u304c\u56fa\u5b9a\uff09\u3002\u914d\u5217\u30d9\u30fc\u30b9\u306e\u30c7\u30fc\u30bf\u69cb\u9020\u306f\u52d5\u7684\u306b\u8981\u7d20\u3092\u8ffd\u52a0\u307e\u305f\u306f\u524a\u9664\u3067\u304d\u307e\u3059\u304c\u3001\u305d\u306e\u5bb9\u91cf\u306f\u56fa\u5b9a\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u30b9\u30bf\u30c3\u30af\u30b5\u30a4\u30ba\u304c\u4e8b\u524d\u306b\u5272\u308a\u5f53\u3066\u3089\u308c\u305f\u30b5\u30a4\u30ba\u3092\u8d85\u3048\u308b\u5834\u5408\u3001\u53e4\u3044\u914d\u5217\u306f\u65b0\u3057\u304f\u4f5c\u6210\u3055\u308c\u305f\u3088\u308a\u5927\u304d\u306a\u914d\u5217\u306b\u30b3\u30d4\u30fc\u3055\u308c\u307e\u3059\u3002</p> <p>Q: \u30b9\u30bf\u30c3\u30af\uff08\u30ad\u30e5\u30fc\uff09\u3092\u69cb\u7bc9\u3059\u308b\u969b\u3001\u305d\u306e\u30b5\u30a4\u30ba\u304c\u6307\u5b9a\u3055\u308c\u3066\u3044\u306a\u3044\u306e\u306b\u3001\u306a\u305c\u300c\u9759\u7684\u30c7\u30fc\u30bf\u69cb\u9020\u300d\u306a\u306e\u3067\u3059\u304b\uff1f</p> <p>\u9ad8\u7d1a\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u3067\u306f\u3001\u30b9\u30bf\u30c3\u30af\uff08\u30ad\u30e5\u30fc\uff09\u306e\u521d\u671f\u5bb9\u91cf\u3092\u624b\u52d5\u3067\u6307\u5b9a\u3059\u308b\u5fc5\u8981\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u3053\u306e\u30bf\u30b9\u30af\u306f\u30af\u30e9\u30b9\u5185\u3067\u81ea\u52d5\u7684\u306b\u5b8c\u4e86\u3055\u308c\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001Java\u306e<code>ArrayList</code>\u306e\u521d\u671f\u5bb9\u91cf\u306f\u901a\u5e3810\u3067\u3059\u3002\u3055\u3089\u306b\u3001\u62e1\u5f35\u64cd\u4f5c\u3082\u81ea\u52d5\u7684\u306b\u5b8c\u4e86\u3055\u308c\u307e\u3059\u3002\u8a73\u7d30\u306b\u3064\u3044\u3066\u306f\u3001\u5f8c\u7d9a\u306e\u300c\u30ea\u30b9\u30c8\u300d\u306e\u7ae0\u3092\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044\u3002</p> <p>Q: \u7b26\u53f7\u7d76\u5bfe\u5024\u30922\u306e\u88dc\u6570\u306b\u5909\u63db\u3059\u308b\u65b9\u6cd5\u306f\u300c\u6700\u521d\u306b\u5426\u5b9a\u3057\u3066\u304b\u30891\u3092\u52a0\u3048\u308b\u300d\u3067\u3059\u306e\u3067\u30012\u306e\u88dc\u6570\u3092\u7b26\u53f7\u7d76\u5bfe\u5024\u306b\u5909\u63db\u3059\u308b\u3053\u3068\u306f\u305d\u306e\u9006\u64cd\u4f5c\u300c\u6700\u521d\u306b1\u3092\u6e1b\u7b97\u3057\u3066\u304b\u3089\u5426\u5b9a\u3059\u308b\u300d\u3067\u3042\u308b\u3079\u304d\u3067\u3059\u3002 \u3057\u304b\u3057\u30012\u306e\u88dc\u6570\u3082\u300c\u6700\u521d\u306b\u5426\u5b9a\u3057\u3066\u304b\u30891\u3092\u52a0\u3048\u308b\u300d\u3092\u901a\u3058\u3066\u7b26\u53f7\u7d76\u5bfe\u5024\u306b\u5909\u63db\u3067\u304d\u307e\u3059\u3002\u306a\u305c\u3067\u3059\u304b\uff1f</p> <p>A: \u3053\u308c\u306f\u3001\u7b26\u53f7\u7d76\u5bfe\u5024\u30682\u306e\u88dc\u6570\u9593\u306e\u76f8\u4e92\u5909\u63db\u304c\u300c\u88dc\u6570\u300d\u306e\u8a08\u7b97\u3068\u7b49\u4fa1\u3060\u304b\u3089\u3067\u3059\u3002\u307e\u305a\u88dc\u6570\u3092\u5b9a\u7fa9\u3057\u307e\u3059\uff1a\\(a + b = c\\)\u3068\u4eee\u5b9a\u3059\u308b\u3068\u3001\\(a\\)\u306f\\(b\\)\u306e\\(c\\)\u306b\u5bfe\u3059\u308b\u88dc\u6570\u3068\u8a00\u3044\u3001\u9006\u306b\\(b\\)\u306f\\(a\\)\u306e\\(c\\)\u306b\u5bfe\u3059\u308b\u88dc\u6570\u3068\u8a00\u3044\u307e\u3059\u3002</p> <p>\u9577\u3055\\(n = 4\\)\u306e\u4e8c\u9032\u6570\\(0010\\)\u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408\u3001\u3053\u306e\u6570\u304c\u7b26\u53f7\u7d76\u5bfe\u5024\uff08\u7b26\u53f7\u30d3\u30c3\u30c8\u3092\u7121\u8996\uff09\u306e\u5834\u5408\u3001\u305d\u306e2\u306e\u88dc\u6570\u306f\u300c\u6700\u521d\u306b\u5426\u5b9a\u3057\u3066\u304b\u30891\u3092\u52a0\u3048\u308b\u300d\u3053\u3068\u3067\u5f97\u3089\u308c\u307e\u3059\uff1a</p> \\[ 0010 \\rightarrow 1101 \\rightarrow 1110 \\] <p>\u7b26\u53f7\u7d76\u5bfe\u5024\u30682\u306e\u88dc\u6570\u306e\u548c\u304c\\(0010 + 1110 = 10000\\)\u3067\u3042\u308b\u3053\u3068\u3092\u89b3\u5bdf\u3057\u307e\u3059\u3002\u3064\u307e\u308a\u30012\u306e\u88dc\u6570\\(1110\\)\u306f\u7b26\u53f7\u7d76\u5bfe\u5024\\(0010\\)\u306e\\(10000\\)\u306b\u5bfe\u3059\u308b\u300c\u88dc\u6570\u300d\u3067\u3059\u3002\u3053\u308c\u306f\u3001\u4e0a\u8a18\u306e\u300c\u6700\u521d\u306b\u5426\u5b9a\u3057\u3066\u304b\u30891\u3092\u52a0\u3048\u308b\u300d\u304c\\(10000\\)\u306b\u5bfe\u3059\u308b\u88dc\u6570\u306e\u8a08\u7b97\u3068\u7b49\u4fa1\u3067\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002</p> <p>\u3067\u306f\u3001\\(1110\\)\u306e\\(10000\\)\u306b\u5bfe\u3059\u308b\u300c\u88dc\u6570\u300d\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\uff1f\u300c\u6700\u521d\u306b\u5426\u5b9a\u3057\u3066\u304b\u30891\u3092\u52a0\u3048\u308b\u300d\u3053\u3068\u3067\u8a08\u7b97\u3067\u304d\u307e\u3059\uff1a</p> \\[ 1110 \\rightarrow 0001 \\rightarrow 0010 \\] <p>\u8a00\u3044\u63db\u3048\u308b\u3068\u3001\u7b26\u53f7\u7d76\u5bfe\u5024\u30682\u306e\u88dc\u6570\u306f\u4e92\u3044\u306b\\(10000\\)\u306b\u5bfe\u3059\u308b\u300c\u88dc\u6570\u300d\u3067\u3042\u308b\u305f\u3081\u3001\u300c\u7b26\u53f7\u7d76\u5bfe\u5024\u304b\u30892\u306e\u88dc\u6570\u300d\u3068\u300c2\u306e\u88dc\u6570\u304b\u3089\u7b26\u53f7\u7d76\u5bfe\u5024\u300d\u306f\u540c\u3058\u64cd\u4f5c\uff08\u6700\u521d\u306b\u5426\u5b9a\u3057\u3066\u304b\u30891\u3092\u52a0\u3048\u308b\uff09\u3067\u5b9f\u88c5\u3067\u304d\u307e\u3059\u3002</p> <p>\u3082\u3061\u308d\u3093\u3001\u300c\u6700\u521d\u306b\u5426\u5b9a\u3057\u3066\u304b\u30891\u3092\u52a0\u3048\u308b\u300d\u306e\u9006\u64cd\u4f5c\u3092\u4f7f\u7528\u3057\u30662\u306e\u88dc\u6570\\(1110\\)\u306e\u7b26\u53f7\u7d76\u5bfe\u5024\u3092\u6c42\u3081\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u300c\u6700\u521d\u306b1\u3092\u6e1b\u7b97\u3057\u3066\u304b\u3089\u5426\u5b9a\u3059\u308b\u300d\uff1a</p> \\[ 1110 \\rightarrow 1101 \\rightarrow 0010 \\] <p>\u8981\u7d04\u3059\u308b\u3068\u3001\u300c\u6700\u521d\u306b\u5426\u5b9a\u3057\u3066\u304b\u30891\u3092\u52a0\u3048\u308b\u300d\u3068\u300c\u6700\u521d\u306b1\u3092\u6e1b\u7b97\u3057\u3066\u304b\u3089\u5426\u5b9a\u3059\u308b\u300d\u306f\u4e21\u65b9\u3068\u3082\\(10000\\)\u306b\u5bfe\u3059\u308b\u88dc\u6570\u3092\u8a08\u7b97\u3057\u3066\u304a\u308a\u3001\u7b49\u4fa1\u3067\u3059\u3002</p> <p>\u672c\u8cea\u7684\u306b\u3001\u300c\u5426\u5b9a\u300d\u64cd\u4f5c\u306f\u5b9f\u969b\u306b\u306f\\(1111\\)\u306b\u5bfe\u3059\u308b\u88dc\u6570\u3092\u6c42\u3081\u308b\u3053\u3068\u3067\u3059\uff08<code>\u7b26\u53f7\u7d76\u5bfe\u5024 + 1\u306e\u88dc\u6570 = 1111</code>\u304c\u5e38\u306b\u6210\u308a\u7acb\u3064\u305f\u3081\uff09\u3002\u305d\u3057\u30661\u306e\u88dc\u6570\u306b1\u3092\u52a0\u3048\u308b\u3053\u3068\u306f\\(10000\\)\u306b\u5bfe\u3059\u308b2\u306e\u88dc\u6570\u3068\u7b49\u3057\u304f\u306a\u308a\u307e\u3059\u3002</p> <p>\u4e0a\u8a18\u3067\u306f\\(n = 4\\)\u3092\u4f8b\u306b\u53d6\u308a\u307e\u3057\u305f\u304c\u3001\u4efb\u610f\u306e\u6841\u6570\u306e\u4efb\u610f\u306e\u4e8c\u9032\u6570\u306b\u4e00\u822c\u5316\u3067\u304d\u307e\u3059\u3002</p>"},{"location":"chapter_divide_and_conquer/","title":"\u7b2c 12 \u7ae0 \u00a0 \u5206\u5272\u7d71\u6cbb","text":"<p>Abstract</p> <p>\u56f0\u96e3\u306a\u554f\u984c\u306f\u5c64\u3092\u91cd\u306d\u3066\u5206\u89e3\u3055\u308c\u3001\u5404\u5206\u89e3\u306b\u3088\u3063\u3066\u3088\u308a\u5358\u7d14\u306b\u306a\u308a\u307e\u3059\u3002</p> <p>\u5206\u5272\u7d71\u6cbb\u306f\u6df1\u3044\u771f\u7406\u3092\u660e\u3089\u304b\u306b\u3057\u307e\u3059\uff1a\u5358\u7d14\u3055\u304b\u3089\u59cb\u3081\u308c\u3070\u3001\u8907\u96d1\u3055\u306f\u89e3\u6c7a\u3055\u308c\u308b\u3002</p>"},{"location":"chapter_divide_and_conquer/#_1","title":"\u7ae0\u306e\u5185\u5bb9","text":"<ul> <li>12.1 \u00a0 \u5206\u5272\u7d71\u6cbb\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0</li> <li>12.2 \u00a0 \u5206\u5272\u7d71\u6cbb\u63a2\u7d22\u6226\u7565</li> <li>12.3 \u00a0 \u4e8c\u5206\u6728\u69cb\u7bc9\u554f\u984c</li> <li>12.4 \u00a0 \u30cf\u30ce\u30a4\u306e\u5854\u554f\u984c</li> <li>12.5 \u00a0 \u307e\u3068\u3081</li> </ul>"},{"location":"chapter_divide_and_conquer/binary_search_recur/","title":"12.2 \u00a0 \u5206\u5272\u7d71\u6cbb\u691c\u7d22\u6226\u7565","text":"<p>\u79c1\u305f\u3061\u306f\u691c\u7d22\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u304c\u4e3b\u306b2\u3064\u306e\u30ab\u30c6\u30b4\u30ea\u306b\u5206\u985e\u3055\u308c\u308b\u3053\u3068\u3092\u5b66\u3073\u307e\u3057\u305f\u3002</p> <ul> <li>\u7dcf\u5f53\u305f\u308a\u691c\u7d22\uff1a\u30c7\u30fc\u30bf\u69cb\u9020\u3092\u8d70\u67fb\u3059\u308b\u3053\u3068\u3067\u5b9f\u88c5\u3055\u308c\u3001\u6642\u9593\u8a08\u7b97\u91cf\u306f \\(O(n)\\) \u3067\u3059\u3002</li> <li>\u9069\u5fdc\u691c\u7d22\uff1a\u72ec\u7279\u306a\u30c7\u30fc\u30bf\u7d44\u7e54\u5f62\u5f0f\u3084\u4e8b\u524d\u60c5\u5831\u3092\u5229\u7528\u3057\u3001\u6642\u9593\u8a08\u7b97\u91cf\u306f \\(O(\\log n)\\) \u307e\u305f\u306f \\(O(1)\\) \u306b\u9054\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002</li> </ul> <p>\u5b9f\u969b\u3001\u6642\u9593\u8a08\u7b97\u91cf\u304c \\(O(\\log n)\\) \u306e\u691c\u7d22\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u901a\u5e38\u5206\u5272\u7d71\u6cbb\u6226\u7565\u306b\u57fa\u3065\u3044\u3066\u3044\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u4e8c\u5206\u63a2\u7d22\u3084\u6728\u306a\u3069\u3067\u3059\u3002</p> <ul> <li>\u4e8c\u5206\u63a2\u7d22\u306e\u5404\u30b9\u30c6\u30c3\u30d7\u306f\u3001\u554f\u984c\uff08\u914d\u5217\u5185\u3067\u30bf\u30fc\u30b2\u30c3\u30c8\u8981\u7d20\u3092\u691c\u7d22\u3059\u308b\uff09\u3092\u3088\u308a\u5c0f\u3055\u306a\u554f\u984c\uff08\u914d\u5217\u306e\u534a\u5206\u3067\u30bf\u30fc\u30b2\u30c3\u30c8\u8981\u7d20\u3092\u691c\u7d22\u3059\u308b\uff09\u306b\u5206\u5272\u3057\u3001\u914d\u5217\u304c\u7a7a\u306b\u306a\u308b\u304b\u30bf\u30fc\u30b2\u30c3\u30c8\u8981\u7d20\u304c\u898b\u3064\u304b\u308b\u307e\u3067\u7d9a\u3051\u307e\u3059\u3002</li> <li>\u6728\u306f\u5206\u5272\u7d71\u6cbb\u306e\u30a2\u30a4\u30c7\u30a2\u3092\u8868\u73fe\u3057\u3001\u4e8c\u5206\u63a2\u7d22\u6728\u3001AVL\u6728\u3001\u30d2\u30fc\u30d7\u306a\u3069\u306e\u30c7\u30fc\u30bf\u69cb\u9020\u3067\u306f\u3001\u69d8\u3005\u306a\u64cd\u4f5c\u306e\u6642\u9593\u8a08\u7b97\u91cf\u306f \\(O(\\log n)\\) \u3067\u3059\u3002</li> </ul> <p>\u4e8c\u5206\u63a2\u7d22\u306e\u5206\u5272\u7d71\u6cbb\u6226\u7565\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\u3002</p> <ul> <li>\u554f\u984c\u3092\u5206\u5272\u3067\u304d\u308b\uff1a\u4e8c\u5206\u63a2\u7d22\u306f\u5143\u306e\u554f\u984c\uff08\u914d\u5217\u5185\u3067\u306e\u691c\u7d22\uff09\u3092\u90e8\u5206\u554f\u984c\uff08\u914d\u5217\u306e\u534a\u5206\u3067\u306e\u691c\u7d22\uff09\u306b\u518d\u5e30\u7684\u306b\u5206\u5272\u3057\u3001\u4e2d\u9593\u8981\u7d20\u3068\u30bf\u30fc\u30b2\u30c3\u30c8\u8981\u7d20\u3092\u6bd4\u8f03\u3059\u308b\u3053\u3068\u3067\u5b9f\u73fe\u3055\u308c\u307e\u3059\u3002</li> <li>\u90e8\u5206\u554f\u984c\u306f\u72ec\u7acb\u3057\u3066\u3044\u308b\uff1a\u4e8c\u5206\u63a2\u7d22\u3067\u306f\u3001\u5404\u30e9\u30a6\u30f3\u30c9\u3067\u4e00\u3064\u306e\u90e8\u5206\u554f\u984c\u3092\u51e6\u7406\u3057\u3001\u4ed6\u306e\u90e8\u5206\u554f\u984c\u306b\u5f71\u97ff\u3055\u308c\u307e\u305b\u3093\u3002</li> <li>\u90e8\u5206\u554f\u984c\u306e\u89e3\u3092\u30de\u30fc\u30b8\u3059\u308b\u5fc5\u8981\u304c\u306a\u3044\uff1a\u4e8c\u5206\u63a2\u7d22\u306f\u7279\u5b9a\u306e\u8981\u7d20\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u3092\u76ee\u7684\u3068\u3057\u3066\u3044\u308b\u305f\u3081\u3001\u90e8\u5206\u554f\u984c\u306e\u89e3\u3092\u30de\u30fc\u30b8\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u305b\u3093\u3002\u90e8\u5206\u554f\u984c\u304c\u89e3\u6c7a\u3055\u308c\u308b\u3068\u3001\u5143\u306e\u554f\u984c\u3082\u89e3\u6c7a\u3055\u308c\u307e\u3059\u3002</li> </ul> <p>\u5206\u5272\u7d71\u6cbb\u306f\u691c\u7d22\u52b9\u7387\u3092\u5411\u4e0a\u3055\u305b\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u306a\u305c\u306a\u3089\u3001\u7dcf\u5f53\u305f\u308a\u691c\u7d22\u306f\u30e9\u30a6\u30f3\u30c9\u3054\u3068\u306b1\u3064\u306e\u9078\u629e\u80a2\u3057\u304b\u9664\u53bb\u3067\u304d\u307e\u305b\u3093\u304c\u3001\u5206\u5272\u7d71\u6cbb\u306f\u9078\u629e\u80a2\u306e\u534a\u5206\u3092\u9664\u53bb\u3067\u304d\u308b\u304b\u3089\u3067\u3059\u3002</p>"},{"location":"chapter_divide_and_conquer/binary_search_recur/#1","title":"1. \u00a0 \u5206\u5272\u7d71\u6cbb\u306b\u57fa\u3065\u304f\u4e8c\u5206\u63a2\u7d22\u306e\u5b9f\u88c5","text":"<p>\u524d\u306e\u7ae0\u3067\u306f\u3001\u4e8c\u5206\u63a2\u7d22\u306f\u53cd\u5fa9\u306b\u57fa\u3065\u3044\u3066\u5b9f\u88c5\u3055\u308c\u307e\u3057\u305f\u3002\u4eca\u5ea6\u306f\u3001\u5206\u5272\u7d71\u6cbb\uff08\u518d\u5e30\uff09\u306b\u57fa\u3065\u3044\u3066\u5b9f\u88c5\u3057\u307e\u3059\u3002</p> <p>Question</p> <p>\u9577\u3055 \\(n\\) \u306e\u9806\u5e8f\u4ed8\u3051\u3089\u308c\u305f\u914d\u5217 <code>nums</code> \u304c\u4e0e\u3048\u3089\u308c\u3001\u3059\u3079\u3066\u306e\u8981\u7d20\u304c\u4e00\u610f\u3067\u3042\u308b\u5834\u5408\u3001\u8981\u7d20 <code>target</code> \u3092\u898b\u3064\u3051\u3066\u304f\u3060\u3055\u3044\u3002</p> <p>\u5206\u5272\u7d71\u6cbb\u306e\u89b3\u70b9\u304b\u3089\u3001\u691c\u7d22\u533a\u9593 \\([i, j]\\) \u306b\u5bfe\u5fdc\u3059\u308b\u90e8\u5206\u554f\u984c\u3092 \\(f(i, j)\\) \u3068\u8868\u3057\u307e\u3059\u3002</p> <p>\u5143\u306e\u554f\u984c \\(f(0, n-1)\\) \u304b\u3089\u958b\u59cb\u3057\u3066\u3001\u4ee5\u4e0b\u306e\u30b9\u30c6\u30c3\u30d7\u3067\u4e8c\u5206\u63a2\u7d22\u3092\u5b9f\u884c\u3057\u307e\u3059\u3002</p> <ol> <li>\u691c\u7d22\u533a\u9593 \\([i, j]\\) \u306e\u4e2d\u70b9 \\(m\\) \u3092\u8a08\u7b97\u3057\u3001\u305d\u308c\u3092\u4f7f\u7528\u3057\u3066\u691c\u7d22\u533a\u9593\u306e\u534a\u5206\u3092\u9664\u53bb\u3057\u307e\u3059\u3002</li> <li>\u534a\u5206\u306e\u30b5\u30a4\u30ba\u306b\u7e2e\u5c0f\u3055\u308c\u305f\u90e8\u5206\u554f\u984c\u3092\u518d\u5e30\u7684\u306b\u89e3\u6c7a\u3057\u307e\u3059\u3002\u3053\u308c\u306f \\(f(i, m-1)\\) \u307e\u305f\u306f \\(f(m+1, j)\\) \u306b\u306a\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002</li> <li><code>target</code> \u304c\u898b\u3064\u304b\u308b\u304b\u533a\u9593\u304c\u7a7a\u306b\u306a\u3063\u3066\u30ea\u30bf\u30fc\u30f3\u3059\u308b\u307e\u3067\u3001\u30b9\u30c6\u30c3\u30d7 <code>1.</code> \u3068 <code>2.</code> \u3092\u7e70\u308a\u8fd4\u3057\u307e\u3059\u3002</li> </ol> <p>\u4ee5\u4e0b\u306e\u56f3\u306f\u3001\u914d\u5217\u5185\u3067\u8981\u7d20 \\(6\\) \u3092\u63a2\u3059\u4e8c\u5206\u63a2\u7d22\u306e\u5206\u5272\u7d71\u6cbb\u904e\u7a0b\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002</p> <p></p> <p> \u56f3 12-4 \u00a0 \u4e8c\u5206\u63a2\u7d22\u306e\u5206\u5272\u7d71\u6cbb\u904e\u7a0b </p> <p>\u5b9f\u88c5\u30b3\u30fc\u30c9\u3067\u306f\u3001\u554f\u984c \\(f(i, j)\\) \u3092\u89e3\u6c7a\u3059\u308b\u305f\u3081\u306b\u518d\u5e30\u95a2\u6570 <code>dfs()</code> \u3092\u5ba3\u8a00\u3057\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig binary_search_recur.py<pre><code>def dfs(nums: list[int], target: int, i: int, j: int) -&gt; int:\n    \"\"\"\u4e8c\u5206\u63a2\u7d22\uff1a\u554f\u984c f(i, j)\"\"\"\n    # \u533a\u9593\u304c\u7a7a\u306e\u5834\u5408\u3001\u5bfe\u8c61\u8981\u7d20\u304c\u306a\u3044\u3053\u3068\u3092\u793a\u3059\u305f\u3081\u3001-1 \u3092\u8fd4\u3059\n    if i &gt; j:\n        return -1\n    # \u4e2d\u70b9\u30a4\u30f3\u30c7\u30c3\u30af\u30b9 m \u3092\u8a08\u7b97\n    m = (i + j) // 2\n    if nums[m] &lt; target:\n        # \u518d\u5e30\u90e8\u5206\u554f\u984c f(m+1, j)\n        return dfs(nums, target, m + 1, j)\n    elif nums[m] &gt; target:\n        # \u518d\u5e30\u90e8\u5206\u554f\u984c f(i, m-1)\n        return dfs(nums, target, i, m - 1)\n    else:\n        # \u5bfe\u8c61\u8981\u7d20\u3092\u767a\u898b\u3057\u305f\u305f\u3081\u3001\u305d\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8fd4\u3059\n        return m\n\ndef binary_search(nums: list[int], target: int) -&gt; int:\n    \"\"\"\u4e8c\u5206\u63a2\u7d22\"\"\"\n    n = len(nums)\n    # \u554f\u984c f(0, n-1) \u3092\u89e3\u304f\n    return dfs(nums, target, 0, n - 1)\n</code></pre> binary_search_recur.cpp<pre><code>/* \u4e8c\u5206\u63a2\u7d22\uff1a\u554f\u984c f(i, j) */\nint dfs(vector&lt;int&gt; &amp;nums, int target, int i, int j) {\n    // \u533a\u9593\u304c\u7a7a\u306e\u5834\u5408\u3001\u5bfe\u8c61\u8981\u7d20\u304c\u5b58\u5728\u3057\u306a\u3044\u3053\u3068\u3092\u793a\u3059\u305f\u3081\u3001-1 \u3092\u8fd4\u3059\n    if (i &gt; j) {\n        return -1;\n    }\n    // \u4e2d\u70b9\u30a4\u30f3\u30c7\u30c3\u30af\u30b9 m \u3092\u8a08\u7b97\n    int m = i + (j - i) / 2;\n    if (nums[m] &lt; target) {\n        // \u518d\u5e30\u7684\u306a\u90e8\u5206\u554f\u984c f(m+1, j)\n        return dfs(nums, target, m + 1, j);\n    } else if (nums[m] &gt; target) {\n        // \u518d\u5e30\u7684\u306a\u90e8\u5206\u554f\u984c f(i, m-1)\n        return dfs(nums, target, i, m - 1);\n    } else {\n        // \u5bfe\u8c61\u8981\u7d20\u304c\u898b\u3064\u304b\u3063\u305f\u305f\u3081\u3001\u305d\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8fd4\u3059\n        return m;\n    }\n}\n\n/* \u4e8c\u5206\u63a2\u7d22 */\nint binarySearch(vector&lt;int&gt; &amp;nums, int target) {\n    int n = nums.size();\n    // \u554f\u984c f(0, n-1) \u3092\u89e3\u304f\n    return dfs(nums, target, 0, n - 1);\n}\n</code></pre> binary_search_recur.java<pre><code>/* \u4e8c\u5206\u63a2\u7d22\uff1a\u554f\u984c f(i, j) */\nint dfs(int[] nums, int target, int i, int j) {\n    // \u533a\u9593\u304c\u7a7a\u306e\u5834\u5408\u3001\u5bfe\u8c61\u8981\u7d20\u304c\u5b58\u5728\u3057\u306a\u3044\u3053\u3068\u3092\u793a\u3059\u305f\u3081\u3001-1 \u3092\u8fd4\u3059\n    if (i &gt; j) {\n        return -1;\n    }\n    // \u4e2d\u70b9\u30a4\u30f3\u30c7\u30c3\u30af\u30b9 m \u3092\u8a08\u7b97\n    int m = i + (j - i) / 2;\n    if (nums[m] &lt; target) {\n        // \u518d\u5e30\u7684\u306a\u90e8\u5206\u554f\u984c f(m+1, j)\n        return dfs(nums, target, m + 1, j);\n    } else if (nums[m] &gt; target) {\n        // \u518d\u5e30\u7684\u306a\u90e8\u5206\u554f\u984c f(i, m-1)\n        return dfs(nums, target, i, m - 1);\n    } else {\n        // \u5bfe\u8c61\u8981\u7d20\u304c\u898b\u3064\u304b\u3063\u305f\u305f\u3081\u3001\u305d\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8fd4\u3059\n        return m;\n    }\n}\n\n/* \u4e8c\u5206\u63a2\u7d22 */\nint binarySearch(int[] nums, int target) {\n    int n = nums.length;\n    // \u554f\u984c f(0, n-1) \u3092\u89e3\u304f\n    return dfs(nums, target, 0, n - 1);\n}\n</code></pre> binary_search_recur.cs<pre><code>[class]{binary_search_recur}-[func]{DFS}\n\n[class]{binary_search_recur}-[func]{BinarySearch}\n</code></pre> binary_search_recur.go<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{binarySearch}\n</code></pre> binary_search_recur.swift<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{binarySearch}\n</code></pre> binary_search_recur.js<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{binarySearch}\n</code></pre> binary_search_recur.ts<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{binarySearch}\n</code></pre> binary_search_recur.dart<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{binarySearch}\n</code></pre> binary_search_recur.rs<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{binary_search}\n</code></pre> binary_search_recur.c<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{binarySearch}\n</code></pre> binary_search_recur.kt<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{binarySearch}\n</code></pre> binary_search_recur.rb<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{binary_search}\n</code></pre> binary_search_recur.zig<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{binarySearch}\n</code></pre>"},{"location":"chapter_divide_and_conquer/build_binary_tree_problem/","title":"12.3 \u00a0 \u4e8c\u5206\u6728\u69cb\u7bc9\u554f\u984c","text":"<p>Question</p> <p>\u4e8c\u5206\u6728\u306e\u524d\u9806\u8d70\u67fb <code>preorder</code> \u30b7\u30fc\u30b1\u30f3\u30b9\u3068\u4e2d\u9806\u8d70\u67fb <code>inorder</code> \u30b7\u30fc\u30b1\u30f3\u30b9\u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408\u3001\u4e8c\u5206\u6728\u3092\u69cb\u7bc9\u3057\u3066\u305d\u306e\u30eb\u30fc\u30c8\u30ce\u30fc\u30c9\u3092\u8fd4\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u4e8c\u5206\u6728\u306b\u91cd\u8907\u3059\u308b\u30ce\u30fc\u30c9\u5024\u304c\u306a\u3044\u3068\u4eee\u5b9a\u3057\u307e\u3059\uff08\u4ee5\u4e0b\u306e\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\uff09\u3002</p> <p></p> <p> \u56f3 12-5 \u00a0 \u4e8c\u5206\u6728\u69cb\u7bc9\u306e\u30b5\u30f3\u30d7\u30eb\u30c7\u30fc\u30bf </p>"},{"location":"chapter_divide_and_conquer/build_binary_tree_problem/#1","title":"1. \u00a0 \u5206\u5272\u7d71\u6cbb\u554f\u984c\u304b\u3069\u3046\u304b\u306e\u5224\u5b9a","text":"<p><code>preorder</code> \u3068 <code>inorder</code> \u30b7\u30fc\u30b1\u30f3\u30b9\u304b\u3089\u4e8c\u5206\u6728\u3092\u69cb\u7bc9\u3059\u308b\u5143\u306e\u554f\u984c\u306f\u3001\u5178\u578b\u7684\u306a\u5206\u5272\u7d71\u6cbb\u554f\u984c\u3067\u3059\u3002</p> <ul> <li>\u554f\u984c\u3092\u5206\u89e3\u3067\u304d\u308b\uff1a\u5206\u5272\u7d71\u6cbb\u306e\u89b3\u70b9\u304b\u3089\u3001\u5143\u306e\u554f\u984c\u30922\u3064\u306e\u90e8\u5206\u554f\u984c\uff08\u5de6\u306e\u90e8\u5206\u6728\u306e\u69cb\u7bc9\u3068\u53f3\u306e\u90e8\u5206\u6728\u306e\u69cb\u7bc9\uff09\u3068\u30eb\u30fc\u30c8\u30ce\u30fc\u30c9\u306e\u521d\u671f\u5316\u3068\u3044\u30461\u3064\u306e\u64cd\u4f5c\u306b\u5206\u5272\u3067\u304d\u307e\u3059\u3002\u5404\u90e8\u5206\u6728\uff08\u90e8\u5206\u554f\u984c\uff09\u306b\u3064\u3044\u3066\u3001\u540c\u3058\u30a2\u30d7\u30ed\u30fc\u30c1\u3092\u7d99\u7d9a\u7684\u306b\u9069\u7528\u3057\u3001\u3088\u308a\u5c0f\u3055\u306a\u90e8\u5206\u6728\uff08\u90e8\u5206\u554f\u984c\uff09\u306b\u5206\u5272\u3057\u3001\u6700\u5c0f\u306e\u90e8\u5206\u554f\u984c\uff08\u7a7a\u306e\u90e8\u5206\u6728\uff09\u306b\u5230\u9054\u3059\u308b\u307e\u3067\u7d9a\u3051\u307e\u3059\u3002</li> <li>\u90e8\u5206\u554f\u984c\u306f\u72ec\u7acb\u3057\u3066\u3044\u308b\uff1a\u5de6\u3068\u53f3\u306e\u90e8\u5206\u6728\u306f\u91cd\u8907\u3057\u307e\u305b\u3093\u3002\u5de6\u306e\u90e8\u5206\u6728\u3092\u69cb\u7bc9\u3059\u308b\u969b\u3001\u5de6\u306e\u90e8\u5206\u6728\u306b\u5bfe\u5fdc\u3059\u308b\u4e2d\u9806\u8d70\u67fb\u3068\u524d\u9806\u8d70\u67fb\u306e\u30bb\u30b0\u30e1\u30f3\u30c8\u306e\u307f\u304c\u5fc5\u8981\u3067\u3059\u3002\u53f3\u306e\u90e8\u5206\u6728\u306b\u3082\u540c\u3058\u30a2\u30d7\u30ed\u30fc\u30c1\u304c\u9069\u7528\u3055\u308c\u307e\u3059\u3002</li> <li>\u90e8\u5206\u554f\u984c\u306e\u89e3\u3092\u7d44\u307f\u5408\u308f\u305b\u308b\u3053\u3068\u304c\u3067\u304d\u308b\uff1a\u5de6\u3068\u53f3\u306e\u90e8\u5206\u6728\uff08\u90e8\u5206\u554f\u984c\u306e\u89e3\uff09\u3092\u69cb\u7bc9\u3057\u305f\u3089\u3001\u305d\u308c\u3089\u3092\u30eb\u30fc\u30c8\u30ce\u30fc\u30c9\u306b\u63a5\u7d9a\u3057\u3066\u5143\u306e\u554f\u984c\u306e\u89e3\u3092\u53d6\u5f97\u3067\u304d\u307e\u3059\u3002</li> </ul>"},{"location":"chapter_divide_and_conquer/build_binary_tree_problem/#2","title":"2. \u00a0 \u90e8\u5206\u6728\u306e\u5206\u5272\u65b9\u6cd5","text":"<p>\u4e0a\u8a18\u306e\u5206\u6790\u306b\u57fa\u3065\u3044\u3066\u3001\u3053\u306e\u554f\u984c\u306f\u5206\u5272\u7d71\u6cbb\u3092\u4f7f\u7528\u3057\u3066\u89e3\u6c7a\u3067\u304d\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u524d\u9806\u8d70\u67fb <code>preorder</code> \u30b7\u30fc\u30b1\u30f3\u30b9\u3068\u4e2d\u9806\u8d70\u67fb <code>inorder</code> \u30b7\u30fc\u30b1\u30f3\u30b9\u3092\u4f7f\u7528\u3057\u3066\u5de6\u3068\u53f3\u306e\u90e8\u5206\u6728\u3092\u3069\u306e\u3088\u3046\u306b\u5206\u5272\u3059\u308c\u3070\u3088\u3044\u3067\u3057\u3087\u3046\u304b\uff1f</p> <p>\u5b9a\u7fa9\u306b\u3088\u308a\u3001<code>preorder</code> \u3068 <code>inorder</code> \u30b7\u30fc\u30b1\u30f3\u30b9\u306e\u4e21\u65b9\u30923\u3064\u306e\u90e8\u5206\u306b\u5206\u5272\u3067\u304d\u307e\u3059\uff1a</p> <ul> <li>\u524d\u9806\u8d70\u67fb\uff1a<code>[ \u30eb\u30fc\u30c8 | \u5de6\u306e\u90e8\u5206\u6728 | \u53f3\u306e\u90e8\u5206\u6728 ]</code>\u3002\u4f8b\u3048\u3070\u3001\u56f3\u3067\u306f\u3001\u6728\u306f <code>[ 3 | 9 | 2 1 7 ]</code> \u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002</li> <li>\u4e2d\u9806\u8d70\u67fb\uff1a<code>[ \u5de6\u306e\u90e8\u5206\u6728 | \u30eb\u30fc\u30c8 | \u53f3\u306e\u90e8\u5206\u6728 ]</code>\u3002\u4f8b\u3048\u3070\u3001\u56f3\u3067\u306f\u3001\u6728\u306f <code>[ 9 | 3 | 1 2 7 ]</code> \u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002</li> </ul> <p>\u524d\u306e\u56f3\u306e\u30c7\u30fc\u30bf\u3092\u4f7f\u7528\u3057\u3066\u3001\u6b21\u306e\u56f3\u306b\u793a\u3059\u30b9\u30c6\u30c3\u30d7\u306b\u5f93\u3063\u3066\u5206\u5272\u7d50\u679c\u3092\u53d6\u5f97\u3067\u304d\u307e\u3059\uff1a</p> <ol> <li>\u524d\u9806\u8d70\u67fb\u306e\u6700\u521d\u306e\u8981\u7d203\u304c\u30eb\u30fc\u30c8\u30ce\u30fc\u30c9\u306e\u5024\u3067\u3059\u3002</li> <li><code>inorder</code> \u30b7\u30fc\u30b1\u30f3\u30b9\u5185\u3067\u30eb\u30fc\u30c8\u30ce\u30fc\u30c93\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u898b\u3064\u3051\u3001\u3053\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u4f7f\u7528\u3057\u3066 <code>inorder</code> \u3092 <code>[ 9 | 3 \uff5c 1 2 7 ]</code> \u306b\u5206\u5272\u3057\u307e\u3059\u3002</li> <li><code>inorder</code> \u30b7\u30fc\u30b1\u30f3\u30b9\u306e\u5206\u5272\u306b\u5f93\u3063\u3066\u3001\u5de6\u3068\u53f3\u306e\u90e8\u5206\u6728\u304c\u305d\u308c\u305e\u308c1\u500b\u30683\u500b\u306e\u30ce\u30fc\u30c9\u3092\u542b\u3080\u3053\u3068\u304c\u7c21\u5358\u306b\u6c7a\u5b9a\u3067\u304d\u308b\u305f\u3081\u3001<code>preorder</code> \u30b7\u30fc\u30b1\u30f3\u30b9\u3092 <code>[ 3 | 9 | 2 1 7 ]</code> \u306b\u5bfe\u5fdc\u3057\u3066\u5206\u5272\u3067\u304d\u307e\u3059\u3002</li> </ol> <p></p> <p> \u56f3 12-6 \u00a0 \u524d\u9806\u8d70\u67fb\u3068\u4e2d\u9806\u8d70\u67fb\u3067\u306e\u90e8\u5206\u6728\u306e\u5206\u5272 </p>"},{"location":"chapter_divide_and_conquer/build_binary_tree_problem/#3","title":"3. \u00a0 \u5909\u6570\u306b\u57fa\u3065\u304f\u90e8\u5206\u6728\u7bc4\u56f2\u306e\u8a18\u8ff0","text":"<p>\u4e0a\u8a18\u306e\u5206\u5272\u65b9\u6cd5\u306b\u57fa\u3065\u3044\u3066\u3001<code>preorder</code> \u3068 <code>inorder</code> \u30b7\u30fc\u30b1\u30f3\u30b9\u306b\u304a\u3051\u308b\u30eb\u30fc\u30c8\u3001\u5de6\u306e\u90e8\u5206\u6728\u3001\u53f3\u306e\u90e8\u5206\u6728\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u7bc4\u56f2\u3092\u53d6\u5f97\u3057\u307e\u3057\u305f\u3002\u3053\u308c\u3089\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u7bc4\u56f2\u3092\u8a18\u8ff0\u3059\u308b\u305f\u3081\u306b\u3001\u3044\u304f\u3064\u304b\u306e\u30dd\u30a4\u30f3\u30bf\u5909\u6570\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002</p> <ul> <li>\u73fe\u5728\u306e\u6728\u306e\u30eb\u30fc\u30c8\u30ce\u30fc\u30c9\u306e <code>preorder</code> \u30b7\u30fc\u30b1\u30f3\u30b9\u3067\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092 \\(i\\) \u3068\u3057\u307e\u3059\u3002</li> <li>\u73fe\u5728\u306e\u6728\u306e\u30eb\u30fc\u30c8\u30ce\u30fc\u30c9\u306e <code>inorder</code> \u30b7\u30fc\u30b1\u30f3\u30b9\u3067\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092 \\(m\\) \u3068\u3057\u307e\u3059\u3002</li> <li>\u73fe\u5728\u306e\u6728\u306e <code>inorder</code> \u30b7\u30fc\u30b1\u30f3\u30b9\u3067\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u7bc4\u56f2\u3092 \\([l, r]\\) \u3068\u3057\u307e\u3059\u3002</li> </ul> <p>\u4ee5\u4e0b\u306e\u8868\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u3053\u308c\u3089\u306e\u5909\u6570\u306f <code>preorder</code> \u30b7\u30fc\u30b1\u30f3\u30b9\u3067\u306e\u30eb\u30fc\u30c8\u30ce\u30fc\u30c9\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3068 <code>inorder</code> \u30b7\u30fc\u30b1\u30f3\u30b9\u3067\u306e\u90e8\u5206\u6728\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u7bc4\u56f2\u3092\u8868\u3057\u307e\u3059\u3002</p> <p> \u8868 12-1 \u00a0 \u524d\u9806\u8d70\u67fb\u3068\u4e2d\u9806\u8d70\u67fb\u3067\u306e\u30eb\u30fc\u30c8\u30ce\u30fc\u30c9\u3068\u90e8\u5206\u6728\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9 </p> <code>preorder</code> \u3067\u306e\u30eb\u30fc\u30c8\u30ce\u30fc\u30c9\u30a4\u30f3\u30c7\u30c3\u30af\u30b9 <code>inorder</code> \u3067\u306e\u90e8\u5206\u6728\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u7bc4\u56f2 \u73fe\u5728\u306e\u6728 \\(i\\) \\([l, r]\\) \u5de6\u306e\u90e8\u5206\u6728 \\(i + 1\\) \\([l, m-1]\\) \u53f3\u306e\u90e8\u5206\u6728 \\(i + 1 + (m - l)\\) \\([m+1, r]\\) <p>\u53f3\u306e\u90e8\u5206\u6728\u306e\u30eb\u30fc\u30c8\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306e \\((m-l)\\) \u306f\u300c\u5de6\u306e\u90e8\u5206\u6728\u306e\u30ce\u30fc\u30c9\u6570\u300d\u3092\u8868\u3059\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u3088\u308a\u660e\u78ba\u306a\u7406\u89e3\u306e\u305f\u3081\u306b\u3001\u4ee5\u4e0b\u306e\u56f3\u3092\u53c2\u7167\u3059\u308b\u3053\u3068\u304c\u5f79\u7acb\u3064\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002</p> <p></p> <p> \u56f3 12-7 \u00a0 \u30eb\u30fc\u30c8\u30ce\u30fc\u30c9\u3068\u5de6\u53f3\u306e\u90e8\u5206\u6728\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9 </p>"},{"location":"chapter_divide_and_conquer/build_binary_tree_problem/#4","title":"4. \u00a0 \u30b3\u30fc\u30c9\u5b9f\u88c5","text":"<p>\\(m\\) \u306e\u554f\u3044\u5408\u308f\u305b\u306e\u52b9\u7387\u3092\u5411\u4e0a\u3055\u305b\u308b\u305f\u3081\u306b\u3001\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb <code>hmap</code> \u3092\u4f7f\u7528\u3057\u3066 <code>inorder</code> \u30b7\u30fc\u30b1\u30f3\u30b9\u306e\u8981\u7d20\u304b\u3089\u305d\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3078\u306e\u30de\u30c3\u30d4\u30f3\u30b0\u3092\u683c\u7d0d\u3057\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig build_tree.py<pre><code>def dfs(\n    preorder: list[int],\n    inorder_map: dict[int, int],\n    i: int,\n    l: int,\n    r: int,\n) -&gt; TreeNode | None:\n    \"\"\"\u4e8c\u5206\u6728\u306e\u69cb\u7bc9\uff1a\u5206\u5272\u7d71\u6cbb\"\"\"\n    # \u90e8\u5206\u6728\u306e\u533a\u9593\u304c\u7a7a\u306e\u3068\u304d\u7d42\u4e86\n    if r - l &lt; 0:\n        return None\n    # \u30eb\u30fc\u30c8\u30ce\u30fc\u30c9\u3092\u521d\u671f\u5316\n    root = TreeNode(preorder[i])\n    # m \u3092\u30af\u30a8\u30ea\u3057\u3066\u5de6\u90e8\u5206\u6728\u3068\u53f3\u90e8\u5206\u6728\u3092\u5206\u5272\n    m = inorder_map[preorder[i]]\n    # \u90e8\u5206\u554f\u984c\uff1a\u5de6\u90e8\u5206\u6728\u3092\u69cb\u7bc9\n    root.left = dfs(preorder, inorder_map, i + 1, l, m - 1)\n    # \u90e8\u5206\u554f\u984c\uff1a\u53f3\u90e8\u5206\u6728\u3092\u69cb\u7bc9\n    root.right = dfs(preorder, inorder_map, i + 1 + m - l, m + 1, r)\n    # \u30eb\u30fc\u30c8\u30ce\u30fc\u30c9\u3092\u8fd4\u3059\n    return root\n\ndef build_tree(preorder: list[int], inorder: list[int]) -&gt; TreeNode | None:\n    \"\"\"\u4e8c\u5206\u6728\u3092\u69cb\u7bc9\"\"\"\n    # \u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u3092\u521d\u671f\u5316\u3001\u4e2d\u9806\u8d70\u67fb\u306e\u8981\u7d20\u304b\u3089\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3078\u306e\u30de\u30c3\u30d4\u30f3\u30b0\u3092\u4fdd\u5b58\n    inorder_map = {val: i for i, val in enumerate(inorder)}\n    root = dfs(preorder, inorder_map, 0, 0, len(inorder) - 1)\n    return root\n</code></pre> build_tree.cpp<pre><code>/* \u4e8c\u5206\u6728\u306e\u69cb\u7bc9\uff1a\u5206\u5272\u7d71\u6cbb */\nTreeNode *dfs(vector&lt;int&gt; &amp;preorder, unordered_map&lt;int, int&gt; &amp;inorderMap, int i, int l, int r) {\n    // \u90e8\u5206\u6728\u306e\u533a\u9593\u304c\u7a7a\u306e\u5834\u5408\u306b\u7d42\u4e86\n    if (r - l &lt; 0)\n        return NULL;\n    // \u30eb\u30fc\u30c8\u30ce\u30fc\u30c9\u3092\u521d\u671f\u5316\n    TreeNode *root = new TreeNode(preorder[i]);\n    // m \u3092\u554f\u3044\u5408\u308f\u305b\u3066\u5de6\u53f3\u306e\u90e8\u5206\u6728\u3092\u5206\u5272\n    int m = inorderMap[preorder[i]];\n    // \u90e8\u5206\u554f\u984c\uff1a\u5de6\u306e\u90e8\u5206\u6728\u3092\u69cb\u7bc9\n    root-&gt;left = dfs(preorder, inorderMap, i + 1, l, m - 1);\n    // \u90e8\u5206\u554f\u984c\uff1a\u53f3\u306e\u90e8\u5206\u6728\u3092\u69cb\u7bc9\n    root-&gt;right = dfs(preorder, inorderMap, i + 1 + m - l, m + 1, r);\n    // \u30eb\u30fc\u30c8\u30ce\u30fc\u30c9\u3092\u8fd4\u3059\n    return root;\n}\n\n/* \u4e8c\u5206\u6728\u306e\u69cb\u7bc9 */\nTreeNode *buildTree(vector&lt;int&gt; &amp;preorder, vector&lt;int&gt; &amp;inorder) {\n    // \u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u3092\u521d\u671f\u5316\u3057\u3001\u4e2d\u9593\u9806\u5e8f\u306e\u8981\u7d20\u304b\u3089\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3078\u306e\u30de\u30c3\u30d4\u30f3\u30b0\u3092\u683c\u7d0d\n    unordered_map&lt;int, int&gt; inorderMap;\n    for (int i = 0; i &lt; inorder.size(); i++) {\n        inorderMap[inorder[i]] = i;\n    }\n    TreeNode *root = dfs(preorder, inorderMap, 0, 0, inorder.size() - 1);\n    return root;\n}\n</code></pre> build_tree.java<pre><code>/* \u4e8c\u5206\u6728\u306e\u69cb\u7bc9\uff1a\u5206\u5272\u7d71\u6cbb */\nTreeNode dfs(int[] preorder, Map&lt;Integer, Integer&gt; inorderMap, int i, int l, int r) {\n    // \u90e8\u5206\u6728\u306e\u533a\u9593\u304c\u7a7a\u306e\u5834\u5408\u306b\u7d42\u4e86\n    if (r - l &lt; 0)\n        return null;\n    // \u30eb\u30fc\u30c8\u30ce\u30fc\u30c9\u3092\u521d\u671f\u5316\n    TreeNode root = new TreeNode(preorder[i]);\n    // m \u3092\u554f\u3044\u5408\u308f\u305b\u3066\u5de6\u53f3\u306e\u90e8\u5206\u6728\u3092\u5206\u5272\n    int m = inorderMap.get(preorder[i]);\n    // \u90e8\u5206\u554f\u984c\uff1a\u5de6\u306e\u90e8\u5206\u6728\u3092\u69cb\u7bc9\n    root.left = dfs(preorder, inorderMap, i + 1, l, m - 1);\n    // \u90e8\u5206\u554f\u984c\uff1a\u53f3\u306e\u90e8\u5206\u6728\u3092\u69cb\u7bc9\n    root.right = dfs(preorder, inorderMap, i + 1 + m - l, m + 1, r);\n    // \u30eb\u30fc\u30c8\u30ce\u30fc\u30c9\u3092\u8fd4\u3059\n    return root;\n}\n\n/* \u4e8c\u5206\u6728\u306e\u69cb\u7bc9 */\nTreeNode buildTree(int[] preorder, int[] inorder) {\n    // \u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u3092\u521d\u671f\u5316\u3057\u3001\u4e2d\u9593\u9806\u5e8f\u306e\u8981\u7d20\u304b\u3089\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3078\u306e\u30de\u30c3\u30d4\u30f3\u30b0\u3092\u683c\u7d0d\n    Map&lt;Integer, Integer&gt; inorderMap = new HashMap&lt;&gt;();\n    for (int i = 0; i &lt; inorder.length; i++) {\n        inorderMap.put(inorder[i], i);\n    }\n    TreeNode root = dfs(preorder, inorderMap, 0, 0, inorder.length - 1);\n    return root;\n}\n</code></pre> build_tree.cs<pre><code>[class]{build_tree}-[func]{DFS}\n\n[class]{build_tree}-[func]{BuildTree}\n</code></pre> build_tree.go<pre><code>[class]{}-[func]{dfsBuildTree}\n\n[class]{}-[func]{buildTree}\n</code></pre> build_tree.swift<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{buildTree}\n</code></pre> build_tree.js<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{buildTree}\n</code></pre> build_tree.ts<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{buildTree}\n</code></pre> build_tree.dart<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{buildTree}\n</code></pre> build_tree.rs<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{build_tree}\n</code></pre> build_tree.c<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{buildTree}\n</code></pre> build_tree.kt<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{buildTree}\n</code></pre> build_tree.rb<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{build_tree}\n</code></pre> build_tree.zig<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{buildTree}\n</code></pre> <p>\u4ee5\u4e0b\u306e\u56f3\u306f\u3001\u4e8c\u5206\u6728\u3092\u69cb\u7bc9\u3059\u308b\u518d\u5e30\u904e\u7a0b\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002\u5404\u30ce\u30fc\u30c9\u306f\u518d\u5e30\u306e\u300c\u4e0b\u964d\u300d\u6bb5\u968e\u3067\u4f5c\u6210\u3055\u308c\u3001\u5404\u30a8\u30c3\u30b8\uff08\u53c2\u7167\uff09\u306f\u300c\u4e0a\u6607\u300d\u6bb5\u968e\u3067\u5f62\u6210\u3055\u308c\u307e\u3059\u3002</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> \u56f3 12-8 \u00a0 \u4e8c\u5206\u6728\u69cb\u7bc9\u306e\u518d\u5e30\u904e\u7a0b </p> <p>\u5404\u518d\u5e30\u95a2\u6570\u306e <code>preorder</code> \u3068 <code>inorder</code> \u30b7\u30fc\u30b1\u30f3\u30b9\u306e\u5206\u5272\u306f\u4ee5\u4e0b\u306e\u56f3\u306b\u793a\u3055\u308c\u3066\u3044\u307e\u3059\u3002</p> <p></p> <p> \u56f3 12-9 \u00a0 \u5404\u518d\u5e30\u95a2\u6570\u3067\u306e\u5206\u5272 </p> <p>\u4e8c\u5206\u6728\u304c \\(n\\) \u500b\u306e\u30ce\u30fc\u30c9\u3092\u6301\u3064\u3068\u4eee\u5b9a\u3059\u308b\u3068\u3001\u5404\u30ce\u30fc\u30c9\u306e\u521d\u671f\u5316\uff08\u518d\u5e30\u95a2\u6570 <code>dfs()</code> \u306e\u547c\u3073\u51fa\u3057\uff09\u306b\u306f \\(O(1)\\) \u6642\u9593\u304c\u304b\u304b\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u5168\u4f53\u306e\u6642\u9593\u8a08\u7b97\u91cf\u306f \\(O(n)\\) \u3067\u3059\u3002</p> <p>\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u306f <code>inorder</code> \u8981\u7d20\u304b\u3089\u305d\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3078\u306e\u30de\u30c3\u30d4\u30f3\u30b0\u3092\u683c\u7d0d\u3059\u308b\u305f\u3081\u3001\\(O(n)\\) \u30b9\u30da\u30fc\u30b9\u304c\u5fc5\u8981\u3067\u3059\u3002\u6700\u60aa\u306e\u5834\u5408\u3001\u4e8c\u5206\u6728\u304c\u9023\u7d50\u30ea\u30b9\u30c8\u306b\u9000\u5316\u3059\u308b\u3068\u3001\u518d\u5e30\u306e\u6df1\u3055\u306f \\(n\\) \u306b\u9054\u3057\u3001\\(O(n)\\) \u306e\u30b9\u30bf\u30c3\u30af\u30b9\u30da\u30fc\u30b9\u3092\u6d88\u8cbb\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u5168\u4f53\u306e\u7a7a\u9593\u8a08\u7b97\u91cf\u306f \\(O(n)\\) \u3067\u3059\u3002</p>"},{"location":"chapter_divide_and_conquer/divide_and_conquer/","title":"12.1 \u00a0 \u5206\u5272\u7d71\u6cbb\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0","text":"<p>\u5206\u5272\u7d71\u6cbb\u306f\u91cd\u8981\u3067\u4eba\u6c17\u306e\u3042\u308b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u6226\u7565\u3067\u3059\u3002\u540d\u524d\u304c\u793a\u3059\u3088\u3046\u306b\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u901a\u5e38\u518d\u5e30\u7684\u306b\u5b9f\u88c5\u3055\u308c\u3001\u300c\u5206\u5272\u300d\u3068\u300c\u7d71\u6cbb\u300d\u306e2\u3064\u306e\u30b9\u30c6\u30c3\u30d7\u304b\u3089\u69cb\u6210\u3055\u308c\u307e\u3059\u3002</p> <ol> <li>\u5206\u5272\uff08\u5206\u5272\u6bb5\u968e\uff09\uff1a\u5143\u306e\u554f\u984c\u3092\u518d\u5e30\u7684\u306b2\u3064\u4ee5\u4e0a\u306e\u5c0f\u3055\u306a\u90e8\u5206\u554f\u984c\u306b\u5206\u89e3\u3057\u3001\u6700\u5c0f\u306e\u90e8\u5206\u554f\u984c\u306b\u5230\u9054\u3059\u308b\u307e\u3067\u7d9a\u3051\u307e\u3059\u3002</li> <li>\u7d71\u6cbb\uff08\u30de\u30fc\u30b8\u6bb5\u968e\uff09\uff1a\u89e3\u6c7a\u65b9\u6cd5\u304c\u65e2\u77e5\u306e\u6700\u5c0f\u306e\u90e8\u5206\u554f\u984c\u304b\u3089\u958b\u59cb\u3057\u3001\u90e8\u5206\u554f\u984c\u306e\u89e3\u3092\u30dc\u30c8\u30e0\u30a2\u30c3\u30d7\u65b9\u5f0f\u3067\u30de\u30fc\u30b8\u3057\u3066\u5143\u306e\u554f\u984c\u306e\u89e3\u3092\u69cb\u7bc9\u3057\u307e\u3059\u3002</li> </ol> <p>\u4ee5\u4e0b\u306e\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u300c\u30de\u30fc\u30b8\u30bd\u30fc\u30c8\u300d\u306f\u5206\u5272\u7d71\u6cbb\u6226\u7565\u306e\u5178\u578b\u7684\u306a\u5fdc\u7528\u306e\u4e00\u3064\u3067\u3059\u3002</p> <ol> <li>\u5206\u5272\uff1a\u5143\u306e\u914d\u5217\uff08\u5143\u306e\u554f\u984c\uff09\u3092\u518d\u5e30\u7684\u306b2\u3064\u306e\u526f\u914d\u5217\uff08\u90e8\u5206\u554f\u984c\uff09\u306b\u5206\u5272\u3057\u3001\u526f\u914d\u5217\u304c1\u3064\u306e\u8981\u7d20\u306e\u307f\u306b\u306a\u308b\u307e\u3067\uff08\u6700\u5c0f\u306e\u90e8\u5206\u554f\u984c\uff09\u7d9a\u3051\u307e\u3059\u3002</li> <li>\u7d71\u6cbb\uff1a\u9806\u5e8f\u4ed8\u3051\u3089\u308c\u305f\u526f\u914d\u5217\uff08\u90e8\u5206\u554f\u984c\u306e\u89e3\uff09\u3092\u30dc\u30c8\u30e0\u30a2\u30c3\u30d7\u3067\u30de\u30fc\u30b8\u3057\u3066\u3001\u9806\u5e8f\u4ed8\u3051\u3089\u308c\u305f\u5143\u306e\u914d\u5217\uff08\u5143\u306e\u554f\u984c\u306e\u89e3\uff09\u3092\u53d6\u5f97\u3057\u307e\u3059\u3002</li> </ol> <p></p> <p> \u56f3 12-1 \u00a0 \u30de\u30fc\u30b8\u30bd\u30fc\u30c8\u306e\u5206\u5272\u7d71\u6cbb\u6226\u7565 </p>"},{"location":"chapter_divide_and_conquer/divide_and_conquer/#1211","title":"12.1.1 \u00a0 \u5206\u5272\u7d71\u6cbb\u554f\u984c\u3092\u7279\u5b9a\u3059\u308b\u65b9\u6cd5","text":"<p>\u554f\u984c\u304c\u5206\u5272\u7d71\u6cbb\u89e3\u6c7a\u306b\u9069\u3057\u3066\u3044\u308b\u304b\u3069\u3046\u304b\u306f\u3001\u901a\u5e38\u4ee5\u4e0b\u306e\u57fa\u6e96\u306b\u57fa\u3065\u3044\u3066\u6c7a\u5b9a\u3067\u304d\u307e\u3059\u3002</p> <ol> <li>\u554f\u984c\u3092\u3088\u308a\u5c0f\u3055\u306a\u3082\u306e\u306b\u5206\u89e3\u3067\u304d\u308b\uff1a\u5143\u306e\u554f\u984c\u3092\u3088\u308a\u5c0f\u3055\u304f\u985e\u4f3c\u3057\u305f\u90e8\u5206\u554f\u984c\u306b\u5206\u5272\u3067\u304d\u3001\u305d\u306e\u3088\u3046\u306a\u904e\u7a0b\u3092\u540c\u3058\u65b9\u6cd5\u3067\u518d\u5e30\u7684\u306b\u5b9f\u884c\u3067\u304d\u307e\u3059\u3002</li> <li>\u90e8\u5206\u554f\u984c\u306f\u72ec\u7acb\u3057\u3066\u3044\u308b\uff1a\u90e8\u5206\u554f\u984c\u9593\u306b\u91cd\u8907\u304c\u306a\u304f\u3001\u72ec\u7acb\u3057\u3066\u304a\u308a\u3001\u500b\u5225\u306b\u89e3\u6c7a\u3067\u304d\u307e\u3059\u3002</li> <li>\u90e8\u5206\u554f\u984c\u306e\u89e3\u3092\u30de\u30fc\u30b8\u3067\u304d\u308b\uff1a\u5143\u306e\u554f\u984c\u306e\u89e3\u306f\u3001\u90e8\u5206\u554f\u984c\u306e\u89e3\u3092\u7d44\u307f\u5408\u308f\u305b\u308b\u3053\u3068\u3067\u5c0e\u51fa\u3055\u308c\u307e\u3059\u3002</li> </ol> <p>\u660e\u3089\u304b\u306b\u3001\u30de\u30fc\u30b8\u30bd\u30fc\u30c8\u306f\u3053\u308c\u30893\u3064\u306e\u57fa\u6e96\u3092\u6e80\u305f\u3057\u3066\u3044\u307e\u3059\u3002</p> <ol> <li>\u554f\u984c\u3092\u3088\u308a\u5c0f\u3055\u306a\u3082\u306e\u306b\u5206\u89e3\u3067\u304d\u308b\uff1a\u914d\u5217\uff08\u5143\u306e\u554f\u984c\uff09\u3092\u518d\u5e30\u7684\u306b2\u3064\u306e\u526f\u914d\u5217\uff08\u90e8\u5206\u554f\u984c\uff09\u306b\u5206\u5272\u3057\u307e\u3059\u3002</li> <li>\u90e8\u5206\u554f\u984c\u306f\u72ec\u7acb\u3057\u3066\u3044\u308b\uff1a\u5404\u526f\u914d\u5217\u306f\u72ec\u7acb\u3057\u3066\u30bd\u30fc\u30c8\u3067\u304d\u307e\u3059\uff08\u90e8\u5206\u554f\u984c\u306f\u72ec\u7acb\u3057\u3066\u89e3\u6c7a\u3067\u304d\u307e\u3059\uff09\u3002</li> <li>\u90e8\u5206\u554f\u984c\u306e\u89e3\u3092\u30de\u30fc\u30b8\u3067\u304d\u308b\uff1a2\u3064\u306e\u9806\u5e8f\u4ed8\u3051\u3089\u308c\u305f\u526f\u914d\u5217\uff08\u90e8\u5206\u554f\u984c\u306e\u89e3\uff09\u30921\u3064\u306e\u9806\u5e8f\u4ed8\u3051\u3089\u308c\u305f\u914d\u5217\uff08\u5143\u306e\u554f\u984c\u306e\u89e3\uff09\u306b\u30de\u30fc\u30b8\u3067\u304d\u307e\u3059\u3002</li> </ol>"},{"location":"chapter_divide_and_conquer/divide_and_conquer/#1212","title":"12.1.2 \u00a0 \u5206\u5272\u7d71\u6cbb\u306b\u3088\u308b\u52b9\u7387\u306e\u5411\u4e0a","text":"<p>\u5206\u5272\u7d71\u6cbb\u6226\u7565\u306f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u554f\u984c\u3092\u52b9\u679c\u7684\u306b\u89e3\u6c7a\u3059\u308b\u3060\u3051\u3067\u306a\u304f\u3001\u3057\u3070\u3057\u3070\u52b9\u7387\u3092\u5411\u4e0a\u3055\u305b\u307e\u3059\u3002\u30bd\u30fc\u30c8\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u306f\u3001\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u3001\u30de\u30fc\u30b8\u30bd\u30fc\u30c8\u3001\u30d2\u30fc\u30d7\u30bd\u30fc\u30c8\u306f\u3001\u5206\u5272\u7d71\u6cbb\u6226\u7565\u3092\u9069\u7528\u3057\u3066\u3044\u308b\u305f\u3081\u3001\u9078\u629e\u30bd\u30fc\u30c8\u3001\u30d0\u30d6\u30eb\u30bd\u30fc\u30c8\u3001\u633f\u5165\u30bd\u30fc\u30c8\u3088\u308a\u3082\u9ad8\u901f\u3067\u3059\u3002</p> <p>\u79c1\u305f\u3061\u306e\u5fc3\u306b\u306f\u7591\u554f\u304c\u3042\u308b\u304b\u3082\u3057\u308c\u307e\u305b\u3093\uff1a\u306a\u305c\u5206\u5272\u7d71\u6cbb\u306f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u52b9\u7387\u3092\u5411\u4e0a\u3055\u305b\u308b\u3053\u3068\u304c\u3067\u304d\u3001\u305d\u306e\u6839\u672c\u7684\u306a\u8ad6\u7406\u306f\u4f55\u3067\u3059\u304b\uff1f \u3064\u307e\u308a\u3001\u554f\u984c\u3092\u90e8\u5206\u554f\u984c\u306b\u5206\u89e3\u3057\u3001\u305d\u308c\u3089\u3092\u89e3\u6c7a\u3057\u3001\u305d\u308c\u3089\u306e\u89e3\u3092\u7d44\u307f\u5408\u308f\u305b\u3066\u5143\u306e\u554f\u984c\u306b\u5bfe\u51e6\u3059\u308b\u3053\u3068\u304c\u3001\u5143\u306e\u554f\u984c\u3092\u76f4\u63a5\u89e3\u6c7a\u3059\u308b\u3088\u308a\u3082\u52b9\u7387\u7684\u3067\u3042\u308b\u7406\u7531\u306f\u4f55\u3067\u3059\u304b\uff1f\u3053\u306e\u8cea\u554f\u306f2\u3064\u306e\u5074\u9762\u304b\u3089\u5206\u6790\u3067\u304d\u307e\u3059\uff1a\u64cd\u4f5c\u6570\u3068\u4e26\u5217\u8a08\u7b97\u3002</p>"},{"location":"chapter_divide_and_conquer/divide_and_conquer/#1","title":"1. \u00a0 \u64cd\u4f5c\u6570\u306e\u6700\u9069\u5316","text":"<p>\u300c\u30d0\u30d6\u30eb\u30bd\u30fc\u30c8\u300d\u3092\u4f8b\u306b\u3068\u308b\u3068\u3001\u9577\u3055 \\(n\\) \u306e\u914d\u5217\u3092\u51e6\u7406\u3059\u308b\u306e\u306b \\(O(n^2)\\) \u6642\u9593\u304c\u5fc5\u8981\u3067\u3059\u3002\u4ee5\u4e0b\u306e\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u914d\u5217\u3092\u4e2d\u70b9\u304b\u30892\u3064\u306e\u526f\u914d\u5217\u306b\u5206\u5272\u3059\u308b\u3068\u3057\u307e\u3059\u3002\u305d\u306e\u3088\u3046\u306a\u5206\u5272\u306b\u306f \\(O(n)\\) \u6642\u9593\u304c\u5fc5\u8981\u3067\u3059\u3002\u5404\u526f\u914d\u5217\u306e\u30bd\u30fc\u30c8\u306b\u306f \\(O((n / 2)^2)\\) \u6642\u9593\u304c\u5fc5\u8981\u3067\u3059\u3002\u305d\u3057\u30662\u3064\u306e\u526f\u914d\u5217\u306e\u30de\u30fc\u30b8\u306b\u306f \\(O(n)\\) \u6642\u9593\u304c\u5fc5\u8981\u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u5168\u4f53\u306e\u6642\u9593\u8a08\u7b97\u91cf\u306f\uff1a</p> \\[ O(n + (\\frac{n}{2})^2 \\times 2 + n) = O(\\frac{n^2}{2} + 2n) \\] <p></p> <p> \u56f3 12-2 \u00a0 \u914d\u5217\u5206\u5272\u524d\u5f8c\u306e\u30d0\u30d6\u30eb\u30bd\u30fc\u30c8 </p> <p>\u4ee5\u4e0b\u306e\u4e0d\u7b49\u5f0f\u3092\u8a08\u7b97\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u5de6\u5074\u306f\u5206\u5272\u524d\u306e\u7dcf\u64cd\u4f5c\u6570\u3092\u8868\u3057\u3001\u53f3\u5074\u306f\u5206\u5272\u5f8c\u306e\u7dcf\u64cd\u4f5c\u6570\u3092\u305d\u308c\u305e\u308c\u8868\u3057\u307e\u3059\uff1a</p> \\[ \\begin{aligned} n^2 &amp; &gt; \\frac{n^2}{2} + 2n \\newline n^2 - \\frac{n^2}{2} - 2n &amp; &gt; 0 \\newline n(n - 4) &amp; &gt; 0 \\end{aligned} \\] <p>\u3053\u308c\u306f \\(n &gt; 4\\) \u306e\u5834\u5408\u3001\u5206\u5272\u5f8c\u306e\u64cd\u4f5c\u6570\u304c\u5c11\u306a\u304f\u3001\u3088\u308a\u826f\u3044\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u306b\u3064\u306a\u304c\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002\u5206\u5272\u5f8c\u306e\u6642\u9593\u8a08\u7b97\u91cf\u306f\u4f9d\u7136\u3068\u3057\u3066\u4e8c\u6b21 \\(O(n^2)\\) \u3067\u3059\u304c\u3001\u8a08\u7b97\u91cf\u306e\u5b9a\u6570\u4fc2\u6570\u304c\u6e1b\u5c11\u3057\u3066\u3044\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002</p> <p>\u3055\u3089\u306b\u9032\u3080\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u526f\u914d\u5217\u3092\u305d\u306e\u4e2d\u70b9\u304b\u3089\u3055\u3089\u306b2\u3064\u306e\u526f\u914d\u5217\u306b\u5206\u5272\u3057\u7d9a\u3051\u3066\u3001\u526f\u914d\u5217\u304c1\u3064\u306e\u8981\u7d20\u306e\u307f\u306b\u306a\u308b\u307e\u3067\u7d9a\u3051\u305f\u3089\u3069\u3046\u3067\u3057\u3087\u3046\u304b\uff1f \u3053\u306e\u30a2\u30a4\u30c7\u30a2\u306f\u5b9f\u969b\u306b\u306f\u300c\u30de\u30fc\u30b8\u30bd\u30fc\u30c8\u300d\u3067\u3001\u6642\u9593\u8a08\u7b97\u91cf\u306f \\(O(n \\log n)\\) \u3067\u3059\u3002</p> <p>\u5c11\u3057\u9055\u3046\u3053\u3068\u3092\u8a66\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u30022\u3064\u3067\u306f\u306a\u304f\u3001\u3088\u308a\u591a\u304f\u306e\u5206\u5272\u306b\u5206\u5272\u3057\u305f\u3089\u3069\u3046\u3067\u3057\u3087\u3046\u304b\uff1f \u4f8b\u3048\u3070\u3001\u5143\u306e\u914d\u5217\u3092 \\(k\\) \u500b\u306e\u526f\u914d\u5217\u306b\u5747\u7b49\u306b\u5206\u5272\u3057\u307e\u3059\u304b\uff1f\u3053\u306e\u30a2\u30d7\u30ed\u30fc\u30c1\u306f\u300c\u30d0\u30b1\u30c3\u30c8\u30bd\u30fc\u30c8\u300d\u3068\u975e\u5e38\u306b\u4f3c\u3066\u304a\u308a\u3001\u5927\u91cf\u306e\u30c7\u30fc\u30bf\u306e\u30bd\u30fc\u30c8\u306b\u975e\u5e38\u306b\u9069\u3057\u3066\u3044\u307e\u3059\u3002\u7406\u8ad6\u7684\u306b\u306f\u3001\u6642\u9593\u8a08\u7b97\u91cf\u306f \\(O(n + k)\\) \u306b\u9054\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002</p>"},{"location":"chapter_divide_and_conquer/divide_and_conquer/#2","title":"2. \u00a0 \u4e26\u5217\u8a08\u7b97\u306b\u3088\u308b\u6700\u9069\u5316","text":"<p>\u5206\u5272\u7d71\u6cbb\u306b\u3088\u3063\u3066\u751f\u6210\u3055\u308c\u308b\u90e8\u5206\u554f\u984c\u306f\u4e92\u3044\u306b\u72ec\u7acb\u3057\u3066\u3044\u308b\u3053\u3068\u304c\u5206\u304b\u3063\u3066\u3044\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u305d\u308c\u3089\u3092\u4e26\u5217\u3067\u89e3\u6c7a\u3067\u304d\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002 \u305d\u306e\u7d50\u679c\u3001\u5206\u5272\u7d71\u6cbb\u306f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u6642\u9593\u8a08\u7b97\u91cf\u3092\u6e1b\u3089\u3059\u3060\u3051\u3067\u306a\u304f\u3001\u73fe\u4ee3\u306e\u30aa\u30da\u30ec\u30fc\u30c6\u30a3\u30f3\u30b0\u30b7\u30b9\u30c6\u30e0\u306b\u3088\u308b\u4e26\u5217\u6700\u9069\u5316\u3082\u4fc3\u9032\u3057\u307e\u3059\u3002</p> <p>\u4e26\u5217\u6700\u9069\u5316\u306f\u3001\u8907\u6570\u306e\u30b3\u30a2\u3084\u30d7\u30ed\u30bb\u30c3\u30b5\u3092\u6301\u3064\u74b0\u5883\u3067\u7279\u306b\u52b9\u679c\u7684\u3067\u3059\u3002\u30b7\u30b9\u30c6\u30e0\u304c\u8907\u6570\u306e\u90e8\u5206\u554f\u984c\u3092\u540c\u6642\u306b\u51e6\u7406\u3067\u304d\u308b\u305f\u3081\u3001\u8a08\u7b97\u30ea\u30bd\u30fc\u30b9\u3092\u5b8c\u5168\u306b\u6d3b\u7528\u3057\u3001\u5168\u4f53\u7684\u306a\u5b9f\u884c\u6642\u9593\u304c\u5927\u5e45\u306b\u77ed\u7e2e\u3055\u308c\u307e\u3059\u3002</p> <p>\u4f8b\u3048\u3070\u3001\u4ee5\u4e0b\u306e\u56f3\u306b\u793a\u3059\u300c\u30d0\u30b1\u30c3\u30c8\u30bd\u30fc\u30c8\u300d\u3067\u306f\u3001\u5927\u91cf\u306e\u30c7\u30fc\u30bf\u3092\u69d8\u3005\u306a\u30d0\u30b1\u30c3\u30c8\u306b\u5747\u7b49\u306b\u5206\u89e3\u3057\u307e\u3059\u3002\u5404\u30d0\u30b1\u30c3\u30c8\u306e\u30bd\u30fc\u30c8\u4f5c\u696d\u306f\u3001\u5229\u7528\u53ef\u80fd\u306a\u8a08\u7b97\u30e6\u30cb\u30c3\u30c8\u306b\u5272\u308a\u5f53\u3066\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3059\u3079\u3066\u306e\u4f5c\u696d\u304c\u5b8c\u4e86\u3059\u308b\u3068\u3001\u3059\u3079\u3066\u306e\u30bd\u30fc\u30c8\u3055\u308c\u305f\u30d0\u30b1\u30c3\u30c8\u304c\u30de\u30fc\u30b8\u3055\u308c\u3066\u6700\u7d42\u7d50\u679c\u304c\u751f\u6210\u3055\u308c\u307e\u3059\u3002</p> <p></p> <p> \u56f3 12-3 \u00a0 \u30d0\u30b1\u30c3\u30c8\u30bd\u30fc\u30c8\u306e\u4e26\u5217\u8a08\u7b97 </p>"},{"location":"chapter_divide_and_conquer/divide_and_conquer/#1213","title":"12.1.3 \u00a0 \u5206\u5272\u7d71\u6cbb\u306e\u4e00\u822c\u7684\u306a\u5fdc\u7528","text":"<p>\u5206\u5272\u7d71\u6cbb\u306f\u591a\u304f\u306e\u53e4\u5178\u7684\u306a\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u554f\u984c\u3092\u89e3\u6c7a\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002</p> <ul> <li>\u6700\u8fd1\u70b9\u5bfe\u306e\u767a\u898b\uff1a\u3053\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u70b9\u306e\u96c6\u5408\u30922\u3064\u306e\u534a\u5206\u306b\u5206\u5272\u3059\u308b\u3053\u3068\u3067\u52d5\u4f5c\u3057\u307e\u3059\u3002\u305d\u3057\u3066\u5404\u534a\u5206\u3067\u518d\u5e30\u7684\u306b\u6700\u8fd1\u70b9\u5bfe\u3092\u898b\u3064\u3051\u307e\u3059\u3002\u6700\u5f8c\u306b\u30012\u3064\u306e\u534a\u5206\u306b\u307e\u305f\u304c\u308b\u30da\u30a2\u3092\u8003\u616e\u3057\u3066\u3001\u5168\u4f53\u306e\u6700\u8fd1\u70b9\u5bfe\u3092\u898b\u3064\u3051\u307e\u3059\u3002</li> <li>\u5927\u6574\u6570\u306e\u4e57\u7b97\uff1a\u4e00\u3064\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306fKaratsuba\u3068\u547c\u3070\u308c\u307e\u3059\u3002\u5927\u6574\u6570\u306e\u4e57\u7b97\u3092\u3044\u304f\u3064\u304b\u306e\u5c0f\u3055\u306a\u6574\u6570\u306e\u4e57\u7b97\u3068\u52a0\u7b97\u306b\u5206\u89e3\u3057\u307e\u3059\u3002</li> <li>\u884c\u5217\u306e\u4e57\u7b97\uff1a\u4e00\u4f8b\u306fStrassen\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u3059\u3002\u5927\u304d\u306a\u884c\u5217\u306e\u4e57\u7b97\u3092\u8907\u6570\u306e\u5c0f\u3055\u306a\u884c\u5217\u306e\u4e57\u7b97\u3068\u52a0\u7b97\u306b\u5206\u89e3\u3057\u307e\u3059\u3002</li> <li>\u30cf\u30ce\u30a4\u306e\u5854\u554f\u984c\uff1a\u30cf\u30ce\u30a4\u306e\u5854\u554f\u984c\u306f\u518d\u5e30\u7684\u306b\u89e3\u6c7a\u3067\u304d\u3001\u5206\u5272\u7d71\u6cbb\u6226\u7565\u306e\u5178\u578b\u7684\u306a\u5fdc\u7528\u3067\u3059\u3002</li> <li>\u8ee2\u5012\u5bfe\u306e\u89e3\u6c7a\uff1a\u30b7\u30fc\u30b1\u30f3\u30b9\u3067\u3001\u524d\u306e\u6570\u304c\u5f8c\u306e\u6570\u3088\u308a\u5927\u304d\u3044\u5834\u5408\u3001\u3053\u308c\u30892\u3064\u306e\u6570\u306f\u8ee2\u5012\u5bfe\u3092\u69cb\u6210\u3057\u307e\u3059\u3002\u8ee2\u5012\u5bfe\u554f\u984c\u306e\u89e3\u6c7a\u306f\u3001\u30de\u30fc\u30b8\u30bd\u30fc\u30c8\u306e\u52a9\u3051\u3092\u501f\u308a\u3066\u3001\u5206\u5272\u7d71\u6cbb\u306e\u30a2\u30a4\u30c7\u30a2\u3092\u5229\u7528\u3067\u304d\u307e\u3059\u3002</li> </ul> <p>\u5206\u5272\u7d71\u6cbb\u306f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3068\u30c7\u30fc\u30bf\u69cb\u9020\u306e\u8a2d\u8a08\u306b\u3082\u5e83\u304f\u5fdc\u7528\u3055\u308c\u3066\u3044\u307e\u3059\u3002</p> <ul> <li>\u4e8c\u5206\u63a2\u7d22\uff1a\u4e8c\u5206\u63a2\u7d22\u306f\u3001\u30bd\u30fc\u30c8\u6e08\u307f\u914d\u5217\u3092\u4e2d\u70b9\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u304b\u30892\u3064\u306e\u534a\u5206\u306b\u5206\u5272\u3057\u307e\u3059\u3002\u305d\u3057\u3066\u3001\u30bf\u30fc\u30b2\u30c3\u30c8\u5024\u3068\u4e2d\u9593\u8981\u7d20\u5024\u306e\u6bd4\u8f03\u7d50\u679c\u306b\u57fa\u3065\u3044\u3066\u3001\u4e00\u65b9\u306e\u534a\u5206\u304c\u7834\u68c4\u3055\u308c\u307e\u3059\u3002\u540c\u3058\u30d7\u30ed\u30bb\u30b9\u3067\u6b8b\u308a\u306e\u534a\u5206\u3067\u691c\u7d22\u304c\u7d9a\u884c\u3055\u308c\u3001\u30bf\u30fc\u30b2\u30c3\u30c8\u304c\u898b\u3064\u304b\u308b\u304b\u6b8b\u308a\u306e\u8981\u7d20\u304c\u306a\u304f\u306a\u308b\u307e\u3067\u7d9a\u304d\u307e\u3059\u3002</li> <li>\u30de\u30fc\u30b8\u30bd\u30fc\u30c8\uff1a\u3053\u306e\u7bc0\u306e\u5192\u982d\u3067\u3059\u3067\u306b\u7d39\u4ecb\u3057\u305f\u305f\u3081\u3001\u3055\u3089\u306a\u308b\u8a73\u8ff0\u306f\u4e0d\u8981\u3067\u3059\u3002</li> <li>\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\uff1a\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u306f\u30d4\u30dc\u30c3\u30c8\u5024\u3092\u9078\u629e\u3057\u3066\u914d\u5217\u30922\u3064\u306e\u526f\u914d\u5217\u306b\u5206\u5272\u3057\u3001\u4e00\u65b9\u306f\u30d4\u30dc\u30c3\u30c8\u3088\u308a\u5c0f\u3055\u3044\u8981\u7d20\u3001\u3082\u3046\u4e00\u65b9\u306f\u30d4\u30dc\u30c3\u30c8\u3088\u308a\u5927\u304d\u3044\u8981\u7d20\u3092\u6301\u3061\u307e\u3059\u3002\u3053\u306e\u30d7\u30ed\u30bb\u30b9\u306f\u3001\u3053\u308c\u30892\u3064\u306e\u526f\u914d\u5217\u306e\u305d\u308c\u305e\u308c\u306b\u5bfe\u3057\u3066\u30011\u3064\u306e\u8981\u7d20\u306e\u307f\u3092\u4fdd\u6301\u3059\u308b\u307e\u3067\u7d9a\u304d\u307e\u3059\u3002</li> <li>\u30d0\u30b1\u30c3\u30c8\u30bd\u30fc\u30c8\uff1a\u30d0\u30b1\u30c3\u30c8\u30bd\u30fc\u30c8\u306e\u57fa\u672c\u7684\u306a\u30a2\u30a4\u30c7\u30a2\u306f\u3001\u30c7\u30fc\u30bf\u3092\u8907\u6570\u306e\u30d0\u30b1\u30c3\u30c8\u306b\u5206\u6563\u3055\u305b\u308b\u3053\u3068\u3067\u3059\u3002\u5404\u30d0\u30b1\u30c3\u30c8\u5185\u306e\u8981\u7d20\u3092\u30bd\u30fc\u30c8\u3057\u305f\u5f8c\u3001\u30d0\u30b1\u30c3\u30c8\u304b\u3089\u9806\u5e8f\u3088\u304f\u8981\u7d20\u3092\u53d6\u5f97\u3057\u3066\u9806\u5e8f\u4ed8\u3051\u3089\u308c\u305f\u914d\u5217\u3092\u53d6\u5f97\u3057\u307e\u3059\u3002</li> <li>\u6728\uff1a\u4f8b\u3048\u3070\u3001\u4e8c\u5206\u63a2\u7d22\u6728\u3001AVL\u6728\u3001\u8d64\u9ed2\u6728\u3001B\u6728\u3001B+\u6728\u306a\u3069\u3002\u305d\u306e\u64cd\u4f5c\uff08\u691c\u7d22\u3001\u633f\u5165\u3001\u524a\u9664\uff09\u306f\u3059\u3079\u3066\u5206\u5272\u7d71\u6cbb\u6226\u7565\u306e\u5fdc\u7528\u3068\u898b\u306a\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002</li> <li>\u30d2\u30fc\u30d7\uff1a\u30d2\u30fc\u30d7\u306f\u7279\u5225\u306a\u30bf\u30a4\u30d7\u306e\u5b8c\u5168\u4e8c\u5206\u6728\u3067\u3059\u3002\u305d\u306e\u69d8\u3005\u306a\u64cd\u4f5c\uff08\u633f\u5165\u3001\u524a\u9664\u3001\u30d2\u30fc\u30d7\u5316\uff09\u306f\u3001\u5b9f\u969b\u306b\u5206\u5272\u7d71\u6cbb\u306e\u30a2\u30a4\u30c7\u30a2\u3092\u542b\u610f\u3057\u3066\u3044\u307e\u3059\u3002</li> <li>\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\uff1a\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u306f\u76f4\u63a5\u5206\u5272\u7d71\u6cbb\u3092\u9069\u7528\u3057\u307e\u305b\u3093\u304c\u3001\u4e00\u90e8\u306e\u30cf\u30c3\u30b7\u30e5\u885d\u7a81\u89e3\u6c7a\u30bd\u30ea\u30e5\u30fc\u30b7\u30e7\u30f3\u306f\u9593\u63a5\u7684\u306b\u3053\u306e\u6226\u7565\u3092\u9069\u7528\u3057\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u30c1\u30a7\u30a4\u30f3\u6cd5\u306e\u9577\u3044\u30ea\u30b9\u30c8\u306f\u3001\u30af\u30a8\u30ea\u52b9\u7387\u3092\u5411\u4e0a\u3055\u305b\u308b\u305f\u3081\u306b\u8d64\u9ed2\u6728\u306b\u5909\u63db\u3055\u308c\u308b\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002</li> </ul> <p>**\u5206\u5272\u7d71\u6cbb\u306f\u5de7\u5999\u306b\u6d78\u900f\u3059\u308b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u30a2\u30a4\u30c7\u30a2**\u3067\u3042\u308a\u3001\u69d8\u3005\u306a\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3068\u30c7\u30fc\u30bf\u69cb\u9020\u306b\u7d44\u307f\u8fbc\u307e\u308c\u3066\u3044\u308b\u3053\u3068\u304c\u5206\u304b\u308a\u307e\u3059\u3002</p>"},{"location":"chapter_divide_and_conquer/hanota_problem/","title":"12.4 \u00a0 \u30cf\u30ce\u30a4\u306e\u5854\u554f\u984c","text":"<p>\u30de\u30fc\u30b8\u30bd\u30fc\u30c8\u3068\u4e8c\u5206\u6728\u69cb\u7bc9\u306e\u4e21\u65b9\u3067\u3001\u5143\u306e\u554f\u984c\u30922\u3064\u306e\u90e8\u5206\u554f\u984c\u306b\u5206\u89e3\u3057\u3001\u305d\u308c\u305e\u308c\u304c\u5143\u306e\u554f\u984c\u306e\u30b5\u30a4\u30ba\u306e\u534a\u5206\u3067\u3057\u305f\u3002\u3057\u304b\u3057\u3001\u30cf\u30ce\u30a4\u306e\u5854\u3067\u306f\u3001\u7570\u306a\u308b\u5206\u89e3\u6226\u7565\u3092\u63a1\u7528\u3057\u307e\u3059\u3002</p> <p>Question</p> <p>3\u3064\u306e\u67f1\u304c\u3042\u308a\u3001\u305d\u308c\u305e\u308c <code>A</code>\u3001<code>B</code>\u3001<code>C</code> \u3068\u8868\u8a18\u3055\u308c\u307e\u3059\u3002\u6700\u521d\u3001\u67f1 <code>A</code> \u306b\u306f \\(n\\) \u679a\u306e\u5186\u76e4\u304c\u3042\u308a\u3001\u4e0a\u304b\u3089\u4e0b\u306b\u5411\u304b\u3063\u3066\u6607\u9806\u306e\u30b5\u30a4\u30ba\u3067\u914d\u7f6e\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u79c1\u305f\u3061\u306e\u30bf\u30b9\u30af\u306f\u3001\u3053\u308c\u3089\u306e \\(n\\) \u679a\u306e\u5186\u76e4\u3092\u67f1 <code>C</code> \u306b\u79fb\u52d5\u3057\u3001\u5143\u306e\u9806\u5e8f\u3092\u7dad\u6301\u3059\u308b\u3053\u3068\u3067\u3059\uff08\u4ee5\u4e0b\u306e\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\uff09\u3002\u79fb\u52d5\u4e2d\u306b\u306f\u4ee5\u4e0b\u306e\u30eb\u30fc\u30eb\u304c\u9069\u7528\u3055\u308c\u307e\u3059\uff1a</p> <ol> <li>\u5186\u76e4\u306f\u67f1\u306e\u4e0a\u90e8\u304b\u3089\u306e\u307f\u53d6\u308a\u9664\u304f\u3053\u3068\u304c\u3067\u304d\u3001\u5225\u306e\u67f1\u306e\u4e0a\u90e8\u306b\u7f6e\u304f\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002</li> <li>\u4e00\u5ea6\u306b\u79fb\u52d5\u3067\u304d\u308b\u306e\u306f1\u679a\u306e\u5186\u76e4\u306e\u307f\u3067\u3059\u3002</li> <li>\u5c0f\u3055\u3044\u5186\u76e4\u306f\u5e38\u306b\u5927\u304d\u3044\u5186\u76e4\u306e\u4e0a\u306b\u3042\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002</li> </ol> <p></p> <p> \u56f3 12-10 \u00a0 \u30cf\u30ce\u30a4\u306e\u5854\u306e\u4f8b </p> <p>\u30b5\u30a4\u30ba \\(i\\) \u306e\u30cf\u30ce\u30a4\u306e\u5854\u554f\u984c\u3092 \\(f(i)\\) \u3068\u8868\u8a18\u3057\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\\(f(3)\\) \u306f3\u679a\u306e\u5186\u76e4\u3092\u67f1 <code>A</code> \u304b\u3089\u67f1 <code>C</code> \u306b\u79fb\u52d5\u3059\u308b\u3053\u3068\u3092\u8868\u3057\u307e\u3059\u3002</p>"},{"location":"chapter_divide_and_conquer/hanota_problem/#1","title":"1. \u00a0 \u57fa\u672c\u30b1\u30fc\u30b9\u3092\u8003\u3048\u308b","text":"<p>\u4ee5\u4e0b\u306e\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u554f\u984c \\(f(1)\\)\uff08\u5186\u76e4\u304c1\u679a\u306e\u307f\uff09\u306b\u3064\u3044\u3066\u306f\u3001<code>A</code> \u304b\u3089 <code>C</code> \u306b\u76f4\u63a5\u79fb\u52d5\u3067\u304d\u307e\u3059\u3002</p> &lt;1&gt;&lt;2&gt; <p></p> <p></p> <p> \u56f3 12-11 \u00a0 \u30b5\u30a4\u30ba1\u306e\u554f\u984c\u306e\u89e3 </p> <p>\\(f(2)\\)\uff08\u5186\u76e4\u304c2\u679a\uff09\u306b\u3064\u3044\u3066\u306f\u3001**\u67f1 <code>B</code> \u306e\u52a9\u3051\u3092\u501f\u308a\u3066\u5c0f\u3055\u3044\u5186\u76e4\u3092\u5927\u304d\u3044\u5186\u76e4\u306e\u4e0a\u306b\u4fdd\u3064**\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u4ee5\u4e0b\u306e\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\uff1a</p> <ol> <li>\u307e\u305a\u3001\u5c0f\u3055\u3044\u5186\u76e4\u3092 <code>A</code> \u304b\u3089 <code>B</code> \u306b\u79fb\u52d5\u3057\u307e\u3059\u3002</li> <li>\u6b21\u306b\u3001\u5927\u304d\u3044\u5186\u76e4\u3092 <code>A</code> \u304b\u3089 <code>C</code> \u306b\u79fb\u52d5\u3057\u307e\u3059\u3002</li> <li>\u6700\u5f8c\u306b\u3001\u5c0f\u3055\u3044\u5186\u76e4\u3092 <code>B</code> \u304b\u3089 <code>C</code> \u306b\u79fb\u52d5\u3057\u307e\u3059\u3002</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt; <p></p> <p></p> <p></p> <p></p> <p> \u56f3 12-12 \u00a0 \u30b5\u30a4\u30ba2\u306e\u554f\u984c\u306e\u89e3 </p> <p>\\(f(2)\\) \u3092\u89e3\u6c7a\u3059\u308b\u904e\u7a0b\u306f\u6b21\u306e\u3088\u3046\u306b\u8981\u7d04\u3067\u304d\u307e\u3059\uff1a<code>B</code> \u306e\u52a9\u3051\u3092\u501f\u308a\u30662\u679a\u306e\u5186\u76e4\u3092 <code>A</code> \u304b\u3089 <code>C</code> \u306b\u79fb\u52d5\u3059\u308b\u3002\u3053\u3053\u3067\u3001<code>C</code> \u3092\u30bf\u30fc\u30b2\u30c3\u30c8\u67f1\u3001<code>B</code> \u3092\u30d0\u30c3\u30d5\u30a1\u67f1\u3068\u547c\u3073\u307e\u3059\u3002</p>"},{"location":"chapter_divide_and_conquer/hanota_problem/#2","title":"2. \u00a0 \u90e8\u5206\u554f\u984c\u306e\u5206\u89e3","text":"<p>\u554f\u984c \\(f(3)\\)\uff08\u3064\u307e\u308a\u3001\u5186\u76e4\u304c3\u679a\u306e\u5834\u5408\uff09\u306b\u3064\u3044\u3066\u306f\u3001\u72b6\u6cc1\u304c\u3084\u3084\u8907\u96d1\u306b\u306a\u308a\u307e\u3059\u3002</p> <p>\u3059\u3067\u306b \\(f(1)\\) \u3068 \\(f(2)\\) \u306e\u89e3\u304c\u5206\u304b\u3063\u3066\u3044\u308b\u306e\u3067\u3001\u5206\u5272\u7d71\u6cbb\u306e\u89b3\u70b9\u3092\u63a1\u7528\u3057\u3001<code>A</code> \u306e\u4e0a\u306e2\u679a\u306e\u5186\u76e4\u30921\u3064\u306e\u5358\u4f4d\u3068\u3057\u3066\u6271\u3044\u3001\u4ee5\u4e0b\u306e\u56f3\u306b\u793a\u3059\u30b9\u30c6\u30c3\u30d7\u3092\u5b9f\u884c\u3067\u304d\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u30013\u679a\u306e\u5186\u76e4\u3092 <code>A</code> \u304b\u3089 <code>C</code> \u306b\u6b63\u5e38\u306b\u79fb\u52d5\u3067\u304d\u307e\u3059\u3002</p> <ol> <li><code>B</code> \u3092\u30bf\u30fc\u30b2\u30c3\u30c8\u67f1\u3001<code>C</code> \u3092\u30d0\u30c3\u30d5\u30a1\u67f1\u3068\u3057\u3066\u30012\u679a\u306e\u5186\u76e4\u3092 <code>A</code> \u304b\u3089 <code>B</code> \u306b\u79fb\u52d5\u3057\u307e\u3059\u3002</li> <li>\u6b8b\u308a\u306e\u5186\u76e4\u3092 <code>A</code> \u304b\u3089\u76f4\u63a5 <code>C</code> \u306b\u79fb\u52d5\u3057\u307e\u3059\u3002</li> <li><code>C</code> \u3092\u30bf\u30fc\u30b2\u30c3\u30c8\u67f1\u3001<code>A</code> \u3092\u30d0\u30c3\u30d5\u30a1\u67f1\u3068\u3057\u3066\u30012\u679a\u306e\u5186\u76e4\u3092 <code>B</code> \u304b\u3089 <code>C</code> \u306b\u79fb\u52d5\u3057\u307e\u3059\u3002</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt; <p></p> <p></p> <p></p> <p></p> <p> \u56f3 12-13 \u00a0 \u30b5\u30a4\u30ba3\u306e\u554f\u984c\u306e\u89e3 </p> <p>\u672c\u8cea\u7684\u306b\u3001\\(f(3)\\) \u30922\u3064\u306e \\(f(2)\\) \u90e8\u5206\u554f\u984c\u30681\u3064\u306e \\(f(1)\\) \u90e8\u5206\u554f\u984c\u306b\u5206\u89e3\u3057\u307e\u3059\u3002\u3053\u308c\u30893\u3064\u306e\u90e8\u5206\u554f\u984c\u3092\u9806\u6b21\u89e3\u6c7a\u3059\u308b\u3053\u3068\u3067\u3001\u5143\u306e\u554f\u984c\u304c\u89e3\u6c7a\u3055\u308c\u3001\u90e8\u5206\u554f\u984c\u304c\u72ec\u7acb\u3057\u3066\u304a\u308a\u3001\u305d\u308c\u3089\u306e\u89e3\u3092\u30de\u30fc\u30b8\u3067\u304d\u308b\u3053\u3068\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002</p> <p>\u3053\u3053\u304b\u3089\u3001\u4ee5\u4e0b\u306e\u56f3\u306b\u793a\u3059\u30cf\u30ce\u30a4\u306e\u5854\u306e\u5206\u5272\u7d71\u6cbb\u6226\u7565\u3092\u8981\u7d04\u3067\u304d\u307e\u3059\u3002\u5143\u306e\u554f\u984c \\(f(n)\\) \u30922\u3064\u306e\u90e8\u5206\u554f\u984c \\(f(n-1)\\) \u30681\u3064\u306e\u90e8\u5206\u554f\u984c \\(f(1)\\) \u306b\u5206\u5272\u3057\u3001\u4ee5\u4e0b\u306e\u9806\u5e8f\u3067\u3053\u308c\u30893\u3064\u306e\u90e8\u5206\u554f\u984c\u3092\u89e3\u6c7a\u3057\u307e\u3059\uff1a</p> <ol> <li><code>C</code> \u3092\u30d0\u30c3\u30d5\u30a1\u3068\u3057\u3066\u4f7f\u7528\u3057\u3001\\(n-1\\) \u679a\u306e\u5186\u76e4\u3092 <code>A</code> \u304b\u3089 <code>B</code> \u306b\u79fb\u52d5\u3057\u307e\u3059\u3002</li> <li>\u6b8b\u308a\u306e\u5186\u76e4\u3092 <code>A</code> \u304b\u3089\u76f4\u63a5 <code>C</code> \u306b\u79fb\u52d5\u3057\u307e\u3059\u3002</li> <li><code>A</code> \u3092\u30d0\u30c3\u30d5\u30a1\u3068\u3057\u3066\u4f7f\u7528\u3057\u3001\\(n-1\\) \u679a\u306e\u5186\u76e4\u3092 <code>B</code> \u304b\u3089 <code>C</code> \u306b\u79fb\u52d5\u3057\u307e\u3059\u3002</li> </ol> <p>\u5404 \\(f(n-1)\\) \u90e8\u5206\u554f\u984c\u306b\u3064\u3044\u3066\u3001\u540c\u3058\u518d\u5e30\u5206\u5272\u3092\u9069\u7528\u3067\u304d\u3001\u6700\u5c0f\u306e\u90e8\u5206\u554f\u984c \\(f(1)\\) \u306b\u5230\u9054\u3059\u308b\u307e\u3067\u7d9a\u3051\u307e\u3059\u3002\\(f(1)\\) \u306f\u5358\u4e00\u306e\u79fb\u52d5\u306e\u307f\u304c\u5fc5\u8981\u3067\u3042\u308b\u3053\u3068\u304c\u3059\u3067\u306b\u5206\u304b\u3063\u3066\u3044\u308b\u305f\u3081\u3001\u89e3\u6c7a\u3059\u308b\u306e\u306f\u7c21\u5358\u3067\u3059\u3002</p> <p></p> <p> \u56f3 12-14 \u00a0 \u30cf\u30ce\u30a4\u306e\u5854\u3092\u89e3\u6c7a\u3059\u308b\u305f\u3081\u306e\u5206\u5272\u7d71\u6cbb\u6226\u7565 </p>"},{"location":"chapter_divide_and_conquer/hanota_problem/#3","title":"3. \u00a0 \u30b3\u30fc\u30c9\u5b9f\u88c5","text":"<p>\u30b3\u30fc\u30c9\u3067\u306f\u3001\u518d\u5e30\u95a2\u6570 <code>dfs(i, src, buf, tar)</code> \u3092\u5b9a\u7fa9\u3057\u307e\u3059\u3002\u3053\u308c\u306f\u67f1 <code>src</code> \u304b\u3089\u4e0a\u306e \\(i\\) \u679a\u306e\u5186\u76e4\u3092\u67f1 <code>tar</code> \u306b\u79fb\u52d5\u3057\u3001\u67f1 <code>buf</code> \u3092\u30d0\u30c3\u30d5\u30a1\u3068\u3057\u3066\u4f7f\u7528\u3057\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig hanota.py<pre><code>def move(src: list[int], tar: list[int]):\n    \"\"\"\u5186\u76e4\u3092\u79fb\u52d5\"\"\"\n    # src \u306e\u4e0a\u304b\u3089\u5186\u76e4\u3092\u53d6\u308a\u51fa\u3059\n    pan = src.pop()\n    # \u5186\u76e4\u3092 tar \u306e\u4e0a\u306b\u7f6e\u304f\n    tar.append(pan)\n\ndef dfs(i: int, src: list[int], buf: list[int], tar: list[int]):\n    \"\"\"\u30cf\u30ce\u30a4\u306e\u5854\u554f\u984c f(i) \u3092\u89e3\u304f\"\"\"\n    # src \u306b\u5186\u76e4\u304c 1 \u3064\u3060\u3051\u6b8b\u3063\u3066\u3044\u308b\u5834\u5408\u3001\u305d\u308c\u3092 tar \u306b\u79fb\u52d5\n    if i == 1:\n        move(src, tar)\n        return\n    # \u90e8\u5206\u554f\u984c f(i-1)\uff1atar \u306e\u52a9\u3051\u3092\u501f\u308a\u3066 src \u306e\u4e0a\u306e i-1 \u500b\u306e\u5186\u76e4\u3092 buf \u306b\u79fb\u52d5\n    dfs(i - 1, src, tar, buf)\n    # \u90e8\u5206\u554f\u984c f(1)\uff1a\u6b8b\u308a\u306e 1 \u500b\u306e\u5186\u76e4\u3092 src \u304b\u3089 tar \u306b\u79fb\u52d5\n    move(src, tar)\n    # \u90e8\u5206\u554f\u984c f(i-1)\uff1asrc \u306e\u52a9\u3051\u3092\u501f\u308a\u3066 buf \u306e\u4e0a\u306e i-1 \u500b\u306e\u5186\u76e4\u3092 tar \u306b\u79fb\u52d5\n    dfs(i - 1, buf, src, tar)\n\ndef solve_hanota(A: list[int], B: list[int], C: list[int]):\n    \"\"\"\u30cf\u30ce\u30a4\u306e\u5854\u554f\u984c\u3092\u89e3\u304f\"\"\"\n    n = len(A)\n    # B \u306e\u52a9\u3051\u3092\u501f\u308a\u3066 A \u306e\u4e0a\u306e n \u500b\u306e\u5186\u76e4\u3092 C \u306b\u79fb\u52d5\n    dfs(n, A, B, C)\n</code></pre> hanota.cpp<pre><code>/* \u5186\u76e4\u3092\u79fb\u52d5 */\nvoid move(vector&lt;int&gt; &amp;src, vector&lt;int&gt; &amp;tar) {\n    // src \u306e\u6700\u4e0a\u90e8\u304b\u3089\u5186\u76e4\u3092\u53d6\u308a\u51fa\u3059\n    int pan = src.back();\n    src.pop_back();\n    // \u5186\u76e4\u3092 tar \u306e\u6700\u4e0a\u90e8\u306b\u914d\u7f6e\n    tar.push_back(pan);\n}\n\n/* \u30cf\u30ce\u30a4\u306e\u5854\u554f\u984c f(i) \u3092\u89e3\u304f */\nvoid dfs(int i, vector&lt;int&gt; &amp;src, vector&lt;int&gt; &amp;buf, vector&lt;int&gt; &amp;tar) {\n    // src \u306b\u5186\u76e4\u304c1\u3064\u3060\u3051\u6b8b\u3063\u3066\u3044\u308b\u5834\u5408\u3001\u305d\u308c\u3092 tar \u306b\u79fb\u52d5\n    if (i == 1) {\n        move(src, tar);\n        return;\n    }\n    // \u90e8\u5206\u554f\u984c f(i-1)\uff1atar \u306e\u52a9\u3051\u3092\u501f\u308a\u3066\u3001\u4e0a\u4f4d i-1 \u500b\u306e\u5186\u76e4\u3092 src \u304b\u3089 buf \u306b\u79fb\u52d5\n    dfs(i - 1, src, tar, buf);\n    // \u90e8\u5206\u554f\u984c f(1)\uff1a\u6b8b\u308a\u306e1\u3064\u306e\u5186\u76e4\u3092 src \u304b\u3089 tar \u306b\u79fb\u52d5\n    move(src, tar);\n    // \u90e8\u5206\u554f\u984c f(i-1)\uff1asrc \u306e\u52a9\u3051\u3092\u501f\u308a\u3066\u3001\u4e0a\u4f4d i-1 \u500b\u306e\u5186\u76e4\u3092 buf \u304b\u3089 tar \u306b\u79fb\u52d5\n    dfs(i - 1, buf, src, tar);\n}\n\n/* \u30cf\u30ce\u30a4\u306e\u5854\u554f\u984c\u3092\u89e3\u304f */\nvoid solveHanota(vector&lt;int&gt; &amp;A, vector&lt;int&gt; &amp;B, vector&lt;int&gt; &amp;C) {\n    int n = A.size();\n    // B \u306e\u52a9\u3051\u3092\u501f\u308a\u3066\u3001\u4e0a\u4f4d n \u500b\u306e\u5186\u76e4\u3092 A \u304b\u3089 C \u306b\u79fb\u52d5\n    dfs(n, A, B, C);\n}\n</code></pre> hanota.java<pre><code>/* \u5186\u76e4\u3092\u79fb\u52d5 */\nvoid move(List&lt;Integer&gt; src, List&lt;Integer&gt; tar) {\n    // src \u306e\u6700\u4e0a\u90e8\u304b\u3089\u5186\u76e4\u3092\u53d6\u308a\u51fa\u3059\n    Integer pan = src.remove(src.size() - 1);\n    // \u5186\u76e4\u3092 tar \u306e\u6700\u4e0a\u90e8\u306b\u914d\u7f6e\n    tar.add(pan);\n}\n\n/* \u30cf\u30ce\u30a4\u306e\u5854\u554f\u984c f(i) \u3092\u89e3\u304f */\nvoid dfs(int i, List&lt;Integer&gt; src, List&lt;Integer&gt; buf, List&lt;Integer&gt; tar) {\n    // src \u306b\u5186\u76e4\u304c1\u3064\u3060\u3051\u6b8b\u3063\u3066\u3044\u308b\u5834\u5408\u3001\u305d\u308c\u3092 tar \u306b\u79fb\u52d5\n    if (i == 1) {\n        move(src, tar);\n        return;\n    }\n    // \u90e8\u5206\u554f\u984c f(i-1)\uff1atar \u306e\u52a9\u3051\u3092\u501f\u308a\u3066\u3001\u4e0a\u4f4d i-1 \u500b\u306e\u5186\u76e4\u3092 src \u304b\u3089 buf \u306b\u79fb\u52d5\n    dfs(i - 1, src, tar, buf);\n    // \u90e8\u5206\u554f\u984c f(1)\uff1a\u6b8b\u308a\u306e1\u3064\u306e\u5186\u76e4\u3092 src \u304b\u3089 tar \u306b\u79fb\u52d5\n    move(src, tar);\n    // \u90e8\u5206\u554f\u984c f(i-1)\uff1asrc \u306e\u52a9\u3051\u3092\u501f\u308a\u3066\u3001\u4e0a\u4f4d i-1 \u500b\u306e\u5186\u76e4\u3092 buf \u304b\u3089 tar \u306b\u79fb\u52d5\n    dfs(i - 1, buf, src, tar);\n}\n\n/* \u30cf\u30ce\u30a4\u306e\u5854\u554f\u984c\u3092\u89e3\u304f */\nvoid solveHanota(List&lt;Integer&gt; A, List&lt;Integer&gt; B, List&lt;Integer&gt; C) {\n    int n = A.size();\n    // B \u306e\u52a9\u3051\u3092\u501f\u308a\u3066\u3001\u4e0a\u4f4d n \u500b\u306e\u5186\u76e4\u3092 A \u304b\u3089 C \u306b\u79fb\u52d5\n    dfs(n, A, B, C);\n}\n</code></pre> hanota.cs<pre><code>[class]{hanota}-[func]{Move}\n\n[class]{hanota}-[func]{DFS}\n\n[class]{hanota}-[func]{SolveHanota}\n</code></pre> hanota.go<pre><code>[class]{}-[func]{move}\n\n[class]{}-[func]{dfsHanota}\n\n[class]{}-[func]{solveHanota}\n</code></pre> hanota.swift<pre><code>[class]{}-[func]{move}\n\n[class]{}-[func]{dfs}\n\n[class]{}-[func]{solveHanota}\n</code></pre> hanota.js<pre><code>[class]{}-[func]{move}\n\n[class]{}-[func]{dfs}\n\n[class]{}-[func]{solveHanota}\n</code></pre> hanota.ts<pre><code>[class]{}-[func]{move}\n\n[class]{}-[func]{dfs}\n\n[class]{}-[func]{solveHanota}\n</code></pre> hanota.dart<pre><code>[class]{}-[func]{move}\n\n[class]{}-[func]{dfs}\n\n[class]{}-[func]{solveHanota}\n</code></pre> hanota.rs<pre><code>[class]{}-[func]{move_pan}\n\n[class]{}-[func]{dfs}\n\n[class]{}-[func]{solve_hanota}\n</code></pre> hanota.c<pre><code>[class]{}-[func]{move}\n\n[class]{}-[func]{dfs}\n\n[class]{}-[func]{solveHanota}\n</code></pre> hanota.kt<pre><code>[class]{}-[func]{move}\n\n[class]{}-[func]{dfs}\n\n[class]{}-[func]{solveHanota}\n</code></pre> hanota.rb<pre><code>[class]{}-[func]{move}\n\n[class]{}-[func]{dfs}\n\n[class]{}-[func]{solve_hanota}\n</code></pre> hanota.zig<pre><code>[class]{}-[func]{move}\n\n[class]{}-[func]{dfs}\n\n[class]{}-[func]{solveHanota}\n</code></pre> <p>\u4ee5\u4e0b\u306e\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u30cf\u30ce\u30a4\u306e\u5854\u554f\u984c\u306f\u9ad8\u3055 \\(n\\) \u306e\u518d\u5e30\u6728\u3068\u3057\u3066\u8996\u899a\u5316\u3067\u304d\u307e\u3059\u3002\u5404\u30ce\u30fc\u30c9\u306f\u90e8\u5206\u554f\u984c\u3092\u8868\u3057\u3001<code>dfs()</code> \u306e\u547c\u3073\u51fa\u3057\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u6642\u9593\u8a08\u7b97\u91cf\u306f \\(O(2^n)\\)\u3001\u7a7a\u9593\u8a08\u7b97\u91cf\u306f \\(O(n)\\) \u3067\u3059\u3002</p> <p></p> <p> \u56f3 12-15 \u00a0 \u30cf\u30ce\u30a4\u306e\u5854\u306e\u518d\u5e30\u6728 </p> <p>Quote</p> <p>\u30cf\u30ce\u30a4\u306e\u5854\u306f\u53e4\u4ee3\u306e\u4f1d\u8aac\u306b\u7531\u6765\u3057\u307e\u3059\u3002\u53e4\u4ee3\u30a4\u30f3\u30c9\u306e\u5bfa\u9662\u3067\u3001\u50e7\u4fb6\u305f\u3061\u306f3\u672c\u306e\u9ad8\u3044\u30c0\u30a4\u30e4\u30e2\u30f3\u30c9\u306e\u67f1\u3068\u3001\u7570\u306a\u308b\u30b5\u30a4\u30ba\u306e \\(64\\) \u679a\u306e\u91d1\u306e\u5186\u76e4\u3092\u6301\u3063\u3066\u3044\u307e\u3057\u305f\u3002\u5f7c\u3089\u306f\u3001\u6700\u5f8c\u306e\u5186\u76e4\u304c\u6b63\u3057\u304f\u7f6e\u304b\u308c\u305f\u3068\u304d\u3001\u4e16\u754c\u304c\u7d42\u308f\u308b\u3068\u4fe1\u3058\u3066\u3044\u307e\u3057\u305f\u3002</p> <p>\u3057\u304b\u3057\u3001\u50e7\u4fb6\u305f\u3061\u304c1\u79d2\u306b1\u679a\u306e\u5186\u76e4\u3092\u79fb\u52d5\u3057\u305f\u3068\u3057\u3066\u3082\u3001\u7d04 \\(2^{64} \\approx 1.84\u00d710^{19}\\) \u2014\u7d045850\u5104\u5e74\u2014\u304b\u304b\u308a\u3001\u5b87\u5b99\u306e\u5e74\u9f62\u306e\u73fe\u5728\u306e\u63a8\u5b9a\u3092\u306f\u308b\u304b\u306b\u8d85\u3048\u3066\u3044\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u3053\u306e\u4f1d\u8aac\u304c\u771f\u5b9f\u3067\u3042\u308c\u3070\u3001\u4e16\u754c\u306e\u7d42\u308f\u308a\u306b\u3064\u3044\u3066\u5fc3\u914d\u3059\u308b\u5fc5\u8981\u306f\u304a\u305d\u3089\u304f\u306a\u3044\u3067\u3057\u3087\u3046\u3002</p>"},{"location":"chapter_divide_and_conquer/summary/","title":"12.5 \u00a0 \u307e\u3068\u3081","text":"<ul> <li>\u5206\u5272\u7d71\u6cbb\u306f\u4e00\u822c\u7684\u306a\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u8a2d\u8a08\u6226\u7565\u3067\u3001\u5206\u5272\uff08\u5206\u5272\uff09\u3068\u7d71\u6cbb\uff08\u30de\u30fc\u30b8\uff09\u306e2\u3064\u306e\u6bb5\u968e\u304b\u3089\u69cb\u6210\u3055\u308c\u3001\u4e00\u822c\u7684\u306b\u518d\u5e30\u3092\u4f7f\u7528\u3057\u3066\u5b9f\u88c5\u3055\u308c\u307e\u3059\u3002</li> <li>\u554f\u984c\u304c\u5206\u5272\u7d71\u6cbb\u30a2\u30d7\u30ed\u30fc\u30c1\u306b\u9069\u3057\u3066\u3044\u308b\u304b\u3069\u3046\u304b\u3092\u5224\u65ad\u3059\u308b\u305f\u3081\u306b\u3001\u554f\u984c\u304c\u5206\u89e3\u53ef\u80fd\u304b\u3069\u3046\u304b\u3001\u90e8\u5206\u554f\u984c\u304c\u72ec\u7acb\u3057\u3066\u3044\u308b\u304b\u3069\u3046\u304b\u3001\u90e8\u5206\u554f\u984c\u3092\u30de\u30fc\u30b8\u3067\u304d\u308b\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\u3057\u307e\u3059\u3002</li> <li>\u30de\u30fc\u30b8\u30bd\u30fc\u30c8\u306f\u5206\u5272\u7d71\u6cbb\u6226\u7565\u306e\u5178\u578b\u7684\u306a\u4f8b\u3067\u3059\u3002\u914d\u5217\u3092\u518d\u5e30\u7684\u306b2\u3064\u306e\u7b49\u3057\u3044\u9577\u3055\u306e\u526f\u914d\u5217\u306b\u5206\u5272\u3057\u30011\u3064\u306e\u8981\u7d20\u306e\u307f\u304c\u6b8b\u308b\u307e\u3067\u7d9a\u3051\u3001\u6b21\u306b\u3053\u308c\u3089\u306e\u526f\u914d\u5217\u3092\u5c64\u3054\u3068\u306b\u30de\u30fc\u30b8\u3057\u3066\u30bd\u30fc\u30c8\u3092\u5b8c\u4e86\u3057\u307e\u3059\u3002</li> <li>\u5206\u5272\u7d71\u6cbb\u6226\u7565\u306e\u5c0e\u5165\u306f\u3001\u3057\u3070\u3057\u3070\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u52b9\u7387\u3092\u5411\u4e0a\u3055\u305b\u307e\u3059\u3002\u4e00\u65b9\u3067\u306f\u64cd\u4f5c\u6570\u3092\u6e1b\u3089\u3057\u3001\u4ed6\u65b9\u3067\u306f\u5206\u5272\u5f8c\u306e\u30b7\u30b9\u30c6\u30e0\u306e\u4e26\u5217\u6700\u9069\u5316\u3092\u4fc3\u9032\u3057\u307e\u3059\u3002</li> <li>\u5206\u5272\u7d71\u6cbb\u306f\u591a\u6570\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u554f\u984c\u306b\u9069\u7528\u3067\u304d\u3001\u30c7\u30fc\u30bf\u69cb\u9020\u3068\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u8a2d\u8a08\u3067\u5e83\u304f\u4f7f\u7528\u3055\u308c\u3001\u591a\u304f\u306e\u30b7\u30ca\u30ea\u30aa\u306b\u73fe\u308c\u307e\u3059\u3002</li> <li>\u7dcf\u5f53\u305f\u308a\u691c\u7d22\u3068\u6bd4\u8f03\u3057\u3066\u3001\u9069\u5fdc\u691c\u7d22\u306f\u3088\u308a\u52b9\u7387\u7684\u3067\u3059\u3002\u6642\u9593\u8a08\u7b97\u91cf\u304c \\(O(\\log n)\\) \u306e\u691c\u7d22\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u3001\u901a\u5e38\u5206\u5272\u7d71\u6cbb\u6226\u7565\u306b\u57fa\u3065\u3044\u3066\u3044\u307e\u3059\u3002</li> <li>\u4e8c\u5206\u63a2\u7d22\u306f\u5206\u5272\u7d71\u6cbb\u6226\u7565\u306e\u3082\u3046\u4e00\u3064\u306e\u53e4\u5178\u7684\u306a\u5fdc\u7528\u3067\u3059\u3002\u90e8\u5206\u554f\u984c\u306e\u89e3\u306e\u30de\u30fc\u30b8\u3092\u542b\u307e\u305a\u3001\u518d\u5e30\u7684\u306a\u5206\u5272\u7d71\u6cbb\u30a2\u30d7\u30ed\u30fc\u30c1\u3067\u5b9f\u88c5\u3067\u304d\u307e\u3059\u3002</li> <li>\u4e8c\u5206\u6728\u69cb\u7bc9\u554f\u984c\u3067\u306f\u3001\u6728\u306e\u69cb\u7bc9\uff08\u5143\u306e\u554f\u984c\uff09\u3092\u5de6\u306e\u90e8\u5206\u6728\u3068\u53f3\u306e\u90e8\u5206\u6728\u306e\u69cb\u7bc9\uff08\u90e8\u5206\u554f\u984c\uff09\u306b\u5206\u5272\u3067\u304d\u307e\u3059\u3002\u3053\u308c\u306f\u524d\u9806\u8d70\u67fb\u3068\u4e2d\u9806\u8d70\u67fb\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u7bc4\u56f2\u3092\u5206\u5272\u3059\u308b\u3053\u3068\u3067\u5b9f\u73fe\u3067\u304d\u307e\u3059\u3002</li> <li>\u30cf\u30ce\u30a4\u306e\u5854\u554f\u984c\u3067\u306f\u3001\u30b5\u30a4\u30ba \\(n\\) \u306e\u554f\u984c\u3092\u30b5\u30a4\u30ba \\(n-1\\) \u306e2\u3064\u306e\u90e8\u5206\u554f\u984c\u3068\u30b5\u30a4\u30ba \\(1\\) \u306e1\u3064\u306e\u90e8\u5206\u554f\u984c\u306b\u5206\u89e3\u3067\u304d\u307e\u3059\u3002\u3053\u308c\u30893\u3064\u306e\u90e8\u5206\u554f\u984c\u3092\u9806\u6b21\u89e3\u6c7a\u3059\u308b\u3053\u3068\u3067\u3001\u5143\u306e\u554f\u984c\u304c\u89e3\u6c7a\u3055\u308c\u307e\u3059\u3002</li> </ul>"},{"location":"chapter_dynamic_programming/","title":"\u7b2c 14 \u7ae0 \u00a0 \u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0","text":"<p>Abstract</p> <p>\u5ddd\u304c\u6d41\u308c\u3066\u6d77\u306b\u6ce8\u3050\u3088\u3046\u306b\u3001</p> <p>\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u306f\u5c0f\u3055\u306a\u554f\u984c\u306e\u89e3\u3092\u7e54\u308a\u5408\u308f\u305b\u3066\u3001\u3088\u308a\u5927\u304d\u306a\u554f\u984c\u306e\u89e3\u3078\u3068\u5c0e\u304d\u307e\u3059\u3002\u4e00\u6b69\u4e00\u6b69\u9032\u3093\u3067\u3001\u6700\u7d42\u7684\u306a\u7b54\u3048\u304c\u5f85\u3064\u5f7c\u5cb8\u3078\u3068\u5411\u304b\u3044\u307e\u3059\u3002</p>"},{"location":"chapter_dynamic_programming/#_1","title":"\u7ae0\u306e\u5185\u5bb9","text":"<ul> <li>14.1 \u00a0 \u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u5165\u9580</li> <li>14.2 \u00a0 DP\u554f\u984c\u306e\u7279\u6027</li> <li>14.3 \u00a0 DP\u554f\u984c\u89e3\u6c7a\u30a2\u30d7\u30ed\u30fc\u30c1</li> <li>14.4 \u00a0 0-1\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c</li> <li>14.5 \u00a0 \u7121\u5236\u9650\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c</li> <li>14.6 \u00a0 \u7de8\u96c6\u8ddd\u96e2\u554f\u984c</li> <li>14.7 \u00a0 \u307e\u3068\u3081</li> </ul>"},{"location":"chapter_dynamic_programming/dp_problem_features/","title":"14.2 \u00a0 \u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u554f\u984c\u306e\u7279\u5fb4","text":"<p>\u524d\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u3067\u306f\u3001\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u304c\u554f\u984c\u3092\u90e8\u5206\u554f\u984c\u306b\u5206\u89e3\u3059\u308b\u3053\u3068\u3067\u5143\u306e\u554f\u984c\u3092\u89e3\u6c7a\u3059\u308b\u65b9\u6cd5\u3092\u5b66\u3073\u307e\u3057\u305f\u3002\u5b9f\u969b\u3001\u90e8\u5206\u554f\u984c\u306e\u5206\u89e3\u306f\u4e00\u822c\u7684\u306a\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u30a2\u30d7\u30ed\u30fc\u30c1\u3067\u3042\u308a\u3001\u5206\u5272\u7d71\u6cbb\u6cd5\u3001\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u3001\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u3067\u306f\u7570\u306a\u308b\u91cd\u70b9\u304c\u3042\u308a\u307e\u3059\u3002</p> <ul> <li>\u5206\u5272\u7d71\u6cbb\u6cd5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u5143\u306e\u554f\u984c\u3092\u8907\u6570\u306e\u72ec\u7acb\u3057\u305f\u90e8\u5206\u554f\u984c\u306b\u518d\u5e30\u7684\u306b\u5206\u5272\u3057\u3001\u6700\u5c0f\u306e\u90e8\u5206\u554f\u984c\u306b\u5230\u9054\u3059\u308b\u307e\u3067\u7d9a\u3051\u3001\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u6642\u306b\u90e8\u5206\u554f\u984c\u306e\u89e3\u3092\u7d44\u307f\u5408\u308f\u305b\u3066\u6700\u7d42\u7684\u306b\u5143\u306e\u554f\u984c\u306e\u89e3\u3092\u5f97\u307e\u3059\u3002</li> <li>\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u3082\u554f\u984c\u3092\u518d\u5e30\u7684\u306b\u5206\u89e3\u3057\u307e\u3059\u304c\u3001\u5206\u5272\u7d71\u6cbb\u6cd5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3068\u306e\u4e3b\u306a\u9055\u3044\u306f\u3001\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u306e\u90e8\u5206\u554f\u984c\u304c\u76f8\u4e92\u4f9d\u5b58\u7684\u3067\u3042\u308a\u3001\u5206\u89e3\u30d7\u30ed\u30bb\u30b9\u4e2d\u306b\u591a\u304f\u306e\u91cd\u8907\u3059\u308b\u90e8\u5206\u554f\u984c\u304c\u73fe\u308c\u308b\u3053\u3068\u3067\u3059\u3002</li> <li>\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u8a66\u884c\u932f\u8aa4\u306b\u3088\u3063\u3066\u3059\u3079\u3066\u306e\u53ef\u80fd\u306a\u89e3\u3092\u7db2\u7f85\u3057\u3001\u679d\u5208\u308a\u306b\u3088\u3063\u3066\u4e0d\u5fc5\u8981\u306a\u63a2\u7d22\u5206\u5c90\u3092\u907f\u3051\u307e\u3059\u3002\u5143\u306e\u554f\u984c\u306e\u89e3\u306f\u4e00\u9023\u306e\u6c7a\u5b9a\u30b9\u30c6\u30c3\u30d7\u304b\u3089\u69cb\u6210\u3055\u308c\u3001\u5404\u6c7a\u5b9a\u30b9\u30c6\u30c3\u30d7\u524d\u306e\u5404\u90e8\u5206\u30b7\u30fc\u30b1\u30f3\u30b9\u3092\u90e8\u5206\u554f\u984c\u3068\u3057\u3066\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002</li> </ul> <p>\u5b9f\u969b\u3001\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u306f\u6700\u9069\u5316\u554f\u984c\u3092\u89e3\u6c7a\u3059\u308b\u305f\u3081\u306b\u3088\u304f\u4f7f\u7528\u3055\u308c\u3001\u3053\u308c\u3089\u306f\u91cd\u8907\u3059\u308b\u90e8\u5206\u554f\u984c\u3092\u542b\u3080\u3060\u3051\u3067\u306a\u304f\u3001\u4ed6\u306b2\u3064\u306e\u4e3b\u8981\u306a\u7279\u5fb4\u304c\u3042\u308a\u307e\u3059\uff1a\u6700\u9069\u90e8\u5206\u69cb\u9020\u3068\u7121\u8a18\u61b6\u6027\u3067\u3059\u3002</p>"},{"location":"chapter_dynamic_programming/dp_problem_features/#1421","title":"14.2.1 \u00a0 \u6700\u9069\u90e8\u5206\u69cb\u9020","text":"<p>\u968e\u6bb5\u767b\u308a\u554f\u984c\u3092\u5c11\u3057\u4fee\u6b63\u3057\u3066\u3001\u6700\u9069\u90e8\u5206\u69cb\u9020\u306e\u6982\u5ff5\u3092\u5b9f\u8a3c\u3059\u308b\u306e\u306b\u3088\u308a\u9069\u3057\u305f\u3082\u306e\u306b\u3057\u307e\u3059\u3002</p> <p>\u968e\u6bb5\u767b\u308a\u306e\u6700\u5c0f\u30b3\u30b9\u30c8</p> <p>\u968e\u6bb5\u304c\u3042\u308a\u3001\u4e00\u5ea6\u306b1\u6bb5\u307e\u305f\u306f2\u6bb5\u4e0a\u308b\u3053\u3068\u304c\u3067\u304d\u3001\u968e\u6bb5\u306e\u5404\u6bb5\u306b\u306f\u305d\u306e\u6bb5\u3067\u652f\u6255\u3046\u5fc5\u8981\u304c\u3042\u308b\u30b3\u30b9\u30c8\u3092\u8868\u3059\u975e\u8ca0\u306e\u6574\u6570\u304c\u3042\u308a\u307e\u3059\u3002\u975e\u8ca0\u306e\u6574\u6570\u914d\u5217 \\(cost\\) \u304c\u4e0e\u3048\u3089\u308c\u3001\\(cost[i]\\) \u306f \\(i\\) \u6bb5\u76ee\u3067\u652f\u6255\u3046\u5fc5\u8981\u304c\u3042\u308b\u30b3\u30b9\u30c8\u3092\u8868\u3057\u3001\\(cost[0]\\) \u306f\u5730\u9762\uff08\u958b\u59cb\u70b9\uff09\u3067\u3059\u3002\u9802\u4e0a\u306b\u5230\u9054\u3059\u308b\u305f\u3081\u306b\u5fc5\u8981\u306a\u6700\u5c0f\u30b3\u30b9\u30c8\u306f\u4f55\u3067\u3059\u304b\uff1f</p> <p>\u4e0b\u306e\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u30011\u6bb5\u76ee\u30012\u6bb5\u76ee\u30013\u6bb5\u76ee\u306e\u30b3\u30b9\u30c8\u304c\u305d\u308c\u305e\u308c \\(1\\)\u3001\\(10\\)\u3001\\(1\\) \u306e\u5834\u5408\u3001\u5730\u9762\u304b\u30893\u6bb5\u76ee\u306b\u767b\u308b\u6700\u5c0f\u30b3\u30b9\u30c8\u306f \\(2\\) \u3067\u3059\u3002</p> <p></p> <p> \u56f3 14-6 \u00a0 3\u6bb5\u76ee\u306b\u767b\u308b\u6700\u5c0f\u30b3\u30b9\u30c8 </p> <p>\\(dp[i]\\) \u3092 \\(i\\) \u6bb5\u76ee\u306b\u767b\u308b\u7d2f\u7a4d\u30b3\u30b9\u30c8\u3068\u3057\u307e\u3059\u3002\\(i\\) \u6bb5\u76ee\u306f \\(i-1\\) \u6bb5\u76ee\u307e\u305f\u306f \\(i-2\\) \u6bb5\u76ee\u304b\u3089\u306e\u307f\u6765\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u305f\u3081\u3001\\(dp[i]\\) \u306f \\(dp[i-1] + cost[i]\\) \u307e\u305f\u306f \\(dp[i-2] + cost[i]\\) \u306e\u3044\u305a\u308c\u304b\u3057\u304b\u3042\u308a\u3048\u307e\u305b\u3093\u3002\u30b3\u30b9\u30c8\u3092\u6700\u5c0f\u5316\u3059\u308b\u305f\u3081\u306b\u30012\u3064\u306e\u3046\u3061\u5c0f\u3055\u3044\u65b9\u3092\u9078\u629e\u3059\u3079\u304d\u3067\u3059\uff1a</p> \\[ dp[i] = \\min(dp[i-1], dp[i-2]) + cost[i] \\] <p>\u3053\u308c\u306b\u3088\u308a\u6700\u9069\u90e8\u5206\u69cb\u9020\u306e\u610f\u5473\u304c\u308f\u304b\u308a\u307e\u3059\uff1a\u5143\u306e\u554f\u984c\u306e\u6700\u9069\u89e3\u306f\u90e8\u5206\u554f\u984c\u306e\u6700\u9069\u89e3\u304b\u3089\u69cb\u7bc9\u3055\u308c\u308b\u3002</p> <p>\u3053\u306e\u554f\u984c\u306f\u660e\u3089\u304b\u306b\u6700\u9069\u90e8\u5206\u69cb\u9020\u3092\u6301\u3063\u3066\u3044\u307e\u3059\uff1a2\u3064\u306e\u90e8\u5206\u554f\u984c \\(dp[i-1]\\) \u3068 \\(dp[i-2]\\) \u306e\u6700\u9069\u89e3\u304b\u3089\u3088\u308a\u826f\u3044\u65b9\u3092\u9078\u629e\u3057\u3001\u305d\u308c\u3092\u4f7f\u7528\u3057\u3066\u5143\u306e\u554f\u984c \\(dp[i]\\) \u306e\u6700\u9069\u89e3\u3092\u69cb\u7bc9\u3057\u307e\u3059\u3002</p> <p>\u3067\u306f\u3001\u524d\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u306e\u968e\u6bb5\u767b\u308a\u554f\u984c\u306f\u6700\u9069\u90e8\u5206\u69cb\u9020\u3092\u6301\u3063\u3066\u3044\u308b\u3067\u3057\u3087\u3046\u304b\uff1f\u305d\u306e\u76ee\u6a19\u306f\u89e3\u306e\u6570\u3092\u6c42\u3081\u308b\u3053\u3068\u3067\u3001\u3053\u308c\u306f\u6570\u3048\u4e0a\u3052\u554f\u984c\u306e\u3088\u3046\u3067\u3059\u304c\u3001\u5225\u306e\u65b9\u6cd5\u3067\u5c0b\u306d\u3066\u307f\u307e\u3057\u3087\u3046\uff1a\u300c\u89e3\u306e\u6700\u5927\u6570\u3092\u6c42\u3081\u308b\u300d\u3002\u9a5a\u304f\u3053\u3068\u306b\u3001**\u554f\u984c\u304c\u5909\u308f\u3063\u305f\u306b\u3082\u304b\u304b\u308f\u3089\u305a\u3001\u6700\u9069\u90e8\u5206\u69cb\u9020\u304c\u73fe\u308c\u305f**\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\uff1a\\(n\\) \u6bb5\u76ee\u3067\u306e\u89e3\u306e\u6700\u5927\u6570\u306f\u3001\\(n-1\\) \u6bb5\u76ee\u3068 \\(n-2\\) \u6bb5\u76ee\u3067\u306e\u89e3\u306e\u6700\u5927\u6570\u306e\u548c\u306b\u7b49\u3057\u3044\u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u6700\u9069\u90e8\u5206\u69cb\u9020\u306e\u89e3\u91c8\u306f\u975e\u5e38\u306b\u67d4\u8edf\u3067\u3001\u7570\u306a\u308b\u554f\u984c\u3067\u306f\u7570\u306a\u308b\u610f\u5473\u3092\u6301\u3061\u307e\u3059\u3002</p> <p>\u72b6\u614b\u9077\u79fb\u65b9\u7a0b\u5f0f\u3068\u521d\u671f\u72b6\u614b \\(dp[1] = cost[1]\\) \u304a\u3088\u3073 \\(dp[2] = cost[2]\\) \u306b\u5f93\u3063\u3066\u3001\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u30b3\u30fc\u30c9\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig min_cost_climbing_stairs_dp.py<pre><code>def min_cost_climbing_stairs_dp(cost: list[int]) -&gt; int:\n    \"\"\"\u6700\u5c0f\u30b3\u30b9\u30c8\u968e\u6bb5\u767b\u308a\uff1a\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\"\"\"\n    n = len(cost) - 1\n    if n == 1 or n == 2:\n        return cost[n]\n    # dp \u30c6\u30fc\u30d6\u30eb\u3092\u521d\u671f\u5316\u3001\u90e8\u5206\u554f\u984c\u306e\u89e3\u3092\u683c\u7d0d\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\n    dp = [0] * (n + 1)\n    # \u521d\u671f\u72b6\u614b\uff1a\u6700\u5c0f\u306e\u90e8\u5206\u554f\u984c\u306e\u89e3\u3092\u4e8b\u524d\u8a2d\u5b9a\n    dp[1], dp[2] = cost[1], cost[2]\n    # \u72b6\u614b\u9077\u79fb\uff1a\u5c0f\u3055\u3044\u90e8\u5206\u554f\u984c\u304b\u3089\u5927\u304d\u3044\u90e8\u5206\u554f\u984c\u3092\u6bb5\u968e\u7684\u306b\u89e3\u304f\n    for i in range(3, n + 1):\n        dp[i] = min(dp[i - 1], dp[i - 2]) + cost[i]\n    return dp[n]\n</code></pre> min_cost_climbing_stairs_dp.cpp<pre><code>/* \u6700\u5c0f\u30b3\u30b9\u30c8\u968e\u6bb5\u767b\u308a\uff1a\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0 */\nint minCostClimbingStairsDP(vector&lt;int&gt; &amp;cost) {\n    int n = cost.size() - 1;\n    if (n == 1 || n == 2)\n        return cost[n];\n    // DP\u30c6\u30fc\u30d6\u30eb\u3092\u521d\u671f\u5316\u3057\u3001\u90e8\u5206\u554f\u984c\u306e\u89e3\u3092\u683c\u7d0d\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\n    vector&lt;int&gt; dp(n + 1);\n    // \u521d\u671f\u72b6\u614b\uff1a\u6700\u5c0f\u306e\u90e8\u5206\u554f\u984c\u306e\u89e3\u3092\u4e8b\u524d\u8a2d\u5b9a\n    dp[1] = cost[1];\n    dp[2] = cost[2];\n    // \u72b6\u614b\u9077\u79fb\uff1a\u5c0f\u3055\u306a\u554f\u984c\u304b\u3089\u5927\u304d\u306a\u90e8\u5206\u554f\u984c\u3092\u6bb5\u968e\u7684\u306b\u89e3\u304f\n    for (int i = 3; i &lt;= n; i++) {\n        dp[i] = min(dp[i - 1], dp[i - 2]) + cost[i];\n    }\n    return dp[n];\n}\n</code></pre> min_cost_climbing_stairs_dp.java<pre><code>/* \u6700\u5c0f\u30b3\u30b9\u30c8\u968e\u6bb5\u767b\u308a\uff1a\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0 */\nint minCostClimbingStairsDP(int[] cost) {\n    int n = cost.length - 1;\n    if (n == 1 || n == 2)\n        return cost[n];\n    // DP\u30c6\u30fc\u30d6\u30eb\u3092\u521d\u671f\u5316\u3057\u3001\u90e8\u5206\u554f\u984c\u306e\u89e3\u3092\u683c\u7d0d\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\n    int[] dp = new int[n + 1];\n    // \u521d\u671f\u72b6\u614b\uff1a\u6700\u5c0f\u306e\u90e8\u5206\u554f\u984c\u306e\u89e3\u3092\u4e8b\u524d\u8a2d\u5b9a\n    dp[1] = cost[1];\n    dp[2] = cost[2];\n    // \u72b6\u614b\u9077\u79fb\uff1a\u5c0f\u3055\u306a\u554f\u984c\u304b\u3089\u5927\u304d\u306a\u90e8\u5206\u554f\u984c\u3092\u6bb5\u968e\u7684\u306b\u89e3\u304f\n    for (int i = 3; i &lt;= n; i++) {\n        dp[i] = Math.min(dp[i - 1], dp[i - 2]) + cost[i];\n    }\n    return dp[n];\n}\n</code></pre> min_cost_climbing_stairs_dp.cs<pre><code>[class]{min_cost_climbing_stairs_dp}-[func]{MinCostClimbingStairsDP}\n</code></pre> min_cost_climbing_stairs_dp.go<pre><code>[class]{}-[func]{minCostClimbingStairsDP}\n</code></pre> min_cost_climbing_stairs_dp.swift<pre><code>[class]{}-[func]{minCostClimbingStairsDP}\n</code></pre> min_cost_climbing_stairs_dp.js<pre><code>[class]{}-[func]{minCostClimbingStairsDP}\n</code></pre> min_cost_climbing_stairs_dp.ts<pre><code>[class]{}-[func]{minCostClimbingStairsDP}\n</code></pre> min_cost_climbing_stairs_dp.dart<pre><code>[class]{}-[func]{minCostClimbingStairsDP}\n</code></pre> min_cost_climbing_stairs_dp.rs<pre><code>[class]{}-[func]{min_cost_climbing_stairs_dp}\n</code></pre> min_cost_climbing_stairs_dp.c<pre><code>[class]{}-[func]{minCostClimbingStairsDP}\n</code></pre> min_cost_climbing_stairs_dp.kt<pre><code>[class]{}-[func]{minCostClimbingStairsDP}\n</code></pre> min_cost_climbing_stairs_dp.rb<pre><code>[class]{}-[func]{min_cost_climbing_stairs_dp}\n</code></pre> min_cost_climbing_stairs_dp.zig<pre><code>[class]{}-[func]{minCostClimbingStairsDP}\n</code></pre> <p>\u4e0b\u306e\u56f3\u306f\u4e0a\u8a18\u30b3\u30fc\u30c9\u306e\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u30d7\u30ed\u30bb\u30b9\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002</p> <p></p> <p> \u56f3 14-7 \u00a0 \u968e\u6bb5\u767b\u308a\u306e\u6700\u5c0f\u30b3\u30b9\u30c8\u306e\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u30d7\u30ed\u30bb\u30b9 </p> <p>\u3053\u306e\u554f\u984c\u3082\u7a7a\u9593\u6700\u9069\u5316\u304c\u53ef\u80fd\u3067\u30011\u6b21\u5143\u30920\u306b\u5727\u7e2e\u3057\u3001\u7a7a\u9593\u8a08\u7b97\u91cf\u3092 \\(O(n)\\) \u304b\u3089 \\(O(1)\\) \u306b\u524a\u6e1b\u3067\u304d\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig min_cost_climbing_stairs_dp.py<pre><code>def min_cost_climbing_stairs_dp_comp(cost: list[int]) -&gt; int:\n    \"\"\"\u6700\u5c0f\u30b3\u30b9\u30c8\u968e\u6bb5\u767b\u308a\uff1a\u7a7a\u9593\u6700\u9069\u5316\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\"\"\"\n    n = len(cost) - 1\n    if n == 1 or n == 2:\n        return cost[n]\n    a, b = cost[1], cost[2]\n    for i in range(3, n + 1):\n        a, b = b, min(a, b) + cost[i]\n    return b\n</code></pre> min_cost_climbing_stairs_dp.cpp<pre><code>/* \u6700\u5c0f\u30b3\u30b9\u30c8\u968e\u6bb5\u767b\u308a\uff1a\u7a7a\u9593\u6700\u9069\u5316\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0 */\nint minCostClimbingStairsDPComp(vector&lt;int&gt; &amp;cost) {\n    int n = cost.size() - 1;\n    if (n == 1 || n == 2)\n        return cost[n];\n    int a = cost[1], b = cost[2];\n    for (int i = 3; i &lt;= n; i++) {\n        int tmp = b;\n        b = min(a, tmp) + cost[i];\n        a = tmp;\n    }\n    return b;\n}\n</code></pre> min_cost_climbing_stairs_dp.java<pre><code>/* \u6700\u5c0f\u30b3\u30b9\u30c8\u968e\u6bb5\u767b\u308a\uff1a\u7a7a\u9593\u6700\u9069\u5316\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0 */\nint minCostClimbingStairsDPComp(int[] cost) {\n    int n = cost.length - 1;\n    if (n == 1 || n == 2)\n        return cost[n];\n    int a = cost[1], b = cost[2];\n    for (int i = 3; i &lt;= n; i++) {\n        int tmp = b;\n        b = Math.min(a, tmp) + cost[i];\n        a = tmp;\n    }\n    return b;\n}\n</code></pre> min_cost_climbing_stairs_dp.cs<pre><code>[class]{min_cost_climbing_stairs_dp}-[func]{MinCostClimbingStairsDPComp}\n</code></pre> min_cost_climbing_stairs_dp.go<pre><code>[class]{}-[func]{minCostClimbingStairsDPComp}\n</code></pre> min_cost_climbing_stairs_dp.swift<pre><code>[class]{}-[func]{minCostClimbingStairsDPComp}\n</code></pre> min_cost_climbing_stairs_dp.js<pre><code>[class]{}-[func]{minCostClimbingStairsDPComp}\n</code></pre> min_cost_climbing_stairs_dp.ts<pre><code>[class]{}-[func]{minCostClimbingStairsDPComp}\n</code></pre> min_cost_climbing_stairs_dp.dart<pre><code>[class]{}-[func]{minCostClimbingStairsDPComp}\n</code></pre> min_cost_climbing_stairs_dp.rs<pre><code>[class]{}-[func]{min_cost_climbing_stairs_dp_comp}\n</code></pre> min_cost_climbing_stairs_dp.c<pre><code>[class]{}-[func]{minCostClimbingStairsDPComp}\n</code></pre> min_cost_climbing_stairs_dp.kt<pre><code>[class]{}-[func]{minCostClimbingStairsDPComp}\n</code></pre> min_cost_climbing_stairs_dp.rb<pre><code>[class]{}-[func]{min_cost_climbing_stairs_dp_comp}\n</code></pre> min_cost_climbing_stairs_dp.zig<pre><code>[class]{}-[func]{minCostClimbingStairsDPComp}\n</code></pre>"},{"location":"chapter_dynamic_programming/dp_problem_features/#1422","title":"14.2.2 \u00a0 \u7121\u8a18\u61b6\u6027","text":"<p>\u7121\u8a18\u61b6\u6027\u306f\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u304c\u554f\u984c\u89e3\u6c7a\u306b\u52b9\u679c\u7684\u3067\u3042\u308b\u3053\u3068\u3092\u53ef\u80fd\u306b\u3059\u308b\u91cd\u8981\u306a\u7279\u5fb4\u306e1\u3064\u3067\u3059\u3002\u305d\u306e\u5b9a\u7fa9\u306f\uff1a\u7279\u5b9a\u306e\u72b6\u614b\u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u304d\u3001\u305d\u306e\u5c06\u6765\u306e\u767a\u5c55\u306f\u73fe\u5728\u306e\u72b6\u614b\u306e\u307f\u306b\u95a2\u9023\u3057\u3001\u904e\u53bb\u306b\u7d4c\u9a13\u3057\u305f\u3059\u3079\u3066\u306e\u72b6\u614b\u3068\u306f\u7121\u95a2\u4fc2\u3067\u3042\u308b\u3002</p> <p>\u968e\u6bb5\u767b\u308a\u554f\u984c\u3092\u4f8b\u306b\u53d6\u308b\u3068\u3001\u72b6\u614b \\(i\\) \u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u304d\u3001\u305d\u308c\u306f\u72b6\u614b \\(i+1\\) \u3068 \\(i+2\\) \u306b\u767a\u5c55\u3057\u3001\u305d\u308c\u305e\u308c1\u6bb5\u30b8\u30e3\u30f3\u30d7\u30682\u6bb5\u30b8\u30e3\u30f3\u30d7\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002\u3053\u308c\u30892\u3064\u306e\u9078\u629e\u3092\u3059\u308b\u3068\u304d\u3001\u72b6\u614b \\(i\\) \u3088\u308a\u524d\u306e\u72b6\u614b\u3092\u8003\u616e\u3059\u308b\u5fc5\u8981\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u306a\u305c\u306a\u3089\u3001\u305d\u308c\u3089\u306f\u72b6\u614b \\(i\\) \u306e\u5c06\u6765\u306b\u5f71\u97ff\u3057\u306a\u3044\u304b\u3089\u3067\u3059\u3002</p> <p>\u3057\u304b\u3057\u3001\u968e\u6bb5\u767b\u308a\u554f\u984c\u306b\u5236\u7d04\u3092\u8ffd\u52a0\u3059\u308b\u3068\u3001\u72b6\u6cc1\u304c\u5909\u308f\u308a\u307e\u3059\u3002</p> <p>\u5236\u7d04\u4ed8\u304d\u968e\u6bb5\u767b\u308a</p> <p>\\(n\\) \u6bb5\u306e\u968e\u6bb5\u304c\u3042\u308a\u3001\u6bce\u56de1\u6bb5\u307e\u305f\u306f2\u6bb5\u4e0a\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u304c\u30011\u6bb5\u30922\u56de\u9023\u7d9a\u3067\u30b8\u30e3\u30f3\u30d7\u3059\u308b\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093\u3002\u9802\u4e0a\u306b\u767b\u308b\u65b9\u6cd5\u306f\u4f55\u901a\u308a\u3042\u308a\u307e\u3059\u304b\uff1f</p> <p>\u4e0b\u306e\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u30013\u6bb5\u76ee\u306b\u767b\u308b\u5b9f\u884c\u53ef\u80fd\u306a\u9078\u629e\u80a2\u306f2\u3064\u3060\u3051\u3067\u30011\u6bb5\u30923\u56de\u9023\u7d9a\u3067\u30b8\u30e3\u30f3\u30d7\u3059\u308b\u9078\u629e\u80a2\u306f\u5236\u7d04\u6761\u4ef6\u3092\u6e80\u305f\u3055\u306a\u3044\u305f\u3081\u7834\u68c4\u3055\u308c\u307e\u3059\u3002</p> <p></p> <p> \u56f3 14-8 \u00a0 \u5236\u7d04\u4ed8\u304d\u30673\u6bb5\u76ee\u306b\u767b\u308b\u5b9f\u884c\u53ef\u80fd\u306a\u9078\u629e\u80a2\u306e\u6570 </p> <p>\u3053\u306e\u554f\u984c\u3067\u306f\u3001\u524d\u56de\u304c1\u6bb5\u30b8\u30e3\u30f3\u30d7\u3060\u3063\u305f\u5834\u5408\u3001\u6b21\u56de\u306f\u5fc5\u305a2\u6bb5\u30b8\u30e3\u30f3\u30d7\u3067\u306a\u3051\u308c\u3070\u306a\u308a\u307e\u305b\u3093\u3002\u3053\u308c\u306f**\u6b21\u306e\u30b9\u30c6\u30c3\u30d7\u306e\u9078\u629e\u304c\u73fe\u5728\u306e\u72b6\u614b\uff08\u73fe\u5728\u306e\u968e\u6bb5\u6bb5\u6570\uff09\u3060\u3051\u3067\u306f\u72ec\u7acb\u3057\u3066\u6c7a\u5b9a\u3067\u304d\u305a\u3001\u524d\u306e\u72b6\u614b\uff08\u524d\u56de\u306e\u968e\u6bb5\u6bb5\u6570\uff09\u306b\u3082\u4f9d\u5b58\u3059\u308b**\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002</p> <p>\u3053\u306e\u554f\u984c\u304c\u3082\u306f\u3084\u7121\u8a18\u61b6\u6027\u3092\u6e80\u305f\u3055\u305a\u3001\u72b6\u614b\u9077\u79fb\u65b9\u7a0b\u5f0f \\(dp[i] = dp[i-1] + dp[i-2]\\) \u3082\u5931\u6557\u3059\u308b\u3053\u3068\u306f\u5bb9\u6613\u306b\u308f\u304b\u308a\u307e\u3059\u3002\u306a\u305c\u306a\u3089 \\(dp[i-1]\\) \u306f\u4eca\u56de\u306e1\u6bb5\u30b8\u30e3\u30f3\u30d7\u3092\u8868\u3057\u307e\u3059\u304c\u3001\u591a\u304f\u306e\u300c\u524d\u56de\u304c1\u6bb5\u30b8\u30e3\u30f3\u30d7\u3060\u3063\u305f\u300d\u9078\u629e\u80a2\u3092\u542b\u3093\u3067\u304a\u308a\u3001\u5236\u7d04\u3092\u6e80\u305f\u3059\u305f\u3081\u306b\u306f\u3053\u308c\u3089\u3092\u76f4\u63a5 \\(dp[i]\\) \u306b\u542b\u3081\u308b\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093\u3002</p> <p>\u3053\u306e\u305f\u3081\u3001\u72b6\u614b\u5b9a\u7fa9\u3092\u62e1\u5f35\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\uff1a\u72b6\u614b \\([i, j]\\) \u306f \\(i\\) \u6bb5\u76ee\u306b\u3044\u3066\u3001\u524d\u56de\u304c \\(j\\) \u6bb5\u30b8\u30e3\u30f3\u30d7\u3060\u3063\u305f\u3053\u3068\u3092\u8868\u3059\u3002\u3053\u3053\u3067 \\(j \\in \\{1, 2\\}\\) \u3067\u3059\u3002\u3053\u306e\u72b6\u614b\u5b9a\u7fa9\u306f\u524d\u56de\u304c1\u6bb5\u30b8\u30e3\u30f3\u30d7\u3060\u3063\u305f\u304b2\u6bb5\u30b8\u30e3\u30f3\u30d7\u3060\u3063\u305f\u304b\u3092\u52b9\u679c\u7684\u306b\u533a\u5225\u3057\u3001\u73fe\u5728\u306e\u72b6\u614b\u304c\u3069\u3053\u304b\u3089\u6765\u305f\u304b\u3092\u9069\u5207\u306b\u5224\u65ad\u3067\u304d\u307e\u3059\u3002</p> <ul> <li>\u524d\u56de\u304c1\u6bb5\u30b8\u30e3\u30f3\u30d7\u3060\u3063\u305f\u5834\u5408\u3001\u524d\u3005\u56de\u306f\u5fc5\u305a2\u6bb5\u30b8\u30e3\u30f3\u30d7\u3092\u9078\u629e\u3057\u3066\u3044\u305f\u306f\u305a\u3067\u3059\u3002\u3064\u307e\u308a\u3001\\(dp[i, 1]\\) \u306f \\(dp[i-1, 2]\\) \u304b\u3089\u306e\u307f\u9077\u79fb\u3067\u304d\u307e\u3059\u3002</li> <li>\u524d\u56de\u304c2\u6bb5\u30b8\u30e3\u30f3\u30d7\u3060\u3063\u305f\u5834\u5408\u3001\u524d\u3005\u56de\u306f1\u6bb5\u30b8\u30e3\u30f3\u30d7\u307e\u305f\u306f2\u6bb5\u30b8\u30e3\u30f3\u30d7\u3092\u9078\u629e\u3067\u304d\u307e\u3057\u305f\u3002\u3064\u307e\u308a\u3001\\(dp[i, 2]\\) \u306f \\(dp[i-2, 1]\\) \u307e\u305f\u306f \\(dp[i-2, 2]\\) \u304b\u3089\u9077\u79fb\u3067\u304d\u307e\u3059\u3002</li> </ul> <p>\u4e0b\u306e\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\\(dp[i, j]\\) \u306f\u72b6\u614b \\([i, j]\\) \u306e\u89e3\u306e\u6570\u3092\u8868\u3057\u307e\u3059\u3002\u3053\u306e\u6642\u70b9\u3067\u3001\u72b6\u614b\u9077\u79fb\u65b9\u7a0b\u5f0f\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff1a</p> \\[ \\begin{cases} dp[i, 1] = dp[i-1, 2] \\\\ dp[i, 2] = dp[i-2, 1] + dp[i-2, 2] \\end{cases} \\] <p></p> <p> \u56f3 14-9 \u00a0 \u5236\u7d04\u3092\u8003\u616e\u3057\u305f\u518d\u5e30\u95a2\u4fc2 </p> <p>\u6700\u7d42\u7684\u306b\u3001\\(dp[n, 1] + dp[n, 2]\\) \u3092\u8fd4\u305b\u3070\u3088\u304f\u3001\u3053\u306e2\u3064\u306e\u5408\u8a08\u304c \\(n\\) \u6bb5\u76ee\u306b\u767b\u308b\u89e3\u306e\u7dcf\u6570\u3092\u8868\u3057\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig climbing_stairs_constraint_dp.py<pre><code>def climbing_stairs_constraint_dp(n: int) -&gt; int:\n    \"\"\"\u5236\u7d04\u4ed8\u304d\u968e\u6bb5\u767b\u308a\uff1a\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\"\"\"\n    if n == 1 or n == 2:\n        return 1\n    # dp \u30c6\u30fc\u30d6\u30eb\u3092\u521d\u671f\u5316\u3001\u90e8\u5206\u554f\u984c\u306e\u89e3\u3092\u683c\u7d0d\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\n    dp = [[0] * 3 for _ in range(n + 1)]\n    # \u521d\u671f\u72b6\u614b\uff1a\u6700\u5c0f\u306e\u90e8\u5206\u554f\u984c\u306e\u89e3\u3092\u4e8b\u524d\u8a2d\u5b9a\n    dp[1][1], dp[1][2] = 1, 0\n    dp[2][1], dp[2][2] = 0, 1\n    # \u72b6\u614b\u9077\u79fb\uff1a\u5c0f\u3055\u3044\u90e8\u5206\u554f\u984c\u304b\u3089\u5927\u304d\u3044\u90e8\u5206\u554f\u984c\u3092\u6bb5\u968e\u7684\u306b\u89e3\u304f\n    for i in range(3, n + 1):\n        dp[i][1] = dp[i - 1][2]\n        dp[i][2] = dp[i - 2][1] + dp[i - 2][2]\n    return dp[n][1] + dp[n][2]\n</code></pre> climbing_stairs_constraint_dp.cpp<pre><code>/* \u5236\u7d04\u4ed8\u304d\u968e\u6bb5\u767b\u308a\uff1a\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0 */\nint climbingStairsConstraintDP(int n) {\n    if (n == 1 || n == 2) {\n        return 1;\n    }\n    // DP\u30c6\u30fc\u30d6\u30eb\u3092\u521d\u671f\u5316\u3057\u3001\u90e8\u5206\u554f\u984c\u306e\u89e3\u3092\u683c\u7d0d\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\n    vector&lt;vector&lt;int&gt;&gt; dp(n + 1, vector&lt;int&gt;(3, 0));\n    // \u521d\u671f\u72b6\u614b\uff1a\u6700\u5c0f\u306e\u90e8\u5206\u554f\u984c\u306e\u89e3\u3092\u4e8b\u524d\u8a2d\u5b9a\n    dp[1][1] = 1;\n    dp[1][2] = 0;\n    dp[2][1] = 0;\n    dp[2][2] = 1;\n    // \u72b6\u614b\u9077\u79fb\uff1a\u5c0f\u3055\u306a\u554f\u984c\u304b\u3089\u5927\u304d\u306a\u90e8\u5206\u554f\u984c\u3092\u6bb5\u968e\u7684\u306b\u89e3\u304f\n    for (int i = 3; i &lt;= n; i++) {\n        dp[i][1] = dp[i - 1][2];\n        dp[i][2] = dp[i - 2][1] + dp[i - 2][2];\n    }\n    return dp[n][1] + dp[n][2];\n}\n</code></pre> climbing_stairs_constraint_dp.java<pre><code>/* \u5236\u7d04\u4ed8\u304d\u968e\u6bb5\u767b\u308a\uff1a\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0 */\nint climbingStairsConstraintDP(int n) {\n    if (n == 1 || n == 2) {\n        return 1;\n    }\n    // DP\u30c6\u30fc\u30d6\u30eb\u3092\u521d\u671f\u5316\u3057\u3001\u90e8\u5206\u554f\u984c\u306e\u89e3\u3092\u683c\u7d0d\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\n    int[][] dp = new int[n + 1][3];\n    // \u521d\u671f\u72b6\u614b\uff1a\u6700\u5c0f\u306e\u90e8\u5206\u554f\u984c\u306e\u89e3\u3092\u4e8b\u524d\u8a2d\u5b9a\n    dp[1][1] = 1;\n    dp[1][2] = 0;\n    dp[2][1] = 0;\n    dp[2][2] = 1;\n    // \u72b6\u614b\u9077\u79fb\uff1a\u5c0f\u3055\u306a\u554f\u984c\u304b\u3089\u5927\u304d\u306a\u90e8\u5206\u554f\u984c\u3092\u6bb5\u968e\u7684\u306b\u89e3\u304f\n    for (int i = 3; i &lt;= n; i++) {\n        dp[i][1] = dp[i - 1][2];\n        dp[i][2] = dp[i - 2][1] + dp[i - 2][2];\n    }\n    return dp[n][1] + dp[n][2];\n}\n</code></pre> climbing_stairs_constraint_dp.cs<pre><code>[class]{climbing_stairs_constraint_dp}-[func]{ClimbingStairsConstraintDP}\n</code></pre> climbing_stairs_constraint_dp.go<pre><code>[class]{}-[func]{climbingStairsConstraintDP}\n</code></pre> climbing_stairs_constraint_dp.swift<pre><code>[class]{}-[func]{climbingStairsConstraintDP}\n</code></pre> climbing_stairs_constraint_dp.js<pre><code>[class]{}-[func]{climbingStairsConstraintDP}\n</code></pre> climbing_stairs_constraint_dp.ts<pre><code>[class]{}-[func]{climbingStairsConstraintDP}\n</code></pre> climbing_stairs_constraint_dp.dart<pre><code>[class]{}-[func]{climbingStairsConstraintDP}\n</code></pre> climbing_stairs_constraint_dp.rs<pre><code>[class]{}-[func]{climbing_stairs_constraint_dp}\n</code></pre> climbing_stairs_constraint_dp.c<pre><code>[class]{}-[func]{climbingStairsConstraintDP}\n</code></pre> climbing_stairs_constraint_dp.kt<pre><code>[class]{}-[func]{climbingStairsConstraintDP}\n</code></pre> climbing_stairs_constraint_dp.rb<pre><code>[class]{}-[func]{climbing_stairs_constraint_dp}\n</code></pre> climbing_stairs_constraint_dp.zig<pre><code>[class]{}-[func]{climbingStairsConstraintDP}\n</code></pre> <p>\u4e0a\u8a18\u306e\u30b1\u30fc\u30b9\u3067\u306f\u3001\u524d\u306e\u72b6\u614b\u306e\u307f\u3092\u8003\u616e\u3059\u308c\u3070\u3088\u3044\u305f\u3081\u3001\u72b6\u614b\u5b9a\u7fa9\u3092\u62e1\u5f35\u3059\u308b\u3053\u3068\u3067\u4f9d\u7136\u3068\u3057\u3066\u7121\u8a18\u61b6\u6027\u3092\u6e80\u305f\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u4e00\u90e8\u306e\u554f\u984c\u3067\u306f\u975e\u5e38\u306b\u6df1\u523b\u306a\u300c\u72b6\u614b\u52b9\u679c\u300d\u304c\u3042\u308a\u307e\u3059\u3002</p> <p>\u969c\u5bb3\u7269\u751f\u6210\u4ed8\u304d\u968e\u6bb5\u767b\u308a</p> <p>\\(n\\) \u6bb5\u306e\u968e\u6bb5\u304c\u3042\u308a\u3001\u6bce\u56de1\u6bb5\u307e\u305f\u306f2\u6bb5\u4e0a\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002**\\(i\\) \u6bb5\u76ee\u306b\u767b\u3063\u305f\u3068\u304d\u3001\u30b7\u30b9\u30c6\u30e0\u304c\u81ea\u52d5\u7684\u306b \\(2i\\) \u6bb5\u76ee\u306b\u969c\u5bb3\u7269\u3092\u7f6e\u304d\u3001\u305d\u306e\u5f8c\u306e\u3059\u3079\u3066\u306e\u30e9\u30a6\u30f3\u30c9\u3067 \\(2i\\) \u6bb5\u76ee\u306b\u30b8\u30e3\u30f3\u30d7\u3059\u308b\u3053\u3068\u304c\u7981\u6b62\u3055\u308c\u308b**\u3068\u898f\u5b9a\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u6700\u521d\u306e2\u30e9\u30a6\u30f3\u30c9\u30672\u6bb5\u76ee\u30683\u6bb5\u76ee\u306b\u30b8\u30e3\u30f3\u30d7\u3057\u305f\u5834\u5408\u3001\u305d\u306e\u5f8c\u306f4\u6bb5\u76ee\u30686\u6bb5\u76ee\u306b\u30b8\u30e3\u30f3\u30d7\u3067\u304d\u307e\u305b\u3093\u3002\u9802\u4e0a\u306b\u767b\u308b\u65b9\u6cd5\u306f\u4f55\u901a\u308a\u3042\u308a\u307e\u3059\u304b\uff1f</p> <p>\u3053\u306e\u554f\u984c\u3067\u306f\u3001\u6b21\u306e\u30b8\u30e3\u30f3\u30d7\u306f\u3059\u3079\u3066\u306e\u904e\u53bb\u306e\u72b6\u614b\u306b\u4f9d\u5b58\u3057\u307e\u3059\u3002\u5404\u30b8\u30e3\u30f3\u30d7\u304c\u3088\u308a\u9ad8\u3044\u6bb5\u306b\u969c\u5bb3\u7269\u3092\u7f6e\u304d\u3001\u5c06\u6765\u306e\u30b8\u30e3\u30f3\u30d7\u306b\u5f71\u97ff\u3059\u308b\u304b\u3089\u3067\u3059\u3002\u3053\u306e\u3088\u3046\u306a\u554f\u984c\u3067\u306f\u3001\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u306f\u3057\u3070\u3057\u3070\u89e3\u6c7a\u306b\u82e6\u52b4\u3057\u307e\u3059\u3002</p> <p>\u5b9f\u969b\u3001\u591a\u304f\u306e\u8907\u96d1\u306a\u7d44\u307f\u5408\u308f\u305b\u6700\u9069\u5316\u554f\u984c\uff08\u5de1\u56de\u30bb\u30fc\u30eb\u30b9\u30de\u30f3\u554f\u984c\u306a\u3069\uff09\u306f\u7121\u8a18\u61b6\u6027\u3092\u6e80\u305f\u3057\u307e\u305b\u3093\u3002\u3053\u306e\u3088\u3046\u306a\u554f\u984c\u306b\u5bfe\u3057\u3066\u306f\u3001\u901a\u5e38\u3001\u30d2\u30e5\u30fc\u30ea\u30b9\u30c6\u30a3\u30c3\u30af\u63a2\u7d22\u3001\u907a\u4f1d\u7684\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3001\u5f37\u5316\u5b66\u7fd2\u306a\u3069\u306e\u4ed6\u306e\u65b9\u6cd5\u3092\u9078\u629e\u3057\u3066\u3001\u9650\u3089\u308c\u305f\u6642\u9593\u5185\u306b\u4f7f\u7528\u53ef\u80fd\u306a\u5c40\u6240\u6700\u9069\u89e3\u3092\u5f97\u307e\u3059\u3002</p>"},{"location":"chapter_dynamic_programming/dp_solution_pipeline/","title":"14.3 \u00a0 \u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u554f\u984c\u89e3\u6c7a\u30a2\u30d7\u30ed\u30fc\u30c1","text":"<p>\u524d\u306e2\u3064\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u3067\u306f\u3001\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u554f\u984c\u306e\u4e3b\u8981\u306a\u7279\u5fb4\u3092\u7d39\u4ecb\u3057\u307e\u3057\u305f\u3002\u6b21\u306b\u3001\u3088\u308a\u5b9f\u7528\u7684\u306a2\u3064\u306e\u554f\u984c\u3092\u4e00\u7dd2\u306b\u63a2\u7d22\u3057\u307e\u3057\u3087\u3046\u3002</p> <ol> <li>\u554f\u984c\u304c\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u554f\u984c\u304b\u3069\u3046\u304b\u3092\u3069\u306e\u3088\u3046\u306b\u5224\u65ad\u3059\u308b\u304b\uff1f</li> <li>\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u554f\u984c\u3092\u89e3\u6c7a\u3059\u308b\u5b8c\u5168\u306a\u30b9\u30c6\u30c3\u30d7\u306f\u4f55\u304b\uff1f</li> </ol>"},{"location":"chapter_dynamic_programming/dp_solution_pipeline/#1431","title":"14.3.1 \u00a0 \u554f\u984c\u306e\u5224\u5b9a","text":"<p>\u4e00\u822c\u7684\u306b\u8a00\u3048\u3070\u3001\u554f\u984c\u304c\u91cd\u8907\u3059\u308b\u90e8\u5206\u554f\u984c\u3001\u6700\u9069\u90e8\u5206\u69cb\u9020\u3092\u542b\u307f\u3001\u7121\u8a18\u61b6\u6027\u3092\u793a\u3059\u5834\u5408\u3001\u901a\u5e38\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u89e3\u6cd5\u306b\u9069\u3057\u3066\u3044\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u554f\u984c\u306e\u8aac\u660e\u304b\u3089\u76f4\u63a5\u3053\u308c\u3089\u306e\u7279\u5fb4\u3092\u62bd\u51fa\u3059\u308b\u3053\u3068\u306f\u3057\u3070\u3057\u3070\u56f0\u96e3\u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u901a\u5e38\u306f\u6761\u4ef6\u3092\u7de9\u548c\u3057\u3001**\u307e\u305a\u554f\u984c\u304c\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\uff08\u5168\u63a2\u7d22\uff09\u3092\u4f7f\u7528\u3057\u305f\u89e3\u6c7a\u306b\u9069\u3057\u3066\u3044\u308b\u304b\u3069\u3046\u304b\u3092\u89b3\u5bdf**\u3057\u307e\u3059\u3002</p> <p>**\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u306b\u9069\u3057\u305f\u554f\u984c\u306f\u901a\u5e38\u300c\u6c7a\u5b9a\u6728\u30e2\u30c7\u30eb\u300d\u306b\u9069\u5408**\u3057\u3001\u3053\u308c\u306f\u6728\u69cb\u9020\u3092\u4f7f\u7528\u3057\u3066\u8a18\u8ff0\u3067\u304d\u3001\u5404\u30ce\u30fc\u30c9\u306f\u6c7a\u5b9a\u3092\u8868\u3057\u3001\u5404\u30d1\u30b9\u306f\u6c7a\u5b9a\u306e\u30b7\u30fc\u30b1\u30f3\u30b9\u3092\u8868\u3057\u307e\u3059\u3002</p> <p>\u8a00\u3044\u63db\u3048\u308b\u3068\u3001\u554f\u984c\u304c\u660e\u793a\u7684\u306a\u6c7a\u5b9a\u6982\u5ff5\u3092\u542b\u307f\u3001\u89e3\u304c\u4e00\u9023\u306e\u6c7a\u5b9a\u3092\u901a\u3058\u3066\u751f\u6210\u3055\u308c\u308b\u5834\u5408\u3001\u305d\u308c\u306f\u6c7a\u5b9a\u6728\u30e2\u30c7\u30eb\u306b\u9069\u5408\u3057\u3001\u901a\u5e38\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u3092\u4f7f\u7528\u3057\u3066\u89e3\u6c7a\u3067\u304d\u307e\u3059\u3002</p> <p>\u3053\u306e\u57fa\u790e\u306e\u4e0a\u3067\u3001\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u554f\u984c\u3092\u5224\u5b9a\u3059\u308b\u305f\u3081\u306e\u300c\u30dc\u30fc\u30ca\u30b9\u30dd\u30a4\u30f3\u30c8\u300d\u304c\u3042\u308a\u307e\u3059\u3002</p> <ul> <li>\u554f\u984c\u306b\u6700\u5927\u5316\uff08\u6700\u5c0f\u5316\uff09\u307e\u305f\u306f\u6700\u3082\uff08\u6700\u3082\u5c11\u306a\u3044\uff09\u6700\u9069\u306a\u89e3\u3092\u898b\u3064\u3051\u308b\u3068\u3044\u3046\u8a18\u8ff0\u304c\u542b\u307e\u308c\u3066\u3044\u308b\u3002</li> <li>\u554f\u984c\u306e\u72b6\u614b\u304c\u30ea\u30b9\u30c8\u3001\u591a\u6b21\u5143\u884c\u5217\u3001\u307e\u305f\u306f\u6728\u3092\u4f7f\u7528\u3057\u3066\u8868\u73fe\u3067\u304d\u3001\u72b6\u614b\u304c\u305d\u306e\u5468\u56f2\u306e\u72b6\u614b\u3068\u518d\u5e30\u95a2\u4fc2\u3092\u6301\u3063\u3066\u3044\u308b\u3002</li> </ul> <p>\u5bfe\u5fdc\u3057\u3066\u3001\u300c\u30da\u30ca\u30eb\u30c6\u30a3\u30dd\u30a4\u30f3\u30c8\u300d\u3082\u3042\u308a\u307e\u3059\u3002</p> <ul> <li>\u554f\u984c\u306e\u76ee\u6a19\u306f\u6700\u9069\u89e3\u3060\u3051\u3067\u306a\u304f\u3001\u3059\u3079\u3066\u306e\u53ef\u80fd\u306a\u89e3\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u3067\u3042\u308b\u3002</li> <li>\u554f\u984c\u306e\u8aac\u660e\u306b\u9806\u5217\u3068\u7d44\u307f\u5408\u308f\u305b\u306e\u660e\u3089\u304b\u306a\u7279\u5fb4\u304c\u3042\u308a\u3001\u7279\u5b9a\u306e\u8907\u6570\u306e\u89e3\u3092\u8fd4\u3059\u5fc5\u8981\u304c\u3042\u308b\u3002</li> </ul> <p>\u554f\u984c\u304c\u6c7a\u5b9a\u6728\u30e2\u30c7\u30eb\u306b\u9069\u5408\u3057\u3001\u6bd4\u8f03\u7684\u660e\u3089\u304b\u306a\u300c\u30dc\u30fc\u30ca\u30b9\u30dd\u30a4\u30f3\u30c8\u300d\u3092\u6301\u3064\u5834\u5408\u3001\u305d\u308c\u304c\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u554f\u984c\u3067\u3042\u308b\u3068\u4eee\u5b9a\u3057\u3001\u89e3\u6c7a\u30d7\u30ed\u30bb\u30b9\u4e2d\u306b\u691c\u8a3c\u3067\u304d\u307e\u3059\u3002</p>"},{"location":"chapter_dynamic_programming/dp_solution_pipeline/#1432","title":"14.3.2 \u00a0 \u554f\u984c\u89e3\u6c7a\u30b9\u30c6\u30c3\u30d7","text":"<p>\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u554f\u984c\u89e3\u6c7a\u30d7\u30ed\u30bb\u30b9\u306f\u554f\u984c\u306e\u6027\u8cea\u3068\u96e3\u6613\u5ea6\u306b\u3088\u3063\u3066\u7570\u306a\u308a\u307e\u3059\u304c\u3001\u4e00\u822c\u7684\u306b\u6b21\u306e\u30b9\u30c6\u30c3\u30d7\u306b\u5f93\u3044\u307e\u3059\uff1a\u6c7a\u5b9a\u306e\u8a18\u8ff0\u3001\u72b6\u614b\u306e\u5b9a\u7fa9\u3001\\(dp\\) \u30c6\u30fc\u30d6\u30eb\u306e\u78ba\u7acb\u3001\u72b6\u614b\u9077\u79fb\u65b9\u7a0b\u5f0f\u306e\u5c0e\u51fa\u3001\u5883\u754c\u6761\u4ef6\u306e\u6c7a\u5b9a\u306a\u3069\u3002</p> <p>\u554f\u984c\u89e3\u6c7a\u30b9\u30c6\u30c3\u30d7\u3092\u3088\u308a\u5177\u4f53\u7684\u306b\u8aac\u660e\u3059\u308b\u305f\u3081\u306b\u3001\u53e4\u5178\u7684\u306a\u554f\u984c\u300c\u6700\u5c0f\u7d4c\u8def\u548c\u300d\u3092\u4f8b\u3068\u3057\u3066\u4f7f\u7528\u3057\u307e\u3059\u3002</p> <p>Question</p> <p>\\(n \\times m\\) \u306e\u4e8c\u6b21\u5143\u30b0\u30ea\u30c3\u30c9 <code>grid</code> \u304c\u4e0e\u3048\u3089\u308c\u3001\u30b0\u30ea\u30c3\u30c9\u306e\u5404\u30bb\u30eb\u306b\u306f\u8ca0\u3067\u306a\u3044\u6574\u6570\u304c\u542b\u307e\u308c\u3001\u305d\u306e\u30bb\u30eb\u306e\u30b3\u30b9\u30c8\u3092\u8868\u3057\u307e\u3059\u3002\u30ed\u30dc\u30c3\u30c8\u306f\u5de6\u4e0a\u306e\u30bb\u30eb\u304b\u3089\u59cb\u307e\u308a\u3001\u5404\u30b9\u30c6\u30c3\u30d7\u3067\u4e0b\u307e\u305f\u306f\u53f3\u306b\u306e\u307f\u79fb\u52d5\u3067\u304d\u3001\u53f3\u4e0b\u306e\u30bb\u30eb\u306b\u5230\u9054\u3059\u308b\u307e\u3067\u7d9a\u3051\u307e\u3059\u3002\u5de6\u4e0a\u304b\u3089\u53f3\u4e0b\u3078\u306e\u6700\u5c0f\u7d4c\u8def\u548c\u3092\u8fd4\u3057\u3066\u304f\u3060\u3055\u3044\u3002</p> <p>\u4e0b\u306e\u56f3\u306f\u4f8b\u3092\u793a\u3057\u3066\u304a\u308a\u3001\u4e0e\u3048\u3089\u308c\u305f\u30b0\u30ea\u30c3\u30c9\u306e\u6700\u5c0f\u7d4c\u8def\u548c\u306f \\(13\\) \u3067\u3059\u3002</p> <p></p> <p> \u56f3 14-10 \u00a0 \u6700\u5c0f\u7d4c\u8def\u548c\u306e\u4f8b\u30c7\u30fc\u30bf </p> <p>\u7b2c1\u30b9\u30c6\u30c3\u30d7\uff1a\u5404\u30e9\u30a6\u30f3\u30c9\u306e\u6c7a\u5b9a\u3092\u8003\u3048\u3001\u72b6\u614b\u3092\u5b9a\u7fa9\u3057\u3001\u305d\u308c\u306b\u3088\u308a \\(dp\\) \u30c6\u30fc\u30d6\u30eb\u3092\u5f97\u308b</p> <p>\u3053\u306e\u554f\u984c\u306e\u5404\u30e9\u30a6\u30f3\u30c9\u306e\u6c7a\u5b9a\u306f\u3001\u73fe\u5728\u306e\u30bb\u30eb\u304b\u3089\u4e0b\u307e\u305f\u306f\u53f3\u306b1\u30b9\u30c6\u30c3\u30d7\u79fb\u52d5\u3059\u308b\u3053\u3068\u3067\u3059\u3002\u73fe\u5728\u306e\u30bb\u30eb\u306e\u884c\u3068\u5217\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u304c \\([i, j]\\) \u3067\u3042\u308b\u3068\u4eee\u5b9a\u3059\u308b\u3068\u3001\u4e0b\u307e\u305f\u306f\u53f3\u306b\u79fb\u52d5\u3057\u305f\u5f8c\u3001\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306f \\([i+1, j]\\) \u307e\u305f\u306f \\([i, j+1]\\) \u306b\u306a\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u72b6\u614b\u306b\u306f2\u3064\u306e\u5909\u6570\u304c\u542b\u307e\u308c\u308b\u3079\u304d\u3067\u3059\uff1a\u884c\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3068\u5217\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3001\\([i, j]\\) \u3068\u8868\u8a18\u3055\u308c\u307e\u3059\u3002</p> <p>\u72b6\u614b \\([i, j]\\) \u306f\u90e8\u5206\u554f\u984c\u306b\u5bfe\u5fdc\u3057\u307e\u3059\uff1a\u958b\u59cb\u70b9 \\([0, 0]\\) \u304b\u3089 \\([i, j]\\) \u3078\u306e\u6700\u5c0f\u7d4c\u8def\u548c\u3001\\(dp[i, j]\\) \u3068\u8868\u8a18\u3055\u308c\u307e\u3059\u3002</p> <p>\u3053\u306e\u3088\u3046\u306b\u3057\u3066\u3001\u4e0b\u306e\u56f3\u306b\u793a\u3059\u4e8c\u6b21\u5143 \\(dp\\) \u884c\u5217\u3092\u5f97\u307e\u3059\u3002\u305d\u306e\u30b5\u30a4\u30ba\u306f\u5165\u529b\u30b0\u30ea\u30c3\u30c9 \\(grid\\) \u3068\u540c\u3058\u3067\u3059\u3002</p> <p></p> <p> \u56f3 14-11 \u00a0 \u72b6\u614b\u5b9a\u7fa9\u3068DP\u30c6\u30fc\u30d6\u30eb </p> <p>Note</p> <p>\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u3068\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u306f\u6c7a\u5b9a\u306e\u30b7\u30fc\u30b1\u30f3\u30b9\u3068\u3057\u3066\u8a18\u8ff0\u3067\u304d\u3001\u72b6\u614b\u306f\u3059\u3079\u3066\u306e\u6c7a\u5b9a\u5909\u6570\u304b\u3089\u69cb\u6210\u3055\u308c\u307e\u3059\u3002\u554f\u984c\u89e3\u6c7a\u306e\u9032\u884c\u3092\u8a18\u8ff0\u3059\u308b\u3059\u3079\u3066\u306e\u5909\u6570\u3092\u542b\u3080\u3079\u304d\u3067\u3001\u6b21\u306e\u72b6\u614b\u3092\u5c0e\u51fa\u3059\u308b\u306e\u306b\u5341\u5206\u306a\u60c5\u5831\u3092\u542b\u3093\u3067\u3044\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002</p> <p>\u5404\u72b6\u614b\u306f\u90e8\u5206\u554f\u984c\u306b\u5bfe\u5fdc\u3057\u3001\u3059\u3079\u3066\u306e\u90e8\u5206\u554f\u984c\u306e\u89e3\u3092\u4fdd\u5b58\u3059\u308b\u305f\u3081\u306e \\(dp\\) \u30c6\u30fc\u30d6\u30eb\u3092\u5b9a\u7fa9\u3057\u307e\u3059\u3002\u72b6\u614b\u306e\u5404\u72ec\u7acb\u5909\u6570\u306f \\(dp\\) \u30c6\u30fc\u30d6\u30eb\u306e\u6b21\u5143\u3067\u3059\u3002\u672c\u8cea\u7684\u306b\u3001\\(dp\\) \u30c6\u30fc\u30d6\u30eb\u306f\u72b6\u614b\u3068\u90e8\u5206\u554f\u984c\u306e\u89e3\u306e\u9593\u306e\u30de\u30c3\u30d4\u30f3\u30b0\u3067\u3059\u3002</p> <p>\u7b2c2\u30b9\u30c6\u30c3\u30d7\uff1a\u6700\u9069\u90e8\u5206\u69cb\u9020\u3092\u7279\u5b9a\u3057\u3001\u72b6\u614b\u9077\u79fb\u65b9\u7a0b\u5f0f\u3092\u5c0e\u51fa\u3059\u308b</p> <p>\u72b6\u614b \\([i, j]\\) \u306b\u3064\u3044\u3066\u3001\u305d\u308c\u306f\u4e0a\u306e\u30bb\u30eb \\([i-1, j]\\) \u307e\u305f\u306f\u5de6\u306e\u30bb\u30eb \\([i, j-1]\\) \u304b\u3089\u306e\u307f\u5c0e\u51fa\u3067\u304d\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u6700\u9069\u90e8\u5206\u69cb\u9020\u306f\uff1a\\([i, j]\\) \u306b\u5230\u9054\u3059\u308b\u6700\u5c0f\u7d4c\u8def\u548c\u306f\u3001\\([i, j-1]\\) \u3068 \\([i-1, j]\\) \u306e\u6700\u5c0f\u7d4c\u8def\u548c\u306e\u5c0f\u3055\u3044\u65b9\u306b\u3088\u3063\u3066\u6c7a\u5b9a\u3055\u308c\u307e\u3059\u3002</p> <p>\u4e0a\u8a18\u306e\u5206\u6790\u306b\u57fa\u3065\u3044\u3066\u3001\u4e0b\u306e\u56f3\u306b\u793a\u3059\u72b6\u614b\u9077\u79fb\u65b9\u7a0b\u5f0f\u3092\u5c0e\u51fa\u3067\u304d\u307e\u3059\uff1a</p> \\[ dp[i, j] = \\min(dp[i-1, j], dp[i, j-1]) + grid[i, j] \\] <p></p> <p> \u56f3 14-12 \u00a0 \u6700\u9069\u90e8\u5206\u69cb\u9020\u3068\u72b6\u614b\u9077\u79fb\u65b9\u7a0b\u5f0f </p> <p>Note</p> <p>\u5b9a\u7fa9\u3055\u308c\u305f \\(dp\\) \u30c6\u30fc\u30d6\u30eb\u306b\u57fa\u3065\u3044\u3066\u3001\u5143\u306e\u554f\u984c\u3068\u90e8\u5206\u554f\u984c\u306e\u95a2\u4fc2\u3092\u8003\u3048\u3001\u90e8\u5206\u554f\u984c\u306e\u6700\u9069\u89e3\u304b\u3089\u5143\u306e\u554f\u984c\u306e\u6700\u9069\u89e3\u3092\u3069\u306e\u3088\u3046\u306b\u69cb\u7bc9\u3059\u308b\u304b\u3001\u3064\u307e\u308a\u6700\u9069\u90e8\u5206\u69cb\u9020\u3092\u898b\u3064\u3051\u307e\u3059\u3002</p> <p>\u6700\u9069\u90e8\u5206\u69cb\u9020\u3092\u7279\u5b9a\u3057\u305f\u3089\u3001\u305d\u308c\u3092\u4f7f\u7528\u3057\u3066\u72b6\u614b\u9077\u79fb\u65b9\u7a0b\u5f0f\u3092\u69cb\u7bc9\u3067\u304d\u307e\u3059\u3002</p> <p>\u7b2c3\u30b9\u30c6\u30c3\u30d7\uff1a\u5883\u754c\u6761\u4ef6\u3068\u72b6\u614b\u9077\u79fb\u9806\u5e8f\u3092\u6c7a\u5b9a\u3059\u308b</p> <p>\u3053\u306e\u554f\u984c\u3067\u306f\u3001\u6700\u521d\u306e\u884c\u306e\u72b6\u614b\u306f\u5de6\u306e\u72b6\u614b\u304b\u3089\u306e\u307f\u6765\u308b\u3053\u3068\u304c\u3067\u304d\u3001\u6700\u521d\u306e\u5217\u306e\u72b6\u614b\u306f\u4e0a\u306e\u72b6\u614b\u304b\u3089\u306e\u307f\u6765\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u305f\u3081\u3001\u6700\u521d\u306e\u884c \\(i = 0\\) \u3068\u6700\u521d\u306e\u5217 \\(j = 0\\) \u304c\u5883\u754c\u6761\u4ef6\u3067\u3059\u3002</p> <p>\u4e0b\u306e\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u5404\u30bb\u30eb\u306f\u5de6\u306e\u30bb\u30eb\u3068\u4e0a\u306e\u30bb\u30eb\u304b\u3089\u5c0e\u51fa\u3055\u308c\u308b\u305f\u3081\u3001\u30eb\u30fc\u30d7\u3092\u4f7f\u7528\u3057\u3066\u884c\u5217\u3092\u8d70\u67fb\u3057\u3001\u5916\u5074\u306e\u30eb\u30fc\u30d7\u306f\u884c\u3092\u53cd\u5fa9\u3057\u3001\u5185\u5074\u306e\u30eb\u30fc\u30d7\u306f\u5217\u3092\u53cd\u5fa9\u3057\u307e\u3059\u3002</p> <p></p> <p> \u56f3 14-13 \u00a0 \u5883\u754c\u6761\u4ef6\u3068\u72b6\u614b\u9077\u79fb\u9806\u5e8f </p> <p>Note</p> <p>\u5883\u754c\u6761\u4ef6\u306f\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u3067 \\(dp\\) \u30c6\u30fc\u30d6\u30eb\u3092\u521d\u671f\u5316\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u3001\u63a2\u7d22\u3067\u306f\u679d\u5208\u308a\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002</p> <p>\u72b6\u614b\u9077\u79fb\u9806\u5e8f\u306e\u6838\u5fc3\u306f\u3001\u73fe\u5728\u306e\u554f\u984c\u306e\u89e3\u3092\u8a08\u7b97\u3059\u308b\u3068\u304d\u3001\u305d\u308c\u304c\u4f9d\u5b58\u3059\u308b\u3059\u3079\u3066\u306e\u5c0f\u3055\u306a\u90e8\u5206\u554f\u984c\u304c\u65e2\u306b\u6b63\u3057\u304f\u8a08\u7b97\u3055\u308c\u3066\u3044\u308b\u3053\u3068\u3092\u78ba\u4fdd\u3059\u308b\u3053\u3068\u3067\u3059\u3002</p> <p>\u4e0a\u8a18\u306e\u5206\u6790\u306b\u57fa\u3065\u3044\u3066\u3001\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u30b3\u30fc\u30c9\u3092\u76f4\u63a5\u66f8\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u90e8\u5206\u554f\u984c\u306e\u5206\u89e3\u306f\u30c8\u30c3\u30d7\u30c0\u30a6\u30f3\u30a2\u30d7\u30ed\u30fc\u30c1\u3067\u3042\u308b\u305f\u3081\u3001\u300c\u529b\u4efb\u305b\u63a2\u7d22 \u2192 \u30e1\u30e2\u5316\u63a2\u7d22 \u2192 \u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u300d\u306e\u9806\u5e8f\u3067\u5b9f\u88c5\u3059\u308b\u3053\u3068\u304c\u7fd2\u6163\u7684\u306a\u601d\u8003\u306b\u3088\u308a\u9069\u5408\u3057\u307e\u3059\u3002</p>"},{"location":"chapter_dynamic_programming/dp_solution_pipeline/#1-1","title":"1. \u00a0 \u65b9\u6cd51\uff1a\u529b\u4efb\u305b\u63a2\u7d22","text":"<p>\u72b6\u614b \\([i, j]\\) \u304b\u3089\u63a2\u7d22\u3092\u958b\u59cb\u3057\u3001\u305d\u308c\u3092\u5e38\u306b\u3088\u308a\u5c0f\u3055\u306a\u72b6\u614b \\([i-1, j]\\) \u3068 \\([i, j-1]\\) \u306b\u5206\u89e3\u3057\u307e\u3059\u3002\u518d\u5e30\u95a2\u6570\u306b\u306f\u4ee5\u4e0b\u306e\u8981\u7d20\u304c\u542b\u307e\u308c\u307e\u3059\u3002</p> <ul> <li>\u518d\u5e30\u30d1\u30e9\u30e1\u30fc\u30bf\uff1a\u72b6\u614b \\([i, j]\\)\u3002</li> <li>\u623b\u308a\u5024\uff1a\\([0, 0]\\) \u304b\u3089 \\([i, j]\\) \u3078\u306e\u6700\u5c0f\u7d4c\u8def\u548c \\(dp[i, j]\\)\u3002</li> <li>\u7d42\u4e86\u6761\u4ef6\uff1a\\(i = 0\\) \u304b\u3064 \\(j = 0\\) \u306e\u3068\u304d\u3001\u30b3\u30b9\u30c8 \\(grid[0, 0]\\) \u3092\u8fd4\u3059\u3002</li> <li>\u679d\u5208\u308a\uff1a\\(i &lt; 0\\) \u307e\u305f\u306f \\(j &lt; 0\\) \u3067\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u304c\u7bc4\u56f2\u5916\u306e\u3068\u304d\u3001\u30b3\u30b9\u30c8 \\(+\\infty\\) \u3092\u8fd4\u3057\u3001\u5b9f\u884c\u4e0d\u53ef\u80fd\u6027\u3092\u8868\u3059\u3002</li> </ul> <p>\u5b9f\u88c5\u30b3\u30fc\u30c9\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig min_path_sum.py<pre><code>def min_path_sum_dfs(grid: list[list[int]], i: int, j: int) -&gt; int:\n    \"\"\"\u6700\u5c0f\u30d1\u30b9\u548c\uff1a\u30d6\u30eb\u30fc\u30c8\u30d5\u30a9\u30fc\u30b9\u63a2\u7d22\"\"\"\n    # \u5de6\u4e0a\u306e\u30bb\u30eb\u306e\u5834\u5408\u3001\u63a2\u7d22\u3092\u7d42\u4e86\n    if i == 0 and j == 0:\n        return grid[0][0]\n    # \u884c\u307e\u305f\u306f\u5217\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u304c\u7bc4\u56f2\u5916\u306e\u5834\u5408\u3001+\u221e \u30b3\u30b9\u30c8\u3092\u8fd4\u3059\n    if i &lt; 0 or j &lt; 0:\n        return inf\n    # \u5de6\u4e0a\u304b\u3089 (i-1, j) \u3068 (i, j-1) \u3078\u306e\u6700\u5c0f\u30d1\u30b9\u30b3\u30b9\u30c8\u3092\u8a08\u7b97\n    up = min_path_sum_dfs(grid, i - 1, j)\n    left = min_path_sum_dfs(grid, i, j - 1)\n    # \u5de6\u4e0a\u304b\u3089 (i, j) \u3078\u306e\u6700\u5c0f\u30d1\u30b9\u30b3\u30b9\u30c8\u3092\u8fd4\u3059\n    return min(left, up) + grid[i][j]\n</code></pre> min_path_sum.cpp<pre><code>/* \u6700\u5c0f\u30d1\u30b9\u548c\uff1a\u30d6\u30eb\u30fc\u30c8\u30d5\u30a9\u30fc\u30b9\u63a2\u7d22 */\nint minPathSumDFS(vector&lt;vector&lt;int&gt;&gt; &amp;grid, int i, int j) {\n    // \u5de6\u4e0a\u306e\u30bb\u30eb\u306e\u5834\u5408\u3001\u63a2\u7d22\u3092\u7d42\u4e86\n    if (i == 0 &amp;&amp; j == 0) {\n        return grid[0][0];\n    }\n    // \u884c\u307e\u305f\u306f\u5217\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u304c\u7bc4\u56f2\u5916\u306e\u5834\u5408\u3001+\u221e \u306e\u30b3\u30b9\u30c8\u3092\u8fd4\u3059\n    if (i &lt; 0 || j &lt; 0) {\n        return INT_MAX;\n    }\n    // \u5de6\u4e0a\u304b\u3089 (i-1, j) \u3068 (i, j-1) \u3078\u306e\u6700\u5c0f\u30d1\u30b9\u30b3\u30b9\u30c8\u3092\u8a08\u7b97\n    int up = minPathSumDFS(grid, i - 1, j);\n    int left = minPathSumDFS(grid, i, j - 1);\n    // \u5de6\u4e0a\u304b\u3089 (i, j) \u3078\u306e\u6700\u5c0f\u30d1\u30b9\u30b3\u30b9\u30c8\u3092\u8fd4\u3059\n    return min(left, up) + grid[i][j];\n}\n</code></pre> min_path_sum.java<pre><code>/* \u6700\u5c0f\u30d1\u30b9\u548c\uff1a\u30d6\u30eb\u30fc\u30c8\u30d5\u30a9\u30fc\u30b9\u63a2\u7d22 */\nint minPathSumDFS(int[][] grid, int i, int j) {\n    // \u5de6\u4e0a\u306e\u30bb\u30eb\u306e\u5834\u5408\u3001\u63a2\u7d22\u3092\u7d42\u4e86\n    if (i == 0 &amp;&amp; j == 0) {\n        return grid[0][0];\n    }\n    // \u884c\u307e\u305f\u306f\u5217\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u304c\u7bc4\u56f2\u5916\u306e\u5834\u5408\u3001+\u221e \u306e\u30b3\u30b9\u30c8\u3092\u8fd4\u3059\n    if (i &lt; 0 || j &lt; 0) {\n        return Integer.MAX_VALUE;\n    }\n    // \u5de6\u4e0a\u304b\u3089 (i-1, j) \u3068 (i, j-1) \u3078\u306e\u6700\u5c0f\u30d1\u30b9\u30b3\u30b9\u30c8\u3092\u8a08\u7b97\n    int up = minPathSumDFS(grid, i - 1, j);\n    int left = minPathSumDFS(grid, i, j - 1);\n    // \u5de6\u4e0a\u304b\u3089 (i, j) \u3078\u306e\u6700\u5c0f\u30d1\u30b9\u30b3\u30b9\u30c8\u3092\u8fd4\u3059\n    return Math.min(left, up) + grid[i][j];\n}\n</code></pre> min_path_sum.cs<pre><code>[class]{min_path_sum}-[func]{MinPathSumDFS}\n</code></pre> min_path_sum.go<pre><code>[class]{}-[func]{minPathSumDFS}\n</code></pre> min_path_sum.swift<pre><code>[class]{}-[func]{minPathSumDFS}\n</code></pre> min_path_sum.js<pre><code>[class]{}-[func]{minPathSumDFS}\n</code></pre> min_path_sum.ts<pre><code>[class]{}-[func]{minPathSumDFS}\n</code></pre> min_path_sum.dart<pre><code>[class]{}-[func]{minPathSumDFS}\n</code></pre> min_path_sum.rs<pre><code>[class]{}-[func]{min_path_sum_dfs}\n</code></pre> min_path_sum.c<pre><code>[class]{}-[func]{minPathSumDFS}\n</code></pre> min_path_sum.kt<pre><code>[class]{}-[func]{minPathSumDFS}\n</code></pre> min_path_sum.rb<pre><code>[class]{}-[func]{min_path_sum_dfs}\n</code></pre> min_path_sum.zig<pre><code>[class]{}-[func]{minPathSumDFS}\n</code></pre> <p>\u4e0b\u306e\u56f3\u306f \\(dp[2, 1]\\) \u3092\u6839\u3068\u3059\u308b\u518d\u5e30\u6728\u3092\u793a\u3057\u3066\u304a\u308a\u3001\u3044\u304f\u3064\u304b\u306e\u91cd\u8907\u3059\u308b\u90e8\u5206\u554f\u984c\u3092\u542b\u307f\u3001\u305d\u306e\u6570\u306f\u30b0\u30ea\u30c3\u30c9 <code>grid</code> \u306e\u30b5\u30a4\u30ba\u304c\u5897\u52a0\u3059\u308b\u3068\u6025\u6fc0\u306b\u5897\u52a0\u3057\u307e\u3059\u3002</p> <p>\u672c\u8cea\u7684\u306b\u3001\u91cd\u8907\u3059\u308b\u90e8\u5206\u554f\u984c\u306e\u7406\u7531\u306f\uff1a**\u5de6\u4e0a\u9685\u304b\u3089\u7279\u5b9a\u306e\u30bb\u30eb\u306b\u5230\u9054\u3059\u308b\u8907\u6570\u306e\u30d1\u30b9\u304c\u5b58\u5728\u3059\u308b**\u3053\u3068\u3067\u3059\u3002</p> <p></p> <p> \u56f3 14-14 \u00a0 \u529b\u4efb\u305b\u63a2\u7d22\u306e\u518d\u5e30\u6728 </p> <p>\u5404\u72b6\u614b\u306b\u306f\u4e0b\u3068\u53f3\u306e2\u3064\u306e\u9078\u629e\u304c\u3042\u308b\u305f\u3081\u3001\u5de6\u4e0a\u9685\u304b\u3089\u53f3\u4e0b\u9685\u307e\u3067\u306e\u7dcf\u30b9\u30c6\u30c3\u30d7\u6570\u306f \\(m + n - 2\\) \u3067\u3001\u6700\u60aa\u6642\u9593\u8a08\u7b97\u91cf\u306f \\(O(2^{m + n})\\) \u3067\u3059\u3002\u3053\u306e\u8a08\u7b97\u65b9\u6cd5\u306f\u30b0\u30ea\u30c3\u30c9\u30a8\u30c3\u30b8\u8fd1\u304f\u306e\u72b6\u6cc1\u3092\u8003\u616e\u3057\u3066\u3044\u306a\u3044\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u30a8\u30c3\u30b8\u306b\u5230\u9054\u3057\u305f\u3068\u304d\u3001\u9078\u629e\u80a2\u304c1\u3064\u3057\u304b\u6b8b\u3089\u306a\u3044\u305f\u3081\u3001\u5b9f\u969b\u306e\u30d1\u30b9\u6570\u306f\u3088\u308a\u5c11\u306a\u304f\u306a\u308a\u307e\u3059\u3002</p>"},{"location":"chapter_dynamic_programming/dp_solution_pipeline/#2-2","title":"2. \u00a0 \u65b9\u6cd52\uff1a\u30e1\u30e2\u5316\u63a2\u7d22","text":"<p>\u30b0\u30ea\u30c3\u30c9 <code>grid</code> \u3068\u540c\u3058\u30b5\u30a4\u30ba\u306e\u30e1\u30e2\u30ea\u30b9\u30c8 <code>mem</code> \u3092\u5c0e\u5165\u3057\u3001\u69d8\u3005\u306a\u90e8\u5206\u554f\u984c\u306e\u89e3\u3092\u8a18\u9332\u3057\u3001\u91cd\u8907\u3059\u308b\u90e8\u5206\u554f\u984c\u3092\u679d\u5208\u308a\u3057\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig min_path_sum.py<pre><code>def min_path_sum_dfs_mem(\n    grid: list[list[int]], mem: list[list[int]], i: int, j: int\n) -&gt; int:\n    \"\"\"\u6700\u5c0f\u30d1\u30b9\u548c\uff1a\u8a18\u61b6\u5316\u63a2\u7d22\"\"\"\n    # \u5de6\u4e0a\u306e\u30bb\u30eb\u306e\u5834\u5408\u3001\u63a2\u7d22\u3092\u7d42\u4e86\n    if i == 0 and j == 0:\n        return grid[0][0]\n    # \u884c\u307e\u305f\u306f\u5217\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u304c\u7bc4\u56f2\u5916\u306e\u5834\u5408\u3001+\u221e \u30b3\u30b9\u30c8\u3092\u8fd4\u3059\n    if i &lt; 0 or j &lt; 0:\n        return inf\n    # \u8a18\u9332\u304c\u3042\u308b\u5834\u5408\u3001\u305d\u308c\u3092\u8fd4\u3059\n    if mem[i][j] != -1:\n        return mem[i][j]\n    # \u5de6\u3068\u4e0a\u306e\u30bb\u30eb\u304b\u3089\u306e\u6700\u5c0f\u30d1\u30b9\u30b3\u30b9\u30c8\n    up = min_path_sum_dfs_mem(grid, mem, i - 1, j)\n    left = min_path_sum_dfs_mem(grid, mem, i, j - 1)\n    # \u5de6\u4e0a\u304b\u3089 (i, j) \u3078\u306e\u6700\u5c0f\u30d1\u30b9\u30b3\u30b9\u30c8\u3092\u8a18\u9332\u3057\u3066\u8fd4\u3059\n    mem[i][j] = min(left, up) + grid[i][j]\n    return mem[i][j]\n</code></pre> min_path_sum.cpp<pre><code>[class]{}-[func]{minPathSumDFSMem}\n</code></pre> min_path_sum.java<pre><code>/* \u6700\u5c0f\u30d1\u30b9\u548c\uff1a\u30e1\u30e2\u5316\u63a2\u7d22 */\nint minPathSumDFSMem(int[][] grid, int[][] mem, int i, int j) {\n    // \u5de6\u4e0a\u306e\u30bb\u30eb\u306e\u5834\u5408\u3001\u63a2\u7d22\u3092\u7d42\u4e86\n    if (i == 0 &amp;&amp; j == 0) {\n        return grid[0][0];\n    }\n    // \u884c\u307e\u305f\u306f\u5217\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u304c\u7bc4\u56f2\u5916\u306e\u5834\u5408\u3001+\u221e \u306e\u30b3\u30b9\u30c8\u3092\u8fd4\u3059\n    if (i &lt; 0 || j &lt; 0) {\n        return Integer.MAX_VALUE;\n    }\n    // \u8a18\u9332\u304c\u3042\u308b\u5834\u5408\u3001\u305d\u308c\u3092\u8fd4\u3059\n    if (mem[i][j] != -1) {\n        return mem[i][j];\n    }\n    // \u5de6\u3068\u4e0a\u306e\u30bb\u30eb\u304b\u3089\u306e\u6700\u5c0f\u30d1\u30b9\u30b3\u30b9\u30c8\n    int up = minPathSumDFSMem(grid, mem, i - 1, j);\n    int left = minPathSumDFSMem(grid, mem, i, j - 1);\n    // \u5de6\u4e0a\u304b\u3089 (i, j) \u3078\u306e\u6700\u5c0f\u30d1\u30b9\u30b3\u30b9\u30c8\u3092\u8a18\u9332\u3057\u3066\u8fd4\u3059\n    mem[i][j] = Math.min(left, up) + grid[i][j];\n    return mem[i][j];\n}\n</code></pre> min_path_sum.cs<pre><code>[class]{min_path_sum}-[func]{MinPathSumDFSMem}\n</code></pre> min_path_sum.go<pre><code>[class]{}-[func]{minPathSumDFSMem}\n</code></pre> min_path_sum.swift<pre><code>[class]{}-[func]{minPathSumDFSMem}\n</code></pre> min_path_sum.js<pre><code>[class]{}-[func]{minPathSumDFSMem}\n</code></pre> min_path_sum.ts<pre><code>[class]{}-[func]{minPathSumDFSMem}\n</code></pre> min_path_sum.dart<pre><code>[class]{}-[func]{minPathSumDFSMem}\n</code></pre> min_path_sum.rs<pre><code>[class]{}-[func]{min_path_sum_dfs_mem}\n</code></pre> min_path_sum.c<pre><code>[class]{}-[func]{minPathSumDFSMem}\n</code></pre> min_path_sum.kt<pre><code>[class]{}-[func]{minPathSumDFSMem}\n</code></pre> min_path_sum.rb<pre><code>[class]{}-[func]{min_path_sum_dfs_mem}\n</code></pre> min_path_sum.zig<pre><code>[class]{}-[func]{minPathSumDFSMem}\n</code></pre> <p>\u4e0b\u306e\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u30e1\u30e2\u5316\u3092\u5c0e\u5165\u3057\u305f\u5f8c\u3001\u3059\u3079\u3066\u306e\u90e8\u5206\u554f\u984c\u306e\u89e3\u306f\u4e00\u5ea6\u3060\u3051\u8a08\u7b97\u3055\u308c\u308b\u5fc5\u8981\u304c\u3042\u308b\u305f\u3081\u3001\u6642\u9593\u8a08\u7b97\u91cf\u306f\u72b6\u614b\u306e\u7dcf\u6570\u3001\u3064\u307e\u308a\u30b0\u30ea\u30c3\u30c9\u30b5\u30a4\u30ba \\(O(nm)\\) \u306b\u4f9d\u5b58\u3057\u307e\u3059\u3002</p> <p></p> <p> \u56f3 14-15 \u00a0 \u30e1\u30e2\u5316\u63a2\u7d22\u306e\u518d\u5e30\u6728 </p>"},{"location":"chapter_dynamic_programming/dp_solution_pipeline/#3-3","title":"3. \u00a0 \u65b9\u6cd53\uff1a\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0","text":"<p>\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u89e3\u6cd5\u3092\u53cd\u5fa9\u7684\u306b\u5b9f\u88c5\u3057\u307e\u3059\u3002\u30b3\u30fc\u30c9\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig min_path_sum.py<pre><code>def min_path_sum_dp(grid: list[list[int]]) -&gt; int:\n    \"\"\"\u6700\u5c0f\u30d1\u30b9\u548c\uff1a\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\"\"\"\n    n, m = len(grid), len(grid[0])\n    # dp \u30c6\u30fc\u30d6\u30eb\u3092\u521d\u671f\u5316\n    dp = [[0] * m for _ in range(n)]\n    dp[0][0] = grid[0][0]\n    # \u72b6\u614b\u9077\u79fb\uff1a\u6700\u521d\u306e\u884c\n    for j in range(1, m):\n        dp[0][j] = dp[0][j - 1] + grid[0][j]\n    # \u72b6\u614b\u9077\u79fb\uff1a\u6700\u521d\u306e\u5217\n    for i in range(1, n):\n        dp[i][0] = dp[i - 1][0] + grid[i][0]\n    # \u72b6\u614b\u9077\u79fb\uff1a\u6b8b\u308a\u306e\u884c\u3068\u5217\n    for i in range(1, n):\n        for j in range(1, m):\n            dp[i][j] = min(dp[i][j - 1], dp[i - 1][j]) + grid[i][j]\n    return dp[n - 1][m - 1]\n</code></pre> min_path_sum.cpp<pre><code>/* \u6700\u5c0f\u30d1\u30b9\u548c\uff1a\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0 */\nint minPathSumDP(vector&lt;vector&lt;int&gt;&gt; &amp;grid) {\n    int n = grid.size(), m = grid[0].size();\n    // DP\u30c6\u30fc\u30d6\u30eb\u3092\u521d\u671f\u5316\n    vector&lt;vector&lt;int&gt;&gt; dp(n, vector&lt;int&gt;(m));\n    dp[0][0] = grid[0][0];\n    // \u72b6\u614b\u9077\u79fb\uff1a\u6700\u521d\u306e\u884c\n    for (int j = 1; j &lt; m; j++) {\n        dp[0][j] = dp[0][j - 1] + grid[0][j];\n    }\n    // \u72b6\u614b\u9077\u79fb\uff1a\u6700\u521d\u306e\u5217\n    for (int i = 1; i &lt; n; i++) {\n        dp[i][0] = dp[i - 1][0] + grid[i][0];\n    }\n    // \u72b6\u614b\u9077\u79fb\uff1a\u6b8b\u308a\u306e\u884c\u3068\u5217\n    for (int i = 1; i &lt; n; i++) {\n        for (int j = 1; j &lt; m; j++) {\n            dp[i][j] = min(dp[i][j - 1], dp[i - 1][j]) + grid[i][j];\n        }\n    }\n    return dp[n - 1][m - 1];\n}\n</code></pre> min_path_sum.java<pre><code>/* \u6700\u5c0f\u30d1\u30b9\u548c\uff1a\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0 */\nint minPathSumDP(int[][] grid) {\n    int n = grid.length, m = grid[0].length;\n    // DP\u30c6\u30fc\u30d6\u30eb\u3092\u521d\u671f\u5316\n    int[][] dp = new int[n][m];\n    dp[0][0] = grid[0][0];\n    // \u72b6\u614b\u9077\u79fb\uff1a\u6700\u521d\u306e\u884c\n    for (int j = 1; j &lt; m; j++) {\n        dp[0][j] = dp[0][j - 1] + grid[0][j];\n    }\n    // \u72b6\u614b\u9077\u79fb\uff1a\u6700\u521d\u306e\u5217\n    for (int i = 1; i &lt; n; i++) {\n        dp[i][0] = dp[i - 1][0] + grid[i][0];\n    }\n    // \u72b6\u614b\u9077\u79fb\uff1a\u6b8b\u308a\u306e\u884c\u3068\u5217\n    for (int i = 1; i &lt; n; i++) {\n        for (int j = 1; j &lt; m; j++) {\n            dp[i][j] = Math.min(dp[i][j - 1], dp[i - 1][j]) + grid[i][j];\n        }\n    }\n    return dp[n - 1][m - 1];\n}\n</code></pre> min_path_sum.cs<pre><code>[class]{min_path_sum}-[func]{MinPathSumDP}\n</code></pre> min_path_sum.go<pre><code>[class]{}-[func]{minPathSumDP}\n</code></pre> min_path_sum.swift<pre><code>[class]{}-[func]{minPathSumDP}\n</code></pre> min_path_sum.js<pre><code>[class]{}-[func]{minPathSumDP}\n</code></pre> min_path_sum.ts<pre><code>[class]{}-[func]{minPathSumDP}\n</code></pre> min_path_sum.dart<pre><code>[class]{}-[func]{minPathSumDP}\n</code></pre> min_path_sum.rs<pre><code>[class]{}-[func]{min_path_sum_dp}\n</code></pre> min_path_sum.c<pre><code>[class]{}-[func]{minPathSumDP}\n</code></pre> min_path_sum.kt<pre><code>[class]{}-[func]{minPathSumDP}\n</code></pre> min_path_sum.rb<pre><code>[class]{}-[func]{min_path_sum_dp}\n</code></pre> min_path_sum.zig<pre><code>[class]{}-[func]{minPathSumDP}\n</code></pre> <p>\u4e0b\u306e\u56f3\u306f\u6700\u5c0f\u7d4c\u8def\u548c\u306e\u72b6\u614b\u9077\u79fb\u30d7\u30ed\u30bb\u30b9\u3092\u793a\u3057\u3001\u30b0\u30ea\u30c3\u30c9\u5168\u4f53\u3092\u8d70\u67fb\u3059\u308b\u305f\u3081\u3001\u6642\u9593\u8a08\u7b97\u91cf\u306f \\(O(nm)\\) \u3067\u3059\u3002</p> <p>\u914d\u5217 <code>dp</code> \u306e\u30b5\u30a4\u30ba\u306f \\(n \\times m\\) \u3067\u3042\u308b\u305f\u3081\u3001\u7a7a\u9593\u8a08\u7b97\u91cf\u306f \\(O(nm)\\) \u3067\u3059\u3002</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt;&lt;12&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> \u56f3 14-16 \u00a0 \u6700\u5c0f\u7d4c\u8def\u548c\u306e\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u30d7\u30ed\u30bb\u30b9 </p>"},{"location":"chapter_dynamic_programming/dp_solution_pipeline/#4","title":"4. \u00a0 \u7a7a\u9593\u6700\u9069\u5316","text":"<p>\u5404\u30bb\u30eb\u306f\u5de6\u3068\u4e0a\u306e\u30bb\u30eb\u306e\u307f\u306b\u95a2\u9023\u3059\u308b\u305f\u3081\u3001\u5358\u4e00\u884c\u914d\u5217\u3092\u4f7f\u7528\u3057\u3066 \\(dp\\) \u30c6\u30fc\u30d6\u30eb\u3092\u5b9f\u88c5\u3067\u304d\u307e\u3059\u3002</p> <p>\u914d\u5217 <code>dp</code> \u306f1\u884c\u306e\u72b6\u614b\u306e\u307f\u3092\u8868\u73fe\u3067\u304d\u308b\u305f\u3081\u3001\u6700\u521d\u306e\u5217\u306e\u72b6\u614b\u3092\u4e8b\u524d\u306b\u521d\u671f\u5316\u3067\u304d\u305a\u3001\u5404\u884c\u3092\u8d70\u67fb\u3059\u308b\u3068\u304d\u306b\u66f4\u65b0\u3059\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig min_path_sum.py<pre><code>def min_path_sum_dp_comp(grid: list[list[int]]) -&gt; int:\n    \"\"\"\u6700\u5c0f\u30d1\u30b9\u548c\uff1a\u7a7a\u9593\u6700\u9069\u5316\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\"\"\"\n    n, m = len(grid), len(grid[0])\n    # dp \u30c6\u30fc\u30d6\u30eb\u3092\u521d\u671f\u5316\n    dp = [0] * m\n    # \u72b6\u614b\u9077\u79fb\uff1a\u6700\u521d\u306e\u884c\n    dp[0] = grid[0][0]\n    for j in range(1, m):\n        dp[j] = dp[j - 1] + grid[0][j]\n    # \u72b6\u614b\u9077\u79fb\uff1a\u6b8b\u308a\u306e\u884c\n    for i in range(1, n):\n        # \u72b6\u614b\u9077\u79fb\uff1a\u6700\u521d\u306e\u5217\n        dp[0] = dp[0] + grid[i][0]\n        # \u72b6\u614b\u9077\u79fb\uff1a\u6b8b\u308a\u306e\u5217\n        for j in range(1, m):\n            dp[j] = min(dp[j - 1], dp[j]) + grid[i][j]\n    return dp[m - 1]\n</code></pre> min_path_sum.cpp<pre><code>[class]{}-[func]{minPathSumDPComp}\n</code></pre> min_path_sum.java<pre><code>/* \u6700\u5c0f\u30d1\u30b9\u548c\uff1a\u7a7a\u9593\u6700\u9069\u5316\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0 */\nint minPathSumDPComp(int[][] grid) {\n    int n = grid.length, m = grid[0].length;\n    // DP\u30c6\u30fc\u30d6\u30eb\u3092\u521d\u671f\u5316\n    int[] dp = new int[m];\n    // \u72b6\u614b\u9077\u79fb\uff1a\u6700\u521d\u306e\u884c\n    dp[0] = grid[0][0];\n    for (int j = 1; j &lt; m; j++) {\n        dp[j] = dp[j - 1] + grid[0][j];\n    }\n    // \u72b6\u614b\u9077\u79fb\uff1a\u6b8b\u308a\u306e\u884c\n    for (int i = 1; i &lt; n; i++) {\n        // \u72b6\u614b\u9077\u79fb\uff1a\u6700\u521d\u306e\u5217\n        dp[0] = dp[0] + grid[i][0];\n        // \u72b6\u614b\u9077\u79fb\uff1a\u6b8b\u308a\u306e\u5217\n        for (int j = 1; j &lt; m; j++) {\n            dp[j] = Math.min(dp[j - 1], dp[j]) + grid[i][j];\n        }\n    }\n    return dp[m - 1];\n}\n</code></pre> min_path_sum.cs<pre><code>[class]{min_path_sum}-[func]{MinPathSumDPComp}\n</code></pre> min_path_sum.go<pre><code>[class]{}-[func]{minPathSumDPComp}\n</code></pre> min_path_sum.swift<pre><code>[class]{}-[func]{minPathSumDPComp}\n</code></pre> min_path_sum.js<pre><code>[class]{}-[func]{minPathSumDPComp}\n</code></pre> min_path_sum.ts<pre><code>[class]{}-[func]{minPathSumDPComp}\n</code></pre> min_path_sum.dart<pre><code>[class]{}-[func]{minPathSumDPComp}\n</code></pre> min_path_sum.rs<pre><code>[class]{}-[func]{min_path_sum_dp_comp}\n</code></pre> min_path_sum.c<pre><code>[class]{}-[func]{minPathSumDPComp}\n</code></pre> min_path_sum.kt<pre><code>[class]{}-[func]{minPathSumDPComp}\n</code></pre> min_path_sum.rb<pre><code>[class]{}-[func]{min_path_sum_dp_comp}\n</code></pre> min_path_sum.zig<pre><code>[class]{}-[func]{minPathSumDPComp}\n</code></pre>"},{"location":"chapter_dynamic_programming/edit_distance_problem/","title":"14.6 \u00a0 \u7de8\u96c6\u8ddd\u96e2\u554f\u984c","text":"<p>\u7de8\u96c6\u8ddd\u96e2\u306f\u3001\u30ec\u30fc\u30d9\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u8ddd\u96e2\u3068\u3082\u547c\u3070\u308c\u3001\u4e00\u3064\u306e\u6587\u5b57\u5217\u3092\u5225\u306e\u6587\u5b57\u5217\u306b\u5909\u63db\u3059\u308b\u305f\u3081\u306b\u5fc5\u8981\u306a\u6700\u5c0f\u4fee\u6b63\u56de\u6570\u3092\u6307\u3057\u3001\u60c5\u5831\u691c\u7d22\u3084\u81ea\u7136\u8a00\u8a9e\u51e6\u7406\u30672\u3064\u306e\u30b7\u30fc\u30b1\u30f3\u30b9\u9593\u306e\u985e\u4f3c\u5ea6\u3092\u6e2c\u5b9a\u3059\u308b\u305f\u3081\u306b\u3088\u304f\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002</p> <p>Question</p> <p>2\u3064\u306e\u6587\u5b57\u5217 \\(s\\) \u3068 \\(t\\) \u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u304d\u3001\\(s\\) \u3092 \\(t\\) \u306b\u5909\u63db\u3059\u308b\u305f\u3081\u306b\u5fc5\u8981\u306a\u6700\u5c0f\u7de8\u96c6\u56de\u6570\u3092\u8fd4\u3057\u3066\u304f\u3060\u3055\u3044\u3002</p> <p>\u6587\u5b57\u5217\u306b\u5bfe\u3057\u30663\u7a2e\u985e\u306e\u7de8\u96c6\u3092\u5b9f\u884c\u3067\u304d\u307e\u3059\uff1a\u6587\u5b57\u306e\u633f\u5165\u3001\u6587\u5b57\u306e\u524a\u9664\u3001\u307e\u305f\u306f\u6587\u5b57\u3092\u4ed6\u306e\u4efb\u610f\u306e\u6587\u5b57\u306b\u7f6e\u63db\u3002</p> <p>\u4e0b\u306e\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001<code>kitten</code> \u3092 <code>sitting</code> \u306b\u5909\u63db\u3059\u308b\u306b\u306f3\u56de\u306e\u7de8\u96c6\u304c\u5fc5\u8981\u3067\u30012\u56de\u306e\u7f6e\u63db\u30681\u56de\u306e\u633f\u5165\u3092\u542b\u307f\u307e\u3059\u3002<code>hello</code> \u3092 <code>algo</code> \u306b\u5909\u63db\u3059\u308b\u306b\u306f3\u30b9\u30c6\u30c3\u30d7\u304c\u5fc5\u8981\u3067\u30012\u56de\u306e\u7f6e\u63db\u30681\u56de\u306e\u524a\u9664\u3092\u542b\u307f\u307e\u3059\u3002</p> <p></p> <p> \u56f3 14-27 \u00a0 \u7de8\u96c6\u8ddd\u96e2\u306e\u4f8b\u30c7\u30fc\u30bf </p> <p>\u7de8\u96c6\u8ddd\u96e2\u554f\u984c\u306f\u6c7a\u5b9a\u6728\u30e2\u30c7\u30eb\u3067\u81ea\u7136\u306b\u8aac\u660e\u3067\u304d\u307e\u3059\u3002\u6587\u5b57\u5217\u306f\u6728\u306e\u30ce\u30fc\u30c9\u306b\u5bfe\u5fdc\u3057\u30011\u30e9\u30a6\u30f3\u30c9\u306e\u6c7a\u5b9a\uff08\u7de8\u96c6\u64cd\u4f5c\uff09\u306f\u6728\u306e\u30a8\u30c3\u30b8\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002</p> <p>\u4e0b\u306e\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u64cd\u4f5c\u306b\u5236\u9650\u304c\u306a\u3044\u5834\u5408\u3001\u5404\u30ce\u30fc\u30c9\u306f\u591a\u304f\u306e\u30a8\u30c3\u30b8\u3092\u5c0e\u51fa\u3067\u304d\u3001\u305d\u308c\u305e\u308c\u304c1\u3064\u306e\u64cd\u4f5c\u306b\u5bfe\u5fdc\u3059\u308b\u305f\u3081\u3001<code>hello</code> \u3092 <code>algo</code> \u306b\u5909\u63db\u3059\u308b\u53ef\u80fd\u306a\u7d4c\u8def\u306f\u591a\u6570\u3042\u308a\u307e\u3059\u3002</p> <p>\u6c7a\u5b9a\u6728\u306e\u89b3\u70b9\u304b\u3089\u3001\u3053\u306e\u554f\u984c\u306e\u76ee\u6a19\u306f\u3001\u30ce\u30fc\u30c9 <code>hello</code> \u3068\u30ce\u30fc\u30c9 <code>algo</code> \u306e\u9593\u306e\u6700\u77ed\u7d4c\u8def\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u3067\u3059\u3002</p> <p></p> <p> \u56f3 14-28 \u00a0 \u6c7a\u5b9a\u6728\u30e2\u30c7\u30eb\u306b\u57fa\u3065\u3044\u3066\u8868\u73fe\u3055\u308c\u305f\u7de8\u96c6\u8ddd\u96e2\u554f\u984c </p>"},{"location":"chapter_dynamic_programming/edit_distance_problem/#1","title":"1. \u00a0 \u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u30a2\u30d7\u30ed\u30fc\u30c1","text":"<p>\u30b9\u30c6\u30c3\u30d71\uff1a\u5404\u30e9\u30a6\u30f3\u30c9\u306e\u6c7a\u5b9a\u3092\u8003\u3048\u3001\u72b6\u614b\u3092\u5b9a\u7fa9\u3057\u3001\u305d\u308c\u306b\u3088\u308a \\(dp\\) \u30c6\u30fc\u30d6\u30eb\u3092\u5f97\u308b</p> <p>\u5404\u30e9\u30a6\u30f3\u30c9\u306e\u6c7a\u5b9a\u306f\u3001\u6587\u5b57\u5217 \\(s\\) \u306b\u5bfe\u3057\u30661\u3064\u306e\u7de8\u96c6\u64cd\u4f5c\u3092\u5b9f\u884c\u3059\u308b\u3053\u3068\u3092\u542b\u307f\u307e\u3059\u3002</p> <p>\u7de8\u96c6\u30d7\u30ed\u30bb\u30b9\u4e2d\u306b\u554f\u984c\u306e\u30b5\u30a4\u30ba\u3092\u6bb5\u968e\u7684\u306b\u7e2e\u5c0f\u3059\u308b\u3053\u3068\u3092\u76ee\u6307\u3057\u3001\u3053\u308c\u306b\u3088\u308a\u90e8\u5206\u554f\u984c\u3092\u69cb\u7bc9\u3067\u304d\u307e\u3059\u3002\u6587\u5b57\u5217 \\(s\\) \u3068 \\(t\\) \u306e\u9577\u3055\u3092\u305d\u308c\u305e\u308c \\(n\\) \u3068 \\(m\\) \u3068\u3057\u307e\u3059\u3002\u307e\u305a\u3001\u4e21\u65b9\u306e\u6587\u5b57\u5217\u306e\u672b\u5c3e\u6587\u5b57 \\(s[n-1]\\) \u3068 \\(t[m-1]\\) \u3092\u8003\u616e\u3057\u307e\u3059\u3002</p> <ul> <li>\\(s[n-1]\\) \u3068 \\(t[m-1]\\) \u304c\u540c\u3058\u5834\u5408\u3001\u305d\u308c\u3089\u3092\u30b9\u30ad\u30c3\u30d7\u3057\u3066\u76f4\u63a5 \\(s[n-2]\\) \u3068 \\(t[m-2]\\) \u3092\u8003\u616e\u3067\u304d\u307e\u3059\u3002</li> <li>\\(s[n-1]\\) \u3068 \\(t[m-1]\\) \u304c\u7570\u306a\u308b\u5834\u5408\u3001\\(s\\) \u306b\u5bfe\u3057\u30661\u3064\u306e\u7de8\u96c6\uff08\u633f\u5165\u3001\u524a\u9664\u3001\u7f6e\u63db\uff09\u3092\u5b9f\u884c\u3057\u3066\u30012\u3064\u306e\u6587\u5b57\u5217\u306e\u672b\u5c3e\u6587\u5b57\u3092\u4e00\u81f4\u3055\u305b\u3001\u305d\u308c\u3089\u3092\u30b9\u30ad\u30c3\u30d7\u3057\u3066\u3088\u308a\u5c0f\u898f\u6a21\u306a\u554f\u984c\u3092\u8003\u616e\u3067\u304d\u308b\u3088\u3046\u306b\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002</li> </ul> <p>\u3057\u305f\u304c\u3063\u3066\u3001\u6587\u5b57\u5217 \\(s\\) \u3067\u306e\u5404\u30e9\u30a6\u30f3\u30c9\u306e\u6c7a\u5b9a\uff08\u7de8\u96c6\u64cd\u4f5c\uff09\u306f\u3001\\(s\\) \u3068 \\(t\\) \u3067\u30de\u30c3\u30c1\u3055\u308c\u308b\u6b8b\u308a\u306e\u6587\u5b57\u3092\u5909\u66f4\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u72b6\u614b\u306f \\(s\\) \u3068 \\(t\\) \u3067\u73fe\u5728\u8003\u616e\u3055\u308c\u3066\u3044\u308b \\(i\\) \u756a\u76ee\u3068 \\(j\\) \u756a\u76ee\u306e\u6587\u5b57\u3067\u3042\u308a\u3001\\([i, j]\\) \u3068\u8868\u8a18\u3055\u308c\u307e\u3059\u3002</p> <p>\u72b6\u614b \\([i, j]\\) \u306f\u90e8\u5206\u554f\u984c\u306b\u5bfe\u5fdc\u3057\u307e\u3059\uff1a\\(s\\) \u306e\u6700\u521d\u306e \\(i\\) \u6587\u5b57\u3092 \\(t\\) \u306e\u6700\u521d\u306e \\(j\\) \u6587\u5b57\u306b\u5909\u66f4\u3059\u308b\u305f\u3081\u306b\u5fc5\u8981\u306a\u6700\u5c0f\u7de8\u96c6\u56de\u6570\u3002</p> <p>\u3053\u308c\u304b\u3089\u3001\u30b5\u30a4\u30ba \\((i+1) \\times (j+1)\\) \u306e\u4e8c\u6b21\u5143 \\(dp\\) \u30c6\u30fc\u30d6\u30eb\u3092\u5f97\u307e\u3059\u3002</p> <p>\u30b9\u30c6\u30c3\u30d72\uff1a\u6700\u9069\u90e8\u5206\u69cb\u9020\u3092\u7279\u5b9a\u3057\u3001\u72b6\u614b\u9077\u79fb\u65b9\u7a0b\u5f0f\u3092\u5c0e\u51fa\u3059\u308b</p> <p>\u90e8\u5206\u554f\u984c \\(dp[i, j]\\) \u3092\u8003\u616e\u3059\u308b\u3068\u3001\u3053\u308c\u306b\u5bfe\u5fdc\u3059\u308b2\u3064\u306e\u6587\u5b57\u5217\u306e\u672b\u5c3e\u6587\u5b57\u306f \\(s[i-1]\\) \u3068 \\(t[j-1]\\) \u3067\u3042\u308a\u3001\u4e0b\u306e\u56f3\u306b\u793a\u3059\u3088\u3046\u306b3\u3064\u306e\u30b7\u30ca\u30ea\u30aa\u306b\u5206\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002</p> <ol> <li>\\(s[i-1]\\) \u306e\u5f8c\u306b \\(t[j-1]\\) \u3092\u8ffd\u52a0\u3059\u308b\u3068\u3001\u6b8b\u308a\u306e\u90e8\u5206\u554f\u984c\u306f \\(dp[i, j-1]\\) \u3067\u3059\u3002</li> <li>\\(s[i-1]\\) \u3092\u524a\u9664\u3059\u308b\u3068\u3001\u6b8b\u308a\u306e\u90e8\u5206\u554f\u984c\u306f \\(dp[i-1, j]\\) \u3067\u3059\u3002</li> <li>\\(s[i-1]\\) \u3092 \\(t[j-1]\\) \u306b\u7f6e\u63db\u3059\u308b\u3068\u3001\u6b8b\u308a\u306e\u90e8\u5206\u554f\u984c\u306f \\(dp[i-1, j-1]\\) \u3067\u3059\u3002</li> </ol> <p></p> <p> \u56f3 14-29 \u00a0 \u7de8\u96c6\u8ddd\u96e2\u306e\u72b6\u614b\u9077\u79fb </p> <p>\u4e0a\u8a18\u306e\u5206\u6790\u306b\u57fa\u3065\u3044\u3066\u3001\u6700\u9069\u90e8\u5206\u69cb\u9020\u3092\u6c7a\u5b9a\u3067\u304d\u307e\u3059\uff1a\\(dp[i, j]\\) \u306e\u6700\u5c0f\u7de8\u96c6\u56de\u6570\u306f\u3001\\(dp[i, j-1]\\)\u3001\\(dp[i-1, j]\\)\u3001\\(dp[i-1, j-1]\\) \u306e\u4e2d\u306e\u6700\u5c0f\u5024\u306b\u7de8\u96c6\u30b9\u30c6\u30c3\u30d7 \\(1\\) \u3092\u52a0\u3048\u305f\u3082\u306e\u3067\u3059\u3002\u5bfe\u5fdc\u3059\u308b\u72b6\u614b\u9077\u79fb\u65b9\u7a0b\u5f0f\u306f\uff1a</p> \\[ dp[i, j] = \\min(dp[i, j-1], dp[i-1, j], dp[i-1, j-1]) + 1 \\] <p>\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002\\(s[i-1]\\) \u3068 \\(t[j-1]\\) \u304c\u540c\u3058\u5834\u5408\u3001\u73fe\u5728\u306e\u6587\u5b57\u306b\u5bfe\u3057\u3066\u7de8\u96c6\u306f\u5fc5\u8981\u3042\u308a\u307e\u305b\u3093\u3002\u3053\u306e\u5834\u5408\u3001\u72b6\u614b\u9077\u79fb\u65b9\u7a0b\u5f0f\u306f\uff1a</p> \\[ dp[i, j] = dp[i-1, j-1] \\] <p>\u30b9\u30c6\u30c3\u30d73\uff1a\u5883\u754c\u6761\u4ef6\u3068\u72b6\u614b\u9077\u79fb\u306e\u9806\u5e8f\u3092\u6c7a\u5b9a\u3059\u308b</p> <p>\u4e21\u65b9\u306e\u6587\u5b57\u5217\u304c\u7a7a\u306e\u5834\u5408\u3001\u7de8\u96c6\u56de\u6570\u306f \\(0\\) \u3067\u3059\u3002\u3064\u307e\u308a\u3001\\(dp[0, 0] = 0\\) \u3067\u3059\u3002\\(s\\) \u304c\u7a7a\u3067 \\(t\\) \u304c\u7a7a\u3067\u306a\u3044\u5834\u5408\u3001\u6700\u5c0f\u7de8\u96c6\u56de\u6570\u306f \\(t\\) \u306e\u9577\u3055\u306b\u7b49\u3057\u304f\u3001\u3064\u307e\u308a\u6700\u521d\u306e\u884c \\(dp[0, j] = j\\) \u3067\u3059\u3002\\(s\\) \u304c\u7a7a\u3067\u306a\u304f \\(t\\) \u304c\u7a7a\u306e\u5834\u5408\u3001\u6700\u5c0f\u7de8\u96c6\u56de\u6570\u306f \\(s\\) \u306e\u9577\u3055\u306b\u7b49\u3057\u304f\u3001\u3064\u307e\u308a\u6700\u521d\u306e\u5217 \\(dp[i, 0] = i\\) \u3067\u3059\u3002</p> <p>\u72b6\u614b\u9077\u79fb\u65b9\u7a0b\u5f0f\u3092\u89b3\u5bdf\u3059\u308b\u3068\u3001\\(dp[i, j]\\) \u306e\u89e3\u6c7a\u306f\u5de6\u3001\u4e0a\u3001\u5de6\u4e0a\u306e\u89e3\u306b\u4f9d\u5b58\u3059\u308b\u305f\u3081\u3001\u4e8c\u91cd\u30eb\u30fc\u30d7\u3092\u4f7f\u7528\u3057\u3066\u6b63\u3057\u3044\u9806\u5e8f\u3067 \\(dp\\) \u30c6\u30fc\u30d6\u30eb\u5168\u4f53\u3092\u8d70\u67fb\u3067\u304d\u307e\u3059\u3002</p>"},{"location":"chapter_dynamic_programming/edit_distance_problem/#2","title":"2. \u00a0 \u30b3\u30fc\u30c9\u5b9f\u88c5","text":"PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig edit_distance.py<pre><code>def edit_distance_dp(s: str, t: str) -&gt; int:\n    \"\"\"\u7de8\u96c6\u8ddd\u96e2\uff1a\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\"\"\"\n    n, m = len(s), len(t)\n    dp = [[0] * (m + 1) for _ in range(n + 1)]\n    # \u72b6\u614b\u9077\u79fb\uff1a\u6700\u521d\u306e\u884c\u3068\u6700\u521d\u306e\u5217\n    for i in range(1, n + 1):\n        dp[i][0] = i\n    for j in range(1, m + 1):\n        dp[0][j] = j\n    # \u72b6\u614b\u9077\u79fb\uff1a\u6b8b\u308a\u306e\u884c\u3068\u5217\n    for i in range(1, n + 1):\n        for j in range(1, m + 1):\n            if s[i - 1] == t[j - 1]:\n                # 2 \u3064\u306e\u6587\u5b57\u304c\u7b49\u3057\u3044\u5834\u5408\u3001\u3053\u308c\u3089 2 \u3064\u306e\u6587\u5b57\u3092\u30b9\u30ad\u30c3\u30d7\n                dp[i][j] = dp[i - 1][j - 1]\n            else:\n                # \u6700\u5c0f\u7de8\u96c6\u6570 = 3 \u3064\u306e\u64cd\u4f5c\uff08\u633f\u5165\u3001\u524a\u9664\u3001\u7f6e\u63db\uff09\u304b\u3089\u306e\u6700\u5c0f\u7de8\u96c6\u6570 + 1\n                dp[i][j] = min(dp[i][j - 1], dp[i - 1][j], dp[i - 1][j - 1]) + 1\n    return dp[n][m]\n</code></pre> edit_distance.cpp<pre><code>/* \u7de8\u96c6\u8ddd\u96e2\uff1a\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0 */\nint editDistanceDP(string s, string t) {\n    int n = s.length(), m = t.length();\n    vector&lt;vector&lt;int&gt;&gt; dp(n + 1, vector&lt;int&gt;(m + 1, 0));\n    // \u72b6\u614b\u9077\u79fb\uff1a\u6700\u521d\u306e\u884c\u3068\u6700\u521d\u306e\u5217\n    for (int i = 1; i &lt;= n; i++) {\n        dp[i][0] = i;\n    }\n    for (int j = 1; j &lt;= m; j++) {\n        dp[0][j] = j;\n    }\n    // \u72b6\u614b\u9077\u79fb\uff1a\u6b8b\u308a\u306e\u884c\u3068\u5217\n    for (int i = 1; i &lt;= n; i++) {\n        for (int j = 1; j &lt;= m; j++) {\n            if (s[i - 1] == t[j - 1]) {\n                // 2\u3064\u306e\u6587\u5b57\u304c\u7b49\u3057\u3044\u5834\u5408\u3001\u3053\u308c\u30892\u3064\u306e\u6587\u5b57\u3092\u30b9\u30ad\u30c3\u30d7\n                dp[i][j] = dp[i - 1][j - 1];\n            } else {\n                // \u6700\u5c0f\u7de8\u96c6\u6570 = 3\u3064\u306e\u64cd\u4f5c\uff08\u633f\u5165\u3001\u524a\u9664\u3001\u7f6e\u63db\uff09\u304b\u3089\u306e\u6700\u5c0f\u7de8\u96c6\u6570 + 1\n                dp[i][j] = min(min(dp[i][j - 1], dp[i - 1][j]), dp[i - 1][j - 1]) + 1;\n            }\n        }\n    }\n    return dp[n][m];\n}\n</code></pre> edit_distance.java<pre><code>/* \u7de8\u96c6\u8ddd\u96e2\uff1a\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0 */\nint editDistanceDP(String s, String t) {\n    int n = s.length(), m = t.length();\n    int[][] dp = new int[n + 1][m + 1];\n    // \u72b6\u614b\u9077\u79fb\uff1a\u6700\u521d\u306e\u884c\u3068\u6700\u521d\u306e\u5217\n    for (int i = 1; i &lt;= n; i++) {\n        dp[i][0] = i;\n    }\n    for (int j = 1; j &lt;= m; j++) {\n        dp[0][j] = j;\n    }\n    // \u72b6\u614b\u9077\u79fb\uff1a\u6b8b\u308a\u306e\u884c\u3068\u5217\n    for (int i = 1; i &lt;= n; i++) {\n        for (int j = 1; j &lt;= m; j++) {\n            if (s.charAt(i - 1) == t.charAt(j - 1)) {\n                // 2\u3064\u306e\u6587\u5b57\u304c\u7b49\u3057\u3044\u5834\u5408\u3001\u3053\u308c\u30892\u3064\u306e\u6587\u5b57\u3092\u30b9\u30ad\u30c3\u30d7\n                dp[i][j] = dp[i - 1][j - 1];\n            } else {\n                // \u6700\u5c0f\u7de8\u96c6\u6570 = 3\u3064\u306e\u64cd\u4f5c\uff08\u633f\u5165\u3001\u524a\u9664\u3001\u7f6e\u63db\uff09\u304b\u3089\u306e\u6700\u5c0f\u7de8\u96c6\u6570 + 1\n                dp[i][j] = Math.min(Math.min(dp[i][j - 1], dp[i - 1][j]), dp[i - 1][j - 1]) + 1;\n            }\n        }\n    }\n    return dp[n][m];\n}\n</code></pre> edit_distance.cs<pre><code>[class]{edit_distance}-[func]{EditDistanceDP}\n</code></pre> edit_distance.go<pre><code>[class]{}-[func]{editDistanceDP}\n</code></pre> edit_distance.swift<pre><code>[class]{}-[func]{editDistanceDP}\n</code></pre> edit_distance.js<pre><code>[class]{}-[func]{editDistanceDP}\n</code></pre> edit_distance.ts<pre><code>[class]{}-[func]{editDistanceDP}\n</code></pre> edit_distance.dart<pre><code>[class]{}-[func]{editDistanceDP}\n</code></pre> edit_distance.rs<pre><code>[class]{}-[func]{edit_distance_dp}\n</code></pre> edit_distance.c<pre><code>[class]{}-[func]{editDistanceDP}\n</code></pre> edit_distance.kt<pre><code>[class]{}-[func]{editDistanceDP}\n</code></pre> edit_distance.rb<pre><code>[class]{}-[func]{edit_distance_dp}\n</code></pre> edit_distance.zig<pre><code>[class]{}-[func]{editDistanceDP}\n</code></pre> <p>\u4e0b\u306e\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u7de8\u96c6\u8ddd\u96e2\u554f\u984c\u306e\u72b6\u614b\u9077\u79fb\u30d7\u30ed\u30bb\u30b9\u306f\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c\u3068\u975e\u5e38\u306b\u4f3c\u3066\u304a\u308a\u3001\u4e8c\u6b21\u5143\u30b0\u30ea\u30c3\u30c9\u3092\u57cb\u3081\u308b\u3053\u3068\u3068\u898b\u306a\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt;&lt;12&gt;&lt;13&gt;&lt;14&gt;&lt;15&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> \u56f3 14-30 \u00a0 \u7de8\u96c6\u8ddd\u96e2\u306e\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u30d7\u30ed\u30bb\u30b9 </p>"},{"location":"chapter_dynamic_programming/edit_distance_problem/#3","title":"3. \u00a0 \u7a7a\u9593\u6700\u9069\u5316","text":"<p>\\(dp[i, j]\\) \u306f\u4e0a\u306e \\(dp[i-1, j]\\)\u3001\u5de6\u306e \\(dp[i, j-1]\\)\u3001\u5de6\u4e0a\u306e \\(dp[i-1, j-1]\\) \u306e\u89e3\u304b\u3089\u5c0e\u51fa\u3055\u308c\u3001\u76f4\u63a5\u8d70\u67fb\u3067\u306f\u5de6\u4e0a\u306e\u89e3 \\(dp[i-1, j-1]\\) \u304c\u5931\u308f\u308c\u3001\u9006\u8d70\u67fb\u3067\u306f\u4e8b\u524d\u306b \\(dp[i, j-1]\\) \u3092\u69cb\u7bc9\u3067\u304d\u306a\u3044\u305f\u3081\u3001\u3069\u3061\u3089\u306e\u8d70\u67fb\u9806\u5e8f\u3082\u5b9f\u884c\u53ef\u80fd\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002</p> <p>\u3053\u306e\u7406\u7531\u3067\u3001\u5909\u6570 <code>leftup</code> \u3092\u4f7f\u7528\u3057\u3066\u5de6\u4e0a\u306e \\(dp[i-1, j-1]\\) \u304b\u3089\u306e\u89e3\u3092\u4e00\u6642\u7684\u306b\u4fdd\u5b58\u3057\u3001\u5de6\u3068\u4e0a\u306e\u89e3\u306e\u307f\u3092\u8003\u616e\u3059\u308c\u3070\u3088\u304f\u306a\u308a\u307e\u3059\u3002\u3053\u306e\u72b6\u6cc1\u306f\u7121\u5236\u9650\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c\u3068\u4f3c\u3066\u304a\u308a\u3001\u76f4\u63a5\u8d70\u67fb\u304c\u53ef\u80fd\u3067\u3059\u3002\u30b3\u30fc\u30c9\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig edit_distance.py<pre><code>def edit_distance_dp_comp(s: str, t: str) -&gt; int:\n    \"\"\"\u7de8\u96c6\u8ddd\u96e2\uff1a\u7a7a\u9593\u6700\u9069\u5316\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\"\"\"\n    n, m = len(s), len(t)\n    dp = [0] * (m + 1)\n    # \u72b6\u614b\u9077\u79fb\uff1a\u6700\u521d\u306e\u884c\n    for j in range(1, m + 1):\n        dp[j] = j\n    # \u72b6\u614b\u9077\u79fb\uff1a\u6b8b\u308a\u306e\u884c\n    for i in range(1, n + 1):\n        # \u72b6\u614b\u9077\u79fb\uff1a\u6700\u521d\u306e\u5217\n        leftup = dp[0]  # dp[i-1, j-1] \u3092\u4e00\u6642\u7684\u306b\u4fdd\u5b58\n        dp[0] += 1\n        # \u72b6\u614b\u9077\u79fb\uff1a\u6b8b\u308a\u306e\u5217\n        for j in range(1, m + 1):\n            temp = dp[j]\n            if s[i - 1] == t[j - 1]:\n                # 2 \u3064\u306e\u6587\u5b57\u304c\u7b49\u3057\u3044\u5834\u5408\u3001\u3053\u308c\u3089 2 \u3064\u306e\u6587\u5b57\u3092\u30b9\u30ad\u30c3\u30d7\n                dp[j] = leftup\n            else:\n                # \u6700\u5c0f\u7de8\u96c6\u6570 = 3 \u3064\u306e\u64cd\u4f5c\uff08\u633f\u5165\u3001\u524a\u9664\u3001\u7f6e\u63db\uff09\u304b\u3089\u306e\u6700\u5c0f\u7de8\u96c6\u6570 + 1\n                dp[j] = min(dp[j - 1], dp[j], leftup) + 1\n            leftup = temp  # \u6b21\u306e dp[i-1, j-1] \u306e\u305f\u3081\u306b\u66f4\u65b0\n    return dp[m]\n</code></pre> edit_distance.cpp<pre><code>[class]{}-[func]{editDistanceDPComp}\n</code></pre> edit_distance.java<pre><code>/* \u7de8\u96c6\u8ddd\u96e2\uff1a\u7a7a\u9593\u6700\u9069\u5316\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0 */\nint editDistanceDPComp(String s, String t) {\n    int n = s.length(), m = t.length();\n    int[] dp = new int[m + 1];\n    // \u72b6\u614b\u9077\u79fb\uff1a\u6700\u521d\u306e\u884c\n    for (int j = 1; j &lt;= m; j++) {\n        dp[j] = j;\n    }\n    // \u72b6\u614b\u9077\u79fb\uff1a\u6b8b\u308a\u306e\u884c\n    for (int i = 1; i &lt;= n; i++) {\n        // \u72b6\u614b\u9077\u79fb\uff1a\u6700\u521d\u306e\u5217\n        int leftup = dp[0]; // dp[i-1, j-1] \u3092\u4e00\u6642\u7684\u306b\u683c\u7d0d\n        dp[0] = i;\n        // \u72b6\u614b\u9077\u79fb\uff1a\u6b8b\u308a\u306e\u5217\n        for (int j = 1; j &lt;= m; j++) {\n            int temp = dp[j];\n            if (s.charAt(i - 1) == t.charAt(j - 1)) {\n                // 2\u3064\u306e\u6587\u5b57\u304c\u7b49\u3057\u3044\u5834\u5408\u3001\u3053\u308c\u30892\u3064\u306e\u6587\u5b57\u3092\u30b9\u30ad\u30c3\u30d7\n                dp[j] = leftup;\n            } else {\n                // \u6700\u5c0f\u7de8\u96c6\u6570 = 3\u3064\u306e\u64cd\u4f5c\uff08\u633f\u5165\u3001\u524a\u9664\u3001\u7f6e\u63db\uff09\u304b\u3089\u306e\u6700\u5c0f\u7de8\u96c6\u6570 + 1\n                dp[j] = Math.min(Math.min(dp[j - 1], dp[j]), leftup) + 1;\n            }\n            leftup = temp; // \u6b21\u306e\u30e9\u30a6\u30f3\u30c9\u306e dp[i-1, j-1] \u306e\u305f\u3081\u306b\u66f4\u65b0\n        }\n    }\n    return dp[m];\n}\n</code></pre> edit_distance.cs<pre><code>[class]{edit_distance}-[func]{EditDistanceDPComp}\n</code></pre> edit_distance.go<pre><code>[class]{}-[func]{editDistanceDPComp}\n</code></pre> edit_distance.swift<pre><code>[class]{}-[func]{editDistanceDPComp}\n</code></pre> edit_distance.js<pre><code>[class]{}-[func]{editDistanceDPComp}\n</code></pre> edit_distance.ts<pre><code>[class]{}-[func]{editDistanceDPComp}\n</code></pre> edit_distance.dart<pre><code>[class]{}-[func]{editDistanceDPComp}\n</code></pre> edit_distance.rs<pre><code>[class]{}-[func]{edit_distance_dp_comp}\n</code></pre> edit_distance.c<pre><code>[class]{}-[func]{editDistanceDPComp}\n</code></pre> edit_distance.kt<pre><code>[class]{}-[func]{editDistanceDPComp}\n</code></pre> edit_distance.rb<pre><code>[class]{}-[func]{edit_distance_dp_comp}\n</code></pre> edit_distance.zig<pre><code>[class]{}-[func]{editDistanceDPComp}\n</code></pre>"},{"location":"chapter_dynamic_programming/intro_to_dynamic_programming/","title":"14.1 \u00a0 \u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u306e\u7d39\u4ecb","text":"<p>\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u306f\u91cd\u8981\u306a\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u30d1\u30e9\u30c0\u30a4\u30e0\u3067\u3042\u308a\u3001\u554f\u984c\u3092\u4e00\u9023\u306e\u5c0f\u3055\u306a\u90e8\u5206\u554f\u984c\u306b\u5206\u89e3\u3057\u3001\u3053\u308c\u3089\u306e\u90e8\u5206\u554f\u984c\u306e\u89e3\u3092\u4fdd\u5b58\u3059\u308b\u3053\u3068\u3067\u5197\u9577\u306a\u8a08\u7b97\u3092\u907f\u3051\u3001\u6642\u9593\u52b9\u7387\u3092\u5927\u5e45\u306b\u5411\u4e0a\u3055\u305b\u307e\u3059\u3002</p> <p>\u3053\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u3067\u306f\u3001\u53e4\u5178\u7684\u306a\u554f\u984c\u304b\u3089\u59cb\u3081\u3066\u3001\u307e\u305a\u529b\u4efb\u305b\u306e\u63a2\u7d22\u6cd5\u306b\u3088\u308b\u89e3\u6cd5\u3092\u63d0\u793a\u3057\u3001\u91cd\u8907\u3059\u308b\u90e8\u5206\u554f\u984c\u3092\u7279\u5b9a\u3057\u3066\u304b\u3089\u3001\u3088\u308a\u52b9\u7387\u7684\u306a\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u89e3\u6cd5\u3092\u6bb5\u968e\u7684\u306b\u5c0e\u51fa\u3057\u307e\u3059\u3002</p> <p>\u968e\u6bb5\u767b\u308a</p> <p>\\(n\\) \u6bb5\u306e\u968e\u6bb5\u304c\u3042\u308a\u3001\u4e00\u5ea6\u306b \\(1\\) \u6bb5\u307e\u305f\u306f \\(2\\) \u6bb5\u4e0a\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u9802\u4e0a\u306b\u5230\u9054\u3059\u308b\u65b9\u6cd5\u306f\u4f55\u901a\u308a\u3042\u308a\u307e\u3059\u304b\uff1f</p> <p>\u4e0b\u306e\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\\(3\\) \u6bb5\u306e\u968e\u6bb5\u306e\u9802\u4e0a\u306b\u5230\u9054\u3059\u308b\u65b9\u6cd5\u306f \\(3\\) \u901a\u308a\u3042\u308a\u307e\u3059\u3002</p> <p></p> <p> \u56f3 14-1 \u00a0 3\u6bb5\u76ee\u306b\u5230\u9054\u3059\u308b\u65b9\u6cd5\u306e\u6570 </p> <p>\u3053\u306e\u554f\u984c\u306f**\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u3092\u7528\u3044\u3066\u3059\u3079\u3066\u306e\u53ef\u80fd\u6027\u3092\u7db2\u7f85**\u3059\u308b\u3053\u3068\u3067\u65b9\u6cd5\u306e\u6570\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u3092\u76ee\u7684\u3068\u3057\u3066\u3044\u307e\u3059\u3002\u5177\u4f53\u7684\u306b\u306f\u3001\u968e\u6bb5\u767b\u308a\u306e\u554f\u984c\u3092\u591a\u6bb5\u968e\u9078\u629e\u30d7\u30ed\u30bb\u30b9\u3068\u3057\u3066\u8003\u3048\u307e\u3059\uff1a\u5730\u9762\u304b\u3089\u59cb\u3081\u3066\u3001\u6bce\u56de \\(1\\) \u6bb5\u307e\u305f\u306f \\(2\\) \u6bb5\u4e0a\u308b\u304b\u3092\u9078\u629e\u3057\u3001\u968e\u6bb5\u306e\u9802\u4e0a\u306b\u5230\u9054\u3057\u305f\u3089\u65b9\u6cd5\u306e\u6570\u3092\u30ab\u30a6\u30f3\u30c8\u3057\u3001\u9802\u4e0a\u3092\u8d85\u3048\u305f\u5834\u5408\u306f\u30d7\u30eb\u30fc\u30cb\u30f3\u30b0\uff08\u679d\u5208\u308a\uff09\u3092\u884c\u3044\u307e\u3059\u3002\u30b3\u30fc\u30c9\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig climbing_stairs_backtrack.py<pre><code>def backtrack(choices: list[int], state: int, n: int, res: list[int]) -&gt; int:\n    \"\"\"\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\"\"\"\n    # n \u6bb5\u76ee\u306b\u767b\u3063\u305f\u3068\u304d\u3001\u89e3\u306e\u6570\u306b 1 \u3092\u52a0\u3048\u308b\n    if state == n:\n        res[0] += 1\n    # \u3059\u3079\u3066\u306e\u9078\u629e\u80a2\u3092\u8d70\u67fb\n    for choice in choices:\n        # \u679d\u5208\u308a\uff1an \u6bb5\u3092\u8d85\u3048\u3066\u767b\u308b\u3053\u3068\u3092\u8a31\u53ef\u3057\u306a\u3044\n        if state + choice &gt; n:\n            continue\n        # \u8a66\u884c\uff1a\u9078\u629e\u3092\u884c\u3044\u3001\u72b6\u614b\u3092\u66f4\u65b0\n        backtrack(choices, state + choice, n, res)\n        # \u64a4\u56de\n\ndef climbing_stairs_backtrack(n: int) -&gt; int:\n    \"\"\"\u968e\u6bb5\u767b\u308a\uff1a\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\"\"\"\n    choices = [1, 2]  # 1 \u6bb5\u307e\u305f\u306f 2 \u6bb5\u767b\u308b\u3053\u3068\u3092\u9078\u629e\u53ef\u80fd\n    state = 0  # 0 \u6bb5\u76ee\u304b\u3089\u767b\u308a\u59cb\u3081\u308b\n    res = [0]  # res[0] \u3092\u4f7f\u7528\u3057\u3066\u89e3\u306e\u6570\u3092\u8a18\u9332\n    backtrack(choices, state, n, res)\n    return res[0]\n</code></pre> climbing_stairs_backtrack.cpp<pre><code>/* \u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0 */\nvoid backtrack(vector&lt;int&gt; &amp;choices, int state, int n, vector&lt;int&gt; &amp;res) {\n    // n\u6bb5\u76ee\u306b\u5230\u9054\u3057\u305f\u3068\u304d\u3001\u89e3\u306e\u6570\u306b1\u3092\u52a0\u3048\u308b\n    if (state == n)\n        res[0]++;\n    // \u3059\u3079\u3066\u306e\u9078\u629e\u80a2\u3092\u8d70\u67fb\n    for (auto &amp;choice : choices) {\n        // \u526a\u5b9a\uff1an\u6bb5\u3092\u8d85\u3048\u3066\u767b\u308b\u3053\u3068\u3092\u8a31\u53ef\u3057\u306a\u3044\n        if (state + choice &gt; n)\n            continue;\n        // \u8a66\u884c\uff1a\u9078\u629e\u3092\u884c\u3044\u3001\u72b6\u614b\u3092\u66f4\u65b0\n        backtrack(choices, state + choice, n, res);\n        // \u64a4\u56de\n    }\n}\n\n/* \u968e\u6bb5\u767b\u308a\uff1a\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0 */\nint climbingStairsBacktrack(int n) {\n    vector&lt;int&gt; choices = {1, 2}; // 1\u6bb5\u307e\u305f\u306f2\u6bb5\u767b\u308b\u3053\u3068\u3092\u9078\u629e\u53ef\u80fd\n    int state = 0;                // 0\u6bb5\u76ee\u304b\u3089\u767b\u308a\u59cb\u3081\u308b\n    vector&lt;int&gt; res = {0};        // res[0] \u3092\u4f7f\u7528\u3057\u3066\u89e3\u306e\u6570\u3092\u8a18\u9332\n    backtrack(choices, state, n, res);\n    return res[0];\n}\n</code></pre> climbing_stairs_backtrack.java<pre><code>/* \u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0 */\nvoid backtrack(List&lt;Integer&gt; choices, int state, int n, List&lt;Integer&gt; res) {\n    // n\u6bb5\u76ee\u306b\u5230\u9054\u3057\u305f\u3068\u304d\u3001\u89e3\u306e\u6570\u306b1\u3092\u52a0\u3048\u308b\n    if (state == n)\n        res.set(0, res.get(0) + 1);\n    // \u3059\u3079\u3066\u306e\u9078\u629e\u80a2\u3092\u8d70\u67fb\n    for (Integer choice : choices) {\n        // \u526a\u5b9a\uff1an\u6bb5\u3092\u8d85\u3048\u3066\u767b\u308b\u3053\u3068\u3092\u8a31\u53ef\u3057\u306a\u3044\n        if (state + choice &gt; n)\n            continue;\n        // \u8a66\u884c\uff1a\u9078\u629e\u3092\u884c\u3044\u3001\u72b6\u614b\u3092\u66f4\u65b0\n        backtrack(choices, state + choice, n, res);\n        // \u64a4\u56de\n    }\n}\n\n/* \u968e\u6bb5\u767b\u308a\uff1a\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0 */\nint climbingStairsBacktrack(int n) {\n    List&lt;Integer&gt; choices = Arrays.asList(1, 2); // 1\u6bb5\u307e\u305f\u306f2\u6bb5\u767b\u308b\u3053\u3068\u3092\u9078\u629e\u53ef\u80fd\n    int state = 0; // 0\u6bb5\u76ee\u304b\u3089\u767b\u308a\u59cb\u3081\u308b\n    List&lt;Integer&gt; res = new ArrayList&lt;&gt;();\n    res.add(0); // res[0] \u3092\u4f7f\u7528\u3057\u3066\u89e3\u306e\u6570\u3092\u8a18\u9332\n    backtrack(choices, state, n, res);\n    return res.get(0);\n}\n</code></pre> climbing_stairs_backtrack.cs<pre><code>[class]{climbing_stairs_backtrack}-[func]{Backtrack}\n\n[class]{climbing_stairs_backtrack}-[func]{ClimbingStairsBacktrack}\n</code></pre> climbing_stairs_backtrack.go<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{climbingStairsBacktrack}\n</code></pre> climbing_stairs_backtrack.swift<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{climbingStairsBacktrack}\n</code></pre> climbing_stairs_backtrack.js<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{climbingStairsBacktrack}\n</code></pre> climbing_stairs_backtrack.ts<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{climbingStairsBacktrack}\n</code></pre> climbing_stairs_backtrack.dart<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{climbingStairsBacktrack}\n</code></pre> climbing_stairs_backtrack.rs<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{climbing_stairs_backtrack}\n</code></pre> climbing_stairs_backtrack.c<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{climbingStairsBacktrack}\n</code></pre> climbing_stairs_backtrack.kt<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{climbingStairsBacktrack}\n</code></pre> climbing_stairs_backtrack.rb<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{climbing_stairs_backtrack}\n</code></pre> climbing_stairs_backtrack.zig<pre><code>[class]{}-[func]{backtrack}\n\n[class]{}-[func]{climbingStairsBacktrack}\n</code></pre>"},{"location":"chapter_dynamic_programming/intro_to_dynamic_programming/#1411-1","title":"14.1.1 \u00a0 \u65b9\u6cd51\uff1a\u529b\u4efb\u305b\u63a2\u7d22","text":"<p>\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u554f\u984c\u3092\u660e\u793a\u7684\u306b\u90e8\u5206\u554f\u984c\u306b\u5206\u89e3\u3057\u307e\u305b\u3093\u3002\u4ee3\u308f\u308a\u306b\u3001\u554f\u984c\u3092\u4e00\u9023\u306e\u6c7a\u5b9a\u30b9\u30c6\u30c3\u30d7\u3068\u3057\u3066\u6271\u3044\u3001\u8a66\u884c\u3068\u679d\u5208\u308a\u3092\u901a\u3058\u3066\u3059\u3079\u3066\u306e\u53ef\u80fd\u6027\u3092\u63a2\u7d22\u3057\u307e\u3059\u3002</p> <p>\u3053\u306e\u554f\u984c\u3092\u5206\u89e3\u30a2\u30d7\u30ed\u30fc\u30c1\u3092\u4f7f\u3063\u3066\u5206\u6790\u3067\u304d\u307e\u3059\u3002\\(dp[i]\\) \u3092 \\(i\\) \u6bb5\u76ee\u306b\u5230\u9054\u3059\u308b\u65b9\u6cd5\u306e\u6570\u3068\u3057\u307e\u3059\u3002\u3053\u306e\u5834\u5408\u3001\\(dp[i]\\) \u304c\u5143\u306e\u554f\u984c\u3067\u3042\u308a\u3001\u305d\u306e\u90e8\u5206\u554f\u984c\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff1a</p> \\[ dp[i-1], dp[i-2], \\dots, dp[2], dp[1] \\] <p>\u5404\u79fb\u52d5\u306f \\(1\\) \u6bb5\u307e\u305f\u306f \\(2\\) \u6bb5\u3057\u304b\u9032\u3081\u306a\u3044\u305f\u3081\u3001\\(i\\) \u6bb5\u76ee\u306b\u7acb\u3063\u3066\u3044\u308b\u3068\u304d\u3001\u524d\u306e\u30b9\u30c6\u30c3\u30d7\u306f \\(i-1\\) \u6bb5\u76ee\u307e\u305f\u306f \\(i-2\\) \u6bb5\u76ee\u306e\u3044\u305a\u308c\u304b\u306b\u3044\u305f\u306f\u305a\u3067\u3059\u3002\u3064\u307e\u308a\u3001\\(i\\) \u6bb5\u76ee\u306b\u306f \\(i-1\\) \u6bb5\u76ee\u307e\u305f\u306f \\(i-2\\) \u6bb5\u76ee\u304b\u3089\u3057\u304b\u5230\u9054\u3067\u304d\u307e\u305b\u3093\u3002</p> <p>\u3053\u308c\u306b\u3088\u308a\u91cd\u8981\u306a\u7d50\u8ad6\u304c\u5f97\u3089\u308c\u307e\u3059\uff1a\\(i-1\\) \u6bb5\u76ee\u306b\u5230\u9054\u3059\u308b\u65b9\u6cd5\u306e\u6570\u306b \\(i-2\\) \u6bb5\u76ee\u306b\u5230\u9054\u3059\u308b\u65b9\u6cd5\u306e\u6570\u3092\u52a0\u3048\u305f\u3082\u306e\u304c\u3001\\(i\\) \u6bb5\u76ee\u306b\u5230\u9054\u3059\u308b\u65b9\u6cd5\u306e\u6570\u306b\u7b49\u3057\u3044\u3002\u5f0f\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\uff1a</p> \\[ dp[i] = dp[i-1] + dp[i-2] \\] <p>\u3053\u308c\u306f\u3001\u968e\u6bb5\u767b\u308a\u554f\u984c\u306b\u304a\u3044\u3066\u90e8\u5206\u554f\u984c\u9593\u306b\u518d\u5e30\u95a2\u4fc2\u304c\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u3001\u5143\u306e\u554f\u984c\u306e\u89e3\u306f\u90e8\u5206\u554f\u984c\u306e\u89e3\u304b\u3089\u69cb\u7bc9\u3067\u304d\u307e\u3059\u3002\u4e0b\u306e\u56f3\u306f\u3053\u306e\u518d\u5e30\u95a2\u4fc2\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002</p> <p></p> <p> \u56f3 14-2 \u00a0 \u89e3\u306e\u6570\u306e\u518d\u5e30\u95a2\u4fc2 </p> <p>\u518d\u5e30\u5f0f\u306b\u5f93\u3063\u3066\u529b\u4efb\u305b\u63a2\u7d22\u89e3\u6cd5\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\\(dp[n]\\) \u304b\u3089\u59cb\u3081\u3066\u3001**\u3088\u308a\u5927\u304d\u306a\u554f\u984c\u3092\u518d\u5e30\u7684\u306b2\u3064\u306e\u5c0f\u3055\u306a\u90e8\u5206\u554f\u984c\u306e\u548c\u306b\u5206\u89e3**\u3057\u3001\u89e3\u304c\u65e2\u77e5\u306e\u6700\u5c0f\u306e\u90e8\u5206\u554f\u984c \\(dp[1]\\) \u3068 \\(dp[2]\\) \u306b\u5230\u9054\u3059\u308b\u307e\u3067\u7d9a\u3051\u307e\u3059\u3002\\(dp[1] = 1\\) \u3068 \\(dp[2] = 2\\) \u3067\u3001\u305d\u308c\u305e\u308c1\u6bb5\u76ee\u30682\u6bb5\u76ee\u306b\u767b\u308b\u65b9\u6cd5\u304c \\(1\\) \u901a\u308a\u3068 \\(2\\) \u901a\u308a\u3042\u308b\u3053\u3068\u3092\u8868\u3057\u307e\u3059\u3002</p> <p>\u4ee5\u4e0b\u306e\u30b3\u30fc\u30c9\u3092\u89b3\u5bdf\u3059\u308b\u3068\u3001\u6a19\u6e96\u7684\u306a\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30b3\u30fc\u30c9\u3068\u540c\u69d8\u306b\u6df1\u3055\u512a\u5148\u63a2\u7d22\u306b\u5c5e\u3057\u307e\u3059\u304c\u3001\u3088\u308a\u7c21\u6f54\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig climbing_stairs_dfs.py<pre><code>def dfs(i: int) -&gt; int:\n    \"\"\"\u63a2\u7d22\"\"\"\n    # \u65e2\u77e5\u306e dp[1] \u3068 dp[2] \u306f\u3001\u305d\u308c\u3089\u3092\u8fd4\u3059\n    if i == 1 or i == 2:\n        return i\n    # dp[i] = dp[i-1] + dp[i-2]\n    count = dfs(i - 1) + dfs(i - 2)\n    return count\n\ndef climbing_stairs_dfs(n: int) -&gt; int:\n    \"\"\"\u968e\u6bb5\u767b\u308a\uff1a\u63a2\u7d22\"\"\"\n    return dfs(n)\n</code></pre> climbing_stairs_dfs.cpp<pre><code>/* \u63a2\u7d22 */\nint dfs(int i) {\n    // \u65e2\u77e5\u306e dp[1] \u3068 dp[2] \u3092\u8fd4\u3059\n    if (i == 1 || i == 2)\n        return i;\n    // dp[i] = dp[i-1] + dp[i-2]\n    int count = dfs(i - 1) + dfs(i - 2);\n    return count;\n}\n\n/* \u968e\u6bb5\u767b\u308a\uff1a\u63a2\u7d22 */\nint climbingStairsDFS(int n) {\n    return dfs(n);\n}\n</code></pre> climbing_stairs_dfs.java<pre><code>/* \u63a2\u7d22 */\nint dfs(int i) {\n    // \u65e2\u77e5\u306e dp[1] \u3068 dp[2] \u3092\u8fd4\u3059\n    if (i == 1 || i == 2)\n        return i;\n    // dp[i] = dp[i-1] + dp[i-2]\n    int count = dfs(i - 1) + dfs(i - 2);\n    return count;\n}\n\n/* \u968e\u6bb5\u767b\u308a\uff1a\u63a2\u7d22 */\nint climbingStairsDFS(int n) {\n    return dfs(n);\n}\n</code></pre> climbing_stairs_dfs.cs<pre><code>[class]{climbing_stairs_dfs}-[func]{DFS}\n\n[class]{climbing_stairs_dfs}-[func]{ClimbingStairsDFS}\n</code></pre> climbing_stairs_dfs.go<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{climbingStairsDFS}\n</code></pre> climbing_stairs_dfs.swift<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{climbingStairsDFS}\n</code></pre> climbing_stairs_dfs.js<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{climbingStairsDFS}\n</code></pre> climbing_stairs_dfs.ts<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{climbingStairsDFS}\n</code></pre> climbing_stairs_dfs.dart<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{climbingStairsDFS}\n</code></pre> climbing_stairs_dfs.rs<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{climbing_stairs_dfs}\n</code></pre> climbing_stairs_dfs.c<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{climbingStairsDFS}\n</code></pre> climbing_stairs_dfs.kt<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{climbingStairsDFS}\n</code></pre> climbing_stairs_dfs.rb<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{climbing_stairs_dfs}\n</code></pre> climbing_stairs_dfs.zig<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{climbingStairsDFS}\n</code></pre> <p>\u4e0b\u306e\u56f3\u306f\u529b\u4efb\u305b\u63a2\u7d22\u306b\u3088\u3063\u3066\u5f62\u6210\u3055\u308c\u308b\u518d\u5e30\u6728\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002\u554f\u984c \\(dp[n]\\) \u306b\u3064\u3044\u3066\u3001\u305d\u306e\u518d\u5e30\u6728\u306e\u6df1\u3055\u306f \\(n\\) \u3067\u3001\u6642\u9593\u8a08\u7b97\u91cf\u306f \\(O(2^n)\\) \u3067\u3059\u3002\u3053\u306e\u6307\u6570\u7684\u5897\u52a0\u306b\u3088\u308a\u3001\\(n\\) \u304c\u5927\u304d\u3044\u3068\u30d7\u30ed\u30b0\u30e9\u30e0\u306e\u5b9f\u884c\u304c\u306f\u308b\u304b\u306b\u9045\u304f\u306a\u308a\u3001\u9577\u3044\u5f85\u6a5f\u6642\u9593\u304c\u751f\u3058\u307e\u3059\u3002</p> <p></p> <p> \u56f3 14-3 \u00a0 \u968e\u6bb5\u767b\u308a\u306e\u518d\u5e30\u6728 </p> <p>\u4e0a\u306e\u56f3\u3092\u89b3\u5bdf\u3059\u308b\u3068\u3001**\u6307\u6570\u6642\u9593\u8a08\u7b97\u91cf\u306f\u300c\u91cd\u8907\u3059\u308b\u90e8\u5206\u554f\u984c\u300d\u306b\u3088\u3063\u3066\u5f15\u304d\u8d77\u3053\u3055\u308c\u308b**\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\\(dp[9]\\) \u306f \\(dp[8]\\) \u3068 \\(dp[7]\\) \u306b\u5206\u89e3\u3055\u308c\u3001\\(dp[8]\\) \u306f\u3055\u3089\u306b \\(dp[7]\\) \u3068 \\(dp[6]\\) \u306b\u5206\u89e3\u3055\u308c\u3001\u4e21\u65b9\u3068\u3082\u90e8\u5206\u554f\u984c \\(dp[7]\\) \u3092\u542b\u3093\u3067\u3044\u307e\u3059\u3002</p> <p>\u3053\u306e\u3088\u3046\u306b\u3001\u90e8\u5206\u554f\u984c\u306b\u306f\u3055\u3089\u306b\u5c0f\u3055\u306a\u91cd\u8907\u3059\u308b\u90e8\u5206\u554f\u984c\u304c\u542b\u307e\u308c\u3001\u3053\u308c\u306f\u7121\u9650\u306b\u7d9a\u304d\u307e\u3059\u3002\u8a08\u7b97\u30ea\u30bd\u30fc\u30b9\u306e\u5927\u90e8\u5206\u304c\u3053\u308c\u3089\u306e\u91cd\u8907\u3059\u308b\u90e8\u5206\u554f\u984c\u306b\u6d6a\u8cbb\u3055\u308c\u3066\u3044\u307e\u3059\u3002</p>"},{"location":"chapter_dynamic_programming/intro_to_dynamic_programming/#1412-2","title":"14.1.2 \u00a0 \u65b9\u6cd52\uff1a\u30e1\u30e2\u5316\u63a2\u7d22","text":"<p>\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u52b9\u7387\u3092\u5411\u4e0a\u3055\u305b\u308b\u305f\u3081\u3001**\u3059\u3079\u3066\u306e\u91cd\u8907\u3059\u308b\u90e8\u5206\u554f\u984c\u3092\u4e00\u5ea6\u3060\u3051\u8a08\u7b97\u3057\u305f\u3044**\u3068\u8003\u3048\u307e\u3059\u3002\u3053\u306e\u76ee\u7684\u306e\u305f\u3081\u3001\u5404\u90e8\u5206\u554f\u984c\u306e\u89e3\u3092\u8a18\u9332\u3059\u308b\u914d\u5217 <code>mem</code> \u3092\u5ba3\u8a00\u3057\u3001\u63a2\u7d22\u30d7\u30ed\u30bb\u30b9\u4e2d\u306b\u91cd\u8907\u3059\u308b\u90e8\u5206\u554f\u984c\u3092\u679d\u5208\u308a\u3057\u307e\u3059\u3002</p> <ol> <li>\\(dp[i]\\) \u304c\u521d\u3081\u3066\u8a08\u7b97\u3055\u308c\u308b\u3068\u304d\u3001\u5f8c\u3067\u4f7f\u7528\u3059\u308b\u305f\u3081\u306b <code>mem[i]</code> \u306b\u8a18\u9332\u3057\u307e\u3059\u3002</li> <li>\\(dp[i]\\) \u3092\u518d\u5ea6\u8a08\u7b97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u3068\u304d\u3001<code>mem[i]</code> \u304b\u3089\u76f4\u63a5\u7d50\u679c\u3092\u53d6\u5f97\u3067\u304d\u3001\u305d\u306e\u90e8\u5206\u554f\u984c\u306e\u5197\u9577\u306a\u8a08\u7b97\u3092\u907f\u3051\u3089\u308c\u307e\u3059\u3002</li> </ol> <p>\u30b3\u30fc\u30c9\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig climbing_stairs_dfs_mem.py<pre><code>def dfs(i: int, mem: list[int]) -&gt; int:\n    \"\"\"\u8a18\u61b6\u5316\u63a2\u7d22\"\"\"\n    # \u65e2\u77e5\u306e dp[1] \u3068 dp[2] \u306f\u3001\u305d\u308c\u3089\u3092\u8fd4\u3059\n    if i == 1 or i == 2:\n        return i\n    # dp[i] \u306e\u8a18\u9332\u304c\u3042\u308b\u5834\u5408\u3001\u305d\u308c\u3092\u8fd4\u3059\n    if mem[i] != -1:\n        return mem[i]\n    # dp[i] = dp[i-1] + dp[i-2]\n    count = dfs(i - 1, mem) + dfs(i - 2, mem)\n    # dp[i] \u3092\u8a18\u9332\n    mem[i] = count\n    return count\n\ndef climbing_stairs_dfs_mem(n: int) -&gt; int:\n    \"\"\"\u968e\u6bb5\u767b\u308a\uff1a\u8a18\u61b6\u5316\u63a2\u7d22\"\"\"\n    # mem[i] \u306f i \u6bb5\u76ee\u306b\u767b\u308b\u89e3\u306e\u7dcf\u6570\u3092\u8a18\u9332\u3001-1 \u306f\u8a18\u9332\u306a\u3057\u3092\u610f\u5473\u3059\u308b\n    mem = [-1] * (n + 1)\n    return dfs(n, mem)\n</code></pre> climbing_stairs_dfs_mem.cpp<pre><code>/* \u30e1\u30e2\u5316\u63a2\u7d22 */\nint dfs(int i, vector&lt;int&gt; &amp;mem) {\n    // \u65e2\u77e5\u306e dp[1] \u3068 dp[2] \u3092\u8fd4\u3059\n    if (i == 1 || i == 2)\n        return i;\n    // dp[i] \u306e\u8a18\u9332\u304c\u3042\u308b\u5834\u5408\u3001\u305d\u308c\u3092\u8fd4\u3059\n    if (mem[i] != -1)\n        return mem[i];\n    // dp[i] = dp[i-1] + dp[i-2]\n    int count = dfs(i - 1, mem) + dfs(i - 2, mem);\n    // dp[i] \u3092\u8a18\u9332\n    mem[i] = count;\n    return count;\n}\n\n/* \u968e\u6bb5\u767b\u308a\uff1a\u30e1\u30e2\u5316\u63a2\u7d22 */\nint climbingStairsDFSMem(int n) {\n    // mem[i] \u306f i \u6bb5\u76ee\u306b\u767b\u308b\u7dcf\u89e3\u6570\u3092\u8a18\u9332\u3001-1 \u306f\u8a18\u9332\u306a\u3057\u3092\u610f\u5473\u3059\u308b\n    vector&lt;int&gt; mem(n + 1, -1);\n    return dfs(n, mem);\n}\n</code></pre> climbing_stairs_dfs_mem.java<pre><code>/* \u30e1\u30e2\u5316\u63a2\u7d22 */\nint dfs(int i, int[] mem) {\n    // \u65e2\u77e5\u306e dp[1] \u3068 dp[2] \u3092\u8fd4\u3059\n    if (i == 1 || i == 2)\n        return i;\n    // dp[i] \u306e\u8a18\u9332\u304c\u3042\u308b\u5834\u5408\u3001\u305d\u308c\u3092\u8fd4\u3059\n    if (mem[i] != -1)\n        return mem[i];\n    // dp[i] = dp[i-1] + dp[i-2]\n    int count = dfs(i - 1, mem) + dfs(i - 2, mem);\n    // dp[i] \u3092\u8a18\u9332\n    mem[i] = count;\n    return count;\n}\n\n/* \u968e\u6bb5\u767b\u308a\uff1a\u30e1\u30e2\u5316\u63a2\u7d22 */\nint climbingStairsDFSMem(int n) {\n    // mem[i] \u306f i \u6bb5\u76ee\u306b\u767b\u308b\u7dcf\u89e3\u6570\u3092\u8a18\u9332\u3001-1 \u306f\u8a18\u9332\u306a\u3057\u3092\u610f\u5473\u3059\u308b\n    int[] mem = new int[n + 1];\n    Arrays.fill(mem, -1);\n    return dfs(n, mem);\n}\n</code></pre> climbing_stairs_dfs_mem.cs<pre><code>[class]{climbing_stairs_dfs_mem}-[func]{DFS}\n\n[class]{climbing_stairs_dfs_mem}-[func]{ClimbingStairsDFSMem}\n</code></pre> climbing_stairs_dfs_mem.go<pre><code>[class]{}-[func]{dfsMem}\n\n[class]{}-[func]{climbingStairsDFSMem}\n</code></pre> climbing_stairs_dfs_mem.swift<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{climbingStairsDFSMem}\n</code></pre> climbing_stairs_dfs_mem.js<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{climbingStairsDFSMem}\n</code></pre> climbing_stairs_dfs_mem.ts<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{climbingStairsDFSMem}\n</code></pre> climbing_stairs_dfs_mem.dart<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{climbingStairsDFSMem}\n</code></pre> climbing_stairs_dfs_mem.rs<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{climbing_stairs_dfs_mem}\n</code></pre> climbing_stairs_dfs_mem.c<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{climbingStairsDFSMem}\n</code></pre> climbing_stairs_dfs_mem.kt<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{climbingStairsDFSMem}\n</code></pre> climbing_stairs_dfs_mem.rb<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{climbing_stairs_dfs_mem}\n</code></pre> climbing_stairs_dfs_mem.zig<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{climbingStairsDFSMem}\n</code></pre> <p>\u4e0b\u306e\u56f3\u3092\u89b3\u5bdf\u3059\u308b\u3068\u3001**\u30e1\u30e2\u5316\u5f8c\u3001\u3059\u3079\u3066\u306e\u91cd\u8907\u3059\u308b\u90e8\u5206\u554f\u984c\u306f\u4e00\u5ea6\u3060\u3051\u8a08\u7b97\u3055\u308c\u308b\u5fc5\u8981\u304c\u3042\u308a\u3001\u6642\u9593\u8a08\u7b97\u91cf\u3092 \\(O(n)\\) \u306b\u6700\u9069\u5316**\u3057\u307e\u3059\u3002\u3053\u308c\u306f\u5927\u5e45\u306a\u6539\u5584\u3067\u3059\u3002</p> <p></p> <p> \u56f3 14-4 \u00a0 \u30e1\u30e2\u5316\u63a2\u7d22\u306b\u3088\u308b\u518d\u5e30\u6728 </p>"},{"location":"chapter_dynamic_programming/intro_to_dynamic_programming/#1413-3","title":"14.1.3 \u00a0 \u65b9\u6cd53\uff1a\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0","text":"<p>**\u30e1\u30e2\u5316\u63a2\u7d22\u306f\u300c\u30c8\u30c3\u30d7\u30c0\u30a6\u30f3\u300d\u65b9\u5f0f**\u3067\u3059\uff1a\u5143\u306e\u554f\u984c\uff08\u6839\u30ce\u30fc\u30c9\uff09\u304b\u3089\u59cb\u3081\u3066\u3001\u3088\u308a\u5927\u304d\u306a\u90e8\u5206\u554f\u984c\u3092\u3088\u308a\u5c0f\u3055\u306a\u3082\u306e\u306b\u518d\u5e30\u7684\u306b\u5206\u89e3\u3057\u3001\u6700\u5c0f\u306e\u65e2\u77e5\u306e\u90e8\u5206\u554f\u984c\uff08\u8449\u30ce\u30fc\u30c9\uff09\u306e\u89e3\u306b\u5230\u9054\u3059\u308b\u307e\u3067\u7d9a\u3051\u307e\u3059\u3002\u305d\u306e\u5f8c\u3001\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u306b\u3088\u308a\u90e8\u5206\u554f\u984c\u306e\u89e3\u3092\u53ce\u96c6\u3057\u3001\u5143\u306e\u554f\u984c\u306e\u89e3\u3092\u69cb\u7bc9\u3057\u307e\u3059\u3002</p> <p>\u4e00\u65b9\u3001**\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u306f\u300c\u30dc\u30c8\u30e0\u30a2\u30c3\u30d7\u300d\u65b9\u5f0f**\u3067\u3059\uff1a\u6700\u5c0f\u306e\u90e8\u5206\u554f\u984c\u306e\u89e3\u304b\u3089\u59cb\u3081\u3066\u3001\u5143\u306e\u554f\u984c\u304c\u89e3\u6c7a\u3055\u308c\u308b\u307e\u3067\u3001\u3088\u308a\u5927\u304d\u306a\u90e8\u5206\u554f\u984c\u306e\u89e3\u3092\u53cd\u5fa9\u7684\u306b\u69cb\u7bc9\u3057\u307e\u3059\u3002</p> <p>\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u306f\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u3092\u5fc5\u8981\u3068\u3057\u306a\u3044\u305f\u3081\u3001\u30eb\u30fc\u30d7\u3092\u4f7f\u3063\u305f\u53cd\u5fa9\u306e\u307f\u304c\u5fc5\u8981\u3067\u3001\u518d\u5e30\u306f\u4e0d\u8981\u3067\u3059\u3002\u4ee5\u4e0b\u306e\u30b3\u30fc\u30c9\u3067\u306f\u3001\u914d\u5217 <code>dp</code> \u3092\u521d\u671f\u5316\u3057\u3066\u90e8\u5206\u554f\u984c\u306e\u89e3\u3092\u4fdd\u5b58\u3057\u3001\u30e1\u30e2\u5316\u63a2\u7d22\u306e\u914d\u5217 <code>mem</code> \u3068\u540c\u3058\u8a18\u9332\u6a5f\u80fd\u3092\u679c\u305f\u3057\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig climbing_stairs_dp.py<pre><code>def climbing_stairs_dp(n: int) -&gt; int:\n    \"\"\"\u968e\u6bb5\u767b\u308a\uff1a\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\"\"\"\n    if n == 1 or n == 2:\n        return n\n    # dp \u30c6\u30fc\u30d6\u30eb\u3092\u521d\u671f\u5316\u3001\u90e8\u5206\u554f\u984c\u306e\u89e3\u3092\u683c\u7d0d\u3059\u308b\u305f\u3081\u4f7f\u7528\n    dp = [0] * (n + 1)\n    # \u521d\u671f\u72b6\u614b\uff1a\u6700\u5c0f\u306e\u90e8\u5206\u554f\u984c\u306e\u89e3\u3092\u4e8b\u524d\u8a2d\u5b9a\n    dp[1], dp[2] = 1, 2\n    # \u72b6\u614b\u9077\u79fb\uff1a\u5c0f\u3055\u3044\u90e8\u5206\u554f\u984c\u304b\u3089\u5927\u304d\u3044\u90e8\u5206\u554f\u984c\u3092\u6bb5\u968e\u7684\u306b\u89e3\u304f\n    for i in range(3, n + 1):\n        dp[i] = dp[i - 1] + dp[i - 2]\n    return dp[n]\n</code></pre> climbing_stairs_dp.cpp<pre><code>/* \u968e\u6bb5\u767b\u308a\uff1a\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0 */\nint climbingStairsDP(int n) {\n    if (n == 1 || n == 2)\n        return n;\n    // DP\u30c6\u30fc\u30d6\u30eb\u3092\u521d\u671f\u5316\u3057\u3001\u90e8\u5206\u554f\u984c\u306e\u89e3\u3092\u683c\u7d0d\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\n    vector&lt;int&gt; dp(n + 1);\n    // \u521d\u671f\u72b6\u614b\uff1a\u6700\u5c0f\u306e\u90e8\u5206\u554f\u984c\u306e\u89e3\u3092\u4e8b\u524d\u8a2d\u5b9a\n    dp[1] = 1;\n    dp[2] = 2;\n    // \u72b6\u614b\u9077\u79fb\uff1a\u5c0f\u3055\u306a\u554f\u984c\u304b\u3089\u5927\u304d\u306a\u90e8\u5206\u554f\u984c\u3092\u6bb5\u968e\u7684\u306b\u89e3\u304f\n    for (int i = 3; i &lt;= n; i++) {\n        dp[i] = dp[i - 1] + dp[i - 2];\n    }\n    return dp[n];\n}\n</code></pre> climbing_stairs_dp.java<pre><code>/* \u968e\u6bb5\u767b\u308a\uff1a\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0 */\nint climbingStairsDP(int n) {\n    if (n == 1 || n == 2)\n        return n;\n    // DP\u30c6\u30fc\u30d6\u30eb\u3092\u521d\u671f\u5316\u3057\u3001\u90e8\u5206\u554f\u984c\u306e\u89e3\u3092\u683c\u7d0d\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\n    int[] dp = new int[n + 1];\n    // \u521d\u671f\u72b6\u614b\uff1a\u6700\u5c0f\u306e\u90e8\u5206\u554f\u984c\u306e\u89e3\u3092\u4e8b\u524d\u8a2d\u5b9a\n    dp[1] = 1;\n    dp[2] = 2;\n    // \u72b6\u614b\u9077\u79fb\uff1a\u5c0f\u3055\u306a\u554f\u984c\u304b\u3089\u5927\u304d\u306a\u90e8\u5206\u554f\u984c\u3092\u6bb5\u968e\u7684\u306b\u89e3\u304f\n    for (int i = 3; i &lt;= n; i++) {\n        dp[i] = dp[i - 1] + dp[i - 2];\n    }\n    return dp[n];\n}\n</code></pre> climbing_stairs_dp.cs<pre><code>[class]{climbing_stairs_dp}-[func]{ClimbingStairsDP}\n</code></pre> climbing_stairs_dp.go<pre><code>[class]{}-[func]{climbingStairsDP}\n</code></pre> climbing_stairs_dp.swift<pre><code>[class]{}-[func]{climbingStairsDP}\n</code></pre> climbing_stairs_dp.js<pre><code>[class]{}-[func]{climbingStairsDP}\n</code></pre> climbing_stairs_dp.ts<pre><code>[class]{}-[func]{climbingStairsDP}\n</code></pre> climbing_stairs_dp.dart<pre><code>[class]{}-[func]{climbingStairsDP}\n</code></pre> climbing_stairs_dp.rs<pre><code>[class]{}-[func]{climbing_stairs_dp}\n</code></pre> climbing_stairs_dp.c<pre><code>[class]{}-[func]{climbingStairsDP}\n</code></pre> climbing_stairs_dp.kt<pre><code>[class]{}-[func]{climbingStairsDP}\n</code></pre> climbing_stairs_dp.rb<pre><code>[class]{}-[func]{climbing_stairs_dp}\n</code></pre> climbing_stairs_dp.zig<pre><code>[class]{}-[func]{climbingStairsDP}\n</code></pre> <p>\u4e0b\u306e\u56f3\u306f\u4e0a\u8a18\u30b3\u30fc\u30c9\u306e\u5b9f\u884c\u30d7\u30ed\u30bb\u30b9\u3092\u30b7\u30df\u30e5\u30ec\u30fc\u30c8\u3057\u3066\u3044\u307e\u3059\u3002</p> <p></p> <p> \u56f3 14-5 \u00a0 \u968e\u6bb5\u767b\u308a\u306e\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u30d7\u30ed\u30bb\u30b9 </p> <p>\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3068\u540c\u69d8\u306b\u3001\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u3082\u300c\u72b6\u614b\u300d\u306e\u6982\u5ff5\u3092\u4f7f\u7528\u3057\u3066\u554f\u984c\u89e3\u6c7a\u306e\u7279\u5b9a\u306e\u6bb5\u968e\u3092\u8868\u73fe\u3057\u3001\u5404\u72b6\u614b\u306f\u90e8\u5206\u554f\u984c\u3068\u305d\u306e\u5c40\u6240\u6700\u9069\u89e3\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u968e\u6bb5\u767b\u308a\u554f\u984c\u306e\u72b6\u614b\u306f\u73fe\u5728\u306e\u30b9\u30c6\u30c3\u30d7\u756a\u53f7 \\(i\\) \u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002</p> <p>\u4e0a\u8a18\u306e\u5185\u5bb9\u306b\u57fa\u3065\u3044\u3066\u3001\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u3067\u3088\u304f\u4f7f\u7528\u3055\u308c\u308b\u7528\u8a9e\u3092\u307e\u3068\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002</p> <ul> <li>\u914d\u5217 <code>dp</code> \u306fDP\u30c6\u30fc\u30d6\u30eb\u3068\u547c\u3070\u308c\u3001\\(dp[i]\\) \u306f\u72b6\u614b \\(i\\) \u306b\u5bfe\u5fdc\u3059\u308b\u90e8\u5206\u554f\u984c\u306e\u89e3\u3092\u8868\u3057\u307e\u3059\u3002</li> <li>\u6700\u5c0f\u306e\u90e8\u5206\u554f\u984c\uff08\u30b9\u30c6\u30c3\u30d7 \\(1\\) \u3068 \\(2\\)\uff09\u306b\u5bfe\u5fdc\u3059\u308b\u72b6\u614b\u306f\u521d\u671f\u72b6\u614b\u3068\u547c\u3070\u308c\u307e\u3059\u3002</li> <li>\u518d\u5e30\u5f0f \\(dp[i] = dp[i-1] + dp[i-2]\\) \u306f\u72b6\u614b\u9077\u79fb\u65b9\u7a0b\u5f0f\u3068\u547c\u3070\u308c\u307e\u3059\u3002</li> </ul>"},{"location":"chapter_dynamic_programming/intro_to_dynamic_programming/#1414","title":"14.1.4 \u00a0 \u7a7a\u9593\u6700\u9069\u5316","text":"<p>\u6ce8\u610f\u6df1\u3044\u8aad\u8005\u306f**\\(dp[i]\\) \u306f \\(dp[i-1]\\) \u3068 \\(dp[i-2]\\) \u306e\u307f\u306b\u95a2\u9023\u3059\u308b\u305f\u3081\u3001\u3059\u3079\u3066\u306e\u90e8\u5206\u554f\u984c\u306e\u89e3\u3092\u4fdd\u5b58\u3059\u308b\u305f\u3081\u306b\u914d\u5217 <code>dp</code> \u3092\u4f7f\u7528\u3059\u308b\u5fc5\u8981\u304c\u306a\u3044**\u3053\u3068\u306b\u6c17\u3065\u304f\u3067\u3057\u3087\u3046\u3002\u5358\u306b2\u3064\u306e\u5909\u6570\u3092\u4f7f\u3063\u3066\u53cd\u5fa9\u7684\u306b\u9032\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u30b3\u30fc\u30c9\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig climbing_stairs_dp.py<pre><code>def climbing_stairs_dp_comp(n: int) -&gt; int:\n    \"\"\"\u968e\u6bb5\u767b\u308a\uff1a\u7a7a\u9593\u6700\u9069\u5316\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\"\"\"\n    if n == 1 or n == 2:\n        return n\n    a, b = 1, 2\n    for _ in range(3, n + 1):\n        a, b = b, a + b\n    return b\n</code></pre> climbing_stairs_dp.cpp<pre><code>/* \u968e\u6bb5\u767b\u308a\uff1a\u7a7a\u9593\u6700\u9069\u5316\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0 */\nint climbingStairsDPComp(int n) {\n    if (n == 1 || n == 2)\n        return n;\n    int a = 1, b = 2;\n    for (int i = 3; i &lt;= n; i++) {\n        int tmp = b;\n        b = a + b;\n        a = tmp;\n    }\n    return b;\n}\n</code></pre> climbing_stairs_dp.java<pre><code>/* \u968e\u6bb5\u767b\u308a\uff1a\u7a7a\u9593\u6700\u9069\u5316\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0 */\nint climbingStairsDPComp(int n) {\n    if (n == 1 || n == 2)\n        return n;\n    int a = 1, b = 2;\n    for (int i = 3; i &lt;= n; i++) {\n        int tmp = b;\n        b = a + b;\n        a = tmp;\n    }\n    return b;\n}\n</code></pre> climbing_stairs_dp.cs<pre><code>[class]{climbing_stairs_dp}-[func]{ClimbingStairsDPComp}\n</code></pre> climbing_stairs_dp.go<pre><code>[class]{}-[func]{climbingStairsDPComp}\n</code></pre> climbing_stairs_dp.swift<pre><code>[class]{}-[func]{climbingStairsDPComp}\n</code></pre> climbing_stairs_dp.js<pre><code>[class]{}-[func]{climbingStairsDPComp}\n</code></pre> climbing_stairs_dp.ts<pre><code>[class]{}-[func]{climbingStairsDPComp}\n</code></pre> climbing_stairs_dp.dart<pre><code>[class]{}-[func]{climbingStairsDPComp}\n</code></pre> climbing_stairs_dp.rs<pre><code>[class]{}-[func]{climbing_stairs_dp_comp}\n</code></pre> climbing_stairs_dp.c<pre><code>[class]{}-[func]{climbingStairsDPComp}\n</code></pre> climbing_stairs_dp.kt<pre><code>[class]{}-[func]{climbingStairsDPComp}\n</code></pre> climbing_stairs_dp.rb<pre><code>[class]{}-[func]{climbing_stairs_dp_comp}\n</code></pre> climbing_stairs_dp.zig<pre><code>[class]{}-[func]{climbingStairsDPComp}\n</code></pre> <p>\u4e0a\u8a18\u306e\u30b3\u30fc\u30c9\u3092\u89b3\u5bdf\u3059\u308b\u3068\u3001\u914d\u5217 <code>dp</code> \u304c\u5360\u6709\u3057\u3066\u3044\u305f\u7a7a\u9593\u304c\u524a\u9664\u3055\u308c\u308b\u305f\u3081\u3001\u7a7a\u9593\u8a08\u7b97\u91cf\u306f \\(O(n)\\) \u304b\u3089 \\(O(1)\\) \u306b\u524a\u6e1b\u3055\u308c\u307e\u3059\u3002</p> <p>\u591a\u304f\u306e\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u554f\u984c\u3067\u306f\u3001\u73fe\u5728\u306e\u72b6\u614b\u306f\u9650\u3089\u308c\u305f\u6570\u306e\u524d\u306e\u72b6\u614b\u306e\u307f\u306b\u4f9d\u5b58\u3059\u308b\u305f\u3081\u3001\u5fc5\u8981\u306a\u72b6\u614b\u306e\u307f\u3092\u4fdd\u6301\u3057\u3001\u300c\u6b21\u5143\u524a\u6e1b\u300d\u306b\u3088\u3063\u3066\u30e1\u30e2\u30ea\u7a7a\u9593\u3092\u7bc0\u7d04\u3067\u304d\u307e\u3059\u3002\u3053\u306e\u7a7a\u9593\u6700\u9069\u5316\u6280\u8853\u306f\u300c\u30ed\u30fc\u30ea\u30f3\u30b0\u5909\u6570\u300d\u307e\u305f\u306f\u300c\u30ed\u30fc\u30ea\u30f3\u30b0\u914d\u5217\u300d\u3068\u3057\u3066\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\u3002</p>"},{"location":"chapter_dynamic_programming/knapsack_problem/","title":"14.4 \u00a0 0-1\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c","text":"<p>\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c\u306f\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u306e\u512a\u308c\u305f\u5165\u9580\u554f\u984c\u3067\u3042\u308a\u3001\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u3067\u6700\u3082\u4e00\u822c\u7684\u306a\u554f\u984c\u30bf\u30a4\u30d7\u3067\u3059\u30020-1\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c\u3001\u7121\u5236\u9650\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c\u3001\u8907\u6570\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c\u306a\u3069\u3001\u591a\u304f\u306e\u5909\u7a2e\u304c\u3042\u308a\u307e\u3059\u3002</p> <p>\u3053\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u3067\u306f\u3001\u307e\u305a\u6700\u3082\u4e00\u822c\u7684\u306a0-1\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c\u3092\u89e3\u6c7a\u3057\u307e\u3059\u3002</p> <p>Question</p> <p>\\(n\\) \u500b\u306e\u30a2\u30a4\u30c6\u30e0\u304c\u4e0e\u3048\u3089\u308c\u3001\\(i\\) \u756a\u76ee\u306e\u30a2\u30a4\u30c6\u30e0\u306e\u91cd\u91cf\u306f \\(wgt[i-1]\\) \u3067\u5024\u306f \\(val[i-1]\\) \u3067\u3059\u3002\u5bb9\u91cf\u304c \\(cap\\) \u306e\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u304c\u3042\u308a\u307e\u3059\u3002\u5404\u30a2\u30a4\u30c6\u30e0\u306f1\u56de\u306e\u307f\u9078\u629e\u3067\u304d\u307e\u3059\u3002\u5bb9\u91cf\u5236\u9650\u4e0b\u3067\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u306b\u5165\u308c\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u30a2\u30a4\u30c6\u30e0\u306e\u6700\u5927\u5024\u306f\u4f55\u3067\u3059\u304b\uff1f</p> <p>\u4e0b\u306e\u56f3\u3092\u89b3\u5bdf\u3059\u308b\u3068\u3001\u30a2\u30a4\u30c6\u30e0\u756a\u53f7 \\(i\\) \u306f1\u304b\u3089\u6570\u3048\u59cb\u3081\u3001\u914d\u5217\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306f0\u304b\u3089\u59cb\u307e\u308b\u305f\u3081\u3001\u30a2\u30a4\u30c6\u30e0 \\(i\\) \u306e\u91cd\u91cf\u306f \\(wgt[i-1]\\) \u306b\u5bfe\u5fdc\u3057\u3001\u5024\u306f \\(val[i-1]\\) \u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002</p> <p></p> <p> \u56f3 14-17 \u00a0 0-1\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u306e\u4f8b\u30c7\u30fc\u30bf </p> <p>0-1\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c\u3092 \\(n\\) \u30e9\u30a6\u30f3\u30c9\u306e\u6c7a\u5b9a\u304b\u3089\u69cb\u6210\u3055\u308c\u308b\u30d7\u30ed\u30bb\u30b9\u3068\u3057\u3066\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u5404\u30a2\u30a4\u30c6\u30e0\u306b\u3064\u3044\u3066\u5165\u308c\u306a\u3044\u3001\u307e\u305f\u306f\u5165\u308c\u308b\u3068\u3044\u30462\u3064\u306e\u6c7a\u5b9a\u304c\u3042\u308a\u3001\u3057\u305f\u304c\u3063\u3066\u554f\u984c\u306f\u6c7a\u5b9a\u6728\u30e2\u30c7\u30eb\u306b\u9069\u5408\u3057\u307e\u3059\u3002</p> <p>\u3053\u306e\u554f\u984c\u306e\u76ee\u7684\u306f\u300c\u9650\u3089\u308c\u305f\u5bb9\u91cf\u306e\u4e0b\u3067\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u306b\u5165\u308c\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u30a2\u30a4\u30c6\u30e0\u306e\u5024\u3092\u6700\u5927\u5316\u3059\u308b\u300d\u3053\u3068\u3067\u3042\u308a\u3001\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u554f\u984c\u3067\u3042\u308b\u53ef\u80fd\u6027\u304c\u9ad8\u3044\u3067\u3059\u3002</p> <p>\u7b2c1\u30b9\u30c6\u30c3\u30d7\uff1a\u5404\u30e9\u30a6\u30f3\u30c9\u306e\u6c7a\u5b9a\u3092\u8003\u3048\u3001\u72b6\u614b\u3092\u5b9a\u7fa9\u3057\u3001\u305d\u308c\u306b\u3088\u308a \\(dp\\) \u30c6\u30fc\u30d6\u30eb\u3092\u5f97\u308b</p> <p>\u5404\u30a2\u30a4\u30c6\u30e0\u306b\u3064\u3044\u3066\u3001\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u306b\u5165\u308c\u306a\u3051\u308c\u3070\u5bb9\u91cf\u306f\u5909\u308f\u3089\u305a\u3001\u5165\u308c\u308c\u3070\u5bb9\u91cf\u306f\u6e1b\u5c11\u3057\u307e\u3059\u3002\u3053\u308c\u304b\u3089\u72b6\u614b\u5b9a\u7fa9\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\uff1a\u73fe\u5728\u306e\u30a2\u30a4\u30c6\u30e0\u756a\u53f7 \\(i\\) \u3068\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u5bb9\u91cf \\(c\\)\u3001\\([i, c]\\) \u3068\u8868\u8a18\u3055\u308c\u307e\u3059\u3002</p> <p>\u72b6\u614b \\([i, c]\\) \u306f\u90e8\u5206\u554f\u984c\u306b\u5bfe\u5fdc\u3057\u307e\u3059\uff1a\u5bb9\u91cf \\(c\\) \u306e\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u3067\u306e\u6700\u521d\u306e \\(i\\) \u500b\u306e\u30a2\u30a4\u30c6\u30e0\u306e\u6700\u5927\u5024\u3001\\(dp[i, c]\\) \u3068\u8868\u8a18\u3055\u308c\u307e\u3059\u3002</p> <p>\u63a2\u3057\u3066\u3044\u308b\u89e3\u306f \\(dp[n, cap]\\) \u3067\u3042\u308b\u305f\u3081\u3001\u30b5\u30a4\u30ba \\((n+1) \\times (cap+1)\\) \u306e\u4e8c\u6b21\u5143 \\(dp\\) \u30c6\u30fc\u30d6\u30eb\u304c\u5fc5\u8981\u3067\u3059\u3002</p> <p>\u7b2c2\u30b9\u30c6\u30c3\u30d7\uff1a\u6700\u9069\u90e8\u5206\u69cb\u9020\u3092\u7279\u5b9a\u3057\u3001\u72b6\u614b\u9077\u79fb\u65b9\u7a0b\u5f0f\u3092\u5c0e\u51fa\u3059\u308b</p> <p>\u30a2\u30a4\u30c6\u30e0 \\(i\\) \u306e\u6c7a\u5b9a\u3092\u884c\u3063\u305f\u5f8c\u3001\u6b8b\u308b\u306e\u306f\u6700\u521d\u306e \\(i-1\\) \u500b\u306e\u30a2\u30a4\u30c6\u30e0\u306e\u6c7a\u5b9a\u306e\u90e8\u5206\u554f\u984c\u3067\u3042\u308a\u3001\u3053\u308c\u306f2\u3064\u306e\u30b1\u30fc\u30b9\u306b\u5206\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002</p> <ul> <li>\u30a2\u30a4\u30c6\u30e0 \\(i\\) \u3092\u5165\u308c\u306a\u3044\uff1a\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u5bb9\u91cf\u306f\u5909\u308f\u3089\u305a\u3001\u72b6\u614b\u306f \\([i-1, c]\\) \u306b\u5909\u308f\u308a\u307e\u3059\u3002</li> <li>\u30a2\u30a4\u30c6\u30e0 \\(i\\) \u3092\u5165\u308c\u308b\uff1a\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u5bb9\u91cf\u306f \\(wgt[i-1]\\) \u3060\u3051\u6e1b\u5c11\u3057\u3001\u5024\u306f \\(val[i-1]\\) \u3060\u3051\u5897\u52a0\u3057\u3001\u72b6\u614b\u306f \\([i-1, c-wgt[i-1]]\\) \u306b\u5909\u308f\u308a\u307e\u3059\u3002</li> </ul> <p>\u4e0a\u8a18\u306e\u5206\u6790\u306b\u3088\u308a\u3001\u3053\u306e\u554f\u984c\u306e\u6700\u9069\u90e8\u5206\u69cb\u9020\u304c\u660e\u3089\u304b\u306b\u306a\u308a\u307e\u3059\uff1a\u6700\u5927\u5024 \\(dp[i, c]\\) \u306f\u3001\u30a2\u30a4\u30c6\u30e0 \\(i\\) \u3092\u5165\u308c\u306a\u3044\u65b9\u6848\u3068\u30a2\u30a4\u30c6\u30e0 \\(i\\) \u3092\u5165\u308c\u308b\u65b9\u6848\u306e2\u3064\u306e\u3046\u3061\u3001\u3088\u308a\u5927\u304d\u306a\u5024\u306b\u7b49\u3057\u3044\u3002\u3053\u308c\u304b\u3089\u72b6\u614b\u9077\u79fb\u65b9\u7a0b\u5f0f\u3092\u5c0e\u51fa\u3067\u304d\u307e\u3059\uff1a</p> \\[ dp[i, c] = \\max(dp[i-1, c], dp[i-1, c - wgt[i-1]] + val[i-1]) \\] <p>\u73fe\u5728\u306e\u30a2\u30a4\u30c6\u30e0\u306e\u91cd\u91cf \\(wgt[i - 1]\\) \u304c\u6b8b\u308a\u306e\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u5bb9\u91cf \\(c\\) \u3092\u8d85\u3048\u308b\u5834\u5408\u3001\u552f\u4e00\u306e\u9078\u629e\u80a2\u306f\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u306b\u5165\u308c\u306a\u3044\u3053\u3068\u3067\u3042\u308b\u3053\u3068\u306b\u6ce8\u610f\u3059\u308b\u3053\u3068\u304c\u91cd\u8981\u3067\u3059\u3002</p> <p>\u7b2c3\u30b9\u30c6\u30c3\u30d7\uff1a\u5883\u754c\u6761\u4ef6\u3068\u72b6\u614b\u9077\u79fb\u306e\u9806\u5e8f\u3092\u6c7a\u5b9a\u3059\u308b</p> <p>\u30a2\u30a4\u30c6\u30e0\u304c\u306a\u3044\u5834\u5408\u307e\u305f\u306f\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u5bb9\u91cf\u304c \\(0\\) \u306e\u5834\u5408\u3001\u6700\u5927\u5024\u306f \\(0\\) \u3067\u3059\u3002\u3064\u307e\u308a\u3001\u6700\u521d\u306e\u5217 \\(dp[i, 0]\\) \u3068\u6700\u521d\u306e\u884c \\(dp[0, c]\\) \u306f\u3069\u3061\u3089\u3082 \\(0\\) \u306b\u7b49\u3057\u3044\u3067\u3059\u3002</p> <p>\u73fe\u5728\u306e\u72b6\u614b \\([i, c]\\) \u306f\u76f4\u63a5\u4e0a\u306e\u72b6\u614b \\([i-1, c]\\) \u3068\u5de6\u4e0a\u306e\u72b6\u614b \\([i-1, c-wgt[i-1]]\\) \u304b\u3089\u9077\u79fb\u3059\u308b\u305f\u3081\u30012\u5c64\u306e\u30eb\u30fc\u30d7\u3092\u901a\u3058\u3066 \\(dp\\) \u30c6\u30fc\u30d6\u30eb\u5168\u4f53\u3092\u9806\u5e8f\u901a\u308a\u306b\u8d70\u67fb\u3057\u307e\u3059\u3002</p> <p>\u4e0a\u8a18\u306e\u5206\u6790\u306b\u5f93\u3063\u3066\u3001\u6b21\u306b\u529b\u4efb\u305b\u63a2\u7d22\u3001\u30e1\u30e2\u5316\u63a2\u7d22\u3001\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u306e\u9806\u5e8f\u3067\u89e3\u6cd5\u3092\u5b9f\u88c5\u3057\u307e\u3059\u3002</p>"},{"location":"chapter_dynamic_programming/knapsack_problem/#1-1","title":"1. \u00a0 \u65b9\u6cd51\uff1a\u529b\u4efb\u305b\u63a2\u7d22","text":"<p>\u63a2\u7d22\u30b3\u30fc\u30c9\u306b\u306f\u4ee5\u4e0b\u306e\u8981\u7d20\u304c\u542b\u307e\u308c\u307e\u3059\u3002</p> <ul> <li>\u518d\u5e30\u30d1\u30e9\u30e1\u30fc\u30bf\uff1a\u72b6\u614b \\([i, c]\\)\u3002</li> <li>\u623b\u308a\u5024\uff1a\u90e8\u5206\u554f\u984c \\(dp[i, c]\\) \u306e\u89e3\u3002</li> <li>\u7d42\u4e86\u6761\u4ef6\uff1a\u30a2\u30a4\u30c6\u30e0\u756a\u53f7\u304c\u7bc4\u56f2\u5916 \\(i = 0\\) \u307e\u305f\u306f\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u306e\u6b8b\u308a\u5bb9\u91cf\u304c \\(0\\) \u306e\u3068\u304d\u3001\u518d\u5e30\u3092\u7d42\u4e86\u3057\u5024 \\(0\\) \u3092\u8fd4\u3059\u3002</li> <li>\u679d\u5208\u308a\uff1a\u73fe\u5728\u306e\u30a2\u30a4\u30c6\u30e0\u306e\u91cd\u91cf\u304c\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u306e\u6b8b\u308a\u5bb9\u91cf\u3092\u8d85\u3048\u308b\u5834\u5408\u3001\u552f\u4e00\u306e\u9078\u629e\u80a2\u306f\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u306b\u5165\u308c\u306a\u3044\u3053\u3068\u3067\u3059\u3002</li> </ul> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig knapsack.py<pre><code>def knapsack_dfs(wgt: list[int], val: list[int], i: int, c: int) -&gt; int:\n    \"\"\"0-1 \u30ca\u30c3\u30d7\u30b5\u30c3\u30af\uff1a\u30d6\u30eb\u30fc\u30c8\u30d5\u30a9\u30fc\u30b9\u63a2\u7d22\"\"\"\n    # \u3059\u3079\u3066\u306e\u30a2\u30a4\u30c6\u30e0\u304c\u9078\u629e\u3055\u308c\u305f\u304b\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u306b\u6b8b\u308a\u5bb9\u91cf\u304c\u306a\u3044\u5834\u5408\u3001\u5024 0 \u3092\u8fd4\u3059\n    if i == 0 or c == 0:\n        return 0\n    # \u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u5bb9\u91cf\u3092\u8d85\u3048\u308b\u5834\u5408\u3001\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u306b\u5165\u308c\u306a\u3044\u3053\u3068\u3057\u304b\u9078\u629e\u3067\u304d\u306a\u3044\n    if wgt[i - 1] &gt; c:\n        return knapsack_dfs(wgt, val, i - 1, c)\n    # \u30a2\u30a4\u30c6\u30e0 i \u3092\u5165\u308c\u306a\u3044\u306e\u3068\u5165\u308c\u308b\u306e\u3068\u306e\u6700\u5927\u5024\u3092\u8a08\u7b97\n    no = knapsack_dfs(wgt, val, i - 1, c)\n    yes = knapsack_dfs(wgt, val, i - 1, c - wgt[i - 1]) + val[i - 1]\n    # 2 \u3064\u306e\u9078\u629e\u80a2\u306e\u3046\u3061\u5927\u304d\u3044\u5024\u3092\u8fd4\u3059\n    return max(no, yes)\n</code></pre> knapsack.cpp<pre><code>/* 0-1 \u30ca\u30c3\u30d7\u30b5\u30c3\u30af\uff1a\u30d6\u30eb\u30fc\u30c8\u30d5\u30a9\u30fc\u30b9\u63a2\u7d22 */\nint knapsackDFS(vector&lt;int&gt; &amp;wgt, vector&lt;int&gt; &amp;val, int i, int c) {\n    // \u3059\u3079\u3066\u306e\u30a2\u30a4\u30c6\u30e0\u304c\u9078\u629e\u3055\u308c\u305f\u304b\u3001\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u306b\u6b8b\u308a\u5bb9\u91cf\u304c\u306a\u3044\u5834\u5408\u3001\u5024 0 \u3092\u8fd4\u3059\n    if (i == 0 || c == 0) {\n        return 0;\n    }\n    // \u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u306e\u5bb9\u91cf\u3092\u8d85\u3048\u308b\u5834\u5408\u3001\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u306b\u5165\u308c\u306a\u3044\u3053\u3068\u3057\u304b\u9078\u629e\u3067\u304d\u306a\u3044\n    if (wgt[i - 1] &gt; c) {\n        return knapsackDFS(wgt, val, i - 1, c);\n    }\n    // \u30a2\u30a4\u30c6\u30e0 i \u3092\u5165\u308c\u306a\u3044\u5834\u5408\u3068\u5165\u308c\u308b\u5834\u5408\u306e\u6700\u5927\u5024\u3092\u8a08\u7b97\n    int no = knapsackDFS(wgt, val, i - 1, c);\n    int yes = knapsackDFS(wgt, val, i - 1, c - wgt[i - 1]) + val[i - 1];\n    // 2\u3064\u306e\u9078\u629e\u80a2\u306e\u3088\u308a\u5927\u304d\u3044\u5024\u3092\u8fd4\u3059\n    return max(no, yes);\n}\n</code></pre> knapsack.java<pre><code>/* 0-1 \u30ca\u30c3\u30d7\u30b5\u30c3\u30af\uff1a\u30d6\u30eb\u30fc\u30c8\u30d5\u30a9\u30fc\u30b9\u63a2\u7d22 */\nint knapsackDFS(int[] wgt, int[] val, int i, int c) {\n    // \u3059\u3079\u3066\u306e\u30a2\u30a4\u30c6\u30e0\u304c\u9078\u629e\u3055\u308c\u305f\u304b\u3001\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u306b\u6b8b\u308a\u5bb9\u91cf\u304c\u306a\u3044\u5834\u5408\u3001\u5024 0 \u3092\u8fd4\u3059\n    if (i == 0 || c == 0) {\n        return 0;\n    }\n    // \u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u306e\u5bb9\u91cf\u3092\u8d85\u3048\u308b\u5834\u5408\u3001\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u306b\u5165\u308c\u306a\u3044\u3053\u3068\u3057\u304b\u9078\u629e\u3067\u304d\u306a\u3044\n    if (wgt[i - 1] &gt; c) {\n        return knapsackDFS(wgt, val, i - 1, c);\n    }\n    // \u30a2\u30a4\u30c6\u30e0 i \u3092\u5165\u308c\u306a\u3044\u5834\u5408\u3068\u5165\u308c\u308b\u5834\u5408\u306e\u6700\u5927\u5024\u3092\u8a08\u7b97\n    int no = knapsackDFS(wgt, val, i - 1, c);\n    int yes = knapsackDFS(wgt, val, i - 1, c - wgt[i - 1]) + val[i - 1];\n    // 2\u3064\u306e\u9078\u629e\u80a2\u306e\u3088\u308a\u5927\u304d\u3044\u5024\u3092\u8fd4\u3059\n    return Math.max(no, yes);\n}\n</code></pre> knapsack.cs<pre><code>[class]{knapsack}-[func]{KnapsackDFS}\n</code></pre> knapsack.go<pre><code>[class]{}-[func]{knapsackDFS}\n</code></pre> knapsack.swift<pre><code>[class]{}-[func]{knapsackDFS}\n</code></pre> knapsack.js<pre><code>[class]{}-[func]{knapsackDFS}\n</code></pre> knapsack.ts<pre><code>[class]{}-[func]{knapsackDFS}\n</code></pre> knapsack.dart<pre><code>[class]{}-[func]{knapsackDFS}\n</code></pre> knapsack.rs<pre><code>[class]{}-[func]{knapsack_dfs}\n</code></pre> knapsack.c<pre><code>[class]{}-[func]{knapsackDFS}\n</code></pre> knapsack.kt<pre><code>[class]{}-[func]{knapsackDFS}\n</code></pre> knapsack.rb<pre><code>[class]{}-[func]{knapsack_dfs}\n</code></pre> knapsack.zig<pre><code>[class]{}-[func]{knapsackDFS}\n</code></pre> <p>\u4e0b\u306e\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u5404\u30a2\u30a4\u30c6\u30e0\u306f\u9078\u629e\u3057\u306a\u3044\u3068\u9078\u629e\u3059\u308b\u3068\u3044\u30462\u3064\u306e\u63a2\u7d22\u5206\u5c90\u3092\u751f\u6210\u3059\u308b\u305f\u3081\u3001\u6642\u9593\u8a08\u7b97\u91cf\u306f \\(O(2^n)\\) \u3067\u3059\u3002</p> <p>\u518d\u5e30\u6728\u3092\u89b3\u5bdf\u3059\u308b\u3068\u3001\\(dp[1, 10]\\) \u306a\u3069\u306e\u91cd\u8907\u3059\u308b\u90e8\u5206\u554f\u984c\u304c\u3042\u308b\u3053\u3068\u304c\u5bb9\u6613\u306b\u308f\u304b\u308a\u307e\u3059\u3002\u30a2\u30a4\u30c6\u30e0\u304c\u591a\u304f\u3001\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u5bb9\u91cf\u304c\u5927\u304d\u3044\u5834\u5408\u3001\u7279\u306b\u540c\u3058\u91cd\u91cf\u306e\u30a2\u30a4\u30c6\u30e0\u304c\u591a\u3044\u5834\u5408\u3001\u91cd\u8907\u3059\u308b\u90e8\u5206\u554f\u984c\u306e\u6570\u306f\u5927\u5e45\u306b\u5897\u52a0\u3057\u307e\u3059\u3002</p> <p></p> <p> \u56f3 14-18 \u00a0 0-1\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c\u306e\u529b\u4efb\u305b\u63a2\u7d22\u518d\u5e30\u6728 </p>"},{"location":"chapter_dynamic_programming/knapsack_problem/#2-2","title":"2. \u00a0 \u65b9\u6cd52\uff1a\u30e1\u30e2\u5316\u63a2\u7d22","text":"<p>\u91cd\u8907\u3059\u308b\u90e8\u5206\u554f\u984c\u304c\u4e00\u5ea6\u3060\u3051\u8a08\u7b97\u3055\u308c\u308b\u3053\u3068\u3092\u78ba\u4fdd\u3059\u308b\u305f\u3081\u306b\u3001\u90e8\u5206\u554f\u984c\u306e\u89e3\u3092\u8a18\u9332\u3059\u308b\u30e1\u30e2\u5316\u30ea\u30b9\u30c8 <code>mem</code> \u3092\u4f7f\u7528\u3057\u307e\u3059\u3002\u3053\u3053\u3067 <code>mem[i][c]</code> \u306f \\(dp[i, c]\\) \u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002</p> <p>\u30e1\u30e2\u5316\u3092\u5c0e\u5165\u3057\u305f\u5f8c\u3001**\u6642\u9593\u8a08\u7b97\u91cf\u306f\u90e8\u5206\u554f\u984c\u306e\u6570\u306b\u4f9d\u5b58**\u3057\u3001\\(O(n \\times cap)\\) \u306b\u306a\u308a\u307e\u3059\u3002\u5b9f\u88c5\u30b3\u30fc\u30c9\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig knapsack.py<pre><code>def knapsack_dfs_mem(\n    wgt: list[int], val: list[int], mem: list[list[int]], i: int, c: int\n) -&gt; int:\n    \"\"\"0-1 \u30ca\u30c3\u30d7\u30b5\u30c3\u30af\uff1a\u8a18\u61b6\u5316\u63a2\u7d22\"\"\"\n    # \u3059\u3079\u3066\u306e\u30a2\u30a4\u30c6\u30e0\u304c\u9078\u629e\u3055\u308c\u305f\u304b\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u306b\u6b8b\u308a\u5bb9\u91cf\u304c\u306a\u3044\u5834\u5408\u3001\u5024 0 \u3092\u8fd4\u3059\n    if i == 0 or c == 0:\n        return 0\n    # \u8a18\u9332\u304c\u3042\u308b\u5834\u5408\u3001\u305d\u308c\u3092\u8fd4\u3059\n    if mem[i][c] != -1:\n        return mem[i][c]\n    # \u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u5bb9\u91cf\u3092\u8d85\u3048\u308b\u5834\u5408\u3001\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u306b\u5165\u308c\u306a\u3044\u3053\u3068\u3057\u304b\u9078\u629e\u3067\u304d\u306a\u3044\n    if wgt[i - 1] &gt; c:\n        return knapsack_dfs_mem(wgt, val, mem, i - 1, c)\n    # \u30a2\u30a4\u30c6\u30e0 i \u3092\u5165\u308c\u306a\u3044\u306e\u3068\u5165\u308c\u308b\u306e\u3068\u306e\u6700\u5927\u5024\u3092\u8a08\u7b97\n    no = knapsack_dfs_mem(wgt, val, mem, i - 1, c)\n    yes = knapsack_dfs_mem(wgt, val, mem, i - 1, c - wgt[i - 1]) + val[i - 1]\n    # 2 \u3064\u306e\u9078\u629e\u80a2\u306e\u3046\u3061\u5927\u304d\u3044\u5024\u3092\u8a18\u9332\u3057\u3066\u8fd4\u3059\n    mem[i][c] = max(no, yes)\n    return mem[i][c]\n</code></pre> knapsack.cpp<pre><code>[class]{}-[func]{knapsackDFSMem}\n</code></pre> knapsack.java<pre><code>/* 0-1 \u30ca\u30c3\u30d7\u30b5\u30c3\u30af\uff1a\u30e1\u30e2\u5316\u63a2\u7d22 */\nint knapsackDFSMem(int[] wgt, int[] val, int[][] mem, int i, int c) {\n    // \u3059\u3079\u3066\u306e\u30a2\u30a4\u30c6\u30e0\u304c\u9078\u629e\u3055\u308c\u305f\u304b\u3001\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u306b\u6b8b\u308a\u5bb9\u91cf\u304c\u306a\u3044\u5834\u5408\u3001\u5024 0 \u3092\u8fd4\u3059\n    if (i == 0 || c == 0) {\n        return 0;\n    }\n    // \u8a18\u9332\u304c\u3042\u308b\u5834\u5408\u3001\u305d\u308c\u3092\u8fd4\u3059\n    if (mem[i][c] != -1) {\n        return mem[i][c];\n    }\n    // \u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u306e\u5bb9\u91cf\u3092\u8d85\u3048\u308b\u5834\u5408\u3001\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u306b\u5165\u308c\u306a\u3044\u3053\u3068\u3057\u304b\u9078\u629e\u3067\u304d\u306a\u3044\n    if (wgt[i - 1] &gt; c) {\n        return knapsackDFSMem(wgt, val, mem, i - 1, c);\n    }\n    // \u30a2\u30a4\u30c6\u30e0 i \u3092\u5165\u308c\u306a\u3044\u5834\u5408\u3068\u5165\u308c\u308b\u5834\u5408\u306e\u6700\u5927\u5024\u3092\u8a08\u7b97\n    int no = knapsackDFSMem(wgt, val, mem, i - 1, c);\n    int yes = knapsackDFSMem(wgt, val, mem, i - 1, c - wgt[i - 1]) + val[i - 1];\n    // 2\u3064\u306e\u9078\u629e\u80a2\u306e\u3088\u308a\u5927\u304d\u3044\u5024\u3092\u8a18\u9332\u3057\u3066\u8fd4\u3059\n    mem[i][c] = Math.max(no, yes);\n    return mem[i][c];\n}\n</code></pre> knapsack.cs<pre><code>[class]{knapsack}-[func]{KnapsackDFSMem}\n</code></pre> knapsack.go<pre><code>[class]{}-[func]{knapsackDFSMem}\n</code></pre> knapsack.swift<pre><code>[class]{}-[func]{knapsackDFSMem}\n</code></pre> knapsack.js<pre><code>[class]{}-[func]{knapsackDFSMem}\n</code></pre> knapsack.ts<pre><code>[class]{}-[func]{knapsackDFSMem}\n</code></pre> knapsack.dart<pre><code>[class]{}-[func]{knapsackDFSMem}\n</code></pre> knapsack.rs<pre><code>[class]{}-[func]{knapsack_dfs_mem}\n</code></pre> knapsack.c<pre><code>[class]{}-[func]{knapsackDFSMem}\n</code></pre> knapsack.kt<pre><code>[class]{}-[func]{knapsackDFSMem}\n</code></pre> knapsack.rb<pre><code>[class]{}-[func]{knapsack_dfs_mem}\n</code></pre> knapsack.zig<pre><code>[class]{}-[func]{knapsackDFSMem}\n</code></pre> <p>\u4e0b\u306e\u56f3\u306f\u30e1\u30e2\u5316\u63a2\u7d22\u3067\u679d\u5208\u308a\u3055\u308c\u308b\u63a2\u7d22\u5206\u5c90\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002</p> <p></p> <p> \u56f3 14-19 \u00a0 0-1\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c\u306e\u30e1\u30e2\u5316\u63a2\u7d22\u518d\u5e30\u6728 </p>"},{"location":"chapter_dynamic_programming/knapsack_problem/#3-3","title":"3. \u00a0 \u65b9\u6cd53\uff1a\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0","text":"<p>\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u306f\u672c\u8cea\u7684\u306b\u72b6\u614b\u9077\u79fb\u4e2d\u306b \\(dp\\) \u30c6\u30fc\u30d6\u30eb\u3092\u57cb\u3081\u308b\u3053\u3068\u3092\u542b\u307f\u307e\u3059\u3002\u30b3\u30fc\u30c9\u306f\u4e0b\u306e\u56f3\u306b\u793a\u3055\u308c\u3066\u3044\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig knapsack.py<pre><code>def knapsack_dp(wgt: list[int], val: list[int], cap: int) -&gt; int:\n    \"\"\"0-1 \u30ca\u30c3\u30d7\u30b5\u30c3\u30af\uff1a\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\"\"\"\n    n = len(wgt)\n    # dp \u30c6\u30fc\u30d6\u30eb\u3092\u521d\u671f\u5316\n    dp = [[0] * (cap + 1) for _ in range(n + 1)]\n    # \u72b6\u614b\u9077\u79fb\n    for i in range(1, n + 1):\n        for c in range(1, cap + 1):\n            if wgt[i - 1] &gt; c:\n                # \u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u5bb9\u91cf\u3092\u8d85\u3048\u308b\u5834\u5408\u3001\u30a2\u30a4\u30c6\u30e0 i \u3092\u9078\u629e\u3057\u306a\u3044\n                dp[i][c] = dp[i - 1][c]\n            else:\n                # \u30a2\u30a4\u30c6\u30e0 i \u3092\u9078\u629e\u3057\u306a\u3044\u306e\u3068\u9078\u629e\u3059\u308b\u306e\u3068\u3067\u5927\u304d\u3044\u5024\n                dp[i][c] = max(dp[i - 1][c], dp[i - 1][c - wgt[i - 1]] + val[i - 1])\n    return dp[n][cap]\n</code></pre> knapsack.cpp<pre><code>/* 0-1 \u30ca\u30c3\u30d7\u30b5\u30c3\u30af\uff1a\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0 */\nint knapsackDP(vector&lt;int&gt; &amp;wgt, vector&lt;int&gt; &amp;val, int cap) {\n    int n = wgt.size();\n    // DP\u30c6\u30fc\u30d6\u30eb\u3092\u521d\u671f\u5316\n    vector&lt;vector&lt;int&gt;&gt; dp(n + 1, vector&lt;int&gt;(cap + 1, 0));\n    // \u72b6\u614b\u9077\u79fb\n    for (int i = 1; i &lt;= n; i++) {\n        for (int c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // \u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u306e\u5bb9\u91cf\u3092\u8d85\u3048\u308b\u5834\u5408\u3001\u30a2\u30a4\u30c6\u30e0 i \u3092\u9078\u629e\u3057\u306a\u3044\n                dp[i][c] = dp[i - 1][c];\n            } else {\n                // \u9078\u629e\u3057\u306a\u3044\u5834\u5408\u3068\u30a2\u30a4\u30c6\u30e0 i \u3092\u9078\u629e\u3059\u308b\u5834\u5408\u306e\u3088\u308a\u5927\u304d\u3044\u5024\n                dp[i][c] = max(dp[i - 1][c], dp[i - 1][c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[n][cap];\n}\n</code></pre> knapsack.java<pre><code>/* 0-1 \u30ca\u30c3\u30d7\u30b5\u30c3\u30af\uff1a\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0 */\nint knapsackDP(int[] wgt, int[] val, int cap) {\n    int n = wgt.length;\n    // DP\u30c6\u30fc\u30d6\u30eb\u3092\u521d\u671f\u5316\n    int[][] dp = new int[n + 1][cap + 1];\n    // \u72b6\u614b\u9077\u79fb\n    for (int i = 1; i &lt;= n; i++) {\n        for (int c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // \u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u306e\u5bb9\u91cf\u3092\u8d85\u3048\u308b\u5834\u5408\u3001\u30a2\u30a4\u30c6\u30e0 i \u3092\u9078\u629e\u3057\u306a\u3044\n                dp[i][c] = dp[i - 1][c];\n            } else {\n                // \u9078\u629e\u3057\u306a\u3044\u5834\u5408\u3068\u30a2\u30a4\u30c6\u30e0 i \u3092\u9078\u629e\u3059\u308b\u5834\u5408\u306e\u3088\u308a\u5927\u304d\u3044\u5024\n                dp[i][c] = Math.max(dp[i - 1][c], dp[i - 1][c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[n][cap];\n}\n</code></pre> knapsack.cs<pre><code>[class]{knapsack}-[func]{KnapsackDP}\n</code></pre> knapsack.go<pre><code>[class]{}-[func]{knapsackDP}\n</code></pre> knapsack.swift<pre><code>[class]{}-[func]{knapsackDP}\n</code></pre> knapsack.js<pre><code>[class]{}-[func]{knapsackDP}\n</code></pre> knapsack.ts<pre><code>[class]{}-[func]{knapsackDP}\n</code></pre> knapsack.dart<pre><code>[class]{}-[func]{knapsackDP}\n</code></pre> knapsack.rs<pre><code>[class]{}-[func]{knapsack_dp}\n</code></pre> knapsack.c<pre><code>[class]{}-[func]{knapsackDP}\n</code></pre> knapsack.kt<pre><code>[class]{}-[func]{knapsackDP}\n</code></pre> knapsack.rb<pre><code>[class]{}-[func]{knapsack_dp}\n</code></pre> knapsack.zig<pre><code>[class]{}-[func]{knapsackDP}\n</code></pre> <p>\u4e0b\u306e\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u6642\u9593\u8a08\u7b97\u91cf\u3068\u7a7a\u9593\u8a08\u7b97\u91cf\u306e\u4e21\u65b9\u304c\u914d\u5217 <code>dp</code> \u306e\u30b5\u30a4\u30ba\u3001\u3064\u307e\u308a \\(O(n \\times cap)\\) \u306b\u3088\u3063\u3066\u6c7a\u5b9a\u3055\u308c\u307e\u3059\u3002</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt;&lt;12&gt;&lt;13&gt;&lt;14&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> \u56f3 14-20 \u00a0 0-1\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c\u306e\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u30d7\u30ed\u30bb\u30b9 </p>"},{"location":"chapter_dynamic_programming/knapsack_problem/#4","title":"4. \u00a0 \u7a7a\u9593\u6700\u9069\u5316","text":"<p>\u5404\u72b6\u614b\u306f\u4e0a\u306e\u884c\u306e\u72b6\u614b\u306e\u307f\u306b\u95a2\u9023\u3059\u308b\u305f\u3081\u30012\u3064\u306e\u914d\u5217\u3092\u4f7f\u7528\u3057\u3066\u30ed\u30fc\u30ea\u30f3\u30b0\u524d\u9032\u3055\u305b\u3001\u7a7a\u9593\u8a08\u7b97\u91cf\u3092 \\(O(n^2)\\) \u304b\u3089 \\(O(n)\\) \u306b\u524a\u6e1b\u3067\u304d\u307e\u3059\u3002</p> <p>\u3055\u3089\u306b\u8003\u3048\u3066\u307f\u308b\u3068\u30011\u3064\u306e\u914d\u5217\u3060\u3051\u3067\u7a7a\u9593\u6700\u9069\u5316\u3092\u9054\u6210\u3067\u304d\u308b\u3067\u3057\u3087\u3046\u304b\uff1f\u5404\u72b6\u614b\u304c\u76f4\u63a5\u4e0a\u306e\u30bb\u30eb\u307e\u305f\u306f\u5de6\u4e0a\u306e\u30bb\u30eb\u304b\u3089\u9077\u79fb\u3059\u308b\u3053\u3068\u304c\u89b3\u5bdf\u3067\u304d\u307e\u3059\u3002\u914d\u5217\u304c1\u3064\u3057\u304b\u306a\u3044\u5834\u5408\u3001\\(i\\) \u884c\u76ee\u306e\u8d70\u67fb\u3092\u958b\u59cb\u3059\u308b\u3068\u304d\u3001\u305d\u306e\u914d\u5217\u306f\u307e\u3060 \\(i-1\\) \u884c\u76ee\u306e\u72b6\u614b\u3092\u4fdd\u5b58\u3057\u3066\u3044\u307e\u3059\u3002</p> <ul> <li>\u901a\u5e38\u306e\u9806\u5e8f\u3067\u8d70\u67fb\u3059\u308b\u5834\u5408\u3001\\(dp[i, j]\\) \u306b\u8d70\u67fb\u3057\u305f\u3068\u304d\u3001\u5de6\u4e0a\u306e \\(dp[i-1, 1]\\) \uff5e \\(dp[i-1, j-1]\\) \u306e\u5024\u304c\u3059\u3067\u306b\u4e0a\u66f8\u304d\u3055\u308c\u3066\u3044\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u3001\u6b63\u3057\u3044\u72b6\u614b\u9077\u79fb\u7d50\u679c\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u305b\u3093\u3002</li> <li>\u9006\u9806\u3067\u8d70\u67fb\u3059\u308b\u5834\u5408\u3001\u4e0a\u66f8\u304d\u554f\u984c\u306f\u306a\u304f\u3001\u72b6\u614b\u9077\u79fb\u3092\u6b63\u3057\u304f\u5b9f\u884c\u3067\u304d\u307e\u3059\u3002</li> </ul> <p>\u4e0b\u306e\u56f3\u306f\u5358\u4e00\u914d\u5217\u3067\u306e \\(i = 1\\) \u884c\u76ee\u304b\u3089 \\(i = 2\\) \u884c\u76ee\u3078\u306e\u9077\u79fb\u30d7\u30ed\u30bb\u30b9\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002\u901a\u5e38\u9806\u5e8f\u8d70\u67fb\u3068\u9006\u9806\u8d70\u67fb\u306e\u9055\u3044\u306b\u3064\u3044\u3066\u8003\u3048\u3066\u307f\u3066\u304f\u3060\u3055\u3044\u3002</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> \u56f3 14-21 \u00a0 0-1\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u306e\u7a7a\u9593\u6700\u9069\u5316\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u30d7\u30ed\u30bb\u30b9 </p> <p>\u30b3\u30fc\u30c9\u5b9f\u88c5\u3067\u306f\u3001\u914d\u5217 <code>dp</code> \u306e\u6700\u521d\u306e\u6b21\u5143 \\(i\\) \u3092\u524a\u9664\u3057\u3001\u5185\u5074\u306e\u30eb\u30fc\u30d7\u3092\u9006\u8d70\u67fb\u306b\u5909\u66f4\u3059\u308b\u3060\u3051\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig knapsack.py<pre><code>def knapsack_dp_comp(wgt: list[int], val: list[int], cap: int) -&gt; int:\n    \"\"\"0-1 \u30ca\u30c3\u30d7\u30b5\u30c3\u30af\uff1a\u7a7a\u9593\u6700\u9069\u5316\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\"\"\"\n    n = len(wgt)\n    # dp \u30c6\u30fc\u30d6\u30eb\u3092\u521d\u671f\u5316\n    dp = [0] * (cap + 1)\n    # \u72b6\u614b\u9077\u79fb\n    for i in range(1, n + 1):\n        # \u9006\u9806\u3067\u8d70\u67fb\n        for c in range(cap, 0, -1):\n            if wgt[i - 1] &gt; c:\n                # \u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u5bb9\u91cf\u3092\u8d85\u3048\u308b\u5834\u5408\u3001\u30a2\u30a4\u30c6\u30e0 i \u3092\u9078\u629e\u3057\u306a\u3044\n                dp[c] = dp[c]\n            else:\n                # \u30a2\u30a4\u30c6\u30e0 i \u3092\u9078\u629e\u3057\u306a\u3044\u306e\u3068\u9078\u629e\u3059\u308b\u306e\u3068\u3067\u5927\u304d\u3044\u5024\n                dp[c] = max(dp[c], dp[c - wgt[i - 1]] + val[i - 1])\n    return dp[cap]\n</code></pre> knapsack.cpp<pre><code>/* 0-1 \u30ca\u30c3\u30d7\u30b5\u30c3\u30af\uff1a\u7a7a\u9593\u6700\u9069\u5316\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0 */\nint knapsackDPComp(vector&lt;int&gt; &amp;wgt, vector&lt;int&gt; &amp;val, int cap) {\n    int n = wgt.size();\n    // DP\u30c6\u30fc\u30d6\u30eb\u3092\u521d\u671f\u5316\n    vector&lt;int&gt; dp(cap + 1, 0);\n    // \u72b6\u614b\u9077\u79fb\n    for (int i = 1; i &lt;= n; i++) {\n        // \u9006\u9806\u3067\u8d70\u67fb\n        for (int c = cap; c &gt;= 1; c--) {\n            if (wgt[i - 1] &lt;= c) {\n                // \u9078\u629e\u3057\u306a\u3044\u5834\u5408\u3068\u30a2\u30a4\u30c6\u30e0 i \u3092\u9078\u629e\u3059\u308b\u5834\u5408\u306e\u3088\u308a\u5927\u304d\u3044\u5024\n                dp[c] = max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[cap];\n}\n</code></pre> knapsack.java<pre><code>/* 0-1 \u30ca\u30c3\u30d7\u30b5\u30c3\u30af\uff1a\u7a7a\u9593\u6700\u9069\u5316\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0 */\nint knapsackDPComp(int[] wgt, int[] val, int cap) {\n    int n = wgt.length;\n    // DP\u30c6\u30fc\u30d6\u30eb\u3092\u521d\u671f\u5316\n    int[] dp = new int[cap + 1];\n    // \u72b6\u614b\u9077\u79fb\n    for (int i = 1; i &lt;= n; i++) {\n        // \u9006\u9806\u3067\u8d70\u67fb\n        for (int c = cap; c &gt;= 1; c--) {\n            if (wgt[i - 1] &lt;= c) {\n                // \u9078\u629e\u3057\u306a\u3044\u5834\u5408\u3068\u30a2\u30a4\u30c6\u30e0 i \u3092\u9078\u629e\u3059\u308b\u5834\u5408\u306e\u3088\u308a\u5927\u304d\u3044\u5024\n                dp[c] = Math.max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[cap];\n}\n</code></pre> knapsack.cs<pre><code>[class]{knapsack}-[func]{KnapsackDPComp}\n</code></pre> knapsack.go<pre><code>[class]{}-[func]{knapsackDPComp}\n</code></pre> knapsack.swift<pre><code>[class]{}-[func]{knapsackDPComp}\n</code></pre> knapsack.js<pre><code>[class]{}-[func]{knapsackDPComp}\n</code></pre> knapsack.ts<pre><code>[class]{}-[func]{knapsackDPComp}\n</code></pre> knapsack.dart<pre><code>[class]{}-[func]{knapsackDPComp}\n</code></pre> knapsack.rs<pre><code>[class]{}-[func]{knapsack_dp_comp}\n</code></pre> knapsack.c<pre><code>[class]{}-[func]{knapsackDPComp}\n</code></pre> knapsack.kt<pre><code>[class]{}-[func]{knapsackDPComp}\n</code></pre> knapsack.rb<pre><code>[class]{}-[func]{knapsack_dp_comp}\n</code></pre> knapsack.zig<pre><code>[class]{}-[func]{knapsackDPComp}\n</code></pre>"},{"location":"chapter_dynamic_programming/summary/","title":"14.7 \u00a0 \u307e\u3068\u3081","text":"<ul> <li>\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u306f\u554f\u984c\u3092\u5206\u89e3\u3057\u3001\u90e8\u5206\u554f\u984c\u306e\u89e3\u3092\u4fdd\u5b58\u3059\u308b\u3053\u3068\u3067\u5197\u9577\u306a\u8a08\u7b97\u3092\u907f\u3051\u3001\u8a08\u7b97\u52b9\u7387\u3092\u5411\u4e0a\u3055\u305b\u307e\u3059\u3002</li> <li>\u6642\u9593\u3092\u8003\u616e\u3057\u306a\u3051\u308c\u3070\u3001\u3059\u3079\u3066\u306e\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u554f\u984c\u306f\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\uff08\u529b\u4efb\u305b\u63a2\u7d22\uff09\u3092\u4f7f\u7528\u3057\u3066\u89e3\u6c7a\u3067\u304d\u307e\u3059\u304c\u3001\u518d\u5e30\u6728\u306b\u306f\u591a\u304f\u306e\u91cd\u8907\u3059\u308b\u90e8\u5206\u554f\u984c\u304c\u3042\u308a\u3001\u52b9\u7387\u304c\u975e\u5e38\u306b\u4f4e\u304f\u306a\u308a\u307e\u3059\u3002\u8a18\u61b6\u5316\u30ea\u30b9\u30c8\u3092\u5c0e\u5165\u3059\u308b\u3053\u3068\u3067\u3001\u8a08\u7b97\u3055\u308c\u305f\u3059\u3079\u3066\u306e\u90e8\u5206\u554f\u984c\u306e\u89e3\u3092\u4fdd\u5b58\u3057\u3001\u91cd\u8907\u3059\u308b\u90e8\u5206\u554f\u984c\u304c\u4e00\u5ea6\u3060\u3051\u8a08\u7b97\u3055\u308c\u308b\u3053\u3068\u3092\u4fdd\u8a3c\u3067\u304d\u307e\u3059\u3002</li> <li>\u8a18\u61b6\u5316\u63a2\u7d22\u306f\u30c8\u30c3\u30d7\u30c0\u30a6\u30f3\u306e\u518d\u5e30\u89e3\u6cd5\u3067\u3042\u308a\u3001\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u306f\u30dc\u30c8\u30e0\u30a2\u30c3\u30d7\u306e\u53cd\u5fa9\u30a2\u30d7\u30ed\u30fc\u30c1\u306b\u5bfe\u5fdc\u3057\u3001\u300c\u8868\u3092\u57cb\u3081\u308b\u300d\u3053\u3068\u306b\u4f3c\u3066\u3044\u307e\u3059\u3002\u73fe\u5728\u306e\u72b6\u614b\u306f\u7279\u5b9a\u306e\u5c40\u6240\u72b6\u614b\u306e\u307f\u306b\u4f9d\u5b58\u3059\u308b\u305f\u3081\u3001dp\u30c6\u30fc\u30d6\u30eb\u306e1\u6b21\u5143\u3092\u524a\u9664\u3057\u3066\u7a7a\u9593\u8a08\u7b97\u91cf\u3092\u524a\u6e1b\u3067\u304d\u307e\u3059\u3002</li> <li>\u90e8\u5206\u554f\u984c\u306e\u5206\u89e3\u306f\u6c4e\u7528\u7684\u306a\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u30a2\u30d7\u30ed\u30fc\u30c1\u3067\u3042\u308a\u3001\u5206\u5272\u7d71\u6cbb\u6cd5\u3001\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u3001\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u3067\u7279\u5fb4\u304c\u7570\u306a\u308a\u307e\u3059\u3002</li> <li>\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u554f\u984c\u306b\u306f3\u3064\u306e\u4e3b\u8981\u306a\u7279\u5fb4\u304c\u3042\u308a\u307e\u3059\uff1a\u91cd\u8907\u3059\u308b\u90e8\u5206\u554f\u984c\u3001\u6700\u9069\u90e8\u5206\u69cb\u9020\u3001\u7121\u8a18\u61b6\u6027\u3002</li> <li>\u5143\u306e\u554f\u984c\u306e\u6700\u9069\u89e3\u304c\u305d\u306e\u90e8\u5206\u554f\u984c\u306e\u6700\u9069\u89e3\u304b\u3089\u69cb\u7bc9\u3067\u304d\u308b\u5834\u5408\u3001\u6700\u9069\u90e8\u5206\u69cb\u9020\u3092\u6301\u3061\u307e\u3059\u3002</li> <li>\u7121\u8a18\u61b6\u6027\u3068\u306f\u3001\u72b6\u614b\u306e\u5c06\u6765\u306e\u767a\u5c55\u304c\u73fe\u5728\u306e\u72b6\u614b\u306e\u307f\u306b\u4f9d\u5b58\u3057\u3001\u904e\u53bb\u306b\u7d4c\u9a13\u3057\u305f\u3059\u3079\u3066\u306e\u72b6\u614b\u306b\u4f9d\u5b58\u3057\u306a\u3044\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002\u591a\u304f\u306e\u7d44\u307f\u5408\u308f\u305b\u6700\u9069\u5316\u554f\u984c\u306b\u306f\u3053\u306e\u7279\u6027\u304c\u306a\u304f\u3001\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u3092\u4f7f\u7528\u3057\u3066\u8fc5\u901f\u306b\u89e3\u6c7a\u3059\u308b\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093\u3002</li> </ul> <p>\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c</p> <ul> <li>\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c\u306f\u6700\u3082\u5178\u578b\u7684\u306a\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u554f\u984c\u306e1\u3064\u3067\u30010-1\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u3001\u7121\u5236\u9650\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u3001\u8907\u6570\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u306a\u3069\u306e\u5909\u7a2e\u304c\u3042\u308a\u307e\u3059\u3002</li> <li>0-1\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u306e\u72b6\u614b\u5b9a\u7fa9\u306f\u3001\u6700\u521d\u306e \\(i\\) \u500b\u306e\u30a2\u30a4\u30c6\u30e0\u3092\u542b\u3080\u5bb9\u91cf \\(c\\) \u306e\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u3067\u306e\u6700\u5927\u5024\u3067\u3059\u3002\u30a2\u30a4\u30c6\u30e0\u3092\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u306b\u5165\u308c\u306a\u3044\u307e\u305f\u306f\u5165\u308c\u308b\u3068\u3044\u3046\u6c7a\u5b9a\u306b\u57fa\u3065\u3044\u3066\u3001\u6700\u9069\u90e8\u5206\u69cb\u9020\u3092\u7279\u5b9a\u3057\u3001\u72b6\u614b\u9077\u79fb\u65b9\u7a0b\u5f0f\u3092\u69cb\u7bc9\u3067\u304d\u307e\u3059\u3002\u7a7a\u9593\u6700\u9069\u5316\u3067\u306f\u3001\u5404\u72b6\u614b\u304c\u76f4\u63a5\u4e0a\u3068\u5de6\u4e0a\u306e\u72b6\u614b\u306b\u4f9d\u5b58\u3059\u308b\u305f\u3081\u3001\u5de6\u4e0a\u306e\u72b6\u614b\u306e\u4e0a\u66f8\u304d\u3092\u907f\u3051\u308b\u305f\u3081\u306b\u30ea\u30b9\u30c8\u3092\u9006\u9806\u3067\u8d70\u67fb\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002</li> <li>\u7121\u5236\u9650\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c\u3067\u306f\u3001\u5404\u7a2e\u985e\u306e\u30a2\u30a4\u30c6\u30e0\u3092\u9078\u629e\u3067\u304d\u308b\u6570\u306b\u5236\u9650\u304c\u306a\u3044\u305f\u3081\u3001\u30a2\u30a4\u30c6\u30e0\u3092\u542b\u3081\u308b\u72b6\u614b\u9077\u79fb\u306f0-1\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u3068\u7570\u306a\u308a\u307e\u3059\u3002\u72b6\u614b\u304c\u76f4\u63a5\u4e0a\u3068\u5de6\u306e\u72b6\u614b\u306b\u4f9d\u5b58\u3059\u308b\u305f\u3081\u3001\u7a7a\u9593\u6700\u9069\u5316\u3067\u306f\u524d\u65b9\u8d70\u67fb\u3092\u542b\u3081\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002</li> <li>\u30b3\u30a4\u30f3\u4ea4\u63db\u554f\u984c\u306f\u7121\u5236\u9650\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c\u306e\u5909\u7a2e\u3067\u3001\u300c\u6700\u5927\u300d\u5024\u3092\u6c42\u3081\u308b\u3053\u3068\u304b\u3089\u300c\u6700\u5c0f\u300d\u30b3\u30a4\u30f3\u6570\u3092\u6c42\u3081\u308b\u3053\u3068\u306b\u5909\u308f\u308a\u3001\u72b6\u614b\u9077\u79fb\u65b9\u7a0b\u5f0f\u306f \\(\\max()\\) \u3092 \\(\\min()\\) \u306b\u5909\u66f4\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u306e\u5bb9\u91cf\u3092\u300c\u8d85\u3048\u306a\u3044\u300d\u3053\u3068\u3092\u8ffd\u6c42\u3059\u308b\u3053\u3068\u304b\u3089\u3001\u6b63\u78ba\u306b\u76ee\u6a19\u91d1\u984d\u3092\u6c42\u3081\u308b\u3053\u3068\u306b\u5909\u308f\u308a\u3001\u300c\u76ee\u6a19\u91d1\u984d\u3092\u69cb\u6210\u3067\u304d\u306a\u3044\u300d\u7121\u52b9\u89e3\u3092\u8868\u3059\u305f\u3081\u306b \\(amt + 1\\) \u3092\u4f7f\u7528\u3057\u307e\u3059\u3002</li> <li>\u30b3\u30a4\u30f3\u4ea4\u63db\u554f\u984cII\u306f\u300c\u6700\u5c0f\u30b3\u30a4\u30f3\u6570\u300d\u3092\u6c42\u3081\u308b\u3053\u3068\u304b\u3089\u300c\u30b3\u30a4\u30f3\u306e\u7d44\u307f\u5408\u308f\u305b\u6570\u300d\u3092\u6c42\u3081\u308b\u3053\u3068\u306b\u5909\u308f\u308a\u3001\u72b6\u614b\u9077\u79fb\u65b9\u7a0b\u5f0f\u3092 \\(\\min()\\) \u304b\u3089\u548c\u7b97\u6f14\u7b97\u5b50\u306b\u5909\u66f4\u3057\u307e\u3059\u3002</li> </ul> <p>\u7de8\u96c6\u8ddd\u96e2\u554f\u984c</p> <ul> <li>\u7de8\u96c6\u8ddd\u96e2\uff08\u30ec\u30fc\u30d9\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u8ddd\u96e2\uff09\u306f2\u3064\u306e\u6587\u5b57\u5217\u9593\u306e\u985e\u4f3c\u5ea6\u3092\u6e2c\u5b9a\u3057\u3001\u4e00\u3064\u306e\u6587\u5b57\u5217\u3092\u5225\u306e\u6587\u5b57\u5217\u306b\u5909\u66f4\u3059\u308b\u305f\u3081\u306b\u5fc5\u8981\u306a\u6700\u5c0f\u7de8\u96c6\u30b9\u30c6\u30c3\u30d7\u6570\u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u3001\u7de8\u96c6\u64cd\u4f5c\u306b\u306f\u8ffd\u52a0\u3001\u524a\u9664\u3001\u7f6e\u63db\u304c\u542b\u307e\u308c\u307e\u3059\u3002</li> <li>\u7de8\u96c6\u8ddd\u96e2\u554f\u984c\u306e\u72b6\u614b\u5b9a\u7fa9\u306f\u3001\\(s\\) \u306e\u6700\u521d\u306e \\(i\\) \u6587\u5b57\u3092 \\(t\\) \u306e\u6700\u521d\u306e \\(j\\) \u6587\u5b57\u306b\u5909\u66f4\u3059\u308b\u305f\u3081\u306b\u5fc5\u8981\u306a\u6700\u5c0f\u7de8\u96c6\u30b9\u30c6\u30c3\u30d7\u6570\u3067\u3059\u3002\\(s[i] \\ne t[j]\\) \u306e\u5834\u5408\u3001\u8ffd\u52a0\u3001\u524a\u9664\u3001\u7f6e\u63db\u306e3\u3064\u306e\u6c7a\u5b9a\u304c\u3042\u308a\u3001\u305d\u308c\u305e\u308c\u306b\u5bfe\u5fdc\u3059\u308b\u6b8b\u4f59\u90e8\u5206\u554f\u984c\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u308c\u304b\u3089\u6700\u9069\u90e8\u5206\u69cb\u9020\u3092\u7279\u5b9a\u3057\u3001\u72b6\u614b\u9077\u79fb\u65b9\u7a0b\u5f0f\u3092\u69cb\u7bc9\u3067\u304d\u307e\u3059\u3002\\(s[i] = t[j]\\) \u306e\u5834\u5408\u3001\u73fe\u5728\u306e\u6587\u5b57\u306e\u7de8\u96c6\u306f\u5fc5\u8981\u3042\u308a\u307e\u305b\u3093\u3002</li> <li>\u7de8\u96c6\u8ddd\u96e2\u3067\u306f\u3001\u72b6\u614b\u304c\u76f4\u63a5\u4e0a\u3001\u5de6\u3001\u5de6\u4e0a\u306e\u72b6\u614b\u306b\u4f9d\u5b58\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u7a7a\u9593\u6700\u9069\u5316\u5f8c\u3001\u524d\u65b9\u8d70\u67fb\u3082\u9006\u8d70\u67fb\u3082\u6b63\u3057\u304f\u72b6\u614b\u9077\u79fb\u3092\u5b9f\u884c\u3067\u304d\u307e\u305b\u3093\u3002\u3053\u308c\u306b\u5bfe\u51e6\u3059\u308b\u305f\u3081\u3001\u5909\u6570\u3092\u4f7f\u7528\u3057\u3066\u5de6\u4e0a\u306e\u72b6\u614b\u3092\u4e00\u6642\u7684\u306b\u4fdd\u5b58\u3057\u3001\u7121\u5236\u9650\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c\u306e\u72b6\u6cc1\u3068\u540c\u7b49\u306b\u3057\u3001\u7a7a\u9593\u6700\u9069\u5316\u5f8c\u306b\u524d\u65b9\u8d70\u67fb\u3092\u53ef\u80fd\u306b\u3057\u307e\u3059\u3002</li> </ul>"},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/","title":"14.5 \u00a0 \u7121\u5236\u9650\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c","text":"<p>\u3053\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u3067\u306f\u3001\u307e\u305a\u5225\u306e\u4e00\u822c\u7684\u306a\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c\u3067\u3042\u308b\u7121\u5236\u9650\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u3092\u89e3\u6c7a\u3057\u3001\u6b21\u306b\u305d\u306e\u7279\u6b8a\u30b1\u30fc\u30b9\u3067\u3042\u308b\u30b3\u30a4\u30f3\u4ea4\u63db\u554f\u984c\u3092\u63a2\u7d22\u3057\u307e\u3059\u3002</p>"},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#1451","title":"14.5.1 \u00a0 \u7121\u5236\u9650\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c","text":"<p>Question</p> <p>\\(n\\) \u500b\u306e\u30a2\u30a4\u30c6\u30e0\u304c\u4e0e\u3048\u3089\u308c\u3001\\(i\\) \u756a\u76ee\u306e\u30a2\u30a4\u30c6\u30e0\u306e\u91cd\u91cf\u306f \\(wgt[i-1]\\) \u3067\u5024\u306f \\(val[i-1]\\) \u3067\u3059\u3002\u5bb9\u91cf\u304c \\(cap\\) \u306e\u30d0\u30c3\u30af\u30d1\u30c3\u30af\u304c\u3042\u308a\u307e\u3059\u3002\u5404\u30a2\u30a4\u30c6\u30e0\u306f\u8907\u6570\u56de\u9078\u629e\u3067\u304d\u307e\u3059\u3002\u5bb9\u91cf\u3092\u8d85\u3048\u308b\u3053\u3068\u306a\u304f\u30d0\u30c3\u30af\u30d1\u30c3\u30af\u306b\u5165\u308c\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u30a2\u30a4\u30c6\u30e0\u306e\u6700\u5927\u5024\u306f\u4f55\u3067\u3059\u304b\uff1f\u4ee5\u4e0b\u306e\u4f8b\u3092\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044\u3002</p> <p></p> <p> \u56f3 14-22 \u00a0 \u7121\u5236\u9650\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c\u306e\u4f8b\u30c7\u30fc\u30bf </p>"},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#1","title":"1. \u00a0 \u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u30a2\u30d7\u30ed\u30fc\u30c1","text":"<p>\u7121\u5236\u9650\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c\u306f0-1\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c\u3068\u975e\u5e38\u306b\u4f3c\u3066\u304a\u308a\u3001\u552f\u4e00\u306e\u9055\u3044\u306f\u30a2\u30a4\u30c6\u30e0\u3092\u9078\u629e\u3067\u304d\u308b\u56de\u6570\u306b\u5236\u9650\u304c\u306a\u3044\u3053\u3068\u3067\u3059\u3002</p> <ul> <li>0-1\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c\u3067\u306f\u3001\u5404\u30a2\u30a4\u30c6\u30e0\u306f1\u3064\u3057\u304b\u306a\u3044\u305f\u3081\u3001\u30a2\u30a4\u30c6\u30e0 \\(i\\) \u3092\u30d0\u30c3\u30af\u30d1\u30c3\u30af\u306b\u5165\u308c\u305f\u5f8c\u306f\u3001\u524d\u306e \\(i-1\\) \u500b\u306e\u30a2\u30a4\u30c6\u30e0\u304b\u3089\u306e\u307f\u9078\u629e\u3067\u304d\u307e\u3059\u3002</li> <li>\u7121\u5236\u9650\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c\u3067\u306f\u3001\u5404\u30a2\u30a4\u30c6\u30e0\u306e\u6570\u91cf\u306f\u7121\u5236\u9650\u3067\u3042\u308b\u305f\u3081\u3001\u30a2\u30a4\u30c6\u30e0 \\(i\\) \u3092\u30d0\u30c3\u30af\u30d1\u30c3\u30af\u306b\u5165\u308c\u305f\u5f8c\u3082\u3001\u524d\u306e \\(i\\) \u500b\u306e\u30a2\u30a4\u30c6\u30e0\u304b\u3089\u5f15\u304d\u7d9a\u304d\u9078\u629e\u3067\u304d\u307e\u3059\u3002</li> </ul> <p>\u7121\u5236\u9650\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c\u306e\u30eb\u30fc\u30eb\u306e\u4e0b\u3067\u3001\u72b6\u614b \\([i, c]\\) \u306f2\u3064\u306e\u65b9\u6cd5\u3067\u5909\u5316\u3067\u304d\u307e\u3059\u3002</p> <ul> <li>\u30a2\u30a4\u30c6\u30e0 \\(i\\) \u3092\u5165\u308c\u306a\u3044\uff1a0-1\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c\u3068\u540c\u69d8\u306b\u3001\\([i-1, c]\\) \u306b\u9077\u79fb\u3057\u307e\u3059\u3002</li> <li>\u30a2\u30a4\u30c6\u30e0 \\(i\\) \u3092\u5165\u308c\u308b\uff1a0-1\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c\u3068\u306f\u7570\u306a\u308a\u3001\\([i, c-wgt[i-1]]\\) \u306b\u9077\u79fb\u3057\u307e\u3059\u3002</li> </ul> <p>\u3057\u305f\u304c\u3063\u3066\u3001\u72b6\u614b\u9077\u79fb\u65b9\u7a0b\u5f0f\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff1a</p> \\[ dp[i, c] = \\max(dp[i-1, c], dp[i, c - wgt[i-1]] + val[i-1]) \\]"},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#2","title":"2. \u00a0 \u30b3\u30fc\u30c9\u5b9f\u88c5","text":"<p>2\u3064\u306e\u554f\u984c\u306e\u30b3\u30fc\u30c9\u3092\u6bd4\u8f03\u3059\u308b\u3068\u3001\u72b6\u614b\u9077\u79fb\u304c \\(i-1\\) \u304b\u3089 \\(i\\) \u306b\u5909\u308f\u308a\u3001\u6b8b\u308a\u306f\u5b8c\u5168\u306b\u540c\u4e00\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig unbounded_knapsack.py<pre><code>def unbounded_knapsack_dp(wgt: list[int], val: list[int], cap: int) -&gt; int:\n    \"\"\"\u5b8c\u5168\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\uff1a\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\"\"\"\n    n = len(wgt)\n    # dp \u30c6\u30fc\u30d6\u30eb\u3092\u521d\u671f\u5316\n    dp = [[0] * (cap + 1) for _ in range(n + 1)]\n    # \u72b6\u614b\u9077\u79fb\n    for i in range(1, n + 1):\n        for c in range(1, cap + 1):\n            if wgt[i - 1] &gt; c:\n                # \u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u5bb9\u91cf\u3092\u8d85\u3048\u308b\u5834\u5408\u3001\u30a2\u30a4\u30c6\u30e0 i \u3092\u9078\u629e\u3057\u306a\u3044\n                dp[i][c] = dp[i - 1][c]\n            else:\n                # \u30a2\u30a4\u30c6\u30e0 i \u3092\u9078\u629e\u3057\u306a\u3044\u306e\u3068\u9078\u629e\u3059\u308b\u306e\u3068\u3067\u5927\u304d\u3044\u5024\n                dp[i][c] = max(dp[i - 1][c], dp[i][c - wgt[i - 1]] + val[i - 1])\n    return dp[n][cap]\n</code></pre> unbounded_knapsack.cpp<pre><code>/* \u5b8c\u5168\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\uff1a\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0 */\nint unboundedKnapsackDP(vector&lt;int&gt; &amp;wgt, vector&lt;int&gt; &amp;val, int cap) {\n    int n = wgt.size();\n    // DP\u30c6\u30fc\u30d6\u30eb\u3092\u521d\u671f\u5316\n    vector&lt;vector&lt;int&gt;&gt; dp(n + 1, vector&lt;int&gt;(cap + 1, 0));\n    // \u72b6\u614b\u9077\u79fb\n    for (int i = 1; i &lt;= n; i++) {\n        for (int c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // \u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u306e\u5bb9\u91cf\u3092\u8d85\u3048\u308b\u5834\u5408\u3001\u30a2\u30a4\u30c6\u30e0 i \u3092\u9078\u629e\u3057\u306a\u3044\n                dp[i][c] = dp[i - 1][c];\n            } else {\n                // \u9078\u629e\u3057\u306a\u3044\u5834\u5408\u3068\u30a2\u30a4\u30c6\u30e0 i \u3092\u9078\u629e\u3059\u308b\u5834\u5408\u306e\u3088\u308a\u5927\u304d\u3044\u5024\n                dp[i][c] = max(dp[i - 1][c], dp[i][c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[n][cap];\n}\n</code></pre> unbounded_knapsack.java<pre><code>/* \u5b8c\u5168\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\uff1a\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0 */\nint unboundedKnapsackDP(int[] wgt, int[] val, int cap) {\n    int n = wgt.length;\n    // DP\u30c6\u30fc\u30d6\u30eb\u3092\u521d\u671f\u5316\n    int[][] dp = new int[n + 1][cap + 1];\n    // \u72b6\u614b\u9077\u79fb\n    for (int i = 1; i &lt;= n; i++) {\n        for (int c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // \u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u306e\u5bb9\u91cf\u3092\u8d85\u3048\u308b\u5834\u5408\u3001\u30a2\u30a4\u30c6\u30e0 i \u3092\u9078\u629e\u3057\u306a\u3044\n                dp[i][c] = dp[i - 1][c];\n            } else {\n                // \u9078\u629e\u3057\u306a\u3044\u5834\u5408\u3068\u30a2\u30a4\u30c6\u30e0 i \u3092\u9078\u629e\u3059\u308b\u5834\u5408\u306e\u3088\u308a\u5927\u304d\u3044\u5024\n                dp[i][c] = Math.max(dp[i - 1][c], dp[i][c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[n][cap];\n}\n</code></pre> unbounded_knapsack.cs<pre><code>[class]{unbounded_knapsack}-[func]{UnboundedKnapsackDP}\n</code></pre> unbounded_knapsack.go<pre><code>[class]{}-[func]{unboundedKnapsackDP}\n</code></pre> unbounded_knapsack.swift<pre><code>[class]{}-[func]{unboundedKnapsackDP}\n</code></pre> unbounded_knapsack.js<pre><code>[class]{}-[func]{unboundedKnapsackDP}\n</code></pre> unbounded_knapsack.ts<pre><code>[class]{}-[func]{unboundedKnapsackDP}\n</code></pre> unbounded_knapsack.dart<pre><code>[class]{}-[func]{unboundedKnapsackDP}\n</code></pre> unbounded_knapsack.rs<pre><code>[class]{}-[func]{unbounded_knapsack_dp}\n</code></pre> unbounded_knapsack.c<pre><code>[class]{}-[func]{unboundedKnapsackDP}\n</code></pre> unbounded_knapsack.kt<pre><code>[class]{}-[func]{unboundedKnapsackDP}\n</code></pre> unbounded_knapsack.rb<pre><code>[class]{}-[func]{unbounded_knapsack_dp}\n</code></pre> unbounded_knapsack.zig<pre><code>[class]{}-[func]{unboundedKnapsackDP}\n</code></pre>"},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#3","title":"3. \u00a0 \u7a7a\u9593\u6700\u9069\u5316","text":"<p>\u73fe\u5728\u306e\u72b6\u614b\u306f\u5de6\u3068\u4e0a\u306e\u72b6\u614b\u304b\u3089\u6765\u308b\u305f\u3081\u3001\u7a7a\u9593\u6700\u9069\u5316\u89e3\u6cd5\u306f \\(dp\\) \u30c6\u30fc\u30d6\u30eb\u306e\u5404\u884c\u306b\u5bfe\u3057\u3066\u524d\u65b9\u8d70\u67fb\u3092\u5b9f\u884c\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002</p> <p>\u3053\u306e\u8d70\u67fb\u9806\u5e8f\u306f0-1\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u306e\u5834\u5408\u3068\u306f\u9006\u3067\u3059\u3002\u9055\u3044\u3092\u7406\u89e3\u3059\u308b\u305f\u3081\u306b\u4e0b\u306e\u56f3\u3092\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044\u3002</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> \u56f3 14-23 \u00a0 \u7a7a\u9593\u6700\u9069\u5316\u5f8c\u306e\u7121\u5236\u9650\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c\u306e\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u30d7\u30ed\u30bb\u30b9 </p> <p>\u30b3\u30fc\u30c9\u5b9f\u88c5\u306f\u975e\u5e38\u306b\u7c21\u5358\u3067\u3001\u914d\u5217 <code>dp</code> \u306e\u6700\u521d\u306e\u6b21\u5143\u3092\u524a\u9664\u3059\u308b\u3060\u3051\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig unbounded_knapsack.py<pre><code>def unbounded_knapsack_dp_comp(wgt: list[int], val: list[int], cap: int) -&gt; int:\n    \"\"\"\u5b8c\u5168\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\uff1a\u7a7a\u9593\u6700\u9069\u5316\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\"\"\"\n    n = len(wgt)\n    # dp \u30c6\u30fc\u30d6\u30eb\u3092\u521d\u671f\u5316\n    dp = [0] * (cap + 1)\n    # \u72b6\u614b\u9077\u79fb\n    for i in range(1, n + 1):\n        # \u9806\u5e8f\u3067\u8d70\u67fb\n        for c in range(1, cap + 1):\n            if wgt[i - 1] &gt; c:\n                # \u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u5bb9\u91cf\u3092\u8d85\u3048\u308b\u5834\u5408\u3001\u30a2\u30a4\u30c6\u30e0 i \u3092\u9078\u629e\u3057\u306a\u3044\n                dp[c] = dp[c]\n            else:\n                # \u30a2\u30a4\u30c6\u30e0 i \u3092\u9078\u629e\u3057\u306a\u3044\u306e\u3068\u9078\u629e\u3059\u308b\u306e\u3068\u3067\u5927\u304d\u3044\u5024\n                dp[c] = max(dp[c], dp[c - wgt[i - 1]] + val[i - 1])\n    return dp[cap]\n</code></pre> unbounded_knapsack.cpp<pre><code>/* \u5b8c\u5168\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\uff1a\u7a7a\u9593\u6700\u9069\u5316\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0 */\nint unboundedKnapsackDPComp(vector&lt;int&gt; &amp;wgt, vector&lt;int&gt; &amp;val, int cap) {\n    int n = wgt.size();\n    // DP\u30c6\u30fc\u30d6\u30eb\u3092\u521d\u671f\u5316\n    vector&lt;int&gt; dp(cap + 1, 0);\n    // \u72b6\u614b\u9077\u79fb\n    for (int i = 1; i &lt;= n; i++) {\n        for (int c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // \u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u306e\u5bb9\u91cf\u3092\u8d85\u3048\u308b\u5834\u5408\u3001\u30a2\u30a4\u30c6\u30e0 i \u3092\u9078\u629e\u3057\u306a\u3044\n                dp[c] = dp[c];\n            } else {\n                // \u9078\u629e\u3057\u306a\u3044\u5834\u5408\u3068\u30a2\u30a4\u30c6\u30e0 i \u3092\u9078\u629e\u3059\u308b\u5834\u5408\u306e\u3088\u308a\u5927\u304d\u3044\u5024\n                dp[c] = max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[cap];\n}\n</code></pre> unbounded_knapsack.java<pre><code>/* \u5b8c\u5168\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\uff1a\u7a7a\u9593\u6700\u9069\u5316\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0 */\nint unboundedKnapsackDPComp(int[] wgt, int[] val, int cap) {\n    int n = wgt.length;\n    // DP\u30c6\u30fc\u30d6\u30eb\u3092\u521d\u671f\u5316\n    int[] dp = new int[cap + 1];\n    // \u72b6\u614b\u9077\u79fb\n    for (int i = 1; i &lt;= n; i++) {\n        for (int c = 1; c &lt;= cap; c++) {\n            if (wgt[i - 1] &gt; c) {\n                // \u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u306e\u5bb9\u91cf\u3092\u8d85\u3048\u308b\u5834\u5408\u3001\u30a2\u30a4\u30c6\u30e0 i \u3092\u9078\u629e\u3057\u306a\u3044\n                dp[c] = dp[c];\n            } else {\n                // \u9078\u629e\u3057\u306a\u3044\u5834\u5408\u3068\u30a2\u30a4\u30c6\u30e0 i \u3092\u9078\u629e\u3059\u308b\u5834\u5408\u306e\u3088\u308a\u5927\u304d\u3044\u5024\n                dp[c] = Math.max(dp[c], dp[c - wgt[i - 1]] + val[i - 1]);\n            }\n        }\n    }\n    return dp[cap];\n}\n</code></pre> unbounded_knapsack.cs<pre><code>[class]{unbounded_knapsack}-[func]{UnboundedKnapsackDPComp}\n</code></pre> unbounded_knapsack.go<pre><code>[class]{}-[func]{unboundedKnapsackDPComp}\n</code></pre> unbounded_knapsack.swift<pre><code>[class]{}-[func]{unboundedKnapsackDPComp}\n</code></pre> unbounded_knapsack.js<pre><code>[class]{}-[func]{unboundedKnapsackDPComp}\n</code></pre> unbounded_knapsack.ts<pre><code>[class]{}-[func]{unboundedKnapsackDPComp}\n</code></pre> unbounded_knapsack.dart<pre><code>[class]{}-[func]{unboundedKnapsackDPComp}\n</code></pre> unbounded_knapsack.rs<pre><code>[class]{}-[func]{unbounded_knapsack_dp_comp}\n</code></pre> unbounded_knapsack.c<pre><code>[class]{}-[func]{unboundedKnapsackDPComp}\n</code></pre> unbounded_knapsack.kt<pre><code>[class]{}-[func]{unboundedKnapsackDPComp}\n</code></pre> unbounded_knapsack.rb<pre><code>[class]{}-[func]{unbounded_knapsack_dp_comp}\n</code></pre> unbounded_knapsack.zig<pre><code>[class]{}-[func]{unboundedKnapsackDPComp}\n</code></pre>"},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#1452","title":"14.5.2 \u00a0 \u30b3\u30a4\u30f3\u4ea4\u63db\u554f\u984c","text":"<p>\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c\u306f\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u554f\u984c\u306e\u5927\u304d\u306a\u30af\u30e9\u30b9\u306e\u4ee3\u8868\u3067\u3042\u308a\u3001\u30b3\u30a4\u30f3\u4ea4\u63db\u554f\u984c\u306a\u3069\u591a\u304f\u306e\u5909\u7a2e\u304c\u3042\u308a\u307e\u3059\u3002</p> <p>Question</p> <p>\\(n\\) \u7a2e\u985e\u306e\u30b3\u30a4\u30f3\u304c\u4e0e\u3048\u3089\u308c\u3001\\(i\\) \u756a\u76ee\u306e\u7a2e\u985e\u306e\u30b3\u30a4\u30f3\u306e\u984d\u9762\u306f \\(coins[i - 1]\\) \u3067\u3001\u76ee\u6a19\u91d1\u984d\u306f \\(amt\\) \u3067\u3059\u3002\u5404\u7a2e\u985e\u306e\u30b3\u30a4\u30f3\u306f\u8907\u6570\u56de\u9078\u629e\u3067\u304d\u307e\u3059\u3002\u76ee\u6a19\u91d1\u984d\u3092\u69cb\u6210\u3059\u308b\u306e\u306b\u5fc5\u8981\u306a\u6700\u5c0f\u30b3\u30a4\u30f3\u6570\u306f\u4f55\u3067\u3059\u304b\uff1f\u76ee\u6a19\u91d1\u984d\u3092\u69cb\u6210\u3067\u304d\u306a\u3044\u5834\u5408\u306f \\(-1\\) \u3092\u8fd4\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u4ee5\u4e0b\u306e\u4f8b\u3092\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044\u3002</p> <p></p> <p> \u56f3 14-24 \u00a0 \u30b3\u30a4\u30f3\u4ea4\u63db\u554f\u984c\u306e\u4f8b\u30c7\u30fc\u30bf </p>"},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#1_1","title":"1. \u00a0 \u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u30a2\u30d7\u30ed\u30fc\u30c1","text":"<p>\u30b3\u30a4\u30f3\u4ea4\u63db\u306f\u7121\u5236\u9650\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c\u306e\u7279\u6b8a\u30b1\u30fc\u30b9\u3068\u898b\u306a\u3059\u3053\u3068\u304c\u3067\u304d\u3001\u4ee5\u4e0b\u306e\u985e\u4f3c\u70b9\u3068\u76f8\u9055\u70b9\u3092\u5171\u6709\u3057\u3066\u3044\u307e\u3059\u3002</p> <ul> <li>2\u3064\u306e\u554f\u984c\u306f\u4e92\u3044\u306b\u5909\u63db\u3067\u304d\u307e\u3059\uff1a\u300c\u30a2\u30a4\u30c6\u30e0\u300d\u306f\u300c\u30b3\u30a4\u30f3\u300d\u306b\u5bfe\u5fdc\u3057\u3001\u300c\u30a2\u30a4\u30c6\u30e0\u306e\u91cd\u91cf\u300d\u306f\u300c\u30b3\u30a4\u30f3\u306e\u984d\u9762\u300d\u306b\u5bfe\u5fdc\u3057\u3001\u300c\u30d0\u30c3\u30af\u30d1\u30c3\u30af\u306e\u5bb9\u91cf\u300d\u306f\u300c\u76ee\u6a19\u91d1\u984d\u300d\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002</li> <li>\u6700\u9069\u5316\u76ee\u6a19\u306f\u9006\u3067\u3059\uff1a\u7121\u5236\u9650\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c\u306f\u30a2\u30a4\u30c6\u30e0\u306e\u5024\u3092\u6700\u5927\u5316\u3059\u308b\u3053\u3068\u3092\u76ee\u7684\u3068\u3057\u3001\u30b3\u30a4\u30f3\u4ea4\u63db\u554f\u984c\u306f\u30b3\u30a4\u30f3\u306e\u6570\u3092\u6700\u5c0f\u5316\u3059\u308b\u3053\u3068\u3092\u76ee\u7684\u3068\u3057\u307e\u3059\u3002</li> <li>\u7121\u5236\u9650\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c\u306f\u30d0\u30c3\u30af\u30d1\u30c3\u30af\u5bb9\u91cf\u3092\u300c\u8d85\u3048\u306a\u3044\u300d\u89e3\u3092\u6c42\u3081\u3001\u30b3\u30a4\u30f3\u4ea4\u63db\u306f\u76ee\u6a19\u91d1\u984d\u3092\u300c\u6b63\u78ba\u306b\u300d\u69cb\u6210\u3059\u308b\u89e3\u3092\u6c42\u3081\u307e\u3059\u3002</li> </ul> <p>\u7b2c1\u30b9\u30c6\u30c3\u30d7\uff1a\u5404\u30e9\u30a6\u30f3\u30c9\u306e\u610f\u601d\u6c7a\u5b9a\u3092\u8003\u3048\u3001\u72b6\u614b\u3092\u5b9a\u7fa9\u3057\u3001\u305d\u308c\u306b\u3088\u308a \\(dp\\) \u30c6\u30fc\u30d6\u30eb\u3092\u5c0e\u51fa\u3059\u308b</p> <p>\u72b6\u614b \\([i, a]\\) \u306f\u90e8\u5206\u554f\u984c\u306b\u5bfe\u5fdc\u3057\u307e\u3059\uff1a\u6700\u521d\u306e \\(i\\) \u7a2e\u985e\u306e\u30b3\u30a4\u30f3\u3092\u4f7f\u7528\u3057\u3066\u91d1\u984d \\(a\\) \u3092\u69cb\u6210\u3067\u304d\u308b\u6700\u5c0f\u30b3\u30a4\u30f3\u6570\u3001\\(dp[i, a]\\) \u3068\u8868\u8a18\u3055\u308c\u307e\u3059\u3002</p> <p>\u4e8c\u6b21\u5143 \\(dp\\) \u30c6\u30fc\u30d6\u30eb\u306e\u30b5\u30a4\u30ba\u306f \\((n+1) \\times (amt+1)\\) \u3067\u3059\u3002</p> <p>\u7b2c2\u30b9\u30c6\u30c3\u30d7\uff1a\u6700\u9069\u90e8\u5206\u69cb\u9020\u3092\u7279\u5b9a\u3057\u3001\u72b6\u614b\u9077\u79fb\u65b9\u7a0b\u5f0f\u3092\u5c0e\u51fa\u3059\u308b</p> <p>\u3053\u306e\u554f\u984c\u306f\u72b6\u614b\u9077\u79fb\u65b9\u7a0b\u5f0f\u306e2\u3064\u306e\u5074\u9762\u3067\u7121\u5236\u9650\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c\u3068\u7570\u306a\u308a\u307e\u3059\u3002</p> <ul> <li>\u3053\u306e\u554f\u984c\u306f\u6700\u5c0f\u5024\u3092\u6c42\u3081\u308b\u305f\u3081\u3001\u6f14\u7b97\u5b50 \\(\\max()\\) \u3092 \\(\\min()\\) \u306b\u5909\u66f4\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002</li> <li>\u6700\u9069\u5316\u306f\u30b3\u30a4\u30f3\u306e\u6570\u306b\u7126\u70b9\u3092\u5f53\u3066\u3066\u3044\u308b\u305f\u3081\u3001\u30b3\u30a4\u30f3\u304c\u9078\u629e\u3055\u308c\u305f\u3068\u304d\u306b\u5358\u7d14\u306b \\(+1\\) \u3092\u8ffd\u52a0\u3057\u307e\u3059\u3002</li> </ul> \\[ dp[i, a] = \\min(dp[i-1, a], dp[i, a - coins[i-1]] + 1) \\] <p>\u7b2c3\u30b9\u30c6\u30c3\u30d7\uff1a\u5883\u754c\u6761\u4ef6\u3068\u72b6\u614b\u9077\u79fb\u9806\u5e8f\u3092\u5b9a\u7fa9\u3059\u308b</p> <p>\u76ee\u6a19\u91d1\u984d\u304c \\(0\\) \u306e\u5834\u5408\u3001\u305d\u308c\u3092\u69cb\u6210\u3059\u308b\u306e\u306b\u5fc5\u8981\u306a\u6700\u5c0f\u30b3\u30a4\u30f3\u6570\u306f \\(0\\) \u3067\u3042\u308b\u305f\u3081\u3001\u6700\u521d\u306e\u5217\u306e\u3059\u3079\u3066\u306e \\(dp[i, 0]\\) \u306f \\(0\\) \u3067\u3059\u3002</p> <p>\u30b3\u30a4\u30f3\u304c\u306a\u3044\u5834\u5408\u3001**\u4efb\u610f\u306e\u91d1\u984d &gt;0 \u3092\u69cb\u6210\u3059\u308b\u3053\u3068\u306f\u4e0d\u53ef\u80fd**\u3067\u3042\u308a\u3001\u3053\u308c\u306f\u7121\u52b9\u306a\u89e3\u3067\u3059\u3002\u72b6\u614b\u9077\u79fb\u65b9\u7a0b\u5f0f\u306e \\(\\min()\\) \u95a2\u6570\u304c\u7121\u52b9\u306a\u89e3\u3092\u8a8d\u8b58\u3057\u3066\u30d5\u30a3\u30eb\u30bf\u30ea\u30f3\u30b0\u3067\u304d\u308b\u3088\u3046\u306b\u3001\\(+\\infty\\) \u3092\u4f7f\u7528\u3057\u3066\u305d\u308c\u3089\u3092\u8868\u73fe\u3059\u308b\u3053\u3068\u3092\u691c\u8a0e\u3057\u3001\u3064\u307e\u308a\u6700\u521d\u306e\u884c\u306e\u3059\u3079\u3066\u306e \\(dp[0, a]\\) \u3092 \\(+\\infty\\) \u306b\u8a2d\u5b9a\u3057\u307e\u3059\u3002</p>"},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#2_1","title":"2. \u00a0 \u30b3\u30fc\u30c9\u5b9f\u88c5","text":"<p>\u307b\u3068\u3093\u3069\u306e\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u306f \\(+\\infty\\) \u5909\u6570\u3092\u63d0\u4f9b\u3057\u3066\u304a\u3089\u305a\u3001\u6574\u6570 <code>int</code> \u306e\u6700\u5927\u5024\u306e\u307f\u3092\u4ee3\u66ff\u3068\u3057\u3066\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u304c\u767a\u751f\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\uff1a\u72b6\u614b\u9077\u79fb\u65b9\u7a0b\u5f0f\u306e \\(+1\\) \u6f14\u7b97\u304c\u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002</p> <p>\u3053\u306e\u7406\u7531\u3067\u3001\u6570\u5024 \\(amt + 1\\) \u3092\u4f7f\u7528\u3057\u3066\u7121\u52b9\u306a\u89e3\u3092\u8868\u3057\u307e\u3059\u3002\u306a\u305c\u306a\u3089\u3001\\(amt\\) \u3092\u69cb\u6210\u3059\u308b\u306e\u306b\u5fc5\u8981\u306a\u6700\u5927\u30b3\u30a4\u30f3\u6570\u306f\u6700\u5927\u3067\u3082 \\(amt\\) \u3060\u304b\u3089\u3067\u3059\u3002\u7d50\u679c\u3092\u8fd4\u3059\u524d\u306b\u3001\\(dp[n, amt]\\) \u304c \\(amt + 1\\) \u306b\u7b49\u3057\u3044\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\u3057\u3001\u305d\u3046\u3067\u3042\u308c\u3070 \\(-1\\) \u3092\u8fd4\u3057\u3001\u76ee\u6a19\u91d1\u984d\u3092\u69cb\u6210\u3067\u304d\u306a\u3044\u3053\u3068\u3092\u793a\u3057\u307e\u3059\u3002\u30b3\u30fc\u30c9\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig coin_change.py<pre><code>def coin_change_dp(coins: list[int], amt: int) -&gt; int:\n    \"\"\"\u786c\u8ca8\u4ea4\u63db\uff1a\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\"\"\"\n    n = len(coins)\n    MAX = amt + 1\n    # dp \u30c6\u30fc\u30d6\u30eb\u3092\u521d\u671f\u5316\n    dp = [[0] * (amt + 1) for _ in range(n + 1)]\n    # \u72b6\u614b\u9077\u79fb\uff1a\u6700\u521d\u306e\u884c\u3068\u6700\u521d\u306e\u5217\n    for a in range(1, amt + 1):\n        dp[0][a] = MAX\n    # \u72b6\u614b\u9077\u79fb\uff1a\u6b8b\u308a\u306e\u884c\u3068\u5217\n    for i in range(1, n + 1):\n        for a in range(1, amt + 1):\n            if coins[i - 1] &gt; a:\n                # \u76ee\u6a19\u91d1\u984d\u3092\u8d85\u3048\u308b\u5834\u5408\u3001\u786c\u8ca8 i \u3092\u9078\u629e\u3057\u306a\u3044\n                dp[i][a] = dp[i - 1][a]\n            else:\n                # \u786c\u8ca8 i \u3092\u9078\u629e\u3057\u306a\u3044\u306e\u3068\u9078\u629e\u3059\u308b\u306e\u3068\u3067\u5c0f\u3055\u3044\u5024\n                dp[i][a] = min(dp[i - 1][a], dp[i][a - coins[i - 1]] + 1)\n    return dp[n][amt] if dp[n][amt] != MAX else -1\n</code></pre> coin_change.cpp<pre><code>/* \u786c\u8ca8\u4e21\u66ff\uff1a\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0 */\nint coinChangeDP(vector&lt;int&gt; &amp;coins, int amt) {\n    int n = coins.size();\n    int MAX = amt + 1;\n    // DP\u30c6\u30fc\u30d6\u30eb\u3092\u521d\u671f\u5316\n    vector&lt;vector&lt;int&gt;&gt; dp(n + 1, vector&lt;int&gt;(amt + 1, 0));\n    // \u72b6\u614b\u9077\u79fb\uff1a\u6700\u521d\u306e\u884c\u3068\u6700\u521d\u306e\u5217\n    for (int a = 1; a &lt;= amt; a++) {\n        dp[0][a] = MAX;\n    }\n    // \u72b6\u614b\u9077\u79fb\uff1a\u6b8b\u308a\u306e\u884c\u3068\u5217\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // \u76ee\u6a19\u91d1\u984d\u3092\u8d85\u3048\u308b\u5834\u5408\u3001\u786c\u8ca8 i \u3092\u9078\u629e\u3057\u306a\u3044\n                dp[i][a] = dp[i - 1][a];\n            } else {\n                // \u9078\u629e\u3057\u306a\u3044\u5834\u5408\u3068\u786c\u8ca8 i \u3092\u9078\u629e\u3059\u308b\u5834\u5408\u306e\u3088\u308a\u5c0f\u3055\u3044\u5024\n                dp[i][a] = min(dp[i - 1][a], dp[i][a - coins[i - 1]] + 1);\n            }\n        }\n    }\n    return dp[n][amt] != MAX ? dp[n][amt] : -1;\n}\n</code></pre> coin_change.java<pre><code>/* \u786c\u8ca8\u4e21\u66ff\uff1a\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0 */\nint coinChangeDP(int[] coins, int amt) {\n    int n = coins.length;\n    int MAX = amt + 1;\n    // DP\u30c6\u30fc\u30d6\u30eb\u3092\u521d\u671f\u5316\n    int[][] dp = new int[n + 1][amt + 1];\n    // \u72b6\u614b\u9077\u79fb\uff1a\u6700\u521d\u306e\u884c\u3068\u6700\u521d\u306e\u5217\n    for (int a = 1; a &lt;= amt; a++) {\n        dp[0][a] = MAX;\n    }\n    // \u72b6\u614b\u9077\u79fb\uff1a\u6b8b\u308a\u306e\u884c\u3068\u5217\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // \u76ee\u6a19\u91d1\u984d\u3092\u8d85\u3048\u308b\u5834\u5408\u3001\u786c\u8ca8 i \u3092\u9078\u629e\u3057\u306a\u3044\n                dp[i][a] = dp[i - 1][a];\n            } else {\n                // \u9078\u629e\u3057\u306a\u3044\u5834\u5408\u3068\u786c\u8ca8 i \u3092\u9078\u629e\u3059\u308b\u5834\u5408\u306e\u3088\u308a\u5c0f\u3055\u3044\u5024\n                dp[i][a] = Math.min(dp[i - 1][a], dp[i][a - coins[i - 1]] + 1);\n            }\n        }\n    }\n    return dp[n][amt] != MAX ? dp[n][amt] : -1;\n}\n</code></pre> coin_change.cs<pre><code>[class]{coin_change}-[func]{CoinChangeDP}\n</code></pre> coin_change.go<pre><code>[class]{}-[func]{coinChangeDP}\n</code></pre> coin_change.swift<pre><code>[class]{}-[func]{coinChangeDP}\n</code></pre> coin_change.js<pre><code>[class]{}-[func]{coinChangeDP}\n</code></pre> coin_change.ts<pre><code>[class]{}-[func]{coinChangeDP}\n</code></pre> coin_change.dart<pre><code>[class]{}-[func]{coinChangeDP}\n</code></pre> coin_change.rs<pre><code>[class]{}-[func]{coin_change_dp}\n</code></pre> coin_change.c<pre><code>[class]{}-[func]{coinChangeDP}\n</code></pre> coin_change.kt<pre><code>[class]{}-[func]{coinChangeDP}\n</code></pre> coin_change.rb<pre><code>[class]{}-[func]{coin_change_dp}\n</code></pre> coin_change.zig<pre><code>[class]{}-[func]{coinChangeDP}\n</code></pre> <p>\u4e0b\u306e\u56f3\u306f\u30b3\u30a4\u30f3\u4ea4\u63db\u554f\u984c\u306e\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u30d7\u30ed\u30bb\u30b9\u3092\u793a\u3057\u3066\u304a\u308a\u3001\u7121\u5236\u9650\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c\u3068\u975e\u5e38\u306b\u4f3c\u3066\u3044\u307e\u3059\u3002</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt;&lt;12&gt;&lt;13&gt;&lt;14&gt;&lt;15&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> \u56f3 14-25 \u00a0 \u30b3\u30a4\u30f3\u4ea4\u63db\u554f\u984c\u306e\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u30d7\u30ed\u30bb\u30b9 </p>"},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#3_1","title":"3. \u00a0 \u7a7a\u9593\u6700\u9069\u5316","text":"<p>\u30b3\u30a4\u30f3\u4ea4\u63db\u554f\u984c\u306e\u7a7a\u9593\u6700\u9069\u5316\u306f\u7121\u5236\u9650\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c\u3068\u540c\u3058\u65b9\u6cd5\u3067\u51e6\u7406\u3055\u308c\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig coin_change.py<pre><code>def coin_change_dp_comp(coins: list[int], amt: int) -&gt; int:\n    \"\"\"\u786c\u8ca8\u4ea4\u63db\uff1a\u7a7a\u9593\u6700\u9069\u5316\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\"\"\"\n    n = len(coins)\n    MAX = amt + 1\n    # dp \u30c6\u30fc\u30d6\u30eb\u3092\u521d\u671f\u5316\n    dp = [MAX] * (amt + 1)\n    dp[0] = 0\n    # \u72b6\u614b\u9077\u79fb\n    for i in range(1, n + 1):\n        # \u9806\u5e8f\u3067\u8d70\u67fb\n        for a in range(1, amt + 1):\n            if coins[i - 1] &gt; a:\n                # \u76ee\u6a19\u91d1\u984d\u3092\u8d85\u3048\u308b\u5834\u5408\u3001\u786c\u8ca8 i \u3092\u9078\u629e\u3057\u306a\u3044\n                dp[a] = dp[a]\n            else:\n                # \u786c\u8ca8 i \u3092\u9078\u629e\u3057\u306a\u3044\u306e\u3068\u9078\u629e\u3059\u308b\u306e\u3068\u3067\u5c0f\u3055\u3044\u5024\n                dp[a] = min(dp[a], dp[a - coins[i - 1]] + 1)\n    return dp[amt] if dp[amt] != MAX else -1\n</code></pre> coin_change.cpp<pre><code>/* \u786c\u8ca8\u4e21\u66ff\uff1a\u7a7a\u9593\u6700\u9069\u5316\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0 */\nint coinChangeDPComp(vector&lt;int&gt; &amp;coins, int amt) {\n    int n = coins.size();\n    int MAX = amt + 1;\n    // DP\u30c6\u30fc\u30d6\u30eb\u3092\u521d\u671f\u5316\n    vector&lt;int&gt; dp(amt + 1, MAX);\n    dp[0] = 0;\n    // \u72b6\u614b\u9077\u79fb\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // \u76ee\u6a19\u91d1\u984d\u3092\u8d85\u3048\u308b\u5834\u5408\u3001\u786c\u8ca8 i \u3092\u9078\u629e\u3057\u306a\u3044\n                dp[a] = dp[a];\n            } else {\n                // \u9078\u629e\u3057\u306a\u3044\u5834\u5408\u3068\u786c\u8ca8 i \u3092\u9078\u629e\u3059\u308b\u5834\u5408\u306e\u3088\u308a\u5c0f\u3055\u3044\u5024\n                dp[a] = min(dp[a], dp[a - coins[i - 1]] + 1);\n            }\n        }\n    }\n    return dp[amt] != MAX ? dp[amt] : -1;\n}\n</code></pre> coin_change.java<pre><code>/* \u786c\u8ca8\u4e21\u66ff\uff1a\u7a7a\u9593\u6700\u9069\u5316\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0 */\nint coinChangeDPComp(int[] coins, int amt) {\n    int n = coins.length;\n    int MAX = amt + 1;\n    // DP\u30c6\u30fc\u30d6\u30eb\u3092\u521d\u671f\u5316\n    int[] dp = new int[amt + 1];\n    Arrays.fill(dp, MAX);\n    dp[0] = 0;\n    // \u72b6\u614b\u9077\u79fb\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // \u76ee\u6a19\u91d1\u984d\u3092\u8d85\u3048\u308b\u5834\u5408\u3001\u786c\u8ca8 i \u3092\u9078\u629e\u3057\u306a\u3044\n                dp[a] = dp[a];\n            } else {\n                // \u9078\u629e\u3057\u306a\u3044\u5834\u5408\u3068\u786c\u8ca8 i \u3092\u9078\u629e\u3059\u308b\u5834\u5408\u306e\u3088\u308a\u5c0f\u3055\u3044\u5024\n                dp[a] = Math.min(dp[a], dp[a - coins[i - 1]] + 1);\n            }\n        }\n    }\n    return dp[amt] != MAX ? dp[amt] : -1;\n}\n</code></pre> coin_change.cs<pre><code>[class]{coin_change}-[func]{CoinChangeDPComp}\n</code></pre> coin_change.go<pre><code>[class]{}-[func]{coinChangeDPComp}\n</code></pre> coin_change.swift<pre><code>[class]{}-[func]{coinChangeDPComp}\n</code></pre> coin_change.js<pre><code>[class]{}-[func]{coinChangeDPComp}\n</code></pre> coin_change.ts<pre><code>[class]{}-[func]{coinChangeDPComp}\n</code></pre> coin_change.dart<pre><code>[class]{}-[func]{coinChangeDPComp}\n</code></pre> coin_change.rs<pre><code>[class]{}-[func]{coin_change_dp_comp}\n</code></pre> coin_change.c<pre><code>[class]{}-[func]{coinChangeDPComp}\n</code></pre> coin_change.kt<pre><code>[class]{}-[func]{coinChangeDPComp}\n</code></pre> coin_change.rb<pre><code>[class]{}-[func]{coin_change_dp_comp}\n</code></pre> coin_change.zig<pre><code>[class]{}-[func]{coinChangeDPComp}\n</code></pre>"},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#1453-ii","title":"14.5.3 \u00a0 \u30b3\u30a4\u30f3\u4ea4\u63db\u554f\u984cII","text":"<p>Question</p> <p>\\(n\\) \u7a2e\u985e\u306e\u30b3\u30a4\u30f3\u304c\u4e0e\u3048\u3089\u308c\u3001\\(i\\) \u756a\u76ee\u306e\u7a2e\u985e\u306e\u30b3\u30a4\u30f3\u306e\u984d\u9762\u306f \\(coins[i - 1]\\) \u3067\u3001\u76ee\u6a19\u91d1\u984d\u306f \\(amt\\) \u3067\u3059\u3002\u5404\u7a2e\u985e\u306e\u30b3\u30a4\u30f3\u306f\u8907\u6570\u56de\u9078\u629e\u3067\u304d\u3001\u76ee\u6a19\u91d1\u984d\u3092\u69cb\u6210\u3067\u304d\u308b\u30b3\u30a4\u30f3\u306e\u7d44\u307f\u5408\u308f\u305b\u306f\u4f55\u901a\u308a\u3042\u308a\u307e\u3059\u304b\u3002\u4ee5\u4e0b\u306e\u4f8b\u3092\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044\u3002</p> <p></p> <p> \u56f3 14-26 \u00a0 \u30b3\u30a4\u30f3\u4ea4\u63db\u554f\u984cII\u306e\u4f8b\u30c7\u30fc\u30bf </p>"},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#1_2","title":"1. \u00a0 \u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u30a2\u30d7\u30ed\u30fc\u30c1","text":"<p>\u524d\u306e\u554f\u984c\u3068\u6bd4\u8f03\u3057\u3066\u3001\u3053\u306e\u554f\u984c\u306e\u76ee\u6a19\u306f\u7d44\u307f\u5408\u308f\u305b\u306e\u6570\u3092\u6c7a\u5b9a\u3059\u308b\u3053\u3068\u3067\u3042\u308b\u305f\u3081\u3001\u90e8\u5206\u554f\u984c\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\uff1a\u6700\u521d\u306e \\(i\\) \u7a2e\u985e\u306e\u30b3\u30a4\u30f3\u3092\u4f7f\u7528\u3057\u3066\u91d1\u984d \\(a\\) \u3092\u69cb\u6210\u3067\u304d\u308b\u7d44\u307f\u5408\u308f\u305b\u306e\u6570\u3002\\(dp\\) \u30c6\u30fc\u30d6\u30eb\u306f\u30b5\u30a4\u30ba \\((n+1) \\times (amt + 1)\\) \u306e\u4e8c\u6b21\u5143\u884c\u5217\u306e\u307e\u307e\u6b8b\u308a\u307e\u3059\u3002</p> <p>\u73fe\u5728\u306e\u72b6\u614b\u306e\u7d44\u307f\u5408\u308f\u305b\u6570\u306f\u3001\u73fe\u5728\u306e\u30b3\u30a4\u30f3\u3092\u9078\u629e\u3057\u306a\u3044\u7d44\u307f\u5408\u308f\u305b\u3068\u73fe\u5728\u306e\u30b3\u30a4\u30f3\u3092\u9078\u629e\u3059\u308b\u7d44\u307f\u5408\u308f\u305b\u306e\u5408\u8a08\u3067\u3059\u3002\u72b6\u614b\u9077\u79fb\u65b9\u7a0b\u5f0f\u306f\uff1a</p> \\[ dp[i, a] = dp[i-1, a] + dp[i, a - coins[i-1]] \\] <p>\u76ee\u6a19\u91d1\u984d\u304c \\(0\\) \u306e\u5834\u5408\u3001\u76ee\u6a19\u91d1\u984d\u3092\u69cb\u6210\u3059\u308b\u306e\u306b\u30b3\u30a4\u30f3\u306f\u5fc5\u8981\u306a\u3044\u305f\u3081\u3001\u6700\u521d\u306e\u5217\u306e\u3059\u3079\u3066\u306e \\(dp[i, 0]\\) \u306f \\(1\\) \u306b\u521d\u671f\u5316\u3055\u308c\u308b\u3079\u304d\u3067\u3059\u3002\u30b3\u30a4\u30f3\u304c\u306a\u3044\u5834\u5408\u3001\u4efb\u610f\u306e\u91d1\u984d &gt;0 \u3092\u69cb\u6210\u3059\u308b\u3053\u3068\u306f\u4e0d\u53ef\u80fd\u3067\u3042\u308b\u305f\u3081\u3001\u6700\u521d\u306e\u884c\u306e\u3059\u3079\u3066\u306e \\(dp[0, a]\\) \u306f \\(0\\) \u306b\u8a2d\u5b9a\u3055\u308c\u308b\u3079\u304d\u3067\u3059\u3002</p>"},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#2_2","title":"2. \u00a0 \u30b3\u30fc\u30c9\u5b9f\u88c5","text":"PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig coin_change_ii.py<pre><code>def coin_change_ii_dp(coins: list[int], amt: int) -&gt; int:\n    \"\"\"\u786c\u8ca8\u4ea4\u63db II\uff1a\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\"\"\"\n    n = len(coins)\n    # dp \u30c6\u30fc\u30d6\u30eb\u3092\u521d\u671f\u5316\n    dp = [[0] * (amt + 1) for _ in range(n + 1)]\n    # \u6700\u521d\u306e\u5217\u3092\u521d\u671f\u5316\n    for i in range(n + 1):\n        dp[i][0] = 1\n    # \u72b6\u614b\u9077\u79fb\n    for i in range(1, n + 1):\n        for a in range(1, amt + 1):\n            if coins[i - 1] &gt; a:\n                # \u76ee\u6a19\u91d1\u984d\u3092\u8d85\u3048\u308b\u5834\u5408\u3001\u786c\u8ca8 i \u3092\u9078\u629e\u3057\u306a\u3044\n                dp[i][a] = dp[i - 1][a]\n            else:\n                # \u786c\u8ca8 i \u3092\u9078\u629e\u3057\u306a\u3044\u306e\u3068\u9078\u629e\u3059\u308b\u306e\u3068\u306e\u4e21\u65b9\u306e\u9078\u629e\u80a2\u306e\u548c\n                dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1]]\n    return dp[n][amt]\n</code></pre> coin_change_ii.cpp<pre><code>/* \u786c\u8ca8\u4e21\u66ff II\uff1a\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0 */\nint coinChangeIIDP(vector&lt;int&gt; &amp;coins, int amt) {\n    int n = coins.size();\n    // DP\u30c6\u30fc\u30d6\u30eb\u3092\u521d\u671f\u5316\n    vector&lt;vector&lt;int&gt;&gt; dp(n + 1, vector&lt;int&gt;(amt + 1, 0));\n    // \u6700\u521d\u306e\u5217\u3092\u521d\u671f\u5316\n    for (int i = 0; i &lt;= n; i++) {\n        dp[i][0] = 1;\n    }\n    // \u72b6\u614b\u9077\u79fb\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // \u76ee\u6a19\u91d1\u984d\u3092\u8d85\u3048\u308b\u5834\u5408\u3001\u786c\u8ca8 i \u3092\u9078\u629e\u3057\u306a\u3044\n                dp[i][a] = dp[i - 1][a];\n            } else {\n                // \u9078\u629e\u3057\u306a\u3044\u5834\u5408\u3068\u786c\u8ca8 i \u3092\u9078\u629e\u3059\u308b\u5834\u5408\u306e2\u3064\u306e\u9078\u629e\u80a2\u306e\u5408\u8a08\n                dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1]];\n            }\n        }\n    }\n    return dp[n][amt];\n}\n</code></pre> coin_change_ii.java<pre><code>/* \u786c\u8ca8\u4e21\u66ff II\uff1a\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0 */\nint coinChangeIIDP(int[] coins, int amt) {\n    int n = coins.length;\n    // DP\u30c6\u30fc\u30d6\u30eb\u3092\u521d\u671f\u5316\n    int[][] dp = new int[n + 1][amt + 1];\n    // \u6700\u521d\u306e\u5217\u3092\u521d\u671f\u5316\n    for (int i = 0; i &lt;= n; i++) {\n        dp[i][0] = 1;\n    }\n    // \u72b6\u614b\u9077\u79fb\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // \u76ee\u6a19\u91d1\u984d\u3092\u8d85\u3048\u308b\u5834\u5408\u3001\u786c\u8ca8 i \u3092\u9078\u629e\u3057\u306a\u3044\n                dp[i][a] = dp[i - 1][a];\n            } else {\n                // \u9078\u629e\u3057\u306a\u3044\u5834\u5408\u3068\u786c\u8ca8 i \u3092\u9078\u629e\u3059\u308b\u5834\u5408\u306e2\u3064\u306e\u9078\u629e\u80a2\u306e\u5408\u8a08\n                dp[i][a] = dp[i - 1][a] + dp[i][a - coins[i - 1]];\n            }\n        }\n    }\n    return dp[n][amt];\n}\n</code></pre> coin_change_ii.cs<pre><code>[class]{coin_change_ii}-[func]{CoinChangeIIDP}\n</code></pre> coin_change_ii.go<pre><code>[class]{}-[func]{coinChangeIIDP}\n</code></pre> coin_change_ii.swift<pre><code>[class]{}-[func]{coinChangeIIDP}\n</code></pre> coin_change_ii.js<pre><code>[class]{}-[func]{coinChangeIIDP}\n</code></pre> coin_change_ii.ts<pre><code>[class]{}-[func]{coinChangeIIDP}\n</code></pre> coin_change_ii.dart<pre><code>[class]{}-[func]{coinChangeIIDP}\n</code></pre> coin_change_ii.rs<pre><code>[class]{}-[func]{coin_change_ii_dp}\n</code></pre> coin_change_ii.c<pre><code>[class]{}-[func]{coinChangeIIDP}\n</code></pre> coin_change_ii.kt<pre><code>[class]{}-[func]{coinChangeIIDP}\n</code></pre> coin_change_ii.rb<pre><code>[class]{}-[func]{coin_change_ii_dp}\n</code></pre> coin_change_ii.zig<pre><code>[class]{}-[func]{coinChangeIIDP}\n</code></pre>"},{"location":"chapter_dynamic_programming/unbounded_knapsack_problem/#3_2","title":"3. \u00a0 \u7a7a\u9593\u6700\u9069\u5316","text":"<p>\u7a7a\u9593\u6700\u9069\u5316\u30a2\u30d7\u30ed\u30fc\u30c1\u306f\u540c\u3058\u3067\u3001\u30b3\u30a4\u30f3\u306e\u6b21\u5143\u3092\u524a\u9664\u3059\u308b\u3060\u3051\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig coin_change_ii.py<pre><code>def coin_change_ii_dp_comp(coins: list[int], amt: int) -&gt; int:\n    \"\"\"\u786c\u8ca8\u4ea4\u63db II\uff1a\u7a7a\u9593\u6700\u9069\u5316\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\"\"\"\n    n = len(coins)\n    # dp \u30c6\u30fc\u30d6\u30eb\u3092\u521d\u671f\u5316\n    dp = [0] * (amt + 1)\n    dp[0] = 1\n    # \u72b6\u614b\u9077\u79fb\n    for i in range(1, n + 1):\n        # \u9806\u5e8f\u3067\u8d70\u67fb\n        for a in range(1, amt + 1):\n            if coins[i - 1] &gt; a:\n                # \u76ee\u6a19\u91d1\u984d\u3092\u8d85\u3048\u308b\u5834\u5408\u3001\u786c\u8ca8 i \u3092\u9078\u629e\u3057\u306a\u3044\n                dp[a] = dp[a]\n            else:\n                # \u786c\u8ca8 i \u3092\u9078\u629e\u3057\u306a\u3044\u306e\u3068\u9078\u629e\u3059\u308b\u306e\u3068\u306e\u4e21\u65b9\u306e\u9078\u629e\u80a2\u306e\u548c\n                dp[a] = dp[a] + dp[a - coins[i - 1]]\n    return dp[amt]\n</code></pre> coin_change_ii.cpp<pre><code>/* \u786c\u8ca8\u4e21\u66ff II\uff1a\u7a7a\u9593\u6700\u9069\u5316\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0 */\nint coinChangeIIDPComp(vector&lt;int&gt; &amp;coins, int amt) {\n    int n = coins.size();\n    // DP\u30c6\u30fc\u30d6\u30eb\u3092\u521d\u671f\u5316\n    vector&lt;int&gt; dp(amt + 1, 0);\n    dp[0] = 1;\n    // \u72b6\u614b\u9077\u79fb\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // \u76ee\u6a19\u91d1\u984d\u3092\u8d85\u3048\u308b\u5834\u5408\u3001\u786c\u8ca8 i \u3092\u9078\u629e\u3057\u306a\u3044\n                dp[a] = dp[a];\n            } else {\n                // \u9078\u629e\u3057\u306a\u3044\u5834\u5408\u3068\u786c\u8ca8 i \u3092\u9078\u629e\u3059\u308b\u5834\u5408\u306e2\u3064\u306e\u9078\u629e\u80a2\u306e\u5408\u8a08\n                dp[a] = dp[a] + dp[a - coins[i - 1]];\n            }\n        }\n    }\n    return dp[amt];\n}\n</code></pre> coin_change_ii.java<pre><code>/* \u786c\u8ca8\u4e21\u66ff II\uff1a\u7a7a\u9593\u6700\u9069\u5316\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0 */\nint coinChangeIIDPComp(int[] coins, int amt) {\n    int n = coins.length;\n    // DP\u30c6\u30fc\u30d6\u30eb\u3092\u521d\u671f\u5316\n    int[] dp = new int[amt + 1];\n    dp[0] = 1;\n    // \u72b6\u614b\u9077\u79fb\n    for (int i = 1; i &lt;= n; i++) {\n        for (int a = 1; a &lt;= amt; a++) {\n            if (coins[i - 1] &gt; a) {\n                // \u76ee\u6a19\u91d1\u984d\u3092\u8d85\u3048\u308b\u5834\u5408\u3001\u786c\u8ca8 i \u3092\u9078\u629e\u3057\u306a\u3044\n                dp[a] = dp[a];\n            } else {\n                // \u9078\u629e\u3057\u306a\u3044\u5834\u5408\u3068\u786c\u8ca8 i \u3092\u9078\u629e\u3059\u308b\u5834\u5408\u306e2\u3064\u306e\u9078\u629e\u80a2\u306e\u5408\u8a08\n                dp[a] = dp[a] + dp[a - coins[i - 1]];\n            }\n        }\n    }\n    return dp[amt];\n}\n</code></pre> coin_change_ii.cs<pre><code>[class]{coin_change_ii}-[func]{CoinChangeIIDPComp}\n</code></pre> coin_change_ii.go<pre><code>[class]{}-[func]{coinChangeIIDPComp}\n</code></pre> coin_change_ii.swift<pre><code>[class]{}-[func]{coinChangeIIDPComp}\n</code></pre> coin_change_ii.js<pre><code>[class]{}-[func]{coinChangeIIDPComp}\n</code></pre> coin_change_ii.ts<pre><code>[class]{}-[func]{coinChangeIIDPComp}\n</code></pre> coin_change_ii.dart<pre><code>[class]{}-[func]{coinChangeIIDPComp}\n</code></pre> coin_change_ii.rs<pre><code>[class]{}-[func]{coin_change_ii_dp_comp}\n</code></pre> coin_change_ii.c<pre><code>[class]{}-[func]{coinChangeIIDPComp}\n</code></pre> coin_change_ii.kt<pre><code>[class]{}-[func]{coinChangeIIDPComp}\n</code></pre> coin_change_ii.rb<pre><code>[class]{}-[func]{coin_change_ii_dp_comp}\n</code></pre> coin_change_ii.zig<pre><code>[class]{}-[func]{coinChangeIIDPComp}\n</code></pre>"},{"location":"chapter_graph/","title":"\u7b2c 9 \u7ae0 \u00a0 \u30b0\u30e9\u30d5","text":"<p>Abstract</p> <p>\u4eba\u751f\u306e\u65c5\u8def\u306b\u304a\u3044\u3066\u3001\u79c1\u305f\u3061\u306e\u4e00\u4eba\u4e00\u4eba\u306f\u30ce\u30fc\u30c9\u3067\u3042\u308a\u3001\u7121\u6570\u306e\u898b\u3048\u306a\u3044\u8fba\u3067\u7d50\u3070\u308c\u3066\u3044\u307e\u3059\u3002</p> <p>\u4e00\u3064\u4e00\u3064\u306e\u51fa\u4f1a\u3044\u3068\u5225\u308c\u304c\u3001\u3053\u306e\u5e83\u5927\u306a\u4eba\u751f\u306e\u30b0\u30e9\u30d5\u306b\u72ec\u7279\u306e\u5370\u3092\u6b8b\u3057\u3066\u3044\u304d\u307e\u3059\u3002</p>"},{"location":"chapter_graph/#_1","title":"\u7ae0\u306e\u5185\u5bb9","text":"<ul> <li>9.1 \u00a0 \u30b0\u30e9\u30d5</li> <li>9.2 \u00a0 \u30b0\u30e9\u30d5\u306e\u57fa\u672c\u64cd\u4f5c</li> <li>9.3 \u00a0 \u30b0\u30e9\u30d5\u306e\u8d70\u67fb</li> <li>9.4 \u00a0 \u307e\u3068\u3081</li> </ul>"},{"location":"chapter_graph/graph/","title":"9.1 \u00a0 \u30b0\u30e9\u30d5","text":"<p>\u30b0\u30e9\u30d5\u306f\u975e\u7dda\u5f62\u30c7\u30fc\u30bf\u69cb\u9020\u306e\u4e00\u7a2e\u3067\u3001\u9802\u70b9\u3068\u8fba\u3067\u69cb\u6210\u3055\u308c\u307e\u3059\u3002\u30b0\u30e9\u30d5\\(G\\)\u306f\u3001\u9802\u70b9\u306e\u96c6\u5408\\(V\\)\u3068\u8fba\u306e\u96c6\u5408\\(E\\)\u306e\u7d44\u307f\u5408\u308f\u305b\u3068\u3057\u3066\u62bd\u8c61\u7684\u306b\u8868\u73fe\u3067\u304d\u307e\u3059\u3002\u4ee5\u4e0b\u306e\u4f8b\u306f\u30015\u3064\u306e\u9802\u70b9\u30687\u3064\u306e\u8fba\u3092\u542b\u3080\u30b0\u30e9\u30d5\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002</p> \\[ \\begin{aligned} V &amp; = \\{ 1, 2, 3, 4, 5 \\} \\newline E &amp; = \\{ (1,2), (1,3), (1,5), (2,3), (2,4), (2,5), (4,5) \\} \\newline G &amp; = \\{ V, E \\} \\newline \\end{aligned} \\] <p>\u9802\u70b9\u3092\u30ce\u30fc\u30c9\u3001\u8fba\u3092\u30ce\u30fc\u30c9\u3092\u63a5\u7d9a\u3059\u308b\u53c2\u7167\uff08\u30dd\u30a4\u30f3\u30bf\uff09\u3068\u898b\u306a\u3059\u3068\u3001\u30b0\u30e9\u30d5\u306f\u9023\u7d50\u30ea\u30b9\u30c8\u304b\u3089\u62e1\u5f35\u3055\u308c\u305f\u30c7\u30fc\u30bf\u69cb\u9020\u3068\u3057\u3066\u898b\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u7dda\u5f62\u95a2\u4fc2\uff08\u9023\u7d50\u30ea\u30b9\u30c8\uff09\u3084\u5206\u5272\u7d71\u6cbb\u95a2\u4fc2\uff08\u6728\uff09\u3068\u6bd4\u8f03\u3057\u3066\u3001\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u95a2\u4fc2\uff08\u30b0\u30e9\u30d5\uff09\u306f\u81ea\u7531\u5ea6\u304c\u9ad8\u3044\u305f\u3081\u3001\u3088\u308a\u8907\u96d1\u3067\u3059\u3002</p> <p></p> <p> \u56f3 9-1 \u00a0 \u9023\u7d50\u30ea\u30b9\u30c8\u3001\u6728\u3001\u30b0\u30e9\u30d5\u306e\u95a2\u4fc2 </p>"},{"location":"chapter_graph/graph/#911","title":"9.1.1 \u00a0 \u30b0\u30e9\u30d5\u306e\u4e00\u822c\u7684\u306a\u7a2e\u985e\u3068\u7528\u8a9e","text":"<p>\u30b0\u30e9\u30d5\u306f\u3001\u8fba\u306b\u65b9\u5411\u304c\u3042\u308b\u304b\u3069\u3046\u304b\u306b\u3088\u3063\u3066\u7121\u5411\u30b0\u30e9\u30d5\u3068\u6709\u5411\u30b0\u30e9\u30d5\u306b\u5206\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\uff08\u4e0b\u56f3\u53c2\u7167\uff09\u3002</p> <ul> <li>\u7121\u5411\u30b0\u30e9\u30d5\u3067\u306f\u3001\u8fba\u306f2\u3064\u306e\u9802\u70b9\u9593\u306e\u300c\u53cc\u65b9\u5411\u300d\u63a5\u7d9a\u3092\u8868\u3057\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001Facebook\u306e\u300c\u53cb\u9054\u300d\u95a2\u4fc2\u3067\u3059\u3002</li> <li>\u6709\u5411\u30b0\u30e9\u30d5\u3067\u306f\u3001\u8fba\u306b\u65b9\u5411\u6027\u304c\u3042\u308a\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u8fba\\(A \\rightarrow B\\)\u3068\\(A \\leftarrow B\\)\u306f\u4e92\u3044\u306b\u72ec\u7acb\u3057\u3066\u3044\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001Instagram\u3084TikTok\u306e\u300c\u30d5\u30a9\u30ed\u30fc\u300d\u3068\u300c\u30d5\u30a9\u30ed\u30ef\u30fc\u300d\u306e\u95a2\u4fc2\u3067\u3059\u3002</li> </ul> <p></p> <p> \u56f3 9-2 \u00a0 \u6709\u5411\u30b0\u30e9\u30d5\u3068\u7121\u5411\u30b0\u30e9\u30d5 </p> <p>\u3059\u3079\u3066\u306e\u9802\u70b9\u304c\u63a5\u7d9a\u3055\u308c\u3066\u3044\u308b\u304b\u3069\u3046\u304b\u306b\u3088\u3063\u3066\u3001\u30b0\u30e9\u30d5\u306f\u9023\u7d50\u30b0\u30e9\u30d5\u3068\u975e\u9023\u7d50\u30b0\u30e9\u30d5\u306b\u5206\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\uff08\u4e0b\u56f3\u53c2\u7167\uff09\u3002</p> <ul> <li>\u9023\u7d50\u30b0\u30e9\u30d5\u3067\u306f\u3001\u4efb\u610f\u306e\u9802\u70b9\u304b\u3089\u958b\u59cb\u3057\u3066\u4ed6\u306e\u4efb\u610f\u306e\u9802\u70b9\u306b\u5230\u9054\u3059\u308b\u3053\u3068\u304c\u53ef\u80fd\u3067\u3059\u3002</li> <li>\u975e\u9023\u7d50\u30b0\u30e9\u30d5\u3067\u306f\u3001\u4efb\u610f\u306e\u958b\u59cb\u9802\u70b9\u304b\u3089\u5230\u9054\u3067\u304d\u306a\u3044\u9802\u70b9\u304c\u5c11\u306a\u304f\u3068\u30821\u3064\u5b58\u5728\u3057\u307e\u3059\u3002</li> </ul> <p></p> <p> \u56f3 9-3 \u00a0 \u9023\u7d50\u30b0\u30e9\u30d5\u3068\u975e\u9023\u7d50\u30b0\u30e9\u30d5 </p> <p>\u8fba\u306b\u91cd\u307f\u5909\u6570\u3092\u8ffd\u52a0\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u3001\u305d\u306e\u7d50\u679c\u3068\u3057\u3066\u91cd\u307f\u4ed8\u304d\u30b0\u30e9\u30d5\u304c\u751f\u307e\u308c\u307e\u3059\uff08\u4e0b\u56f3\u53c2\u7167\uff09\u3002\u4f8b\u3048\u3070\u3001Instagram\u3067\u306f\u3001\u30b7\u30b9\u30c6\u30e0\u304c\u3042\u306a\u305f\u3068\u4ed6\u306e\u30e6\u30fc\u30b6\u30fc\u3068\u306e\u9593\u306e\u76f8\u4e92\u4f5c\u7528\u30ec\u30d9\u30eb\uff08\u3044\u3044\u306d\u3001\u95b2\u89a7\u3001\u30b3\u30e1\u30f3\u30c8\u306a\u3069\uff09\u306b\u3088\u3063\u3066\u30d5\u30a9\u30ed\u30ef\u30fc\u3068\u30d5\u30a9\u30ed\u30fc\u4e2d\u306e\u30ea\u30b9\u30c8\u3092\u30bd\u30fc\u30c8\u3057\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306a\u76f8\u4e92\u4f5c\u7528\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u306f\u91cd\u307f\u4ed8\u304d\u30b0\u30e9\u30d5\u3067\u8868\u73fe\u3067\u304d\u307e\u3059\u3002</p> <p></p> <p> \u56f3 9-4 \u00a0 \u91cd\u307f\u4ed8\u304d\u30b0\u30e9\u30d5\u3068\u91cd\u307f\u306a\u3057\u30b0\u30e9\u30d5 </p> <p>\u30b0\u30e9\u30d5\u30c7\u30fc\u30bf\u69cb\u9020\u306b\u306f\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306a\u4e00\u822c\u7684\u306b\u4f7f\u7528\u3055\u308c\u308b\u7528\u8a9e\u304c\u3042\u308a\u307e\u3059\u3002</p> <ul> <li>\u96a3\u63a5\uff1a2\u3064\u306e\u9802\u70b9\u3092\u63a5\u7d9a\u3059\u308b\u8fba\u304c\u3042\u308b\u5834\u5408\u3001\u3053\u308c\u30892\u3064\u306e\u9802\u70b9\u306f\u300c\u96a3\u63a5\u300d\u3057\u3066\u3044\u308b\u3068\u8a00\u308f\u308c\u307e\u3059\u3002\u4e0a\u56f3\u3067\u306f\u3001\u9802\u70b91\u306e\u96a3\u63a5\u9802\u70b9\u306f\u9802\u70b92\u30013\u30015\u3067\u3059\u3002</li> <li>\u30d1\u30b9\uff1a\u9802\u70b9A\u304b\u3089\u9802\u70b9B\u307e\u3067\u306b\u901a\u904e\u3059\u308b\u8fba\u306e\u30b7\u30fc\u30b1\u30f3\u30b9\u3092\u3001A\u304b\u3089B\u3078\u306e\u30d1\u30b9\u3068\u547c\u3073\u307e\u3059\u3002\u4e0a\u56f3\u3067\u306f\u3001\u8fba\u306e\u30b7\u30fc\u30b1\u30f3\u30b91-5-2-4\u306f\u9802\u70b91\u304b\u3089\u9802\u70b94\u3078\u306e\u30d1\u30b9\u3067\u3059\u3002</li> <li>\u6b21\u6570\uff1a\u9802\u70b9\u304c\u6301\u3064\u8fba\u306e\u6570\u3067\u3059\u3002\u6709\u5411\u30b0\u30e9\u30d5\u306e\u5834\u5408\u3001\u5165\u6b21\u6570\u306f\u305d\u306e\u9802\u70b9\u3092\u6307\u3059\u8fba\u306e\u6570\u3001\u51fa\u6b21\u6570\u306f\u305d\u306e\u9802\u70b9\u304b\u3089\u51fa\u308b\u8fba\u306e\u6570\u3092\u6307\u3057\u307e\u3059\u3002</li> </ul>"},{"location":"chapter_graph/graph/#912","title":"9.1.2 \u00a0 \u30b0\u30e9\u30d5\u306e\u8868\u73fe","text":"<p>\u30b0\u30e9\u30d5\u306e\u4e00\u822c\u7684\u306a\u8868\u73fe\u306b\u306f\u300c\u96a3\u63a5\u884c\u5217\u300d\u3068\u300c\u96a3\u63a5\u30ea\u30b9\u30c8\u300d\u304c\u3042\u308a\u307e\u3059\u3002\u4ee5\u4e0b\u306e\u4f8b\u3067\u306f\u7121\u5411\u30b0\u30e9\u30d5\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002</p>"},{"location":"chapter_graph/graph/#1","title":"1. \u00a0 \u96a3\u63a5\u884c\u5217","text":"<p>\u30b0\u30e9\u30d5\u306e\u9802\u70b9\u6570\u3092\\(n\\)\u3068\u3059\u308b\u3068\u3001\u96a3\u63a5\u884c\u5217\u306f\\(n \\times n\\)\u306e\u884c\u5217\u3092\u4f7f\u7528\u3057\u3066\u30b0\u30e9\u30d5\u3092\u8868\u73fe\u3057\u307e\u3059\u3002\u5404\u884c\uff08\u5217\uff09\u306f\u9802\u70b9\u3092\u8868\u3057\u3001\u884c\u5217\u8981\u7d20\u306f\u8fba\u3092\u8868\u3057\u30012\u3064\u306e\u9802\u70b9\u9593\u306b\u8fba\u304c\u3042\u308b\u304b\u3069\u3046\u304b\u3092\\(1\\)\u307e\u305f\u306f\\(0\\)\u3067\u793a\u3057\u307e\u3059\u3002</p> <p>\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u96a3\u63a5\u884c\u5217\u3092\\(M\\)\u3001\u9802\u70b9\u306e\u30ea\u30b9\u30c8\u3092\\(V\\)\u3068\u3059\u308b\u3068\u3001\u884c\u5217\u8981\u7d20\\(M[i, j] = 1\\)\u306f\u9802\u70b9\\(V[i]\\)\u3068\u9802\u70b9\\(V[j]\\)\u306e\u9593\u306b\u8fba\u304c\u3042\u308b\u3053\u3068\u3092\u793a\u3057\u3001\u9006\u306b\\(M[i, j] = 0\\)\u306f2\u3064\u306e\u9802\u70b9\u9593\u306b\u8fba\u304c\u306a\u3044\u3053\u3068\u3092\u793a\u3057\u307e\u3059\u3002</p> <p></p> <p> \u56f3 9-5 \u00a0 \u96a3\u63a5\u884c\u5217\u306b\u3088\u308b\u30b0\u30e9\u30d5\u306e\u8868\u73fe </p> <p>\u96a3\u63a5\u884c\u5217\u306b\u306f\u4ee5\u4e0b\u306e\u7279\u6027\u304c\u3042\u308a\u307e\u3059\u3002</p> <ul> <li>\u9802\u70b9\u306f\u81ea\u5206\u81ea\u8eab\u306b\u63a5\u7d9a\u3059\u308b\u3053\u3068\u306f\u3067\u304d\u306a\u3044\u305f\u3081\u3001\u96a3\u63a5\u884c\u5217\u306e\u4e3b\u5bfe\u89d2\u7dda\u4e0a\u306e\u8981\u7d20\u306f\u610f\u5473\u304c\u3042\u308a\u307e\u305b\u3093\u3002</li> <li>\u7121\u5411\u30b0\u30e9\u30d5\u306e\u5834\u5408\u3001\u4e21\u65b9\u5411\u306e\u8fba\u306f\u7b49\u4fa1\u3067\u3042\u308b\u305f\u3081\u3001\u96a3\u63a5\u884c\u5217\u306f\u4e3b\u5bfe\u89d2\u7dda\u306b\u95a2\u3057\u3066\u5bfe\u79f0\u3067\u3059\u3002</li> <li>\u96a3\u63a5\u884c\u5217\u306e\u8981\u7d20\u3092\\(1\\)\u3068\\(0\\)\u304b\u3089\u91cd\u307f\u306b\u7f6e\u304d\u63db\u3048\u308b\u3053\u3068\u3067\u3001\u91cd\u307f\u4ed8\u304d\u30b0\u30e9\u30d5\u3092\u8868\u73fe\u3067\u304d\u307e\u3059\u3002</li> </ul> <p>\u96a3\u63a5\u884c\u5217\u3067\u30b0\u30e9\u30d5\u3092\u8868\u73fe\u3059\u308b\u5834\u5408\u3001\u884c\u5217\u8981\u7d20\u306b\u76f4\u63a5\u30a2\u30af\u30bb\u30b9\u3057\u3066\u8fba\u3092\u53d6\u5f97\u3067\u304d\u308b\u305f\u3081\u3001\u8ffd\u52a0\u3001\u524a\u9664\u3001\u691c\u7d22\u3001\u5909\u66f4\u306e\u64cd\u4f5c\u304c\u52b9\u7387\u7684\u3067\u3001\u3059\u3079\u3066\u6642\u9593\u8a08\u7b97\u91cf\\(O(1)\\)\u3067\u3059\u3002\u305f\u3060\u3057\u3001\u884c\u5217\u306e\u7a7a\u9593\u8a08\u7b97\u91cf\u306f\\(O(n^2)\\)\u3067\u3001\u3088\u308a\u591a\u304f\u306e\u30e1\u30e2\u30ea\u3092\u6d88\u8cbb\u3057\u307e\u3059\u3002</p>"},{"location":"chapter_graph/graph/#2","title":"2. \u00a0 \u96a3\u63a5\u30ea\u30b9\u30c8","text":"<p>\u96a3\u63a5\u30ea\u30b9\u30c8\u306f\\(n\\)\u500b\u306e\u9023\u7d50\u30ea\u30b9\u30c8\u3092\u4f7f\u7528\u3057\u3066\u30b0\u30e9\u30d5\u3092\u8868\u73fe\u3057\u3001\u5404\u9023\u7d50\u30ea\u30b9\u30c8\u30ce\u30fc\u30c9\u306f\u9802\u70b9\u3092\u8868\u3057\u307e\u3059\u3002\\(i\\)\u756a\u76ee\u306e\u9023\u7d50\u30ea\u30b9\u30c8\u306f\u9802\u70b9\\(i\\)\u306b\u5bfe\u5fdc\u3057\u3001\u3059\u3079\u3066\u306e\u96a3\u63a5\u9802\u70b9\uff08\u305d\u306e\u9802\u70b9\u306b\u63a5\u7d9a\u3055\u308c\u305f\u9802\u70b9\uff09\u3092\u542b\u307f\u307e\u3059\u3002\u4e0b\u56f3\u306f\u96a3\u63a5\u30ea\u30b9\u30c8\u3092\u4f7f\u7528\u3057\u3066\u683c\u7d0d\u3055\u308c\u305f\u30b0\u30e9\u30d5\u306e\u4f8b\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002</p> <p></p> <p> \u56f3 9-6 \u00a0 \u96a3\u63a5\u30ea\u30b9\u30c8\u306b\u3088\u308b\u30b0\u30e9\u30d5\u306e\u8868\u73fe </p> <p>\u96a3\u63a5\u30ea\u30b9\u30c8\u306f\u5b9f\u969b\u306e\u8fba\u306e\u307f\u3092\u683c\u7d0d\u3057\u3001\u8fba\u306e\u7dcf\u6570\u306f\\(n^2\\)\u3088\u308a\u3082\u306f\u308b\u304b\u306b\u5c11\u306a\u3044\u3053\u3068\u304c\u591a\u304f\u3001\u3088\u308a\u7a7a\u9593\u52b9\u7387\u7684\u3067\u3059\u3002\u305f\u3060\u3057\u3001\u96a3\u63a5\u30ea\u30b9\u30c8\u3067\u8fba\u3092\u898b\u3064\u3051\u308b\u306b\u306f\u9023\u7d50\u30ea\u30b9\u30c8\u3092\u8d70\u67fb\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u305f\u3081\u3001\u305d\u306e\u6642\u9593\u52b9\u7387\u306f\u96a3\u63a5\u884c\u5217\u307b\u3069\u826f\u304f\u3042\u308a\u307e\u305b\u3093\u3002</p> <p>\u4e0a\u56f3\u3092\u89b3\u5bdf\u3059\u308b\u3068\u3001\u96a3\u63a5\u30ea\u30b9\u30c8\u306e\u69cb\u9020\u306f\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u306e\u300c\u30c1\u30a7\u30a4\u30f3\u6cd5\u300d\u3068\u975e\u5e38\u306b\u4f3c\u3066\u3044\u308b\u305f\u3081\u3001\u540c\u69d8\u306e\u65b9\u6cd5\u3092\u4f7f\u7528\u3057\u3066\u52b9\u7387\u3092\u6700\u9069\u5316\u3067\u304d\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u304c\u9577\u3044\u5834\u5408\u3001\u305d\u308c\u3092AVL\u6728\u3084\u8d64\u9ed2\u6728\u306b\u5909\u63db\u3057\u3066\u3001\u6642\u9593\u52b9\u7387\u3092\\(O(n)\\)\u304b\u3089\\(O(\\log n)\\)\u306b\u6700\u9069\u5316\u3067\u304d\u307e\u3059\u3002\u9023\u7d50\u30ea\u30b9\u30c8\u3092\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u306b\u5909\u63db\u3059\u308b\u3053\u3068\u3067\u3001\u6642\u9593\u8a08\u7b97\u91cf\u3092\\(O(1)\\)\u306b\u524a\u6e1b\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002</p>"},{"location":"chapter_graph/graph/#913","title":"9.1.3 \u00a0 \u30b0\u30e9\u30d5\u306e\u4e00\u822c\u7684\u306a\u5fdc\u7528","text":"<p>\u4e0b\u8868\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u591a\u304f\u306e\u73fe\u5b9f\u4e16\u754c\u306e\u30b7\u30b9\u30c6\u30e0\u306f\u30b0\u30e9\u30d5\u3067\u30e2\u30c7\u30eb\u5316\u3067\u304d\u3001\u5bfe\u5fdc\u3059\u308b\u554f\u984c\u306f\u30b0\u30e9\u30d5\u8a08\u7b97\u554f\u984c\u306b\u524a\u6e1b\u3067\u304d\u307e\u3059\u3002</p> <p> \u8868 9-1 \u00a0 \u73fe\u5b9f\u751f\u6d3b\u306e\u4e00\u822c\u7684\u306a\u30b0\u30e9\u30d5 </p> \u9802\u70b9 \u8fba \u30b0\u30e9\u30d5\u8a08\u7b97\u554f\u984c \u30bd\u30fc\u30b7\u30e3\u30eb\u30cd\u30c3\u30c8\u30ef\u30fc\u30af \u30e6\u30fc\u30b6\u30fc \u30d5\u30a9\u30ed\u30fc / \u30d5\u30a9\u30ed\u30ef\u30fc\u95a2\u4fc2 \u6f5c\u5728\u7684\u30d5\u30a9\u30ed\u30fc\u63a8\u85a6 \u5730\u4e0b\u9244\u8def\u7dda \u99c5 \u99c5\u9593\u306e\u63a5\u7d9a\u6027 \u6700\u77ed\u30eb\u30fc\u30c8\u63a8\u85a6 \u592a\u967d\u7cfb \u5929\u4f53 \u5929\u4f53\u9593\u306e\u91cd\u529b \u60d1\u661f\u8ecc\u9053\u8a08\u7b97"},{"location":"chapter_graph/graph_operations/","title":"9.2 \u00a0 \u30b0\u30e9\u30d5\u306e\u57fa\u672c\u64cd\u4f5c","text":"<p>\u30b0\u30e9\u30d5\u306e\u57fa\u672c\u64cd\u4f5c\u306f\u300c\u8fba\u300d\u306b\u5bfe\u3059\u308b\u64cd\u4f5c\u3068\u300c\u9802\u70b9\u300d\u306b\u5bfe\u3059\u308b\u64cd\u4f5c\u306b\u5206\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u300c\u96a3\u63a5\u884c\u5217\u300d\u3068\u300c\u96a3\u63a5\u30ea\u30b9\u30c8\u300d\u306e2\u3064\u306e\u8868\u73fe\u65b9\u6cd5\u306e\u4e0b\u3067\u306f\u3001\u5b9f\u88c5\u304c\u7570\u306a\u308a\u307e\u3059\u3002</p>"},{"location":"chapter_graph/graph_operations/#921","title":"9.2.1 \u00a0 \u96a3\u63a5\u884c\u5217\u306b\u57fa\u3065\u304f\u5b9f\u88c5","text":"<p>\\(n\\)\u500b\u306e\u9802\u70b9\u3092\u6301\u3064\u7121\u5411\u30b0\u30e9\u30d5\u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408\u3001\u3055\u307e\u3056\u307e\u306a\u64cd\u4f5c\u306f\u4e0b\u56f3\u306e\u3088\u3046\u306b\u5b9f\u88c5\u3055\u308c\u307e\u3059\u3002</p> <ul> <li>\u8fba\u306e\u8ffd\u52a0\u307e\u305f\u306f\u524a\u9664\uff1a\u96a3\u63a5\u884c\u5217\u5185\u306e\u6307\u5b9a\u3055\u308c\u305f\u8fba\u3092\u76f4\u63a5\u5909\u66f4\u3057\u3001\\(O(1)\\)\u6642\u9593\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002\u7121\u5411\u30b0\u30e9\u30d5\u3067\u3042\u308b\u305f\u3081\u3001\u4e21\u65b9\u5411\u306e\u8fba\u3092\u540c\u6642\u306b\u66f4\u65b0\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002</li> <li>\u9802\u70b9\u306e\u8ffd\u52a0\uff1a\u96a3\u63a5\u884c\u5217\u306e\u672b\u5c3e\u306b\u884c\u3068\u5217\u3092\u8ffd\u52a0\u3057\u3001\u3059\u3079\u3066\\(0\\)\u3067\u57cb\u3081\u307e\u3059\u3002\\(O(n)\\)\u6642\u9593\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002</li> <li>\u9802\u70b9\u306e\u524a\u9664\uff1a\u96a3\u63a5\u884c\u5217\u5185\u306e\u884c\u3068\u5217\u3092\u524a\u9664\u3057\u307e\u3059\u3002\u6700\u60aa\u306e\u5834\u5408\u306f\u6700\u521d\u306e\u884c\u3068\u5217\u304c\u524a\u9664\u3055\u308c\u308b\u3068\u304d\u3067\u3001\\((n-1)^2\\)\u500b\u306e\u8981\u7d20\u3092\u300c\u4e0a\u3068\u5de6\u306b\u79fb\u52d5\u300d\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u3001\\(O(n^2)\\)\u6642\u9593\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002</li> <li>\u521d\u671f\u5316\uff1a\\(n\\)\u500b\u306e\u9802\u70b9\u3092\u6e21\u3057\u3001\u9577\u3055\\(n\\)\u306e\u9802\u70b9\u30ea\u30b9\u30c8<code>vertices</code>\u3092\u521d\u671f\u5316\u3057\u3001\\(O(n)\\)\u6642\u9593\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002\\(n \\times n\\)\u30b5\u30a4\u30ba\u306e\u96a3\u63a5\u884c\u5217<code>adjMat</code>\u3092\u521d\u671f\u5316\u3057\u3001\\(O(n^2)\\)\u6642\u9593\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002</li> </ul> \u96a3\u63a5\u884c\u5217\u306e\u521d\u671f\u5316\u8fba\u306e\u8ffd\u52a0\u8fba\u306e\u524a\u9664\u9802\u70b9\u306e\u8ffd\u52a0\u9802\u70b9\u306e\u524a\u9664 <p></p> <p></p> <p></p> <p></p> <p></p> <p> \u56f3 9-7 \u00a0 \u96a3\u63a5\u884c\u5217\u3067\u306e\u521d\u671f\u5316\u3001\u8fba\u306e\u8ffd\u52a0\u3068\u524a\u9664\u3001\u9802\u70b9\u306e\u8ffd\u52a0\u3068\u524a\u9664 </p> <p>\u4ee5\u4e0b\u306f\u96a3\u63a5\u884c\u5217\u3092\u4f7f\u7528\u3057\u3066\u8868\u73fe\u3055\u308c\u305f\u30b0\u30e9\u30d5\u306e\u5b9f\u88c5\u30b3\u30fc\u30c9\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig graph_adjacency_matrix.py<pre><code>class GraphAdjMat:\n    \"\"\"\u96a3\u63a5\u884c\u5217\u306b\u57fa\u3065\u304f\u7121\u5411\u30b0\u30e9\u30d5\u30af\u30e9\u30b9\"\"\"\n\n    def __init__(self, vertices: list[int], edges: list[list[int]]):\n        \"\"\"\u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf\"\"\"\n        # \u9802\u70b9\u30ea\u30b9\u30c8\u3001\u8981\u7d20\u306f\u300c\u9802\u70b9\u5024\u300d\u3092\u8868\u3057\u3001\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306f\u300c\u9802\u70b9\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u300d\u3092\u8868\u3059\n        self.vertices: list[int] = []\n        # \u96a3\u63a5\u884c\u5217\u3001\u884c\u3068\u5217\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306f\u300c\u9802\u70b9\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u300d\u306b\u5bfe\u5fdc\n        self.adj_mat: list[list[int]] = []\n        # \u9802\u70b9\u3092\u8ffd\u52a0\n        for val in vertices:\n            self.add_vertex(val)\n        # \u8fba\u3092\u8ffd\u52a0\n        # edges\u8981\u7d20\u306f\u9802\u70b9\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8868\u3059\n        for e in edges:\n            self.add_edge(e[0], e[1])\n\n    def size(self) -&gt; int:\n        \"\"\"\u9802\u70b9\u6570\u3092\u53d6\u5f97\"\"\"\n        return len(self.vertices)\n\n    def add_vertex(self, val: int):\n        \"\"\"\u9802\u70b9\u3092\u8ffd\u52a0\"\"\"\n        n = self.size()\n        # \u9802\u70b9\u30ea\u30b9\u30c8\u306b\u65b0\u3057\u3044\u9802\u70b9\u5024\u3092\u8ffd\u52a0\n        self.vertices.append(val)\n        # \u96a3\u63a5\u884c\u5217\u306b\u884c\u3092\u8ffd\u52a0\n        new_row = [0] * n\n        self.adj_mat.append(new_row)\n        # \u96a3\u63a5\u884c\u5217\u306b\u5217\u3092\u8ffd\u52a0\n        for row in self.adj_mat:\n            row.append(0)\n\n    def remove_vertex(self, index: int):\n        \"\"\"\u9802\u70b9\u3092\u524a\u9664\"\"\"\n        if index &gt;= self.size():\n            raise IndexError()\n        # \u9802\u70b9\u30ea\u30b9\u30c8\u304b\u3089`index`\u306e\u9802\u70b9\u3092\u524a\u9664\n        self.vertices.pop(index)\n        # \u96a3\u63a5\u884c\u5217\u304b\u3089`index`\u306e\u884c\u3092\u524a\u9664\n        self.adj_mat.pop(index)\n        # \u96a3\u63a5\u884c\u5217\u304b\u3089`index`\u306e\u5217\u3092\u524a\u9664\n        for row in self.adj_mat:\n            row.pop(index)\n\n    def add_edge(self, i: int, j: int):\n        \"\"\"\u8fba\u3092\u8ffd\u52a0\"\"\"\n        # \u30d1\u30e9\u30e1\u30fc\u30bfi\u3001j\u306f\u9802\u70b9\u8981\u7d20\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306b\u5bfe\u5fdc\n        # \u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306e\u7bc4\u56f2\u5916\u3068\u7b49\u4fa1\u6027\u3092\u51e6\u7406\n        if i &lt; 0 or j &lt; 0 or i &gt;= self.size() or j &gt;= self.size() or i == j:\n            raise IndexError()\n        # \u7121\u5411\u30b0\u30e9\u30d5\u3067\u306f\u3001\u96a3\u63a5\u884c\u5217\u306f\u4e3b\u5bfe\u89d2\u7dda\u306b\u3064\u3044\u3066\u5bfe\u79f0\u3001\u3059\u306a\u308f\u3061 (i, j) == (j, i) \u3092\u6e80\u305f\u3059\n        self.adj_mat[i][j] = 1\n        self.adj_mat[j][i] = 1\n\n    def remove_edge(self, i: int, j: int):\n        \"\"\"\u8fba\u3092\u524a\u9664\"\"\"\n        # \u30d1\u30e9\u30e1\u30fc\u30bfi\u3001j\u306f\u9802\u70b9\u8981\u7d20\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306b\u5bfe\u5fdc\n        # \u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306e\u7bc4\u56f2\u5916\u3068\u7b49\u4fa1\u6027\u3092\u51e6\u7406\n        if i &lt; 0 or j &lt; 0 or i &gt;= self.size() or j &gt;= self.size() or i == j:\n            raise IndexError()\n        self.adj_mat[i][j] = 0\n        self.adj_mat[j][i] = 0\n\n    def print(self):\n        \"\"\"\u96a3\u63a5\u884c\u5217\u3092\u51fa\u529b\"\"\"\n        print(\"\u9802\u70b9\u30ea\u30b9\u30c8 =\", self.vertices)\n        print(\"\u96a3\u63a5\u884c\u5217 =\")\n        print_matrix(self.adj_mat)\n</code></pre> graph_adjacency_matrix.cpp<pre><code>/* \u96a3\u63a5\u884c\u5217\u306b\u57fa\u3065\u304f\u7121\u5411\u30b0\u30e9\u30d5\u30af\u30e9\u30b9 */\nclass GraphAdjMat {\n    vector&lt;int&gt; vertices;       // \u9802\u70b9\u30ea\u30b9\u30c8\u3001\u8981\u7d20\u306f\u300c\u9802\u70b9\u5024\u300d\u3092\u8868\u3057\u3001\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306f\u300c\u9802\u70b9\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u300d\u3092\u8868\u3059\n    vector&lt;vector&lt;int&gt;&gt; adjMat; // \u96a3\u63a5\u884c\u5217\u3001\u884c\u3068\u5217\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306f\u300c\u9802\u70b9\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u300d\u306b\u5bfe\u5fdc\n\n  public:\n    /* \u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf */\n    GraphAdjMat(const vector&lt;int&gt; &amp;vertices, const vector&lt;vector&lt;int&gt;&gt; &amp;edges) {\n        // \u9802\u70b9\u3092\u8ffd\u52a0\n        for (int val : vertices) {\n            addVertex(val);\n        }\n        // \u8fba\u3092\u8ffd\u52a0\n        // \u8fba\u306e\u8981\u7d20\u306f\u9802\u70b9\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8868\u3059\n        for (const vector&lt;int&gt; &amp;edge : edges) {\n            addEdge(edge[0], edge[1]);\n        }\n    }\n\n    /* \u9802\u70b9\u6570\u3092\u53d6\u5f97 */\n    int size() const {\n        return vertices.size();\n    }\n\n    /* \u9802\u70b9\u3092\u8ffd\u52a0 */\n    void addVertex(int val) {\n        int n = size();\n        // \u9802\u70b9\u30ea\u30b9\u30c8\u306b\u65b0\u3057\u3044\u9802\u70b9\u5024\u3092\u8ffd\u52a0\n        vertices.push_back(val);\n        // \u96a3\u63a5\u884c\u5217\u306b\u884c\u3092\u8ffd\u52a0\n        adjMat.emplace_back(vector&lt;int&gt;(n, 0));\n        // \u96a3\u63a5\u884c\u5217\u306b\u5217\u3092\u8ffd\u52a0\n        for (vector&lt;int&gt; &amp;row : adjMat) {\n            row.push_back(0);\n        }\n    }\n\n    /* \u9802\u70b9\u3092\u524a\u9664 */\n    void removeVertex(int index) {\n        if (index &gt;= size()) {\n            throw out_of_range(\"Vertex does not exist\");\n        }\n        // \u9802\u70b9\u30ea\u30b9\u30c8\u304b\u3089`index`\u306e\u9802\u70b9\u3092\u524a\u9664\n        vertices.erase(vertices.begin() + index);\n        // \u96a3\u63a5\u884c\u5217\u304b\u3089`index`\u306e\u884c\u3092\u524a\u9664\n        adjMat.erase(adjMat.begin() + index);\n        // \u96a3\u63a5\u884c\u5217\u304b\u3089`index`\u306e\u5217\u3092\u524a\u9664\n        for (vector&lt;int&gt; &amp;row : adjMat) {\n            row.erase(row.begin() + index);\n        }\n    }\n\n    /* \u8fba\u3092\u8ffd\u52a0 */\n    // \u30d1\u30e9\u30e1\u30fc\u30bfi\u3001j\u306f\u9802\u70b9\u8981\u7d20\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306b\u5bfe\u5fdc\n    void addEdge(int i, int j) {\n        // \u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u7bc4\u56f2\u5916\u3068\u7b49\u4fa1\u6027\u3092\u51e6\u7406\n        if (i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j) {\n            throw out_of_range(\"Vertex does not exist\");\n        }\n        // \u7121\u5411\u30b0\u30e9\u30d5\u3067\u306f\u3001\u96a3\u63a5\u884c\u5217\u306f\u4e3b\u5bfe\u89d2\u7dda\u306b\u3064\u3044\u3066\u5bfe\u79f0\u3001\u5373\u3061(i, j) == (j, i)\u3092\u6e80\u305f\u3059\n        adjMat[i][j] = 1;\n        adjMat[j][i] = 1;\n    }\n\n    /* \u8fba\u3092\u524a\u9664 */\n    // \u30d1\u30e9\u30e1\u30fc\u30bfi\u3001j\u306f\u9802\u70b9\u8981\u7d20\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306b\u5bfe\u5fdc\n    void removeEdge(int i, int j) {\n        // \u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u7bc4\u56f2\u5916\u3068\u7b49\u4fa1\u6027\u3092\u51e6\u7406\n        if (i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j) {\n            throw out_of_range(\"Vertex does not exist\");\n        }\n        adjMat[i][j] = 0;\n        adjMat[j][i] = 0;\n    }\n\n    /* \u96a3\u63a5\u884c\u5217\u3092\u5370\u5237 */\n    void print() {\n        cout &lt;&lt; \"\u9802\u70b9\u30ea\u30b9\u30c8 = \";\n        printVector(vertices);\n        cout &lt;&lt; \"\u96a3\u63a5\u884c\u5217 =\" &lt;&lt; endl;\n        printVectorMatrix(adjMat);\n    }\n};\n</code></pre> graph_adjacency_matrix.java<pre><code>/* \u96a3\u63a5\u884c\u5217\u306b\u57fa\u3065\u304f\u7121\u5411\u30b0\u30e9\u30d5\u30af\u30e9\u30b9 */\nclass GraphAdjMat {\n    List&lt;Integer&gt; vertices; // \u9802\u70b9\u30ea\u30b9\u30c8\u3001\u8981\u7d20\u306f\u300c\u9802\u70b9\u5024\u300d\u3092\u8868\u3057\u3001\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306f\u300c\u9802\u70b9\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u300d\u3092\u8868\u3059\n    List&lt;List&lt;Integer&gt;&gt; adjMat; // \u96a3\u63a5\u884c\u5217\u3001\u884c\u3068\u5217\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306f\u300c\u9802\u70b9\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u300d\u306b\u5bfe\u5fdc\n\n    /* \u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf */\n    public GraphAdjMat(int[] vertices, int[][] edges) {\n        this.vertices = new ArrayList&lt;&gt;();\n        this.adjMat = new ArrayList&lt;&gt;();\n        // \u9802\u70b9\u3092\u8ffd\u52a0\n        for (int val : vertices) {\n            addVertex(val);\n        }\n        // \u8fba\u3092\u8ffd\u52a0\n        // \u8fba\u306e\u8981\u7d20\u306f\u9802\u70b9\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8868\u3059\n        for (int[] e : edges) {\n            addEdge(e[0], e[1]);\n        }\n    }\n\n    /* \u9802\u70b9\u6570\u3092\u53d6\u5f97 */\n    public int size() {\n        return vertices.size();\n    }\n\n    /* \u9802\u70b9\u3092\u8ffd\u52a0 */\n    public void addVertex(int val) {\n        int n = size();\n        // \u9802\u70b9\u30ea\u30b9\u30c8\u306b\u65b0\u3057\u3044\u9802\u70b9\u5024\u3092\u8ffd\u52a0\n        vertices.add(val);\n        // \u96a3\u63a5\u884c\u5217\u306b\u884c\u3092\u8ffd\u52a0\n        List&lt;Integer&gt; newRow = new ArrayList&lt;&gt;(n);\n        for (int j = 0; j &lt; n; j++) {\n            newRow.add(0);\n        }\n        adjMat.add(newRow);\n        // \u96a3\u63a5\u884c\u5217\u306b\u5217\u3092\u8ffd\u52a0\n        for (List&lt;Integer&gt; row : adjMat) {\n            row.add(0);\n        }\n    }\n\n    /* \u9802\u70b9\u3092\u524a\u9664 */\n    public void removeVertex(int index) {\n        if (index &gt;= size())\n            throw new IndexOutOfBoundsException();\n        // \u9802\u70b9\u30ea\u30b9\u30c8\u304b\u3089 `index` \u306e\u9802\u70b9\u3092\u524a\u9664\n        vertices.remove(index);\n        // \u96a3\u63a5\u884c\u5217\u304b\u3089 `index` \u306e\u884c\u3092\u524a\u9664\n        adjMat.remove(index);\n        // \u96a3\u63a5\u884c\u5217\u304b\u3089 `index` \u306e\u5217\u3092\u524a\u9664\n        for (List&lt;Integer&gt; row : adjMat) {\n            row.remove(index);\n        }\n    }\n\n    /* \u8fba\u3092\u8ffd\u52a0 */\n    // \u30d1\u30e9\u30e1\u30fc\u30bf i\u3001j \u306f\u9802\u70b9\u8981\u7d20\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306b\u5bfe\u5fdc\n    public void addEdge(int i, int j) {\n        // \u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306e\u7bc4\u56f2\u5916\u3068\u7b49\u4fa1\u6027\u3092\u51e6\u7406\n        if (i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j)\n            throw new IndexOutOfBoundsException();\n        // \u7121\u5411\u30b0\u30e9\u30d5\u3067\u306f\u3001\u96a3\u63a5\u884c\u5217\u306f\u4e3b\u5bfe\u89d2\u7dda\u306b\u3064\u3044\u3066\u5bfe\u79f0\u3001\u3059\u306a\u308f\u3061 (i, j) == (j, i) \u3092\u6e80\u305f\u3059\n        adjMat.get(i).set(j, 1);\n        adjMat.get(j).set(i, 1);\n    }\n\n    /* \u8fba\u3092\u524a\u9664 */\n    // \u30d1\u30e9\u30e1\u30fc\u30bf i\u3001j \u306f\u9802\u70b9\u8981\u7d20\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306b\u5bfe\u5fdc\n    public void removeEdge(int i, int j) {\n        // \u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306e\u7bc4\u56f2\u5916\u3068\u7b49\u4fa1\u6027\u3092\u51e6\u7406\n        if (i &lt; 0 || j &lt; 0 || i &gt;= size() || j &gt;= size() || i == j)\n            throw new IndexOutOfBoundsException();\n        adjMat.get(i).set(j, 0);\n        adjMat.get(j).set(i, 0);\n    }\n\n    /* \u96a3\u63a5\u884c\u5217\u3092\u51fa\u529b */\n    public void print() {\n        System.out.print(\"\u9802\u70b9\u30ea\u30b9\u30c8 = \");\n        System.out.println(vertices);\n        System.out.println(\"\u96a3\u63a5\u884c\u5217 =\");\n        PrintUtil.printMatrix(adjMat);\n    }\n}\n</code></pre> graph_adjacency_matrix.cs<pre><code>[class]{GraphAdjMat}-[func]{}\n</code></pre> graph_adjacency_matrix.go<pre><code>[class]{graphAdjMat}-[func]{}\n</code></pre> graph_adjacency_matrix.swift<pre><code>[class]{GraphAdjMat}-[func]{}\n</code></pre> graph_adjacency_matrix.js<pre><code>[class]{GraphAdjMat}-[func]{}\n</code></pre> graph_adjacency_matrix.ts<pre><code>[class]{GraphAdjMat}-[func]{}\n</code></pre> graph_adjacency_matrix.dart<pre><code>[class]{GraphAdjMat}-[func]{}\n</code></pre> graph_adjacency_matrix.rs<pre><code>[class]{GraphAdjMat}-[func]{}\n</code></pre> graph_adjacency_matrix.c<pre><code>[class]{GraphAdjMat}-[func]{}\n</code></pre> graph_adjacency_matrix.kt<pre><code>[class]{GraphAdjMat}-[func]{}\n</code></pre> graph_adjacency_matrix.rb<pre><code>[class]{GraphAdjMat}-[func]{}\n</code></pre> graph_adjacency_matrix.zig<pre><code>[class]{GraphAdjMat}-[func]{}\n</code></pre>"},{"location":"chapter_graph/graph_operations/#922","title":"9.2.2 \u00a0 \u96a3\u63a5\u30ea\u30b9\u30c8\u306b\u57fa\u3065\u304f\u5b9f\u88c5","text":"<p>\u7dcf\u8a08\\(n\\)\u500b\u306e\u9802\u70b9\u3068\\(m\\)\u500b\u306e\u8fba\u3092\u6301\u3064\u7121\u5411\u30b0\u30e9\u30d5\u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408\u3001\u3055\u307e\u3056\u307e\u306a\u64cd\u4f5c\u306f\u4e0b\u56f3\u306e\u3088\u3046\u306b\u5b9f\u88c5\u3067\u304d\u307e\u3059\u3002</p> <ul> <li>\u8fba\u306e\u8ffd\u52a0\uff1a\u5bfe\u5fdc\u3059\u308b\u9802\u70b9\u306e\u9023\u7d50\u30ea\u30b9\u30c8\u306e\u672b\u5c3e\u306b\u8fba\u3092\u8ffd\u52a0\u3059\u308b\u3060\u3051\u3067\u3001\\(O(1)\\)\u6642\u9593\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002\u7121\u5411\u30b0\u30e9\u30d5\u3067\u3042\u308b\u305f\u3081\u3001\u4e21\u65b9\u5411\u306b\u540c\u6642\u306b\u8fba\u3092\u8ffd\u52a0\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002</li> <li>\u8fba\u306e\u524a\u9664\uff1a\u5bfe\u5fdc\u3059\u308b\u9802\u70b9\u306e\u9023\u7d50\u30ea\u30b9\u30c8\u5185\u3067\u6307\u5b9a\u3055\u308c\u305f\u8fba\u3092\u898b\u3064\u3051\u3066\u524a\u9664\u3057\u3001\\(O(m)\\)\u6642\u9593\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002\u7121\u5411\u30b0\u30e9\u30d5\u3067\u306f\u3001\u4e21\u65b9\u5411\u306e\u8fba\u3092\u540c\u6642\u306b\u524a\u9664\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002</li> <li>\u9802\u70b9\u306e\u8ffd\u52a0\uff1a\u96a3\u63a5\u30ea\u30b9\u30c8\u306b\u9023\u7d50\u30ea\u30b9\u30c8\u3092\u8ffd\u52a0\u3057\u3001\u65b0\u3057\u3044\u9802\u70b9\u3092\u30ea\u30b9\u30c8\u306e\u30d8\u30c3\u30c9\u30ce\u30fc\u30c9\u306b\u3057\u3001\\(O(1)\\)\u6642\u9593\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002</li> <li>\u9802\u70b9\u306e\u524a\u9664\uff1a\u96a3\u63a5\u30ea\u30b9\u30c8\u5168\u4f53\u3092\u8d70\u67fb\u3057\u3001\u6307\u5b9a\u3055\u308c\u305f\u9802\u70b9\u3092\u542b\u3080\u3059\u3079\u3066\u306e\u8fba\u3092\u524a\u9664\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u3001\\(O(n + m)\\)\u6642\u9593\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002</li> <li>\u521d\u671f\u5316\uff1a\u96a3\u63a5\u30ea\u30b9\u30c8\u306b\\(n\\)\u500b\u306e\u9802\u70b9\u3068\\(2m\\)\u500b\u306e\u8fba\u3092\u4f5c\u6210\u3057\u3001\\(O(n + m)\\)\u6642\u9593\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002</li> </ul> \u96a3\u63a5\u30ea\u30b9\u30c8\u306e\u521d\u671f\u5316\u8fba\u306e\u8ffd\u52a0\u8fba\u306e\u524a\u9664\u9802\u70b9\u306e\u8ffd\u52a0\u9802\u70b9\u306e\u524a\u9664 <p></p> <p></p> <p></p> <p></p> <p></p> <p> \u56f3 9-8 \u00a0 \u96a3\u63a5\u30ea\u30b9\u30c8\u3067\u306e\u521d\u671f\u5316\u3001\u8fba\u306e\u8ffd\u52a0\u3068\u524a\u9664\u3001\u9802\u70b9\u306e\u8ffd\u52a0\u3068\u524a\u9664 </p> <p>\u4ee5\u4e0b\u306f\u96a3\u63a5\u30ea\u30b9\u30c8\u306e\u30b3\u30fc\u30c9\u5b9f\u88c5\u3067\u3059\u3002\u4e0a\u56f3\u3068\u6bd4\u8f03\u3057\u3066\u3001\u5b9f\u969b\u306e\u30b3\u30fc\u30c9\u306b\u306f\u4ee5\u4e0b\u306e\u9055\u3044\u304c\u3042\u308a\u307e\u3059\u3002</p> <ul> <li>\u9802\u70b9\u306e\u8ffd\u52a0\u3068\u524a\u9664\u306e\u4fbf\u5b9c\u3001\u304a\u3088\u3073\u30b3\u30fc\u30c9\u306e\u7c21\u7d20\u5316\u306e\u305f\u3081\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u306e\u4ee3\u308f\u308a\u306b\u30ea\u30b9\u30c8\uff08\u52d5\u7684\u914d\u5217\uff09\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002</li> <li>\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u3092\u4f7f\u7528\u3057\u3066\u96a3\u63a5\u30ea\u30b9\u30c8\u3092\u683c\u7d0d\u3057\u3001<code>key</code>\u304c\u9802\u70b9\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u3001<code>value</code>\u304c\u305d\u306e\u9802\u70b9\u306e\u96a3\u63a5\u9802\u70b9\u306e\u30ea\u30b9\u30c8\uff08\u9023\u7d50\u30ea\u30b9\u30c8\uff09\u3067\u3059\u3002</li> </ul> <p>\u3055\u3089\u306b\u3001\u96a3\u63a5\u30ea\u30b9\u30c8\u3067\u9802\u70b9\u3092\u8868\u73fe\u3059\u308b\u305f\u3081\u306b<code>Vertex</code>\u30af\u30e9\u30b9\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002\u305d\u306e\u7406\u7531\u306f\uff1a\u96a3\u63a5\u884c\u5217\u306e\u3088\u3046\u306b\u30ea\u30b9\u30c8\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u4f7f\u7528\u3057\u3066\u7570\u306a\u308b\u9802\u70b9\u3092\u533a\u5225\u3059\u308b\u5834\u5408\u3001\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\\(i\\)\u306e\u9802\u70b9\u3092\u524a\u9664\u3057\u305f\u3044\u5834\u5408\u3001\u96a3\u63a5\u30ea\u30b9\u30c8\u5168\u4f53\u3092\u8d70\u67fb\u3057\u3001\\(i\\)\u3088\u308a\u5927\u304d\u3044\u3059\u3079\u3066\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u30921\u3064\u305a\u3064\u6e1b\u5c11\u3055\u305b\u308b\u5fc5\u8981\u304c\u3042\u308a\u3001\u3053\u308c\u306f\u975e\u5e38\u306b\u975e\u52b9\u7387\u7684\u3067\u3059\u3002\u3057\u304b\u3057\u3001\u5404\u9802\u70b9\u304c\u4e00\u610f\u306e<code>Vertex</code>\u30a4\u30f3\u30b9\u30bf\u30f3\u30b9\u3067\u3042\u308b\u5834\u5408\u3001\u9802\u70b9\u3092\u524a\u9664\u3057\u3066\u3082\u4ed6\u306e\u9802\u70b9\u306b\u5909\u66f4\u3092\u52a0\u3048\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u305b\u3093\u3002</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig graph_adjacency_list.py<pre><code>class GraphAdjList:\n    \"\"\"\u96a3\u63a5\u30ea\u30b9\u30c8\u306b\u57fa\u3065\u304f\u7121\u5411\u30b0\u30e9\u30d5\u30af\u30e9\u30b9\"\"\"\n\n    def __init__(self, edges: list[list[Vertex]]):\n        \"\"\"\u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf\"\"\"\n        # \u96a3\u63a5\u30ea\u30b9\u30c8\u3001\u30ad\u30fc: \u9802\u70b9\u3001\u5024: \u305d\u306e\u9802\u70b9\u306e\u96a3\u63a5\u3059\u308b\u5168\u9802\u70b9\n        self.adj_list = dict[Vertex, list[Vertex]]()\n        # \u3059\u3079\u3066\u306e\u9802\u70b9\u3068\u8fba\u3092\u8ffd\u52a0\n        for edge in edges:\n            self.add_vertex(edge[0])\n            self.add_vertex(edge[1])\n            self.add_edge(edge[0], edge[1])\n\n    def size(self) -&gt; int:\n        \"\"\"\u9802\u70b9\u6570\u3092\u53d6\u5f97\"\"\"\n        return len(self.adj_list)\n\n    def add_edge(self, vet1: Vertex, vet2: Vertex):\n        \"\"\"\u8fba\u3092\u8ffd\u52a0\"\"\"\n        if vet1 not in self.adj_list or vet2 not in self.adj_list or vet1 == vet2:\n            raise ValueError()\n        # \u8fba vet1 - vet2 \u3092\u8ffd\u52a0\n        self.adj_list[vet1].append(vet2)\n        self.adj_list[vet2].append(vet1)\n\n    def remove_edge(self, vet1: Vertex, vet2: Vertex):\n        \"\"\"\u8fba\u3092\u524a\u9664\"\"\"\n        if vet1 not in self.adj_list or vet2 not in self.adj_list or vet1 == vet2:\n            raise ValueError()\n        # \u8fba vet1 - vet2 \u3092\u524a\u9664\n        self.adj_list[vet1].remove(vet2)\n        self.adj_list[vet2].remove(vet1)\n\n    def add_vertex(self, vet: Vertex):\n        \"\"\"\u9802\u70b9\u3092\u8ffd\u52a0\"\"\"\n        if vet in self.adj_list:\n            return\n        # \u96a3\u63a5\u30ea\u30b9\u30c8\u306b\u65b0\u3057\u3044\u9023\u7d50\u30ea\u30b9\u30c8\u3092\u8ffd\u52a0\n        self.adj_list[vet] = []\n\n    def remove_vertex(self, vet: Vertex):\n        \"\"\"\u9802\u70b9\u3092\u524a\u9664\"\"\"\n        if vet not in self.adj_list:\n            raise ValueError()\n        # \u96a3\u63a5\u30ea\u30b9\u30c8\u304b\u3089\u9802\u70b9vet\u306b\u5bfe\u5fdc\u3059\u308b\u9023\u7d50\u30ea\u30b9\u30c8\u3092\u524a\u9664\n        self.adj_list.pop(vet)\n        # \u4ed6\u306e\u9802\u70b9\u306e\u9023\u7d50\u30ea\u30b9\u30c8\u3092\u8d70\u67fb\u3057\u3001vet\u3092\u542b\u3080\u3059\u3079\u3066\u306e\u8fba\u3092\u524a\u9664\n        for vertex in self.adj_list:\n            if vet in self.adj_list[vertex]:\n                self.adj_list[vertex].remove(vet)\n\n    def print(self):\n        \"\"\"\u96a3\u63a5\u30ea\u30b9\u30c8\u3092\u51fa\u529b\"\"\"\n        print(\"\u96a3\u63a5\u30ea\u30b9\u30c8 =\")\n        for vertex in self.adj_list:\n            tmp = [v.val for v in self.adj_list[vertex]]\n            print(f\"{vertex.val}: {tmp},\")\n</code></pre> graph_adjacency_list.cpp<pre><code>/* \u96a3\u63a5\u30ea\u30b9\u30c8\u306b\u57fa\u3065\u304f\u7121\u5411\u30b0\u30e9\u30d5\u30af\u30e9\u30b9 */\nclass GraphAdjList {\n  public:\n    // \u96a3\u63a5\u30ea\u30b9\u30c8\u3001\u30ad\u30fc\uff1a\u9802\u70b9\u3001\u5024\uff1a\u305d\u306e\u9802\u70b9\u306e\u3059\u3079\u3066\u306e\u96a3\u63a5\u9802\u70b9\n    unordered_map&lt;Vertex *, vector&lt;Vertex *&gt;&gt; adjList;\n\n    /* \u30d9\u30af\u30bf\u30fc\u304b\u3089\u6307\u5b9a\u3055\u308c\u305f\u30ce\u30fc\u30c9\u3092\u524a\u9664 */\n    void remove(vector&lt;Vertex *&gt; &amp;vec, Vertex *vet) {\n        for (int i = 0; i &lt; vec.size(); i++) {\n            if (vec[i] == vet) {\n                vec.erase(vec.begin() + i);\n                break;\n            }\n        }\n    }\n\n    /* \u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf */\n    GraphAdjList(const vector&lt;vector&lt;Vertex *&gt;&gt; &amp;edges) {\n        // \u3059\u3079\u3066\u306e\u9802\u70b9\u3068\u8fba\u3092\u8ffd\u52a0\n        for (const vector&lt;Vertex *&gt; &amp;edge : edges) {\n            addVertex(edge[0]);\n            addVertex(edge[1]);\n            addEdge(edge[0], edge[1]);\n        }\n    }\n\n    /* \u9802\u70b9\u6570\u3092\u53d6\u5f97 */\n    int size() {\n        return adjList.size();\n    }\n\n    /* \u8fba\u3092\u8ffd\u52a0 */\n    void addEdge(Vertex *vet1, Vertex *vet2) {\n        if (!adjList.count(vet1) || !adjList.count(vet2) || vet1 == vet2)\n            throw invalid_argument(\"Vertex does not exist\");\n        // \u8fba vet1 - vet2 \u3092\u8ffd\u52a0\n        adjList[vet1].push_back(vet2);\n        adjList[vet2].push_back(vet1);\n    }\n\n    /* \u8fba\u3092\u524a\u9664 */\n    void removeEdge(Vertex *vet1, Vertex *vet2) {\n        if (!adjList.count(vet1) || !adjList.count(vet2) || vet1 == vet2)\n            throw invalid_argument(\"Vertex does not exist\");\n        // \u8fba vet1 - vet2 \u3092\u524a\u9664\n        remove(adjList[vet1], vet2);\n        remove(adjList[vet2], vet1);\n    }\n\n    /* \u9802\u70b9\u3092\u8ffd\u52a0 */\n    void addVertex(Vertex *vet) {\n        if (adjList.count(vet))\n            return;\n        // \u96a3\u63a5\u30ea\u30b9\u30c8\u306b\u65b0\u3057\u3044\u9023\u7d50\u30ea\u30b9\u30c8\u3092\u8ffd\u52a0\n        adjList[vet] = vector&lt;Vertex *&gt;();\n    }\n\n    /* \u9802\u70b9\u3092\u524a\u9664 */\n    void removeVertex(Vertex *vet) {\n        if (!adjList.count(vet))\n            throw invalid_argument(\"Vertex does not exist\");\n        // \u96a3\u63a5\u30ea\u30b9\u30c8\u304b\u3089\u9802\u70b9vet\u306b\u5bfe\u5fdc\u3059\u308b\u9023\u7d50\u30ea\u30b9\u30c8\u3092\u524a\u9664\n        adjList.erase(vet);\n        // \u4ed6\u306e\u9802\u70b9\u306e\u9023\u7d50\u30ea\u30b9\u30c8\u3092\u8d70\u67fb\u3057\u3001vet\u3092\u542b\u3080\u3059\u3079\u3066\u306e\u8fba\u3092\u524a\u9664\n        for (auto &amp;adj : adjList) {\n            remove(adj.second, vet);\n        }\n    }\n\n    /* \u96a3\u63a5\u30ea\u30b9\u30c8\u3092\u5370\u5237 */\n    void print() {\n        cout &lt;&lt; \"\u96a3\u63a5\u30ea\u30b9\u30c8 =\" &lt;&lt; endl;\n        for (auto &amp;adj : adjList) {\n            const auto &amp;key = adj.first;\n            const auto &amp;vec = adj.second;\n            cout &lt;&lt; key-&gt;val &lt;&lt; \": \";\n            printVector(vetsToVals(vec));\n        }\n    }\n};\n</code></pre> graph_adjacency_list.java<pre><code>/* \u96a3\u63a5\u30ea\u30b9\u30c8\u306b\u57fa\u3065\u304f\u7121\u5411\u30b0\u30e9\u30d5\u30af\u30e9\u30b9 */\nclass GraphAdjList {\n    // \u96a3\u63a5\u30ea\u30b9\u30c8\u3001\u30ad\u30fc: \u9802\u70b9\u3001\u5024: \u305d\u306e\u9802\u70b9\u306e\u3059\u3079\u3066\u306e\u96a3\u63a5\u9802\u70b9\n    Map&lt;Vertex, List&lt;Vertex&gt;&gt; adjList;\n\n    /* \u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf */\n    public GraphAdjList(Vertex[][] edges) {\n        this.adjList = new HashMap&lt;&gt;();\n        // \u3059\u3079\u3066\u306e\u9802\u70b9\u3068\u8fba\u3092\u8ffd\u52a0\n        for (Vertex[] edge : edges) {\n            addVertex(edge[0]);\n            addVertex(edge[1]);\n            addEdge(edge[0], edge[1]);\n        }\n    }\n\n    /* \u9802\u70b9\u6570\u3092\u53d6\u5f97 */\n    public int size() {\n        return adjList.size();\n    }\n\n    /* \u8fba\u3092\u8ffd\u52a0 */\n    public void addEdge(Vertex vet1, Vertex vet2) {\n        if (!adjList.containsKey(vet1) || !adjList.containsKey(vet2) || vet1 == vet2)\n            throw new IllegalArgumentException();\n        // \u8fba vet1 - vet2 \u3092\u8ffd\u52a0\n        adjList.get(vet1).add(vet2);\n        adjList.get(vet2).add(vet1);\n    }\n\n    /* \u8fba\u3092\u524a\u9664 */\n    public void removeEdge(Vertex vet1, Vertex vet2) {\n        if (!adjList.containsKey(vet1) || !adjList.containsKey(vet2) || vet1 == vet2)\n            throw new IllegalArgumentException();\n        // \u8fba vet1 - vet2 \u3092\u524a\u9664\n        adjList.get(vet1).remove(vet2);\n        adjList.get(vet2).remove(vet1);\n    }\n\n    /* \u9802\u70b9\u3092\u8ffd\u52a0 */\n    public void addVertex(Vertex vet) {\n        if (adjList.containsKey(vet))\n            return;\n        // \u96a3\u63a5\u30ea\u30b9\u30c8\u306b\u65b0\u3057\u3044\u9023\u7d50\u30ea\u30b9\u30c8\u3092\u8ffd\u52a0\n        adjList.put(vet, new ArrayList&lt;&gt;());\n    }\n\n    /* \u9802\u70b9\u3092\u524a\u9664 */\n    public void removeVertex(Vertex vet) {\n        if (!adjList.containsKey(vet))\n            throw new IllegalArgumentException();\n        // \u96a3\u63a5\u30ea\u30b9\u30c8\u304b\u3089\u9802\u70b9 vet \u306b\u5bfe\u5fdc\u3059\u308b\u9023\u7d50\u30ea\u30b9\u30c8\u3092\u524a\u9664\n        adjList.remove(vet);\n        // \u4ed6\u306e\u9802\u70b9\u306e\u9023\u7d50\u30ea\u30b9\u30c8\u3092\u8d70\u67fb\u3057\u3001vet \u3092\u542b\u3080\u3059\u3079\u3066\u306e\u8fba\u3092\u524a\u9664\n        for (List&lt;Vertex&gt; list : adjList.values()) {\n            list.remove(vet);\n        }\n    }\n\n    /* \u96a3\u63a5\u30ea\u30b9\u30c8\u3092\u51fa\u529b */\n    public void print() {\n        System.out.println(\"\u96a3\u63a5\u30ea\u30b9\u30c8 =\");\n        for (Map.Entry&lt;Vertex, List&lt;Vertex&gt;&gt; pair : adjList.entrySet()) {\n            List&lt;Integer&gt; tmp = new ArrayList&lt;&gt;();\n            for (Vertex vertex : pair.getValue())\n                tmp.add(vertex.val);\n            System.out.println(pair.getKey().val + \": \" + tmp + \",\");\n        }\n    }\n}\n</code></pre> graph_adjacency_list.cs<pre><code>[class]{GraphAdjList}-[func]{}\n</code></pre> graph_adjacency_list.go<pre><code>[class]{graphAdjList}-[func]{}\n</code></pre> graph_adjacency_list.swift<pre><code>[class]{GraphAdjList}-[func]{}\n</code></pre> graph_adjacency_list.js<pre><code>[class]{GraphAdjList}-[func]{}\n</code></pre> graph_adjacency_list.ts<pre><code>[class]{GraphAdjList}-[func]{}\n</code></pre> graph_adjacency_list.dart<pre><code>[class]{GraphAdjList}-[func]{}\n</code></pre> graph_adjacency_list.rs<pre><code>[class]{GraphAdjList}-[func]{}\n</code></pre> graph_adjacency_list.c<pre><code>[class]{AdjListNode}-[func]{}\n\n[class]{GraphAdjList}-[func]{}\n</code></pre> graph_adjacency_list.kt<pre><code>[class]{GraphAdjList}-[func]{}\n</code></pre> graph_adjacency_list.rb<pre><code>[class]{GraphAdjList}-[func]{}\n</code></pre> graph_adjacency_list.zig<pre><code>[class]{GraphAdjList}-[func]{}\n</code></pre>"},{"location":"chapter_graph/graph_operations/#923","title":"9.2.3 \u00a0 \u52b9\u7387\u306e\u6bd4\u8f03","text":"<p>\u30b0\u30e9\u30d5\u306b\\(n\\)\u500b\u306e\u9802\u70b9\u3068\\(m\\)\u500b\u306e\u8fba\u304c\u3042\u308b\u3068\u4eee\u5b9a\u3059\u308b\u3068\u3001\u4e0b\u8868\u306f\u96a3\u63a5\u884c\u5217\u3068\u96a3\u63a5\u30ea\u30b9\u30c8\u306e\u6642\u9593\u52b9\u7387\u3068\u7a7a\u9593\u52b9\u7387\u3092\u6bd4\u8f03\u3057\u3066\u3044\u307e\u3059\u3002</p> <p> \u8868 9-2 \u00a0 \u96a3\u63a5\u884c\u5217\u3068\u96a3\u63a5\u30ea\u30b9\u30c8\u306e\u6bd4\u8f03 </p> \u96a3\u63a5\u884c\u5217 \u96a3\u63a5\u30ea\u30b9\u30c8\uff08\u9023\u7d50\u30ea\u30b9\u30c8\uff09 \u96a3\u63a5\u30ea\u30b9\u30c8\uff08\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\uff09 \u96a3\u63a5\u6027\u306e\u5224\u5b9a \\(O(1)\\) \\(O(m)\\) \\(O(1)\\) \u8fba\u306e\u8ffd\u52a0 \\(O(1)\\) \\(O(1)\\) \\(O(1)\\) \u8fba\u306e\u524a\u9664 \\(O(1)\\) \\(O(m)\\) \\(O(1)\\) \u9802\u70b9\u306e\u8ffd\u52a0 \\(O(n)\\) \\(O(1)\\) \\(O(1)\\) \u9802\u70b9\u306e\u524a\u9664 \\(O(n^2)\\) \\(O(n + m)\\) \\(O(n)\\) \u30e1\u30e2\u30ea\u7a7a\u9593\u4f7f\u7528\u91cf \\(O(n^2)\\) \\(O(n + m)\\) \\(O(n + m)\\) <p>\u4e0a\u8868\u3092\u89b3\u5bdf\u3059\u308b\u3068\u3001\u96a3\u63a5\u30ea\u30b9\u30c8\uff08\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\uff09\u304c\u6700\u9ad8\u306e\u6642\u9593\u52b9\u7387\u3068\u7a7a\u9593\u52b9\u7387\u3092\u6301\u3063\u3066\u3044\u308b\u3088\u3046\u306b\u898b\u3048\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u5b9f\u969b\u306b\u306f\u3001\u96a3\u63a5\u884c\u5217\u3067\u306e\u8fba\u306b\u5bfe\u3059\u308b\u64cd\u4f5c\u304c\u3088\u308a\u52b9\u7387\u7684\u3067\u3001\u5358\u4e00\u306e\u914d\u5217\u30a2\u30af\u30bb\u30b9\u307e\u305f\u306f\u4ee3\u5165\u64cd\u4f5c\u306e\u307f\u304c\u5fc5\u8981\u3067\u3059\u3002\u5168\u4f53\u7684\u306b\u3001\u96a3\u63a5\u884c\u5217\u306f\u300c\u7a7a\u9593\u3068\u6642\u9593\u306e\u30c8\u30ec\u30fc\u30c9\u30aa\u30d5\u300d\u306e\u539f\u5247\u3092\u4f8b\u793a\u3057\u3001\u96a3\u63a5\u30ea\u30b9\u30c8\u306f\u300c\u6642\u9593\u3068\u7a7a\u9593\u306e\u30c8\u30ec\u30fc\u30c9\u30aa\u30d5\u300d\u3092\u4f8b\u793a\u3057\u3066\u3044\u307e\u3059\u3002</p>"},{"location":"chapter_graph/graph_traversal/","title":"9.3 \u00a0 \u30b0\u30e9\u30d5\u8d70\u67fb","text":"<p>\u6728\u306f\u300c\u4e00\u5bfe\u591a\u300d\u306e\u95a2\u4fc2\u3092\u8868\u73fe\u3057\u3001\u30b0\u30e9\u30d5\u306f\u3088\u308a\u9ad8\u3044\u81ea\u7531\u5ea6\u3092\u6301\u3061\u3001\u4efb\u610f\u306e\u300c\u591a\u5bfe\u591a\u300d\u306e\u95a2\u4fc2\u3092\u8868\u73fe\u3067\u304d\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u6728\u3092\u30b0\u30e9\u30d5\u306e\u7279\u5225\u306a\u30b1\u30fc\u30b9\u3068\u898b\u306a\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u660e\u3089\u304b\u306b\u3001\u6728\u306e\u8d70\u67fb\u64cd\u4f5c\u3082\u30b0\u30e9\u30d5\u8d70\u67fb\u64cd\u4f5c\u306e\u7279\u5225\u306a\u30b1\u30fc\u30b9\u3067\u3059\u3002</p> <p>\u30b0\u30e9\u30d5\u3068\u6728\u306e\u4e21\u65b9\u3067\u3001\u8d70\u67fb\u64cd\u4f5c\u3092\u5b9f\u88c5\u3059\u308b\u305f\u3081\u306b\u63a2\u7d22\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5fdc\u7528\u304c\u5fc5\u8981\u3067\u3059\u3002\u30b0\u30e9\u30d5\u8d70\u67fb\u306f2\u3064\u306e\u30bf\u30a4\u30d7\u306b\u5206\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\uff1a\u5e45\u512a\u5148\u63a2\u7d22\uff08BFS\uff09\u3068\u6df1\u3055\u512a\u5148\u63a2\u7d22\uff08DFS\uff09\u3067\u3059\u3002</p>"},{"location":"chapter_graph/graph_traversal/#931","title":"9.3.1 \u00a0 \u5e45\u512a\u5148\u63a2\u7d22","text":"<p>\u5e45\u512a\u5148\u63a2\u7d22\u306f\u8fd1\u304f\u304b\u3089\u9060\u304f\u3078\u306e\u8d70\u67fb\u65b9\u6cd5\u3067\u3001\u3042\u308b\u9802\u70b9\u304b\u3089\u958b\u59cb\u3057\u3001\u5e38\u306b\u6700\u3082\u8fd1\u3044\u9802\u70b9\u3092\u512a\u5148\u7684\u306b\u8a2a\u554f\u3057\u3001\u5c64\u3054\u3068\u306b\u5916\u5074\u306b\u5c55\u958b\u3057\u3066\u3044\u304d\u307e\u3059\u3002\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u5de6\u4e0a\u306e\u9802\u70b9\u304b\u3089\u958b\u59cb\u3057\u3001\u307e\u305a\u305d\u306e\u9802\u70b9\u306e\u3059\u3079\u3066\u306e\u96a3\u63a5\u9802\u70b9\u3092\u8d70\u67fb\u3057\u3001\u6b21\u306b\u6b21\u306e\u9802\u70b9\u306e\u3059\u3079\u3066\u306e\u96a3\u63a5\u9802\u70b9\u3092\u8d70\u67fb\u3057\u3001\u4ee5\u4e0b\u540c\u69d8\u306b\u3001\u3059\u3079\u3066\u306e\u9802\u70b9\u304c\u8a2a\u554f\u3055\u308c\u308b\u307e\u3067\u7d9a\u3051\u307e\u3059\u3002</p> <p></p> <p> \u56f3 9-9 \u00a0 \u30b0\u30e9\u30d5\u306e\u5e45\u512a\u5148\u8d70\u67fb </p>"},{"location":"chapter_graph/graph_traversal/#1","title":"1. \u00a0 \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5b9f\u88c5","text":"<p>BFS\u306f\u901a\u5e38\u30ad\u30e5\u30fc\u306e\u52a9\u3051\u3092\u501f\u308a\u3066\u5b9f\u88c5\u3055\u308c\u307e\u3059\uff08\u4e0b\u8a18\u306e\u30b3\u30fc\u30c9\u53c2\u7167\uff09\u3002\u30ad\u30e5\u30fc\u306f\u300c\u5148\u5165\u5148\u51fa\u300d\u3067\u3001\u3053\u308c\u306f\u300c\u8fd1\u304f\u304b\u3089\u9060\u304f\u3078\u300d\u8d70\u67fb\u3059\u308bBFS\u306e\u8003\u3048\u65b9\u3068\u4e00\u81f4\u3057\u307e\u3059\u3002</p> <ol> <li>\u958b\u59cb\u9802\u70b9<code>startVet</code>\u3092\u30ad\u30e5\u30fc\u306b\u8ffd\u52a0\u3057\u3001\u30eb\u30fc\u30d7\u3092\u958b\u59cb\u3057\u307e\u3059\u3002</li> <li>\u30eb\u30fc\u30d7\u306e\u5404\u53cd\u5fa9\u3067\u3001\u30ad\u30e5\u30fc\u306e\u5148\u982d\u306e\u9802\u70b9\u3092\u30dd\u30c3\u30d7\u3057\u3001\u305d\u308c\u3092\u8a2a\u554f\u6e08\u307f\u3068\u3057\u3066\u8a18\u9332\u3057\u3001\u6b21\u306b\u305d\u306e\u9802\u70b9\u306e\u3059\u3079\u3066\u306e\u96a3\u63a5\u9802\u70b9\u3092\u30ad\u30e5\u30fc\u306e\u672b\u5c3e\u306b\u8ffd\u52a0\u3057\u307e\u3059\u3002</li> <li>\u3059\u3079\u3066\u306e\u9802\u70b9\u304c\u8a2a\u554f\u3055\u308c\u308b\u307e\u3067\u624b\u9806<code>2.</code>\u3092\u7e70\u308a\u8fd4\u3057\u307e\u3059\u3002</li> </ol> <p>\u9802\u70b9\u306e\u518d\u8a2a\u554f\u3092\u9632\u3050\u305f\u3081\u306b\u3001\u30cf\u30c3\u30b7\u30e5\u30bb\u30c3\u30c8<code>visited</code>\u3092\u4f7f\u7528\u3057\u3066\u3069\u306e\u30ce\u30fc\u30c9\u304c\u8a2a\u554f\u3055\u308c\u305f\u304b\u3092\u8a18\u9332\u3057\u307e\u3059\u3002</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig graph_bfs.py<pre><code>def graph_bfs(graph: GraphAdjList, start_vet: Vertex) -&gt; list[Vertex]:\n    \"\"\"\u5e45\u512a\u5148\u8d70\u67fb\"\"\"\n    # \u96a3\u63a5\u30ea\u30b9\u30c8\u3092\u4f7f\u7528\u3057\u3066\u30b0\u30e9\u30d5\u3092\u8868\u73fe\u3057\u3001\u6307\u5b9a\u3055\u308c\u305f\u9802\u70b9\u306e\u3059\u3079\u3066\u306e\u96a3\u63a5\u9802\u70b9\u3092\u53d6\u5f97\n    # \u9802\u70b9\u8d70\u67fb\u30b7\u30fc\u30b1\u30f3\u30b9\n    res = []\n    # \u30cf\u30c3\u30b7\u30e5\u30bb\u30c3\u30c8\u3001\u8a2a\u554f\u6e08\u307f\u9802\u70b9\u3092\u8a18\u9332\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\n    visited = set[Vertex]([start_vet])\n    # BFS\u3092\u5b9f\u88c5\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u308b\u30ad\u30e5\u30fc\n    que = deque[Vertex]([start_vet])\n    # \u9802\u70b9vet\u304b\u3089\u958b\u59cb\u3057\u3001\u3059\u3079\u3066\u306e\u9802\u70b9\u304c\u8a2a\u554f\u3055\u308c\u308b\u307e\u3067\u30eb\u30fc\u30d7\n    while len(que) &gt; 0:\n        vet = que.popleft()  # \u30ad\u30e5\u30fc\u306e\u5148\u982d\u306e\u9802\u70b9\u3092\u30c7\u30ad\u30e5\u30fc\n        res.append(vet)  # \u8a2a\u554f\u6e08\u307f\u9802\u70b9\u3092\u8a18\u9332\n        # \u305d\u306e\u9802\u70b9\u306e\u3059\u3079\u3066\u306e\u96a3\u63a5\u9802\u70b9\u3092\u8d70\u67fb\n        for adj_vet in graph.adj_list[vet]:\n            if adj_vet in visited:\n                continue  # \u65e2\u306b\u8a2a\u554f\u6e08\u307f\u306e\u9802\u70b9\u3092\u30b9\u30ad\u30c3\u30d7\n            que.append(adj_vet)  # \u672a\u8a2a\u554f\u306e\u9802\u70b9\u306e\u307f\u3092\u30a8\u30f3\u30ad\u30e5\u30fc\n            visited.add(adj_vet)  # \u9802\u70b9\u3092\u8a2a\u554f\u6e08\u307f\u3068\u3057\u3066\u30de\u30fc\u30af\n    # \u9802\u70b9\u8d70\u67fb\u30b7\u30fc\u30b1\u30f3\u30b9\u3092\u8fd4\u3059\n    return res\n</code></pre> graph_bfs.cpp<pre><code>/* \u5e45\u512a\u5148\u8d70\u67fb */\n// \u96a3\u63a5\u30ea\u30b9\u30c8\u3092\u4f7f\u7528\u3057\u3066\u30b0\u30e9\u30d5\u3092\u8868\u73fe\u3057\u3001\u6307\u5b9a\u3055\u308c\u305f\u9802\u70b9\u306e\u3059\u3079\u3066\u306e\u96a3\u63a5\u9802\u70b9\u3092\u53d6\u5f97\nvector&lt;Vertex *&gt; graphBFS(GraphAdjList &amp;graph, Vertex *startVet) {\n    // \u9802\u70b9\u8d70\u67fb\u9806\u5e8f\n    vector&lt;Vertex *&gt; res;\n    // \u30cf\u30c3\u30b7\u30e5\u30bb\u30c3\u30c8\u3001\u8a2a\u554f\u6e08\u307f\u9802\u70b9\u3092\u8a18\u9332\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\n    unordered_set&lt;Vertex *&gt; visited = {startVet};\n    // BFS\u3092\u5b9f\u88c5\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u308b\u30ad\u30e5\u30fc\n    queue&lt;Vertex *&gt; que;\n    que.push(startVet);\n    // \u9802\u70b9vet\u304b\u3089\u958b\u59cb\u3057\u3001\u3059\u3079\u3066\u306e\u9802\u70b9\u304c\u8a2a\u554f\u3055\u308c\u308b\u307e\u3067\u30eb\u30fc\u30d7\n    while (!que.empty()) {\n        Vertex *vet = que.front();\n        que.pop();          // \u30ad\u30e5\u30fc\u306e\u5148\u982d\u306e\u9802\u70b9\u3092\u30c7\u30ad\u30e5\u30fc\n        res.push_back(vet); // \u8a2a\u554f\u6e08\u307f\u9802\u70b9\u3092\u8a18\u9332\n        // \u305d\u306e\u9802\u70b9\u306e\u3059\u3079\u3066\u306e\u96a3\u63a5\u9802\u70b9\u3092\u8d70\u67fb\n        for (auto adjVet : graph.adjList[vet]) {\n            if (visited.count(adjVet))\n                continue;            // \u3059\u3067\u306b\u8a2a\u554f\u6e08\u307f\u306e\u9802\u70b9\u3092\u30b9\u30ad\u30c3\u30d7\n            que.push(adjVet);        // \u672a\u8a2a\u554f\u306e\u9802\u70b9\u306e\u307f\u3092\u30a8\u30f3\u30ad\u30e5\u30fc\n            visited.emplace(adjVet); // \u9802\u70b9\u3092\u8a2a\u554f\u6e08\u307f\u3068\u3057\u3066\u30de\u30fc\u30af\n        }\n    }\n    // \u9802\u70b9\u8d70\u67fb\u9806\u5e8f\u3092\u8fd4\u3059\n    return res;\n}\n</code></pre> graph_bfs.java<pre><code>/* \u5e45\u512a\u5148\u8d70\u67fb */\n// \u96a3\u63a5\u30ea\u30b9\u30c8\u3092\u4f7f\u7528\u3057\u3066\u30b0\u30e9\u30d5\u3092\u8868\u73fe\u3057\u3001\u6307\u5b9a\u3057\u305f\u9802\u70b9\u306e\u3059\u3079\u3066\u306e\u96a3\u63a5\u9802\u70b9\u3092\u53d6\u5f97\nList&lt;Vertex&gt; graphBFS(GraphAdjList graph, Vertex startVet) {\n    // \u9802\u70b9\u8d70\u67fb\u9806\u5e8f\n    List&lt;Vertex&gt; res = new ArrayList&lt;&gt;();\n    // \u30cf\u30c3\u30b7\u30e5\u30bb\u30c3\u30c8\u3001\u8a2a\u554f\u6e08\u307f\u306e\u9802\u70b9\u3092\u8a18\u9332\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\n    Set&lt;Vertex&gt; visited = new HashSet&lt;&gt;();\n    visited.add(startVet);\n    // BFS \u3092\u5b9f\u88c5\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3059\u308b\u30ad\u30e5\u30fc\n    Queue&lt;Vertex&gt; que = new LinkedList&lt;&gt;();\n    que.offer(startVet);\n    // \u9802\u70b9 vet \u304b\u3089\u958b\u59cb\u3057\u3001\u3059\u3079\u3066\u306e\u9802\u70b9\u304c\u8a2a\u554f\u3055\u308c\u308b\u307e\u3067\u30eb\u30fc\u30d7\n    while (!que.isEmpty()) {\n        Vertex vet = que.poll(); // \u30ad\u30e5\u30fc\u306e\u5148\u982d\u306e\u9802\u70b9\u3092\u30c7\u30ad\u30e5\u30fc\n        res.add(vet);            // \u8a2a\u554f\u3057\u305f\u9802\u70b9\u3092\u8a18\u9332\n        // \u305d\u306e\u9802\u70b9\u306e\u3059\u3079\u3066\u306e\u96a3\u63a5\u9802\u70b9\u3092\u8d70\u67fb\n        for (Vertex adjVet : graph.adjList.get(vet)) {\n            if (visited.contains(adjVet))\n                continue;        // \u3059\u3067\u306b\u8a2a\u554f\u6e08\u307f\u306e\u9802\u70b9\u3092\u30b9\u30ad\u30c3\u30d7\n            que.offer(adjVet);   // \u672a\u8a2a\u554f\u306e\u9802\u70b9\u306e\u307f\u3092\u30a8\u30f3\u30ad\u30e5\u30fc\n            visited.add(adjVet); // \u9802\u70b9\u3092\u8a2a\u554f\u6e08\u307f\u3068\u3057\u3066\u30de\u30fc\u30af\n        }\n    }\n    // \u9802\u70b9\u8d70\u67fb\u9806\u5e8f\u3092\u8fd4\u3059\n    return res;\n}\n</code></pre> graph_bfs.cs<pre><code>[class]{graph_bfs}-[func]{GraphBFS}\n</code></pre> graph_bfs.go<pre><code>[class]{}-[func]{graphBFS}\n</code></pre> graph_bfs.swift<pre><code>[class]{}-[func]{graphBFS}\n</code></pre> graph_bfs.js<pre><code>[class]{}-[func]{graphBFS}\n</code></pre> graph_bfs.ts<pre><code>[class]{}-[func]{graphBFS}\n</code></pre> graph_bfs.dart<pre><code>[class]{}-[func]{graphBFS}\n</code></pre> graph_bfs.rs<pre><code>[class]{}-[func]{graph_bfs}\n</code></pre> graph_bfs.c<pre><code>[class]{Queue}-[func]{}\n\n[class]{}-[func]{isVisited}\n\n[class]{}-[func]{graphBFS}\n</code></pre> graph_bfs.kt<pre><code>[class]{}-[func]{graphBFS}\n</code></pre> graph_bfs.rb<pre><code>[class]{}-[func]{graph_bfs}\n</code></pre> graph_bfs.zig<pre><code>[class]{}-[func]{graphBFS}\n</code></pre> <p>\u30b3\u30fc\u30c9\u306f\u6bd4\u8f03\u7684\u62bd\u8c61\u7684\u3067\u3059\u304c\u3001\u4e0b\u56f3\u3068\u6bd4\u8f03\u3059\u308b\u3053\u3068\u3067\u3088\u308a\u826f\u304f\u7406\u89e3\u3067\u304d\u307e\u3059\u3002</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> \u56f3 9-10 \u00a0 \u30b0\u30e9\u30d5\u306e\u5e45\u512a\u5148\u63a2\u7d22\u306e\u624b\u9806 </p> <p>\u5e45\u512a\u5148\u8d70\u67fb\u306e\u30b7\u30fc\u30b1\u30f3\u30b9\u306f\u4e00\u610f\u3067\u3059\u304b\uff1f</p> <p>\u4e00\u610f\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u5e45\u512a\u5148\u8d70\u67fb\u306f\u300c\u8fd1\u304f\u304b\u3089\u9060\u304f\u300d\u306e\u9806\u5e8f\u3067\u8d70\u67fb\u3059\u308b\u3053\u3068\u306e\u307f\u3092\u8981\u6c42\u3057\u3001\u540c\u3058\u8ddd\u96e2\u306e\u9802\u70b9\u306e\u8d70\u67fb\u9806\u5e8f\u306f\u4efb\u610f\u306b\u3067\u304d\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u4e0a\u56f3\u3067\u306f\u3001\u9802\u70b9\\(1\\)\u3068\\(3\\)\u306e\u8a2a\u554f\u9806\u5e8f\u3092\u4ea4\u63db\u3067\u304d\u307e\u3059\u3057\u3001\u9802\u70b9\\(2\\)\u3001\\(4\\)\u3001\\(6\\)\u306e\u9806\u5e8f\u3082\u540c\u69d8\u3067\u3059\u3002</p>"},{"location":"chapter_graph/graph_traversal/#2","title":"2. \u00a0 \u8a08\u7b97\u91cf\u5206\u6790","text":"<p>\u6642\u9593\u8a08\u7b97\u91cf\uff1a\u3059\u3079\u3066\u306e\u9802\u70b9\u304c\u4e00\u5ea6\u305a\u3064\u30a8\u30f3\u30ad\u30e5\u30fc\u304a\u3088\u3073\u30c7\u30ad\u30e5\u30fc\u3055\u308c\u3001\\(O(|V|)\\)\u6642\u9593\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002\u96a3\u63a5\u9802\u70b9\u3092\u8d70\u67fb\u3059\u308b\u904e\u7a0b\u3067\u3001\u7121\u5411\u30b0\u30e9\u30d5\u3067\u3042\u308b\u305f\u3081\u3001\u3059\u3079\u3066\u306e\u8fba\u304c\\(2\\)\u56de\u8a2a\u554f\u3055\u308c\u3001\\(O(2|E|)\\)\u6642\u9593\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002\u5168\u4f53\u3067\\(O(|V| + |E|)\\)\u6642\u9593\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002</p> <p>\u7a7a\u9593\u8a08\u7b97\u91cf\uff1a\u30ea\u30b9\u30c8<code>res</code>\u3001\u30cf\u30c3\u30b7\u30e5\u30bb\u30c3\u30c8<code>visited</code>\u3001\u30ad\u30e5\u30fc<code>que</code>\u306e\u6700\u5927\u9802\u70b9\u6570\u306f\\(|V|\\)\u3067\u3001\\(O(|V|)\\)\u7a7a\u9593\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002</p>"},{"location":"chapter_graph/graph_traversal/#932","title":"9.3.2 \u00a0 \u6df1\u3055\u512a\u5148\u63a2\u7d22","text":"<p>\u6df1\u3055\u512a\u5148\u63a2\u7d22\u306f\u53ef\u80fd\u306a\u9650\u308a\u9060\u304f\u307e\u3067\u884c\u304d\u3001\u305d\u308c\u4ee5\u4e0a\u306e\u30d1\u30b9\u304c\u306a\u3044\u5834\u5408\u306b\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30af\u3059\u308b\u8d70\u67fb\u65b9\u6cd5\u3067\u3059\u3002\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u5de6\u4e0a\u306e\u9802\u70b9\u304b\u3089\u958b\u59cb\u3057\u3001\u305d\u308c\u4ee5\u4e0a\u306e\u30d1\u30b9\u304c\u306a\u304f\u306a\u308b\u307e\u3067\u73fe\u5728\u306e\u9802\u70b9\u306e\u3044\u305a\u308c\u304b\u306e\u96a3\u63a5\u9802\u70b9\u3092\u8a2a\u554f\u3057\u3001\u6b21\u306b\u623b\u3063\u3066\u7d9a\u884c\u3057\u3001\u3059\u3079\u3066\u306e\u9802\u70b9\u304c\u8d70\u67fb\u3055\u308c\u308b\u307e\u3067\u7d9a\u3051\u307e\u3059\u3002</p> <p></p> <p> \u56f3 9-11 \u00a0 \u30b0\u30e9\u30d5\u306e\u6df1\u3055\u512a\u5148\u8d70\u67fb </p>"},{"location":"chapter_graph/graph_traversal/#1_1","title":"1. \u00a0 \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5b9f\u88c5","text":"<p>\u3053\u306e\u300c\u53ef\u80fd\u306a\u9650\u308a\u9060\u304f\u307e\u3067\u884c\u3063\u3066\u304b\u3089\u623b\u308b\u300d\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u30d1\u30e9\u30c0\u30a4\u30e0\u306f\u901a\u5e38\u518d\u5e30\u306b\u57fa\u3065\u3044\u3066\u5b9f\u88c5\u3055\u308c\u307e\u3059\u3002\u5e45\u512a\u5148\u63a2\u7d22\u3068\u540c\u69d8\u306b\u3001\u6df1\u3055\u512a\u5148\u63a2\u7d22\u3067\u3082\u3001\u518d\u8a2a\u554f\u3092\u907f\u3051\u308b\u305f\u3081\u306b\u8a2a\u554f\u6e08\u307f\u9802\u70b9\u3092\u8a18\u9332\u3059\u308b\u30cf\u30c3\u30b7\u30e5\u30bb\u30c3\u30c8<code>visited</code>\u306e\u52a9\u3051\u304c\u5fc5\u8981\u3067\u3059\u3002</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig graph_dfs.py<pre><code>def dfs(graph: GraphAdjList, visited: set[Vertex], res: list[Vertex], vet: Vertex):\n    \"\"\"\u6df1\u3055\u512a\u5148\u8d70\u67fb\u306e\u30d8\u30eb\u30d1\u30fc\u95a2\u6570\"\"\"\n    res.append(vet)  # \u8a2a\u554f\u6e08\u307f\u9802\u70b9\u3092\u8a18\u9332\n    visited.add(vet)  # \u9802\u70b9\u3092\u8a2a\u554f\u6e08\u307f\u3068\u3057\u3066\u30de\u30fc\u30af\n    # \u305d\u306e\u9802\u70b9\u306e\u3059\u3079\u3066\u306e\u96a3\u63a5\u9802\u70b9\u3092\u8d70\u67fb\n    for adjVet in graph.adj_list[vet]:\n        if adjVet in visited:\n            continue  # \u65e2\u306b\u8a2a\u554f\u6e08\u307f\u306e\u9802\u70b9\u3092\u30b9\u30ad\u30c3\u30d7\n        # \u96a3\u63a5\u9802\u70b9\u3092\u518d\u5e30\u7684\u306b\u8a2a\u554f\n        dfs(graph, visited, res, adjVet)\n\ndef graph_dfs(graph: GraphAdjList, start_vet: Vertex) -&gt; list[Vertex]:\n    \"\"\"\u6df1\u3055\u512a\u5148\u8d70\u67fb\"\"\"\n    # \u96a3\u63a5\u30ea\u30b9\u30c8\u3092\u4f7f\u7528\u3057\u3066\u30b0\u30e9\u30d5\u3092\u8868\u73fe\u3057\u3001\u6307\u5b9a\u3055\u308c\u305f\u9802\u70b9\u306e\u3059\u3079\u3066\u306e\u96a3\u63a5\u9802\u70b9\u3092\u53d6\u5f97\n    # \u9802\u70b9\u8d70\u67fb\u30b7\u30fc\u30b1\u30f3\u30b9\n    res = []\n    # \u30cf\u30c3\u30b7\u30e5\u30bb\u30c3\u30c8\u3001\u8a2a\u554f\u6e08\u307f\u9802\u70b9\u3092\u8a18\u9332\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\n    visited = set[Vertex]()\n    dfs(graph, visited, res, start_vet)\n    return res\n</code></pre> graph_dfs.cpp<pre><code>/* \u6df1\u3055\u512a\u5148\u8d70\u67fb\u30d8\u30eb\u30d1\u30fc\u95a2\u6570 */\nvoid dfs(GraphAdjList &amp;graph, unordered_set&lt;Vertex *&gt; &amp;visited, vector&lt;Vertex *&gt; &amp;res, Vertex *vet) {\n    res.push_back(vet);   // \u8a2a\u554f\u6e08\u307f\u9802\u70b9\u3092\u8a18\u9332\n    visited.emplace(vet); // \u9802\u70b9\u3092\u8a2a\u554f\u6e08\u307f\u3068\u3057\u3066\u30de\u30fc\u30af\n    // \u305d\u306e\u9802\u70b9\u306e\u3059\u3079\u3066\u306e\u96a3\u63a5\u9802\u70b9\u3092\u8d70\u67fb\n    for (Vertex *adjVet : graph.adjList[vet]) {\n        if (visited.count(adjVet))\n            continue; // \u3059\u3067\u306b\u8a2a\u554f\u6e08\u307f\u306e\u9802\u70b9\u3092\u30b9\u30ad\u30c3\u30d7\n        // \u96a3\u63a5\u9802\u70b9\u3092\u518d\u5e30\u7684\u306b\u8a2a\u554f\n        dfs(graph, visited, res, adjVet);\n    }\n}\n\n/* \u6df1\u3055\u512a\u5148\u8d70\u67fb */\n// \u96a3\u63a5\u30ea\u30b9\u30c8\u3092\u4f7f\u7528\u3057\u3066\u30b0\u30e9\u30d5\u3092\u8868\u73fe\u3057\u3001\u6307\u5b9a\u3055\u308c\u305f\u9802\u70b9\u306e\u3059\u3079\u3066\u306e\u96a3\u63a5\u9802\u70b9\u3092\u53d6\u5f97\nvector&lt;Vertex *&gt; graphDFS(GraphAdjList &amp;graph, Vertex *startVet) {\n    // \u9802\u70b9\u8d70\u67fb\u9806\u5e8f\n    vector&lt;Vertex *&gt; res;\n    // \u30cf\u30c3\u30b7\u30e5\u30bb\u30c3\u30c8\u3001\u8a2a\u554f\u6e08\u307f\u9802\u70b9\u3092\u8a18\u9332\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\n    unordered_set&lt;Vertex *&gt; visited;\n    dfs(graph, visited, res, startVet);\n    return res;\n}\n</code></pre> graph_dfs.java<pre><code>/* \u6df1\u3055\u512a\u5148\u8d70\u67fb\u306e\u88dc\u52a9\u95a2\u6570 */\nvoid dfs(GraphAdjList graph, Set&lt;Vertex&gt; visited, List&lt;Vertex&gt; res, Vertex vet) {\n    res.add(vet);     // \u8a2a\u554f\u3057\u305f\u9802\u70b9\u3092\u8a18\u9332\n    visited.add(vet); // \u9802\u70b9\u3092\u8a2a\u554f\u6e08\u307f\u3068\u3057\u3066\u30de\u30fc\u30af\n    // \u305d\u306e\u9802\u70b9\u306e\u3059\u3079\u3066\u306e\u96a3\u63a5\u9802\u70b9\u3092\u8d70\u67fb\n    for (Vertex adjVet : graph.adjList.get(vet)) {\n        if (visited.contains(adjVet))\n            continue; // \u3059\u3067\u306b\u8a2a\u554f\u6e08\u307f\u306e\u9802\u70b9\u3092\u30b9\u30ad\u30c3\u30d7\n        // \u96a3\u63a5\u9802\u70b9\u3092\u518d\u5e30\u7684\u306b\u8a2a\u554f\n        dfs(graph, visited, res, adjVet);\n    }\n}\n\n/* \u6df1\u3055\u512a\u5148\u8d70\u67fb */\n// \u96a3\u63a5\u30ea\u30b9\u30c8\u3092\u4f7f\u7528\u3057\u3066\u30b0\u30e9\u30d5\u3092\u8868\u73fe\u3057\u3001\u6307\u5b9a\u3057\u305f\u9802\u70b9\u306e\u3059\u3079\u3066\u306e\u96a3\u63a5\u9802\u70b9\u3092\u53d6\u5f97\nList&lt;Vertex&gt; graphDFS(GraphAdjList graph, Vertex startVet) {\n    // \u9802\u70b9\u8d70\u67fb\u9806\u5e8f\n    List&lt;Vertex&gt; res = new ArrayList&lt;&gt;();\n    // \u30cf\u30c3\u30b7\u30e5\u30bb\u30c3\u30c8\u3001\u8a2a\u554f\u6e08\u307f\u306e\u9802\u70b9\u3092\u8a18\u9332\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\n    Set&lt;Vertex&gt; visited = new HashSet&lt;&gt;();\n    dfs(graph, visited, res, startVet);\n    return res;\n}\n</code></pre> graph_dfs.cs<pre><code>[class]{graph_dfs}-[func]{DFS}\n\n[class]{graph_dfs}-[func]{GraphDFS}\n</code></pre> graph_dfs.go<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{graphDFS}\n</code></pre> graph_dfs.swift<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{graphDFS}\n</code></pre> graph_dfs.js<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{graphDFS}\n</code></pre> graph_dfs.ts<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{graphDFS}\n</code></pre> graph_dfs.dart<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{graphDFS}\n</code></pre> graph_dfs.rs<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{graph_dfs}\n</code></pre> graph_dfs.c<pre><code>[class]{}-[func]{isVisited}\n\n[class]{}-[func]{dfs}\n\n[class]{}-[func]{graphDFS}\n</code></pre> graph_dfs.kt<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{graphDFS}\n</code></pre> graph_dfs.rb<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{graph_dfs}\n</code></pre> graph_dfs.zig<pre><code>[class]{}-[func]{dfs}\n\n[class]{}-[func]{graphDFS}\n</code></pre> <p>\u6df1\u3055\u512a\u5148\u63a2\u7d22\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u30d7\u30ed\u30bb\u30b9\u3092\u4e0b\u56f3\u306b\u793a\u3057\u307e\u3059\u3002</p> <ul> <li>\u7834\u7dda\u306f\u4e0b\u5411\u304d\u306e\u518d\u5e30\u3092\u8868\u3057\u3001\u65b0\u3057\u3044\u9802\u70b9\u3092\u8a2a\u554f\u3059\u308b\u305f\u3081\u306b\u65b0\u3057\u3044\u518d\u5e30\u30e1\u30bd\u30c3\u30c9\u304c\u958b\u59cb\u3055\u308c\u305f\u3053\u3068\u3092\u793a\u3057\u307e\u3059\u3002</li> <li>\u66f2\u7dda\u306e\u7834\u7dda\u306f\u4e0a\u5411\u304d\u306e\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30af\u3092\u8868\u3057\u3001\u3053\u306e\u518d\u5e30\u30e1\u30bd\u30c3\u30c9\u304c\u3053\u306e\u30e1\u30bd\u30c3\u30c9\u304c\u958b\u59cb\u3055\u308c\u305f\u4f4d\u7f6e\u306b\u623b\u3063\u305f\u3053\u3068\u3092\u793a\u3057\u307e\u3059\u3002</li> </ul> <p>\u7406\u89e3\u3092\u6df1\u3081\u308b\u305f\u3081\u3001\u4e0b\u56f3\u3068\u30b3\u30fc\u30c9\u3092\u7d44\u307f\u5408\u308f\u305b\u3066\u3001DFS\u30d7\u30ed\u30bb\u30b9\u5168\u4f53\u3092\u982d\u306e\u4e2d\u3067\u30b7\u30df\u30e5\u30ec\u30fc\u30c8\uff08\u307e\u305f\u306f\u63cf\u753b\uff09\u3059\u308b\u3053\u3068\u3092\u304a\u52e7\u3081\u3057\u307e\u3059\u3002\u5404\u518d\u5e30\u30e1\u30bd\u30c3\u30c9\u304c\u3044\u3064\u958b\u59cb\u3055\u308c\u3001\u3044\u3064\u623b\u308b\u304b\u3092\u542b\u3081\u3066\u3067\u3059\u3002</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> \u56f3 9-12 \u00a0 \u30b0\u30e9\u30d5\u306e\u6df1\u3055\u512a\u5148\u63a2\u7d22\u306e\u624b\u9806 </p> <p>\u6df1\u3055\u512a\u5148\u8d70\u67fb\u306e\u30b7\u30fc\u30b1\u30f3\u30b9\u306f\u4e00\u610f\u3067\u3059\u304b\uff1f</p> <p>\u5e45\u512a\u5148\u8d70\u67fb\u3068\u540c\u69d8\u306b\u3001\u6df1\u3055\u512a\u5148\u8d70\u67fb\u30b7\u30fc\u30b1\u30f3\u30b9\u306e\u9806\u5e8f\u3082\u4e00\u610f\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u3042\u308b\u9802\u70b9\u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408\u3001\u3069\u306e\u65b9\u5411\u3092\u6700\u521d\u306b\u63a2\u7d22\u3059\u308b\u3053\u3068\u3082\u53ef\u80fd\u3067\u3059\u3002\u3064\u307e\u308a\u3001\u96a3\u63a5\u9802\u70b9\u306e\u9806\u5e8f\u306f\u4efb\u610f\u306b\u30b7\u30e3\u30c3\u30d5\u30eb\u3067\u304d\u307e\u3059\u304c\u3001\u3059\u3079\u3066\u6df1\u3055\u512a\u5148\u8d70\u67fb\u306e\u4e00\u90e8\u3067\u3059\u3002</p> <p>\u6728\u306e\u8d70\u67fb\u3092\u4f8b\u306b\u53d6\u308b\u3068\u3001\u300c\u6839 \\(\\rightarrow\\) \u5de6 \\(\\rightarrow\\) \u53f3\u300d\u3001\u300c\u5de6 \\(\\rightarrow\\) \u6839 \\(\\rightarrow\\) \u53f3\u300d\u3001\u300c\u5de6 \\(\\rightarrow\\) \u53f3 \\(\\rightarrow\\) \u6839\u300d\u306f\u3001\u305d\u308c\u305e\u308c\u524d\u9806\u3001\u4e2d\u9806\u3001\u5f8c\u9806\u8d70\u67fb\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002\u3053\u308c\u3089\u306f3\u3064\u306e\u7570\u306a\u308b\u8d70\u67fb\u512a\u5148\u5ea6\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u304c\u30013\u3064\u3059\u3079\u3066\u304c\u6df1\u3055\u512a\u5148\u8d70\u67fb\u3068\u898b\u306a\u3055\u308c\u307e\u3059\u3002</p>"},{"location":"chapter_graph/graph_traversal/#2_1","title":"2. \u00a0 \u8a08\u7b97\u91cf\u5206\u6790","text":"<p>\u6642\u9593\u8a08\u7b97\u91cf\uff1a\u3059\u3079\u3066\u306e\u9802\u70b9\u304c\u4e00\u5ea6\u8a2a\u554f\u3055\u308c\u3001\\(O(|V|)\\)\u6642\u9593\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002\u3059\u3079\u3066\u306e\u8fba\u304c2\u56de\u8a2a\u554f\u3055\u308c\u3001\\(O(2|E|)\\)\u6642\u9593\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002\u5168\u4f53\u3067\\(O(|V| + |E|)\\)\u6642\u9593\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002</p> <p>\u7a7a\u9593\u8a08\u7b97\u91cf\uff1a\u30ea\u30b9\u30c8<code>res</code>\u3001\u30cf\u30c3\u30b7\u30e5\u30bb\u30c3\u30c8<code>visited</code>\u306e\u6700\u5927\u9802\u70b9\u6570\u306f\\(|V|\\)\u3067\u3001\u6700\u5927\u518d\u5e30\u6df1\u5ea6\u306f\\(|V|\\)\u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\\(O(|V|)\\)\u7a7a\u9593\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002</p>"},{"location":"chapter_graph/summary/","title":"9.4 \u00a0 \u307e\u3068\u3081","text":""},{"location":"chapter_graph/summary/#1","title":"1. \u00a0 \u91cd\u8981\u306a\u5fa9\u7fd2","text":"<ul> <li>\u30b0\u30e9\u30d5\u306f\u9802\u70b9\u3068\u8fba\u3067\u69cb\u6210\u3055\u308c\u307e\u3059\u3002\u9802\u70b9\u306e\u96c6\u5408\u3068\u8fba\u306e\u96c6\u5408\u3068\u3057\u3066\u8a18\u8ff0\u3067\u304d\u307e\u3059\u3002</li> <li>\u7dda\u5f62\u95a2\u4fc2\uff08\u9023\u7d50\u30ea\u30b9\u30c8\u306a\u3069\uff09\u3084\u968e\u5c64\u95a2\u4fc2\uff08\u6728\u306a\u3069\uff09\u3068\u6bd4\u8f03\u3057\u3066\u3001\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u95a2\u4fc2\uff08\u30b0\u30e9\u30d5\uff09\u306f\u3088\u308a\u5927\u304d\u306a\u67d4\u8edf\u6027\u3092\u63d0\u4f9b\u3057\u3001\u3088\u308a\u8907\u96d1\u306b\u306a\u308a\u307e\u3059\u3002</li> <li>\u6709\u5411\u30b0\u30e9\u30d5\u3067\u306f\u3001\u8fba\u306b\u65b9\u5411\u304c\u3042\u308a\u307e\u3059\u3002\u9023\u7d50\u30b0\u30e9\u30d5\u3067\u306f\u3001\u4efb\u610f\u306e\u9802\u70b9\u304b\u3089\u4ed6\u306e\u4efb\u610f\u306e\u9802\u70b9\u306b\u5230\u9054\u3067\u304d\u307e\u3059\u3002\u91cd\u307f\u4ed8\u304d\u30b0\u30e9\u30d5\u3067\u306f\u3001\u5404\u8fba\u306b\u95a2\u9023\u3059\u308b\u91cd\u307f\u5909\u6570\u304c\u3042\u308a\u307e\u3059\u3002</li> <li>\u96a3\u63a5\u884c\u5217\u306f\u3001\u884c\u5217\uff082\u6b21\u5143\u914d\u5217\uff09\u3092\u4f7f\u7528\u3057\u3066\u30b0\u30e9\u30d5\u3092\u8868\u73fe\u3059\u308b\u65b9\u6cd5\u3067\u3059\u3002\u884c\u3068\u5217\u306f\u9802\u70b9\u3092\u8868\u3057\u307e\u3059\u3002\u884c\u5217\u8981\u7d20\u306e\u5024\u306f\u30012\u3064\u306e\u9802\u70b9\u9593\u306b\u8fba\u304c\u3042\u308b\u304b\u3069\u3046\u304b\u3092\u793a\u3057\u3001\u8fba\u304c\u3042\u308b\u5834\u5408\u306f\\(1\\)\u3001\u306a\u3044\u5834\u5408\u306f\\(0\\)\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002\u96a3\u63a5\u884c\u5217\u306f\u8fba\u306e\u8ffd\u52a0\u3001\u524a\u9664\u3001\u30c1\u30a7\u30c3\u30af\u306a\u3069\u306e\u64cd\u4f5c\u306b\u975e\u5e38\u306b\u52b9\u7387\u7684\u3067\u3059\u304c\u3001\u3088\u308a\u591a\u304f\u306e\u30b9\u30da\u30fc\u30b9\u304c\u5fc5\u8981\u3067\u3059\u3002</li> <li>\u96a3\u63a5\u30ea\u30b9\u30c8\u306f\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u306e\u96c6\u5408\u3092\u4f7f\u7528\u3057\u3066\u30b0\u30e9\u30d5\u3092\u8868\u73fe\u3059\u308b\u3082\u3046\u4e00\u3064\u306e\u4e00\u822c\u7684\u306a\u65b9\u6cd5\u3067\u3059\u3002\u30b0\u30e9\u30d5\u5185\u306e\u5404\u9802\u70b9\u306b\u306f\u3001\u305d\u306e\u96a3\u63a5\u3059\u308b\u3059\u3079\u3066\u306e\u9802\u70b9\u3092\u542b\u3080\u30ea\u30b9\u30c8\u304c\u3042\u308a\u307e\u3059\u3002\\(i\\)\u756a\u76ee\u306e\u30ea\u30b9\u30c8\u306f\u9802\u70b9\\(i\\)\u3092\u8868\u3057\u307e\u3059\u3002\u96a3\u63a5\u30ea\u30b9\u30c8\u306f\u96a3\u63a5\u884c\u5217\u3068\u6bd4\u8f03\u3057\u3066\u3088\u308a\u5c11\u306a\u3044\u30b9\u30da\u30fc\u30b9\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002\u305f\u3060\u3057\u3001\u8fba\u3092\u898b\u3064\u3051\u308b\u305f\u3081\u306b\u30ea\u30b9\u30c8\u3092\u8d70\u67fb\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u305f\u3081\u3001\u6642\u9593\u52b9\u7387\u306f\u4f4e\u304f\u306a\u308a\u307e\u3059\u3002</li> <li>\u96a3\u63a5\u30ea\u30b9\u30c8\u306e\u9023\u7d50\u30ea\u30b9\u30c8\u304c\u5341\u5206\u306b\u9577\u304f\u306a\u3063\u305f\u3068\u304d\u3001\u30eb\u30c3\u30af\u30a2\u30c3\u30d7\u52b9\u7387\u3092\u5411\u4e0a\u3055\u305b\u308b\u305f\u3081\u306b\u8d64\u9ed2\u6728\u3084\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u306b\u5909\u63db\u3067\u304d\u307e\u3059\u3002</li> <li>\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u8a2d\u8a08\u306e\u89b3\u70b9\u304b\u3089\u3001\u96a3\u63a5\u884c\u5217\u306f\u300c\u7a7a\u9593\u3068\u6642\u9593\u306e\u30c8\u30ec\u30fc\u30c9\u30aa\u30d5\u300d\u306e\u6982\u5ff5\u3092\u53cd\u6620\u3057\u3001\u96a3\u63a5\u30ea\u30b9\u30c8\u306f\u300c\u6642\u9593\u3068\u7a7a\u9593\u306e\u30c8\u30ec\u30fc\u30c9\u30aa\u30d5\u300d\u3092\u53cd\u6620\u3057\u307e\u3059\u3002</li> <li>\u30b0\u30e9\u30d5\u306f\u3001\u30bd\u30fc\u30b7\u30e3\u30eb\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u3084\u5730\u4e0b\u9244\u8def\u7dda\u306a\u3069\u3001\u3055\u307e\u3056\u307e\u306a\u73fe\u5b9f\u4e16\u754c\u306e\u30b7\u30b9\u30c6\u30e0\u3092\u30e2\u30c7\u30eb\u5316\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002</li> <li>\u6728\u306f\u30b0\u30e9\u30d5\u306e\u7279\u5225\u306a\u30b1\u30fc\u30b9\u3067\u3042\u308a\u3001\u6728\u306e\u8d70\u67fb\u3082\u30b0\u30e9\u30d5\u8d70\u67fb\u306e\u7279\u5225\u306a\u30b1\u30fc\u30b9\u3067\u3059\u3002</li> <li>\u30b0\u30e9\u30d5\u306e\u5e45\u512a\u5148\u8d70\u67fb\u306f\u3001\u8fd1\u304f\u304b\u3089\u9060\u304f\u3078\u3068\u5c64\u3054\u3068\u306b\u62e1\u5f35\u3059\u308b\u63a2\u7d22\u65b9\u6cd5\u3067\u3001\u901a\u5e38\u30ad\u30e5\u30fc\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002</li> <li>\u30b0\u30e9\u30d5\u306e\u6df1\u3055\u512a\u5148\u8d70\u67fb\u306f\u3001\u305d\u308c\u4ee5\u4e0a\u306e\u30d1\u30b9\u304c\u306a\u3044\u5834\u5408\u306b\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30af\u3059\u308b\u524d\u306b\u3001\u307e\u305a\u7d42\u7aef\u306b\u5230\u9054\u3059\u308b\u3053\u3068\u3092\u512a\u5148\u3059\u308b\u63a2\u7d22\u65b9\u6cd5\u3067\u3059\u3002\u3057\u3070\u3057\u3070\u518d\u5e30\u3092\u4f7f\u7528\u3057\u3066\u5b9f\u88c5\u3055\u308c\u307e\u3059\u3002</li> </ul>"},{"location":"chapter_graph/summary/#2-q-a","title":"2. \u00a0 Q &amp; A","text":"<p>Q: \u30d1\u30b9\u306f\u9802\u70b9\u306e\u30b7\u30fc\u30b1\u30f3\u30b9\u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u304b\u3001\u305d\u308c\u3068\u3082\u8fba\u306e\u30b7\u30fc\u30b1\u30f3\u30b9\u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u304b\uff1f</p> <p>\u30b0\u30e9\u30d5\u7406\u8ad6\u3067\u306f\u3001\u30b0\u30e9\u30d5\u5185\u306e\u30d1\u30b9\u306f\u9802\u70b9\u306e\u30b7\u30fc\u30b1\u30f3\u30b9\u3092\u7d50\u3076\u6709\u9650\u307e\u305f\u306f\u7121\u9650\u306e\u8fba\u306e\u30b7\u30fc\u30b1\u30f3\u30b9\u3067\u3059\u3002</p> <p>\u3053\u306e\u6587\u66f8\u3067\u306f\u3001\u30d1\u30b9\u306f\u9802\u70b9\u306e\u30b7\u30fc\u30b1\u30f3\u30b9\u3067\u306f\u306a\u304f\u3001\u8fba\u306e\u30b7\u30fc\u30b1\u30f3\u30b9\u3068\u8003\u3048\u3089\u308c\u307e\u3059\u3002\u3053\u308c\u306f\u30012\u3064\u306e\u9802\u70b9\u3092\u7d50\u3076\u8907\u6570\u306e\u8fba\u304c\u3042\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u3001\u305d\u306e\u5834\u5408\u5404\u8fba\u304c\u30d1\u30b9\u306b\u5bfe\u5fdc\u3059\u308b\u305f\u3081\u3067\u3059\u3002</p> <p>Q: \u975e\u9023\u7d50\u30b0\u30e9\u30d5\u3067\u306f\u3001\u8d70\u67fb\u3067\u304d\u306a\u3044\u70b9\u304c\u3042\u308a\u307e\u3059\u304b\uff1f</p> <p>\u975e\u9023\u7d50\u30b0\u30e9\u30d5\u3067\u306f\u3001\u7279\u5b9a\u306e\u70b9\u304b\u3089\u5230\u9054\u3067\u304d\u306a\u3044\u9802\u70b9\u304c\u5c11\u306a\u304f\u3068\u30821\u3064\u3042\u308a\u307e\u3059\u3002\u975e\u9023\u7d50\u30b0\u30e9\u30d5\u3092\u8d70\u67fb\u3059\u308b\u306b\u306f\u3001\u30b0\u30e9\u30d5\u306e\u3059\u3079\u3066\u306e\u9023\u7d50\u6210\u5206\u3092\u8d70\u67fb\u3059\u308b\u305f\u3081\u306b\u8907\u6570\u306e\u958b\u59cb\u70b9\u3092\u8a2d\u5b9a\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002</p> <p>Q: \u96a3\u63a5\u30ea\u30b9\u30c8\u3067\u3001\u300c\u305d\u306e\u9802\u70b9\u306b\u63a5\u7d9a\u3055\u308c\u305f\u3059\u3079\u3066\u306e\u9802\u70b9\u300d\u306e\u9806\u5e8f\u306f\u91cd\u8981\u3067\u3059\u304b\uff1f</p> <p>\u4efb\u610f\u306e\u9806\u5e8f\u3067\u69cb\u3044\u307e\u305b\u3093\u3002\u305f\u3060\u3057\u3001\u5b9f\u969b\u306e\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u3067\u306f\u3001\u9802\u70b9\u304c\u8ffd\u52a0\u3055\u308c\u305f\u9806\u5e8f\u3084\u9802\u70b9\u5024\u306e\u9806\u5e8f\u306a\u3069\u3001\u7279\u5b9a\u306e\u30eb\u30fc\u30eb\u306b\u5f93\u3063\u3066\u305d\u308c\u3089\u3092\u30bd\u30fc\u30c8\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u7279\u5b9a\u306e\u6975\u5024\u3092\u6301\u3064\u9802\u70b9\u3092\u7d20\u65e9\u304f\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002</p>"},{"location":"chapter_greedy/","title":"\u7b2c 15 \u7ae0 \u00a0 \u8caa\u6b32\u6cd5","text":"<p>Abstract</p> <p>\u3072\u307e\u308f\u308a\u306f\u592a\u967d\u306e\u65b9\u3092\u5411\u304d\u3001\u5e38\u306b\u81ea\u5206\u306b\u3068\u3063\u3066\u6700\u5927\u306e\u6210\u9577\u3092\u6c42\u3081\u307e\u3059\u3002</p> <p>\u8caa\u6b32\u306a\u6226\u7565\u306f\u3001\u4e00\u9023\u306e\u5358\u7d14\u306a\u9078\u629e\u3092\u901a\u3058\u3066\u3001\u6bb5\u968e\u7684\u306b\u6700\u826f\u306e\u7b54\u3048\u3078\u3068\u5c0e\u304d\u307e\u3059\u3002</p>"},{"location":"chapter_greedy/#_1","title":"\u7ae0\u306e\u5185\u5bb9","text":"<ul> <li>15.1 \u00a0 \u8caa\u6b32\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0</li> <li>15.2 \u00a0 \u5206\u6570\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c</li> <li>15.3 \u00a0 \u6700\u5927\u5bb9\u91cf\u554f\u984c</li> <li>15.4 \u00a0 \u6700\u5927\u7a4d\u5207\u65ad\u554f\u984c</li> <li>15.5 \u00a0 \u307e\u3068\u3081</li> </ul>"},{"location":"chapter_greedy/fractional_knapsack_problem/","title":"15.2 \u00a0 \u5206\u6570\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c","text":"<p>Question</p> <p>\\(n\\) \u500b\u306e\u30a2\u30a4\u30c6\u30e0\u304c\u4e0e\u3048\u3089\u308c\u3001\\(i\\) \u756a\u76ee\u306e\u30a2\u30a4\u30c6\u30e0\u306e\u91cd\u91cf\u306f \\(wgt[i-1]\\) \u3067\u5024\u306f \\(val[i-1]\\) \u3067\u3059\u3002\u5bb9\u91cf\u304c \\(cap\\) \u306e\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u304c\u3042\u308a\u307e\u3059\u3002\u5404\u30a2\u30a4\u30c6\u30e0\u306f1\u56de\u306e\u307f\u9078\u629e\u3067\u304d\u307e\u3059\u304c\u3001\u30a2\u30a4\u30c6\u30e0\u306e\u4e00\u90e8\u3092\u9078\u629e\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u3001\u305d\u306e\u5024\u306f\u9078\u629e\u3055\u308c\u305f\u91cd\u91cf\u306e\u5272\u5408\u306b\u57fa\u3065\u3044\u3066\u8a08\u7b97\u3055\u308c\u307e\u3059\u3002\u9650\u3089\u308c\u305f\u5bb9\u91cf\u306e\u4e0b\u3067\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u5185\u306e\u30a2\u30a4\u30c6\u30e0\u306e\u6700\u5927\u5024\u306f\u4f55\u3067\u3059\u304b\uff1f\u4f8b\u3092\u4e0b\u306e\u56f3\u306b\u793a\u3057\u307e\u3059\u3002</p> <p></p> <p> \u56f3 15-3 \u00a0 \u5206\u6570\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c\u306e\u4f8b\u30c7\u30fc\u30bf </p> <p>\u5206\u6570\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c\u306f\u5168\u4f53\u7684\u306b0-1\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c\u3068\u975e\u5e38\u306b\u4f3c\u3066\u304a\u308a\u3001\u73fe\u5728\u306e\u30a2\u30a4\u30c6\u30e0 \\(i\\) \u3068\u5bb9\u91cf \\(c\\) \u3092\u542b\u307f\u3001\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u306e\u9650\u3089\u308c\u305f\u5bb9\u91cf\u5185\u3067\u5024\u3092\u6700\u5927\u5316\u3059\u308b\u3053\u3068\u3092\u76ee\u7684\u3068\u3057\u3066\u3044\u307e\u3059\u3002</p> <p>\u9055\u3044\u306f\u3001\u3053\u306e\u554f\u984c\u3067\u306f\u30a2\u30a4\u30c6\u30e0\u306e\u4e00\u90e8\u306e\u307f\u3092\u9078\u629e\u3067\u304d\u308b\u3053\u3068\u3067\u3059\u3002\u4e0b\u306e\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u30a2\u30a4\u30c6\u30e0\u3092\u4efb\u610f\u306b\u5206\u5272\u3057\u3001\u91cd\u91cf\u306e\u5272\u5408\u306b\u57fa\u3065\u3044\u3066\u5bfe\u5fdc\u3059\u308b\u5024\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002</p> <ol> <li>\u30a2\u30a4\u30c6\u30e0 \\(i\\) \u306b\u3064\u3044\u3066\u3001\u305d\u306e\u5358\u4f4d\u91cd\u91cf\u3042\u305f\u308a\u306e\u5024\u306f \\(val[i-1] / wgt[i-1]\\) \u3067\u3001\u5358\u4f4d\u5024\u3068\u547c\u3070\u308c\u307e\u3059\u3002</li> <li>\u91cd\u91cf \\(w\\) \u306e\u30a2\u30a4\u30c6\u30e0 \\(i\\) \u306e\u4e00\u90e8\u3092\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u306b\u5165\u308c\u308b\u3068\u3059\u308b\u3068\u3001\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u306b\u8ffd\u52a0\u3055\u308c\u308b\u5024\u306f \\(w \\times val[i-1] / wgt[i-1]\\) \u3067\u3059\u3002</li> </ol> <p></p> <p> \u56f3 15-4 \u00a0 \u30a2\u30a4\u30c6\u30e0\u306e\u5358\u4f4d\u91cd\u91cf\u3042\u305f\u308a\u306e\u5024 </p>"},{"location":"chapter_greedy/fractional_knapsack_problem/#1","title":"1. \u00a0 \u8caa\u6b32\u6226\u7565\u306e\u6c7a\u5b9a","text":"<p>\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u5185\u306e\u30a2\u30a4\u30c6\u30e0\u306e\u7dcf\u5024\u3092\u6700\u5927\u5316\u3059\u308b\u3053\u3068\u306f\u3001\u672c\u8cea\u7684\u306b\u5358\u4f4d\u91cd\u91cf\u3042\u305f\u308a\u306e\u5024\u3092\u6700\u5927\u5316\u3059\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002\u3053\u308c\u304b\u3089\u3001\u4e0b\u306e\u56f3\u306b\u793a\u3059\u8caa\u6b32\u6226\u7565\u3092\u5c0e\u51fa\u3067\u304d\u307e\u3059\u3002</p> <ol> <li>\u30a2\u30a4\u30c6\u30e0\u3092\u5358\u4f4d\u5024\u306e\u9ad8\u3044\u9806\u304b\u3089\u4f4e\u3044\u9806\u306b\u30bd\u30fc\u30c8\u3057\u307e\u3059\u3002</li> <li>\u3059\u3079\u3066\u306e\u30a2\u30a4\u30c6\u30e0\u3092\u53cd\u5fa9\u3057\u3001**\u5404\u30e9\u30a6\u30f3\u30c9\u3067\u6700\u3082\u9ad8\u3044\u5358\u4f4d\u5024\u3092\u6301\u3064\u30a2\u30a4\u30c6\u30e0\u3092\u8caa\u6b32\u306b\u9078\u629e**\u3057\u307e\u3059\u3002</li> <li>\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u306e\u6b8b\u308a\u5bb9\u91cf\u304c\u4e0d\u5341\u5206\u306a\u5834\u5408\u3001\u73fe\u5728\u306e\u30a2\u30a4\u30c6\u30e0\u306e\u4e00\u90e8\u3092\u4f7f\u7528\u3057\u3066\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u3092\u6e80\u305f\u3057\u307e\u3059\u3002</li> </ol> <p></p> <p> \u56f3 15-5 \u00a0 \u5206\u6570\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c\u306e\u8caa\u6b32\u6226\u7565 </p>"},{"location":"chapter_greedy/fractional_knapsack_problem/#2","title":"2. \u00a0 \u30b3\u30fc\u30c9\u5b9f\u88c5","text":"<p>\u30a2\u30a4\u30c6\u30e0\u3092\u5358\u4f4d\u5024\u3067\u30bd\u30fc\u30c8\u3059\u308b\u305f\u3081\u306b <code>Item</code> \u30af\u30e9\u30b9\u3092\u4f5c\u6210\u3057\u307e\u3057\u305f\u3002\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u304c\u6e80\u305f\u3055\u308c\u308b\u307e\u3067\u30eb\u30fc\u30d7\u3057\u3066\u8caa\u6b32\u306a\u9078\u629e\u3092\u884c\u3044\u3001\u305d\u306e\u5f8c\u7d42\u4e86\u3057\u3066\u89e3\u3092\u8fd4\u3057\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig fractional_knapsack.py<pre><code>class Item:\n    \"\"\"\u30a2\u30a4\u30c6\u30e0\"\"\"\n\n    def __init__(self, w: int, v: int):\n        self.w = w  # \u30a2\u30a4\u30c6\u30e0\u306e\u91cd\u91cf\n        self.v = v  # \u30a2\u30a4\u30c6\u30e0\u306e\u4fa1\u5024\n\ndef fractional_knapsack(wgt: list[int], val: list[int], cap: int) -&gt; int:\n    \"\"\"\u5206\u6570\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\uff1a\u8caa\u6b32\u6cd5\"\"\"\n    # \u30a2\u30a4\u30c6\u30e0\u30ea\u30b9\u30c8\u3092\u4f5c\u6210\u30012 \u3064\u306e\u5c5e\u6027\u3092\u542b\u3080\uff1a\u91cd\u91cf\u3001\u4fa1\u5024\n    items = [Item(w, v) for w, v in zip(wgt, val)]\n    # \u5358\u4f4d\u4fa1\u5024 item.v / item.w \u3067\u9ad8\u3044\u9806\u306b\u30bd\u30fc\u30c8\n    items.sort(key=lambda item: item.v / item.w, reverse=True)\n    # \u8caa\u6b32\u9078\u629e\u3092\u30eb\u30fc\u30d7\n    res = 0\n    for item in items:\n        if item.w &lt;= cap:\n            # \u6b8b\u308a\u5bb9\u91cf\u304c\u5341\u5206\u306a\u5834\u5408\u3001\u30a2\u30a4\u30c6\u30e0\u5168\u4f53\u3092\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u306b\u5165\u308c\u308b\n            res += item.v\n            cap -= item.w\n        else:\n            # \u6b8b\u308a\u5bb9\u91cf\u304c\u4e0d\u5341\u5206\u306a\u5834\u5408\u3001\u30a2\u30a4\u30c6\u30e0\u306e\u4e00\u90e8\u3092\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u306b\u5165\u308c\u308b\n            res += (item.v / item.w) * cap\n            # \u6b8b\u308a\u5bb9\u91cf\u304c\u306a\u304f\u306a\u3063\u305f\u305f\u3081\u3001\u30eb\u30fc\u30d7\u3092\u4e2d\u65ad\n            break\n    return res\n</code></pre> fractional_knapsack.cpp<pre><code>/* \u30a2\u30a4\u30c6\u30e0 */\nclass Item {\n  public:\n    int w; // \u30a2\u30a4\u30c6\u30e0\u306e\u91cd\u91cf\n    int v; // \u30a2\u30a4\u30c6\u30e0\u306e\u4fa1\u5024\n\n    Item(int w, int v) : w(w), v(v) {\n    }\n};\n\n/* \u5206\u6570\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\uff1a\u8caa\u6b32\u6cd5 */\ndouble fractionalKnapsack(vector&lt;int&gt; &amp;wgt, vector&lt;int&gt; &amp;val, int cap) {\n    // \u30a2\u30a4\u30c6\u30e0\u30ea\u30b9\u30c8\u3092\u4f5c\u6210\u30012\u3064\u306e\u5c5e\u6027\u3092\u542b\u3080\uff1a\u91cd\u91cf\u3001\u4fa1\u5024\n    vector&lt;Item&gt; items;\n    for (int i = 0; i &lt; wgt.size(); i++) {\n        items.push_back(Item(wgt[i], val[i]));\n    }\n    // \u5358\u4f4d\u4fa1\u5024 item.v / item.w \u3067\u9ad8\u3044\u9806\u306b\u30bd\u30fc\u30c8\n    sort(items.begin(), items.end(), [](Item &amp;a, Item &amp;b) { return (double)a.v / a.w &gt; (double)b.v / b.w; });\n    // \u8caa\u6b32\u9078\u629e\u3092\u30eb\u30fc\u30d7\n    double res = 0;\n    for (auto &amp;item : items) {\n        if (item.w &lt;= cap) {\n            // \u6b8b\u308a\u5bb9\u91cf\u304c\u5341\u5206\u306a\u5834\u5408\u3001\u30a2\u30a4\u30c6\u30e0\u5168\u4f53\u3092\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u306b\u5165\u308c\u308b\n            res += item.v;\n            cap -= item.w;\n        } else {\n            // \u6b8b\u308a\u5bb9\u91cf\u304c\u4e0d\u5341\u5206\u306a\u5834\u5408\u3001\u30a2\u30a4\u30c6\u30e0\u306e\u4e00\u90e8\u3092\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u306b\u5165\u308c\u308b\n            res += (double)item.v / item.w * cap;\n            // \u6b8b\u308a\u5bb9\u91cf\u304c\u306a\u304f\u306a\u3063\u305f\u305f\u3081\u3001\u30eb\u30fc\u30d7\u3092\u4e2d\u65ad\n            break;\n        }\n    }\n    return res;\n}\n</code></pre> fractional_knapsack.java<pre><code>/* \u30a2\u30a4\u30c6\u30e0 */\nclass Item {\n    int w; // \u30a2\u30a4\u30c6\u30e0\u306e\u91cd\u91cf\n    int v; // \u30a2\u30a4\u30c6\u30e0\u306e\u4fa1\u5024\n\n    public Item(int w, int v) {\n        this.w = w;\n        this.v = v;\n    }\n}\n\n/* \u5206\u6570\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\uff1a\u8caa\u6b32\u6cd5 */\ndouble fractionalKnapsack(int[] wgt, int[] val, int cap) {\n    // \u30a2\u30a4\u30c6\u30e0\u30ea\u30b9\u30c8\u3092\u4f5c\u6210\u30012\u3064\u306e\u5c5e\u6027\u3092\u542b\u3080\uff1a\u91cd\u91cf\u3001\u4fa1\u5024\n    Item[] items = new Item[wgt.length];\n    for (int i = 0; i &lt; wgt.length; i++) {\n        items[i] = new Item(wgt[i], val[i]);\n    }\n    // \u5358\u4f4d\u4fa1\u5024 item.v / item.w \u3067\u9ad8\u3044\u9806\u306b\u30bd\u30fc\u30c8\n    Arrays.sort(items, Comparator.comparingDouble(item -&gt; -((double) item.v / item.w)));\n    // \u8caa\u6b32\u9078\u629e\u3092\u30eb\u30fc\u30d7\n    double res = 0;\n    for (Item item : items) {\n        if (item.w &lt;= cap) {\n            // \u6b8b\u308a\u5bb9\u91cf\u304c\u5341\u5206\u306a\u5834\u5408\u3001\u30a2\u30a4\u30c6\u30e0\u5168\u4f53\u3092\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u306b\u5165\u308c\u308b\n            res += item.v;\n            cap -= item.w;\n        } else {\n            // \u6b8b\u308a\u5bb9\u91cf\u304c\u4e0d\u5341\u5206\u306a\u5834\u5408\u3001\u30a2\u30a4\u30c6\u30e0\u306e\u4e00\u90e8\u3092\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u306b\u5165\u308c\u308b\n            res += (double) item.v / item.w * cap;\n            // \u6b8b\u308a\u5bb9\u91cf\u304c\u306a\u304f\u306a\u3063\u305f\u305f\u3081\u3001\u30eb\u30fc\u30d7\u3092\u4e2d\u65ad\n            break;\n        }\n    }\n    return res;\n}\n</code></pre> fractional_knapsack.cs<pre><code>[class]{Item}-[func]{}\n\n[class]{fractional_knapsack}-[func]{FractionalKnapsack}\n</code></pre> fractional_knapsack.go<pre><code>[class]{Item}-[func]{}\n\n[class]{}-[func]{fractionalKnapsack}\n</code></pre> fractional_knapsack.swift<pre><code>[class]{Item}-[func]{}\n\n[class]{}-[func]{fractionalKnapsack}\n</code></pre> fractional_knapsack.js<pre><code>[class]{Item}-[func]{}\n\n[class]{}-[func]{fractionalKnapsack}\n</code></pre> fractional_knapsack.ts<pre><code>[class]{Item}-[func]{}\n\n[class]{}-[func]{fractionalKnapsack}\n</code></pre> fractional_knapsack.dart<pre><code>[class]{Item}-[func]{}\n\n[class]{}-[func]{fractionalKnapsack}\n</code></pre> fractional_knapsack.rs<pre><code>[class]{Item}-[func]{}\n\n[class]{}-[func]{fractional_knapsack}\n</code></pre> fractional_knapsack.c<pre><code>[class]{Item}-[func]{}\n\n[class]{}-[func]{fractionalKnapsack}\n</code></pre> fractional_knapsack.kt<pre><code>[class]{Item}-[func]{}\n\n[class]{}-[func]{fractionalKnapsack}\n</code></pre> fractional_knapsack.rb<pre><code>[class]{Item}-[func]{}\n\n[class]{}-[func]{fractional_knapsack}\n</code></pre> fractional_knapsack.zig<pre><code>[class]{Item}-[func]{}\n\n[class]{}-[func]{fractionalKnapsack}\n</code></pre> <p>\u30bd\u30fc\u30c8\u4ee5\u5916\u306b\u3001\u6700\u60aa\u306e\u5834\u5408\u3001\u30a2\u30a4\u30c6\u30e0\u306e\u30ea\u30b9\u30c8\u5168\u4f53\u3092\u8d70\u67fb\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u305f\u3081\u3001\u6642\u9593\u8a08\u7b97\u91cf\u306f \\(O(n)\\) \u3067\u3059\u3002\u3053\u3053\u3067 \\(n\\) \u306f\u30a2\u30a4\u30c6\u30e0\u306e\u6570\u3067\u3059\u3002</p> <p><code>Item</code> \u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u30ea\u30b9\u30c8\u304c\u521d\u671f\u5316\u3055\u308c\u308b\u305f\u3081\u3001\u7a7a\u9593\u8a08\u7b97\u91cf\u306f \\(O(n)\\) \u3067\u3059\u3002</p>"},{"location":"chapter_greedy/fractional_knapsack_problem/#3","title":"3. \u00a0 \u6b63\u3057\u3055\u306e\u8a3c\u660e","text":"<p>\u80cc\u7406\u6cd5\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002\u30a2\u30a4\u30c6\u30e0 \\(x\\) \u304c\u6700\u9ad8\u306e\u5358\u4f4d\u5024\u3092\u6301\u3061\u3001\u3042\u308b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u304c\u6700\u5927\u5024 <code>res</code> \u3092\u751f\u6210\u3059\u308b\u304c\u3001\u89e3\u306b\u30a2\u30a4\u30c6\u30e0 \\(x\\) \u304c\u542b\u307e\u308c\u3066\u3044\u306a\u3044\u3068\u4eee\u5b9a\u3057\u307e\u3059\u3002</p> <p>\u4eca\u3001\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u304b\u3089\u4efb\u610f\u306e\u30a2\u30a4\u30c6\u30e0\u306e\u5358\u4f4d\u91cd\u91cf\u3092\u53d6\u308a\u9664\u304d\u3001\u30a2\u30a4\u30c6\u30e0 \\(x\\) \u306e\u5358\u4f4d\u91cd\u91cf\u3067\u7f6e\u304d\u63db\u3048\u307e\u3059\u3002\u30a2\u30a4\u30c6\u30e0 \\(x\\) \u306e\u5358\u4f4d\u5024\u304c\u6700\u9ad8\u3067\u3042\u308b\u305f\u3081\u3001\u7f6e\u304d\u63db\u3048\u5f8c\u306e\u7dcf\u5024\u306f\u78ba\u5b9f\u306b <code>res</code> \u3088\u308a\u5927\u304d\u304f\u306a\u308a\u307e\u3059\u3002\u3053\u308c\u306f <code>res</code> \u304c\u6700\u9069\u89e3\u3067\u3042\u308b\u3068\u3044\u3046\u4eee\u5b9a\u3068\u77db\u76fe\u3057\u3001\u6700\u9069\u89e3\u306b\u306f\u5fc5\u305a\u30a2\u30a4\u30c6\u30e0 \\(x\\) \u304c\u542b\u307e\u308c\u308b\u3053\u3068\u3092\u8a3c\u660e\u3057\u307e\u3059\u3002</p> <p>\u3053\u306e\u89e3\u306e\u4ed6\u306e\u30a2\u30a4\u30c6\u30e0\u306b\u3064\u3044\u3066\u3082\u3001\u4e0a\u8a18\u306e\u77db\u76fe\u3092\u69cb\u7bc9\u3067\u304d\u307e\u3059\u3002\u5168\u4f53\u7684\u306b\u3001**\u5358\u4f4d\u5024\u304c\u3088\u308a\u5927\u304d\u3044\u30a2\u30a4\u30c6\u30e0\u306f\u5e38\u306b\u3088\u308a\u826f\u3044\u9078\u629e**\u3067\u3042\u308a\u3001\u8caa\u6b32\u6226\u7565\u304c\u52b9\u679c\u7684\u3067\u3042\u308b\u3053\u3068\u3092\u8a3c\u660e\u3057\u307e\u3059\u3002</p> <p>\u4e0b\u306e\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u30a2\u30a4\u30c6\u30e0\u306e\u91cd\u91cf\u3068\u5358\u4f4d\u5024\u3092\u305d\u308c\u305e\u308c\u4e8c\u6b21\u5143\u30c1\u30e3\u30fc\u30c8\u306e\u6a2a\u8ef8\u3068\u7e26\u8ef8\u3068\u898b\u306a\u3059\u3068\u3001\u5206\u6570\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c\u306f\u300c\u9650\u3089\u308c\u305f\u6a2a\u8ef8\u7bc4\u56f2\u5185\u3067\u56f2\u307e\u308c\u308b\u6700\u5927\u9762\u7a4d\u3092\u6c42\u3081\u308b\u300d\u3053\u3068\u306b\u5909\u63db\u3067\u304d\u307e\u3059\u3002\u3053\u306e\u985e\u63a8\u306f\u3001\u5e7e\u4f55\u5b66\u7684\u89b3\u70b9\u304b\u3089\u8caa\u6b32\u6226\u7565\u306e\u52b9\u679c\u3092\u7406\u89e3\u3059\u308b\u306e\u306b\u5f79\u7acb\u3061\u307e\u3059\u3002</p> <p></p> <p> \u56f3 15-6 \u00a0 \u5206\u6570\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c\u306e\u5e7e\u4f55\u5b66\u7684\u8868\u73fe </p>"},{"location":"chapter_greedy/greedy_algorithm/","title":"15.1 \u00a0 \u8caa\u6b32\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0","text":"<p>\u8caa\u6b32\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u6700\u9069\u5316\u554f\u984c\u3092\u89e3\u6c7a\u3059\u308b\u305f\u3081\u306e\u4e00\u822c\u7684\u306a\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u3001\u57fa\u672c\u7684\u306b\u554f\u984c\u306e\u5404\u610f\u601d\u6c7a\u5b9a\u6bb5\u968e\u3067\u6700\u3082\u826f\u3044\u9078\u629e\u3092\u3059\u308b\u3053\u3068\u3001\u3064\u307e\u308a\u5c40\u6240\u7684\u306b\u6700\u9069\u306a\u6c7a\u5b9a\u3092\u8caa\u6b32\u306b\u884c\u3044\u3001\u30b0\u30ed\u30fc\u30d0\u30eb\u306b\u6700\u9069\u306a\u89e3\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u3092\u671b\u307f\u307e\u3059\u3002\u8caa\u6b32\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u7c21\u6f54\u3067\u52b9\u7387\u7684\u3067\u3042\u308a\u3001\u591a\u304f\u306e\u5b9f\u7528\u7684\u306a\u554f\u984c\u3067\u5e83\u304f\u4f7f\u7528\u3055\u308c\u3066\u3044\u307e\u3059\u3002</p> <p>\u8caa\u6b32\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3068\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u306f\u3001\u3069\u3061\u3089\u3082\u6700\u9069\u5316\u554f\u984c\u3092\u89e3\u6c7a\u3059\u308b\u305f\u3081\u306b\u3088\u304f\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u4e21\u8005\u306f\u6700\u9069\u90e8\u5206\u69cb\u9020\u306e\u6027\u8cea\u306b\u4f9d\u5b58\u3059\u308b\u306a\u3069\u3001\u3044\u304f\u3064\u304b\u306e\u985e\u4f3c\u70b9\u3092\u5171\u6709\u3057\u3066\u3044\u307e\u3059\u304c\u3001\u52d5\u4f5c\u65b9\u6cd5\u304c\u7570\u306a\u308a\u307e\u3059\u3002</p> <ul> <li>\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u306f\u73fe\u5728\u306e\u6c7a\u5b9a\u6bb5\u968e\u3067\u3059\u3079\u3066\u306e\u4ee5\u524d\u306e\u6c7a\u5b9a\u3092\u8003\u616e\u3057\u3001\u904e\u53bb\u306e\u90e8\u5206\u554f\u984c\u306e\u89e3\u3092\u4f7f\u7528\u3057\u3066\u73fe\u5728\u306e\u90e8\u5206\u554f\u984c\u306e\u89e3\u3092\u69cb\u7bc9\u3057\u307e\u3059\u3002</li> <li>\u8caa\u6b32\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u904e\u53bb\u306e\u6c7a\u5b9a\u3092\u8003\u616e\u305b\u305a\u3001\u4ee3\u308f\u308a\u306b\u8caa\u6b32\u306a\u9078\u629e\u3092\u7d9a\u3051\u3001\u554f\u984c\u304c\u89e3\u6c7a\u3055\u308c\u308b\u307e\u3067\u554f\u984c\u306e\u7bc4\u56f2\u3092\u7d99\u7d9a\u7684\u306b\u72ed\u3081\u307e\u3059\u3002</li> </ul> <p>\u307e\u305a\u3001\u300c\u5b8c\u5168\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c\u300d\u306e\u7ae0\u3067\u7d39\u4ecb\u3055\u308c\u305f\u300c\u30b3\u30a4\u30f3\u4ea4\u63db\u300d\u306e\u4f8b\u3092\u901a\u3058\u3066\u8caa\u6b32\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u52d5\u4f5c\u539f\u7406\u3092\u7406\u89e3\u3057\u307e\u3057\u3087\u3046\u3002\u3059\u3067\u306b\u3088\u304f\u77e5\u3063\u3066\u3044\u308b\u3068\u601d\u3044\u307e\u3059\u3002</p> <p>Question</p> <p>\\(n\\) \u7a2e\u985e\u306e\u30b3\u30a4\u30f3\u304c\u4e0e\u3048\u3089\u308c\u3001\\(i\\) \u756a\u76ee\u306e\u7a2e\u985e\u306e\u30b3\u30a4\u30f3\u306e\u984d\u9762\u306f \\(coins[i - 1]\\) \u3067\u3001\u76ee\u6a19\u91d1\u984d\u306f \\(amt\\) \u3067\u3059\u3002\u5404\u7a2e\u985e\u306e\u30b3\u30a4\u30f3\u306f\u7121\u5236\u9650\u306b\u5229\u7528\u53ef\u80fd\u3067\u3001\u76ee\u6a19\u91d1\u984d\u3092\u69cb\u6210\u3059\u308b\u306e\u306b\u5fc5\u8981\u306a\u6700\u5c0f\u30b3\u30a4\u30f3\u6570\u306f\u4f55\u3067\u3059\u304b\uff1f\u76ee\u6a19\u91d1\u984d\u3092\u69cb\u6210\u3067\u304d\u306a\u3044\u5834\u5408\u306f \\(-1\\) \u3092\u8fd4\u3057\u3066\u304f\u3060\u3055\u3044\u3002</p> <p>\u3053\u306e\u554f\u984c\u3067\u63a1\u7528\u3055\u308c\u308b\u8caa\u6b32\u6226\u7565\u3092\u4e0b\u306e\u56f3\u306b\u793a\u3057\u307e\u3059\u3002\u76ee\u6a19\u91d1\u984d\u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u304d\u3001**\u305d\u308c\u306b\u6700\u3082\u8fd1\u304f\u3001\u305d\u308c\u3092\u8d85\u3048\u306a\u3044\u30b3\u30a4\u30f3\u3092\u8caa\u6b32\u306b\u9078\u629e**\u3057\u3001\u76ee\u6a19\u91d1\u984d\u304c\u6e80\u305f\u3055\u308c\u308b\u307e\u3067\u3053\u306e\u30b9\u30c6\u30c3\u30d7\u3092\u7e70\u308a\u8fd4\u3057\u307e\u3059\u3002</p> <p></p> <p> \u56f3 15-1 \u00a0 \u30b3\u30a4\u30f3\u4ea4\u63db\u306e\u8caa\u6b32\u6226\u7565 </p> <p>\u5b9f\u88c5\u30b3\u30fc\u30c9\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig coin_change_greedy.py<pre><code>def coin_change_greedy(coins: list[int], amt: int) -&gt; int:\n    \"\"\"\u786c\u8ca8\u4ea4\u63db\uff1a\u8caa\u6b32\u6cd5\"\"\"\n    # coins \u30ea\u30b9\u30c8\u304c\u30bd\u30fc\u30c8\u3055\u308c\u3066\u3044\u308b\u3068\u4eee\u5b9a\n    i = len(coins) - 1\n    count = 0\n    # \u6b8b\u308a\u91d1\u984d\u304c\u306a\u304f\u306a\u308b\u307e\u3067\u8caa\u6b32\u9078\u629e\u3092\u30eb\u30fc\u30d7\n    while amt &gt; 0:\n        # \u6b8b\u308a\u91d1\u984d\u306b\u6700\u3082\u8fd1\u304f\u3001\u305d\u308c\u3088\u308a\u5c0f\u3055\u3044\u786c\u8ca8\u3092\u898b\u3064\u3051\u308b\n        while i &gt; 0 and coins[i] &gt; amt:\n            i -= 1\n        # coins[i] \u3092\u9078\u629e\n        amt -= coins[i]\n        count += 1\n    # \u5b9f\u884c\u53ef\u80fd\u306a\u89e3\u304c\u898b\u3064\u304b\u3089\u306a\u3044\u5834\u5408\u3001-1 \u3092\u8fd4\u3059\n    return count if amt == 0 else -1\n</code></pre> coin_change_greedy.cpp<pre><code>/* \u786c\u8ca8\u4e21\u66ff\uff1a\u8caa\u6b32\u6cd5 */\nint coinChangeGreedy(vector&lt;int&gt; &amp;coins, int amt) {\n    // \u786c\u8ca8\u30ea\u30b9\u30c8\u304c\u9806\u5e8f\u4ed8\u3051\u3055\u308c\u3066\u3044\u308b\u3068\u4eee\u5b9a\n    int i = coins.size() - 1;\n    int count = 0;\n    // \u6b8b\u308a\u91d1\u984d\u304c\u306a\u304f\u306a\u308b\u307e\u3067\u8caa\u6b32\u9078\u629e\u3092\u30eb\u30fc\u30d7\n    while (amt &gt; 0) {\n        // \u6b8b\u308a\u91d1\u984d\u306b\u8fd1\u304f\u3001\u305d\u308c\u4ee5\u4e0b\u306e\u6700\u5c0f\u786c\u8ca8\u3092\u898b\u3064\u3051\u308b\n        while (i &gt; 0 &amp;&amp; coins[i] &gt; amt) {\n            i--;\n        }\n        // coins[i] \u3092\u9078\u629e\n        amt -= coins[i];\n        count++;\n    }\n    // \u5b9f\u884c\u53ef\u80fd\u306a\u89e3\u304c\u898b\u3064\u304b\u3089\u306a\u3044\u5834\u5408\u3001-1 \u3092\u8fd4\u3059\n    return amt == 0 ? count : -1;\n}\n</code></pre> coin_change_greedy.java<pre><code>/* \u786c\u8ca8\u4e21\u66ff\uff1a\u8caa\u6b32\u6cd5 */\nint coinChangeGreedy(int[] coins, int amt) {\n    // \u786c\u8ca8\u30ea\u30b9\u30c8\u304c\u9806\u5e8f\u4ed8\u3051\u3055\u308c\u3066\u3044\u308b\u3068\u4eee\u5b9a\n    int i = coins.length - 1;\n    int count = 0;\n    // \u6b8b\u308a\u91d1\u984d\u304c\u306a\u304f\u306a\u308b\u307e\u3067\u8caa\u6b32\u9078\u629e\u3092\u30eb\u30fc\u30d7\n    while (amt &gt; 0) {\n        // \u6b8b\u308a\u91d1\u984d\u306b\u8fd1\u304f\u3001\u305d\u308c\u4ee5\u4e0b\u306e\u6700\u5c0f\u786c\u8ca8\u3092\u898b\u3064\u3051\u308b\n        while (i &gt; 0 &amp;&amp; coins[i] &gt; amt) {\n            i--;\n        }\n        // coins[i] \u3092\u9078\u629e\n        amt -= coins[i];\n        count++;\n    }\n    // \u5b9f\u884c\u53ef\u80fd\u306a\u89e3\u304c\u898b\u3064\u304b\u3089\u306a\u3044\u5834\u5408\u3001-1 \u3092\u8fd4\u3059\n    return amt == 0 ? count : -1;\n}\n</code></pre> coin_change_greedy.cs<pre><code>[class]{coin_change_greedy}-[func]{CoinChangeGreedy}\n</code></pre> coin_change_greedy.go<pre><code>[class]{}-[func]{coinChangeGreedy}\n</code></pre> coin_change_greedy.swift<pre><code>[class]{}-[func]{coinChangeGreedy}\n</code></pre> coin_change_greedy.js<pre><code>[class]{}-[func]{coinChangeGreedy}\n</code></pre> coin_change_greedy.ts<pre><code>[class]{}-[func]{coinChangeGreedy}\n</code></pre> coin_change_greedy.dart<pre><code>[class]{}-[func]{coinChangeGreedy}\n</code></pre> coin_change_greedy.rs<pre><code>[class]{}-[func]{coin_change_greedy}\n</code></pre> coin_change_greedy.c<pre><code>[class]{}-[func]{coinChangeGreedy}\n</code></pre> coin_change_greedy.kt<pre><code>[class]{}-[func]{coinChangeGreedy}\n</code></pre> coin_change_greedy.rb<pre><code>[class]{}-[func]{coin_change_greedy}\n</code></pre> coin_change_greedy.zig<pre><code>[class]{}-[func]{coinChangeGreedy}\n</code></pre> <p>\u611f\u5606\u3059\u308b\u304b\u3082\u3057\u308c\u307e\u305b\u3093\uff1a\u306a\u3093\u3066\u7c21\u6f54\u306a\u3093\u3060\uff01\u8caa\u6b32\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u7d0410\u884c\u306e\u30b3\u30fc\u30c9\u3067\u30b3\u30a4\u30f3\u4ea4\u63db\u554f\u984c\u3092\u89e3\u6c7a\u3057\u307e\u3059\u3002</p>"},{"location":"chapter_greedy/greedy_algorithm/#1511","title":"15.1.1 \u00a0 \u8caa\u6b32\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5229\u70b9\u3068\u5236\u9650","text":"<p>\u8caa\u6b32\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u76f4\u63a5\u7684\u3067\u5b9f\u88c5\u304c\u7c21\u5358\u3067\u3042\u308b\u3060\u3051\u3067\u306a\u304f\u3001\u901a\u5e38\u975e\u5e38\u306b\u52b9\u7387\u7684\u3067\u3082\u3042\u308a\u307e\u3059\u3002\u4e0a\u8a18\u306e\u30b3\u30fc\u30c9\u3067\u3001\u6700\u5c0f\u306e\u30b3\u30a4\u30f3\u984d\u9762\u3092 \\(\\min(coins)\\) \u3068\u3059\u308b\u3068\u3001\u8caa\u6b32\u306a\u9078\u629e\u30eb\u30fc\u30d7\u306f\u6700\u5927 \\(amt / \\min(coins)\\) \u56de\u5b9f\u884c\u3055\u308c\u3001\u6642\u9593\u8a08\u7b97\u91cf\u306f \\(O(amt / \\min(coins))\\) \u306b\u306a\u308a\u307e\u3059\u3002\u3053\u308c\u306f\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u89e3\u6cd5\u306e\u6642\u9593\u8a08\u7b97\u91cf \\(O(n \\times amt)\\) \u3088\u308a\u3082\u4e00\u6841\u5c0f\u3055\u3044\u3067\u3059\u3002</p> <p>\u3057\u304b\u3057\u3001\u4e00\u90e8\u306e\u30b3\u30a4\u30f3\u984d\u9762\u306e\u7d44\u307f\u5408\u308f\u305b\u3067\u306f\u3001\u8caa\u6b32\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u6700\u9069\u89e3\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u305b\u3093\u3002\u4e0b\u306e\u56f3\u306f2\u3064\u306e\u4f8b\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002</p> <ul> <li>\u6b63\u306e\u4f8b \\(coins = [1, 5, 10, 20, 50, 100]\\)\uff1a\u3053\u306e\u30b3\u30a4\u30f3\u306e\u7d44\u307f\u5408\u308f\u305b\u3067\u306f\u3001\u4efb\u610f\u306e \\(amt\\) \u306b\u5bfe\u3057\u3066\u3001\u8caa\u6b32\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u6700\u9069\u89e3\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002</li> <li>\u8ca0\u306e\u4f8b \\(coins = [1, 20, 50]\\)\uff1a\\(amt = 60\\) \u3068\u3059\u308b\u3068\u3001\u8caa\u6b32\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u7d44\u307f\u5408\u308f\u305b \\(50 + 1 \\times 10\\) \u3057\u304b\u898b\u3064\u3051\u3089\u308c\u305a\u3001\u5408\u8a0811\u679a\u306e\u30b3\u30a4\u30f3\u3067\u3059\u304c\u3001\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u306f\u6700\u9069\u89e3 \\(20 + 20 + 20\\) \u3092\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u30013\u679a\u306e\u30b3\u30a4\u30f3\u306e\u307f\u304c\u5fc5\u8981\u3067\u3059\u3002</li> <li>\u8ca0\u306e\u4f8b \\(coins = [1, 49, 50]\\)\uff1a\\(amt = 98\\) \u3068\u3059\u308b\u3068\u3001\u8caa\u6b32\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u7d44\u307f\u5408\u308f\u305b \\(50 + 1 \\times 48\\) \u3057\u304b\u898b\u3064\u3051\u3089\u308c\u305a\u3001\u5408\u8a0849\u679a\u306e\u30b3\u30a4\u30f3\u3067\u3059\u304c\u3001\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u306f\u6700\u9069\u89e3 \\(49 + 49\\) \u3092\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u30012\u679a\u306e\u30b3\u30a4\u30f3\u306e\u307f\u304c\u5fc5\u8981\u3067\u3059\u3002</li> </ul> <p></p> <p> \u56f3 15-2 \u00a0 \u8caa\u6b32\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u304c\u6700\u9069\u89e3\u3092\u898b\u3064\u3051\u3089\u308c\u306a\u3044\u4f8b </p> <p>\u3053\u308c\u306f\u3001\u30b3\u30a4\u30f3\u4ea4\u63db\u554f\u984c\u306b\u304a\u3044\u3066\u3001\u8caa\u6b32\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u304c\u30b0\u30ed\u30fc\u30d0\u30eb\u306b\u6700\u9069\u306a\u89e3\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u3092\u4fdd\u8a3c\u3067\u304d\u305a\u3001\u975e\u5e38\u306b\u60aa\u3044\u89e3\u3092\u898b\u3064\u3051\u308b\u53ef\u80fd\u6027\u304c\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u306e\u65b9\u304c\u9069\u3057\u3066\u3044\u307e\u3059\u3002</p> <p>\u4e00\u822c\u7684\u306b\u3001\u8caa\u6b32\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u9069\u7528\u6027\u306f2\u3064\u306e\u30ab\u30c6\u30b4\u30ea\u306b\u5206\u985e\u3055\u308c\u307e\u3059\u3002</p> <ol> <li>\u6700\u9069\u89e3\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u4fdd\u8a3c\u3055\u308c\u308b\uff1a\u3053\u308c\u3089\u306e\u5834\u5408\u3001\u8caa\u6b32\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u3057\u3070\u3057\u3070\u6700\u826f\u306e\u9078\u629e\u3067\u3001\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u3084\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u3088\u308a\u3082\u52b9\u7387\u7684\u3067\u3042\u308b\u50be\u5411\u304c\u3042\u308a\u307e\u3059\u3002</li> <li>\u6e96\u6700\u9069\u89e3\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u308b\uff1a\u8caa\u6b32\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u3053\u3053\u3067\u3082\u9069\u7528\u53ef\u80fd\u3067\u3059\u3002\u591a\u304f\u306e\u8907\u96d1\u306a\u554f\u984c\u3067\u306f\u3001\u30b0\u30ed\u30fc\u30d0\u30eb\u6700\u9069\u89e3\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u306f\u975e\u5e38\u306b\u56f0\u96e3\u3067\u3042\u308a\u3001\u9ad8\u52b9\u7387\u306e\u6e96\u6700\u9069\u89e3\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u3082\u975e\u5e38\u306b\u4fa1\u5024\u304c\u3042\u308a\u307e\u3059\u3002</li> </ol>"},{"location":"chapter_greedy/greedy_algorithm/#1512","title":"15.1.2 \u00a0 \u8caa\u6b32\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u7279\u5fb4","text":"<p>\u305d\u308c\u3067\u306f\u3001\u3069\u306e\u3088\u3046\u306a\u554f\u984c\u304c\u8caa\u6b32\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u89e3\u6c7a\u3059\u308b\u306e\u306b\u9069\u3057\u3066\u3044\u308b\u306e\u3067\u3057\u3087\u3046\u304b\uff1f\u8a00\u3044\u63db\u3048\u308c\u3070\u3001\u3069\u306e\u3088\u3046\u306a\u6761\u4ef6\u4e0b\u3067\u8caa\u6b32\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u6700\u9069\u89e3\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u3092\u4fdd\u8a3c\u3067\u304d\u308b\u306e\u3067\u3057\u3087\u3046\u304b\uff1f</p> <p>\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u3068\u6bd4\u8f03\u3057\u3066\u3001\u8caa\u6b32\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u3088\u308a\u53b3\u3057\u3044\u4f7f\u7528\u6761\u4ef6\u3092\u6301\u3061\u3001\u4e3b\u306b\u554f\u984c\u306e2\u3064\u306e\u6027\u8cea\u306b\u7126\u70b9\u3092\u5f53\u3066\u3066\u3044\u307e\u3059\u3002</p> <ul> <li>\u8caa\u6b32\u9078\u629e\u6027\uff1a\u5c40\u6240\u7684\u306b\u6700\u9069\u306a\u9078\u629e\u304c\u5e38\u306b\u30b0\u30ed\u30fc\u30d0\u30eb\u306b\u6700\u9069\u306a\u89e3\u306b\u5c0e\u304f\u3053\u3068\u304c\u3067\u304d\u308b\u5834\u5408\u306e\u307f\u3001\u8caa\u6b32\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u6700\u9069\u89e3\u3092\u5f97\u308b\u3053\u3068\u3092\u4fdd\u8a3c\u3067\u304d\u307e\u3059\u3002</li> <li>\u6700\u9069\u90e8\u5206\u69cb\u9020\uff1a\u5143\u306e\u554f\u984c\u306e\u6700\u9069\u89e3\u306f\u305d\u306e\u90e8\u5206\u554f\u984c\u306e\u6700\u9069\u89e3\u3092\u542b\u307f\u307e\u3059\u3002</li> </ul> <p>\u6700\u9069\u90e8\u5206\u69cb\u9020\u306f\u300c\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u300d\u306e\u7ae0\u3067\u3059\u3067\u306b\u7d39\u4ecb\u3055\u308c\u3066\u3044\u308b\u305f\u3081\u3001\u3053\u3053\u3067\u306f\u3053\u308c\u4ee5\u4e0a\u8b70\u8ad6\u3057\u307e\u305b\u3093\u3002\u4e00\u90e8\u306e\u554f\u984c\u306b\u306f\u660e\u3089\u304b\u306a\u6700\u9069\u90e8\u5206\u69cb\u9020\u304c\u3042\u308a\u307e\u305b\u3093\u304c\u3001\u305d\u308c\u3067\u3082\u8caa\u6b32\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u4f7f\u7528\u3057\u3066\u89e3\u6c7a\u3067\u304d\u308b\u3053\u3068\u306b\u6ce8\u610f\u3059\u308b\u3053\u3068\u304c\u91cd\u8981\u3067\u3059\u3002</p> <p>\u4e3b\u306b\u8caa\u6b32\u9078\u629e\u6027\u3092\u6c7a\u5b9a\u3059\u308b\u65b9\u6cd5\u3092\u63a2\u7d22\u3057\u307e\u3059\u3002\u305d\u306e\u8a18\u8ff0\u306f\u5358\u7d14\u306b\u898b\u3048\u307e\u3059\u304c\u3001\u5b9f\u969b\u306b\u306f\u3001\u591a\u304f\u306e\u554f\u984c\u306e\u8caa\u6b32\u9078\u629e\u6027\u3092\u8a3c\u660e\u3059\u308b\u3053\u3068\u306f\u5bb9\u6613\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002</p> <p>\u4f8b\u3048\u3070\u3001\u30b3\u30a4\u30f3\u4ea4\u63db\u554f\u984c\u3067\u306f\u3001\u8caa\u6b32\u9078\u629e\u6027\u3092\u53cd\u8a3c\u3059\u308b\u305f\u3081\u306b\u53cd\u4f8b\u3092\u7c21\u5358\u306b\u6319\u3052\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u304c\u3001\u305d\u308c\u3092\u8a3c\u660e\u3059\u308b\u3053\u3068\u306f\u306f\u308b\u304b\u306b\u56f0\u96e3\u3067\u3059\u3002**\u30b3\u30a4\u30f3\u306e\u7d44\u307f\u5408\u308f\u305b\u304c\u8caa\u6b32\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u4f7f\u7528\u3057\u3066\u89e3\u6c7a\u3067\u304d\u308b\u305f\u3081\u306b\u306f\u3001\u3069\u306e\u3088\u3046\u306a\u6761\u4ef6\u3092\u6e80\u305f\u3059\u5fc5\u8981\u304c\u3042\u308b\u304b**\u3068\u5c0b\u306d\u3089\u308c\u305f\u5834\u5408\u3001\u53b3\u5bc6\u306a\u6570\u5b66\u7684\u8a3c\u660e\u3092\u63d0\u4f9b\u3059\u308b\u3053\u3068\u304c\u56f0\u96e3\u3067\u3042\u308b\u305f\u3081\u3001\u3057\u3070\u3057\u3070\u76f4\u611f\u3084\u4f8b\u306b\u983c\u3063\u3066\u66d6\u6627\u306a\u7b54\u3048\u3092\u63d0\u4f9b\u3057\u306a\u3051\u308c\u3070\u306a\u308a\u307e\u305b\u3093\u3002</p> <p>Quote</p> <p>\u3042\u308b\u8ad6\u6587\u3067\u306f\u3001\u30b3\u30a4\u30f3\u306e\u7d44\u307f\u5408\u308f\u305b\u304c\u4efb\u610f\u306e\u91d1\u984d\u306b\u5bfe\u3057\u3066\u8caa\u6b32\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u4f7f\u7528\u3057\u3066\u6700\u9069\u89e3\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u304b\u3069\u3046\u304b\u3092\u5224\u5b9a\u3059\u308b\u305f\u3081\u306e\u6642\u9593\u8a08\u7b97\u91cf \\(O(n^3)\\) \u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u304c\u63d0\u793a\u3055\u308c\u3066\u3044\u307e\u3059\u3002</p> <p>Pearson, D. A polynomial-time algorithm for the change-making problem[J]. Operations Research Letters, 2005, 33(3): 231-234.</p>"},{"location":"chapter_greedy/greedy_algorithm/#1513","title":"15.1.3 \u00a0 \u8caa\u6b32\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306b\u3088\u308b\u554f\u984c\u89e3\u6c7a\u306e\u30b9\u30c6\u30c3\u30d7","text":"<p>\u8caa\u6b32\u554f\u984c\u306e\u554f\u984c\u89e3\u6c7a\u30d7\u30ed\u30bb\u30b9\u306f\u3001\u4e00\u822c\u7684\u306b\u4ee5\u4e0b\u306e3\u3064\u306e\u30b9\u30c6\u30c3\u30d7\u306b\u5206\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002</p> <ol> <li>\u554f\u984c\u5206\u6790\uff1a\u554f\u984c\u306e\u7279\u5fb4\u3092\u6574\u7406\u3057\u7406\u89e3\u3059\u308b\u3002\u72b6\u614b\u5b9a\u7fa9\u3001\u6700\u9069\u5316\u76ee\u6a19\u3001\u5236\u7d04\u306a\u3069\u3092\u542b\u307f\u307e\u3059\u3002\u3053\u306e\u30b9\u30c6\u30c3\u30d7\u306f\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u3084\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u3067\u3082\u95a2\u4e0e\u3057\u307e\u3059\u3002</li> <li>\u8caa\u6b32\u6226\u7565\u306e\u6c7a\u5b9a\uff1a\u5404\u30b9\u30c6\u30c3\u30d7\u3067\u8caa\u6b32\u306a\u9078\u629e\u3092\u3059\u308b\u65b9\u6cd5\u3092\u6c7a\u5b9a\u3059\u308b\u3002\u3053\u306e\u6226\u7565\u306f\u5404\u30b9\u30c6\u30c3\u30d7\u3067\u554f\u984c\u306e\u898f\u6a21\u3092\u7e2e\u5c0f\u3057\u3001\u6700\u7d42\u7684\u306b\u554f\u984c\u5168\u4f53\u3092\u89e3\u6c7a\u3067\u304d\u307e\u3059\u3002</li> <li>\u6b63\u78ba\u6027\u306e\u8a3c\u660e\uff1a\u901a\u5e38\u3001\u554f\u984c\u304c\u8caa\u6b32\u9078\u629e\u6027\u3068\u6700\u9069\u90e8\u5206\u69cb\u9020\u306e\u4e21\u65b9\u3092\u6301\u3064\u3053\u3068\u3092\u8a3c\u660e\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u30b9\u30c6\u30c3\u30d7\u306b\u306f\u3001\u5e30\u7d0d\u6cd5\u3084\u80cc\u7406\u6cd5\u306a\u3069\u306e\u6570\u5b66\u7684\u8a3c\u660e\u304c\u5fc5\u8981\u306a\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002</li> </ol> <p>\u8caa\u6b32\u6226\u7565\u306e\u6c7a\u5b9a\u306f\u554f\u984c\u89e3\u6c7a\u306e\u6838\u5fc3\u30b9\u30c6\u30c3\u30d7\u3067\u3059\u304c\u3001\u5b9f\u88c5\u306f\u5bb9\u6613\u3067\u306f\u306a\u3044\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002\u4e3b\u306a\u7406\u7531\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\u3002</p> <ul> <li>\u7570\u306a\u308b\u554f\u984c\u9593\u3067\u8caa\u6b32\u6226\u7565\u306f\u5927\u304d\u304f\u7570\u306a\u308b\u3002\u591a\u304f\u306e\u554f\u984c\u3067\u306f\u3001\u8caa\u6b32\u6226\u7565\u306f\u304b\u306a\u308a\u76f4\u63a5\u7684\u3067\u3001\u4e00\u822c\u7684\u306a\u601d\u8003\u3068\u8a66\u884c\u3092\u901a\u3058\u3066\u601d\u3044\u3064\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u4e00\u90e8\u306e\u8907\u96d1\u306a\u554f\u984c\u3067\u306f\u3001\u8caa\u6b32\u6226\u7565\u306f\u975e\u5e38\u306b\u898b\u3064\u3051\u306b\u304f\u304f\u3001\u3053\u308c\u306f\u500b\u4eba\u306e\u554f\u984c\u89e3\u6c7a\u7d4c\u9a13\u3068\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u80fd\u529b\u306e\u771f\u306e\u30c6\u30b9\u30c8\u3067\u3059\u3002</li> <li>\u4e00\u90e8\u306e\u8caa\u6b32\u6226\u7565\u306f\u975e\u5e38\u306b\u8aa4\u89e3\u3092\u62db\u304f\u3002\u81ea\u4fe1\u3092\u6301\u3063\u3066\u8caa\u6b32\u6226\u7565\u3092\u8a2d\u8a08\u3057\u3001\u30b3\u30fc\u30c9\u3092\u66f8\u3044\u3066\u30c6\u30b9\u30c8\u306b\u63d0\u51fa\u3057\u305f\u3068\u304d\u3001\u4e00\u90e8\u306e\u30c6\u30b9\u30c8\u30b1\u30fc\u30b9\u304c\u901a\u3089\u306a\u3044\u53ef\u80fd\u6027\u304c\u9ad8\u3044\u3067\u3059\u3002\u3053\u308c\u306f\u8a2d\u8a08\u3055\u308c\u305f\u8caa\u6b32\u6226\u7565\u304c\u300c\u90e8\u5206\u7684\u306b\u6b63\u3057\u3044\u300d\u3060\u3051\u3067\u3042\u308b\u305f\u3081\u3067\u3001\u4e0a\u8a18\u306e\u30b3\u30a4\u30f3\u4ea4\u63db\u306e\u4f8b\u3067\u8aac\u660e\u3057\u305f\u901a\u308a\u3067\u3059\u3002</li> </ul> <p>\u6b63\u78ba\u6027\u3092\u78ba\u4fdd\u3059\u308b\u305f\u3081\u306b\u3001\u8caa\u6b32\u6226\u7565\u306b\u5bfe\u3057\u3066\u53b3\u5bc6\u306a\u6570\u5b66\u7684\u8a3c\u660e\u3092\u63d0\u4f9b\u3059\u3079\u304d\u3067\u3001\u901a\u5e38\u306f\u80cc\u7406\u6cd5\u3084\u6570\u5b66\u7684\u5e30\u7d0d\u6cd5\u3092\u542b\u307f\u307e\u3059\u3002</p> <p>\u3057\u304b\u3057\u3001\u6b63\u78ba\u6027\u3092\u8a3c\u660e\u3059\u308b\u3053\u3068\u306f\u5bb9\u6613\u306a\u4f5c\u696d\u3067\u306f\u306a\u3044\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002\u9014\u65b9\u306b\u66ae\u308c\u305f\u5834\u5408\u3001\u901a\u5e38\u306f\u30c6\u30b9\u30c8\u30b1\u30fc\u30b9\u306b\u57fa\u3065\u3044\u3066\u30b3\u30fc\u30c9\u3092\u30c7\u30d0\u30c3\u30b0\u3057\u3001\u8caa\u6b32\u6226\u7565\u3092\u6bb5\u968e\u7684\u306b\u4fee\u6b63\u3057\u691c\u8a3c\u3059\u308b\u3053\u3068\u3092\u9078\u629e\u3057\u307e\u3059\u3002</p>"},{"location":"chapter_greedy/greedy_algorithm/#1514","title":"15.1.4 \u00a0 \u8caa\u6b32\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u89e3\u6c7a\u3055\u308c\u308b\u5178\u578b\u7684\u306a\u554f\u984c","text":"<p>\u8caa\u6b32\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u3001\u8caa\u6b32\u9078\u629e\u3068\u6700\u9069\u90e8\u5206\u69cb\u9020\u306e\u6027\u8cea\u3092\u6e80\u305f\u3059\u6700\u9069\u5316\u554f\u984c\u306b\u3088\u304f\u9069\u7528\u3055\u308c\u307e\u3059\u3002\u4ee5\u4e0b\u306f\u5178\u578b\u7684\u306a\u8caa\u6b32\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u554f\u984c\u306e\u3044\u304f\u3064\u304b\u3067\u3059\u3002</p> <ul> <li>\u30b3\u30a4\u30f3\u4ea4\u63db\u554f\u984c\uff1a\u4e00\u90e8\u306e\u30b3\u30a4\u30f3\u306e\u7d44\u307f\u5408\u308f\u305b\u3067\u306f\u3001\u8caa\u6b32\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u5e38\u306b\u6700\u9069\u89e3\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002</li> <li>\u533a\u9593\u30b9\u30b1\u30b8\u30e5\u30fc\u30ea\u30f3\u30b0\u554f\u984c\uff1a\u3044\u304f\u3064\u304b\u306e\u30bf\u30b9\u30af\u304c\u3042\u308a\u3001\u305d\u308c\u305e\u308c\u304c\u4e00\u5b9a\u671f\u9593\u306b\u308f\u305f\u3063\u3066\u884c\u308f\u308c\u308b\u3068\u3057\u307e\u3059\u3002\u76ee\u6a19\u306f\u3067\u304d\u308b\u3060\u3051\u591a\u304f\u306e\u30bf\u30b9\u30af\u3092\u5b8c\u4e86\u3059\u308b\u3053\u3068\u3067\u3059\u3002\u5e38\u306b\u6700\u3082\u65e9\u304f\u7d42\u4e86\u3059\u308b\u30bf\u30b9\u30af\u3092\u9078\u629e\u3059\u308b\u3068\u3001\u8caa\u6b32\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u6700\u9069\u89e3\u3092\u9054\u6210\u3067\u304d\u307e\u3059\u3002</li> <li>\u5206\u6570\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c\uff1a\u30a2\u30a4\u30c6\u30e0\u306e\u30bb\u30c3\u30c8\u3068\u904b\u642c\u5bb9\u91cf\u304c\u4e0e\u3048\u3089\u308c\u3001\u76ee\u6a19\u306f\u7dcf\u91cd\u91cf\u304c\u904b\u642c\u5bb9\u91cf\u3092\u8d85\u3048\u305a\u3001\u7dcf\u4fa1\u5024\u304c\u6700\u5927\u5316\u3055\u308c\u308b\u3088\u3046\u306a\u30a2\u30a4\u30c6\u30e0\u306e\u30bb\u30c3\u30c8\u3092\u9078\u629e\u3059\u308b\u3053\u3068\u3067\u3059\u3002\u5e38\u306b\u6700\u9ad8\u306e\u4fa1\u5024\u5bfe\u91cd\u91cf\u6bd4\uff08\u4fa1\u5024/\u91cd\u91cf\uff09\u306e\u30a2\u30a4\u30c6\u30e0\u3092\u9078\u629e\u3059\u308b\u3068\u3001\u8caa\u6b32\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u4e00\u90e8\u306e\u30b1\u30fc\u30b9\u3067\u6700\u9069\u89e3\u3092\u9054\u6210\u3067\u304d\u307e\u3059\u3002</li> <li>\u682a\u5f0f\u53d6\u5f15\u554f\u984c\uff1a\u682a\u4fa1\u306e\u5c65\u6b74\u306e\u30bb\u30c3\u30c8\u304c\u4e0e\u3048\u3089\u308c\u3001\u8907\u6570\u56de\u306e\u53d6\u5f15\u3092\u884c\u3046\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u304c\u3001\u3059\u3067\u306b\u682a\u5f0f\u3092\u6240\u6709\u3057\u3066\u3044\u308b\u5834\u5408\u306f\u58f2\u5374\u5f8c\u3067\u306a\u3044\u3068\u518d\u5ea6\u8cfc\u5165\u3067\u304d\u307e\u305b\u3093\u3002\u76ee\u6a19\u306f\u6700\u5927\u5229\u76ca\u3092\u9054\u6210\u3059\u308b\u3053\u3068\u3067\u3059\u3002</li> <li>\u30cf\u30d5\u30de\u30f3\u7b26\u53f7\u5316\uff1a\u30cf\u30d5\u30de\u30f3\u7b26\u53f7\u5316\u306f\u7121\u640d\u5931\u30c7\u30fc\u30bf\u5727\u7e2e\u306b\u4f7f\u7528\u3055\u308c\u308b\u8caa\u6b32\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u3059\u3002\u30cf\u30d5\u30de\u30f3\u6728\u3092\u69cb\u7bc9\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u5e38\u306b\u6700\u4f4e\u983b\u5ea6\u306e2\u3064\u306e\u30ce\u30fc\u30c9\u3092\u7d71\u5408\u3057\u3001\u6700\u5c0f\u91cd\u307f\u4ed8\u304d\u30d1\u30b9\u9577\uff08\u7b26\u53f7\u5316\u9577\uff09\u306e\u30cf\u30d5\u30de\u30f3\u6728\u3092\u751f\u6210\u3057\u307e\u3059\u3002</li> <li>\u30c0\u30a4\u30af\u30b9\u30c8\u30e9\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\uff1a\u3053\u308c\u306f\u4e0e\u3048\u3089\u308c\u305f\u30bd\u30fc\u30b9\u9802\u70b9\u304b\u3089\u4ed6\u306e\u3059\u3079\u3066\u306e\u9802\u70b9\u3078\u306e\u6700\u77ed\u7d4c\u8def\u554f\u984c\u3092\u89e3\u6c7a\u3059\u308b\u305f\u3081\u306e\u8caa\u6b32\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u3059\u3002</li> </ul>"},{"location":"chapter_greedy/max_capacity_problem/","title":"15.3 \u00a0 \u6700\u5927\u5bb9\u91cf\u554f\u984c","text":"<p>Question</p> <p>\u914d\u5217 \\(ht\\) \u3092\u5165\u529b\u3057\u307e\u3059\u3002\u5404\u8981\u7d20\u306f\u5782\u76f4\u4ed5\u5207\u308a\u306e\u9ad8\u3055\u3092\u8868\u3057\u307e\u3059\u3002\u914d\u5217\u5185\u306e\u4efb\u610f\u306e2\u3064\u306e\u4ed5\u5207\u308a\u3068\u3001\u305d\u308c\u3089\u306e\u9593\u306e\u30b9\u30da\u30fc\u30b9\u306b\u3088\u3063\u3066\u30b3\u30f3\u30c6\u30ca\u3092\u5f62\u6210\u3067\u304d\u307e\u3059\u3002</p> <p>\u30b3\u30f3\u30c6\u30ca\u306e\u5bb9\u91cf\u306f\u9ad8\u3055\u3068\u5e45\u306e\u7a4d\uff08\u9762\u7a4d\uff09\u3067\u3001\u9ad8\u3055\u306f\u77ed\u3044\u65b9\u306e\u4ed5\u5207\u308a\u306b\u3088\u3063\u3066\u6c7a\u5b9a\u3055\u308c\u3001\u5e45\u306f2\u3064\u306e\u4ed5\u5207\u308a\u306e\u914d\u5217\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306e\u5dee\u3067\u3059\u3002</p> <p>\u30b3\u30f3\u30c6\u30ca\u306e\u5bb9\u91cf\u3092\u6700\u5927\u5316\u3059\u308b2\u3064\u306e\u4ed5\u5207\u308a\u3092\u914d\u5217\u304b\u3089\u9078\u629e\u3057\u3001\u3053\u306e\u6700\u5927\u5bb9\u91cf\u3092\u8fd4\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u4f8b\u3092\u4e0b\u306e\u56f3\u306b\u793a\u3057\u307e\u3059\u3002</p> <p></p> <p> \u56f3 15-7 \u00a0 \u6700\u5927\u5bb9\u91cf\u554f\u984c\u306e\u4f8b\u30c7\u30fc\u30bf </p> <p>\u30b3\u30f3\u30c6\u30ca\u306f\u4efb\u610f\u306e2\u3064\u306e\u4ed5\u5207\u308a\u306b\u3088\u3063\u3066\u5f62\u6210\u3055\u308c\u308b\u305f\u3081\u3001\u3053\u306e\u554f\u984c\u306e\u72b6\u614b\u306f2\u3064\u306e\u4ed5\u5207\u308a\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3067\u8868\u73fe\u3055\u308c\u3001\\([i, j]\\) \u3068\u8868\u8a18\u3055\u308c\u307e\u3059\u3002</p> <p>\u554f\u984c\u306e\u8a18\u8ff0\u306b\u3088\u308c\u3070\u3001\u5bb9\u91cf\u306f\u9ad8\u3055\u3068\u5e45\u306e\u7a4d\u306b\u7b49\u3057\u304f\u3001\u9ad8\u3055\u306f\u77ed\u3044\u65b9\u306e\u4ed5\u5207\u308a\u306b\u3088\u3063\u3066\u6c7a\u5b9a\u3055\u308c\u3001\u5e45\u306f2\u3064\u306e\u4ed5\u5207\u308a\u306e\u914d\u5217\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306e\u5dee\u3067\u3059\u3002\u5bb9\u91cf \\(cap[i, j]\\) \u306e\u5f0f\u306f\uff1a</p> \\[ cap[i, j] = \\min(ht[i], ht[j]) \\times (j - i) \\] <p>\u914d\u5217\u306e\u9577\u3055\u3092 \\(n\\) \u3068\u4eee\u5b9a\u3059\u308b\u3068\u30012\u3064\u306e\u4ed5\u5207\u308a\u306e\u7d44\u307f\u5408\u308f\u305b\u6570\uff08\u72b6\u614b\u306e\u7dcf\u6570\uff09\u306f \\(C_n^2 = \\frac{n(n - 1)}{2}\\) \u3067\u3059\u3002\u6700\u3082\u76f4\u63a5\u7684\u306a\u30a2\u30d7\u30ed\u30fc\u30c1\u306f**\u3059\u3079\u3066\u306e\u53ef\u80fd\u306a\u72b6\u614b\u3092\u5217\u6319\u3059\u308b**\u3053\u3068\u3067\u3001\u6642\u9593\u8a08\u7b97\u91cf\u306f \\(O(n^2)\\) \u306b\u306a\u308a\u307e\u3059\u3002</p>"},{"location":"chapter_greedy/max_capacity_problem/#1","title":"1. \u00a0 \u8caa\u6b32\u6226\u7565\u306e\u6c7a\u5b9a","text":"<p>\u3053\u306e\u554f\u984c\u306b\u306f\u3088\u308a\u52b9\u7387\u7684\u306a\u89e3\u6cd5\u304c\u3042\u308a\u307e\u3059\u3002\u4e0b\u306e\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u30a4\u30f3\u30c7\u30c3\u30af\u30b9 \\(i &lt; j\\) \u304b\u3064\u9ad8\u3055 \\(ht[i] &lt; ht[j]\\) \u306e\u72b6\u614b \\([i, j]\\) \u3092\u9078\u629e\u3057\u307e\u3059\u3002\u3064\u307e\u308a\u3001\\(i\\) \u306f\u77ed\u3044\u4ed5\u5207\u308a\u3001\\(j\\) \u306f\u9ad8\u3044\u4ed5\u5207\u308a\u3067\u3059\u3002</p> <p></p> <p> \u56f3 15-8 \u00a0 \u521d\u671f\u72b6\u614b </p> <p>\u4e0b\u306e\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u9ad8\u3044\u4ed5\u5207\u308a \\(j\\) \u3092\u77ed\u3044\u4ed5\u5207\u308a \\(i\\) \u306b\u8fd1\u3065\u3051\u3066\u79fb\u52d5\u3059\u308b\u3068\u3001\u5bb9\u91cf\u306f\u78ba\u5b9f\u306b\u6e1b\u5c11\u3057\u307e\u3059\u3002</p> <p>\u3053\u308c\u306f\u3001\u9ad8\u3044\u4ed5\u5207\u308a \\(j\\) \u3092\u79fb\u52d5\u3059\u308b\u3068\u3001\u5e45 \\(j-i\\) \u304c\u78ba\u5b9f\u306b\u6e1b\u5c11\u3059\u308b\u305f\u3081\u3067\u3059\u3002\u9ad8\u3055\u306f\u77ed\u3044\u4ed5\u5207\u308a\u306b\u3088\u3063\u3066\u6c7a\u5b9a\u3055\u308c\u308b\u305f\u3081\u3001\u9ad8\u3055\u306f\u540c\u3058\u307e\u307e\uff08\\(i\\) \u304c\u77ed\u3044\u4ed5\u5207\u308a\u306e\u307e\u307e\uff09\u304b\u6e1b\u5c11\uff08\u79fb\u52d5\u3057\u305f \\(j\\) \u304c\u77ed\u3044\u4ed5\u5207\u308a\u306b\u306a\u308b\uff09\u3057\u304b\u3042\u308a\u307e\u305b\u3093\u3002</p> <p></p> <p> \u56f3 15-9 \u00a0 \u9ad8\u3044\u4ed5\u5207\u308a\u3092\u5185\u5074\u306b\u79fb\u52d5\u3057\u305f\u5f8c\u306e\u72b6\u614b </p> <p>\u9006\u306b\u3001\u77ed\u3044\u4ed5\u5207\u308a \\(i\\) \u3092\u5185\u5074\u306b\u79fb\u52d5\u3059\u308b\u3053\u3068\u306b\u3088\u3063\u3066\u306e\u307f\u5bb9\u91cf\u3092\u5897\u52a0\u3055\u305b\u308b\u3053\u3068\u304c\u53ef\u80fd\u3067\u3059\u3002\u5e45\u306f\u78ba\u5b9f\u306b\u6e1b\u5c11\u3057\u307e\u3059\u304c\u3001\u9ad8\u3055\u304c\u5897\u52a0\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\uff08\u79fb\u52d5\u3057\u305f\u77ed\u3044\u4ed5\u5207\u308a \\(i\\) \u304c\u9ad8\u304f\u306a\u308b\u5834\u5408\uff09\u3002\u4f8b\u3048\u3070\u3001\u4e0b\u306e\u56f3\u3067\u306f\u3001\u77ed\u3044\u4ed5\u5207\u308a\u3092\u79fb\u52d5\u3057\u305f\u5f8c\u306b\u9762\u7a4d\u304c\u5897\u52a0\u3057\u3066\u3044\u307e\u3059\u3002</p> <p></p> <p> \u56f3 15-10 \u00a0 \u77ed\u3044\u4ed5\u5207\u308a\u3092\u5185\u5074\u306b\u79fb\u52d5\u3057\u305f\u5f8c\u306e\u72b6\u614b </p> <p>\u3053\u308c\u306b\u3088\u308a\u3001\u3053\u306e\u554f\u984c\u306e\u8caa\u6b32\u6226\u7565\u304c\u5c0e\u304b\u308c\u307e\u3059\uff1a\u30b3\u30f3\u30c6\u30ca\u306e\u4e21\u7aef\u306b2\u3064\u306e\u30dd\u30a4\u30f3\u30bf\u3092\u521d\u671f\u5316\u3057\u3001\u5404\u30e9\u30a6\u30f3\u30c9\u3067\u77ed\u3044\u4ed5\u5207\u308a\u306b\u5bfe\u5fdc\u3059\u308b\u30dd\u30a4\u30f3\u30bf\u3092\u5185\u5074\u306b\u79fb\u52d5\u3057\u30012\u3064\u306e\u30dd\u30a4\u30f3\u30bf\u304c\u51fa\u4f1a\u3046\u307e\u3067\u7d9a\u3051\u307e\u3059\u3002</p> <p>\u4e0b\u306e\u56f3\u306f\u8caa\u6b32\u6226\u7565\u306e\u5b9f\u884c\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002</p> <ol> <li>\u6700\u521d\u306b\u3001\u30dd\u30a4\u30f3\u30bf \\(i\\) \u3068 \\(j\\) \u304c\u914d\u5217\u306e\u4e21\u7aef\u306b\u914d\u7f6e\u3055\u308c\u307e\u3059\u3002</li> <li>\u73fe\u5728\u306e\u72b6\u614b\u306e\u5bb9\u91cf \\(cap[i, j]\\) \u3092\u8a08\u7b97\u3057\u3001\u6700\u5927\u5bb9\u91cf\u3092\u66f4\u65b0\u3057\u307e\u3059\u3002</li> <li>\u4ed5\u5207\u308a \\(i\\) \u3068 \\(j\\) \u306e\u9ad8\u3055\u3092\u6bd4\u8f03\u3057\u3001\u77ed\u3044\u4ed5\u5207\u308a\u30921\u30b9\u30c6\u30c3\u30d7\u5185\u5074\u306b\u79fb\u52d5\u3057\u307e\u3059\u3002</li> <li>\\(i\\) \u3068 \\(j\\) \u304c\u51fa\u4f1a\u3046\u307e\u3067\u30b9\u30c6\u30c3\u30d7 <code>2.</code> \u3068 <code>3.</code> \u3092\u7e70\u308a\u8fd4\u3057\u307e\u3059\u3002</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> \u56f3 15-11 \u00a0 \u6700\u5927\u5bb9\u91cf\u554f\u984c\u306e\u8caa\u6b32\u30d7\u30ed\u30bb\u30b9 </p>"},{"location":"chapter_greedy/max_capacity_problem/#2","title":"2. \u00a0 \u5b9f\u88c5","text":"<p>\u30b3\u30fc\u30c9\u306f\u6700\u5927 \\(n\\) \u56de\u30eb\u30fc\u30d7\u3059\u308b\u305f\u3081\u3001\u6642\u9593\u8a08\u7b97\u91cf\u306f \\(O(n)\\) \u3067\u3059\u3002</p> <p>\u5909\u6570 \\(i\\)\u3001\\(j\\)\u3001\\(res\\) \u306f\u4e00\u5b9a\u91cf\u306e\u8ffd\u52a0\u30b9\u30da\u30fc\u30b9\u3092\u4f7f\u7528\u3059\u308b\u305f\u3081\u3001\u7a7a\u9593\u8a08\u7b97\u91cf\u306f \\(O(1)\\) \u3067\u3059\u3002</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig max_capacity.py<pre><code>def max_capacity(ht: list[int]) -&gt; int:\n    \"\"\"\u6700\u5927\u5bb9\u91cf\uff1a\u8caa\u6b32\u6cd5\"\"\"\n    # i\u3001j \u3092\u521d\u671f\u5316\u3001\u914d\u5217\u306e\u4e21\u7aef\u3067\u5206\u5272\u3055\u305b\u308b\n    i, j = 0, len(ht) - 1\n    # \u521d\u671f\u6700\u5927\u5bb9\u91cf\u306f 0\n    res = 0\n    # 2 \u3064\u306e\u677f\u304c\u51fa\u4f1a\u3046\u307e\u3067\u8caa\u6b32\u9078\u629e\u3092\u30eb\u30fc\u30d7\n    while i &lt; j:\n        # \u6700\u5927\u5bb9\u91cf\u3092\u66f4\u65b0\n        cap = min(ht[i], ht[j]) * (j - i)\n        res = max(res, cap)\n        # \u77ed\u3044\u677f\u3092\u5185\u5074\u306b\u79fb\u52d5\n        if ht[i] &lt; ht[j]:\n            i += 1\n        else:\n            j -= 1\n    return res\n</code></pre> max_capacity.cpp<pre><code>/* \u6700\u5927\u5bb9\u91cf\uff1a\u8caa\u6b32\u6cd5 */\nint maxCapacity(vector&lt;int&gt; &amp;ht) {\n    // i\u3001j \u3092\u521d\u671f\u5316\u3057\u3001\u914d\u5217\u306e\u4e21\u7aef\u3067\u5206\u5272\u3055\u305b\u308b\n    int i = 0, j = ht.size() - 1;\n    // \u521d\u671f\u6700\u5927\u5bb9\u91cf\u306f 0\n    int res = 0;\n    // 2\u3064\u306e\u677f\u304c\u51fa\u4f1a\u3046\u307e\u3067\u8caa\u6b32\u9078\u629e\u3092\u30eb\u30fc\u30d7\n    while (i &lt; j) {\n        // \u6700\u5927\u5bb9\u91cf\u3092\u66f4\u65b0\n        int cap = min(ht[i], ht[j]) * (j - i);\n        res = max(res, cap);\n        // \u3088\u308a\u77ed\u3044\u677f\u3092\u5185\u5074\u306b\u79fb\u52d5\n        if (ht[i] &lt; ht[j]) {\n            i++;\n        } else {\n            j--;\n        }\n    }\n    return res;\n}\n</code></pre> max_capacity.java<pre><code>/* \u6700\u5927\u5bb9\u91cf\uff1a\u8caa\u6b32\u6cd5 */\nint maxCapacity(int[] ht) {\n    // i\u3001j \u3092\u521d\u671f\u5316\u3057\u3001\u914d\u5217\u306e\u4e21\u7aef\u3067\u5206\u5272\u3055\u305b\u308b\n    int i = 0, j = ht.length - 1;\n    // \u521d\u671f\u6700\u5927\u5bb9\u91cf\u306f 0\n    int res = 0;\n    // 2\u3064\u306e\u677f\u304c\u51fa\u4f1a\u3046\u307e\u3067\u8caa\u6b32\u9078\u629e\u3092\u30eb\u30fc\u30d7\n    while (i &lt; j) {\n        // \u6700\u5927\u5bb9\u91cf\u3092\u66f4\u65b0\n        int cap = Math.min(ht[i], ht[j]) * (j - i);\n        res = Math.max(res, cap);\n        // \u3088\u308a\u77ed\u3044\u677f\u3092\u5185\u5074\u306b\u79fb\u52d5\n        if (ht[i] &lt; ht[j]) {\n            i++;\n        } else {\n            j--;\n        }\n    }\n    return res;\n}\n</code></pre> max_capacity.cs<pre><code>[class]{max_capacity}-[func]{MaxCapacity}\n</code></pre> max_capacity.go<pre><code>[class]{}-[func]{maxCapacity}\n</code></pre> max_capacity.swift<pre><code>[class]{}-[func]{maxCapacity}\n</code></pre> max_capacity.js<pre><code>[class]{}-[func]{maxCapacity}\n</code></pre> max_capacity.ts<pre><code>[class]{}-[func]{maxCapacity}\n</code></pre> max_capacity.dart<pre><code>[class]{}-[func]{maxCapacity}\n</code></pre> max_capacity.rs<pre><code>[class]{}-[func]{max_capacity}\n</code></pre> max_capacity.c<pre><code>[class]{}-[func]{maxCapacity}\n</code></pre> max_capacity.kt<pre><code>[class]{}-[func]{maxCapacity}\n</code></pre> max_capacity.rb<pre><code>[class]{}-[func]{max_capacity}\n</code></pre> max_capacity.zig<pre><code>[class]{}-[func]{maxCapacity}\n</code></pre>"},{"location":"chapter_greedy/max_capacity_problem/#3","title":"3. \u00a0 \u6b63\u3057\u3055\u306e\u8a3c\u660e","text":"<p>\u8caa\u6b32\u6cd5\u304c\u5217\u6319\u3088\u308a\u3082\u9ad8\u901f\u3067\u3042\u308b\u7406\u7531\u306f\u3001\u5404\u30e9\u30a6\u30f3\u30c9\u306e\u8caa\u6b32\u9078\u629e\u304c\u4e00\u90e8\u306e\u72b6\u614b\u3092\u300c\u30b9\u30ad\u30c3\u30d7\u300d\u3059\u308b\u304b\u3089\u3067\u3059\u3002</p> <p>\u4f8b\u3048\u3070\u3001\\(i\\) \u304c\u77ed\u3044\u4ed5\u5207\u308a\u3067 \\(j\\) \u304c\u9ad8\u3044\u4ed5\u5207\u308a\u3067\u3042\u308b\u72b6\u614b \\(cap[i, j]\\) \u306e\u4e0b\u3067\u3001\u77ed\u3044\u4ed5\u5207\u308a \\(i\\) \u3092\u8caa\u6b32\u306b1\u30b9\u30c6\u30c3\u30d7\u5185\u5074\u306b\u79fb\u52d5\u3059\u308b\u3068\u3001\u4e0b\u306e\u56f3\u306b\u793a\u3059\u300c\u30b9\u30ad\u30c3\u30d7\u3055\u308c\u305f\u300d\u72b6\u614b\u306b\u3064\u306a\u304c\u308a\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u3053\u308c\u3089\u306e\u72b6\u614b\u306e\u5bb9\u91cf\u3092\u5f8c\u3067\u691c\u8a3c\u3067\u304d\u306a\u3044\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002</p> \\[ cap[i, i+1], cap[i, i+2], \\dots, cap[i, j-2], cap[i, j-1] \\] <p></p> <p> \u56f3 15-12 \u00a0 \u77ed\u3044\u4ed5\u5207\u308a\u306e\u79fb\u52d5\u306b\u3088\u3063\u3066\u30b9\u30ad\u30c3\u30d7\u3055\u308c\u308b\u72b6\u614b </p> <p>\u89b3\u5bdf\u3059\u308b\u3068\u3001\u3053\u308c\u3089\u306e\u30b9\u30ad\u30c3\u30d7\u3055\u308c\u305f\u72b6\u614b\u306f\u5b9f\u969b\u306b\u306f\u9ad8\u3044\u4ed5\u5207\u308a \\(j\\) \u304c\u5185\u5074\u306b\u79fb\u52d5\u3057\u305f\u3059\u3079\u3066\u306e\u72b6\u614b**\u3067\u3059\u3002\u9ad8\u3044\u4ed5\u5207\u308a\u3092\u5185\u5074\u306b\u79fb\u52d5\u3059\u308b\u3068\u5bb9\u91cf\u304c\u78ba\u5b9f\u306b\u6e1b\u5c11\u3059\u308b\u3053\u3068\u3092\u3059\u3067\u306b\u8a3c\u660e\u3057\u307e\u3057\u305f\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u30b9\u30ad\u30c3\u30d7\u3055\u308c\u305f\u72b6\u614b\u306f\u6700\u9069\u89e3\u3067\u3042\u308b\u53ef\u80fd\u6027\u304c\u306a\u304f\u3001**\u305d\u308c\u3089\u3092\u30b9\u30ad\u30c3\u30d7\u3057\u3066\u3082\u6700\u9069\u89e3\u3092\u898b\u9003\u3059\u3053\u3068\u306f\u3042\u308a\u307e\u305b\u3093\u3002</p> <p>\u5206\u6790\u306b\u3088\u308a\u3001\u77ed\u3044\u4ed5\u5207\u308a\u3092\u79fb\u52d5\u3059\u308b\u64cd\u4f5c\u306f\u300c\u5b89\u5168\u300d\u3067\u3042\u308a\u3001\u8caa\u6b32\u6226\u7565\u304c\u52b9\u679c\u7684\u3067\u3042\u308b\u3053\u3068\u304c\u793a\u3055\u308c\u307e\u3059\u3002</p>"},{"location":"chapter_greedy/max_product_cutting_problem/","title":"15.4 \u00a0 \u6700\u5927\u7a4d\u5207\u65ad\u554f\u984c","text":"<p>Question</p> <p>\u6b63\u306e\u6574\u6570 \\(n\\) \u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u304d\u3001\u305d\u308c\u3092\u5408\u8a08\u304c \\(n\\) \u306b\u306a\u308b\u5c11\u306a\u304f\u3068\u30822\u3064\u306e\u6b63\u306e\u6574\u6570\u306b\u5206\u5272\u3057\u3001\u3053\u308c\u3089\u306e\u6574\u6570\u306e\u6700\u5927\u7a4d\u3092\u6c42\u3081\u3066\u304f\u3060\u3055\u3044\u3002\u4e0b\u306e\u56f3\u306b\u793a\u3059\u3068\u304a\u308a\u3067\u3059\u3002</p> <p></p> <p> \u56f3 15-13 \u00a0 \u6700\u5927\u7a4d\u5207\u65ad\u554f\u984c\u306e\u5b9a\u7fa9 </p> <p>\\(n\\) \u3092 \\(m\\) \u500b\u306e\u6574\u6570\u56e0\u5b50\u306b\u5206\u5272\u3059\u308b\u3068\u4eee\u5b9a\u3057\u3001\\(i\\) \u756a\u76ee\u306e\u56e0\u5b50\u3092 \\(n_i\\) \u3068\u8868\u8a18\u3059\u308b\u3068\u3001</p> \\[ n = \\sum_{i=1}^{m}n_i \\] <p>\u3053\u306e\u554f\u984c\u306e\u76ee\u6a19\u306f\u3001\u3059\u3079\u3066\u306e\u6574\u6570\u56e0\u5b50\u306e\u6700\u5927\u7a4d\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u3067\u3059\u3002\u3059\u306a\u308f\u3061\u3001</p> \\[ \\max(\\prod_{i=1}^{m}n_i) \\] <p>\u8003\u616e\u3059\u3079\u304d\u70b9\uff1a\u5206\u5272\u6570 \\(m\\) \u306f\u3069\u306e\u7a0b\u5ea6\u5927\u304d\u304f\u3059\u3079\u304d\u304b\u3001\u5404 \\(n_i\\) \u306f\u4f55\u3067\u3042\u308b\u3079\u304d\u304b\uff1f</p>"},{"location":"chapter_greedy/max_product_cutting_problem/#1","title":"1. \u00a0 \u8caa\u6b32\u6226\u7565\u306e\u6c7a\u5b9a","text":"<p>\u7d4c\u9a13\u7684\u306b\u30012\u3064\u306e\u6574\u6570\u306e\u7a4d\u306f\u591a\u304f\u306e\u5834\u5408\u305d\u306e\u548c\u3088\u308a\u3082\u5927\u304d\u304f\u306a\u308a\u307e\u3059\u3002\\(n\\) \u304b\u3089\u56e0\u5b50 \\(2\\) \u3092\u5206\u5272\u3059\u308b\u3068\u4eee\u5b9a\u3059\u308b\u3068\u3001\u305d\u306e\u7a4d\u306f \\(2(n-2)\\) \u3067\u3059\u3002\u3053\u306e\u7a4d\u3092 \\(n\\) \u3068\u6bd4\u8f03\u3057\u307e\u3059\uff1a</p> \\[ \\begin{aligned} 2(n-2) &amp; \\geq n \\newline 2n - n - 4 &amp; \\geq 0 \\newline n &amp; \\geq 4 \\end{aligned} \\] <p>\u4e0b\u306e\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\\(n \\geq 4\\) \u306e\u3068\u304d\u3001\\(2\\) \u3092\u5206\u5272\u3059\u308b\u3068\u7a4d\u304c\u5897\u52a0\u3057\u307e\u3059\u3002\u3053\u308c\u306f4\u4ee5\u4e0a\u306e\u6574\u6570\u3092\u5206\u5272\u3059\u3079\u304d\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002</p> <p>\u8caa\u6b32\u6226\u75651\uff1a\u5206\u5272\u30b9\u30ad\u30fc\u30e0\u304c \\(\\geq 4\\) \u306e\u56e0\u5b50\u3092\u542b\u3080\u5834\u5408\u3001\u305d\u308c\u3089\u306f\u3055\u3089\u306b\u5206\u5272\u3055\u308c\u308b\u3079\u304d\u3067\u3059\u3002\u6700\u7d42\u7684\u306a\u5206\u5272\u306f\u56e0\u5b50 \\(1\\)\u3001\\(2\\)\u3001\\(3\\) \u306e\u307f\u3092\u542b\u3080\u3079\u304d\u3067\u3059\u3002</p> <p></p> <p> \u56f3 15-14 \u00a0 \u5206\u5272\u306b\u3088\u308b\u7a4d\u306e\u5897\u52a0 </p> <p>\u6b21\u306b\u3001\u3069\u306e\u56e0\u5b50\u304c\u6700\u9069\u304b\u3092\u8003\u616e\u3057\u307e\u3059\u3002\u56e0\u5b50 \\(1\\)\u3001\\(2\\)\u3001\\(3\\) \u306e\u4e2d\u3067\u3001\u660e\u3089\u304b\u306b \\(1\\) \u304c\u6700\u60aa\u3067\u3059\u3002\\(1 \\times (n-1) &lt; n\\) \u304c\u5e38\u306b\u6210\u308a\u7acb\u3064\u305f\u3081\u3001\\(1\\) \u3092\u5206\u5272\u3059\u308b\u3068\u5b9f\u969b\u306b\u7a4d\u304c\u6e1b\u5c11\u3057\u307e\u3059\u3002</p> <p>\u4e0b\u306e\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\\(n = 6\\) \u306e\u3068\u304d\u3001\\(3 \\times 3 &gt; 2 \\times 2 \\times 2\\) \u3067\u3059\u3002\u3053\u308c\u306f \\(3\\) \u3092\u5206\u5272\u3059\u308b\u65b9\u304c \\(2\\) \u3092\u5206\u5272\u3059\u308b\u3088\u308a\u3082\u826f\u3044\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002</p> <p>\u8caa\u6b32\u6226\u75652\uff1a\u5206\u5272\u30b9\u30ad\u30fc\u30e0\u306b\u306f\u6700\u5927\u30672\u3064\u306e \\(2\\) \u304c\u3042\u308b\u3079\u304d\u3067\u3059\u30023\u3064\u306e \\(2\\) \u306f\u5e38\u306b2\u3064\u306e \\(3\\) \u306b\u7f6e\u304d\u63db\u3048\u3066\u3088\u308a\u9ad8\u3044\u7a4d\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u304b\u3089\u3067\u3059\u3002</p> <p></p> <p> \u56f3 15-15 \u00a0 \u6700\u9069\u306a\u5206\u5272\u56e0\u5b50 </p> <p>\u4e0a\u8a18\u304b\u3089\u3001\u4ee5\u4e0b\u306e\u8caa\u6b32\u6226\u7565\u3092\u5c0e\u51fa\u3067\u304d\u307e\u3059\u3002</p> <ol> <li>\u5165\u529b\u6574\u6570 \\(n\\) \u306b\u3064\u3044\u3066\u3001\u4f59\u308a\u304c \\(0\\)\u3001\\(1\\)\u3001\u307e\u305f\u306f \\(2\\) \u306b\u306a\u308b\u307e\u3067\u56e0\u5b50 \\(3\\) \u3092\u7d99\u7d9a\u7684\u306b\u5206\u5272\u3057\u307e\u3059\u3002</li> <li>\u4f59\u308a\u304c \\(0\\) \u306e\u5834\u5408\u3001\\(n\\) \u304c \\(3\\) \u306e\u500d\u6570\u3067\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3059\u308b\u305f\u3081\u3001\u305d\u308c\u4ee5\u4e0a\u306e\u884c\u52d5\u306f\u53d6\u308a\u307e\u305b\u3093\u3002</li> <li>\u4f59\u308a\u304c \\(2\\) \u306e\u5834\u5408\u3001\u3055\u3089\u306b\u5206\u5272\u3092\u7d9a\u3051\u305a\u3001\u305d\u306e\u307e\u307e\u4fdd\u6301\u3057\u307e\u3059\u3002</li> <li>\u4f59\u308a\u304c \\(1\\) \u306e\u5834\u5408\u3001\\(2 \\times 2 &gt; 1 \\times 3\\) \u3067\u3042\u308b\u305f\u3081\u3001\u6700\u5f8c\u306e \\(3\\) \u3092 \\(2\\) \u306b\u7f6e\u304d\u63db\u3048\u308b\u3079\u304d\u3067\u3059\u3002</li> </ol>"},{"location":"chapter_greedy/max_product_cutting_problem/#2","title":"2. \u00a0 \u30b3\u30fc\u30c9\u5b9f\u88c5","text":"<p>\u4e0b\u306e\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u6574\u6570\u3092\u5206\u5272\u3059\u308b\u305f\u3081\u306b\u30eb\u30fc\u30d7\u3092\u4f7f\u7528\u3059\u308b\u5fc5\u8981\u306f\u306a\u304f\u3001\u5e8a\u9664\u7b97\u6f14\u7b97\u3092\u4f7f\u7528\u3057\u3066 \\(3\\) \u306e\u6570 \\(a\\) \u3092\u53d6\u5f97\u3057\u3001\u5270\u4f59\u6f14\u7b97\u3092\u4f7f\u7528\u3057\u3066\u4f59\u308a \\(b\\) \u3092\u53d6\u5f97\u3067\u304d\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\uff1a</p> \\[ n = 3a + b \\] <p>\\(n \\leq 3\\) \u306e\u5883\u754c\u30b1\u30fc\u30b9\u3067\u306f\u3001\\(1\\) \u3092\u5206\u5272\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u3001\u7a4d\u306f \\(1 \\times (n - 1)\\) \u3067\u3042\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig max_product_cutting.py<pre><code>def max_product_cutting(n: int) -&gt; int:\n    \"\"\"\u5207\u65ad\u306e\u6700\u5927\u7a4d\uff1a\u8caa\u6b32\u6cd5\"\"\"\n    # n &lt;= 3 \u306e\u5834\u5408\u30011 \u3092\u5207\u308a\u51fa\u3059\u5fc5\u8981\u304c\u3042\u308b\n    if n &lt;= 3:\n        return 1 * (n - 1)\n    # \u8caa\u6b32\u7684\u306b 3 \u3092\u5207\u308a\u51fa\u3059\u3001a \u306f 3 \u306e\u500b\u6570\u3001b \u306f\u4f59\u308a\n    a, b = n // 3, n % 3\n    if b == 1:\n        # \u4f59\u308a\u304c 1 \u306e\u5834\u5408\u30011 * 3 \u306e\u30da\u30a2\u3092 2 * 2 \u306b\u5909\u63db\n        return int(math.pow(3, a - 1)) * 2 * 2\n    if b == 2:\n        # \u4f59\u308a\u304c 2 \u306e\u5834\u5408\u3001\u4f55\u3082\u3057\u306a\u3044\n        return int(math.pow(3, a)) * 2\n    # \u4f59\u308a\u304c 0 \u306e\u5834\u5408\u3001\u4f55\u3082\u3057\u306a\u3044\n    return int(math.pow(3, a))\n</code></pre> max_product_cutting.cpp<pre><code>/* \u6700\u5927\u7a4d\u5207\u65ad\uff1a\u8caa\u6b32\u6cd5 */\nint maxProductCutting(int n) {\n    // n &lt;= 3 \u306e\u5834\u5408\u30011 \u3092\u5207\u308a\u51fa\u3059\u5fc5\u8981\u304c\u3042\u308b\n    if (n &lt;= 3) {\n        return 1 * (n - 1);\n    }\n    // \u8caa\u6b32\u306b 3 \u3092\u5207\u308a\u51fa\u3059\u3002a \u306f 3 \u306e\u500b\u6570\u3001b \u306f\u4f59\u308a\n    int a = n / 3;\n    int b = n % 3;\n    if (b == 1) {\n        // \u4f59\u308a\u304c 1 \u306e\u5834\u5408\u30011 * 3 \u306e\u30da\u30a2\u3092 2 * 2 \u306b\u5909\u63db\n        return (int)pow(3, a - 1) * 2 * 2;\n    }\n    if (b == 2) {\n        // \u4f59\u308a\u304c 2 \u306e\u5834\u5408\u3001\u4f55\u3082\u3057\u306a\u3044\n        return (int)pow(3, a) * 2;\n    }\n    // \u4f59\u308a\u304c 0 \u306e\u5834\u5408\u3001\u4f55\u3082\u3057\u306a\u3044\n    return (int)pow(3, a);\n}\n</code></pre> max_product_cutting.java<pre><code>/* \u6700\u5927\u7a4d\u5207\u65ad\uff1a\u8caa\u6b32\u6cd5 */\nint maxProductCutting(int n) {\n    // n &lt;= 3 \u306e\u5834\u5408\u30011 \u3092\u5207\u308a\u51fa\u3059\u5fc5\u8981\u304c\u3042\u308b\n    if (n &lt;= 3) {\n        return 1 * (n - 1);\n    }\n    // \u8caa\u6b32\u306b 3 \u3092\u5207\u308a\u51fa\u3059\u3002a \u306f 3 \u306e\u500b\u6570\u3001b \u306f\u4f59\u308a\n    int a = n / 3;\n    int b = n % 3;\n    if (b == 1) {\n        // \u4f59\u308a\u304c 1 \u306e\u5834\u5408\u30011 * 3 \u306e\u30da\u30a2\u3092 2 * 2 \u306b\u5909\u63db\n        return (int) Math.pow(3, a - 1) * 2 * 2;\n    }\n    if (b == 2) {\n        // \u4f59\u308a\u304c 2 \u306e\u5834\u5408\u3001\u4f55\u3082\u3057\u306a\u3044\n        return (int) Math.pow(3, a) * 2;\n    }\n    // \u4f59\u308a\u304c 0 \u306e\u5834\u5408\u3001\u4f55\u3082\u3057\u306a\u3044\n    return (int) Math.pow(3, a);\n}\n</code></pre> max_product_cutting.cs<pre><code>[class]{max_product_cutting}-[func]{MaxProductCutting}\n</code></pre> max_product_cutting.go<pre><code>[class]{}-[func]{maxProductCutting}\n</code></pre> max_product_cutting.swift<pre><code>[class]{}-[func]{maxProductCutting}\n</code></pre> max_product_cutting.js<pre><code>[class]{}-[func]{maxProductCutting}\n</code></pre> max_product_cutting.ts<pre><code>[class]{}-[func]{maxProductCutting}\n</code></pre> max_product_cutting.dart<pre><code>[class]{}-[func]{maxProductCutting}\n</code></pre> max_product_cutting.rs<pre><code>[class]{}-[func]{max_product_cutting}\n</code></pre> max_product_cutting.c<pre><code>[class]{}-[func]{maxProductCutting}\n</code></pre> max_product_cutting.kt<pre><code>[class]{}-[func]{maxProductCutting}\n</code></pre> max_product_cutting.rb<pre><code>[class]{}-[func]{max_product_cutting}\n</code></pre> max_product_cutting.zig<pre><code>[class]{}-[func]{maxProductCutting}\n</code></pre> <p></p> <p> \u56f3 15-16 \u00a0 \u5207\u65ad\u5f8c\u306e\u6700\u5927\u7a4d\u306e\u8a08\u7b97\u65b9\u6cd5 </p> <p>\u6642\u9593\u8a08\u7b97\u91cf\u306f\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u306e\u3079\u304d\u4e57\u6f14\u7b97\u306e\u5b9f\u88c5\u306b\u4f9d\u5b58\u3057\u307e\u3059\u3002Python\u3067\u306f\u3001\u3088\u304f\u4f7f\u7528\u3055\u308c\u308b\u3079\u304d\u4e57\u8a08\u7b97\u95a2\u6570\u306f3\u7a2e\u985e\u3042\u308a\u307e\u3059\uff1a</p> <ul> <li>\u6f14\u7b97\u5b50 <code>**</code> \u3068\u95a2\u6570 <code>pow()</code> \u306e\u4e21\u65b9\u306e\u6642\u9593\u8a08\u7b97\u91cf\u306f \\(O(\\log\u2061 a)\\) \u3067\u3059\u3002</li> <li><code>math.pow()</code> \u95a2\u6570\u306f\u5185\u90e8\u3067C\u8a00\u8a9e\u30e9\u30a4\u30d6\u30e9\u30ea\u306e <code>pow()</code> \u95a2\u6570\u3092\u547c\u3073\u51fa\u3057\u3001\u6d6e\u52d5\u5c0f\u6570\u70b9\u3079\u304d\u4e57\u3092\u5b9f\u884c\u3057\u3001\u6642\u9593\u8a08\u7b97\u91cf\u306f \\(O(1)\\) \u3067\u3059\u3002</li> </ul> <p>\u5909\u6570 \\(a\\) \u3068 \\(b\\) \u306f\u4e00\u5b9a\u30b5\u30a4\u30ba\u306e\u8ffd\u52a0\u30b9\u30da\u30fc\u30b9\u3092\u4f7f\u7528\u3059\u308b\u305f\u3081\u3001\u7a7a\u9593\u8a08\u7b97\u91cf\u306f \\(O(1)\\) \u3067\u3059\u3002</p>"},{"location":"chapter_greedy/max_product_cutting_problem/#3","title":"3. \u00a0 \u6b63\u3057\u3055\u306e\u8a3c\u660e","text":"<p>\u80cc\u7406\u6cd5\u3092\u4f7f\u7528\u3057\u3001\\(n \\geq 3\\) \u306e\u30b1\u30fc\u30b9\u306e\u307f\u3092\u5206\u6790\u3057\u307e\u3059\u3002</p> <ol> <li>\u3059\u3079\u3066\u306e\u56e0\u5b50 \\(\\leq 3\\)\uff1a\u6700\u9069\u5206\u5272\u30b9\u30ad\u30fc\u30e0\u304c\u56e0\u5b50 \\(x \\geq 4\\) \u3092\u542b\u3080\u3068\u4eee\u5b9a\u3059\u308b\u3068\u3001\u305d\u308c\u3092\u78ba\u5b9f\u306b \\(2(x-2)\\) \u306b\u3055\u3089\u306b\u5206\u5272\u3067\u304d\u3001\u3088\u308a\u5927\u304d\u306a\u7a4d\u3092\u5f97\u3089\u308c\u307e\u3059\u3002\u3053\u308c\u306f\u4eee\u5b9a\u3068\u77db\u76fe\u3057\u307e\u3059\u3002</li> <li>\u5206\u5272\u30b9\u30ad\u30fc\u30e0\u306b \\(1\\) \u304c\u542b\u307e\u308c\u306a\u3044\uff1a\u6700\u9069\u5206\u5272\u30b9\u30ad\u30fc\u30e0\u304c\u56e0\u5b50 \\(1\\) \u3092\u542b\u3080\u3068\u4eee\u5b9a\u3059\u308b\u3068\u3001\u305d\u308c\u3092\u78ba\u5b9f\u306b\u5225\u306e\u56e0\u5b50\u3068\u7d50\u5408\u3057\u3066\u3088\u308a\u5927\u304d\u306a\u7a4d\u3092\u5f97\u3089\u308c\u307e\u3059\u3002\u3053\u308c\u306f\u4eee\u5b9a\u3068\u77db\u76fe\u3057\u307e\u3059\u3002</li> <li>\u5206\u5272\u30b9\u30ad\u30fc\u30e0\u306b\u306f\u6700\u5927\u30672\u3064\u306e \\(2\\) \u304c\u542b\u307e\u308c\u308b\uff1a\u6700\u9069\u5206\u5272\u30b9\u30ad\u30fc\u30e0\u304c3\u3064\u306e \\(2\\) \u3092\u542b\u3080\u3068\u4eee\u5b9a\u3059\u308b\u3068\u3001\u305d\u308c\u3089\u3092\u78ba\u5b9f\u306b2\u3064\u306e \\(3\\) \u306b\u7f6e\u304d\u63db\u3048\u3066\u3001\u3088\u308a\u9ad8\u3044\u7a4d\u3092\u9054\u6210\u3067\u304d\u307e\u3059\u3002\u3053\u308c\u306f\u4eee\u5b9a\u3068\u77db\u76fe\u3057\u307e\u3059\u3002</li> </ol>"},{"location":"chapter_greedy/summary/","title":"15.5 \u00a0 \u307e\u3068\u3081","text":"<ul> <li>\u8caa\u6b32\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u6700\u9069\u5316\u554f\u984c\u3092\u89e3\u6c7a\u3059\u308b\u305f\u3081\u306b\u3088\u304f\u4f7f\u7528\u3055\u308c\u3001\u539f\u7406\u306f\u5404\u6c7a\u5b9a\u6bb5\u968e\u3067\u5c40\u6240\u7684\u306b\u6700\u9069\u306a\u6c7a\u5b9a\u3092\u884c\u3044\u3001\u30b0\u30ed\u30fc\u30d0\u30eb\u306b\u6700\u9069\u306a\u89e3\u3092\u9054\u6210\u3059\u308b\u3053\u3068\u3067\u3059\u3002</li> <li>\u8caa\u6b32\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u8caa\u6b32\u306a\u9078\u629e\u3092\u6b21\u3005\u3068\u53cd\u5fa9\u7684\u306b\u884c\u3044\u3001\u5404\u30e9\u30a6\u30f3\u30c9\u3067\u554f\u984c\u3092\u3088\u308a\u5c0f\u3055\u306a\u90e8\u5206\u554f\u984c\u306b\u5909\u63db\u3057\u3001\u554f\u984c\u304c\u89e3\u6c7a\u3055\u308c\u308b\u307e\u3067\u7d9a\u3051\u307e\u3059\u3002</li> <li>\u8caa\u6b32\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u5b9f\u88c5\u304c\u7c21\u5358\u306a\u3060\u3051\u3067\u306a\u304f\u3001\u554f\u984c\u89e3\u6c7a\u52b9\u7387\u3082\u9ad8\u3044\u3067\u3059\u3002\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u3068\u6bd4\u8f03\u3057\u3066\u3001\u8caa\u6b32\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u4e00\u822c\u7684\u306b\u3088\u308a\u4f4e\u3044\u6642\u9593\u8a08\u7b97\u91cf\u3092\u6301\u3061\u307e\u3059\u3002</li> <li>\u30b3\u30a4\u30f3\u4ea4\u63db\u554f\u984c\u306b\u304a\u3044\u3066\u3001\u8caa\u6b32\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u7279\u5b9a\u306e\u30b3\u30a4\u30f3\u306e\u7d44\u307f\u5408\u308f\u305b\u306b\u5bfe\u3057\u3066\u6700\u9069\u89e3\u3092\u4fdd\u8a3c\u3067\u304d\u307e\u3059\u304c\u3001\u4ed6\u306e\u7d44\u307f\u5408\u308f\u305b\u3067\u306f\u8caa\u6b32\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u304c\u975e\u5e38\u306b\u60aa\u3044\u89e3\u3092\u898b\u3064\u3051\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002</li> <li>\u8caa\u6b32\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u89e3\u6cd5\u306b\u9069\u3057\u305f\u554f\u984c\u306f2\u3064\u306e\u4e3b\u8981\u306a\u6027\u8cea\u3092\u6301\u3061\u307e\u3059\uff1a\u8caa\u6b32\u9078\u629e\u6027\u3068\u6700\u9069\u90e8\u5206\u69cb\u9020\u3002\u8caa\u6b32\u9078\u629e\u6027\u306f\u8caa\u6b32\u6226\u7565\u306e\u52b9\u679c\u3092\u8868\u3057\u307e\u3059\u3002</li> <li>\u4e00\u90e8\u306e\u8907\u96d1\u306a\u554f\u984c\u3067\u306f\u3001\u8caa\u6b32\u9078\u629e\u6027\u3092\u8a3c\u660e\u3059\u308b\u3053\u3068\u306f\u7c21\u5358\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u9006\u306b\u3001\u7121\u52b9\u6027\u3092\u8a3c\u660e\u3059\u308b\u3053\u3068\u306f\u3057\u3070\u3057\u3070\u3088\u308a\u5bb9\u6613\u3067\u3001\u30b3\u30a4\u30f3\u4ea4\u63db\u554f\u984c\u306a\u3069\u304c\u305d\u306e\u4f8b\u3067\u3059\u3002</li> <li>\u8caa\u6b32\u554f\u984c\u306e\u89e3\u6c7a\u306f\u4e3b\u306b3\u3064\u306e\u30b9\u30c6\u30c3\u30d7\u304b\u3089\u69cb\u6210\u3055\u308c\u307e\u3059\uff1a\u554f\u984c\u5206\u6790\u3001\u8caa\u6b32\u6226\u7565\u306e\u6c7a\u5b9a\u3001\u6b63\u3057\u3055\u306e\u8a3c\u660e\u3002\u3053\u306e\u3046\u3061\u3001\u8caa\u6b32\u6226\u7565\u306e\u6c7a\u5b9a\u304c\u91cd\u8981\u306a\u30b9\u30c6\u30c3\u30d7\u3067\u3042\u308a\u3001\u6b63\u3057\u3055\u306e\u8a3c\u660e\u304c\u3057\u3070\u3057\u3070\u6311\u6226\u3068\u306a\u308a\u307e\u3059\u3002</li> <li>\u5206\u6570\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c\u306f0-1\u30ca\u30c3\u30d7\u30b5\u30c3\u30af\u554f\u984c\u306b\u57fa\u3065\u3044\u3066\u30a2\u30a4\u30c6\u30e0\u306e\u4e00\u90e8\u306e\u9078\u629e\u3092\u53ef\u80fd\u306b\u3057\u3001\u3057\u305f\u304c\u3063\u3066\u8caa\u6b32\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u4f7f\u7528\u3057\u3066\u89e3\u6c7a\u3067\u304d\u307e\u3059\u3002\u8caa\u6b32\u6226\u7565\u306e\u6b63\u3057\u3055\u306f\u80cc\u7406\u6cd5\u306b\u3088\u3063\u3066\u8a3c\u660e\u3067\u304d\u307e\u3059\u3002</li> <li>\u6700\u5927\u5bb9\u91cf\u554f\u984c\u306f\u5168\u63a2\u7d22\u6cd5\u3067\u89e3\u6c7a\u3067\u304d\u3001\u6642\u9593\u8a08\u7b97\u91cf\u306f \\(O(n^2)\\) \u3067\u3059\u3002\u8caa\u6b32\u6226\u7565\u3092\u8a2d\u8a08\u3059\u308b\u3053\u3068\u3067\u3001\u5404\u30e9\u30a6\u30f3\u30c9\u3067\u77ed\u3044\u677f\u3092\u5185\u5074\u306b\u79fb\u52d5\u3057\u3001\u6642\u9593\u8a08\u7b97\u91cf\u3092 \\(O(n)\\) \u306b\u6700\u9069\u5316\u3057\u307e\u3059\u3002</li> <li>\u5207\u65ad\u5f8c\u306e\u6700\u5927\u7a4d\u554f\u984c\u306b\u304a\u3044\u3066\u30012\u3064\u306e\u8caa\u6b32\u6226\u7565\u3092\u5c0e\u51fa\u3057\u307e\u3059\uff1a\\(\\geq 4\\) \u306e\u6574\u6570\u306f\u7d99\u7d9a\u7684\u306b\u5207\u65ad\u3055\u308c\u308b\u3079\u304d\u3067\u3001\u6700\u9069\u306a\u5207\u65ad\u56e0\u5b50\u306f \\(3\\) \u3067\u3059\u3002\u30b3\u30fc\u30c9\u306b\u306f\u3079\u304d\u4e57\u6f14\u7b97\u304c\u542b\u307e\u308c\u3001\u6642\u9593\u8a08\u7b97\u91cf\u306f\u3079\u304d\u4e57\u6f14\u7b97\u306e\u5b9f\u88c5\u65b9\u6cd5\u306b\u4f9d\u5b58\u3057\u3001\u4e00\u822c\u7684\u306b \\(O(1)\\) \u307e\u305f\u306f \\(O(\\log n)\\) \u3067\u3059\u3002</li> </ul>"},{"location":"chapter_hashing/","title":"\u7b2c 6 \u7ae0 \u00a0 \u30cf\u30c3\u30b7\u30e5\u8868","text":"<p>Abstract</p> <p>\u30b3\u30f3\u30d4\u30e5\u30fc\u30c6\u30a3\u30f3\u30b0\u306e\u4e16\u754c\u306b\u304a\u3044\u3066\u3001\u30cf\u30c3\u30b7\u30e5\u8868\u306f\u8ce2\u3044\u53f8\u66f8\u306e\u3088\u3046\u306a\u3082\u306e\u3067\u3059\u3002</p> <p>\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u756a\u53f7\u306e\u8a08\u7b97\u65b9\u6cd5\u3092\u7406\u89e3\u3057\u3001\u76ee\u7684\u306e\u672c\u3092\u8fc5\u901f\u306b\u53d6\u5f97\u3059\u308b\u3053\u3068\u3092\u53ef\u80fd\u306b\u3057\u307e\u3059\u3002</p>"},{"location":"chapter_hashing/#_1","title":"\u7ae0\u306e\u5185\u5bb9","text":"<ul> <li>6.1 \u00a0 \u30cf\u30c3\u30b7\u30e5\u8868</li> <li>6.2 \u00a0 \u30cf\u30c3\u30b7\u30e5\u885d\u7a81</li> <li>6.3 \u00a0 \u30cf\u30c3\u30b7\u30e5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0</li> <li>6.4 \u00a0 \u307e\u3068\u3081</li> </ul>"},{"location":"chapter_hashing/hash_algorithm/","title":"6.3 \u00a0 \u30cf\u30c3\u30b7\u30e5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0","text":"<p>\u524d\u306e2\u3064\u306e\u7bc0\u3067\u306f\u3001\u30cf\u30c3\u30b7\u30e5\u8868\u306e\u52d5\u4f5c\u539f\u7406\u3068\u30cf\u30c3\u30b7\u30e5\u885d\u7a81\u3092\u51e6\u7406\u3059\u308b\u65b9\u6cd5\u3092\u7d39\u4ecb\u3057\u307e\u3057\u305f\u3002\u3057\u304b\u3057\u3001\u30aa\u30fc\u30d7\u30f3\u30a2\u30c9\u30ec\u30b9\u6cd5\u3068\u9023\u9396\u6cd5\u306f\u3069\u3061\u3089\u3082**\u885d\u7a81\u304c\u767a\u751f\u3057\u305f\u969b\u306b\u30cf\u30c3\u30b7\u30e5\u8868\u304c\u6b63\u5e38\u306b\u6a5f\u80fd\u3059\u308b\u3053\u3068\u306e\u307f\u3092\u4fdd\u8a3c\u3067\u304d\u3001\u30cf\u30c3\u30b7\u30e5\u885d\u7a81\u306e\u767a\u751f\u983b\u5ea6\u3092\u6e1b\u3089\u3059\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093**\u3002</p> <p>\u30cf\u30c3\u30b7\u30e5\u885d\u7a81\u304c\u3042\u307e\u308a\u306b\u3082\u983b\u7e41\u306b\u767a\u751f\u3059\u308b\u3068\u3001\u30cf\u30c3\u30b7\u30e5\u8868\u306e\u6027\u80fd\u306f\u5287\u7684\u306b\u60aa\u5316\u3057\u307e\u3059\u3002\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u9023\u9396\u6cd5\u30cf\u30c3\u30b7\u30e5\u8868\u3067\u306f\u3001\u7406\u60f3\u7684\u306a\u30b1\u30fc\u30b9\u3067\u306f\u30ad\u30fc\u5024\u30da\u30a2\u304c\u30d0\u30b1\u30c3\u30c8\u9593\u306b\u5747\u7b49\u306b\u5206\u6563\u3055\u308c\u3001\u6700\u9069\u306a\u30af\u30a8\u30ea\u52b9\u7387\u3092\u5b9f\u73fe\u3057\u307e\u3059\u3002\u6700\u60aa\u306e\u30b1\u30fc\u30b9\u3067\u306f\u3001\u3059\u3079\u3066\u306e\u30ad\u30fc\u5024\u30da\u30a2\u304c\u540c\u3058\u30d0\u30b1\u30c3\u30c8\u306b\u683c\u7d0d\u3055\u308c\u3001\u6642\u9593\u8a08\u7b97\u91cf\u304c\\(O(n)\\)\u306b\u60aa\u5316\u3057\u307e\u3059\u3002</p> <p></p> <p> \u56f3 6-8 \u00a0 \u30cf\u30c3\u30b7\u30e5\u885d\u7a81\u306e\u7406\u60f3\u7684\u304a\u3088\u3073\u6700\u60aa\u306e\u30b1\u30fc\u30b9 </p> <p>\u30ad\u30fc\u5024\u30da\u30a2\u306e\u5206\u5e03\u306f\u30cf\u30c3\u30b7\u30e5\u95a2\u6570\u306b\u3088\u3063\u3066\u6c7a\u5b9a\u3055\u308c\u307e\u3059\u3002\u30cf\u30c3\u30b7\u30e5\u95a2\u6570\u306e\u8a08\u7b97\u30b9\u30c6\u30c3\u30d7\u3092\u601d\u3044\u51fa\u3059\u3068\u3001\u307e\u305a\u30cf\u30c3\u30b7\u30e5\u5024\u3092\u8a08\u7b97\u3057\u3001\u6b21\u306b\u914d\u5217\u9577\u3067\u5270\u4f59\u3092\u53d6\u308a\u307e\u3059\uff1a</p> <pre><code>index = hash(key) % capacity\n</code></pre> <p>\u4e0a\u8a18\u306e\u5f0f\u3092\u89b3\u5bdf\u3059\u308b\u3068\u3001\u30cf\u30c3\u30b7\u30e5\u8868\u306e\u5bb9\u91cf<code>capacity</code>\u304c\u56fa\u5b9a\u3055\u308c\u3066\u3044\u308b\u5834\u5408\u3001\u30cf\u30c3\u30b7\u30e5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0<code>hash()</code>\u304c\u51fa\u529b\u5024\u3092\u6c7a\u5b9a\u3057\u3001\u305d\u308c\u306b\u3088\u3063\u3066\u30cf\u30c3\u30b7\u30e5\u8868\u306b\u304a\u3051\u308b\u30ad\u30fc\u5024\u30da\u30a2\u306e\u5206\u5e03\u3092\u6c7a\u5b9a\u3057\u307e\u3059\u3002</p> <p>\u3053\u308c\u306f\u3001\u30cf\u30c3\u30b7\u30e5\u885d\u7a81\u306e\u78ba\u7387\u3092\u6e1b\u3089\u3059\u305f\u3081\u306b\u3001\u30cf\u30c3\u30b7\u30e5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0<code>hash()</code>\u306e\u8a2d\u8a08\u306b\u7126\u70b9\u3092\u5f53\u3066\u308b\u3079\u304d\u3067\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002</p>"},{"location":"chapter_hashing/hash_algorithm/#631","title":"6.3.1 \u00a0 \u30cf\u30c3\u30b7\u30e5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u76ee\u6a19","text":"<p>\u300c\u9ad8\u901f\u3067\u5b89\u5b9a\u3057\u305f\u300d\u30cf\u30c3\u30b7\u30e5\u8868\u30c7\u30fc\u30bf\u69cb\u9020\u3092\u5b9f\u73fe\u3059\u308b\u305f\u3081\u306b\u3001\u30cf\u30c3\u30b7\u30e5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u4ee5\u4e0b\u306e\u7279\u6027\u3092\u6301\u3064\u3079\u304d\u3067\u3059\uff1a</p> <ul> <li>\u6c7a\u5b9a\u6027: \u540c\u3058\u5165\u529b\u306b\u5bfe\u3057\u3066\u3001\u30cf\u30c3\u30b7\u30e5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u5e38\u306b\u540c\u3058\u51fa\u529b\u3092\u751f\u6210\u3059\u308b\u3079\u304d\u3067\u3059\u3002\u305d\u3046\u3067\u306a\u3051\u308c\u3070\u30cf\u30c3\u30b7\u30e5\u8868\u306f\u4fe1\u983c\u3067\u304d\u307e\u305b\u3093\u3002</li> <li>\u9ad8\u52b9\u7387: \u30cf\u30c3\u30b7\u30e5\u5024\u3092\u8a08\u7b97\u3059\u308b\u30d7\u30ed\u30bb\u30b9\u306f\u5341\u5206\u306b\u9ad8\u901f\u3067\u3042\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u8a08\u7b97\u30aa\u30fc\u30d0\u30fc\u30d8\u30c3\u30c9\u304c\u5c0f\u3055\u3044\u307b\u3069\u3001\u30cf\u30c3\u30b7\u30e5\u8868\u306f\u3088\u308a\u5b9f\u7528\u7684\u306b\u306a\u308a\u307e\u3059\u3002</li> <li>\u5747\u7b49\u5206\u6563: \u30cf\u30c3\u30b7\u30e5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u30ad\u30fc\u5024\u30da\u30a2\u304c\u30cf\u30c3\u30b7\u30e5\u8868\u306b\u5747\u7b49\u306b\u5206\u6563\u3055\u308c\u308b\u3053\u3068\u3092\u4fdd\u8a3c\u3059\u308b\u3079\u304d\u3067\u3059\u3002\u5206\u6563\u304c\u5747\u7b49\u3067\u3042\u308b\u307b\u3069\u3001\u30cf\u30c3\u30b7\u30e5\u885d\u7a81\u306e\u78ba\u7387\u306f\u4f4e\u304f\u306a\u308a\u307e\u3059\u3002</li> </ul> <p>\u5b9f\u969b\u3001\u30cf\u30c3\u30b7\u30e5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u30cf\u30c3\u30b7\u30e5\u8868\u306e\u5b9f\u88c5\u3060\u3051\u3067\u306a\u304f\u3001\u4ed6\u306e\u5206\u91ce\u3067\u3082\u5e83\u304f\u5fdc\u7528\u3055\u308c\u3066\u3044\u307e\u3059\u3002</p> <ul> <li>\u30d1\u30b9\u30ef\u30fc\u30c9\u4fdd\u5b58: \u30e6\u30fc\u30b6\u30fc\u30d1\u30b9\u30ef\u30fc\u30c9\u306e\u30bb\u30ad\u30e5\u30ea\u30c6\u30a3\u3092\u4fdd\u8b77\u3059\u308b\u305f\u3081\u306b\u3001\u30b7\u30b9\u30c6\u30e0\u306f\u901a\u5e38\u5e73\u6587\u30d1\u30b9\u30ef\u30fc\u30c9\u3092\u4fdd\u5b58\u305b\u305a\u3001\u30d1\u30b9\u30ef\u30fc\u30c9\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u3092\u4fdd\u5b58\u3057\u307e\u3059\u3002\u30e6\u30fc\u30b6\u30fc\u304c\u30d1\u30b9\u30ef\u30fc\u30c9\u3092\u5165\u529b\u3059\u308b\u3068\u3001\u30b7\u30b9\u30c6\u30e0\u306f\u5165\u529b\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u3092\u8a08\u7b97\u3057\u3001\u4fdd\u5b58\u3055\u308c\u3066\u3044\u308b\u30cf\u30c3\u30b7\u30e5\u5024\u3068\u6bd4\u8f03\u3057\u307e\u3059\u3002\u4e00\u81f4\u3059\u308c\u3070\u3001\u30d1\u30b9\u30ef\u30fc\u30c9\u306f\u6b63\u3057\u3044\u3068\u898b\u306a\u3055\u308c\u307e\u3059\u3002</li> <li>\u30c7\u30fc\u30bf\u6574\u5408\u6027\u30c1\u30a7\u30c3\u30af: \u30c7\u30fc\u30bf\u9001\u4fe1\u8005\u306f\u30c7\u30fc\u30bf\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u3092\u8a08\u7b97\u3057\u3066\u4e00\u7dd2\u306b\u9001\u4fe1\u3067\u304d\u307e\u3059\u3002\u53d7\u4fe1\u8005\u306f\u53d7\u4fe1\u3057\u305f\u30c7\u30fc\u30bf\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u3092\u518d\u8a08\u7b97\u3057\u3001\u53d7\u4fe1\u3057\u305f\u30cf\u30c3\u30b7\u30e5\u5024\u3068\u6bd4\u8f03\u3067\u304d\u307e\u3059\u3002\u4e00\u81f4\u3059\u308c\u3070\u3001\u30c7\u30fc\u30bf\u306f\u5b8c\u5168\u3067\u3042\u308b\u3068\u898b\u306a\u3055\u308c\u307e\u3059\u3002</li> </ul> <p>\u6697\u53f7\u5316\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u3067\u306f\u3001\u30cf\u30c3\u30b7\u30e5\u5024\u304b\u3089\u5143\u306e\u30d1\u30b9\u30ef\u30fc\u30c9\u3092\u63a8\u6e2c\u3059\u308b\u306a\u3069\u306e\u9006\u884c\u5206\u6790\u3092\u9632\u3050\u305f\u3081\u306b\u3001\u30cf\u30c3\u30b7\u30e5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u3088\u308a\u9ad8\u3044\u30ec\u30d9\u30eb\u306e\u30bb\u30ad\u30e5\u30ea\u30c6\u30a3\u6a5f\u80fd\u304c\u5fc5\u8981\u3067\u3059\u3002</p> <ul> <li>\u4e00\u65b9\u5411\u6027: \u30cf\u30c3\u30b7\u30e5\u5024\u304b\u3089\u5165\u529b\u30c7\u30fc\u30bf\u306b\u95a2\u3059\u308b\u60c5\u5831\u3092\u63a8\u6e2c\u3059\u308b\u3053\u3068\u306f\u4e0d\u53ef\u80fd\u3067\u3042\u308b\u3079\u304d\u3067\u3059\u3002</li> <li>\u885d\u7a81\u8010\u6027: \u540c\u3058\u30cf\u30c3\u30b7\u30e5\u5024\u3092\u751f\u6210\u3059\u308b2\u3064\u306e\u7570\u306a\u308b\u5165\u529b\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u306f\u6975\u3081\u3066\u56f0\u96e3\u3067\u3042\u308b\u3079\u304d\u3067\u3059\u3002</li> <li>\u96ea\u5d29\u52b9\u679c: \u5165\u529b\u306e\u5c0f\u3055\u306a\u5909\u66f4\u306f\u3001\u51fa\u529b\u306b\u5927\u304d\u304f\u4e88\u6e2c\u4e0d\u53ef\u80fd\u306a\u5909\u5316\u3092\u3082\u305f\u3089\u3059\u3079\u304d\u3067\u3059\u3002</li> </ul> <p>**\u300c\u5747\u7b49\u5206\u6563\u300d\u3068\u300c\u885d\u7a81\u8010\u6027\u300d\u306f2\u3064\u306e\u5225\u3005\u306e\u6982\u5ff5**\u3067\u3042\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u5747\u7b49\u5206\u6563\u3092\u6e80\u305f\u3057\u3066\u3082\u3001\u5fc5\u305a\u3057\u3082\u885d\u7a81\u8010\u6027\u304c\u3042\u308b\u3068\u306f\u9650\u308a\u307e\u305b\u3093\u3002\u4f8b\u3048\u3070\u3001\u30e9\u30f3\u30c0\u30e0\u306a\u5165\u529b<code>key</code>\u306e\u4e0b\u3067\u3001\u30cf\u30c3\u30b7\u30e5\u95a2\u6570<code>key % 100</code>\u306f\u5747\u7b49\u306b\u5206\u6563\u3055\u308c\u305f\u51fa\u529b\u3092\u751f\u6210\u3067\u304d\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u3053\u306e\u30cf\u30c3\u30b7\u30e5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u904e\u5ea6\u306b\u30b7\u30f3\u30d7\u30eb\u3067\u3001\u4e0b\u4e8c\u6841\u304c\u540c\u3058\u3059\u3079\u3066\u306e<code>key</code>\u306f\u540c\u3058\u51fa\u529b\u3092\u6301\u3064\u305f\u3081\u3001\u30cf\u30c3\u30b7\u30e5\u5024\u304b\u3089\u4f7f\u7528\u53ef\u80fd\u306a<code>key</code>\u3092\u7c21\u5358\u306b\u63a8\u6e2c\u3067\u304d\u3001\u30d1\u30b9\u30ef\u30fc\u30c9\u3092\u7834\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002</p>"},{"location":"chapter_hashing/hash_algorithm/#632","title":"6.3.2 \u00a0 \u30cf\u30c3\u30b7\u30e5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u8a2d\u8a08","text":"<p>\u30cf\u30c3\u30b7\u30e5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u8a2d\u8a08\u306f\u591a\u304f\u306e\u8981\u56e0\u3092\u8003\u616e\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u8907\u96d1\u306a\u554f\u984c\u3067\u3059\u3002\u3057\u304b\u3057\u3001\u8981\u6c42\u304c\u5c11\u306a\u3044\u4e00\u90e8\u306e\u30b7\u30ca\u30ea\u30aa\u3067\u306f\u3001\u3044\u304f\u3064\u304b\u306e\u7c21\u5358\u306a\u30cf\u30c3\u30b7\u30e5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u8a2d\u8a08\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002</p> <ul> <li>\u52a0\u7b97\u30cf\u30c3\u30b7\u30e5: \u5165\u529b\u306e\u5404\u6587\u5b57\u306eASCII\u30b3\u30fc\u30c9\u3092\u5408\u8a08\u3057\u3001\u5408\u8a08\u3092\u30cf\u30c3\u30b7\u30e5\u5024\u3068\u3057\u3066\u4f7f\u7528\u3057\u307e\u3059\u3002</li> <li>\u4e57\u7b97\u30cf\u30c3\u30b7\u30e5: \u4e57\u7b97\u306e\u975e\u76f8\u95a2\u6027\u3092\u5229\u7528\u3057\u3001\u5404\u30e9\u30a6\u30f3\u30c9\u3067\u5b9a\u6570\u3092\u4e57\u7b97\u3057\u3001\u5404\u6587\u5b57\u306eASCII\u30b3\u30fc\u30c9\u3092\u30cf\u30c3\u30b7\u30e5\u5024\u306b\u7d2f\u7a4d\u3057\u307e\u3059\u3002</li> <li>XOR\u30cf\u30c3\u30b7\u30e5: \u5165\u529b\u30c7\u30fc\u30bf\u306e\u5404\u8981\u7d20\u3092XOR\u3059\u308b\u3053\u3068\u3067\u30cf\u30c3\u30b7\u30e5\u5024\u3092\u7d2f\u7a4d\u3057\u307e\u3059\u3002</li> <li>\u56de\u8ee2\u30cf\u30c3\u30b7\u30e5: \u5404\u6587\u5b57\u306eASCII\u30b3\u30fc\u30c9\u3092\u30cf\u30c3\u30b7\u30e5\u5024\u306b\u7d2f\u7a4d\u3057\u3001\u5404\u7d2f\u7a4d\u524d\u306b\u30cf\u30c3\u30b7\u30e5\u5024\u306b\u56de\u8ee2\u64cd\u4f5c\u3092\u5b9f\u884c\u3057\u307e\u3059\u3002</li> </ul> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig simple_hash.py<pre><code>def add_hash(key: str) -&gt; int:\n    \"\"\"\u52a0\u6cd5\u30cf\u30c3\u30b7\u30e5\"\"\"\n    hash = 0\n    modulus = 1000000007\n    for c in key:\n        hash += ord(c)\n    return hash % modulus\n\ndef mul_hash(key: str) -&gt; int:\n    \"\"\"\u4e57\u6cd5\u30cf\u30c3\u30b7\u30e5\"\"\"\n    hash = 0\n    modulus = 1000000007\n    for c in key:\n        hash = 31 * hash + ord(c)\n    return hash % modulus\n\ndef xor_hash(key: str) -&gt; int:\n    \"\"\"XOR\u30cf\u30c3\u30b7\u30e5\"\"\"\n    hash = 0\n    modulus = 1000000007\n    for c in key:\n        hash ^= ord(c)\n    return hash % modulus\n\ndef rot_hash(key: str) -&gt; int:\n    \"\"\"\u56de\u8ee2\u30cf\u30c3\u30b7\u30e5\"\"\"\n    hash = 0\n    modulus = 1000000007\n    for c in key:\n        hash = (hash &lt;&lt; 4) ^ (hash &gt;&gt; 28) ^ ord(c)\n    return hash % modulus\n</code></pre> simple_hash.cpp<pre><code>/* \u52a0\u7b97\u30cf\u30c3\u30b7\u30e5 */\nint addHash(string key) {\n    long long hash = 0;\n    const int MODULUS = 1000000007;\n    for (unsigned char c : key) {\n        hash = (hash + (int)c) % MODULUS;\n    }\n    return (int)hash;\n}\n\n/* \u4e57\u7b97\u30cf\u30c3\u30b7\u30e5 */\nint mulHash(string key) {\n    long long hash = 0;\n    const int MODULUS = 1000000007;\n    for (unsigned char c : key) {\n        hash = (31 * hash + (int)c) % MODULUS;\n    }\n    return (int)hash;\n}\n\n/* XOR\u30cf\u30c3\u30b7\u30e5 */\nint xorHash(string key) {\n    int hash = 0;\n    const int MODULUS = 1000000007;\n    for (unsigned char c : key) {\n        hash ^= (int)c;\n    }\n    return hash &amp; MODULUS;\n}\n\n/* \u56de\u8ee2\u30cf\u30c3\u30b7\u30e5 */\nint rotHash(string key) {\n    long long hash = 0;\n    const int MODULUS = 1000000007;\n    for (unsigned char c : key) {\n        hash = ((hash &lt;&lt; 4) ^ (hash &gt;&gt; 28) ^ (int)c) % MODULUS;\n    }\n    return (int)hash;\n}\n</code></pre> simple_hash.java<pre><code>/* \u52a0\u7b97\u30cf\u30c3\u30b7\u30e5 */\nint addHash(String key) {\n    long hash = 0;\n    final int MODULUS = 1000000007;\n    for (char c : key.toCharArray()) {\n        hash = (hash + (int) c) % MODULUS;\n    }\n    return (int) hash;\n}\n\n/* \u4e57\u7b97\u30cf\u30c3\u30b7\u30e5 */\nint mulHash(String key) {\n    long hash = 0;\n    final int MODULUS = 1000000007;\n    for (char c : key.toCharArray()) {\n        hash = (31 * hash + (int) c) % MODULUS;\n    }\n    return (int) hash;\n}\n\n/* XOR\u30cf\u30c3\u30b7\u30e5 */\nint xorHash(String key) {\n    int hash = 0;\n    final int MODULUS = 1000000007;\n    for (char c : key.toCharArray()) {\n        hash ^= (int) c;\n    }\n    return hash &amp; MODULUS;\n}\n\n/* \u56de\u8ee2\u30cf\u30c3\u30b7\u30e5 */\nint rotHash(String key) {\n    long hash = 0;\n    final int MODULUS = 1000000007;\n    for (char c : key.toCharArray()) {\n        hash = ((hash &lt;&lt; 4) ^ (hash &gt;&gt; 28) ^ (int) c) % MODULUS;\n    }\n    return (int) hash;\n}\n</code></pre> simple_hash.cs<pre><code>[class]{simple_hash}-[func]{AddHash}\n\n[class]{simple_hash}-[func]{MulHash}\n\n[class]{simple_hash}-[func]{XorHash}\n\n[class]{simple_hash}-[func]{RotHash}\n</code></pre> simple_hash.go<pre><code>[class]{}-[func]{addHash}\n\n[class]{}-[func]{mulHash}\n\n[class]{}-[func]{xorHash}\n\n[class]{}-[func]{rotHash}\n</code></pre> simple_hash.swift<pre><code>[class]{}-[func]{addHash}\n\n[class]{}-[func]{mulHash}\n\n[class]{}-[func]{xorHash}\n\n[class]{}-[func]{rotHash}\n</code></pre> simple_hash.js<pre><code>[class]{}-[func]{addHash}\n\n[class]{}-[func]{mulHash}\n\n[class]{}-[func]{xorHash}\n\n[class]{}-[func]{rotHash}\n</code></pre> simple_hash.ts<pre><code>[class]{}-[func]{addHash}\n\n[class]{}-[func]{mulHash}\n\n[class]{}-[func]{xorHash}\n\n[class]{}-[func]{rotHash}\n</code></pre> simple_hash.dart<pre><code>[class]{}-[func]{addHash}\n\n[class]{}-[func]{mulHash}\n\n[class]{}-[func]{xorHash}\n\n[class]{}-[func]{rotHash}\n</code></pre> simple_hash.rs<pre><code>[class]{}-[func]{add_hash}\n\n[class]{}-[func]{mul_hash}\n\n[class]{}-[func]{xor_hash}\n\n[class]{}-[func]{rot_hash}\n</code></pre> simple_hash.c<pre><code>[class]{}-[func]{addHash}\n\n[class]{}-[func]{mulHash}\n\n[class]{}-[func]{xorHash}\n\n[class]{}-[func]{rotHash}\n</code></pre> simple_hash.kt<pre><code>[class]{}-[func]{addHash}\n\n[class]{}-[func]{mulHash}\n\n[class]{}-[func]{xorHash}\n\n[class]{}-[func]{rotHash}\n</code></pre> simple_hash.rb<pre><code>[class]{}-[func]{add_hash}\n\n[class]{}-[func]{mul_hash}\n\n[class]{}-[func]{xor_hash}\n\n[class]{}-[func]{rot_hash}\n</code></pre> simple_hash.zig<pre><code>[class]{}-[func]{addHash}\n\n[class]{}-[func]{mulHash}\n\n[class]{}-[func]{xorHash}\n\n[class]{}-[func]{rotHash}\n</code></pre> <p>\u5404\u30cf\u30c3\u30b7\u30e5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u6700\u5f8c\u306e\u30b9\u30c6\u30c3\u30d7\u304c\u5927\u304d\u306a\u7d20\u6570\\(1000000007\\)\u306e\u5270\u4f59\u3092\u53d6\u308b\u3053\u3068\u3067\u3001\u30cf\u30c3\u30b7\u30e5\u5024\u304c\u9069\u5207\u306a\u7bc4\u56f2\u5185\u306b\u3042\u308b\u3053\u3068\u3092\u4fdd\u8a3c\u3057\u3066\u3044\u308b\u3053\u3068\u304c\u89b3\u5bdf\u3055\u308c\u307e\u3059\u3002\u306a\u305c\u7d20\u6570\u306e\u5270\u4f59\u3092\u53d6\u308b\u3053\u3068\u304c\u5f37\u8abf\u3055\u308c\u308b\u306e\u304b\u3001\u307e\u305f\u306f\u5408\u6210\u6570\u306e\u5270\u4f59\u3092\u53d6\u308b\u3053\u3068\u306e\u6b20\u70b9\u306f\u4f55\u304b\u3092\u8003\u3048\u308b\u4fa1\u5024\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u308c\u306f\u8208\u5473\u6df1\u3044\u8cea\u554f\u3067\u3059\u3002</p> <p>\u7d50\u8ad6\u3068\u3057\u3066\uff1a\u5927\u304d\u306a\u7d20\u6570\u3092\u5270\u4f59\u3068\u3057\u3066\u4f7f\u7528\u3059\u308b\u3053\u3068\u3067\u3001\u30cf\u30c3\u30b7\u30e5\u5024\u306e\u5747\u7b49\u5206\u6563\u3092\u6700\u5927\u5316\u3067\u304d\u307e\u3059\u3002\u7d20\u6570\u306f\u4ed6\u306e\u6570\u3068\u5171\u901a\u56e0\u5b50\u3092\u6301\u305f\u306a\u3044\u305f\u3081\u3001\u5270\u4f59\u6f14\u7b97\u306b\u3088\u3063\u3066\u5f15\u304d\u8d77\u3053\u3055\u308c\u308b\u5468\u671f\u7684\u30d1\u30bf\u30fc\u30f3\u3092\u6e1b\u3089\u3057\u3001\u30cf\u30c3\u30b7\u30e5\u885d\u7a81\u3092\u56de\u907f\u3067\u304d\u307e\u3059\u3002</p> <p>\u4f8b\u3048\u3070\u3001\u5408\u6210\u6570\\(9\\)\u3092\u5270\u4f59\u3068\u3057\u3066\u9078\u629e\u3059\u308b\u3068\u3057\u307e\u3059\u3002\u3053\u308c\u306f\\(3\\)\u3067\u5272\u308a\u5207\u308c\u308b\u305f\u3081\u3001\\(3\\)\u3067\u5272\u308a\u5207\u308c\u308b\u3059\u3079\u3066\u306e<code>key</code>\u306f\u30cf\u30c3\u30b7\u30e5\u5024\\(0\\)\u3001\\(3\\)\u3001\\(6\\)\u306b\u30de\u30c3\u30d4\u30f3\u30b0\u3055\u308c\u307e\u3059\u3002</p> \\[ \\begin{aligned} \\text{modulus} &amp; = 9 \\newline \\text{key} &amp; = \\{ 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, \\dots \\} \\newline \\text{hash} &amp; = \\{ 0, 3, 6, 0, 3, 6, 0, 3, 6, 0, 3, 6,\\dots \\} \\end{aligned} \\] <p>\u5165\u529b<code>key</code>\u304c\u305f\u307e\u305f\u307e\u3053\u306e\u7a2e\u306e\u7b49\u5dee\u6570\u5217\u5206\u5e03\u3092\u6301\u3064\u5834\u5408\u3001\u30cf\u30c3\u30b7\u30e5\u5024\u304c\u30af\u30e9\u30b9\u30bf\u30fc\u3057\u3001\u30cf\u30c3\u30b7\u30e5\u885d\u7a81\u3092\u60aa\u5316\u3055\u305b\u307e\u3059\u3002\u4eca\u5ea6\u306f<code>modulus</code>\u3092\u7d20\u6570\\(13\\)\u306b\u7f6e\u304d\u63db\u3048\u308b\u3068\u3057\u307e\u3059\u3002<code>key</code>\u3068<code>modulus</code>\u306e\u9593\u306b\u5171\u901a\u56e0\u5b50\u304c\u306a\u3044\u305f\u3081\u3001\u51fa\u529b\u30cf\u30c3\u30b7\u30e5\u5024\u306e\u5747\u7b49\u6027\u304c\u5927\u5e45\u306b\u6539\u5584\u3055\u308c\u307e\u3059\u3002</p> \\[ \\begin{aligned} \\text{modulus} &amp; = 13 \\newline \\text{key} &amp; = \\{ 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, \\dots \\} \\newline \\text{hash} &amp; = \\{ 0, 3, 6, 9, 12, 2, 5, 8, 11, 1, 4, 7, \\dots \\} \\end{aligned} \\] <p><code>key</code>\u304c\u30e9\u30f3\u30c0\u30e0\u3067\u5747\u7b49\u306b\u5206\u6563\u3055\u308c\u308b\u3053\u3068\u304c\u4fdd\u8a3c\u3055\u308c\u3066\u3044\u308b\u5834\u5408\u3001\u5270\u4f59\u3068\u3057\u3066\u7d20\u6570\u307e\u305f\u306f\u5408\u6210\u6570\u3092\u9078\u629e\u3057\u3066\u3082\u3001\u4e21\u65b9\u3068\u3082\u5747\u7b49\u306b\u5206\u6563\u3055\u308c\u305f\u30cf\u30c3\u30b7\u30e5\u5024\u3092\u751f\u6210\u3067\u304d\u308b\u3053\u3068\u306f\u6ce8\u76ee\u306b\u5024\u3057\u307e\u3059\u3002\u3057\u304b\u3057\u3001<code>key</code>\u306e\u5206\u5e03\u306b\u3042\u308b\u7a2e\u306e\u5468\u671f\u6027\u304c\u3042\u308b\u5834\u5408\u3001\u5408\u6210\u6570\u306e\u5270\u4f59\u306f\u30af\u30e9\u30b9\u30bf\u30ea\u30f3\u30b0\u3092\u5f15\u304d\u8d77\u3053\u3057\u3084\u3059\u304f\u306a\u308a\u307e\u3059\u3002</p> <p>\u8981\u7d04\u3059\u308b\u3068\u3001\u901a\u5e38\u306f\u7d20\u6570\u3092\u5270\u4f59\u3068\u3057\u3066\u9078\u629e\u3057\u3001\u3053\u306e\u7d20\u6570\u306f\u5468\u671f\u7684\u30d1\u30bf\u30fc\u30f3\u3092\u53ef\u80fd\u306a\u9650\u308a\u6392\u9664\u3057\u3001\u30cf\u30c3\u30b7\u30e5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5805\u7262\u6027\u3092\u5411\u4e0a\u3055\u305b\u308b\u305f\u3081\u306b\u5341\u5206\u5927\u304d\u304f\u3042\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002</p>"},{"location":"chapter_hashing/hash_algorithm/#633","title":"6.3.3 \u00a0 \u4e00\u822c\u7684\u306a\u30cf\u30c3\u30b7\u30e5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0","text":"<p>\u4e0a\u8a18\u3067\u8a00\u53ca\u3057\u305f\u7c21\u5358\u306a\u30cf\u30c3\u30b7\u30e5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u304b\u306a\u308a\u300c\u8106\u5f31\u300d\u3067\u3001\u30cf\u30c3\u30b7\u30e5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u8a2d\u8a08\u76ee\u6a19\u304b\u3089\u7a0b\u9060\u3044\u3053\u3068\u306f\u96e3\u3057\u304f\u3042\u308a\u307e\u305b\u3093\u3002\u4f8b\u3048\u3070\u3001\u52a0\u7b97\u3068XOR\u306f\u4ea4\u63db\u6cd5\u5247\u306b\u5f93\u3046\u305f\u3081\u3001\u52a0\u7b97\u30cf\u30c3\u30b7\u30e5\u3068XOR\u30cf\u30c3\u30b7\u30e5\u306f\u540c\u3058\u5185\u5bb9\u3060\u304c\u9806\u5e8f\u304c\u7570\u306a\u308b\u6587\u5b57\u5217\u3092\u533a\u5225\u3067\u304d\u305a\u3001\u30cf\u30c3\u30b7\u30e5\u885d\u7a81\u3092\u60aa\u5316\u3055\u305b\u3001\u30bb\u30ad\u30e5\u30ea\u30c6\u30a3\u554f\u984c\u3092\u5f15\u304d\u8d77\u3053\u3059\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002</p> <p>\u5b9f\u969b\u306b\u306f\u3001\u901a\u5e38MD5\u3001SHA-1\u3001SHA-2\u3001SHA-3\u306a\u3069\u306e\u6a19\u6e96\u30cf\u30c3\u30b7\u30e5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002\u3053\u308c\u3089\u306f\u4efb\u610f\u306e\u9577\u3055\u306e\u5165\u529b\u30c7\u30fc\u30bf\u3092\u56fa\u5b9a\u9577\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306b\u30de\u30c3\u30d4\u30f3\u30b0\u3067\u304d\u307e\u3059\u3002</p> <p>\u904e\u53bb1\u4e16\u7d00\u306b\u308f\u305f\u3063\u3066\u3001\u30cf\u30c3\u30b7\u30e5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u7d99\u7d9a\u7684\u306a\u30a2\u30c3\u30d7\u30b0\u30ec\u30fc\u30c9\u3068\u6700\u9069\u5316\u306e\u30d7\u30ed\u30bb\u30b9\u306b\u3042\u308a\u307e\u3057\u305f\u3002\u4e00\u90e8\u306e\u7814\u7a76\u8005\u306f\u30cf\u30c3\u30b7\u30e5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u6027\u80fd\u5411\u4e0a\u306b\u52aa\u3081\u3001\u30cf\u30c3\u30ab\u30fc\u3092\u542b\u3080\u4ed6\u306e\u4eba\u3005\u306f\u30cf\u30c3\u30b7\u30e5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u30bb\u30ad\u30e5\u30ea\u30c6\u30a3\u554f\u984c\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u306b\u5c02\u5ff5\u3057\u3066\u3044\u307e\u3059\u3002\u4ee5\u4e0b\u306e\u8868\u306f\u3001\u5b9f\u7528\u7684\u306a\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u3067\u4e00\u822c\u7684\u306b\u4f7f\u7528\u3055\u308c\u308b\u30cf\u30c3\u30b7\u30e5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002</p> <ul> <li>MD5\u3068SHA-1\u306f\u8907\u6570\u56de\u653b\u6483\u306b\u6210\u529f\u3057\u3066\u304a\u308a\u3001\u3055\u307e\u3056\u307e\u306a\u30bb\u30ad\u30e5\u30ea\u30c6\u30a3\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u3067\u653e\u68c4\u3055\u308c\u3066\u3044\u307e\u3059\u3002</li> <li>SHA-2\u30b7\u30ea\u30fc\u30ba\u3001\u7279\u306bSHA-256\u306f\u3001\u73fe\u5728\u6700\u3082\u5b89\u5168\u306a\u30cf\u30c3\u30b7\u30e5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e1\u3064\u3067\u3001\u6210\u529f\u3057\u305f\u653b\u6483\u306f\u5831\u544a\u3055\u308c\u3066\u304a\u3089\u305a\u3001\u3055\u307e\u3056\u307e\u306a\u30bb\u30ad\u30e5\u30ea\u30c6\u30a3\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u3068\u30d7\u30ed\u30c8\u30b3\u30eb\u3067\u4e00\u822c\u7684\u306b\u4f7f\u7528\u3055\u308c\u3066\u3044\u307e\u3059\u3002</li> <li>SHA-3\u306fSHA-2\u3068\u6bd4\u8f03\u3057\u3066\u5b9f\u88c5\u30b3\u30b9\u30c8\u304c\u4f4e\u304f\u3001\u8a08\u7b97\u52b9\u7387\u304c\u9ad8\u3044\u3067\u3059\u304c\u3001\u73fe\u5728\u306e\u4f7f\u7528\u7bc4\u56f2\u306fSHA-2\u30b7\u30ea\u30fc\u30ba\u307b\u3069\u5e83\u7bc4\u56f2\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002</li> </ul> <p> \u8868 6-2 \u00a0 \u4e00\u822c\u7684\u306a\u30cf\u30c3\u30b7\u30e5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0 </p> MD5 SHA-1 SHA-2 SHA-3 \u30ea\u30ea\u30fc\u30b9\u5e74 1992 1995 2002 2008 \u51fa\u529b\u9577 128 bit 160 bit 256/512 bit 224/256/384/512 bit \u30cf\u30c3\u30b7\u30e5\u885d\u7a81 \u983b\u7e41 \u983b\u7e41 \u307e\u308c \u307e\u308c \u30bb\u30ad\u30e5\u30ea\u30c6\u30a3\u30ec\u30d9\u30eb \u4f4e\u3001\u653b\u6483\u306b\u6210\u529f\u3057\u3066\u3044\u308b \u4f4e\u3001\u653b\u6483\u306b\u6210\u529f\u3057\u3066\u3044\u308b \u9ad8 \u9ad8 \u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3 \u653e\u68c4\u3001\u30c7\u30fc\u30bf\u6574\u5408\u6027\u30c1\u30a7\u30c3\u30af\u306b\u307e\u3060\u4f7f\u7528 \u653e\u68c4 \u6697\u53f7\u901a\u8ca8\u53d6\u5f15\u691c\u8a3c\u3001\u30c7\u30b8\u30bf\u30eb\u7f72\u540d\u306a\u3069 SHA-2\u306e\u4ee3\u66ff\u3068\u3057\u3066\u4f7f\u7528\u53ef\u80fd"},{"location":"chapter_hashing/hash_algorithm/#_1","title":"\u30c7\u30fc\u30bf\u69cb\u9020\u306b\u304a\u3051\u308b\u30cf\u30c3\u30b7\u30e5\u5024","text":"<p>\u30cf\u30c3\u30b7\u30e5\u8868\u306e\u30ad\u30fc\u306f\u6574\u6570\u3001\u5c0f\u6570\u3001\u6587\u5b57\u5217\u306a\u3069\u306e\u3055\u307e\u3056\u307e\u306a\u30c7\u30fc\u30bf\u578b\u306b\u3067\u304d\u308b\u3053\u3068\u3092\u77e5\u3063\u3066\u3044\u307e\u3059\u3002\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u306f\u901a\u5e38\u3001\u3053\u308c\u3089\u306e\u30c7\u30fc\u30bf\u578b\u306b\u5bfe\u3057\u3066\u7d44\u307f\u8fbc\u307f\u306e\u30cf\u30c3\u30b7\u30e5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u63d0\u4f9b\u3057\u3001\u30cf\u30c3\u30b7\u30e5\u8868\u306e\u30d0\u30b1\u30c3\u30c8\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002Python\u3092\u4f8b\u306b\u53d6\u308b\u3068\u3001<code>hash()</code>\u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u3055\u307e\u3056\u307e\u306a\u30c7\u30fc\u30bf\u578b\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002</p> <ul> <li>\u6574\u6570\u3068\u30d6\u30fc\u30eb\u5024\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306f\u3001\u305d\u308c\u3089\u81ea\u8eab\u306e\u5024\u3067\u3059\u3002</li> <li>\u6d6e\u52d5\u5c0f\u6570\u70b9\u6570\u3068\u6587\u5b57\u5217\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306e\u8a08\u7b97\u306f\u3088\u308a\u8907\u96d1\u3067\u3001\u8208\u5473\u306e\u3042\u308b\u8aad\u8005\u306f\u81ea\u5206\u3067\u7814\u7a76\u3059\u308b\u3053\u3068\u3092\u304a\u52e7\u3081\u3057\u307e\u3059\u3002</li> <li>\u30bf\u30d7\u30eb\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306f\u3001\u305d\u306e\u5404\u8981\u7d20\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306e\u7d44\u307f\u5408\u308f\u305b\u3067\u3001\u5358\u4e00\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306b\u306a\u308a\u307e\u3059\u3002</li> <li>\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306f\u3001\u305d\u306e\u30e1\u30e2\u30ea\u30a2\u30c9\u30ec\u30b9\u306b\u57fa\u3065\u3044\u3066\u751f\u6210\u3055\u308c\u307e\u3059\u3002\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u306e\u30cf\u30c3\u30b7\u30e5\u30e1\u30bd\u30c3\u30c9\u3092\u30aa\u30fc\u30d0\u30fc\u30e9\u30a4\u30c9\u3059\u308b\u3053\u3068\u3067\u3001\u5185\u5bb9\u306b\u57fa\u3065\u3044\u3066\u30cf\u30c3\u30b7\u30e5\u5024\u3092\u751f\u6210\u3067\u304d\u307e\u3059\u3002</li> </ul> <p>Tip</p> <p>\u7570\u306a\u308b\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u306b\u304a\u3051\u308b\u7d44\u307f\u8fbc\u307f\u30cf\u30c3\u30b7\u30e5\u5024\u8a08\u7b97\u95a2\u6570\u306e\u5b9a\u7fa9\u3068\u65b9\u6cd5\u306f\u7570\u306a\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinZig built_in_hash.py<pre><code>num = 3\nhash_num = hash(num)\n# \u6574\u65703\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306f3\n\nbol = True\nhash_bol = hash(bol)\n# \u30d6\u30fc\u30eb\u5024True\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306f1\n\ndec = 3.14159\nhash_dec = hash(dec)\n# \u5c0f\u65703.14159\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306f326484311674566659\n\nstr = \"Hello \u7b97\u6cd5\"\nhash_str = hash(str)\n# \u6587\u5b57\u5217\"Hello \u7b97\u6cd5\"\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306f4617003410720528961\n\ntup = (12836, \"\u5c0f\u54c8\")\nhash_tup = hash(tup)\n# \u30bf\u30d7\u30eb(12836, '\u5c0f\u54c8')\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306f1029005403108185979\n\nobj = ListNode(0)\nhash_obj = hash(obj)\n# ListNode\u30aa\u30d6\u30b8\u30a7\u30af\u30c80x1058fd810\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306f274267521\n</code></pre> built_in_hash.cpp<pre><code>int num = 3;\nsize_t hashNum = hash&lt;int&gt;()(num);\n// \u6574\u65703\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306f3\n\nbool bol = true;\nsize_t hashBol = hash&lt;bool&gt;()(bol);\n// \u30d6\u30fc\u30eb\u50241\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306f1\n\ndouble dec = 3.14159;\nsize_t hashDec = hash&lt;double&gt;()(dec);\n// \u5c0f\u65703.14159\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306f4614256650576692846\n\nstring str = \"Hello \u7b97\u6cd5\";\nsize_t hashStr = hash&lt;string&gt;()(str);\n// \u6587\u5b57\u5217\"Hello \u7b97\u6cd5\"\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306f15466937326284535026\n\n// C++\u3067\u306f\u3001\u7d44\u307f\u8fbc\u307fstd::hash()\u306f\u57fa\u672c\u30c7\u30fc\u30bf\u578b\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306e\u307f\u3092\u63d0\u4f9b\n// \u914d\u5217\u3068\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306f\u5225\u9014\u5b9f\u88c5\u304c\u5fc5\u8981\n</code></pre> built_in_hash.java<pre><code>int num = 3;\nint hashNum = Integer.hashCode(num);\n// \u6574\u65703\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306f3\n\nboolean bol = true;\nint hashBol = Boolean.hashCode(bol);\n// \u30d6\u30fc\u30eb\u5024true\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306f1231\n\ndouble dec = 3.14159;\nint hashDec = Double.hashCode(dec);\n// \u5c0f\u65703.14159\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306f-1340954729\n\nString str = \"Hello \u7b97\u6cd5\";\nint hashStr = str.hashCode();\n// \u6587\u5b57\u5217\"Hello \u7b97\u6cd5\"\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306f-727081396\n\nObject[] arr = { 12836, \"\u5c0f\u54c8\" };\nint hashTup = Arrays.hashCode(arr);\n// \u914d\u5217[12836, \u5c0f\u54c8]\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306f1151158\n\nListNode obj = new ListNode(0);\nint hashObj = obj.hashCode();\n// ListNode\u30aa\u30d6\u30b8\u30a7\u30af\u30c8utils.ListNode@7dc5e7b4\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306f2110121908\n</code></pre> built_in_hash.cs<pre><code>int num = 3;\nint hashNum = num.GetHashCode();\n// \u6574\u65703\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306f3;\n\nbool bol = true;\nint hashBol = bol.GetHashCode();\n// \u30d6\u30fc\u30eb\u5024true\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306f1;\n\ndouble dec = 3.14159;\nint hashDec = dec.GetHashCode();\n// \u5c0f\u65703.14159\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306f-1340954729;\n\nstring str = \"Hello \u7b97\u6cd5\";\nint hashStr = str.GetHashCode();\n// \u6587\u5b57\u5217\"Hello \u7b97\u6cd5\"\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306f-586107568;\n\nobject[] arr = [12836, \"\u5c0f\u54c8\"];\nint hashTup = arr.GetHashCode();\n// \u914d\u5217[12836, \u5c0f\u54c8]\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306f42931033;\n\nListNode obj = new(0);\nint hashObj = obj.GetHashCode();\n// ListNode\u30aa\u30d6\u30b8\u30a7\u30af\u30c80\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306f39053774;\n</code></pre> built_in_hash.go<pre><code>// Go\u306b\u306f\u7d44\u307f\u8fbc\u307f\u306e\u30cf\u30c3\u30b7\u30e5\u30b3\u30fc\u30c9\u95a2\u6570\u304c\u63d0\u4f9b\u3055\u308c\u3066\u3044\u307e\u305b\u3093\n</code></pre> built_in_hash.swift<pre><code>let num = 3\nlet hashNum = num.hashValue\n// \u6574\u65703\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306f9047044699613009734\n\nlet bol = true\nlet hashBol = bol.hashValue\n// \u30d6\u30fc\u30eb\u5024true\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306f-4431640247352757451\n\nlet dec = 3.14159\nlet hashDec = dec.hashValue\n// \u5c0f\u65703.14159\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306f-2465384235396674631\n\nlet str = \"Hello \u7b97\u6cd5\"\nlet hashStr = str.hashValue\n// \u6587\u5b57\u5217\"Hello \u7b97\u6cd5\"\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306f-7850626797806988787\n\nlet arr = [AnyHashable(12836), AnyHashable(\"\u5c0f\u54c8\")]\nlet hashTup = arr.hashValue\n// \u914d\u5217[AnyHashable(12836), AnyHashable(\"\u5c0f\u54c8\")]\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306f-2308633508154532996\n\nlet obj = ListNode(x: 0)\nlet hashObj = obj.hashValue\n// ListNode\u30aa\u30d6\u30b8\u30a7\u30af\u30c8utils.ListNode\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306f-2434780518035996159\n</code></pre> built_in_hash.js<pre><code>// JavaScript\u306b\u306f\u7d44\u307f\u8fbc\u307f\u306e\u30cf\u30c3\u30b7\u30e5\u30b3\u30fc\u30c9\u95a2\u6570\u304c\u63d0\u4f9b\u3055\u308c\u3066\u3044\u307e\u305b\u3093\n</code></pre> built_in_hash.ts<pre><code>// TypeScript\u306b\u306f\u7d44\u307f\u8fbc\u307f\u306e\u30cf\u30c3\u30b7\u30e5\u30b3\u30fc\u30c9\u95a2\u6570\u304c\u63d0\u4f9b\u3055\u308c\u3066\u3044\u307e\u305b\u3093\n</code></pre> built_in_hash.dart<pre><code>int num = 3;\nint hashNum = num.hashCode;\n// \u6574\u65703\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306f34803\n\nbool bol = true;\nint hashBol = bol.hashCode;\n// \u30d6\u30fc\u30eb\u5024true\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306f1231\n\ndouble dec = 3.14159;\nint hashDec = dec.hashCode;\n// \u5c0f\u65703.14159\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306f2570631074981783\n\nString str = \"Hello \u7b97\u6cd5\";\nint hashStr = str.hashCode;\n// \u6587\u5b57\u5217\"Hello \u7b97\u6cd5\"\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306f468167534\n\nList arr = [12836, \"\u5c0f\u54c8\"];\nint hashArr = arr.hashCode;\n// \u914d\u5217[12836, \u5c0f\u54c8]\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306f976512528\n\nListNode obj = new ListNode(0);\nint hashObj = obj.hashCode;\n// ListNode\u30aa\u30d6\u30b8\u30a7\u30af\u30c8Instance of 'ListNode'\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306f1033450432\n</code></pre> built_in_hash.rs<pre><code>use std::collections::hash_map::DefaultHasher;\nuse std::hash::{Hash, Hasher};\n\nlet num = 3;\nlet mut num_hasher = DefaultHasher::new();\nnum.hash(&amp;mut num_hasher);\nlet hash_num = num_hasher.finish();\n// \u6574\u65703\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306f568126464209439262\n\nlet bol = true;\nlet mut bol_hasher = DefaultHasher::new();\nbol.hash(&amp;mut bol_hasher);\nlet hash_bol = bol_hasher.finish();\n// \u30d6\u30fc\u30eb\u5024true\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306f4952851536318644461\n\nlet dec: f32 = 3.14159;\nlet mut dec_hasher = DefaultHasher::new();\ndec.to_bits().hash(&amp;mut dec_hasher);\nlet hash_dec = dec_hasher.finish();\n// \u5c0f\u65703.14159\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306f2566941990314602357\n\nlet str = \"Hello \u7b97\u6cd5\";\nlet mut str_hasher = DefaultHasher::new();\nstr.hash(&amp;mut str_hasher);\nlet hash_str = str_hasher.finish();\n// \u6587\u5b57\u5217\"Hello \u7b97\u6cd5\"\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306f16092673739211250988\n\nlet arr = (&amp;12836, &amp;\"\u5c0f\u54c8\");\nlet mut tup_hasher = DefaultHasher::new();\narr.hash(&amp;mut tup_hasher);\nlet hash_tup = tup_hasher.finish();\n// \u30bf\u30d7\u30eb(12836, \"\u5c0f\u54c8\")\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306f1885128010422702749\n\nlet node = ListNode::new(42);\nlet mut hasher = DefaultHasher::new();\nnode.borrow().val.hash(&amp;mut hasher);\nlet hash = hasher.finish();\n// ListNode\u30aa\u30d6\u30b8\u30a7\u30af\u30c8RefCell { value: ListNode { val: 42, next: None } }\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u306f15387811073369036852\n</code></pre> built_in_hash.c<pre><code>// C\u306b\u306f\u7d44\u307f\u8fbc\u307f\u306e\u30cf\u30c3\u30b7\u30e5\u30b3\u30fc\u30c9\u95a2\u6570\u304c\u63d0\u4f9b\u3055\u308c\u3066\u3044\u307e\u305b\u3093\n</code></pre> built_in_hash.kt<pre><code>\n</code></pre> built_in_hash.zig<pre><code>\n</code></pre> <p>\u591a\u304f\u306e\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u3067\u306f\u3001\u4e0d\u5909\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u306e\u307f\u304c\u30cf\u30c3\u30b7\u30e5\u8868\u306e<code>key</code>\u3068\u3057\u3066\u6a5f\u80fd\u3067\u304d\u307e\u3059\u3002\u30ea\u30b9\u30c8\uff08\u52d5\u7684\u914d\u5217\uff09\u3092<code>key</code>\u3068\u3057\u3066\u4f7f\u7528\u3059\u308b\u5834\u5408\u3001\u30ea\u30b9\u30c8\u306e\u5185\u5bb9\u304c\u5909\u66f4\u3055\u308c\u308b\u3068\u3001\u305d\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u3082\u5909\u66f4\u3055\u308c\u3001\u30cf\u30c3\u30b7\u30e5\u8868\u3067\u5143\u306e<code>value</code>\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u306a\u304f\u306a\u308a\u307e\u3059\u3002</p> <p>\u30ab\u30b9\u30bf\u30e0\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\uff08\u9023\u7d50\u30ea\u30b9\u30c8\u30ce\u30fc\u30c9\u306a\u3069\uff09\u306e\u30e1\u30f3\u30d0\u30fc\u5909\u6570\u306f\u53ef\u5909\u3067\u3059\u304c\u3001\u30cf\u30c3\u30b7\u30e5\u53ef\u80fd\u3067\u3059\u3002\u3053\u308c\u306f\u3001\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u306e\u30cf\u30c3\u30b7\u30e5\u5024\u304c\u901a\u5e38\u305d\u306e\u30e1\u30e2\u30ea\u30a2\u30c9\u30ec\u30b9\u306b\u57fa\u3065\u3044\u3066\u751f\u6210\u3055\u308c\u308b\u305f\u3081\u3067\u3059\u3002\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u306e\u5185\u5bb9\u304c\u5909\u66f4\u3055\u308c\u3066\u3082\u3001\u30e1\u30e2\u30ea\u30a2\u30c9\u30ec\u30b9\u306f\u540c\u3058\u307e\u307e\u306a\u306e\u3067\u3001\u30cf\u30c3\u30b7\u30e5\u5024\u306f\u5909\u66f4\u3055\u308c\u307e\u305b\u3093\u3002</p> <p>\u7570\u306a\u308b\u30b3\u30f3\u30bd\u30fc\u30eb\u3067\u51fa\u529b\u3055\u308c\u308b\u30cf\u30c3\u30b7\u30e5\u5024\u304c\u7570\u306a\u308b\u3053\u3068\u306b\u6c17\u3065\u3044\u305f\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u3002\u3053\u308c\u306f\u3001Python\u30a4\u30f3\u30bf\u30fc\u30d7\u30ea\u30bf\u30fc\u304c\u8d77\u52d5\u3059\u308b\u305f\u3073\u306b\u6587\u5b57\u5217\u30cf\u30c3\u30b7\u30e5\u95a2\u6570\u306b\u30e9\u30f3\u30c0\u30e0\u30bd\u30eb\u30c8\u3092\u8ffd\u52a0\u3059\u308b\u305f\u3081\u3067\u3059\u3002\u3053\u306e\u30a2\u30d7\u30ed\u30fc\u30c1\u306fHashDoS\u653b\u6483\u3092\u52b9\u679c\u7684\u306b\u9632\u304e\u3001\u30cf\u30c3\u30b7\u30e5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u30bb\u30ad\u30e5\u30ea\u30c6\u30a3\u3092\u5411\u4e0a\u3055\u305b\u307e\u3059\u3002</p>"},{"location":"chapter_hashing/hash_collision/","title":"6.2 \u00a0 \u30cf\u30c3\u30b7\u30e5\u885d\u7a81","text":"<p>\u524d\u7bc0\u3067\u8ff0\u3079\u305f\u3088\u3046\u306b\u3001**\u307b\u3068\u3093\u3069\u306e\u5834\u5408\u3001\u30cf\u30c3\u30b7\u30e5\u95a2\u6570\u306e\u5165\u529b\u7a7a\u9593\u306f\u51fa\u529b\u7a7a\u9593\u3088\u308a\u3082\u306f\u308b\u304b\u306b\u5927\u304d\u3044**\u305f\u3081\u3001\u7406\u8ad6\u7684\u306b\u306f\u30cf\u30c3\u30b7\u30e5\u885d\u7a81\u306f\u907f\u3051\u3089\u308c\u307e\u305b\u3093\u3002\u4f8b\u3048\u3070\u3001\u5165\u529b\u7a7a\u9593\u304c\u3059\u3079\u3066\u306e\u6574\u6570\u3067\u3001\u51fa\u529b\u7a7a\u9593\u304c\u914d\u5217\u5bb9\u91cf\u306e\u30b5\u30a4\u30ba\u306e\u5834\u5408\u3001\u8907\u6570\u306e\u6574\u6570\u304c\u5fc5\u7136\u7684\u306b\u540c\u3058\u30d0\u30b1\u30c3\u30c8\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306b\u30de\u30c3\u30d4\u30f3\u30b0\u3055\u308c\u307e\u3059\u3002</p> <p>\u30cf\u30c3\u30b7\u30e5\u885d\u7a81\u306f\u8aa4\u3063\u305f\u30af\u30a8\u30ea\u7d50\u679c\u306b\u3064\u306a\u304c\u308a\u3001\u30cf\u30c3\u30b7\u30e5\u8868\u306e\u4f7f\u3044\u3084\u3059\u3055\u306b\u6df1\u523b\u306a\u5f71\u97ff\u3092\u4e0e\u3048\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u554f\u984c\u306b\u5bfe\u51e6\u3059\u308b\u305f\u3081\u306b\u3001\u30cf\u30c3\u30b7\u30e5\u885d\u7a81\u304c\u767a\u751f\u3059\u308b\u305f\u3073\u306b\u3001\u885d\u7a81\u304c\u6d88\u3048\u308b\u307e\u3067\u30cf\u30c3\u30b7\u30e5\u8868\u306e\u30ea\u30b5\u30a4\u30ba\u3092\u5b9f\u884c\u3057\u307e\u3059\u3002\u3053\u306e\u30a2\u30d7\u30ed\u30fc\u30c1\u306f\u975e\u5e38\u306b\u30b7\u30f3\u30d7\u30eb\u3067\u76f4\u63a5\u7684\u3067\u3042\u308a\u3001\u3046\u307e\u304f\u6a5f\u80fd\u3057\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u30c6\u30fc\u30d6\u30eb\u306e\u62e1\u5f35\u306b\u306f\u5927\u91cf\u306e\u30c7\u30fc\u30bf\u79fb\u884c\u3068\u30cf\u30c3\u30b7\u30e5\u30b3\u30fc\u30c9\u306e\u518d\u8a08\u7b97\u304c\u542b\u307e\u308c\u3001\u3053\u308c\u3089\u306f\u9ad8\u30b3\u30b9\u30c8\u3067\u3042\u308b\u305f\u3081\u3001\u975e\u5e38\u306b\u975e\u52b9\u7387\u7684\u306b\u898b\u3048\u307e\u3059\u3002\u52b9\u7387\u3092\u5411\u4e0a\u3055\u305b\u308b\u305f\u3081\u306b\u3001\u4ee5\u4e0b\u306e\u6226\u7565\u3092\u63a1\u7528\u3067\u304d\u307e\u3059\uff1a</p> <ol> <li>**\u30cf\u30c3\u30b7\u30e5\u885d\u7a81\u304c\u767a\u751f\u3057\u305f\u5834\u5408\u3067\u3082\u3001\u30bf\u30fc\u30b2\u30c3\u30c8\u8981\u7d20\u306e\u691c\u7d22\u304c\u9069\u5207\u306b\u6a5f\u80fd\u3059\u308b**\u3088\u3046\u306b\u30cf\u30c3\u30b7\u30e5\u8868\u306e\u30c7\u30fc\u30bf\u69cb\u9020\u3092\u6539\u5584\u3059\u308b\u3002</li> <li>\u6df1\u523b\u306a\u885d\u7a81\u304c\u89b3\u5bdf\u3055\u308c\u3001\u5fc5\u8981\u306b\u306a\u308b\u524d\u306b\u3001\u62e1\u5f35\u306f\u6700\u5f8c\u306e\u624b\u6bb5\u3068\u3059\u308b\u3002</li> </ol> <p>\u30cf\u30c3\u30b7\u30e5\u8868\u306e\u69cb\u9020\u3092\u6539\u5584\u3059\u308b\u4e3b\u306a\u65b9\u6cd5\u306f2\u3064\u3042\u308a\u307e\u3059\uff1a\u300c\u9023\u9396\u6cd5\u300d\u3068\u300c\u30aa\u30fc\u30d7\u30f3\u30a2\u30c9\u30ec\u30b9\u6cd5\u300d\u3067\u3059\u3002</p>"},{"location":"chapter_hashing/hash_collision/#621","title":"6.2.1 \u00a0 \u9023\u9396\u6cd5","text":"<p>\u5143\u306e\u30cf\u30c3\u30b7\u30e5\u8868\u3067\u306f\u3001\u5404\u30d0\u30b1\u30c3\u30c8\u306f1\u3064\u306e\u30ad\u30fc\u5024\u30da\u30a2\u306e\u307f\u3092\u683c\u7d0d\u3067\u304d\u307e\u3059\u3002\u9023\u9396\u6cd5\u306f\u5358\u4e00\u306e\u8981\u7d20\u3092\u9023\u7d50\u30ea\u30b9\u30c8\u306b\u5909\u63db\u3057\u3001\u30ad\u30fc\u5024\u30da\u30a2\u3092\u30ea\u30b9\u30c8\u30ce\u30fc\u30c9\u3068\u3057\u3066\u6271\u3044\u3001\u885d\u7a81\u3059\u308b\u3059\u3079\u3066\u306e\u30ad\u30fc\u5024\u30da\u30a2\u3092\u540c\u3058\u9023\u7d50\u30ea\u30b9\u30c8\u306b\u683c\u7d0d\u3057\u307e\u3059\u3002\u4e0b\u56f3\u306f\u9023\u9396\u6cd5\u3092\u4f7f\u7528\u3057\u305f\u30cf\u30c3\u30b7\u30e5\u8868\u306e\u4f8b\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002</p> <p></p> <p> \u56f3 6-5 \u00a0 \u9023\u9396\u6cd5\u30cf\u30c3\u30b7\u30e5\u8868 </p> <p>\u9023\u9396\u6cd5\u3067\u5b9f\u88c5\u3055\u308c\u305f\u30cf\u30c3\u30b7\u30e5\u8868\u306e\u64cd\u4f5c\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5909\u66f4\u3055\u308c\u307e\u3059\uff1a</p> <ul> <li>\u8981\u7d20\u306e\u30af\u30a8\u30ea: <code>key</code>\u3092\u5165\u529b\u3057\u3001\u30cf\u30c3\u30b7\u30e5\u95a2\u6570\u3092\u901a\u3057\u3066\u30d0\u30b1\u30c3\u30c8\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u53d6\u5f97\u3057\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u306e\u30d8\u30c3\u30c9\u30ce\u30fc\u30c9\u306b\u30a2\u30af\u30bb\u30b9\u3057\u307e\u3059\u3002\u9023\u7d50\u30ea\u30b9\u30c8\u3092\u8d70\u67fb\u3057\u3066\u30ad\u30fc\u3092\u6bd4\u8f03\u3057\u3001\u30bf\u30fc\u30b2\u30c3\u30c8\u30ad\u30fc\u5024\u30da\u30a2\u3092\u898b\u3064\u3051\u307e\u3059\u3002</li> <li>\u8981\u7d20\u306e\u8ffd\u52a0: \u30cf\u30c3\u30b7\u30e5\u95a2\u6570\u3092\u901a\u3057\u3066\u9023\u7d50\u30ea\u30b9\u30c8\u306e\u30d8\u30c3\u30c9\u30ce\u30fc\u30c9\u306b\u30a2\u30af\u30bb\u30b9\u3057\u3001\u30ce\u30fc\u30c9\uff08\u30ad\u30fc\u5024\u30da\u30a2\uff09\u3092\u30ea\u30b9\u30c8\u306b\u8ffd\u52a0\u3057\u307e\u3059\u3002</li> <li>\u8981\u7d20\u306e\u524a\u9664: \u30cf\u30c3\u30b7\u30e5\u95a2\u6570\u306e\u7d50\u679c\u306b\u57fa\u3065\u3044\u3066\u9023\u7d50\u30ea\u30b9\u30c8\u306e\u30d8\u30c3\u30c9\u306b\u30a2\u30af\u30bb\u30b9\u3057\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u3092\u8d70\u67fb\u3057\u3066\u30bf\u30fc\u30b2\u30c3\u30c8\u30ce\u30fc\u30c9\u3092\u898b\u3064\u3051\u3066\u524a\u9664\u3057\u307e\u3059\u3002</li> </ul> <p>\u9023\u9396\u6cd5\u306b\u306f\u4ee5\u4e0b\u306e\u5236\u9650\u304c\u3042\u308a\u307e\u3059\uff1a</p> <ul> <li>\u7a7a\u9593\u4f7f\u7528\u91cf\u306e\u5897\u52a0: \u9023\u7d50\u30ea\u30b9\u30c8\u306b\u306f\u30ce\u30fc\u30c9\u30dd\u30a4\u30f3\u30bf\u304c\u542b\u307e\u308c\u3066\u304a\u308a\u3001\u914d\u5217\u3088\u308a\u3082\u591a\u304f\u306e\u30e1\u30e2\u30ea\u7a7a\u9593\u3092\u6d88\u8cbb\u3057\u307e\u3059\u3002</li> <li>\u30af\u30a8\u30ea\u52b9\u7387\u306e\u4f4e\u4e0b: \u5bfe\u5fdc\u3059\u308b\u8981\u7d20\u3092\u898b\u3064\u3051\u308b\u305f\u3081\u306b\u9023\u7d50\u30ea\u30b9\u30c8\u306e\u7dda\u5f62\u8d70\u67fb\u304c\u5fc5\u8981\u306b\u306a\u308b\u305f\u3081\u3067\u3059\u3002</li> </ul> <p>\u4ee5\u4e0b\u306e\u30b3\u30fc\u30c9\u306f\u9023\u9396\u6cd5\u30cf\u30c3\u30b7\u30e5\u8868\u306e\u7c21\u5358\u306a\u5b9f\u88c5\u3092\u63d0\u4f9b\u3057\u3001\u6ce8\u610f\u3059\u3079\u304d2\u3064\u306e\u70b9\u304c\u3042\u308a\u307e\u3059\uff1a</p> <ul> <li>\u7c21\u5358\u306b\u3059\u308b\u305f\u3081\u306b\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u306e\u4ee3\u308f\u308a\u306b\u30ea\u30b9\u30c8\uff08\u52d5\u7684\u914d\u5217\uff09\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002\u3053\u306e\u8a2d\u5b9a\u3067\u306f\u3001\u30cf\u30c3\u30b7\u30e5\u8868\uff08\u914d\u5217\uff09\u306f\u8907\u6570\u306e\u30d0\u30b1\u30c3\u30c8\u3092\u542b\u307f\u3001\u5404\u30d0\u30b1\u30c3\u30c8\u306f\u30ea\u30b9\u30c8\u3067\u3059\u3002</li> <li>\u3053\u306e\u5b9f\u88c5\u306b\u306f\u30cf\u30c3\u30b7\u30e5\u8868\u306e\u30ea\u30b5\u30a4\u30ba\u30e1\u30bd\u30c3\u30c9\u304c\u542b\u307e\u308c\u3066\u3044\u307e\u3059\u3002\u8ca0\u8377\u7387\u304c\\(\\frac{2}{3}\\)\u3092\u8d85\u3048\u308b\u3068\u3001\u30cf\u30c3\u30b7\u30e5\u8868\u3092\u5143\u306e\u30b5\u30a4\u30ba\u306e2\u500d\u306b\u62e1\u5f35\u3057\u307e\u3059\u3002</li> </ul> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig hash_map_chaining.py<pre><code>class HashMapChaining:\n    \"\"\"\u30c1\u30a7\u30fc\u30f3\u30a2\u30c9\u30ec\u30b9\u6cd5\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\"\"\"\n\n    def __init__(self):\n        \"\"\"\u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf\"\"\"\n        self.size = 0  # \u30ad\u30fc\u5024\u30da\u30a2\u306e\u6570\n        self.capacity = 4  # \u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u306e\u5bb9\u91cf\n        self.load_thres = 2.0 / 3.0  # \u62e1\u5f35\u3092\u30c8\u30ea\u30ac\u30fc\u3059\u308b\u8ca0\u8377\u7387\u306e\u95be\u5024\n        self.extend_ratio = 2  # \u62e1\u5f35\u306e\u500d\u6570\n        self.buckets = [[] for _ in range(self.capacity)]  # \u30d0\u30b1\u30c3\u30c8\u914d\u5217\n\n    def hash_func(self, key: int) -&gt; int:\n        \"\"\"\u30cf\u30c3\u30b7\u30e5\u95a2\u6570\"\"\"\n        return key % self.capacity\n\n    def load_factor(self) -&gt; float:\n        \"\"\"\u8ca0\u8377\u7387\"\"\"\n        return self.size / self.capacity\n\n    def get(self, key: int) -&gt; str | None:\n        \"\"\"\u7167\u4f1a\u64cd\u4f5c\"\"\"\n        index = self.hash_func(key)\n        bucket = self.buckets[index]\n        # \u30d0\u30b1\u30c3\u30c8\u3092\u8d70\u67fb\u3057\u3001\u30ad\u30fc\u304c\u898b\u3064\u304b\u308c\u3070\u5bfe\u5fdc\u3059\u308b val \u3092\u8fd4\u3059\n        for pair in bucket:\n            if pair.key == key:\n                return pair.val\n        # \u30ad\u30fc\u304c\u898b\u3064\u304b\u3089\u306a\u3044\u5834\u5408\u3001None \u3092\u8fd4\u3059\n        return None\n\n    def put(self, key: int, val: str):\n        \"\"\"\u8ffd\u52a0\u64cd\u4f5c\"\"\"\n        # \u8ca0\u8377\u7387\u304c\u95be\u5024\u3092\u8d85\u3048\u305f\u5834\u5408\u3001\u62e1\u5f35\u3092\u5b9f\u884c\n        if self.load_factor() &gt; self.load_thres:\n            self.extend()\n        index = self.hash_func(key)\n        bucket = self.buckets[index]\n        # \u30d0\u30b1\u30c3\u30c8\u3092\u8d70\u67fb\u3057\u3001\u6307\u5b9a\u3055\u308c\u305f\u30ad\u30fc\u306b\u906d\u9047\u3057\u305f\u5834\u5408\u3001\u5bfe\u5fdc\u3059\u308b val \u3092\u66f4\u65b0\u3057\u3066\u8fd4\u3059\n        for pair in bucket:\n            if pair.key == key:\n                pair.val = val\n                return\n        # \u30ad\u30fc\u304c\u898b\u3064\u304b\u3089\u306a\u3044\u5834\u5408\u3001\u30ad\u30fc\u5024\u30da\u30a2\u3092\u672b\u5c3e\u306b\u8ffd\u52a0\n        pair = Pair(key, val)\n        bucket.append(pair)\n        self.size += 1\n\n    def remove(self, key: int):\n        \"\"\"\u524a\u9664\u64cd\u4f5c\"\"\"\n        index = self.hash_func(key)\n        bucket = self.buckets[index]\n        # \u30d0\u30b1\u30c3\u30c8\u3092\u8d70\u67fb\u3057\u3001\u305d\u306e\u4e2d\u304b\u3089\u30ad\u30fc\u5024\u30da\u30a2\u3092\u524a\u9664\n        for pair in bucket:\n            if pair.key == key:\n                bucket.remove(pair)\n                self.size -= 1\n                break\n\n    def extend(self):\n        \"\"\"\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u3092\u62e1\u5f35\"\"\"\n        # \u5143\u306e\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u3092\u4e00\u6642\u7684\u306b\u4fdd\u5b58\n        buckets = self.buckets\n        # \u62e1\u5f35\u3055\u308c\u305f\u65b0\u3057\u3044\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u3092\u521d\u671f\u5316\n        self.capacity *= self.extend_ratio\n        self.buckets = [[] for _ in range(self.capacity)]\n        self.size = 0\n        # \u5143\u306e\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u304b\u3089\u65b0\u3057\u3044\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u306b\u30ad\u30fc\u5024\u30da\u30a2\u3092\u79fb\u52d5\n        for bucket in buckets:\n            for pair in bucket:\n                self.put(pair.key, pair.val)\n\n    def print(self):\n        \"\"\"\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u3092\u51fa\u529b\"\"\"\n        for bucket in self.buckets:\n            res = []\n            for pair in bucket:\n                res.append(str(pair.key) + \" -&gt; \" + pair.val)\n            print(res)\n</code></pre> hash_map_chaining.cpp<pre><code>/* \u30c1\u30a7\u30a4\u30f3\u6cd5\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb */\nclass HashMapChaining {\n  private:\n    int size;                       // \u30ad\u30fc\u5024\u30da\u30a2\u306e\u6570\n    int capacity;                   // \u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u306e\u5bb9\u91cf\n    double loadThres;               // \u62e1\u5f35\u3092\u30c8\u30ea\u30ac\u30fc\u3059\u308b\u8ca0\u8377\u7387\u306e\u95be\u5024\n    int extendRatio;                // \u62e1\u5f35\u500d\u7387\n    vector&lt;vector&lt;Pair *&gt;&gt; buckets; // \u30d0\u30b1\u30c3\u30c8\u914d\u5217\n\n  public:\n    /* \u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf */\n    HashMapChaining() : size(0), capacity(4), loadThres(2.0 / 3.0), extendRatio(2) {\n        buckets.resize(capacity);\n    }\n\n    /* \u30c7\u30b9\u30c8\u30e9\u30af\u30bf */\n    ~HashMapChaining() {\n        for (auto &amp;bucket : buckets) {\n            for (Pair *pair : bucket) {\n                // \u30e1\u30e2\u30ea\u3092\u89e3\u653e\n                delete pair;\n            }\n        }\n    }\n\n    /* \u30cf\u30c3\u30b7\u30e5\u95a2\u6570 */\n    int hashFunc(int key) {\n        return key % capacity;\n    }\n\n    /* \u8ca0\u8377\u7387 */\n    double loadFactor() {\n        return (double)size / (double)capacity;\n    }\n\n    /* \u30af\u30a8\u30ea\u64cd\u4f5c */\n    string get(int key) {\n        int index = hashFunc(key);\n        // \u30d0\u30b1\u30c3\u30c8\u3092\u8d70\u67fb\u3001\u30ad\u30fc\u304c\u898b\u3064\u304b\u3063\u305f\u5834\u5408\u3001\u5bfe\u5fdc\u3059\u308bval\u3092\u8fd4\u5374\n        for (Pair *pair : buckets[index]) {\n            if (pair-&gt;key == key) {\n                return pair-&gt;val;\n            }\n        }\n        // \u30ad\u30fc\u304c\u898b\u3064\u304b\u3089\u306a\u3044\u5834\u5408\u3001\u7a7a\u6587\u5b57\u5217\u3092\u8fd4\u5374\n        return \"\";\n    }\n\n    /* \u8ffd\u52a0\u64cd\u4f5c */\n    void put(int key, string val) {\n        // \u8ca0\u8377\u7387\u304c\u95be\u5024\u3092\u8d85\u3048\u305f\u5834\u5408\u3001\u62e1\u5f35\u3092\u5b9f\u884c\n        if (loadFactor() &gt; loadThres) {\n            extend();\n        }\n        int index = hashFunc(key);\n        // \u30d0\u30b1\u30c3\u30c8\u3092\u8d70\u67fb\u3001\u6307\u5b9a\u30ad\u30fc\u306b\u906d\u9047\u3057\u305f\u5834\u5408\u3001\u5bfe\u5fdc\u3059\u308bval\u3092\u66f4\u65b0\u3057\u3066\u8fd4\u5374\n        for (Pair *pair : buckets[index]) {\n            if (pair-&gt;key == key) {\n                pair-&gt;val = val;\n                return;\n            }\n        }\n        // \u30ad\u30fc\u304c\u898b\u3064\u304b\u3089\u306a\u3044\u5834\u5408\u3001\u30ad\u30fc\u5024\u30da\u30a2\u3092\u672b\u5c3e\u306b\u8ffd\u52a0\n        buckets[index].push_back(new Pair(key, val));\n        size++;\n    }\n\n    /* \u524a\u9664\u64cd\u4f5c */\n    void remove(int key) {\n        int index = hashFunc(key);\n        auto &amp;bucket = buckets[index];\n        // \u30d0\u30b1\u30c3\u30c8\u3092\u8d70\u67fb\u3001\u30ad\u30fc\u5024\u30da\u30a2\u3092\u524a\u9664\n        for (int i = 0; i &lt; bucket.size(); i++) {\n            if (bucket[i]-&gt;key == key) {\n                Pair *tmp = bucket[i];\n                bucket.erase(bucket.begin() + i); // \u30ad\u30fc\u5024\u30da\u30a2\u3092\u524a\u9664\n                delete tmp;                       // \u30e1\u30e2\u30ea\u3092\u89e3\u653e\n                size--;\n                return;\n            }\n        }\n    }\n\n    /* \u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u3092\u62e1\u5f35 */\n    void extend() {\n        // \u5143\u306e\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u3092\u4e00\u6642\u4fdd\u5b58\n        vector&lt;vector&lt;Pair *&gt;&gt; bucketsTmp = buckets;\n        // \u62e1\u5f35\u3055\u308c\u305f\u65b0\u3057\u3044\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u3092\u521d\u671f\u5316\n        capacity *= extendRatio;\n        buckets.clear();\n        buckets.resize(capacity);\n        size = 0;\n        // \u5143\u306e\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u304b\u3089\u65b0\u3057\u3044\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u306b\u30ad\u30fc\u5024\u30da\u30a2\u3092\u79fb\u52d5\n        for (auto &amp;bucket : bucketsTmp) {\n            for (Pair *pair : bucket) {\n                put(pair-&gt;key, pair-&gt;val);\n                // \u30e1\u30e2\u30ea\u3092\u89e3\u653e\n                delete pair;\n            }\n        }\n    }\n\n    /* \u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u3092\u5370\u5237 */\n    void print() {\n        for (auto &amp;bucket : buckets) {\n            cout &lt;&lt; \"[\";\n            for (Pair *pair : bucket) {\n                cout &lt;&lt; pair-&gt;key &lt;&lt; \" -&gt; \" &lt;&lt; pair-&gt;val &lt;&lt; \", \";\n            }\n            cout &lt;&lt; \"]\\n\";\n        }\n    }\n};\n</code></pre> hash_map_chaining.java<pre><code>/* \u30c1\u30a7\u30a4\u30f3\u6cd5\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb */\nclass HashMapChaining {\n    int size; // \u30ad\u30fc\u5024\u30da\u30a2\u306e\u6570\n    int capacity; // \u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u306e\u5bb9\u91cf\n    double loadThres; // \u62e1\u5f35\u3092\u30c8\u30ea\u30ac\u30fc\u3059\u308b\u8ca0\u8377\u7387\u306e\u95be\u5024\n    int extendRatio; // \u62e1\u5f35\u500d\u7387\n    List&lt;List&lt;Pair&gt;&gt; buckets; // \u30d0\u30b1\u30c3\u30c8\u914d\u5217\n\n    /* \u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf */\n    public HashMapChaining() {\n        size = 0;\n        capacity = 4;\n        loadThres = 2.0 / 3.0;\n        extendRatio = 2;\n        buckets = new ArrayList&lt;&gt;(capacity);\n        for (int i = 0; i &lt; capacity; i++) {\n            buckets.add(new ArrayList&lt;&gt;());\n        }\n    }\n\n    /* \u30cf\u30c3\u30b7\u30e5\u95a2\u6570 */\n    int hashFunc(int key) {\n        return key % capacity;\n    }\n\n    /* \u8ca0\u8377\u7387 */\n    double loadFactor() {\n        return (double) size / capacity;\n    }\n\n    /* \u30af\u30a8\u30ea\u64cd\u4f5c */\n    String get(int key) {\n        int index = hashFunc(key);\n        List&lt;Pair&gt; bucket = buckets.get(index);\n        // \u30d0\u30b1\u30c3\u30c8\u3092\u8d70\u67fb\u3001\u30ad\u30fc\u304c\u898b\u3064\u304b\u3063\u305f\u5834\u5408\u5bfe\u5fdc\u3059\u308bval\u3092\u8fd4\u3059\n        for (Pair pair : bucket) {\n            if (pair.key == key) {\n                return pair.val;\n            }\n        }\n        // \u30ad\u30fc\u304c\u898b\u3064\u304b\u3089\u306a\u3044\u5834\u5408\u3001null\u3092\u8fd4\u3059\n        return null;\n    }\n\n    /* \u8ffd\u52a0\u64cd\u4f5c */\n    void put(int key, String val) {\n        // \u8ca0\u8377\u7387\u304c\u95be\u5024\u3092\u8d85\u3048\u305f\u5834\u5408\u3001\u62e1\u5f35\u3092\u5b9f\u884c\n        if (loadFactor() &gt; loadThres) {\n            extend();\n        }\n        int index = hashFunc(key);\n        List&lt;Pair&gt; bucket = buckets.get(index);\n        // \u30d0\u30b1\u30c3\u30c8\u3092\u8d70\u67fb\u3001\u6307\u5b9a\u3057\u305f\u30ad\u30fc\u306b\u906d\u9047\u3057\u305f\u5834\u5408\u3001\u5bfe\u5fdc\u3059\u308bval\u3092\u66f4\u65b0\u3057\u3066\u623b\u308b\n        for (Pair pair : bucket) {\n            if (pair.key == key) {\n                pair.val = val;\n                return;\n            }\n        }\n        // \u30ad\u30fc\u304c\u898b\u3064\u304b\u3089\u306a\u3044\u5834\u5408\u3001\u30ad\u30fc\u5024\u30da\u30a2\u3092\u672b\u5c3e\u306b\u8ffd\u52a0\n        Pair pair = new Pair(key, val);\n        bucket.add(pair);\n        size++;\n    }\n\n    /* \u524a\u9664\u64cd\u4f5c */\n    void remove(int key) {\n        int index = hashFunc(key);\n        List&lt;Pair&gt; bucket = buckets.get(index);\n        // \u30d0\u30b1\u30c3\u30c8\u3092\u8d70\u67fb\u3001\u305d\u306e\u4e2d\u304b\u3089\u30ad\u30fc\u5024\u30da\u30a2\u3092\u524a\u9664\n        for (Pair pair : bucket) {\n            if (pair.key == key) {\n                bucket.remove(pair);\n                size--;\n                break;\n            }\n        }\n    }\n\n    /* \u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u3092\u62e1\u5f35 */\n    void extend() {\n        // \u5143\u306e\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u3092\u4e00\u6642\u7684\u306b\u4fdd\u5b58\n        List&lt;List&lt;Pair&gt;&gt; bucketsTmp = buckets;\n        // \u62e1\u5f35\u3055\u308c\u305f\u65b0\u3057\u3044\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u3092\u521d\u671f\u5316\n        capacity *= extendRatio;\n        buckets = new ArrayList&lt;&gt;(capacity);\n        for (int i = 0; i &lt; capacity; i++) {\n            buckets.add(new ArrayList&lt;&gt;());\n        }\n        size = 0;\n        // \u5143\u306e\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u304b\u3089\u65b0\u3057\u3044\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u306b\u30ad\u30fc\u5024\u30da\u30a2\u3092\u79fb\u52d5\n        for (List&lt;Pair&gt; bucket : bucketsTmp) {\n            for (Pair pair : bucket) {\n                put(pair.key, pair.val);\n            }\n        }\n    }\n\n    /* \u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u3092\u5370\u5237 */\n    void print() {\n        for (List&lt;Pair&gt; bucket : buckets) {\n            List&lt;String&gt; res = new ArrayList&lt;&gt;();\n            for (Pair pair : bucket) {\n                res.add(pair.key + \" -&gt; \" + pair.val);\n            }\n            System.out.println(res);\n        }\n    }\n}\n</code></pre> hash_map_chaining.cs<pre><code>[class]{HashMapChaining}-[func]{}\n</code></pre> hash_map_chaining.go<pre><code>[class]{hashMapChaining}-[func]{}\n</code></pre> hash_map_chaining.swift<pre><code>[class]{HashMapChaining}-[func]{}\n</code></pre> hash_map_chaining.js<pre><code>[class]{HashMapChaining}-[func]{}\n</code></pre> hash_map_chaining.ts<pre><code>[class]{HashMapChaining}-[func]{}\n</code></pre> hash_map_chaining.dart<pre><code>[class]{HashMapChaining}-[func]{}\n</code></pre> hash_map_chaining.rs<pre><code>[class]{HashMapChaining}-[func]{}\n</code></pre> hash_map_chaining.c<pre><code>[class]{Node}-[func]{}\n\n[class]{HashMapChaining}-[func]{}\n</code></pre> hash_map_chaining.kt<pre><code>[class]{HashMapChaining}-[func]{}\n</code></pre> hash_map_chaining.rb<pre><code>[class]{HashMapChaining}-[func]{}\n</code></pre> hash_map_chaining.zig<pre><code>[class]{HashMapChaining}-[func]{}\n</code></pre> <p>\u9023\u7d50\u30ea\u30b9\u30c8\u304c\u975e\u5e38\u306b\u9577\u3044\u5834\u5408\u3001\u30af\u30a8\u30ea\u52b9\u7387\\(O(n)\\)\u304c\u60aa\u3044\u3053\u3068\u306f\u6ce8\u76ee\u306b\u5024\u3057\u307e\u3059\u3002\u3053\u306e\u5834\u5408\u3001\u30ea\u30b9\u30c8\u3092\u300cAVL\u6728\u300d\u307e\u305f\u306f\u300c\u8d64\u9ed2\u6728\u300d\u306b\u5909\u63db\u3057\u3066\u3001\u30af\u30a8\u30ea\u64cd\u4f5c\u306e\u6642\u9593\u8a08\u7b97\u91cf\u3092\\(O(\\log n)\\)\u306b\u6700\u9069\u5316\u3067\u304d\u307e\u3059\u3002</p>"},{"location":"chapter_hashing/hash_collision/#622","title":"6.2.2 \u00a0 \u30aa\u30fc\u30d7\u30f3\u30a2\u30c9\u30ec\u30b9\u6cd5","text":"<p>\u30aa\u30fc\u30d7\u30f3\u30a2\u30c9\u30ec\u30b9\u6cd5\u306f\u8ffd\u52a0\u306e\u30c7\u30fc\u30bf\u69cb\u9020\u3092\u5c0e\u5165\u305b\u305a\u3001\u4ee3\u308f\u308a\u306b\u300c\u8907\u6570\u56de\u30d7\u30ed\u30fc\u30d6\u300d\u3092\u901a\u3057\u3066\u30cf\u30c3\u30b7\u30e5\u885d\u7a81\u3092\u51e6\u7406\u3057\u307e\u3059\u3002\u30d7\u30ed\u30fc\u30d6\u65b9\u6cd5\u306b\u306f\u4e3b\u306b\u7dda\u5f62\u30d7\u30ed\u30fc\u30d6\u3001\u4e8c\u6b21\u30d7\u30ed\u30fc\u30d6\u3001\u4e8c\u91cd\u30cf\u30c3\u30b7\u30e5\u304c\u3042\u308a\u307e\u3059\u3002</p> <p>\u7dda\u5f62\u30d7\u30ed\u30fc\u30d6\u3092\u4f8b\u306b\u3057\u3066\u3001\u30aa\u30fc\u30d7\u30f3\u30a2\u30c9\u30ec\u30b9\u6cd5\u30cf\u30c3\u30b7\u30e5\u8868\u306e\u30e1\u30ab\u30cb\u30ba\u30e0\u3092\u7d39\u4ecb\u3057\u307e\u3057\u3087\u3046\u3002</p>"},{"location":"chapter_hashing/hash_collision/#1","title":"1. \u00a0 \u7dda\u5f62\u30d7\u30ed\u30fc\u30d6","text":"<p>\u7dda\u5f62\u30d7\u30ed\u30fc\u30d6\u306f\u56fa\u5b9a\u30b9\u30c6\u30c3\u30d7\u306e\u7dda\u5f62\u691c\u7d22\u3092\u30d7\u30ed\u30fc\u30d6\u306b\u4f7f\u7528\u3057\u3001\u901a\u5e38\u306e\u30cf\u30c3\u30b7\u30e5\u8868\u3068\u306f\u7570\u306a\u308a\u307e\u3059\u3002</p> <ul> <li>\u8981\u7d20\u306e\u633f\u5165: \u30cf\u30c3\u30b7\u30e5\u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u30d0\u30b1\u30c3\u30c8\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002\u30d0\u30b1\u30c3\u30c8\u306b\u65e2\u306b\u8981\u7d20\u304c\u542b\u307e\u308c\u3066\u3044\u308b\u5834\u5408\u3001\u885d\u7a81\u4f4d\u7f6e\u304b\u3089\u7dda\u5f62\u306b\u524d\u65b9\u306b\u8d70\u67fb\u3057\uff08\u901a\u5e38\u30b9\u30c6\u30c3\u30d7\u30b5\u30a4\u30ba\u306f\\(1\\)\uff09\u3001\u7a7a\u306e\u30d0\u30b1\u30c3\u30c8\u304c\u898b\u3064\u304b\u308b\u307e\u3067\u9032\u307f\u3001\u8981\u7d20\u3092\u633f\u5165\u3057\u307e\u3059\u3002</li> <li>\u8981\u7d20\u306e\u691c\u7d22: \u30cf\u30c3\u30b7\u30e5\u885d\u7a81\u306b\u906d\u9047\u3057\u305f\u5834\u5408\u3001\u540c\u3058\u30b9\u30c6\u30c3\u30d7\u30b5\u30a4\u30ba\u3092\u4f7f\u7528\u3057\u3066\u7dda\u5f62\u306b\u524d\u65b9\u306b\u8d70\u67fb\u3057\u3001\u5bfe\u5fdc\u3059\u308b\u8981\u7d20\u304c\u898b\u3064\u304b\u3063\u305f\u3089<code>value</code>\u3092\u8fd4\u3057\u307e\u3059\u3002\u7a7a\u306e\u30d0\u30b1\u30c3\u30c8\u306b\u906d\u9047\u3057\u305f\u5834\u5408\u3001\u30bf\u30fc\u30b2\u30c3\u30c8\u8981\u7d20\u304c\u30cf\u30c3\u30b7\u30e5\u8868\u306b\u306a\u3044\u3053\u3068\u3092\u610f\u5473\u3059\u308b\u305f\u3081\u3001<code>None</code>\u3092\u8fd4\u3057\u307e\u3059\u3002</li> </ul> <p>\u4e0b\u56f3\u306f\u30aa\u30fc\u30d7\u30f3\u30a2\u30c9\u30ec\u30b9\u6cd5\uff08\u7dda\u5f62\u30d7\u30ed\u30fc\u30d6\uff09\u30cf\u30c3\u30b7\u30e5\u8868\u306b\u304a\u3051\u308b\u30ad\u30fc\u5024\u30da\u30a2\u306e\u5206\u5e03\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002\u3053\u306e\u30cf\u30c3\u30b7\u30e5\u95a2\u6570\u306b\u3088\u308b\u3068\u3001\u4e0b\u4e8c\u6841\u304c\u540c\u3058\u30ad\u30fc\u306f\u540c\u3058\u30d0\u30b1\u30c3\u30c8\u306b\u30de\u30c3\u30d4\u30f3\u30b0\u3055\u308c\u307e\u3059\u3002\u7dda\u5f62\u30d7\u30ed\u30fc\u30d6\u3092\u901a\u3057\u3066\u3001\u305d\u308c\u3089\u306f\u305d\u306e\u30d0\u30b1\u30c3\u30c8\u3068\u305d\u306e\u4e0b\u306e\u30d0\u30b1\u30c3\u30c8\u306b\u9806\u6b21\u683c\u7d0d\u3055\u308c\u307e\u3059\u3002</p> <p></p> <p> \u56f3 6-6 \u00a0 \u30aa\u30fc\u30d7\u30f3\u30a2\u30c9\u30ec\u30b9\u6cd5\uff08\u7dda\u5f62\u30d7\u30ed\u30fc\u30d6\uff09\u30cf\u30c3\u30b7\u30e5\u8868\u306b\u304a\u3051\u308b\u30ad\u30fc\u5024\u30da\u30a2\u306e\u5206\u5e03 </p> <p>\u3057\u304b\u3057\u3001\u7dda\u5f62\u30d7\u30ed\u30fc\u30d6\u306f\u300c\u30af\u30e9\u30b9\u30bf\u30ea\u30f3\u30b0\u300d\u3092\u4f5c\u308a\u3084\u3059\u3044\u50be\u5411\u304c\u3042\u308a\u307e\u3059\u3002\u5177\u4f53\u7684\u306b\u306f\u3001\u914d\u5217\u5185\u306e\u9023\u7d9a\u7684\u306b\u5360\u6709\u3055\u308c\u305f\u4f4d\u7f6e\u304c\u9577\u3044\u307b\u3069\u3001\u3053\u308c\u3089\u306e\u9023\u7d9a\u3057\u305f\u4f4d\u7f6e\u3067\u30cf\u30c3\u30b7\u30e5\u885d\u7a81\u304c\u767a\u751f\u3059\u308b\u78ba\u7387\u304c\u9ad8\u304f\u306a\u308a\u3001\u305d\u306e\u4f4d\u7f6e\u3067\u306e\u30af\u30e9\u30b9\u30bf\u30ea\u30f3\u30b0\u306e\u6210\u9577\u3092\u3055\u3089\u306b\u4fc3\u9032\u3057\u3001\u60aa\u5faa\u74b0\u3092\u5f62\u6210\u3057\u3001\u6700\u7d42\u7684\u306b\u633f\u5165\u3001\u524a\u9664\u3001\u30af\u30a8\u30ea\u3001\u66f4\u65b0\u64cd\u4f5c\u306e\u52b9\u7387\u4f4e\u4e0b\u306b\u3064\u306a\u304c\u308a\u307e\u3059\u3002</p> <p>**\u30aa\u30fc\u30d7\u30f3\u30a2\u30c9\u30ec\u30b9\u6cd5\u30cf\u30c3\u30b7\u30e5\u8868\u3067\u306f\u8981\u7d20\u3092\u76f4\u63a5\u524a\u9664\u3067\u304d\u306a\u3044**\u3053\u3068\u306b\u6ce8\u610f\u3059\u308b\u3053\u3068\u304c\u91cd\u8981\u3067\u3059\u3002\u8981\u7d20\u3092\u524a\u9664\u3059\u308b\u3068\u3001\u914d\u5217\u306b\u7a7a\u306e\u30d0\u30b1\u30c3\u30c8<code>None</code>\u304c\u4f5c\u6210\u3055\u308c\u307e\u3059\u3002\u8981\u7d20\u3092\u691c\u7d22\u3059\u308b\u969b\u3001\u7dda\u5f62\u30d7\u30ed\u30fc\u30d6\u304c\u3053\u306e\u7a7a\u306e\u30d0\u30b1\u30c3\u30c8\u306b\u906d\u9047\u3059\u308b\u3068\u623b\u3063\u3066\u3057\u307e\u3044\u3001\u3053\u306e\u30d0\u30b1\u30c3\u30c8\u306e\u4e0b\u306e\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9\u3067\u304d\u306a\u304f\u306a\u308a\u307e\u3059\u3002\u30d7\u30ed\u30b0\u30e9\u30e0\u306f\u3053\u308c\u3089\u306e\u8981\u7d20\u304c\u5b58\u5728\u3057\u306a\u3044\u3068\u8aa4\u3063\u3066\u4eee\u5b9a\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002\u4e0b\u56f3\u306b\u793a\u3059\u3068\u304a\u308a\u3067\u3059\u3002</p> <p></p> <p> \u56f3 6-7 \u00a0 \u30aa\u30fc\u30d7\u30f3\u30a2\u30c9\u30ec\u30b9\u6cd5\u3067\u306e\u524a\u9664\u306b\u3088\u308b\u30af\u30a8\u30ea\u554f\u984c </p> <p>\u3053\u306e\u554f\u984c\u3092\u89e3\u6c7a\u3059\u308b\u305f\u3081\u306b\u3001\u9045\u5ef6\u524a\u9664\u30e1\u30ab\u30cb\u30ba\u30e0\u3092\u63a1\u7528\u3067\u304d\u307e\u3059\uff1a\u30cf\u30c3\u30b7\u30e5\u8868\u304b\u3089\u8981\u7d20\u3092\u76f4\u63a5\u524a\u9664\u3059\u308b\u4ee3\u308f\u308a\u306b\u3001\u5b9a\u6570<code>TOMBSTONE</code>\u3092\u4f7f\u7528\u3057\u3066\u30d0\u30b1\u30c3\u30c8\u3092\u30de\u30fc\u30af\u3057\u307e\u3059\u3002\u3053\u306e\u30e1\u30ab\u30cb\u30ba\u30e0\u3067\u306f\u3001<code>None</code>\u3068<code>TOMBSTONE</code>\u306e\u4e21\u65b9\u304c\u7a7a\u306e\u30d0\u30b1\u30c3\u30c8\u3092\u8868\u3057\u3001\u30ad\u30fc\u5024\u30da\u30a2\u3092\u4fdd\u6301\u3067\u304d\u307e\u3059\u3002\u305f\u3060\u3057\u3001\u7dda\u5f62\u30d7\u30ed\u30fc\u30d6\u304c<code>TOMBSTONE</code>\u306b\u906d\u9047\u3057\u305f\u5834\u5408\u3001\u305d\u306e\u4e0b\u306b\u307e\u3060\u30ad\u30fc\u5024\u30da\u30a2\u304c\u3042\u308b\u53ef\u80fd\u6027\u304c\u3042\u308b\u305f\u3081\u3001\u8d70\u67fb\u3092\u7d9a\u3051\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002</p> <p>\u3057\u304b\u3057\u3001\u9045\u5ef6\u524a\u9664\u306f\u30cf\u30c3\u30b7\u30e5\u8868\u306e\u6027\u80fd\u52a3\u5316\u3092\u52a0\u901f\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002\u524a\u9664\u64cd\u4f5c\u306e\u305f\u3073\u306b\u524a\u9664\u30de\u30fc\u30af\u304c\u751f\u6210\u3055\u308c\u3001<code>TOMBSTONE</code>\u304c\u5897\u52a0\u3059\u308b\u3068\u3001\u7dda\u5f62\u30d7\u30ed\u30fc\u30d6\u304c\u30bf\u30fc\u30b2\u30c3\u30c8\u8981\u7d20\u3092\u898b\u3064\u3051\u308b\u305f\u3081\u306b\u8907\u6570\u306e<code>TOMBSTONE</code>\u3092\u30b9\u30ad\u30c3\u30d7\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u53ef\u80fd\u6027\u304c\u3042\u308b\u305f\u3081\u3001\u691c\u7d22\u6642\u9593\u3082\u5897\u52a0\u3057\u307e\u3059\u3002</p> <p>\u3053\u308c\u306b\u5bfe\u51e6\u3059\u308b\u305f\u3081\u306b\u3001\u7dda\u5f62\u30d7\u30ed\u30fc\u30d6\u4e2d\u306b\u6700\u521d\u306b\u906d\u9047\u3057\u305f<code>TOMBSTONE</code>\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8a18\u9332\u3057\u3001\u691c\u7d22\u3055\u308c\u305f\u30bf\u30fc\u30b2\u30c3\u30c8\u8981\u7d20\u3068\u305d\u306e<code>TOMBSTONE</code>\u306e\u4f4d\u7f6e\u3092\u4ea4\u63db\u3059\u308b\u3053\u3068\u3092\u691c\u8a0e\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u3053\u308c\u3092\u884c\u3046\u5229\u70b9\u306f\u3001\u8981\u7d20\u304c\u30af\u30a8\u30ea\u307e\u305f\u306f\u8ffd\u52a0\u3055\u308c\u308b\u305f\u3073\u306b\u3001\u8981\u7d20\u304c\u305d\u306e\u7406\u60f3\u7684\u306a\u4f4d\u7f6e\uff08\u30d7\u30ed\u30fc\u30d6\u306e\u958b\u59cb\u70b9\uff09\u306b\u3088\u308a\u8fd1\u3044\u30d0\u30b1\u30c3\u30c8\u306b\u79fb\u52d5\u3055\u308c\u3001\u30af\u30a8\u30ea\u52b9\u7387\u304c\u6700\u9069\u5316\u3055\u308c\u308b\u3053\u3068\u3067\u3059\u3002</p> <p>\u4ee5\u4e0b\u306e\u30b3\u30fc\u30c9\u306f\u3001\u9045\u5ef6\u524a\u9664\u3092\u4f7f\u7528\u3057\u305f\u30aa\u30fc\u30d7\u30f3\u30a2\u30c9\u30ec\u30b9\u6cd5\uff08\u7dda\u5f62\u30d7\u30ed\u30fc\u30d6\uff09\u30cf\u30c3\u30b7\u30e5\u8868\u3092\u5b9f\u88c5\u3057\u3066\u3044\u307e\u3059\u3002\u30cf\u30c3\u30b7\u30e5\u8868\u306e\u7a7a\u9593\u3092\u3088\u308a\u6709\u52b9\u306b\u6d3b\u7528\u3059\u308b\u305f\u3081\u306b\u3001\u30cf\u30c3\u30b7\u30e5\u8868\u3092\u300c\u5faa\u74b0\u914d\u5217\u300d\u3068\u3057\u3066\u6271\u3044\u307e\u3059\u3002\u914d\u5217\u306e\u7d42\u308f\u308a\u3092\u8d85\u3048\u308b\u3068\u3001\u6700\u521d\u306b\u623b\u3063\u3066\u8d70\u67fb\u3092\u7d9a\u3051\u307e\u3059\u3002</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig hash_map_open_addressing.py<pre><code>class HashMapOpenAddressing:\n    \"\"\"\u30aa\u30fc\u30d7\u30f3\u30a2\u30c9\u30ec\u30b9\u6cd5\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\"\"\"\n\n    def __init__(self):\n        \"\"\"\u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf\"\"\"\n        self.size = 0  # \u30ad\u30fc\u5024\u30da\u30a2\u306e\u6570\n        self.capacity = 4  # \u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u306e\u5bb9\u91cf\n        self.load_thres = 2.0 / 3.0  # \u62e1\u5f35\u3092\u30c8\u30ea\u30ac\u30fc\u3059\u308b\u8ca0\u8377\u7387\u306e\u95be\u5024\n        self.extend_ratio = 2  # \u62e1\u5f35\u306e\u500d\u6570\n        self.buckets: list[Pair | None] = [None] * self.capacity  # \u30d0\u30b1\u30c3\u30c8\u914d\u5217\n        self.TOMBSTONE = Pair(-1, \"-1\")  # \u524a\u9664\u30de\u30fc\u30af\n\n    def hash_func(self, key: int) -&gt; int:\n        \"\"\"\u30cf\u30c3\u30b7\u30e5\u95a2\u6570\"\"\"\n        return key % self.capacity\n\n    def load_factor(self) -&gt; float:\n        \"\"\"\u8ca0\u8377\u7387\"\"\"\n        return self.size / self.capacity\n\n    def find_bucket(self, key: int) -&gt; int:\n        \"\"\"key \u306b\u5bfe\u5fdc\u3059\u308b\u30d0\u30b1\u30c3\u30c8\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u691c\u7d22\"\"\"\n        index = self.hash_func(key)\n        first_tombstone = -1\n        # \u7dda\u5f62\u63a2\u67fb\u3001\u7a7a\u306e\u30d0\u30b1\u30c3\u30c8\u306b\u906d\u9047\u3057\u305f\u3089\u30d6\u30ec\u30fc\u30af\n        while self.buckets[index] is not None:\n            # \u30ad\u30fc\u306b\u906d\u9047\u3057\u305f\u5834\u5408\u3001\u5bfe\u5fdc\u3059\u308b\u30d0\u30b1\u30c3\u30c8\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8fd4\u3059\n            if self.buckets[index].key == key:\n                # \u524a\u9664\u30de\u30fc\u30af\u304c\u4ee5\u524d\u306b\u906d\u9047\u3057\u3066\u3044\u305f\u5834\u5408\u3001\u30ad\u30fc\u5024\u30da\u30a2\u3092\u305d\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306b\u79fb\u52d5\n                if first_tombstone != -1:\n                    self.buckets[first_tombstone] = self.buckets[index]\n                    self.buckets[index] = self.TOMBSTONE\n                    return first_tombstone  # \u79fb\u52d5\u3055\u308c\u305f\u30d0\u30b1\u30c3\u30c8\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8fd4\u3059\n                return index  # \u30d0\u30b1\u30c3\u30c8\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8fd4\u3059\n            # \u6700\u521d\u306b\u906d\u9047\u3057\u305f\u524a\u9664\u30de\u30fc\u30af\u3092\u8a18\u9332\n            if first_tombstone == -1 and self.buckets[index] is self.TOMBSTONE:\n                first_tombstone = index\n            # \u30d0\u30b1\u30c3\u30c8\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8a08\u7b97\u3001\u672b\u5c3e\u3092\u8d85\u3048\u305f\u5834\u5408\u306f\u5148\u982d\u306b\u623b\u308b\n            index = (index + 1) % self.capacity\n        # \u30ad\u30fc\u304c\u5b58\u5728\u3057\u306a\u3044\u5834\u5408\u3001\u633f\u5165\u30dd\u30a4\u30f3\u30c8\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8fd4\u3059\n        return index if first_tombstone == -1 else first_tombstone\n\n    def get(self, key: int) -&gt; str:\n        \"\"\"\u7167\u4f1a\u64cd\u4f5c\"\"\"\n        # key \u306b\u5bfe\u5fdc\u3059\u308b\u30d0\u30b1\u30c3\u30c8\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u691c\u7d22\n        index = self.find_bucket(key)\n        # \u30ad\u30fc\u5024\u30da\u30a2\u304c\u898b\u3064\u304b\u308c\u3070\u3001\u5bfe\u5fdc\u3059\u308b val \u3092\u8fd4\u3059\n        if self.buckets[index] not in [None, self.TOMBSTONE]:\n            return self.buckets[index].val\n        # \u30ad\u30fc\u5024\u30da\u30a2\u304c\u5b58\u5728\u3057\u306a\u3044\u5834\u5408\u3001None \u3092\u8fd4\u3059\n        return None\n\n    def put(self, key: int, val: str):\n        \"\"\"\u8ffd\u52a0\u64cd\u4f5c\"\"\"\n        # \u8ca0\u8377\u7387\u304c\u95be\u5024\u3092\u8d85\u3048\u305f\u5834\u5408\u3001\u62e1\u5f35\u3092\u5b9f\u884c\n        if self.load_factor() &gt; self.load_thres:\n            self.extend()\n        # key \u306b\u5bfe\u5fdc\u3059\u308b\u30d0\u30b1\u30c3\u30c8\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u691c\u7d22\n        index = self.find_bucket(key)\n        # \u30ad\u30fc\u5024\u30da\u30a2\u304c\u898b\u3064\u304b\u308c\u3070\u3001val \u3092\u4e0a\u66f8\u304d\u3057\u3066\u8fd4\u3059\n        if self.buckets[index] not in [None, self.TOMBSTONE]:\n            self.buckets[index].val = val\n            return\n        # \u30ad\u30fc\u5024\u30da\u30a2\u304c\u5b58\u5728\u3057\u306a\u3044\u5834\u5408\u3001\u30ad\u30fc\u5024\u30da\u30a2\u3092\u8ffd\u52a0\n        self.buckets[index] = Pair(key, val)\n        self.size += 1\n\n    def remove(self, key: int):\n        \"\"\"\u524a\u9664\u64cd\u4f5c\"\"\"\n        # key \u306b\u5bfe\u5fdc\u3059\u308b\u30d0\u30b1\u30c3\u30c8\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u691c\u7d22\n        index = self.find_bucket(key)\n        # \u30ad\u30fc\u5024\u30da\u30a2\u304c\u898b\u3064\u304b\u308c\u3070\u3001\u524a\u9664\u30de\u30fc\u30af\u3067\u8986\u3046\n        if self.buckets[index] not in [None, self.TOMBSTONE]:\n            self.buckets[index] = self.TOMBSTONE\n            self.size -= 1\n\n    def extend(self):\n        \"\"\"\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u3092\u62e1\u5f35\"\"\"\n        # \u5143\u306e\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u3092\u4e00\u6642\u7684\u306b\u4fdd\u5b58\n        buckets_tmp = self.buckets\n        # \u62e1\u5f35\u3055\u308c\u305f\u65b0\u3057\u3044\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u3092\u521d\u671f\u5316\n        self.capacity *= self.extend_ratio\n        self.buckets = [None] * self.capacity\n        self.size = 0\n        # \u5143\u306e\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u304b\u3089\u65b0\u3057\u3044\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u306b\u30ad\u30fc\u5024\u30da\u30a2\u3092\u79fb\u52d5\n        for pair in buckets_tmp:\n            if pair not in [None, self.TOMBSTONE]:\n                self.put(pair.key, pair.val)\n\n    def print(self):\n        \"\"\"\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u3092\u51fa\u529b\"\"\"\n        for pair in self.buckets:\n            if pair is None:\n                print(\"None\")\n            elif pair is self.TOMBSTONE:\n                print(\"TOMBSTONE\")\n            else:\n                print(pair.key, \"-&gt;\", pair.val)\n</code></pre> hash_map_open_addressing.cpp<pre><code>/* \u30aa\u30fc\u30d7\u30f3\u30a2\u30c9\u30ec\u30b9\u6cd5\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb */\nclass HashMapOpenAddressing {\n  private:\n    int size;                             // \u30ad\u30fc\u5024\u30da\u30a2\u306e\u6570\n    int capacity = 4;                     // \u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u306e\u5bb9\u91cf\n    const double loadThres = 2.0 / 3.0;     // \u62e1\u5f35\u3092\u30c8\u30ea\u30ac\u30fc\u3059\u308b\u8ca0\u8377\u7387\u306e\u95be\u5024\n    const int extendRatio = 2;            // \u62e1\u5f35\u500d\u7387\n    vector&lt;Pair *&gt; buckets;               // \u30d0\u30b1\u30c3\u30c8\u914d\u5217\n    Pair *TOMBSTONE = new Pair(-1, \"-1\"); // \u524a\u9664\u30de\u30fc\u30af\n\n  public:\n    /* \u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf */\n    HashMapOpenAddressing() : size(0), buckets(capacity, nullptr) {\n    }\n\n    /* \u30c7\u30b9\u30c8\u30e9\u30af\u30bf */\n    ~HashMapOpenAddressing() {\n        for (Pair *pair : buckets) {\n            if (pair != nullptr &amp;&amp; pair != TOMBSTONE) {\n                delete pair;\n            }\n        }\n        delete TOMBSTONE;\n    }\n\n    /* \u30cf\u30c3\u30b7\u30e5\u95a2\u6570 */\n    int hashFunc(int key) {\n        return key % capacity;\n    }\n\n    /* \u8ca0\u8377\u7387 */\n    double loadFactor() {\n        return (double)size / capacity;\n    }\n\n    /* key\u306b\u5bfe\u5fdc\u3059\u308b\u30d0\u30b1\u30c3\u30c8\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u691c\u7d22 */\n    int findBucket(int key) {\n        int index = hashFunc(key);\n        int firstTombstone = -1;\n        // \u7dda\u5f62\u63a2\u67fb\u3001\u7a7a\u306e\u30d0\u30b1\u30c3\u30c8\u306b\u906d\u9047\u3057\u305f\u3089\u4e2d\u65ad\n        while (buckets[index] != nullptr) {\n            // key\u306b\u906d\u9047\u3057\u305f\u5834\u5408\u3001\u5bfe\u5fdc\u3059\u308b\u30d0\u30b1\u30c3\u30c8\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8fd4\u5374\n            if (buckets[index]-&gt;key == key) {\n                // \u4ee5\u524d\u306b\u524a\u9664\u30de\u30fc\u30af\u306b\u906d\u9047\u3057\u3066\u3044\u305f\u5834\u5408\u3001\u30ad\u30fc\u5024\u30da\u30a2\u3092\u305d\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306b\u79fb\u52d5\n                if (firstTombstone != -1) {\n                    buckets[firstTombstone] = buckets[index];\n                    buckets[index] = TOMBSTONE;\n                    return firstTombstone; // \u79fb\u52d5\u3055\u308c\u305f\u30d0\u30b1\u30c3\u30c8\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8fd4\u5374\n                }\n                return index; // \u30d0\u30b1\u30c3\u30c8\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8fd4\u5374\n            }\n            // \u6700\u521d\u306b\u906d\u9047\u3057\u305f\u524a\u9664\u30de\u30fc\u30af\u3092\u8a18\u9332\n            if (firstTombstone == -1 &amp;&amp; buckets[index] == TOMBSTONE) {\n                firstTombstone = index;\n            }\n            // \u30d0\u30b1\u30c3\u30c8\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8a08\u7b97\u3001\u672b\u5c3e\u3092\u8d85\u3048\u305f\u5834\u5408\u306f\u5148\u982d\u306b\u623b\u308b\n            index = (index + 1) % capacity;\n        }\n        // key\u304c\u5b58\u5728\u3057\u306a\u3044\u5834\u5408\u3001\u633f\u5165\u30dd\u30a4\u30f3\u30c8\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8fd4\u5374\n        return firstTombstone == -1 ? index : firstTombstone;\n    }\n\n    /* \u30af\u30a8\u30ea\u64cd\u4f5c */\n    string get(int key) {\n        // key\u306b\u5bfe\u5fdc\u3059\u308b\u30d0\u30b1\u30c3\u30c8\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u691c\u7d22\n        int index = findBucket(key);\n        // \u30ad\u30fc\u5024\u30da\u30a2\u304c\u898b\u3064\u304b\u3063\u305f\u5834\u5408\u3001\u5bfe\u5fdc\u3059\u308bval\u3092\u8fd4\u5374\n        if (buckets[index] != nullptr &amp;&amp; buckets[index] != TOMBSTONE) {\n            return buckets[index]-&gt;val;\n        }\n        // \u30ad\u30fc\u5024\u30da\u30a2\u304c\u5b58\u5728\u3057\u306a\u3044\u5834\u5408\u3001\u7a7a\u6587\u5b57\u5217\u3092\u8fd4\u5374\n        return \"\";\n    }\n\n    /* \u8ffd\u52a0\u64cd\u4f5c */\n    void put(int key, string val) {\n        // \u8ca0\u8377\u7387\u304c\u95be\u5024\u3092\u8d85\u3048\u305f\u5834\u5408\u3001\u62e1\u5f35\u3092\u5b9f\u884c\n        if (loadFactor() &gt; loadThres) {\n            extend();\n        }\n        // key\u306b\u5bfe\u5fdc\u3059\u308b\u30d0\u30b1\u30c3\u30c8\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u691c\u7d22\n        int index = findBucket(key);\n        // \u30ad\u30fc\u5024\u30da\u30a2\u304c\u898b\u3064\u304b\u3063\u305f\u5834\u5408\u3001val\u3092\u4e0a\u66f8\u304d\u3057\u3066\u8fd4\u5374\n        if (buckets[index] != nullptr &amp;&amp; buckets[index] != TOMBSTONE) {\n            buckets[index]-&gt;val = val;\n            return;\n        }\n        // \u30ad\u30fc\u5024\u30da\u30a2\u304c\u5b58\u5728\u3057\u306a\u3044\u5834\u5408\u3001\u30ad\u30fc\u5024\u30da\u30a2\u3092\u8ffd\u52a0\n        buckets[index] = new Pair(key, val);\n        size++;\n    }\n\n    /* \u524a\u9664\u64cd\u4f5c */\n    void remove(int key) {\n        // key\u306b\u5bfe\u5fdc\u3059\u308b\u30d0\u30b1\u30c3\u30c8\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u691c\u7d22\n        int index = findBucket(key);\n        // \u30ad\u30fc\u5024\u30da\u30a2\u304c\u898b\u3064\u304b\u3063\u305f\u5834\u5408\u3001\u524a\u9664\u30de\u30fc\u30af\u3067\u8986\u3046\n        if (buckets[index] != nullptr &amp;&amp; buckets[index] != TOMBSTONE) {\n            delete buckets[index];\n            buckets[index] = TOMBSTONE;\n            size--;\n        }\n    }\n\n    /* \u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u3092\u62e1\u5f35 */\n    void extend() {\n        // \u5143\u306e\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u3092\u4e00\u6642\u4fdd\u5b58\n        vector&lt;Pair *&gt; bucketsTmp = buckets;\n        // \u62e1\u5f35\u3055\u308c\u305f\u65b0\u3057\u3044\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u3092\u521d\u671f\u5316\n        capacity *= extendRatio;\n        buckets = vector&lt;Pair *&gt;(capacity, nullptr);\n        size = 0;\n        // \u5143\u306e\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u304b\u3089\u65b0\u3057\u3044\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u306b\u30ad\u30fc\u5024\u30da\u30a2\u3092\u79fb\u52d5\n        for (Pair *pair : bucketsTmp) {\n            if (pair != nullptr &amp;&amp; pair != TOMBSTONE) {\n                put(pair-&gt;key, pair-&gt;val);\n                delete pair;\n            }\n        }\n    }\n\n    /* \u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u3092\u5370\u5237 */\n    void print() {\n        for (Pair *pair : buckets) {\n            if (pair == nullptr) {\n                cout &lt;&lt; \"nullptr\" &lt;&lt; endl;\n            } else if (pair == TOMBSTONE) {\n                cout &lt;&lt; \"TOMBSTONE\" &lt;&lt; endl;\n            } else {\n                cout &lt;&lt; pair-&gt;key &lt;&lt; \" -&gt; \" &lt;&lt; pair-&gt;val &lt;&lt; endl;\n            }\n        }\n    }\n};\n</code></pre> hash_map_open_addressing.java<pre><code>/* \u30aa\u30fc\u30d7\u30f3\u30a2\u30c9\u30ec\u30b9\u6cd5\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb */\nclass HashMapOpenAddressing {\n    private int size; // \u30ad\u30fc\u5024\u30da\u30a2\u306e\u6570\n    private int capacity = 4; // \u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u306e\u5bb9\u91cf\n    private final double loadThres = 2.0 / 3.0; // \u62e1\u5f35\u3092\u30c8\u30ea\u30ac\u30fc\u3059\u308b\u8ca0\u8377\u7387\u306e\u95be\u5024\n    private final int extendRatio = 2; // \u62e1\u5f35\u500d\u7387\n    private Pair[] buckets; // \u30d0\u30b1\u30c3\u30c8\u914d\u5217\n    private final Pair TOMBSTONE = new Pair(-1, \"-1\"); // \u524a\u9664\u30de\u30fc\u30af\n\n    /* \u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf */\n    public HashMapOpenAddressing() {\n        size = 0;\n        buckets = new Pair[capacity];\n    }\n\n    /* \u30cf\u30c3\u30b7\u30e5\u95a2\u6570 */\n    private int hashFunc(int key) {\n        return key % capacity;\n    }\n\n    /* \u8ca0\u8377\u7387 */\n    private double loadFactor() {\n        return (double) size / capacity;\n    }\n\n    /* key\u306b\u5bfe\u5fdc\u3059\u308b\u30d0\u30b1\u30c3\u30c8\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u691c\u7d22 */\n    private int findBucket(int key) {\n        int index = hashFunc(key);\n        int firstTombstone = -1;\n        // \u7dda\u5f62\u63a2\u67fb\u3001\u7a7a\u306e\u30d0\u30b1\u30c3\u30c8\u306b\u906d\u9047\u3057\u305f\u3089\u7d42\u4e86\n        while (buckets[index] != null) {\n            // key\u306b\u906d\u9047\u3057\u305f\u5834\u5408\u3001\u5bfe\u5fdc\u3059\u308b\u30d0\u30b1\u30c3\u30c8\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8fd4\u3059\n            if (buckets[index].key == key) {\n                // \u4ee5\u524d\u306b\u524a\u9664\u30de\u30fc\u30af\u306b\u906d\u9047\u3057\u3066\u3044\u305f\u5834\u5408\u3001\u30ad\u30fc\u5024\u30da\u30a2\u3092\u305d\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306b\u79fb\u52d5\n                if (firstTombstone != -1) {\n                    buckets[firstTombstone] = buckets[index];\n                    buckets[index] = TOMBSTONE;\n                    return firstTombstone; // \u79fb\u52d5\u5f8c\u306e\u30d0\u30b1\u30c3\u30c8\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8fd4\u3059\n                }\n                return index; // \u30d0\u30b1\u30c3\u30c8\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8fd4\u3059\n            }\n            // \u6700\u521d\u306b\u906d\u9047\u3057\u305f\u524a\u9664\u30de\u30fc\u30af\u3092\u8a18\u9332\n            if (firstTombstone == -1 &amp;&amp; buckets[index] == TOMBSTONE) {\n                firstTombstone = index;\n            }\n            // \u30d0\u30b1\u30c3\u30c8\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8a08\u7b97\u3001\u672b\u5c3e\u3092\u8d85\u3048\u305f\u5834\u5408\u306f\u5148\u982d\u306b\u623b\u308b\n            index = (index + 1) % capacity;\n        }\n        // key\u304c\u5b58\u5728\u3057\u306a\u3044\u5834\u5408\u3001\u633f\u5165\u30dd\u30a4\u30f3\u30c8\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8fd4\u3059\n        return firstTombstone == -1 ? index : firstTombstone;\n    }\n\n    /* \u30af\u30a8\u30ea\u64cd\u4f5c */\n    public String get(int key) {\n        // key\u306b\u5bfe\u5fdc\u3059\u308b\u30d0\u30b1\u30c3\u30c8\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u691c\u7d22\n        int index = findBucket(key);\n        // \u30ad\u30fc\u5024\u30da\u30a2\u304c\u898b\u3064\u304b\u3063\u305f\u5834\u5408\u3001\u5bfe\u5fdc\u3059\u308bval\u3092\u8fd4\u3059\n        if (buckets[index] != null &amp;&amp; buckets[index] != TOMBSTONE) {\n            return buckets[index].val;\n        }\n        // \u30ad\u30fc\u5024\u30da\u30a2\u304c\u5b58\u5728\u3057\u306a\u3044\u5834\u5408\u3001null\u3092\u8fd4\u3059\n        return null;\n    }\n\n    /* \u8ffd\u52a0\u64cd\u4f5c */\n    public void put(int key, String val) {\n        // \u8ca0\u8377\u7387\u304c\u95be\u5024\u3092\u8d85\u3048\u305f\u5834\u5408\u3001\u62e1\u5f35\u3092\u5b9f\u884c\n        if (loadFactor() &gt; loadThres) {\n            extend();\n        }\n        // key\u306b\u5bfe\u5fdc\u3059\u308b\u30d0\u30b1\u30c3\u30c8\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u691c\u7d22\n        int index = findBucket(key);\n        // \u30ad\u30fc\u5024\u30da\u30a2\u304c\u898b\u3064\u304b\u3063\u305f\u5834\u5408\u3001val\u3092\u4e0a\u66f8\u304d\u3057\u3066\u623b\u308b\n        if (buckets[index] != null &amp;&amp; buckets[index] != TOMBSTONE) {\n            buckets[index].val = val;\n            return;\n        }\n        // \u30ad\u30fc\u5024\u30da\u30a2\u304c\u5b58\u5728\u3057\u306a\u3044\u5834\u5408\u3001\u30ad\u30fc\u5024\u30da\u30a2\u3092\u8ffd\u52a0\n        buckets[index] = new Pair(key, val);\n        size++;\n    }\n\n    /* \u524a\u9664\u64cd\u4f5c */\n    public void remove(int key) {\n        // key\u306b\u5bfe\u5fdc\u3059\u308b\u30d0\u30b1\u30c3\u30c8\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u691c\u7d22\n        int index = findBucket(key);\n        // \u30ad\u30fc\u5024\u30da\u30a2\u304c\u898b\u3064\u304b\u3063\u305f\u5834\u5408\u3001\u524a\u9664\u30de\u30fc\u30af\u3067\u8986\u3046\n        if (buckets[index] != null &amp;&amp; buckets[index] != TOMBSTONE) {\n            buckets[index] = TOMBSTONE;\n            size--;\n        }\n    }\n\n    /* \u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u3092\u62e1\u5f35 */\n    private void extend() {\n        // \u5143\u306e\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u3092\u4e00\u6642\u7684\u306b\u4fdd\u5b58\n        Pair[] bucketsTmp = buckets;\n        // \u62e1\u5f35\u3055\u308c\u305f\u65b0\u3057\u3044\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u3092\u521d\u671f\u5316\n        capacity *= extendRatio;\n        buckets = new Pair[capacity];\n        size = 0;\n        // \u5143\u306e\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u304b\u3089\u65b0\u3057\u3044\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u306b\u30ad\u30fc\u5024\u30da\u30a2\u3092\u79fb\u52d5\n        for (Pair pair : bucketsTmp) {\n            if (pair != null &amp;&amp; pair != TOMBSTONE) {\n                put(pair.key, pair.val);\n            }\n        }\n    }\n\n    /* \u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u3092\u5370\u5237 */\n    public void print() {\n        for (Pair pair : buckets) {\n            if (pair == null) {\n                System.out.println(\"null\");\n            } else if (pair == TOMBSTONE) {\n                System.out.println(\"TOMBSTONE\");\n            } else {\n                System.out.println(pair.key + \" -&gt; \" + pair.val);\n            }\n        }\n    }\n}\n</code></pre> hash_map_open_addressing.cs<pre><code>[class]{HashMapOpenAddressing}-[func]{}\n</code></pre> hash_map_open_addressing.go<pre><code>[class]{hashMapOpenAddressing}-[func]{}\n</code></pre> hash_map_open_addressing.swift<pre><code>[class]{HashMapOpenAddressing}-[func]{}\n</code></pre> hash_map_open_addressing.js<pre><code>[class]{HashMapOpenAddressing}-[func]{}\n</code></pre> hash_map_open_addressing.ts<pre><code>[class]{HashMapOpenAddressing}-[func]{}\n</code></pre> hash_map_open_addressing.dart<pre><code>[class]{HashMapOpenAddressing}-[func]{}\n</code></pre> hash_map_open_addressing.rs<pre><code>[class]{HashMapOpenAddressing}-[func]{}\n</code></pre> hash_map_open_addressing.c<pre><code>[class]{HashMapOpenAddressing}-[func]{}\n</code></pre> hash_map_open_addressing.kt<pre><code>[class]{HashMapOpenAddressing}-[func]{}\n</code></pre> hash_map_open_addressing.rb<pre><code>[class]{HashMapOpenAddressing}-[func]{}\n</code></pre> hash_map_open_addressing.zig<pre><code>[class]{HashMapOpenAddressing}-[func]{}\n</code></pre>"},{"location":"chapter_hashing/hash_collision/#2","title":"2. \u00a0 \u4e8c\u6b21\u30d7\u30ed\u30fc\u30d6","text":"<p>\u4e8c\u6b21\u30d7\u30ed\u30fc\u30d6\u306f\u7dda\u5f62\u30d7\u30ed\u30fc\u30d6\u306b\u4f3c\u3066\u304a\u308a\u3001\u30aa\u30fc\u30d7\u30f3\u30a2\u30c9\u30ec\u30b9\u6cd5\u306e\u4e00\u822c\u7684\u306a\u6226\u7565\u306e1\u3064\u3067\u3059\u3002\u885d\u7a81\u304c\u767a\u751f\u3057\u305f\u5834\u5408\u3001\u4e8c\u6b21\u30d7\u30ed\u30fc\u30d6\u306f\u5358\u7d14\u306b\u56fa\u5b9a\u30b9\u30c6\u30c3\u30d7\u6570\u3092\u30b9\u30ad\u30c3\u30d7\u3059\u308b\u306e\u3067\u306f\u306a\u304f\u3001\u300c\u30d7\u30ed\u30fc\u30d6\u56de\u6570\u306e\u4e8c\u4e57\u300d\u306b\u7b49\u3057\u3044\u30b9\u30c6\u30c3\u30d7\u6570\u3001\u3064\u307e\u308a\\(1, 4, 9, \\dots\\)\u30b9\u30c6\u30c3\u30d7\u3092\u30b9\u30ad\u30c3\u30d7\u3057\u307e\u3059\u3002</p> <p>\u4e8c\u6b21\u30d7\u30ed\u30fc\u30d6\u306b\u306f\u4ee5\u4e0b\u306e\u5229\u70b9\u304c\u3042\u308a\u307e\u3059\uff1a</p> <ul> <li>\u4e8c\u6b21\u30d7\u30ed\u30fc\u30d6\u306f\u3001\u30d7\u30ed\u30fc\u30d6\u56de\u6570\u306e\u4e8c\u4e57\u306e\u8ddd\u96e2\u3092\u30b9\u30ad\u30c3\u30d7\u3059\u308b\u3053\u3068\u3067\u3001\u7dda\u5f62\u30d7\u30ed\u30fc\u30d6\u306e\u30af\u30e9\u30b9\u30bf\u30ea\u30f3\u30b0\u52b9\u679c\u3092\u8efd\u6e1b\u3057\u3088\u3046\u3068\u3057\u307e\u3059\u3002</li> <li>\u4e8c\u6b21\u30d7\u30ed\u30fc\u30d6\u306f\u3088\u308a\u5927\u304d\u306a\u8ddd\u96e2\u3092\u30b9\u30ad\u30c3\u30d7\u3057\u3066\u7a7a\u306e\u4f4d\u7f6e\u3092\u898b\u3064\u3051\u3001\u30c7\u30fc\u30bf\u3092\u3088\u308a\u5747\u7b49\u306b\u5206\u6563\u3059\u308b\u306e\u306b\u5f79\u7acb\u3061\u307e\u3059\u3002</li> </ul> <p>\u3057\u304b\u3057\u3001\u4e8c\u6b21\u30d7\u30ed\u30fc\u30d6\u306f\u5b8c\u74a7\u3067\u306f\u3042\u308a\u307e\u305b\u3093\uff1a</p> <ul> <li>\u30af\u30e9\u30b9\u30bf\u30ea\u30f3\u30b0\u306f\u4f9d\u7136\u3068\u3057\u3066\u5b58\u5728\u3057\u3001\u3064\u307e\u308a\u4e00\u90e8\u306e\u4f4d\u7f6e\u306f\u4ed6\u306e\u4f4d\u7f6e\u3088\u308a\u3082\u5360\u6709\u3055\u308c\u308b\u53ef\u80fd\u6027\u304c\u9ad8\u3044\u3067\u3059\u3002</li> <li>\u4e8c\u4e57\u306e\u6210\u9577\u306b\u3088\u308a\u3001\u4e8c\u6b21\u30d7\u30ed\u30fc\u30d6\u306f\u30cf\u30c3\u30b7\u30e5\u8868\u5168\u4f53\u3092\u30d7\u30ed\u30fc\u30d6\u3067\u304d\u306a\u3044\u53ef\u80fd\u6027\u304c\u3042\u308a\u3001\u30cf\u30c3\u30b7\u30e5\u8868\u306b\u7a7a\u306e\u30d0\u30b1\u30c3\u30c8\u304c\u3042\u3063\u3066\u3082\u3001\u4e8c\u6b21\u30d7\u30ed\u30fc\u30d6\u304c\u30a2\u30af\u30bb\u30b9\u3067\u304d\u306a\u3044\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002</li> </ul>"},{"location":"chapter_hashing/hash_collision/#3","title":"3. \u00a0 \u4e8c\u91cd\u30cf\u30c3\u30b7\u30e5","text":"<p>\u540d\u524d\u304c\u793a\u3059\u3088\u3046\u306b\u3001\u4e8c\u91cd\u30cf\u30c3\u30b7\u30e5\u6cd5\u306f\u8907\u6570\u306e\u30cf\u30c3\u30b7\u30e5\u95a2\u6570\\(f_1(x)\\)\u3001\\(f_2(x)\\)\u3001\\(f_3(x)\\)\u3001\\(\\dots\\)\u3092\u30d7\u30ed\u30fc\u30d6\u306b\u4f7f\u7528\u3057\u307e\u3059\u3002</p> <ul> <li>\u8981\u7d20\u306e\u633f\u5165: \u30cf\u30c3\u30b7\u30e5\u95a2\u6570\\(f_1(x)\\)\u304c\u885d\u7a81\u306b\u906d\u9047\u3057\u305f\u5834\u5408\u3001\\(f_2(x)\\)\u3092\u8a66\u3057\u3001\u4ee5\u4e0b\u540c\u69d8\u306b\u3001\u7a7a\u306e\u4f4d\u7f6e\u304c\u898b\u3064\u304b\u3063\u3066\u8981\u7d20\u304c\u633f\u5165\u3055\u308c\u308b\u307e\u3067\u7d9a\u3051\u307e\u3059\u3002</li> <li>\u8981\u7d20\u306e\u691c\u7d22: \u540c\u3058\u30cf\u30c3\u30b7\u30e5\u95a2\u6570\u306e\u9806\u5e8f\u3067\u691c\u7d22\u3057\u3001\u30bf\u30fc\u30b2\u30c3\u30c8\u8981\u7d20\u304c\u898b\u3064\u304b\u3063\u3066\u8fd4\u3055\u308c\u308b\u307e\u3067\u3001\u307e\u305f\u306f\u7a7a\u306e\u4f4d\u7f6e\u306b\u906d\u9047\u3059\u308b\u304b\u3059\u3079\u3066\u306e\u30cf\u30c3\u30b7\u30e5\u95a2\u6570\u304c\u8a66\u3055\u308c\u308b\u307e\u3067\u7d9a\u3051\u3001\u8981\u7d20\u304c\u30cf\u30c3\u30b7\u30e5\u8868\u306b\u306a\u3044\u3053\u3068\u3092\u793a\u3057\u3001<code>None</code>\u3092\u8fd4\u3057\u307e\u3059\u3002</li> </ul> <p>\u7dda\u5f62\u30d7\u30ed\u30fc\u30d6\u3068\u6bd4\u8f03\u3057\u3066\u3001\u4e8c\u91cd\u30cf\u30c3\u30b7\u30e5\u6cd5\u306f\u30af\u30e9\u30b9\u30bf\u30ea\u30f3\u30b0\u304c\u8d77\u3053\u308a\u306b\u304f\u3044\u3067\u3059\u304c\u3001\u8907\u6570\u306e\u30cf\u30c3\u30b7\u30e5\u95a2\u6570\u306f\u8ffd\u52a0\u306e\u8a08\u7b97\u30aa\u30fc\u30d0\u30fc\u30d8\u30c3\u30c9\u3092\u5c0e\u5165\u3057\u307e\u3059\u3002</p> <p>Tip</p> <p>\u30aa\u30fc\u30d7\u30f3\u30a2\u30c9\u30ec\u30b9\u6cd5\uff08\u7dda\u5f62\u30d7\u30ed\u30fc\u30d6\u3001\u4e8c\u6b21\u30d7\u30ed\u30fc\u30d6\u3001\u4e8c\u91cd\u30cf\u30c3\u30b7\u30e5\uff09\u30cf\u30c3\u30b7\u30e5\u8868\u306f\u3059\u3079\u3066\u300c\u8981\u7d20\u3092\u76f4\u63a5\u524a\u9664\u3067\u304d\u306a\u3044\u300d\u3068\u3044\u3046\u554f\u984c\u304c\u3042\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002</p>"},{"location":"chapter_hashing/hash_collision/#623","title":"6.2.3 \u00a0 \u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u306e\u9078\u629e","text":"<p>\u7570\u306a\u308b\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u306f\u7570\u306a\u308b\u30cf\u30c3\u30b7\u30e5\u8868\u5b9f\u88c5\u6226\u7565\u3092\u63a1\u7528\u3057\u3066\u3044\u307e\u3059\u3002\u4ee5\u4e0b\u306b\u3044\u304f\u3064\u304b\u306e\u4f8b\u3092\u793a\u3057\u307e\u3059\uff1a</p> <ul> <li>Python\u306f\u30aa\u30fc\u30d7\u30f3\u30a2\u30c9\u30ec\u30b9\u6cd5\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002<code>dict</code>\u8f9e\u66f8\u306f\u30d7\u30ed\u30fc\u30d6\u306b\u7591\u4f3c\u4e71\u6570\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002</li> <li>Java\u306f\u9023\u9396\u6cd5\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002JDK 1.8\u4ee5\u964d\u3001<code>HashMap</code>\u306e\u914d\u5217\u9577\u304c64\u306b\u9054\u3057\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u306e\u9577\u3055\u304c8\u306b\u9054\u3059\u308b\u3068\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u306f\u691c\u7d22\u6027\u80fd\u3092\u5411\u4e0a\u3055\u305b\u308b\u305f\u3081\u306b\u8d64\u9ed2\u6728\u306b\u5909\u63db\u3055\u308c\u307e\u3059\u3002</li> <li>Go\u306f\u9023\u9396\u6cd5\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002Go\u306f\u5404\u30d0\u30b1\u30c3\u30c8\u304c\u6700\u59278\u3064\u306e\u30ad\u30fc\u5024\u30da\u30a2\u3092\u683c\u7d0d\u3067\u304d\u308b\u3053\u3068\u3092\u898f\u5b9a\u3057\u3001\u5bb9\u91cf\u3092\u8d85\u3048\u305f\u5834\u5408\u306f\u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u30d0\u30b1\u30c3\u30c8\u304c\u9023\u7d50\u3055\u308c\u307e\u3059\u3002\u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u30d0\u30b1\u30c3\u30c8\u304c\u591a\u3059\u304e\u308b\u5834\u5408\u3001\u6027\u80fd\u3092\u78ba\u4fdd\u3059\u308b\u305f\u3081\u306b\u7279\u5225\u306a\u7b49\u5bb9\u91cf\u30ea\u30b5\u30a4\u30ba\u64cd\u4f5c\u304c\u5b9f\u884c\u3055\u308c\u307e\u3059\u3002</li> </ul>"},{"location":"chapter_hashing/hash_map/","title":"6.1 \u00a0 \u30cf\u30c3\u30b7\u30e5\u8868","text":"<p>\u30cf\u30c3\u30b7\u30e5\u8868\u306f\u30cf\u30c3\u30b7\u30e5\u30de\u30c3\u30d7\u3068\u3082\u547c\u3070\u308c\u3001\u30ad\u30fc\u3068\u5024\u306e\u9593\u306e\u30de\u30c3\u30d4\u30f3\u30b0\u3092\u78ba\u7acb\u3057\u3001\u52b9\u7387\u7684\u306a\u8981\u7d20\u306e\u53d6\u5f97\u3092\u53ef\u80fd\u306b\u3059\u308b\u30c7\u30fc\u30bf\u69cb\u9020\u3067\u3059\u3002\u5177\u4f53\u7684\u306b\u306f\u3001\u30cf\u30c3\u30b7\u30e5\u8868\u306b<code>key</code>\u3092\u5165\u529b\u3059\u308b\u3068\u3001\\(O(1)\\)\u306e\u6642\u9593\u8a08\u7b97\u91cf\u3067\u5bfe\u5fdc\u3059\u308b<code>value</code>\u3092\u53d6\u5f97\u3067\u304d\u307e\u3059\u3002</p> <p>\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\\(n\\)\u4eba\u306e\u5b66\u751f\u304c\u3044\u3066\u3001\u5404\u5b66\u751f\u306b\u306f\u300c\u540d\u524d\u300d\u3068\u300c\u5b66\u7c4d\u756a\u53f7\u300d\u306e2\u3064\u306e\u30c7\u30fc\u30bf\u30d5\u30a3\u30fc\u30eb\u30c9\u304c\u3042\u308b\u3068\u3057\u307e\u3059\u3002\u5b66\u7c4d\u756a\u53f7\u3092\u5165\u529b\u3068\u3057\u3066\u5bfe\u5fdc\u3059\u308b\u540d\u524d\u3092\u8fd4\u3059\u30af\u30a8\u30ea\u6a5f\u80fd\u3092\u5b9f\u88c5\u3057\u305f\u3044\u5834\u5408\u3001\u4e0b\u56f3\u306b\u793a\u3059\u30cf\u30c3\u30b7\u30e5\u8868\u3092\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002</p> <p></p> <p> \u56f3 6-1 \u00a0 \u30cf\u30c3\u30b7\u30e5\u8868\u306e\u62bd\u8c61\u7684\u306a\u8868\u73fe </p> <p>\u30cf\u30c3\u30b7\u30e5\u8868\u306b\u52a0\u3048\u3066\u3001\u914d\u5217\u3084\u9023\u7d50\u30ea\u30b9\u30c8\u3082\u30af\u30a8\u30ea\u6a5f\u80fd\u306e\u5b9f\u88c5\u306b\u4f7f\u7528\u3067\u304d\u307e\u3059\u304c\u3001\u6642\u9593\u8a08\u7b97\u91cf\u304c\u7570\u306a\u308a\u307e\u3059\u3002\u52b9\u7387\u306f\u4ee5\u4e0b\u306e\u8868\u3067\u6bd4\u8f03\u3055\u308c\u3066\u3044\u307e\u3059\uff1a</p> <ul> <li>\u8981\u7d20\u306e\u633f\u5165: \u914d\u5217\uff08\u307e\u305f\u306f\u9023\u7d50\u30ea\u30b9\u30c8\uff09\u306e\u672b\u5c3e\u306b\u8981\u7d20\u3092\u8ffd\u52a0\u3059\u308b\u3060\u3051\u3067\u3059\u3002\u3053\u306e\u64cd\u4f5c\u306e\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O(1)\\)\u3067\u3059\u3002</li> <li>\u8981\u7d20\u306e\u691c\u7d22: \u914d\u5217\uff08\u307e\u305f\u306f\u9023\u7d50\u30ea\u30b9\u30c8\uff09\u304c\u30bd\u30fc\u30c8\u3055\u308c\u3066\u3044\u306a\u3044\u305f\u3081\u3001\u8981\u7d20\u3092\u691c\u7d22\u3059\u308b\u306b\u306f\u3059\u3079\u3066\u306e\u8981\u7d20\u3092\u8d70\u67fb\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u64cd\u4f5c\u306e\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O(n)\\)\u3067\u3059\u3002</li> <li>\u8981\u7d20\u306e\u524a\u9664: \u8981\u7d20\u3092\u524a\u9664\u3059\u308b\u306b\u306f\u3001\u307e\u305a\u305d\u306e\u8981\u7d20\u3092\u898b\u3064\u3051\u3066\u304b\u3089\u3001\u914d\u5217\uff08\u307e\u305f\u306f\u9023\u7d50\u30ea\u30b9\u30c8\uff09\u304b\u3089\u524a\u9664\u3057\u307e\u3059\u3002\u3053\u306e\u64cd\u4f5c\u306e\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O(n)\\)\u3067\u3059\u3002</li> </ul> <p> \u8868 6-1 \u00a0 \u4e00\u822c\u7684\u306a\u64cd\u4f5c\u306e\u6642\u9593\u52b9\u7387\u306e\u6bd4\u8f03 </p> \u914d\u5217 \u9023\u7d50\u30ea\u30b9\u30c8 \u30cf\u30c3\u30b7\u30e5\u8868 \u8981\u7d20\u306e\u691c\u7d22 \\(O(n)\\) \\(O(n)\\) \\(O(1)\\) \u8981\u7d20\u306e\u633f\u5165 \\(O(1)\\) \\(O(1)\\) \\(O(1)\\) \u8981\u7d20\u306e\u524a\u9664 \\(O(n)\\) \\(O(n)\\) \\(O(1)\\) <p>\u89b3\u5bdf\u3055\u308c\u308b\u3088\u3046\u306b\u3001**\u30cf\u30c3\u30b7\u30e5\u8868\u306b\u304a\u3051\u308b\u64cd\u4f5c\uff08\u633f\u5165\u3001\u524a\u9664\u3001\u691c\u7d22\u3001\u5909\u66f4\uff09\u306e\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O(1)\\)**\u3067\u3001\u975e\u5e38\u306b\u52b9\u7387\u7684\u3067\u3059\u3002</p>"},{"location":"chapter_hashing/hash_map/#611","title":"6.1.1 \u00a0 \u30cf\u30c3\u30b7\u30e5\u8868\u306e\u4e00\u822c\u7684\u306a\u64cd\u4f5c","text":"<p>\u30cf\u30c3\u30b7\u30e5\u8868\u306e\u4e00\u822c\u7684\u306a\u64cd\u4f5c\u306b\u306f\u3001\u521d\u671f\u5316\u3001\u30af\u30a8\u30ea\u3001\u30ad\u30fc\u5024\u30da\u30a2\u306e\u8ffd\u52a0\u3001\u30ad\u30fc\u5024\u30da\u30a2\u306e\u524a\u9664\u304c\u3042\u308a\u307e\u3059\u3002\u4ee5\u4e0b\u306f\u30b3\u30fc\u30c9\u4f8b\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinZig hash_map.py<pre><code># \u30cf\u30c3\u30b7\u30e5\u8868\u3092\u521d\u671f\u5316\nhmap: dict = {}\n\n# \u8ffd\u52a0\u64cd\u4f5c\n# \u30cf\u30c3\u30b7\u30e5\u8868\u306b\u30ad\u30fc\u5024\u30da\u30a2 (key, value) \u3092\u8ffd\u52a0\nhmap[12836] = \"\u5c0f\u54c8\"\nhmap[15937] = \"\u5c0f\u5570\"\nhmap[16750] = \"\u5c0f\u7b97\"\nhmap[13276] = \"\u5c0f\u6cd5\"\nhmap[10583] = \"\u5c0f\u9e2d\"\n\n# \u30af\u30a8\u30ea\u64cd\u4f5c\n# \u30cf\u30c3\u30b7\u30e5\u8868\u306b\u30ad\u30fc\u3092\u5165\u529b\u3057\u3001\u5024\u3092\u53d6\u5f97\nname: str = hmap[15937]\n\n# \u524a\u9664\u64cd\u4f5c\n# \u30cf\u30c3\u30b7\u30e5\u8868\u304b\u3089\u30ad\u30fc\u5024\u30da\u30a2 (key, value) \u3092\u524a\u9664\nhmap.pop(10583)\n</code></pre> hash_map.cpp<pre><code>/* \u30cf\u30c3\u30b7\u30e5\u8868\u3092\u521d\u671f\u5316 */\nunordered_map&lt;int, string&gt; map;\n\n/* \u8ffd\u52a0\u64cd\u4f5c */\n// \u30cf\u30c3\u30b7\u30e5\u8868\u306b\u30ad\u30fc\u5024\u30da\u30a2 (key, value) \u3092\u8ffd\u52a0\nmap[12836] = \"\u5c0f\u54c8\";\nmap[15937] = \"\u5c0f\u5570\";\nmap[16750] = \"\u5c0f\u7b97\";\nmap[13276] = \"\u5c0f\u6cd5\";\nmap[10583] = \"\u5c0f\u9e2d\";\n\n/* \u30af\u30a8\u30ea\u64cd\u4f5c */\n// \u30cf\u30c3\u30b7\u30e5\u8868\u306b\u30ad\u30fc\u3092\u5165\u529b\u3057\u3001\u5024\u3092\u53d6\u5f97\nstring name = map[15937];\n\n/* \u524a\u9664\u64cd\u4f5c */\n// \u30cf\u30c3\u30b7\u30e5\u8868\u304b\u3089\u30ad\u30fc\u5024\u30da\u30a2 (key, value) \u3092\u524a\u9664\nmap.erase(10583);\n</code></pre> hash_map.java<pre><code>/* \u30cf\u30c3\u30b7\u30e5\u8868\u3092\u521d\u671f\u5316 */\nMap&lt;Integer, String&gt; map = new HashMap&lt;&gt;();\n\n/* \u8ffd\u52a0\u64cd\u4f5c */\n// \u30cf\u30c3\u30b7\u30e5\u8868\u306b\u30ad\u30fc\u5024\u30da\u30a2 (key, value) \u3092\u8ffd\u52a0\nmap.put(12836, \"\u5c0f\u54c8\");\nmap.put(15937, \"\u5c0f\u5570\");\nmap.put(16750, \"\u5c0f\u7b97\");\nmap.put(13276, \"\u5c0f\u6cd5\");\nmap.put(10583, \"\u5c0f\u9e2d\");\n\n/* \u30af\u30a8\u30ea\u64cd\u4f5c */\n// \u30cf\u30c3\u30b7\u30e5\u8868\u306b\u30ad\u30fc\u3092\u5165\u529b\u3057\u3001\u5024\u3092\u53d6\u5f97\nString name = map.get(15937);\n\n/* \u524a\u9664\u64cd\u4f5c */\n// \u30cf\u30c3\u30b7\u30e5\u8868\u304b\u3089\u30ad\u30fc\u5024\u30da\u30a2 (key, value) \u3092\u524a\u9664\nmap.remove(10583);\n</code></pre> hash_map.cs<pre><code>/* \u30cf\u30c3\u30b7\u30e5\u8868\u3092\u521d\u671f\u5316 */\nDictionary&lt;int, string&gt; map = new() {\n    /* \u8ffd\u52a0\u64cd\u4f5c */\n    // \u30cf\u30c3\u30b7\u30e5\u8868\u306b\u30ad\u30fc\u5024\u30da\u30a2 (key, value) \u3092\u8ffd\u52a0\n    { 12836, \"\u5c0f\u54c8\" },\n    { 15937, \"\u5c0f\u5570\" },\n    { 16750, \"\u5c0f\u7b97\" },\n    { 13276, \"\u5c0f\u6cd5\" },\n    { 10583, \"\u5c0f\u9e2d\" }\n};\n\n/* \u30af\u30a8\u30ea\u64cd\u4f5c */\n// \u30cf\u30c3\u30b7\u30e5\u8868\u306b\u30ad\u30fc\u3092\u5165\u529b\u3057\u3001\u5024\u3092\u53d6\u5f97\nstring name = map[15937];\n\n/* \u524a\u9664\u64cd\u4f5c */\n// \u30cf\u30c3\u30b7\u30e5\u8868\u304b\u3089\u30ad\u30fc\u5024\u30da\u30a2 (key, value) \u3092\u524a\u9664\nmap.Remove(10583);\n</code></pre> hash_map_test.go<pre><code>/* \u30cf\u30c3\u30b7\u30e5\u8868\u3092\u521d\u671f\u5316 */\nhmap := make(map[int]string)\n\n/* \u8ffd\u52a0\u64cd\u4f5c */\n// \u30cf\u30c3\u30b7\u30e5\u8868\u306b\u30ad\u30fc\u5024\u30da\u30a2 (key, value) \u3092\u8ffd\u52a0\nhmap[12836] = \"\u5c0f\u54c8\"\nhmap[15937] = \"\u5c0f\u5570\"\nhmap[16750] = \"\u5c0f\u7b97\"\nhmap[13276] = \"\u5c0f\u6cd5\"\nhmap[10583] = \"\u5c0f\u9e2d\"\n\n/* \u30af\u30a8\u30ea\u64cd\u4f5c */\n// \u30cf\u30c3\u30b7\u30e5\u8868\u306b\u30ad\u30fc\u3092\u5165\u529b\u3057\u3001\u5024\u3092\u53d6\u5f97\nname := hmap[15937]\n\n/* \u524a\u9664\u64cd\u4f5c */\n// \u30cf\u30c3\u30b7\u30e5\u8868\u304b\u3089\u30ad\u30fc\u5024\u30da\u30a2 (key, value) \u3092\u524a\u9664\ndelete(hmap, 10583)\n</code></pre> hash_map.swift<pre><code>/* \u30cf\u30c3\u30b7\u30e5\u8868\u3092\u521d\u671f\u5316 */\nvar map: [Int: String] = [:]\n\n/* \u8ffd\u52a0\u64cd\u4f5c */\n// \u30cf\u30c3\u30b7\u30e5\u8868\u306b\u30ad\u30fc\u5024\u30da\u30a2 (key, value) \u3092\u8ffd\u52a0\nmap[12836] = \"\u5c0f\u54c8\"\nmap[15937] = \"\u5c0f\u5570\"\nmap[16750] = \"\u5c0f\u7b97\"\nmap[13276] = \"\u5c0f\u6cd5\"\nmap[10583] = \"\u5c0f\u9e2d\"\n\n/* \u30af\u30a8\u30ea\u64cd\u4f5c */\n// \u30cf\u30c3\u30b7\u30e5\u8868\u306b\u30ad\u30fc\u3092\u5165\u529b\u3057\u3001\u5024\u3092\u53d6\u5f97\nlet name = map[15937]!\n\n/* \u524a\u9664\u64cd\u4f5c */\n// \u30cf\u30c3\u30b7\u30e5\u8868\u304b\u3089\u30ad\u30fc\u5024\u30da\u30a2 (key, value) \u3092\u524a\u9664\nmap.removeValue(forKey: 10583)\n</code></pre> hash_map.js<pre><code>/* \u30cf\u30c3\u30b7\u30e5\u8868\u3092\u521d\u671f\u5316 */\nconst map = new Map();\n/* \u8ffd\u52a0\u64cd\u4f5c */\n// \u30cf\u30c3\u30b7\u30e5\u8868\u306b\u30ad\u30fc\u5024\u30da\u30a2 (key, value) \u3092\u8ffd\u52a0\nmap.set(12836, '\u5c0f\u54c8');\nmap.set(15937, '\u5c0f\u5570');\nmap.set(16750, '\u5c0f\u7b97');\nmap.set(13276, '\u5c0f\u6cd5');\nmap.set(10583, '\u5c0f\u9e2d');\n\n/* \u30af\u30a8\u30ea\u64cd\u4f5c */\n// \u30cf\u30c3\u30b7\u30e5\u8868\u306b\u30ad\u30fc\u3092\u5165\u529b\u3057\u3001\u5024\u3092\u53d6\u5f97\nlet name = map.get(15937);\n\n/* \u524a\u9664\u64cd\u4f5c */\n// \u30cf\u30c3\u30b7\u30e5\u8868\u304b\u3089\u30ad\u30fc\u5024\u30da\u30a2 (key, value) \u3092\u524a\u9664\nmap.delete(10583);\n</code></pre> hash_map.ts<pre><code>/* \u30cf\u30c3\u30b7\u30e5\u8868\u3092\u521d\u671f\u5316 */\nconst map = new Map&lt;number, string&gt;();\n/* \u8ffd\u52a0\u64cd\u4f5c */\n// \u30cf\u30c3\u30b7\u30e5\u8868\u306b\u30ad\u30fc\u5024\u30da\u30a2 (key, value) \u3092\u8ffd\u52a0\nmap.set(12836, '\u5c0f\u54c8');\nmap.set(15937, '\u5c0f\u5570');\nmap.set(16750, '\u5c0f\u7b97');\nmap.set(13276, '\u5c0f\u6cd5');\nmap.set(10583, '\u5c0f\u9e2d');\nconsole.info('\\n\u8ffd\u52a0\u5f8c\u3001\u30cf\u30c3\u30b7\u30e5\u8868\u306f\\nKey -&gt; Value');\nconsole.info(map);\n\n/* \u30af\u30a8\u30ea\u64cd\u4f5c */\n// \u30cf\u30c3\u30b7\u30e5\u8868\u306b\u30ad\u30fc\u3092\u5165\u529b\u3057\u3001\u5024\u3092\u53d6\u5f97\nlet name = map.get(15937);\nconsole.info('\\n\u5b66\u7c4d\u756a\u53f715937\u3092\u5165\u529b\u3001\u540d\u524d\u3092\u554f\u3044\u5408\u308f\u305b ' + name);\n\n/* \u524a\u9664\u64cd\u4f5c */\n// \u30cf\u30c3\u30b7\u30e5\u8868\u304b\u3089\u30ad\u30fc\u5024\u30da\u30a2 (key, value) \u3092\u524a\u9664\nmap.delete(10583);\nconsole.info('\\n10583\u3092\u524a\u9664\u5f8c\u3001\u30cf\u30c3\u30b7\u30e5\u8868\u306f\\nKey -&gt; Value');\nconsole.info(map);\n</code></pre> hash_map.dart<pre><code>/* \u30cf\u30c3\u30b7\u30e5\u8868\u3092\u521d\u671f\u5316 */\nMap&lt;int, String&gt; map = {};\n\n/* \u8ffd\u52a0\u64cd\u4f5c */\n// \u30cf\u30c3\u30b7\u30e5\u8868\u306b\u30ad\u30fc\u5024\u30da\u30a2 (key, value) \u3092\u8ffd\u52a0\nmap[12836] = \"\u5c0f\u54c8\";\nmap[15937] = \"\u5c0f\u5570\";\nmap[16750] = \"\u5c0f\u7b97\";\nmap[13276] = \"\u5c0f\u6cd5\";\nmap[10583] = \"\u5c0f\u9e2d\";\n\n/* \u30af\u30a8\u30ea\u64cd\u4f5c */\n// \u30cf\u30c3\u30b7\u30e5\u8868\u306b\u30ad\u30fc\u3092\u5165\u529b\u3057\u3001\u5024\u3092\u53d6\u5f97\nString name = map[15937];\n\n/* \u524a\u9664\u64cd\u4f5c */\n// \u30cf\u30c3\u30b7\u30e5\u8868\u304b\u3089\u30ad\u30fc\u5024\u30da\u30a2 (key, value) \u3092\u524a\u9664\nmap.remove(10583);\n</code></pre> hash_map.rs<pre><code>use std::collections::HashMap;\n\n/* \u30cf\u30c3\u30b7\u30e5\u8868\u3092\u521d\u671f\u5316 */\nlet mut map: HashMap&lt;i32, String&gt; = HashMap::new();\n\n/* \u8ffd\u52a0\u64cd\u4f5c */\n// \u30cf\u30c3\u30b7\u30e5\u8868\u306b\u30ad\u30fc\u5024\u30da\u30a2 (key, value) \u3092\u8ffd\u52a0\nmap.insert(12836, \"\u5c0f\u54c8\".to_string());\nmap.insert(15937, \"\u5c0f\u5570\".to_string());\nmap.insert(16750, \"\u5c0f\u7b97\".to_string());\nmap.insert(13279, \"\u5c0f\u6cd5\".to_string());\nmap.insert(10583, \"\u5c0f\u9e2d\".to_string());\n\n/* \u30af\u30a8\u30ea\u64cd\u4f5c */\n// \u30cf\u30c3\u30b7\u30e5\u8868\u306b\u30ad\u30fc\u3092\u5165\u529b\u3057\u3001\u5024\u3092\u53d6\u5f97\nlet _name: Option&lt;&amp;String&gt; = map.get(&amp;15937);\n\n/* \u524a\u9664\u64cd\u4f5c */\n// \u30cf\u30c3\u30b7\u30e5\u8868\u304b\u3089\u30ad\u30fc\u5024\u30da\u30a2 (key, value) \u3092\u524a\u9664\nlet _removed_value: Option&lt;String&gt; = map.remove(&amp;10583);\n</code></pre> hash_map.c<pre><code>// C\u306b\u306f\u7d44\u307f\u8fbc\u307f\u306e\u30cf\u30c3\u30b7\u30e5\u8868\u304c\u63d0\u4f9b\u3055\u308c\u3066\u3044\u307e\u305b\u3093\n</code></pre> hash_map.kt<pre><code>\n</code></pre> hash_map.zig<pre><code>\n</code></pre> <p>\u30cf\u30c3\u30b7\u30e5\u8868\u3092\u8d70\u67fb\u3059\u308b\u4e00\u822c\u7684\u306a\u65b9\u6cd5\u306f3\u3064\u3042\u308a\u307e\u3059\uff1a\u30ad\u30fc\u5024\u30da\u30a2\u306e\u8d70\u67fb\u3001\u30ad\u30fc\u306e\u8d70\u67fb\u3001\u5024\u306e\u8d70\u67fb\u3002\u4ee5\u4e0b\u306f\u30b3\u30fc\u30c9\u4f8b\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinZig hash_map.py<pre><code># \u30cf\u30c3\u30b7\u30e5\u8868\u3092\u8d70\u67fb\n# \u30ad\u30fc\u5024\u30da\u30a2 key-&gt;value \u3092\u8d70\u67fb\nfor key, value in hmap.items():\n    print(key, \"-&gt;\", value)\n# \u30ad\u30fc\u306e\u307f\u3092\u8d70\u67fb\nfor key in hmap.keys():\n    print(key)\n# \u5024\u306e\u307f\u3092\u8d70\u67fb\nfor value in hmap.values():\n    print(value)\n</code></pre> hash_map.cpp<pre><code>/* \u30cf\u30c3\u30b7\u30e5\u8868\u3092\u8d70\u67fb */\n// \u30ad\u30fc\u5024\u30da\u30a2 key-&gt;value \u3092\u8d70\u67fb\nfor (auto kv: map) {\n    cout &lt;&lt; kv.first &lt;&lt; \" -&gt; \" &lt;&lt; kv.second &lt;&lt; endl;\n}\n// \u30a4\u30c6\u30ec\u30fc\u30bf\u3092\u4f7f\u7528\u3057\u3066\u30ad\u30fc\u5024\u30da\u30a2 key-&gt;value \u3092\u8d70\u67fb\nfor (auto iter = map.begin(); iter != map.end(); iter++) {\n    cout &lt;&lt; iter-&gt;first &lt;&lt; \"-&gt;\" &lt;&lt; iter-&gt;second &lt;&lt; endl;\n}\n</code></pre> hash_map.java<pre><code>/* \u30cf\u30c3\u30b7\u30e5\u8868\u3092\u8d70\u67fb */\n// \u30ad\u30fc\u5024\u30da\u30a2 key-&gt;value \u3092\u8d70\u67fb\nfor (Map.Entry&lt;Integer, String&gt; kv: map.entrySet()) {\n    System.out.println(kv.getKey() + \" -&gt; \" + kv.getValue());\n}\n// \u30ad\u30fc\u306e\u307f\u3092\u8d70\u67fb\nfor (int key: map.keySet()) {\n    System.out.println(key);\n}\n// \u5024\u306e\u307f\u3092\u8d70\u67fb\nfor (String val: map.values()) {\n    System.out.println(val);\n}\n</code></pre> hash_map.cs<pre><code>/* \u30cf\u30c3\u30b7\u30e5\u8868\u3092\u8d70\u67fb */\n// \u30ad\u30fc\u5024\u30da\u30a2 Key-&gt;Value \u3092\u8d70\u67fb\nforeach (var kv in map) {\n    Console.WriteLine(kv.Key + \" -&gt; \" + kv.Value);\n}\n// \u30ad\u30fc\u306e\u307f\u3092\u8d70\u67fb\nforeach (int key in map.Keys) {\n    Console.WriteLine(key);\n}\n// \u5024\u306e\u307f\u3092\u8d70\u67fb\nforeach (string val in map.Values) {\n    Console.WriteLine(val);\n}\n</code></pre> hash_map_test.go<pre><code>/* \u30cf\u30c3\u30b7\u30e5\u8868\u3092\u8d70\u67fb */\n// \u30ad\u30fc\u5024\u30da\u30a2 key-&gt;value \u3092\u8d70\u67fb\nfor key, value := range hmap {\n    fmt.Println(key, \"-&gt;\", value)\n}\n// \u30ad\u30fc\u306e\u307f\u3092\u8d70\u67fb\nfor key := range hmap {\n    fmt.Println(key)\n}\n// \u5024\u306e\u307f\u3092\u8d70\u67fb\nfor _, value := range hmap {\n    fmt.Println(value)\n}\n</code></pre> hash_map.swift<pre><code>/* \u30cf\u30c3\u30b7\u30e5\u8868\u3092\u8d70\u67fb */\n// \u30ad\u30fc\u5024\u30da\u30a2 Key-&gt;Value \u3092\u8d70\u67fb\nfor (key, value) in map {\n    print(\"\\(key) -&gt; \\(value)\")\n}\n// \u30ad\u30fc\u306e\u307f\u3092\u8d70\u67fb\nfor key in map.keys {\n    print(key)\n}\n// \u5024\u306e\u307f\u3092\u8d70\u67fb\nfor value in map.values {\n    print(value)\n}\n</code></pre> hash_map.js<pre><code>/* \u30cf\u30c3\u30b7\u30e5\u8868\u3092\u8d70\u67fb */\nconsole.info('\\n\u30ad\u30fc\u5024\u30da\u30a2 Key-&gt;Value \u3092\u8d70\u67fb');\nfor (const [k, v] of map.entries()) {\n    console.info(k + ' -&gt; ' + v);\n}\nconsole.info('\\n\u30ad\u30fc\u306e\u307f\u3092\u8d70\u67fb Key');\nfor (const k of map.keys()) {\n    console.info(k);\n}\nconsole.info('\\n\u5024\u306e\u307f\u3092\u8d70\u67fb Value');\nfor (const v of map.values()) {\n    console.info(v);\n}\n</code></pre> hash_map.ts<pre><code>/* \u30cf\u30c3\u30b7\u30e5\u8868\u3092\u8d70\u67fb */\nconsole.info('\\n\u30ad\u30fc\u5024\u30da\u30a2 Key-&gt;Value \u3092\u8d70\u67fb');\nfor (const [k, v] of map.entries()) {\n    console.info(k + ' -&gt; ' + v);\n}\nconsole.info('\\n\u30ad\u30fc\u306e\u307f\u3092\u8d70\u67fb Key');\nfor (const k of map.keys()) {\n    console.info(k);\n}\nconsole.info('\\n\u5024\u306e\u307f\u3092\u8d70\u67fb Value');\nfor (const v of map.values()) {\n    console.info(v);\n}\n</code></pre> hash_map.dart<pre><code>/* \u30cf\u30c3\u30b7\u30e5\u8868\u3092\u8d70\u67fb */\n// \u30ad\u30fc\u5024\u30da\u30a2 Key-&gt;Value \u3092\u8d70\u67fb\nmap.forEach((key, value) {\nprint('$key -&gt; $value');\n});\n\n// \u30ad\u30fc\u306e\u307f\u3092\u8d70\u67fb Key\nmap.keys.forEach((key) {\nprint(key);\n});\n\n// \u5024\u306e\u307f\u3092\u8d70\u67fb Value\nmap.values.forEach((value) {\nprint(value);\n});\n</code></pre> hash_map.rs<pre><code>/* \u30cf\u30c3\u30b7\u30e5\u8868\u3092\u8d70\u67fb */\n// \u30ad\u30fc\u5024\u30da\u30a2 Key-&gt;Value \u3092\u8d70\u67fb\nfor (key, value) in &amp;map {\n    println!(\"{key} -&gt; {value}\");\n}\n\n// \u30ad\u30fc\u306e\u307f\u3092\u8d70\u67fb Key\nfor key in map.keys() {\n    println!(\"{key}\");\n}\n\n// \u5024\u306e\u307f\u3092\u8d70\u67fb Value\nfor value in map.values() {\n    println!(\"{value}\");\n}\n</code></pre> hash_map.c<pre><code>// C\u306b\u306f\u7d44\u307f\u8fbc\u307f\u306e\u30cf\u30c3\u30b7\u30e5\u8868\u304c\u63d0\u4f9b\u3055\u308c\u3066\u3044\u307e\u305b\u3093\n</code></pre> hash_map.kt<pre><code>\n</code></pre> hash_map.zig<pre><code>// Zig\u306e\u4f8b\u306f\u63d0\u4f9b\u3055\u308c\u3066\u3044\u307e\u305b\u3093\n</code></pre>"},{"location":"chapter_hashing/hash_map/#612","title":"6.1.2 \u00a0 \u30cf\u30c3\u30b7\u30e5\u8868\u306e\u7c21\u5358\u306a\u5b9f\u88c5","text":"<p>\u307e\u305a\u3001\u6700\u3082\u7c21\u5358\u306a\u30b1\u30fc\u30b9\u3092\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\uff1a\u914d\u5217\u306e\u307f\u3092\u4f7f\u3063\u3066\u30cf\u30c3\u30b7\u30e5\u8868\u3092\u5b9f\u88c5\u3059\u308b\u3053\u3068\u3002\u30cf\u30c3\u30b7\u30e5\u8868\u306b\u304a\u3044\u3066\u3001\u914d\u5217\u306e\u5404\u7a7a\u304d\u30b9\u30ed\u30c3\u30c8\u306f\u30d0\u30b1\u30c3\u30c8\u3068\u547c\u3070\u308c\u3001\u5404\u30d0\u30b1\u30c3\u30c8\u306f\u30ad\u30fc\u5024\u30da\u30a2\u3092\u683c\u7d0d\u3067\u304d\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u30af\u30a8\u30ea\u64cd\u4f5c\u306f<code>key</code>\u306b\u5bfe\u5fdc\u3059\u308b\u30d0\u30b1\u30c3\u30c8\u3092\u898b\u3064\u3051\u3001\u305d\u3053\u304b\u3089<code>value</code>\u3092\u53d6\u5f97\u3059\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059\u3002</p> <p>\u3067\u306f\u3001<code>key</code>\u306b\u57fa\u3065\u3044\u3066\u5bfe\u5fdc\u3059\u308b\u30d0\u30b1\u30c3\u30c8\u3092\u3069\u306e\u3088\u3046\u306b\u7279\u5b9a\u3059\u308b\u306e\u3067\u3057\u3087\u3046\u304b\uff1f\u3053\u308c\u306f\u30cf\u30c3\u30b7\u30e5\u95a2\u6570\u306b\u3088\u3063\u3066\u5b9f\u73fe\u3055\u308c\u307e\u3059\u3002\u30cf\u30c3\u30b7\u30e5\u95a2\u6570\u306e\u5f79\u5272\u306f\u3001\u3088\u308a\u5927\u304d\u306a\u5165\u529b\u7a7a\u9593\u3092\u3088\u308a\u5c0f\u3055\u306a\u51fa\u529b\u7a7a\u9593\u306b\u30de\u30c3\u30d4\u30f3\u30b0\u3059\u308b\u3053\u3068\u3067\u3059\u3002\u30cf\u30c3\u30b7\u30e5\u8868\u3067\u306f\u3001\u5165\u529b\u7a7a\u9593\u306f\u3059\u3079\u3066\u306e\u30ad\u30fc\u3067\u69cb\u6210\u3055\u308c\u3001\u51fa\u529b\u7a7a\u9593\u306f\u3059\u3079\u3066\u306e\u30d0\u30b1\u30c3\u30c8\uff08\u914d\u5217\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\uff09\u3067\u69cb\u6210\u3055\u308c\u307e\u3059\u3002\u3064\u307e\u308a\u3001<code>key</code>\u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408\u3001\u30cf\u30c3\u30b7\u30e5\u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u5bfe\u5fdc\u3059\u308b\u30ad\u30fc\u5024\u30da\u30a2\u306e\u914d\u5217\u5185\u306e\u683c\u7d0d\u4f4d\u7f6e\u3092\u6c7a\u5b9a\u3067\u304d\u307e\u3059\u3002</p> <p>\u4e0e\u3048\u3089\u308c\u305f<code>key</code>\u306b\u5bfe\u3057\u3066\u3001\u30cf\u30c3\u30b7\u30e5\u95a2\u6570\u306e\u8a08\u7b97\u306f2\u3064\u306e\u30b9\u30c6\u30c3\u30d7\u3067\u69cb\u6210\u3055\u308c\u307e\u3059\uff1a</p> <ol> <li>\u7279\u5b9a\u306e\u30cf\u30c3\u30b7\u30e5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0<code>hash()</code>\u3092\u4f7f\u7528\u3057\u3066\u30cf\u30c3\u30b7\u30e5\u5024\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002</li> <li>\u30cf\u30c3\u30b7\u30e5\u5024\u3092\u30d0\u30b1\u30c3\u30c8\u6570\uff08\u914d\u5217\u9577\uff09<code>capacity</code>\u3067\u5270\u4f59\u3092\u53d6\u308a\u3001\u30ad\u30fc\u306b\u5bfe\u5fdc\u3059\u308b\u914d\u5217<code>index</code>\u3092\u53d6\u5f97\u3057\u307e\u3059\u3002</li> </ol> <pre><code>index = hash(key) % capacity\n</code></pre> <p>\u305d\u306e\u5f8c\u3001<code>index</code>\u3092\u4f7f\u7528\u3057\u3066\u30cf\u30c3\u30b7\u30e5\u8868\u5185\u306e\u5bfe\u5fdc\u3059\u308b\u30d0\u30b1\u30c3\u30c8\u306b\u30a2\u30af\u30bb\u30b9\u3057\u3001<code>value</code>\u3092\u53d6\u5f97\u3067\u304d\u307e\u3059\u3002</p> <p>\u914d\u5217\u9577\u304c<code>capacity = 100</code>\u3067\u3001\u30cf\u30c3\u30b7\u30e5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u304c<code>hash(key) = key</code>\u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u3066\u3044\u308b\u3068\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u30cf\u30c3\u30b7\u30e5\u95a2\u6570\u306f<code>key % 100</code>\u3068\u3057\u3066\u8868\u73fe\u3067\u304d\u307e\u3059\u3002\u4ee5\u4e0b\u306e\u56f3\u306f\u3001<code>key</code>\u3092\u5b66\u7c4d\u756a\u53f7\u3001<code>value</code>\u3092\u540d\u524d\u3068\u3057\u3066\u3001\u30cf\u30c3\u30b7\u30e5\u95a2\u6570\u306e\u52d5\u4f5c\u539f\u7406\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002</p> <p></p> <p> \u56f3 6-2 \u00a0 \u30cf\u30c3\u30b7\u30e5\u95a2\u6570\u306e\u52d5\u4f5c\u539f\u7406 </p> <p>\u4ee5\u4e0b\u306e\u30b3\u30fc\u30c9\u306f\u7c21\u5358\u306a\u30cf\u30c3\u30b7\u30e5\u8868\u3092\u5b9f\u88c5\u3057\u3066\u3044\u307e\u3059\u3002\u3053\u3053\u3067\u306f\u3001<code>key</code>\u3068<code>value</code>\u3092<code>Pair</code>\u30af\u30e9\u30b9\u306b\u30ab\u30d7\u30bb\u30eb\u5316\u3057\u3066\u30ad\u30fc\u5024\u30da\u30a2\u3092\u8868\u73fe\u3057\u3066\u3044\u307e\u3059\u3002</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig array_hash_map.py<pre><code>class Pair:\n    \"\"\"\u30ad\u30fc\u5024\u30da\u30a2\"\"\"\n\n    def __init__(self, key: int, val: str):\n        self.key = key\n        self.val = val\n\nclass ArrayHashMap:\n    \"\"\"\u914d\u5217\u5b9f\u88c5\u306b\u57fa\u3065\u304f\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\"\"\"\n\n    def __init__(self):\n        \"\"\"\u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf\"\"\"\n        # 100\u500b\u306e\u30d0\u30b1\u30c3\u30c8\u3092\u542b\u3080\u914d\u5217\u3092\u521d\u671f\u5316\n        self.buckets: list[Pair | None] = [None] * 100\n\n    def hash_func(self, key: int) -&gt; int:\n        \"\"\"\u30cf\u30c3\u30b7\u30e5\u95a2\u6570\"\"\"\n        index = key % 100\n        return index\n\n    def get(self, key: int) -&gt; str:\n        \"\"\"\u7167\u4f1a\u64cd\u4f5c\"\"\"\n        index: int = self.hash_func(key)\n        pair: Pair = self.buckets[index]\n        if pair is None:\n            return None\n        return pair.val\n\n    def put(self, key: int, val: str):\n        \"\"\"\u8ffd\u52a0\u64cd\u4f5c\"\"\"\n        pair = Pair(key, val)\n        index: int = self.hash_func(key)\n        self.buckets[index] = pair\n\n    def remove(self, key: int):\n        \"\"\"\u524a\u9664\u64cd\u4f5c\"\"\"\n        index: int = self.hash_func(key)\n        # None \u306b\u8a2d\u5b9a\u3057\u3001\u524a\u9664\u3092\u8868\u73fe\n        self.buckets[index] = None\n\n    def entry_set(self) -&gt; list[Pair]:\n        \"\"\"\u3059\u3079\u3066\u306e\u30ad\u30fc\u5024\u30da\u30a2\u3092\u53d6\u5f97\"\"\"\n        result: list[Pair] = []\n        for pair in self.buckets:\n            if pair is not None:\n                result.append(pair)\n        return result\n\n    def key_set(self) -&gt; list[int]:\n        \"\"\"\u3059\u3079\u3066\u306e\u30ad\u30fc\u3092\u53d6\u5f97\"\"\"\n        result = []\n        for pair in self.buckets:\n            if pair is not None:\n                result.append(pair.key)\n        return result\n\n    def value_set(self) -&gt; list[str]:\n        \"\"\"\u3059\u3079\u3066\u306e\u5024\u3092\u53d6\u5f97\"\"\"\n        result = []\n        for pair in self.buckets:\n            if pair is not None:\n                result.append(pair.val)\n        return result\n\n    def print(self):\n        \"\"\"\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u3092\u51fa\u529b\"\"\"\n        for pair in self.buckets:\n            if pair is not None:\n                print(pair.key, \"-&gt;\", pair.val)\n</code></pre> array_hash_map.cpp<pre><code>/* \u30ad\u30fc\u5024\u30da\u30a2 */\nstruct Pair {\n  public:\n    int key;\n    string val;\n    Pair(int key, string val) {\n        this-&gt;key = key;\n        this-&gt;val = val;\n    }\n};\n\n/* \u914d\u5217\u5b9f\u88c5\u306b\u57fa\u3065\u304f\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb */\nclass ArrayHashMap {\n  private:\n    vector&lt;Pair *&gt; buckets;\n\n  public:\n    ArrayHashMap() {\n        // \u914d\u5217\u3092\u521d\u671f\u5316\u3001100\u500b\u306e\u30d0\u30b1\u30c3\u30c8\u3092\u542b\u3080\n        buckets = vector&lt;Pair *&gt;(100);\n    }\n\n    ~ArrayHashMap() {\n        // \u30e1\u30e2\u30ea\u3092\u89e3\u653e\n        for (const auto &amp;bucket : buckets) {\n            delete bucket;\n        }\n        buckets.clear();\n    }\n\n    /* \u30cf\u30c3\u30b7\u30e5\u95a2\u6570 */\n    int hashFunc(int key) {\n        int index = key % 100;\n        return index;\n    }\n\n    /* \u30af\u30a8\u30ea\u64cd\u4f5c */\n    string get(int key) {\n        int index = hashFunc(key);\n        Pair *pair = buckets[index];\n        if (pair == nullptr)\n            return \"\";\n        return pair-&gt;val;\n    }\n\n    /* \u8ffd\u52a0\u64cd\u4f5c */\n    void put(int key, string val) {\n        Pair *pair = new Pair(key, val);\n        int index = hashFunc(key);\n        buckets[index] = pair;\n    }\n\n    /* \u524a\u9664\u64cd\u4f5c */\n    void remove(int key) {\n        int index = hashFunc(key);\n        // \u30e1\u30e2\u30ea\u3092\u89e3\u653e\u3057\u3066nullptr\u306b\u8a2d\u5b9a\n        delete buckets[index];\n        buckets[index] = nullptr;\n    }\n\n    /* \u3059\u3079\u3066\u306e\u30ad\u30fc\u5024\u30da\u30a2\u3092\u53d6\u5f97 */\n    vector&lt;Pair *&gt; pairSet() {\n        vector&lt;Pair *&gt; pairSet;\n        for (Pair *pair : buckets) {\n            if (pair != nullptr) {\n                pairSet.push_back(pair);\n            }\n        }\n        return pairSet;\n    }\n\n    /* \u3059\u3079\u3066\u306e\u30ad\u30fc\u3092\u53d6\u5f97 */\n    vector&lt;int&gt; keySet() {\n        vector&lt;int&gt; keySet;\n        for (Pair *pair : buckets) {\n            if (pair != nullptr) {\n                keySet.push_back(pair-&gt;key);\n            }\n        }\n        return keySet;\n    }\n\n    /* \u3059\u3079\u3066\u306e\u5024\u3092\u53d6\u5f97 */\n    vector&lt;string&gt; valueSet() {\n        vector&lt;string&gt; valueSet;\n        for (Pair *pair : buckets) {\n            if (pair != nullptr) {\n                valueSet.push_back(pair-&gt;val);\n            }\n        }\n        return valueSet;\n    }\n\n    /* \u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u3092\u5370\u5237 */\n    void print() {\n        for (Pair *kv : pairSet()) {\n            cout &lt;&lt; kv-&gt;key &lt;&lt; \" -&gt; \" &lt;&lt; kv-&gt;val &lt;&lt; endl;\n        }\n    }\n};\n</code></pre> array_hash_map.java<pre><code>/* \u30ad\u30fc\u5024\u30da\u30a2 */\nclass Pair {\n    public int key;\n    public String val;\n\n    public Pair(int key, String val) {\n        this.key = key;\n        this.val = val;\n    }\n}\n\n/* \u914d\u5217\u5b9f\u88c5\u306b\u57fa\u3065\u304f\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb */\nclass ArrayHashMap {\n    private List&lt;Pair&gt; buckets;\n\n    public ArrayHashMap() {\n        // 100\u500b\u306e\u30d0\u30b1\u30c3\u30c8\u3092\u542b\u3080\u914d\u5217\u3092\u521d\u671f\u5316\n        buckets = new ArrayList&lt;&gt;();\n        for (int i = 0; i &lt; 100; i++) {\n            buckets.add(null);\n        }\n    }\n\n    /* \u30cf\u30c3\u30b7\u30e5\u95a2\u6570 */\n    private int hashFunc(int key) {\n        int index = key % 100;\n        return index;\n    }\n\n    /* \u30af\u30a8\u30ea\u64cd\u4f5c */\n    public String get(int key) {\n        int index = hashFunc(key);\n        Pair pair = buckets.get(index);\n        if (pair == null)\n            return null;\n        return pair.val;\n    }\n\n    /* \u8ffd\u52a0\u64cd\u4f5c */\n    public void put(int key, String val) {\n        Pair pair = new Pair(key, val);\n        int index = hashFunc(key);\n        buckets.set(index, pair);\n    }\n\n    /* \u524a\u9664\u64cd\u4f5c */\n    public void remove(int key) {\n        int index = hashFunc(key);\n        // null\u306b\u8a2d\u5b9a\u3057\u3066\u524a\u9664\u3092\u793a\u3059\n        buckets.set(index, null);\n    }\n\n    /* \u3059\u3079\u3066\u306e\u30ad\u30fc\u5024\u30da\u30a2\u3092\u53d6\u5f97 */\n    public List&lt;Pair&gt; pairSet() {\n        List&lt;Pair&gt; pairSet = new ArrayList&lt;&gt;();\n        for (Pair pair : buckets) {\n            if (pair != null)\n                pairSet.add(pair);\n        }\n        return pairSet;\n    }\n\n    /* \u3059\u3079\u3066\u306e\u30ad\u30fc\u3092\u53d6\u5f97 */\n    public List&lt;Integer&gt; keySet() {\n        List&lt;Integer&gt; keySet = new ArrayList&lt;&gt;();\n        for (Pair pair : buckets) {\n            if (pair != null)\n                keySet.add(pair.key);\n        }\n        return keySet;\n    }\n\n    /* \u3059\u3079\u3066\u306e\u5024\u3092\u53d6\u5f97 */\n    public List&lt;String&gt; valueSet() {\n        List&lt;String&gt; valueSet = new ArrayList&lt;&gt;();\n        for (Pair pair : buckets) {\n            if (pair != null)\n                valueSet.add(pair.val);\n        }\n        return valueSet;\n    }\n\n    /* \u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u3092\u5370\u5237 */\n    public void print() {\n        for (Pair kv : pairSet()) {\n            System.out.println(kv.key + \" -&gt; \" + kv.val);\n        }\n    }\n}\n</code></pre> array_hash_map.cs<pre><code>[class]{Pair}-[func]{}\n\n[class]{ArrayHashMap}-[func]{}\n</code></pre> array_hash_map.go<pre><code>[class]{pair}-[func]{}\n\n[class]{arrayHashMap}-[func]{}\n</code></pre> array_hash_map.swift<pre><code>[file]{utils/pair.swift}-[class]{Pair}-[func]{}\n\n[class]{ArrayHashMap}-[func]{}\n</code></pre> array_hash_map.js<pre><code>[class]{Pair}-[func]{}\n\n[class]{ArrayHashMap}-[func]{}\n</code></pre> array_hash_map.ts<pre><code>[class]{Pair}-[func]{}\n\n[class]{ArrayHashMap}-[func]{}\n</code></pre> array_hash_map.dart<pre><code>[class]{Pair}-[func]{}\n\n[class]{ArrayHashMap}-[func]{}\n</code></pre> array_hash_map.rs<pre><code>[class]{Pair}-[func]{}\n\n[class]{ArrayHashMap}-[func]{}\n</code></pre> array_hash_map.c<pre><code>[class]{Pair}-[func]{}\n\n[class]{ArrayHashMap}-[func]{}\n</code></pre> array_hash_map.kt<pre><code>[class]{Pair}-[func]{}\n\n[class]{ArrayHashMap}-[func]{}\n</code></pre> array_hash_map.rb<pre><code>[class]{Pair}-[func]{}\n\n[class]{ArrayHashMap}-[func]{}\n</code></pre> array_hash_map.zig<pre><code>[class]{Pair}-[func]{}\n\n[class]{ArrayHashMap}-[func]{}\n</code></pre>"},{"location":"chapter_hashing/hash_map/#613","title":"6.1.3 \u00a0 \u30cf\u30c3\u30b7\u30e5\u885d\u7a81\u3068\u30ea\u30b5\u30a4\u30ba","text":"<p>\u672c\u8cea\u7684\u306b\u3001\u30cf\u30c3\u30b7\u30e5\u95a2\u6570\u306e\u5f79\u5272\u306f\u3001\u3059\u3079\u3066\u306e\u30ad\u30fc\u306e\u5165\u529b\u7a7a\u9593\u5168\u4f53\u3092\u3001\u3059\u3079\u3066\u306e\u914d\u5217\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306e\u51fa\u529b\u7a7a\u9593\u306b\u30de\u30c3\u30d4\u30f3\u30b0\u3059\u308b\u3053\u3068\u3067\u3059\u3002\u3057\u304b\u3057\u3001\u5165\u529b\u7a7a\u9593\u306f\u51fa\u529b\u7a7a\u9593\u3088\u308a\u3082\u306f\u308b\u304b\u306b\u5927\u304d\u3044\u3053\u3068\u304c\u3088\u304f\u3042\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u7406\u8ad6\u7684\u306b\u306f\u3001\u300c\u8907\u6570\u306e\u5165\u529b\u304c\u540c\u3058\u51fa\u529b\u306b\u5bfe\u5fdc\u3059\u308b\u300d\u30b1\u30fc\u30b9\u304c\u5e38\u306b\u5b58\u5728\u3057\u307e\u3059\u3002</p> <p>\u4e0a\u8a18\u306e\u4f8b\u3067\u306f\u3001\u4e0e\u3048\u3089\u308c\u305f\u30cf\u30c3\u30b7\u30e5\u95a2\u6570\u3067\u3001\u5165\u529b<code>key</code>\u306e\u4e0b\u4e8c\u6841\u304c\u540c\u3058\u5834\u5408\u3001\u30cf\u30c3\u30b7\u30e5\u95a2\u6570\u306f\u540c\u3058\u51fa\u529b\u3092\u751f\u6210\u3057\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u5b66\u7c4d\u756a\u53f712836\u306820336\u306e2\u4eba\u306e\u5b66\u751f\u3092\u30af\u30a8\u30ea\u3059\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\uff1a</p> <pre><code>12836 % 100 = 36\n20336 % 100 = 36\n</code></pre> <p>\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u4e21\u65b9\u306e\u5b66\u7c4d\u756a\u53f7\u304c\u540c\u3058\u540d\u524d\u3092\u6307\u3057\u3066\u304a\u308a\u3001\u3053\u308c\u306f\u660e\u3089\u304b\u306b\u9593\u9055\u3063\u3066\u3044\u307e\u3059\u3002\u3053\u306e\u8907\u6570\u306e\u5165\u529b\u304c\u540c\u3058\u51fa\u529b\u306b\u5bfe\u5fdc\u3059\u308b\u72b6\u6cc1\u3092\u30cf\u30c3\u30b7\u30e5\u885d\u7a81\u3068\u547c\u3073\u307e\u3059\u3002</p> <p></p> <p> \u56f3 6-3 \u00a0 \u30cf\u30c3\u30b7\u30e5\u885d\u7a81\u306e\u4f8b </p> <p>\u30cf\u30c3\u30b7\u30e5\u8868\u306e\u5bb9\u91cf\\(n\\)\u304c\u5897\u52a0\u3059\u308b\u306b\u3064\u308c\u3066\u3001\u8907\u6570\u306e\u30ad\u30fc\u304c\u540c\u3058\u30d0\u30b1\u30c3\u30c8\u306b\u5272\u308a\u5f53\u3066\u3089\u308c\u308b\u78ba\u7387\u304c\u6e1b\u5c11\u3057\u3001\u885d\u7a81\u304c\u5c11\u306a\u304f\u306a\u308b\u3053\u3068\u306f\u7406\u89e3\u3057\u3084\u3059\u3044\u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u30cf\u30c3\u30b7\u30e5\u8868\u3092\u30ea\u30b5\u30a4\u30ba\u3059\u308b\u3053\u3068\u3067\u30cf\u30c3\u30b7\u30e5\u885d\u7a81\u3092\u6e1b\u3089\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002</p> <p>\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u30ea\u30b5\u30a4\u30ba\u524d\u306f\u3001\u30ad\u30fc\u5024\u30da\u30a2<code>(136, A)</code>\u3068<code>(236, D)</code>\u304c\u885d\u7a81\u3057\u3066\u3044\u307e\u3057\u305f\u3002\u3057\u304b\u3057\u3001\u30ea\u30b5\u30a4\u30ba\u5f8c\u306f\u885d\u7a81\u304c\u89e3\u6c7a\u3055\u308c\u3066\u3044\u307e\u3059\u3002</p> <p></p> <p> \u56f3 6-4 \u00a0 \u30cf\u30c3\u30b7\u30e5\u8868\u306e\u30ea\u30b5\u30a4\u30ba </p> <p>\u914d\u5217\u306e\u62e1\u5f35\u3068\u540c\u69d8\u306b\u3001\u30cf\u30c3\u30b7\u30e5\u8868\u306e\u30ea\u30b5\u30a4\u30ba\u306b\u306f\u3059\u3079\u3066\u306e\u30ad\u30fc\u5024\u30da\u30a2\u3092\u5143\u306e\u30cf\u30c3\u30b7\u30e5\u8868\u304b\u3089\u65b0\u3057\u3044\u3082\u306e\u306b\u79fb\u884c\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u3001\u6642\u9593\u304c\u304b\u304b\u308a\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u30cf\u30c3\u30b7\u30e5\u8868\u306e<code>capacity</code>\u304c\u5909\u66f4\u3055\u308c\u308b\u305f\u3081\u3001\u30cf\u30c3\u30b7\u30e5\u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066\u3059\u3079\u3066\u306e\u30ad\u30fc\u5024\u30da\u30a2\u306e\u683c\u7d0d\u4f4d\u7f6e\u3092\u518d\u8a08\u7b97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u3001\u30ea\u30b5\u30a4\u30ba\u30d7\u30ed\u30bb\u30b9\u306e\u8a08\u7b97\u30aa\u30fc\u30d0\u30fc\u30d8\u30c3\u30c9\u304c\u3055\u3089\u306b\u5897\u52a0\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u306f\u983b\u7e41\u306a\u30ea\u30b5\u30a4\u30ba\u3092\u9632\u3050\u305f\u3081\u306b\u3001\u30cf\u30c3\u30b7\u30e5\u8868\u306b\u5341\u5206\u5927\u304d\u306a\u5bb9\u91cf\u3092\u5272\u308a\u5f53\u3066\u308b\u3053\u3068\u304c\u3088\u304f\u3042\u308a\u307e\u3059\u3002</p> <p>\u8ca0\u8377\u7387\u306f\u30cf\u30c3\u30b7\u30e5\u8868\u306e\u91cd\u8981\u306a\u6982\u5ff5\u3067\u3059\u3002\u30cf\u30c3\u30b7\u30e5\u8868\u5185\u306e\u8981\u7d20\u6570\u3068\u30d0\u30b1\u30c3\u30c8\u6570\u306e\u6bd4\u7387\u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002\u30cf\u30c3\u30b7\u30e5\u885d\u7a81\u306e\u6df1\u523b\u5ea6\u3092\u6e2c\u5b9a\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u3001\u3057\u3070\u3057\u3070\u30cf\u30c3\u30b7\u30e5\u8868\u306e\u30ea\u30b5\u30a4\u30ba\u306e\u30c8\u30ea\u30ac\u30fc\u3068\u3057\u3066\u3082\u6a5f\u80fd\u3057\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001Java\u3067\u306f\u3001\u8ca0\u8377\u7387\u304c\\(0.75\\)\u3092\u8d85\u3048\u308b\u3068\u3001\u30b7\u30b9\u30c6\u30e0\u306f\u30cf\u30c3\u30b7\u30e5\u8868\u3092\u5143\u306e\u30b5\u30a4\u30ba\u306e2\u500d\u306b\u30ea\u30b5\u30a4\u30ba\u3057\u307e\u3059\u3002</p>"},{"location":"chapter_hashing/summary/","title":"6.4 \u00a0 \u307e\u3068\u3081","text":""},{"location":"chapter_hashing/summary/#1","title":"1. \u00a0 \u91cd\u8981\u306a\u30dd\u30a4\u30f3\u30c8","text":"<ul> <li>\u5165\u529b<code>key</code>\u304c\u4e0e\u3048\u3089\u308c\u308b\u3068\u3001\u30cf\u30c3\u30b7\u30e5\u8868\u306f\\(O(1)\\)\u306e\u6642\u9593\u3067\u5bfe\u5fdc\u3059\u308b<code>value</code>\u3092\u53d6\u5f97\u3067\u304d\u3001\u975e\u5e38\u306b\u52b9\u7387\u7684\u3067\u3059\u3002</li> <li>\u4e00\u822c\u7684\u306a\u30cf\u30c3\u30b7\u30e5\u8868\u306e\u64cd\u4f5c\u306b\u306f\u3001\u30af\u30a8\u30ea\u3001\u30ad\u30fc\u5024\u30da\u30a2\u306e\u8ffd\u52a0\u3001\u30ad\u30fc\u5024\u30da\u30a2\u306e\u524a\u9664\u3001\u30cf\u30c3\u30b7\u30e5\u8868\u306e\u8d70\u67fb\u304c\u3042\u308a\u307e\u3059\u3002</li> <li>\u30cf\u30c3\u30b7\u30e5\u95a2\u6570\u306f<code>key</code>\u3092\u914d\u5217\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306b\u30de\u30c3\u30d4\u30f3\u30b0\u3057\u3001\u5bfe\u5fdc\u3059\u308b\u30d0\u30b1\u30c3\u30c8\u306b\u30a2\u30af\u30bb\u30b9\u3057\u3066<code>value</code>\u3092\u53d6\u5f97\u3067\u304d\u308b\u3088\u3046\u306b\u3057\u307e\u3059\u3002</li> <li>2\u3064\u306e\u7570\u306a\u308b\u30ad\u30fc\u304c\u30cf\u30c3\u30b7\u30e5\u5316\u5f8c\u306b\u540c\u3058\u914d\u5217\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306b\u306a\u308b\u5834\u5408\u304c\u3042\u308a\u3001\u8aa4\u3063\u305f\u30af\u30a8\u30ea\u7d50\u679c\u306b\u3064\u306a\u304c\u308a\u307e\u3059\u3002\u3053\u306e\u73fe\u8c61\u306f\u30cf\u30c3\u30b7\u30e5\u885d\u7a81\u3068\u3057\u3066\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\u3002</li> <li>\u30cf\u30c3\u30b7\u30e5\u8868\u306e\u5bb9\u91cf\u304c\u5927\u304d\u3044\u307b\u3069\u3001\u30cf\u30c3\u30b7\u30e5\u885d\u7a81\u306e\u78ba\u7387\u306f\u4f4e\u304f\u306a\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u30cf\u30c3\u30b7\u30e5\u8868\u306e\u30ea\u30b5\u30a4\u30ba\u306f\u30cf\u30c3\u30b7\u30e5\u885d\u7a81\u3092\u7de9\u548c\u3067\u304d\u307e\u3059\u3002\u914d\u5217\u306e\u30ea\u30b5\u30a4\u30ba\u3068\u540c\u69d8\u306b\u3001\u30cf\u30c3\u30b7\u30e5\u8868\u306e\u30ea\u30b5\u30a4\u30ba\u306f\u30b3\u30b9\u30c8\u304c\u9ad8\u3044\u3067\u3059\u3002</li> <li>\u8981\u7d20\u6570\u3092\u30d0\u30b1\u30c3\u30c8\u6570\u3067\u5272\u3063\u305f\u8ca0\u8377\u7387\u306f\u3001\u30cf\u30c3\u30b7\u30e5\u885d\u7a81\u306e\u6df1\u523b\u5ea6\u3092\u53cd\u6620\u3057\u3001\u3057\u3070\u3057\u3070\u30cf\u30c3\u30b7\u30e5\u8868\u30ea\u30b5\u30a4\u30ba\u306e\u30c8\u30ea\u30ac\u30fc\u6761\u4ef6\u3068\u3057\u3066\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002</li> <li>\u9023\u9396\u6cd5\u306f\u5404\u8981\u7d20\u3092\u9023\u7d50\u30ea\u30b9\u30c8\u306b\u5909\u63db\u3057\u3001\u885d\u7a81\u3059\u308b\u3059\u3079\u3066\u306e\u8981\u7d20\u3092\u540c\u3058\u30ea\u30b9\u30c8\u306b\u683c\u7d0d\u3059\u308b\u3053\u3068\u3067\u30cf\u30c3\u30b7\u30e5\u885d\u7a81\u306b\u5bfe\u51e6\u3057\u307e\u3059\u3002\u305f\u3060\u3057\u3001\u904e\u5ea6\u306b\u9577\u3044\u30ea\u30b9\u30c8\u306f\u30af\u30a8\u30ea\u52b9\u7387\u3092\u4f4e\u4e0b\u3055\u305b\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u3001\u30ea\u30b9\u30c8\u3092\u8d64\u9ed2\u6728\u306b\u5909\u63db\u3059\u308b\u3053\u3068\u3067\u6539\u5584\u3067\u304d\u307e\u3059\u3002</li> <li>\u30aa\u30fc\u30d7\u30f3\u30a2\u30c9\u30ec\u30b9\u6cd5\u306f\u8907\u6570\u56de\u306e\u30d7\u30ed\u30fc\u30d6\u3092\u901a\u3057\u3066\u30cf\u30c3\u30b7\u30e5\u885d\u7a81\u3092\u51e6\u7406\u3057\u307e\u3059\u3002\u7dda\u5f62\u30d7\u30ed\u30fc\u30d6\u306f\u56fa\u5b9a\u30b9\u30c6\u30c3\u30d7\u30b5\u30a4\u30ba\u3092\u4f7f\u7528\u3057\u307e\u3059\u304c\u3001\u8981\u7d20\u3092\u524a\u9664\u3067\u304d\u305a\u3001\u30af\u30e9\u30b9\u30bf\u30ea\u30f3\u30b0\u3092\u8d77\u3053\u3057\u3084\u3059\u3044\u50be\u5411\u304c\u3042\u308a\u307e\u3059\u3002\u591a\u91cd\u30cf\u30c3\u30b7\u30e5\u306f\u30d7\u30ed\u30fc\u30d6\u306b\u8907\u6570\u306e\u30cf\u30c3\u30b7\u30e5\u95a2\u6570\u3092\u4f7f\u7528\u3057\u3001\u7dda\u5f62\u30d7\u30ed\u30fc\u30d6\u3068\u6bd4\u8f03\u3057\u3066\u30af\u30e9\u30b9\u30bf\u30ea\u30f3\u30b0\u3092\u6e1b\u3089\u3057\u307e\u3059\u304c\u3001\u8a08\u7b97\u30aa\u30fc\u30d0\u30fc\u30d8\u30c3\u30c9\u304c\u5897\u52a0\u3057\u307e\u3059\u3002</li> <li>\u7570\u306a\u308b\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u306f\u3055\u307e\u3056\u307e\u306a\u30cf\u30c3\u30b7\u30e5\u8868\u5b9f\u88c5\u3092\u63a1\u7528\u3057\u3066\u3044\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001Java\u306e<code>HashMap</code>\u306f\u9023\u9396\u6cd5\u3092\u4f7f\u7528\u3057\u3001Python\u306e<code>dict</code>\u306f\u30aa\u30fc\u30d7\u30f3\u30a2\u30c9\u30ec\u30b9\u6cd5\u3092\u63a1\u7528\u3057\u3066\u3044\u307e\u3059\u3002</li> <li>\u30cf\u30c3\u30b7\u30e5\u8868\u3067\u306f\u3001\u6c7a\u5b9a\u6027\u3001\u9ad8\u52b9\u7387\u3001\u5747\u7b49\u5206\u6563\u3092\u6301\u3064\u30cf\u30c3\u30b7\u30e5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u304c\u671b\u307e\u308c\u307e\u3059\u3002\u6697\u53f7\u5316\u3067\u306f\u3001\u30cf\u30c3\u30b7\u30e5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u885d\u7a81\u8010\u6027\u3068\u96ea\u5d29\u52b9\u679c\u3082\u6301\u3064\u3079\u304d\u3067\u3059\u3002</li> <li>\u30cf\u30c3\u30b7\u30e5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u901a\u5e38\u3001\u30cf\u30c3\u30b7\u30e5\u5024\u306e\u5747\u7b49\u5206\u6563\u3092\u4fdd\u8a3c\u3057\u3001\u30cf\u30c3\u30b7\u30e5\u885d\u7a81\u3092\u6e1b\u3089\u3059\u305f\u3081\u306b\u3001\u5927\u304d\u306a\u7d20\u6570\u3092\u5270\u4f59\u3068\u3057\u3066\u4f7f\u7528\u3057\u307e\u3059\u3002</li> <li>\u4e00\u822c\u7684\u306a\u30cf\u30c3\u30b7\u30e5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306b\u306f\u3001MD5\u3001SHA-1\u3001SHA-2\u3001SHA-3\u304c\u3042\u308a\u307e\u3059\u3002MD5\u306f\u30d5\u30a1\u30a4\u30eb\u6574\u5408\u6027\u30c1\u30a7\u30c3\u30af\u306b\u3088\u304f\u4f7f\u7528\u3055\u308c\u3001SHA-2\u306f\u5b89\u5168\u306a\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u3068\u30d7\u30ed\u30c8\u30b3\u30eb\u3067\u4e00\u822c\u7684\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002</li> <li>\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u306f\u901a\u5e38\u3001\u30cf\u30c3\u30b7\u30e5\u8868\u306e\u30d0\u30b1\u30c3\u30c8\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8a08\u7b97\u3059\u308b\u305f\u3081\u306b\u3001\u30c7\u30fc\u30bf\u578b\u306b\u5bfe\u3057\u3066\u7d44\u307f\u8fbc\u307f\u306e\u30cf\u30c3\u30b7\u30e5\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u4e00\u822c\u7684\u306b\u3001\u4e0d\u5909\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u306e\u307f\u304c\u30cf\u30c3\u30b7\u30e5\u53ef\u80fd\u3067\u3059\u3002</li> </ul>"},{"location":"chapter_hashing/summary/#2-q-a","title":"2. \u00a0 Q &amp; A","text":"<p>Q: \u30cf\u30c3\u30b7\u30e5\u8868\u306e\u6642\u9593\u8a08\u7b97\u91cf\u304c\\(O(n)\\)\u306b\u60aa\u5316\u3059\u308b\u306e\u306f\u3044\u3064\u3067\u3059\u304b\uff1f</p> <p>\u30cf\u30c3\u30b7\u30e5\u8868\u306e\u6642\u9593\u8a08\u7b97\u91cf\u306f\u3001\u30cf\u30c3\u30b7\u30e5\u885d\u7a81\u304c\u6df1\u523b\u306a\u5834\u5408\u306b\\(O(n)\\)\u306b\u60aa\u5316\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002\u30cf\u30c3\u30b7\u30e5\u95a2\u6570\u304c\u9069\u5207\u306b\u8a2d\u8a08\u3055\u308c\u3001\u5bb9\u91cf\u304c\u9069\u5207\u306b\u8a2d\u5b9a\u3055\u308c\u3001\u885d\u7a81\u304c\u5747\u7b49\u306b\u5206\u6563\u3055\u308c\u3066\u3044\u308b\u5834\u5408\u3001\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O(1)\\)\u3067\u3059\u3002\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u306e\u7d44\u307f\u8fbc\u307f\u30cf\u30c3\u30b7\u30e5\u8868\u3092\u4f7f\u7528\u3059\u308b\u5834\u5408\u3001\u901a\u5e38\u306f\u6642\u9593\u8a08\u7b97\u91cf\u3092\\(O(1)\\)\u3068\u8003\u3048\u307e\u3059\u3002</p> <p>Q: \u306a\u305c\u30cf\u30c3\u30b7\u30e5\u95a2\u6570\\(f(x) = x\\)\u3092\u4f7f\u7528\u3057\u306a\u3044\u306e\u3067\u3059\u304b\uff1f\u3053\u308c\u306a\u3089\u885d\u7a81\u3092\u6392\u9664\u3067\u304d\u307e\u3059\u3002</p> <p>\u30cf\u30c3\u30b7\u30e5\u95a2\u6570\\(f(x) = x\\)\u3067\u306f\u3001\u5404\u8981\u7d20\u304c\u4e00\u610f\u306e\u30d0\u30b1\u30c3\u30c8\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306b\u5bfe\u5fdc\u3057\u3001\u3053\u308c\u306f\u914d\u5217\u3068\u540c\u7b49\u3067\u3059\u3002\u3057\u304b\u3057\u3001\u5165\u529b\u7a7a\u9593\u306f\u901a\u5e38\u51fa\u529b\u7a7a\u9593\uff08\u914d\u5217\u9577\uff09\u3088\u308a\u3082\u306f\u308b\u304b\u306b\u5927\u304d\u3044\u305f\u3081\u3001\u30cf\u30c3\u30b7\u30e5\u95a2\u6570\u306e\u6700\u5f8c\u306e\u30b9\u30c6\u30c3\u30d7\u306f\u914d\u5217\u9577\u306e\u5270\u4f59\u3092\u53d6\u308b\u3053\u3068\u304c\u3088\u304f\u3042\u308a\u307e\u3059\u3002\u8a00\u3044\u63db\u3048\u308b\u3068\u3001\u30cf\u30c3\u30b7\u30e5\u8868\u306e\u76ee\u6a19\u306f\u3001\\(O(1)\\)\u306e\u30af\u30a8\u30ea\u52b9\u7387\u3092\u63d0\u4f9b\u3057\u306a\u304c\u3089\u3001\u3088\u308a\u5927\u304d\u306a\u72b6\u614b\u7a7a\u9593\u3092\u3088\u308a\u5c0f\u3055\u306a\u3082\u306e\u306b\u30de\u30c3\u30d4\u30f3\u30b0\u3059\u308b\u3053\u3068\u3067\u3059\u3002</p> <p>Q: \u30cf\u30c3\u30b7\u30e5\u8868\u304c\u3053\u308c\u3089\u306e\u69cb\u9020\u3092\u4f7f\u3063\u3066\u5b9f\u88c5\u3055\u308c\u3066\u3044\u308b\u306b\u3082\u304b\u304b\u308f\u3089\u305a\u3001\u306a\u305c\u914d\u5217\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u3001\u4e8c\u5206\u6728\u3088\u308a\u3082\u52b9\u7387\u7684\u306b\u306a\u308c\u308b\u306e\u3067\u3059\u304b\uff1f</p> <p>\u307e\u305a\u3001\u30cf\u30c3\u30b7\u30e5\u8868\u306f\u6642\u9593\u52b9\u7387\u304c\u9ad8\u3044\u3067\u3059\u304c\u3001\u7a7a\u9593\u52b9\u7387\u306f\u4f4e\u3044\u3067\u3059\u3002\u30cf\u30c3\u30b7\u30e5\u8868\u306e\u30e1\u30e2\u30ea\u306e\u5927\u90e8\u5206\u306f\u672a\u4f7f\u7528\u306e\u307e\u307e\u3067\u3059\u3002</p> <p>\u6b21\u306b\u3001\u30cf\u30c3\u30b7\u30e5\u8868\u306f\u7279\u5b9a\u306e\u30e6\u30fc\u30b9\u30b1\u30fc\u30b9\u3067\u306e\u307f\u6642\u9593\u52b9\u7387\u304c\u9ad8\u3044\u3067\u3059\u3002\u914d\u5217\u3084\u9023\u7d50\u30ea\u30b9\u30c8\u3092\u4f7f\u7528\u3057\u3066\u540c\u3058\u6642\u9593\u8a08\u7b97\u91cf\u3067\u6a5f\u80fd\u3092\u5b9f\u88c5\u3067\u304d\u308b\u5834\u5408\u3001\u901a\u5e38\u306f\u30cf\u30c3\u30b7\u30e5\u8868\u3092\u4f7f\u7528\u3059\u308b\u3088\u308a\u3082\u9ad8\u901f\u3067\u3059\u3002\u3053\u308c\u306f\u3001\u30cf\u30c3\u30b7\u30e5\u95a2\u6570\u306e\u8a08\u7b97\u304c\u30aa\u30fc\u30d0\u30fc\u30d8\u30c3\u30c9\u3092\u767a\u751f\u3055\u305b\u3001\u6642\u9593\u8a08\u7b97\u91cf\u306e\u5b9a\u6570\u56e0\u5b50\u304c\u5927\u304d\u304f\u306a\u308b\u305f\u3081\u3067\u3059\u3002</p> <p>\u6700\u5f8c\u306b\u3001\u30cf\u30c3\u30b7\u30e5\u8868\u306e\u6642\u9593\u8a08\u7b97\u91cf\u306f\u60aa\u5316\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u9023\u9396\u6cd5\u3067\u306f\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u3084\u8d64\u9ed2\u6728\u3067\u691c\u7d22\u64cd\u4f5c\u3092\u5b9f\u884c\u3057\u3001\u3053\u308c\u306f\u4f9d\u7136\u3068\u3057\u3066\\(O(n)\\)\u6642\u9593\u306b\u60aa\u5316\u3059\u308b\u30ea\u30b9\u30af\u304c\u3042\u308a\u307e\u3059\u3002</p> <p>Q: \u591a\u91cd\u30cf\u30c3\u30b7\u30e5\u306b\u3082\u8981\u7d20\u3092\u76f4\u63a5\u524a\u9664\u3067\u304d\u306a\u3044\u3068\u3044\u3046\u6b20\u9665\u304c\u3042\u308a\u307e\u3059\u304b\uff1f\u524a\u9664\u3068\u3057\u3066\u30de\u30fc\u30af\u3055\u308c\u305f\u7a7a\u9593\u306f\u518d\u5229\u7528\u3067\u304d\u307e\u3059\u304b\uff1f</p> <p>\u591a\u91cd\u30cf\u30c3\u30b7\u30e5\u306f\u30aa\u30fc\u30d7\u30f3\u30a2\u30c9\u30ec\u30b9\u6cd5\u306e\u4e00\u5f62\u614b\u3067\u3042\u308a\u3001\u3059\u3079\u3066\u306e\u30aa\u30fc\u30d7\u30f3\u30a2\u30c9\u30ec\u30b9\u6cd5\u306b\u306f\u8981\u7d20\u3092\u76f4\u63a5\u524a\u9664\u3067\u304d\u306a\u3044\u3068\u3044\u3046\u6b20\u70b9\u304c\u3042\u308a\u307e\u3059\u3002\u8981\u7d20\u3092\u524a\u9664\u6e08\u307f\u3068\u3057\u3066\u30de\u30fc\u30af\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u30de\u30fc\u30af\u3055\u308c\u305f\u7a7a\u9593\u306f\u518d\u5229\u7528\u3067\u304d\u307e\u3059\u3002\u30cf\u30c3\u30b7\u30e5\u8868\u306b\u65b0\u3057\u3044\u8981\u7d20\u3092\u633f\u5165\u3059\u308b\u969b\u3001\u30cf\u30c3\u30b7\u30e5\u95a2\u6570\u304c\u524a\u9664\u6e08\u307f\u3068\u3057\u3066\u30de\u30fc\u30af\u3055\u308c\u305f\u4f4d\u7f6e\u3092\u6307\u3057\u3066\u3044\u308b\u5834\u5408\u3001\u305d\u306e\u4f4d\u7f6e\u306f\u65b0\u3057\u3044\u8981\u7d20\u306b\u3088\u3063\u3066\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u30cf\u30c3\u30b7\u30e5\u8868\u306e\u30d7\u30ed\u30fc\u30d6\u30b7\u30fc\u30b1\u30f3\u30b9\u3092\u7dad\u6301\u3057\u306a\u304c\u3089\u3001\u7a7a\u9593\u306e\u52b9\u7387\u7684\u306a\u4f7f\u7528\u304c\u4fdd\u8a3c\u3055\u308c\u307e\u3059\u3002</p> <p>Q: \u306a\u305c\u7dda\u5f62\u30d7\u30ed\u30fc\u30d6\u306e\u691c\u7d22\u30d7\u30ed\u30bb\u30b9\u4e2d\u306b\u30cf\u30c3\u30b7\u30e5\u885d\u7a81\u304c\u767a\u751f\u3059\u308b\u306e\u3067\u3059\u304b\uff1f</p> <p>\u691c\u7d22\u30d7\u30ed\u30bb\u30b9\u4e2d\u3001\u30cf\u30c3\u30b7\u30e5\u95a2\u6570\u306f\u5bfe\u5fdc\u3059\u308b\u30d0\u30b1\u30c3\u30c8\u3068\u30ad\u30fc\u5024\u30da\u30a2\u3092\u6307\u3057\u307e\u3059\u3002<code>key</code>\u304c\u4e00\u81f4\u3057\u306a\u3044\u5834\u5408\u3001\u30cf\u30c3\u30b7\u30e5\u885d\u7a81\u3092\u793a\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u7dda\u5f62\u30d7\u30ed\u30fc\u30d6\u306f\u6b63\u3057\u3044\u30ad\u30fc\u5024\u30da\u30a2\u304c\u898b\u3064\u304b\u308b\u304b\u691c\u7d22\u304c\u5931\u6557\u3059\u308b\u307e\u3067\u3001\u4e8b\u524d\u306b\u6c7a\u3081\u3089\u308c\u305f\u30b9\u30c6\u30c3\u30d7\u30b5\u30a4\u30ba\u3067\u4e0b\u65b9\u5411\u306b\u691c\u7d22\u3057\u307e\u3059\u3002</p> <p>Q: \u306a\u305c\u30cf\u30c3\u30b7\u30e5\u8868\u306e\u30ea\u30b5\u30a4\u30ba\u304c\u30cf\u30c3\u30b7\u30e5\u885d\u7a81\u3092\u7de9\u548c\u3067\u304d\u308b\u306e\u3067\u3059\u304b\uff1f</p> <p>\u30cf\u30c3\u30b7\u30e5\u95a2\u6570\u306e\u6700\u5f8c\u306e\u30b9\u30c6\u30c3\u30d7\u306f\u3001\u51fa\u529b\u3092\u914d\u5217\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u7bc4\u56f2\u5185\u306b\u4fdd\u3064\u305f\u3081\u306b\u3001\u914d\u5217\u9577\\(n\\)\u306e\u5270\u4f59\u3092\u53d6\u308b\u3053\u3068\u304c\u3088\u304f\u3042\u308a\u307e\u3059\u3002\u30ea\u30b5\u30a4\u30ba\u6642\u3001\u914d\u5217\u9577\\(n\\)\u304c\u5909\u5316\u3057\u3001\u30ad\u30fc\u306b\u5bfe\u5fdc\u3059\u308b\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3082\u5909\u5316\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002\u4ee5\u524d\u306b\u540c\u3058\u30d0\u30b1\u30c3\u30c8\u306b\u30de\u30c3\u30d4\u30f3\u30b0\u3055\u308c\u3066\u3044\u305f\u30ad\u30fc\u304c\u3001\u30ea\u30b5\u30a4\u30ba\u5f8c\u306b\u8907\u6570\u306e\u30d0\u30b1\u30c3\u30c8\u306b\u5206\u6563\u3055\u308c\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u3001\u305d\u308c\u306b\u3088\u3063\u3066\u30cf\u30c3\u30b7\u30e5\u885d\u7a81\u304c\u7de9\u548c\u3055\u308c\u307e\u3059\u3002</p>"},{"location":"chapter_heap/","title":"\u7b2c 8 \u7ae0 \u00a0 \u30d2\u30fc\u30d7","text":"<p>Abstract</p> <p>\u30d2\u30fc\u30d7\u306f\u5c71\u3068\u305d\u306e\u967a\u3057\u3044\u5cf0\u306e\u3088\u3046\u306b\u3001\u5c64\u3092\u306a\u3057\u3066\u8d77\u4f0f\u3057\u3001\u305d\u308c\u305e\u308c\u304c\u72ec\u7279\u306e\u5f62\u3092\u6301\u3063\u3066\u3044\u307e\u3059\u3002</p> <p>\u5404\u5c71\u306e\u9802\u306f\u6563\u3089\u3070\u3063\u305f\u9ad8\u3055\u3067\u4e0a\u4e0b\u3057\u307e\u3059\u304c\u3001\u6700\u3082\u9ad8\u3044\u3082\u306e\u304c\u5e38\u306b\u6700\u521d\u306b\u6ce8\u76ee\u3092\u96c6\u3081\u307e\u3059\u3002</p>"},{"location":"chapter_heap/#_1","title":"\u7ae0\u306e\u5185\u5bb9","text":"<ul> <li>8.1 \u00a0 \u30d2\u30fc\u30d7</li> <li>8.2 \u00a0 \u30d2\u30fc\u30d7\u306e\u69cb\u7bc9</li> <li>8.3 \u00a0 Top-k\u554f\u984c</li> <li>8.4 \u00a0 \u307e\u3068\u3081</li> </ul>"},{"location":"chapter_heap/build_heap/","title":"8.2 \u00a0 \u30d2\u30fc\u30d7\u69cb\u7bc9\u64cd\u4f5c","text":"<p>\u5834\u5408\u306b\u3088\u3063\u3066\u306f\u3001\u30ea\u30b9\u30c8\u306e\u3059\u3079\u3066\u306e\u8981\u7d20\u3092\u4f7f\u7528\u3057\u3066\u30d2\u30fc\u30d7\u3092\u69cb\u7bc9\u3057\u305f\u3044\u3053\u3068\u304c\u3042\u308a\u3001\u3053\u306e\u30d7\u30ed\u30bb\u30b9\u306f\u300c\u30d2\u30fc\u30d7\u69cb\u7bc9\u64cd\u4f5c\u300d\u3068\u3057\u3066\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\u3002</p>"},{"location":"chapter_heap/build_heap/#821","title":"8.2.1 \u00a0 \u30d2\u30fc\u30d7\u633f\u5165\u64cd\u4f5c\u306b\u3088\u308b\u5b9f\u88c5","text":"<p>\u307e\u305a\u3001\u7a7a\u306e\u30d2\u30fc\u30d7\u3092\u4f5c\u6210\u3057\u3001\u6b21\u306b\u30ea\u30b9\u30c8\u3092\u53cd\u5fa9\u51e6\u7406\u3057\u3066\u3001\u5404\u8981\u7d20\u306b\u5bfe\u3057\u3066\u9806\u756a\u306b\u300c\u30d2\u30fc\u30d7\u633f\u5165\u64cd\u4f5c\u300d\u3092\u5b9f\u884c\u3057\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u8981\u7d20\u3092\u30d2\u30fc\u30d7\u306e\u672b\u5c3e\u306b\u8ffd\u52a0\u3057\u3001\u6b21\u306b\u4e0b\u304b\u3089\u4e0a\u306b\u300c\u30d2\u30fc\u30d7\u5316\u300d\u3059\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002</p> <p>\u30d2\u30fc\u30d7\u306b\u8981\u7d20\u304c\u8ffd\u52a0\u3055\u308c\u308b\u305f\u3073\u306b\u3001\u30d2\u30fc\u30d7\u306e\u9577\u3055\u306f1\u3064\u305a\u3064\u5897\u52a0\u3057\u307e\u3059\u3002\u30ce\u30fc\u30c9\u306f\u4e8c\u5206\u6728\u306b\u4e0a\u304b\u3089\u4e0b\u306b\u8ffd\u52a0\u3055\u308c\u308b\u305f\u3081\u3001\u30d2\u30fc\u30d7\u306f\u300c\u4e0a\u304b\u3089\u4e0b\u306b\u300d\u69cb\u7bc9\u3055\u308c\u307e\u3059\u3002</p> <p>\u8981\u7d20\u6570\u3092\\(n\\)\u3068\u3059\u308b\u3068\u3001\u5404\u8981\u7d20\u306e\u633f\u5165\u64cd\u4f5c\u306f\\(O(\\log{n})\\)\u6642\u9593\u304b\u304b\u308b\u305f\u3081\u3001\u3053\u306e\u30d2\u30fc\u30d7\u69cb\u7bc9\u65b9\u6cd5\u306e\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O(n \\log n)\\)\u3067\u3059\u3002</p>"},{"location":"chapter_heap/build_heap/#822","title":"8.2.2 \u00a0 \u8d70\u67fb\u306b\u3088\u308b\u30d2\u30fc\u30d7\u5316\u306e\u5b9f\u88c5","text":"<p>\u5b9f\u969b\u306b\u306f\u30012\u3064\u306e\u30b9\u30c6\u30c3\u30d7\u3067\u3088\u308a\u52b9\u7387\u7684\u306a\u30d2\u30fc\u30d7\u69cb\u7bc9\u65b9\u6cd5\u3092\u5b9f\u88c5\u3067\u304d\u307e\u3059\u3002</p> <ol> <li>\u30ea\u30b9\u30c8\u306e\u3059\u3079\u3066\u306e\u8981\u7d20\u3092\u305d\u306e\u307e\u307e\u30d2\u30fc\u30d7\u306b\u8ffd\u52a0\u3057\u307e\u3059\u3002\u3053\u306e\u6642\u70b9\u3067\u306f\u3001\u30d2\u30fc\u30d7\u306e\u6027\u8cea\u306f\u307e\u3060\u6e80\u305f\u3055\u308c\u3066\u3044\u307e\u305b\u3093\u3002</li> <li>\u30d2\u30fc\u30d7\u3092\u9006\u9806\uff08\u30ec\u30d9\u30eb\u9806\u8d70\u67fb\u306e\u9006\uff09\u3067\u8d70\u67fb\u3057\u3001\u5404\u975e\u8449\u30ce\u30fc\u30c9\u306b\u5bfe\u3057\u3066\u300c\u4e0a\u304b\u3089\u4e0b\u306e\u30d2\u30fc\u30d7\u5316\u300d\u3092\u5b9f\u884c\u3057\u307e\u3059\u3002</li> </ol> <p>\u30ce\u30fc\u30c9\u3092\u30d2\u30fc\u30d7\u5316\u3057\u305f\u5f8c\u3001\u305d\u306e\u30ce\u30fc\u30c9\u3092\u6839\u3068\u3059\u308b\u90e8\u5206\u6728\u306f\u6709\u52b9\u306a\u90e8\u5206\u30d2\u30fc\u30d7\u306b\u306a\u308a\u307e\u3059\u3002\u8d70\u67fb\u304c\u9006\u9806\u3067\u3042\u308b\u305f\u3081\u3001\u30d2\u30fc\u30d7\u306f\u300c\u4e0b\u304b\u3089\u4e0a\u306b\u300d\u69cb\u7bc9\u3055\u308c\u307e\u3059\u3002</p> <p>\u9006\u8d70\u67fb\u3092\u9078\u629e\u3059\u308b\u7406\u7531\u306f\u3001\u73fe\u5728\u306e\u30ce\u30fc\u30c9\u306e\u4e0b\u306e\u90e8\u5206\u6728\u304c\u3059\u3067\u306b\u6709\u52b9\u306a\u90e8\u5206\u30d2\u30fc\u30d7\u3067\u3042\u308b\u3053\u3068\u3092\u4fdd\u8a3c\u3057\u3001\u73fe\u5728\u306e\u30ce\u30fc\u30c9\u306e\u30d2\u30fc\u30d7\u5316\u3092\u52b9\u679c\u7684\u306b\u3059\u308b\u305f\u3081\u3067\u3059\u3002</p> <p>\u8a00\u53ca\u3059\u308b\u4fa1\u5024\u304c\u3042\u308b\u306e\u306f\u3001**\u8449\u30ce\u30fc\u30c9\u306f\u5b50\u3092\u6301\u305f\u306a\u3044\u305f\u3081\u3001\u81ea\u7136\u306b\u6709\u52b9\u306a\u90e8\u5206\u30d2\u30fc\u30d7\u3092\u5f62\u6210\u3057\u3001\u30d2\u30fc\u30d7\u5316\u3059\u308b\u5fc5\u8981\u304c\u306a\u3044**\u3068\u3044\u3046\u3053\u3068\u3067\u3059\u3002\u4ee5\u4e0b\u306e\u30b3\u30fc\u30c9\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u6700\u5f8c\u306e\u975e\u8449\u30ce\u30fc\u30c9\u306f\u6700\u5f8c\u306e\u30ce\u30fc\u30c9\u306e\u89aa\u3067\u3059\u3002\u305d\u3053\u304b\u3089\u958b\u59cb\u3057\u3066\u9006\u9806\u306b\u8d70\u67fb\u3057\u3066\u30d2\u30fc\u30d7\u5316\u3092\u5b9f\u884c\u3057\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig my_heap.py<pre><code>def __init__(self, nums: list[int]):\n    \"\"\"\u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf\u3001\u5165\u529b\u30ea\u30b9\u30c8\u306b\u57fa\u3065\u3044\u3066\u30d2\u30fc\u30d7\u3092\u69cb\u7bc9\"\"\"\n    # \u3059\u3079\u3066\u306e\u30ea\u30b9\u30c8\u8981\u7d20\u3092\u30d2\u30fc\u30d7\u306b\u8ffd\u52a0\n    self.max_heap = nums\n    # \u8449\u4ee5\u5916\u306e\u3059\u3079\u3066\u306e\u30ce\u30fc\u30c9\u3092\u30d2\u30fc\u30d7\u5316\n    for i in range(self.parent(self.size() - 1), -1, -1):\n        self.sift_down(i)\n</code></pre> my_heap.cpp<pre><code>/* \u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf\u3001\u5165\u529b\u30ea\u30b9\u30c8\u306b\u57fa\u3065\u3044\u3066\u30d2\u30fc\u30d7\u3092\u69cb\u7bc9 */\nMaxHeap(vector&lt;int&gt; nums) {\n    // \u3059\u3079\u3066\u306e\u30ea\u30b9\u30c8\u8981\u7d20\u3092\u30d2\u30fc\u30d7\u306b\u8ffd\u52a0\n    maxHeap = nums;\n    // \u8449\u4ee5\u5916\u306e\u3059\u3079\u3066\u306e\u30ce\u30fc\u30c9\u3092\u30d2\u30fc\u30d7\u5316\n    for (int i = parent(size() - 1); i &gt;= 0; i--) {\n        siftDown(i);\n    }\n}\n</code></pre> my_heap.java<pre><code>/* \u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf\u3001\u5165\u529b\u30ea\u30b9\u30c8\u306b\u57fa\u3065\u3044\u3066\u30d2\u30fc\u30d7\u3092\u69cb\u7bc9 */\nMaxHeap(List&lt;Integer&gt; nums) {\n    // \u3059\u3079\u3066\u306e\u30ea\u30b9\u30c8\u8981\u7d20\u3092\u30d2\u30fc\u30d7\u306b\u8ffd\u52a0\n    maxHeap = new ArrayList&lt;&gt;(nums);\n    // \u8449\u3092\u9664\u304f\u3059\u3079\u3066\u306e\u30ce\u30fc\u30c9\u3092\u30d2\u30fc\u30d7\u5316\n    for (int i = parent(size() - 1); i &gt;= 0; i--) {\n        siftDown(i);\n    }\n}\n</code></pre> my_heap.cs<pre><code>[class]{MaxHeap}-[func]{MaxHeap}\n</code></pre> my_heap.go<pre><code>[class]{maxHeap}-[func]{newMaxHeap}\n</code></pre> my_heap.swift<pre><code>[class]{MaxHeap}-[func]{init}\n</code></pre> my_heap.js<pre><code>[class]{MaxHeap}-[func]{constructor}\n</code></pre> my_heap.ts<pre><code>[class]{MaxHeap}-[func]{constructor}\n</code></pre> my_heap.dart<pre><code>[class]{MaxHeap}-[func]{MaxHeap}\n</code></pre> my_heap.rs<pre><code>[class]{MaxHeap}-[func]{new}\n</code></pre> my_heap.c<pre><code>[class]{MaxHeap}-[func]{newMaxHeap}\n</code></pre> my_heap.kt<pre><code>[class]{MaxHeap}-[func]{}\n</code></pre> my_heap.rb<pre><code>[class]{MaxHeap}-[func]{initialize}\n</code></pre> my_heap.zig<pre><code>[class]{MaxHeap}-[func]{init}\n</code></pre>"},{"location":"chapter_heap/build_heap/#823","title":"8.2.3 \u00a0 \u8a08\u7b97\u91cf\u5206\u6790","text":"<p>\u6b21\u306b\u3001\u3053\u306e\u7b2c2\u306e\u30d2\u30fc\u30d7\u69cb\u7bc9\u65b9\u6cd5\u306e\u6642\u9593\u8a08\u7b97\u91cf\u3092\u8a08\u7b97\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002</p> <ul> <li>\u5b8c\u5099\u4e8c\u5206\u6728\u306e\u30ce\u30fc\u30c9\u6570\u3092\\(n\\)\u3068\u4eee\u5b9a\u3059\u308b\u3068\u3001\u8449\u30ce\u30fc\u30c9\u306e\u6570\u306f\\((n + 1) / 2\\)\u3067\u3059\u3002\u3053\u3053\u3067\\(/\\) \u306f\u6574\u6570\u9664\u7b97\u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u30d2\u30fc\u30d7\u5316\u304c\u5fc5\u8981\u306a\u30ce\u30fc\u30c9\u306e\u6570\u306f\\((n - 1) / 2\\)\u3067\u3059\u3002</li> <li>\u300c\u4e0a\u304b\u3089\u4e0b\u306e\u30d2\u30fc\u30d7\u5316\u300d\u306e\u30d7\u30ed\u30bb\u30b9\u3067\u306f\u3001\u5404\u30ce\u30fc\u30c9\u306f\u6700\u5927\u3067\u8449\u30ce\u30fc\u30c9\u307e\u3067\u30d2\u30fc\u30d7\u5316\u3055\u308c\u308b\u305f\u3081\u3001\u6700\u5927\u53cd\u5fa9\u56de\u6570\u306f\u4e8c\u5206\u6728\u306e\u9ad8\u3055\\(\\log n\\)\u3067\u3059\u3002</li> </ul> <p>\u3053\u306e2\u3064\u3092\u639b\u3051\u5408\u308f\u305b\u308b\u3068\u3001\u30d2\u30fc\u30d7\u69cb\u7bc9\u30d7\u30ed\u30bb\u30b9\u306e\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O(n \\log n)\\)\u3068\u306a\u308a\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u3053\u306e\u63a8\u5b9a\u306f\u6b63\u78ba\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u4e8c\u5206\u6728\u306e\u4e0b\u4f4d\u30ec\u30d9\u30eb\u306b\u306f\u4e0a\u4f4d\u3088\u308a\u3082\u306f\u308b\u304b\u306b\u591a\u304f\u306e\u30ce\u30fc\u30c9\u304c\u3042\u308b\u3068\u3044\u3046\u6027\u8cea\u3092\u8003\u616e\u3057\u3066\u3044\u306a\u3044\u304b\u3089\u3067\u3059\u3002</p> <p>\u3088\u308a\u6b63\u78ba\u306a\u8a08\u7b97\u3092\u884c\u3044\u307e\u3057\u3087\u3046\u3002\u8a08\u7b97\u3092\u7c21\u7d20\u5316\u3059\u308b\u305f\u3081\u3001\\(n\\)\u500b\u306e\u30ce\u30fc\u30c9\u3068\u9ad8\u3055\\(h\\)\u3092\u6301\u3064\u300c\u5b8c\u5168\u4e8c\u5206\u6728\u300d\u3092\u4eee\u5b9a\u3057\u307e\u3059\u3002\u3053\u306e\u4eee\u5b9a\u306f\u7d50\u679c\u306e\u6b63\u78ba\u6027\u306b\u5f71\u97ff\u3057\u307e\u305b\u3093\u3002</p> <p></p> <p> \u56f3 8-5 \u00a0 \u5b8c\u5168\u4e8c\u5206\u6728\u306e\u5404\u30ec\u30d9\u30eb\u306e\u30ce\u30fc\u30c9\u6570 </p> <p>\u4e0a\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u30ce\u30fc\u30c9\u304c\u300c\u4e0a\u304b\u3089\u4e0b\u306b\u30d2\u30fc\u30d7\u5316\u3055\u308c\u308b\u300d\u6700\u5927\u53cd\u5fa9\u56de\u6570\u306f\u3001\u305d\u306e\u30ce\u30fc\u30c9\u304b\u3089\u8449\u30ce\u30fc\u30c9\u307e\u3067\u306e\u8ddd\u96e2\u3068\u7b49\u3057\u304f\u3001\u3053\u308c\u306f\u6b63\u78ba\u306b\u300c\u30ce\u30fc\u30c9\u306e\u9ad8\u3055\u300d\u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u5404\u30ec\u30d9\u30eb\u3067\u300c\u30ce\u30fc\u30c9\u6570\u00d7\u30ce\u30fc\u30c9\u306e\u9ad8\u3055\u300d\u3092\u5408\u8a08\u3057\u3066\u3001**\u3059\u3079\u3066\u306e\u30ce\u30fc\u30c9\u306e\u7dcf\u30d2\u30fc\u30d7\u5316\u53cd\u5fa9\u56de\u6570\u3092\u5f97\u308b**\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002</p> \\[ T(h) = 2^0h + 2^1(h-1) + 2^2(h-2) + \\dots + 2^{(h-1)}\\times1 \\] <p>\u4e0a\u8a18\u306e\u65b9\u7a0b\u5f0f\u3092\u7c21\u7d20\u5316\u3059\u308b\u305f\u3081\u306b\u3001\u9ad8\u6821\u306e\u6570\u5217\u306e\u77e5\u8b58\u3092\u4f7f\u7528\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u307e\u305a\\(T(h)\\)\u306b\\(2\\)\u3092\u639b\u3051\u3066\u4ee5\u4e0b\u3092\u5f97\u307e\u3059\uff1a</p> \\[ \\begin{aligned} T(h) &amp; = 2^0h + 2^1(h-1) + 2^2(h-2) + \\dots + 2^{h-1}\\times1 \\newline 2T(h) &amp; = 2^1h + 2^2(h-1) + 2^3(h-2) + \\dots + 2^h\\times1 \\newline \\end{aligned} \\] <p>\u5909\u4f4d\u6cd5\u3092\u4f7f\u7528\u3057\u3066\\(2T(h)\\)\u304b\u3089\\(T(h)\\)\u3092\u6e1b\u7b97\u3059\u308b\u3068\u3001\u4ee5\u4e0b\u3092\u5f97\u307e\u3059\uff1a</p> \\[ 2T(h) - T(h) = T(h) = -2^0h + 2^1 + 2^2 + \\dots + 2^{h-1} + 2^h \\] <p>\u65b9\u7a0b\u5f0f\u3092\u89b3\u5bdf\u3059\u308b\u3068\u3001\\(T(h)\\)\u306f\u7b49\u6bd4\u6570\u5217\u3067\u3042\u308a\u3001\u548c\u306e\u516c\u5f0f\u3092\u4f7f\u7528\u3057\u3066\u76f4\u63a5\u8a08\u7b97\u3067\u304d\u3001\u6642\u9593\u8a08\u7b97\u91cf\u306f\u4ee5\u4e0b\u306b\u306a\u308a\u307e\u3059\uff1a</p> \\[ \\begin{aligned} T(h) &amp; = 2 \\frac{1 - 2^h}{1 - 2} - h \\newline &amp; = 2^{h+1} - h - 2 \\newline &amp; = O(2^h) \\end{aligned} \\] <p>\u3055\u3089\u306b\u3001\u9ad8\u3055\\(h\\)\u306e\u5b8c\u5168\u4e8c\u5206\u6728\u306f\\(n = 2^{h+1} - 1\\)\u500b\u306e\u30ce\u30fc\u30c9\u3092\u6301\u3064\u305f\u3081\u3001\u8a08\u7b97\u91cf\u306f\\(O(2^h) = O(n)\\)\u3067\u3059\u3002\u3053\u306e\u8a08\u7b97\u306f\u3001**\u30ea\u30b9\u30c8\u3092\u5165\u529b\u3057\u3066\u30d2\u30fc\u30d7\u3092\u69cb\u7bc9\u3059\u308b\u6642\u9593\u8a08\u7b97\u91cf\u304c\\(O(n)\\)\u3067\u3042\u308a\u3001\u975e\u5e38\u306b\u52b9\u7387\u7684\u3067\u3042\u308b**\u3053\u3068\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002</p>"},{"location":"chapter_heap/heap/","title":"8.1 \u00a0 \u30d2\u30fc\u30d7","text":"<p>\u30d2\u30fc\u30d7\u306f\u7279\u5b9a\u306e\u6761\u4ef6\u3092\u6e80\u305f\u3059\u5b8c\u5099\u4e8c\u5206\u6728\u3067\u3001\u4e3b\u306b\u6b21\u306e2\u3064\u306e\u30bf\u30a4\u30d7\u306b\u5206\u985e\u3055\u308c\u307e\u3059\uff08\u4e0b\u56f3\u53c2\u7167\uff09\u3002</p> <ul> <li>\u6700\u5c0f\u30d2\u30fc\u30d7\uff1a\u4efb\u610f\u306e\u30ce\u30fc\u30c9\u306e\u5024 \\(\\leq\\) \u305d\u306e\u5b50\u30ce\u30fc\u30c9\u306e\u5024\u3002</li> <li>\u6700\u5927\u30d2\u30fc\u30d7\uff1a\u4efb\u610f\u306e\u30ce\u30fc\u30c9\u306e\u5024 \\(\\geq\\) \u305d\u306e\u5b50\u30ce\u30fc\u30c9\u306e\u5024\u3002</li> </ul> <p></p> <p> \u56f3 8-1 \u00a0 \u6700\u5c0f\u30d2\u30fc\u30d7\u3068\u6700\u5927\u30d2\u30fc\u30d7 </p> <p>\u5b8c\u5099\u4e8c\u5206\u6728\u306e\u7279\u5225\u306a\u30b1\u30fc\u30b9\u3068\u3057\u3066\u3001\u30d2\u30fc\u30d7\u306b\u306f\u4ee5\u4e0b\u306e\u7279\u6027\u304c\u3042\u308a\u307e\u3059\uff1a</p> <ul> <li>\u6700\u4e0b\u4f4d\u5c64\u306e\u30ce\u30fc\u30c9\u306f\u5de6\u304b\u3089\u53f3\u306b\u57cb\u3081\u3089\u308c\u3001\u4ed6\u306e\u5c64\u306e\u30ce\u30fc\u30c9\u306f\u5b8c\u5168\u306b\u57cb\u3081\u3089\u308c\u3066\u3044\u307e\u3059\u3002</li> <li>\u4e8c\u5206\u6728\u306e\u6839\u30ce\u30fc\u30c9\u3092\u30d2\u30fc\u30d7\u306e\u300c\u5148\u982d\u300d\u3068\u547c\u3073\u3001\u6700\u3082\u53f3\u4e0b\u306e\u30ce\u30fc\u30c9\u3092\u30d2\u30fc\u30d7\u306e\u300c\u672b\u5c3e\u300d\u3068\u547c\u3073\u307e\u3059\u3002</li> <li>\u6700\u5927\u30d2\u30fc\u30d7\uff08\u6700\u5c0f\u30d2\u30fc\u30d7\uff09\u306e\u5834\u5408\u3001\u5148\u982d\u8981\u7d20\uff08\u6839\uff09\u306e\u5024\u306f\u3059\u3079\u3066\u306e\u8981\u7d20\u306e\u4e2d\u3067\u6700\u5927\uff08\u6700\u5c0f\uff09\u3067\u3059\u3002</li> </ul>"},{"location":"chapter_heap/heap/#811","title":"8.1.1 \u00a0 \u30d2\u30fc\u30d7\u306e\u4e00\u822c\u7684\u306a\u64cd\u4f5c","text":"<p>\u591a\u304f\u306e\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u304c\u512a\u5148\u5ea6\u30ad\u30e5\u30fc\u3092\u63d0\u4f9b\u3057\u3066\u3044\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u3053\u308c\u306f\u512a\u5148\u5ea6\u4ed8\u304d\u30bd\u30fc\u30c8\u3092\u6301\u3064\u30ad\u30e5\u30fc\u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u308b\u62bd\u8c61\u30c7\u30fc\u30bf\u69cb\u9020\u3067\u3059\u3002</p> <p>\u5b9f\u969b\u306b\u306f\u3001\u30d2\u30fc\u30d7\u306f\u512a\u5148\u5ea6\u30ad\u30e5\u30fc\u3092\u5b9f\u88c5\u3059\u308b\u305f\u3081\u306b\u3088\u304f\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u6700\u5927\u30d2\u30fc\u30d7\u306f\u3001\u8981\u7d20\u304c\u964d\u9806\u3067\u30c7\u30ad\u30e5\u30fc\u3055\u308c\u308b\u512a\u5148\u5ea6\u30ad\u30e5\u30fc\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002\u4f7f\u7528\u306e\u89b3\u70b9\u304b\u3089\u3001\u300c\u512a\u5148\u5ea6\u30ad\u30e5\u30fc\u300d\u3068\u300c\u30d2\u30fc\u30d7\u300d\u3092\u540c\u7b49\u306e\u30c7\u30fc\u30bf\u69cb\u9020\u3068\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u3053\u306e\u672c\u3067\u306f\u4e21\u8005\u3092\u7279\u5225\u306b\u533a\u5225\u305b\u305a\u3001\u7d71\u4e00\u3057\u3066\u300c\u30d2\u30fc\u30d7\u300d\u3068\u547c\u3073\u307e\u3059\u3002</p> <p>\u30d2\u30fc\u30d7\u306e\u4e00\u822c\u7684\u306a\u64cd\u4f5c\u3092\u4e0b\u8868\u306b\u793a\u3057\u307e\u3059\u3002\u30e1\u30bd\u30c3\u30c9\u540d\u306f\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u306b\u3088\u3063\u3066\u7570\u306a\u308b\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002</p> <p> \u8868 8-1 \u00a0 \u30d2\u30fc\u30d7\u64cd\u4f5c\u306e\u52b9\u7387 </p> \u30e1\u30bd\u30c3\u30c9\u540d \u8aac\u660e \u6642\u9593\u8a08\u7b97\u91cf <code>push()</code> \u30d2\u30fc\u30d7\u306b\u8981\u7d20\u3092\u8ffd\u52a0 \\(O(\\log n)\\) <code>pop()</code> \u30d2\u30fc\u30d7\u304b\u3089\u5148\u982d\u8981\u7d20\u3092\u524a\u9664 \\(O(\\log n)\\) <code>peek()</code> \u5148\u982d\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9\uff08\u6700\u5927/\u6700\u5c0f\u30d2\u30fc\u30d7\u306e\u5834\u5408\u3001\u6700\u5927/\u6700\u5c0f\u5024\uff09 \\(O(1)\\) <code>size()</code> \u30d2\u30fc\u30d7\u5185\u306e\u8981\u7d20\u6570\u3092\u53d6\u5f97 \\(O(1)\\) <code>isEmpty()</code> \u30d2\u30fc\u30d7\u304c\u7a7a\u304b\u3069\u3046\u304b\u3092\u30c1\u30a7\u30c3\u30af \\(O(1)\\) <p>\u5b9f\u969b\u306b\u306f\u3001\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u306b\u3088\u3063\u3066\u63d0\u4f9b\u3055\u308c\u308b\u30d2\u30fc\u30d7\u30af\u30e9\u30b9\uff08\u307e\u305f\u306f\u512a\u5148\u5ea6\u30ad\u30e5\u30fc\u30af\u30e9\u30b9\uff09\u3092\u76f4\u63a5\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002</p> <p>\u30bd\u30fc\u30c8\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u300c\u6607\u9806\u300d\u3068\u300c\u964d\u9806\u300d\u304c\u3042\u308b\u3088\u3046\u306b\u3001<code>flag</code>\u3092\u8a2d\u5b9a\u3059\u308b\u304b<code>Comparator</code>\u3092\u5909\u66f4\u3059\u308b\u3053\u3068\u3067\u300c\u6700\u5c0f\u30d2\u30fc\u30d7\u300d\u3068\u300c\u6700\u5927\u30d2\u30fc\u30d7\u300d\u3092\u5207\u308a\u66ff\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u30b3\u30fc\u30c9\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig heap.py<pre><code># \u6700\u5c0f\u30d2\u30fc\u30d7\u306e\u521d\u671f\u5316\nmin_heap, flag = [], 1\n# \u6700\u5927\u30d2\u30fc\u30d7\u306e\u521d\u671f\u5316\nmax_heap, flag = [], -1\n\n# Python\u306eheapq\u30e2\u30b8\u30e5\u30fc\u30eb\u306f\u30c7\u30d5\u30a9\u30eb\u30c8\u3067\u6700\u5c0f\u30d2\u30fc\u30d7\u3092\u5b9f\u88c5\n# \u8981\u7d20\u3092\u30d2\u30fc\u30d7\u306b\u30d7\u30c3\u30b7\u30e5\u3059\u308b\u524d\u306b\u8ca0\u306e\u5024\u306b\u3059\u308b\u3053\u3068\u3067\u3001\u9806\u5e8f\u3092\u53cd\u8ee2\u3055\u305b\u3001\u6700\u5927\u30d2\u30fc\u30d7\u3092\u5b9f\u88c5\n# \u3053\u306e\u4f8b\u3067\u306f\u3001flag = 1\u306f\u6700\u5c0f\u30d2\u30fc\u30d7\u306b\u5bfe\u5fdc\u3057\u3001flag = -1\u306f\u6700\u5927\u30d2\u30fc\u30d7\u306b\u5bfe\u5fdc\n\n# \u30d2\u30fc\u30d7\u306b\u8981\u7d20\u3092\u30d7\u30c3\u30b7\u30e5\nheapq.heappush(max_heap, flag * 1)\nheapq.heappush(max_heap, flag * 3)\nheapq.heappush(max_heap, flag * 2)\nheapq.heappush(max_heap, flag * 5)\nheapq.heappush(max_heap, flag * 4)\n\n# \u30d2\u30fc\u30d7\u306e\u5148\u982d\u8981\u7d20\u3092\u53d6\u5f97\npeek: int = flag * max_heap[0] # 5\n\n# \u30d2\u30fc\u30d7\u306e\u5148\u982d\u8981\u7d20\u3092\u30dd\u30c3\u30d7\n# \u30dd\u30c3\u30d7\u3055\u308c\u305f\u8981\u7d20\u306f\u964d\u9806\u306e\u30b7\u30fc\u30b1\u30f3\u30b9\u3092\u5f62\u6210\nval = flag * heapq.heappop(max_heap) # 5\nval = flag * heapq.heappop(max_heap) # 4\nval = flag * heapq.heappop(max_heap) # 3\nval = flag * heapq.heappop(max_heap) # 2\nval = flag * heapq.heappop(max_heap) # 1\n\n# \u30d2\u30fc\u30d7\u306e\u30b5\u30a4\u30ba\u3092\u53d6\u5f97\nsize: int = len(max_heap)\n\n# \u30d2\u30fc\u30d7\u304c\u7a7a\u304b\u3069\u3046\u304b\u3092\u30c1\u30a7\u30c3\u30af\nis_empty: bool = not max_heap\n\n# \u30ea\u30b9\u30c8\u304b\u3089\u30d2\u30fc\u30d7\u3092\u4f5c\u6210\nmin_heap: list[int] = [1, 3, 2, 5, 4]\nheapq.heapify(min_heap)\n</code></pre> heap.cpp<pre><code>/* \u30d2\u30fc\u30d7\u306e\u521d\u671f\u5316 */\n// \u6700\u5c0f\u30d2\u30fc\u30d7\u306e\u521d\u671f\u5316\npriority_queue&lt;int, vector&lt;int&gt;, greater&lt;int&gt;&gt; minHeap;\n// \u6700\u5927\u30d2\u30fc\u30d7\u306e\u521d\u671f\u5316\npriority_queue&lt;int, vector&lt;int&gt;, less&lt;int&gt;&gt; maxHeap;\n\n/* \u30d2\u30fc\u30d7\u306b\u8981\u7d20\u3092\u30d7\u30c3\u30b7\u30e5 */\nmaxHeap.push(1);\nmaxHeap.push(3);\nmaxHeap.push(2);\nmaxHeap.push(5);\nmaxHeap.push(4);\n\n/* \u30d2\u30fc\u30d7\u306e\u5148\u982d\u8981\u7d20\u3092\u53d6\u5f97 */\nint peek = maxHeap.top(); // 5\n\n/* \u30d2\u30fc\u30d7\u306e\u5148\u982d\u8981\u7d20\u3092\u30dd\u30c3\u30d7 */\n// \u30dd\u30c3\u30d7\u3055\u308c\u305f\u8981\u7d20\u306f\u964d\u9806\u306e\u30b7\u30fc\u30b1\u30f3\u30b9\u3092\u5f62\u6210\nmaxHeap.pop(); // 5\nmaxHeap.pop(); // 4\nmaxHeap.pop(); // 3\nmaxHeap.pop(); // 2\nmaxHeap.pop(); // 1\n\n/* \u30d2\u30fc\u30d7\u306e\u30b5\u30a4\u30ba\u3092\u53d6\u5f97 */\nint size = maxHeap.size();\n\n/* \u30d2\u30fc\u30d7\u304c\u7a7a\u304b\u3069\u3046\u304b\u3092\u30c1\u30a7\u30c3\u30af */\nbool isEmpty = maxHeap.empty();\n\n/* \u30ea\u30b9\u30c8\u304b\u3089\u30d2\u30fc\u30d7\u3092\u4f5c\u6210 */\nvector&lt;int&gt; input{1, 3, 2, 5, 4};\npriority_queue&lt;int, vector&lt;int&gt;, greater&lt;int&gt;&gt; minHeap(input.begin(), input.end());\n</code></pre> heap.java<pre><code>/* \u30d2\u30fc\u30d7\u306e\u521d\u671f\u5316 */\n// \u6700\u5c0f\u30d2\u30fc\u30d7\u306e\u521d\u671f\u5316\nQueue&lt;Integer&gt; minHeap = new PriorityQueue&lt;&gt;();\n// \u6700\u5927\u30d2\u30fc\u30d7\u306e\u521d\u671f\u5316\uff08\u30e9\u30e0\u30c0\u5f0f\u3067Comparator\u3092\u5909\u66f4\u3059\u308b\u3060\u3051\uff09\nQueue&lt;Integer&gt; maxHeap = new PriorityQueue&lt;&gt;((a, b) -&gt; b - a);\n\n/* \u30d2\u30fc\u30d7\u306b\u8981\u7d20\u3092\u30d7\u30c3\u30b7\u30e5 */\nmaxHeap.offer(1);\nmaxHeap.offer(3);\nmaxHeap.offer(2);\nmaxHeap.offer(5);\nmaxHeap.offer(4);\n\n/* \u30d2\u30fc\u30d7\u306e\u5148\u982d\u8981\u7d20\u3092\u53d6\u5f97 */\nint peek = maxHeap.peek(); // 5\n\n/* \u30d2\u30fc\u30d7\u306e\u5148\u982d\u8981\u7d20\u3092\u30dd\u30c3\u30d7 */\n// \u30dd\u30c3\u30d7\u3055\u308c\u305f\u8981\u7d20\u306f\u964d\u9806\u306e\u30b7\u30fc\u30b1\u30f3\u30b9\u3092\u5f62\u6210\npeek = maxHeap.poll(); // 5\npeek = maxHeap.poll(); // 4\npeek = maxHeap.poll(); // 3\npeek = maxHeap.poll(); // 2\npeek = maxHeap.poll(); // 1\n\n/* \u30d2\u30fc\u30d7\u306e\u30b5\u30a4\u30ba\u3092\u53d6\u5f97 */\nint size = maxHeap.size();\n\n/* \u30d2\u30fc\u30d7\u304c\u7a7a\u304b\u3069\u3046\u304b\u3092\u30c1\u30a7\u30c3\u30af */\nboolean isEmpty = maxHeap.isEmpty();\n\n/* \u30ea\u30b9\u30c8\u304b\u3089\u30d2\u30fc\u30d7\u3092\u4f5c\u6210 */\nminHeap = new PriorityQueue&lt;&gt;(Arrays.asList(1, 3, 2, 5, 4));\n</code></pre> heap.cs<pre><code>/* \u30d2\u30fc\u30d7\u306e\u521d\u671f\u5316 */\n// \u6700\u5c0f\u30d2\u30fc\u30d7\u306e\u521d\u671f\u5316\nPriorityQueue&lt;int, int&gt; minHeap = new();\n// \u6700\u5927\u30d2\u30fc\u30d7\u306e\u521d\u671f\u5316\uff08\u30e9\u30e0\u30c0\u5f0f\u3067Comparator\u3092\u5909\u66f4\u3059\u308b\u3060\u3051\uff09\nPriorityQueue&lt;int, int&gt; maxHeap = new(Comparer&lt;int&gt;.Create((x, y) =&gt; y - x));\n\n/* \u30d2\u30fc\u30d7\u306b\u8981\u7d20\u3092\u30d7\u30c3\u30b7\u30e5 */\nmaxHeap.Enqueue(1, 1);\nmaxHeap.Enqueue(3, 3);\nmaxHeap.Enqueue(2, 2);\nmaxHeap.Enqueue(5, 5);\nmaxHeap.Enqueue(4, 4);\n\n/* \u30d2\u30fc\u30d7\u306e\u5148\u982d\u8981\u7d20\u3092\u53d6\u5f97 */\nint peek = maxHeap.Peek();//5\n\n/* \u30d2\u30fc\u30d7\u306e\u5148\u982d\u8981\u7d20\u3092\u30dd\u30c3\u30d7 */\n// \u30dd\u30c3\u30d7\u3055\u308c\u305f\u8981\u7d20\u306f\u964d\u9806\u306e\u30b7\u30fc\u30b1\u30f3\u30b9\u3092\u5f62\u6210\npeek = maxHeap.Dequeue();  // 5\npeek = maxHeap.Dequeue();  // 4\npeek = maxHeap.Dequeue();  // 3\npeek = maxHeap.Dequeue();  // 2\npeek = maxHeap.Dequeue();  // 1\n\n/* \u30d2\u30fc\u30d7\u306e\u30b5\u30a4\u30ba\u3092\u53d6\u5f97 */\nint size = maxHeap.Count;\n\n/* \u30d2\u30fc\u30d7\u304c\u7a7a\u304b\u3069\u3046\u304b\u3092\u30c1\u30a7\u30c3\u30af */\nbool isEmpty = maxHeap.Count == 0;\n\n/* \u30ea\u30b9\u30c8\u304b\u3089\u30d2\u30fc\u30d7\u3092\u4f5c\u6210 */\nminHeap = new PriorityQueue&lt;int, int&gt;([(1, 1), (3, 3), (2, 2), (5, 5), (4, 4)]);\n</code></pre> heap.go<pre><code>// Go\u3067\u306f\u3001heap.Interface\u3092\u5b9f\u88c5\u3059\u308b\u3053\u3068\u3067\u6574\u6570\u306e\u6700\u5927\u30d2\u30fc\u30d7\u3092\u69cb\u7bc9\u3067\u304d\u307e\u3059\n// heap.Interface\u3092\u5b9f\u88c5\u3059\u308b\u306b\u306f\u3001sort.Interface\u3082\u5b9f\u88c5\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\ntype intHeap []any\n\n// heap.Interface\u306ePush\u30e1\u30bd\u30c3\u30c9\u3001\u8981\u7d20\u3092\u30d2\u30fc\u30d7\u306b\u30d7\u30c3\u30b7\u30e5\nfunc (h *intHeap) Push(x any) {\n    // Push\u3068Pop\u306e\u4e21\u65b9\u3067\u30dd\u30a4\u30f3\u30bf\u30ec\u30b7\u30fc\u30d0\u30fc\u3092\u4f7f\u7528\n    // \u30b9\u30e9\u30a4\u30b9\u306e\u8981\u7d20\u3092\u8abf\u6574\u3059\u308b\u3060\u3051\u3067\u306a\u304f\u3001\u305d\u306e\u9577\u3055\u3082\u5909\u66f4\u3059\u308b\u305f\u3081\n    *h = append(*h, x.(int))\n}\n\n// heap.Interface\u306ePop\u30e1\u30bd\u30c3\u30c9\u3001\u30d2\u30fc\u30d7\u306e\u5148\u982d\u8981\u7d20\u3092\u524a\u9664\nfunc (h *intHeap) Pop() any {\n    // \u30d2\u30fc\u30d7\u304b\u3089\u30dd\u30c3\u30d7\u3059\u308b\u8981\u7d20\u306f\u672b\u5c3e\u306b\u683c\u7d0d\n    last := (*h)[len(*h)-1]\n    *h = (*h)[:len(*h)-1]\n    return last\n}\n\n// sort.Interface\u306eLen\u30e1\u30bd\u30c3\u30c9\nfunc (h *intHeap) Len() int {\n    return len(*h)\n}\n\n// sort.Interface\u306eLess\u30e1\u30bd\u30c3\u30c9\nfunc (h *intHeap) Less(i, j int) bool {\n    // \u6700\u5c0f\u30d2\u30fc\u30d7\u3092\u5b9f\u88c5\u3057\u305f\u3044\u5834\u5408\u306f\u3001\u3053\u308c\u3092\u5c0f\u306a\u308a\u6bd4\u8f03\u306b\u5909\u66f4\n    return (*h)[i].(int) &gt; (*h)[j].(int)\n}\n\n// sort.Interface\u306eSwap\u30e1\u30bd\u30c3\u30c9\nfunc (h *intHeap) Swap(i, j int) {\n    (*h)[i], (*h)[j] = (*h)[j], (*h)[i]\n}\n\n// Top \u30d2\u30fc\u30d7\u306e\u5148\u982d\u8981\u7d20\u3092\u53d6\u5f97\nfunc (h *intHeap) Top() any {\n    return (*h)[0]\n}\n\n/* \u30c9\u30e9\u30a4\u30d0\u30fc\u30b3\u30fc\u30c9 */\nfunc TestHeap(t *testing.T) {\n    /* \u30d2\u30fc\u30d7\u306e\u521d\u671f\u5316 */\n    // \u6700\u5927\u30d2\u30fc\u30d7\u306e\u521d\u671f\u5316\n    maxHeap := &amp;intHeap{}\n    heap.Init(maxHeap)\n    /* \u30d2\u30fc\u30d7\u306b\u8981\u7d20\u3092\u30d7\u30c3\u30b7\u30e5 */\n    // heap.Interface\u306e\u30e1\u30bd\u30c3\u30c9\u3092\u547c\u3073\u51fa\u3057\u3066\u8981\u7d20\u3092\u8ffd\u52a0\n    heap.Push(maxHeap, 1)\n    heap.Push(maxHeap, 3)\n    heap.Push(maxHeap, 2)\n    heap.Push(maxHeap, 4)\n    heap.Push(maxHeap, 5)\n\n    /* \u30d2\u30fc\u30d7\u306e\u5148\u982d\u8981\u7d20\u3092\u53d6\u5f97 */\n    top := maxHeap.Top()\n    fmt.Printf(\"\u30d2\u30fc\u30d7\u306e\u5148\u982d\u8981\u7d20\u306f %d\\n\", top)\n\n    /* \u30d2\u30fc\u30d7\u306e\u5148\u982d\u8981\u7d20\u3092\u30dd\u30c3\u30d7 */\n    // heap.Interface\u306e\u30e1\u30bd\u30c3\u30c9\u3092\u547c\u3073\u51fa\u3057\u3066\u8981\u7d20\u3092\u524a\u9664\n    heap.Pop(maxHeap) // 5\n    heap.Pop(maxHeap) // 4\n    heap.Pop(maxHeap) // 3\n    heap.Pop(maxHeap) // 2\n    heap.Pop(maxHeap) // 1\n\n    /* \u30d2\u30fc\u30d7\u306e\u30b5\u30a4\u30ba\u3092\u53d6\u5f97 */\n    size := len(*maxHeap)\n    fmt.Printf(\"\u30d2\u30fc\u30d7\u5185\u306e\u8981\u7d20\u6570\u306f %d\\n\", size)\n\n    /* \u30d2\u30fc\u30d7\u304c\u7a7a\u304b\u3069\u3046\u304b\u3092\u30c1\u30a7\u30c3\u30af */\n    isEmpty := len(*maxHeap) == 0\n    fmt.Printf(\"\u30d2\u30fc\u30d7\u306f\u7a7a\u3067\u3059\u304b\uff1f %t\\n\", isEmpty)\n}\n</code></pre> heap.swift<pre><code>/* \u30d2\u30fc\u30d7\u306e\u521d\u671f\u5316 */\n// Swift\u306eHeap\u578b\u306f\u6700\u5927\u30d2\u30fc\u30d7\u3068\u6700\u5c0f\u30d2\u30fc\u30d7\u306e\u4e21\u65b9\u3092\u30b5\u30dd\u30fc\u30c8\u3057\u3001swift-collections\u30e9\u30a4\u30d6\u30e9\u30ea\u304c\u5fc5\u8981\nvar heap = Heap&lt;Int&gt;()\n\n/* \u30d2\u30fc\u30d7\u306b\u8981\u7d20\u3092\u30d7\u30c3\u30b7\u30e5 */\nheap.insert(1)\nheap.insert(3)\nheap.insert(2)\nheap.insert(5)\nheap.insert(4)\n\n/* \u30d2\u30fc\u30d7\u306e\u5148\u982d\u8981\u7d20\u3092\u53d6\u5f97 */\nvar peek = heap.max()!\n\n/* \u30d2\u30fc\u30d7\u306e\u5148\u982d\u8981\u7d20\u3092\u30dd\u30c3\u30d7 */\npeek = heap.removeMax() // 5\npeek = heap.removeMax() // 4\npeek = heap.removeMax() // 3\npeek = heap.removeMax() // 2\npeek = heap.removeMax() // 1\n\n/* \u30d2\u30fc\u30d7\u306e\u30b5\u30a4\u30ba\u3092\u53d6\u5f97 */\nlet size = heap.count\n\n/* \u30d2\u30fc\u30d7\u304c\u7a7a\u304b\u3069\u3046\u304b\u3092\u30c1\u30a7\u30c3\u30af */\nlet isEmpty = heap.isEmpty\n\n/* \u30ea\u30b9\u30c8\u304b\u3089\u30d2\u30fc\u30d7\u3092\u4f5c\u6210 */\nlet heap2 = Heap([1, 3, 2, 5, 4])\n</code></pre> heap.js<pre><code>// JavaScript\u306f\u7d44\u307f\u8fbc\u307f\u306eHeap\u30af\u30e9\u30b9\u3092\u63d0\u4f9b\u3057\u3066\u3044\u307e\u305b\u3093\n</code></pre> heap.ts<pre><code>// TypeScript\u306f\u7d44\u307f\u8fbc\u307f\u306eHeap\u30af\u30e9\u30b9\u3092\u63d0\u4f9b\u3057\u3066\u3044\u307e\u305b\u3093\n</code></pre> heap.dart<pre><code>// Dart\u306f\u7d44\u307f\u8fbc\u307f\u306eHeap\u30af\u30e9\u30b9\u3092\u63d0\u4f9b\u3057\u3066\u3044\u307e\u305b\u3093\n</code></pre> heap.rs<pre><code>use std::collections::BinaryHeap;\nuse std::cmp::Reverse;\n\n/* \u30d2\u30fc\u30d7\u306e\u521d\u671f\u5316 */\n// \u6700\u5c0f\u30d2\u30fc\u30d7\u306e\u521d\u671f\u5316\nlet mut min_heap = BinaryHeap::&lt;Reverse&lt;i32&gt;&gt;::new();\n// \u6700\u5927\u30d2\u30fc\u30d7\u306e\u521d\u671f\u5316\nlet mut max_heap = BinaryHeap::new();\n\n/* \u30d2\u30fc\u30d7\u306b\u8981\u7d20\u3092\u30d7\u30c3\u30b7\u30e5 */\nmax_heap.push(1);\nmax_heap.push(3);\nmax_heap.push(2);\nmax_heap.push(5);\nmax_heap.push(4);\n\n/* \u30d2\u30fc\u30d7\u306e\u5148\u982d\u8981\u7d20\u3092\u53d6\u5f97 */\nlet peek = max_heap.peek().unwrap();  // 5\n\n/* \u30d2\u30fc\u30d7\u306e\u5148\u982d\u8981\u7d20\u3092\u30dd\u30c3\u30d7 */\n// \u30dd\u30c3\u30d7\u3055\u308c\u305f\u8981\u7d20\u306f\u964d\u9806\u306e\u30b7\u30fc\u30b1\u30f3\u30b9\u3092\u5f62\u6210\nlet peek = max_heap.pop().unwrap();   // 5\nlet peek = max_heap.pop().unwrap();   // 4\nlet peek = max_heap.pop().unwrap();   // 3\nlet peek = max_heap.pop().unwrap();   // 2\nlet peek = max_heap.pop().unwrap();   // 1\n\n/* \u30d2\u30fc\u30d7\u306e\u30b5\u30a4\u30ba\u3092\u53d6\u5f97 */\nlet size = max_heap.len();\n\n/* \u30d2\u30fc\u30d7\u304c\u7a7a\u304b\u3069\u3046\u304b\u3092\u30c1\u30a7\u30c3\u30af */\nlet is_empty = max_heap.is_empty();\n\n/* \u30ea\u30b9\u30c8\u304b\u3089\u30d2\u30fc\u30d7\u3092\u4f5c\u6210 */\nlet min_heap = BinaryHeap::from(vec![Reverse(1), Reverse(3), Reverse(2), Reverse(5), Reverse(4)]);\n</code></pre> heap.c<pre><code>// C\u306f\u7d44\u307f\u8fbc\u307f\u306eHeap\u30af\u30e9\u30b9\u3092\u63d0\u4f9b\u3057\u3066\u3044\u307e\u305b\u3093\n</code></pre> heap.kt<pre><code>/* \u30d2\u30fc\u30d7\u306e\u521d\u671f\u5316 */\n// \u6700\u5c0f\u30d2\u30fc\u30d7\u306e\u521d\u671f\u5316\nvar minHeap = PriorityQueue&lt;Int&gt;()\n// \u6700\u5927\u30d2\u30fc\u30d7\u306e\u521d\u671f\u5316\uff08\u30e9\u30e0\u30c0\u5f0f\u3067Comparator\u3092\u5909\u66f4\u3059\u308b\u3060\u3051\uff09\nval maxHeap = PriorityQueue { a: Int, b: Int -&gt; b - a }\n\n/* \u30d2\u30fc\u30d7\u306b\u8981\u7d20\u3092\u30d7\u30c3\u30b7\u30e5 */\nmaxHeap.offer(1)\nmaxHeap.offer(3)\nmaxHeap.offer(2)\nmaxHeap.offer(5)\nmaxHeap.offer(4)\n\n/* \u30d2\u30fc\u30d7\u306e\u5148\u982d\u8981\u7d20\u3092\u53d6\u5f97 */\nvar peek = maxHeap.peek() // 5\n\n/* \u30d2\u30fc\u30d7\u306e\u5148\u982d\u8981\u7d20\u3092\u30dd\u30c3\u30d7 */\n// \u30dd\u30c3\u30d7\u3055\u308c\u305f\u8981\u7d20\u306f\u964d\u9806\u306e\u30b7\u30fc\u30b1\u30f3\u30b9\u3092\u5f62\u6210\npeek = maxHeap.poll() // 5\npeek = maxHeap.poll() // 4\npeek = maxHeap.poll() // 3\npeek = maxHeap.poll() // 2\npeek = maxHeap.poll() // 1\n\n/* \u30d2\u30fc\u30d7\u306e\u30b5\u30a4\u30ba\u3092\u53d6\u5f97 */\nval size = maxHeap.size\n\n/* \u30d2\u30fc\u30d7\u304c\u7a7a\u304b\u3069\u3046\u304b\u3092\u30c1\u30a7\u30c3\u30af */\nval isEmpty = maxHeap.isEmpty()\n\n/* \u30ea\u30b9\u30c8\u304b\u3089\u30d2\u30fc\u30d7\u3092\u4f5c\u6210 */\nminHeap = PriorityQueue(mutableListOf(1, 3, 2, 5, 4))\n</code></pre> heap.rb<pre><code>\n</code></pre> heap.zig<pre><code>\n</code></pre>"},{"location":"chapter_heap/heap/#812","title":"8.1.2 \u00a0 \u30d2\u30fc\u30d7\u306e\u5b9f\u88c5","text":"<p>\u4ee5\u4e0b\u306e\u5b9f\u88c5\u306f\u6700\u5927\u30d2\u30fc\u30d7\u3067\u3059\u3002\u6700\u5c0f\u30d2\u30fc\u30d7\u306b\u5909\u63db\u3059\u308b\u306b\u306f\u3001\u3059\u3079\u3066\u306e\u30b5\u30a4\u30ba\u8ad6\u7406\u6bd4\u8f03\u3092\u53cd\u8ee2\u3055\u305b\u308b\u3060\u3051\u3067\u3059\uff08\u4f8b\u3048\u3070\u3001\\(\\geq\\)\u3092\\(\\leq\\)\u306b\u7f6e\u304d\u63db\u3048\u308b\uff09\u3002\u8208\u5473\u306e\u3042\u308b\u8aad\u8005\u306f\u81ea\u5206\u3067\u5b9f\u88c5\u3059\u308b\u3053\u3068\u3092\u304a\u52e7\u3081\u3057\u307e\u3059\u3002</p>"},{"location":"chapter_heap/heap/#1","title":"1. \u00a0 \u30d2\u30fc\u30d7\u306e\u683c\u7d0d\u3068\u8868\u73fe","text":"<p>\u300c\u4e8c\u5206\u6728\u300d\u306e\u7bc0\u3067\u8ff0\u3079\u305f\u3088\u3046\u306b\u3001\u5b8c\u5099\u4e8c\u5206\u6728\u306f\u914d\u5217\u8868\u73fe\u306b\u975e\u5e38\u306b\u9069\u3057\u3066\u3044\u307e\u3059\u3002\u30d2\u30fc\u30d7\u306f\u5b8c\u5099\u4e8c\u5206\u6728\u306e\u4e00\u7a2e\u306a\u306e\u3067\u3001\u914d\u5217\u3092\u4f7f\u7528\u3057\u3066\u30d2\u30fc\u30d7\u3092\u683c\u7d0d\u3057\u307e\u3059\u3002</p> <p>\u914d\u5217\u3092\u4f7f\u7528\u3057\u3066\u4e8c\u5206\u6728\u3092\u8868\u73fe\u3059\u308b\u5834\u5408\u3001\u8981\u7d20\u306f\u30ce\u30fc\u30c9\u5024\u3092\u8868\u3057\u3001\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306f\u4e8c\u5206\u6728\u5185\u306e\u30ce\u30fc\u30c9\u4f4d\u7f6e\u3092\u8868\u3057\u307e\u3059\u3002\u30ce\u30fc\u30c9\u30dd\u30a4\u30f3\u30bf\u306f\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u30de\u30c3\u30d4\u30f3\u30b0\u516c\u5f0f\u3092\u901a\u3058\u3066\u5b9f\u88c5\u3055\u308c\u307e\u3059\u3002</p> <p>\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\\(i\\)\u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408\u3001\u305d\u306e\u5de6\u306e\u5b50\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306f\\(2i + 1\\)\u3001\u53f3\u306e\u5b50\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306f\\(2i + 2\\)\u3001\u89aa\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306f\\((i - 1) / 2\\)\uff08\u5e8a\u9664\u7b97\uff09\u3067\u3059\u3002\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u304c\u7bc4\u56f2\u5916\u306e\u5834\u5408\u3001null\u30ce\u30fc\u30c9\u307e\u305f\u306f\u30ce\u30fc\u30c9\u304c\u5b58\u5728\u3057\u306a\u3044\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002</p> <p></p> <p> \u56f3 8-2 \u00a0 \u30d2\u30fc\u30d7\u306e\u8868\u73fe\u3068\u683c\u7d0d </p> <p>\u5f8c\u3067\u4fbf\u5229\u306b\u4f7f\u7528\u3059\u308b\u305f\u3081\u3001\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u30de\u30c3\u30d4\u30f3\u30b0\u516c\u5f0f\u3092\u95a2\u6570\u306b\u30ab\u30d7\u30bb\u30eb\u5316\u3067\u304d\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig my_heap.py<pre><code>def left(self, i: int) -&gt; int:\n    \"\"\"\u5de6\u306e\u5b50\u30ce\u30fc\u30c9\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u53d6\u5f97\"\"\"\n    return 2 * i + 1\n\ndef right(self, i: int) -&gt; int:\n    \"\"\"\u53f3\u306e\u5b50\u30ce\u30fc\u30c9\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u53d6\u5f97\"\"\"\n    return 2 * i + 2\n\ndef parent(self, i: int) -&gt; int:\n    \"\"\"\u89aa\u30ce\u30fc\u30c9\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u53d6\u5f97\"\"\"\n    return (i - 1) // 2  # \u6574\u6570\u9664\u7b97\u3067\u5207\u308a\u4e0b\u3052\n</code></pre> my_heap.cpp<pre><code>/* \u5de6\u306e\u5b50\u30ce\u30fc\u30c9\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u53d6\u5f97 */\nint left(int i) {\n    return 2 * i + 1;\n}\n\n/* \u53f3\u306e\u5b50\u30ce\u30fc\u30c9\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u53d6\u5f97 */\nint right(int i) {\n    return 2 * i + 2;\n}\n\n/* \u89aa\u30ce\u30fc\u30c9\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u53d6\u5f97 */\nint parent(int i) {\n    return (i - 1) / 2; // \u6574\u6570\u9664\u7b97\u3067\u5207\u308a\u4e0b\u3052\n}\n</code></pre> my_heap.java<pre><code>/* \u5de6\u306e\u5b50\u30ce\u30fc\u30c9\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u53d6\u5f97 */\nint left(int i) {\n    return 2 * i + 1;\n}\n\n/* \u53f3\u306e\u5b50\u30ce\u30fc\u30c9\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u53d6\u5f97 */\nint right(int i) {\n    return 2 * i + 2;\n}\n\n/* \u89aa\u30ce\u30fc\u30c9\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u53d6\u5f97 */\nint parent(int i) {\n    return (i - 1) / 2; // \u6574\u6570\u9664\u7b97\u3067\u5207\u308a\u4e0b\u3052\n}\n</code></pre> my_heap.cs<pre><code>[class]{MaxHeap}-[func]{Left}\n\n[class]{MaxHeap}-[func]{Right}\n\n[class]{MaxHeap}-[func]{Parent}\n</code></pre> my_heap.go<pre><code>[class]{maxHeap}-[func]{left}\n\n[class]{maxHeap}-[func]{right}\n\n[class]{maxHeap}-[func]{parent}\n</code></pre> my_heap.swift<pre><code>[class]{MaxHeap}-[func]{left}\n\n[class]{MaxHeap}-[func]{right}\n\n[class]{MaxHeap}-[func]{parent}\n</code></pre> my_heap.js<pre><code>[class]{MaxHeap}-[func]{left}\n\n[class]{MaxHeap}-[func]{right}\n\n[class]{MaxHeap}-[func]{parent}\n</code></pre> my_heap.ts<pre><code>[class]{MaxHeap}-[func]{left}\n\n[class]{MaxHeap}-[func]{right}\n\n[class]{MaxHeap}-[func]{parent}\n</code></pre> my_heap.dart<pre><code>[class]{MaxHeap}-[func]{_left}\n\n[class]{MaxHeap}-[func]{_right}\n\n[class]{MaxHeap}-[func]{_parent}\n</code></pre> my_heap.rs<pre><code>[class]{MaxHeap}-[func]{left}\n\n[class]{MaxHeap}-[func]{right}\n\n[class]{MaxHeap}-[func]{parent}\n</code></pre> my_heap.c<pre><code>[class]{MaxHeap}-[func]{left}\n\n[class]{MaxHeap}-[func]{right}\n\n[class]{MaxHeap}-[func]{parent}\n</code></pre> my_heap.kt<pre><code>[class]{MaxHeap}-[func]{left}\n\n[class]{MaxHeap}-[func]{right}\n\n[class]{MaxHeap}-[func]{parent}\n</code></pre> my_heap.rb<pre><code>[class]{MaxHeap}-[func]{left}\n\n[class]{MaxHeap}-[func]{right}\n\n[class]{MaxHeap}-[func]{parent}\n</code></pre> my_heap.zig<pre><code>[class]{MaxHeap}-[func]{left}\n\n[class]{MaxHeap}-[func]{right}\n\n[class]{MaxHeap}-[func]{parent}\n</code></pre>"},{"location":"chapter_heap/heap/#2","title":"2. \u00a0 \u30d2\u30fc\u30d7\u306e\u5148\u982d\u8981\u7d20\u3078\u306e\u30a2\u30af\u30bb\u30b9","text":"<p>\u30d2\u30fc\u30d7\u306e\u5148\u982d\u8981\u7d20\u306f\u4e8c\u5206\u6728\u306e\u6839\u30ce\u30fc\u30c9\u3067\u3001\u30ea\u30b9\u30c8\u306e\u6700\u521d\u306e\u8981\u7d20\u3067\u3082\u3042\u308a\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig my_heap.py<pre><code>def peek(self) -&gt; int:\n    \"\"\"\u30d2\u30fc\u30d7\u306e\u5148\u982d\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9\"\"\"\n    return self.max_heap[0]\n</code></pre> my_heap.cpp<pre><code>/* \u30d2\u30fc\u30d7\u306e\u5148\u982d\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\nint peek() {\n    return maxHeap[0];\n}\n</code></pre> my_heap.java<pre><code>/* \u30d2\u30fc\u30d7\u306e\u5148\u982d\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\nint peek() {\n    return maxHeap.get(0);\n}\n</code></pre> my_heap.cs<pre><code>[class]{MaxHeap}-[func]{Peek}\n</code></pre> my_heap.go<pre><code>[class]{maxHeap}-[func]{peek}\n</code></pre> my_heap.swift<pre><code>[class]{MaxHeap}-[func]{peek}\n</code></pre> my_heap.js<pre><code>[class]{MaxHeap}-[func]{peek}\n</code></pre> my_heap.ts<pre><code>[class]{MaxHeap}-[func]{peek}\n</code></pre> my_heap.dart<pre><code>[class]{MaxHeap}-[func]{peek}\n</code></pre> my_heap.rs<pre><code>[class]{MaxHeap}-[func]{peek}\n</code></pre> my_heap.c<pre><code>[class]{MaxHeap}-[func]{peek}\n</code></pre> my_heap.kt<pre><code>[class]{MaxHeap}-[func]{peek}\n</code></pre> my_heap.rb<pre><code>[class]{MaxHeap}-[func]{peek}\n</code></pre> my_heap.zig<pre><code>[class]{MaxHeap}-[func]{peek}\n</code></pre>"},{"location":"chapter_heap/heap/#3","title":"3. \u00a0 \u30d2\u30fc\u30d7\u3078\u306e\u8981\u7d20\u633f\u5165","text":"<p>\u8981\u7d20<code>val</code>\u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408\u3001\u307e\u305a\u305d\u308c\u3092\u30d2\u30fc\u30d7\u306e\u5e95\u306b\u8ffd\u52a0\u3057\u307e\u3059\u3002\u8ffd\u52a0\u5f8c\u3001<code>val</code>\u304c\u30d2\u30fc\u30d7\u5185\u306e\u4ed6\u306e\u8981\u7d20\u3088\u308a\u5927\u304d\u3044\u53ef\u80fd\u6027\u304c\u3042\u308b\u305f\u3081\u3001\u30d2\u30fc\u30d7\u306e\u5b8c\u5168\u6027\u304c\u640d\u306a\u308f\u308c\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u633f\u5165\u3055\u308c\u305f\u30ce\u30fc\u30c9\u304b\u3089\u6839\u30ce\u30fc\u30c9\u307e\u3067\u306e\u30d1\u30b9\u3092\u4fee\u5fa9\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u64cd\u4f5c\u306f\u30d2\u30fc\u30d7\u5316\u3068\u547c\u3070\u308c\u307e\u3059\u3002</p> <p>\u633f\u5165\u3055\u308c\u305f\u30ce\u30fc\u30c9\u304b\u3089\u958b\u59cb\u3057\u3066\u3001\u4e0b\u304b\u3089\u4e0a\u306b\u30d2\u30fc\u30d7\u5316\u3092\u5b9f\u884c\u3057\u307e\u3059\u3002\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u633f\u5165\u3055\u308c\u305f\u30ce\u30fc\u30c9\u306e\u5024\u3092\u305d\u306e\u89aa\u30ce\u30fc\u30c9\u3068\u6bd4\u8f03\u3057\u3001\u633f\u5165\u3055\u308c\u305f\u30ce\u30fc\u30c9\u304c\u5927\u304d\u3044\u5834\u5408\u306f\u305d\u308c\u3089\u3092\u4ea4\u63db\u3057\u307e\u3059\u3002\u6b21\u306b\u3053\u306e\u64cd\u4f5c\u3092\u7d9a\u884c\u3057\u3001\u6839\u306b\u5230\u9054\u3059\u308b\u304b\u3001\u4ea4\u63db\u304c\u4e0d\u8981\u306a\u30ce\u30fc\u30c9\u306b\u906d\u9047\u3059\u308b\u307e\u3067\u3001\u4e0b\u304b\u3089\u4e0a\u306b\u30d2\u30fc\u30d7\u5185\u306e\u5404\u30ce\u30fc\u30c9\u3092\u4fee\u5fa9\u3057\u307e\u3059\u3002</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> \u56f3 8-3 \u00a0 \u30d2\u30fc\u30d7\u3078\u306e\u8981\u7d20\u633f\u5165\u306e\u624b\u9806 </p> <p>\u7dcf\u30ce\u30fc\u30c9\u6570\u3092\\(n\\)\u3068\u3059\u308b\u3068\u3001\u6728\u306e\u9ad8\u3055\u306f\\(O(\\log n)\\)\u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u30d2\u30fc\u30d7\u5316\u64cd\u4f5c\u306e\u30eb\u30fc\u30d7\u53cd\u5fa9\u56de\u6570\u306f\u6700\u5927\\(O(\\log n)\\)\u3067\u3001\u8981\u7d20\u633f\u5165\u64cd\u4f5c\u306e\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O(\\log n)\\)\u306b\u306a\u308a\u307e\u3059\u3002\u30b3\u30fc\u30c9\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig my_heap.py<pre><code>def push(self, val: int):\n    \"\"\"\u30d2\u30fc\u30d7\u306b\u8981\u7d20\u3092\u30d7\u30c3\u30b7\u30e5\"\"\"\n    # \u30ce\u30fc\u30c9\u3092\u8ffd\u52a0\n    self.max_heap.append(val)\n    # \u4e0b\u304b\u3089\u4e0a\u3078\u30d2\u30fc\u30d7\u5316\n    self.sift_up(self.size() - 1)\n\ndef sift_up(self, i: int):\n    \"\"\"\u30ce\u30fc\u30c9i\u304b\u3089\u958b\u59cb\u3057\u3066\u3001\u4e0b\u304b\u3089\u4e0a\u3078\u30d2\u30fc\u30d7\u5316\"\"\"\n    while True:\n        # \u30ce\u30fc\u30c9i\u306e\u89aa\u30ce\u30fc\u30c9\u3092\u53d6\u5f97\n        p = self.parent(i)\n        # \u300c\u30eb\u30fc\u30c8\u30ce\u30fc\u30c9\u3092\u8d8a\u3048\u308b\u300d\u307e\u305f\u306f\u300c\u30ce\u30fc\u30c9\u304c\u4fee\u5fa9\u4e0d\u8981\u300d\u306e\u5834\u5408\u3001\u30d2\u30fc\u30d7\u5316\u3092\u7d42\u4e86\n        if p &lt; 0 or self.max_heap[i] &lt;= self.max_heap[p]:\n            break\n        # 2\u3064\u306e\u30ce\u30fc\u30c9\u3092\u4ea4\u63db\n        self.swap(i, p)\n        # \u4e0a\u5411\u304d\u306e\u30eb\u30fc\u30d7\u30d2\u30fc\u30d7\u5316\n        i = p\n</code></pre> my_heap.cpp<pre><code>/* \u30d2\u30fc\u30d7\u306b\u8981\u7d20\u3092\u30d7\u30c3\u30b7\u30e5 */\nvoid push(int val) {\n    // \u30ce\u30fc\u30c9\u3092\u8ffd\u52a0\n    maxHeap.push_back(val);\n    // \u4e0b\u304b\u3089\u4e0a\u3078\u30d2\u30fc\u30d7\u5316\n    siftUp(size() - 1);\n}\n\n/* \u30ce\u30fc\u30c9i\u304b\u3089\u4e0a\u5411\u304d\u306b\u30d2\u30fc\u30d7\u5316\u3092\u958b\u59cb */\nvoid siftUp(int i) {\n    while (true) {\n        // \u30ce\u30fc\u30c9i\u306e\u89aa\u30ce\u30fc\u30c9\u3092\u53d6\u5f97\n        int p = parent(i);\n        // \u300c\u30eb\u30fc\u30c8\u30ce\u30fc\u30c9\u3092\u8d85\u3048\u308b\u300d\u307e\u305f\u306f\u300c\u30ce\u30fc\u30c9\u304c\u4fee\u5fa9\u4e0d\u8981\u300d\u306e\u5834\u5408\u3001\u30d2\u30fc\u30d7\u5316\u3092\u7d42\u4e86\n        if (p &lt; 0 || maxHeap[i] &lt;= maxHeap[p])\n            break;\n        // 2\u3064\u306e\u30ce\u30fc\u30c9\u3092\u4ea4\u63db\n        swap(maxHeap[i], maxHeap[p]);\n        // \u4e0a\u5411\u304d\u306b\u30eb\u30fc\u30d7\u3057\u3066\u30d2\u30fc\u30d7\u5316\n        i = p;\n    }\n}\n</code></pre> my_heap.java<pre><code>/* \u8981\u7d20\u3092\u30d2\u30fc\u30d7\u306b\u30d7\u30c3\u30b7\u30e5 */\nvoid push(int val) {\n    // \u30ce\u30fc\u30c9\u3092\u8ffd\u52a0\n    maxHeap.add(val);\n    // \u4e0b\u304b\u3089\u4e0a\u3078\u30d2\u30fc\u30d7\u5316\n    siftUp(size() - 1);\n}\n\n/* \u30ce\u30fc\u30c9 i \u304b\u3089\u4e0a\u5411\u304d\u306b\u30d2\u30fc\u30d7\u5316\u3092\u958b\u59cb */\nvoid siftUp(int i) {\n    while (true) {\n        // \u30ce\u30fc\u30c9 i \u306e\u89aa\u30ce\u30fc\u30c9\u3092\u53d6\u5f97\n        int p = parent(i);\n        // \u300c\u6839\u30ce\u30fc\u30c9\u3092\u8d8a\u3048\u308b\u300d\u307e\u305f\u306f\u300c\u30ce\u30fc\u30c9\u304c\u4fee\u5fa9\u4e0d\u8981\u300d\u306e\u5834\u5408\u3001\u30d2\u30fc\u30d7\u5316\u3092\u7d42\u4e86\n        if (p &lt; 0 || maxHeap.get(i) &lt;= maxHeap.get(p))\n            break;\n        // 2\u3064\u306e\u30ce\u30fc\u30c9\u3092\u4ea4\u63db\n        swap(i, p);\n        // \u4e0a\u5411\u304d\u306b\u30d2\u30fc\u30d7\u5316\u3092\u30eb\u30fc\u30d7\n        i = p;\n    }\n}\n</code></pre> my_heap.cs<pre><code>[class]{MaxHeap}-[func]{Push}\n\n[class]{MaxHeap}-[func]{SiftUp}\n</code></pre> my_heap.go<pre><code>[class]{maxHeap}-[func]{push}\n\n[class]{maxHeap}-[func]{siftUp}\n</code></pre> my_heap.swift<pre><code>[class]{MaxHeap}-[func]{push}\n\n[class]{MaxHeap}-[func]{siftUp}\n</code></pre> my_heap.js<pre><code>[class]{MaxHeap}-[func]{push}\n\n[class]{MaxHeap}-[func]{siftUp}\n</code></pre> my_heap.ts<pre><code>[class]{MaxHeap}-[func]{push}\n\n[class]{MaxHeap}-[func]{siftUp}\n</code></pre> my_heap.dart<pre><code>[class]{MaxHeap}-[func]{push}\n\n[class]{MaxHeap}-[func]{siftUp}\n</code></pre> my_heap.rs<pre><code>[class]{MaxHeap}-[func]{push}\n\n[class]{MaxHeap}-[func]{sift_up}\n</code></pre> my_heap.c<pre><code>[class]{MaxHeap}-[func]{push}\n\n[class]{MaxHeap}-[func]{siftUp}\n</code></pre> my_heap.kt<pre><code>[class]{MaxHeap}-[func]{push}\n\n[class]{MaxHeap}-[func]{siftUp}\n</code></pre> my_heap.rb<pre><code>[class]{MaxHeap}-[func]{push}\n\n[class]{MaxHeap}-[func]{sift_up}\n</code></pre> my_heap.zig<pre><code>[class]{MaxHeap}-[func]{push}\n\n[class]{MaxHeap}-[func]{siftUp}\n</code></pre>"},{"location":"chapter_heap/heap/#4","title":"4. \u00a0 \u30d2\u30fc\u30d7\u304b\u3089\u306e\u5148\u982d\u8981\u7d20\u524a\u9664","text":"<p>\u30d2\u30fc\u30d7\u306e\u5148\u982d\u8981\u7d20\u306f\u4e8c\u5206\u6728\u306e\u6839\u30ce\u30fc\u30c9\u3001\u3064\u307e\u308a\u30ea\u30b9\u30c8\u306e\u6700\u521d\u306e\u8981\u7d20\u3067\u3059\u3002\u30ea\u30b9\u30c8\u304b\u3089\u6700\u521d\u306e\u8981\u7d20\u3092\u76f4\u63a5\u524a\u9664\u3059\u308b\u3068\u3001\u4e8c\u5206\u6728\u5185\u306e\u3059\u3079\u3066\u306e\u30ce\u30fc\u30c9\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u304c\u5909\u66f4\u3055\u308c\u3001\u5f8c\u7d9a\u306e\u4fee\u5fa9\u306b\u30d2\u30fc\u30d7\u5316\u3092\u4f7f\u7528\u3059\u308b\u3053\u3068\u304c\u56f0\u96e3\u306b\u306a\u308a\u307e\u3059\u3002\u8981\u7d20\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306e\u5909\u66f4\u3092\u6700\u5c0f\u9650\u306b\u6291\u3048\u308b\u305f\u3081\u3001\u6b21\u306e\u624b\u9806\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002</p> <ol> <li>\u30d2\u30fc\u30d7\u306e\u5148\u982d\u8981\u7d20\u3068\u5e95\u306e\u8981\u7d20\u3092\u4ea4\u63db\u3057\u307e\u3059\uff08\u6839\u30ce\u30fc\u30c9\u3068\u6700\u3082\u53f3\u306e\u8449\u30ce\u30fc\u30c9\u3092\u4ea4\u63db\uff09\u3002</li> <li>\u4ea4\u63db\u5f8c\u3001\u30ea\u30b9\u30c8\u304b\u3089\u30d2\u30fc\u30d7\u306e\u5e95\u3092\u524a\u9664\u3057\u307e\u3059\uff08\u4ea4\u63db\u3055\u308c\u3066\u3044\u308b\u305f\u3081\u3001\u5b9f\u969b\u306b\u306f\u5143\u306e\u5148\u982d\u8981\u7d20\u304c\u524a\u9664\u3055\u308c\u308b\uff09\u3002</li> <li>\u6839\u30ce\u30fc\u30c9\u304b\u3089\u958b\u59cb\u3057\u3066\u3001\u4e0a\u304b\u3089\u4e0b\u306b\u30d2\u30fc\u30d7\u5316\u3092\u5b9f\u884c\u3057\u307e\u3059\u3002</li> </ol> <p>\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u300c\u4e0a\u304b\u3089\u4e0b\u306e\u30d2\u30fc\u30d7\u5316\u300d\u306e\u65b9\u5411\u306f\u300c\u4e0b\u304b\u3089\u4e0a\u306e\u30d2\u30fc\u30d7\u5316\u300d\u3068\u53cd\u5bfe\u3067\u3059\u3002\u6839\u30ce\u30fc\u30c9\u306e\u5024\u3092\u305d\u306e2\u3064\u306e\u5b50\u3068\u6bd4\u8f03\u3057\u3001\u6700\u5927\u306e\u5b50\u3068\u4ea4\u63db\u3057\u307e\u3059\u3002\u6b21\u306b\u3001\u8449\u30ce\u30fc\u30c9\u306b\u5230\u9054\u3059\u308b\u304b\u3001\u4ea4\u63db\u304c\u4e0d\u8981\u306a\u30ce\u30fc\u30c9\u306b\u906d\u9047\u3059\u308b\u307e\u3067\u3001\u3053\u306e\u64cd\u4f5c\u3092\u7e70\u308a\u8fd4\u3057\u307e\u3059\u3002</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> \u56f3 8-4 \u00a0 \u30d2\u30fc\u30d7\u304b\u3089\u306e\u5148\u982d\u8981\u7d20\u524a\u9664\u306e\u624b\u9806 </p> <p>\u8981\u7d20\u633f\u5165\u64cd\u4f5c\u3068\u540c\u69d8\u306b\u3001\u5148\u982d\u8981\u7d20\u524a\u9664\u64cd\u4f5c\u306e\u6642\u9593\u8a08\u7b97\u91cf\u3082\\(O(\\log n)\\)\u3067\u3059\u3002\u30b3\u30fc\u30c9\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig my_heap.py<pre><code>def pop(self) -&gt; int:\n    \"\"\"\u8981\u7d20\u3092\u30d2\u30fc\u30d7\u304b\u3089\u51fa\u3059\"\"\"\n    # \u7a7a\u306e\u51e6\u7406\n    if self.is_empty():\n        raise IndexError(\"Heap is empty\")\n    # \u30eb\u30fc\u30c8\u30ce\u30fc\u30c9\u3068\u6700\u53f3\u7aef\u306e\u8449\u30ce\u30fc\u30c9\u3092\u4ea4\u63db\uff08\u6700\u521d\u306e\u8981\u7d20\u3068\u6700\u5f8c\u306e\u8981\u7d20\u3092\u4ea4\u63db\uff09\n    self.swap(0, self.size() - 1)\n    # \u30ce\u30fc\u30c9\u3092\u524a\u9664\n    val = self.max_heap.pop()\n    # \u4e0a\u304b\u3089\u4e0b\u3078\u30d2\u30fc\u30d7\u5316\n    self.sift_down(0)\n    # \u30d2\u30fc\u30d7\u306e\u5148\u982d\u8981\u7d20\u3092\u8fd4\u3059\n    return val\n\ndef sift_down(self, i: int):\n    \"\"\"\u30ce\u30fc\u30c9i\u304b\u3089\u958b\u59cb\u3057\u3066\u3001\u4e0a\u304b\u3089\u4e0b\u3078\u30d2\u30fc\u30d7\u5316\"\"\"\n    while True:\n        # i\u3001l\u3001r\u306e\u4e2d\u3067\u6700\u5927\u306e\u30ce\u30fc\u30c9\u3092\u6c7a\u5b9a\u3057\u3001ma\u3068\u3059\u308b\n        l, r, ma = self.left(i), self.right(i), i\n        if l &lt; self.size() and self.max_heap[l] &gt; self.max_heap[ma]:\n            ma = l\n        if r &lt; self.size() and self.max_heap[r] &gt; self.max_heap[ma]:\n            ma = r\n        # \u30ce\u30fc\u30c9i\u304c\u6700\u5927\u307e\u305f\u306f\u30a4\u30f3\u30c7\u30c3\u30af\u30b9l\u3001r\u304c\u7bc4\u56f2\u5916\u306e\u5834\u5408\u3001\u3055\u3089\u306a\u308b\u30d2\u30fc\u30d7\u5316\u306f\u4e0d\u8981\u3001\u30d6\u30ec\u30fc\u30af\n        if ma == i:\n            break\n        # 2\u3064\u306e\u30ce\u30fc\u30c9\u3092\u4ea4\u63db\n        self.swap(i, ma)\n        # \u4e0b\u5411\u304d\u306e\u30eb\u30fc\u30d7\u30d2\u30fc\u30d7\u5316\n        i = ma\n</code></pre> my_heap.cpp<pre><code>/* \u8981\u7d20\u304c\u30d2\u30fc\u30d7\u304b\u3089\u9000\u51fa */\nvoid pop() {\n    // \u7a7a\u306e\u51e6\u7406\n    if (isEmpty()) {\n        throw out_of_range(\"Heap is empty\");\n    }\n    // \u30eb\u30fc\u30c8\u30ce\u30fc\u30c9\u3092\u6700\u3082\u53f3\u306e\u8449\u30ce\u30fc\u30c9\u3068\u4ea4\u63db\uff08\u6700\u521d\u306e\u8981\u7d20\u3068\u6700\u5f8c\u306e\u8981\u7d20\u3092\u4ea4\u63db\uff09\n    swap(maxHeap[0], maxHeap[size() - 1]);\n    // \u30ce\u30fc\u30c9\u3092\u524a\u9664\n    maxHeap.pop_back();\n    // \u4e0a\u304b\u3089\u4e0b\u3078\u30d2\u30fc\u30d7\u5316\n    siftDown(0);\n}\n\n/* \u30ce\u30fc\u30c9i\u304b\u3089\u4e0b\u5411\u304d\u306b\u30d2\u30fc\u30d7\u5316\u3092\u958b\u59cb */\nvoid siftDown(int i) {\n    while (true) {\n        // i\u3001l\u3001r\u306e\u4e2d\u3067\u6700\u5927\u306e\u30ce\u30fc\u30c9\u3092\u6c7a\u5b9a\u3057\u3001ma\u3068\u3057\u3066\u8a18\u9332\n        int l = left(i), r = right(i), ma = i;\n        if (l &lt; size() &amp;&amp; maxHeap[l] &gt; maxHeap[ma])\n            ma = l;\n        if (r &lt; size() &amp;&amp; maxHeap[r] &gt; maxHeap[ma])\n            ma = r;\n        // \u30ce\u30fc\u30c9i\u304c\u6700\u5927\u3001\u307e\u305f\u306f\u30a4\u30f3\u30c7\u30c3\u30af\u30b9l\u3001r\u304c\u7bc4\u56f2\u5916\u306e\u5834\u5408\u3001\u3053\u308c\u4ee5\u4e0a\u306e\u30d2\u30fc\u30d7\u5316\u306f\u4e0d\u8981\u3001\u30d6\u30ec\u30fc\u30af\n        if (ma == i)\n            break;\n        swap(maxHeap[i], maxHeap[ma]);\n        // \u4e0b\u5411\u304d\u306b\u30eb\u30fc\u30d7\u3057\u3066\u30d2\u30fc\u30d7\u5316\n        i = ma;\n    }\n}\n</code></pre> my_heap.java<pre><code>/* \u8981\u7d20\u304c\u30d2\u30fc\u30d7\u304b\u3089\u9000\u51fa */\nint pop() {\n    // \u7a7a\u306e\u51e6\u7406\n    if (isEmpty())\n        throw new IndexOutOfBoundsException();\n    // \u6839\u30ce\u30fc\u30c9\u3092\u6700\u3082\u53f3\u306e\u8449\u30ce\u30fc\u30c9\u3068\u4ea4\u63db\uff08\u6700\u521d\u306e\u8981\u7d20\u3092\u6700\u5f8c\u306e\u8981\u7d20\u3068\u4ea4\u63db\uff09\n    swap(0, size() - 1);\n    // \u30ce\u30fc\u30c9\u3092\u524a\u9664\n    int val = maxHeap.remove(size() - 1);\n    // \u4e0a\u304b\u3089\u4e0b\u3078\u30d2\u30fc\u30d7\u5316\n    siftDown(0);\n    // \u30d2\u30fc\u30d7\u306e\u5148\u982d\u8981\u7d20\u3092\u8fd4\u3059\n    return val;\n}\n\n/* \u30ce\u30fc\u30c9 i \u304b\u3089\u4e0b\u5411\u304d\u306b\u30d2\u30fc\u30d7\u5316\u3092\u958b\u59cb */\nvoid siftDown(int i) {\n    while (true) {\n        // i\u3001l\u3001r \u306e\u4e2d\u3067\u6700\u5927\u306e\u30ce\u30fc\u30c9\u3092\u6c7a\u5b9a\u3057\u3001ma \u3068\u3059\u308b\n        int l = left(i), r = right(i), ma = i;\n        if (l &lt; size() &amp;&amp; maxHeap.get(l) &gt; maxHeap.get(ma))\n            ma = l;\n        if (r &lt; size() &amp;&amp; maxHeap.get(r) &gt; maxHeap.get(ma))\n            ma = r;\n        // \u30ce\u30fc\u30c9 i \u304c\u6700\u5927\u306e\u5834\u5408\u3001\u307e\u305f\u306f\u30a4\u30f3\u30c7\u30c3\u30af\u30b9 l\u3001r \u304c\u7bc4\u56f2\u5916\u306e\u5834\u5408\u3001\u3055\u3089\u306a\u308b\u30d2\u30fc\u30d7\u5316\u306f\u4e0d\u8981\u3001\u7d42\u4e86\n        if (ma == i)\n            break;\n        // 2\u3064\u306e\u30ce\u30fc\u30c9\u3092\u4ea4\u63db\n        swap(i, ma);\n        // \u4e0b\u5411\u304d\u306b\u30d2\u30fc\u30d7\u5316\u3092\u30eb\u30fc\u30d7\n        i = ma;\n    }\n}\n</code></pre> my_heap.cs<pre><code>[class]{MaxHeap}-[func]{Pop}\n\n[class]{MaxHeap}-[func]{SiftDown}\n</code></pre> my_heap.go<pre><code>[class]{maxHeap}-[func]{pop}\n\n[class]{maxHeap}-[func]{siftDown}\n</code></pre> my_heap.swift<pre><code>[class]{MaxHeap}-[func]{pop}\n\n[class]{MaxHeap}-[func]{siftDown}\n</code></pre> my_heap.js<pre><code>[class]{MaxHeap}-[func]{pop}\n\n[class]{MaxHeap}-[func]{siftDown}\n</code></pre> my_heap.ts<pre><code>[class]{MaxHeap}-[func]{pop}\n\n[class]{MaxHeap}-[func]{siftDown}\n</code></pre> my_heap.dart<pre><code>[class]{MaxHeap}-[func]{pop}\n\n[class]{MaxHeap}-[func]{siftDown}\n</code></pre> my_heap.rs<pre><code>[class]{MaxHeap}-[func]{pop}\n\n[class]{MaxHeap}-[func]{sift_down}\n</code></pre> my_heap.c<pre><code>[class]{MaxHeap}-[func]{pop}\n\n[class]{MaxHeap}-[func]{siftDown}\n</code></pre> my_heap.kt<pre><code>[class]{MaxHeap}-[func]{pop}\n\n[class]{MaxHeap}-[func]{siftDown}\n</code></pre> my_heap.rb<pre><code>[class]{MaxHeap}-[func]{pop}\n\n[class]{MaxHeap}-[func]{sift_down}\n</code></pre> my_heap.zig<pre><code>[class]{MaxHeap}-[func]{pop}\n\n[class]{MaxHeap}-[func]{siftDown}\n</code></pre>"},{"location":"chapter_heap/heap/#813","title":"8.1.3 \u00a0 \u30d2\u30fc\u30d7\u306e\u4e00\u822c\u7684\u306a\u5fdc\u7528","text":"<ul> <li>\u512a\u5148\u5ea6\u30ad\u30e5\u30fc\uff1a\u30d2\u30fc\u30d7\u306f\u512a\u5148\u5ea6\u30ad\u30e5\u30fc\u3092\u5b9f\u88c5\u3059\u308b\u305f\u3081\u306e\u597d\u307e\u3057\u3044\u30c7\u30fc\u30bf\u69cb\u9020\u3067\u3001\u30a8\u30f3\u30ad\u30e5\u30fc\u64cd\u4f5c\u3068\u30c7\u30ad\u30e5\u30fc\u64cd\u4f5c\u306e\u4e21\u65b9\u306e\u6642\u9593\u8a08\u7b97\u91cf\u304c\\(O(\\log n)\\)\u3001\u30ad\u30e5\u30fc\u69cb\u7bc9\u306e\u6642\u9593\u8a08\u7b97\u91cf\u304c\\(O(n)\\)\u3067\u3001\u3059\u3079\u3066\u975e\u5e38\u306b\u52b9\u7387\u7684\u3067\u3059\u3002</li> <li>\u30d2\u30fc\u30d7\u30bd\u30fc\u30c8\uff1a\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408\u3001\u305d\u308c\u3089\u304b\u3089\u30d2\u30fc\u30d7\u3092\u4f5c\u6210\u3057\u3001\u6b21\u306b\u8981\u7d20\u524a\u9664\u64cd\u4f5c\u3092\u7d99\u7d9a\u7684\u306b\u5b9f\u884c\u3057\u3066\u9806\u5e8f\u4ed8\u3051\u3055\u308c\u305f\u30c7\u30fc\u30bf\u3092\u53d6\u5f97\u3067\u304d\u307e\u3059\u3002\u305f\u3060\u3057\u3001\u30d2\u30fc\u30d7\u30bd\u30fc\u30c8\u3092\u5b9f\u88c5\u3059\u308b\u3088\u308a\u6d17\u7df4\u3055\u308c\u305f\u65b9\u6cd5\u304c\u3042\u308a\u3001\u300c\u30d2\u30fc\u30d7\u30bd\u30fc\u30c8\u300d\u306e\u7ae0\u3067\u8aac\u660e\u3055\u308c\u3066\u3044\u307e\u3059\u3002</li> <li>\u6700\u5927\\(k\\)\u500b\u306e\u8981\u7d20\u306e\u767a\u898b\uff1a\u3053\u308c\u306f\u53e4\u5178\u7684\u306a\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u554f\u984c\u3067\u3042\u308a\u3001\u4e00\u822c\u7684\u306a\u4f7f\u7528\u4f8b\u3067\u3082\u3042\u308a\u307e\u3059\u3002Weibo\u30db\u30c3\u30c8\u691c\u7d22\u306e\u30c8\u30c3\u30d710\u30db\u30c3\u30c8\u30cb\u30e5\u30fc\u30b9\u306e\u9078\u629e\u3084\u3001\u30c8\u30c3\u30d710\u306e\u58f2\u308c\u7b4b\u5546\u54c1\u306e\u9078\u629e\u306a\u3069\u3067\u3059\u3002</li> </ul>"},{"location":"chapter_heap/summary/","title":"8.4 \u00a0 \u307e\u3068\u3081","text":""},{"location":"chapter_heap/summary/#1","title":"1. \u00a0 \u91cd\u8981\u306a\u5fa9\u7fd2","text":"<ul> <li>\u30d2\u30fc\u30d7\u306f\u5b8c\u5099\u4e8c\u5206\u6728\u3067\u3001\u305d\u306e\u69cb\u7bc9\u6027\u8cea\u306b\u57fa\u3065\u3044\u3066\u6700\u5927\u30d2\u30fc\u30d7\u307e\u305f\u306f\u6700\u5c0f\u30d2\u30fc\u30d7\u306b\u5206\u985e\u3067\u304d\u307e\u3059\u3002\u6700\u5927\u30d2\u30fc\u30d7\u306e\u5148\u982d\u8981\u7d20\u306f\u6700\u5927\u3067\u3001\u6700\u5c0f\u30d2\u30fc\u30d7\u306e\u5148\u982d\u8981\u7d20\u306f\u6700\u5c0f\u3067\u3059\u3002</li> <li>\u512a\u5148\u5ea6\u30ad\u30e5\u30fc\u306f\u3001\u30c7\u30ad\u30e5\u30fc\u306e\u512a\u5148\u5ea6\u3092\u6301\u3064\u30ad\u30e5\u30fc\u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u3001\u901a\u5e38\u30d2\u30fc\u30d7\u3092\u4f7f\u7528\u3057\u3066\u5b9f\u88c5\u3055\u308c\u307e\u3059\u3002</li> <li>\u30d2\u30fc\u30d7\u306e\u4e00\u822c\u7684\u306a\u64cd\u4f5c\u3068\u305d\u308c\u306b\u5bfe\u5fdc\u3059\u308b\u6642\u9593\u8a08\u7b97\u91cf\u306b\u306f\u4ee5\u4e0b\u304c\u3042\u308a\u307e\u3059\uff1a\u30d2\u30fc\u30d7\u3078\u306e\u8981\u7d20\u633f\u5165\\(O(\\log n)\\)\u3001\u30d2\u30fc\u30d7\u304b\u3089\u306e\u5148\u982d\u8981\u7d20\u524a\u9664\\(O(\\log n)\\)\u3001\u30d2\u30fc\u30d7\u306e\u5148\u982d\u8981\u7d20\u3078\u306e\u30a2\u30af\u30bb\u30b9\\(O(1)\\)\u3002</li> <li>\u5b8c\u5099\u4e8c\u5206\u6728\u306f\u914d\u5217\u3067\u8868\u73fe\u3059\u308b\u306e\u306b\u9069\u3057\u3066\u3044\u308b\u305f\u3081\u3001\u30d2\u30fc\u30d7\u306f\u4e00\u822c\u7684\u306b\u914d\u5217\u3092\u4f7f\u7528\u3057\u3066\u683c\u7d0d\u3055\u308c\u307e\u3059\u3002</li> <li>\u30d2\u30fc\u30d7\u5316\u64cd\u4f5c\u306f\u30d2\u30fc\u30d7\u306e\u6027\u8cea\u3092\u7dad\u6301\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u3001\u30d2\u30fc\u30d7\u306e\u633f\u5165\u64cd\u4f5c\u3068\u524a\u9664\u64cd\u4f5c\u306e\u4e21\u65b9\u3067\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002</li> <li>\\(n\\)\u500b\u306e\u8981\u7d20\u304c\u5165\u529b\u3068\u3057\u3066\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408\u306e\u30d2\u30fc\u30d7\u69cb\u7bc9\u306e\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O(n)\\)\u306b\u6700\u9069\u5316\u3067\u304d\u3001\u3053\u308c\u306f\u975e\u5e38\u306b\u52b9\u7387\u7684\u3067\u3059\u3002</li> <li>Top-k\u306f\u53e4\u5178\u7684\u306a\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u554f\u984c\u3067\u3001\u30d2\u30fc\u30d7\u30c7\u30fc\u30bf\u69cb\u9020\u3092\u4f7f\u7528\u3057\u3066\u52b9\u7387\u7684\u306b\u89e3\u6c7a\u3067\u304d\u3001\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O(n \\log k)\\)\u3067\u3059\u3002</li> </ul>"},{"location":"chapter_heap/summary/#2-q-a","title":"2. \u00a0 Q &amp; A","text":"<p>Q: \u30c7\u30fc\u30bf\u69cb\u9020\u306e\u300c\u30d2\u30fc\u30d7\u300d\u3068\u30e1\u30e2\u30ea\u7ba1\u7406\u306e\u300c\u30d2\u30fc\u30d7\u300d\u306f\u540c\u3058\u6982\u5ff5\u3067\u3059\u304b\uff1f</p> <p>\u3053\u306e2\u3064\u306f\u3001\u3069\u3061\u3089\u3082\u300c\u30d2\u30fc\u30d7\u300d\u3068\u547c\u3070\u308c\u307e\u3059\u304c\u3001\u540c\u3058\u6982\u5ff5\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u30b7\u30b9\u30c6\u30e0\u30e1\u30e2\u30ea\u306e\u30d2\u30fc\u30d7\u306f\u52d5\u7684\u30e1\u30e2\u30ea\u5272\u308a\u5f53\u3066\u306e\u4e00\u90e8\u3067\u3001\u30d7\u30ed\u30b0\u30e9\u30e0\u304c\u5b9f\u884c\u4e2d\u306b\u30c7\u30fc\u30bf\u3092\u683c\u7d0d\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002\u30d7\u30ed\u30b0\u30e9\u30e0\u306f\u3001\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u3084\u914d\u5217\u306a\u3069\u306e\u8907\u96d1\u306a\u69cb\u9020\u3092\u683c\u7d0d\u3059\u308b\u305f\u3081\u306b\u3001\u4e00\u5b9a\u91cf\u306e\u30d2\u30fc\u30d7\u30e1\u30e2\u30ea\u3092\u8981\u6c42\u3067\u304d\u307e\u3059\u3002\u5272\u308a\u5f53\u3066\u3089\u308c\u305f\u30c7\u30fc\u30bf\u304c\u4e0d\u8981\u306b\u306a\u3063\u305f\u3068\u304d\u306f\u3001\u30e1\u30e2\u30ea\u30ea\u30fc\u30af\u3092\u9632\u3050\u305f\u3081\u306b\u30d7\u30ed\u30b0\u30e9\u30e0\u304c\u3053\u306e\u30e1\u30e2\u30ea\u3092\u89e3\u653e\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u30b9\u30bf\u30c3\u30af\u30e1\u30e2\u30ea\u3068\u6bd4\u8f03\u3057\u3066\u3001\u30d2\u30fc\u30d7\u30e1\u30e2\u30ea\u306e\u7ba1\u7406\u3068\u4f7f\u7528\u306b\u306f\u3088\u308a\u591a\u304f\u306e\u6ce8\u610f\u304c\u5fc5\u8981\u3067\u3001\u4e0d\u9069\u5207\u306a\u4f7f\u7528\u306f\u30e1\u30e2\u30ea\u30ea\u30fc\u30af\u3084\u30c0\u30f3\u30b0\u30ea\u30f3\u30b0\u30dd\u30a4\u30f3\u30bf\u306b\u3064\u306a\u304c\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002</p>"},{"location":"chapter_heap/top_k/","title":"8.3 \u00a0 Top-k\u554f\u984c","text":"<p>Question</p> <p>\u9577\u3055\\(n\\)\u306e\u9806\u5e8f\u4ed8\u3051\u3089\u308c\u3066\u3044\u306a\u3044\u914d\u5217<code>nums</code>\u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u304d\u3001\u914d\u5217\u5185\u306e\u6700\u5927\\(k\\)\u500b\u306e\u8981\u7d20\u3092\u8fd4\u3057\u3066\u304f\u3060\u3055\u3044\u3002</p> <p>\u3053\u306e\u554f\u984c\u306b\u3064\u3044\u3066\u3001\u307e\u305a2\u3064\u306e\u76f4\u63a5\u7684\u306a\u89e3\u6cd5\u3092\u7d39\u4ecb\u3057\u3001\u6b21\u306b\u3088\u308a\u52b9\u7387\u7684\u306a\u30d2\u30fc\u30d7\u30d9\u30fc\u30b9\u306e\u65b9\u6cd5\u3092\u8aac\u660e\u3057\u307e\u3059\u3002</p>"},{"location":"chapter_heap/top_k/#831-1","title":"8.3.1 \u00a0 \u65b9\u6cd51\uff1a\u53cd\u5fa9\u9078\u629e","text":"<p>\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\\(k\\)\u56de\u306e\u53cd\u5fa9\u3092\u5b9f\u884c\u3057\u3001\u5404\u56de\u3067\\(1\\)\u756a\u76ee\u3001\\(2\\)\u756a\u76ee\u3001\\(\\dots\\)\u3001\\(k\\)\u756a\u76ee\u306b\u5927\u304d\u3044\u8981\u7d20\u3092\u62bd\u51fa\u3067\u304d\u307e\u3059\u3002\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O(nk)\\)\u3067\u3059\u3002</p> <p>\u3053\u306e\u65b9\u6cd5\u306f\\(k \\ll n\\)\u306e\u5834\u5408\u306b\u306e\u307f\u9069\u3057\u3066\u3044\u307e\u3059\u3002\\(k\\)\u304c\\(n\\)\u306b\u8fd1\u3044\u5834\u5408\u3001\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O(n^2)\\)\u306b\u8fd1\u3065\u304d\u3001\u975e\u5e38\u306b\u6642\u9593\u304c\u304b\u304b\u308a\u307e\u3059\u3002</p> <p></p> <p> \u56f3 8-6 \u00a0 \u6700\u5927k\u500b\u306e\u8981\u7d20\u3092\u53cd\u5fa9\u7684\u306b\u898b\u3064\u3051\u308b </p> <p>Tip</p> <p>\\(k = n\\)\u306e\u5834\u5408\u3001\u5b8c\u5168\u306b\u9806\u5e8f\u4ed8\u3051\u3089\u308c\u305f\u30b7\u30fc\u30b1\u30f3\u30b9\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u3001\u3053\u308c\u306f\u300c\u9078\u629e\u30bd\u30fc\u30c8\u300d\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3068\u540c\u7b49\u3067\u3059\u3002</p>"},{"location":"chapter_heap/top_k/#832-2","title":"8.3.2 \u00a0 \u65b9\u6cd52\uff1a\u30bd\u30fc\u30c8","text":"<p>\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u307e\u305a\u914d\u5217<code>nums</code>\u3092\u30bd\u30fc\u30c8\u3057\u3001\u6b21\u306b\u6700\u5f8c\u306e\\(k\\)\u500b\u306e\u8981\u7d20\u3092\u8fd4\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O(n \\log n)\\)\u3067\u3059\u3002</p> <p>\u660e\u3089\u304b\u306b\u3001\u3053\u306e\u65b9\u6cd5\u306f\u30bf\u30b9\u30af\u3092\u300c\u3084\u308a\u3059\u304e\u300d\u3066\u3044\u307e\u3059\u3002\u6700\u5927\\(k\\)\u500b\u306e\u8981\u7d20\u3092\u898b\u3064\u3051\u308b\u3060\u3051\u3067\u3088\u304f\u3001\u4ed6\u306e\u8981\u7d20\u3092\u30bd\u30fc\u30c8\u3059\u308b\u5fc5\u8981\u306f\u3042\u308a\u307e\u305b\u3093\u3002</p> <p></p> <p> \u56f3 8-7 \u00a0 \u30bd\u30fc\u30c8\u306b\u3088\u308b\u6700\u5927k\u500b\u306e\u8981\u7d20\u306e\u767a\u898b </p>"},{"location":"chapter_heap/top_k/#833-3","title":"8.3.3 \u00a0 \u65b9\u6cd53\uff1a\u30d2\u30fc\u30d7","text":"<p>\u4ee5\u4e0b\u306e\u30d7\u30ed\u30bb\u30b9\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u30d2\u30fc\u30d7\u306b\u57fa\u3065\u3044\u3066Top-k\u554f\u984c\u3092\u3088\u308a\u52b9\u7387\u7684\u306b\u89e3\u6c7a\u3067\u304d\u307e\u3059\u3002</p> <ol> <li>\u6700\u5c0f\u30d2\u30fc\u30d7\u3092\u521d\u671f\u5316\u3057\u307e\u3059\u3002\u5148\u982d\u8981\u7d20\u304c\u6700\u5c0f\u306b\u306a\u308a\u307e\u3059\u3002</li> <li>\u307e\u305a\u3001\u914d\u5217\u306e\u6700\u521d\u306e\\(k\\)\u500b\u306e\u8981\u7d20\u3092\u30d2\u30fc\u30d7\u306b\u633f\u5165\u3057\u307e\u3059\u3002</li> <li>\\(k + 1\\)\u756a\u76ee\u306e\u8981\u7d20\u304b\u3089\u958b\u59cb\u3057\u3001\u73fe\u5728\u306e\u8981\u7d20\u304c\u30d2\u30fc\u30d7\u306e\u5148\u982d\u8981\u7d20\u3088\u308a\u5927\u304d\u3044\u5834\u5408\u3001\u30d2\u30fc\u30d7\u306e\u5148\u982d\u8981\u7d20\u3092\u524a\u9664\u3057\u3001\u73fe\u5728\u306e\u8981\u7d20\u3092\u30d2\u30fc\u30d7\u306b\u633f\u5165\u3057\u307e\u3059\u3002</li> <li>\u8d70\u67fb\u3092\u5b8c\u4e86\u3057\u305f\u5f8c\u3001\u30d2\u30fc\u30d7\u306b\u306f\u6700\u5927\\(k\\)\u500b\u306e\u8981\u7d20\u304c\u542b\u307e\u308c\u3066\u3044\u307e\u3059\u3002</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> \u56f3 8-8 \u00a0 \u30d2\u30fc\u30d7\u306b\u57fa\u3065\u304f\u6700\u5927k\u500b\u306e\u8981\u7d20\u306e\u767a\u898b </p> <p>\u30b5\u30f3\u30d7\u30eb\u30b3\u30fc\u30c9\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig top_k.py<pre><code>def top_k_heap(nums: list[int], k: int) -&gt; list[int]:\n    \"\"\"\u30d2\u30fc\u30d7\u3092\u4f7f\u7528\u3057\u3066\u914d\u5217\u5185\u306e\u6700\u5927k\u500b\u306e\u8981\u7d20\u3092\u898b\u3064\u3051\u308b\"\"\"\n    # \u6700\u5c0f\u30d2\u30fc\u30d7\u3092\u521d\u671f\u5316\n    heap = []\n    # \u914d\u5217\u306e\u6700\u521d\u306ek\u500b\u306e\u8981\u7d20\u3092\u30d2\u30fc\u30d7\u306b\u5165\u529b\n    for i in range(k):\n        heapq.heappush(heap, nums[i])\n    # k+1\u756a\u76ee\u306e\u8981\u7d20\u304b\u3089\u3001\u30d2\u30fc\u30d7\u306e\u9577\u3055\u3092k\u306b\u4fdd\u3064\n    for i in range(k, len(nums)):\n        # \u73fe\u5728\u306e\u8981\u7d20\u304c\u30d2\u30fc\u30d7\u306e\u5148\u982d\u8981\u7d20\u3088\u308a\u5927\u304d\u3044\u5834\u5408\u3001\u30d2\u30fc\u30d7\u306e\u5148\u982d\u8981\u7d20\u3092\u524a\u9664\u3057\u3001\u73fe\u5728\u306e\u8981\u7d20\u3092\u30d2\u30fc\u30d7\u306b\u5165\u529b\n        if nums[i] &gt; heap[0]:\n            heapq.heappop(heap)\n            heapq.heappush(heap, nums[i])\n    return heap\n</code></pre> top_k.cpp<pre><code>/* \u30d2\u30fc\u30d7\u3092\u4f7f\u7528\u3057\u3066\u914d\u5217\u5185\u306e\u6700\u5927k\u500b\u306e\u8981\u7d20\u3092\u898b\u3064\u3051\u308b */\npriority_queue&lt;int, vector&lt;int&gt;, greater&lt;int&gt;&gt; topKHeap(vector&lt;int&gt; &amp;nums, int k) {\n    // \u6700\u5c0f\u30d2\u30fc\u30d7\u3092\u521d\u671f\u5316\n    priority_queue&lt;int, vector&lt;int&gt;, greater&lt;int&gt;&gt; heap;\n    // \u914d\u5217\u306e\u6700\u521d\u306ek\u500b\u306e\u8981\u7d20\u3092\u30d2\u30fc\u30d7\u306b\u5165\u529b\n    for (int i = 0; i &lt; k; i++) {\n        heap.push(nums[i]);\n    }\n    // k+1\u756a\u76ee\u306e\u8981\u7d20\u304b\u3089\u3001\u30d2\u30fc\u30d7\u306e\u9577\u3055\u3092k\u306b\u4fdd\u3064\n    for (int i = k; i &lt; nums.size(); i++) {\n        // \u73fe\u5728\u306e\u8981\u7d20\u304c\u30d2\u30fc\u30d7\u306e\u5148\u982d\u8981\u7d20\u3088\u308a\u5927\u304d\u3044\u5834\u5408\u3001\u30d2\u30fc\u30d7\u306e\u5148\u982d\u8981\u7d20\u3092\u524a\u9664\u3057\u3001\u73fe\u5728\u306e\u8981\u7d20\u3092\u30d2\u30fc\u30d7\u306b\u5165\u529b\n        if (nums[i] &gt; heap.top()) {\n            heap.pop();\n            heap.push(nums[i]);\n        }\n    }\n    return heap;\n}\n</code></pre> top_k.java<pre><code>/* \u30d2\u30fc\u30d7\u3092\u4f7f\u7528\u3057\u3066\u914d\u5217\u5185\u306e\u6700\u5927 k \u500b\u306e\u8981\u7d20\u3092\u691c\u7d22 */\nQueue&lt;Integer&gt; topKHeap(int[] nums, int k) {\n    // \u6700\u5c0f\u30d2\u30fc\u30d7\u3092\u521d\u671f\u5316\n    Queue&lt;Integer&gt; heap = new PriorityQueue&lt;Integer&gt;();\n    // \u914d\u5217\u306e\u6700\u521d\u306e k \u500b\u306e\u8981\u7d20\u3092\u30d2\u30fc\u30d7\u306b\u5165\u529b\n    for (int i = 0; i &lt; k; i++) {\n        heap.offer(nums[i]);\n    }\n    // k+1 \u756a\u76ee\u306e\u8981\u7d20\u304b\u3089\u3001\u30d2\u30fc\u30d7\u306e\u9577\u3055\u3092 k \u306b\u4fdd\u3064\n    for (int i = k; i &lt; nums.length; i++) {\n        // \u73fe\u5728\u306e\u8981\u7d20\u304c\u30d2\u30fc\u30d7\u306e\u5148\u982d\u8981\u7d20\u3088\u308a\u5927\u304d\u3044\u5834\u5408\u3001\u30d2\u30fc\u30d7\u306e\u5148\u982d\u8981\u7d20\u3092\u524a\u9664\u3057\u3001\u73fe\u5728\u306e\u8981\u7d20\u3092\u30d2\u30fc\u30d7\u306b\u5165\u529b\n        if (nums[i] &gt; heap.peek()) {\n            heap.poll();\n            heap.offer(nums[i]);\n        }\n    }\n    return heap;\n}\n</code></pre> top_k.cs<pre><code>[class]{top_k}-[func]{TopKHeap}\n</code></pre> top_k.go<pre><code>[class]{}-[func]{topKHeap}\n</code></pre> top_k.swift<pre><code>[class]{}-[func]{topKHeap}\n</code></pre> top_k.js<pre><code>[class]{}-[func]{pushMinHeap}\n\n[class]{}-[func]{popMinHeap}\n\n[class]{}-[func]{peekMinHeap}\n\n[class]{}-[func]{getMinHeap}\n\n[class]{}-[func]{topKHeap}\n</code></pre> top_k.ts<pre><code>[class]{}-[func]{pushMinHeap}\n\n[class]{}-[func]{popMinHeap}\n\n[class]{}-[func]{peekMinHeap}\n\n[class]{}-[func]{getMinHeap}\n\n[class]{}-[func]{topKHeap}\n</code></pre> top_k.dart<pre><code>[class]{}-[func]{topKHeap}\n</code></pre> top_k.rs<pre><code>[class]{}-[func]{top_k_heap}\n</code></pre> top_k.c<pre><code>[class]{}-[func]{pushMinHeap}\n\n[class]{}-[func]{popMinHeap}\n\n[class]{}-[func]{peekMinHeap}\n\n[class]{}-[func]{getMinHeap}\n\n[class]{}-[func]{topKHeap}\n</code></pre> top_k.kt<pre><code>[class]{}-[func]{topKHeap}\n</code></pre> top_k.rb<pre><code>[class]{}-[func]{top_k_heap}\n</code></pre> top_k.zig<pre><code>[class]{}-[func]{topKHeap}\n</code></pre> <p>\u5408\u8a08\\(n\\)\u56de\u306e\u30d2\u30fc\u30d7\u633f\u5165\u3068\u524a\u9664\u304c\u5b9f\u884c\u3055\u308c\u3001\u6700\u5927\u30d2\u30fc\u30d7\u30b5\u30a4\u30ba\u304c\\(k\\)\u3067\u3042\u308b\u305f\u3081\u3001\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O(n \\log k)\\)\u3067\u3059\u3002\u3053\u306e\u65b9\u6cd5\u306f\u975e\u5e38\u306b\u52b9\u7387\u7684\u3067\u3001\\(k\\)\u304c\u5c0f\u3055\u3044\u5834\u5408\u3001\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O(n)\\)\u306b\u8fd1\u3065\u304d\u3001\\(k\\)\u304c\u5927\u304d\u3044\u5834\u5408\u3067\u3082\u3001\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O(n \\log n)\\)\u3092\u8d85\u3048\u307e\u305b\u3093\u3002</p> <p>\u3055\u3089\u306b\u3001\u3053\u306e\u65b9\u6cd5\u306f\u52d5\u7684\u30c7\u30fc\u30bf\u30b9\u30c8\u30ea\u30fc\u30e0\u306e\u30b7\u30ca\u30ea\u30aa\u306b\u9069\u3057\u3066\u3044\u307e\u3059\u3002\u30c7\u30fc\u30bf\u3092\u7d99\u7d9a\u7684\u306b\u8ffd\u52a0\u3059\u308b\u3053\u3068\u3067\u3001\u30d2\u30fc\u30d7\u5185\u306e\u8981\u7d20\u3092\u7dad\u6301\u3057\u3001\u6700\u5927\\(k\\)\u500b\u306e\u8981\u7d20\u306e\u52d5\u7684\u66f4\u65b0\u3092\u5b9f\u73fe\u3067\u304d\u307e\u3059\u3002</p>"},{"location":"chapter_hello_algo/","title":"\u306f\u3058\u3081\u306b","text":"<p>\u6570\u5e74\u524d\u3001\u79c1\u306fLeetCode\u3067\u300c\u5263\u6307Offer\u300d\u306e\u554f\u984c\u89e3\u7b54\u3092\u5171\u6709\u3057\u3001\u591a\u304f\u306e\u8aad\u8005\u304b\u3089\u52b1\u307e\u3057\u3068\u30b5\u30dd\u30fc\u30c8\u3092\u53d7\u3051\u307e\u3057\u305f\u3002\u8aad\u8005\u3068\u306e\u3084\u308a\u53d6\u308a\u306e\u4e2d\u3067\u3001\u6700\u3082\u3088\u304f\u805e\u304b\u308c\u305f\u8cea\u554f\u306f\u300c\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u52c9\u5f37\u3092\u3069\u3046\u59cb\u3081\u305f\u3089\u3088\u3044\u304b\u300d\u3067\u3057\u305f\u3002\u6b21\u7b2c\u306b\u3001\u79c1\u306f\u3053\u306e\u8cea\u554f\u306b\u5f37\u3044\u95a2\u5fc3\u3092\u62b1\u304f\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u305f\u3002</p> <p>\u554f\u984c\u3092\u76f4\u63a5\u89e3\u304f\u3053\u3068\u304c\u6700\u3082\u4eba\u6c17\u306e\u3042\u308b\u65b9\u6cd5\u306e\u3088\u3046\u3067\u3059\u3002\u3053\u308c\u306f\u30b7\u30f3\u30d7\u30eb\u3067\u76f4\u63a5\u7684\u3067\u52b9\u679c\u7684\u3067\u3059\u3002\u3057\u304b\u3057\u3001\u554f\u984c\u89e3\u6c7a\u306f\u30de\u30a4\u30f3\u30b9\u30a4\u30fc\u30d1\u30fc\u3092\u30d7\u30ec\u30a4\u3059\u308b\u3088\u3046\u306a\u3082\u306e\u3067\u3059\u3002\u81ea\u5b66\u81ea\u7fd2\u306e\u80fd\u529b\u304c\u9ad8\u3044\u4eba\u306f\u3001\u5730\u96f7\u3092\u4e00\u3064\u305a\u3064\u56de\u907f\u3057\u3066\u3044\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u304c\u3001\u3057\u3063\u304b\u308a\u3068\u3057\u305f\u57fa\u790e\u304c\u306a\u3044\u4eba\u306f\u3001\u4f55\u5ea6\u3082\u3064\u307e\u305a\u3044\u3066\u632b\u6298\u3057\u306a\u304c\u3089\u5f8c\u9000\u3059\u308b\u3053\u3068\u306b\u306a\u308b\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u3002\u6559\u79d1\u66f8\u3092\u8aad\u3080\u3053\u3068\u3082\u4e00\u822c\u7684\u306a\u65b9\u6cd5\u3067\u3059\u304c\u3001\u5c31\u8077\u6d3b\u52d5\u4e2d\u306e\u4eba\u306b\u3068\u3063\u3066\u3001\u5352\u696d\u8ad6\u6587\u306e\u57f7\u7b46\u3001\u5c65\u6b74\u66f8\u306e\u63d0\u51fa\u3001\u7b46\u8a18\u8a66\u9a13\u3084\u9762\u63a5\u306e\u6e96\u5099\u304c\u65e2\u306b\u30a8\u30cd\u30eb\u30ae\u30fc\u306e\u5927\u90e8\u5206\u3092\u6d88\u8cbb\u3057\u3066\u304a\u308a\u3001\u5206\u539a\u3044\u672c\u3092\u8aad\u3080\u3053\u3068\u306f\u3057\u3070\u3057\u3070\u56f0\u96e3\u306a\u6311\u6226\u3068\u306a\u308a\u307e\u3059\u3002</p> <p>\u3082\u3057\u3042\u306a\u305f\u304c\u540c\u69d8\u306e\u60a9\u307f\u3092\u62b1\u3048\u3066\u3044\u308b\u306a\u3089\u3001\u3053\u306e\u672c\u304c\u3042\u306a\u305f\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u3066\u5e78\u904b\u3067\u3059\u3002\u3053\u306e\u672c\u306f\u3001\u3053\u306e\u8cea\u554f\u306b\u5bfe\u3059\u308b\u79c1\u306e\u7b54\u3048\u3067\u3059\u3002\u3053\u308c\u304c\u6700\u826f\u306e\u89e3\u6c7a\u7b56\u3067\u306f\u306a\u3044\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u304c\u3001\u5c11\u306a\u304f\u3068\u3082\u7a4d\u6975\u7684\u306a\u8a66\u307f\u3067\u3059\u3002\u3053\u306e\u672c\u304c\u3042\u306a\u305f\u306b\u76f4\u63a5\u5185\u5b9a\u3092\u3082\u305f\u3089\u3059\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093\u304c\u3001\u30c7\u30fc\u30bf\u69cb\u9020\u3068\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u300c\u77e5\u8b58\u5730\u56f3\u300d\u3092\u63a2\u7d22\u3059\u308b\u624b\u5f15\u304d\u3068\u306a\u308a\u3001\u3055\u307e\u3056\u307e\u306a\u300c\u5730\u96f7\u300d\u306e\u5f62\u3001\u5927\u304d\u3055\u3001\u4f4d\u7f6e\u3092\u7406\u89e3\u3057\u3001\u3055\u307e\u3056\u307e\u306a\u300c\u5730\u96f7\u9664\u53bb\u65b9\u6cd5\u300d\u3092\u30de\u30b9\u30bf\u30fc\u3067\u304d\u308b\u3088\u3046\u304a\u624b\u4f1d\u3044\u3057\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u30b9\u30ad\u30eb\u304c\u3042\u308c\u3070\u3001\u3088\u308a\u5feb\u9069\u306b\u554f\u984c\u3092\u89e3\u304d\u3001\u6587\u732e\u3092\u8aad\u3080\u3053\u3068\u304c\u3067\u304d\u3001\u5f90\u3005\u306b\u77e5\u8b58\u4f53\u7cfb\u3092\u69cb\u7bc9\u3067\u304d\u308b\u3068\u4fe1\u3058\u3066\u3044\u307e\u3059\u3002</p> <p>\u79c1\u306f\u3001\u30d5\u30a1\u30a4\u30f3\u30de\u30f3\u6559\u6388\u306e\u8a00\u8449\u306b\u6df1\u304f\u540c\u611f\u3057\u307e\u3059\u3002\u300c\u77e5\u8b58\u306f\u7121\u6599\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u6ce8\u610f\u3092\u6255\u308f\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044\u306e\u3067\u3059\u3002\u300d\u3053\u306e\u610f\u5473\u3067\u3001\u3053\u306e\u672c\u306f\u5b8c\u5168\u306b\u300c\u7121\u6599\u300d\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u3053\u306e\u672c\u306b\u5bfe\u3059\u308b\u3042\u306a\u305f\u306e\u8cb4\u91cd\u306a\u300c\u6ce8\u610f\u300d\u306b\u5fdc\u3048\u308b\u305f\u3081\u306b\u3001\u79c1\u306f\u6700\u5584\u3092\u5c3d\u304f\u3057\u3001\u6700\u5927\u306e\u300c\u6ce8\u610f\u300d\u3092\u6255\u3063\u3066\u3053\u306e\u672c\u3092\u66f8\u304d\u307e\u3059\u3002</p> <p>\u81ea\u5206\u306e\u9650\u754c\u3092\u8a8d\u8b58\u3057\u3066\u304a\u308a\u3001\u3053\u306e\u672c\u306e\u5185\u5bb9\u304c\u6642\u9593\u3092\u304b\u3051\u3066\u6d17\u7df4\u3055\u308c\u305f\u306b\u3082\u304b\u304b\u308f\u3089\u305a\u3001\u9593\u9055\u3044\u306f\u78ba\u5b9f\u306b\u6b8b\u3063\u3066\u3044\u308b\u3053\u3068\u3092\u7406\u89e3\u3057\u3066\u3044\u307e\u3059\u3002\u5148\u751f\u65b9\u3084\u5b66\u751f\u306e\u7686\u69d8\u304b\u3089\u306e\u6279\u8a55\u3068\u8a02\u6b63\u3092\u5fc3\u304b\u3089\u6b53\u8fce\u3044\u305f\u3057\u307e\u3059\u3002</p> <p></p> Hello, Algo! <p>\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u306e\u51fa\u73fe\u306f\u4e16\u754c\u306b\u5927\u304d\u306a\u5909\u5316\u3092\u3082\u305f\u3089\u3057\u307e\u3057\u305f\u3002\u9ad8\u901f\u306a\u8a08\u7b97\u80fd\u529b\u3068\u512a\u308c\u305f\u30d7\u30ed\u30b0\u30e9\u30e0\u53ef\u80fd\u6027\u306b\u3088\u308a\u3001\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u306f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u5b9f\u884c\u3057\u30c7\u30fc\u30bf\u3092\u51e6\u7406\u3059\u308b\u305f\u3081\u306e\u7406\u60f3\u7684\u306a\u5a92\u4f53\u3068\u306a\u308a\u307e\u3057\u305f\u3002\u30d3\u30c7\u30aa\u30b2\u30fc\u30e0\u306e\u30ea\u30a2\u30eb\u306a\u30b0\u30e9\u30d5\u30a3\u30c3\u30af\u30b9\u3001\u81ea\u52d5\u904b\u8ee2\u306e\u77e5\u7684\u306a\u5224\u65ad\u3001AlphaGo\u306e\u898b\u4e8b\u306a\u56f2\u7881\u30b2\u30fc\u30e0\u3001ChatGPT\u306e\u81ea\u7136\u306a\u5bfe\u8a71\u306a\u3069\u3001\u3053\u308c\u3089\u306e\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u306f\u3059\u3079\u3066\u3001\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u4e0a\u3067\u52d5\u4f5c\u3059\u308b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u7cbe\u5de7\u306a\u5b9f\u6f14\u3067\u3059\u3002</p> <p>\u5b9f\u969b\u3001\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u306e\u51fa\u73fe\u4ee5\u524d\u304b\u3089\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3068\u30c7\u30fc\u30bf\u69cb\u9020\u306f\u4e16\u754c\u306e\u81f3\u308b\u6240\u306b\u5b58\u5728\u3057\u3066\u3044\u307e\u3057\u305f\u3002\u521d\u671f\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u6bd4\u8f03\u7684\u30b7\u30f3\u30d7\u30eb\u3067\u3001\u53e4\u4ee3\u306e\u8a08\u6570\u65b9\u6cd5\u3084\u9053\u5177\u4f5c\u308a\u306e\u624b\u9806\u306a\u3069\u304c\u3042\u308a\u307e\u3057\u305f\u3002\u6587\u660e\u304c\u9032\u6b69\u3059\u308b\u306b\u3064\u308c\u3066\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u3088\u308a\u6d17\u7df4\u3055\u308c\u8907\u96d1\u306b\u306a\u308a\u307e\u3057\u305f\u3002\u8077\u4eba\u306e\u7cbe\u5de7\u306a\u6280\u8853\u304b\u3089\u3001\u751f\u7523\u529b\u3092\u89e3\u653e\u3059\u308b\u5de5\u696d\u88fd\u54c1\u3001\u5b87\u5b99\u3092\u652f\u914d\u3059\u308b\u79d1\u5b66\u6cd5\u5247\u307e\u3067\u3001\u307b\u307c\u3059\u3079\u3066\u306e\u5e73\u51e1\u307e\u305f\u306f\u9a5a\u7570\u7684\u306a\u3053\u3068\u306e\u80cc\u5f8c\u306b\u306f\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5de7\u5999\u306a\u601d\u8003\u304c\u3042\u308a\u307e\u3059\u3002</p> <p>\u540c\u69d8\u306b\u3001\u30c7\u30fc\u30bf\u69cb\u9020\u306f\u81f3\u308b\u6240\u306b\u3042\u308a\u307e\u3059\u3002\u30bd\u30fc\u30b7\u30e3\u30eb\u30cd\u30c3\u30c8\u30ef\u30fc\u30af\u304b\u3089\u5730\u4e0b\u9244\u8def\u7dda\u307e\u3067\u3001\u591a\u304f\u306e\u30b7\u30b9\u30c6\u30e0\u306f\u300c\u30b0\u30e9\u30d5\u300d\u3068\u3057\u3066\u30e2\u30c7\u30eb\u5316\u3067\u304d\u307e\u3059\u3002\u56fd\u304b\u3089\u5bb6\u65cf\u307e\u3067\u3001\u793e\u4f1a\u7d44\u7e54\u306e\u4e3b\u8981\u306a\u5f62\u614b\u306f\u300c\u6728\u300d\u306e\u7279\u5fb4\u3092\u793a\u3057\u307e\u3059\u3002\u51ac\u670d\u306f\u300c\u30b9\u30bf\u30c3\u30af\u300d\u306e\u3088\u3046\u3067\u3001\u6700\u521d\u306b\u7740\u305f\u3082\u306e\u304c\u6700\u5f8c\u306b\u8131\u304c\u308c\u307e\u3059\u3002\u30d0\u30c9\u30df\u30f3\u30c8\u30f3\u306e\u30b7\u30e3\u30c8\u30eb\u7b52\u306f\u300c\u30ad\u30e5\u30fc\u300d\u306b\u4f3c\u3066\u304a\u308a\u3001\u4e00\u65b9\u306e\u7aef\u3067\u633f\u5165\u3057\u3001\u3082\u3046\u4e00\u65b9\u306e\u7aef\u3067\u53d6\u308a\u51fa\u3057\u307e\u3059\u3002\u8f9e\u66f8\u306f\u300c\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u300d\u306e\u3088\u3046\u3067\u3001\u76ee\u6a19\u30a8\u30f3\u30c8\u30ea\u3092\u7d20\u65e9\u304f\u691c\u7d22\u3067\u304d\u307e\u3059\u3002</p> <p>\u3053\u306e\u672c\u306f\u3001\u660e\u78ba\u3067\u7406\u89e3\u3057\u3084\u3059\u3044\u30a2\u30cb\u30e1\u30fc\u30b7\u30e7\u30f3\u56f3\u89e3\u3068\u5b9f\u884c\u53ef\u80fd\u306a\u30b3\u30fc\u30c9\u4f8b\u3092\u901a\u3058\u3066\u3001\u8aad\u8005\u304c\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3068\u30c7\u30fc\u30bf\u69cb\u9020\u306e\u6838\u5fc3\u6982\u5ff5\u3092\u7406\u89e3\u3057\u3001\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u3092\u901a\u3058\u3066\u305d\u308c\u3089\u3092\u5b9f\u88c5\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308b\u3053\u3068\u3092\u76ee\u6307\u3057\u3066\u3044\u307e\u3059\u3002\u3053\u306e\u57fa\u76e4\u306e\u4e0a\u3067\u3001\u3053\u306e\u672c\u306f\u8907\u96d1\u306a\u4e16\u754c\u306b\u304a\u3051\u308b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u751f\u304d\u751f\u304d\u3068\u3057\u305f\u73fe\u308c\u3092\u660e\u3089\u304b\u306b\u3057\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u7f8e\u3057\u3055\u3092\u793a\u3059\u3053\u3068\u306b\u52aa\u3081\u3066\u3044\u307e\u3059\u3002\u3053\u306e\u672c\u304c\u3042\u306a\u305f\u306e\u304a\u5f79\u306b\u7acb\u3066\u308b\u3053\u3068\u3092\u9858\u3063\u3066\u3044\u307e\u3059\uff01</p>"},{"location":"chapter_introduction/","title":"\u7b2c 1 \u7ae0 \u00a0 \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3068\u306e\u51fa\u4f1a\u3044","text":"<p>Abstract</p> <p>\u512a\u96c5\u306a\u4e59\u5973\u304c\u8e0a\u308a\u307e\u3059\u3002\u30c7\u30fc\u30bf\u3068\u7d61\u307f\u5408\u3044\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u30e1\u30ed\u30c7\u30a3\u30fc\u306b\u5408\u308f\u305b\u3066\u30b9\u30ab\u30fc\u30c8\u3092\u306a\u3073\u304b\u305b\u306a\u304c\u3089\u3002</p> <p>\u5f7c\u5973\u304c\u3042\u306a\u305f\u3092\u30c0\u30f3\u30b9\u306b\u8a98\u3044\u307e\u3059\u3002\u5f7c\u5973\u306e\u30b9\u30c6\u30c3\u30d7\u306b\u5f93\u3063\u3066\u3001\u8ad6\u7406\u3068\u7f8e\u306b\u6e80\u3061\u305f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u4e16\u754c\u306b\u5165\u308a\u307e\u3057\u3087\u3046\u3002</p>"},{"location":"chapter_introduction/#_1","title":"\u7ae0\u306e\u5185\u5bb9","text":"<ul> <li>1.1 \u00a0 \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u3069\u3053\u306b\u3067\u3082\u3042\u308b</li> <li>1.2 \u00a0 \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3068\u306f\u4f55\u304b</li> <li>1.3 \u00a0 \u307e\u3068\u3081</li> </ul>"},{"location":"chapter_introduction/algorithms_are_everywhere/","title":"1.1 \u00a0 \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u81f3\u308b\u6240\u306b\u3042\u308b","text":"<p>\u300c\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u300d\u3068\u3044\u3046\u8a00\u8449\u3092\u805e\u304f\u3068\u3001\u81ea\u7136\u306b\u6570\u5b66\u3092\u601d\u3044\u6d6e\u304b\u3079\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u591a\u304f\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u8907\u96d1\u306a\u6570\u5b66\u3092\u542b\u307e\u305a\u3001\u57fa\u672c\u7684\u306a\u8ad6\u7406\u306b\u3088\u308a\u591a\u304f\u4f9d\u5b58\u3057\u3066\u304a\u308a\u3001\u3053\u308c\u306f\u79c1\u305f\u3061\u306e\u65e5\u5e38\u751f\u6d3b\u306e\u81f3\u308b\u6240\u3067\u898b\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002</p> <p>\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306b\u3064\u3044\u3066\u6b63\u5f0f\u306b\u8b70\u8ad6\u3092\u59cb\u3081\u308b\u524d\u306b\u3001\u8208\u5473\u6df1\u3044\u4e8b\u5b9f\u3092\u5171\u6709\u3059\u308b\u4fa1\u5024\u304c\u3042\u308a\u307e\u3059\u3002\u3042\u306a\u305f\u306f\u7121\u610f\u8b58\u306e\u3046\u3061\u306b\u591a\u304f\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u5b66\u3073\u3001\u65e5\u5e38\u751f\u6d3b\u3067\u305d\u308c\u3089\u3092\u5fdc\u7528\u3059\u308b\u3053\u3068\u306b\u6163\u308c\u3066\u3044\u307e\u3059\u3002\u3053\u3053\u3067\u3001\u3053\u306e\u70b9\u3092\u8a3c\u660e\u3059\u308b\u305f\u3081\u306b\u3044\u304f\u3064\u304b\u306e\u5177\u4f53\u7684\u306a\u4f8b\u3092\u6319\u3052\u307e\u3059\u3002</p> <p>\u4f8b1\uff1a\u8f9e\u66f8\u306e\u5f15\u304d\u65b9\u3002\u82f1\u8a9e\u306e\u8f9e\u66f8\u3067\u306f\u3001\u5358\u8a9e\u304c\u30a2\u30eb\u30d5\u30a1\u30d9\u30c3\u30c8\u9806\u306b\u4e26\u3093\u3067\u3044\u307e\u3059\u3002\\(r\\)\u3067\u59cb\u307e\u308b\u5358\u8a9e\u3092\u63a2\u3057\u3066\u3044\u308b\u3068\u4eee\u5b9a\u3059\u308b\u3068\u3001\u901a\u5e38\u306f\u4ee5\u4e0b\u306e\u65b9\u6cd5\u3067\u884c\u3044\u307e\u3059\uff1a</p> <ol> <li>\u8f9e\u66f8\u3092\u5927\u4f53\u534a\u5206\u3050\u3089\u3044\u306e\u3068\u3053\u308d\u3067\u958b\u304d\u3001\u305d\u306e\u30da\u30fc\u30b8\u306e\u6700\u521d\u306e\u8a9e\u5f59\u3092\u78ba\u8a8d\u3057\u307e\u3059\u3002\u4f8b\u3048\u3070\\(m\\)\u3067\u59cb\u307e\u308b\u6587\u5b57\u3060\u3068\u3057\u307e\u3057\u3087\u3046\u3002</li> <li>\\(r\\)\u306f\u30a2\u30eb\u30d5\u30a1\u30d9\u30c3\u30c8\u3067\\(m\\)\u306e\u5f8c\u306b\u6765\u308b\u306e\u3067\u3001\u524d\u534a\u3092\u7121\u8996\u3057\u3066\u3001\u63a2\u7d22\u7a7a\u9593\u3092\u5f8c\u534a\u306b\u7d5e\u308a\u307e\u3059\u3002</li> <li>\\(r\\)\u3067\u59cb\u307e\u308b\u5358\u8a9e\u3092\u898b\u3064\u3051\u308b\u307e\u3067\u3001\u30b9\u30c6\u30c3\u30d7<code>1.</code>\u3068<code>2.</code>\u3092\u7e70\u308a\u8fd4\u3057\u307e\u3059\u3002</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p> \u56f3 1-1 \u00a0 \u8f9e\u66f8\u3092\u5f15\u304f\u904e\u7a0b </p> <p>\u8f9e\u66f8\u3092\u5f15\u304f\u3053\u3068\u306f\u3001\u5c0f\u5b66\u751f\u306b\u3068\u3063\u3066\u5fc5\u9808\u306e\u30b9\u30ad\u30eb\u3067\u3059\u304c\u3001\u5b9f\u969b\u306b\u306f\u6709\u540d\u306a\u300c\u4e8c\u5206\u63a2\u7d22\u300d\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u3059\u3002\u30c7\u30fc\u30bf\u69cb\u9020\u306e\u89b3\u70b9\u304b\u3089\u3001\u8f9e\u66f8\u3092\u30bd\u30fc\u30c8\u3055\u308c\u305f\u300c\u914d\u5217\u300d\u3068\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u89b3\u70b9\u304b\u3089\u3001\u8f9e\u66f8\u3067\u5358\u8a9e\u3092\u63a2\u3059\u305f\u3081\u306b\u53d6\u3089\u308c\u308b\u4e00\u9023\u306e\u884c\u52d5\u306f\u3001\u300c\u4e8c\u5206\u63a2\u7d22\u300d\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3068\u898b\u306a\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002</p> <p>\u4f8b2\uff1a\u30c8\u30e9\u30f3\u30d7\u306e\u6574\u7406\u3002\u30c8\u30e9\u30f3\u30d7\u3092\u30d7\u30ec\u30a4\u3059\u308b\u3068\u304d\u3001\u624b\u672d\u3092\u6607\u9806\u306b\u4e26\u3079\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u4ee5\u4e0b\u306e\u904e\u7a0b\u3067\u793a\u3055\u308c\u307e\u3059\u3002</p> <ol> <li>\u30c8\u30e9\u30f3\u30d7\u3092\u300c\u6574\u5217\u6e08\u307f\u300d\u3068\u300c\u672a\u6574\u5217\u300d\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u306b\u5206\u3051\u307e\u3059\u3002\u6700\u521d\u306f\u4e00\u756a\u5de6\u306e\u30ab\u30fc\u30c9\u304c\u65e2\u306b\u6574\u5217\u3057\u3066\u3044\u308b\u3068\u4eee\u5b9a\u3057\u307e\u3059\u3002</li> <li>\u672a\u6574\u5217\u30bb\u30af\u30b7\u30e7\u30f3\u304b\u3089\u30ab\u30fc\u30c9\u30921\u679a\u53d6\u308a\u51fa\u3057\u3001\u6574\u5217\u6e08\u307f\u30bb\u30af\u30b7\u30e7\u30f3\u306e\u6b63\u3057\u3044\u4f4d\u7f6e\u306b\u633f\u5165\u3057\u307e\u3059\u3002\u3053\u306e\u5f8c\u3001\u5de6\u7aef\u306e2\u679a\u306e\u30ab\u30fc\u30c9\u304c\u6574\u5217\u3057\u307e\u3059\u3002</li> <li>\u3059\u3079\u3066\u306e\u30ab\u30fc\u30c9\u304c\u6574\u5217\u3059\u308b\u307e\u3067\u3001\u30b9\u30c6\u30c3\u30d7<code>2</code>\u3092\u7e70\u308a\u8fd4\u3057\u307e\u3059\u3002</li> </ol> <p></p> <p> \u56f3 1-2 \u00a0 \u30c8\u30e9\u30f3\u30d7\u306e\u6574\u7406\u904e\u7a0b </p> <p>\u4e0a\u8a18\u306e\u30c8\u30e9\u30f3\u30d7\u3092\u6574\u7406\u3059\u308b\u65b9\u6cd5\u306f\u3001\u5b9f\u8cea\u7684\u306b\u300c\u633f\u5165\u30bd\u30fc\u30c8\u300d\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u3042\u308a\u3001\u5c0f\u3055\u306a\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u306b\u5bfe\u3057\u3066\u975e\u5e38\u306b\u52b9\u7387\u7684\u3067\u3059\u3002\u591a\u304f\u306e\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u306e\u30bd\u30fc\u30c8\u95a2\u6570\u306b\u306f\u633f\u5165\u30bd\u30fc\u30c8\u304c\u542b\u307e\u308c\u3066\u3044\u307e\u3059\u3002</p> <p>\u4f8b3\uff1a\u304a\u91e3\u308a\u306e\u8a08\u7b97\u3002\u30b9\u30fc\u30d1\u30fc\u30de\u30fc\u30b1\u30c3\u30c8\u3067\\(69\\)\u306e\u8cb7\u3044\u7269\u3092\u3057\u305f\u3068\u4eee\u5b9a\u3057\u307e\u3059\u3002\u30ec\u30b8\u4fc2\u306b\\(100\\)\u3092\u6e21\u3059\u3068\u3001\\(31\\)\u306e\u304a\u91e3\u308a\u3092\u63d0\u4f9b\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u904e\u7a0b\u306f\u4ee5\u4e0b\u306e\u56f3\u3067\u660e\u78ba\u306b\u7406\u89e3\u3067\u304d\u307e\u3059\u3002</p> <ol> <li>\u9078\u629e\u80a2\u306f\\(31\\)\u4ee5\u4e0b\u306e\u4fa1\u5024\u306e\u3042\u308b\u901a\u8ca8\u3067\u3001\\(1\\)\u3001\\(5\\)\u3001\\(10\\)\u3001\\(20\\)\u304c\u542b\u307e\u308c\u307e\u3059\u3002</li> <li>\u9078\u629e\u80a2\u304b\u3089\u6700\u5927\u306e\\(20\\)\u3092\u53d6\u308a\u51fa\u3057\u3001\\(31 - 20 = 11\\)\u304c\u6b8b\u308a\u307e\u3059\u3002</li> <li>\u6b8b\u308a\u306e\u9078\u629e\u80a2\u304b\u3089\u6700\u5927\u306e\\(10\\)\u3092\u53d6\u308a\u51fa\u3057\u3001\\(11 - 10 = 1\\)\u304c\u6b8b\u308a\u307e\u3059\u3002</li> <li>\u6b8b\u308a\u306e\u9078\u629e\u80a2\u304b\u3089\u6700\u5927\u306e\\(1\\)\u3092\u53d6\u308a\u51fa\u3057\u3001\\(1 - 1 = 0\\)\u304c\u6b8b\u308a\u307e\u3059\u3002</li> <li>\u304a\u91e3\u308a\u306e\u8a08\u7b97\u304c\u5b8c\u4e86\u3057\u3001\u89e3\u7b54\u306f\\(20 + 10 + 1 = 31\\)\u3067\u3059\u3002</li> </ol> <p></p> <p> \u56f3 1-3 \u00a0 \u304a\u91e3\u308a\u306e\u8a08\u7b97\u904e\u7a0b </p> <p>\u8a18\u8ff0\u3055\u308c\u305f\u30b9\u30c6\u30c3\u30d7\u3067\u306f\u3001\u5229\u7528\u53ef\u80fd\u306a\u6700\u5927\u306e\u984d\u9762\u3092\u4f7f\u7528\u3057\u3066\u5404\u6bb5\u968e\u3067\u6700\u826f\u306e\u9078\u629e\u80a2\u3092\u9078\u3076\u3053\u3068\u3067\u3001\u52b9\u679c\u7684\u306a\u304a\u91e3\u308a\u8a08\u7b97\u6226\u7565\u306b\u3064\u306a\u304c\u308a\u307e\u3059\u3002\u30c7\u30fc\u30bf\u69cb\u9020\u3068\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u89b3\u70b9\u304b\u3089\u3001\u3053\u306e\u30a2\u30d7\u30ed\u30fc\u30c1\u306f\u300c\u8caa\u6b32\u300d\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3068\u3057\u3066\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\u3002</p> <p>\u6599\u7406\u306e\u6e96\u5099\u304b\u3089\u5b87\u5b99\u65c5\u884c\u307e\u3067\u3001\u307b\u307c\u3059\u3079\u3066\u306e\u554f\u984c\u89e3\u6c7a\u306b\u306f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u304c\u95a2\u308f\u3063\u3066\u3044\u307e\u3059\u3002\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u306e\u51fa\u73fe\u306b\u3088\u308a\u3001\u30e1\u30e2\u30ea\u306b\u30c7\u30fc\u30bf\u69cb\u9020\u3092\u683c\u7d0d\u3057\u3001CPU\u3068GPU\u3092\u547c\u3073\u51fa\u3057\u3066\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u5b9f\u884c\u3059\u308b\u30b3\u30fc\u30c9\u3092\u66f8\u304f\u3053\u3068\u304c\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u305f\u3002\u3053\u306e\u3088\u3046\u306b\u3057\u3066\u3001\u73fe\u5b9f\u4e16\u754c\u306e\u554f\u984c\u3092\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u306b\u79fb\u3057\u3001\u3088\u308a\u52b9\u7387\u7684\u306a\u65b9\u6cd5\u3067\u3055\u307e\u3056\u307e\u306a\u8907\u96d1\u306a\u554f\u984c\u3092\u89e3\u6c7a\u3067\u304d\u307e\u3059\u3002</p> <p>Tip</p> <p>\u30c7\u30fc\u30bf\u69cb\u9020\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3001\u914d\u5217\u3001\u4e8c\u5206\u63a2\u7d22\u306a\u3069\u306e\u6982\u5ff5\u306b\u3064\u3044\u3066\u307e\u3060\u6df7\u4e71\u3057\u3066\u3044\u308b\u5834\u5408\u306f\u3001\u8aad\u307f\u7d9a\u3051\u308b\u3053\u3068\u3092\u304a\u52e7\u3081\u3057\u307e\u3059\u3002\u3053\u306e\u672c\u306f\u3001\u30c7\u30fc\u30bf\u69cb\u9020\u3068\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u7406\u89e3\u306e\u9818\u57df\u3078\u3068\u512a\u3057\u304f\u5c0e\u3044\u3066\u304f\u308c\u308b\u3067\u3057\u3087\u3046\u3002</p>"},{"location":"chapter_introduction/summary/","title":"1.3 \u00a0 \u307e\u3068\u3081","text":"<ul> <li>\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u65e5\u5e38\u751f\u6d3b\u306b\u3042\u308a\u3075\u308c\u3066\u304a\u308a\u3001\u601d\u3063\u3066\u3044\u308b\u307b\u3069\u30a2\u30af\u30bb\u30b9\u3057\u306b\u304f\u304f\u8907\u96d1\u306a\u3082\u306e\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u5b9f\u969b\u3001\u79c1\u305f\u3061\u306f\u65e2\u306b\u7121\u610f\u8b58\u306e\u3046\u3061\u306b\u591a\u304f\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u5b66\u3073\u3001\u751f\u6d3b\u306e\u69d8\u3005\u306a\u554f\u984c\u3092\u89e3\u6c7a\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3057\u3066\u3044\u307e\u3059\u3002</li> <li>\u8f9e\u66f8\u3067\u5358\u8a9e\u3092\u5f15\u304f\u539f\u7406\u306f\u4e8c\u5206\u63a2\u7d22\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3068\u4e00\u81f4\u3057\u3066\u3044\u307e\u3059\u3002\u4e8c\u5206\u63a2\u7d22\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u5206\u5272\u7d71\u6cbb\u3068\u3044\u3046\u91cd\u8981\u306a\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u6982\u5ff5\u3092\u4f53\u73fe\u3057\u3066\u3044\u307e\u3059\u3002</li> <li>\u30c8\u30e9\u30f3\u30d7\u3092\u6574\u7406\u3059\u308b\u904e\u7a0b\u306f\u633f\u5165\u30bd\u30fc\u30c8\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3068\u975e\u5e38\u306b\u4f3c\u3066\u3044\u307e\u3059\u3002\u633f\u5165\u30bd\u30fc\u30c8\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u5c0f\u3055\u306a\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u306e\u30bd\u30fc\u30c8\u306b\u9069\u3057\u3066\u3044\u307e\u3059\u3002</li> <li>\u901a\u8ca8\u3067\u304a\u91e3\u308a\u3092\u8a08\u7b97\u3059\u308b\u30b9\u30c6\u30c3\u30d7\u306f\u672c\u8cea\u7684\u306b\u8caa\u6b32\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306b\u5f93\u3063\u3066\u304a\u308a\u3001\u5404\u30b9\u30c6\u30c3\u30d7\u3067\u305d\u306e\u6642\u70b9\u3067\u306e\u6700\u826f\u306e\u9078\u629e\u3092\u3057\u307e\u3059\u3002</li> <li>\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u6709\u9650\u6642\u9593\u5185\u3067\u7279\u5b9a\u306e\u554f\u984c\u3092\u89e3\u6c7a\u3059\u308b\u305f\u3081\u306e\u6bb5\u968e\u7684\u306a\u6307\u793a\u306e\u30bb\u30c3\u30c8\u3067\u3059\u304c\u3001\u30c7\u30fc\u30bf\u69cb\u9020\u306f\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u3067\u306e\u30c7\u30fc\u30bf\u306e\u7d44\u7e54\u5316\u3068\u4fdd\u5b58\u65b9\u6cd5\u3092\u5b9a\u7fa9\u3057\u307e\u3059\u3002</li> <li>\u30c7\u30fc\u30bf\u69cb\u9020\u3068\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u5bc6\u63a5\u306b\u95a2\u9023\u3057\u3066\u3044\u307e\u3059\u3002\u30c7\u30fc\u30bf\u69cb\u9020\u306f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u57fa\u790e\u3067\u3042\u308a\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u30c7\u30fc\u30bf\u69cb\u9020\u306e\u6a5f\u80fd\u3092\u6d3b\u7528\u3059\u308b\u30b9\u30c6\u30fc\u30b8\u3067\u3059\u3002</li> <li>\u30c7\u30fc\u30bf\u69cb\u9020\u3068\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u30d6\u30ed\u30c3\u30af\u306e\u7d44\u307f\u7acb\u3066\u306b\u4f8b\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u30d6\u30ed\u30c3\u30af\u306f\u30c7\u30fc\u30bf\u3092\u8868\u3057\u3001\u30d6\u30ed\u30c3\u30af\u306e\u5f62\u72b6\u3068\u63a5\u7d9a\u65b9\u6cd5\u306f\u30c7\u30fc\u30bf\u69cb\u9020\u3092\u8868\u3057\u3001\u30d6\u30ed\u30c3\u30af\u3092\u7d44\u307f\u7acb\u3066\u308b\u30b9\u30c6\u30c3\u30d7\u306f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002</li> </ul>"},{"location":"chapter_introduction/summary/#1-q-a","title":"1. \u00a0 Q &amp; A","text":"<p>Q\uff1a\u30d7\u30ed\u30b0\u30e9\u30de\u30fc\u3068\u3057\u3066\u3001\u65e5\u5e38\u306e\u4ed5\u4e8b\u3067\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u624b\u52d5\u3067\u5b9f\u88c5\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u3053\u3068\u306f\u3081\u3063\u305f\u306b\u3042\u308a\u307e\u305b\u3093\u3002\u6700\u3082\u4e00\u822c\u7684\u306b\u4f7f\u7528\u3055\u308c\u308b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u3001\u65e2\u306b\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u3068\u30e9\u30a4\u30d6\u30e9\u30ea\u306b\u7d44\u307f\u8fbc\u307e\u308c\u3066\u304a\u308a\u3001\u3059\u3050\u306b\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u79c1\u305f\u3061\u304c\u4ed5\u4e8b\u3067\u906d\u9047\u3059\u308b\u554f\u984c\u304c\u3001\u30ab\u30b9\u30bf\u30e0\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u8a2d\u8a08\u3092\u5fc5\u8981\u3068\u3059\u308b\u8907\u96d1\u3055\u306e\u30ec\u30d9\u30eb\u306b\u307e\u3060\u9054\u3057\u3066\u3044\u306a\u3044\u3053\u3068\u3092\u793a\u5506\u3057\u3066\u3044\u307e\u3059\u304b\uff1f</p> <p>\u7279\u5b9a\u306e\u4ed5\u4e8b\u30b9\u30ad\u30eb\u304c\u6b66\u8853\u306e\u300c\u6280\u300d\u306e\u3088\u3046\u306a\u3082\u306e\u3060\u3068\u3059\u308c\u3070\u3001\u57fa\u790e\u79d1\u76ee\u306f\u300c\u5185\u529f\u300d\u306e\u3088\u3046\u306a\u3082\u306e\u3067\u3059\u3002</p> <p>\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\uff08\u304a\u3088\u3073\u305d\u306e\u4ed6\u306e\u57fa\u790e\u79d1\u76ee\uff09\u3092\u5b66\u3076\u610f\u7fa9\u306f\u3001\u5fc5\u305a\u3057\u3082\u4ed5\u4e8b\u3067\u305d\u308c\u3089\u3092\u4e00\u304b\u3089\u5b9f\u88c5\u3059\u308b\u3053\u3068\u3067\u306f\u306a\u304f\u3001\u6982\u5ff5\u306e\u78ba\u56fa\u305f\u308b\u7406\u89e3\u306b\u57fa\u3065\u3044\u3066\u3001\u3088\u308a\u5c02\u9580\u7684\u306a\u610f\u601d\u6c7a\u5b9a\u3068\u554f\u984c\u89e3\u6c7a\u3092\u53ef\u80fd\u306b\u3057\u3001\u305d\u308c\u306b\u3088\u3063\u3066\u4ed5\u4e8b\u306e\u5168\u4f53\u7684\u306a\u8cea\u3092\u5411\u4e0a\u3055\u305b\u308b\u3053\u3068\u3060\u3068\u79c1\u306f\u4fe1\u3058\u3066\u3044\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u3059\u3079\u3066\u306e\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u306b\u306f\u7d44\u307f\u8fbc\u307f\u306e\u30bd\u30fc\u30c8\u95a2\u6570\u304c\u3042\u308a\u307e\u3059\uff1a</p> <ul> <li>\u30c7\u30fc\u30bf\u69cb\u9020\u3068\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u5b66\u3093\u3067\u3044\u306a\u3044\u5834\u5408\u3001\u3069\u3093\u306a\u30c7\u30fc\u30bf\u304c\u4e0e\u3048\u3089\u308c\u3066\u3082\u3001\u3053\u306e\u30bd\u30fc\u30c8\u95a2\u6570\u306b\u6e21\u3059\u3060\u3051\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u3002\u30b9\u30e0\u30fc\u30ba\u306b\u52d5\u4f5c\u3057\u3001\u826f\u3044\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u3092\u793a\u3057\u3001\u554f\u984c\u304c\u306a\u3044\u3088\u3046\u306b\u898b\u3048\u307e\u3059\u3002</li> <li>\u3057\u304b\u3057\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u5b66\u3093\u3060\u3053\u3068\u304c\u3042\u308c\u3070\u3001\u7d44\u307f\u8fbc\u307f\u306e\u30bd\u30fc\u30c8\u95a2\u6570\u306e\u6642\u9593\u8907\u96d1\u5ea6\u306f\u901a\u5e38\\(O(n \\log n)\\)\u3067\u3042\u308b\u3053\u3068\u3092\u7406\u89e3\u3057\u3066\u3044\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u30c7\u30fc\u30bf\u304c\u56fa\u5b9a\u6841\u6570\u306e\u6574\u6570\uff08\u5b66\u751fID\u306a\u3069\uff09\u3067\u69cb\u6210\u3055\u308c\u3066\u3044\u308b\u5834\u5408\u3001\u57fa\u6570\u30bd\u30fc\u30c8\u306e\u3088\u3046\u306a\u3088\u308a\u52b9\u7387\u7684\u306a\u30a2\u30d7\u30ed\u30fc\u30c1\u3092\u9069\u7528\u3067\u304d\u3001\u6642\u9593\u8907\u96d1\u5ea6\u3092O(nk)\u306b\u524a\u6e1b\u3067\u304d\u307e\u3059\u3002\u3053\u3053\u3067k\u306f\u6841\u6570\u3067\u3059\u3002\u5927\u91cf\u306e\u30c7\u30fc\u30bf\u3092\u51e6\u7406\u3059\u308b\u969b\u3001\u7bc0\u7d04\u3055\u308c\u305f\u6642\u9593\u306f\u91cd\u8981\u306a\u4fa1\u5024\u306b\u5909\u308f\u308a\u307e\u3059 \u2014 \u30b3\u30b9\u30c8\u306e\u524a\u6e1b\u3001\u30e6\u30fc\u30b6\u30fc\u30a8\u30af\u30b9\u30da\u30ea\u30a8\u30f3\u30b9\u306e\u5411\u4e0a\u3001\u30b7\u30b9\u30c6\u30e0\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u306e\u5411\u4e0a\u3002</li> </ul> <p>\u30a8\u30f3\u30b8\u30cb\u30a2\u30ea\u30f3\u30b0\u3067\u306f\u3001\u591a\u304f\u306e\u554f\u984c\u3092\u6700\u9069\u306b\u89e3\u6c7a\u3059\u308b\u3053\u3068\u306f\u56f0\u96e3\u3067\u3059\u3002\u307b\u3068\u3093\u3069\u306f\u300c\u6e96\u6700\u9069\u300d\u89e3\u6c7a\u7b56\u3067\u5bfe\u51e6\u3055\u308c\u307e\u3059\u3002\u554f\u984c\u306e\u96e3\u3057\u3055\u306f\u3001\u305d\u306e\u56fa\u6709\u306e\u8907\u96d1\u3055\u3060\u3051\u3067\u306a\u304f\u3001\u305d\u308c\u306b\u53d6\u308a\u7d44\u3080\u4eba\u306e\u77e5\u8b58\u3068\u7d4c\u9a13\u306b\u3082\u4f9d\u5b58\u3057\u307e\u3059\u3002\u5c02\u9580\u77e5\u8b58\u3068\u7d4c\u9a13\u304c\u6df1\u3044\u307b\u3069\u3001\u5206\u6790\u304c\u3088\u308a\u5fb9\u5e95\u7684\u306b\u306a\u308a\u3001\u554f\u984c\u3092\u3088\u308a\u512a\u96c5\u306b\u89e3\u6c7a\u3067\u304d\u307e\u3059\u3002</p>"},{"location":"chapter_introduction/what_is_dsa/","title":"1.2 \u00a0 \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3068\u306f\u4f55\u304b","text":""},{"location":"chapter_introduction/what_is_dsa/#121","title":"1.2.1 \u00a0 \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5b9a\u7fa9","text":"<p>\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u3001\u6709\u9650\u6642\u9593\u5185\u3067\u7279\u5b9a\u306e\u554f\u984c\u3092\u89e3\u6c7a\u3059\u308b\u305f\u3081\u306e\u4e00\u9023\u306e\u6307\u793a\u307e\u305f\u306f\u30b9\u30c6\u30c3\u30d7\u3067\u3059\u3002\u4ee5\u4e0b\u306e\u7279\u5fb4\u304c\u3042\u308a\u307e\u3059\uff1a</p> <ul> <li>\u554f\u984c\u304c\u660e\u78ba\u306b\u5b9a\u7fa9\u3055\u308c\u3066\u304a\u308a\u3001\u5165\u529b\u3068\u51fa\u529b\u306e\u660e\u78ba\u306a\u5b9a\u7fa9\u304c\u542b\u307e\u308c\u3066\u3044\u307e\u3059\u3002</li> <li>\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u5b9f\u884c\u53ef\u80fd\u3067\u3001\u6709\u9650\u306e\u56de\u6570\u306e\u30b9\u30c6\u30c3\u30d7\u3001\u6642\u9593\u3001\u30e1\u30e2\u30ea\u7a7a\u9593\u5185\u3067\u5b8c\u4e86\u3067\u304d\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002</li> <li>\u5404\u30b9\u30c6\u30c3\u30d7\u306b\u306f\u660e\u78ba\u306a\u610f\u5473\u304c\u3042\u308a\u307e\u3059\u3002\u540c\u3058\u5165\u529b\u3068\u6761\u4ef6\u306e\u4e0b\u3067\u51fa\u529b\u306f\u4e00\u8cab\u3057\u3066\u540c\u3058\u3067\u3059\u3002</li> </ul>"},{"location":"chapter_introduction/what_is_dsa/#122","title":"1.2.2 \u00a0 \u30c7\u30fc\u30bf\u69cb\u9020\u306e\u5b9a\u7fa9","text":"<p>\u30c7\u30fc\u30bf\u69cb\u9020\u306f\u3001\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u5185\u3067\u30c7\u30fc\u30bf\u3092\u7d44\u7e54\u3057\u4fdd\u5b58\u3059\u308b\u65b9\u6cd5\u3067\u3001\u4ee5\u4e0b\u306e\u8a2d\u8a08\u76ee\u6a19\u304c\u3042\u308a\u307e\u3059\uff1a</p> <ul> <li>\u30b3\u30f3\u30d4\u30e5\u30fc\u30bf\u306e\u30e1\u30e2\u30ea\u3092\u7bc0\u7d04\u3059\u308b\u305f\u3081\u306b\u7a7a\u9593\u5360\u6709\u3092\u6700\u5c0f\u5316\u3059\u308b\u3002</li> <li>\u30c7\u30fc\u30bf\u64cd\u4f5c\u3092\u53ef\u80fd\u306a\u9650\u308a\u9ad8\u901f\u306b\u3057\u3001\u30c7\u30fc\u30bf\u306e\u30a2\u30af\u30bb\u30b9\u3001\u8ffd\u52a0\u3001\u524a\u9664\u3001\u66f4\u65b0\u306a\u3069\u3092\u30ab\u30d0\u30fc\u3059\u308b\u3002</li> <li>\u52b9\u7387\u7684\u306a\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u5b9f\u884c\u3092\u53ef\u80fd\u306b\u3059\u308b\u305f\u3081\u306b\u3001\u7c21\u6f54\u306a\u30c7\u30fc\u30bf\u8868\u73fe\u3068\u8ad6\u7406\u60c5\u5831\u3092\u63d0\u4f9b\u3059\u308b\u3002</li> </ul> <p>\u30c7\u30fc\u30bf\u69cb\u9020\u306e\u8a2d\u8a08\u306f\u30d0\u30e9\u30f3\u30b9\u3092\u53d6\u308b\u884c\u70ba\u3067\u3042\u308a\u3001\u3057\u3070\u3057\u3070\u30c8\u30ec\u30fc\u30c9\u30aa\u30d5\u304c\u5fc5\u8981\u3067\u3059\u3002\u4e00\u3064\u306e\u5074\u9762\u3092\u6539\u5584\u3057\u305f\u3044\u5834\u5408\u3001\u3057\u3070\u3057\u3070\u5225\u306e\u5074\u9762\u3067\u59a5\u5354\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u4ee5\u4e0b\u306f2\u3064\u306e\u4f8b\u3067\u3059\uff1a</p> <ul> <li>\u914d\u5217\u3068\u6bd4\u8f03\u3057\u3066\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u306f\u30c7\u30fc\u30bf\u306e\u8ffd\u52a0\u3068\u524a\u9664\u306b\u304a\u3044\u3066\u3088\u308a\u4fbf\u5229\u3067\u3059\u304c\u3001\u30c7\u30fc\u30bf\u30a2\u30af\u30bb\u30b9\u901f\u5ea6\u3092\u72a0\u7272\u306b\u3057\u307e\u3059\u3002</li> <li>\u9023\u7d50\u30ea\u30b9\u30c8\u3068\u6bd4\u8f03\u3057\u3066\u3001\u30b0\u30e9\u30d5\u306f\u3088\u308a\u8c4a\u5bcc\u306a\u8ad6\u7406\u60c5\u5831\u3092\u63d0\u4f9b\u3057\u307e\u3059\u304c\u3001\u3088\u308a\u591a\u304f\u306e\u30e1\u30e2\u30ea\u7a7a\u9593\u304c\u5fc5\u8981\u3067\u3059\u3002</li> </ul>"},{"location":"chapter_introduction/what_is_dsa/#123","title":"1.2.3 \u00a0 \u30c7\u30fc\u30bf\u69cb\u9020\u3068\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u95a2\u4fc2","text":"<p>\u4ee5\u4e0b\u306e\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u30c7\u30fc\u30bf\u69cb\u9020\u3068\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u9ad8\u5ea6\u306b\u95a2\u9023\u3057\u3001\u5bc6\u63a5\u306b\u7d71\u5408\u3055\u308c\u3066\u304a\u308a\u3001\u5177\u4f53\u7684\u306b\u306f\u4ee5\u4e0b\u306e3\u3064\u306e\u5074\u9762\u304c\u3042\u308a\u307e\u3059\uff1a</p> <ul> <li>\u30c7\u30fc\u30bf\u69cb\u9020\u306f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u57fa\u790e\u3067\u3059\u3002\u69cb\u9020\u5316\u3055\u308c\u305f\u30c7\u30fc\u30bf\u4fdd\u5b58\u3068\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u305f\u3081\u306e\u30c7\u30fc\u30bf\u64cd\u4f5c\u65b9\u6cd5\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002</li> <li>\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u30c7\u30fc\u30bf\u69cb\u9020\u306b\u6d3b\u529b\u3092\u6ce8\u5165\u3057\u307e\u3059\u3002\u30c7\u30fc\u30bf\u69cb\u9020\u3060\u3051\u3067\u306f\u30c7\u30fc\u30bf\u60c5\u5831\u3092\u4fdd\u5b58\u3059\u308b\u3060\u3051\u3067\u3059\u3002\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5fdc\u7528\u306b\u3088\u3063\u3066\u3001\u7279\u5b9a\u306e\u554f\u984c\u3092\u89e3\u6c7a\u3067\u304d\u307e\u3059\u3002</li> <li>\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u7570\u306a\u308b\u30c7\u30fc\u30bf\u69cb\u9020\u306b\u57fa\u3065\u3044\u3066\u5b9f\u88c5\u3067\u304d\u308b\u3053\u3068\u304c\u591a\u3044\u3067\u3059\u304c\u3001\u5b9f\u884c\u52b9\u7387\u306f\u5927\u304d\u304f\u7570\u306a\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002\u9069\u5207\u306a\u30c7\u30fc\u30bf\u69cb\u9020\u3092\u9078\u629e\u3059\u308b\u3053\u3068\u304c\u9375\u3067\u3059\u3002</li> </ul> <p></p> <p> \u56f3 1-4 \u00a0 \u30c7\u30fc\u30bf\u69cb\u9020\u3068\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u95a2\u4fc2 </p> <p>\u30c7\u30fc\u30bf\u69cb\u9020\u3068\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u3001\u4ee5\u4e0b\u306e\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u30d6\u30ed\u30c3\u30af\u306e\u30bb\u30c3\u30c8\u306b\u4f8b\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u30d6\u30ed\u30c3\u30af\u30bb\u30c3\u30c8\u306b\u306f\u591a\u6570\u306e\u30d4\u30fc\u30b9\u304c\u542b\u307e\u308c\u3001\u8a73\u7d30\u306a\u7d44\u307f\u7acb\u3066\u8aac\u660e\u66f8\u304c\u4ed8\u3044\u3066\u3044\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u8aac\u660e\u66f8\u306b\u6bb5\u968e\u7684\u306b\u5f93\u3046\u3053\u3068\u3067\u3001\u8907\u96d1\u306a\u30d6\u30ed\u30c3\u30af\u30e2\u30c7\u30eb\u3092\u69cb\u7bc9\u3067\u304d\u307e\u3059\u3002</p> <p></p> <p> \u56f3 1-5 \u00a0 \u30d6\u30ed\u30c3\u30af\u306e\u7d44\u307f\u7acb\u3066 </p> <p>\u4e21\u8005\u306e\u8a73\u7d30\u306a\u5bfe\u5fdc\u95a2\u4fc2\u306f\u4ee5\u4e0b\u306e\u8868\u306b\u793a\u3055\u308c\u3066\u3044\u307e\u3059\u3002</p> <p> \u8868 1-1 \u00a0 \u30c7\u30fc\u30bf\u69cb\u9020\u3068\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u30d6\u30ed\u30c3\u30af\u3068\u6bd4\u8f03 </p> \u30c7\u30fc\u30bf\u69cb\u9020\u3068\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0 \u30d6\u30ed\u30c3\u30af \u5165\u529b\u30c7\u30fc\u30bf \u672a\u7d44\u307f\u7acb\u3066\u306e\u30d6\u30ed\u30c3\u30af \u30c7\u30fc\u30bf\u69cb\u9020 \u30d6\u30ed\u30c3\u30af\u306e\u7d44\u7e54\u3001\u5f62\u72b6\u3001\u30b5\u30a4\u30ba\u3001\u63a5\u7d9a\u306a\u3069\u3092\u542b\u3080 \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0 \u30d6\u30ed\u30c3\u30af\u3092\u671b\u307e\u3057\u3044\u5f62\u72b6\u306b\u7d44\u307f\u7acb\u3066\u308b\u4e00\u9023\u306e\u30b9\u30c6\u30c3\u30d7 \u51fa\u529b\u30c7\u30fc\u30bf \u5b8c\u6210\u3057\u305f\u30d6\u30ed\u30c3\u30af\u30e2\u30c7\u30eb <p>\u30c7\u30fc\u30bf\u69cb\u9020\u3068\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u304b\u3089\u72ec\u7acb\u3057\u3066\u3044\u308b\u3053\u3068\u306f\u6ce8\u76ee\u306b\u5024\u3057\u307e\u3059\u3002\u3053\u306e\u7406\u7531\u306b\u3088\u308a\u3001\u3053\u306e\u672c\u306f\u8907\u6570\u306e\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u3067\u306e\u5b9f\u88c5\u3092\u63d0\u4f9b\u3067\u304d\u307e\u3059\u3002</p> <p>\u6163\u7fd2\u7684\u306a\u7565\u8a9e</p> <p>\u5b9f\u751f\u6d3b\u306e\u8b70\u8ad6\u3067\u306f\u3001\u300c\u30c7\u30fc\u30bf\u69cb\u9020\u3068\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u300d\u3092\u5358\u7d14\u306b\u300c\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u300d\u3068\u547c\u3076\u3053\u3068\u304c\u3088\u304f\u3042\u308a\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u3088\u304f\u77e5\u3089\u308c\u305fLeetCode\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u554f\u984c\u306f\u3001\u5b9f\u969b\u306b\u306f\u30c7\u30fc\u30bf\u69cb\u9020\u3068\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u4e21\u65b9\u306e\u77e5\u8b58\u3092\u30c6\u30b9\u30c8\u3057\u3066\u3044\u307e\u3059\u3002</p>"},{"location":"chapter_preface/","title":"\u7b2c 0 \u7ae0 \u00a0 \u5e8f\u6587","text":"<p>Abstract</p> <p>\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u7f8e\u3057\u3044\u4ea4\u97ff\u66f2\u306e\u3088\u3046\u3067\u3001\u30b3\u30fc\u30c9\u306e\u4e00\u884c\u4e00\u884c\u304c\u30ea\u30ba\u30e0\u306e\u3088\u3046\u306b\u6d41\u308c\u3066\u3044\u307e\u3059\u3002</p> <p>\u3053\u306e\u672c\u304c\u3042\u306a\u305f\u306e\u5fc3\u306e\u4e2d\u3067\u9759\u304b\u306b\u97ff\u304d\u3001\u72ec\u7279\u3067\u6df1\u3044\u65cb\u5f8b\u3092\u6b8b\u3059\u3053\u3068\u3092\u9858\u3063\u3066\u3044\u307e\u3059\u3002</p>"},{"location":"chapter_preface/#_1","title":"\u7ae0\u306e\u5185\u5bb9","text":"<ul> <li>0.1 \u00a0 \u3053\u306e\u672c\u306b\u3064\u3044\u3066</li> <li>0.2 \u00a0 \u672c\u66f8\u306e\u4f7f\u3044\u65b9</li> <li>0.3 \u00a0 \u307e\u3068\u3081</li> </ul>"},{"location":"chapter_preface/about_the_book/","title":"0.1 \u00a0 \u3053\u306e\u672c\u306b\u3064\u3044\u3066","text":"<p>\u3053\u306e\u30aa\u30fc\u30d7\u30f3\u30bd\u30fc\u30b9\u30d7\u30ed\u30b8\u30a7\u30af\u30c8\u306f\u3001\u30c7\u30fc\u30bf\u69cb\u9020\u3068\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306b\u95a2\u3059\u308b\u7121\u6599\u3067\u521d\u5fc3\u8005\u306b\u3084\u3055\u3057\u3044\u30af\u30e9\u30c3\u30b7\u30e5\u30b3\u30fc\u30b9\u306e\u4f5c\u6210\u3092\u76ee\u6307\u3057\u3066\u3044\u307e\u3059\u3002</p> <ul> <li>\u30a2\u30cb\u30e1\u30fc\u30b7\u30e7\u30f3\u4ed8\u304d\u306e\u56f3\u89e3\u3001\u7406\u89e3\u3057\u3084\u3059\u3044\u5185\u5bb9\u3001\u6ed1\u3089\u304b\u306a\u5b66\u7fd2\u66f2\u7dda\u306b\u3088\u308a\u3001\u521d\u5fc3\u8005\u304c\u30c7\u30fc\u30bf\u69cb\u9020\u3068\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u300c\u77e5\u8b58\u30de\u30c3\u30d7\u300d\u3092\u63a2\u7d22\u3059\u308b\u306e\u306b\u5f79\u7acb\u3061\u307e\u3059\u3002</li> <li>\u30ef\u30f3\u30af\u30ea\u30c3\u30af\u3067\u30b3\u30fc\u30c9\u3092\u5b9f\u884c\u3067\u304d\u308b\u305f\u3081\u3001\u8aad\u8005\u306e\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u30b9\u30ad\u30eb\u306e\u5411\u4e0a\u3068\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u52d5\u4f5c\u539f\u7406\u304a\u3088\u3073\u30c7\u30fc\u30bf\u69cb\u9020\u306e\u57fa\u790e\u5b9f\u88c5\u306e\u7406\u89e3\u306b\u5f79\u7acb\u3061\u307e\u3059\u3002</li> <li>\u6559\u3048\u308b\u3053\u3068\u306b\u3088\u308b\u5b66\u7fd2\u3092\u4fc3\u9032\u3057\u3001\u8cea\u554f\u3084\u6d1e\u5bdf\u306e\u5171\u6709\u3092\u81ea\u7531\u306b\u884c\u3063\u3066\u304f\u3060\u3055\u3044\u3002\u8b70\u8ad6\u3092\u901a\u3058\u3066\u4e00\u7dd2\u306b\u6210\u9577\u3057\u307e\u3057\u3087\u3046\u3002</li> </ul>"},{"location":"chapter_preface/about_the_book/#011","title":"0.1.1 \u00a0 \u5bfe\u8c61\u8aad\u8005","text":"<p>\u3082\u3057\u3042\u306a\u305f\u304c\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306b\u89e6\u308c\u305f\u3070\u304b\u308a\u3067\u7d4c\u9a13\u304c\u9650\u3089\u308c\u3066\u3044\u308b\u5834\u5408\u3001\u307e\u305f\u306f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u3042\u308b\u7a0b\u5ea6\u306e\u7d4c\u9a13\u3092\u7a4d\u3093\u3067\u3044\u3066\u3082\u3001\u30c7\u30fc\u30bf\u69cb\u9020\u3068\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306b\u3064\u3044\u3066\u66d6\u6627\u306a\u7406\u89e3\u3057\u304b\u306a\u304f\u3001\u5e38\u306b\u300c\u5206\u304b\u3063\u305f\u300d\u3068\u300c\u3046\u30fc\u3093\u300d\u306e\u9593\u3092\u884c\u304d\u6765\u3057\u3066\u3044\u308b\u5834\u5408\u3001\u3053\u306e\u672c\u306f\u3042\u306a\u305f\u306e\u305f\u3081\u306e\u3082\u306e\u3067\u3059\uff01</p> <p>\u3059\u3067\u306b\u3042\u308b\u7a0b\u5ea6\u306e\u554f\u984c\u89e3\u6c7a\u7d4c\u9a13\u3092\u7a4d\u3093\u3067\u304a\u308a\u3001\u307b\u3068\u3093\u3069\u306e\u30bf\u30a4\u30d7\u306e\u554f\u984c\u306b\u7cbe\u901a\u3057\u3066\u3044\u308b\u5834\u5408\u3001\u3053\u306e\u672c\u306f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u77e5\u8b58\u4f53\u7cfb\u3092\u5fa9\u7fd2\u3057\u6574\u7406\u3059\u308b\u306e\u306b\u5f79\u7acb\u3061\u307e\u3059\u3002\u30ea\u30dd\u30b8\u30c8\u30ea\u306e\u30bd\u30fc\u30b9\u30b3\u30fc\u30c9\u306f\u300c\u554f\u984c\u89e3\u6c7a\u30c4\u30fc\u30eb\u30ad\u30c3\u30c8\u300d\u3084\u300c\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u30c1\u30fc\u30c8\u30b7\u30fc\u30c8\u300d\u3068\u3057\u3066\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002</p> <p>\u3082\u3057\u3042\u306a\u305f\u304c\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5c02\u9580\u5bb6\u3067\u3042\u308c\u3070\u3001\u8cb4\u91cd\u306a\u63d0\u6848\u3092\u3044\u305f\u3060\u304f\u304b\u3001\u53c2\u52a0\u3057\u3066\u5354\u529b\u3057\u3066\u3044\u305f\u3060\u3051\u308c\u3070\u3068\u601d\u3044\u307e\u3059\u3002</p> <p>\u524d\u63d0\u6761\u4ef6</p> <p>\u5c11\u306a\u304f\u3068\u3082\u4e00\u3064\u306e\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u3067\u7c21\u5358\u306a\u30b3\u30fc\u30c9\u3092\u66f8\u3044\u3066\u8aad\u3080\u3053\u3068\u304c\u3067\u304d\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002</p>"},{"location":"chapter_preface/about_the_book/#012","title":"0.1.2 \u00a0 \u5185\u5bb9\u69cb\u6210","text":"<p>\u672c\u66f8\u306e\u4e3b\u306a\u5185\u5bb9\u3092\u4e0b\u56f3\u306b\u793a\u3057\u307e\u3059\u3002</p> <ul> <li>\u8a08\u7b97\u91cf\u89e3\u6790: \u30c7\u30fc\u30bf\u69cb\u9020\u3068\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u8a55\u4fa1\u3059\u308b\u5074\u9762\u3068\u65b9\u6cd5\u3092\u63a2\u6c42\u3057\u307e\u3059\u3002\u6642\u9593\u8a08\u7b97\u91cf\u3068\u7a7a\u9593\u8a08\u7b97\u91cf\u3092\u5c0e\u51fa\u3059\u308b\u65b9\u6cd5\u3001\u304a\u3088\u3073\u4e00\u822c\u7684\u306a\u30bf\u30a4\u30d7\u3068\u4f8b\u3092\u6271\u3044\u307e\u3059\u3002</li> <li>\u30c7\u30fc\u30bf\u69cb\u9020: \u57fa\u672c\u7684\u306a\u30c7\u30fc\u30bf\u578b\u3001\u5206\u985e\u65b9\u6cd5\u3001\u5b9a\u7fa9\u3001\u9577\u6240\u3068\u77ed\u6240\u3001\u4e00\u822c\u7684\u306a\u64cd\u4f5c\u3001\u30bf\u30a4\u30d7\u3001\u5fdc\u7528\u3001\u304a\u3088\u3073\u914d\u5217\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u3001\u30b9\u30bf\u30c3\u30af\u3001\u30ad\u30e5\u30fc\u3001\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u3001\u6728\u3001\u30d2\u30fc\u30d7\u3001\u30b0\u30e9\u30d5\u306a\u3069\u306e\u30c7\u30fc\u30bf\u69cb\u9020\u306e\u5b9f\u88c5\u65b9\u6cd5\u306b\u7126\u70b9\u3092\u5f53\u3066\u307e\u3059\u3002</li> <li>\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0: \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u5b9a\u7fa9\u3057\u3001\u305d\u306e\u9577\u6240\u3068\u77ed\u6240\u3001\u52b9\u7387\u6027\u3001\u5fdc\u7528\u30b7\u30ca\u30ea\u30aa\u3001\u554f\u984c\u89e3\u6c7a\u30b9\u30c6\u30c3\u30d7\u306b\u3064\u3044\u3066\u8b70\u8ad6\u3057\u3001\u691c\u7d22\u3001\u30bd\u30fc\u30c8\u3001\u5206\u5272\u7d71\u6cbb\u3001\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u3001\u52d5\u7684\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u3001\u8caa\u6b32\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306a\u3069\u3001\u3055\u307e\u3056\u307e\u306a\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u30b5\u30f3\u30d7\u30eb\u554f\u984c\u3092\u542b\u307f\u307e\u3059\u3002</li> </ul> <p></p> <p> \u56f3 0-1 \u00a0 \u672c\u66f8\u306e\u4e3b\u306a\u5185\u5bb9 </p>"},{"location":"chapter_preface/about_the_book/#013","title":"0.1.3 \u00a0 \u8b1d\u8f9e","text":"<p>\u3053\u306e\u672c\u306f\u3001\u30aa\u30fc\u30d7\u30f3\u30bd\u30fc\u30b9\u30b3\u30df\u30e5\u30cb\u30c6\u30a3\u306e\u591a\u304f\u306e\u8ca2\u732e\u8005\u306e\u5171\u540c\u52aa\u529b\u306b\u3088\u308a\u7d99\u7d9a\u7684\u306b\u6539\u5584\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u6642\u9593\u3068\u30a8\u30cd\u30eb\u30ae\u30fc\u3092\u6295\u8cc7\u3057\u3066\u304f\u3060\u3055\u3063\u305f\u5404\u57f7\u7b46\u8005\u306b\u611f\u8b1d\u3044\u305f\u3057\u307e\u3059\u3002GitHub\u3067\u751f\u6210\u3055\u308c\u305f\u9806\u5e8f\u3067\u8a18\u8f09\u3055\u308c\u3066\u3044\u307e\u3059: krahets, coderonion, Gonglja, nuomi1, Reanon, justin-tse, hpstory, danielsss, curtishd, night-cruise, S-N-O-R-L-A-X, msk397, gvenusleo, khoaxuantu, RiverTwilight, rongyi, gyt95, zhuoqinyue, K3v123, Zuoxun, mingXta, hello-ikun, FangYuan33, GN-Yu, yuelinxin, longsizhuo, Cathay-Chen, guowei-gong, xBLACKICEx, IsChristina, JoseHung, qualifier1024, QiLOL, pengchzn, Guanngxu, L-Super, WSL0809, Slone123c, lhxsm, yuan0221, what-is-me, theNefelibatas, longranger2, cy-by-side, xiongsp, JeffersonHuang, Transmigration-zhou, magentaqin, Wonderdch, malone6, xiaomiusa87, gaofer, bluebean-cloud, a16su, Shyam-Chen, nanlei, hongyun-robot, Phoenix0415, MolDuM, Nigh, he-weilai, junminhong, mgisr, iron-irax, yd-j, XiaChuerwu, XC-Zero, seven1240, SamJin98, wodray, reeswell, NI-SW, Horbin-Magician, Enlightenus, xjr7670, YangXuanyi, DullSword, boloboloda, iStig, qq909244296, jiaxianhua, wenjianmin, keshida, kilikilikid, lclc6, lwbaptx, liuxjerry, lucaswangdev, lyl625760, hts0000, gledfish, fbigm, echo1937, szu17dmy, dshlstarr, Yucao-cy, coderlef, czruby, bongbongbakudan, beintentional, ZongYangL, ZhongYuuu, luluxia, xb534, bitsmi, ElaBosak233, baagod, zhouLion, yishangzhang, yi427, yabo083, weibk, wangwang105, th1nk3r-ing, tao363, 4yDX3906, syd168, steventimes, sslmj2020, smilelsb, siqyka, selear, sdshaoda, Xi-Row, popozhu, nuquist19, noobcodemaker, XiaoK29, chadyi, ZhongGuanbin, shanghai-Jerry, JackYang-hellobobo, Javesun99, lipusheng, BlindTerran, ShiMaRing, FreddieLi, FloranceYeh, iFleey, fanchenggang, gltianwen, goerll, Dr-XYZ, nedchu, curly210102, CuB3y0nd, KraHsu, CarrotDLaw, youshaoXG, bubble9um, fanenr, eagleanurag, LifeGoesOnionOnionOnion, 52coder, foursevenlove, KorsChen, hezhizhen, linzeyan, ZJKung, GaochaoZhu, hopkings2008, yang-le, Evilrabbit520, Turing-1024-Lee, thomasq0, Suremotoo, Allen-Scai, Risuntsy, Richard-Zhang1019, qingpeng9802, primexiao, nidhoggfgg, 1ch0, MwumLi, martinx, ZnYang2018, hugtyftg, logan-qiu, psychelzh, Keynman, KeiichiKasai and 0130w.</p> <p>\u3053\u306e\u672c\u306e\u30b3\u30fc\u30c9\u30ec\u30d3\u30e5\u30fc\u4f5c\u696d\u306f\u3001coderonion, Gonglja, gvenusleo, hpstory, justin\u2010tse, khoaxuantu, krahets, night-cruise, nuomi1, Reanon and rongyi\uff08\u30a2\u30eb\u30d5\u30a1\u30d9\u30c3\u30c8\u9806\uff09\u306b\u3088\u3063\u3066\u5b8c\u4e86\u3055\u308c\u307e\u3057\u305f\u3002\u5f7c\u3089\u306e\u6642\u9593\u3068\u52aa\u529b\u306b\u611f\u8b1d\u3057\u3001\u69d8\u3005\u306a\u8a00\u8a9e\u3067\u306e\u30b3\u30fc\u30c9\u306e\u6a19\u6e96\u5316\u3068\u7d71\u4e00\u6027\u3092\u78ba\u4fdd\u3057\u3066\u304f\u3060\u3055\u3044\u307e\u3057\u305f\u3002</p> <p>\u3053\u306e\u672c\u306e\u7e41\u4f53\u5b57\u4e2d\u56fd\u8a9e\u7248\u306f Shyam-Chen \u3068 Dr-XYZ \u306b\u3088\u3063\u3066\u30ec\u30d3\u30e5\u30fc\u3055\u308c\u3001\u82f1\u8a9e\u7248\u306f yuelinxin, K3v123, QiLOL, Phoenix0415, SamJin98, yanedie, RafaelCaso, pengchzn, thomasq0, and magentaqin \u306b\u3088\u3063\u3066\u30ec\u30d3\u30e5\u30fc\u3055\u308c\u307e\u3057\u305f\u3002\u5f7c\u3089\u306e\u7d99\u7d9a\u7684\u306a\u8ca2\u732e\u306b\u3088\u308a\u3001\u3053\u306e\u672c\u304c\u3088\u308a\u5e83\u3044\u8aad\u8005\u306b\u5c4a\u304d\u3001\u5f79\u7acb\u3064\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002</p> <p>\u3053\u306e\u672c\u306e\u5236\u4f5c\u904e\u7a0b\u306b\u304a\u3044\u3066\u3001\u591a\u304f\u306e\u65b9\u3005\u304b\u3089\u8cb4\u91cd\u306a\u652f\u63f4\u3092\u3044\u305f\u3060\u304d\u307e\u3057\u305f\u3002\u3053\u308c\u3089\u306b\u9650\u5b9a\u3055\u308c\u307e\u305b\u3093\u304c\uff1a</p> <ul> <li>\u4f1a\u793e\u3067\u306e\u30e1\u30f3\u30bf\u30fc\u3001\u674e\u7199\u535a\u58eb\u306b\u611f\u8b1d\u3057\u307e\u3059\u3002\u3042\u308b\u4f1a\u8a71\u3067\u300c\u65e9\u304f\u884c\u52d5\u3057\u308d\u300d\u3068\u52b1\u307e\u3057\u3066\u3044\u305f\u3060\u304d\u3001\u3053\u306e\u672c\u3092\u66f8\u304f\u6c7a\u610f\u3092\u56fa\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002</li> <li>\u30ac\u30fc\u30eb\u30d5\u30ec\u30f3\u30c9\u306eBubble\u306b\u611f\u8b1d\u3057\u307e\u3059\u3002\u3053\u306e\u672c\u306e\u6700\u521d\u306e\u8aad\u8005\u3068\u3057\u3066\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u521d\u5fc3\u8005\u306e\u8996\u70b9\u304b\u3089\u591a\u304f\u306e\u8cb4\u91cd\u306a\u63d0\u6848\u3092\u3044\u305f\u3060\u304d\u3001\u3053\u306e\u672c\u3092\u521d\u5fc3\u8005\u306b\u3088\u308a\u9069\u3057\u305f\u3082\u306e\u306b\u3057\u3066\u304f\u3060\u3055\u3044\u307e\u3057\u305f\u3002</li> <li>Tengbao\u3001Qibao\u3001Feibao\u306b\u611f\u8b1d\u3057\u307e\u3059\u3002\u3053\u306e\u672c\u306e\u30af\u30ea\u30a8\u30a4\u30c6\u30a3\u30d6\u306a\u540d\u524d\u3092\u8003\u3048\u3066\u304f\u3060\u3055\u308a\u3001\u307f\u3093\u306a\u304c\u521d\u3081\u3066\u300cHello World!\u300d\u3092\u66f8\u3044\u305f\u6642\u306e\u7d20\u6674\u3089\u3057\u3044\u601d\u3044\u51fa\u3092\u547c\u3073\u8d77\u3053\u3057\u3066\u304f\u308c\u307e\u3057\u305f\u3002</li> <li>Xiaoquan\u306b\u611f\u8b1d\u3057\u307e\u3059\u3002\u77e5\u7684\u8ca1\u7523\u306b\u95a2\u3059\u308b\u5c02\u9580\u7684\u306a\u652f\u63f4\u3092\u63d0\u4f9b\u3057\u3066\u304f\u3060\u3055\u308a\u3001\u3053\u306e\u30aa\u30fc\u30d7\u30f3\u30bd\u30fc\u30b9\u672c\u306e\u958b\u767a\u306b\u304a\u3044\u3066\u91cd\u8981\u306a\u5f79\u5272\u3092\u679c\u305f\u3057\u3066\u304f\u3060\u3055\u3044\u307e\u3057\u305f\u3002</li> <li>Sutong\u306b\u611f\u8b1d\u3057\u307e\u3059\u3002\u3053\u306e\u672c\u306e\u7f8e\u3057\u3044\u30ab\u30d0\u30fc\u3068\u30ed\u30b4\u3092\u30c7\u30b6\u30a4\u30f3\u3057\u3066\u304f\u3060\u3055\u308a\u3001\u79c1\u306e\u8981\u6c42\u3067\u4f55\u5ea6\u3082\u4fee\u6b63\u3092\u8f9b\u62b1\u5f37\u304f\u884c\u3063\u3066\u304f\u3060\u3055\u3044\u307e\u3057\u305f\u3002</li> <li>@squidfunk \u306b\u611f\u8b1d\u3057\u307e\u3059\u3002\u57f7\u7b46\u3068\u7d44\u7248\u306e\u63d0\u6848\u3001\u304a\u3088\u3073\u5f7c\u304c\u958b\u767a\u3057\u305f\u30aa\u30fc\u30d7\u30f3\u30bd\u30fc\u30b9\u30c9\u30ad\u30e5\u30e1\u30f3\u30c8\u30c6\u30fc\u30de Material-for-MkDocs \u3092\u63d0\u4f9b\u3057\u3066\u304f\u3060\u3055\u3044\u307e\u3057\u305f\u3002</li> </ul> <p>\u57f7\u7b46\u306e\u904e\u7a0b\u3067\u3001\u30c7\u30fc\u30bf\u69cb\u9020\u3068\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306b\u95a2\u3059\u308b\u591a\u6570\u306e\u6559\u79d1\u66f8\u3084\u8a18\u4e8b\u3092\u6df1\u304f\u7814\u7a76\u3057\u307e\u3057\u305f\u3002\u3053\u308c\u3089\u306e\u4f5c\u54c1\u306f\u6a21\u7bc4\u7684\u306a\u30e2\u30c7\u30eb\u3068\u3057\u3066\u6a5f\u80fd\u3057\u3001\u3053\u306e\u672c\u306e\u5185\u5bb9\u306e\u6b63\u78ba\u6027\u3068\u54c1\u8cea\u3092\u78ba\u4fdd\u3057\u3066\u304f\u3060\u3055\u3044\u307e\u3057\u305f\u3002\u5148\u4eba\u306e\u65b9\u3005\u306e\u8cb4\u91cd\u306a\u8ca2\u732e\u306b\u611f\u8b1d\u3044\u305f\u3057\u307e\u3059\uff01</p> <p>\u3053\u306e\u672c\u306f\u3001\u7406\u8ad6\u3068\u5b9f\u8df5\u3092\u7d44\u307f\u5408\u308f\u305b\u305f\u5b66\u7fd2\u3092\u63d0\u5531\u3057\u3066\u304a\u308a\u3001\u3053\u306e\u70b9\u3067 \"Dive into Deep Learning\" \u304b\u3089\u30a4\u30f3\u30b9\u30d4\u30ec\u30fc\u30b7\u30e7\u30f3\u3092\u53d7\u3051\u3066\u3044\u307e\u3059\u3002\u3053\u306e\u512a\u308c\u305f\u672c\u3092\u3059\u3079\u3066\u306e\u8aad\u8005\u306b\u5f37\u304f\u304a\u52e7\u3081\u3057\u307e\u3059\u3002</p> <p>\u7d99\u7d9a\u7684\u306a\u652f\u63f4\u3068\u52b1\u307e\u3057\u306b\u3088\u308a\u3001\u3053\u306e\u8208\u5473\u6df1\u3044\u4ed5\u4e8b\u3092\u3059\u308b\u3053\u3068\u3092\u53ef\u80fd\u306b\u3057\u3066\u304f\u3060\u3055\u3063\u305f\u4e21\u89aa\u306b\u5fc3\u304b\u3089\u611f\u8b1d\u3044\u305f\u3057\u307e\u3059\u3002</p>"},{"location":"chapter_preface/suggestions/","title":"0.2 \u00a0 \u8aad\u307f\u65b9","text":"<p>Tip</p> <p>\u6700\u826f\u306e\u8aad\u66f8\u4f53\u9a13\u306e\u305f\u3081\u306b\u3001\u3053\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u3092\u901a\u8aad\u3059\u308b\u3053\u3068\u3092\u304a\u52e7\u3081\u3057\u307e\u3059\u3002</p>"},{"location":"chapter_preface/suggestions/#021","title":"0.2.1 \u00a0 \u8a18\u8ff0\u898f\u5247","text":"<ul> <li>\u30bf\u30a4\u30c8\u30eb\u306e\u5f8c\u306b\u300c*\u300d\u304c\u4ed8\u3044\u305f\u7ae0\u306f\u4efb\u610f\u3067\u3042\u308a\u3001\u6bd4\u8f03\u7684\u96e3\u6613\u5ea6\u306e\u9ad8\u3044\u5185\u5bb9\u304c\u542b\u307e\u308c\u3066\u3044\u307e\u3059\u3002\u6642\u9593\u306b\u5236\u7d04\u304c\u3042\u308b\u5834\u5408\u306f\u3001\u3053\u308c\u3089\u3092\u30b9\u30ad\u30c3\u30d7\u3059\u308b\u3053\u3068\u3092\u304a\u52e7\u3081\u3057\u307e\u3059\u3002</li> <li>\u6280\u8853\u7528\u8a9e\u306f\u592a\u5b57\uff08\u5370\u5237\u7248\u304a\u3088\u3073PDF\u7248\uff09\u307e\u305f\u306f\u4e0b\u7dda\uff08Web\u7248\uff09\u3067\u8868\u793a\u3055\u308c\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u914d\u5217\u306a\u3069\u3067\u3059\u3002\u6280\u8853\u6587\u66f8\u3092\u3088\u308a\u826f\u304f\u7406\u89e3\u3059\u308b\u305f\u3081\u306b\u3001\u3053\u308c\u3089\u306b\u6163\u308c\u308b\u3053\u3068\u3092\u304a\u52e7\u3081\u3057\u307e\u3059\u3002</li> <li>**\u592a\u5b57\u306e\u30c6\u30ad\u30b9\u30c8**\u306f\u91cd\u8981\u306a\u5185\u5bb9\u3084\u8981\u7d04\u6587\u3092\u793a\u3057\u3001\u7279\u5225\u306a\u6ce8\u610f\u3092\u6255\u3046\u4fa1\u5024\u304c\u3042\u308a\u307e\u3059\u3002</li> <li>\u7279\u5b9a\u306e\u610f\u5473\u3092\u6301\u3064\u5358\u8a9e\u3084\u53e5\u306f\u300c\u5f15\u7528\u7b26\u300d\u3067\u793a\u3055\u308c\u3001\u66d6\u6627\u3055\u3092\u907f\u3051\u307e\u3059\u3002</li> <li>\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u9593\u3067\u4e00\u81f4\u3057\u306a\u3044\u7528\u8a9e\u306b\u3064\u3044\u3066\u306f\u3001\u3053\u306e\u672c\u306fPython\u306b\u5f93\u3044\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001<code>null</code>\u3092\u610f\u5473\u3059\u308b\u305f\u3081\u306b<code>None</code>\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002</li> <li>\u3053\u306e\u672c\u306f\u3001\u3088\u308a\u30b3\u30f3\u30d1\u30af\u30c8\u306a\u30b3\u30f3\u30c6\u30f3\u30c4\u30ec\u30a4\u30a2\u30a6\u30c8\u3068\u5f15\u304d\u63db\u3048\u306b\u3001\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u306e\u30b3\u30e1\u30f3\u30c8\u898f\u7d04\u3092\u90e8\u5206\u7684\u306b\u7121\u8996\u3057\u3066\u3044\u307e\u3059\u3002\u30b3\u30e1\u30f3\u30c8\u306f\u4e3b\u306b3\u3064\u306e\u30bf\u30a4\u30d7\u3067\u69cb\u6210\u3055\u308c\u3066\u3044\u307e\u3059\uff1a\u30bf\u30a4\u30c8\u30eb\u30b3\u30e1\u30f3\u30c8\u3001\u5185\u5bb9\u30b3\u30e1\u30f3\u30c8\u3001\u8907\u6570\u884c\u30b3\u30e1\u30f3\u30c8\u3002</li> </ul> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinZig <pre><code>\"\"\"\u95a2\u6570\u3001\u30af\u30e9\u30b9\u3001\u30c6\u30b9\u30c8\u30b5\u30f3\u30d7\u30eb\u306a\u3069\u3092\u30e9\u30d9\u30eb\u4ed8\u3051\u3059\u308b\u305f\u3081\u306e\u30d8\u30c3\u30c0\u30fc\u30b3\u30e1\u30f3\u30c8\"\"\"\n\n# \u8a73\u7d30\u3092\u8aac\u660e\u3059\u308b\u305f\u3081\u306e\u30b3\u30e1\u30f3\u30c8\n\n\"\"\"\n\u8907\u6570\u884c\n\u30b3\u30e1\u30f3\u30c8\n\"\"\"\n</code></pre> <pre><code>/* \u95a2\u6570\u3001\u30af\u30e9\u30b9\u3001\u30c6\u30b9\u30c8\u30b5\u30f3\u30d7\u30eb\u306a\u3069\u3092\u30e9\u30d9\u30eb\u4ed8\u3051\u3059\u308b\u305f\u3081\u306e\u30d8\u30c3\u30c0\u30fc\u30b3\u30e1\u30f3\u30c8 */\n\n// \u8a73\u7d30\u3092\u8aac\u660e\u3059\u308b\u305f\u3081\u306e\u30b3\u30e1\u30f3\u30c8\n\n/**\n * \u8907\u6570\u884c\n * \u30b3\u30e1\u30f3\u30c8\n */\n</code></pre> <pre><code>/* \u95a2\u6570\u3001\u30af\u30e9\u30b9\u3001\u30c6\u30b9\u30c8\u30b5\u30f3\u30d7\u30eb\u306a\u3069\u3092\u30e9\u30d9\u30eb\u4ed8\u3051\u3059\u308b\u305f\u3081\u306e\u30d8\u30c3\u30c0\u30fc\u30b3\u30e1\u30f3\u30c8 */\n\n// \u8a73\u7d30\u3092\u8aac\u660e\u3059\u308b\u305f\u3081\u306e\u30b3\u30e1\u30f3\u30c8\n\n/**\n * \u8907\u6570\u884c\n * \u30b3\u30e1\u30f3\u30c8\n */\n</code></pre> <pre><code>/* \u95a2\u6570\u3001\u30af\u30e9\u30b9\u3001\u30c6\u30b9\u30c8\u30b5\u30f3\u30d7\u30eb\u306a\u3069\u3092\u30e9\u30d9\u30eb\u4ed8\u3051\u3059\u308b\u305f\u3081\u306e\u30d8\u30c3\u30c0\u30fc\u30b3\u30e1\u30f3\u30c8 */\n\n// \u8a73\u7d30\u3092\u8aac\u660e\u3059\u308b\u305f\u3081\u306e\u30b3\u30e1\u30f3\u30c8\n\n/**\n * \u8907\u6570\u884c\n * \u30b3\u30e1\u30f3\u30c8\n */\n</code></pre> <pre><code>/* \u95a2\u6570\u3001\u30af\u30e9\u30b9\u3001\u30c6\u30b9\u30c8\u30b5\u30f3\u30d7\u30eb\u306a\u3069\u3092\u30e9\u30d9\u30eb\u4ed8\u3051\u3059\u308b\u305f\u3081\u306e\u30d8\u30c3\u30c0\u30fc\u30b3\u30e1\u30f3\u30c8 */\n\n// \u8a73\u7d30\u3092\u8aac\u660e\u3059\u308b\u305f\u3081\u306e\u30b3\u30e1\u30f3\u30c8\n\n/**\n * \u8907\u6570\u884c\n * \u30b3\u30e1\u30f3\u30c8\n */\n</code></pre> <pre><code>/* \u95a2\u6570\u3001\u30af\u30e9\u30b9\u3001\u30c6\u30b9\u30c8\u30b5\u30f3\u30d7\u30eb\u306a\u3069\u3092\u30e9\u30d9\u30eb\u4ed8\u3051\u3059\u308b\u305f\u3081\u306e\u30d8\u30c3\u30c0\u30fc\u30b3\u30e1\u30f3\u30c8 */\n\n// \u8a73\u7d30\u3092\u8aac\u660e\u3059\u308b\u305f\u3081\u306e\u30b3\u30e1\u30f3\u30c8\n\n/**\n * \u8907\u6570\u884c\n * \u30b3\u30e1\u30f3\u30c8\n */\n</code></pre> <pre><code>/* \u95a2\u6570\u3001\u30af\u30e9\u30b9\u3001\u30c6\u30b9\u30c8\u30b5\u30f3\u30d7\u30eb\u306a\u3069\u3092\u30e9\u30d9\u30eb\u4ed8\u3051\u3059\u308b\u305f\u3081\u306e\u30d8\u30c3\u30c0\u30fc\u30b3\u30e1\u30f3\u30c8 */\n\n// \u8a73\u7d30\u3092\u8aac\u660e\u3059\u308b\u305f\u3081\u306e\u30b3\u30e1\u30f3\u30c8\n\n/**\n * \u8907\u6570\u884c\n * \u30b3\u30e1\u30f3\u30c8\n */\n</code></pre> <pre><code>/* \u95a2\u6570\u3001\u30af\u30e9\u30b9\u3001\u30c6\u30b9\u30c8\u30b5\u30f3\u30d7\u30eb\u306a\u3069\u3092\u30e9\u30d9\u30eb\u4ed8\u3051\u3059\u308b\u305f\u3081\u306e\u30d8\u30c3\u30c0\u30fc\u30b3\u30e1\u30f3\u30c8 */\n\n// \u8a73\u7d30\u3092\u8aac\u660e\u3059\u308b\u305f\u3081\u306e\u30b3\u30e1\u30f3\u30c8\n\n/**\n * \u8907\u6570\u884c\n * \u30b3\u30e1\u30f3\u30c8\n */\n</code></pre> <pre><code>/* \u95a2\u6570\u3001\u30af\u30e9\u30b9\u3001\u30c6\u30b9\u30c8\u30b5\u30f3\u30d7\u30eb\u306a\u3069\u3092\u30e9\u30d9\u30eb\u4ed8\u3051\u3059\u308b\u305f\u3081\u306e\u30d8\u30c3\u30c0\u30fc\u30b3\u30e1\u30f3\u30c8 */\n\n// \u8a73\u7d30\u3092\u8aac\u660e\u3059\u308b\u305f\u3081\u306e\u30b3\u30e1\u30f3\u30c8\n\n/**\n * \u8907\u6570\u884c\n * \u30b3\u30e1\u30f3\u30c8\n */\n</code></pre> <pre><code>/* \u95a2\u6570\u3001\u30af\u30e9\u30b9\u3001\u30c6\u30b9\u30c8\u30b5\u30f3\u30d7\u30eb\u306a\u3069\u3092\u30e9\u30d9\u30eb\u4ed8\u3051\u3059\u308b\u305f\u3081\u306e\u30d8\u30c3\u30c0\u30fc\u30b3\u30e1\u30f3\u30c8 */\n\n// \u8a73\u7d30\u3092\u8aac\u660e\u3059\u308b\u305f\u3081\u306e\u30b3\u30e1\u30f3\u30c8\n\n/**\n * \u8907\u6570\u884c\n * \u30b3\u30e1\u30f3\u30c8\n */\n</code></pre> <pre><code>/* \u95a2\u6570\u3001\u30af\u30e9\u30b9\u3001\u30c6\u30b9\u30c8\u30b5\u30f3\u30d7\u30eb\u306a\u3069\u3092\u30e9\u30d9\u30eb\u4ed8\u3051\u3059\u308b\u305f\u3081\u306e\u30d8\u30c3\u30c0\u30fc\u30b3\u30e1\u30f3\u30c8 */\n\n// \u8a73\u7d30\u3092\u8aac\u660e\u3059\u308b\u305f\u3081\u306e\u30b3\u30e1\u30f3\u30c8\n\n/**\n * \u8907\u6570\u884c\n * \u30b3\u30e1\u30f3\u30c8\n */\n</code></pre> <pre><code>/* \u95a2\u6570\u3001\u30af\u30e9\u30b9\u3001\u30c6\u30b9\u30c8\u30b5\u30f3\u30d7\u30eb\u306a\u3069\u3092\u30e9\u30d9\u30eb\u4ed8\u3051\u3059\u308b\u305f\u3081\u306e\u30d8\u30c3\u30c0\u30fc\u30b3\u30e1\u30f3\u30c8 */\n\n// \u8a73\u7d30\u3092\u8aac\u660e\u3059\u308b\u305f\u3081\u306e\u30b3\u30e1\u30f3\u30c8\n\n/**\n * \u8907\u6570\u884c\n * \u30b3\u30e1\u30f3\u30c8\n */\n</code></pre> <pre><code>// \u95a2\u6570\u3001\u30af\u30e9\u30b9\u3001\u30c6\u30b9\u30c8\u30b5\u30f3\u30d7\u30eb\u306a\u3069\u3092\u30e9\u30d9\u30eb\u4ed8\u3051\u3059\u308b\u305f\u3081\u306e\u30d8\u30c3\u30c0\u30fc\u30b3\u30e1\u30f3\u30c8\n\n// \u8a73\u7d30\u3092\u8aac\u660e\u3059\u308b\u305f\u3081\u306e\u30b3\u30e1\u30f3\u30c8\n\n// \u8907\u6570\u884c\n// \u30b3\u30e1\u30f3\u30c8\n</code></pre>"},{"location":"chapter_preface/suggestions/#022","title":"0.2.2 \u00a0 \u30a2\u30cb\u30e1\u30fc\u30b7\u30e7\u30f3\u56f3\u89e3\u306b\u3088\u308b\u52b9\u7387\u7684\u5b66\u7fd2","text":"<p>\u30c6\u30ad\u30b9\u30c8\u3068\u6bd4\u8f03\u3057\u3066\u3001\u52d5\u753b\u3084\u753b\u50cf\u306f\u60c5\u5831\u5bc6\u5ea6\u304c\u9ad8\u304f\u3001\u3088\u308a\u69cb\u9020\u5316\u3055\u308c\u3066\u304a\u308a\u3001\u7406\u89e3\u3057\u3084\u3059\u304f\u306a\u3063\u3066\u3044\u307e\u3059\u3002\u3053\u306e\u672c\u3067\u306f\u3001\u91cd\u8981\u3067\u96e3\u3057\u3044\u6982\u5ff5\u306f\u4e3b\u306b\u30a2\u30cb\u30e1\u30fc\u30b7\u30e7\u30f3\u3068\u56f3\u89e3\u3092\u901a\u3058\u3066\u63d0\u793a\u3055\u308c\u3001\u30c6\u30ad\u30b9\u30c8\u306f\u8aac\u660e\u3068\u88dc\u8db3\u3068\u3057\u3066\u6a5f\u80fd\u3057\u307e\u3059\u3002</p> <p>\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306a\u30a2\u30cb\u30e1\u30fc\u30b7\u30e7\u30f3\u3084\u56f3\u89e3\u306e\u3042\u308b\u5185\u5bb9\u306b\u906d\u9047\u3057\u305f\u5834\u5408\u3001\u56f3\u306e\u7406\u89e3\u3092\u512a\u5148\u3057\u3001\u30c6\u30ad\u30b9\u30c8\u3092\u88dc\u8db3\u3068\u3057\u3066\u3001\u4e21\u65b9\u3092\u7d71\u5408\u3057\u3066\u5305\u62ec\u7684\u306a\u7406\u89e3\u3092\u5f97\u3066\u304f\u3060\u3055\u3044\u3002</p> <p></p> <p> \u56f3 0-2 \u00a0 \u30a2\u30cb\u30e1\u30fc\u30b7\u30e7\u30f3\u56f3\u89e3\u306e\u4f8b </p>"},{"location":"chapter_preface/suggestions/#023","title":"0.2.3 \u00a0 \u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u5b9f\u8df5\u306b\u3088\u308b\u7406\u89e3\u306e\u6df1\u5316","text":"<p>\u3053\u306e\u672c\u306e\u30bd\u30fc\u30b9\u30b3\u30fc\u30c9\u306fGitHub\u30ea\u30dd\u30b8\u30c8\u30ea\u3067\u30db\u30b9\u30c8\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u30bd\u30fc\u30b9\u30b3\u30fc\u30c9\u306b\u306f\u30c6\u30b9\u30c8\u4f8b\u304c\u4ed8\u5c5e\u3057\u3066\u304a\u308a\u3001\u30ef\u30f3\u30af\u30ea\u30c3\u30af\u3067\u5b9f\u884c\u3067\u304d\u307e\u3059\u3002</p> <p>\u6642\u9593\u306b\u4f59\u88d5\u304c\u3042\u308b\u5834\u5408\u306f\u3001\u81ea\u5206\u3067\u30b3\u30fc\u30c9\u3092\u30bf\u30a4\u30d7\u3059\u308b\u3053\u3068\u3092\u304a\u52e7\u3081\u3057\u307e\u3059\u3002\u6642\u9593\u304c\u306a\u3044\u5834\u5408\u306f\u3001\u5c11\u306a\u304f\u3068\u3082\u3059\u3079\u3066\u306e\u30b3\u30fc\u30c9\u3092\u8aad\u3093\u3067\u5b9f\u884c\u3057\u3066\u304f\u3060\u3055\u3044\u3002</p> <p>\u30b3\u30fc\u30c9\u3092\u8aad\u3080\u3060\u3051\u3068\u6bd4\u8f03\u3057\u3066\u3001\u30b3\u30fc\u30c9\u3092\u66f8\u304f\u3053\u3068\u306f\u591a\u304f\u306e\u5834\u5408\u3001\u3088\u308a\u591a\u304f\u306e\u5b66\u7fd2\u3092\u3082\u305f\u3089\u3057\u307e\u3059\u3002\u5b9f\u8df5\u306b\u3088\u308b\u5b66\u7fd2\u3053\u305d\u304c\u771f\u306e\u5b66\u7fd2\u65b9\u6cd5\u3067\u3059\u3002</p> <p></p> <p> \u56f3 0-3 \u00a0 \u30b3\u30fc\u30c9\u5b9f\u884c\u4f8b </p> <p>\u30b3\u30fc\u30c9\u3092\u5b9f\u884c\u3059\u308b\u305f\u3081\u306e\u8a2d\u5b9a\u306b\u306f\u3001\u4e3b\u306b3\u3064\u306e\u30b9\u30c6\u30c3\u30d7\u304c\u542b\u307e\u308c\u307e\u3059\u3002</p> <p>\u30b9\u30c6\u30c3\u30d71\uff1a\u30ed\u30fc\u30ab\u30eb\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u74b0\u5883\u3092\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3002\u4ed8\u9332\u306e\u30c1\u30e5\u30fc\u30c8\u30ea\u30a2\u30eb\u306b\u5f93\u3063\u3066\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3059\u308b\u304b\u3001\u3059\u3067\u306b\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3055\u308c\u3066\u3044\u308b\u5834\u5408\u306f\u3053\u306e\u30b9\u30c6\u30c3\u30d7\u3092\u30b9\u30ad\u30c3\u30d7\u3057\u3066\u304f\u3060\u3055\u3044\u3002</p> <p>\u30b9\u30c6\u30c3\u30d72\uff1a\u30b3\u30fc\u30c9\u30ea\u30dd\u30b8\u30c8\u30ea\u3092\u30af\u30ed\u30fc\u30f3\u307e\u305f\u306f\u30c0\u30a6\u30f3\u30ed\u30fc\u30c9\u3002GitHub\u30ea\u30dd\u30b8\u30c8\u30ea\u3092\u8a2a\u554f\u3057\u3066\u304f\u3060\u3055\u3044\u3002</p> <p>Git\u304c\u30a4\u30f3\u30b9\u30c8\u30fc\u30eb\u3055\u308c\u3066\u3044\u308b\u5834\u5408\u306f\u3001\u6b21\u306e\u30b3\u30de\u30f3\u30c9\u3092\u4f7f\u7528\u3057\u3066\u30ea\u30dd\u30b8\u30c8\u30ea\u3092\u30af\u30ed\u30fc\u30f3\u3057\u307e\u3059\uff1a</p> <pre><code>git clone https://github.com/krahets/hello-algo.git\n</code></pre> <p>\u307e\u305f\u306f\u3001\u4e0b\u56f3\u306b\u793a\u3059\u5834\u6240\u306b\u3042\u308b\u300cDownload ZIP\u300d\u30dc\u30bf\u30f3\u3092\u30af\u30ea\u30c3\u30af\u3057\u3066\u3001\u30b3\u30fc\u30c9\u3092\u5727\u7e2eZIP\u30d5\u30a1\u30a4\u30eb\u3068\u3057\u3066\u76f4\u63a5\u30c0\u30a6\u30f3\u30ed\u30fc\u30c9\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002\u305d\u306e\u5f8c\u3001\u30ed\u30fc\u30ab\u30eb\u3067\u5c55\u958b\u3059\u308b\u3060\u3051\u3067\u3059\u3002</p> <p></p> <p> \u56f3 0-4 \u00a0 \u30ea\u30dd\u30b8\u30c8\u30ea\u306e\u30af\u30ed\u30fc\u30f3\u3068\u30b3\u30fc\u30c9\u306e\u30c0\u30a6\u30f3\u30ed\u30fc\u30c9 </p> <p>\u30b9\u30c6\u30c3\u30d73\uff1a\u30bd\u30fc\u30b9\u30b3\u30fc\u30c9\u3092\u5b9f\u884c\u3002\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u4e0a\u90e8\u306b\u30d5\u30a1\u30a4\u30eb\u540d\u304c\u8a18\u8f09\u3055\u308c\u305f\u30b3\u30fc\u30c9\u30d6\u30ed\u30c3\u30af\u306b\u3064\u3044\u3066\u306f\u3001\u30ea\u30dd\u30b8\u30c8\u30ea\u306e<code>codes</code>\u30d5\u30a9\u30eb\u30c0\u3067\u5bfe\u5fdc\u3059\u308b\u30bd\u30fc\u30b9\u30b3\u30fc\u30c9\u30d5\u30a1\u30a4\u30eb\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u30d5\u30a1\u30a4\u30eb\u306f\u30ef\u30f3\u30af\u30ea\u30c3\u30af\u3067\u5b9f\u884c\u3067\u304d\u3001\u4e0d\u8981\u306a\u30c7\u30d0\u30c3\u30b0\u6642\u9593\u3092\u7bc0\u7d04\u3057\u3001\u5b66\u7fd2\u306b\u96c6\u4e2d\u3067\u304d\u307e\u3059\u3002</p> <p></p> <p> \u56f3 0-5 \u00a0 \u30b3\u30fc\u30c9\u30d6\u30ed\u30c3\u30af\u3068\u5bfe\u5fdc\u3059\u308b\u30bd\u30fc\u30b9\u30b3\u30fc\u30c9\u30d5\u30a1\u30a4\u30eb </p>"},{"location":"chapter_preface/suggestions/#024","title":"0.2.4 \u00a0 \u8b70\u8ad6\u306b\u3088\u308b\u5171\u540c\u5b66\u7fd2","text":"<p>\u3053\u306e\u672c\u3092\u8aad\u3093\u3067\u3044\u308b\u9593\u3001\u5b66\u3079\u306a\u304b\u3063\u305f\u70b9\u3092\u98db\u3070\u3055\u306a\u3044\u3067\u304f\u3060\u3055\u3044\u3002\u30b3\u30e1\u30f3\u30c8\u30bb\u30af\u30b7\u30e7\u30f3\u3067\u6c17\u8efd\u306b\u8cea\u554f\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u559c\u3093\u3067\u304a\u7b54\u3048\u3057\u3001\u901a\u5e382\u65e5\u4ee5\u5185\u306b\u56de\u7b54\u3067\u304d\u307e\u3059\u3002</p> <p>\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u5404\u7ae0\u306e\u4e0b\u90e8\u306b\u30b3\u30e1\u30f3\u30c8\u30bb\u30af\u30b7\u30e7\u30f3\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u30b3\u30e1\u30f3\u30c8\u306b\u6ce8\u610f\u3092\u6255\u3046\u3053\u3068\u3092\u304a\u52e7\u3081\u3057\u307e\u3059\u3002\u4ed6\u306e\u4eba\u304c\u906d\u9047\u3057\u305f\u554f\u984c\u3092\u77e5\u308b\u3053\u3068\u3067\u3001\u77e5\u8b58\u306e\u30ae\u30e3\u30c3\u30d7\u3092\u7279\u5b9a\u3057\u3001\u3088\u308a\u6df1\u3044\u601d\u7d22\u3092\u4fc3\u3059\u3060\u3051\u3067\u306a\u304f\u3001\u4ef2\u9593\u306e\u8aad\u8005\u306e\u8cea\u554f\u306b\u7b54\u3048\u305f\u308a\u3001\u6d1e\u5bdf\u3092\u5171\u6709\u3057\u305f\u308a\u3001\u76f8\u4e92\u306e\u5411\u4e0a\u3092\u4fc3\u9032\u3057\u305f\u308a\u3059\u308b\u3053\u3068\u3067\u5bdb\u5927\u306b\u8ca2\u732e\u3059\u308b\u3053\u3068\u3082\u62db\u5f85\u3057\u307e\u3059\u3002</p> <p></p> <p> \u56f3 0-6 \u00a0 \u30b3\u30e1\u30f3\u30c8\u30bb\u30af\u30b7\u30e7\u30f3\u306e\u4f8b </p>"},{"location":"chapter_preface/suggestions/#025","title":"0.2.5 \u00a0 \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u5b66\u7fd2\u30d1\u30b9","text":"<p>\u5168\u4f53\u7684\u306b\u3001\u30c7\u30fc\u30bf\u69cb\u9020\u3068\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u30de\u30b9\u30bf\u30fc\u3059\u308b\u65c5\u306f3\u3064\u306e\u6bb5\u968e\u306b\u5206\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\uff1a</p> <ol> <li>\u6bb5\u968e1\uff1a\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5165\u9580\u3002\u3055\u307e\u3056\u307e\u306a\u30c7\u30fc\u30bf\u69cb\u9020\u306e\u7279\u6027\u3068\u4f7f\u7528\u6cd5\u306b\u6163\u308c\u3001\u7570\u306a\u308b\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u539f\u7406\u3001\u30d7\u30ed\u30bb\u30b9\u3001\u7528\u9014\u3001\u52b9\u7387\u306b\u3064\u3044\u3066\u5b66\u3076\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002</li> <li>\u6bb5\u968e2\uff1a\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u554f\u984c\u306e\u7df4\u7fd2\u3002Sword for Offer\u3084LeetCode Hot 100\u306a\u3069\u306e\u4eba\u6c17\u306e\u3042\u308b\u554f\u984c\u304b\u3089\u59cb\u3081\u308b\u3053\u3068\u3092\u304a\u52e7\u3081\u3057\u3001\u5c11\u306a\u304f\u3068\u3082100\u554f\u3092\u84c4\u7a4d\u3057\u3066\u4e3b\u6d41\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u554f\u984c\u306b\u6163\u308c\u308b\u3053\u3068\u3067\u3059\u3002\u7df4\u7fd2\u3092\u59cb\u3081\u308b\u3068\u5fd8\u5374\u304c\u8ab2\u984c\u306b\u306a\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u304c\u3001\u3053\u308c\u306f\u6b63\u5e38\u306a\u3053\u3068\u3067\u3059\u306e\u3067\u3054\u5b89\u5fc3\u304f\u3060\u3055\u3044\u3002\u300c\u30a8\u30d3\u30f3\u30b0\u30cf\u30a6\u30b9\u306e\u5fd8\u5374\u66f2\u7dda\u300d\u306b\u5f93\u3063\u3066\u554f\u984c\u3092\u5fa9\u7fd2\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u3001\u901a\u5e383\u301c5\u56de\u306e\u53cd\u5fa9\u306e\u5f8c\u3001\u305d\u308c\u3089\u3092\u899a\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3067\u3057\u3087\u3046\u3002</li> <li>\u6bb5\u968e3\uff1a\u77e5\u8b58\u4f53\u7cfb\u306e\u69cb\u7bc9\u3002\u5b66\u7fd2\u306e\u9762\u3067\u306f\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u30b3\u30e9\u30e0\u8a18\u4e8b\u3001\u89e3\u6cd5\u30d5\u30ec\u30fc\u30e0\u30ef\u30fc\u30af\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u6559\u79d1\u66f8\u3092\u8aad\u3093\u3067\u77e5\u8b58\u4f53\u7cfb\u3092\u7d99\u7d9a\u7684\u306b\u8c4a\u304b\u306b\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u7df4\u7fd2\u306e\u9762\u3067\u306f\u3001\u30c8\u30d4\u30c3\u30af\u5225\u5206\u985e\u3001\u4e00\u3064\u306e\u554f\u984c\u306b\u5bfe\u3059\u308b\u8907\u6570\u306e\u89e3\u6cd5\u3001\u8907\u6570\u306e\u554f\u984c\u306b\u5bfe\u3059\u308b\u4e00\u3064\u306e\u89e3\u6cd5\u306a\u3069\u3001\u9ad8\u5ea6\u306a\u6226\u7565\u3092\u8a66\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u6226\u7565\u306b\u95a2\u3059\u308b\u6d1e\u5bdf\u306f\u3001\u3055\u307e\u3056\u307e\u306a\u30b3\u30df\u30e5\u30cb\u30c6\u30a3\u3067\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002</li> </ol> <p>\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u3053\u306e\u672c\u306f\u4e3b\u306b\u300c\u6bb5\u968e1\u300d\u3092\u30ab\u30d0\u30fc\u3057\u3066\u304a\u308a\u3001\u6bb5\u968e2\u30683\u306b\u3088\u308a\u52b9\u7387\u7684\u306b\u53d6\u308a\u7d44\u3080\u306e\u306b\u5f79\u7acb\u3064\u3053\u3068\u3092\u76ee\u7684\u3068\u3057\u3066\u3044\u307e\u3059\u3002</p> <p></p> <p> \u56f3 0-7 \u00a0 \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u5b66\u7fd2\u30d1\u30b9 </p>"},{"location":"chapter_preface/summary/","title":"0.3 \u00a0 \u307e\u3068\u3081","text":"<ul> <li>\u3053\u306e\u672c\u306e\u4e3b\u306a\u8aad\u8005\u306f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u521d\u5fc3\u8005\u3067\u3059\u3002\u3059\u3067\u306b\u57fa\u672c\u7684\u306a\u77e5\u8b58\u3092\u304a\u6301\u3061\u306e\u5834\u5408\u3001\u3053\u306e\u672c\u306f\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u77e5\u8b58\u3092\u4f53\u7cfb\u7684\u306b\u5fa9\u7fd2\u3059\u308b\u306e\u306b\u5f79\u7acb\u3061\u3001\u3053\u306e\u672c\u306e\u30bd\u30fc\u30b9\u30b3\u30fc\u30c9\u306f\u300c\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u30c4\u30fc\u30eb\u30ad\u30c3\u30c8\u300d\u3068\u3057\u3066\u3082\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002</li> <li>\u3053\u306e\u672c\u306f3\u3064\u306e\u4e3b\u8981\u306a\u30bb\u30af\u30b7\u30e7\u30f3\u3001\u8a08\u7b97\u91cf\u89e3\u6790\u3001\u30c7\u30fc\u30bf\u69cb\u9020\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u69cb\u6210\u3055\u308c\u3066\u304a\u308a\u3001\u3053\u306e\u5206\u91ce\u306e\u307b\u3068\u3093\u3069\u306e\u30c8\u30d4\u30c3\u30af\u3092\u30ab\u30d0\u30fc\u3057\u3066\u3044\u307e\u3059\u3002</li> <li>\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u521d\u5fc3\u8005\u306b\u3068\u3063\u3066\u3001\u591a\u304f\u306e\u56de\u308a\u9053\u3084\u4e00\u822c\u7684\u306a\u843d\u3068\u3057\u7a74\u3092\u907f\u3051\u308b\u305f\u3081\u306b\u3001\u521d\u671f\u6bb5\u968e\u3067\u5165\u9580\u66f8\u3092\u8aad\u3080\u3053\u3068\u304c\u91cd\u8981\u3067\u3059\u3002</li> <li>\u672c\u66f8\u5185\u306e\u30a2\u30cb\u30e1\u30fc\u30b7\u30e7\u30f3\u3068\u56f3\u306f\u901a\u5e38\u3001\u91cd\u8981\u306a\u30dd\u30a4\u30f3\u30c8\u3068\u96e3\u3057\u3044\u77e5\u8b58\u3092\u7d39\u4ecb\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u672c\u3092\u8aad\u3080\u969b\u306b\u306f\u3053\u308c\u3089\u306b\u3088\u308a\u591a\u304f\u306e\u6ce8\u610f\u3092\u6255\u3046\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002</li> <li>\u5b9f\u8df5\u306f\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u3092\u5b66\u3076\u6700\u826f\u306e\u65b9\u6cd5\u3067\u3059\u3002\u30bd\u30fc\u30b9\u30b3\u30fc\u30c9\u3092\u5b9f\u884c\u3057\u3001\u81ea\u5206\u3067\u30b3\u30fc\u30c9\u3092\u30bf\u30a4\u30d7\u3059\u308b\u3053\u3068\u3092\u5f37\u304f\u304a\u52e7\u3081\u3057\u307e\u3059\u3002</li> <li>\u3053\u306e\u672c\u306eWeb\u7248\u306e\u5404\u7ae0\u306b\u306f\u8b70\u8ad6\u30bb\u30af\u30b7\u30e7\u30f3\u304c\u3042\u308a\u3001\u3044\u3064\u3067\u3082\u8cea\u554f\u3084\u6d1e\u5bdf\u3092\u5171\u6709\u3059\u308b\u3053\u3068\u3092\u6b53\u8fce\u3057\u307e\u3059\u3002</li> </ul>"},{"location":"chapter_reference/","title":"\u53c2\u8003\u6587\u732e","text":"<p>[1] Thomas H. Cormen, et al. Introduction to Algorithms (3<sup>rd</sup> Edition).</p> <p>[2] Aditya Bhargava. Grokking Algorithms: An Illustrated Guide for Programmers and Other Curious People (1<sup>st</sup> Edition).</p> <p>[3] Robert Sedgewick, et al. Algorithms (4<sup>th</sup> Edition).</p> <p>[4] Yan Weimin. Data Structures (C Language Version).</p> <p>[5] Deng Junhui. Data Structures (C++ Language Version, Third Edition).</p> <p>[6] Mark Allen Weiss, translated by Chen Yue. Data Structures and Algorithm Analysis in Java (Third Edition).</p> <p>[7] Cheng Jie. Speaking of Data Structures.</p> <p>[8] Wang Zheng. The Beauty of Data Structures and Algorithms.</p> <p>[9] Gayle Laakmann McDowell. Cracking the Coding Interview: 189 Programming Questions and Solutions (6<sup>th</sup> Edition).</p> <p>[10] Aston Zhang, et al. Dive into Deep Learning.</p>"},{"location":"chapter_searching/","title":"\u7b2c 10 \u7ae0 \u00a0 \u63a2\u7d22","text":"<p>Abstract</p> <p>\u63a2\u7d22\u306f\u672a\u77e5\u3078\u306e\u5192\u967a\u3067\u3059\u3002\u795e\u79d8\u7684\u306a\u7a7a\u9593\u306e\u9685\u3005\u307e\u3067\u5de1\u308b\u5fc5\u8981\u304c\u3042\u308b\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u3057\u3001\u3042\u308b\u3044\u306f\u3059\u3050\u306b\u76ee\u6a19\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u3002</p> <p>\u3053\u306e\u767a\u898b\u306e\u65c5\u306b\u304a\u3044\u3066\u3001\u305d\u308c\u305e\u308c\u306e\u63a2\u67fb\u306f\u4e88\u671f\u3057\u306a\u3044\u7b54\u3048\u3067\u7d42\u308f\u308b\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u3002</p>"},{"location":"chapter_searching/#_1","title":"\u7ae0\u306e\u5185\u5bb9","text":"<ul> <li>10.1 \u00a0 \u4e8c\u5206\u63a2\u7d22</li> <li>10.2 \u00a0 \u4e8c\u5206\u63a2\u7d22\u633f\u5165\u70b9</li> <li>10.3 \u00a0 \u4e8c\u5206\u63a2\u7d22\u306e\u5883\u754c</li> <li>10.4 \u00a0 \u30cf\u30c3\u30b7\u30e5\u6700\u9069\u5316\u6226\u7565</li> <li>10.5 \u00a0 \u63a2\u7d22\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u518d\u8003</li> <li>10.6 \u00a0 \u307e\u3068\u3081</li> </ul>"},{"location":"chapter_searching/binary_search/","title":"10.1 \u00a0 \u4e8c\u5206\u63a2\u7d22","text":"<p>\u4e8c\u5206\u63a2\u7d22\u306f\u5206\u5272\u7d71\u6cbb\u6226\u7565\u3092\u7528\u3044\u308b\u52b9\u7387\u7684\u306a\u63a2\u7d22\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u3059\u3002\u914d\u5217\u5185\u306e\u8981\u7d20\u306e\u6574\u5217\u9806\u5e8f\u3092\u5229\u7528\u3057\u3001\u5404\u53cd\u5fa9\u3067\u63a2\u7d22\u533a\u9593\u3092\u534a\u5206\u306b\u6e1b\u3089\u3057\u306a\u304c\u3089\u3001\u76ee\u6a19\u8981\u7d20\u304c\u898b\u3064\u304b\u308b\u304b\u63a2\u7d22\u533a\u9593\u304c\u7a7a\u306b\u306a\u308b\u307e\u3067\u7d9a\u884c\u3057\u307e\u3059\u3002</p> <p>Question</p> <p>\u9577\u3055\\(n\\)\u306e\u914d\u5217<code>nums</code>\u304c\u4e0e\u3048\u3089\u308c\u3001\u8981\u7d20\u306f\u91cd\u8907\u306a\u3057\u3067\u6607\u9806\u306b\u914d\u5217\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u3053\u306e\u914d\u5217\u5185\u306e\u8981\u7d20<code>target</code>\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u898b\u3064\u3051\u3066\u8fd4\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u914d\u5217\u306b\u8981\u7d20\u304c\u542b\u307e\u308c\u3066\u3044\u306a\u3044\u5834\u5408\u306f\\(-1\\)\u3092\u8fd4\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u4f8b\u3092\u4e0b\u56f3\u306b\u793a\u3057\u307e\u3059\u3002</p> <p></p> <p> \u56f3 10-1 \u00a0 Binary search example data </p> <p>\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u307e\u305a\\(i = 0\\)\u3068\\(j = n - 1\\)\u3067\u30dd\u30a4\u30f3\u30bf\u3092\u521d\u671f\u5316\u3057\u3001\u305d\u308c\u305e\u308c\u914d\u5217\u306e\u6700\u521d\u3068\u6700\u5f8c\u306e\u8981\u7d20\u3092\u6307\u3057\u307e\u3059\u3002\u3053\u308c\u3089\u306f\u307e\u305f\u5168\u4f53\u306e\u63a2\u7d22\u533a\u9593\\([0, n - 1]\\)\u3092\u8868\u3057\u307e\u3059\u3002\u89d2\u62ec\u5f27\u306f\u9589\u533a\u9593\u3092\u793a\u3057\u3001\u5883\u754c\u5024\u81ea\u8eab\u3082\u542b\u3080\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002</p> <p>\u305d\u3057\u3066\u3001\u4ee5\u4e0b\u306e2\u3064\u306e\u30b9\u30c6\u30c3\u30d7\u3092\u30eb\u30fc\u30d7\u3067\u5b9f\u884c\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002</p> <ol> <li>\u4e2d\u70b9\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\\(m = \\lfloor {(i + j) / 2} \\rfloor\\)\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002\u3053\u3053\u3067\\(\\lfloor \\: \\rfloor\\)\u306f\u5e8a\u95a2\u6570\u3092\u8868\u3057\u307e\u3059\u3002</li> <li><code>nums[m]</code>\u3068<code>target</code>\u306e\u6bd4\u8f03\u306b\u57fa\u3065\u3044\u3066\u3001\u4ee5\u4e0b\u306e3\u3064\u306e\u30b1\u30fc\u30b9\u306e\u3046\u30611\u3064\u3092\u9078\u629e\u3057\u3066\u5b9f\u884c\u3057\u307e\u3059\u3002<ol> <li><code>nums[m] &lt; target</code>\u306e\u5834\u5408\u3001<code>target</code>\u306f\u533a\u9593\\([m + 1, j]\\)\u306b\u3042\u308b\u3053\u3068\u3092\u793a\u3059\u305f\u3081\u3001\\(i = m + 1\\)\u3068\u3057\u307e\u3059\u3002</li> <li><code>nums[m] &gt; target</code>\u306e\u5834\u5408\u3001<code>target</code>\u306f\u533a\u9593\\([i, m - 1]\\)\u306b\u3042\u308b\u3053\u3068\u3092\u793a\u3059\u305f\u3081\u3001\\(j = m - 1\\)\u3068\u3057\u307e\u3059\u3002</li> <li><code>nums[m] = target</code>\u306e\u5834\u5408\u3001<code>target</code>\u304c\u898b\u3064\u304b\u3063\u305f\u3053\u3068\u3092\u793a\u3059\u305f\u3081\u3001\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\\(m\\)\u3092\u8fd4\u3057\u307e\u3059\u3002</li> </ol> </li> </ol> <p>\u914d\u5217\u306b\u76ee\u6a19\u8981\u7d20\u304c\u542b\u307e\u308c\u3066\u3044\u306a\u3044\u5834\u5408\u3001\u63a2\u7d22\u533a\u9593\u306f\u6700\u7d42\u7684\u306b\u7a7a\u306b\u306a\u308a\u3001\\(-1\\)\u3092\u8fd4\u3057\u3066\u7d42\u4e86\u3057\u307e\u3059\u3002</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> \u56f3 10-2 \u00a0 Binary search process </p> <p>\\(i\\)\u3068\\(j\\)\u304c\u4e21\u65b9\u3068\u3082<code>int</code>\u578b\u3067\u3042\u308b\u305f\u3081\u3001**\\(i + j\\)\u306f<code>int</code>\u578b\u306e\u7bc4\u56f2\u3092\u8d85\u3048\u308b\u53ef\u80fd\u6027\u304c\u3042\u308b**\u3053\u3068\u306f\u6ce8\u76ee\u306b\u5024\u3057\u307e\u3059\u3002\u5927\u304d\u306a\u6570\u306e\u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u3092\u907f\u3051\u308b\u305f\u3081\u3001\u901a\u5e38\u306f\u5f0f\\(m = \\lfloor {i + (j - i) / 2} \\rfloor\\)\u3092\u4f7f\u7528\u3057\u3066\u4e2d\u70b9\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002</p> <p>\u30b3\u30fc\u30c9\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig binary_search.py<pre><code>def binary_search(nums: list[int], target: int) -&gt; int:\n    \"\"\"\u4e8c\u5206\u63a2\u7d22\uff08\u4e21\u7aef\u9589\u533a\u9593\uff09\"\"\"\n    # \u4e21\u7aef\u9589\u533a\u9593 [0, n-1] \u3092\u521d\u671f\u5316\u3001\u3059\u306a\u308f\u3061 i, j \u306f\u305d\u308c\u305e\u308c\u914d\u5217\u306e\u6700\u521d\u306e\u8981\u7d20\u3068\u6700\u5f8c\u306e\u8981\u7d20\u3092\u6307\u3059\n    i, j = 0, len(nums) - 1\n    # \u691c\u7d22\u533a\u9593\u304c\u7a7a\u306b\u306a\u308b\u307e\u3067\u30eb\u30fc\u30d7\uff08i &gt; j \u306e\u3068\u304d\u7a7a\uff09\n    while i &lt;= j:\n        # \u7406\u8ad6\u7684\u306b\u306f\u3001Python\u306e\u6570\u5024\u306f\u7121\u9650\u306b\u5927\u304d\u304f\u306a\u308b\u3053\u3068\u304c\u3067\u304d\u308b\uff08\u30e1\u30e2\u30ea\u30b5\u30a4\u30ba\u306b\u4f9d\u5b58\uff09\u305f\u3081\u3001\u5927\u304d\u306a\u6570\u306e\u30aa\u30fc\u30d0\u30fc\u30d5\u30ed\u30fc\u3092\u8003\u616e\u3059\u308b\u5fc5\u8981\u306f\u306a\u3044\n        m = i + (j - i) // 2  # \u4e2d\u70b9\u30a4\u30f3\u30c7\u30c3\u30af\u30b9 m \u3092\u8a08\u7b97\n        if nums[m] &lt; target:\n            i = m + 1  # \u3053\u306e\u5834\u5408\u3001target \u306f\u533a\u9593 [m+1, j] \u306b\u3042\u308b\u3053\u3068\u3092\u793a\u3059\n        elif nums[m] &gt; target:\n            j = m - 1  # \u3053\u306e\u5834\u5408\u3001target \u306f\u533a\u9593 [i, m-1] \u306b\u3042\u308b\u3053\u3068\u3092\u793a\u3059\n        else:\n            return m  # \u30bf\u30fc\u30b2\u30c3\u30c8\u8981\u7d20\u304c\u898b\u3064\u304b\u3063\u305f\u305f\u3081\u3001\u305d\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8fd4\u3059\n    return -1  # \u30bf\u30fc\u30b2\u30c3\u30c8\u8981\u7d20\u304c\u898b\u3064\u304b\u3089\u306a\u304b\u3063\u305f\u305f\u3081\u3001-1 \u3092\u8fd4\u3059\n</code></pre> binary_search.cpp<pre><code>/* \u4e8c\u5206\u63a2\u7d22\uff08\u4e21\u7aef\u9589\u533a\u9593\uff09 */\nint binarySearch(vector&lt;int&gt; &amp;nums, int target) {\n    // \u4e21\u7aef\u9589\u533a\u9593[0, n-1]\u3092\u521d\u671f\u5316\u3001\u3059\u306a\u308f\u3061i\u3001j\u306f\u305d\u308c\u305e\u308c\u914d\u5217\u306e\u6700\u521d\u306e\u8981\u7d20\u3068\u6700\u5f8c\u306e\u8981\u7d20\u3092\u6307\u3059\n    int i = 0, j = nums.size() - 1;\n    // \u63a2\u7d22\u533a\u9593\u304c\u7a7a\u306b\u306a\u308b\u307e\u3067\u30eb\u30fc\u30d7\uff08i &gt; j\u306e\u6642\u7a7a\u306b\u306a\u308b\uff09\n    while (i &lt;= j) {\n        int m = i + (j - i) / 2; // \u4e2d\u70b9\u30a4\u30f3\u30c7\u30c3\u30af\u30b9m\u3092\u8a08\u7b97\n        if (nums[m] &lt; target)    // \u3053\u306e\u72b6\u6cc1\u306ftarget\u304c\u533a\u9593[m+1, j]\u306b\u3042\u308b\u3053\u3068\u3092\u793a\u3059\n            i = m + 1;\n        else if (nums[m] &gt; target) // \u3053\u306e\u72b6\u6cc1\u306ftarget\u304c\u533a\u9593[i, m-1]\u306b\u3042\u308b\u3053\u3068\u3092\u793a\u3059\n            j = m - 1;\n        else // \u30bf\u30fc\u30b2\u30c3\u30c8\u8981\u7d20\u304c\u898b\u3064\u304b\u3063\u305f\u305f\u3081\u3001\u305d\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8fd4\u3059\n            return m;\n    }\n    // \u30bf\u30fc\u30b2\u30c3\u30c8\u8981\u7d20\u304c\u898b\u3064\u304b\u3089\u306a\u304b\u3063\u305f\u305f\u3081\u3001-1\u3092\u8fd4\u3059\n    return -1;\n}\n</code></pre> binary_search.java<pre><code>/* \u4e8c\u5206\u63a2\u7d22\uff08\u4e21\u7aef\u9589\u533a\u9593\uff09 */\nint binarySearch(int[] nums, int target) {\n    // \u4e21\u7aef\u9589\u533a\u9593 [0, n-1] \u3092\u521d\u671f\u5316\u3001\u3059\u306a\u308f\u3061 i, j \u306f\u305d\u308c\u305e\u308c\u914d\u5217\u306e\u6700\u521d\u306e\u8981\u7d20\u3068\u6700\u5f8c\u306e\u8981\u7d20\u3092\u6307\u3059\n    int i = 0, j = nums.length - 1;\n    // \u63a2\u7d22\u533a\u9593\u304c\u7a7a\u306b\u306a\u308b\u307e\u3067\u30eb\u30fc\u30d7\uff08i &gt; j \u306e\u3068\u304d\u7a7a\uff09\n    while (i &lt;= j) {\n        int m = i + (j - i) / 2; // \u4e2d\u70b9\u30a4\u30f3\u30c7\u30c3\u30af\u30b9 m \u3092\u8a08\u7b97\n        if (nums[m] &lt; target) // \u3053\u306e\u72b6\u6cc1\u306f target \u304c\u533a\u9593 [m+1, j] \u306b\u3042\u308b\u3053\u3068\u3092\u793a\u3059\n            i = m + 1;\n        else if (nums[m] &gt; target) // \u3053\u306e\u72b6\u6cc1\u306f target \u304c\u533a\u9593 [i, m-1] \u306b\u3042\u308b\u3053\u3068\u3092\u793a\u3059\n            j = m - 1;\n        else // \u76ee\u6a19\u8981\u7d20\u3092\u898b\u3064\u3051\u305f\u306e\u3067\u3001\u305d\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8fd4\u3059\n            return m;\n    }\n    // \u76ee\u6a19\u8981\u7d20\u3092\u898b\u3064\u3051\u3089\u308c\u306a\u304b\u3063\u305f\u306e\u3067\u3001-1 \u3092\u8fd4\u3059\n    return -1;\n}\n</code></pre> binary_search.cs<pre><code>[class]{binary_search}-[func]{BinarySearch}\n</code></pre> binary_search.go<pre><code>[class]{}-[func]{binarySearch}\n</code></pre> binary_search.swift<pre><code>[class]{}-[func]{binarySearch}\n</code></pre> binary_search.js<pre><code>[class]{}-[func]{binarySearch}\n</code></pre> binary_search.ts<pre><code>[class]{}-[func]{binarySearch}\n</code></pre> binary_search.dart<pre><code>[class]{}-[func]{binarySearch}\n</code></pre> binary_search.rs<pre><code>[class]{}-[func]{binary_search}\n</code></pre> binary_search.c<pre><code>[class]{}-[func]{binarySearch}\n</code></pre> binary_search.kt<pre><code>[class]{}-[func]{binarySearch}\n</code></pre> binary_search.rb<pre><code>[class]{}-[func]{binary_search}\n</code></pre> binary_search.zig<pre><code>[class]{}-[func]{binarySearch}\n</code></pre> <p>\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O(\\log n)\\)\u3067\u3059\uff1a\u4e8c\u5206\u30eb\u30fc\u30d7\u306b\u304a\u3044\u3066\u3001\u533a\u9593\u306f\u5404\u30e9\u30a6\u30f3\u30c9\u3067\u534a\u5206\u306b\u6e1b\u5c11\u3059\u308b\u305f\u3081\u3001\u53cd\u5fa9\u56de\u6570\u306f\\(\\log_2 n\\)\u3068\u306a\u308a\u307e\u3059\u3002</p> <p>\u7a7a\u9593\u8a08\u7b97\u91cf\u306f\\(O(1)\\)\u3067\u3059\uff1a\u30dd\u30a4\u30f3\u30bf\\(i\\)\u3068\\(j\\)\u306f\u5b9a\u6570\u30b5\u30a4\u30ba\u306e\u7a7a\u9593\u3092\u5360\u6709\u3057\u307e\u3059\u3002</p>"},{"location":"chapter_searching/binary_search/#1011","title":"10.1.1 \u00a0 \u533a\u9593\u8868\u73fe\u65b9\u6cd5","text":"<p>\u4e0a\u8a18\u306e\u9589\u533a\u9593\u306e\u4ed6\u306b\u3001\u3082\u3046\u4e00\u3064\u306e\u4e00\u822c\u7684\u306a\u533a\u9593\u8868\u73fe\u306f\u300c\u5de6\u9589\u53f3\u958b\u300d\u533a\u9593\u3067\u3001\\([0, n)\\)\u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u3001\u5de6\u5883\u754c\u306f\u81ea\u8eab\u3092\u542b\u307f\u3001\u53f3\u5883\u754c\u306f\u542b\u307f\u307e\u305b\u3093\u3002\u3053\u306e\u8868\u73fe\u3067\u306f\u3001\\(i = j\\)\u306e\u3068\u304d\u533a\u9593\\([i, j)\\)\u306f\u7a7a\u306b\u306a\u308a\u307e\u3059\u3002</p> <p>\u3053\u306e\u8868\u73fe\u306b\u57fa\u3065\u3044\u3066\u540c\u3058\u6a5f\u80fd\u3092\u6301\u3064\u4e8c\u5206\u63a2\u7d22\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u5b9f\u88c5\u3067\u304d\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig binary_search.py<pre><code>def binary_search_lcro(nums: list[int], target: int) -&gt; int:\n    \"\"\"\u4e8c\u5206\u63a2\u7d22\uff08\u5de6\u9589\u53f3\u958b\u533a\u9593\uff09\"\"\"\n    # \u5de6\u9589\u53f3\u958b\u533a\u9593 [0, n) \u3092\u521d\u671f\u5316\u3001\u3059\u306a\u308f\u3061 i, j \u306f\u305d\u308c\u305e\u308c\u914d\u5217\u306e\u6700\u521d\u306e\u8981\u7d20\u3068\u6700\u5f8c\u306e\u8981\u7d20+1\u3092\u6307\u3059\n    i, j = 0, len(nums)\n    # \u691c\u7d22\u533a\u9593\u304c\u7a7a\u306b\u306a\u308b\u307e\u3067\u30eb\u30fc\u30d7\uff08i = j \u306e\u3068\u304d\u7a7a\uff09\n    while i &lt; j:\n        m = i + (j - i) // 2  # \u4e2d\u70b9\u30a4\u30f3\u30c7\u30c3\u30af\u30b9 m \u3092\u8a08\u7b97\n        if nums[m] &lt; target:\n            i = m + 1  # \u3053\u306e\u5834\u5408\u3001target \u306f\u533a\u9593 [m+1, j) \u306b\u3042\u308b\u3053\u3068\u3092\u793a\u3059\n        elif nums[m] &gt; target:\n            j = m  # \u3053\u306e\u5834\u5408\u3001target \u306f\u533a\u9593 [i, m) \u306b\u3042\u308b\u3053\u3068\u3092\u793a\u3059\n        else:\n            return m  # \u30bf\u30fc\u30b2\u30c3\u30c8\u8981\u7d20\u304c\u898b\u3064\u304b\u3063\u305f\u305f\u3081\u3001\u305d\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8fd4\u3059\n    return -1  # \u30bf\u30fc\u30b2\u30c3\u30c8\u8981\u7d20\u304c\u898b\u3064\u304b\u3089\u306a\u304b\u3063\u305f\u305f\u3081\u3001-1 \u3092\u8fd4\u3059\n</code></pre> binary_search.cpp<pre><code>/* \u4e8c\u5206\u63a2\u7d22\uff08\u5de6\u9589\u53f3\u958b\u533a\u9593\uff09 */\nint binarySearchLCRO(vector&lt;int&gt; &amp;nums, int target) {\n    // \u5de6\u9589\u53f3\u958b\u533a\u9593[0, n)\u3092\u521d\u671f\u5316\u3001\u3059\u306a\u308f\u3061i\u3001j\u306f\u305d\u308c\u305e\u308c\u914d\u5217\u306e\u6700\u521d\u306e\u8981\u7d20\u3068\u6700\u5f8c\u306e\u8981\u7d20+1\u3092\u6307\u3059\n    int i = 0, j = nums.size();\n    // \u63a2\u7d22\u533a\u9593\u304c\u7a7a\u306b\u306a\u308b\u307e\u3067\u30eb\u30fc\u30d7\uff08i = j\u306e\u6642\u7a7a\u306b\u306a\u308b\uff09\n    while (i &lt; j) {\n        int m = i + (j - i) / 2; // \u4e2d\u70b9\u30a4\u30f3\u30c7\u30c3\u30af\u30b9m\u3092\u8a08\u7b97\n        if (nums[m] &lt; target)    // \u3053\u306e\u72b6\u6cc1\u306ftarget\u304c\u533a\u9593[m+1, j)\u306b\u3042\u308b\u3053\u3068\u3092\u793a\u3059\n            i = m + 1;\n        else if (nums[m] &gt; target) // \u3053\u306e\u72b6\u6cc1\u306ftarget\u304c\u533a\u9593[i, m)\u306b\u3042\u308b\u3053\u3068\u3092\u793a\u3059\n            j = m;\n        else // \u30bf\u30fc\u30b2\u30c3\u30c8\u8981\u7d20\u304c\u898b\u3064\u304b\u3063\u305f\u305f\u3081\u3001\u305d\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8fd4\u3059\n            return m;\n    }\n    // \u30bf\u30fc\u30b2\u30c3\u30c8\u8981\u7d20\u304c\u898b\u3064\u304b\u3089\u306a\u304b\u3063\u305f\u305f\u3081\u3001-1\u3092\u8fd4\u3059\n    return -1;\n}\n</code></pre> binary_search.java<pre><code>/* \u4e8c\u5206\u63a2\u7d22\uff08\u5de6\u9589\u53f3\u958b\u533a\u9593\uff09 */\nint binarySearchLCRO(int[] nums, int target) {\n    // \u5de6\u9589\u53f3\u958b\u533a\u9593 [0, n) \u3092\u521d\u671f\u5316\u3001\u3059\u306a\u308f\u3061 i, j \u306f\u305d\u308c\u305e\u308c\u914d\u5217\u306e\u6700\u521d\u306e\u8981\u7d20\u3068\u6700\u5f8c\u306e\u8981\u7d20+1\u3092\u6307\u3059\n    int i = 0, j = nums.length;\n    // \u63a2\u7d22\u533a\u9593\u304c\u7a7a\u306b\u306a\u308b\u307e\u3067\u30eb\u30fc\u30d7\uff08i = j \u306e\u3068\u304d\u7a7a\uff09\n    while (i &lt; j) {\n        int m = i + (j - i) / 2; // \u4e2d\u70b9\u30a4\u30f3\u30c7\u30c3\u30af\u30b9 m \u3092\u8a08\u7b97\n        if (nums[m] &lt; target) // \u3053\u306e\u72b6\u6cc1\u306f target \u304c\u533a\u9593 [m+1, j) \u306b\u3042\u308b\u3053\u3068\u3092\u793a\u3059\n            i = m + 1;\n        else if (nums[m] &gt; target) // \u3053\u306e\u72b6\u6cc1\u306f target \u304c\u533a\u9593 [i, m) \u306b\u3042\u308b\u3053\u3068\u3092\u793a\u3059\n            j = m;\n        else // \u76ee\u6a19\u8981\u7d20\u3092\u898b\u3064\u3051\u305f\u306e\u3067\u3001\u305d\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8fd4\u3059\n            return m;\n    }\n    // \u76ee\u6a19\u8981\u7d20\u3092\u898b\u3064\u3051\u3089\u308c\u306a\u304b\u3063\u305f\u306e\u3067\u3001-1 \u3092\u8fd4\u3059\n    return -1;\n}\n</code></pre> binary_search.cs<pre><code>[class]{binary_search}-[func]{BinarySearchLCRO}\n</code></pre> binary_search.go<pre><code>[class]{}-[func]{binarySearchLCRO}\n</code></pre> binary_search.swift<pre><code>[class]{}-[func]{binarySearchLCRO}\n</code></pre> binary_search.js<pre><code>[class]{}-[func]{binarySearchLCRO}\n</code></pre> binary_search.ts<pre><code>[class]{}-[func]{binarySearchLCRO}\n</code></pre> binary_search.dart<pre><code>[class]{}-[func]{binarySearchLCRO}\n</code></pre> binary_search.rs<pre><code>[class]{}-[func]{binary_search_lcro}\n</code></pre> binary_search.c<pre><code>[class]{}-[func]{binarySearchLCRO}\n</code></pre> binary_search.kt<pre><code>[class]{}-[func]{binarySearchLCRO}\n</code></pre> binary_search.rb<pre><code>[class]{}-[func]{binary_search_lcro}\n</code></pre> binary_search.zig<pre><code>[class]{}-[func]{binarySearchLCRO}\n</code></pre> <p>\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u30012\u3064\u306e\u533a\u9593\u8868\u73fe\u30bf\u30a4\u30d7\u306b\u304a\u3044\u3066\u3001\u4e8c\u5206\u63a2\u7d22\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u521d\u671f\u5316\u3001\u30eb\u30fc\u30d7\u6761\u4ef6\u3001\u533a\u9593\u7e2e\u5c0f\u64cd\u4f5c\u304c\u7570\u306a\u308a\u307e\u3059\u3002</p> <p>\u300c\u9589\u533a\u9593\u300d\u8868\u73fe\u3067\u306f\u4e21\u65b9\u306e\u5883\u754c\u304c\u5305\u542b\u7684\u3067\u3042\u308b\u305f\u3081\u3001\u30dd\u30a4\u30f3\u30bf\\(i\\)\u3068\\(j\\)\u306b\u3088\u308b\u533a\u9593\u7e2e\u5c0f\u64cd\u4f5c\u3082\u5bfe\u79f0\u7684\u3067\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u30a8\u30e9\u30fc\u304c\u767a\u751f\u3057\u306b\u304f\u304f\u306a\u308b\u305f\u3081\u3001\u4e00\u822c\u7684\u306b\u300c\u9589\u533a\u9593\u300d\u30a2\u30d7\u30ed\u30fc\u30c1\u306e\u4f7f\u7528\u304c\u63a8\u5968\u3055\u308c\u307e\u3059\u3002</p> <p></p> <p> \u56f3 10-3 \u00a0 Two types of interval definitions </p>"},{"location":"chapter_searching/binary_search/#1012","title":"10.1.2 \u00a0 \u5229\u70b9\u3068\u5236\u9650","text":"<p>\u4e8c\u5206\u63a2\u7d22\u306f\u6642\u9593\u3068\u7a7a\u9593\u306e\u4e21\u65b9\u306e\u9762\u3067\u826f\u597d\u306a\u6027\u80fd\u3092\u793a\u3057\u307e\u3059\u3002</p> <ul> <li>\u4e8c\u5206\u63a2\u7d22\u306f\u6642\u9593\u52b9\u7387\u304c\u826f\u3044\u3067\u3059\u3002\u5927\u304d\u306a\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u3067\u306f\u3001\u5bfe\u6570\u6642\u9593\u8a08\u7b97\u91cf\u304c\u5927\u304d\u306a\u5229\u70b9\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u30b5\u30a4\u30ba\\(n = 2^{20}\\)\u306e\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408\u3001\u7dda\u5f62\u63a2\u7d22\u306f\\(2^{20} = 1048576\\)\u56de\u306e\u53cd\u5fa9\u304c\u5fc5\u8981\u3067\u3059\u304c\u3001\u4e8c\u5206\u63a2\u7d22\u306f\\(\\log_2 2^{20} = 20\\)\u56de\u306e\u30eb\u30fc\u30d7\u306e\u307f\u3067\u6e08\u307f\u307e\u3059\u3002</li> <li>\u4e8c\u5206\u63a2\u7d22\u306b\u306f\u8ffd\u52a0\u306e\u7a7a\u9593\u304c\u5fc5\u8981\u3042\u308a\u307e\u305b\u3093\u3002\u8ffd\u52a0\u306e\u7a7a\u9593\u306b\u4f9d\u5b58\u3059\u308b\u63a2\u7d22\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\uff08\u30cf\u30c3\u30b7\u30e5\u63a2\u7d22\u306a\u3069\uff09\u3068\u6bd4\u8f03\u3057\u3066\u3001\u4e8c\u5206\u63a2\u7d22\u306f\u3088\u308a\u7a7a\u9593\u52b9\u7387\u7684\u3067\u3059\u3002</li> </ul> <p>\u3057\u304b\u3057\u3001\u4e8c\u5206\u63a2\u7d22\u306f\u4ee5\u4e0b\u306e\u61f8\u5ff5\u306b\u3088\u308a\u3001\u3059\u3079\u3066\u306e\u30b7\u30ca\u30ea\u30aa\u306b\u9069\u3057\u3066\u3044\u308b\u3068\u306f\u9650\u308a\u307e\u305b\u3093\u3002</p> <ul> <li>\u4e8c\u5206\u63a2\u7d22\u306f\u30bd\u30fc\u30c8\u6e08\u307f\u30c7\u30fc\u30bf\u306b\u306e\u307f\u9069\u7528\u3067\u304d\u307e\u3059\u3002\u672a\u30bd\u30fc\u30c8\u306e\u30c7\u30fc\u30bf\u306f\u4e8c\u5206\u63a2\u7d22\u3092\u9069\u7528\u3059\u308b\u524d\u306b\u30bd\u30fc\u30c8\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u3001\u30bd\u30fc\u30c8\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u901a\u5e38\\(O(n \\log n)\\)\u306e\u6642\u9593\u8a08\u7b97\u91cf\u3092\u6301\u3064\u305f\u3081\u3001\u3053\u308c\u306f\u4fa1\u5024\u304c\u306a\u3044\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u3002\u3053\u306e\u30b3\u30b9\u30c8\u306f\u7dda\u5f62\u63a2\u7d22\u3088\u308a\u3082\u9ad8\u304f\u3001\u4e8c\u5206\u63a2\u7d22\u81ea\u4f53\u306f\u8a00\u3046\u307e\u3067\u3082\u3042\u308a\u307e\u305b\u3093\u3002\u983b\u7e41\u306a\u633f\u5165\u304c\u3042\u308b\u30b7\u30ca\u30ea\u30aa\u3067\u306f\u3001\u914d\u5217\u3092\u9806\u5e8f\u306b\u4fdd\u3064\u30b3\u30b9\u30c8\u306f\u975e\u5e38\u306b\u9ad8\u304f\u3001\u7279\u5b9a\u306e\u4f4d\u7f6e\u306b\u65b0\u3057\u3044\u8981\u7d20\u3092\u633f\u5165\u3059\u308b\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O(n)\\)\u3067\u3059\u3002</li> <li>\u4e8c\u5206\u63a2\u7d22\u306f\u914d\u5217\u306e\u307f\u3092\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002\u4e8c\u5206\u63a2\u7d22\u306b\u306f\u975e\u9023\u7d9a\uff08\u30b8\u30e3\u30f3\u30d7\uff09\u8981\u7d20\u30a2\u30af\u30bb\u30b9\u304c\u5fc5\u8981\u3067\u3001\u3053\u308c\u306f\u9023\u7d50\u30ea\u30b9\u30c8\u3067\u306f\u975e\u52b9\u7387\u7684\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u3084\u9023\u7d50\u30ea\u30b9\u30c8\u306b\u57fa\u3065\u304f\u30c7\u30fc\u30bf\u69cb\u9020\u306f\u3053\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306b\u9069\u3057\u3066\u3044\u306a\u3044\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002</li> <li>\u7dda\u5f62\u63a2\u7d22\u306f\u5c0f\u3055\u306a\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u3067\u3088\u308a\u826f\u3044\u6027\u80fd\u3092\u793a\u3057\u307e\u3059\u3002\u7dda\u5f62\u63a2\u7d22\u3067\u306f\u5404\u53cd\u5fa9\u30671\u3064\u306e\u5224\u5b9a\u64cd\u4f5c\u306e\u307f\u304c\u5fc5\u8981\u3067\u3059\u304c\u3001\u4e8c\u5206\u63a2\u7d22\u3067\u306f1\u3064\u306e\u52a0\u7b97\u30011\u3064\u306e\u9664\u7b97\u30011\u3064\u304b\u30893\u3064\u306e\u5224\u5b9a\u64cd\u4f5c\u30011\u3064\u306e\u52a0\u7b97\uff08\u6e1b\u7b97\uff09\u3092\u542b\u307f\u3001\u5408\u8a084\u3064\u304b\u30896\u3064\u306e\u64cd\u4f5c\u304c\u5fc5\u8981\u3067\u3059\u3002\u305d\u306e\u305f\u3081\u3001\u30c7\u30fc\u30bf\u30b5\u30a4\u30ba\\(n\\)\u304c\u5c0f\u3055\u3044\u5834\u5408\u3001\u7dda\u5f62\u63a2\u7d22\u306f\u4e8c\u5206\u63a2\u7d22\u3088\u308a\u3082\u9ad8\u901f\u3067\u3059\u3002</li> </ul>"},{"location":"chapter_searching/binary_search_edge/","title":"10.3 \u00a0 \u4e8c\u5206\u63a2\u7d22\u306e\u5883\u754c","text":""},{"location":"chapter_searching/binary_search_edge/#1031","title":"10.3.1 \u00a0 \u5de6\u5883\u754c\u3092\u898b\u3064\u3051\u308b","text":"<p>Question</p> <p>\u91cd\u8907\u8981\u7d20\u3092\u542b\u3080\u53ef\u80fd\u6027\u304c\u3042\u308b\u9577\u3055\\(n\\)\u306e\u30bd\u30fc\u30c8\u6e08\u307f\u914d\u5217<code>nums</code>\u304c\u4e0e\u3048\u3089\u308c\u3001\u6700\u3082\u5de6\u306e\u8981\u7d20<code>target</code>\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8fd4\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u8981\u7d20\u304c\u914d\u5217\u306b\u5b58\u5728\u3057\u306a\u3044\u5834\u5408\u306f\u3001\\(-1\\)\u3092\u8fd4\u3057\u3066\u304f\u3060\u3055\u3044\u3002</p> <p>\u633f\u5165\u4f4d\u7f6e\u306e\u4e8c\u5206\u63a2\u7d22\u65b9\u6cd5\u3092\u601d\u3044\u51fa\u3059\u3068\u3001\u63a2\u7d22\u5b8c\u4e86\u5f8c\u3001\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\\(i\\)\u306f<code>target</code>\u306e\u6700\u3082\u5de6\u306e\u51fa\u73fe\u3092\u6307\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u633f\u5165\u4f4d\u7f6e\u306e\u63a2\u7d22\u306f\u672c\u8cea\u7684\u306b\u6700\u3082\u5de6\u306e<code>target</code>\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u3068\u540c\u3058\u3067\u3059\u3002</p> <p>\u633f\u5165\u4f4d\u7f6e\u3092\u898b\u3064\u3051\u308b\u95a2\u6570\u3092\u4f7f\u7528\u3057\u3066<code>target</code>\u306e\u5de6\u5883\u754c\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u914d\u5217\u306b<code>target</code>\u304c\u542b\u307e\u308c\u3066\u3044\u306a\u3044\u53ef\u80fd\u6027\u304c\u3042\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u3053\u308c\u306f\u4ee5\u4e0b\u306e2\u3064\u306e\u7d50\u679c\u306b\u3064\u306a\u304c\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\uff1a</p> <ul> <li>\u633f\u5165\u4f4d\u7f6e\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\\(i\\)\u304c\u7bc4\u56f2\u5916\u3067\u3059\u3002</li> <li>\u8981\u7d20<code>nums[i]</code>\u304c<code>target</code>\u3068\u7b49\u3057\u304f\u3042\u308a\u307e\u305b\u3093\u3002</li> </ul> <p>\u3053\u308c\u3089\u306e\u5834\u5408\u3001\u5358\u306b\\(-1\\)\u3092\u8fd4\u3057\u307e\u3059\u3002\u30b3\u30fc\u30c9\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig binary_search_edge.py<pre><code>def binary_search_left_edge(nums: list[int], target: int) -&gt; int:\n    \"\"\"\u6700\u5de6\u7aef\u306e\u30bf\u30fc\u30b2\u30c3\u30c8\u306e\u4e8c\u5206\u63a2\u7d22\"\"\"\n    # \u30bf\u30fc\u30b2\u30c3\u30c8\u306e\u633f\u5165\u4f4d\u7f6e\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u3068\u540c\u7b49\n    i = binary_search_insertion(nums, target)\n    # \u30bf\u30fc\u30b2\u30c3\u30c8\u304c\u898b\u3064\u304b\u3089\u306a\u304b\u3063\u305f\u5834\u5408\u3001-1 \u3092\u8fd4\u3059\n    if i == len(nums) or nums[i] != target:\n        return -1\n    # \u30bf\u30fc\u30b2\u30c3\u30c8\u304c\u898b\u3064\u304b\u3063\u305f\u5834\u5408\u3001\u30a4\u30f3\u30c7\u30c3\u30af\u30b9 i \u3092\u8fd4\u3059\n    return i\n</code></pre> binary_search_edge.cpp<pre><code>/* \u6700\u5de6\u306e\u30bf\u30fc\u30b2\u30c3\u30c8\u306e\u4e8c\u5206\u63a2\u7d22 */\nint binarySearchLeftEdge(vector&lt;int&gt; &amp;nums, int target) {\n    // target\u306e\u633f\u5165\u30dd\u30a4\u30f3\u30c8\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u3068\u7b49\u4fa1\n    int i = binarySearchInsertion(nums, target);\n    // target\u304c\u898b\u3064\u304b\u3089\u306a\u304b\u3063\u305f\u305f\u3081\u3001-1\u3092\u8fd4\u3059\n    if (i == nums.size() || nums[i] != target) {\n        return -1;\n    }\n    // target\u304c\u898b\u3064\u304b\u3063\u305f\u305f\u3081\u3001\u30a4\u30f3\u30c7\u30c3\u30af\u30b9i\u3092\u8fd4\u3059\n    return i;\n}\n</code></pre> binary_search_edge.java<pre><code>/* \u6700\u3082\u5de6\u306e target \u3092\u4e8c\u5206\u63a2\u7d22 */\nint binarySearchLeftEdge(int[] nums, int target) {\n    // target \u306e\u633f\u5165\u70b9\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u3068\u7b49\u4fa1\n    int i = binary_search_insertion.binarySearchInsertion(nums, target);\n    // target \u3092\u898b\u3064\u3051\u3089\u308c\u306a\u304b\u3063\u305f\u306e\u3067\u3001-1 \u3092\u8fd4\u3059\n    if (i == nums.length || nums[i] != target) {\n        return -1;\n    }\n    // target \u3092\u898b\u3064\u3051\u305f\u306e\u3067\u3001\u30a4\u30f3\u30c7\u30c3\u30af\u30b9 i \u3092\u8fd4\u3059\n    return i;\n}\n</code></pre> binary_search_edge.cs<pre><code>[class]{binary_search_edge}-[func]{BinarySearchLeftEdge}\n</code></pre> binary_search_edge.go<pre><code>[class]{}-[func]{binarySearchLeftEdge}\n</code></pre> binary_search_edge.swift<pre><code>[class]{}-[func]{binarySearchLeftEdge}\n</code></pre> binary_search_edge.js<pre><code>[class]{}-[func]{binarySearchLeftEdge}\n</code></pre> binary_search_edge.ts<pre><code>[class]{}-[func]{binarySearchLeftEdge}\n</code></pre> binary_search_edge.dart<pre><code>[class]{}-[func]{binarySearchLeftEdge}\n</code></pre> binary_search_edge.rs<pre><code>[class]{}-[func]{binary_search_left_edge}\n</code></pre> binary_search_edge.c<pre><code>[class]{}-[func]{binarySearchLeftEdge}\n</code></pre> binary_search_edge.kt<pre><code>[class]{}-[func]{binarySearchLeftEdge}\n</code></pre> binary_search_edge.rb<pre><code>[class]{}-[func]{binary_search_left_edge}\n</code></pre> binary_search_edge.zig<pre><code>[class]{}-[func]{binarySearchLeftEdge}\n</code></pre>"},{"location":"chapter_searching/binary_search_edge/#1032","title":"10.3.2 \u00a0 \u53f3\u5883\u754c\u3092\u898b\u3064\u3051\u308b","text":"<p><code>target</code>\u306e\u6700\u3082\u53f3\u306e\u51fa\u73fe\u3092\u3069\u306e\u3088\u3046\u306b\u898b\u3064\u3051\u308b\u3067\u3057\u3087\u3046\u304b\uff1f\u6700\u3082\u76f4\u63a5\u7684\u306a\u65b9\u6cd5\u306f\u3001<code>nums[m] == target</code>\u306e\u5834\u5408\u306b\u63a2\u7d22\u5883\u754c\u3092\u8abf\u6574\u3059\u308b\u65b9\u6cd5\u3092\u5909\u66f4\u3057\u3066\u3001\u5f93\u6765\u306e\u4e8c\u5206\u63a2\u7d22\u30ed\u30b8\u30c3\u30af\u3092\u4fee\u6b63\u3059\u308b\u3053\u3068\u3067\u3059\u3002\u30b3\u30fc\u30c9\u306f\u3053\u3053\u3067\u306f\u7701\u7565\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u8208\u5473\u304c\u3042\u308b\u5834\u5408\u306f\u3001\u81ea\u5206\u3067\u30b3\u30fc\u30c9\u3092\u5b9f\u88c5\u3057\u3066\u307f\u3066\u304f\u3060\u3055\u3044\u3002</p> <p>\u4ee5\u4e0b\u3067\u306f\u3001\u3055\u3089\u306b2\u3064\u306e\u5de7\u5999\u306a\u65b9\u6cd5\u3092\u7d39\u4ecb\u3057\u307e\u3059\u3002</p>"},{"location":"chapter_searching/binary_search_edge/#1","title":"1. \u00a0 \u5de6\u5883\u754c\u63a2\u7d22\u3092\u518d\u5229\u7528\u3059\u308b","text":"<p><code>target</code>\u306e\u6700\u3082\u53f3\u306e\u51fa\u73fe\u3092\u898b\u3064\u3051\u308b\u306b\u306f\u3001\u6700\u3082\u5de6\u306e<code>target</code>\u3092\u898b\u3064\u3051\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u305f\u95a2\u6570\u3092\u518d\u5229\u7528\u3067\u304d\u307e\u3059\u3002\u5177\u4f53\u7684\u306b\u306f\u3001\u6700\u3082\u53f3\u306e\u30bf\u30fc\u30b2\u30c3\u30c8\u306e\u63a2\u7d22\u3092\u6700\u3082\u5de6\u306e\u30bf\u30fc\u30b2\u30c3\u30c8 + 1\u306e\u63a2\u7d22\u306b\u5909\u63db\u3057\u307e\u3059\u3002</p> <p>\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u63a2\u7d22\u5b8c\u4e86\u5f8c\u3001\u30dd\u30a4\u30f3\u30bf\\(i\\)\u306f\u6700\u3082\u5de6\u306e<code>target + 1</code>\uff08\u5b58\u5728\u3059\u308b\u5834\u5408\uff09\u3092\u6307\u3057\u3001\u30dd\u30a4\u30f3\u30bf\\(j\\)\u306f<code>target</code>\u306e\u6700\u3082\u53f3\u306e\u51fa\u73fe\u3092\u6307\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\\(j\\)\u3092\u8fd4\u3059\u3053\u3068\u3067\u53f3\u5883\u754c\u304c\u5f97\u3089\u308c\u307e\u3059\u3002</p> <p></p> <p> \u56f3 10-7 \u00a0 Transforming the search for the right boundary into the search for the left boundary </p> <p>\u8fd4\u3055\u308c\u308b\u633f\u5165\u4f4d\u7f6e\u306f\\(i\\)\u3067\u3042\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u3057\u305f\u304c\u3063\u3066\u3001\\(j\\)\u3092\u5f97\u308b\u305f\u3081\u306b\u306f1\u3092\u5f15\u304f\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig binary_search_edge.py<pre><code>def binary_search_right_edge(nums: list[int], target: int) -&gt; int:\n    \"\"\"\u6700\u53f3\u7aef\u306e\u30bf\u30fc\u30b2\u30c3\u30c8\u306e\u4e8c\u5206\u63a2\u7d22\"\"\"\n    # \u6700\u5de6\u7aef\u306e\u30bf\u30fc\u30b2\u30c3\u30c8 + 1 \u3092\u898b\u3064\u3051\u308b\u3053\u3068\u306b\u5909\u63db\n    i = binary_search_insertion(nums, target + 1)\n    # j \u306f\u6700\u53f3\u7aef\u306e\u30bf\u30fc\u30b2\u30c3\u30c8\u3092\u6307\u3057\u3001i \u306f\u30bf\u30fc\u30b2\u30c3\u30c8\u3088\u308a\u5927\u304d\u3044\u6700\u521d\u306e\u8981\u7d20\u3092\u6307\u3059\n    j = i - 1\n    # \u30bf\u30fc\u30b2\u30c3\u30c8\u304c\u898b\u3064\u304b\u3089\u306a\u304b\u3063\u305f\u5834\u5408\u3001-1 \u3092\u8fd4\u3059\n    if j == -1 or nums[j] != target:\n        return -1\n    # \u30bf\u30fc\u30b2\u30c3\u30c8\u304c\u898b\u3064\u304b\u3063\u305f\u5834\u5408\u3001\u30a4\u30f3\u30c7\u30c3\u30af\u30b9 j \u3092\u8fd4\u3059\n    return j\n</code></pre> binary_search_edge.cpp<pre><code>/* \u6700\u53f3\u306e\u30bf\u30fc\u30b2\u30c3\u30c8\u306e\u4e8c\u5206\u63a2\u7d22 */\nint binarySearchRightEdge(vector&lt;int&gt; &amp;nums, int target) {\n    // \u6700\u5de6\u306etarget + 1\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u306b\u5909\u63db\n    int i = binarySearchInsertion(nums, target + 1);\n    // j\u306f\u6700\u53f3\u306e\u30bf\u30fc\u30b2\u30c3\u30c8\u3092\u6307\u3057\u3001i\u306ftarget\u3088\u308a\u5927\u304d\u3044\u6700\u521d\u306e\u8981\u7d20\u3092\u6307\u3059\n    int j = i - 1;\n    // target\u304c\u898b\u3064\u304b\u3089\u306a\u304b\u3063\u305f\u305f\u3081\u3001-1\u3092\u8fd4\u3059\n    if (j == -1 || nums[j] != target) {\n        return -1;\n    }\n    // target\u304c\u898b\u3064\u304b\u3063\u305f\u305f\u3081\u3001\u30a4\u30f3\u30c7\u30c3\u30af\u30b9j\u3092\u8fd4\u3059\n    return j;\n}\n</code></pre> binary_search_edge.java<pre><code>/* \u6700\u3082\u53f3\u306e target \u3092\u4e8c\u5206\u63a2\u7d22 */\nint binarySearchRightEdge(int[] nums, int target) {\n    // \u6700\u3082\u5de6\u306e target + 1 \u3092\u898b\u3064\u3051\u308b\u3053\u3068\u306b\u5909\u63db\n    int i = binary_search_insertion.binarySearchInsertion(nums, target + 1);\n    // j \u306f\u6700\u3082\u53f3\u306e target \u3092\u6307\u3057\u3001i \u306f target \u3088\u308a\u5927\u304d\u3044\u6700\u521d\u306e\u8981\u7d20\u3092\u6307\u3059\n    int j = i - 1;\n    // target \u3092\u898b\u3064\u3051\u3089\u308c\u306a\u304b\u3063\u305f\u306e\u3067\u3001-1 \u3092\u8fd4\u3059\n    if (j == -1 || nums[j] != target) {\n        return -1;\n    }\n    // target \u3092\u898b\u3064\u3051\u305f\u306e\u3067\u3001\u30a4\u30f3\u30c7\u30c3\u30af\u30b9 j \u3092\u8fd4\u3059\n    return j;\n}\n</code></pre> binary_search_edge.cs<pre><code>[class]{binary_search_edge}-[func]{BinarySearchRightEdge}\n</code></pre> binary_search_edge.go<pre><code>[class]{}-[func]{binarySearchRightEdge}\n</code></pre> binary_search_edge.swift<pre><code>[class]{}-[func]{binarySearchRightEdge}\n</code></pre> binary_search_edge.js<pre><code>[class]{}-[func]{binarySearchRightEdge}\n</code></pre> binary_search_edge.ts<pre><code>[class]{}-[func]{binarySearchRightEdge}\n</code></pre> binary_search_edge.dart<pre><code>[class]{}-[func]{binarySearchRightEdge}\n</code></pre> binary_search_edge.rs<pre><code>[class]{}-[func]{binary_search_right_edge}\n</code></pre> binary_search_edge.c<pre><code>[class]{}-[func]{binarySearchRightEdge}\n</code></pre> binary_search_edge.kt<pre><code>[class]{}-[func]{binarySearchRightEdge}\n</code></pre> binary_search_edge.rb<pre><code>[class]{}-[func]{binary_search_right_edge}\n</code></pre> binary_search_edge.zig<pre><code>[class]{}-[func]{binarySearchRightEdge}\n</code></pre>"},{"location":"chapter_searching/binary_search_edge/#2","title":"2. \u00a0 \u8981\u7d20\u63a2\u7d22\u306b\u5909\u63db\u3059\u308b","text":"<p>\u914d\u5217\u306b<code>target</code>\u304c\u542b\u307e\u308c\u3066\u3044\u306a\u3044\u5834\u5408\u3001\\(i\\)\u3068\\(j\\)\u306f\u6700\u7d42\u7684\u306b<code>target</code>\u3088\u308a\u5927\u304d\u3044\u6700\u521d\u306e\u8981\u7d20\u3068\u5c0f\u3055\u3044\u6700\u521d\u306e\u8981\u7d20\u3092\u305d\u308c\u305e\u308c\u6307\u3057\u307e\u3059\u3002</p> <p>\u3057\u305f\u304c\u3063\u3066\u3001\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u914d\u5217\u306b\u5b58\u5728\u3057\u306a\u3044\u8981\u7d20\u3092\u69cb\u7bc9\u3057\u3066\u3001\u5de6\u3068\u53f3\u306e\u5883\u754c\u3092\u63a2\u7d22\u3067\u304d\u307e\u3059\u3002</p> <ul> <li>\u6700\u3082\u5de6\u306e<code>target</code>\u3092\u898b\u3064\u3051\u308b\u306b\u306f\uff1a<code>target - 0.5</code>\u3092\u63a2\u7d22\u3059\u308b\u3053\u3068\u306b\u5909\u63db\u3067\u304d\u3001\u30dd\u30a4\u30f3\u30bf\\(i\\)\u3092\u8fd4\u3057\u307e\u3059\u3002</li> <li>\u6700\u3082\u53f3\u306e<code>target</code>\u3092\u898b\u3064\u3051\u308b\u306b\u306f\uff1a<code>target + 0.5</code>\u3092\u63a2\u7d22\u3059\u308b\u3053\u3068\u306b\u5909\u63db\u3067\u304d\u3001\u30dd\u30a4\u30f3\u30bf\\(j\\)\u3092\u8fd4\u3057\u307e\u3059\u3002</li> </ul> <p></p> <p> \u56f3 10-8 \u00a0 Transforming the search for boundaries into the search for an element </p> <p>\u30b3\u30fc\u30c9\u306f\u3053\u3053\u3067\u306f\u7701\u7565\u3055\u308c\u3066\u3044\u307e\u3059\u304c\u3001\u3053\u306e\u30a2\u30d7\u30ed\u30fc\u30c1\u306b\u3064\u3044\u3066\u6ce8\u610f\u3059\u3079\u304d2\u3064\u306e\u91cd\u8981\u306a\u70b9\u304c\u3042\u308a\u307e\u3059\u3002</p> <ul> <li>\u4e0e\u3048\u3089\u308c\u305f\u914d\u5217<code>nums</code>\u306b\u306f\u5c0f\u6570\u304c\u542b\u307e\u308c\u3066\u3044\u306a\u3044\u305f\u3081\u3001\u7b49\u3057\u3044\u5834\u5408\u306e\u51e6\u7406\u306f\u5fc3\u914d\u3042\u308a\u307e\u305b\u3093\u3002</li> <li>\u305f\u3060\u3057\u3001\u3053\u306e\u30a2\u30d7\u30ed\u30fc\u30c1\u3067\u5c0f\u6570\u3092\u5c0e\u5165\u3059\u308b\u306b\u306f\u3001<code>target</code>\u5909\u6570\u3092\u6d6e\u52d5\u5c0f\u6570\u70b9\u578b\u306b\u5909\u66f4\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\uff08Python\u3067\u306f\u5909\u66f4\u306f\u4e0d\u8981\u3067\u3059\uff09\u3002</li> </ul>"},{"location":"chapter_searching/binary_search_insertion/","title":"10.2 \u00a0 \u4e8c\u5206\u63a2\u7d22\u306b\u3088\u308b\u633f\u5165","text":"<p>\u4e8c\u5206\u63a2\u7d22\u306f\u76ee\u6a19\u8981\u7d20\u3092\u63a2\u7d22\u3059\u308b\u3060\u3051\u3067\u306a\u304f\u3001\u76ee\u6a19\u8981\u7d20\u306e\u633f\u5165\u4f4d\u7f6e\u3092\u63a2\u7d22\u3059\u308b\u306a\u3069\u3001\u591a\u304f\u306e\u5909\u7a2e\u554f\u984c\u3092\u89e3\u6c7a\u3059\u308b\u305f\u3081\u306b\u3082\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002</p>"},{"location":"chapter_searching/binary_search_insertion/#1021","title":"10.2.1 \u00a0 \u91cd\u8907\u8981\u7d20\u304c\u306a\u3044\u5834\u5408","text":"<p>Question</p> <p>\u4e00\u610f\u306e\u8981\u7d20\u3092\u6301\u3064\u9577\u3055\\(n\\)\u306e\u30bd\u30fc\u30c8\u6e08\u307f\u914d\u5217<code>nums</code>\u3068\u8981\u7d20<code>target</code>\u304c\u4e0e\u3048\u3089\u308c\u3001\u30bd\u30fc\u30c8\u9806\u3092\u7dad\u6301\u3057\u306a\u304c\u3089<code>target</code>\u3092<code>nums</code>\u306b\u633f\u5165\u3057\u307e\u3059\u3002<code>target</code>\u304c\u914d\u5217\u306b\u3059\u3067\u306b\u5b58\u5728\u3059\u308b\u5834\u5408\u306f\u3001\u65e2\u5b58\u306e\u8981\u7d20\u306e\u5de6\u5074\u306b\u633f\u5165\u3057\u307e\u3059\u3002\u633f\u5165\u5f8c\u306e\u914d\u5217\u306b\u304a\u3051\u308b<code>target</code>\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8fd4\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u4e0b\u56f3\u306b\u793a\u3059\u4f8b\u3092\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044\u3002</p> <p></p> <p> \u56f3 10-4 \u00a0 Example data for binary search insertion point </p> <p>\u524d\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u306e\u4e8c\u5206\u63a2\u7d22\u30b3\u30fc\u30c9\u3092\u518d\u5229\u7528\u3057\u305f\u3044\u5834\u5408\u3001\u4ee5\u4e0b\u306e2\u3064\u306e\u8cea\u554f\u306b\u7b54\u3048\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002</p> <p>\u8cea\u554f1\uff1a\u914d\u5217\u306b\u3059\u3067\u306b<code>target</code>\u304c\u542b\u307e\u308c\u3066\u3044\u308b\u5834\u5408\u3001\u633f\u5165\u4f4d\u7f6e\u306f\u65e2\u5b58\u8981\u7d20\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306b\u306a\u308a\u307e\u3059\u304b\uff1f</p> <p><code>target</code>\u3092\u7b49\u3057\u3044\u8981\u7d20\u306e\u5de6\u5074\u306b\u633f\u5165\u3059\u308b\u3068\u3044\u3046\u8981\u4ef6\u306f\u3001\u65b0\u3057\u304f\u633f\u5165\u3055\u308c\u308b<code>target</code>\u304c\u5143\u306e<code>target</code>\u306e\u4f4d\u7f6e\u3092\u7f6e\u304d\u63db\u3048\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u914d\u5217\u306b<code>target</code>\u304c\u542b\u307e\u308c\u3066\u3044\u308b\u5834\u5408\u3001\u633f\u5165\u4f4d\u7f6e\u306f\u78ba\u304b\u306b\u305d\u306e<code>target</code>\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3067\u3059\u3002</p> <p>\u8cea\u554f2\uff1a\u914d\u5217\u306b<code>target</code>\u304c\u542b\u307e\u308c\u3066\u3044\u306a\u3044\u5834\u5408\u3001\u3069\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306b\u633f\u5165\u3055\u308c\u307e\u3059\u304b\uff1f</p> <p>\u4e8c\u5206\u63a2\u7d22\u30d7\u30ed\u30bb\u30b9\u3092\u3055\u3089\u306b\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\uff1a<code>nums[m] &lt; target</code>\u306e\u3068\u304d\u3001\u30dd\u30a4\u30f3\u30bf\\(i\\)\u304c\u79fb\u52d5\u3057\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u30dd\u30a4\u30f3\u30bf\\(i\\)\u304c<code>target</code>\u4ee5\u4e0a\u306e\u8981\u7d20\u306b\u8fd1\u3065\u3044\u3066\u3044\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002\u540c\u69d8\u306b\u3001\u30dd\u30a4\u30f3\u30bf\\(j\\)\u306f\u5e38\u306b<code>target</code>\u4ee5\u4e0b\u306e\u8981\u7d20\u306b\u8fd1\u3065\u3044\u3066\u3044\u307e\u3059\u3002</p> <p>\u3057\u305f\u304c\u3063\u3066\u3001\u4e8c\u5206\u306e\u7d42\u4e86\u6642\u306b\u306f\u78ba\u5b9f\u306b\uff1a\\(i\\)\u306f<code>target</code>\u3088\u308a\u5927\u304d\u3044\u6700\u521d\u306e\u8981\u7d20\u3092\u6307\u3057\u3001\\(j\\)\u306f<code>target</code>\u3088\u308a\u5c0f\u3055\u3044\u6700\u521d\u306e\u8981\u7d20\u3092\u6307\u3057\u307e\u3059\u3002\u914d\u5217\u306b<code>target</code>\u304c\u542b\u307e\u308c\u3066\u3044\u306a\u3044\u5834\u5408\u3001\u633f\u5165\u4f4d\u7f6e\u306f\\(i\\)\u3067\u3042\u308b\u3053\u3068\u306f\u660e\u3089\u304b\u3067\u3059\u3002\u30b3\u30fc\u30c9\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig binary_search_insertion.py<pre><code>def binary_search_insertion_simple(nums: list[int], target: int) -&gt; int:\n    \"\"\"\u633f\u5165\u4f4d\u7f6e\u306e\u4e8c\u5206\u63a2\u7d22\uff08\u91cd\u8907\u8981\u7d20\u306a\u3057\uff09\"\"\"\n    i, j = 0, len(nums) - 1  # \u4e21\u7aef\u9589\u533a\u9593 [0, n-1] \u3092\u521d\u671f\u5316\n    while i &lt;= j:\n        m = i + (j - i) // 2  # \u4e2d\u70b9\u30a4\u30f3\u30c7\u30c3\u30af\u30b9 m \u3092\u8a08\u7b97\n        if nums[m] &lt; target:\n            i = m + 1  # \u30bf\u30fc\u30b2\u30c3\u30c8\u306f\u533a\u9593 [m+1, j] \u306b\u3042\u308b\n        elif nums[m] &gt; target:\n            j = m - 1  # \u30bf\u30fc\u30b2\u30c3\u30c8\u306f\u533a\u9593 [i, m-1] \u306b\u3042\u308b\n        else:\n            return m  # \u30bf\u30fc\u30b2\u30c3\u30c8\u304c\u898b\u3064\u304b\u3063\u305f\u5834\u5408\u3001\u633f\u5165\u4f4d\u7f6e m \u3092\u8fd4\u3059\n    # \u30bf\u30fc\u30b2\u30c3\u30c8\u304c\u898b\u3064\u304b\u3089\u306a\u304b\u3063\u305f\u5834\u5408\u3001\u633f\u5165\u4f4d\u7f6e i \u3092\u8fd4\u3059\n    return i\n</code></pre> binary_search_insertion.cpp<pre><code>/* \u633f\u5165\u30dd\u30a4\u30f3\u30c8\u306e\u4e8c\u5206\u63a2\u7d22\uff08\u91cd\u8907\u8981\u7d20\u306a\u3057\uff09 */\nint binarySearchInsertionSimple(vector&lt;int&gt; &amp;nums, int target) {\n    int i = 0, j = nums.size() - 1; // \u4e21\u7aef\u9589\u533a\u9593[0, n-1]\u3092\u521d\u671f\u5316\n    while (i &lt;= j) {\n        int m = i + (j - i) / 2; // \u4e2d\u70b9\u30a4\u30f3\u30c7\u30c3\u30af\u30b9m\u3092\u8a08\u7b97\n        if (nums[m] &lt; target) {\n            i = m + 1; // \u30bf\u30fc\u30b2\u30c3\u30c8\u306f\u533a\u9593[m+1, j]\u306b\u3042\u308b\n        } else if (nums[m] &gt; target) {\n            j = m - 1; // \u30bf\u30fc\u30b2\u30c3\u30c8\u306f\u533a\u9593[i, m-1]\u306b\u3042\u308b\n        } else {\n            return m; // \u30bf\u30fc\u30b2\u30c3\u30c8\u304c\u898b\u3064\u304b\u3063\u305f\u305f\u3081\u3001\u633f\u5165\u30dd\u30a4\u30f3\u30c8m\u3092\u8fd4\u3059\n        }\n    }\n    // \u30bf\u30fc\u30b2\u30c3\u30c8\u304c\u898b\u3064\u304b\u3089\u306a\u304b\u3063\u305f\u305f\u3081\u3001\u633f\u5165\u30dd\u30a4\u30f3\u30c8i\u3092\u8fd4\u3059\n    return i;\n}\n</code></pre> binary_search_insertion.java<pre><code>/* \u633f\u5165\u70b9\u306e\u4e8c\u5206\u63a2\u7d22\uff08\u91cd\u8907\u8981\u7d20\u306a\u3057\uff09 */\nint binarySearchInsertionSimple(int[] nums, int target) {\n    int i = 0, j = nums.length - 1; // \u4e21\u7aef\u9589\u533a\u9593 [0, n-1] \u3092\u521d\u671f\u5316\n    while (i &lt;= j) {\n        int m = i + (j - i) / 2; // \u4e2d\u70b9\u30a4\u30f3\u30c7\u30c3\u30af\u30b9 m \u3092\u8a08\u7b97\n        if (nums[m] &lt; target) {\n            i = m + 1; // target \u306f\u533a\u9593 [m+1, j] \u306b\u3042\u308b\n        } else if (nums[m] &gt; target) {\n            j = m - 1; // target \u306f\u533a\u9593 [i, m-1] \u306b\u3042\u308b\n        } else {\n            return m; // target \u3092\u898b\u3064\u3051\u305f\u306e\u3067\u3001\u633f\u5165\u70b9 m \u3092\u8fd4\u3059\n        }\n    }\n    // target \u3092\u898b\u3064\u3051\u3089\u308c\u306a\u304b\u3063\u305f\u306e\u3067\u3001\u633f\u5165\u70b9 i \u3092\u8fd4\u3059\n    return i;\n}\n</code></pre> binary_search_insertion.cs<pre><code>[class]{binary_search_insertion}-[func]{BinarySearchInsertionSimple}\n</code></pre> binary_search_insertion.go<pre><code>[class]{}-[func]{binarySearchInsertionSimple}\n</code></pre> binary_search_insertion.swift<pre><code>[class]{}-[func]{binarySearchInsertionSimple}\n</code></pre> binary_search_insertion.js<pre><code>[class]{}-[func]{binarySearchInsertionSimple}\n</code></pre> binary_search_insertion.ts<pre><code>[class]{}-[func]{binarySearchInsertionSimple}\n</code></pre> binary_search_insertion.dart<pre><code>[class]{}-[func]{binarySearchInsertionSimple}\n</code></pre> binary_search_insertion.rs<pre><code>[class]{}-[func]{binary_search_insertion_simple}\n</code></pre> binary_search_insertion.c<pre><code>[class]{}-[func]{binarySearchInsertionSimple}\n</code></pre> binary_search_insertion.kt<pre><code>[class]{}-[func]{binarySearchInsertionSimple}\n</code></pre> binary_search_insertion.rb<pre><code>[class]{}-[func]{binary_search_insertion_simple}\n</code></pre> binary_search_insertion.zig<pre><code>[class]{}-[func]{binarySearchInsertionSimple}\n</code></pre>"},{"location":"chapter_searching/binary_search_insertion/#1022","title":"10.2.2 \u00a0 \u91cd\u8907\u8981\u7d20\u304c\u3042\u308b\u5834\u5408","text":"<p>Question</p> <p>\u524d\u306e\u8cea\u554f\u306b\u57fa\u3065\u3044\u3066\u3001\u914d\u5217\u306b\u91cd\u8907\u8981\u7d20\u304c\u542b\u307e\u308c\u3066\u3044\u308b\u53ef\u80fd\u6027\u304c\u3042\u308b\u3068\u4eee\u5b9a\u3057\u3001\u4ed6\u306f\u3059\u3079\u3066\u540c\u3058\u3068\u3057\u307e\u3059\u3002</p> <p>\u914d\u5217\u306b<code>target</code>\u306e\u8907\u6570\u306e\u51fa\u73fe\u304c\u3042\u308b\u5834\u5408\u3001\u901a\u5e38\u306e\u4e8c\u5206\u63a2\u7d22\u306f<code>target</code>\u306e1\u3064\u306e\u51fa\u73fe\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306e\u307f\u3092\u8fd4\u3059\u3053\u3068\u304c\u3067\u304d\u3001\u305d\u306e\u4f4d\u7f6e\u306e\u5de6\u53f3\u306b<code>target</code>\u306e\u51fa\u73fe\u304c\u3044\u304f\u3064\u3042\u308b\u304b\u3092\u7279\u5b9a\u3059\u308b\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093\u3002</p> <p>\u554f\u984c\u3067\u306f\u76ee\u6a19\u8981\u7d20\u3092\u6700\u3082\u5de6\u306e\u4f4d\u7f6e\u306b\u633f\u5165\u3059\u308b\u3053\u3068\u304c\u8981\u6c42\u3055\u308c\u3066\u3044\u308b\u305f\u3081\u3001\u914d\u5217\u5185\u306e\u6700\u3082\u5de6\u306e<code>target</code>\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u898b\u3064\u3051\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u6700\u521d\u306b\u4e0b\u56f3\u306b\u793a\u3059\u30b9\u30c6\u30c3\u30d7\u3092\u901a\u3057\u3066\u3053\u308c\u3092\u5b9f\u88c5\u3059\u308b\u3053\u3068\u3092\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\u3002</p> <ol> <li>\u4e8c\u5206\u63a2\u7d22\u3092\u5b9f\u884c\u3057\u3066<code>target</code>\u306e\u4efb\u610f\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3001\u4f8b\u3048\u3070\\(k\\)\u3092\u898b\u3064\u3051\u307e\u3059\u3002</li> <li>\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\\(k\\)\u304b\u3089\u958b\u59cb\u3057\u3066\u3001\u6700\u3082\u5de6\u306e<code>target</code>\u306e\u51fa\u73fe\u304c\u898b\u3064\u304b\u308b\u307e\u3067\u5de6\u306b\u7dda\u5f62\u63a2\u7d22\u3092\u884c\u3044\u3001\u3053\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8fd4\u3057\u307e\u3059\u3002</li> </ol> <p></p> <p> \u56f3 10-5 \u00a0 Linear search for the insertion point of duplicate elements </p> <p>\u3053\u306e\u65b9\u6cd5\u306f\u5b9f\u73fe\u53ef\u80fd\u3067\u3059\u304c\u3001\u7dda\u5f62\u63a2\u7d22\u3092\u542b\u3080\u305f\u3081\u3001\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O(n)\\)\u3067\u3059\u3002\u3053\u306e\u65b9\u6cd5\u306f\u3001\u914d\u5217\u306b\u591a\u304f\u306e\u91cd\u8907\u3059\u308b<code>target</code>\u304c\u542b\u307e\u308c\u3066\u3044\u308b\u5834\u5408\u306b\u975e\u52b9\u7387\u3067\u3059\u3002</p> <p>\u4eca\u5ea6\u306f\u4e8c\u5206\u63a2\u7d22\u30b3\u30fc\u30c9\u3092\u62e1\u5f35\u3059\u308b\u3053\u3068\u3092\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u5168\u4f53\u7684\u306a\u30d7\u30ed\u30bb\u30b9\u306f\u540c\u3058\u307e\u307e\u3067\u3059\u3002\u5404\u30e9\u30a6\u30f3\u30c9\u3067\u3001\u307e\u305a\u4e2d\u9593\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\\(m\\)\u3092\u8a08\u7b97\u3057\u3001\u6b21\u306b<code>target</code>\u3068<code>nums[m]</code>\u306e\u5024\u3092\u6bd4\u8f03\u3057\u3066\u3001\u4ee5\u4e0b\u306e\u30b1\u30fc\u30b9\u306b\u306a\u308a\u307e\u3059\u3002</p> <ul> <li><code>nums[m] &lt; target</code>\u307e\u305f\u306f<code>nums[m] &gt; target</code>\u306e\u3068\u304d\u3001\u3053\u308c\u306f<code>target</code>\u304c\u307e\u3060\u898b\u3064\u304b\u3063\u3066\u3044\u306a\u3044\u3053\u3068\u3092\u610f\u5473\u3059\u308b\u305f\u3081\u3001\u901a\u5e38\u306e\u4e8c\u5206\u63a2\u7d22\u3092\u4f7f\u7528\u3057\u3066\u63a2\u7d22\u7bc4\u56f2\u3092\u72ed\u3081\u3001\u30dd\u30a4\u30f3\u30bf\\(i\\)\u3068\\(j\\)\u3092<code>target</code>\u306b\u8fd1\u3065\u3051\u307e\u3059\u3002</li> <li><code>nums[m] == target</code>\u306e\u3068\u304d\u3001\u3053\u308c\u306f<code>target</code>\u3088\u308a\u5c0f\u3055\u3044\u8981\u7d20\u304c\u7bc4\u56f2\\([i, m - 1]\\)\u306b\u3042\u308b\u3053\u3068\u3092\u793a\u3059\u305f\u3081\u3001\\(j = m - 1\\)\u3092\u4f7f\u7528\u3057\u3066\u7bc4\u56f2\u3092\u72ed\u3081\u3001\u30dd\u30a4\u30f3\u30bf\\(j\\)\u3092<code>target</code>\u3088\u308a\u5c0f\u3055\u3044\u8981\u7d20\u306b\u8fd1\u3065\u3051\u307e\u3059\u3002</li> </ul> <p>\u30eb\u30fc\u30d7\u5f8c\u3001\\(i\\)\u306f\u6700\u3082\u5de6\u306e<code>target</code>\u3092\u6307\u3057\u3001\\(j\\)\u306f<code>target</code>\u3088\u308a\u5c0f\u3055\u3044\u6700\u521d\u306e\u8981\u7d20\u3092\u6307\u3059\u305f\u3081\u3001\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\\(i\\)\u304c\u633f\u5165\u4f4d\u7f6e\u3067\u3059\u3002</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> \u56f3 10-6 \u00a0 Steps for binary search insertion point of duplicate elements </p> <p>\u4ee5\u4e0b\u306e\u30b3\u30fc\u30c9\u3092\u89b3\u5bdf\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u5206\u5c90<code>nums[m] &gt; target</code>\u3068<code>nums[m] == target</code>\u306e\u64cd\u4f5c\u306f\u540c\u3058\u3067\u3042\u308b\u305f\u3081\u3001\u3053\u308c\u30892\u3064\u306e\u5206\u5c90\u3092\u30de\u30fc\u30b8\u3067\u304d\u307e\u3059\u3002</p> <p>\u305d\u308c\u3067\u3082\u3001\u30ed\u30b8\u30c3\u30af\u304c\u3088\u308a\u660e\u78ba\u306b\u306a\u308a\u3001\u53ef\u8aad\u6027\u304c\u5411\u4e0a\u3059\u308b\u305f\u3081\u3001\u6761\u4ef6\u3092\u5c55\u958b\u3057\u305f\u307e\u307e\u306b\u3057\u3066\u304a\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig binary_search_insertion.py<pre><code>def binary_search_insertion(nums: list[int], target: int) -&gt; int:\n    \"\"\"\u633f\u5165\u4f4d\u7f6e\u306e\u4e8c\u5206\u63a2\u7d22\uff08\u91cd\u8907\u8981\u7d20\u3042\u308a\uff09\"\"\"\n    i, j = 0, len(nums) - 1  # \u4e21\u7aef\u9589\u533a\u9593 [0, n-1] \u3092\u521d\u671f\u5316\n    while i &lt;= j:\n        m = i + (j - i) // 2  # \u4e2d\u70b9\u30a4\u30f3\u30c7\u30c3\u30af\u30b9 m \u3092\u8a08\u7b97\n        if nums[m] &lt; target:\n            i = m + 1  # \u30bf\u30fc\u30b2\u30c3\u30c8\u306f\u533a\u9593 [m+1, j] \u306b\u3042\u308b\n        elif nums[m] &gt; target:\n            j = m - 1  # \u30bf\u30fc\u30b2\u30c3\u30c8\u306f\u533a\u9593 [i, m-1] \u306b\u3042\u308b\n        else:\n            j = m - 1  # \u30bf\u30fc\u30b2\u30c3\u30c8\u672a\u6e80\u306e\u6700\u521d\u306e\u8981\u7d20\u306f\u533a\u9593 [i, m-1] \u306b\u3042\u308b\n    # \u633f\u5165\u4f4d\u7f6e i \u3092\u8fd4\u3059\n    return i\n</code></pre> binary_search_insertion.cpp<pre><code>/* \u633f\u5165\u30dd\u30a4\u30f3\u30c8\u306e\u4e8c\u5206\u63a2\u7d22\uff08\u91cd\u8907\u8981\u7d20\u3042\u308a\uff09 */\nint binarySearchInsertion(vector&lt;int&gt; &amp;nums, int target) {\n    int i = 0, j = nums.size() - 1; // \u4e21\u7aef\u9589\u533a\u9593[0, n-1]\u3092\u521d\u671f\u5316\n    while (i &lt;= j) {\n        int m = i + (j - i) / 2; // \u4e2d\u70b9\u30a4\u30f3\u30c7\u30c3\u30af\u30b9m\u3092\u8a08\u7b97\n        if (nums[m] &lt; target) {\n            i = m + 1; // \u30bf\u30fc\u30b2\u30c3\u30c8\u306f\u533a\u9593[m+1, j]\u306b\u3042\u308b\n        } else if (nums[m] &gt; target) {\n            j = m - 1; // \u30bf\u30fc\u30b2\u30c3\u30c8\u306f\u533a\u9593[i, m-1]\u306b\u3042\u308b\n        } else {\n            j = m - 1; // \u30bf\u30fc\u30b2\u30c3\u30c8\u672a\u6e80\u306e\u6700\u521d\u306e\u8981\u7d20\u306f\u533a\u9593[i, m-1]\u306b\u3042\u308b\n        }\n    }\n    // \u633f\u5165\u30dd\u30a4\u30f3\u30c8i\u3092\u8fd4\u3059\n    return i;\n}\n</code></pre> binary_search_insertion.java<pre><code>/* \u633f\u5165\u70b9\u306e\u4e8c\u5206\u63a2\u7d22\uff08\u91cd\u8907\u8981\u7d20\u3042\u308a\uff09 */\nint binarySearchInsertion(int[] nums, int target) {\n    int i = 0, j = nums.length - 1; // \u4e21\u7aef\u9589\u533a\u9593 [0, n-1] \u3092\u521d\u671f\u5316\n    while (i &lt;= j) {\n        int m = i + (j - i) / 2; // \u4e2d\u70b9\u30a4\u30f3\u30c7\u30c3\u30af\u30b9 m \u3092\u8a08\u7b97\n        if (nums[m] &lt; target) {\n            i = m + 1; // target \u306f\u533a\u9593 [m+1, j] \u306b\u3042\u308b\n        } else if (nums[m] &gt; target) {\n            j = m - 1; // target \u306f\u533a\u9593 [i, m-1] \u306b\u3042\u308b\n        } else {\n            j = m - 1; // target \u3088\u308a\u5c0f\u3055\u3044\u6700\u521d\u306e\u8981\u7d20\u306f\u533a\u9593 [i, m-1] \u306b\u3042\u308b\n        }\n    }\n    // \u633f\u5165\u70b9 i \u3092\u8fd4\u3059\n    return i;\n}\n</code></pre> binary_search_insertion.cs<pre><code>[class]{binary_search_insertion}-[func]{BinarySearchInsertion}\n</code></pre> binary_search_insertion.go<pre><code>[class]{}-[func]{binarySearchInsertion}\n</code></pre> binary_search_insertion.swift<pre><code>[class]{}-[func]{binarySearchInsertion}\n</code></pre> binary_search_insertion.js<pre><code>[class]{}-[func]{binarySearchInsertion}\n</code></pre> binary_search_insertion.ts<pre><code>[class]{}-[func]{binarySearchInsertion}\n</code></pre> binary_search_insertion.dart<pre><code>[class]{}-[func]{binarySearchInsertion}\n</code></pre> binary_search_insertion.rs<pre><code>[class]{}-[func]{binary_search_insertion}\n</code></pre> binary_search_insertion.c<pre><code>[class]{}-[func]{binarySearchInsertion}\n</code></pre> binary_search_insertion.kt<pre><code>[class]{}-[func]{binarySearchInsertion}\n</code></pre> binary_search_insertion.rb<pre><code>[class]{}-[func]{binary_search_insertion}\n</code></pre> binary_search_insertion.zig<pre><code>[class]{}-[func]{binarySearchInsertion}\n</code></pre> <p>Tip</p> <p>\u3053\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u306e\u30b3\u30fc\u30c9\u306f\u300c\u9589\u533a\u9593\u300d\u3092\u4f7f\u7528\u3057\u3066\u3044\u307e\u3059\u3002\u300c\u5de6\u9589\u53f3\u958b\u300d\u306b\u8208\u5473\u304c\u3042\u308b\u5834\u5408\u306f\u3001\u81ea\u5206\u3067\u30b3\u30fc\u30c9\u3092\u5b9f\u88c5\u3057\u3066\u307f\u3066\u304f\u3060\u3055\u3044\u3002</p> <p>\u8981\u7d04\u3059\u308b\u3068\u3001\u4e8c\u5206\u63a2\u7d22\u306f\u672c\u8cea\u7684\u306b\u30dd\u30a4\u30f3\u30bf\\(i\\)\u3068\\(j\\)\u306e\u63a2\u7d22\u76ee\u6a19\u3092\u8a2d\u5b9a\u3059\u308b\u3053\u3068\u3067\u3059\u3002\u3053\u308c\u3089\u306e\u76ee\u6a19\u306f\u7279\u5b9a\u306e\u8981\u7d20\uff08<code>target</code>\u306a\u3069\uff09\u307e\u305f\u306f\u8981\u7d20\u306e\u7bc4\u56f2\uff08<code>target</code>\u3088\u308a\u5c0f\u3055\u3044\u3082\u306e\u306a\u3069\uff09\u3067\u3042\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002</p> <p>\u4e8c\u5206\u63a2\u7d22\u306e\u9023\u7d9a\u30eb\u30fc\u30d7\u306b\u304a\u3044\u3066\u3001\u30dd\u30a4\u30f3\u30bf\\(i\\)\u3068\\(j\\)\u306f\u6bb5\u968e\u7684\u306b\u4e8b\u524d\u5b9a\u7fa9\u3055\u308c\u305f\u76ee\u6a19\u306b\u8fd1\u3065\u304d\u307e\u3059\u3002\u6700\u7d42\u7684\u306b\u3001\u305d\u308c\u3089\u306f\u7b54\u3048\u3092\u898b\u3064\u3051\u308b\u304b\u3001\u5883\u754c\u3092\u8d8a\u3048\u305f\u5f8c\u306b\u505c\u6b62\u3057\u307e\u3059\u3002</p>"},{"location":"chapter_searching/replace_linear_by_hashing/","title":"10.4 \u00a0 \u30cf\u30c3\u30b7\u30e5\u6700\u9069\u5316\u6226\u7565","text":"<p>\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u554f\u984c\u306b\u304a\u3044\u3066\u3001\u7dda\u5f62\u63a2\u7d22\u3092\u30cf\u30c3\u30b7\u30e5\u30d9\u30fc\u30b9\u306e\u63a2\u7d22\u306b\u7f6e\u304d\u63db\u3048\u308b\u3053\u3068\u3067\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u6642\u9593\u8a08\u7b97\u91cf\u3092\u524a\u6e1b\u3059\u308b\u3053\u3068\u304c\u3088\u304f\u3042\u308a\u307e\u3059\u3002\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u554f\u984c\u3092\u4f7f\u7528\u3057\u3066\u7406\u89e3\u3092\u6df1\u3081\u307e\u3057\u3087\u3046\u3002</p> <p>Question</p> <p>\u6574\u6570\u914d\u5217<code>nums</code>\u3068\u76ee\u6a19\u8981\u7d20<code>target</code>\u304c\u4e0e\u3048\u3089\u308c\u3001\u914d\u5217\u5185\u3067\u300c\u548c\u300d\u304c<code>target</code>\u306b\u7b49\u3057\u30442\u3064\u306e\u8981\u7d20\u3092\u63a2\u7d22\u3057\u3001\u305d\u308c\u3089\u306e\u914d\u5217\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8fd4\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u4efb\u610f\u306e\u89e3\u304c\u53d7\u3051\u5165\u308c\u3089\u308c\u307e\u3059\u3002</p>"},{"location":"chapter_searching/replace_linear_by_hashing/#1041","title":"10.4.1 \u00a0 \u7dda\u5f62\u63a2\u7d22\uff1a\u6642\u9593\u3092\u7a7a\u9593\u3068\u4ea4\u63db","text":"<p>\u3059\u3079\u3066\u306e\u53ef\u80fd\u306a\u7d44\u307f\u5408\u308f\u305b\u3092\u76f4\u63a5\u6a2a\u65ad\u3059\u308b\u3053\u3068\u3092\u8003\u3048\u3066\u307f\u307e\u3059\u3002\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u30cd\u30b9\u30c8\u3057\u305f\u30eb\u30fc\u30d7\u3092\u958b\u59cb\u3057\u3001\u5404\u53cd\u5fa9\u30672\u3064\u306e\u6574\u6570\u306e\u548c\u304c<code>target</code>\u306b\u7b49\u3057\u3044\u304b\u3069\u3046\u304b\u3092\u5224\u65ad\u3057\u307e\u3059\u3002\u305d\u3046\u3067\u3042\u308c\u3070\u3001\u305d\u308c\u3089\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8fd4\u3057\u307e\u3059\u3002</p> <p></p> <p> \u56f3 10-9 \u00a0 Linear search solution for two-sum problem </p> <p>\u30b3\u30fc\u30c9\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig two_sum.py<pre><code>def two_sum_brute_force(nums: list[int], target: int) -&gt; list[int]:\n    \"\"\"\u65b9\u6cd5\u4e00\uff1a\u30d6\u30eb\u30fc\u30c8\u30d5\u30a9\u30fc\u30b9\u5217\u6319\"\"\"\n    # \u4e8c\u91cd\u30eb\u30fc\u30d7\u3001\u6642\u9593\u8a08\u7b97\u91cf\u306f O(n^2)\n    for i in range(len(nums) - 1):\n        for j in range(i + 1, len(nums)):\n            if nums[i] + nums[j] == target:\n                return [i, j]\n    return []\n</code></pre> two_sum.cpp<pre><code>/* \u65b9\u6cd5\u4e00\uff1a\u30d6\u30eb\u30fc\u30c8\u30d5\u30a9\u30fc\u30b9\u5217\u6319 */\nvector&lt;int&gt; twoSumBruteForce(vector&lt;int&gt; &amp;nums, int target) {\n    int size = nums.size();\n    // \u4e8c\u91cd\u30eb\u30fc\u30d7\u3001\u6642\u9593\u8a08\u7b97\u91cf\u306fO(n^2)\n    for (int i = 0; i &lt; size - 1; i++) {\n        for (int j = i + 1; j &lt; size; j++) {\n            if (nums[i] + nums[j] == target)\n                return {i, j};\n        }\n    }\n    return {};\n}\n</code></pre> two_sum.java<pre><code>/* \u65b9\u6cd5\u4e00: \u66b4\u529b\u5217\u6319 */\nint[] twoSumBruteForce(int[] nums, int target) {\n    int size = nums.length;\n    // \u4e8c\u91cd\u30eb\u30fc\u30d7\u3001\u6642\u9593\u8a08\u7b97\u91cf\u306f O(n^2)\n    for (int i = 0; i &lt; size - 1; i++) {\n        for (int j = i + 1; j &lt; size; j++) {\n            if (nums[i] + nums[j] == target)\n                return new int[] { i, j };\n        }\n    }\n    return new int[0];\n}\n</code></pre> two_sum.cs<pre><code>[class]{two_sum}-[func]{TwoSumBruteForce}\n</code></pre> two_sum.go<pre><code>[class]{}-[func]{twoSumBruteForce}\n</code></pre> two_sum.swift<pre><code>[class]{}-[func]{twoSumBruteForce}\n</code></pre> two_sum.js<pre><code>[class]{}-[func]{twoSumBruteForce}\n</code></pre> two_sum.ts<pre><code>[class]{}-[func]{twoSumBruteForce}\n</code></pre> two_sum.dart<pre><code>[class]{}-[func]{twoSumBruteForce}\n</code></pre> two_sum.rs<pre><code>[class]{}-[func]{two_sum_brute_force}\n</code></pre> two_sum.c<pre><code>[class]{}-[func]{twoSumBruteForce}\n</code></pre> two_sum.kt<pre><code>[class]{}-[func]{twoSumBruteForce}\n</code></pre> two_sum.rb<pre><code>[class]{}-[func]{two_sum_brute_force}\n</code></pre> two_sum.zig<pre><code>[class]{}-[func]{twoSumBruteForce}\n</code></pre> <p>\u3053\u306e\u65b9\u6cd5\u306e\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O(n^2)\\)\u3001\u7a7a\u9593\u8a08\u7b97\u91cf\u306f\\(O(1)\\)\u3067\u3001\u5927\u5bb9\u91cf\u30c7\u30fc\u30bf\u3067\u306f\u975e\u5e38\u306b\u6642\u9593\u304c\u304b\u304b\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002</p>"},{"location":"chapter_searching/replace_linear_by_hashing/#1042","title":"10.4.2 \u00a0 \u30cf\u30c3\u30b7\u30e5\u63a2\u7d22\uff1a\u7a7a\u9593\u3092\u6642\u9593\u3068\u4ea4\u63db","text":"<p>\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u306e\u4f7f\u7528\u3092\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u30ad\u30fc\u3068\u5024\u306e\u30da\u30a2\u306f\u305d\u308c\u305e\u308c\u914d\u5217\u8981\u7d20\u3068\u305d\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3067\u3059\u3002\u914d\u5217\u3092\u30eb\u30fc\u30d7\u3057\u3001\u5404\u53cd\u5fa9\u4e2d\u306b\u4e0b\u56f3\u306b\u793a\u3059\u30b9\u30c6\u30c3\u30d7\u3092\u5b9f\u884c\u3057\u307e\u3059\u3002</p> <ol> <li>\u6570\u5024<code>target - nums[i]</code>\u304c\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u306b\u3042\u308b\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\u3057\u307e\u3059\u3002\u3042\u308b\u5834\u5408\u306f\u3001\u3053\u308c\u30892\u3064\u306e\u8981\u7d20\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u76f4\u63a5\u8fd4\u3057\u307e\u3059\u3002</li> <li>\u30ad\u30fc\u3068\u5024\u306e\u30da\u30a2<code>nums[i]</code>\u3068\u30a4\u30f3\u30c7\u30c3\u30af\u30b9<code>i</code>\u3092\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u306b\u8ffd\u52a0\u3057\u307e\u3059\u3002</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt; <p></p> <p></p> <p></p> <p> \u56f3 10-10 \u00a0 Help hash table solve two-sum </p> <p>\u5b9f\u88c5\u30b3\u30fc\u30c9\u306f\u4ee5\u4e0b\u306b\u793a\u3055\u308c\u3001\u5358\u4e00\u306e\u30eb\u30fc\u30d7\u306e\u307f\u304c\u5fc5\u8981\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig two_sum.py<pre><code>def two_sum_hash_table(nums: list[int], target: int) -&gt; list[int]:\n    \"\"\"\u65b9\u6cd5\u4e8c\uff1a\u88dc\u52a9\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\"\"\"\n    # \u88dc\u52a9\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u3001\u7a7a\u9593\u8a08\u7b97\u91cf\u306f O(n)\n    dic = {}\n    # \u5358\u4e00\u30eb\u30fc\u30d7\u3001\u6642\u9593\u8a08\u7b97\u91cf\u306f O(n)\n    for i in range(len(nums)):\n        if target - nums[i] in dic:\n            return [dic[target - nums[i]], i]\n        dic[nums[i]] = i\n    return []\n</code></pre> two_sum.cpp<pre><code>/* \u65b9\u6cd5\u4e8c\uff1a\u88dc\u52a9\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb */\nvector&lt;int&gt; twoSumHashTable(vector&lt;int&gt; &amp;nums, int target) {\n    int size = nums.size();\n    // \u88dc\u52a9\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u3001\u7a7a\u9593\u8a08\u7b97\u91cf\u306fO(n)\n    unordered_map&lt;int, int&gt; dic;\n    // \u5358\u5c64\u30eb\u30fc\u30d7\u3001\u6642\u9593\u8a08\u7b97\u91cf\u306fO(n)\n    for (int i = 0; i &lt; size; i++) {\n        if (dic.find(target - nums[i]) != dic.end()) {\n            return {dic[target - nums[i]], i};\n        }\n        dic.emplace(nums[i], i);\n    }\n    return {};\n}\n</code></pre> two_sum.java<pre><code>/* \u65b9\u6cd5\u4e8c: \u88dc\u52a9\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb */\nint[] twoSumHashTable(int[] nums, int target) {\n    int size = nums.length;\n    // \u88dc\u52a9\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u3001\u7a7a\u9593\u8a08\u7b97\u91cf\u306f O(n)\n    Map&lt;Integer, Integer&gt; dic = new HashMap&lt;&gt;();\n    // \u5358\u4e00\u5c64\u30eb\u30fc\u30d7\u3001\u6642\u9593\u8a08\u7b97\u91cf\u306f O(n)\n    for (int i = 0; i &lt; size; i++) {\n        if (dic.containsKey(target - nums[i])) {\n            return new int[] { dic.get(target - nums[i]), i };\n        }\n        dic.put(nums[i], i);\n    }\n    return new int[0];\n}\n</code></pre> two_sum.cs<pre><code>[class]{two_sum}-[func]{TwoSumHashTable}\n</code></pre> two_sum.go<pre><code>[class]{}-[func]{twoSumHashTable}\n</code></pre> two_sum.swift<pre><code>[class]{}-[func]{twoSumHashTable}\n</code></pre> two_sum.js<pre><code>[class]{}-[func]{twoSumHashTable}\n</code></pre> two_sum.ts<pre><code>[class]{}-[func]{twoSumHashTable}\n</code></pre> two_sum.dart<pre><code>[class]{}-[func]{twoSumHashTable}\n</code></pre> two_sum.rs<pre><code>[class]{}-[func]{two_sum_hash_table}\n</code></pre> two_sum.c<pre><code>[class]{HashTable}-[func]{}\n\n[class]{}-[func]{twoSumHashTable}\n</code></pre> two_sum.kt<pre><code>[class]{}-[func]{twoSumHashTable}\n</code></pre> two_sum.rb<pre><code>[class]{}-[func]{two_sum_hash_table}\n</code></pre> two_sum.zig<pre><code>[class]{}-[func]{twoSumHashTable}\n</code></pre> <p>\u3053\u306e\u65b9\u6cd5\u306f\u3001\u30cf\u30c3\u30b7\u30e5\u63a2\u7d22\u3092\u4f7f\u7528\u3059\u308b\u3053\u3068\u3067\u6642\u9593\u8a08\u7b97\u91cf\u3092\\(O(n^2)\\)\u304b\u3089\\(O(n)\\)\u306b\u524a\u6e1b\u3057\u3001\u5b9f\u884c\u6642\u52b9\u7387\u3092\u5927\u5e45\u306b\u5411\u4e0a\u3055\u305b\u307e\u3059\u3002</p> <p>\u8ffd\u52a0\u306e\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u3092\u7dad\u6301\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u305f\u3081\u3001\u7a7a\u9593\u8a08\u7b97\u91cf\u306f\\(O(n)\\)\u3067\u3059\u3002\u305d\u308c\u306b\u3082\u304b\u304b\u308f\u3089\u305a\u3001\u3053\u306e\u65b9\u6cd5\u306f\u5168\u4f53\u7684\u306b\u3088\u308a\u5747\u8861\u306e\u3068\u308c\u305f\u6642\u7a7a\u9593\u52b9\u7387\u3092\u6301\u3061\u3001\u3053\u306e\u554f\u984c\u306e\u6700\u9069\u89e3\u3068\u306a\u308a\u307e\u3059\u3002</p>"},{"location":"chapter_searching/searching_algorithm_revisited/","title":"10.5 \u00a0 \u63a2\u7d22\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u518d\u691c\u8a0e","text":"<p>\u63a2\u7d22\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\uff08\u691c\u7d22\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\uff09\u306f\u3001\u914d\u5217\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u3001\u6728\u3001\u30b0\u30e9\u30d5\u306a\u3069\u306e\u30c7\u30fc\u30bf\u69cb\u9020\u5185\u3067\u7279\u5b9a\u306e\u57fa\u6e96\u3092\u6e80\u305f\u30591\u3064\u4ee5\u4e0a\u306e\u8981\u7d20\u3092\u53d6\u5f97\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002</p> <p>\u63a2\u7d22\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u3001\u305d\u306e\u30a2\u30d7\u30ed\u30fc\u30c1\u306b\u57fa\u3065\u3044\u3066\u4ee5\u4e0b\u306e2\u3064\u306e\u30ab\u30c6\u30b4\u30ea\u306b\u5206\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002</p> <ul> <li>\u30c7\u30fc\u30bf\u69cb\u9020\u3092\u6a2a\u65ad\u3059\u308b\u3053\u3068\u3067\u76ee\u6a19\u8981\u7d20\u3092\u7279\u5b9a\u3059\u308b\uff1a\u914d\u5217\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u3001\u6728\u3001\u30b0\u30e9\u30d5\u306e\u6a2a\u65ad\u306a\u3069\u3002</li> <li>\u30c7\u30fc\u30bf\u306e\u7d44\u7e54\u69cb\u9020\u3084\u65e2\u5b58\u306e\u30c7\u30fc\u30bf\u3092\u4f7f\u7528\u3057\u3066\u52b9\u7387\u7684\u306a\u8981\u7d20\u63a2\u7d22\u3092\u5b9f\u73fe\u3059\u308b\uff1a\u4e8c\u5206\u63a2\u7d22\u3001\u30cf\u30c3\u30b7\u30e5\u63a2\u7d22\u3001\u4e8c\u5206\u63a2\u7d22\u6728\u63a2\u7d22\u306a\u3069\u3002</li> </ul> <p>\u3053\u308c\u3089\u306e\u30c8\u30d4\u30c3\u30af\u306f\u524d\u306e\u7ae0\u3067\u7d39\u4ecb\u3055\u308c\u305f\u305f\u3081\u3001\u79c1\u305f\u3061\u306b\u306f\u99b4\u67d3\u307f\u306e\u306a\u3044\u3082\u306e\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u3053\u306e\u30bb\u30af\u30b7\u30e7\u30f3\u3067\u306f\u3001\u3088\u308a\u4f53\u7cfb\u7684\u306a\u89b3\u70b9\u304b\u3089\u63a2\u7d22\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u518d\u691c\u8a0e\u3057\u307e\u3059\u3002</p>"},{"location":"chapter_searching/searching_algorithm_revisited/#1051","title":"10.5.1 \u00a0 \u7dcf\u5f53\u305f\u308a\u63a2\u7d22","text":"<p>\u7dcf\u5f53\u305f\u308a\u63a2\u7d22\u306f\u3001\u30c7\u30fc\u30bf\u69cb\u9020\u306e\u3059\u3079\u3066\u306e\u8981\u7d20\u3092\u6a2a\u65ad\u3059\u308b\u3053\u3068\u3067\u76ee\u6a19\u8981\u7d20\u3092\u7279\u5b9a\u3057\u307e\u3059\u3002</p> <ul> <li>\u300c\u7dda\u5f62\u63a2\u7d22\u300d\u306f\u914d\u5217\u3084\u9023\u7d50\u30ea\u30b9\u30c8\u306a\u3069\u306e\u7dda\u5f62\u30c7\u30fc\u30bf\u69cb\u9020\u306b\u9069\u3057\u3066\u3044\u307e\u3059\u3002\u30c7\u30fc\u30bf\u69cb\u9020\u306e\u4e00\u7aef\u304b\u3089\u958b\u59cb\u3057\u3001\u76ee\u6a19\u8981\u7d20\u304c\u898b\u3064\u304b\u308b\u304b\u3001\u76ee\u6a19\u8981\u7d20\u3092\u898b\u3064\u3051\u308b\u3053\u3068\u306a\u304f\u4ed6\u7aef\u306b\u5230\u9054\u3059\u308b\u307e\u3067\u3001\u5404\u8981\u7d20\u306b\u4e00\u3064\u305a\u3064\u30a2\u30af\u30bb\u30b9\u3057\u307e\u3059\u3002</li> <li>\u300c\u5e45\u512a\u5148\u63a2\u7d22\u300d\u3068\u300c\u6df1\u3055\u512a\u5148\u63a2\u7d22\u300d\u306f\u3001\u30b0\u30e9\u30d5\u3068\u6728\u306e2\u3064\u306e\u6a2a\u65ad\u6226\u7565\u3067\u3059\u3002\u5e45\u512a\u5148\u63a2\u7d22\u306f\u521d\u671f\u30ce\u30fc\u30c9\u304b\u3089\u958b\u59cb\u3057\u3001\u5c64\u3054\u3068\uff08\u5de6\u304b\u3089\u53f3\u3078\uff09\u306b\u63a2\u7d22\u3057\u3001\u8fd1\u304f\u304b\u3089\u9060\u304f\u306e\u30ce\u30fc\u30c9\u306b\u30a2\u30af\u30bb\u30b9\u3057\u307e\u3059\u3002\u6df1\u3055\u512a\u5148\u63a2\u7d22\u306f\u521d\u671f\u30ce\u30fc\u30c9\u304b\u3089\u958b\u59cb\u3057\u3001\u30d1\u30b9\u306e\u7d42\u7aef\uff08\u4e0a\u304b\u3089\u4e0b\u3078\uff09\u307e\u3067\u8ffd\u8de1\u3057\u3001\u305d\u306e\u5f8c\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30af\u3057\u3066\u4ed6\u306e\u30d1\u30b9\u3092\u8a66\u3057\u3001\u30c7\u30fc\u30bf\u69cb\u9020\u5168\u4f53\u304c\u6a2a\u65ad\u3055\u308c\u308b\u307e\u3067\u7d9a\u884c\u3057\u307e\u3059\u3002</li> </ul> <p>\u7dcf\u5f53\u305f\u308a\u63a2\u7d22\u306e\u5229\u70b9\u306f\u3001\u305d\u306e\u5358\u7d14\u3055\u3068\u6c4e\u7528\u6027\u3067\u3042\u308a\u3001**\u30c7\u30fc\u30bf\u306e\u524d\u51e6\u7406\u3084\u8ffd\u52a0\u306e\u30c7\u30fc\u30bf\u69cb\u9020\u306e\u52a9\u3051\u304c\u4e0d\u8981**\u3067\u3059\u3002</p> <p>\u305f\u3060\u3057\u3001**\u3053\u306e\u30bf\u30a4\u30d7\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O(n)\\)**\u3067\u3001\\(n\\)\u306f\u8981\u7d20\u6570\u3067\u3042\u308b\u305f\u3081\u3001\u5927\u898f\u6a21\u306a\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u3067\u306f\u6027\u80fd\u304c\u60aa\u304f\u306a\u308a\u307e\u3059\u3002</p>"},{"location":"chapter_searching/searching_algorithm_revisited/#1052","title":"10.5.2 \u00a0 \u9069\u5fdc\u7684\u63a2\u7d22","text":"<p>\u9069\u5fdc\u7684\u63a2\u7d22\u306f\u3001\u30c7\u30fc\u30bf\u306e\u56fa\u6709\u306e\u6027\u8cea\uff08\u9806\u5e8f\u306a\u3069\uff09\u3092\u4f7f\u7528\u3057\u3066\u63a2\u7d22\u30d7\u30ed\u30bb\u30b9\u3092\u6700\u9069\u5316\u3057\u3001\u305d\u308c\u306b\u3088\u308a\u76ee\u6a19\u8981\u7d20\u3092\u3088\u308a\u52b9\u7387\u7684\u306b\u7279\u5b9a\u3057\u307e\u3059\u3002</p> <ul> <li>\u300c\u4e8c\u5206\u63a2\u7d22\u300d\u306f\u30c7\u30fc\u30bf\u306e\u6574\u5217\u6027\u3092\u4f7f\u7528\u3057\u3066\u52b9\u7387\u7684\u306a\u63a2\u7d22\u3092\u5b9f\u73fe\u3057\u3001\u914d\u5217\u306b\u306e\u307f\u9069\u7528\u53ef\u80fd\u3067\u3059\u3002</li> <li>\u300c\u30cf\u30c3\u30b7\u30e5\u63a2\u7d22\u300d\u306f\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u3092\u4f7f\u7528\u3057\u3066\u63a2\u7d22\u30c7\u30fc\u30bf\u3068\u76ee\u6a19\u30c7\u30fc\u30bf\u306e\u9593\u306b\u30ad\u30fc\u3068\u5024\u306e\u30de\u30c3\u30d4\u30f3\u30b0\u3092\u78ba\u7acb\u3057\u3001\u305d\u308c\u306b\u3088\u308a\u30af\u30a8\u30ea\u64cd\u4f5c\u3092\u5b9f\u88c5\u3057\u307e\u3059\u3002</li> <li>\u7279\u5b9a\u306e\u6728\u69cb\u9020\uff08\u4e8c\u5206\u63a2\u7d22\u6728\u306a\u3069\uff09\u3067\u306e\u300c\u6728\u63a2\u7d22\u300d\u306f\u3001\u30ce\u30fc\u30c9\u5024\u306e\u6bd4\u8f03\u306b\u57fa\u3065\u3044\u3066\u30ce\u30fc\u30c9\u3092\u8fc5\u901f\u306b\u9664\u5916\u3057\u3001\u305d\u308c\u306b\u3088\u308a\u76ee\u6a19\u8981\u7d20\u3092\u7279\u5b9a\u3057\u307e\u3059\u3002</li> </ul> <p>\u3053\u308c\u3089\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5229\u70b9\u306f\u9ad8\u52b9\u7387\u3067\u3042\u308a\u3001\u6642\u9593\u8a08\u7b97\u91cf\u304c\\(O(\\log n)\\)\u307e\u305f\u306f\\(O(1)\\)\u306b\u307e\u3067\u9054\u3057\u307e\u3059\u3002</p> <p>\u305f\u3060\u3057\u3001\u3053\u308c\u3089\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u4f7f\u7528\u3059\u308b\u306b\u306f\u3001\u591a\u304f\u306e\u5834\u5408\u30c7\u30fc\u30bf\u306e\u524d\u51e6\u7406\u304c\u5fc5\u8981\u3067\u3059\u3002\u4f8b\u3048\u3070\u3001\u4e8c\u5206\u63a2\u7d22\u3067\u306f\u4e8b\u524d\u306b\u914d\u5217\u3092\u30bd\u30fc\u30c8\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u3001\u30cf\u30c3\u30b7\u30e5\u63a2\u7d22\u3068\u6728\u63a2\u7d22\u306e\u4e21\u65b9\u3067\u8ffd\u52a0\u306e\u30c7\u30fc\u30bf\u69cb\u9020\u306e\u52a9\u3051\u304c\u5fc5\u8981\u3067\u3059\u3002\u3053\u308c\u3089\u306e\u69cb\u9020\u3092\u7dad\u6301\u3059\u308b\u3053\u3068\u3082\u3001\u6642\u9593\u3068\u7a7a\u9593\u306e\u9762\u3067\u3088\u308a\u591a\u304f\u306e\u30aa\u30fc\u30d0\u30fc\u30d8\u30c3\u30c9\u304c\u5fc5\u8981\u3067\u3059\u3002</p> <p>Tip</p> <p>\u9069\u5fdc\u7684\u63a2\u7d22\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u3001\u591a\u304f\u306e\u5834\u5408\u63a2\u7d22\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3068\u547c\u3070\u308c\u3001\u4e3b\u306b\u7279\u5b9a\u306e\u30c7\u30fc\u30bf\u69cb\u9020\u5185\u3067\u76ee\u6a19\u8981\u7d20\u3092\u8fc5\u901f\u306b\u53d6\u5f97\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002</p>"},{"location":"chapter_searching/searching_algorithm_revisited/#1053","title":"10.5.3 \u00a0 \u63a2\u7d22\u65b9\u6cd5\u306e\u9078\u629e","text":"<p>\u30b5\u30a4\u30ba\\(n\\)\u306e\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408\u3001\u7dda\u5f62\u63a2\u7d22\u3001\u4e8c\u5206\u63a2\u7d22\u3001\u6728\u63a2\u7d22\u3001\u30cf\u30c3\u30b7\u30e5\u63a2\u7d22\u3001\u307e\u305f\u306f\u305d\u306e\u4ed6\u306e\u65b9\u6cd5\u3092\u4f7f\u7528\u3057\u3066\u76ee\u6a19\u8981\u7d20\u3092\u53d6\u5f97\u3067\u304d\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u65b9\u6cd5\u306e\u52d5\u4f5c\u539f\u7406\u3092\u4e0b\u56f3\u306b\u793a\u3057\u307e\u3059\u3002</p> <p></p> <p> \u56f3 10-11 \u00a0 Various search strategies </p> <p>\u524d\u8ff0\u306e\u65b9\u6cd5\u306e\u7279\u6027\u3068\u64cd\u4f5c\u52b9\u7387\u3092\u4ee5\u4e0b\u306e\u8868\u306b\u793a\u3057\u307e\u3059\u3002</p> <p> \u8868 10-1 \u00a0 \u63a2\u7d22\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u52b9\u7387\u306e\u6bd4\u8f03 </p> \u7dda\u5f62\u63a2\u7d22 \u4e8c\u5206\u63a2\u7d22 \u6728\u63a2\u7d22 \u30cf\u30c3\u30b7\u30e5\u63a2\u7d22 \u8981\u7d20\u63a2\u7d22 \\(O(n)\\) \\(O(\\log n)\\) \\(O(\\log n)\\) \\(O(1)\\) \u8981\u7d20\u633f\u5165 \\(O(1)\\) \\(O(n)\\) \\(O(\\log n)\\) \\(O(1)\\) \u8981\u7d20\u524a\u9664 \\(O(n)\\) \\(O(n)\\) \\(O(\\log n)\\) \\(O(1)\\) \u8ffd\u52a0\u7a7a\u9593 \\(O(1)\\) \\(O(1)\\) \\(O(n)\\) \\(O(n)\\) \u30c7\u30fc\u30bf\u524d\u51e6\u7406 / \u30bd\u30fc\u30c8 \\(O(n \\log n)\\) \u6728\u69cb\u7bc9 \\(O(n \\log n)\\) \u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u69cb\u7bc9 \\(O(n)\\) \u30c7\u30fc\u30bf\u9806\u5e8f\u6027 \u7121\u9806\u5e8f \u9806\u5e8f \u9806\u5e8f \u7121\u9806\u5e8f <p>\u63a2\u7d22\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u9078\u629e\u306f\u3001\u30c7\u30fc\u30bf\u91cf\u3001\u63a2\u7d22\u6027\u80fd\u8981\u4ef6\u3001\u30c7\u30fc\u30bf\u30af\u30a8\u30ea\u3068\u66f4\u65b0\u306e\u983b\u5ea6\u306a\u3069\u306b\u3082\u4f9d\u5b58\u3057\u307e\u3059\u3002</p> <p>\u7dda\u5f62\u63a2\u7d22</p> <ul> <li>\u6c4e\u7528\u6027\u304c\u826f\u304f\u3001\u30c7\u30fc\u30bf\u524d\u51e6\u7406\u64cd\u4f5c\u304c\u4e0d\u8981\u3067\u3059\u3002\u30c7\u30fc\u30bf\u3092\u4e00\u5ea6\u3060\u3051\u30af\u30a8\u30ea\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u5834\u5408\u3001\u4ed6\u306e3\u3064\u306e\u65b9\u6cd5\u306e\u30c7\u30fc\u30bf\u524d\u51e6\u7406\u6642\u9593\u306f\u7dda\u5f62\u63a2\u7d22\u306e\u6642\u9593\u3088\u308a\u3082\u9577\u304f\u306a\u308a\u307e\u3059\u3002</li> <li>\u5c0f\u5bb9\u91cf\u306e\u30c7\u30fc\u30bf\u306b\u9069\u3057\u3066\u304a\u308a\u3001\u6642\u9593\u8a08\u7b97\u91cf\u304c\u52b9\u7387\u306b\u4e0e\u3048\u308b\u5f71\u97ff\u306f\u5c0f\u3055\u3044\u3067\u3059\u3002</li> <li>\u30c7\u30fc\u30bf\u66f4\u65b0\u304c\u975e\u5e38\u306b\u983b\u7e41\u306a\u30b7\u30ca\u30ea\u30aa\u306b\u9069\u3057\u3066\u3044\u307e\u3059\u3002\u3053\u306e\u65b9\u6cd5\u306f\u30c7\u30fc\u30bf\u306e\u8ffd\u52a0\u30e1\u30f3\u30c6\u30ca\u30f3\u30b9\u3092\u5fc5\u8981\u3068\u3057\u306a\u3044\u305f\u3081\u3067\u3059\u3002</li> </ul> <p>\u4e8c\u5206\u63a2\u7d22</p> <ul> <li>\u3088\u308a\u5927\u304d\u306a\u30c7\u30fc\u30bf\u91cf\u306b\u9069\u3057\u3066\u304a\u308a\u3001\u5b89\u5b9a\u3057\u305f\u6027\u80fd\u3068\u6700\u60aa\u30b1\u30fc\u30b9\u306e\u6642\u9593\u8a08\u7b97\u91cf\\(O(\\log n)\\)\u3092\u6301\u3061\u307e\u3059\u3002</li> <li>\u305f\u3060\u3057\u3001\u30c7\u30fc\u30bf\u91cf\u304c\u5927\u304d\u3059\u304e\u308b\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093\u3002\u914d\u5217\u306e\u4fdd\u5b58\u306b\u306f\u9023\u7d9a\u3057\u305f\u30e1\u30e2\u30ea\u7a7a\u9593\u304c\u5fc5\u8981\u3060\u304b\u3089\u3067\u3059\u3002</li> <li>\u983b\u7e41\u306a\u8ffd\u52a0\u3068\u524a\u9664\u304c\u3042\u308b\u30b7\u30ca\u30ea\u30aa\u306b\u306f\u9069\u3057\u3066\u3044\u307e\u305b\u3093\u3002\u9806\u5e8f\u4ed8\u304d\u914d\u5217\u306e\u7dad\u6301\u306b\u591a\u304f\u306e\u30aa\u30fc\u30d0\u30fc\u30d8\u30c3\u30c9\u304c\u767a\u751f\u3059\u308b\u305f\u3081\u3067\u3059\u3002</li> </ul> <p>\u30cf\u30c3\u30b7\u30e5\u63a2\u7d22</p> <ul> <li>\u9ad8\u901f\u30af\u30a8\u30ea\u6027\u80fd\u304c\u4e0d\u53ef\u6b20\u306a\u30b7\u30ca\u30ea\u30aa\u306b\u9069\u3057\u3066\u304a\u308a\u3001\u5e73\u5747\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O(1)\\)\u3067\u3059\u3002</li> <li>\u9806\u5e8f\u4ed8\u304d\u30c7\u30fc\u30bf\u3084\u7bc4\u56f2\u63a2\u7d22\u304c\u5fc5\u8981\u306a\u30b7\u30ca\u30ea\u30aa\u306b\u306f\u9069\u3057\u3066\u3044\u307e\u305b\u3093\u3002\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u306f\u30c7\u30fc\u30bf\u306e\u9806\u5e8f\u6027\u3092\u7dad\u6301\u3067\u304d\u306a\u3044\u305f\u3081\u3067\u3059\u3002</li> <li>\u30cf\u30c3\u30b7\u30e5\u95a2\u6570\u3068\u30cf\u30c3\u30b7\u30e5\u885d\u7a81\u51e6\u7406\u6226\u7565\u3078\u306e\u4f9d\u5b58\u5ea6\u304c\u9ad8\u304f\u3001\u6027\u80fd\u52a3\u5316\u306e\u30ea\u30b9\u30af\u304c\u5927\u304d\u3044\u3067\u3059\u3002</li> <li>\u904e\u5ea6\u306b\u5927\u5bb9\u91cf\u306e\u30c7\u30fc\u30bf\u306b\u306f\u9069\u3057\u3066\u3044\u307e\u305b\u3093\u3002\u30cf\u30c3\u30b7\u30e5\u30c6\u30fc\u30d6\u30eb\u306f\u885d\u7a81\u3092\u6700\u5c0f\u5316\u3057\u3001\u826f\u597d\u306a\u30af\u30a8\u30ea\u6027\u80fd\u3092\u63d0\u4f9b\u3059\u308b\u305f\u3081\u306b\u8ffd\u52a0\u306e\u7a7a\u9593\u304c\u5fc5\u8981\u3060\u304b\u3089\u3067\u3059\u3002</li> </ul> <p>\u6728\u63a2\u7d22</p> <ul> <li>\u5927\u5bb9\u91cf\u30c7\u30fc\u30bf\u306b\u9069\u3057\u3066\u3044\u307e\u3059\u3002\u6728\u30ce\u30fc\u30c9\u306f\u30e1\u30e2\u30ea\u5185\u306b\u5206\u6563\u3057\u3066\u4fdd\u5b58\u3055\u308c\u308b\u305f\u3081\u3067\u3059\u3002</li> <li>\u9806\u5e8f\u4ed8\u304d\u30c7\u30fc\u30bf\u306e\u7dad\u6301\u3084\u7bc4\u56f2\u63a2\u7d22\u306b\u9069\u3057\u3066\u3044\u307e\u3059\u3002</li> <li>\u30ce\u30fc\u30c9\u306e\u7d99\u7d9a\u7684\u306a\u8ffd\u52a0\u3068\u524a\u9664\u306b\u3088\u308a\u3001\u4e8c\u5206\u63a2\u7d22\u6728\u306f\u504f\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u3001\u6642\u9593\u8a08\u7b97\u91cf\u304c\\(O(n)\\)\u306b\u52a3\u5316\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002</li> <li>AVL\u6728\u3084\u8d64\u9ed2\u6728\u3092\u4f7f\u7528\u3059\u308b\u5834\u5408\u3001\u64cd\u4f5c\u306f\\(O(\\log n)\\)\u52b9\u7387\u3067\u5b89\u5b9a\u3057\u3066\u5b9f\u884c\u3067\u304d\u307e\u3059\u304c\u3001\u6728\u306e\u30d0\u30e9\u30f3\u30b9\u3092\u7dad\u6301\u3059\u308b\u64cd\u4f5c\u306b\u3088\u308a\u8ffd\u52a0\u306e\u30aa\u30fc\u30d0\u30fc\u30d8\u30c3\u30c9\u304c\u8ffd\u52a0\u3055\u308c\u307e\u3059\u3002</li> </ul>"},{"location":"chapter_searching/summary/","title":"10.6 \u00a0 \u307e\u3068\u3081","text":"<ul> <li>\u4e8c\u5206\u63a2\u7d22\u306f\u30c7\u30fc\u30bf\u306e\u9806\u5e8f\u306b\u4f9d\u5b58\u3057\u3001\u63a2\u7d22\u533a\u9593\u3092\u53cd\u5fa9\u7684\u306b\u534a\u5206\u306b\u3059\u308b\u3053\u3068\u3067\u63a2\u7d22\u3092\u5b9f\u884c\u3057\u307e\u3059\u3002\u5165\u529b\u30c7\u30fc\u30bf\u304c\u30bd\u30fc\u30c8\u6e08\u307f\u3067\u3042\u308b\u5fc5\u8981\u304c\u3042\u308a\u3001\u914d\u5217\u307e\u305f\u306f\u914d\u5217\u30d9\u30fc\u30b9\u306e\u30c7\u30fc\u30bf\u69cb\u9020\u306b\u306e\u307f\u9069\u7528\u53ef\u80fd\u3067\u3059\u3002</li> <li>\u7121\u9806\u5e8f\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u5185\u306e\u30a8\u30f3\u30c8\u30ea\u3092\u898b\u3064\u3051\u308b\u306b\u306f\u3001\u7dcf\u5f53\u305f\u308a\u63a2\u7d22\u304c\u5fc5\u8981\u306a\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002\u30c7\u30fc\u30bf\u69cb\u9020\u306b\u57fa\u3065\u3044\u3066\u7570\u306a\u308b\u63a2\u7d22\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u9069\u7528\u3067\u304d\u307e\u3059\uff1a\u7dda\u5f62\u63a2\u7d22\u306f\u914d\u5217\u3068\u9023\u7d50\u30ea\u30b9\u30c8\u306b\u9069\u3057\u3066\u304a\u308a\u3001\u5e45\u512a\u5148\u63a2\u7d22\uff08BFS\uff09\u3068\u6df1\u3055\u512a\u5148\u63a2\u7d22\uff08DFS\uff09\u306f\u30b0\u30e9\u30d5\u3068\u6728\u306b\u9069\u3057\u3066\u3044\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u975e\u5e38\u306b\u6c4e\u7528\u6027\u304c\u9ad8\u304f\u3001\u30c7\u30fc\u30bf\u306e\u524d\u51e6\u7406\u304c\u4e0d\u8981\u3067\u3059\u304c\u3001\\(O(n)\\)\u3068\u3044\u3046\u9ad8\u3044\u6642\u9593\u8a08\u7b97\u91cf\u3092\u6301\u3061\u307e\u3059\u3002</li> <li>\u30cf\u30c3\u30b7\u30e5\u63a2\u7d22\u3001\u6728\u63a2\u7d22\u3001\u4e8c\u5206\u63a2\u7d22\u306f\u52b9\u7387\u7684\u306a\u63a2\u7d22\u65b9\u6cd5\u3067\u3001\u7279\u5b9a\u306e\u30c7\u30fc\u30bf\u69cb\u9020\u5185\u3067\u76ee\u6a19\u8981\u7d20\u3092\u8fc5\u901f\u306b\u7279\u5b9a\u3067\u304d\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u975e\u5e38\u306b\u52b9\u7387\u7684\u3067\u3001\u6642\u9593\u8a08\u7b97\u91cf\u304c\\(O(\\log n)\\)\u307e\u305f\u306f\\(O(1)\\)\u306b\u307e\u3067\u9054\u3057\u307e\u3059\u304c\u3001\u901a\u5e38\u306f\u8ffd\u52a0\u306e\u30c7\u30fc\u30bf\u69cb\u9020\u3092\u53ce\u5bb9\u3059\u308b\u305f\u3081\u306b\u8ffd\u52a0\u306e\u7a7a\u9593\u304c\u5fc5\u8981\u3067\u3059\u3002</li> <li>\u5b9f\u969b\u306b\u306f\u3001\u30c7\u30fc\u30bf\u91cf\u3001\u63a2\u7d22\u6027\u80fd\u8981\u4ef6\u3001\u30c7\u30fc\u30bf\u30af\u30a8\u30ea\u3068\u66f4\u65b0\u983b\u5ea6\u306a\u3069\u306e\u8981\u56e0\u3092\u5206\u6790\u3057\u3066\u3001\u9069\u5207\u306a\u63a2\u7d22\u65b9\u6cd5\u3092\u9078\u629e\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002</li> <li>\u7dda\u5f62\u63a2\u7d22\u306f\u5c0f\u3055\u306a\u30c7\u30fc\u30bf\u3084\u983b\u7e41\u306b\u66f4\u65b0\u3055\u308c\u308b\uff08\u5909\u52d5\u6027\u306e\u9ad8\u3044\uff09\u30c7\u30fc\u30bf\u306b\u7406\u60f3\u7684\u3067\u3059\u3002\u4e8c\u5206\u63a2\u7d22\u306f\u5927\u304d\u304f\u3066\u30bd\u30fc\u30c8\u6e08\u307f\u306e\u30c7\u30fc\u30bf\u306b\u9069\u3057\u3066\u3044\u307e\u3059\u3002\u30cf\u30c3\u30b7\u30e5\u63a2\u7d22\u306f\u9ad8\u3044\u30af\u30a8\u30ea\u52b9\u7387\u304c\u5fc5\u8981\u3067\u7bc4\u56f2\u30af\u30a8\u30ea\u304c\u4e0d\u8981\u306a\u30c7\u30fc\u30bf\u306b\u9069\u3057\u3066\u3044\u307e\u3059\u3002\u6728\u63a2\u7d22\u306f\u9806\u5e8f\u3092\u7dad\u6301\u3057\u3001\u7bc4\u56f2\u30af\u30a8\u30ea\u3092\u30b5\u30dd\u30fc\u30c8\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u5927\u304d\u306a\u52d5\u7684\u30c7\u30fc\u30bf\u306b\u6700\u3082\u9069\u3057\u3066\u3044\u307e\u3059\u3002</li> <li>\u7dda\u5f62\u63a2\u7d22\u3092\u30cf\u30c3\u30b7\u30e5\u63a2\u7d22\u306b\u7f6e\u304d\u63db\u3048\u308b\u3053\u3068\u306f\u3001\u5b9f\u884c\u6642\u6027\u80fd\u3092\u6700\u9069\u5316\u3059\u308b\u4e00\u822c\u7684\u306a\u6226\u7565\u3067\u3001\u6642\u9593\u8a08\u7b97\u91cf\u3092\\(O(n)\\)\u304b\u3089\\(O(1)\\)\u306b\u524a\u6e1b\u3057\u307e\u3059\u3002</li> </ul>"},{"location":"chapter_sorting/","title":"\u7b2c 11 \u7ae0 \u00a0 \u30bd\u30fc\u30c8","text":"<p>Abstract</p> <p>\u30bd\u30fc\u30c8\u306f\u6df7\u6c8c\u3092\u79e9\u5e8f\u306b\u5909\u3048\u308b\u9b54\u6cd5\u306e\u9375\u306e\u3088\u3046\u306a\u3082\u306e\u3067\u3001\u30c7\u30fc\u30bf\u3092\u3088\u308a\u52b9\u7387\u7684\u306b\u7406\u89e3\u3057\u51e6\u7406\u3059\u308b\u3053\u3068\u3092\u53ef\u80fd\u306b\u3057\u307e\u3059\u3002</p> <p>\u5358\u7d14\u306a\u6607\u9806\u3067\u3042\u308d\u3046\u3068\u8907\u96d1\u306a\u30ab\u30c6\u30b4\u30ea\u914d\u5217\u3067\u3042\u308d\u3046\u3068\u3001\u30bd\u30fc\u30c8\u306f\u30c7\u30fc\u30bf\u306e\u8abf\u548c\u7f8e\u3092\u660e\u3089\u304b\u306b\u3057\u307e\u3059\u3002</p>"},{"location":"chapter_sorting/#_1","title":"\u7ae0\u306e\u5185\u5bb9","text":"<ul> <li>11.1 \u00a0 \u30bd\u30fc\u30c8\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0</li> <li>11.2 \u00a0 \u9078\u629e\u30bd\u30fc\u30c8</li> <li>11.3 \u00a0 \u30d0\u30d6\u30eb\u30bd\u30fc\u30c8</li> <li>11.4 \u00a0 \u633f\u5165\u30bd\u30fc\u30c8</li> <li>11.5 \u00a0 \u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8</li> <li>11.6 \u00a0 \u30de\u30fc\u30b8\u30bd\u30fc\u30c8</li> <li>11.7 \u00a0 \u30d2\u30fc\u30d7\u30bd\u30fc\u30c8</li> <li>11.8 \u00a0 \u30d0\u30b1\u30c3\u30c8\u30bd\u30fc\u30c8</li> <li>11.9 \u00a0 \u8a08\u6570\u30bd\u30fc\u30c8</li> <li>11.10 \u00a0 \u57fa\u6570\u30bd\u30fc\u30c8</li> <li>11.11 \u00a0 \u307e\u3068\u3081</li> </ul>"},{"location":"chapter_sorting/bubble_sort/","title":"11.3 \u00a0 \u30d0\u30d6\u30eb\u30bd\u30fc\u30c8","text":"<p>\u30d0\u30d6\u30eb\u30bd\u30fc\u30c8\u306f\u3001\u96a3\u63a5\u3059\u308b\u8981\u7d20\u3092\u7d99\u7d9a\u7684\u306b\u6bd4\u8f03\u3057\u4ea4\u63db\u3059\u308b\u3053\u3068\u3067\u52d5\u4f5c\u3057\u307e\u3059\u3002\u3053\u306e\u30d7\u30ed\u30bb\u30b9\u306f\u6ce1\u304c\u5e95\u304b\u3089\u4e0a\u306b\u4e0a\u6607\u3059\u308b\u3088\u3046\u306a\u3082\u306e\u306a\u306e\u3067\u3001\u300c\u30d0\u30d6\u30eb\u30bd\u30fc\u30c8\u300d\u3068\u540d\u4ed8\u3051\u3089\u308c\u307e\u3057\u305f\u3002</p> <p>\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u30d0\u30d6\u30ea\u30f3\u30b0\u30d7\u30ed\u30bb\u30b9\u306f\u8981\u7d20\u4ea4\u63db\u3092\u4f7f\u7528\u3057\u3066\u30b7\u30df\u30e5\u30ec\u30fc\u30c8\u3067\u304d\u307e\u3059\uff1a\u914d\u5217\u306e\u5de6\u7aef\u304b\u3089\u958b\u59cb\u3057\u3066\u53f3\u306b\u79fb\u52d5\u3057\u3001\u96a3\u63a5\u3059\u308b\u8981\u7d20\u306e\u5404\u30da\u30a2\u3092\u6bd4\u8f03\u3057\u307e\u3059\u3002\u5de6\u306e\u8981\u7d20\u304c\u53f3\u306e\u8981\u7d20\u3088\u308a\u5927\u304d\u3044\u5834\u5408\u306f\u3001\u305d\u308c\u3089\u3092\u4ea4\u63db\u3057\u307e\u3059\u3002\u6a2a\u65ad\u5f8c\u3001\u6700\u5927\u8981\u7d20\u306f\u914d\u5217\u306e\u53f3\u7aef\u306b\u30d0\u30d6\u30eb\u30a2\u30c3\u30d7\u3057\u307e\u3059\u3002</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> \u56f3 11-4 \u00a0 Simulating bubble process using element swap </p>"},{"location":"chapter_sorting/bubble_sort/#1131","title":"11.3.1 \u00a0 \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u30d7\u30ed\u30bb\u30b9","text":"<p>\u914d\u5217\u306e\u9577\u3055\u3092\\(n\\)\u3068\u3057\u307e\u3059\u3002\u30d0\u30d6\u30eb\u30bd\u30fc\u30c8\u306e\u30b9\u30c6\u30c3\u30d7\u306f\u4e0b\u56f3\u306b\u793a\u3055\u308c\u307e\u3059\uff1a</p> <ol> <li>\u307e\u305a\u3001\\(n\\)\u500b\u306e\u8981\u7d20\u306b\u5bfe\u3057\u30661\u56de\u306e\u300c\u30d0\u30d6\u30eb\u300d\u30d1\u30b9\u3092\u5b9f\u884c\u3057\u3001\u6700\u5927\u8981\u7d20\u3092\u6b63\u3057\u3044\u4f4d\u7f6e\u306b\u4ea4\u63db\u3057\u307e\u3059\u3002</li> <li>\u6b21\u306b\u3001\u6b8b\u308a\u306e\\(n - 1\\)\u500b\u306e\u8981\u7d20\u306b\u5bfe\u3057\u3066\u300c\u30d0\u30d6\u30eb\u300d\u30d1\u30b9\u3092\u5b9f\u884c\u3057\u30012\u756a\u76ee\u306b\u5927\u304d\u3044\u8981\u7d20\u3092\u6b63\u3057\u3044\u4f4d\u7f6e\u306b\u4ea4\u63db\u3057\u307e\u3059\u3002</li> <li>\u3053\u306e\u65b9\u6cd5\u3067\u7d9a\u884c\u3057\u307e\u3059\uff1b\\(n - 1\\)\u56de\u306e\u30d1\u30b9\u306e\u5f8c\u3001\u6700\u5927\\(n - 1\\)\u500b\u306e\u8981\u7d20\u304c\u6b63\u3057\u3044\u4f4d\u7f6e\u306b\u79fb\u52d5\u3055\u308c\u307e\u3059\u3002</li> <li>\u6b8b\u308a\u306e\u552f\u4e00\u306e\u8981\u7d20\u306f**\u5fc5\u305a**\u6700\u5c0f\u3067\u3042\u308b\u305f\u3081\u3001**\u3055\u3089\u306a\u308b**\u30bd\u30fc\u30c8\u306f\u5fc5\u8981\u3042\u308a\u307e\u305b\u3093\u3002\u3053\u306e\u6642\u70b9\u3067\u3001\u914d\u5217\u306f\u30bd\u30fc\u30c8\u3055\u308c\u307e\u3059\u3002</li> </ol> <p></p> <p> \u56f3 11-5 \u00a0 Bubble sort process </p> <p>\u30b3\u30fc\u30c9\u4f8b\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig bubble_sort.py<pre><code>def bubble_sort(nums: list[int]):\n    \"\"\"\u30d0\u30d6\u30eb\u30bd\u30fc\u30c8\"\"\"\n    n = len(nums)\n    # \u5916\u5074\u306e\u30eb\u30fc\u30d7\uff1a\u672a\u30bd\u30fc\u30c8\u7bc4\u56f2\u306f [0, i]\n    for i in range(n - 1, 0, -1):\n        # \u5185\u5074\u306e\u30eb\u30fc\u30d7\uff1a\u672a\u30bd\u30fc\u30c8\u7bc4\u56f2 [0, i] \u306e\u6700\u5927\u8981\u7d20\u3092\u7bc4\u56f2\u306e\u53f3\u7aef\u306b\u79fb\u52d5\n        for j in range(i):\n            if nums[j] &gt; nums[j + 1]:\n                # nums[j] \u3068 nums[j + 1] \u3092\u4ea4\u63db\n                nums[j], nums[j + 1] = nums[j + 1], nums[j]\n</code></pre> bubble_sort.cpp<pre><code>/* \u30d0\u30d6\u30eb\u30bd\u30fc\u30c8 */\nvoid bubbleSort(vector&lt;int&gt; &amp;nums) {\n    // \u5916\u5074\u30eb\u30fc\u30d7\uff1a\u672a\u30bd\u30fc\u30c8\u7bc4\u56f2\u306f[0, i]\n    for (int i = nums.size() - 1; i &gt; 0; i--) {\n        // \u5185\u5074\u30eb\u30fc\u30d7\uff1a\u672a\u30bd\u30fc\u30c8\u7bc4\u56f2[0, i]\u5185\u306e\u6700\u5927\u8981\u7d20\u3092\u7bc4\u56f2\u306e\u53f3\u7aef\u306b\u4ea4\u63db\n        for (int j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // nums[j]\u3068nums[j + 1]\u3092\u4ea4\u63db\n                // \u3053\u3053\u3067\u306fstd\u306eswap\u3092\u4f7f\u7528\n                swap(nums[j], nums[j + 1]);\n            }\n        }\n    }\n}\n</code></pre> bubble_sort.java<pre><code>/* \u30d0\u30d6\u30eb\u30bd\u30fc\u30c8 */\nvoid bubbleSort(int[] nums) {\n    // \u5916\u5074\u30eb\u30fc\u30d7: \u672a\u30bd\u30fc\u30c8\u7bc4\u56f2\u306f [0, i]\n    for (int i = nums.length - 1; i &gt; 0; i--) {\n        // \u5185\u5074\u30eb\u30fc\u30d7: \u672a\u30bd\u30fc\u30c8\u7bc4\u56f2 [0, i] \u306e\u6700\u5927\u8981\u7d20\u3092\u7bc4\u56f2\u306e\u53f3\u7aef\u306b\u4ea4\u63db\n        for (int j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // nums[j] \u3068 nums[j + 1] \u3092\u4ea4\u63db\n                int tmp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = tmp;\n            }\n        }\n    }\n}\n</code></pre> bubble_sort.cs<pre><code>[class]{bubble_sort}-[func]{BubbleSort}\n</code></pre> bubble_sort.go<pre><code>[class]{}-[func]{bubbleSort}\n</code></pre> bubble_sort.swift<pre><code>[class]{}-[func]{bubbleSort}\n</code></pre> bubble_sort.js<pre><code>[class]{}-[func]{bubbleSort}\n</code></pre> bubble_sort.ts<pre><code>[class]{}-[func]{bubbleSort}\n</code></pre> bubble_sort.dart<pre><code>[class]{}-[func]{bubbleSort}\n</code></pre> bubble_sort.rs<pre><code>[class]{}-[func]{bubble_sort}\n</code></pre> bubble_sort.c<pre><code>[class]{}-[func]{bubbleSort}\n</code></pre> bubble_sort.kt<pre><code>[class]{}-[func]{bubbleSort}\n</code></pre> bubble_sort.rb<pre><code>[class]{}-[func]{bubble_sort}\n</code></pre> bubble_sort.zig<pre><code>[class]{}-[func]{bubbleSort}\n</code></pre>"},{"location":"chapter_sorting/bubble_sort/#1132","title":"11.3.2 \u00a0 \u52b9\u7387\u306e\u6700\u9069\u5316","text":"<p>\u300c\u30d0\u30d6\u30ea\u30f3\u30b0\u300d\u306e\u30e9\u30a6\u30f3\u30c9\u4e2d\u306b\u4ea4\u63db\u304c\u767a\u751f\u3057\u306a\u3044\u5834\u5408\u3001\u914d\u5217\u306f\u3059\u3067\u306b\u30bd\u30fc\u30c8\u3055\u308c\u3066\u3044\u308b\u305f\u3081\u3001\u3059\u3050\u306b\u623b\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u3053\u308c\u3092\u691c\u51fa\u3059\u308b\u305f\u3081\u306b\u3001<code>flag</code>\u5909\u6570\u3092\u8ffd\u52a0\u3067\u304d\u307e\u3059\uff1b\u30d1\u30b9\u3067\u4ea4\u63db\u304c\u884c\u308f\u308c\u306a\u3044\u5834\u5408\u306f\u3001\u30d5\u30e9\u30b0\u3092\u8a2d\u5b9a\u3057\u3066\u65e9\u671f\u306b\u623b\u308a\u307e\u3059\u3002</p> <p>\u3053\u306e\u6700\u9069\u5316\u304c\u3042\u3063\u3066\u3082\u3001\u30d0\u30d6\u30eb\u30bd\u30fc\u30c8\u306e\u6700\u60aa\u6642\u9593\u8a08\u7b97\u91cf\u3068\u5e73\u5747\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O(n^2)\\)\u306e\u307e\u307e\u3067\u3059\u3002\u305f\u3060\u3057\u3001\u5165\u529b\u914d\u5217\u304c\u3059\u3067\u306b\u30bd\u30fc\u30c8\u3055\u308c\u3066\u3044\u308b\u5834\u5408\u3001\u6700\u826f\u30b1\u30fc\u30b9\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O(n)\\)\u307e\u3067\u4f4e\u304f\u306a\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig bubble_sort.py<pre><code>def bubble_sort_with_flag(nums: list[int]):\n    \"\"\"\u30d0\u30d6\u30eb\u30bd\u30fc\u30c8\uff08\u30d5\u30e9\u30b0\u306b\u3088\u308b\u6700\u9069\u5316\uff09\"\"\"\n    n = len(nums)\n    # \u5916\u5074\u306e\u30eb\u30fc\u30d7\uff1a\u672a\u30bd\u30fc\u30c8\u7bc4\u56f2\u306f [0, i]\n    for i in range(n - 1, 0, -1):\n        flag = False  # \u30d5\u30e9\u30b0\u3092\u521d\u671f\u5316\n        # \u5185\u5074\u306e\u30eb\u30fc\u30d7\uff1a\u672a\u30bd\u30fc\u30c8\u7bc4\u56f2 [0, i] \u306e\u6700\u5927\u8981\u7d20\u3092\u7bc4\u56f2\u306e\u53f3\u7aef\u306b\u79fb\u52d5\n        for j in range(i):\n            if nums[j] &gt; nums[j + 1]:\n                # nums[j] \u3068 nums[j + 1] \u3092\u4ea4\u63db\n                nums[j], nums[j + 1] = nums[j + 1], nums[j]\n                flag = True  # \u8981\u7d20\u3092\u4ea4\u63db\u3057\u305f\u3053\u3068\u3092\u8a18\u9332\n        if not flag:\n            break  # \u3053\u306e\u56de\u306e\u300c\u30d0\u30d6\u30ea\u30f3\u30b0\u300d\u3067\u8981\u7d20\u304c\u4ea4\u63db\u3055\u308c\u306a\u304b\u3063\u305f\u5834\u5408\u3001\u7d42\u4e86\n</code></pre> bubble_sort.cpp<pre><code>/* \u30d0\u30d6\u30eb\u30bd\u30fc\u30c8\uff08\u30d5\u30e9\u30b0\u6700\u9069\u5316\u7248\uff09*/\nvoid bubbleSortWithFlag(vector&lt;int&gt; &amp;nums) {\n    // \u5916\u5074\u30eb\u30fc\u30d7\uff1a\u672a\u30bd\u30fc\u30c8\u7bc4\u56f2\u306f[0, i]\n    for (int i = nums.size() - 1; i &gt; 0; i--) {\n        bool flag = false; // \u30d5\u30e9\u30b0\u3092\u521d\u671f\u5316\n        // \u5185\u5074\u30eb\u30fc\u30d7\uff1a\u672a\u30bd\u30fc\u30c8\u7bc4\u56f2[0, i]\u5185\u306e\u6700\u5927\u8981\u7d20\u3092\u7bc4\u56f2\u306e\u53f3\u7aef\u306b\u4ea4\u63db\n        for (int j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // nums[j]\u3068nums[j + 1]\u3092\u4ea4\u63db\n                // \u3053\u3053\u3067\u306fstd\u306eswap\u3092\u4f7f\u7528\n                swap(nums[j], nums[j + 1]);\n                flag = true; // \u4ea4\u63db\u3055\u308c\u305f\u8981\u7d20\u3092\u8a18\u9332\n            }\n        }\n        if (!flag)\n            break; // \u3053\u306e\u56de\u306e\u300c\u30d0\u30d6\u30ea\u30f3\u30b0\u300d\u3067\u8981\u7d20\u304c\u4ea4\u63db\u3055\u308c\u306a\u304b\u3063\u305f\u5834\u5408\u3001\u7d42\u4e86\n    }\n}\n</code></pre> bubble_sort.java<pre><code>/* \u30d0\u30d6\u30eb\u30bd\u30fc\u30c8\uff08\u30d5\u30e9\u30b0\u306b\u3088\u308b\u6700\u9069\u5316\uff09 */\nvoid bubbleSortWithFlag(int[] nums) {\n    // \u5916\u5074\u30eb\u30fc\u30d7: \u672a\u30bd\u30fc\u30c8\u7bc4\u56f2\u306f [0, i]\n    for (int i = nums.length - 1; i &gt; 0; i--) {\n        boolean flag = false; // \u30d5\u30e9\u30b0\u3092\u521d\u671f\u5316\n        // \u5185\u5074\u30eb\u30fc\u30d7: \u672a\u30bd\u30fc\u30c8\u7bc4\u56f2 [0, i] \u306e\u6700\u5927\u8981\u7d20\u3092\u7bc4\u56f2\u306e\u53f3\u7aef\u306b\u4ea4\u63db\n        for (int j = 0; j &lt; i; j++) {\n            if (nums[j] &gt; nums[j + 1]) {\n                // nums[j] \u3068 nums[j + 1] \u3092\u4ea4\u63db\n                int tmp = nums[j];\n                nums[j] = nums[j + 1];\n                nums[j + 1] = tmp;\n                flag = true; // \u4ea4\u63db\u3055\u308c\u305f\u8981\u7d20\u3092\u8a18\u9332\n            }\n        }\n        if (!flag)\n            break; // \u3053\u306e\u300c\u30d0\u30d6\u30ea\u30f3\u30b0\u300d\u30e9\u30a6\u30f3\u30c9\u3067\u8981\u7d20\u304c\u4ea4\u63db\u3055\u308c\u306a\u304b\u3063\u305f\u5834\u5408\u3001\u7d42\u4e86\n    }\n}\n</code></pre> bubble_sort.cs<pre><code>[class]{bubble_sort}-[func]{BubbleSortWithFlag}\n</code></pre> bubble_sort.go<pre><code>[class]{}-[func]{bubbleSortWithFlag}\n</code></pre> bubble_sort.swift<pre><code>[class]{}-[func]{bubbleSortWithFlag}\n</code></pre> bubble_sort.js<pre><code>[class]{}-[func]{bubbleSortWithFlag}\n</code></pre> bubble_sort.ts<pre><code>[class]{}-[func]{bubbleSortWithFlag}\n</code></pre> bubble_sort.dart<pre><code>[class]{}-[func]{bubbleSortWithFlag}\n</code></pre> bubble_sort.rs<pre><code>[class]{}-[func]{bubble_sort_with_flag}\n</code></pre> bubble_sort.c<pre><code>[class]{}-[func]{bubbleSortWithFlag}\n</code></pre> bubble_sort.kt<pre><code>[class]{}-[func]{bubbleSortWithFlag}\n</code></pre> bubble_sort.rb<pre><code>[class]{}-[func]{bubble_sort_with_flag}\n</code></pre> bubble_sort.zig<pre><code>[class]{}-[func]{bubbleSortWithFlag}\n</code></pre>"},{"location":"chapter_sorting/bubble_sort/#1133","title":"11.3.3 \u00a0 \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u7279\u6027","text":"<ul> <li>\\(O(n^2)\\)\u306e\u6642\u9593\u8a08\u7b97\u91cf\u3001\u9069\u5fdc\u30bd\u30fc\u30c8\u3002 \u5404\u300c\u30d0\u30d6\u30ea\u30f3\u30b0\u300d\u30e9\u30a6\u30f3\u30c9\u306f\u9577\u3055\\(n - 1\\)\u3001\\(n - 2\\)\u3001\\(\\dots\\)\u3001\\(2\\)\u3001\\(1\\)\u306e\u914d\u5217\u30bb\u30b0\u30e1\u30f3\u30c8\u3092\u6a2a\u65ad\u3057\u3001\u5408\u8a08\u306f\\((n - 1) n / 2\\)\u3068\u306a\u308a\u307e\u3059\u3002<code>flag</code>\u6700\u9069\u5316\u306b\u3088\u308a\u3001\u914d\u5217\u304c\u3059\u3067\u306b\u30bd\u30fc\u30c8\u3055\u308c\u3066\u3044\u308b\u5834\u5408\u3001\u6700\u826f\u30b1\u30fc\u30b9\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O(n)\\)\u306b\u9054\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002</li> <li>\\(O(1)\\)\u306e\u7a7a\u9593\u8a08\u7b97\u91cf\u3001\u30a4\u30f3\u30d7\u30ec\u30fc\u30b9\u30bd\u30fc\u30c8\u3002 \u30dd\u30a4\u30f3\u30bf\\(i\\)\u3068\\(j\\)\u306b\u3088\u3063\u3066\u5b9a\u6570\u91cf\u306e\u8ffd\u52a0\u7a7a\u9593\u306e\u307f\u304c\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002</li> <li>\u5b89\u5b9a\u30bd\u30fc\u30c8\u3002 \u7b49\u3057\u3044\u8981\u7d20\u306f\u300c\u30d0\u30d6\u30ea\u30f3\u30b0\u300d\u4e2d\u306b\u4ea4\u63db\u3055\u308c\u306a\u3044\u305f\u3081\u3001\u5143\u306e\u9806\u5e8f\u304c\u4fdd\u6301\u3055\u308c\u3001\u3053\u308c\u306f\u5b89\u5b9a\u30bd\u30fc\u30c8\u306b\u306a\u308a\u307e\u3059\u3002</li> </ul>"},{"location":"chapter_sorting/bucket_sort/","title":"11.8 \u00a0 \u30d0\u30b1\u30c3\u30c8\u30bd\u30fc\u30c8","text":"<p>\u524d\u8ff0\u306e\u30bd\u30fc\u30c8\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u3059\u3079\u3066\u300c\u6bd4\u8f03\u30d9\u30fc\u30b9\u306e\u30bd\u30fc\u30c8\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u300d\u3067\u3001\u5024\u3092\u6bd4\u8f03\u3059\u308b\u3053\u3068\u3067\u8981\u7d20\u3092\u30bd\u30fc\u30c8\u3057\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306a\u30bd\u30fc\u30c8\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f \\(O(n \\log n)\\) \u3088\u308a\u826f\u3044\u6642\u9593\u8a08\u7b97\u91cf\u3092\u6301\u3064\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093\u3002\u6b21\u306b\u3001\u7dda\u5f62\u6642\u9593\u8a08\u7b97\u91cf\u3092\u9054\u6210\u3067\u304d\u308b\u3044\u304f\u3064\u304b\u306e\u300c\u975e\u6bd4\u8f03\u30bd\u30fc\u30c8\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u300d\u306b\u3064\u3044\u3066\u8b70\u8ad6\u3057\u307e\u3059\u3002</p> <p>\u30d0\u30b1\u30c3\u30c8\u30bd\u30fc\u30c8\u306f\u5206\u5272\u7d71\u6cbb\u6226\u7565\u306e\u5178\u578b\u7684\u306a\u5fdc\u7528\u3067\u3059\u3002\u4e00\u9023\u306e\u9806\u5e8f\u4ed8\u3051\u3089\u308c\u305f\u30d0\u30b1\u30c3\u30c8\u3092\u8a2d\u5b9a\u3057\u3001\u5404\u30d0\u30b1\u30c3\u30c8\u304c\u30c7\u30fc\u30bf\u306e\u7bc4\u56f2\u3092\u542b\u307f\u3001\u5165\u529b\u30c7\u30fc\u30bf\u3092\u3053\u308c\u3089\u306e\u30d0\u30b1\u30c3\u30c8\u306b\u5747\u7b49\u306b\u5206\u6563\u3055\u305b\u308b\u3053\u3068\u3067\u52d5\u4f5c\u3057\u307e\u3059\u3002\u305d\u3057\u3066\u3001\u5404\u30d0\u30b1\u30c3\u30c8\u5185\u306e\u30c7\u30fc\u30bf\u3092\u500b\u5225\u306b\u30bd\u30fc\u30c8\u3057\u307e\u3059\u3002\u6700\u5f8c\u306b\u3001\u3059\u3079\u3066\u306e\u30d0\u30b1\u30c3\u30c8\u304b\u3089\u306e\u30bd\u30fc\u30c8\u6e08\u307f\u30c7\u30fc\u30bf\u3092\u9806\u6b21\u30de\u30fc\u30b8\u3057\u3066\u6700\u7d42\u7d50\u679c\u3092\u751f\u6210\u3057\u307e\u3059\u3002</p>"},{"location":"chapter_sorting/bucket_sort/#1181","title":"11.8.1 \u00a0 \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u904e\u7a0b","text":"<p>\u9577\u3055 \\(n\\) \u306e\u914d\u5217\u3067\u3001\\([0, 1)\\) \u306e\u7bc4\u56f2\u306e\u6d6e\u52d5\u5c0f\u6570\u70b9\u6570\u3092\u8003\u3048\u3066\u307f\u307e\u3059\u3002\u30d0\u30b1\u30c3\u30c8\u30bd\u30fc\u30c8\u306e\u904e\u7a0b\u306f\u4ee5\u4e0b\u306e\u56f3\u306b\u793a\u3055\u308c\u3066\u3044\u307e\u3059\u3002</p> <ol> <li>\\(k\\) \u500b\u306e\u30d0\u30b1\u30c3\u30c8\u3092\u521d\u671f\u5316\u3057\u3001\\(n\\) \u500b\u306e\u8981\u7d20\u3092\u3053\u308c\u3089\u306e \\(k\\) \u500b\u306e\u30d0\u30b1\u30c3\u30c8\u306b\u5206\u6563\u3055\u305b\u307e\u3059\u3002</li> <li>\u5404\u30d0\u30b1\u30c3\u30c8\u3092\u500b\u5225\u306b\u30bd\u30fc\u30c8\u3057\u307e\u3059\uff08\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u306e\u7d44\u307f\u8fbc\u307f\u30bd\u30fc\u30c8\u95a2\u6570\u3092\u4f7f\u7528\uff09\u3002</li> <li>\u6700\u5c0f\u304b\u3089\u6700\u5927\u306e\u30d0\u30b1\u30c3\u30c8\u306e\u9806\u5e8f\u3067\u7d50\u679c\u3092\u30de\u30fc\u30b8\u3057\u307e\u3059\u3002</li> </ol> <p></p> <p> \u56f3 11-13 \u00a0 \u30d0\u30b1\u30c3\u30c8\u30bd\u30fc\u30c8\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u904e\u7a0b </p> <p>\u30b3\u30fc\u30c9\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig bucket_sort.py<pre><code>def bucket_sort(nums: list[float]):\n    \"\"\"\u30d0\u30b1\u30c3\u30c8\u30bd\u30fc\u30c8\"\"\"\n    # k = n/2 \u500b\u306e\u30d0\u30b1\u30c3\u30c8\u3092\u521d\u671f\u5316\u3001\u5404\u30d0\u30b1\u30c3\u30c8\u306b\u5e73\u57472\u500b\u306e\u8981\u7d20\u3092\u914d\u7f6e\u3059\u308b\u3053\u3068\u3092\u671f\u5f85\n    k = len(nums) // 2\n    buckets = [[] for _ in range(k)]\n    # 1. \u914d\u5217\u8981\u7d20\u3092\u5404\u30d0\u30b1\u30c3\u30c8\u306b\u5206\u6563\n    for num in nums:\n        # \u5165\u529b\u30c7\u30fc\u30bf\u7bc4\u56f2\u306f [0, 1)\u3001num * k \u3092\u4f7f\u7528\u3057\u3066\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u7bc4\u56f2 [0, k-1] \u306b\u30de\u30c3\u30d4\u30f3\u30b0\n        i = int(num * k)\n        # num \u3092\u30d0\u30b1\u30c3\u30c8 i \u306b\u8ffd\u52a0\n        buckets[i].append(num)\n    # 2. \u5404\u30d0\u30b1\u30c3\u30c8\u3092\u30bd\u30fc\u30c8\n    for bucket in buckets:\n        # \u7d44\u307f\u8fbc\u307f\u30bd\u30fc\u30c8\u95a2\u6570\u3092\u4f7f\u7528\u3001\u4ed6\u306e\u30bd\u30fc\u30c8\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306b\u7f6e\u304d\u63db\u3048\u308b\u3053\u3068\u3082\u53ef\u80fd\n        bucket.sort()\n    # 3. \u30d0\u30b1\u30c3\u30c8\u3092\u8d70\u67fb\u3057\u3066\u7d50\u679c\u3092\u30de\u30fc\u30b8\n    i = 0\n    for bucket in buckets:\n        for num in bucket:\n            nums[i] = num\n            i += 1\n</code></pre> bucket_sort.cpp<pre><code>/* \u30d0\u30b1\u30c3\u30c8\u30bd\u30fc\u30c8 */\nvoid bucketSort(vector&lt;float&gt; &amp;nums) {\n    // k = n/2\u500b\u306e\u30d0\u30b1\u30c3\u30c8\u3092\u521d\u671f\u5316\u3001\u5404\u30d0\u30b1\u30c3\u30c8\u306b2\u3064\u306e\u8981\u7d20\u3092\u5272\u308a\u5f53\u3066\u308b\u3053\u3068\u3092\u671f\u5f85\n    int k = nums.size() / 2;\n    vector&lt;vector&lt;float&gt;&gt; buckets(k);\n    // 1. \u914d\u5217\u8981\u7d20\u3092\u5404\u30d0\u30b1\u30c3\u30c8\u306b\u5206\u914d\n    for (float num : nums) {\n        // \u5165\u529b\u30c7\u30fc\u30bf\u7bc4\u56f2\u306f[0, 1)\u3001num * k\u3092\u4f7f\u7528\u3057\u3066\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u7bc4\u56f2[0, k-1]\u306b\u30de\u30c3\u30d7\n        int i = num * k;\n        // bucket_idx\u30d0\u30b1\u30c3\u30c8\u306b\u6570\u5024\u3092\u8ffd\u52a0\n        buckets[i].push_back(num);\n    }\n    // 2. \u5404\u30d0\u30b1\u30c3\u30c8\u3092\u30bd\u30fc\u30c8\n    for (vector&lt;float&gt; &amp;bucket : buckets) {\n        // \u7d44\u307f\u8fbc\u307f\u30bd\u30fc\u30c8\u95a2\u6570\u3092\u4f7f\u7528\u3001\u4ed6\u306e\u30bd\u30fc\u30c8\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306b\u7f6e\u304d\u63db\u3048\u308b\u3053\u3068\u3082\u53ef\u80fd\n        sort(bucket.begin(), bucket.end());\n    }\n    // 3. \u30d0\u30b1\u30c3\u30c8\u3092\u8d70\u67fb\u3057\u3066\u7d50\u679c\u3092\u30de\u30fc\u30b8\n    int i = 0;\n    for (vector&lt;float&gt; &amp;bucket : buckets) {\n        for (float num : bucket) {\n            nums[i++] = num;\n        }\n    }\n}\n</code></pre> bucket_sort.java<pre><code>/* \u30d0\u30b1\u30c3\u30c8\u30bd\u30fc\u30c8 */\nvoid bucketSort(float[] nums) {\n    // k = n/2 \u500b\u306e\u30d0\u30b1\u30c3\u30c8\u3092\u521d\u671f\u5316\u3001\u5404\u30d0\u30b1\u30c3\u30c8\u306b\u671f\u5f85\u3055\u308c\u308b\u8981\u7d20\u6570\u306f 2 \u500b\n    int k = nums.length / 2;\n    List&lt;List&lt;Float&gt;&gt; buckets = new ArrayList&lt;&gt;();\n    for (int i = 0; i &lt; k; i++) {\n        buckets.add(new ArrayList&lt;&gt;());\n    }\n    // 1. \u914d\u5217\u8981\u7d20\u3092\u5404\u30d0\u30b1\u30c3\u30c8\u306b\u5206\u6563\n    for (float num : nums) {\n        // \u5165\u529b\u30c7\u30fc\u30bf\u7bc4\u56f2\u306f [0, 1)\u3001num * k \u3092\u4f7f\u3063\u3066\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u7bc4\u56f2 [0, k-1] \u306b\u30de\u30c3\u30d4\u30f3\u30b0\n        int i = (int) (num * k);\n        // num \u3092\u30d0\u30b1\u30c3\u30c8 i \u306b\u8ffd\u52a0\n        buckets.get(i).add(num);\n    }\n    // 2. \u5404\u30d0\u30b1\u30c3\u30c8\u3092\u30bd\u30fc\u30c8\n    for (List&lt;Float&gt; bucket : buckets) {\n        // \u7d44\u307f\u8fbc\u307f\u30bd\u30fc\u30c8\u95a2\u6570\u3092\u4f7f\u7528\u3001\u4ed6\u306e\u30bd\u30fc\u30c8\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306b\u7f6e\u304d\u63db\u3048\u308b\u3053\u3068\u3082\u53ef\u80fd\n        Collections.sort(bucket);\n    }\n    // 3. \u30d0\u30b1\u30c3\u30c8\u3092\u8d70\u67fb\u3057\u3066\u7d50\u679c\u3092\u30de\u30fc\u30b8\n    int i = 0;\n    for (List&lt;Float&gt; bucket : buckets) {\n        for (float num : bucket) {\n            nums[i++] = num;\n        }\n    }\n}\n</code></pre> bucket_sort.cs<pre><code>[class]{bucket_sort}-[func]{BucketSort}\n</code></pre> bucket_sort.go<pre><code>[class]{}-[func]{bucketSort}\n</code></pre> bucket_sort.swift<pre><code>[class]{}-[func]{bucketSort}\n</code></pre> bucket_sort.js<pre><code>[class]{}-[func]{bucketSort}\n</code></pre> bucket_sort.ts<pre><code>[class]{}-[func]{bucketSort}\n</code></pre> bucket_sort.dart<pre><code>[class]{}-[func]{bucketSort}\n</code></pre> bucket_sort.rs<pre><code>[class]{}-[func]{bucket_sort}\n</code></pre> bucket_sort.c<pre><code>[class]{}-[func]{bucketSort}\n</code></pre> bucket_sort.kt<pre><code>[class]{}-[func]{bucketSort}\n</code></pre> bucket_sort.rb<pre><code>[class]{}-[func]{bucket_sort}\n</code></pre> bucket_sort.zig<pre><code>[class]{}-[func]{bucketSort}\n</code></pre>"},{"location":"chapter_sorting/bucket_sort/#1182","title":"11.8.2 \u00a0 \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u7279\u5fb4","text":"<p>\u30d0\u30b1\u30c3\u30c8\u30bd\u30fc\u30c8\u306f\u975e\u5e38\u306b\u5927\u304d\u306a\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u306e\u51e6\u7406\u306b\u9069\u3057\u3066\u3044\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u5165\u529b\u30c7\u30fc\u30bf\u306b100\u4e07\u500b\u306e\u8981\u7d20\u304c\u542b\u307e\u308c\u3001\u30b7\u30b9\u30c6\u30e0\u30e1\u30e2\u30ea\u306e\u5236\u9650\u306b\u3088\u308a\u3059\u3079\u3066\u306e\u30c7\u30fc\u30bf\u3092\u540c\u6642\u306b\u30ed\u30fc\u30c9\u3067\u304d\u306a\u3044\u5834\u5408\u3001\u30c7\u30fc\u30bf\u30921,000\u500b\u306e\u30d0\u30b1\u30c3\u30c8\u306b\u5206\u5272\u3057\u3001\u5404\u30d0\u30b1\u30c3\u30c8\u3092\u500b\u5225\u306b\u30bd\u30fc\u30c8\u3057\u3066\u304b\u3089\u7d50\u679c\u3092\u30de\u30fc\u30b8\u3067\u304d\u307e\u3059\u3002</p> <ul> <li>\u6642\u9593\u8a08\u7b97\u91cf\u306f \\(O(n + k)\\)\uff1a\u8981\u7d20\u304c\u30d0\u30b1\u30c3\u30c8\u9593\u3067\u5747\u7b49\u306b\u5206\u6563\u3055\u308c\u3066\u3044\u308b\u3068\u4eee\u5b9a\u3059\u308b\u3068\u3001\u5404\u30d0\u30b1\u30c3\u30c8\u5185\u306e\u8981\u7d20\u6570\u306f \\(n/k\\) \u3067\u3059\u3002\u5358\u4e00\u306e\u30d0\u30b1\u30c3\u30c8\u306e\u30bd\u30fc\u30c8\u306b \\(O(n/k \\log(n/k))\\) \u6642\u9593\u304c\u304b\u304b\u308b\u3068\u4eee\u5b9a\u3059\u308b\u3068\u3001\u3059\u3079\u3066\u306e\u30d0\u30b1\u30c3\u30c8\u306e\u30bd\u30fc\u30c8\u306b \\(O(n \\log(n/k))\\) \u6642\u9593\u304c\u304b\u304b\u308a\u307e\u3059\u3002\u30d0\u30b1\u30c3\u30c8\u6570 \\(k\\) \u304c\u6bd4\u8f03\u7684\u5927\u304d\u3044\u3068\u304d\u3001\u6642\u9593\u8a08\u7b97\u91cf\u306f \\(O(n)\\) \u306b\u8fd1\u3065\u304d\u307e\u3059\u3002\u7d50\u679c\u306e\u30de\u30fc\u30b8\u306b\u306f\u3001\u3059\u3079\u3066\u306e\u30d0\u30b1\u30c3\u30c8\u3068\u8981\u7d20\u3092\u8d70\u67fb\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u3001\\(O(n + k)\\) \u6642\u9593\u304c\u304b\u304b\u308a\u307e\u3059\u3002\u6700\u60aa\u306e\u5834\u5408\u3001\u3059\u3079\u3066\u306e\u30c7\u30fc\u30bf\u304c\u5358\u4e00\u306e\u30d0\u30b1\u30c3\u30c8\u306b\u5206\u6563\u3055\u308c\u3001\u305d\u306e\u30d0\u30b1\u30c3\u30c8\u306e\u30bd\u30fc\u30c8\u306b\u306f \\(O(n^2)\\) \u6642\u9593\u304c\u304b\u304b\u308a\u307e\u3059\u3002</li> <li>\u7a7a\u9593\u8a08\u7b97\u91cf\u306f \\(O(n + k)\\)\u3001\u975e\u30a4\u30f3\u30d7\u30ec\u30fc\u30b9\u30bd\u30fc\u30c8\uff1a\\(k\\) \u500b\u306e\u30d0\u30b1\u30c3\u30c8\u3068\u5408\u8a08 \\(n\\) \u500b\u306e\u8981\u7d20\u306e\u305f\u3081\u306e\u8ffd\u52a0\u30b9\u30da\u30fc\u30b9\u304c\u5fc5\u8981\u3067\u3059\u3002</li> <li>\u30d0\u30b1\u30c3\u30c8\u30bd\u30fc\u30c8\u304c\u5b89\u5b9a\u304b\u3069\u3046\u304b\u306f\u3001\u5404\u30d0\u30b1\u30c3\u30c8\u5185\u3067\u4f7f\u7528\u3055\u308c\u308b\u30bd\u30fc\u30c8\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u304c\u5b89\u5b9a\u304b\u3069\u3046\u304b\u306b\u4f9d\u5b58\u3057\u307e\u3059\u3002</li> </ul>"},{"location":"chapter_sorting/bucket_sort/#1183","title":"11.8.3 \u00a0 \u5747\u7b49\u5206\u6563\u3092\u9054\u6210\u3059\u308b\u65b9\u6cd5","text":"<p>\u30d0\u30b1\u30c3\u30c8\u30bd\u30fc\u30c8\u306e\u7406\u8ad6\u7684\u6642\u9593\u8a08\u7b97\u91cf\u306f \\(O(n)\\) \u306b\u9054\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u91cd\u8981\u306a\u3053\u3068\u306f\u3001\u3059\u3079\u3066\u306e\u30d0\u30b1\u30c3\u30c8\u306b\u8981\u7d20\u3092\u5747\u7b49\u306b\u5206\u6563\u3055\u305b\u308b\u3053\u3068\u3067\u3059\u3002\u5b9f\u4e16\u754c\u306e\u30c7\u30fc\u30bf\u306f\u3057\u3070\u3057\u3070\u5747\u4e00\u306b\u5206\u6563\u3055\u308c\u3066\u3044\u306a\u3044\u304b\u3089\u3067\u3059\u3002\u4f8b\u3048\u3070\u3001eBay\u306e\u3059\u3079\u3066\u306e\u5546\u54c1\u3092\u4fa1\u683c\u7bc4\u56f2\u306710\u500b\u306e\u30d0\u30b1\u30c3\u30c8\u306b\u5747\u7b49\u306b\u5206\u6563\u3055\u305b\u305f\u3044\u3068\u3057\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u5546\u54c1\u4fa1\u683c\u306e\u5206\u6563\u306f\u5747\u7b49\u3067\u306a\u3044\u53ef\u80fd\u6027\u304c\u3042\u308a\u3001100\u30c9\u30eb\u672a\u6e80\u306e\u5546\u54c1\u304c\u591a\u304f\u3001500\u30c9\u30eb\u4ee5\u4e0a\u306e\u5546\u54c1\u304c\u5c11\u306a\u3044\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u3002\u4fa1\u683c\u7bc4\u56f2\u3092\u5747\u7b49\u306b10\u5206\u5272\u3059\u308b\u3068\u3001\u5404\u30d0\u30b1\u30c3\u30c8\u306e\u5546\u54c1\u6570\u306e\u5dee\u304c\u5927\u304d\u304f\u306a\u308a\u307e\u3059\u3002</p> <p>\u5747\u7b49\u5206\u6563\u3092\u9054\u6210\u3059\u308b\u305f\u3081\u306b\u3001\u6700\u521d\u306b\u304a\u304a\u3088\u305d\u306e\u5883\u754c\u3092\u8a2d\u5b9a\u3057\u3066\u3001\u30c7\u30fc\u30bf\u30923\u3064\u306e\u30d0\u30b1\u30c3\u30c8\u306b\u5927\u307e\u304b\u306b\u5206\u5272\u3067\u304d\u307e\u3059\u3002\u5206\u6563\u304c\u5b8c\u4e86\u3057\u305f\u5f8c\u3001\u3088\u308a\u591a\u304f\u306e\u30a2\u30a4\u30c6\u30e0\u3092\u6301\u3064\u30d0\u30b1\u30c3\u30c8\u3092\u3055\u3089\u306b3\u3064\u306e\u30d0\u30b1\u30c3\u30c8\u306b\u5206\u5272\u3057\u3001\u3059\u3079\u3066\u306e\u30d0\u30b1\u30c3\u30c8\u306e\u8981\u7d20\u6570\u304c\u307b\u307c\u7b49\u3057\u304f\u306a\u308b\u307e\u3067\u7d9a\u3051\u307e\u3059\u3002</p> <p>\u4ee5\u4e0b\u306e\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u3053\u306e\u65b9\u6cd5\u306f\u672c\u8cea\u7684\u306b\u518d\u5e30\u6728\u3092\u69cb\u7bc9\u3057\u3001\u8449\u30ce\u30fc\u30c9\u306e\u8981\u7d20\u6570\u304c\u3067\u304d\u308b\u3060\u3051\u5747\u7b49\u306b\u306a\u308b\u3053\u3068\u3092\u76ee\u6307\u3057\u307e\u3059\u3002\u3082\u3061\u308d\u3093\u3001\u5404\u30e9\u30a6\u30f3\u30c9\u3067\u30c7\u30fc\u30bf\u30923\u3064\u306e\u30d0\u30b1\u30c3\u30c8\u306b\u5206\u5272\u3059\u308b\u5fc5\u8981\u306f\u3042\u308a\u307e\u305b\u3093 - \u5206\u5272\u6226\u7565\u306f\u30c7\u30fc\u30bf\u306e\u72ec\u7279\u306a\u7279\u6027\u306b\u9069\u5fdc\u7684\u306b\u8abf\u6574\u3067\u304d\u307e\u3059\u3002</p> <p></p> <p> \u56f3 11-14 \u00a0 \u30d0\u30b1\u30c3\u30c8\u306e\u518d\u5e30\u7684\u5206\u5272 </p> <p>\u5546\u54c1\u4fa1\u683c\u306e\u78ba\u7387\u5206\u5e03\u3092\u4e8b\u524d\u306b\u77e5\u3063\u3066\u3044\u308b\u5834\u5408\u3001\u30c7\u30fc\u30bf\u306e\u78ba\u7387\u5206\u5e03\u306b\u57fa\u3065\u3044\u3066\u5404\u30d0\u30b1\u30c3\u30c8\u306e\u4fa1\u683c\u5883\u754c\u3092\u8a2d\u5b9a\u3067\u304d\u307e\u3059\u3002\u30c7\u30fc\u30bf\u5206\u5e03\u3092\u5177\u4f53\u7684\u306b\u8a08\u7b97\u3059\u308b\u5fc5\u8981\u306f\u5fc5\u305a\u3057\u3082\u306a\u304f\u3001\u4ee3\u308f\u308a\u306b\u78ba\u7387\u30e2\u30c7\u30eb\u3092\u4f7f\u7528\u3057\u3066\u30c7\u30fc\u30bf\u7279\u6027\u306b\u57fa\u3065\u3044\u3066\u8fd1\u4f3c\u3067\u304d\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002</p> <p>\u4ee5\u4e0b\u306e\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u5546\u54c1\u4fa1\u683c\u304c\u6b63\u898f\u5206\u5e03\u306b\u5f93\u3046\u3068\u4eee\u5b9a\u3059\u308b\u3068\u3001\u30d0\u30b1\u30c3\u30c8\u9593\u3067\u30a2\u30a4\u30c6\u30e0\u306e\u5206\u6563\u306e\u30d0\u30e9\u30f3\u30b9\u3092\u53d6\u308b\u305f\u3081\u306b\u5408\u7406\u7684\u306a\u4fa1\u683c\u533a\u9593\u3092\u5b9a\u7fa9\u3067\u304d\u307e\u3059\u3002</p> <p></p> <p> \u56f3 11-15 \u00a0 \u78ba\u7387\u5206\u5e03\u306b\u57fa\u3065\u304f\u30d0\u30b1\u30c3\u30c8\u5206\u5272 </p>"},{"location":"chapter_sorting/counting_sort/","title":"11.9 \u00a0 \u8a08\u6570\u30bd\u30fc\u30c8","text":"<p>\u8a08\u6570\u30bd\u30fc\u30c8\u306f\u8981\u7d20\u306e\u6570\u3092\u30ab\u30a6\u30f3\u30c8\u3059\u308b\u3053\u3068\u3067\u30bd\u30fc\u30c8\u3092\u5b9f\u73fe\u3057\u3001\u901a\u5e38\u306f\u6574\u6570\u914d\u5217\u306b\u9069\u7528\u3055\u308c\u307e\u3059\u3002</p>"},{"location":"chapter_sorting/counting_sort/#1191","title":"11.9.1 \u00a0 \u7c21\u5358\u306a\u5b9f\u88c5","text":"<p>\u7c21\u5358\u306a\u4f8b\u304b\u3089\u59cb\u3081\u307e\u3057\u3087\u3046\u3002\u9577\u3055 \\(n\\) \u306e\u914d\u5217 <code>nums</code> \u304c\u4e0e\u3048\u3089\u308c\u3001\u3059\u3079\u3066\u306e\u8981\u7d20\u304c\u300c\u975e\u8ca0\u6574\u6570\u300d\u3067\u3042\u308b\u5834\u5408\u3001\u8a08\u6570\u30bd\u30fc\u30c8\u306e\u5168\u4f53\u7684\u306a\u904e\u7a0b\u306f\u4ee5\u4e0b\u306e\u56f3\u306b\u793a\u3055\u308c\u3066\u3044\u307e\u3059\u3002</p> <ol> <li>\u914d\u5217\u3092\u8d70\u67fb\u3057\u3066\u6700\u5927\u6570\u3092\u898b\u3064\u3051\u3001\u305d\u308c\u3092 \\(m\\) \u3068\u3057\u3001\u9577\u3055 \\(m + 1\\) \u306e\u88dc\u52a9\u914d\u5217 <code>counter</code> \u3092\u4f5c\u6210\u3057\u307e\u3059\u3002</li> <li><code>counter</code> \u3092\u4f7f\u7528\u3057\u3066 <code>nums</code> \u5185\u306e\u5404\u6570\u306e\u51fa\u73fe\u56de\u6570\u3092\u30ab\u30a6\u30f3\u30c8\u3057\u307e\u3059\u3002\u3053\u3053\u3067 <code>counter[num]</code> \u306f\u6570 <code>num</code> \u306e\u51fa\u73fe\u56de\u6570\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002\u30ab\u30a6\u30f3\u30c8\u65b9\u6cd5\u306f\u7c21\u5358\u3067\u3001<code>nums</code> \u3092\u8d70\u67fb\u3057\uff08\u73fe\u5728\u306e\u6570\u3092 <code>num</code> \u3068\u3059\u308b\uff09\u3001\u5404\u30e9\u30a6\u30f3\u30c9\u3067 <code>counter[num]</code> \u3092 \\(1\\) \u5897\u3084\u3057\u307e\u3059\u3002</li> <li><code>counter</code> \u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306f\u81ea\u7136\u306b\u9806\u5e8f\u4ed8\u3051\u3089\u308c\u3066\u3044\u308b\u305f\u3081\u3001\u3059\u3079\u3066\u306e\u6570\u306f\u672c\u8cea\u7684\u306b\u3059\u3067\u306b\u30bd\u30fc\u30c8\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u6b21\u306b\u3001<code>counter</code> \u3092\u8d70\u67fb\u3057\u3001\u51fa\u73fe\u9806\u306b <code>nums</code> \u3092\u6607\u9806\u3067\u57cb\u3081\u307e\u3059\u3002</li> </ol> <p></p> <p> \u56f3 11-16 \u00a0 \u8a08\u6570\u30bd\u30fc\u30c8\u306e\u904e\u7a0b </p> <p>\u30b3\u30fc\u30c9\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig counting_sort.py<pre><code>def counting_sort_naive(nums: list[int]):\n    \"\"\"\u8a08\u6570\u30bd\u30fc\u30c8\"\"\"\n    # \u30b7\u30f3\u30d7\u30eb\u306a\u5b9f\u88c5\u3001\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u306e\u30bd\u30fc\u30c8\u306b\u306f\u4f7f\u7528\u3067\u304d\u306a\u3044\n    # 1. \u914d\u5217\u5185\u306e\u6700\u5927\u8981\u7d20 m \u3092\u7d71\u8a08\n    m = 0\n    for num in nums:\n        m = max(m, num)\n    # 2. \u5404\u6570\u5b57\u306e\u51fa\u73fe\u56de\u6570\u3092\u7d71\u8a08\n    # counter[num] \u306f num \u306e\u51fa\u73fe\u56de\u6570\u3092\u8868\u3059\n    counter = [0] * (m + 1)\n    for num in nums:\n        counter[num] += 1\n    # 3. counter \u3092\u8d70\u67fb\u3057\u3001\u5404\u8981\u7d20\u3092\u5143\u306e\u914d\u5217 nums \u306b\u57cb\u3081\u623b\u3057\n    i = 0\n    for num in range(m + 1):\n        for _ in range(counter[num]):\n            nums[i] = num\n            i += 1\n</code></pre> counting_sort.cpp<pre><code>/* \u30ab\u30a6\u30f3\u30c8\u30bd\u30fc\u30c8 */\n// \u7c21\u5358\u306a\u5b9f\u88c5\u3001\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u306e\u30bd\u30fc\u30c8\u306b\u306f\u4f7f\u7528\u3067\u304d\u306a\u3044\nvoid countingSortNaive(vector&lt;int&gt; &amp;nums) {\n    // 1. \u914d\u5217\u306e\u6700\u5927\u8981\u7d20m\u3092\u7d71\u8a08\n    int m = 0;\n    for (int num : nums) {\n        m = max(m, num);\n    }\n    // 2. \u5404\u6570\u5b57\u306e\u51fa\u73fe\u56de\u6570\u3092\u7d71\u8a08\n    // counter[num]\u306fnum\u306e\u51fa\u73fe\u56de\u6570\u3092\u8868\u3059\n    vector&lt;int&gt; counter(m + 1, 0);\n    for (int num : nums) {\n        counter[num]++;\n    }\n    // 3. counter\u3092\u8d70\u67fb\u3057\u3001\u5404\u8981\u7d20\u3092\u5143\u306e\u914d\u5217nums\u306b\u623b\u3059\n    int i = 0;\n    for (int num = 0; num &lt; m + 1; num++) {\n        for (int j = 0; j &lt; counter[num]; j++, i++) {\n            nums[i] = num;\n        }\n    }\n}\n</code></pre> counting_sort.java<pre><code>/* \u8a08\u6570\u30bd\u30fc\u30c8 */\n// \u7c21\u5358\u306a\u5b9f\u88c5\u3001\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u306e\u30bd\u30fc\u30c8\u306b\u306f\u4f7f\u7528\u3067\u304d\u306a\u3044\nvoid countingSortNaive(int[] nums) {\n    // 1. \u914d\u5217\u306e\u6700\u5927\u8981\u7d20 m \u3092\u7d71\u8a08\n    int m = 0;\n    for (int num : nums) {\n        m = Math.max(m, num);\n    }\n    // 2. \u5404\u6570\u5b57\u306e\u51fa\u73fe\u56de\u6570\u3092\u7d71\u8a08\n    // counter[num] \u306f num \u306e\u51fa\u73fe\u56de\u6570\u3092\u8868\u3059\n    int[] counter = new int[m + 1];\n    for (int num : nums) {\n        counter[num]++;\n    }\n    // 3. counter \u3092\u8d70\u67fb\u3057\u3001\u5404\u8981\u7d20\u3092\u5143\u306e\u914d\u5217 nums \u306b\u623b\u3059\n    int i = 0;\n    for (int num = 0; num &lt; m + 1; num++) {\n        for (int j = 0; j &lt; counter[num]; j++, i++) {\n            nums[i] = num;\n        }\n    }\n}\n</code></pre> counting_sort.cs<pre><code>[class]{counting_sort}-[func]{CountingSortNaive}\n</code></pre> counting_sort.go<pre><code>[class]{}-[func]{countingSortNaive}\n</code></pre> counting_sort.swift<pre><code>[class]{}-[func]{countingSortNaive}\n</code></pre> counting_sort.js<pre><code>[class]{}-[func]{countingSortNaive}\n</code></pre> counting_sort.ts<pre><code>[class]{}-[func]{countingSortNaive}\n</code></pre> counting_sort.dart<pre><code>[class]{}-[func]{countingSortNaive}\n</code></pre> counting_sort.rs<pre><code>[class]{}-[func]{counting_sort_naive}\n</code></pre> counting_sort.c<pre><code>[class]{}-[func]{countingSortNaive}\n</code></pre> counting_sort.kt<pre><code>[class]{}-[func]{countingSortNaive}\n</code></pre> counting_sort.rb<pre><code>[class]{}-[func]{counting_sort_naive}\n</code></pre> counting_sort.zig<pre><code>[class]{}-[func]{countingSortNaive}\n</code></pre> <p>\u8a08\u6570\u30bd\u30fc\u30c8\u3068\u30d0\u30b1\u30c3\u30c8\u30bd\u30fc\u30c8\u306e\u95a2\u4fc2</p> <p>\u30d0\u30b1\u30c3\u30c8\u30bd\u30fc\u30c8\u306e\u89b3\u70b9\u304b\u3089\u3001\u8a08\u6570\u30bd\u30fc\u30c8\u306b\u304a\u3051\u308b\u8a08\u6570\u914d\u5217 <code>counter</code> \u306e\u5404\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u30d0\u30b1\u30c3\u30c8\u3068\u8003\u3048\u3001\u30ab\u30a6\u30f3\u30c8\u306e\u904e\u7a0b\u3092\u8981\u7d20\u3092\u5bfe\u5fdc\u3059\u308b\u30d0\u30b1\u30c3\u30c8\u306b\u5206\u6563\u3055\u305b\u308b\u3053\u3068\u3068\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u672c\u8cea\u7684\u306b\u3001\u8a08\u6570\u30bd\u30fc\u30c8\u306f\u6574\u6570\u30c7\u30fc\u30bf\u306e\u305f\u3081\u306e\u30d0\u30b1\u30c3\u30c8\u30bd\u30fc\u30c8\u306e\u7279\u5225\u306a\u30b1\u30fc\u30b9\u3067\u3059\u3002</p>"},{"location":"chapter_sorting/counting_sort/#1192","title":"11.9.2 \u00a0 \u5b8c\u5168\u306a\u5b9f\u88c5","text":"<p>\u6ce8\u610f\u6df1\u3044\u8aad\u8005\u306f\u6c17\u4ed8\u304f\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u304c\u3001\u5165\u529b\u30c7\u30fc\u30bf\u304c\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u306e\u5834\u5408\u3001\u4e0a\u8a18\u306e\u624b\u9806 <code>3.</code> \u306f\u7121\u52b9\u3067\u3059\u3002\u5165\u529b\u30c7\u30fc\u30bf\u304c\u5546\u54c1\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u3067\u3001\u4fa1\u683c\uff08\u30af\u30e9\u30b9\u30e1\u30f3\u30d0\u5909\u6570\uff09\u3067\u5546\u54c1\u3092\u30bd\u30fc\u30c8\u3057\u305f\u3044\u3068\u3057\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u4e0a\u8a18\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u7d50\u679c\u3068\u3057\u3066\u30bd\u30fc\u30c8\u6e08\u307f\u306e\u4fa1\u683c\u306e\u307f\u3092\u63d0\u4f9b\u3067\u304d\u307e\u3059\u3002</p> <p>\u3067\u306f\u3001\u5143\u306e\u30c7\u30fc\u30bf\u306e\u30bd\u30fc\u30c8\u7d50\u679c\u3092\u3069\u306e\u3088\u3046\u306b\u53d6\u5f97\u3067\u304d\u308b\u3067\u3057\u3087\u3046\u304b\uff1f\u307e\u305a\u3001<code>counter</code> \u306e\u300c\u524d\u7f6e\u548c\u300d\u3092\u8a08\u7b97\u3057\u307e\u3059\u3002\u540d\u524d\u304c\u793a\u3059\u3088\u3046\u306b\u3001\u30a4\u30f3\u30c7\u30c3\u30af\u30b9 <code>i</code> \u3067\u306e\u524d\u7f6e\u548c <code>prefix[i]</code> \u306f\u3001\u914d\u5217\u306e\u6700\u521d\u306e <code>i</code> \u500b\u306e\u8981\u7d20\u306e\u548c\u306b\u7b49\u3057\u3044\u3067\u3059\uff1a</p> \\[ \\text{prefix}[i] = \\sum_{j=0}^i \\text{counter[j]} \\] <p>\u524d\u7f6e\u548c\u306b\u306f\u660e\u78ba\u306a\u610f\u5473\u304c\u3042\u308a\u307e\u3059\u3002<code>prefix[num] - 1</code> \u306f\u7d50\u679c\u914d\u5217 <code>res</code> \u306b\u304a\u3051\u308b\u8981\u7d20 <code>num</code> \u306e\u6700\u5f8c\u306e\u51fa\u73fe\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8868\u3057\u307e\u3059\u3002\u3053\u306e\u60c5\u5831\u306f\u91cd\u8981\u3067\u3001\u5404\u8981\u7d20\u304c\u7d50\u679c\u914d\u5217\u306e\u3069\u3053\u306b\u73fe\u308c\u308b\u3079\u304d\u304b\u3092\u6559\u3048\u3066\u304f\u308c\u307e\u3059\u3002\u6b21\u306b\u3001\u5143\u306e\u914d\u5217 <code>nums</code> \u306e\u5404\u8981\u7d20 <code>num</code> \u3092\u9006\u9806\u3067\u8d70\u67fb\u3057\u3001\u5404\u53cd\u5fa9\u3067\u4ee5\u4e0b\u306e2\u3064\u306e\u624b\u9806\u3092\u5b9f\u884c\u3057\u307e\u3059\u3002</p> <ol> <li>\u30a4\u30f3\u30c7\u30c3\u30af\u30b9 <code>prefix[num] - 1</code> \u3067\u914d\u5217 <code>res</code> \u306b <code>num</code> \u3092\u57cb\u3081\u307e\u3059\u3002</li> <li>\u524d\u7f6e\u548c <code>prefix[num]</code> \u3092 \\(1\\) \u6e1b\u3089\u3057\u3066\u3001<code>num</code> \u3092\u914d\u7f6e\u3059\u308b\u6b21\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u53d6\u5f97\u3057\u307e\u3059\u3002</li> </ol> <p>\u8d70\u67fb\u5f8c\u3001\u914d\u5217 <code>res</code> \u306b\u306f\u30bd\u30fc\u30c8\u3055\u308c\u305f\u7d50\u679c\u304c\u542b\u307e\u308c\u3001\u6700\u5f8c\u306b <code>res</code> \u304c\u5143\u306e\u914d\u5217 <code>nums</code> \u3092\u7f6e\u304d\u63db\u3048\u307e\u3059\u3002\u5b8c\u5168\u306a\u8a08\u6570\u30bd\u30fc\u30c8\u306e\u904e\u7a0b\u306f\u4ee5\u4e0b\u306e\u56f3\u306b\u793a\u3055\u308c\u3066\u3044\u307e\u3059\u3002</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> \u56f3 11-17 \u00a0 \u8a08\u6570\u30bd\u30fc\u30c8\u306e\u904e\u7a0b </p> <p>\u8a08\u6570\u30bd\u30fc\u30c8\u306e\u5b9f\u88c5\u30b3\u30fc\u30c9\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig counting_sort.py<pre><code>def counting_sort(nums: list[int]):\n    \"\"\"\u8a08\u6570\u30bd\u30fc\u30c8\"\"\"\n    # \u5b8c\u5168\u306a\u5b9f\u88c5\u3001\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u306e\u30bd\u30fc\u30c8\u304c\u53ef\u80fd\u3067\u3001\u5b89\u5b9a\u30bd\u30fc\u30c8\n    # 1. \u914d\u5217\u5185\u306e\u6700\u5927\u8981\u7d20 m \u3092\u7d71\u8a08\n    m = max(nums)\n    # 2. \u5404\u6570\u5b57\u306e\u51fa\u73fe\u56de\u6570\u3092\u7d71\u8a08\n    # counter[num] \u306f num \u306e\u51fa\u73fe\u56de\u6570\u3092\u8868\u3059\n    counter = [0] * (m + 1)\n    for num in nums:\n        counter[num] += 1\n    # 3. counter \u306e\u524d\u7f6e\u548c\u3092\u8a08\u7b97\u3057\u3001\u300c\u51fa\u73fe\u56de\u6570\u300d\u3092\u300c\u672b\u5c3e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u300d\u306b\u5909\u63db\n    # counter[num]-1 \u306f res \u306b\u304a\u3044\u3066 num \u304c\u6700\u5f8c\u306b\u51fa\u73fe\u3059\u308b\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\n    for i in range(m):\n        counter[i + 1] += counter[i]\n    # 4. nums \u3092\u9006\u9806\u306b\u8d70\u67fb\u3057\u3001\u5404\u8981\u7d20\u3092\u7d50\u679c\u914d\u5217 res \u306b\u914d\u7f6e\n    # \u7d50\u679c\u3092\u8a18\u9332\u3059\u308b\u305f\u3081\u306e\u914d\u5217 res \u3092\u521d\u671f\u5316\n    n = len(nums)\n    res = [0] * n\n    for i in range(n - 1, -1, -1):\n        num = nums[i]\n        res[counter[num] - 1] = num  # num \u3092\u5bfe\u5fdc\u3059\u308b\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306b\u914d\u7f6e\n        counter[num] -= 1  # \u524d\u7f6e\u548c\u30921\u6e1b\u3089\u3057\u3001num \u3092\u914d\u7f6e\u3059\u308b\u6b21\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u53d6\u5f97\n    # \u7d50\u679c\u914d\u5217 res \u3092\u4f7f\u7528\u3057\u3066\u5143\u306e\u914d\u5217 nums \u3092\u4e0a\u66f8\u304d\n    for i in range(n):\n        nums[i] = res[i]\n</code></pre> counting_sort.cpp<pre><code>/* \u30ab\u30a6\u30f3\u30c8\u30bd\u30fc\u30c8 */\n// \u5b8c\u5168\u306a\u5b9f\u88c5\u3001\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u306e\u30bd\u30fc\u30c8\u304c\u53ef\u80fd\u3067\u5b89\u5b9a\u30bd\u30fc\u30c8\nvoid countingSort(vector&lt;int&gt; &amp;nums) {\n    // 1. \u914d\u5217\u306e\u6700\u5927\u8981\u7d20m\u3092\u7d71\u8a08\n    int m = 0;\n    for (int num : nums) {\n        m = max(m, num);\n    }\n    // 2. \u5404\u6570\u5b57\u306e\u51fa\u73fe\u56de\u6570\u3092\u7d71\u8a08\n    // counter[num]\u306fnum\u306e\u51fa\u73fe\u56de\u6570\u3092\u8868\u3059\n    vector&lt;int&gt; counter(m + 1, 0);\n    for (int num : nums) {\n        counter[num]++;\n    }\n    // 3. counter\u306e\u524d\u7f00\u548c\u3092\u8a08\u7b97\u3057\u3001\u300c\u51fa\u73fe\u56de\u6570\u300d\u3092\u300c\u672b\u5c3e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u300d\u306b\u5909\u63db\n    // counter[num]-1\u306fnum\u304cres\u3067\u73fe\u308c\u308b\u6700\u5f8c\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\n    for (int i = 0; i &lt; m; i++) {\n        counter[i + 1] += counter[i];\n    }\n    // 4. nums\u3092\u9006\u9806\u3067\u8d70\u67fb\u3057\u3001\u5404\u8981\u7d20\u3092\u7d50\u679c\u914d\u5217res\u306b\u914d\u7f6e\n    // \u7d50\u679c\u3092\u8a18\u9332\u3059\u308b\u914d\u5217res\u3092\u521d\u671f\u5316\n    int n = nums.size();\n    vector&lt;int&gt; res(n);\n    for (int i = n - 1; i &gt;= 0; i--) {\n        int num = nums[i];\n        res[counter[num] - 1] = num; // num\u3092\u5bfe\u5fdc\u3059\u308b\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306b\u914d\u7f6e\n        counter[num]--;              // \u524d\u7f00\u548c\u30921\u6e1b\u3089\u3057\u3001num\u3092\u914d\u7f6e\u3059\u308b\u6b21\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u53d6\u5f97\n    }\n    // \u7d50\u679c\u914d\u5217res\u3067\u5143\u306e\u914d\u5217nums\u3092\u4e0a\u66f8\u304d\n    nums = res;\n}\n</code></pre> counting_sort.java<pre><code>/* \u8a08\u6570\u30bd\u30fc\u30c8 */\n// \u5b8c\u5168\u306a\u5b9f\u88c5\u3001\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u3092\u30bd\u30fc\u30c8\u3067\u304d\u3001\u5b89\u5b9a\u30bd\u30fc\u30c8\nvoid countingSort(int[] nums) {\n    // 1. \u914d\u5217\u306e\u6700\u5927\u8981\u7d20 m \u3092\u7d71\u8a08\n    int m = 0;\n    for (int num : nums) {\n        m = Math.max(m, num);\n    }\n    // 2. \u5404\u6570\u5b57\u306e\u51fa\u73fe\u56de\u6570\u3092\u7d71\u8a08\n    // counter[num] \u306f num \u306e\u51fa\u73fe\u56de\u6570\u3092\u8868\u3059\n    int[] counter = new int[m + 1];\n    for (int num : nums) {\n        counter[num]++;\n    }\n    // 3. counter \u306e\u7d2f\u7a4d\u548c\u3092\u8a08\u7b97\u3057\u3001\u300c\u51fa\u73fe\u56de\u6570\u300d\u3092\u300c\u5c3b\u5c3e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u300d\u306b\u5909\u63db\n    // counter[num]-1 \u306f res \u5185\u3067 num \u304c\u51fa\u73fe\u3059\u308b\u6700\u5f8c\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\n    for (int i = 0; i &lt; m; i++) {\n        counter[i + 1] += counter[i];\n    }\n    // 4. nums \u3092\u9006\u9806\u306b\u8d70\u67fb\u3057\u3001\u5404\u8981\u7d20\u3092\u7d50\u679c\u914d\u5217 res \u306b\u914d\u7f6e\n    // \u7d50\u679c\u3092\u8a18\u9332\u3059\u308b\u914d\u5217 res \u3092\u521d\u671f\u5316\n    int n = nums.length;\n    int[] res = new int[n];\n    for (int i = n - 1; i &gt;= 0; i--) {\n        int num = nums[i];\n        res[counter[num] - 1] = num; // num \u3092\u5bfe\u5fdc\u3059\u308b\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306b\u914d\u7f6e\n        counter[num]--; // \u7d2f\u7a4d\u548c\u3092 1 \u6e1b\u7b97\u3057\u3001num \u3092\u914d\u7f6e\u3059\u308b\u6b21\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u53d6\u5f97\n    }\n    // \u7d50\u679c\u914d\u5217 res \u3092\u4f7f\u3063\u3066\u5143\u306e\u914d\u5217 nums \u3092\u4e0a\u66f8\u304d\n    for (int i = 0; i &lt; n; i++) {\n        nums[i] = res[i];\n    }\n}\n</code></pre> counting_sort.cs<pre><code>[class]{counting_sort}-[func]{CountingSort}\n</code></pre> counting_sort.go<pre><code>[class]{}-[func]{countingSort}\n</code></pre> counting_sort.swift<pre><code>[class]{}-[func]{countingSort}\n</code></pre> counting_sort.js<pre><code>[class]{}-[func]{countingSort}\n</code></pre> counting_sort.ts<pre><code>[class]{}-[func]{countingSort}\n</code></pre> counting_sort.dart<pre><code>[class]{}-[func]{countingSort}\n</code></pre> counting_sort.rs<pre><code>[class]{}-[func]{counting_sort}\n</code></pre> counting_sort.c<pre><code>[class]{}-[func]{countingSort}\n</code></pre> counting_sort.kt<pre><code>[class]{}-[func]{countingSort}\n</code></pre> counting_sort.rb<pre><code>[class]{}-[func]{counting_sort}\n</code></pre> counting_sort.zig<pre><code>[class]{}-[func]{countingSort}\n</code></pre>"},{"location":"chapter_sorting/counting_sort/#1193","title":"11.9.3 \u00a0 \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u7279\u5fb4","text":"<ul> <li>\u6642\u9593\u8a08\u7b97\u91cf\u306f \\(O(n + m)\\)\u3001\u975e\u9069\u5fdc\u30bd\u30fc\u30c8\uff1a<code>nums</code> \u3068 <code>counter</code> \u306e\u8d70\u67fb\u304c\u542b\u307e\u308c\u3001\u3069\u3061\u3089\u3082\u7dda\u5f62\u6642\u9593\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002\u4e00\u822c\u7684\u306b\u3001\\(n \\gg m\\) \u3067\u3042\u308a\u3001\u6642\u9593\u8a08\u7b97\u91cf\u306f \\(O(n)\\) \u306b\u8fd1\u3065\u304d\u307e\u3059\u3002</li> <li>\u7a7a\u9593\u8a08\u7b97\u91cf\u306f \\(O(n + m)\\)\u3001\u975e\u30a4\u30f3\u30d7\u30ec\u30fc\u30b9\u30bd\u30fc\u30c8\uff1a\u9577\u3055 \\(n\\) \u306e\u914d\u5217 <code>res</code> \u3068\u9577\u3055 \\(m\\) \u306e\u914d\u5217 <code>counter</code> \u3092\u305d\u308c\u305e\u308c\u4f7f\u7528\u3057\u307e\u3059\u3002</li> <li>\u5b89\u5b9a\u30bd\u30fc\u30c8\uff1a\u8981\u7d20\u304c\u300c\u53f3\u304b\u3089\u5de6\u300d\u306e\u9806\u5e8f\u3067 <code>res</code> \u306b\u57cb\u3081\u3089\u308c\u308b\u305f\u3081\u3001<code>nums</code> \u306e\u8d70\u67fb\u3092\u9006\u9806\u306b\u3059\u308b\u3053\u3068\u3067\u3001\u7b49\u3057\u3044\u8981\u7d20\u9593\u306e\u76f8\u5bfe\u4f4d\u7f6e\u306e\u5909\u5316\u3092\u9632\u304e\u3001\u5b89\u5b9a\u3057\u305f\u30bd\u30fc\u30c8\u3092\u5b9f\u73fe\u3067\u304d\u307e\u3059\u3002\u5b9f\u969b\u3001<code>nums</code> \u3092\u9806\u756a\u306b\u8d70\u67fb\u3057\u3066\u3082\u6b63\u3057\u3044\u30bd\u30fc\u30c8\u7d50\u679c\u3092\u751f\u6210\u3067\u304d\u307e\u3059\u304c\u3001\u7d50\u679c\u306f\u4e0d\u5b89\u5b9a\u3067\u3059\u3002</li> </ul>"},{"location":"chapter_sorting/counting_sort/#1194","title":"11.9.4 \u00a0 \u5236\u9650\u4e8b\u9805","text":"<p>\u4eca\u307e\u3067\u306b\u3001\u8a08\u6570\u30bd\u30fc\u30c8\u306f\u975e\u5e38\u306b\u5de7\u5999\u3060\u3068\u611f\u3058\u308b\u304b\u3082\u3057\u308c\u307e\u305b\u3093\u3002\u5358\u306b\u91cf\u3092\u30ab\u30a6\u30f3\u30c8\u3059\u308b\u3060\u3051\u3067\u52b9\u7387\u7684\u306a\u30bd\u30fc\u30c8\u3092\u5b9f\u73fe\u3067\u304d\u308b\u304b\u3089\u3067\u3059\u3002\u3057\u304b\u3057\u3001\u8a08\u6570\u30bd\u30fc\u30c8\u3092\u4f7f\u7528\u3059\u308b\u305f\u3081\u306e\u524d\u63d0\u6761\u4ef6\u306f\u6bd4\u8f03\u7684\u53b3\u3057\u3044\u3067\u3059\u3002</p> <p>\u8a08\u6570\u30bd\u30fc\u30c8\u306f\u975e\u8ca0\u6574\u6570\u306b\u306e\u307f\u9069\u7528\u3067\u304d\u307e\u3059\u3002\u4ed6\u306e\u30bf\u30a4\u30d7\u306e\u30c7\u30fc\u30bf\u306b\u9069\u7528\u3057\u305f\u3044\u5834\u5408\u3001\u3053\u308c\u3089\u306e\u30c7\u30fc\u30bf\u304c\u8981\u7d20\u306e\u5143\u306e\u9806\u5e8f\u3092\u5909\u66f4\u3059\u308b\u3053\u3068\u306a\u304f\u975e\u8ca0\u6574\u6570\u306b\u5909\u63db\u3067\u304d\u308b\u3053\u3068\u3092\u4fdd\u8a3c\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u8ca0\u306e\u6574\u6570\u3092\u542b\u3080\u914d\u5217\u306e\u5834\u5408\u3001\u6700\u521d\u306b\u3059\u3079\u3066\u306e\u6570\u306b\u5b9a\u6570\u3092\u52a0\u3048\u3066\u3001\u3059\u3079\u3066\u3092\u6b63\u306e\u6570\u306b\u5909\u63db\u3057\u3001\u30bd\u30fc\u30c8\u5b8c\u4e86\u5f8c\u306b\u5143\u306b\u623b\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002</p> <p>\u8a08\u6570\u30bd\u30fc\u30c8\u306f\u5024\u306e\u7bc4\u56f2\u304c\u5c0f\u3055\u3044\u5927\u304d\u306a\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u306b\u9069\u3057\u3066\u3044\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u4e0a\u8a18\u306e\u4f8b\u3067\u306f\u3001\\(m\\) \u306f\u5927\u304d\u3059\u304e\u308b\u3079\u304d\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u305d\u3046\u3067\u306a\u3051\u308c\u3070\u3001\u3042\u307e\u308a\u306b\u3082\u591a\u304f\u306e\u30b9\u30da\u30fc\u30b9\u3092\u5360\u6709\u3057\u3066\u3057\u307e\u3044\u307e\u3059\u3002\u305d\u3057\u3066 \\(n \\ll m\\) \u306e\u5834\u5408\u3001\u8a08\u6570\u30bd\u30fc\u30c8\u306f \\(O(m)\\) \u6642\u9593\u3092\u4f7f\u7528\u3057\u3001\\(O(n \\log n)\\) \u30bd\u30fc\u30c8\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3088\u308a\u9045\u3044\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002</p>"},{"location":"chapter_sorting/heap_sort/","title":"11.7 \u00a0 \u30d2\u30fc\u30d7\u30bd\u30fc\u30c8","text":"<p>Tip</p> <p>\u3053\u306e\u7bc0\u3092\u8aad\u3080\u524d\u306b\u3001\u300c\u30d2\u30fc\u30d7\u300d\u306e\u7ae0\u3092\u5fc5\u305a\u5b8c\u4e86\u3055\u305b\u3066\u304f\u3060\u3055\u3044\u3002</p> <p>\u30d2\u30fc\u30d7\u30bd\u30fc\u30c8\u306f\u3001\u30d2\u30fc\u30d7\u30c7\u30fc\u30bf\u69cb\u9020\u306b\u57fa\u3065\u304f\u52b9\u7387\u7684\u306a\u30bd\u30fc\u30c8\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u3059\u3002\u3059\u3067\u306b\u5b66\u7fd2\u3057\u305f\u300c\u30d2\u30fc\u30d7\u306e\u69cb\u7bc9\u300d\u3068\u300c\u8981\u7d20\u306e\u62bd\u51fa\u300d\u64cd\u4f5c\u3092\u4f7f\u7528\u3057\u3066\u30d2\u30fc\u30d7\u30bd\u30fc\u30c8\u3092\u5b9f\u88c5\u3067\u304d\u307e\u3059\u3002</p> <ol> <li>\u914d\u5217\u3092\u5165\u529b\u3057\u3001\u6700\u5c0f\u30d2\u30fc\u30d7\u3092\u69cb\u7bc9\u3057\u307e\u3059\u3002\u3053\u3053\u3067\u3001\u6700\u5c0f\u8981\u7d20\u304c\u30d2\u30fc\u30d7\u306e\u9802\u4e0a\u306b\u4f4d\u7f6e\u3057\u307e\u3059\u3002</li> <li>\u7d99\u7d9a\u7684\u306b\u62bd\u51fa\u64cd\u4f5c\u3092\u5b9f\u884c\u3057\u3001\u62bd\u51fa\u3055\u308c\u305f\u8981\u7d20\u3092\u9806\u6b21\u8a18\u9332\u3057\u3066\u3001\u6700\u5c0f\u304b\u3089\u6700\u5927\u307e\u3067\u306e\u30bd\u30fc\u30c8\u6e08\u307f\u30ea\u30b9\u30c8\u3092\u53d6\u5f97\u3057\u307e\u3059\u3002</li> </ol> <p>\u4e0a\u8a18\u306e\u65b9\u6cd5\u306f\u5b9f\u73fe\u53ef\u80fd\u3067\u3059\u304c\u3001\u30dd\u30c3\u30d7\u3055\u308c\u305f\u8981\u7d20\u3092\u683c\u7d0d\u3059\u308b\u305f\u3081\u306e\u8ffd\u52a0\u306e\u914d\u5217\u304c\u5fc5\u8981\u3067\u3001\u3084\u3084\u7a7a\u9593\u3092\u6d88\u8cbb\u3057\u307e\u3059\u3002\u5b9f\u969b\u306b\u306f\u3001\u901a\u5e38\u3001\u3088\u308a\u512a\u96c5\u306a\u5b9f\u88c5\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002</p>"},{"location":"chapter_sorting/heap_sort/#1171","title":"11.7.1 \u00a0 \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u6d41\u308c","text":"<p>\u914d\u5217\u306e\u9577\u3055\u3092 \\(n\\) \u3068\u3059\u308b\u3068\u3001\u30d2\u30fc\u30d7\u30bd\u30fc\u30c8\u306e\u904e\u7a0b\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\u3002</p> <ol> <li>\u914d\u5217\u3092\u5165\u529b\u3057\u3001\u6700\u5927\u30d2\u30fc\u30d7\u3092\u69cb\u7bc9\u3057\u307e\u3059\u3002\u3053\u306e\u624b\u9806\u306e\u5f8c\u3001\u6700\u5927\u8981\u7d20\u304c\u30d2\u30fc\u30d7\u306e\u9802\u4e0a\u306b\u4f4d\u7f6e\u3057\u307e\u3059\u3002</li> <li>\u30d2\u30fc\u30d7\u306e\u9802\u4e0a\u8981\u7d20\uff08\u6700\u521d\u306e\u8981\u7d20\uff09\u3068\u30d2\u30fc\u30d7\u306e\u5e95\u90e8\u8981\u7d20\uff08\u6700\u5f8c\u306e\u8981\u7d20\uff09\u3092\u4ea4\u63db\u3057\u307e\u3059\u3002\u3053\u306e\u4ea4\u63db\u306e\u5f8c\u3001\u30d2\u30fc\u30d7\u306e\u9577\u3055\u3092 \\(1\\) \u6e1b\u3089\u3057\u3001\u30bd\u30fc\u30c8\u6e08\u307f\u8981\u7d20\u306e\u6570\u3092 \\(1\\) \u5897\u3084\u3057\u307e\u3059\u3002</li> <li>\u30d2\u30fc\u30d7\u306e\u9802\u4e0a\u304b\u3089\u958b\u59cb\u3057\u3066\u3001\u4e0a\u304b\u3089\u4e0b\u3078\u306esift-down\u64cd\u4f5c\u3092\u5b9f\u884c\u3057\u307e\u3059\u3002sift-down\u306e\u5f8c\u3001\u30d2\u30fc\u30d7\u306e\u6027\u8cea\u304c\u5fa9\u5143\u3055\u308c\u307e\u3059\u3002</li> <li>\u624b\u9806 <code>2.</code> \u3068 <code>3.</code> \u3092\u7e70\u308a\u8fd4\u3057\u307e\u3059\u3002\\(n - 1\\) \u30e9\u30a6\u30f3\u30c9\u30eb\u30fc\u30d7\u3057\u3066\u3001\u914d\u5217\u306e\u30bd\u30fc\u30c8\u3092\u5b8c\u4e86\u3057\u307e\u3059\u3002</li> </ol> <p>Tip</p> <p>\u5b9f\u969b\u3001\u8981\u7d20\u62bd\u51fa\u64cd\u4f5c\u3082\u624b\u9806 <code>2.</code> \u3068 <code>3.</code> \u3092\u542b\u307f\u3001\u62bd\u51fa\u3055\u308c\u305f\u8981\u7d20\u3092\u30d2\u30fc\u30d7\u304b\u3089\u524a\u9664\u3059\u308b\u8ffd\u52a0\u306e\u624b\u9806\u304c\u3042\u308a\u307e\u3059\u3002</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt;&lt;12&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> \u56f3 11-12 \u00a0 \u30d2\u30fc\u30d7\u30bd\u30fc\u30c8\u306e\u904e\u7a0b </p> <p>\u30b3\u30fc\u30c9\u306e\u5b9f\u88c5\u3067\u306f\u3001\u300c\u30d2\u30fc\u30d7\u300d\u306e\u7ae0\u304b\u3089\u306esift-down\u95a2\u6570 <code>sift_down()</code> \u3092\u4f7f\u7528\u3057\u307e\u3057\u305f\u3002\u6700\u5927\u8981\u7d20\u304c\u62bd\u51fa\u3055\u308c\u308b\u306b\u3064\u308c\u3066\u30d2\u30fc\u30d7\u306e\u9577\u3055\u304c\u6e1b\u5c11\u3059\u308b\u305f\u3081\u3001<code>sift_down()</code> \u95a2\u6570\u306b\u9577\u3055\u30d1\u30e9\u30e1\u30fc\u30bf \\(n\\) \u3092\u8ffd\u52a0\u3057\u3066\u3001\u30d2\u30fc\u30d7\u306e\u73fe\u5728\u306e\u6709\u52b9\u9577\u3092\u6307\u5b9a\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u3053\u3068\u306b\u6ce8\u610f\u3059\u308b\u3053\u3068\u304c\u91cd\u8981\u3067\u3059\u3002\u30b3\u30fc\u30c9\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig heap_sort.py<pre><code>def sift_down(nums: list[int], n: int, i: int):\n    \"\"\"\u30d2\u30fc\u30d7\u306e\u9577\u3055\u304c n\u3001\u30ce\u30fc\u30c9 i \u304b\u3089\u4e0a\u304b\u3089\u4e0b\u3078\u30d2\u30fc\u30d7\u5316\u3092\u958b\u59cb\"\"\"\n    while True:\n        # i\u3001l\u3001r \u306e\u4e2d\u3067\u6700\u5927\u306e\u30ce\u30fc\u30c9\u3092\u5224\u5b9a\u3057\u3001ma \u3068\u3059\u308b\n        l = 2 * i + 1\n        r = 2 * i + 2\n        ma = i\n        if l &lt; n and nums[l] &gt; nums[ma]:\n            ma = l\n        if r &lt; n and nums[r] &gt; nums[ma]:\n            ma = r\n        # \u30ce\u30fc\u30c9 i \u304c\u6700\u5927\u307e\u305f\u306f l\u3001r \u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u304c\u7bc4\u56f2\u5916\u306e\u5834\u5408\u3001\u3055\u3089\u306a\u308b\u30d2\u30fc\u30d7\u5316\u306f\u4e0d\u8981\u3001\u30eb\u30fc\u30d7\u3092\u629c\u3051\u308b\n        if ma == i:\n            break\n        # 2\u3064\u306e\u30ce\u30fc\u30c9\u3092\u4ea4\u63db\n        nums[i], nums[ma] = nums[ma], nums[i]\n        # \u4e0b\u5411\u304d\u306b\u30d2\u30fc\u30d7\u5316\u3092\u30eb\u30fc\u30d7\n        i = ma\n\ndef heap_sort(nums: list[int]):\n    \"\"\"\u30d2\u30fc\u30d7\u30bd\u30fc\u30c8\"\"\"\n    # \u30d2\u30fc\u30d7\u69cb\u7bc9\u64cd\u4f5c\uff1a\u8449\u30ce\u30fc\u30c9\u4ee5\u5916\u306e\u3059\u3079\u3066\u306e\u30ce\u30fc\u30c9\u3092\u30d2\u30fc\u30d7\u5316\n    for i in range(len(nums) // 2 - 1, -1, -1):\n        sift_down(nums, len(nums), i)\n    # \u30d2\u30fc\u30d7\u304b\u3089\u6700\u5927\u8981\u7d20\u3092\u62bd\u51fa\u3057\u3001n-1 \u56de\u7e70\u308a\u8fd4\u3059\n    for i in range(len(nums) - 1, 0, -1):\n        # \u30eb\u30fc\u30c8\u30ce\u30fc\u30c9\u3068\u6700\u3082\u53f3\u306e\u8449\u30ce\u30fc\u30c9\u3092\u4ea4\u63db\uff08\u6700\u521d\u306e\u8981\u7d20\u3068\u6700\u5f8c\u306e\u8981\u7d20\u3092\u4ea4\u63db\uff09\n        nums[0], nums[i] = nums[i], nums[0]\n        # \u30eb\u30fc\u30c8\u30ce\u30fc\u30c9\u304b\u3089\u4e0a\u304b\u3089\u4e0b\u3078\u30d2\u30fc\u30d7\u5316\u3092\u958b\u59cb\n        sift_down(nums, i, 0)\n</code></pre> heap_sort.cpp<pre><code>/* \u30d2\u30fc\u30d7\u306e\u9577\u3055\u306fn\u3001\u30ce\u30fc\u30c9i\u304b\u3089\u4e0a\u304b\u3089\u4e0b\u3078\u30d2\u30fc\u30d7\u5316\u3092\u958b\u59cb */\nvoid siftDown(vector&lt;int&gt; &amp;nums, int n, int i) {\n    while (true) {\n        // i\u3001l\u3001r \u306e\u4e2d\u3067\u6700\u5927\u306e\u30ce\u30fc\u30c9\u3092\u6c7a\u5b9a\u3057\u3001ma\u3068\u3057\u3066\u8a18\u9332\n        int l = 2 * i + 1;\n        int r = 2 * i + 2;\n        int ma = i;\n        if (l &lt; n &amp;&amp; nums[l] &gt; nums[ma])\n            ma = l;\n        if (r &lt; n &amp;&amp; nums[r] &gt; nums[ma])\n            ma = r;\n        // \u30ce\u30fc\u30c9i\u304c\u6700\u5927\u304b\u3001\u30a4\u30f3\u30c7\u30c3\u30af\u30b9l\u3001r\u304c\u5883\u754c\u5916\u306e\u5834\u5408\u3001\u305d\u308c\u4ee5\u4e0a\u306e\u30d2\u30fc\u30d7\u5316\u306f\u4e0d\u8981\u3067\u7d42\u4e86\n        if (ma == i) {\n            break;\n        }\n        // \u4e8c\u3064\u306e\u30ce\u30fc\u30c9\u3092\u4ea4\u63db\n        swap(nums[i], nums[ma]);\n        // \u4e0b\u5411\u304d\u306b\u30d2\u30fc\u30d7\u5316\u3092\u30eb\u30fc\u30d7\n        i = ma;\n    }\n}\n\n/* \u30d2\u30fc\u30d7\u30bd\u30fc\u30c8 */\nvoid heapSort(vector&lt;int&gt; &amp;nums) {\n    // \u30d2\u30fc\u30d7\u69cb\u7bc9\u64cd\u4f5c\uff1a\u8449\u4ee5\u5916\u306e\u3059\u3079\u3066\u306e\u30ce\u30fc\u30c9\u3092\u30d2\u30fc\u30d7\u5316\n    for (int i = nums.size() / 2 - 1; i &gt;= 0; --i) {\n        siftDown(nums, nums.size(), i);\n    }\n    // \u30d2\u30fc\u30d7\u304b\u3089\u6700\u5927\u8981\u7d20\u3092\u62bd\u51fa\u3057\u3001n-1\u56de\u7e70\u308a\u8fd4\u3059\n    for (int i = nums.size() - 1; i &gt; 0; --i) {\n        // \u30eb\u30fc\u30c8\u30ce\u30fc\u30c9\u3092\u6700\u53f3\u8449\u30ce\u30fc\u30c9\u3068\u4ea4\u63db\uff08\u6700\u521d\u306e\u8981\u7d20\u3092\u6700\u5f8c\u306e\u8981\u7d20\u3068\u4ea4\u63db\uff09\n        swap(nums[0], nums[i]);\n        // \u30eb\u30fc\u30c8\u30ce\u30fc\u30c9\u304b\u3089\u4e0a\u304b\u3089\u4e0b\u3078\u30d2\u30fc\u30d7\u5316\u3092\u958b\u59cb\n        siftDown(nums, i, 0);\n    }\n}\n</code></pre> heap_sort.java<pre><code>/* \u30d2\u30fc\u30d7\u306e\u9577\u3055\u306f n\u3001\u30ce\u30fc\u30c9 i \u304b\u3089\u4e0a\u304b\u3089\u4e0b\u3078\u30d2\u30fc\u30d7\u5316\u958b\u59cb */\nvoid siftDown(int[] nums, int n, int i) {\n    while (true) {\n        // i, l, r \u306e\u4e2d\u3067\u6700\u5927\u306e\u30ce\u30fc\u30c9\u3092\u5224\u5b9a\u3057\u3001ma \u3068\u3059\u308b\n        int l = 2 * i + 1;\n        int r = 2 * i + 2;\n        int ma = i;\n        if (l &lt; n &amp;&amp; nums[l] &gt; nums[ma])\n            ma = l;\n        if (r &lt; n &amp;&amp; nums[r] &gt; nums[ma])\n            ma = r;\n        // \u30ce\u30fc\u30c9 i \u304c\u6700\u5927\u3001\u307e\u305f\u306f\u30a4\u30f3\u30c7\u30c3\u30af\u30b9 l, r \u304c\u7bc4\u56f2\u5916\u306e\u5834\u5408\u3001\u3055\u3089\u306a\u308b\u30d2\u30fc\u30d7\u5316\u306f\u4e0d\u8981\u3001\u30d6\u30ec\u30fc\u30af\n        if (ma == i)\n            break;\n        // 2\u3064\u306e\u30ce\u30fc\u30c9\u3092\u4ea4\u63db\n        int temp = nums[i];\n        nums[i] = nums[ma];\n        nums[ma] = temp;\n        // \u4e0b\u5411\u304d\u306b\u30d2\u30fc\u30d7\u5316\u3092\u30eb\u30fc\u30d7\n        i = ma;\n    }\n}\n\n/* \u30d2\u30fc\u30d7\u30bd\u30fc\u30c8 */\nvoid heapSort(int[] nums) {\n    // \u30d2\u30fc\u30d7\u69cb\u7bc9\u64cd\u4f5c: \u8449\u30ce\u30fc\u30c9\u4ee5\u5916\u306e\u3059\u3079\u3066\u306e\u30ce\u30fc\u30c9\u3092\u30d2\u30fc\u30d7\u5316\n    for (int i = nums.length / 2 - 1; i &gt;= 0; i--) {\n        siftDown(nums, nums.length, i);\n    }\n    // \u30d2\u30fc\u30d7\u304b\u3089\u6700\u5927\u8981\u7d20\u3092\u62bd\u51fa\u3057\u3001n-1 \u56de\u7e70\u308a\u8fd4\u3057\n    for (int i = nums.length - 1; i &gt; 0; i--) {\n        // \u30eb\u30fc\u30c8\u30ce\u30fc\u30c9\u3068\u6700\u3082\u53f3\u306e\u8449\u30ce\u30fc\u30c9\u3092\u4ea4\u63db\uff08\u6700\u521d\u306e\u8981\u7d20\u3068\u6700\u5f8c\u306e\u8981\u7d20\u3092\u4ea4\u63db\uff09\n        int tmp = nums[0];\n        nums[0] = nums[i];\n        nums[i] = tmp;\n        // \u30eb\u30fc\u30c8\u30ce\u30fc\u30c9\u304b\u3089\u4e0a\u304b\u3089\u4e0b\u3078\u30d2\u30fc\u30d7\u5316\u958b\u59cb\n        siftDown(nums, i, 0);\n    }\n}\n</code></pre> heap_sort.cs<pre><code>[class]{heap_sort}-[func]{SiftDown}\n\n[class]{heap_sort}-[func]{HeapSort}\n</code></pre> heap_sort.go<pre><code>[class]{}-[func]{siftDown}\n\n[class]{}-[func]{heapSort}\n</code></pre> heap_sort.swift<pre><code>[class]{}-[func]{siftDown}\n\n[class]{}-[func]{heapSort}\n</code></pre> heap_sort.js<pre><code>[class]{}-[func]{siftDown}\n\n[class]{}-[func]{heapSort}\n</code></pre> heap_sort.ts<pre><code>[class]{}-[func]{siftDown}\n\n[class]{}-[func]{heapSort}\n</code></pre> heap_sort.dart<pre><code>[class]{}-[func]{siftDown}\n\n[class]{}-[func]{heapSort}\n</code></pre> heap_sort.rs<pre><code>[class]{}-[func]{sift_down}\n\n[class]{}-[func]{heap_sort}\n</code></pre> heap_sort.c<pre><code>[class]{}-[func]{siftDown}\n\n[class]{}-[func]{heapSort}\n</code></pre> heap_sort.kt<pre><code>[class]{}-[func]{siftDown}\n\n[class]{}-[func]{heapSort}\n</code></pre> heap_sort.rb<pre><code>[class]{}-[func]{sift_down}\n\n[class]{}-[func]{heap_sort}\n</code></pre> heap_sort.zig<pre><code>[class]{}-[func]{siftDown}\n\n[class]{}-[func]{heapSort}\n</code></pre>"},{"location":"chapter_sorting/heap_sort/#1172","title":"11.7.2 \u00a0 \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u7279\u5fb4","text":"<ul> <li>\u6642\u9593\u8a08\u7b97\u91cf\u306f \\(O(n \\log n)\\)\u3001\u975e\u9069\u5fdc\u30bd\u30fc\u30c8\uff1a\u30d2\u30fc\u30d7\u306e\u69cb\u7bc9\u306f \\(O(n)\\) \u6642\u9593\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002\u30d2\u30fc\u30d7\u304b\u3089\u6700\u5927\u8981\u7d20\u3092\u62bd\u51fa\u3059\u308b\u306b\u306f \\(O(\\log n)\\) \u6642\u9593\u304c\u304b\u304b\u308a\u3001\\(n - 1\\) \u30e9\u30a6\u30f3\u30c9\u30eb\u30fc\u30d7\u3057\u307e\u3059\u3002</li> <li>\u7a7a\u9593\u8a08\u7b97\u91cf\u306f \\(O(1)\\)\u3001\u30a4\u30f3\u30d7\u30ec\u30fc\u30b9\u30bd\u30fc\u30c8\uff1a\u3044\u304f\u3064\u304b\u306e\u30dd\u30a4\u30f3\u30bf\u5909\u6570\u304c \\(O(1)\\) \u7a7a\u9593\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002\u8981\u7d20\u306e\u4ea4\u63db\u3068\u30d2\u30fc\u30d7\u5316\u64cd\u4f5c\u306f\u5143\u306e\u914d\u5217\u3067\u5b9f\u884c\u3055\u308c\u307e\u3059\u3002</li> <li>\u975e\u5b89\u5b9a\u30bd\u30fc\u30c8\uff1a\u30d2\u30fc\u30d7\u306e\u9802\u4e0a\u3068\u5e95\u90e8\u8981\u7d20\u306e\u4ea4\u63db\u4e2d\u306b\u3001\u7b49\u3057\u3044\u8981\u7d20\u306e\u76f8\u5bfe\u4f4d\u7f6e\u304c\u5909\u308f\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002</li> </ul>"},{"location":"chapter_sorting/insertion_sort/","title":"11.4 \u00a0 \u633f\u5165\u30bd\u30fc\u30c8","text":"<p>\u633f\u5165\u30bd\u30fc\u30c8\u306f\u3001\u30c8\u30e9\u30f3\u30d7\u306e\u30c7\u30c3\u30ad\u3092\u624b\u52d5\u3067\u30bd\u30fc\u30c8\u3059\u308b\u30d7\u30ed\u30bb\u30b9\u306b\u3088\u304f\u4f3c\u305f\u52d5\u4f5c\u3092\u3059\u308b\u30b7\u30f3\u30d7\u30eb\u306a\u30bd\u30fc\u30c8\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u3059\u3002</p> <p>\u5177\u4f53\u7684\u306b\u306f\u3001\u672a\u30bd\u30fc\u30c8\u533a\u9593\u304b\u3089\u30d9\u30fc\u30b9\u8981\u7d20\u3092\u9078\u629e\u3057\u3001\u305d\u306e\u5de6\u5074\u306e\u30bd\u30fc\u30c8\u6e08\u307f\u533a\u9593\u306e\u8981\u7d20\u3068\u6bd4\u8f03\u3057\u3066\u3001\u8981\u7d20\u3092\u6b63\u3057\u3044\u4f4d\u7f6e\u306b\u633f\u5165\u3057\u307e\u3059\u3002</p> <p>\u4e0b\u56f3\u306f\u3001\u8981\u7d20\u304c\u914d\u5217\u306b\u633f\u5165\u3055\u308c\u308b\u65b9\u6cd5\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002\u30d9\u30fc\u30b9\u8981\u7d20\u3092<code>base</code>\u3068\u3059\u308b\u3068\u3001\u30bf\u30fc\u30b2\u30c3\u30c8\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u304b\u3089<code>base</code>\u307e\u3067\u306e\u3059\u3079\u3066\u306e\u8981\u7d20\u3092\u53f3\u306b1\u3064\u305a\u3064\u30b7\u30d5\u30c8\u3057\u3001\u305d\u306e\u5f8c<code>base</code>\u3092\u30bf\u30fc\u30b2\u30c3\u30c8\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306b\u5272\u308a\u5f53\u3066\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002</p> <p></p> <p> \u56f3 11-6 \u00a0 Single insertion operation </p>"},{"location":"chapter_sorting/insertion_sort/#1141","title":"11.4.1 \u00a0 \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u30d7\u30ed\u30bb\u30b9","text":"<p>\u633f\u5165\u30bd\u30fc\u30c8\u306e\u5168\u4f53\u7684\u306a\u30d7\u30ed\u30bb\u30b9\u306f\u4e0b\u56f3\u306b\u793a\u3055\u308c\u307e\u3059\u3002</p> <ol> <li>\u914d\u5217\u306e\u6700\u521d\u306e\u8981\u7d20\u3092\u30bd\u30fc\u30c8\u6e08\u307f\u3068\u307f\u306a\u3057\u307e\u3059\u3002</li> <li>2\u756a\u76ee\u306e\u8981\u7d20\u3092<code>base</code>\u3068\u3057\u3066\u9078\u629e\u3057\u3001\u6b63\u3057\u3044\u4f4d\u7f6e\u306b\u633f\u5165\u3057\u3066\u3001\u6700\u521d\u306e2\u3064\u306e\u8981\u7d20\u3092\u30bd\u30fc\u30c8\u6e08\u307f\u306b\u3057\u307e\u3059\u3002</li> <li>3\u756a\u76ee\u306e\u8981\u7d20\u3092<code>base</code>\u3068\u3057\u3066\u9078\u629e\u3057\u3001\u6b63\u3057\u3044\u4f4d\u7f6e\u306b\u633f\u5165\u3057\u3066\u3001\u6700\u521d\u306e3\u3064\u306e\u8981\u7d20\u3092\u30bd\u30fc\u30c8\u6e08\u307f\u306b\u3057\u307e\u3059\u3002</li> <li>\u3053\u306e\u65b9\u6cd5\u3067\u7d9a\u884c\u3057\u3001\u6700\u5f8c\u306e\u53cd\u5fa9\u3067\u306f\u3001\u6700\u5f8c\u306e\u8981\u7d20\u3092<code>base</code>\u3068\u3057\u3066\u53d6\u308a\u3001\u6b63\u3057\u3044\u4f4d\u7f6e\u306b\u633f\u5165\u3057\u305f\u5f8c\u3001\u3059\u3079\u3066\u306e\u8981\u7d20\u304c\u30bd\u30fc\u30c8\u3055\u308c\u307e\u3059\u3002</li> </ol> <p></p> <p> \u56f3 11-7 \u00a0 Insertion sort process </p> <p>\u30b3\u30fc\u30c9\u4f8b\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig insertion_sort.py<pre><code>def insertion_sort(nums: list[int]):\n    \"\"\"\u633f\u5165\u30bd\u30fc\u30c8\"\"\"\n    # \u5916\u5074\u306e\u30eb\u30fc\u30d7\uff1a\u30bd\u30fc\u30c8\u6e08\u307f\u7bc4\u56f2\u306f [0, i-1]\n    for i in range(1, len(nums)):\n        base = nums[i]\n        j = i - 1\n        # \u5185\u5074\u306e\u30eb\u30fc\u30d7\uff1abase \u3092\u30bd\u30fc\u30c8\u6e08\u307f\u7bc4\u56f2 [0, i-1] \u306e\u6b63\u3057\u3044\u4f4d\u7f6e\u306b\u633f\u5165\n        while j &gt;= 0 and nums[j] &gt; base:\n            nums[j + 1] = nums[j]  # nums[j] \u3092\u53f3\u306b1\u3064\u79fb\u52d5\n            j -= 1\n        nums[j + 1] = base  # base \u3092\u6b63\u3057\u3044\u4f4d\u7f6e\u306b\u4ee3\u5165\n</code></pre> insertion_sort.cpp<pre><code>/* \u633f\u5165\u30bd\u30fc\u30c8 */\nvoid insertionSort(vector&lt;int&gt; &amp;nums) {\n    // \u5916\u5074\u30eb\u30fc\u30d7\uff1a\u30bd\u30fc\u30c8\u6e08\u307f\u7bc4\u56f2\u306f[0, i-1]\n    for (int i = 1; i &lt; nums.size(); i++) {\n        int base = nums[i], j = i - 1;\n        // \u5185\u5074\u30eb\u30fc\u30d7\uff1abase\u3092\u30bd\u30fc\u30c8\u6e08\u307f\u7bc4\u56f2[0, i-1]\u5185\u306e\u6b63\u3057\u3044\u4f4d\u7f6e\u306b\u633f\u5165\n        while (j &gt;= 0 &amp;&amp; nums[j] &gt; base) {\n            nums[j + 1] = nums[j]; // nums[j]\u3092\u4e00\u3064\u53f3\u306b\u79fb\u52d5\n            j--;\n        }\n        nums[j + 1] = base; // base\u3092\u6b63\u3057\u3044\u4f4d\u7f6e\u306b\u4ee3\u5165\n    }\n}\n</code></pre> insertion_sort.java<pre><code>/* \u633f\u5165\u30bd\u30fc\u30c8 */\nvoid insertionSort(int[] nums) {\n    // \u5916\u5074\u30eb\u30fc\u30d7: \u30bd\u30fc\u30c8\u6e08\u307f\u7bc4\u56f2\u306f [0, i-1]\n    for (int i = 1; i &lt; nums.length; i++) {\n        int base = nums[i], j = i - 1;\n        // \u5185\u5074\u30eb\u30fc\u30d7: base \u3092\u30bd\u30fc\u30c8\u6e08\u307f\u7bc4\u56f2 [0, i-1] \u306e\u6b63\u3057\u3044\u4f4d\u7f6e\u306b\u633f\u5165\n        while (j &gt;= 0 &amp;&amp; nums[j] &gt; base) {\n            nums[j + 1] = nums[j]; // nums[j] \u3092\u53f3\u306b1\u3064\u79fb\u52d5\n            j--;\n        }\n        nums[j + 1] = base;        // base \u3092\u6b63\u3057\u3044\u4f4d\u7f6e\u306b\u4ee3\u5165\n    }\n}\n</code></pre> insertion_sort.cs<pre><code>[class]{insertion_sort}-[func]{InsertionSort}\n</code></pre> insertion_sort.go<pre><code>[class]{}-[func]{insertionSort}\n</code></pre> insertion_sort.swift<pre><code>[class]{}-[func]{insertionSort}\n</code></pre> insertion_sort.js<pre><code>[class]{}-[func]{insertionSort}\n</code></pre> insertion_sort.ts<pre><code>[class]{}-[func]{insertionSort}\n</code></pre> insertion_sort.dart<pre><code>[class]{}-[func]{insertionSort}\n</code></pre> insertion_sort.rs<pre><code>[class]{}-[func]{insertion_sort}\n</code></pre> insertion_sort.c<pre><code>[class]{}-[func]{insertionSort}\n</code></pre> insertion_sort.kt<pre><code>[class]{}-[func]{insertionSort}\n</code></pre> insertion_sort.rb<pre><code>[class]{}-[func]{insertion_sort}\n</code></pre> insertion_sort.zig<pre><code>[class]{}-[func]{insertionSort}\n</code></pre>"},{"location":"chapter_sorting/insertion_sort/#1142","title":"11.4.2 \u00a0 \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u7279\u6027","text":"<ul> <li>\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O(n^2)\\)\u3001\u9069\u5fdc\u30bd\u30fc\u30c8\uff1a\u6700\u60aa\u306e\u5834\u5408\u3001\u5404\u633f\u5165\u64cd\u4f5c\u306b\u306f\\(n - 1\\)\u3001\\(n-2\\)\u3001...\u3001\\(2\\)\u3001\\(1\\)\u306e\u30eb\u30fc\u30d7\u304c\u5fc5\u8981\u3067\u3001\u5408\u8a08\u306f\\((n - 1) n / 2\\)\u3068\u306a\u308a\u3001\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O(n^2)\\)\u3067\u3059\u3002\u9806\u5e8f\u4ed8\u304d\u30c7\u30fc\u30bf\u306e\u5834\u5408\u3001\u633f\u5165\u64cd\u4f5c\u306f\u65e9\u671f\u306b\u7d42\u4e86\u3057\u307e\u3059\u3002\u5165\u529b\u914d\u5217\u304c\u5b8c\u5168\u306b\u9806\u5e8f\u4ed8\u3051\u3089\u308c\u3066\u3044\u308b\u5834\u5408\u3001\u633f\u5165\u30bd\u30fc\u30c8\u306f\u6700\u826f\u6642\u9593\u8a08\u7b97\u91cf\\(O(n)\\)\u3092\u5b9f\u73fe\u3057\u307e\u3059\u3002</li> <li>\u7a7a\u9593\u8a08\u7b97\u91cf\u306f\\(O(1)\\)\u3001\u30a4\u30f3\u30d7\u30ec\u30fc\u30b9\u30bd\u30fc\u30c8\uff1a\u30dd\u30a4\u30f3\u30bf\\(i\\)\u3068\\(j\\)\u306f\u5b9a\u6570\u91cf\u306e\u8ffd\u52a0\u7a7a\u9593\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002</li> <li>\u5b89\u5b9a\u30bd\u30fc\u30c8\uff1a\u633f\u5165\u64cd\u4f5c\u4e2d\u3001\u7b49\u3057\u3044\u8981\u7d20\u306e\u53f3\u5074\u306b\u8981\u7d20\u3092\u633f\u5165\u3057\u3001\u9806\u5e8f\u3092\u5909\u66f4\u3057\u307e\u305b\u3093\u3002</li> </ul>"},{"location":"chapter_sorting/insertion_sort/#1143","title":"11.4.3 \u00a0 \u633f\u5165\u30bd\u30fc\u30c8\u306e\u5229\u70b9","text":"<p>\u633f\u5165\u30bd\u30fc\u30c8\u306e\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O(n^2)\\)\u3067\u3001\u6b21\u306b\u5b66\u7fd2\u3059\u308b\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u306e\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O(n \\log n)\\)\u3067\u3059\u3002\u633f\u5165\u30bd\u30fc\u30c8\u306f\u3088\u308a\u9ad8\u3044\u6642\u9593\u8a08\u7b97\u91cf\u3092\u6301\u3061\u307e\u3059\u304c\u3001\u5c0f\u3055\u306a\u5165\u529b\u30b5\u30a4\u30ba\u3067\u306f\u901a\u5e38\u3088\u308a\u9ad8\u901f\u3067\u3059\u3002</p> <p>\u3053\u306e\u7d50\u8ad6\u306f\u7dda\u5f62\u63a2\u7d22\u3068\u4e8c\u5206\u63a2\u7d22\u306e\u7d50\u8ad6\u3068\u4f3c\u3066\u3044\u307e\u3059\u3002\u6642\u9593\u8a08\u7b97\u91cf\u304c\\(O(n \\log n)\\)\u3067\u5206\u5272\u7d71\u6cbb\u6226\u7565\u306b\u57fa\u3065\u304f\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u306a\u3069\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u3001\u591a\u304f\u306e\u5834\u5408\u3088\u308a\u591a\u304f\u306e\u5358\u4f4d\u64cd\u4f5c\u3092\u542b\u307f\u307e\u3059\u3002\u5c0f\u3055\u306a\u5165\u529b\u30b5\u30a4\u30ba\u3067\u306f\u3001\\(n^2\\)\u3068\\(n \\log n\\)\u306e\u6570\u5024\u306f\u8fd1\u304f\u3001\u8a08\u7b97\u91cf\u304c\u652f\u914d\u7684\u3067\u306a\u304f\u3001\u30e9\u30a6\u30f3\u30c9\u3042\u305f\u308a\u306e\u5358\u4f4d\u64cd\u4f5c\u6570\u304c\u6c7a\u5b9a\u7684\u306a\u5f79\u5272\u3092\u679c\u305f\u3057\u307e\u3059\u3002</p> <p>\u5b9f\u969b\u3001\u591a\u304f\u306e\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\uff08Java\u306a\u3069\uff09\u306f\u3001\u7d44\u307f\u8fbc\u307f\u30bd\u30fc\u30c8\u95a2\u6570\u5185\u3067\u633f\u5165\u30bd\u30fc\u30c8\u3092\u4f7f\u7528\u3057\u3066\u3044\u307e\u3059\u3002\u4e00\u822c\u7684\u306a\u30a2\u30d7\u30ed\u30fc\u30c1\u306f\uff1a\u9577\u3044\u914d\u5217\u306b\u5bfe\u3057\u3066\u306f\u3001\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u306a\u3069\u306e\u5206\u5272\u7d71\u6cbb\u6226\u7565\u306b\u57fa\u3065\u304f\u30bd\u30fc\u30c8\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u4f7f\u7528\u3057\u3001\u77ed\u3044\u914d\u5217\u306b\u5bfe\u3057\u3066\u306f\u633f\u5165\u30bd\u30fc\u30c8\u3092\u76f4\u63a5\u4f7f\u7528\u3057\u307e\u3059\u3002</p> <p>\u30d0\u30d6\u30eb\u30bd\u30fc\u30c8\u3001\u9078\u629e\u30bd\u30fc\u30c8\u3001\u633f\u5165\u30bd\u30fc\u30c8\u306f\u3059\u3079\u3066\u6642\u9593\u8a08\u7b97\u91cf\\(O(n^2)\\)\u3092\u6301\u3061\u307e\u3059\u304c\u3001\u5b9f\u969b\u306b\u306f\u3001\u633f\u5165\u30bd\u30fc\u30c8\u306f\u30d0\u30d6\u30eb\u30bd\u30fc\u30c8\u3084\u9078\u629e\u30bd\u30fc\u30c8\u3088\u308a\u3082\u4e00\u822c\u7684\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u4e3b\u306a\u7406\u7531\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\u3002</p> <ul> <li>\u30d0\u30d6\u30eb\u30bd\u30fc\u30c8\u306f\u8981\u7d20\u4ea4\u63db\u306b\u57fa\u3065\u304d\u3001\u4e00\u6642\u5909\u6570\u306e\u4f7f\u7528\u304c\u5fc5\u8981\u3067\u30013\u3064\u306e\u5358\u4f4d\u64cd\u4f5c\u3092\u542b\u307f\u307e\u3059\uff1b\u633f\u5165\u30bd\u30fc\u30c8\u306f\u8981\u7d20\u4ee3\u5165\u306b\u57fa\u3065\u304d\u30011\u3064\u306e\u5358\u4f4d\u64cd\u4f5c\u306e\u307f\u304c\u5fc5\u8981\u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u30d0\u30d6\u30eb\u30bd\u30fc\u30c8\u306e\u8a08\u7b97\u30aa\u30fc\u30d0\u30fc\u30d8\u30c3\u30c9\u306f\u4e00\u822c\u7684\u306b\u633f\u5165\u30bd\u30fc\u30c8\u3088\u308a\u3082\u9ad8\u304f\u306a\u308a\u307e\u3059\u3002</li> <li>\u9078\u629e\u30bd\u30fc\u30c8\u306e\u6642\u9593\u8a08\u7b97\u91cf\u306f\u5e38\u306b\\(O(n^2)\\)\u3067\u3059\u3002\u90e8\u5206\u7684\u306b\u9806\u5e8f\u4ed8\u3051\u3089\u308c\u305f\u30c7\u30fc\u30bf\u306e\u30bb\u30c3\u30c8\u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408\u3001\u633f\u5165\u30bd\u30fc\u30c8\u306f\u901a\u5e38\u9078\u629e\u30bd\u30fc\u30c8\u3088\u308a\u3082\u52b9\u7387\u7684\u3067\u3059\u3002</li> <li>\u9078\u629e\u30bd\u30fc\u30c8\u306f\u4e0d\u5b89\u5b9a\u3067\u3001\u30de\u30eb\u30c1\u30ec\u30d9\u30eb\u30bd\u30fc\u30c8\u306b\u9069\u7528\u3067\u304d\u307e\u305b\u3093\u3002</li> </ul>"},{"location":"chapter_sorting/merge_sort/","title":"11.6 \u00a0 \u30de\u30fc\u30b8\u30bd\u30fc\u30c8","text":"<p>\u30de\u30fc\u30b8\u30bd\u30fc\u30c8\u306f\u5206\u5272\u7d71\u6cbb\u6226\u7565\u306b\u57fa\u3065\u304f\u30bd\u30fc\u30c8\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u3001\u4e0b\u56f3\u306b\u793a\u3059\u300c\u5206\u5272\u300d\u3068\u300c\u30de\u30fc\u30b8\u300d\u30d5\u30a7\u30fc\u30ba\u3092\u542b\u307f\u307e\u3059\u3002</p> <ol> <li>\u5206\u5272\u30d5\u30a7\u30fc\u30ba\uff1a\u4e2d\u70b9\u304b\u3089\u914d\u5217\u3092\u518d\u5e30\u7684\u306b\u5206\u5272\u3057\u3001\u9577\u3044\u914d\u5217\u306e\u30bd\u30fc\u30c8\u554f\u984c\u3092\u3088\u308a\u77ed\u3044\u914d\u5217\u306b\u5909\u63db\u3057\u307e\u3059\u3002</li> <li>\u30de\u30fc\u30b8\u30d5\u30a7\u30fc\u30ba\uff1a\u30b5\u30d6\u914d\u5217\u306e\u9577\u3055\u304c1\u306b\u306a\u3063\u305f\u3068\u304d\u306b\u5206\u5272\u3092\u505c\u6b62\u3057\u3001\u305d\u306e\u5f8c\u30de\u30fc\u30b8\u3092\u958b\u59cb\u3057\u307e\u3059\u30022\u3064\u306e\u77ed\u3044\u30bd\u30fc\u30c8\u6e08\u307f\u914d\u5217\u3092\u9023\u7d9a\u7684\u306b\u3088\u308a\u9577\u3044\u30bd\u30fc\u30c8\u6e08\u307f\u914d\u5217\u306b\u30de\u30fc\u30b8\u3057\u3001\u30d7\u30ed\u30bb\u30b9\u304c\u5b8c\u4e86\u3059\u308b\u307e\u3067\u7d9a\u884c\u3057\u307e\u3059\u3002</li> </ol> <p></p> <p> \u56f3 11-10 \u00a0 The divide and merge phases of merge sort </p>"},{"location":"chapter_sorting/merge_sort/#1161","title":"11.6.1 \u00a0 \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u30ef\u30fc\u30af\u30d5\u30ed\u30fc","text":"<p>\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u300c\u5206\u5272\u30d5\u30a7\u30fc\u30ba\u300d\u306f\u4e2d\u70b9\u304b\u3089\u914d\u5217\u3092\u4e0a\u304b\u3089\u4e0b\u306b2\u3064\u306e\u30b5\u30d6\u914d\u5217\u306b\u518d\u5e30\u7684\u306b\u5206\u5272\u3057\u307e\u3059\u3002</p> <ol> <li>\u4e2d\u70b9<code>mid</code>\u3092\u8a08\u7b97\u3057\u3001\u5de6\u30b5\u30d6\u914d\u5217\uff08\u533a\u9593<code>[left, mid]</code>\uff09\u3068\u53f3\u30b5\u30d6\u914d\u5217\uff08\u533a\u9593<code>[mid + 1, right]</code>\uff09\u3092\u518d\u5e30\u7684\u306b\u5206\u5272\u3057\u307e\u3059\u3002</li> <li>\u30b5\u30d6\u914d\u5217\u306e\u9577\u3055\u304c1\u306b\u306a\u308b\u307e\u3067\u30b9\u30c6\u30c3\u30d7<code>1.</code>\u3092\u518d\u5e30\u7684\u306b\u7d9a\u884c\u3057\u3001\u305d\u306e\u5f8c\u505c\u6b62\u3057\u307e\u3059\u3002</li> </ol> <p>\u300c\u30de\u30fc\u30b8\u30d5\u30a7\u30fc\u30ba\u300d\u306f\u5de6\u3068\u53f3\u306e\u30b5\u30d6\u914d\u5217\u3092\u4e0b\u304b\u3089\u4e0a\u306b\u30bd\u30fc\u30c8\u6e08\u307f\u914d\u5217\u306b\u7d50\u5408\u3057\u307e\u3059\u3002\u91cd\u8981\u306a\u306e\u306f\u3001\u30de\u30fc\u30b8\u304c\u9577\u30551\u306e\u30b5\u30d6\u914d\u5217\u304b\u3089\u958b\u59cb\u3055\u308c\u3001\u30de\u30fc\u30b8\u30d5\u30a7\u30fc\u30ba\u4e2d\u306b\u5404\u30b5\u30d6\u914d\u5217\u304c\u30bd\u30fc\u30c8\u3055\u308c\u308b\u3053\u3068\u3067\u3059\u3002</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> \u56f3 11-11 \u00a0 Merge sort process </p> <p>\u30de\u30fc\u30b8\u30bd\u30fc\u30c8\u306e\u518d\u5e30\u9806\u5e8f\u306f\u4e8c\u5206\u6728\u306e\u5f8c\u9806\u6a2a\u65ad\u3068\u4e00\u81f4\u3059\u308b\u3053\u3068\u304c\u89b3\u5bdf\u3067\u304d\u307e\u3059\u3002</p> <ul> <li>\u5f8c\u9806\u6a2a\u65ad\uff1a\u307e\u305a\u5de6\u306e\u30b5\u30d6\u30c4\u30ea\u30fc\u3092\u518d\u5e30\u7684\u306b\u6a2a\u65ad\u3057\u3001\u6b21\u306b\u53f3\u306e\u30b5\u30d6\u30c4\u30ea\u30fc\u3092\u6a2a\u65ad\u3057\u3001\u6700\u5f8c\u306b\u30eb\u30fc\u30c8\u30ce\u30fc\u30c9\u3092\u51e6\u7406\u3057\u307e\u3059\u3002</li> <li>\u30de\u30fc\u30b8\u30bd\u30fc\u30c8\uff1a\u307e\u305a\u5de6\u306e\u30b5\u30d6\u914d\u5217\u3092\u518d\u5e30\u7684\u306b\u51e6\u7406\u3057\u3001\u6b21\u306b\u53f3\u306e\u30b5\u30d6\u914d\u5217\u3092\u51e6\u7406\u3057\u3001\u6700\u5f8c\u306b\u30de\u30fc\u30b8\u3092\u5b9f\u884c\u3057\u307e\u3059\u3002</li> </ul> <p>\u30de\u30fc\u30b8\u30bd\u30fc\u30c8\u306e\u5b9f\u88c5\u306f\u4ee5\u4e0b\u306e\u30b3\u30fc\u30c9\u306b\u793a\u3055\u308c\u307e\u3059\u3002<code>nums</code>\u3067\u30de\u30fc\u30b8\u3055\u308c\u308b\u533a\u9593\u306f<code>[left, right]</code>\u3067\u3001<code>tmp</code>\u306e\u5bfe\u5fdc\u3059\u308b\u533a\u9593\u306f<code>[0, right - left]</code>\u3067\u3042\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig merge_sort.py<pre><code>def merge(nums: list[int], left: int, mid: int, right: int):\n    \"\"\"\u5de6\u30b5\u30d6\u914d\u5217\u3068\u53f3\u30b5\u30d6\u914d\u5217\u3092\u30de\u30fc\u30b8\"\"\"\n    # \u5de6\u30b5\u30d6\u914d\u5217\u533a\u9593\u306f [left, mid]\u3001\u53f3\u30b5\u30d6\u914d\u5217\u533a\u9593\u306f [mid+1, right]\n    # \u4e00\u6642\u914d\u5217 tmp \u3092\u4f5c\u6210\u3057\u3066\u30de\u30fc\u30b8\u7d50\u679c\u3092\u683c\u7d0d\n    tmp = [0] * (right - left + 1)\n    # \u5de6\u53f3\u30b5\u30d6\u914d\u5217\u306e\u958b\u59cb\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u521d\u671f\u5316\n    i, j, k = left, mid + 1, 0\n    # \u4e21\u65b9\u306e\u30b5\u30d6\u914d\u5217\u306b\u8981\u7d20\u304c\u6b8b\u3063\u3066\u3044\u308b\u9593\u3001\u3088\u308a\u5c0f\u3055\u3044\u8981\u7d20\u3092\u4e00\u6642\u914d\u5217\u306b\u30b3\u30d4\u30fc\n    while i &lt;= mid and j &lt;= right:\n        if nums[i] &lt;= nums[j]:\n            tmp[k] = nums[i]\n            i += 1\n        else:\n            tmp[k] = nums[j]\n            j += 1\n        k += 1\n    # \u6b8b\u3063\u305f\u5de6\u53f3\u30b5\u30d6\u914d\u5217\u306e\u8981\u7d20\u3092\u4e00\u6642\u914d\u5217\u306b\u30b3\u30d4\u30fc\n    while i &lt;= mid:\n        tmp[k] = nums[i]\n        i += 1\n        k += 1\n    while j &lt;= right:\n        tmp[k] = nums[j]\n        j += 1\n        k += 1\n    # \u4e00\u6642\u914d\u5217 tmp \u306e\u8981\u7d20\u3092\u5143\u306e\u914d\u5217 nums \u306e\u5bfe\u5fdc\u3059\u308b\u533a\u9593\u306b\u30b3\u30d4\u30fc\u30d0\u30c3\u30af\n    for k in range(0, len(tmp)):\n        nums[left + k] = tmp[k]\n\ndef merge_sort(nums: list[int], left: int, right: int):\n    \"\"\"\u30de\u30fc\u30b8\u30bd\u30fc\u30c8\"\"\"\n    # \u7d42\u4e86\u6761\u4ef6\n    if left &gt;= right:\n        return  # \u30b5\u30d6\u914d\u5217\u306e\u9577\u3055\u304c1\u306e\u3068\u304d\u306b\u518d\u5e30\u3092\u7d42\u4e86\n    # \u5206\u5272\u6bb5\u968e\n    mid = left + (right - left) // 2  # \u4e2d\u70b9\u3092\u8a08\u7b97\n    merge_sort(nums, left, mid)  # \u5de6\u30b5\u30d6\u914d\u5217\u3092\u518d\u5e30\u7684\u306b\u51e6\u7406\n    merge_sort(nums, mid + 1, right)  # \u53f3\u30b5\u30d6\u914d\u5217\u3092\u518d\u5e30\u7684\u306b\u51e6\u7406\n    # \u30de\u30fc\u30b8\u6bb5\u968e\n    merge(nums, left, mid, right)\n</code></pre> merge_sort.cpp<pre><code>/* \u5de6\u30b5\u30d6\u914d\u5217\u3068\u53f3\u30b5\u30d6\u914d\u5217\u3092\u30de\u30fc\u30b8 */\nvoid merge(vector&lt;int&gt; &amp;nums, int left, int mid, int right) {\n    // \u5de6\u30b5\u30d6\u914d\u5217\u306e\u533a\u9593\u306f[left, mid]\u3001\u53f3\u30b5\u30d6\u914d\u5217\u306e\u533a\u9593\u306f[mid+1, right]\n    // \u30de\u30fc\u30b8\u7d50\u679c\u3092\u4fdd\u5b58\u3059\u308b\u4e00\u6642\u914d\u5217tmp\u3092\u4f5c\u6210\n    vector&lt;int&gt; tmp(right - left + 1);\n    // \u5de6\u53f3\u30b5\u30d6\u914d\u5217\u306e\u958b\u59cb\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u521d\u671f\u5316\n    int i = left, j = mid + 1, k = 0;\n    // \u4e21\u30b5\u30d6\u914d\u5217\u306b\u8981\u7d20\u304c\u3042\u308b\u9593\u3001\u5c0f\u3055\u3044\u65b9\u306e\u8981\u7d20\u3092\u4e00\u6642\u914d\u5217\u306b\u30b3\u30d4\u30fc\n    while (i &lt;= mid &amp;&amp; j &lt;= right) {\n        if (nums[i] &lt;= nums[j])\n            tmp[k++] = nums[i++];\n        else\n            tmp[k++] = nums[j++];\n    }\n    // \u5de6\u53f3\u30b5\u30d6\u914d\u5217\u306e\u6b8b\u308a\u306e\u8981\u7d20\u3092\u4e00\u6642\u914d\u5217\u306b\u30b3\u30d4\u30fc\n    while (i &lt;= mid) {\n        tmp[k++] = nums[i++];\n    }\n    while (j &lt;= right) {\n        tmp[k++] = nums[j++];\n    }\n    // \u4e00\u6642\u914d\u5217tmp\u306e\u8981\u7d20\u3092\u5143\u306e\u914d\u5217nums\u306e\u5bfe\u5fdc\u3059\u308b\u533a\u9593\u306b\u30b3\u30d4\u30fc\n    for (k = 0; k &lt; tmp.size(); k++) {\n        nums[left + k] = tmp[k];\n    }\n}\n\n/* \u30de\u30fc\u30b8\u30bd\u30fc\u30c8 */\nvoid mergeSort(vector&lt;int&gt; &amp;nums, int left, int right) {\n    // \u7d42\u4e86\u6761\u4ef6\n    if (left &gt;= right)\n        return; // \u30b5\u30d6\u914d\u5217\u306e\u9577\u3055\u304c1\u306e\u6642\u3001\u518d\u5e30\u3092\u7d42\u4e86\n    // \u5206\u5272\u6bb5\u968e\n    int mid = left + (right - left) / 2;    // \u4e2d\u70b9\u3092\u8a08\u7b97\n    mergeSort(nums, left, mid);      // \u5de6\u30b5\u30d6\u914d\u5217\u3092\u518d\u5e30\u7684\u306b\u51e6\u7406\n    mergeSort(nums, mid + 1, right); // \u53f3\u30b5\u30d6\u914d\u5217\u3092\u518d\u5e30\u7684\u306b\u51e6\u7406\n    // \u30de\u30fc\u30b8\u6bb5\u968e\n    merge(nums, left, mid, right);\n}\n</code></pre> merge_sort.java<pre><code>/* \u5de6\u90e8\u5206\u914d\u5217\u3068\u53f3\u90e8\u5206\u914d\u5217\u3092\u30de\u30fc\u30b8 */\nvoid merge(int[] nums, int left, int mid, int right) {\n    // \u5de6\u90e8\u5206\u914d\u5217\u533a\u9593\u306f [left, mid]\u3001\u53f3\u90e8\u5206\u914d\u5217\u533a\u9593\u306f [mid+1, right]\n    // \u4e00\u6642\u914d\u5217 tmp \u3092\u4f5c\u6210\u3057\u3066\u30de\u30fc\u30b8\u7d50\u679c\u3092\u683c\u7d0d\n    int[] tmp = new int[right - left + 1];\n    // \u5de6\u53f3\u90e8\u5206\u914d\u5217\u306e\u958b\u59cb\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u521d\u671f\u5316\n    int i = left, j = mid + 1, k = 0;\n    // \u4e21\u90e8\u5206\u914d\u5217\u306b\u307e\u3060\u8981\u7d20\u304c\u3042\u308b\u9593\u3001\u6bd4\u8f03\u3057\u3066\u3088\u308a\u5c0f\u3055\u3044\u8981\u7d20\u3092\u4e00\u6642\u914d\u5217\u306b\u30b3\u30d4\u30fc\n    while (i &lt;= mid &amp;&amp; j &lt;= right) {\n        if (nums[i] &lt;= nums[j])\n            tmp[k++] = nums[i++];\n        else\n            tmp[k++] = nums[j++];\n    }\n    // \u5de6\u53f3\u90e8\u5206\u914d\u5217\u306e\u6b8b\u308a\u306e\u8981\u7d20\u3092\u4e00\u6642\u914d\u5217\u306b\u30b3\u30d4\u30fc\n    while (i &lt;= mid) {\n        tmp[k++] = nums[i++];\n    }\n    while (j &lt;= right) {\n        tmp[k++] = nums[j++];\n    }\n    // \u4e00\u6642\u914d\u5217 tmp \u306e\u8981\u7d20\u3092\u5143\u306e\u914d\u5217 nums \u306e\u5bfe\u5fdc\u3059\u308b\u533a\u9593\u306b\u30b3\u30d4\u30fc\u30d0\u30c3\u30af\n    for (k = 0; k &lt; tmp.length; k++) {\n        nums[left + k] = tmp[k];\n    }\n}\n\n/* \u30de\u30fc\u30b8\u30bd\u30fc\u30c8 */\nvoid mergeSort(int[] nums, int left, int right) {\n    // \u7d42\u4e86\u6761\u4ef6\n    if (left &gt;= right)\n        return; // \u90e8\u5206\u914d\u5217\u306e\u9577\u3055\u304c 1 \u306e\u3068\u304d\u518d\u5e30\u3092\u7d42\u4e86\n    // \u5206\u5272\u6bb5\u968e\n    int mid = left + (right - left) / 2; // \u4e2d\u70b9\u3092\u8a08\u7b97\n    mergeSort(nums, left, mid); // \u5de6\u90e8\u5206\u914d\u5217\u3092\u518d\u5e30\u7684\u306b\u51e6\u7406\n    mergeSort(nums, mid + 1, right); // \u53f3\u90e8\u5206\u914d\u5217\u3092\u518d\u5e30\u7684\u306b\u51e6\u7406\n    // \u30de\u30fc\u30b8\u6bb5\u968e\n    merge(nums, left, mid, right);\n}\n</code></pre> merge_sort.cs<pre><code>[class]{merge_sort}-[func]{Merge}\n\n[class]{merge_sort}-[func]{MergeSort}\n</code></pre> merge_sort.go<pre><code>[class]{}-[func]{merge}\n\n[class]{}-[func]{mergeSort}\n</code></pre> merge_sort.swift<pre><code>[class]{}-[func]{merge}\n\n[class]{}-[func]{mergeSort}\n</code></pre> merge_sort.js<pre><code>[class]{}-[func]{merge}\n\n[class]{}-[func]{mergeSort}\n</code></pre> merge_sort.ts<pre><code>[class]{}-[func]{merge}\n\n[class]{}-[func]{mergeSort}\n</code></pre> merge_sort.dart<pre><code>[class]{}-[func]{merge}\n\n[class]{}-[func]{mergeSort}\n</code></pre> merge_sort.rs<pre><code>[class]{}-[func]{merge}\n\n[class]{}-[func]{merge_sort}\n</code></pre> merge_sort.c<pre><code>[class]{}-[func]{merge}\n\n[class]{}-[func]{mergeSort}\n</code></pre> merge_sort.kt<pre><code>[class]{}-[func]{merge}\n\n[class]{}-[func]{mergeSort}\n</code></pre> merge_sort.rb<pre><code>[class]{}-[func]{merge}\n\n[class]{}-[func]{merge_sort}\n</code></pre> merge_sort.zig<pre><code>[class]{}-[func]{merge}\n\n[class]{}-[func]{mergeSort}\n</code></pre>"},{"location":"chapter_sorting/merge_sort/#1162","title":"11.6.2 \u00a0 \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u7279\u6027","text":"<ul> <li>\\(O(n \\log n)\\)\u306e\u6642\u9593\u8a08\u7b97\u91cf\u3001\u975e\u9069\u5fdc\u30bd\u30fc\u30c8\uff1a\u5206\u5272\u306b\u3088\u308a\u9ad8\u3055\\(\\log n\\)\u306e\u518d\u5e30\u30c4\u30ea\u30fc\u304c\u4f5c\u6210\u3055\u308c\u3001\u5404\u5c64\u3067\u5408\u8a08\\(n\\)\u56de\u306e\u64cd\u4f5c\u3092\u30de\u30fc\u30b8\u3057\u3001\u5168\u4f53\u7684\u306a\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O(n \\log n)\\)\u3068\u306a\u308a\u307e\u3059\u3002</li> <li>\\(O(n)\\)\u306e\u7a7a\u9593\u8a08\u7b97\u91cf\u3001\u975e\u30a4\u30f3\u30d7\u30ec\u30fc\u30b9\u30bd\u30fc\u30c8\uff1a\u518d\u5e30\u6df1\u5ea6\u306f\\(\\log n\\)\u3067\u3001\\(O(\\log n)\\)\u306e\u30b9\u30bf\u30c3\u30af\u30d5\u30ec\u30fc\u30e0\u7a7a\u9593\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002\u30de\u30fc\u30b8\u64cd\u4f5c\u306b\u306f\u88dc\u52a9\u914d\u5217\u304c\u5fc5\u8981\u3067\u3001\u8ffd\u52a0\u306e\\(O(n)\\)\u7a7a\u9593\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002</li> <li>\u5b89\u5b9a\u30bd\u30fc\u30c8\uff1a\u30de\u30fc\u30b8\u30d7\u30ed\u30bb\u30b9\u4e2d\u3001\u7b49\u3057\u3044\u8981\u7d20\u306e\u9806\u5e8f\u306f\u5909\u66f4\u3055\u308c\u307e\u305b\u3093\u3002</li> </ul>"},{"location":"chapter_sorting/merge_sort/#1163","title":"11.6.3 \u00a0 \u9023\u7d50\u30ea\u30b9\u30c8\u306e\u30bd\u30fc\u30c8","text":"<p>\u9023\u7d50\u30ea\u30b9\u30c8\u306e\u5834\u5408\u3001\u30de\u30fc\u30b8\u30bd\u30fc\u30c8\u306f\u4ed6\u306e\u30bd\u30fc\u30c8\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3088\u308a\u3082\u5927\u304d\u306a\u5229\u70b9\u304c\u3042\u308a\u307e\u3059\u3002\u9023\u7d50\u30ea\u30b9\u30c8\u30bd\u30fc\u30c8\u30bf\u30b9\u30af\u306e\u7a7a\u9593\u8a08\u7b97\u91cf\u3092\\(O(1)\\)\u306b\u6700\u9069\u5316\u3067\u304d\u307e\u3059\u3002</p> <ul> <li>\u5206\u5272\u30d5\u30a7\u30fc\u30ba\uff1a\u300c\u518d\u5e30\u300d\u306e\u4ee3\u308f\u308a\u306b\u300c\u53cd\u5fa9\u300d\u3092\u4f7f\u7528\u3057\u3066\u9023\u7d50\u30ea\u30b9\u30c8\u5206\u5272\u4f5c\u696d\u3092\u5b9f\u884c\u3067\u304d\u308b\u305f\u3081\u3001\u518d\u5e30\u3067\u4f7f\u7528\u3055\u308c\u308b\u30b9\u30bf\u30c3\u30af\u30d5\u30ec\u30fc\u30e0\u7a7a\u9593\u3092\u7bc0\u7d04\u3067\u304d\u307e\u3059\u3002</li> <li>\u30de\u30fc\u30b8\u30d5\u30a7\u30fc\u30ba\uff1a\u9023\u7d50\u30ea\u30b9\u30c8\u3067\u306f\u3001\u30ce\u30fc\u30c9\u306e\u633f\u5165\u3068\u524a\u9664\u64cd\u4f5c\u306f\u53c2\u7167\uff08\u30dd\u30a4\u30f3\u30bf\uff09\u3092\u5909\u66f4\u3059\u308b\u3053\u3068\u3067\u5b9f\u73fe\u3067\u304d\u308b\u305f\u3081\u3001\u30de\u30fc\u30b8\u30d5\u30a7\u30fc\u30ba\uff082\u3064\u306e\u77ed\u3044\u9806\u5e8f\u4ed8\u304d\u30ea\u30b9\u30c8\u30921\u3064\u306e\u9577\u3044\u9806\u5e8f\u4ed8\u304d\u30ea\u30b9\u30c8\u306b\u7d50\u5408\uff09\u4e2d\u306b\u8ffd\u52a0\u306e\u30ea\u30b9\u30c8\u3092\u4f5c\u6210\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u305b\u3093\u3002</li> </ul> <p>\u5b9f\u88c5\u306e\u8a73\u7d30\u306f\u6bd4\u8f03\u7684\u8907\u96d1\u3067\u3001\u8208\u5473\u306e\u3042\u308b\u8aad\u8005\u306f\u95a2\u9023\u8cc7\u6599\u3092\u53c2\u7167\u3057\u3066\u5b66\u7fd2\u3057\u3066\u304f\u3060\u3055\u3044\u3002</p>"},{"location":"chapter_sorting/quick_sort/","title":"11.5 \u00a0 \u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8","text":"<p>\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u306f\u5206\u5272\u7d71\u6cbb\u6226\u7565\u306b\u57fa\u3065\u304f\u30bd\u30fc\u30c8\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3067\u3001\u305d\u306e\u52b9\u7387\u6027\u3068\u5e45\u5e83\u3044\u5fdc\u7528\u3067\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\u3002</p> <p>\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u306e\u30b3\u30a2\u64cd\u4f5c\u306f\u300c\u30d4\u30dc\u30c3\u30c8\u5206\u5272\u300d\u3067\u3001\u914d\u5217\u304b\u3089\u8981\u7d20\u3092\u300c\u30d4\u30dc\u30c3\u30c8\u300d\u3068\u3057\u3066\u9078\u629e\u3057\u3001\u30d4\u30dc\u30c3\u30c8\u3088\u308a\u5c0f\u3055\u3044\u3059\u3079\u3066\u306e\u8981\u7d20\u3092\u305d\u306e\u5de6\u5074\u306b\u79fb\u52d5\u3057\u3001\u30d4\u30dc\u30c3\u30c8\u3088\u308a\u5927\u304d\u3044\u3059\u3079\u3066\u306e\u8981\u7d20\u3092\u305d\u306e\u53f3\u5074\u306b\u79fb\u52d5\u3059\u308b\u3053\u3068\u3092\u76ee\u7684\u3068\u3057\u3066\u3044\u307e\u3059\u3002\u5177\u4f53\u7684\u306b\u3001\u30d4\u30dc\u30c3\u30c8\u5206\u5272\u306e\u30d7\u30ed\u30bb\u30b9\u306f\u4e0b\u56f3\u306b\u793a\u3055\u308c\u307e\u3059\u3002</p> <ol> <li>\u914d\u5217\u306e\u6700\u3082\u5de6\u306e\u8981\u7d20\u3092\u30d4\u30dc\u30c3\u30c8\u3068\u3057\u3066\u9078\u629e\u3057\u30012\u3064\u306e\u30dd\u30a4\u30f3\u30bf<code>i</code>\u3068<code>j</code>\u3092\u521d\u671f\u5316\u3057\u3066\u914d\u5217\u306e\u4e21\u7aef\u3092\u305d\u308c\u305e\u308c\u6307\u3059\u3088\u3046\u306b\u3057\u307e\u3059\u3002</li> <li>\u5404\u30e9\u30a6\u30f3\u30c9\u3067<code>i</code>\uff08<code>j</code>\uff09\u3092\u4f7f\u7528\u3057\u3066\u30d4\u30dc\u30c3\u30c8\u3088\u308a\u5927\u304d\u3044\uff08\u5c0f\u3055\u3044\uff09\u6700\u521d\u306e\u8981\u7d20\u3092\u63a2\u7d22\u3057\u3001\u6b21\u306b\u3053\u308c\u30892\u3064\u306e\u8981\u7d20\u3092\u4ea4\u63db\u3059\u308b\u30eb\u30fc\u30d7\u3092\u8a2d\u5b9a\u3057\u307e\u3059\u3002</li> <li><code>i</code>\u3068<code>j</code>\u304c\u51fa\u4f1a\u3046\u307e\u3067\u30b9\u30c6\u30c3\u30d7<code>2.</code>\u3092\u7e70\u308a\u8fd4\u3057\u3001\u6700\u5f8c\u306b\u30d4\u30dc\u30c3\u30c8\u30922\u3064\u306e\u30b5\u30d6\u914d\u5217\u306e\u5883\u754c\u306b\u4ea4\u63db\u3057\u307e\u3059\u3002</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> \u56f3 11-8 \u00a0 Pivot division process </p> <p>\u30d4\u30dc\u30c3\u30c8\u5206\u5272\u5f8c\u3001\u5143\u306e\u914d\u5217\u306f3\u3064\u306e\u90e8\u5206\u306b\u5206\u5272\u3055\u308c\u307e\u3059\uff1a\u5de6\u30b5\u30d6\u914d\u5217\u3001\u30d4\u30dc\u30c3\u30c8\u3001\u53f3\u30b5\u30d6\u914d\u5217\u3067\u3001\u300c\u5de6\u30b5\u30d6\u914d\u5217\u306e\u4efb\u610f\u306e\u8981\u7d20 \\(\\leq\\) \u30d4\u30dc\u30c3\u30c8 \\(\\leq\\) \u53f3\u30b5\u30d6\u914d\u5217\u306e\u4efb\u610f\u306e\u8981\u7d20\u300d\u3092\u6e80\u305f\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u3053\u308c\u30892\u3064\u306e\u30b5\u30d6\u914d\u5217\u306e\u307f\u3092\u30bd\u30fc\u30c8\u3059\u308c\u3070\u3088\u3044\u306e\u3067\u3059\u3002</p> <p>\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u306e\u5206\u5272\u7d71\u6cbb\u6226\u7565</p> <p>\u30d4\u30dc\u30c3\u30c8\u5206\u5272\u306e\u672c\u8cea\u306f\u3001\u3088\u308a\u9577\u3044\u914d\u5217\u306e\u30bd\u30fc\u30c8\u554f\u984c\u3092\u3088\u308a\u77ed\u30442\u3064\u306e\u914d\u5217\u306b\u7c21\u7d20\u5316\u3059\u308b\u3053\u3068\u3067\u3059\u3002</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig quick_sort.py<pre><code>def partition(self, nums: list[int], left: int, right: int) -&gt; int:\n    \"\"\"\u5206\u5272\"\"\"\n    # nums[left] \u3092\u30d4\u30dc\u30c3\u30c8\u3068\u3057\u3066\u4f7f\u7528\n    i, j = left, right\n    while i &lt; j:\n        while i &lt; j and nums[j] &gt;= nums[left]:\n            j -= 1  # \u53f3\u304b\u3089\u5de6\u3078\u30d4\u30dc\u30c3\u30c8\u3088\u308a\u5c0f\u3055\u3044\u6700\u521d\u306e\u8981\u7d20\u3092\u63a2\u3059\n        while i &lt; j and nums[i] &lt;= nums[left]:\n            i += 1  # \u5de6\u304b\u3089\u53f3\u3078\u30d4\u30dc\u30c3\u30c8\u3088\u308a\u5927\u304d\u3044\u6700\u521d\u306e\u8981\u7d20\u3092\u63a2\u3059\n        # \u8981\u7d20\u3092\u4ea4\u63db\n        nums[i], nums[j] = nums[j], nums[i]\n    # \u30d4\u30dc\u30c3\u30c8\u30922\u3064\u306e\u30b5\u30d6\u914d\u5217\u306e\u5883\u754c\u306b\u4ea4\u63db\n    nums[i], nums[left] = nums[left], nums[i]\n    return i  # \u30d4\u30dc\u30c3\u30c8\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8fd4\u3059\n</code></pre> quick_sort.cpp<pre><code>/* \u5206\u5272 */\nint partition(vector&lt;int&gt; &amp;nums, int left, int right) {\n    // nums[left]\u3092\u30d4\u30dc\u30c3\u30c8\u3068\u3057\u3066\u4f7f\u7528\n    int i = left, j = right;\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\n            j--; // \u53f3\u304b\u3089\u5de6\u3078\u30d4\u30dc\u30c3\u30c8\u3088\u308a\u5c0f\u3055\u3044\u6700\u521d\u306e\u8981\u7d20\u3092\u691c\u7d22\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\n            i++;          // \u5de6\u304b\u3089\u53f3\u3078\u30d4\u30dc\u30c3\u30c8\u3088\u308a\u5927\u304d\u3044\u6700\u521d\u306e\u8981\u7d20\u3092\u691c\u7d22\n        swap(nums, i, j); // \u3053\u308c\u3089\u4e8c\u3064\u306e\u8981\u7d20\u3092\u4ea4\u63db\n    }\n    swap(nums, i, left); // \u30d4\u30dc\u30c3\u30c8\u3092\u4e8c\u3064\u306e\u30b5\u30d6\u914d\u5217\u306e\u5883\u754c\u306b\u4ea4\u63db\n    return i;            // \u30d4\u30dc\u30c3\u30c8\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8fd4\u3059\n}\n</code></pre> quick_sort.java<pre><code>/* \u8981\u7d20\u3092\u4ea4\u63db */\nvoid swap(int[] nums, int i, int j) {\n    int tmp = nums[i];\n    nums[i] = nums[j];\n    nums[j] = tmp;\n}\n\n/* \u5206\u5272 */\nint partition(int[] nums, int left, int right) {\n    // nums[left] \u3092\u57fa\u6e96\u5024\u3068\u3057\u3066\u4f7f\u7528\n    int i = left, j = right;\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\n            j--;          // \u53f3\u304b\u3089\u5de6\u3078\u3001\u57fa\u6e96\u5024\u3088\u308a\u5c0f\u3055\u3044\u6700\u521d\u306e\u8981\u7d20\u3092\u691c\u7d22\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\n            i++;          // \u5de6\u304b\u3089\u53f3\u3078\u3001\u57fa\u6e96\u5024\u3088\u308a\u5927\u304d\u3044\u6700\u521d\u306e\u8981\u7d20\u3092\u691c\u7d22\n        swap(nums, i, j); // \u3053\u308c\u30892\u3064\u306e\u8981\u7d20\u3092\u4ea4\u63db\n    }\n    swap(nums, i, left);  // \u57fa\u6e96\u5024\u30922\u3064\u306e\u90e8\u5206\u914d\u5217\u306e\u5883\u754c\u306b\u4ea4\u63db\n    return i;             // \u57fa\u6e96\u5024\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8fd4\u3059\n}\n</code></pre> quick_sort.cs<pre><code>[class]{quickSort}-[func]{Swap}\n\n[class]{quickSort}-[func]{Partition}\n</code></pre> quick_sort.go<pre><code>[class]{quickSort}-[func]{partition}\n</code></pre> quick_sort.swift<pre><code>[class]{}-[func]{partition}\n</code></pre> quick_sort.js<pre><code>[class]{QuickSort}-[func]{swap}\n\n[class]{QuickSort}-[func]{partition}\n</code></pre> quick_sort.ts<pre><code>[class]{QuickSort}-[func]{swap}\n\n[class]{QuickSort}-[func]{partition}\n</code></pre> quick_sort.dart<pre><code>[class]{QuickSort}-[func]{_swap}\n\n[class]{QuickSort}-[func]{_partition}\n</code></pre> quick_sort.rs<pre><code>[class]{QuickSort}-[func]{partition}\n</code></pre> quick_sort.c<pre><code>[class]{}-[func]{swap}\n\n[class]{}-[func]{partition}\n</code></pre> quick_sort.kt<pre><code>[class]{}-[func]{swap}\n\n[class]{}-[func]{partition}\n</code></pre> quick_sort.rb<pre><code>[class]{QuickSort}-[func]{partition}\n</code></pre> quick_sort.zig<pre><code>[class]{QuickSort}-[func]{swap}\n\n[class]{QuickSort}-[func]{partition}\n</code></pre>"},{"location":"chapter_sorting/quick_sort/#1151","title":"11.5.1 \u00a0 \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u30d7\u30ed\u30bb\u30b9","text":"<p>\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u306e\u5168\u4f53\u7684\u306a\u30d7\u30ed\u30bb\u30b9\u306f\u4e0b\u56f3\u306b\u793a\u3055\u308c\u307e\u3059\u3002</p> <ol> <li>\u307e\u305a\u3001\u5143\u306e\u914d\u5217\u306b\u5bfe\u3057\u3066\u300c\u30d4\u30dc\u30c3\u30c8\u5206\u5272\u300d\u3092\u5b9f\u884c\u3057\u3001\u672a\u30bd\u30fc\u30c8\u306e\u5de6\u3068\u53f3\u306e\u30b5\u30d6\u914d\u5217\u3092\u53d6\u5f97\u3057\u307e\u3059\u3002</li> <li>\u6b21\u306b\u3001\u5de6\u3068\u53f3\u306e\u30b5\u30d6\u914d\u5217\u306b\u5bfe\u3057\u3066\u305d\u308c\u305e\u308c\u518d\u5e30\u7684\u306b\u300c\u30d4\u30dc\u30c3\u30c8\u5206\u5272\u300d\u3092\u5b9f\u884c\u3057\u307e\u3059\u3002</li> <li>\u30b5\u30d6\u914d\u5217\u306e\u9577\u3055\u304c1\u306b\u306a\u308b\u307e\u3067\u518d\u5e30\u3092\u7d9a\u3051\u3001\u914d\u5217\u5168\u4f53\u306e\u30bd\u30fc\u30c8\u3092\u5b8c\u4e86\u3057\u307e\u3059\u3002</li> </ol> <p></p> <p> \u56f3 11-9 \u00a0 Quick sort process </p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig quick_sort.py<pre><code>def quick_sort(self, nums: list[int], left: int, right: int):\n    \"\"\"\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\"\"\"\n    # \u30b5\u30d6\u914d\u5217\u306e\u9577\u3055\u304c1\u306e\u3068\u304d\u306b\u518d\u5e30\u3092\u7d42\u4e86\n    if left &gt;= right:\n        return\n    # \u5206\u5272\n    pivot = self.partition(nums, left, right)\n    # \u5de6\u30b5\u30d6\u914d\u5217\u3068\u53f3\u30b5\u30d6\u914d\u5217\u3092\u518d\u5e30\u7684\u306b\u51e6\u7406\n    self.quick_sort(nums, left, pivot - 1)\n    self.quick_sort(nums, pivot + 1, right)\n</code></pre> quick_sort.cpp<pre><code>/* \u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8 */\nvoid quickSort(vector&lt;int&gt; &amp;nums, int left, int right) {\n    // \u30b5\u30d6\u914d\u5217\u306e\u9577\u3055\u304c1\u306e\u6642\u3001\u518d\u5e30\u3092\u7d42\u4e86\n    if (left &gt;= right)\n        return;\n    // \u5206\u5272\n    int pivot = partition(nums, left, right);\n    // \u5de6\u30b5\u30d6\u914d\u5217\u3068\u53f3\u30b5\u30d6\u914d\u5217\u3092\u518d\u5e30\u7684\u306b\u51e6\u7406\n    quickSort(nums, left, pivot - 1);\n    quickSort(nums, pivot + 1, right);\n}\n</code></pre> quick_sort.java<pre><code>/* \u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8 */\nvoid quickSort(int[] nums, int left, int right) {\n    // \u90e8\u5206\u914d\u5217\u306e\u9577\u3055\u304c 1 \u306e\u3068\u304d\u518d\u5e30\u3092\u7d42\u4e86\n    if (left &gt;= right)\n        return;\n    // \u5206\u5272\n    int pivot = partition(nums, left, right);\n    // \u5de6\u90e8\u5206\u914d\u5217\u3068\u53f3\u90e8\u5206\u914d\u5217\u3092\u518d\u5e30\u7684\u306b\u51e6\u7406\n    quickSort(nums, left, pivot - 1);\n    quickSort(nums, pivot + 1, right);\n}\n</code></pre> quick_sort.cs<pre><code>[class]{quickSort}-[func]{QuickSort}\n</code></pre> quick_sort.go<pre><code>[class]{quickSort}-[func]{quickSort}\n</code></pre> quick_sort.swift<pre><code>[class]{}-[func]{quickSort}\n</code></pre> quick_sort.js<pre><code>[class]{QuickSort}-[func]{quickSort}\n</code></pre> quick_sort.ts<pre><code>[class]{QuickSort}-[func]{quickSort}\n</code></pre> quick_sort.dart<pre><code>[class]{QuickSort}-[func]{quickSort}\n</code></pre> quick_sort.rs<pre><code>[class]{QuickSort}-[func]{quick_sort}\n</code></pre> quick_sort.c<pre><code>[class]{}-[func]{quickSort}\n</code></pre> quick_sort.kt<pre><code>[class]{}-[func]{quickSort}\n</code></pre> quick_sort.rb<pre><code>[class]{QuickSort}-[func]{quick_sort}\n</code></pre> quick_sort.zig<pre><code>[class]{QuickSort}-[func]{quickSort}\n</code></pre>"},{"location":"chapter_sorting/quick_sort/#1152","title":"11.5.2 \u00a0 \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u7279\u5fb4","text":"<ul> <li>\\(O(n \\log n)\\)\u306e\u6642\u9593\u8a08\u7b97\u91cf\u3001\u975e\u9069\u5fdc\u30bd\u30fc\u30c8\uff1a\u5e73\u5747\u7684\u306a\u30b1\u30fc\u30b9\u3067\u306f\u3001\u30d4\u30dc\u30c3\u30c8\u5206\u5272\u306e\u518d\u5e30\u30ec\u30d9\u30eb\u306f\\(\\log n\\)\u3067\u3001\u30ec\u30d9\u30eb\u3042\u305f\u308a\u306e\u30eb\u30fc\u30d7\u306e\u7dcf\u6570\u306f\\(n\\)\u3067\u3042\u308a\u3001\u5168\u4f53\u3067\\(O(n \\log n)\\)\u306e\u6642\u9593\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002\u6700\u60aa\u306e\u5834\u5408\u3001\u5404\u30e9\u30a6\u30f3\u30c9\u306e\u30d4\u30dc\u30c3\u30c8\u5206\u5272\u306f\u9577\u3055\\(n\\)\u306e\u914d\u5217\u3092\u9577\u3055\\(0\\)\u3068\\(n - 1\\)\u306e2\u3064\u306e\u30b5\u30d6\u914d\u5217\u306b\u5206\u5272\u3057\u3001\u518d\u5e30\u30ec\u30d9\u30eb\u6570\u304c\\(n\\)\u306b\u9054\u3059\u308b\u3068\u3001\u5404\u30ec\u30d9\u30eb\u306e\u30eb\u30fc\u30d7\u6570\u306f\\(n\\)\u3067\u3001\u4f7f\u7528\u3055\u308c\u308b\u7dcf\u6642\u9593\u306f\\(O(n^2)\\)\u3067\u3059\u3002</li> <li>\\(O(n)\\)\u306e\u7a7a\u9593\u8a08\u7b97\u91cf\u3001\u30a4\u30f3\u30d7\u30ec\u30fc\u30b9\u30bd\u30fc\u30c8\uff1a\u5165\u529b\u914d\u5217\u304c\u5b8c\u5168\u306b\u9006\u9806\u306e\u5834\u5408\u3001\u6700\u60aa\u306e\u518d\u5e30\u6df1\u5ea6\u306f\\(n\\)\u306b\u9054\u3057\u3001\\(O(n)\\)\u306e\u30b9\u30bf\u30c3\u30af\u30d5\u30ec\u30fc\u30e0\u7a7a\u9593\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002\u30bd\u30fc\u30c8\u64cd\u4f5c\u306f\u8ffd\u52a0\u306e\u914d\u5217\u306e\u52a9\u3051\u306a\u3057\u306b\u5143\u306e\u914d\u5217\u3067\u5b9f\u884c\u3055\u308c\u307e\u3059\u3002</li> <li>\u975e\u5b89\u5b9a\u30bd\u30fc\u30c8\uff1a\u30d4\u30dc\u30c3\u30c8\u5206\u5272\u306e\u6700\u7d42\u30b9\u30c6\u30c3\u30d7\u3067\u3001\u30d4\u30dc\u30c3\u30c8\u306f\u7b49\u3057\u3044\u8981\u7d20\u306e\u53f3\u5074\u306b\u4ea4\u63db\u3055\u308c\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002</li> </ul>"},{"location":"chapter_sorting/quick_sort/#1153","title":"11.5.3 \u00a0 \u306a\u305c\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u306f\u9ad8\u901f\u306a\u306e\u304b","text":"<p>\u540d\u524d\u304c\u793a\u3059\u3088\u3046\u306b\u3001\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u306f\u52b9\u7387\u6027\u306e\u9762\u3067\u4e00\u5b9a\u306e\u5229\u70b9\u3092\u6301\u3064\u3079\u304d\u3067\u3059\u3002\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u306e\u5e73\u5747\u6642\u9593\u8a08\u7b97\u91cf\u306f\u300c\u30de\u30fc\u30b8\u30bd\u30fc\u30c8\u300d\u3084\u300c\u30d2\u30fc\u30d7\u30bd\u30fc\u30c8\u300d\u3068\u540c\u3058\u3067\u3059\u304c\u3001\u4ee5\u4e0b\u306e\u7406\u7531\u3067\u4e00\u822c\u7684\u306b\u3088\u308a\u52b9\u7387\u7684\u3067\u3059\u3002</p> <ul> <li>\u6700\u60aa\u30b1\u30fc\u30b9\u30b7\u30ca\u30ea\u30aa\u306e\u4f4e\u3044\u78ba\u7387\uff1a\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u306e\u6700\u60aa\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O(n^2)\\)\u3067\u3001\u30de\u30fc\u30b8\u30bd\u30fc\u30c8\u307b\u3069\u5b89\u5b9a\u3057\u3066\u3044\u307e\u305b\u3093\u304c\u3001\u307b\u3068\u3093\u3069\u306e\u5834\u5408\u3001\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u306f\\(O(n \\log n)\\)\u306e\u6642\u9593\u8a08\u7b97\u91cf\u3067\u52d5\u4f5c\u3067\u304d\u307e\u3059\u3002</li> <li>\u9ad8\u3044\u30ad\u30e3\u30c3\u30b7\u30e5\u5229\u7528\u7387\uff1a\u30d4\u30dc\u30c3\u30c8\u5206\u5272\u64cd\u4f5c\u4e2d\u3001\u30b7\u30b9\u30c6\u30e0\u306f\u30b5\u30d6\u914d\u5217\u5168\u4f53\u3092\u30ad\u30e3\u30c3\u30b7\u30e5\u306b\u30ed\u30fc\u30c9\u3067\u304d\u308b\u305f\u3081\u3001\u8981\u7d20\u306b\u3088\u308a\u52b9\u7387\u7684\u306b\u30a2\u30af\u30bb\u30b9\u3067\u304d\u307e\u3059\u3002\u5bfe\u7167\u7684\u306b\u3001\u300c\u30d2\u30fc\u30d7\u30bd\u30fc\u30c8\u300d\u306a\u3069\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u8981\u7d20\u306b\u30b8\u30e3\u30f3\u30d7\u65b9\u5f0f\u3067\u30a2\u30af\u30bb\u30b9\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u3001\u3053\u306e\u7279\u5fb4\u3092\u6b20\u3044\u3066\u3044\u307e\u3059\u3002</li> <li>\u8a08\u7b97\u91cf\u306e\u5c0f\u3055\u306a\u5b9a\u6570\u4fc2\u6570\uff1a\u4e0a\u8a183\u3064\u306e\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u4e2d\u3067\u3001\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u306f\u6bd4\u8f03\u3001\u4ee3\u5165\u3001\u4ea4\u63db\u306a\u3069\u306e\u64cd\u4f5c\u306e\u7dcf\u6570\u304c\u6700\u3082\u5c11\u306a\u3044\u3067\u3059\u3002\u3053\u308c\u306f\u300c\u633f\u5165\u30bd\u30fc\u30c8\u300d\u304c\u300c\u30d0\u30d6\u30eb\u30bd\u30fc\u30c8\u300d\u3088\u308a\u3082\u9ad8\u901f\u306a\u7406\u7531\u3068\u4f3c\u3066\u3044\u307e\u3059\u3002</li> </ul>"},{"location":"chapter_sorting/quick_sort/#1154","title":"11.5.4 \u00a0 \u30d4\u30dc\u30c3\u30c8\u6700\u9069\u5316","text":"<p>\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u306e\u6642\u9593\u52b9\u7387\u306f\u7279\u5b9a\u306e\u5165\u529b\u3067\u52a3\u5316\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u5165\u529b\u914d\u5217\u304c\u5b8c\u5168\u306b\u9006\u9806\u306e\u5834\u5408\u3001\u6700\u3082\u5de6\u306e\u8981\u7d20\u3092\u30d4\u30dc\u30c3\u30c8\u3068\u3057\u3066\u9078\u629e\u3059\u308b\u305f\u3081\u3001\u30d4\u30dc\u30c3\u30c8\u5206\u5272\u5f8c\u3001\u30d4\u30dc\u30c3\u30c8\u306f\u914d\u5217\u306e\u53f3\u7aef\u306b\u4ea4\u63db\u3055\u308c\u3001\u5de6\u30b5\u30d6\u914d\u5217\u306e\u9577\u3055\u304c\\(n - 1\\)\u3001\u53f3\u30b5\u30d6\u914d\u5217\u306e\u9577\u3055\u304c\\(0\\)\u306b\u306a\u308a\u307e\u3059\u3002\u3053\u306e\u65b9\u6cd5\u3092\u7d9a\u3051\u308b\u3068\u3001\u5404\u30e9\u30a6\u30f3\u30c9\u306e\u30d4\u30dc\u30c3\u30c8\u5206\u5272\u3067\u30b5\u30d6\u914d\u5217\u306e\u9577\u3055\u304c\\(0\\)\u306b\u306a\u308a\u3001\u5206\u5272\u7d71\u6cbb\u6226\u7565\u304c\u5931\u6557\u3057\u3001\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u306f\u300c\u30d0\u30d6\u30eb\u30bd\u30fc\u30c8\u300d\u306b\u4f3c\u305f\u5f62\u306b\u52a3\u5316\u3057\u307e\u3059\u3002</p> <p>\u3053\u306e\u72b6\u6cc1\u3092\u907f\u3051\u308b\u305f\u3081\u3001\u30d4\u30dc\u30c3\u30c8\u5206\u5272\u3067\u30d4\u30dc\u30c3\u30c8\u9078\u629e\u6226\u7565\u3092\u6700\u9069\u5316\u3067\u304d\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u8981\u7d20\u3092\u30e9\u30f3\u30c0\u30e0\u306b\u9078\u629e\u3057\u3066\u30d4\u30dc\u30c3\u30c8\u3068\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u305f\u3060\u3057\u3001\u904b\u304c\u60aa\u304f\u3001\u4e00\u8cab\u3057\u3066\u6700\u9069\u3067\u306a\u3044\u30d4\u30dc\u30c3\u30c8\u3092\u9078\u629e\u3057\u305f\u5834\u5408\u3001\u52b9\u7387\u306f\u307e\u3060\u6e80\u8db3\u3067\u304d\u307e\u305b\u3093\u3002</p> <p>\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u306f\u901a\u5e38\u300c\u7591\u4f3c\u4e71\u6570\u300d\u3092\u751f\u6210\u3059\u308b\u3053\u3068\u306b\u6ce8\u610f\u3059\u308b\u3053\u3068\u304c\u91cd\u8981\u3067\u3059\u3002\u7591\u4f3c\u4e71\u6570\u30b7\u30fc\u30b1\u30f3\u30b9\u306b\u5bfe\u3057\u3066\u7279\u5b9a\u306e\u30c6\u30b9\u30c8\u30b1\u30fc\u30b9\u3092\u69cb\u7bc9\u3059\u308b\u3068\u3001\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u306e\u52b9\u7387\u306f\u307e\u3060\u52a3\u5316\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002</p> <p>\u3055\u3089\u306a\u308b\u6539\u5584\u306e\u305f\u3081\u30013\u3064\u306e\u5019\u88dc\u8981\u7d20\uff08\u901a\u5e38\u306f\u914d\u5217\u306e\u6700\u521d\u3001\u6700\u5f8c\u3001\u4e2d\u70b9\u306e\u8981\u7d20\uff09\u3092\u9078\u629e\u3057\u3001**\u3053\u308c\u30893\u3064\u306e\u5019\u88dc\u8981\u7d20\u306e\u4e2d\u592e\u5024\u3092\u30d4\u30dc\u30c3\u30c8\u3068\u3057\u3066\u4f7f\u7528**\u3067\u304d\u307e\u3059\u3002\u3053\u306e\u65b9\u6cd5\u3067\u3001\u30d4\u30dc\u30c3\u30c8\u304c\u300c\u5c0f\u3055\u3059\u304e\u305a\u5927\u304d\u3059\u304e\u306a\u3044\u300d\u78ba\u7387\u304c\u5927\u5e45\u306b\u5897\u52a0\u3057\u307e\u3059\u3002\u3082\u3061\u308d\u3093\u3001\u3055\u3089\u306b\u591a\u304f\u306e\u5019\u88dc\u8981\u7d20\u3092\u9078\u629e\u3057\u3066\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5805\u7262\u6027\u3092\u3055\u3089\u306b\u5411\u4e0a\u3055\u305b\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002\u3053\u306e\u65b9\u6cd5\u306b\u3088\u308a\u3001\u6642\u9593\u8a08\u7b97\u91cf\u304c\\(O(n^2)\\)\u306b\u52a3\u5316\u3059\u308b\u78ba\u7387\u304c\u5927\u5e45\u306b\u524a\u6e1b\u3055\u308c\u307e\u3059\u3002</p> <p>\u30b5\u30f3\u30d7\u30eb\u30b3\u30fc\u30c9\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig quick_sort.py<pre><code>def median_three(self, nums: list[int], left: int, mid: int, right: int) -&gt; int:\n    \"\"\"3\u3064\u306e\u5019\u88dc\u8981\u7d20\u306e\u4e2d\u592e\u5024\u3092\u9078\u629e\"\"\"\n    l, m, r = nums[left], nums[mid], nums[right]\n    if (l &lt;= m &lt;= r) or (r &lt;= m &lt;= l):\n        return mid  # m \u306f l \u3068 r \u306e\u9593\n    if (m &lt;= l &lt;= r) or (r &lt;= l &lt;= m):\n        return left  # l \u306f m \u3068 r \u306e\u9593\n    return right\n\ndef partition(self, nums: list[int], left: int, right: int) -&gt; int:\n    \"\"\"\u5206\u5272\uff08\u4e09\u70b9\u4e2d\u592e\u5024\uff09\"\"\"\n    # nums[left] \u3092\u30d4\u30dc\u30c3\u30c8\u3068\u3057\u3066\u4f7f\u7528\n    med = self.median_three(nums, left, (left + right) // 2, right)\n    # \u4e2d\u592e\u5024\u3092\u914d\u5217\u306e\u6700\u5de6\u7aef\u306b\u4ea4\u63db\n    nums[left], nums[med] = nums[med], nums[left]\n    # nums[left] \u3092\u30d4\u30dc\u30c3\u30c8\u3068\u3057\u3066\u4f7f\u7528\n    i, j = left, right\n    while i &lt; j:\n        while i &lt; j and nums[j] &gt;= nums[left]:\n            j -= 1  # \u53f3\u304b\u3089\u5de6\u3078\u30d4\u30dc\u30c3\u30c8\u3088\u308a\u5c0f\u3055\u3044\u6700\u521d\u306e\u8981\u7d20\u3092\u63a2\u3059\n        while i &lt; j and nums[i] &lt;= nums[left]:\n            i += 1  # \u5de6\u304b\u3089\u53f3\u3078\u30d4\u30dc\u30c3\u30c8\u3088\u308a\u5927\u304d\u3044\u6700\u521d\u306e\u8981\u7d20\u3092\u63a2\u3059\n        # \u8981\u7d20\u3092\u4ea4\u63db\n        nums[i], nums[j] = nums[j], nums[i]\n    # \u30d4\u30dc\u30c3\u30c8\u30922\u3064\u306e\u30b5\u30d6\u914d\u5217\u306e\u5883\u754c\u306b\u4ea4\u63db\n    nums[i], nums[left] = nums[left], nums[i]\n    return i  # \u30d4\u30dc\u30c3\u30c8\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8fd4\u3059\n</code></pre> quick_sort.cpp<pre><code>/* \u4e09\u3064\u306e\u5019\u88dc\u8981\u7d20\u306e\u4e2d\u592e\u5024\u3092\u9078\u629e */\nint medianThree(vector&lt;int&gt; &amp;nums, int left, int mid, int right) {\n    int l = nums[left], m = nums[mid], r = nums[right];\n    if ((l &lt;= m &amp;&amp; m &lt;= r) || (r &lt;= m &amp;&amp; m &lt;= l))\n        return mid; // m\u306fl\u3068r\u306e\u9593\n    if ((m &lt;= l &amp;&amp; l &lt;= r) || (r &lt;= l &amp;&amp; l &lt;= m))\n        return left; // l\u306fm\u3068r\u306e\u9593\n    return right;\n}\n\n/* \u5206\u5272\uff08\u4e09\u3064\u306e\u4e2d\u592e\u5024\uff09 */\nint partition(vector&lt;int&gt; &amp;nums, int left, int right) {\n    // \u4e09\u3064\u306e\u5019\u88dc\u8981\u7d20\u306e\u4e2d\u592e\u5024\u3092\u9078\u629e\n    int med = medianThree(nums, left, (left + right) / 2, right);\n    // \u4e2d\u592e\u5024\u3092\u914d\u5217\u306e\u6700\u5de6\u4f4d\u7f6e\u306b\u4ea4\u63db\n    swap(nums, left, med);\n    // nums[left]\u3092\u30d4\u30dc\u30c3\u30c8\u3068\u3057\u3066\u4f7f\u7528\n    int i = left, j = right;\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\n            j--; // \u53f3\u304b\u3089\u5de6\u3078\u30d4\u30dc\u30c3\u30c8\u3088\u308a\u5c0f\u3055\u3044\u6700\u521d\u306e\u8981\u7d20\u3092\u691c\u7d22\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\n            i++;          // \u5de6\u304b\u3089\u53f3\u3078\u30d4\u30dc\u30c3\u30c8\u3088\u308a\u5927\u304d\u3044\u6700\u521d\u306e\u8981\u7d20\u3092\u691c\u7d22\n        swap(nums, i, j); // \u3053\u308c\u3089\u4e8c\u3064\u306e\u8981\u7d20\u3092\u4ea4\u63db\n    }\n    swap(nums, i, left); // \u30d4\u30dc\u30c3\u30c8\u3092\u4e8c\u3064\u306e\u30b5\u30d6\u914d\u5217\u306e\u5883\u754c\u306b\u4ea4\u63db\n    return i;            // \u30d4\u30dc\u30c3\u30c8\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8fd4\u3059\n}\n</code></pre> quick_sort.java<pre><code>/* 3\u3064\u306e\u5019\u88dc\u8981\u7d20\u306e\u4e2d\u592e\u5024\u3092\u9078\u629e */\nint medianThree(int[] nums, int left, int mid, int right) {\n    int l = nums[left], m = nums[mid], r = nums[right];\n    if ((l &lt;= m &amp;&amp; m &lt;= r) || (r &lt;= m &amp;&amp; m &lt;= l))\n        return mid; // m \u306f l \u3068 r \u306e\u9593\n    if ((m &lt;= l &amp;&amp; l &lt;= r) || (r &lt;= l &amp;&amp; l &lt;= m))\n        return left; // l \u306f m \u3068 r \u306e\u9593\n    return right;\n}\n\n/* \u5206\u5272\uff083\u3064\u306e\u4e2d\u592e\u5024\uff09 */\nint partition(int[] nums, int left, int right) {\n    // 3\u3064\u306e\u5019\u88dc\u8981\u7d20\u306e\u4e2d\u592e\u5024\u3092\u9078\u629e\n    int med = medianThree(nums, left, (left + right) / 2, right);\n    // \u4e2d\u592e\u5024\u3092\u914d\u5217\u306e\u6700\u5de6\u7aef\u306e\u4f4d\u7f6e\u306b\u4ea4\u63db\n    swap(nums, left, med);\n    // nums[left] \u3092\u57fa\u6e96\u5024\u3068\u3057\u3066\u4f7f\u7528\n    int i = left, j = right;\n    while (i &lt; j) {\n        while (i &lt; j &amp;&amp; nums[j] &gt;= nums[left])\n            j--;          // \u53f3\u304b\u3089\u5de6\u3078\u3001\u57fa\u6e96\u5024\u3088\u308a\u5c0f\u3055\u3044\u6700\u521d\u306e\u8981\u7d20\u3092\u691c\u7d22\n        while (i &lt; j &amp;&amp; nums[i] &lt;= nums[left])\n            i++;          // \u5de6\u304b\u3089\u53f3\u3078\u3001\u57fa\u6e96\u5024\u3088\u308a\u5927\u304d\u3044\u6700\u521d\u306e\u8981\u7d20\u3092\u691c\u7d22\n        swap(nums, i, j); // \u3053\u308c\u30892\u3064\u306e\u8981\u7d20\u3092\u4ea4\u63db\n    }\n    swap(nums, i, left);  // \u57fa\u6e96\u5024\u30922\u3064\u306e\u90e8\u5206\u914d\u5217\u306e\u5883\u754c\u306b\u4ea4\u63db\n    return i;             // \u57fa\u6e96\u5024\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8fd4\u3059\n}\n</code></pre> quick_sort.cs<pre><code>[class]{QuickSortMedian}-[func]{MedianThree}\n\n[class]{QuickSortMedian}-[func]{Partition}\n</code></pre> quick_sort.go<pre><code>[class]{quickSortMedian}-[func]{medianThree}\n\n[class]{quickSortMedian}-[func]{partition}\n</code></pre> quick_sort.swift<pre><code>[class]{}-[func]{medianThree}\n\n[class]{}-[func]{partitionMedian}\n</code></pre> quick_sort.js<pre><code>[class]{QuickSortMedian}-[func]{medianThree}\n\n[class]{QuickSortMedian}-[func]{partition}\n</code></pre> quick_sort.ts<pre><code>[class]{QuickSortMedian}-[func]{medianThree}\n\n[class]{QuickSortMedian}-[func]{partition}\n</code></pre> quick_sort.dart<pre><code>[class]{QuickSortMedian}-[func]{_medianThree}\n\n[class]{QuickSortMedian}-[func]{_partition}\n</code></pre> quick_sort.rs<pre><code>[class]{QuickSortMedian}-[func]{median_three}\n\n[class]{QuickSortMedian}-[func]{partition}\n</code></pre> quick_sort.c<pre><code>[class]{}-[func]{medianThree}\n\n[class]{}-[func]{partitionMedian}\n</code></pre> quick_sort.kt<pre><code>[class]{}-[func]{medianThree}\n\n[class]{}-[func]{partitionMedian}\n</code></pre> quick_sort.rb<pre><code>[class]{QuickSortMedian}-[func]{median_three}\n\n[class]{QuickSortMedian}-[func]{partition}\n</code></pre> quick_sort.zig<pre><code>[class]{QuickSortMedian}-[func]{medianThree}\n\n[class]{QuickSortMedian}-[func]{partition}\n</code></pre>"},{"location":"chapter_sorting/quick_sort/#1155","title":"11.5.5 \u00a0 \u672b\u5c3e\u518d\u5e30\u6700\u9069\u5316","text":"<p>\u7279\u5b9a\u306e\u5165\u529b\u3067\u306f\u3001\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u306f\u3088\u308a\u591a\u304f\u306e\u7a7a\u9593\u3092\u5360\u6709\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u5b8c\u5168\u306b\u9806\u5e8f\u4ed8\u3051\u3089\u308c\u305f\u5165\u529b\u914d\u5217\u3092\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u518d\u5e30\u3067\u306e\u30b5\u30d6\u914d\u5217\u306e\u9577\u3055\u3092\\(m\\)\u3068\u3057\u307e\u3059\u3002\u5404\u30e9\u30a6\u30f3\u30c9\u306e\u30d4\u30dc\u30c3\u30c8\u5206\u5272\u3067\u3001\u9577\u3055\\(0\\)\u306e\u5de6\u30b5\u30d6\u914d\u5217\u3068\u9577\u3055\\(m - 1\\)\u306e\u53f3\u30b5\u30d6\u914d\u5217\u304c\u751f\u6210\u3055\u308c\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u518d\u5e30\u547c\u3073\u51fa\u3057\u3054\u3068\u306b\u554f\u984c\u30b5\u30a4\u30ba\u304c1\u3064\u306e\u8981\u7d20\u306e\u307f\u6e1b\u5c11\u3059\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u3001\u5404\u30ec\u30d9\u30eb\u306e\u518d\u5e30\u3067\u306e\u524a\u6e1b\u304c\u975e\u5e38\u306b\u5c0f\u3055\u304f\u306a\u308a\u307e\u3059\u3002 \u7d50\u679c\u3068\u3057\u3066\u3001\u518d\u5e30\u30c4\u30ea\u30fc\u306e\u9ad8\u3055\u306f\\(n \u2212 1\\)\u306b\u9054\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u3001\u3053\u308c\u306b\u306f\\(O(n)\\)\u306e\u30b9\u30bf\u30c3\u30af\u30d5\u30ec\u30fc\u30e0\u7a7a\u9593\u304c\u5fc5\u8981\u3067\u3059\u3002</p> <p>\u30b9\u30bf\u30c3\u30af\u30d5\u30ec\u30fc\u30e0\u7a7a\u9593\u306e\u84c4\u7a4d\u3092\u9632\u3050\u305f\u3081\u3001\u5404\u30e9\u30a6\u30f3\u30c9\u306e\u30d4\u30dc\u30c3\u30c8\u30bd\u30fc\u30c8\u5f8c\u306b2\u3064\u306e\u30b5\u30d6\u914d\u5217\u306e\u9577\u3055\u3092\u6bd4\u8f03\u3057\u3001**\u3088\u308a\u77ed\u3044\u30b5\u30d6\u914d\u5217\u306e\u307f\u3092\u518d\u5e30\u7684\u306b\u30bd\u30fc\u30c8**\u3067\u304d\u307e\u3059\u3002\u3088\u308a\u77ed\u3044\u30b5\u30d6\u914d\u5217\u306e\u9577\u3055\u306f\\(n / 2\\)\u3092\u8d85\u3048\u306a\u3044\u305f\u3081\u3001\u3053\u306e\u65b9\u6cd5\u306f\u518d\u5e30\u6df1\u5ea6\u304c\\(\\log n\\)\u3092\u8d85\u3048\u306a\u3044\u3053\u3068\u3092\u4fdd\u8a3c\u3057\u3001\u6700\u60aa\u7a7a\u9593\u8a08\u7b97\u91cf\u3092\\(O(\\log n)\\)\u306b\u6700\u9069\u5316\u3057\u307e\u3059\u3002\u30b3\u30fc\u30c9\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig quick_sort.py<pre><code>def quick_sort(self, nums: list[int], left: int, right: int):\n    \"\"\"\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\uff08\u672b\u5c3e\u518d\u5e30\u6700\u9069\u5316\uff09\"\"\"\n    # \u30b5\u30d6\u914d\u5217\u306e\u9577\u3055\u304c1\u306e\u3068\u304d\u306b\u7d42\u4e86\n    while left &lt; right:\n        # \u5206\u5272\u64cd\u4f5c\n        pivot = self.partition(nums, left, right)\n        # 2\u3064\u306e\u30b5\u30d6\u914d\u5217\u306e\u3046\u3061\u77ed\u3044\u65b9\u306b\u5bfe\u3057\u3066\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u3092\u5b9f\u884c\n        if pivot - left &lt; right - pivot:\n            self.quick_sort(nums, left, pivot - 1)  # \u5de6\u30b5\u30d6\u914d\u5217\u3092\u518d\u5e30\u7684\u306b\u30bd\u30fc\u30c8\n            left = pivot + 1  # \u6b8b\u308a\u306e\u672a\u30bd\u30fc\u30c8\u533a\u9593\u306f [pivot + 1, right]\n        else:\n            self.quick_sort(nums, pivot + 1, right)  # \u53f3\u30b5\u30d6\u914d\u5217\u3092\u518d\u5e30\u7684\u306b\u30bd\u30fc\u30c8\n            right = pivot - 1  # \u6b8b\u308a\u306e\u672a\u30bd\u30fc\u30c8\u533a\u9593\u306f [left, pivot - 1]\n</code></pre> quick_sort.cpp<pre><code>/* \u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\uff08\u672b\u5c3e\u518d\u5e30\u6700\u9069\u5316\uff09 */\nvoid quickSort(vector&lt;int&gt; &amp;nums, int left, int right) {\n    // \u30b5\u30d6\u914d\u5217\u306e\u9577\u3055\u304c1\u306e\u6642\u7d42\u4e86\n    while (left &lt; right) {\n        // \u5206\u5272\u64cd\u4f5c\n        int pivot = partition(nums, left, right);\n        // \u4e8c\u3064\u306e\u30b5\u30d6\u914d\u5217\u306e\u3046\u3061\u77ed\u3044\u65b9\u3067\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u3092\u5b9f\u884c\n        if (pivot - left &lt; right - pivot) {\n            quickSort(nums, left, pivot - 1); // \u5de6\u30b5\u30d6\u914d\u5217\u3092\u518d\u5e30\u7684\u306b\u30bd\u30fc\u30c8\n            left = pivot + 1;                 // \u6b8b\u308a\u306e\u672a\u30bd\u30fc\u30c8\u533a\u9593\u306f[pivot + 1, right]\n        } else {\n            quickSort(nums, pivot + 1, right); // \u53f3\u30b5\u30d6\u914d\u5217\u3092\u518d\u5e30\u7684\u306b\u30bd\u30fc\u30c8\n            right = pivot - 1;                 // \u6b8b\u308a\u306e\u672a\u30bd\u30fc\u30c8\u533a\u9593\u306f[left, pivot - 1]\n        }\n    }\n}\n</code></pre> quick_sort.java<pre><code>/* \u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\uff08\u672b\u5c3e\u518d\u5e30\u6700\u9069\u5316\uff09 */\nvoid quickSort(int[] nums, int left, int right) {\n    // \u90e8\u5206\u914d\u5217\u306e\u9577\u3055\u304c 1 \u306e\u3068\u304d\u7d42\u4e86\n    while (left &lt; right) {\n        // \u5206\u5272\u64cd\u4f5c\n        int pivot = partition(nums, left, right);\n        // 2\u3064\u306e\u90e8\u5206\u914d\u5217\u306e\u3046\u3061\u77ed\u3044\u65b9\u306b\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u3092\u5b9f\u884c\n        if (pivot - left &lt; right - pivot) {\n            quickSort(nums, left, pivot - 1); // \u5de6\u90e8\u5206\u914d\u5217\u3092\u518d\u5e30\u7684\u306b\u30bd\u30fc\u30c8\n            left = pivot + 1; // \u6b8b\u308a\u306e\u672a\u30bd\u30fc\u30c8\u533a\u9593\u306f [pivot + 1, right]\n        } else {\n            quickSort(nums, pivot + 1, right); // \u53f3\u90e8\u5206\u914d\u5217\u3092\u518d\u5e30\u7684\u306b\u30bd\u30fc\u30c8\n            right = pivot - 1; // \u6b8b\u308a\u306e\u672a\u30bd\u30fc\u30c8\u533a\u9593\u306f [left, pivot - 1]\n        }\n    }\n}\n</code></pre> quick_sort.cs<pre><code>[class]{QuickSortTailCall}-[func]{QuickSort}\n</code></pre> quick_sort.go<pre><code>[class]{quickSortTailCall}-[func]{quickSort}\n</code></pre> quick_sort.swift<pre><code>[class]{}-[func]{quickSortTailCall}\n</code></pre> quick_sort.js<pre><code>[class]{QuickSortTailCall}-[func]{quickSort}\n</code></pre> quick_sort.ts<pre><code>[class]{QuickSortTailCall}-[func]{quickSort}\n</code></pre> quick_sort.dart<pre><code>[class]{QuickSortTailCall}-[func]{quickSort}\n</code></pre> quick_sort.rs<pre><code>[class]{QuickSortTailCall}-[func]{quick_sort}\n</code></pre> quick_sort.c<pre><code>[class]{}-[func]{quickSortTailCall}\n</code></pre> quick_sort.kt<pre><code>[class]{}-[func]{quickSortTailCall}\n</code></pre> quick_sort.rb<pre><code>[class]{QuickSortTailCall}-[func]{quick_sort}\n</code></pre> quick_sort.zig<pre><code>[class]{QuickSortTailCall}-[func]{quickSort}\n</code></pre>"},{"location":"chapter_sorting/radix_sort/","title":"11.10 \u00a0 \u57fa\u6570\u30bd\u30fc\u30c8","text":"<p>\u524d\u306e\u7bc0\u3067\u306f\u8a08\u6570\u30bd\u30fc\u30c8\u3092\u7d39\u4ecb\u3057\u307e\u3057\u305f\u3002\u3053\u308c\u306f\u3001\u30c7\u30fc\u30bf\u30b5\u30a4\u30ba \\(n\\) \u304c\u5927\u304d\u3044\u304c\u30c7\u30fc\u30bf\u7bc4\u56f2 \\(m\\) \u304c\u5c0f\u3055\u3044\u30b7\u30ca\u30ea\u30aa\u306b\u9069\u3057\u3066\u3044\u307e\u3059\u3002\\(n = 10^6\\) \u306e\u5b66\u751fID\u3092\u30bd\u30fc\u30c8\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u3001\u5404ID\u304c \\(8\\) \u6841\u306e\u6570\u5b57\u3067\u3042\u308b\u3068\u3057\u307e\u3059\u3002\u3053\u308c\u306f\u3001\u30c7\u30fc\u30bf\u7bc4\u56f2 \\(m = 10^8\\) \u304c\u975e\u5e38\u306b\u5927\u304d\u3044\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002\u3053\u306e\u5834\u5408\u3001\u8a08\u6570\u30bd\u30fc\u30c8\u3092\u4f7f\u7528\u3059\u308b\u3068\u3001\u5927\u91cf\u306e\u30e1\u30e2\u30ea\u30b9\u30da\u30fc\u30b9\u304c\u5fc5\u8981\u306b\u306a\u308a\u307e\u3059\u3002\u57fa\u6570\u30bd\u30fc\u30c8\u306f\u3053\u306e\u72b6\u6cc1\u3092\u56de\u907f\u3067\u304d\u307e\u3059\u3002</p> <p>\u57fa\u6570\u30bd\u30fc\u30c8\u306f\u8a08\u6570\u30bd\u30fc\u30c8\u3068\u540c\u3058\u6838\u5fc3\u6982\u5ff5\u3092\u5171\u6709\u3057\u3001\u8981\u7d20\u306e\u983b\u5ea6\u3092\u30ab\u30a6\u30f3\u30c8\u3059\u308b\u3053\u3068\u3067\u30bd\u30fc\u30c8\u3057\u307e\u3059\u3002\u540c\u6642\u306b\u3001\u57fa\u6570\u30bd\u30fc\u30c8\u306f\u6570\u5b57\u306e\u6841\u9593\u306e\u6f38\u9032\u7684\u95a2\u4fc2\u3092\u5229\u7528\u3057\u3066\u3053\u308c\u3092\u57fa\u76e4\u3068\u3057\u3066\u3044\u307e\u3059\u3002\u6841\u3092\u4e00\u5ea6\u306b\u4e00\u3064\u305a\u3064\u51e6\u7406\u3057\u3066\u30bd\u30fc\u30c8\u3057\u3001\u6700\u7d42\u7684\u306a\u30bd\u30fc\u30c8\u9806\u5e8f\u3092\u9054\u6210\u3057\u307e\u3059\u3002</p>"},{"location":"chapter_sorting/radix_sort/#11101","title":"11.10.1 \u00a0 \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u904e\u7a0b","text":"<p>\u5b66\u751fID\u30c7\u30fc\u30bf\u3092\u4f8b\u3068\u3057\u3066\u3001\u6700\u4e0b\u4f4d\u6841\u3092 \\(1\\) \u756a\u76ee\u3001\u6700\u4e0a\u4f4d\u6841\u3092 \\(8\\) \u756a\u76ee\u3068\u3059\u308b\u3068\u3001\u57fa\u6570\u30bd\u30fc\u30c8\u306e\u904e\u7a0b\u306f\u4ee5\u4e0b\u306e\u56f3\u306b\u793a\u3055\u308c\u3066\u3044\u307e\u3059\u3002</p> <ol> <li>\u6841 \\(k = 1\\) \u3092\u521d\u671f\u5316\u3057\u307e\u3059\u3002</li> <li>\u5b66\u751fID\u306e \\(k\\) \u756a\u76ee\u306e\u6841\u306b\u5bfe\u3057\u3066\u300c\u8a08\u6570\u30bd\u30fc\u30c8\u300d\u3092\u5b9f\u884c\u3057\u307e\u3059\u3002\u5b8c\u4e86\u5f8c\u3001\u30c7\u30fc\u30bf\u306f \\(k\\) \u756a\u76ee\u306e\u6841\u306b\u57fa\u3065\u3044\u3066\u6700\u5c0f\u304b\u3089\u6700\u5927\u307e\u3067\u30bd\u30fc\u30c8\u3055\u308c\u307e\u3059\u3002</li> <li>\\(k\\) \u3092 \\(1\\) \u5897\u3084\u3057\u3001\u624b\u9806 <code>2.</code> \u306b\u623b\u3063\u3066\u53cd\u5fa9\u3092\u7d9a\u3051\u3001\u3059\u3079\u3066\u306e\u6841\u304c\u30bd\u30fc\u30c8\u3055\u308c\u308b\u307e\u3067\u7d9a\u3051\u307e\u3059\u3002\u3053\u306e\u6642\u70b9\u3067\u904e\u7a0b\u304c\u7d42\u4e86\u3057\u307e\u3059\u3002</li> </ol> <p></p> <p> \u56f3 11-18 \u00a0 \u57fa\u6570\u30bd\u30fc\u30c8\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u904e\u7a0b </p> <p>\u4ee5\u4e0b\u3001\u30b3\u30fc\u30c9\u5b9f\u88c5\u3092\u8a73\u3057\u304f\u898b\u3066\u307f\u307e\u3059\u3002\u57fa\u6570 \\(d\\) \u3067\u306e\u6570 \\(x\\) \u306b\u5bfe\u3057\u3066\u3001\u305d\u306e \\(k\\) \u756a\u76ee\u306e\u6841 \\(x_k\\) \u3092\u53d6\u5f97\u3059\u308b\u306b\u306f\u3001\u4ee5\u4e0b\u306e\u8a08\u7b97\u5f0f\u3092\u4f7f\u7528\u3067\u304d\u307e\u3059\uff1a</p> \\[ x_k = \\lfloor\\frac{x}{d^{k-1}}\\rfloor \\bmod d \\] <p>\u3053\u3053\u3067 \\(\\lfloor a \\rfloor\\) \u306f\u6d6e\u52d5\u5c0f\u6570\u70b9\u6570 \\(a\\) \u306e\u5207\u308a\u6368\u3066\u3092\u8868\u3057\u3001\\(\\bmod \\: d\\) \u306f \\(d\\) \u306b\u3088\u308b\u5270\u4f59\u3092\u8868\u3057\u307e\u3059\u3002\u5b66\u751fID\u30c7\u30fc\u30bf\u306e\u5834\u5408\u3001\\(d = 10\\) \u3067 \\(k \\in [1, 8]\\) \u3067\u3059\u3002</p> <p>\u3055\u3089\u306b\u3001\\(k\\) \u756a\u76ee\u306e\u6841\u306b\u57fa\u3065\u3044\u3066\u30bd\u30fc\u30c8\u3067\u304d\u308b\u3088\u3046\u306b\u3001\u8a08\u6570\u30bd\u30fc\u30c8\u306e\u30b3\u30fc\u30c9\u3092\u5c11\u3057\u4fee\u6b63\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig radix_sort.py<pre><code>def digit(num: int, exp: int) -&gt; int:\n    \"\"\"\u8981\u7d20 num \u306e k \u756a\u76ee\u306e\u6841\u3092\u53d6\u5f97\u3001exp = 10^(k-1)\"\"\"\n    # k \u306e\u4ee3\u308f\u308a\u306b exp \u3092\u6e21\u3059\u3053\u3068\u3067\u3001\u3053\u3053\u3067\u30b3\u30b9\u30c8\u306e\u9ad8\u3044\u7d2f\u4e57\u8a08\u7b97\u3092\u907f\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u308b\n    return (num // exp) % 10\n\ndef counting_sort_digit(nums: list[int], exp: int):\n    \"\"\"\u8a08\u6570\u30bd\u30fc\u30c8\uff08nums \u306e k \u756a\u76ee\u306e\u6841\u306b\u57fa\u3065\u304f\uff09\"\"\"\n    # 10\u9032\u6570\u306e\u6841\u306e\u7bc4\u56f2\u306f 0~9\u3001\u3057\u305f\u304c\u3063\u3066\u9577\u305510\u306e\u30d0\u30b1\u30c3\u30c8\u914d\u5217\u304c\u5fc5\u8981\n    counter = [0] * 10\n    n = len(nums)\n    # \u6570\u5b57 0~9 \u306e\u51fa\u73fe\u56de\u6570\u3092\u7d71\u8a08\n    for i in range(n):\n        d = digit(nums[i], exp)  # nums[i] \u306e k \u756a\u76ee\u306e\u6841\u3092\u53d6\u5f97\u3001d \u3068\u3059\u308b\n        counter[d] += 1  # \u6570\u5b57 d \u306e\u51fa\u73fe\u56de\u6570\u3092\u7d71\u8a08\n    # \u524d\u7f6e\u548c\u3092\u8a08\u7b97\u3057\u3001\u300c\u51fa\u73fe\u56de\u6570\u300d\u3092\u300c\u914d\u5217\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u300d\u306b\u5909\u63db\n    for i in range(1, 10):\n        counter[i] += counter[i - 1]\n    # \u9006\u9806\u306b\u8d70\u67fb\u3057\u3001\u30d0\u30b1\u30c3\u30c8\u7d71\u8a08\u306b\u57fa\u3065\u3044\u3066\u5404\u8981\u7d20\u3092 res \u306b\u914d\u7f6e\n    res = [0] * n\n    for i in range(n - 1, -1, -1):\n        d = digit(nums[i], exp)\n        j = counter[d] - 1  # \u914d\u5217\u5185\u306e d \u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9 j \u3092\u53d6\u5f97\n        res[j] = nums[i]  # \u73fe\u5728\u306e\u8981\u7d20\u3092\u30a4\u30f3\u30c7\u30c3\u30af\u30b9 j \u306b\u914d\u7f6e\n        counter[d] -= 1  # d \u306e\u6570\u30921\u6e1b\u3089\u3059\n    # \u7d50\u679c\u3092\u4f7f\u7528\u3057\u3066\u5143\u306e\u914d\u5217 nums \u3092\u4e0a\u66f8\u304d\n    for i in range(n):\n        nums[i] = res[i]\n\ndef radix_sort(nums: list[int]):\n    \"\"\"\u57fa\u6570\u30bd\u30fc\u30c8\"\"\"\n    # \u914d\u5217\u306e\u6700\u5927\u8981\u7d20\u3092\u53d6\u5f97\u3057\u3001\u6700\u5927\u6841\u6570\u3092\u5224\u5b9a\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\n    m = max(nums)\n    # \u6700\u4e0b\u4f4d\u6841\u304b\u3089\u6700\u4e0a\u4f4d\u6841\u307e\u3067\u8d70\u67fb\n    exp = 1\n    while exp &lt;= m:\n        # \u914d\u5217\u8981\u7d20\u306e k \u756a\u76ee\u306e\u6841\u306b\u5bfe\u3057\u3066\u8a08\u6570\u30bd\u30fc\u30c8\u3092\u5b9f\u884c\n        # k = 1 -&gt; exp = 1\n        # k = 2 -&gt; exp = 10\n        # \u3064\u307e\u308a\u3001exp = 10^(k-1)\n        counting_sort_digit(nums, exp)\n        exp *= 10\n</code></pre> radix_sort.cpp<pre><code>/* \u8981\u7d20num\u306ek\u756a\u76ee\u306e\u6841\u3092\u53d6\u5f97\u3001exp = 10^(k-1) */\nint digit(int num, int exp) {\n    // k\u306e\u4ee3\u308f\u308a\u306bexp\u3092\u6e21\u3059\u3053\u3068\u3067\u3001\u3053\u3053\u3067\u7e70\u308a\u8fd4\u3055\u308c\u308b\u9ad8\u4fa1\u306a\u51aa\u4e57\u8a08\u7b97\u3092\u907f\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u308b\n    return (num / exp) % 10;\n}\n\n/* \u30ab\u30a6\u30f3\u30c8\u30bd\u30fc\u30c8\uff08nums\u306ek\u756a\u76ee\u306e\u6841\u306b\u57fa\u3065\u304f\uff09 */\nvoid countingSortDigit(vector&lt;int&gt; &amp;nums, int exp) {\n    // 10\u9032\u6570\u306e\u6841\u7bc4\u56f2\u306f0~9\u306a\u306e\u3067\u3001\u9577\u305510\u306e\u30d0\u30b1\u30c3\u30c8\u914d\u5217\u304c\u5fc5\u8981\n    vector&lt;int&gt; counter(10, 0);\n    int n = nums.size();\n    // \u6570\u5b570~9\u306e\u51fa\u73fe\u56de\u6570\u3092\u7d71\u8a08\n    for (int i = 0; i &lt; n; i++) {\n        int d = digit(nums[i], exp); // nums[i]\u306ek\u756a\u76ee\u306e\u6841\u3092\u53d6\u5f97\u3001d\u3068\u3057\u3066\u8a18\u9332\n        counter[d]++;                // \u6570\u5b57d\u306e\u51fa\u73fe\u56de\u6570\u3092\u7d71\u8a08\n    }\n    // \u524d\u7f00\u548c\u3092\u8a08\u7b97\u3057\u3001\u300c\u51fa\u73fe\u56de\u6570\u300d\u3092\u300c\u914d\u5217\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u300d\u306b\u5909\u63db\n    for (int i = 1; i &lt; 10; i++) {\n        counter[i] += counter[i - 1];\n    }\n    // \u9006\u9806\u3067\u8d70\u67fb\u3057\u3001\u30d0\u30b1\u30c3\u30c8\u7d71\u8a08\u306b\u57fa\u3065\u3044\u3066\u5404\u8981\u7d20\u3092res\u306b\u914d\u7f6e\n    vector&lt;int&gt; res(n, 0);\n    for (int i = n - 1; i &gt;= 0; i--) {\n        int d = digit(nums[i], exp);\n        int j = counter[d] - 1; // d\u304c\u914d\u5217\u5185\u306b\u3042\u308b\u30a4\u30f3\u30c7\u30c3\u30af\u30b9j\u3092\u53d6\u5f97\n        res[j] = nums[i];       // \u73fe\u5728\u306e\u8981\u7d20\u3092\u30a4\u30f3\u30c7\u30c3\u30af\u30b9j\u306b\u914d\u7f6e\n        counter[d]--;           // d\u306e\u30ab\u30a6\u30f3\u30c8\u30921\u6e1b\u3089\u3059\n    }\n    // \u7d50\u679c\u3067\u5143\u306e\u914d\u5217nums\u3092\u4e0a\u66f8\u304d\n    for (int i = 0; i &lt; n; i++)\n        nums[i] = res[i];\n}\n\n/* \u57fa\u6570\u30bd\u30fc\u30c8 */\nvoid radixSort(vector&lt;int&gt; &amp;nums) {\n    // \u914d\u5217\u306e\u6700\u5927\u8981\u7d20\u3092\u53d6\u5f97\u3001\u6700\u5927\u6841\u6570\u3092\u5224\u5b9a\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\n    int m = *max_element(nums.begin(), nums.end());\n    // \u6700\u4e0b\u4f4d\u6841\u304b\u3089\u6700\u4e0a\u4f4d\u6841\u307e\u3067\u8d70\u67fb\n    for (int exp = 1; exp &lt;= m; exp *= 10)\n        // \u914d\u5217\u8981\u7d20\u306ek\u756a\u76ee\u306e\u6841\u3067\u30ab\u30a6\u30f3\u30c8\u30bd\u30fc\u30c8\u3092\u5b9f\u884c\n        // k = 1 -&gt; exp = 1\n        // k = 2 -&gt; exp = 10\n        // \u3064\u307e\u308a\u3001exp = 10^(k-1)\n        countingSortDigit(nums, exp);\n}\n</code></pre> radix_sort.java<pre><code>/* \u8981\u7d20 num \u306e k \u756a\u76ee\u306e\u6841\u3092\u53d6\u5f97\u3001exp = 10^(k-1) */\nint digit(int num, int exp) {\n    // k \u306e\u4ee3\u308f\u308a\u306b exp \u3092\u6e21\u3059\u3053\u3068\u3067\u3001\u3053\u3053\u3067\u30b3\u30b9\u30c8\u306e\u9ad8\u3044\u7d2f\u4e57\u8a08\u7b97\u306e\u7e70\u308a\u8fd4\u3057\u3092\u907f\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u308b\n    return (num / exp) % 10;\n}\n\n/* \u8a08\u6570\u30bd\u30fc\u30c8\uff08nums \u306e k \u756a\u76ee\u306e\u6841\u306b\u57fa\u3065\u304f\uff09 */\nvoid countingSortDigit(int[] nums, int exp) {\n    // 10\u9032\u6570\u306e\u6841\u306e\u7bc4\u56f2\u306f 0~9\u3001\u3057\u305f\u304c\u3063\u3066\u9577\u3055 10 \u306e\u30d0\u30b1\u30c3\u30c8\u914d\u5217\u304c\u5fc5\u8981\n    int[] counter = new int[10];\n    int n = nums.length;\n    // \u6841 0~9 \u306e\u51fa\u73fe\u56de\u6570\u3092\u7d71\u8a08\n    for (int i = 0; i &lt; n; i++) {\n        int d = digit(nums[i], exp); // nums[i] \u306e k \u756a\u76ee\u306e\u6841\u3092\u53d6\u5f97\u3001d \u3068\u3059\u308b\n        counter[d]++;                // \u6841 d \u306e\u51fa\u73fe\u56de\u6570\u3092\u7d71\u8a08\n    }\n    // \u7d2f\u7a4d\u548c\u3092\u8a08\u7b97\u3057\u3001\u300c\u51fa\u73fe\u56de\u6570\u300d\u3092\u300c\u914d\u5217\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u300d\u306b\u5909\u63db\n    for (int i = 1; i &lt; 10; i++) {\n        counter[i] += counter[i - 1];\n    }\n    // \u9006\u9806\u306b\u8d70\u67fb\u3057\u3001\u30d0\u30b1\u30c3\u30c8\u7d71\u8a08\u306b\u57fa\u3065\u3044\u3066\u5404\u8981\u7d20\u3092 res \u306b\u914d\u7f6e\n    int[] res = new int[n];\n    for (int i = n - 1; i &gt;= 0; i--) {\n        int d = digit(nums[i], exp);\n        int j = counter[d] - 1; // \u914d\u5217\u5185\u3067\u306e d \u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9 j \u3092\u53d6\u5f97\n        res[j] = nums[i];       // \u73fe\u5728\u306e\u8981\u7d20\u3092\u30a4\u30f3\u30c7\u30c3\u30af\u30b9 j \u306b\u914d\u7f6e\n        counter[d]--;           // d \u306e\u30ab\u30a6\u30f3\u30c8\u3092 1 \u6e1b\u3089\u3059\n    }\n    // \u7d50\u679c\u3067\u5143\u306e\u914d\u5217 nums \u3092\u4e0a\u66f8\u304d\n    for (int i = 0; i &lt; n; i++)\n        nums[i] = res[i];\n}\n\n/* \u57fa\u6570\u30bd\u30fc\u30c8 */\nvoid radixSort(int[] nums) {\n    // \u914d\u5217\u306e\u6700\u5927\u8981\u7d20\u3092\u53d6\u5f97\u3057\u3001\u6700\u5927\u6841\u6570\u3092\u5224\u5b9a\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\n    int m = Integer.MIN_VALUE;\n    for (int num : nums)\n        if (num &gt; m)\n            m = num;\n    // \u6700\u4e0b\u4f4d\u6841\u304b\u3089\u6700\u4e0a\u4f4d\u6841\u307e\u3067\u8d70\u67fb\n    for (int exp = 1; exp &lt;= m; exp *= 10) {\n        // \u914d\u5217\u8981\u7d20\u306e k \u756a\u76ee\u306e\u6841\u306b\u5bfe\u3057\u3066\u8a08\u6570\u30bd\u30fc\u30c8\u3092\u5b9f\u884c\n        // k = 1 -&gt; exp = 1\n        // k = 2 -&gt; exp = 10\n        // \u3059\u306a\u308f\u3061 exp = 10^(k-1)\n        countingSortDigit(nums, exp);\n    }\n}\n</code></pre> radix_sort.cs<pre><code>[class]{radix_sort}-[func]{Digit}\n\n[class]{radix_sort}-[func]{CountingSortDigit}\n\n[class]{radix_sort}-[func]{RadixSort}\n</code></pre> radix_sort.go<pre><code>[class]{}-[func]{digit}\n\n[class]{}-[func]{countingSortDigit}\n\n[class]{}-[func]{radixSort}\n</code></pre> radix_sort.swift<pre><code>[class]{}-[func]{digit}\n\n[class]{}-[func]{countingSortDigit}\n\n[class]{}-[func]{radixSort}\n</code></pre> radix_sort.js<pre><code>[class]{}-[func]{digit}\n\n[class]{}-[func]{countingSortDigit}\n\n[class]{}-[func]{radixSort}\n</code></pre> radix_sort.ts<pre><code>[class]{}-[func]{digit}\n\n[class]{}-[func]{countingSortDigit}\n\n[class]{}-[func]{radixSort}\n</code></pre> radix_sort.dart<pre><code>[class]{}-[func]{digit}\n\n[class]{}-[func]{countingSortDigit}\n\n[class]{}-[func]{radixSort}\n</code></pre> radix_sort.rs<pre><code>[class]{}-[func]{digit}\n\n[class]{}-[func]{counting_sort_digit}\n\n[class]{}-[func]{radix_sort}\n</code></pre> radix_sort.c<pre><code>[class]{}-[func]{digit}\n\n[class]{}-[func]{countingSortDigit}\n\n[class]{}-[func]{radixSort}\n</code></pre> radix_sort.kt<pre><code>[class]{}-[func]{digit}\n\n[class]{}-[func]{countingSortDigit}\n\n[class]{}-[func]{radixSort}\n</code></pre> radix_sort.rb<pre><code>[class]{}-[func]{digit}\n\n[class]{}-[func]{counting_sort_digit}\n\n[class]{}-[func]{radix_sort}\n</code></pre> radix_sort.zig<pre><code>[class]{}-[func]{digit}\n\n[class]{}-[func]{countingSortDigit}\n\n[class]{}-[func]{radixSort}\n</code></pre> <p>\u306a\u305c\u6700\u4e0b\u4f4d\u6841\u304b\u3089\u958b\u59cb\u3059\u308b\u306e\u304b\uff1f</p> <p>\u9023\u7d9a\u3059\u308b\u30bd\u30fc\u30c8\u30e9\u30a6\u30f3\u30c9\u3067\u306f\u3001\u5f8c\u306e\u30e9\u30a6\u30f3\u30c9\u306e\u7d50\u679c\u304c\u524d\u306e\u30e9\u30a6\u30f3\u30c9\u306e\u7d50\u679c\u3092\u4e0a\u66f8\u304d\u3057\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u6700\u521d\u306e\u30e9\u30a6\u30f3\u30c9\u306e\u7d50\u679c\u304c \\(a &lt; b\\) \u3067\u30012\u756a\u76ee\u306e\u30e9\u30a6\u30f3\u30c9\u304c \\(a &gt; b\\) \u306e\u5834\u5408\u30012\u756a\u76ee\u306e\u30e9\u30a6\u30f3\u30c9\u306e\u7d50\u679c\u304c\u6700\u521d\u306e\u30e9\u30a6\u30f3\u30c9\u306e\u7d50\u679c\u3092\u7f6e\u304d\u63db\u3048\u307e\u3059\u3002\u4e0a\u4f4d\u6841\u306f\u4e0b\u4f4d\u6841\u3088\u308a\u512a\u5148\u3055\u308c\u308b\u305f\u3081\u3001\u4e0a\u4f4d\u6841\u306e\u524d\u306b\u4e0b\u4f4d\u6841\u3092\u30bd\u30fc\u30c8\u3059\u308b\u3053\u3068\u304c\u7406\u306b\u304b\u306a\u3063\u3066\u3044\u307e\u3059\u3002</p>"},{"location":"chapter_sorting/radix_sort/#11102","title":"11.10.2 \u00a0 \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u7279\u5fb4","text":"<p>\u8a08\u6570\u30bd\u30fc\u30c8\u3068\u6bd4\u8f03\u3057\u3066\u3001\u57fa\u6570\u30bd\u30fc\u30c8\u306f\u3088\u308a\u5927\u304d\u306a\u6570\u5024\u7bc4\u56f2\u306b\u9069\u3057\u3066\u3044\u307e\u3059\u304c\u3001\u30c7\u30fc\u30bf\u304c\u56fa\u5b9a\u6841\u6570\u3067\u8868\u73fe\u3067\u304d\u3001\u6841\u6570\u304c\u3042\u307e\u308a\u5927\u304d\u304f\u306a\u3044\u3053\u3068\u3092\u524d\u63d0\u3068\u3057\u3066\u3044\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u6d6e\u52d5\u5c0f\u6570\u70b9\u6570\u306f\u6841\u6570 \\(k\\) \u304c\u5927\u304d\u3044\u53ef\u80fd\u6027\u304c\u3042\u308a\u3001\u6642\u9593\u8a08\u7b97\u91cf \\(O(nk) \\gg O(n^2)\\) \u306b\u3064\u306a\u304c\u308b\u53ef\u80fd\u6027\u304c\u3042\u308b\u305f\u3081\u3001\u57fa\u6570\u30bd\u30fc\u30c8\u306b\u306f\u9069\u3057\u3066\u3044\u307e\u305b\u3093\u3002</p> <ul> <li>\u6642\u9593\u8a08\u7b97\u91cf\u306f \\(O(nk)\\)\u3001\u975e\u9069\u5fdc\u30bd\u30fc\u30c8\uff1a\u30c7\u30fc\u30bf\u30b5\u30a4\u30ba\u3092 \\(n\\)\u3001\u30c7\u30fc\u30bf\u304c\u57fa\u6570 \\(d\\)\u3001\u6700\u5927\u6841\u6570\u3092 \\(k\\) \u3068\u3059\u308b\u3068\u3001\u5358\u4e00\u6841\u306e\u30bd\u30fc\u30c8\u306b\u306f \\(O(n + d)\\) \u6642\u9593\u304c\u304b\u304b\u308a\u3001\u3059\u3079\u3066\u306e \\(k\\) \u6841\u306e\u30bd\u30fc\u30c8\u306b\u306f \\(O((n + d)k)\\) \u6642\u9593\u304c\u304b\u304b\u308a\u307e\u3059\u3002\u4e00\u822c\u7684\u306b\u3001\\(d\\) \u3068 \\(k\\) \u306f\u3069\u3061\u3089\u3082\u6bd4\u8f03\u7684\u5c0f\u3055\u304f\u3001\u6642\u9593\u8a08\u7b97\u91cf\u306f \\(O(n)\\) \u306b\u8fd1\u3065\u304d\u307e\u3059\u3002</li> <li>\u7a7a\u9593\u8a08\u7b97\u91cf\u306f \\(O(n + d)\\)\u3001\u975e\u30a4\u30f3\u30d7\u30ec\u30fc\u30b9\u30bd\u30fc\u30c8\uff1a\u8a08\u6570\u30bd\u30fc\u30c8\u3068\u540c\u69d8\u306b\u3001\u57fa\u6570\u30bd\u30fc\u30c8\u306f\u9577\u3055 \\(n\\) \u3068 \\(d\\) \u306e\u914d\u5217 <code>res</code> \u3068 <code>counter</code> \u306b\u305d\u308c\u305e\u308c\u4f9d\u5b58\u3057\u307e\u3059\u3002</li> <li>\u5b89\u5b9a\u30bd\u30fc\u30c8\uff1a\u8a08\u6570\u30bd\u30fc\u30c8\u304c\u5b89\u5b9a\u306a\u5834\u5408\u3001\u57fa\u6570\u30bd\u30fc\u30c8\u3082\u5b89\u5b9a\u3067\u3059\u3002\u8a08\u6570\u30bd\u30fc\u30c8\u304c\u4e0d\u5b89\u5b9a\u306a\u5834\u5408\u3001\u57fa\u6570\u30bd\u30fc\u30c8\u306f\u6b63\u3057\u3044\u30bd\u30fc\u30c8\u9806\u5e8f\u3092\u4fdd\u8a3c\u3067\u304d\u307e\u305b\u3093\u3002</li> </ul>"},{"location":"chapter_sorting/selection_sort/","title":"11.2 \u00a0 \u9078\u629e\u30bd\u30fc\u30c8","text":"<p>\u9078\u629e\u30bd\u30fc\u30c8\u306f\u975e\u5e38\u306b\u30b7\u30f3\u30d7\u30eb\u306a\u539f\u7406\u3067\u52d5\u4f5c\u3057\u307e\u3059\uff1a\u5404\u53cd\u5fa9\u3067\u672a\u30bd\u30fc\u30c8\u533a\u9593\u304b\u3089\u6700\u5c0f\u8981\u7d20\u3092\u9078\u629e\u3057\u3001\u30bd\u30fc\u30c8\u6e08\u307f\u30bb\u30af\u30b7\u30e7\u30f3\u306e\u672b\u5c3e\u306b\u79fb\u52d5\u3059\u308b\u30eb\u30fc\u30d7\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002</p> <p>\u914d\u5217\u306e\u9577\u3055\u3092\\(n\\)\u3068\u3059\u308b\u3068\u3001\u9078\u629e\u30bd\u30fc\u30c8\u306e\u30b9\u30c6\u30c3\u30d7\u306f\u4e0b\u56f3\u306b\u793a\u3055\u308c\u307e\u3059\u3002</p> <ol> <li>\u6700\u521d\u306b\u3001\u3059\u3079\u3066\u306e\u8981\u7d20\u306f\u672a\u30bd\u30fc\u30c8\u3067\u3001\u3064\u307e\u308a\u672a\u30bd\u30fc\u30c8\uff08\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\uff09\u533a\u9593\u306f\\([0, n-1]\\)\u3067\u3059\u3002</li> <li>\u533a\u9593\\([0, n-1]\\)\u306e\u6700\u5c0f\u8981\u7d20\u3092\u9078\u629e\u3057\u3001\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\\(0\\)\u306e\u8981\u7d20\u3068\u4ea4\u63db\u3057\u307e\u3059\u3002\u3053\u306e\u5f8c\u3001\u914d\u5217\u306e\u6700\u521d\u306e\u8981\u7d20\u304c\u30bd\u30fc\u30c8\u3055\u308c\u307e\u3059\u3002</li> <li>\u533a\u9593\\([1, n-1]\\)\u306e\u6700\u5c0f\u8981\u7d20\u3092\u9078\u629e\u3057\u3001\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\\(1\\)\u306e\u8981\u7d20\u3068\u4ea4\u63db\u3057\u307e\u3059\u3002\u3053\u306e\u5f8c\u3001\u914d\u5217\u306e\u6700\u521d\u306e2\u3064\u306e\u8981\u7d20\u304c\u30bd\u30fc\u30c8\u3055\u308c\u307e\u3059\u3002</li> <li>\u3053\u306e\u65b9\u6cd5\u3067\u7d9a\u884c\u3057\u307e\u3059\u3002\\(n - 1\\)\u30e9\u30a6\u30f3\u30c9\u306e\u9078\u629e\u3068\u4ea4\u63db\u306e\u5f8c\u3001\u6700\u521d\u306e\\(n - 1\\)\u500b\u306e\u8981\u7d20\u304c\u30bd\u30fc\u30c8\u3055\u308c\u307e\u3059\u3002</li> <li>\u6b8b\u308a\u306e\u552f\u4e00\u306e\u8981\u7d20\u306f\u7d50\u679c\u7684\u306b\u6700\u5927\u8981\u7d20\u3067\u3042\u308a\u3001\u30bd\u30fc\u30c8\u3059\u308b\u5fc5\u8981\u304c\u306a\u3044\u305f\u3081\u3001\u914d\u5217\u306f\u30bd\u30fc\u30c8\u3055\u308c\u307e\u3059\u3002</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> \u56f3 11-2 \u00a0 Selection sort process </p> <p>\u30b3\u30fc\u30c9\u3067\u306f\u3001\\(k\\)\u3092\u4f7f\u7528\u3057\u3066\u672a\u30bd\u30fc\u30c8\u533a\u9593\u5185\u306e\u6700\u5c0f\u8981\u7d20\u3092\u8a18\u9332\u3057\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig selection_sort.py<pre><code>def selection_sort(nums: list[int]):\n    \"\"\"\u9078\u629e\u30bd\u30fc\u30c8\"\"\"\n    n = len(nums)\n    # \u5916\u5074\u306e\u30eb\u30fc\u30d7\uff1a\u672a\u30bd\u30fc\u30c8\u7bc4\u56f2\u306f [i, n-1]\n    for i in range(n - 1):\n        # \u5185\u5074\u306e\u30eb\u30fc\u30d7\uff1a\u672a\u30bd\u30fc\u30c8\u7bc4\u56f2\u5185\u3067\u6700\u5c0f\u8981\u7d20\u3092\u898b\u3064\u3051\u308b\n        k = i\n        for j in range(i + 1, n):\n            if nums[j] &lt; nums[k]:\n                k = j  # \u6700\u5c0f\u8981\u7d20\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8a18\u9332\n        # \u6700\u5c0f\u8981\u7d20\u3092\u672a\u30bd\u30fc\u30c8\u7bc4\u56f2\u306e\u5148\u982d\u8981\u7d20\u3068\u4ea4\u63db\n        nums[i], nums[k] = nums[k], nums[i]\n</code></pre> selection_sort.cpp<pre><code>/* \u9078\u629e\u30bd\u30fc\u30c8 */\nvoid selectionSort(vector&lt;int&gt; &amp;nums) {\n    int n = nums.size();\n    // \u5916\u5074\u30eb\u30fc\u30d7\uff1a\u672a\u30bd\u30fc\u30c8\u7bc4\u56f2\u306f[i, n-1]\n    for (int i = 0; i &lt; n - 1; i++) {\n        // \u5185\u5074\u30eb\u30fc\u30d7\uff1a\u672a\u30bd\u30fc\u30c8\u7bc4\u56f2\u5185\u3067\u6700\u5c0f\u8981\u7d20\u3092\u898b\u3064\u3051\u308b\n        int k = i;\n        for (int j = i + 1; j &lt; n; j++) {\n            if (nums[j] &lt; nums[k])\n                k = j; // \u6700\u5c0f\u8981\u7d20\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8a18\u9332\n        }\n        // \u6700\u5c0f\u8981\u7d20\u3092\u672a\u30bd\u30fc\u30c8\u7bc4\u56f2\u306e\u6700\u521d\u306e\u8981\u7d20\u3068\u4ea4\u63db\n        swap(nums[i], nums[k]);\n    }\n}\n</code></pre> selection_sort.java<pre><code>/* \u9078\u629e\u30bd\u30fc\u30c8 */\nvoid selectionSort(int[] nums) {\n    int n = nums.length;\n    // \u5916\u5074\u30eb\u30fc\u30d7: \u672a\u30bd\u30fc\u30c8\u7bc4\u56f2\u306f [i, n-1]\n    for (int i = 0; i &lt; n - 1; i++) {\n        // \u5185\u5074\u30eb\u30fc\u30d7: \u672a\u30bd\u30fc\u30c8\u7bc4\u56f2\u5185\u3067\u6700\u5c0f\u8981\u7d20\u3092\u898b\u3064\u3051\u308b\n        int k = i;\n        for (int j = i + 1; j &lt; n; j++) {\n            if (nums[j] &lt; nums[k])\n                k = j; // \u6700\u5c0f\u8981\u7d20\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8a18\u9332\n        }\n        // \u6700\u5c0f\u8981\u7d20\u3068\u672a\u30bd\u30fc\u30c8\u7bc4\u56f2\u306e\u6700\u521d\u306e\u8981\u7d20\u3092\u4ea4\u63db\n        int temp = nums[i];\n        nums[i] = nums[k];\n        nums[k] = temp;\n    }\n}\n</code></pre> selection_sort.cs<pre><code>[class]{selection_sort}-[func]{SelectionSort}\n</code></pre> selection_sort.go<pre><code>[class]{}-[func]{selectionSort}\n</code></pre> selection_sort.swift<pre><code>[class]{}-[func]{selectionSort}\n</code></pre> selection_sort.js<pre><code>[class]{}-[func]{selectionSort}\n</code></pre> selection_sort.ts<pre><code>[class]{}-[func]{selectionSort}\n</code></pre> selection_sort.dart<pre><code>[class]{}-[func]{selectionSort}\n</code></pre> selection_sort.rs<pre><code>[class]{}-[func]{selection_sort}\n</code></pre> selection_sort.c<pre><code>[class]{}-[func]{selectionSort}\n</code></pre> selection_sort.kt<pre><code>[class]{}-[func]{selectionSort}\n</code></pre> selection_sort.rb<pre><code>[class]{}-[func]{selection_sort}\n</code></pre> selection_sort.zig<pre><code>[class]{}-[func]{selectionSort}\n</code></pre>"},{"location":"chapter_sorting/selection_sort/#1121","title":"11.2.1 \u00a0 \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u7279\u6027","text":"<ul> <li>\\(O(n^2)\\)\u306e\u6642\u9593\u8a08\u7b97\u91cf\u3001\u975e\u9069\u5fdc\u30bd\u30fc\u30c8\uff1a\u5916\u5074\u30eb\u30fc\u30d7\u306b\\(n - 1\\)\u56de\u306e\u53cd\u5fa9\u304c\u3042\u308a\u3001\u672a\u30bd\u30fc\u30c8\u30bb\u30af\u30b7\u30e7\u30f3\u306e\u9577\u3055\u306f\u6700\u521d\u306e\u53cd\u5fa9\u3067\\(n\\)\u304b\u3089\u59cb\u307e\u308a\u3001\u6700\u5f8c\u306e\u53cd\u5fa9\u3067\\(2\\)\u307e\u3067\u6e1b\u5c11\u3057\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u5404\u5916\u5074\u30eb\u30fc\u30d7\u53cd\u5fa9\u306b\u306f\u305d\u308c\u305e\u308c\\(n\\)\u3001\\(n - 1\\)\u3001\\(\\dots\\)\u3001\\(3\\)\u3001\\(2\\)\u56de\u306e\u5185\u5074\u30eb\u30fc\u30d7\u53cd\u5fa9\u304c\u542b\u307e\u308c\u3001\u5408\u8a08\u306f\\(\\frac{(n - 1)(n + 2)}{2}\\)\u3068\u306a\u308a\u307e\u3059\u3002</li> <li>\\(O(1)\\)\u306e\u7a7a\u9593\u8a08\u7b97\u91cf\u3001\u30a4\u30f3\u30d7\u30ec\u30fc\u30b9\u30bd\u30fc\u30c8\uff1a\u30dd\u30a4\u30f3\u30bf\\(i\\)\u3068\\(j\\)\u3067\u5b9a\u6570\u306e\u8ffd\u52a0\u7a7a\u9593\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002</li> <li>\u975e\u5b89\u5b9a\u30bd\u30fc\u30c8\uff1a\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u8981\u7d20<code>nums[i]</code>\u306f\u7b49\u3057\u3044\u8981\u7d20\u306e\u53f3\u5074\u306b\u4ea4\u63db\u3055\u308c\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u3001\u76f8\u5bfe\u9806\u5e8f\u304c\u5909\u308f\u308b\u539f\u56e0\u3068\u306a\u308a\u307e\u3059\u3002</li> </ul> <p> \u56f3 11-3 \u00a0 Selection sort instability example </p>"},{"location":"chapter_sorting/sorting_algorithm/","title":"11.1 \u00a0 \u30bd\u30fc\u30c8\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0","text":"<p>\u30bd\u30fc\u30c8\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u3001\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u3092\u7279\u5b9a\u306e\u9806\u5e8f\u3067\u914d\u5217\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u30bd\u30fc\u30c8\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u3001\u9806\u5e8f\u4ed8\u3051\u3089\u308c\u305f\u30c7\u30fc\u30bf\u306f\u901a\u5e38\u3001\u3088\u308a\u52b9\u7387\u7684\u306b\u63a2\u7d22\u3001\u5206\u6790\u3001\u51e6\u7406\u3067\u304d\u308b\u305f\u3081\u3001\u5e45\u5e83\u3044\u5fdc\u7528\u304c\u3042\u308a\u307e\u3059\u3002</p> <p>\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u30bd\u30fc\u30c8\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u30c7\u30fc\u30bf\u578b\u306f\u6574\u6570\u3001\u6d6e\u52d5\u5c0f\u6570\u70b9\u6570\u3001\u6587\u5b57\u3001\u6587\u5b57\u5217\u306a\u3069\u3067\u3059\u3002\u30bd\u30fc\u30c8\u57fa\u6e96\u306f\u3001\u6570\u5024\u30b5\u30a4\u30ba\u3001\u6587\u5b57ASCII\u9806\u5e8f\u3001\u307e\u305f\u306f\u30ab\u30b9\u30bf\u30e0\u57fa\u6e96\u306a\u3069\u3001\u5fc5\u8981\u306b\u5fdc\u3058\u3066\u8a2d\u5b9a\u3067\u304d\u307e\u3059\u3002</p> <p></p> <p> \u56f3 11-1 \u00a0 Data types and comparator examples </p>"},{"location":"chapter_sorting/sorting_algorithm/#1111","title":"11.1.1 \u00a0 \u8a55\u4fa1\u6b21\u5143","text":"<p>\u5b9f\u884c\u52b9\u7387\uff1a\u30bd\u30fc\u30c8\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u6642\u9593\u8a08\u7b97\u91cf\u304c\u3067\u304d\u308b\u3060\u3051\u4f4e\u3044\u3053\u3068\u3092\u671f\u5f85\u3057\u3001\u5168\u4f53\u7684\u306a\u64cd\u4f5c\u6570\u3082\u5c11\u306a\u3044\u3053\u3068\uff08\u6642\u9593\u8a08\u7b97\u91cf\u306e\u5b9a\u6570\u9805\u3092\u4e0b\u3052\u308b\uff09\u3092\u671b\u307f\u307e\u3059\u3002\u5927\u5bb9\u91cf\u30c7\u30fc\u30bf\u3067\u306f\u3001\u5b9f\u884c\u52b9\u7387\u304c\u7279\u306b\u91cd\u8981\u3067\u3059\u3002</p> <p>\u30a4\u30f3\u30d7\u30ec\u30fc\u30b9\u6027\uff1a\u540d\u524d\u304c\u793a\u3059\u3068\u304a\u308a\u3001\u30a4\u30f3\u30d7\u30ec\u30fc\u30b9\u30bd\u30fc\u30c8\u306f\u5143\u306e\u914d\u5217\u3092\u76f4\u63a5\u64cd\u4f5c\u3059\u308b\u3053\u3068\u3067\u5b9f\u73fe\u3055\u308c\u3001\u8ffd\u52a0\u306e\u30d8\u30eb\u30d1\u30fc\u914d\u5217\u304c\u4e0d\u8981\u3067\u3042\u308b\u305f\u3081\u3001\u30e1\u30e2\u30ea\u3092\u7bc0\u7d04\u3057\u307e\u3059\u3002\u4e00\u822c\u7684\u306b\u3001\u30a4\u30f3\u30d7\u30ec\u30fc\u30b9\u30bd\u30fc\u30c8\u306f\u30c7\u30fc\u30bf\u79fb\u52d5\u64cd\u4f5c\u304c\u5c11\u306a\u304f\u3001\u9ad8\u901f\u3067\u3059\u3002</p> <p>\u5b89\u5b9a\u6027\uff1a\u5b89\u5b9a\u30bd\u30fc\u30c8\u306f\u3001\u30bd\u30fc\u30c8\u5f8c\u306b\u914d\u5217\u5185\u306e\u7b49\u3057\u3044\u8981\u7d20\u306e\u76f8\u5bfe\u9806\u5e8f\u304c\u5909\u308f\u3089\u306a\u3044\u3053\u3068\u3092\u4fdd\u8a3c\u3057\u307e\u3059\u3002</p> <p>\u5b89\u5b9a\u30bd\u30fc\u30c8\u306f\u3001\u30de\u30eb\u30c1\u30ad\u30fc\u30bd\u30fc\u30c8\u30b7\u30ca\u30ea\u30aa\u306b\u304a\u3044\u3066\u5fc5\u8981\u6761\u4ef6\u3067\u3059\u3002\u5b66\u751f\u60c5\u5831\u3092\u683c\u7d0d\u3059\u308b\u30c6\u30fc\u30d6\u30eb\u304c\u3042\u308a\u3001\u7b2c1\u5217\u3068\u7b2c2\u5217\u304c\u305d\u308c\u305e\u308c\u540d\u524d\u3068\u5e74\u9f62\u3067\u3042\u308b\u3068\u3057\u307e\u3059\u3002\u3053\u306e\u5834\u5408\u3001\u4e0d\u5b89\u5b9a\u30bd\u30fc\u30c8\u306f\u5165\u529b\u30c7\u30fc\u30bf\u306e\u9806\u5e8f\u3092\u5931\u3046\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\uff1a</p> <pre><code># \u5165\u529b\u30c7\u30fc\u30bf\u306f\u540d\u524d\u3067\u30bd\u30fc\u30c8\u6e08\u307f\n# (\u540d\u524d, \u5e74\u9f62)\n  ('A', 19)\n  ('B', 18)\n  ('C', 21)\n  ('D', 19)\n  ('E', 23)\n\n# \u4e0d\u5b89\u5b9a\u30bd\u30fc\u30c8\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u4f7f\u7528\u3057\u3066\u30ea\u30b9\u30c8\u3092\u5e74\u9f62\u3067\u30bd\u30fc\u30c8\u3059\u308b\u3068\u4eee\u5b9a\u3059\u308b\u3068\u3001\n# \u7d50\u679c\u306f('D', 19)\u3068('A', 19)\u306e\u76f8\u5bfe\u4f4d\u7f6e\u3092\u5909\u66f4\u3057\u3001\n# \u5165\u529b\u30c7\u30fc\u30bf\u304c\u540d\u524d\u3067\u30bd\u30fc\u30c8\u6e08\u307f\u3067\u3042\u308b\u3068\u3044\u3046\u6027\u8cea\u304c\u5931\u308f\u308c\u308b\n  ('B', 18)\n  ('D', 19)\n  ('A', 19)\n  ('C', 21)\n  ('E', 23)\n</code></pre> <p>\u9069\u5fdc\u6027\uff1a\u9069\u5fdc\u30bd\u30fc\u30c8\u306f\u5165\u529b\u30c7\u30fc\u30bf\u5185\u306e\u65e2\u5b58\u306e\u9806\u5e8f\u60c5\u5831\u3092\u6d3b\u7528\u3057\u3066\u8a08\u7b97\u8ca0\u8377\u3092\u524a\u6e1b\u3057\u3001\u3088\u308a\u6700\u9069\u306a\u6642\u9593\u52b9\u7387\u3092\u5b9f\u73fe\u3057\u307e\u3059\u3002\u9069\u5fdc\u30bd\u30fc\u30c8\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u6700\u826f\u30b1\u30fc\u30b9\u6642\u9593\u8a08\u7b97\u91cf\u306f\u3001\u901a\u5e38\u5e73\u5747\u30b1\u30fc\u30b9\u6642\u9593\u8a08\u7b97\u91cf\u3088\u308a\u3082\u512a\u308c\u3066\u3044\u307e\u3059\u3002</p> <p>\u6bd4\u8f03\u30d9\u30fc\u30b9\u307e\u305f\u306f\u975e\u6bd4\u8f03\u30d9\u30fc\u30b9\uff1a\u6bd4\u8f03\u30d9\u30fc\u30b9\u30bd\u30fc\u30c8\u306f\u6bd4\u8f03\u6f14\u7b97\u5b50\uff08\\(&lt;\\)\u3001\\(=\\)\u3001\\(&gt;\\)\uff09\u306b\u4f9d\u5b58\u3057\u3066\u8981\u7d20\u306e\u76f8\u5bfe\u9806\u5e8f\u3092\u6c7a\u5b9a\u3057\u3001\u914d\u5217\u5168\u4f53\u3092\u30bd\u30fc\u30c8\u3057\u307e\u3059\u3002\u7406\u8ad6\u7684\u6700\u9069\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O(n \\log n)\\)\u3067\u3059\u3002\u4e00\u65b9\u3001\u975e\u6bd4\u8f03\u30bd\u30fc\u30c8\u306f\u6bd4\u8f03\u6f14\u7b97\u5b50\u3092\u4f7f\u7528\u305b\u305a\u3001\\(O(n)\\)\u306e\u6642\u9593\u8a08\u7b97\u91cf\u3092\u5b9f\u73fe\u3067\u304d\u307e\u3059\u304c\u3001\u6c4e\u7528\u6027\u306f\u6bd4\u8f03\u7684\u52a3\u308a\u307e\u3059\u3002</p>"},{"location":"chapter_sorting/sorting_algorithm/#1112","title":"11.1.2 \u00a0 \u7406\u60f3\u7684\u306a\u30bd\u30fc\u30c8\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0","text":"<p>\u9ad8\u901f\u5b9f\u884c\u3001\u30a4\u30f3\u30d7\u30ec\u30fc\u30b9\u3001\u5b89\u5b9a\u3001\u9069\u5fdc\u3001\u6c4e\u7528\u3002\u660e\u3089\u304b\u306b\u3001\u3053\u308c\u3089\u306e\u3059\u3079\u3066\u306e\u7279\u5fb4\u3092\u7d44\u307f\u5408\u308f\u305b\u305f\u30bd\u30fc\u30c8\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u4eca\u65e5\u307e\u3067\u898b\u3064\u304b\u3063\u3066\u3044\u307e\u305b\u3093\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u30bd\u30fc\u30c8\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u9078\u629e\u3059\u308b\u969b\u306f\u3001\u30c7\u30fc\u30bf\u306e\u7279\u5b9a\u306e\u7279\u5fb4\u3068\u554f\u984c\u306e\u8981\u4ef6\u306b\u57fa\u3065\u3044\u3066\u6c7a\u5b9a\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002</p> <p>\u6b21\u306b\u3001\u3055\u307e\u3056\u307e\u306a\u30bd\u30fc\u30c8\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u4e00\u7dd2\u306b\u5b66\u3073\u3001\u4e0a\u8a18\u306e\u8a55\u4fa1\u6b21\u5143\u306b\u57fa\u3065\u3044\u3066\u305d\u308c\u305e\u308c\u306e\u5229\u70b9\u3068\u6b20\u70b9\u3092\u5206\u6790\u3057\u307e\u3059\u3002</p>"},{"location":"chapter_sorting/summary/","title":"11.11 \u00a0 \u307e\u3068\u3081","text":""},{"location":"chapter_sorting/summary/#1","title":"1. \u00a0 \u91cd\u8981\u306a\u5fa9\u7fd2","text":"<ul> <li>\u30d0\u30d6\u30eb\u30bd\u30fc\u30c8\u306f\u96a3\u63a5\u3059\u308b\u8981\u7d20\u3092\u4ea4\u63db\u3059\u308b\u3053\u3068\u3067\u52d5\u4f5c\u3057\u307e\u3059\u3002\u30d5\u30e9\u30b0\u3092\u8ffd\u52a0\u3057\u3066\u65e9\u671f\u30ea\u30bf\u30fc\u30f3\u3092\u53ef\u80fd\u306b\u3059\u308b\u3053\u3068\u3067\u3001\u30d0\u30d6\u30eb\u30bd\u30fc\u30c8\u306e\u6700\u826f\u30b1\u30fc\u30b9\u306e\u6642\u9593\u8a08\u7b97\u91cf\u3092 \\(O(n)\\) \u306b\u6700\u9069\u5316\u3067\u304d\u307e\u3059\u3002</li> <li>\u633f\u5165\u30bd\u30fc\u30c8\u306f\u3001\u672a\u30bd\u30fc\u30c8\u533a\u9593\u304b\u3089\u8981\u7d20\u3092\u53d6\u308a\u51fa\u3057\u3066\u30bd\u30fc\u30c8\u6e08\u307f\u533a\u9593\u306e\u6b63\u3057\u3044\u4f4d\u7f6e\u306b\u633f\u5165\u3059\u308b\u3053\u3068\u3067\u5404\u30e9\u30a6\u30f3\u30c9\u3092\u30bd\u30fc\u30c8\u3057\u307e\u3059\u3002\u633f\u5165\u30bd\u30fc\u30c8\u306e\u6642\u9593\u8a08\u7b97\u91cf\u306f \\(O(n^2)\\) \u3067\u3059\u304c\u3001\u5358\u4f4d\u3042\u305f\u308a\u306e\u64cd\u4f5c\u304c\u6bd4\u8f03\u7684\u5c11\u306a\u3044\u305f\u3081\u3001\u5c11\u91cf\u306e\u30c7\u30fc\u30bf\u306e\u30bd\u30fc\u30c8\u3067\u306f\u975e\u5e38\u306b\u4eba\u6c17\u304c\u3042\u308a\u307e\u3059\u3002</li> <li>\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u306f\u6b69\u54e8\u5206\u5272\u64cd\u4f5c\u306b\u57fa\u3065\u3044\u3066\u3044\u307e\u3059\u3002\u6b69\u54e8\u5206\u5272\u3067\u306f\u3001\u5e38\u306b\u6700\u60aa\u306e\u30d4\u30dc\u30c3\u30c8\u3092\u9078\u3076\u53ef\u80fd\u6027\u304c\u3042\u308a\u3001\u6642\u9593\u8a08\u7b97\u91cf\u304c \\(O(n^2)\\) \u306b\u52a3\u5316\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002\u4e2d\u592e\u5024\u3084\u30e9\u30f3\u30c0\u30e0\u30d4\u30dc\u30c3\u30c8\u3092\u5c0e\u5165\u3059\u308b\u3053\u3068\u3067\u3001\u305d\u306e\u3088\u3046\u306a\u52a3\u5316\u306e\u78ba\u7387\u3092\u6e1b\u3089\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u672b\u5c3e\u518d\u5e30\u306f\u518d\u5e30\u306e\u6df1\u3055\u3092\u52b9\u679c\u7684\u306b\u6e1b\u3089\u3057\u3001\u7a7a\u9593\u8a08\u7b97\u91cf\u3092 \\(O(\\log n)\\) \u306b\u6700\u9069\u5316\u3057\u307e\u3059\u3002</li> <li>\u30de\u30fc\u30b8\u30bd\u30fc\u30c8\u306b\u306f\u5206\u5272\u3068\u30de\u30fc\u30b8\u306e2\u3064\u306e\u6bb5\u968e\u304c\u3042\u308a\u3001\u901a\u5e38\u5206\u5272\u7d71\u6cbb\u6226\u7565\u3092\u4f53\u73fe\u3057\u3066\u3044\u307e\u3059\u3002\u30de\u30fc\u30b8\u30bd\u30fc\u30c8\u3067\u306f\u3001\u914d\u5217\u306e\u30bd\u30fc\u30c8\u306b\u306f\u88dc\u52a9\u914d\u5217\u306e\u4f5c\u6210\u304c\u5fc5\u8981\u3067\u3001\u7a7a\u9593\u8a08\u7b97\u91cf\u306f \\(O(n)\\) \u306b\u306a\u308a\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u30ea\u30b9\u30c8\u306e\u30bd\u30fc\u30c8\u306e\u7a7a\u9593\u8a08\u7b97\u91cf\u306f \\(O(1)\\) \u306b\u6700\u9069\u5316\u3067\u304d\u307e\u3059\u3002</li> <li>\u30d0\u30b1\u30c3\u30c8\u30bd\u30fc\u30c8\u306f3\u3064\u306e\u624b\u9806\u304b\u3089\u69cb\u6210\u3055\u308c\u307e\u3059\uff1a\u30c7\u30fc\u30bf\u3092\u30d0\u30b1\u30c3\u30c8\u306b\u5206\u6563\u3001\u5404\u30d0\u30b1\u30c3\u30c8\u5185\u3067\u306e\u30bd\u30fc\u30c8\u3001\u30d0\u30b1\u30c3\u30c8\u9806\u3067\u306e\u7d50\u679c\u306e\u30de\u30fc\u30b8\u3002\u3053\u308c\u3082\u5206\u5272\u7d71\u6cbb\u6226\u7565\u3092\u4f53\u73fe\u3057\u3001\u975e\u5e38\u306b\u5927\u304d\u306a\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u306b\u9069\u3057\u3066\u3044\u307e\u3059\u3002\u30d0\u30b1\u30c3\u30c8\u30bd\u30fc\u30c8\u306e\u9375\u306f\u30c7\u30fc\u30bf\u306e\u5747\u7b49\u5206\u6563\u3067\u3059\u3002</li> <li>\u8a08\u6570\u30bd\u30fc\u30c8\u306f\u30d0\u30b1\u30c3\u30c8\u30bd\u30fc\u30c8\u306e\u5909\u5f62\u3067\u3001\u5404\u30c7\u30fc\u30bf\u30dd\u30a4\u30f3\u30c8\u306e\u51fa\u73fe\u56de\u6570\u3092\u30ab\u30a6\u30f3\u30c8\u3059\u308b\u3053\u3068\u3067\u30bd\u30fc\u30c8\u3057\u307e\u3059\u3002\u8a08\u6570\u30bd\u30fc\u30c8\u306f\u9650\u3089\u308c\u305f\u7bc4\u56f2\u306e\u30c7\u30fc\u30bf\u3092\u6301\u3064\u5927\u304d\u306a\u30c7\u30fc\u30bf\u30bb\u30c3\u30c8\u306b\u9069\u3057\u3066\u304a\u308a\u3001\u30c7\u30fc\u30bf\u3092\u6b63\u306e\u6574\u6570\u306b\u5909\u63db\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002</li> <li>\u57fa\u6570\u30bd\u30fc\u30c8\u306f\u6841\u3054\u3068\u306b\u30bd\u30fc\u30c8\u3059\u308b\u3053\u3068\u3067\u30c7\u30fc\u30bf\u3092\u51e6\u7406\u3057\u3001\u30c7\u30fc\u30bf\u304c\u56fa\u5b9a\u9577\u306e\u6570\u5024\u3068\u3057\u3066\u8868\u73fe\u3055\u308c\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002</li> <li>\u5168\u4f53\u7684\u306b\u3001\u79c1\u305f\u3061\u306f\u9ad8\u52b9\u7387\u3001\u5b89\u5b9a\u6027\u3001\u30a4\u30f3\u30d7\u30ec\u30fc\u30b9\u64cd\u4f5c\u3001\u9069\u5fdc\u6027\u3092\u6301\u3064\u30bd\u30fc\u30c8\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u6c42\u3081\u3066\u3044\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u4ed6\u306e\u30c7\u30fc\u30bf\u69cb\u9020\u3084\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3068\u540c\u69d8\u306b\u3001\u3053\u308c\u3089\u3059\u3079\u3066\u306e\u6761\u4ef6\u3092\u540c\u6642\u306b\u6e80\u305f\u3059\u30bd\u30fc\u30c8\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306f\u5b58\u5728\u3057\u307e\u305b\u3093\u3002\u5b9f\u969b\u306e\u5fdc\u7528\u3067\u306f\u3001\u30c7\u30fc\u30bf\u306e\u7279\u6027\u306b\u57fa\u3065\u3044\u3066\u9069\u5207\u306a\u30bd\u30fc\u30c8\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u9078\u629e\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002</li> <li>\u4ee5\u4e0b\u306e\u56f3\u306f\u3001\u52b9\u7387\u6027\u3001\u5b89\u5b9a\u6027\u3001\u30a4\u30f3\u30d7\u30ec\u30fc\u30b9\u6027\u3001\u9069\u5fdc\u6027\u306e\u89b3\u70b9\u304b\u3089\u4e3b\u6d41\u306e\u30bd\u30fc\u30c8\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u6bd4\u8f03\u3057\u3066\u3044\u307e\u3059\u3002</li> </ul> <p> \u56f3 11-19 \u00a0 \u30bd\u30fc\u30c8\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u6bd4\u8f03 </p>"},{"location":"chapter_sorting/summary/#2-q-a","title":"2. \u00a0 Q &amp; A","text":"<p>Q: \u30bd\u30fc\u30c8\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u5b89\u5b9a\u6027\u306f\u3044\u3064\u5fc5\u8981\u3067\u3059\u304b\uff1f</p> <p>\u5b9f\u969b\u306b\u306f\u3001\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u306e\u4e00\u3064\u306e\u5c5e\u6027\u306b\u57fa\u3065\u3044\u3066\u30bd\u30fc\u30c8\u3059\u308b\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u5b66\u751f\u306f\u540d\u524d\u3068\u8eab\u9577\u306e\u5c5e\u6027\u3092\u6301\u3061\u3001\u591a\u6bb5\u968e\u30bd\u30fc\u30c8\u3092\u5b9f\u88c5\u3059\u308b\u3053\u3068\u3092\u76ee\u6307\u3057\u307e\u3059\uff1a\u6700\u521d\u306b\u540d\u524d\u3067 <code>(A, 180) (B, 185) (C, 170) (D, 170)</code> \u3092\u53d6\u5f97\u3057\u3001\u6b21\u306b\u8eab\u9577\u3067\u3002\u30bd\u30fc\u30c8\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u304c\u4e0d\u5b89\u5b9a\u306a\u305f\u3081\u3001<code>(D, 170) (C, 170) (A, 180) (B, 185)</code> \u306b\u306a\u3063\u3066\u3057\u307e\u3046\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002</p> <p>\u5b66\u751fD\u3068C\u306e\u4f4d\u7f6e\u304c\u4ea4\u63db\u3055\u308c\u3001\u540d\u524d\u306e\u9806\u5e8f\u6027\u304c\u7834\u3089\u308c\u3066\u3044\u308b\u306e\u304c\u5206\u304b\u308a\u307e\u3059\u3002\u3053\u308c\u306f\u671b\u307e\u3057\u304f\u3042\u308a\u307e\u305b\u3093\u3002</p> <p>Q: \u6b69\u54e8\u5206\u5272\u3067\u306e\u300c\u53f3\u304b\u3089\u5de6\u3078\u306e\u691c\u7d22\u300d\u3068\u300c\u5de6\u304b\u3089\u53f3\u3078\u306e\u691c\u7d22\u300d\u306e\u9806\u5e8f\u3092\u4ea4\u63db\u3067\u304d\u307e\u3059\u304b\uff1f</p> <p>\u3044\u3044\u3048\u3001\u6700\u5de6\u8981\u7d20\u3092\u30d4\u30dc\u30c3\u30c8\u3068\u3057\u3066\u4f7f\u7528\u3059\u308b\u5834\u5408\u3001\u6700\u521d\u306b\u300c\u53f3\u304b\u3089\u5de6\u3078\u306e\u691c\u7d22\u300d\u3092\u884c\u3044\u3001\u6b21\u306b\u300c\u5de6\u304b\u3089\u53f3\u3078\u306e\u691c\u7d22\u300d\u3092\u884c\u3046\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u7d50\u8ad6\u306f\u3084\u3084\u76f4\u89b3\u306b\u53cd\u3059\u308b\u306e\u3067\u3001\u7406\u7531\u3092\u5206\u6790\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002</p> <p>\u6b69\u54e8\u5206\u5272 <code>partition()</code> \u306e\u6700\u5f8c\u306e\u30b9\u30c6\u30c3\u30d7\u306f <code>nums[left]</code> \u3068 <code>nums[i]</code> \u3092\u4ea4\u63db\u3059\u308b\u3053\u3068\u3067\u3059\u3002\u4ea4\u63db\u5f8c\u3001\u30d4\u30dc\u30c3\u30c8\u306e\u5de6\u5074\u306e\u8981\u7d20\u306f\u3059\u3079\u3066\u30d4\u30dc\u30c3\u30c8\u4ee5\u4e0b\u306b\u306a\u308a\u307e\u3059\u3002\u3053\u308c\u306b\u306f\u6700\u5f8c\u306e\u4ea4\u63db\u524d\u306b <code>nums[left] &gt;= nums[i]</code> \u304c\u6210\u308a\u7acb\u3064\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u300c\u5de6\u304b\u3089\u53f3\u3078\u306e\u691c\u7d22\u300d\u3092\u6700\u521d\u306b\u884c\u3044\u3001\u30d4\u30dc\u30c3\u30c8\u3088\u308a\u5927\u304d\u3044\u8981\u7d20\u304c\u898b\u3064\u304b\u3089\u306a\u3044\u5834\u5408\u3001<code>i == j</code> \u3067\u30eb\u30fc\u30d7\u3092\u7d42\u4e86\u3057\u3001<code>nums[j] == nums[i] &gt; nums[left]</code> \u3068\u306a\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u6700\u7d42\u4ea4\u63db\u64cd\u4f5c\u306f\u30d4\u30dc\u30c3\u30c8\u3088\u308a\u5927\u304d\u3044\u8981\u7d20\u3092\u914d\u5217\u306e\u5de6\u7aef\u306b\u4ea4\u63db\u3057\u3001\u6b69\u54e8\u5206\u5272\u3092\u5931\u6557\u3055\u305b\u307e\u3059\u3002</p> <p>\u4f8b\u3048\u3070\u3001\u914d\u5217 <code>[0, 0, 0, 0, 1]</code> \u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408\u3001\u6700\u521d\u306b\u300c\u5de6\u304b\u3089\u53f3\u3078\u306e\u691c\u7d22\u300d\u3092\u884c\u3046\u3068\u3001\u6b69\u54e8\u5206\u5272\u5f8c\u306e\u914d\u5217\u306f <code>[1, 0, 0, 0, 0]</code> \u3068\u306a\u308a\u3001\u3053\u308c\u306f\u6b63\u3057\u304f\u3042\u308a\u307e\u305b\u3093\u3002</p> <p>\u3055\u3089\u306b\u8003\u3048\u308b\u3068\u3001<code>nums[right]</code> \u3092\u30d4\u30dc\u30c3\u30c8\u3068\u3057\u3066\u9078\u629e\u3059\u308b\u5834\u5408\u3001\u307e\u3063\u305f\u304f\u9006\u3067\u3001\u6700\u521d\u306b\u300c\u5de6\u304b\u3089\u53f3\u3078\u306e\u691c\u7d22\u300d\u3092\u884c\u3046\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002</p> <p>Q: \u672b\u5c3e\u518d\u5e30\u6700\u9069\u5316\u306b\u3064\u3044\u3066\u3001\u77ed\u3044\u914d\u5217\u3092\u9078\u629e\u3059\u308b\u3053\u3068\u3067\u518d\u5e30\u306e\u6df1\u3055\u304c \\(\\log n\\) \u3092\u8d85\u3048\u306a\u3044\u3053\u3068\u3092\u4fdd\u8a3c\u3059\u308b\u306e\u306f\u306a\u305c\u3067\u3059\u304b\uff1f</p> <p>\u518d\u5e30\u306e\u6df1\u3055\u306f\u73fe\u5728\u30ea\u30bf\u30fc\u30f3\u3057\u3066\u3044\u306a\u3044\u518d\u5e30\u30e1\u30bd\u30c3\u30c9\u306e\u6570\u3067\u3059\u3002\u6b69\u54e8\u5206\u5272\u306e\u5404\u30e9\u30a6\u30f3\u30c9\u306f\u5143\u306e\u914d\u5217\u30922\u3064\u306e\u526f\u914d\u5217\u306b\u5206\u5272\u3057\u307e\u3059\u3002\u672b\u5c3e\u518d\u5e30\u6700\u9069\u5316\u306b\u3088\u308a\u3001\u518d\u5e30\u7684\u306b\u7d9a\u884c\u3059\u308b\u526f\u914d\u5217\u306e\u9577\u3055\u306f\u6700\u5927\u3067\u3082\u5143\u306e\u914d\u5217\u9577\u306e\u534a\u5206\u3067\u3059\u3002\u6700\u60aa\u306e\u5834\u5408\u5e38\u306b\u9577\u3055\u3092\u534a\u5206\u306b\u3059\u308b\u3068\u4eee\u5b9a\u3059\u308b\u3068\u3001\u6700\u7d42\u7684\u306a\u518d\u5e30\u306e\u6df1\u3055\u306f \\(\\log n\\) \u306b\u306a\u308a\u307e\u3059\u3002</p> <p>\u5143\u306e\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u3092\u898b\u76f4\u3059\u3068\u3001\u3088\u308a\u5927\u304d\u306a\u914d\u5217\u3092\u7d99\u7d9a\u7684\u306b\u518d\u5e30\u51e6\u7406\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u3001\u6700\u60aa\u306e\u5834\u5408 \\(n\\)\u3001\\(n - 1\\)\u3001...\u3001\\(2\\)\u3001\\(1\\) \u3067\u3001\u518d\u5e30\u306e\u6df1\u3055\u306f \\(n\\) \u306b\u306a\u308a\u307e\u3059\u3002\u672b\u5c3e\u518d\u5e30\u6700\u9069\u5316\u306f\u3053\u306e\u30b7\u30ca\u30ea\u30aa\u3092\u56de\u907f\u3067\u304d\u307e\u3059\u3002</p> <p>Q: \u914d\u5217\u306e\u3059\u3079\u3066\u306e\u8981\u7d20\u304c\u7b49\u3057\u3044\u5834\u5408\u3001\u30af\u30a4\u30c3\u30af\u30bd\u30fc\u30c8\u306e\u6642\u9593\u8a08\u7b97\u91cf\u306f \\(O(n^2)\\) \u3067\u3059\u304b\uff1f\u3053\u306e\u52a3\u5316\u30b1\u30fc\u30b9\u3092\u3069\u3046\u51e6\u7406\u3059\u3079\u304d\u3067\u3059\u304b\uff1f</p> <p>\u306f\u3044\u3002\u3053\u306e\u72b6\u6cc1\u306b\u3064\u3044\u3066\u306f\u3001\u6b69\u54e8\u5206\u5272\u3092\u4f7f\u7528\u3057\u3066\u914d\u5217\u3092\u30d4\u30dc\u30c3\u30c8\u3088\u308a\u5c0f\u3055\u3044\u3001\u7b49\u3057\u3044\u3001\u5927\u304d\u3044\u306e3\u3064\u306e\u90e8\u5206\u306b\u5206\u5272\u3059\u308b\u3053\u3068\u3092\u691c\u8a0e\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u5c0f\u3055\u3044\u90e8\u5206\u3068\u5927\u304d\u3044\u90e8\u5206\u306e\u307f\u3092\u518d\u5e30\u7684\u306b\u9032\u3081\u307e\u3059\u3002\u3053\u306e\u65b9\u6cd5\u3067\u306f\u3001\u3059\u3079\u3066\u306e\u5165\u529b\u8981\u7d20\u304c\u7b49\u3057\u3044\u914d\u5217\u30921\u30e9\u30a6\u30f3\u30c9\u306e\u6b69\u54e8\u5206\u5272\u3060\u3051\u3067\u30bd\u30fc\u30c8\u3067\u304d\u307e\u3059\u3002</p> <p>Q: \u306a\u305c\u30d0\u30b1\u30c3\u30c8\u30bd\u30fc\u30c8\u306e\u6700\u60aa\u30b1\u30fc\u30b9\u6642\u9593\u8a08\u7b97\u91cf\u306f \\(O(n^2)\\) \u3067\u3059\u304b\uff1f</p> <p>\u6700\u60aa\u306e\u5834\u5408\u3001\u3059\u3079\u3066\u306e\u8981\u7d20\u304c\u540c\u3058\u30d0\u30b1\u30c3\u30c8\u306b\u914d\u7f6e\u3055\u308c\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u8981\u7d20\u3092\u30bd\u30fc\u30c8\u3059\u308b\u305f\u3081\u306b \\(O(n^2)\\) \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3092\u4f7f\u7528\u3059\u308b\u5834\u5408\u3001\u6642\u9593\u8a08\u7b97\u91cf\u306f \\(O(n^2)\\) \u306b\u306a\u308a\u307e\u3059\u3002</p>"},{"location":"chapter_stack_and_queue/","title":"\u7b2c 5 \u7ae0 \u00a0 \u30b9\u30bf\u30c3\u30af\u3068\u30ad\u30e5\u30fc","text":"<p>Abstract</p> <p>\u30b9\u30bf\u30c3\u30af\u306f\u7a4d\u307f\u91cd\u306d\u3089\u308c\u305f\u732b\u306e\u3088\u3046\u306a\u3082\u306e\u3067\u3001\u30ad\u30e5\u30fc\u306f\u4e00\u5217\u306b\u4e26\u3093\u3060\u732b\u306e\u3088\u3046\u306a\u3082\u306e\u3067\u3059\u3002</p> <p>\u305d\u308c\u3089\u306f\u305d\u308c\u305e\u308c\u3001\u5f8c\u5165\u5148\u51fa\uff08LIFO\uff09\u3068\u5148\u5165\u5148\u51fa\uff08FIFO\uff09\u306e\u8ad6\u7406\u95a2\u4fc2\u3092\u8868\u3057\u3066\u3044\u307e\u3059\u3002</p>"},{"location":"chapter_stack_and_queue/#_1","title":"\u7ae0\u306e\u5185\u5bb9","text":"<ul> <li>5.1 \u00a0 \u30b9\u30bf\u30c3\u30af</li> <li>5.2 \u00a0 \u30ad\u30e5\u30fc</li> <li>5.3 \u00a0 \u4e21\u7aef\u30ad\u30e5\u30fc</li> <li>5.4 \u00a0 \u307e\u3068\u3081</li> </ul>"},{"location":"chapter_stack_and_queue/deque/","title":"5.3 \u00a0 \u4e21\u7aef\u30ad\u30e5\u30fc","text":"<p>\u30ad\u30e5\u30fc\u3067\u306f\u3001\u5148\u982d\u304b\u3089\u306e\u8981\u7d20\u306e\u524a\u9664\u3084\u672b\u5c3e\u3078\u306e\u8981\u7d20\u306e\u8ffd\u52a0\u306e\u307f\u304c\u53ef\u80fd\u3067\u3059\u3002\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u4e21\u7aef\u30ad\u30e5\u30fc\uff08deque\uff09\u306f\u3088\u308a\u67d4\u8edf\u6027\u3092\u63d0\u4f9b\u3057\u3001\u5148\u982d\u3068\u672b\u5c3e\u306e\u4e21\u65b9\u3067\u8981\u7d20\u306e\u8ffd\u52a0\u3084\u524a\u9664\u3092\u53ef\u80fd\u306b\u3057\u307e\u3059\u3002</p> <p></p> <p> \u56f3 5-7 \u00a0 \u4e21\u7aef\u30ad\u30e5\u30fc\u306e\u64cd\u4f5c </p>"},{"location":"chapter_stack_and_queue/deque/#531","title":"5.3.1 \u00a0 \u4e21\u7aef\u30ad\u30e5\u30fc\u306e\u4e00\u822c\u7684\u306a\u64cd\u4f5c","text":"<p>\u4e21\u7aef\u30ad\u30e5\u30fc\u306e\u4e00\u822c\u7684\u306a\u64cd\u4f5c\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\u3002\u5177\u4f53\u7684\u306a\u30e1\u30bd\u30c3\u30c9\u540d\u306f\u4f7f\u7528\u3059\u308b\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u306b\u3088\u3063\u3066\u7570\u306a\u308a\u307e\u3059\u3002</p> <p> \u8868 5-3 \u00a0 \u4e21\u7aef\u30ad\u30e5\u30fc\u306e\u64cd\u4f5c\u52b9\u7387 </p> \u30e1\u30bd\u30c3\u30c9\u540d \u8aac\u660e \u6642\u9593\u8a08\u7b97\u91cf <code>pushFirst()</code> \u5148\u982d\u306b\u8981\u7d20\u3092\u8ffd\u52a0 \\(O(1)\\) <code>pushLast()</code> \u672b\u5c3e\u306b\u8981\u7d20\u3092\u8ffd\u52a0 \\(O(1)\\) <code>popFirst()</code> \u5148\u982d\u8981\u7d20\u3092\u524a\u9664 \\(O(1)\\) <code>popLast()</code> \u672b\u5c3e\u8981\u7d20\u3092\u524a\u9664 \\(O(1)\\) <code>peekFirst()</code> \u5148\u982d\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 \\(O(1)\\) <code>peekLast()</code> \u672b\u5c3e\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 \\(O(1)\\) <p>\u540c\u69d8\u306b\u3001\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u3067\u5b9f\u88c5\u3055\u308c\u305f\u4e21\u7aef\u30ad\u30e5\u30fc\u30af\u30e9\u30b9\u3092\u76f4\u63a5\u4f7f\u7528\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinZig deque.py<pre><code>from collections import deque\n\n# \u4e21\u7aef\u30ad\u30e5\u30fc\u3092\u521d\u671f\u5316\ndeq: deque[int] = deque()\n\n# \u8981\u7d20\u3092\u30a8\u30f3\u30ad\u30e5\u30fc\ndeq.append(2)      # \u672b\u5c3e\u306b\u8ffd\u52a0\ndeq.append(5)\ndeq.append(4)\ndeq.appendleft(3)  # \u5148\u982d\u306b\u8ffd\u52a0\ndeq.appendleft(1)\n\n# \u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9\nfront: int = deq[0]  # \u5148\u982d\u8981\u7d20\nrear: int = deq[-1]  # \u672b\u5c3e\u8981\u7d20\n\n# \u8981\u7d20\u3092\u30c7\u30ad\u30e5\u30fc\npop_front: int = deq.popleft()  # \u5148\u982d\u8981\u7d20\u3092\u30c7\u30ad\u30e5\u30fc\npop_rear: int = deq.pop()       # \u672b\u5c3e\u8981\u7d20\u3092\u30c7\u30ad\u30e5\u30fc\n\n# \u4e21\u7aef\u30ad\u30e5\u30fc\u306e\u9577\u3055\u3092\u53d6\u5f97\nsize: int = len(deq)\n\n# \u4e21\u7aef\u30ad\u30e5\u30fc\u304c\u7a7a\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d\nis_empty: bool = len(deq) == 0\n</code></pre> deque.cpp<pre><code>/* \u4e21\u7aef\u30ad\u30e5\u30fc\u3092\u521d\u671f\u5316 */\ndeque&lt;int&gt; deque;\n\n/* \u8981\u7d20\u3092\u30a8\u30f3\u30ad\u30e5\u30fc */\ndeque.push_back(2);   // \u672b\u5c3e\u306b\u8ffd\u52a0\ndeque.push_back(5);\ndeque.push_back(4);\ndeque.push_front(3);  // \u5148\u982d\u306b\u8ffd\u52a0\ndeque.push_front(1);\n\n/* \u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\nint front = deque.front(); // \u5148\u982d\u8981\u7d20\nint back = deque.back();   // \u672b\u5c3e\u8981\u7d20\n\n/* \u8981\u7d20\u3092\u30c7\u30ad\u30e5\u30fc */\ndeque.pop_front();  // \u5148\u982d\u8981\u7d20\u3092\u30c7\u30ad\u30e5\u30fc\ndeque.pop_back();   // \u672b\u5c3e\u8981\u7d20\u3092\u30c7\u30ad\u30e5\u30fc\n\n/* \u4e21\u7aef\u30ad\u30e5\u30fc\u306e\u9577\u3055\u3092\u53d6\u5f97 */\nint size = deque.size();\n\n/* \u4e21\u7aef\u30ad\u30e5\u30fc\u304c\u7a7a\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d */\nbool empty = deque.empty();\n</code></pre> deque.java<pre><code>/* \u4e21\u7aef\u30ad\u30e5\u30fc\u3092\u521d\u671f\u5316 */\nDeque&lt;Integer&gt; deque = new LinkedList&lt;&gt;();\n\n/* \u8981\u7d20\u3092\u30a8\u30f3\u30ad\u30e5\u30fc */\ndeque.offerLast(2);   // \u672b\u5c3e\u306b\u8ffd\u52a0\ndeque.offerLast(5);\ndeque.offerLast(4);\ndeque.offerFirst(3);  // \u5148\u982d\u306b\u8ffd\u52a0\ndeque.offerFirst(1);\n\n/* \u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\nint peekFirst = deque.peekFirst();  // \u5148\u982d\u8981\u7d20\nint peekLast = deque.peekLast();    // \u672b\u5c3e\u8981\u7d20\n\n/* \u8981\u7d20\u3092\u30c7\u30ad\u30e5\u30fc */\nint popFirst = deque.pollFirst();  // \u5148\u982d\u8981\u7d20\u3092\u30c7\u30ad\u30e5\u30fc\nint popLast = deque.pollLast();    // \u672b\u5c3e\u8981\u7d20\u3092\u30c7\u30ad\u30e5\u30fc\n\n/* \u4e21\u7aef\u30ad\u30e5\u30fc\u306e\u9577\u3055\u3092\u53d6\u5f97 */\nint size = deque.size();\n\n/* \u4e21\u7aef\u30ad\u30e5\u30fc\u304c\u7a7a\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d */\nboolean isEmpty = deque.isEmpty();\n</code></pre> deque.cs<pre><code>/* \u4e21\u7aef\u30ad\u30e5\u30fc\u3092\u521d\u671f\u5316 */\n// C#\u3067\u306f\u3001LinkedList\u3092\u4e21\u7aef\u30ad\u30e5\u30fc\u3068\u3057\u3066\u4f7f\u7528\nLinkedList&lt;int&gt; deque = new();\n\n/* \u8981\u7d20\u3092\u30a8\u30f3\u30ad\u30e5\u30fc */\ndeque.AddLast(2);   // \u672b\u5c3e\u306b\u8ffd\u52a0\ndeque.AddLast(5);\ndeque.AddLast(4);\ndeque.AddFirst(3);  // \u5148\u982d\u306b\u8ffd\u52a0\ndeque.AddFirst(1);\n\n/* \u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\nint peekFirst = deque.First.Value;  // \u5148\u982d\u8981\u7d20\nint peekLast = deque.Last.Value;    // \u672b\u5c3e\u8981\u7d20\n\n/* \u8981\u7d20\u3092\u30c7\u30ad\u30e5\u30fc */\ndeque.RemoveFirst();  // \u5148\u982d\u8981\u7d20\u3092\u30c7\u30ad\u30e5\u30fc\ndeque.RemoveLast();   // \u672b\u5c3e\u8981\u7d20\u3092\u30c7\u30ad\u30e5\u30fc\n\n/* \u4e21\u7aef\u30ad\u30e5\u30fc\u306e\u9577\u3055\u3092\u53d6\u5f97 */\nint size = deque.Count;\n\n/* \u4e21\u7aef\u30ad\u30e5\u30fc\u304c\u7a7a\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d */\nbool isEmpty = deque.Count == 0;\n</code></pre> deque_test.go<pre><code>/* \u4e21\u7aef\u30ad\u30e5\u30fc\u3092\u521d\u671f\u5316 */\n// Go\u3067\u306f\u3001list\u3092\u4e21\u7aef\u30ad\u30e5\u30fc\u3068\u3057\u3066\u4f7f\u7528\ndeque := list.New()\n\n/* \u8981\u7d20\u3092\u30a8\u30f3\u30ad\u30e5\u30fc */\ndeque.PushBack(2)      // \u672b\u5c3e\u306b\u8ffd\u52a0\ndeque.PushBack(5)\ndeque.PushBack(4)\ndeque.PushFront(3)     // \u5148\u982d\u306b\u8ffd\u52a0\ndeque.PushFront(1)\n\n/* \u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\nfront := deque.Front() // \u5148\u982d\u8981\u7d20\nrear := deque.Back()   // \u672b\u5c3e\u8981\u7d20\n\n/* \u8981\u7d20\u3092\u30c7\u30ad\u30e5\u30fc */\ndeque.Remove(front)    // \u5148\u982d\u8981\u7d20\u3092\u30c7\u30ad\u30e5\u30fc\ndeque.Remove(rear)     // \u672b\u5c3e\u8981\u7d20\u3092\u30c7\u30ad\u30e5\u30fc\n\n/* \u4e21\u7aef\u30ad\u30e5\u30fc\u306e\u9577\u3055\u3092\u53d6\u5f97 */\nsize := deque.Len()\n\n/* \u4e21\u7aef\u30ad\u30e5\u30fc\u304c\u7a7a\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d */\nisEmpty := deque.Len() == 0\n</code></pre> deque.swift<pre><code>/* \u4e21\u7aef\u30ad\u30e5\u30fc\u3092\u521d\u671f\u5316 */\n// Swift\u306b\u306f\u7d44\u307f\u8fbc\u307f\u306e\u4e21\u7aef\u30ad\u30e5\u30fc\u30af\u30e9\u30b9\u304c\u306a\u3044\u305f\u3081\u3001Array\u3092\u4e21\u7aef\u30ad\u30e5\u30fc\u3068\u3057\u3066\u4f7f\u7528\nvar deque: [Int] = []\n\n/* \u8981\u7d20\u3092\u30a8\u30f3\u30ad\u30e5\u30fc */\ndeque.append(2) // \u672b\u5c3e\u306b\u8ffd\u52a0\ndeque.append(5)\ndeque.append(4)\ndeque.insert(3, at: 0) // \u5148\u982d\u306b\u8ffd\u52a0\ndeque.insert(1, at: 0)\n\n/* \u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\nlet peekFirst = deque.first! // \u5148\u982d\u8981\u7d20\nlet peekLast = deque.last!   // \u672b\u5c3e\u8981\u7d20\n\n/* \u8981\u7d20\u3092\u30c7\u30ad\u30e5\u30fc */\n// Array\u3092\u4f7f\u7528\u3059\u308b\u5834\u5408\u3001popFirst\u306e\u8a08\u7b97\u91cf\u306fO(n)\nlet popFirst = deque.removeFirst() // \u5148\u982d\u8981\u7d20\u3092\u30c7\u30ad\u30e5\u30fc\nlet popLast = deque.removeLast()   // \u672b\u5c3e\u8981\u7d20\u3092\u30c7\u30ad\u30e5\u30fc\n\n/* \u4e21\u7aef\u30ad\u30e5\u30fc\u306e\u9577\u3055\u3092\u53d6\u5f97 */\nlet size = deque.count\n\n/* \u4e21\u7aef\u30ad\u30e5\u30fc\u304c\u7a7a\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d */\nlet isEmpty = deque.isEmpty\n</code></pre> deque.js<pre><code>/* \u4e21\u7aef\u30ad\u30e5\u30fc\u3092\u521d\u671f\u5316 */\n// JavaScript\u306b\u306f\u7d44\u307f\u8fbc\u307f\u306e\u4e21\u7aef\u30ad\u30e5\u30fc\u304c\u306a\u3044\u305f\u3081\u3001Array\u3092\u4e21\u7aef\u30ad\u30e5\u30fc\u3068\u3057\u3066\u4f7f\u7528\nconst deque = [];\n\n/* \u8981\u7d20\u3092\u30a8\u30f3\u30ad\u30e5\u30fc */\ndeque.push(2);\ndeque.push(5);\ndeque.push(4);\n// \u6ce8\u610f\uff1aunshift()\u306f\u914d\u5217\u306e\u305f\u3081\u6642\u9593\u8a08\u7b97\u91cf\u304cO(n)\ndeque.unshift(3);\ndeque.unshift(1);\n\n/* \u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\nconst peekFirst = deque[0]; // \u5148\u982d\u8981\u7d20\nconst peekLast = deque[deque.length - 1]; // \u672b\u5c3e\u8981\u7d20\n\n/* \u8981\u7d20\u3092\u30c7\u30ad\u30e5\u30fc */\n// \u6ce8\u610f\uff1ashift()\u306f\u914d\u5217\u306e\u305f\u3081\u6642\u9593\u8a08\u7b97\u91cf\u304cO(n)\nconst popFront = deque.shift(); // \u5148\u982d\u8981\u7d20\u3092\u30c7\u30ad\u30e5\u30fc\nconst popBack = deque.pop();    // \u672b\u5c3e\u8981\u7d20\u3092\u30c7\u30ad\u30e5\u30fc\n\n/* \u4e21\u7aef\u30ad\u30e5\u30fc\u306e\u9577\u3055\u3092\u53d6\u5f97 */\nconst size = deque.length;\n\n/* \u4e21\u7aef\u30ad\u30e5\u30fc\u304c\u7a7a\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d */\nconst isEmpty = size === 0;\n</code></pre> deque.ts<pre><code>/* \u4e21\u7aef\u30ad\u30e5\u30fc\u3092\u521d\u671f\u5316 */\n// TypeScript\u306b\u306f\u7d44\u307f\u8fbc\u307f\u306e\u4e21\u7aef\u30ad\u30e5\u30fc\u304c\u306a\u3044\u305f\u3081\u3001Array\u3092\u4e21\u7aef\u30ad\u30e5\u30fc\u3068\u3057\u3066\u4f7f\u7528\nconst deque: number[] = [];\n\n/* \u8981\u7d20\u3092\u30a8\u30f3\u30ad\u30e5\u30fc */\ndeque.push(2);\ndeque.push(5);\ndeque.push(4);\n// \u6ce8\u610f\uff1aunshift()\u306f\u914d\u5217\u306e\u305f\u3081\u6642\u9593\u8a08\u7b97\u91cf\u304cO(n)\ndeque.unshift(3);\ndeque.unshift(1);\n\n/* \u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\nconst peekFirst: number = deque[0]; // \u5148\u982d\u8981\u7d20\nconst peekLast: number = deque[deque.length - 1]; // \u672b\u5c3e\u8981\u7d20\n\n/* \u8981\u7d20\u3092\u30c7\u30ad\u30e5\u30fc */\n// \u6ce8\u610f\uff1ashift()\u306f\u914d\u5217\u306e\u305f\u3081\u6642\u9593\u8a08\u7b97\u91cf\u304cO(n)\nconst popFront: number = deque.shift() as number; // \u5148\u982d\u8981\u7d20\u3092\u30c7\u30ad\u30e5\u30fc\nconst popBack: number = deque.pop() as number;    // \u672b\u5c3e\u8981\u7d20\u3092\u30c7\u30ad\u30e5\u30fc\n\n/* \u4e21\u7aef\u30ad\u30e5\u30fc\u306e\u9577\u3055\u3092\u53d6\u5f97 */\nconst size: number = deque.length;\n\n/* \u4e21\u7aef\u30ad\u30e5\u30fc\u304c\u7a7a\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d */\nconst isEmpty: boolean = size === 0;\n</code></pre> deque.dart<pre><code>/* \u4e21\u7aef\u30ad\u30e5\u30fc\u3092\u521d\u671f\u5316 */\n// Dart\u3067\u306f\u3001Queue\u304c\u4e21\u7aef\u30ad\u30e5\u30fc\u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u308b\nQueue&lt;int&gt; deque = Queue&lt;int&gt;();\n\n/* \u8981\u7d20\u3092\u30a8\u30f3\u30ad\u30e5\u30fc */\ndeque.addLast(2);  // \u672b\u5c3e\u306b\u8ffd\u52a0\ndeque.addLast(5);\ndeque.addLast(4);\ndeque.addFirst(3); // \u5148\u982d\u306b\u8ffd\u52a0\ndeque.addFirst(1);\n\n/* \u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\nint peekFirst = deque.first; // \u5148\u982d\u8981\u7d20\nint peekLast = deque.last;   // \u672b\u5c3e\u8981\u7d20\n\n/* \u8981\u7d20\u3092\u30c7\u30ad\u30e5\u30fc */\nint popFirst = deque.removeFirst(); // \u5148\u982d\u8981\u7d20\u3092\u30c7\u30ad\u30e5\u30fc\nint popLast = deque.removeLast();   // \u672b\u5c3e\u8981\u7d20\u3092\u30c7\u30ad\u30e5\u30fc\n\n/* \u4e21\u7aef\u30ad\u30e5\u30fc\u306e\u9577\u3055\u3092\u53d6\u5f97 */\nint size = deque.length;\n\n/* \u4e21\u7aef\u30ad\u30e5\u30fc\u304c\u7a7a\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d */\nbool isEmpty = deque.isEmpty;\n</code></pre> deque.rs<pre><code>/* \u4e21\u7aef\u30ad\u30e5\u30fc\u3092\u521d\u671f\u5316 */\nlet mut deque: VecDeque&lt;u32&gt; = VecDeque::new();\n\n/* \u8981\u7d20\u3092\u30a8\u30f3\u30ad\u30e5\u30fc */\ndeque.push_back(2);  // \u672b\u5c3e\u306b\u8ffd\u52a0\ndeque.push_back(5);\ndeque.push_back(4);\ndeque.push_front(3); // \u5148\u982d\u306b\u8ffd\u52a0\ndeque.push_front(1);\n\n/* \u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\nif let Some(front) = deque.front() { // \u5148\u982d\u8981\u7d20\n}\nif let Some(rear) = deque.back() {   // \u672b\u5c3e\u8981\u7d20\n}\n\n/* \u8981\u7d20\u3092\u30c7\u30ad\u30e5\u30fc */\nif let Some(pop_front) = deque.pop_front() { // \u5148\u982d\u8981\u7d20\u3092\u30c7\u30ad\u30e5\u30fc\n}\nif let Some(pop_rear) = deque.pop_back() {   // \u672b\u5c3e\u8981\u7d20\u3092\u30c7\u30ad\u30e5\u30fc\n}\n\n/* \u4e21\u7aef\u30ad\u30e5\u30fc\u306e\u9577\u3055\u3092\u53d6\u5f97 */\nlet size = deque.len();\n\n/* \u4e21\u7aef\u30ad\u30e5\u30fc\u304c\u7a7a\u304b\u3069\u3046\u304b\u3092\u78ba\u8a8d */\nlet is_empty = deque.is_empty();\n</code></pre> deque.c<pre><code>// C\u306b\u306f\u7d44\u307f\u8fbc\u307f\u306e\u4e21\u7aef\u30ad\u30e5\u30fc\u304c\u63d0\u4f9b\u3055\u308c\u3066\u3044\u307e\u305b\u3093\n</code></pre> deque.kt<pre><code>\n</code></pre> deque.zig<pre><code>\n</code></pre>"},{"location":"chapter_stack_and_queue/deque/#532","title":"5.3.2 \u00a0 \u4e21\u7aef\u30ad\u30e5\u30fc\u306e\u5b9f\u88c5 *","text":"<p>\u4e21\u7aef\u30ad\u30e5\u30fc\u306e\u5b9f\u88c5\u306f\u901a\u5e38\u306e\u30ad\u30e5\u30fc\u306e\u5b9f\u88c5\u3068\u4f3c\u3066\u304a\u308a\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u307e\u305f\u306f\u914d\u5217\u3092\u57fa\u76e4\u3068\u306a\u308b\u30c7\u30fc\u30bf\u69cb\u9020\u3068\u3057\u3066\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002</p>"},{"location":"chapter_stack_and_queue/deque/#1","title":"1. \u00a0 \u53cc\u65b9\u5411\u9023\u7d50\u30ea\u30b9\u30c8\u306b\u57fa\u3065\u304f\u5b9f\u88c5","text":"<p>\u524d\u7bc0\u3067\u3001\u901a\u5e38\u306e\u5358\u4e00\u9023\u7d50\u30ea\u30b9\u30c8\u3092\u4f7f\u3063\u3066\u30ad\u30e5\u30fc\u3092\u5b9f\u88c5\u3057\u305f\u3053\u3068\u3092\u601d\u3044\u51fa\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u3053\u308c\u306f\u5148\u982d\u304b\u3089\u306e\u524a\u9664\uff08\u30c7\u30ad\u30e5\u30fc\u64cd\u4f5c\u306b\u5bfe\u5fdc\uff09\u3068\u672b\u5c3e\u3078\u306e\u65b0\u3057\u3044\u8981\u7d20\u306e\u8ffd\u52a0\uff08\u30a8\u30f3\u30ad\u30e5\u30fc\u64cd\u4f5c\u306b\u5bfe\u5fdc\uff09\u3092\u4fbf\u5229\u306b\u884c\u3048\u308b\u305f\u3081\u3067\u3057\u305f\u3002</p> <p>\u4e21\u7aef\u30ad\u30e5\u30fc\u3067\u306f\u3001\u5148\u982d\u3068\u672b\u5c3e\u306e\u4e21\u65b9\u3067\u30a8\u30f3\u30ad\u30e5\u30fc\u3068\u30c7\u30ad\u30e5\u30fc\u64cd\u4f5c\u3092\u5b9f\u884c\u3067\u304d\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u4e21\u7aef\u30ad\u30e5\u30fc\u306f\u9006\u65b9\u5411\u306e\u64cd\u4f5c\u3082\u5b9f\u88c5\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u305f\u3081\u3001\u4e21\u7aef\u30ad\u30e5\u30fc\u306e\u57fa\u76e4\u3068\u306a\u308b\u30c7\u30fc\u30bf\u69cb\u9020\u3068\u3057\u3066\u300c\u53cc\u65b9\u5411\u9023\u7d50\u30ea\u30b9\u30c8\u300d\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002</p> <p>\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u53cc\u65b9\u5411\u9023\u7d50\u30ea\u30b9\u30c8\u306e\u5148\u982d\u30ce\u30fc\u30c9\u3068\u672b\u5c3e\u30ce\u30fc\u30c9\u3092\u305d\u308c\u305e\u308c\u4e21\u7aef\u30ad\u30e5\u30fc\u306e\u524d\u7aef\u3068\u5f8c\u7aef\u3068\u3057\u3066\u6271\u3044\u3001\u4e21\u7aef\u3067\u306e\u30ce\u30fc\u30c9\u306e\u8ffd\u52a0\u3068\u524a\u9664\u6a5f\u80fd\u3092\u5b9f\u88c5\u3057\u307e\u3059\u3002</p> LinkedListDequepushLast()pushFirst()popLast()popFirst() <p></p> <p></p> <p></p> <p></p> <p></p> <p> \u56f3 5-8 \u00a0 \u53cc\u65b9\u5411\u9023\u7d50\u30ea\u30b9\u30c8\u306b\u3088\u308b\u4e21\u7aef\u30ad\u30e5\u30fc\u306e\u30a8\u30f3\u30ad\u30e5\u30fc\u3068\u30c7\u30ad\u30e5\u30fc\u64cd\u4f5c\u306e\u5b9f\u88c5 </p> <p>\u5b9f\u88c5\u30b3\u30fc\u30c9\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig linkedlist_deque.py<pre><code>class ListNode:\n    \"\"\"\u53cc\u65b9\u5411\u9023\u7d50\u30ea\u30b9\u30c8\u30ce\u30fc\u30c9\"\"\"\n\n    def __init__(self, val: int):\n        \"\"\"\u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf\"\"\"\n        self.val: int = val\n        self.next: ListNode | None = None  # \u5f8c\u7d9a\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\n        self.prev: ListNode | None = None  # \u524d\u99c6\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\n\nclass LinkedListDeque:\n    \"\"\"\u53cc\u65b9\u5411\u9023\u7d50\u30ea\u30b9\u30c8\u30d9\u30fc\u30b9\u306e\u53cc\u7aef\u30ad\u30e5\u30fc\u30af\u30e9\u30b9\"\"\"\n\n    def __init__(self):\n        \"\"\"\u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf\"\"\"\n        self._front: ListNode | None = None  # \u30d8\u30c3\u30c9\u30ce\u30fc\u30c9 front\n        self._rear: ListNode | None = None  # \u30c6\u30fc\u30eb\u30ce\u30fc\u30c9 rear\n        self._size: int = 0  # \u53cc\u7aef\u30ad\u30e5\u30fc\u306e\u9577\u3055\n\n    def size(self) -&gt; int:\n        \"\"\"\u53cc\u7aef\u30ad\u30e5\u30fc\u306e\u9577\u3055\u3092\u53d6\u5f97\"\"\"\n        return self._size\n\n    def is_empty(self) -&gt; bool:\n        \"\"\"\u53cc\u7aef\u30ad\u30e5\u30fc\u304c\u7a7a\u304b\u3069\u3046\u304b\u3092\u5224\u5b9a\"\"\"\n        return self._size == 0\n\n    def push(self, num: int, is_front: bool):\n        \"\"\"\u30a8\u30f3\u30ad\u30e5\u30fc\u64cd\u4f5c\"\"\"\n        node = ListNode(num)\n        # \u30ea\u30b9\u30c8\u304c\u7a7a\u306e\u5834\u5408\u3001front \u3068 rear \u306e\u4e21\u65b9\u3092 node \u306b\u5411\u3051\u308b\n        if self.is_empty():\n            self._front = self._rear = node\n        # \u524d\u7aef\u30a8\u30f3\u30ad\u30e5\u30fc\u64cd\u4f5c\n        elif is_front:\n            # \u30ce\u30fc\u30c9\u3092\u30ea\u30b9\u30c8\u306e\u5148\u982d\u306b\u8ffd\u52a0\n            self._front.prev = node\n            node.next = self._front\n            self._front = node  # \u30d8\u30c3\u30c9\u30ce\u30fc\u30c9\u3092\u66f4\u65b0\n        # \u5f8c\u7aef\u30a8\u30f3\u30ad\u30e5\u30fc\u64cd\u4f5c\n        else:\n            # \u30ce\u30fc\u30c9\u3092\u30ea\u30b9\u30c8\u306e\u672b\u5c3e\u306b\u8ffd\u52a0\n            self._rear.next = node\n            node.prev = self._rear\n            self._rear = node  # \u30c6\u30fc\u30eb\u30ce\u30fc\u30c9\u3092\u66f4\u65b0\n        self._size += 1  # \u30ad\u30e5\u30fc\u306e\u9577\u3055\u3092\u66f4\u65b0\n\n    def push_first(self, num: int):\n        \"\"\"\u524d\u7aef\u30a8\u30f3\u30ad\u30e5\u30fc\"\"\"\n        self.push(num, True)\n\n    def push_last(self, num: int):\n        \"\"\"\u5f8c\u7aef\u30a8\u30f3\u30ad\u30e5\u30fc\"\"\"\n        self.push(num, False)\n\n    def pop(self, is_front: bool) -&gt; int:\n        \"\"\"\u30c7\u30ad\u30e5\u30fc\u64cd\u4f5c\"\"\"\n        if self.is_empty():\n            raise IndexError(\"Double-ended queue is empty\")\n        # \u524d\u7aef\u30c7\u30ad\u30e5\u30fc\u64cd\u4f5c\n        if is_front:\n            val: int = self._front.val  # \u30d8\u30c3\u30c9\u30ce\u30fc\u30c9\u306e\u5024\u3092\u4e00\u6642\u7684\u306b\u4fdd\u5b58\n            # \u30d8\u30c3\u30c9\u30ce\u30fc\u30c9\u3092\u524a\u9664\n            fnext: ListNode | None = self._front.next\n            if fnext is not None:\n                fnext.prev = None\n                self._front.next = None\n            self._front = fnext  # \u30d8\u30c3\u30c9\u30ce\u30fc\u30c9\u3092\u66f4\u65b0\n        # \u5f8c\u7aef\u30c7\u30ad\u30e5\u30fc\u64cd\u4f5c\n        else:\n            val: int = self._rear.val  # \u30c6\u30fc\u30eb\u30ce\u30fc\u30c9\u306e\u5024\u3092\u4e00\u6642\u7684\u306b\u4fdd\u5b58\n            # \u30c6\u30fc\u30eb\u30ce\u30fc\u30c9\u3092\u524a\u9664\n            rprev: ListNode | None = self._rear.prev\n            if rprev is not None:\n                rprev.next = None\n                self._rear.prev = None\n            self._rear = rprev  # \u30c6\u30fc\u30eb\u30ce\u30fc\u30c9\u3092\u66f4\u65b0\n        self._size -= 1  # \u30ad\u30e5\u30fc\u306e\u9577\u3055\u3092\u66f4\u65b0\n        return val\n\n    def pop_first(self) -&gt; int:\n        \"\"\"\u524d\u7aef\u30c7\u30ad\u30e5\u30fc\"\"\"\n        return self.pop(True)\n\n    def pop_last(self) -&gt; int:\n        \"\"\"\u5f8c\u7aef\u30c7\u30ad\u30e5\u30fc\"\"\"\n        return self.pop(False)\n\n    def peek_first(self) -&gt; int:\n        \"\"\"\u524d\u7aef\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9\"\"\"\n        if self.is_empty():\n            raise IndexError(\"Double-ended queue is empty\")\n        return self._front.val\n\n    def peek_last(self) -&gt; int:\n        \"\"\"\u5f8c\u7aef\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9\"\"\"\n        if self.is_empty():\n            raise IndexError(\"Double-ended queue is empty\")\n        return self._rear.val\n\n    def to_array(self) -&gt; list[int]:\n        \"\"\"\u51fa\u529b\u7528\u306e\u914d\u5217\u3092\u8fd4\u3059\"\"\"\n        node = self._front\n        res = [0] * self.size()\n        for i in range(self.size()):\n            res[i] = node.val\n            node = node.next\n        return res\n</code></pre> linkedlist_deque.cpp<pre><code>/* \u53cc\u65b9\u5411\u9023\u7d50\u30ea\u30b9\u30c8\u30ce\u30fc\u30c9 */\nstruct DoublyListNode {\n    int val;              // \u30ce\u30fc\u30c9\u306e\u5024\n    DoublyListNode *next; // \u5f8c\u7d9a\u30ce\u30fc\u30c9\u3078\u306e\u30dd\u30a4\u30f3\u30bf\n    DoublyListNode *prev; // \u524d\u7d9a\u30ce\u30fc\u30c9\u3078\u306e\u30dd\u30a4\u30f3\u30bf\n    DoublyListNode(int val) : val(val), prev(nullptr), next(nullptr) {\n    }\n};\n\n/* \u53cc\u65b9\u5411\u9023\u7d50\u30ea\u30b9\u30c8\u306b\u57fa\u3065\u304f\u4e21\u7aef\u30ad\u30e5\u30fc\u30af\u30e9\u30b9 */\nclass LinkedListDeque {\n  private:\n    DoublyListNode *front, *rear; // \u5148\u982d\u30ce\u30fc\u30c9front\u3001\u672b\u5c3e\u30ce\u30fc\u30c9rear\n    int queSize = 0;              // \u4e21\u7aef\u30ad\u30e5\u30fc\u306e\u9577\u3055\n\n  public:\n    /* \u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf */\n    LinkedListDeque() : front(nullptr), rear(nullptr) {\n    }\n\n    /* \u30c7\u30b9\u30c8\u30e9\u30af\u30bf */\n    ~LinkedListDeque() {\n        // \u9023\u7d50\u30ea\u30b9\u30c8\u3092\u8d70\u67fb\u3001\u30ce\u30fc\u30c9\u3092\u524a\u9664\u3001\u30e1\u30e2\u30ea\u3092\u89e3\u653e\n        DoublyListNode *pre, *cur = front;\n        while (cur != nullptr) {\n            pre = cur;\n            cur = cur-&gt;next;\n            delete pre;\n        }\n    }\n\n    /* \u4e21\u7aef\u30ad\u30e5\u30fc\u306e\u9577\u3055\u3092\u53d6\u5f97 */\n    int size() {\n        return queSize;\n    }\n\n    /* \u4e21\u7aef\u30ad\u30e5\u30fc\u304c\u7a7a\u304b\u3069\u3046\u304b\u3092\u5224\u5b9a */\n    bool isEmpty() {\n        return size() == 0;\n    }\n\n    /* \u30a8\u30f3\u30ad\u30e5\u30fc\u64cd\u4f5c */\n    void push(int num, bool isFront) {\n        DoublyListNode *node = new DoublyListNode(num);\n        // \u30ea\u30b9\u30c8\u304c\u7a7a\u306e\u5834\u5408\u3001front\u3068rear\u306e\u4e21\u65b9\u3092node\u306b\u5411\u3051\u308b\n        if (isEmpty())\n            front = rear = node;\n        // \u5148\u982d\u30a8\u30f3\u30ad\u30e5\u30fc\u64cd\u4f5c\n        else if (isFront) {\n            // \u30ce\u30fc\u30c9\u3092\u30ea\u30b9\u30c8\u306e\u5148\u982d\u306b\u8ffd\u52a0\n            front-&gt;prev = node;\n            node-&gt;next = front;\n            front = node; // \u5148\u982d\u30ce\u30fc\u30c9\u3092\u66f4\u65b0\n        // \u672b\u5c3e\u30a8\u30f3\u30ad\u30e5\u30fc\u64cd\u4f5c\n        } else {\n            // \u30ce\u30fc\u30c9\u3092\u30ea\u30b9\u30c8\u306e\u672b\u5c3e\u306b\u8ffd\u52a0\n            rear-&gt;next = node;\n            node-&gt;prev = rear;\n            rear = node; // \u672b\u5c3e\u30ce\u30fc\u30c9\u3092\u66f4\u65b0\n        }\n        queSize++; // \u30ad\u30e5\u30fc\u9577\u3092\u66f4\u65b0\n    }\n\n    /* \u5148\u982d\u30a8\u30f3\u30ad\u30e5\u30fc */\n    void pushFirst(int num) {\n        push(num, true);\n    }\n\n    /* \u672b\u5c3e\u30a8\u30f3\u30ad\u30e5\u30fc */\n    void pushLast(int num) {\n        push(num, false);\n    }\n\n    /* \u30c7\u30ad\u30e5\u30fc\u64cd\u4f5c */\n    int pop(bool isFront) {\n        if (isEmpty())\n            throw out_of_range(\"Queue is empty\");\n        int val;\n        // \u5148\u982d\u30c7\u30ad\u30e5\u30fc\u64cd\u4f5c\n        if (isFront) {\n            val = front-&gt;val; // \u5148\u982d\u30ce\u30fc\u30c9\u306e\u5024\u3092\u4e00\u6642\u4fdd\u5b58\n            // \u5148\u982d\u30ce\u30fc\u30c9\u3092\u524a\u9664\n            DoublyListNode *fNext = front-&gt;next;\n            if (fNext != nullptr) {\n                fNext-&gt;prev = nullptr;\n                front-&gt;next = nullptr;\n            }\n            delete front;\n            front = fNext; // \u5148\u982d\u30ce\u30fc\u30c9\u3092\u66f4\u65b0\n        // \u672b\u5c3e\u30c7\u30ad\u30e5\u30fc\u64cd\u4f5c\n        } else {\n            val = rear-&gt;val; // \u672b\u5c3e\u30ce\u30fc\u30c9\u306e\u5024\u3092\u4e00\u6642\u4fdd\u5b58\n            // \u672b\u5c3e\u30ce\u30fc\u30c9\u3092\u524a\u9664\n            DoublyListNode *rPrev = rear-&gt;prev;\n            if (rPrev != nullptr) {\n                rPrev-&gt;next = nullptr;\n                rear-&gt;prev = nullptr;\n            }\n            delete rear;\n            rear = rPrev; // \u672b\u5c3e\u30ce\u30fc\u30c9\u3092\u66f4\u65b0\n        }\n        queSize--; // \u30ad\u30e5\u30fc\u9577\u3092\u66f4\u65b0\n        return val;\n    }\n\n    /* \u5148\u982d\u30c7\u30ad\u30e5\u30fc */\n    int popFirst() {\n        return pop(true);\n    }\n\n    /* \u672b\u5c3e\u30c7\u30ad\u30e5\u30fc */\n    int popLast() {\n        return pop(false);\n    }\n\n    /* \u5148\u982d\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\n    int peekFirst() {\n        if (isEmpty())\n            throw out_of_range(\"Double-ended queue is empty\");\n        return front-&gt;val;\n    }\n\n    /* \u672b\u5c3e\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\n    int peekLast() {\n        if (isEmpty())\n            throw out_of_range(\"Double-ended queue is empty\");\n        return rear-&gt;val;\n    }\n\n    /* \u5370\u5237\u7528\u306b\u914d\u5217\u3092\u8fd4\u5374 */\n    vector&lt;int&gt; toVector() {\n        DoublyListNode *node = front;\n        vector&lt;int&gt; res(size());\n        for (int i = 0; i &lt; res.size(); i++) {\n            res[i] = node-&gt;val;\n            node = node-&gt;next;\n        }\n        return res;\n    }\n};\n</code></pre> linkedlist_deque.java<pre><code>/* \u53cc\u65b9\u5411\u9023\u7d50\u30ea\u30b9\u30c8\u30ce\u30fc\u30c9 */\nclass ListNode {\n    int val; // \u30ce\u30fc\u30c9\u5024\n    ListNode next; // \u5f8c\u7d9a\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\n    ListNode prev; // \u524d\u4efb\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\n\n    ListNode(int val) {\n        this.val = val;\n        prev = next = null;\n    }\n}\n\n/* \u53cc\u65b9\u5411\u9023\u7d50\u30ea\u30b9\u30c8\u306b\u57fa\u3065\u304f\u4e21\u7aef\u30ad\u30e5\u30fc\u30af\u30e9\u30b9 */\nclass LinkedListDeque {\n    private ListNode front, rear; // \u5148\u982d\u30ce\u30fc\u30c9 front\u3001\u672b\u5c3e\u30ce\u30fc\u30c9 rear\n    private int queSize = 0; // \u4e21\u7aef\u30ad\u30e5\u30fc\u306e\u9577\u3055\n\n    public LinkedListDeque() {\n        front = rear = null;\n    }\n\n    /* \u4e21\u7aef\u30ad\u30e5\u30fc\u306e\u9577\u3055\u3092\u53d6\u5f97 */\n    public int size() {\n        return queSize;\n    }\n\n    /* \u4e21\u7aef\u30ad\u30e5\u30fc\u304c\u7a7a\u304b\u3069\u3046\u304b\u3092\u5224\u5b9a */\n    public boolean isEmpty() {\n        return size() == 0;\n    }\n\n    /* \u30a8\u30f3\u30ad\u30e5\u30fc\u64cd\u4f5c */\n    private void push(int num, boolean isFront) {\n        ListNode node = new ListNode(num);\n        // \u30ea\u30b9\u30c8\u304c\u7a7a\u306e\u5834\u5408\u3001front \u3068 rear \u306e\u4e21\u65b9\u3092 node \u306b\u6307\u3059\n        if (isEmpty())\n            front = rear = node;\n        // \u5148\u982d\u30a8\u30f3\u30ad\u30e5\u30fc\u64cd\u4f5c\n        else if (isFront) {\n            // node \u3092\u30ea\u30b9\u30c8\u306e\u5148\u982d\u306b\u8ffd\u52a0\n            front.prev = node;\n            node.next = front;\n            front = node; // front \u3092\u66f4\u65b0\n        // \u672b\u5c3e\u30a8\u30f3\u30ad\u30e5\u30fc\u64cd\u4f5c\n        } else {\n            // node \u3092\u30ea\u30b9\u30c8\u306e\u672b\u5c3e\u306b\u8ffd\u52a0\n            rear.next = node;\n            node.prev = rear;\n            rear = node; // rear \u3092\u66f4\u65b0\n        }\n        queSize++; // \u9577\u3055\u3092\u66f4\u65b0\n    }\n\n    /* \u5148\u982d\u30a8\u30f3\u30ad\u30e5\u30fc */\n    public void pushFirst(int num) {\n        push(num, true);\n    }\n\n    /* \u672b\u5c3e\u30a8\u30f3\u30ad\u30e5\u30fc */\n    public void pushLast(int num) {\n        push(num, false);\n    }\n\n    /* \u30c7\u30ad\u30e5\u30fc\u64cd\u4f5c */\n    private int pop(boolean isFront) {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        int val;\n        // \u5148\u982d\u30c7\u30ad\u30e5\u30fc\u64cd\u4f5c\n        if (isFront) {\n            val = front.val; // \u4e00\u6642\u7684\u306b\u5148\u982d\u30ce\u30fc\u30c9\u5024\u3092\u4fdd\u5b58\n            // \u6b21\u306e\u30ce\u30fc\u30c9\u3092\u524a\u9664\n            ListNode fNext = front.next;\n            if (fNext != null) {\n                fNext.prev = null;\n                front.next = null;\n            }\n            front = fNext; // front \u3092\u66f4\u65b0\n        // \u672b\u5c3e\u30c7\u30ad\u30e5\u30fc\u64cd\u4f5c\n        } else {\n            val = rear.val; // \u4e00\u6642\u7684\u306b\u672b\u5c3e\u30ce\u30fc\u30c9\u5024\u3092\u4fdd\u5b58\n            // \u524d\u306e\u30ce\u30fc\u30c9\u3092\u524a\u9664\n            ListNode rPrev = rear.prev;\n            if (rPrev != null) {\n                rPrev.next = null;\n                rear.prev = null;\n            }\n            rear = rPrev; // rear \u3092\u66f4\u65b0\n        }\n        queSize--; // \u9577\u3055\u3092\u66f4\u65b0\n        return val;\n    }\n\n    /* \u5148\u982d\u30c7\u30ad\u30e5\u30fc */\n    public int popFirst() {\n        return pop(true);\n    }\n\n    /* \u672b\u5c3e\u30c7\u30ad\u30e5\u30fc */\n    public int popLast() {\n        return pop(false);\n    }\n\n    /* \u5148\u982d\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\n    public int peekFirst() {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        return front.val;\n    }\n\n    /* \u672b\u5c3e\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\n    public int peekLast() {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        return rear.val;\n    }\n\n    /* \u914d\u5217\u3092\u8fd4\u3059 */\n    public int[] toArray() {\n        ListNode node = front;\n        int[] res = new int[size()];\n        for (int i = 0; i &lt; res.length; i++) {\n            res[i] = node.val;\n            node = node.next;\n        }\n        return res;\n    }\n}\n</code></pre> linkedlist_deque.cs<pre><code>[class]{ListNode}-[func]{}\n\n[class]{LinkedListDeque}-[func]{}\n</code></pre> linkedlist_deque.go<pre><code>[class]{linkedListDeque}-[func]{}\n</code></pre> linkedlist_deque.swift<pre><code>[class]{ListNode}-[func]{}\n\n[class]{LinkedListDeque}-[func]{}\n</code></pre> linkedlist_deque.js<pre><code>[class]{ListNode}-[func]{}\n\n[class]{LinkedListDeque}-[func]{}\n</code></pre> linkedlist_deque.ts<pre><code>[class]{ListNode}-[func]{}\n\n[class]{LinkedListDeque}-[func]{}\n</code></pre> linkedlist_deque.dart<pre><code>[class]{ListNode}-[func]{}\n\n[class]{LinkedListDeque}-[func]{}\n</code></pre> linkedlist_deque.rs<pre><code>[class]{ListNode}-[func]{}\n\n[class]{LinkedListDeque}-[func]{}\n</code></pre> linkedlist_deque.c<pre><code>[class]{DoublyListNode}-[func]{}\n\n[class]{LinkedListDeque}-[func]{}\n</code></pre> linkedlist_deque.kt<pre><code>[class]{ListNode}-[func]{}\n\n[class]{LinkedListDeque}-[func]{}\n</code></pre> linkedlist_deque.rb<pre><code>[class]{ListNode}-[func]{}\n\n[class]{LinkedListDeque}-[func]{}\n</code></pre> linkedlist_deque.zig<pre><code>[class]{ListNode}-[func]{}\n\n[class]{LinkedListDeque}-[func]{}\n</code></pre>"},{"location":"chapter_stack_and_queue/deque/#2","title":"2. \u00a0 \u914d\u5217\u306b\u57fa\u3065\u304f\u5b9f\u88c5","text":"<p>\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u914d\u5217\u3067\u30ad\u30e5\u30fc\u3092\u5b9f\u88c5\u3059\u308b\u306e\u3068\u540c\u69d8\u306b\u3001\u5faa\u74b0\u914d\u5217\u3092\u4f7f\u3063\u3066\u4e21\u7aef\u30ad\u30e5\u30fc\u3092\u5b9f\u88c5\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002</p> ArrayDequepushLast()pushFirst()popLast()popFirst() <p></p> <p></p> <p></p> <p></p> <p></p> <p> \u56f3 5-9 \u00a0 \u914d\u5217\u306b\u3088\u308b\u4e21\u7aef\u30ad\u30e5\u30fc\u306e\u30a8\u30f3\u30ad\u30e5\u30fc\u3068\u30c7\u30ad\u30e5\u30fc\u64cd\u4f5c\u306e\u5b9f\u88c5 </p> <p>\u5b9f\u88c5\u3067\u306f\u300c\u524d\u7aef\u30a8\u30f3\u30ad\u30e5\u30fc\u300d\u3068\u300c\u5f8c\u7aef\u30c7\u30ad\u30e5\u30fc\u300d\u306e\u30e1\u30bd\u30c3\u30c9\u3092\u8ffd\u52a0\u3059\u308b\u3060\u3051\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig array_deque.py<pre><code>class ArrayDeque:\n    \"\"\"\u5faa\u74b0\u914d\u5217\u30d9\u30fc\u30b9\u306e\u53cc\u7aef\u30ad\u30e5\u30fc\u30af\u30e9\u30b9\"\"\"\n\n    def __init__(self, capacity: int):\n        \"\"\"\u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf\"\"\"\n        self._nums: list[int] = [0] * capacity\n        self._front: int = 0\n        self._size: int = 0\n\n    def capacity(self) -&gt; int:\n        \"\"\"\u53cc\u7aef\u30ad\u30e5\u30fc\u306e\u5bb9\u91cf\u3092\u53d6\u5f97\"\"\"\n        return len(self._nums)\n\n    def size(self) -&gt; int:\n        \"\"\"\u53cc\u7aef\u30ad\u30e5\u30fc\u306e\u9577\u3055\u3092\u53d6\u5f97\"\"\"\n        return self._size\n\n    def is_empty(self) -&gt; bool:\n        \"\"\"\u53cc\u7aef\u30ad\u30e5\u30fc\u304c\u7a7a\u304b\u3069\u3046\u304b\u3092\u5224\u5b9a\"\"\"\n        return self._size == 0\n\n    def index(self, i: int) -&gt; int:\n        \"\"\"\u5faa\u74b0\u914d\u5217\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8a08\u7b97\"\"\"\n        # \u30e2\u30b8\u30e5\u30ed\u6f14\u7b97\u306b\u3088\u3063\u3066\u5faa\u74b0\u914d\u5217\u3092\u5b9f\u88c5\n        # i \u304c\u914d\u5217\u306e\u672b\u5c3e\u3092\u8d85\u3048\u305f\u5834\u5408\u3001\u5148\u982d\u306b\u623b\u308b\n        # i \u304c\u914d\u5217\u306e\u5148\u982d\u3092\u8d85\u3048\u305f\u5834\u5408\u3001\u672b\u5c3e\u306b\u623b\u308b\n        return (i + self.capacity()) % self.capacity()\n\n    def push_first(self, num: int):\n        \"\"\"\u524d\u7aef\u30a8\u30f3\u30ad\u30e5\u30fc\"\"\"\n        if self._size == self.capacity():\n            print(\"\u53cc\u7aef\u30ad\u30e5\u30fc\u304c\u6e80\u676f\u3067\u3059\")\n            return\n        # \u30d5\u30ed\u30f3\u30c8\u30dd\u30a4\u30f3\u30bf\u3092\u5de6\u306b1\u3064\u79fb\u52d5\n        # \u30e2\u30b8\u30e5\u30ed\u6f14\u7b97\u306b\u3088\u3063\u3066\u30d5\u30ed\u30f3\u30c8\u304c\u914d\u5217\u306e\u5148\u982d\u3092\u8d85\u3048\u3066\u672b\u5c3e\u306b\u623b\u308b\u3053\u3068\u3092\u5b9f\u88c5\n        self._front = self.index(self._front - 1)\n        # num \u3092\u524d\u7aef\u306b\u8ffd\u52a0\n        self._nums[self._front] = num\n        self._size += 1\n\n    def push_last(self, num: int):\n        \"\"\"\u5f8c\u7aef\u30a8\u30f3\u30ad\u30e5\u30fc\"\"\"\n        if self._size == self.capacity():\n            print(\"\u53cc\u7aef\u30ad\u30e5\u30fc\u304c\u6e80\u676f\u3067\u3059\")\n            return\n        # \u30ea\u30a2\u30dd\u30a4\u30f3\u30bf\u3092\u8a08\u7b97\u3001\u30ea\u30a2\u30a4\u30f3\u30c7\u30c3\u30af\u30b9 + 1 \u3092\u6307\u3059\n        rear = self.index(self._front + self._size)\n        # num \u3092\u5f8c\u7aef\u306b\u8ffd\u52a0\n        self._nums[rear] = num\n        self._size += 1\n\n    def pop_first(self) -&gt; int:\n        \"\"\"\u524d\u7aef\u30c7\u30ad\u30e5\u30fc\"\"\"\n        num = self.peek_first()\n        # \u30d5\u30ed\u30f3\u30c8\u30dd\u30a4\u30f3\u30bf\u30921\u3064\u5f8c\u308d\u306b\u79fb\u52d5\n        self._front = self.index(self._front + 1)\n        self._size -= 1\n        return num\n\n    def pop_last(self) -&gt; int:\n        \"\"\"\u5f8c\u7aef\u30c7\u30ad\u30e5\u30fc\"\"\"\n        num = self.peek_last()\n        self._size -= 1\n        return num\n\n    def peek_first(self) -&gt; int:\n        \"\"\"\u524d\u7aef\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9\"\"\"\n        if self.is_empty():\n            raise IndexError(\"Double-ended queue is empty\")\n        return self._nums[self._front]\n\n    def peek_last(self) -&gt; int:\n        \"\"\"\u5f8c\u7aef\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9\"\"\"\n        if self.is_empty():\n            raise IndexError(\"Double-ended queue is empty\")\n        # \u5f8c\u7aef\u8981\u7d20\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8a08\u7b97\n        last = self.index(self._front + self._size - 1)\n        return self._nums[last]\n\n    def to_array(self) -&gt; list[int]:\n        \"\"\"\u51fa\u529b\u7528\u306e\u914d\u5217\u3092\u8fd4\u3059\"\"\"\n        # \u6709\u52b9\u306a\u9577\u3055\u7bc4\u56f2\u5185\u306e\u8981\u7d20\u306e\u307f\u3092\u5909\u63db\n        res = []\n        for i in range(self._size):\n            res.append(self._nums[self.index(self._front + i)])\n        return res\n</code></pre> array_deque.cpp<pre><code>/* \u5faa\u74b0\u914d\u5217\u306b\u57fa\u3065\u304f\u4e21\u7aef\u30ad\u30e5\u30fc\u30af\u30e9\u30b9 */\nclass ArrayDeque {\n  private:\n    vector&lt;int&gt; nums; // \u4e21\u7aef\u30ad\u30e5\u30fc\u306e\u8981\u7d20\u3092\u683c\u7d0d\u3059\u308b\u914d\u5217\n    int front;        // \u5148\u982d\u30dd\u30a4\u30f3\u30bf\u3001\u5148\u982d\u8981\u7d20\u3092\u6307\u3059\n    int queSize;      // \u4e21\u7aef\u30ad\u30e5\u30fc\u306e\u9577\u3055\n\n  public:\n    /* \u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf */\n    ArrayDeque(int capacity) {\n        nums.resize(capacity);\n        front = queSize = 0;\n    }\n\n    /* \u4e21\u7aef\u30ad\u30e5\u30fc\u306e\u5bb9\u91cf\u3092\u53d6\u5f97 */\n    int capacity() {\n        return nums.size();\n    }\n\n    /* \u4e21\u7aef\u30ad\u30e5\u30fc\u306e\u9577\u3055\u3092\u53d6\u5f97 */\n    int size() {\n        return queSize;\n    }\n\n    /* \u4e21\u7aef\u30ad\u30e5\u30fc\u304c\u7a7a\u304b\u3069\u3046\u304b\u3092\u5224\u5b9a */\n    bool isEmpty() {\n        return queSize == 0;\n    }\n\n    /* \u5faa\u74b0\u914d\u5217\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8a08\u7b97 */\n    int index(int i) {\n        // \u5270\u4f59\u6f14\u7b97\u3067\u5faa\u74b0\u914d\u5217\u3092\u5b9f\u73fe\n        // i\u304c\u914d\u5217\u306e\u672b\u5c3e\u3092\u8d85\u3048\u305f\u5834\u5408\u3001\u5148\u982d\u306b\u623b\u308b\n        // i\u304c\u914d\u5217\u306e\u5148\u982d\u3092\u8d85\u3048\u305f\u5834\u5408\u3001\u672b\u5c3e\u306b\u623b\u308b\n        return (i + capacity()) % capacity();\n    }\n\n    /* \u5148\u982d\u30a8\u30f3\u30ad\u30e5\u30fc */\n    void pushFirst(int num) {\n        if (queSize == capacity()) {\n            cout &lt;&lt; \"Double-ended queue is full\" &lt;&lt; endl;\n            return;\n        }\n        // \u5148\u982d\u30dd\u30a4\u30f3\u30bf\u30921\u3064\u5de6\u306b\u79fb\u52d5\n        // \u5270\u4f59\u6f14\u7b97\u3067front\u304c\u914d\u5217\u306e\u5148\u982d\u3092\u8d8a\u3048\u3066\u672b\u5c3e\u306b\u623b\u308b\u3053\u3068\u3092\u5b9f\u73fe\n        front = index(front - 1);\n        // num\u3092\u5148\u982d\u306b\u8ffd\u52a0\n        nums[front] = num;\n        queSize++;\n    }\n\n    /* \u672b\u5c3e\u30a8\u30f3\u30ad\u30e5\u30fc */\n    void pushLast(int num) {\n        if (queSize == capacity()) {\n            cout &lt;&lt; \"Double-ended queue is full\" &lt;&lt; endl;\n            return;\n        }\n        // \u672b\u5c3e\u30dd\u30a4\u30f3\u30bf\u3092\u8a08\u7b97\u3001\u672b\u5c3e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9 + 1\u3092\u6307\u3059\n        int rear = index(front + queSize);\n        // num\u3092\u672b\u5c3e\u306b\u8ffd\u52a0\n        nums[rear] = num;\n        queSize++;\n    }\n\n    /* \u5148\u982d\u30c7\u30ad\u30e5\u30fc */\n    int popFirst() {\n        int num = peekFirst();\n        // \u5148\u982d\u30dd\u30a4\u30f3\u30bf\u30921\u3064\u5f8c\u308d\u306b\u79fb\u52d5\n        front = index(front + 1);\n        queSize--;\n        return num;\n    }\n\n    /* \u672b\u5c3e\u30c7\u30ad\u30e5\u30fc */\n    int popLast() {\n        int num = peekLast();\n        queSize--;\n        return num;\n    }\n\n    /* \u5148\u982d\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\n    int peekFirst() {\n        if (isEmpty())\n            throw out_of_range(\"Double-ended queue is empty\");\n        return nums[front];\n    }\n\n    /* \u672b\u5c3e\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\n    int peekLast() {\n        if (isEmpty())\n            throw out_of_range(\"Double-ended queue is empty\");\n        // \u672b\u5c3e\u8981\u7d20\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8a08\u7b97\n        int last = index(front + queSize - 1);\n        return nums[last];\n    }\n\n    /* \u5370\u5237\u7528\u306b\u914d\u5217\u3092\u8fd4\u5374 */\n    vector&lt;int&gt; toVector() {\n        // \u6709\u52b9\u306a\u9577\u3055\u7bc4\u56f2\u5185\u306e\u8981\u7d20\u306e\u307f\u3092\u5909\u63db\n        vector&lt;int&gt; res(queSize);\n        for (int i = 0, j = front; i &lt; queSize; i++, j++) {\n            res[i] = nums[index(j)];\n        }\n        return res;\n    }\n};\n</code></pre> array_deque.java<pre><code>/* \u5faa\u74b0\u914d\u5217\u306b\u57fa\u3065\u304f\u4e21\u7aef\u30ad\u30e5\u30fc\u30af\u30e9\u30b9 */\nclass ArrayDeque {\n    private int[] nums; // \u4e21\u7aef\u30ad\u30e5\u30fc\u306e\u8981\u7d20\u3092\u683c\u7d0d\u3059\u308b\u914d\u5217\n    private int front; // \u5148\u982d\u30dd\u30a4\u30f3\u30bf\u3001\u5148\u982d\u8981\u7d20\u3092\u6307\u3059\n    private int queSize; // \u4e21\u7aef\u30ad\u30e5\u30fc\u306e\u9577\u3055\n\n    /* \u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf */\n    public ArrayDeque(int capacity) {\n        this.nums = new int[capacity];\n        front = queSize = 0;\n    }\n\n    /* \u4e21\u7aef\u30ad\u30e5\u30fc\u306e\u5bb9\u91cf\u3092\u53d6\u5f97 */\n    public int capacity() {\n        return nums.length;\n    }\n\n    /* \u4e21\u7aef\u30ad\u30e5\u30fc\u306e\u9577\u3055\u3092\u53d6\u5f97 */\n    public int size() {\n        return queSize;\n    }\n\n    /* \u4e21\u7aef\u30ad\u30e5\u30fc\u304c\u7a7a\u304b\u3069\u3046\u304b\u3092\u5224\u5b9a */\n    public boolean isEmpty() {\n        return queSize == 0;\n    }\n\n    /* \u5faa\u74b0\u914d\u5217\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8a08\u7b97 */\n    private int index(int i) {\n        // \u30e2\u30b8\u30e5\u30ed\u6f14\u7b97\u306b\u3088\u308a\u5faa\u74b0\u914d\u5217\u3092\u5b9f\u88c5\n        // i \u304c\u914d\u5217\u306e\u672b\u5c3e\u3092\u8d85\u3048\u308b\u5834\u5408\u3001\u5148\u982d\u306b\u623b\u308b\n        // i \u304c\u914d\u5217\u306e\u5148\u982d\u3092\u8d85\u3048\u308b\u5834\u5408\u3001\u672b\u5c3e\u306b\u623b\u308b\n        return (i + capacity()) % capacity();\n    }\n\n    /* \u5148\u982d\u30a8\u30f3\u30ad\u30e5\u30fc */\n    public void pushFirst(int num) {\n        if (queSize == capacity()) {\n            System.out.println(\"\u4e21\u7aef\u30ad\u30e5\u30fc\u304c\u6e80\u676f\u3067\u3059\");\n            return;\n        }\n        // \u5148\u982d\u30dd\u30a4\u30f3\u30bf\u3092\u5de6\u306b\u79fb\u52d5\u3057\u3001\u5883\u754c\u3092\u8d8a\u3048\u308b\u5834\u5408\u306f\u914d\u5217\u306e\u672b\u5c3e\u306b\u56de\u308b\n        front = index(front - 1);\n        // \u5148\u982d\u306b num \u3092\u8ffd\u52a0\n        nums[front] = num;\n        queSize++;\n    }\n\n    /* \u672b\u5c3e\u30a8\u30f3\u30ad\u30e5\u30fc */\n    public void pushLast(int num) {\n        if (queSize == capacity()) {\n            System.out.println(\"\u4e21\u7aef\u30ad\u30e5\u30fc\u304c\u6e80\u676f\u3067\u3059\");\n            return;\n        }\n        // \u672b\u5c3e\u30dd\u30a4\u30f3\u30bf\u3092\u8a08\u7b97\u3057\u3001\u672b\u5c3e\u306b\u8981\u7d20\u3092\u8ffd\u52a0\n        int rear = index(front + queSize);\n        nums[rear] = num;\n        queSize++;\n    }\n\n    /* \u5148\u982d\u30c7\u30ad\u30e5\u30fc */\n    public int popFirst() {\n        int num = peekFirst();\n        // \u5148\u982d\u30dd\u30a4\u30f3\u30bf\u3092\u53f3\u306b\u79fb\u52d5\n        front = index(front + 1);\n        queSize--;\n        return num;\n    }\n\n    /* \u672b\u5c3e\u30c7\u30ad\u30e5\u30fc */\n    public int popLast() {\n        int num = peekLast();\n        queSize--;\n        return num;\n    }\n\n    /* \u5148\u982d\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\n    public int peekFirst() {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        return nums[front];\n    }\n\n    /* \u672b\u5c3e\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\n    public int peekLast() {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        // \u672b\u5c3e\u8981\u7d20\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u8a08\u7b97\n        int last = index(front + queSize - 1);\n        return nums[last];\n    }\n\n    /* \u914d\u5217\u3092\u8fd4\u3059 */\n    public int[] toArray() {\n        // front \u304b\u3089\u958b\u59cb\u3057\u3066 queSize \u500b\u306e\u8981\u7d20\u306e\u307f\u3092\u30b3\u30d4\u30fc\n        int[] res = new int[queSize];\n        for (int i = 0, j = front; i &lt; queSize; i++, j++) {\n            res[i] = nums[index(j)];\n        }\n        return res;\n    }\n}\n</code></pre> array_deque.cs<pre><code>[class]{ArrayDeque}-[func]{}\n</code></pre> array_deque.go<pre><code>[class]{arrayDeque}-[func]{}\n</code></pre> array_deque.swift<pre><code>[class]{ArrayDeque}-[func]{}\n</code></pre> array_deque.js<pre><code>[class]{ArrayDeque}-[func]{}\n</code></pre> array_deque.ts<pre><code>[class]{ArrayDeque}-[func]{}\n</code></pre> array_deque.dart<pre><code>[class]{ArrayDeque}-[func]{}\n</code></pre> array_deque.rs<pre><code>[class]{ArrayDeque}-[func]{}\n</code></pre> array_deque.c<pre><code>[class]{ArrayDeque}-[func]{}\n</code></pre> array_deque.kt<pre><code>[class]{ArrayDeque}-[func]{}\n</code></pre> array_deque.rb<pre><code>[class]{ArrayDeque}-[func]{}\n</code></pre> array_deque.zig<pre><code>[class]{ArrayDeque}-[func]{}\n</code></pre>"},{"location":"chapter_stack_and_queue/deque/#533","title":"5.3.3 \u00a0 \u4e21\u7aef\u30ad\u30e5\u30fc\u306e\u5fdc\u7528","text":"<p>\u4e21\u7aef\u30ad\u30e5\u30fc\u306f\u30b9\u30bf\u30c3\u30af\u3068\u30ad\u30e5\u30fc\u306e\u4e21\u65b9\u306e\u30ed\u30b8\u30c3\u30af\u3092\u7d44\u307f\u5408\u308f\u305b\u3066\u3044\u308b\u305f\u3081\u3001\u305d\u308c\u305e\u308c\u306e\u3059\u3079\u3066\u306e\u30e6\u30fc\u30b9\u30b1\u30fc\u30b9\u3092\u5b9f\u88c5\u3067\u304d\u3001\u3088\u308a\u5927\u304d\u306a\u67d4\u8edf\u6027\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002</p> <p>\u30bd\u30d5\u30c8\u30a6\u30a7\u30a2\u306e\u300c\u5143\u306b\u623b\u3059\u300d\u6a5f\u80fd\u306f\u901a\u5e38\u30b9\u30bf\u30c3\u30af\u3092\u4f7f\u3063\u3066\u5b9f\u88c5\u3055\u308c\u308b\u3053\u3068\u3092\u77e5\u3063\u3066\u3044\u307e\u3059\uff1a\u30b7\u30b9\u30c6\u30e0\u306f\u5404\u5909\u66f4\u64cd\u4f5c\u3092\u30b9\u30bf\u30c3\u30af\u306b<code>push</code>\u3057\u3001\u6b21\u306b<code>pop</code>\u3057\u3066\u5143\u306b\u623b\u3059\u3053\u3068\u3092\u5b9f\u88c5\u3057\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u30b7\u30b9\u30c6\u30e0\u30ea\u30bd\u30fc\u30b9\u306e\u5236\u9650\u3092\u8003\u616e\u3057\u3066\u3001\u30bd\u30d5\u30c8\u30a6\u30a7\u30a2\u306f\u5143\u306b\u623b\u3059\u30b9\u30c6\u30c3\u30d7\u306e\u6570\u3092\u5236\u9650\u3059\u308b\u3053\u3068\u304c\u3088\u304f\u3042\u308a\u307e\u3059\uff08\u4f8b\u3048\u3070\u3001\u6700\u5f8c\u306e50\u30b9\u30c6\u30c3\u30d7\u306e\u307f\u3092\u8a31\u53ef\uff09\u3002\u30b9\u30bf\u30c3\u30af\u306e\u9577\u3055\u304c50\u3092\u8d85\u3048\u305f\u5834\u5408\u3001\u30bd\u30d5\u30c8\u30a6\u30a7\u30a2\u306f\u30b9\u30bf\u30c3\u30af\u306e\u5e95\u90e8\uff08\u30ad\u30e5\u30fc\u306e\u524d\u7aef\uff09\u3067\u524a\u9664\u64cd\u4f5c\u3092\u5b9f\u884c\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u901a\u5e38\u306e\u30b9\u30bf\u30c3\u30af\u3067\u306f\u3053\u306e\u6a5f\u80fd\u3092\u5b9f\u884c\u3067\u304d\u306a\u3044\u305f\u3081\u3001\u4e21\u7aef\u30ad\u30e5\u30fc\u304c\u5fc5\u8981\u306b\u306a\u308a\u307e\u3059\u3002\u300c\u5143\u306b\u623b\u3059\u300d\u306e\u30b3\u30a2\u30ed\u30b8\u30c3\u30af\u306f\u4f9d\u7136\u3068\u3057\u3066\u30b9\u30bf\u30c3\u30af\u306e\u5f8c\u5165\u308c\u5148\u51fa\u3057\u539f\u5247\u306b\u5f93\u3044\u307e\u3059\u304c\u3001\u4e21\u7aef\u30ad\u30e5\u30fc\u306f\u3088\u308a\u67d4\u8edf\u306b\u3044\u304f\u3064\u304b\u306e\u8ffd\u52a0\u30ed\u30b8\u30c3\u30af\u3092\u5b9f\u88c5\u3067\u304d\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002</p>"},{"location":"chapter_stack_and_queue/queue/","title":"5.2 \u00a0 \u30ad\u30e5\u30fc","text":"<p>\u30ad\u30e5\u30fc\u306f\u3001\u5148\u5165\u5148\u51fa\uff08FIFO\uff09\u30eb\u30fc\u30eb\u306b\u5f93\u3046\u7dda\u5f62\u30c7\u30fc\u30bf\u69cb\u9020\u3067\u3059\u3002\u540d\u524d\u304c\u793a\u3059\u3088\u3046\u306b\u3001\u30ad\u30e5\u30fc\u306f\u884c\u5217\u306e\u73fe\u8c61\u3092\u30b7\u30df\u30e5\u30ec\u30fc\u30c8\u3057\u3001\u65b0\u53c2\u8005\u306f\u5217\u306e\u5f8c\u308d\u306b\u4e26\u3073\u3001\u524d\u306e\u4eba\u304c\u6700\u521d\u306b\u5217\u3092\u96e2\u308c\u307e\u3059\u3002</p> <p>\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u30ad\u30e5\u30fc\u306e\u524d\u9762\u3092\u300c\u30d8\u30c3\u30c9\u300d\u3001\u5f8c\u9762\u3092\u300c\u30c6\u30fc\u30eb\u300d\u3068\u547c\u3073\u307e\u3059\u3002\u30ad\u30e5\u30fc\u306e\u5f8c\u308d\u306b\u8981\u7d20\u3092\u8ffd\u52a0\u3059\u308b\u64cd\u4f5c\u3092\u300c\u30a8\u30f3\u30ad\u30e5\u30fc\u300d\u3001\u524d\u304b\u3089\u8981\u7d20\u3092\u524a\u9664\u3059\u308b\u64cd\u4f5c\u3092\u300c\u30c7\u30ad\u30e5\u30fc\u300d\u3068\u547c\u3073\u307e\u3059\u3002</p> <p></p> <p> \u56f3 5-4 \u00a0 \u30ad\u30e5\u30fc\u306e\u5148\u5165\u5148\u51fa\u30eb\u30fc\u30eb </p>"},{"location":"chapter_stack_and_queue/queue/#521","title":"5.2.1 \u00a0 \u30ad\u30e5\u30fc\u306e\u4e00\u822c\u7684\u306a\u64cd\u4f5c","text":"<p>\u30ad\u30e5\u30fc\u306e\u4e00\u822c\u7684\u306a\u64cd\u4f5c\u3092\u4e0b\u8868\u306b\u793a\u3057\u307e\u3059\u3002\u30e1\u30bd\u30c3\u30c9\u540d\u306f\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u306b\u3088\u3063\u3066\u7570\u306a\u308b\u5834\u5408\u304c\u3042\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u3053\u3053\u3067\u306f\u3001\u30b9\u30bf\u30c3\u30af\u3067\u4f7f\u7528\u3057\u305f\u306e\u3068\u540c\u3058\u547d\u540d\u898f\u5247\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002</p> <p> \u8868 5-2 \u00a0 \u30ad\u30e5\u30fc\u64cd\u4f5c\u306e\u52b9\u7387 </p> \u30e1\u30bd\u30c3\u30c9\u540d \u8aac\u660e \u6642\u9593\u8a08\u7b97\u91cf <code>push()</code> \u8981\u7d20\u3092\u30a8\u30f3\u30ad\u30e5\u30fc\u3001\u30c6\u30fc\u30eb\u306b\u8ffd\u52a0 \\(O(1)\\) <code>pop()</code> \u30d8\u30c3\u30c9\u8981\u7d20\u3092\u30c7\u30ad\u30e5\u30fc \\(O(1)\\) <code>peek()</code> \u30d8\u30c3\u30c9\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 \\(O(1)\\) <p>\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u3067\u7528\u610f\u3055\u308c\u3066\u3044\u308b\u30ad\u30e5\u30fc\u30af\u30e9\u30b9\u3092\u76f4\u63a5\u4f7f\u7528\u3067\u304d\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinZig queue.py<pre><code>from collections import deque\n\n# \u30ad\u30e5\u30fc\u3092\u521d\u671f\u5316\n# Python\u3067\u306f\u3001\u4e00\u822c\u7684\u306bdeque\u30af\u30e9\u30b9\u3092\u30ad\u30e5\u30fc\u3068\u3057\u3066\u4f7f\u7528\u3057\u307e\u3059\n# queue.Queue()\u306f\u7d14\u7c8b\u306a\u30ad\u30e5\u30fc\u30af\u30e9\u30b9\u3067\u3059\u304c\u3001\u4f7f\u3044\u306b\u304f\u3044\u305f\u3081\u63a8\u5968\u3055\u308c\u307e\u305b\u3093\nque: deque[int] = deque()\n\n# \u8981\u7d20\u3092\u30a8\u30f3\u30ad\u30e5\u30fc\nque.append(1)\nque.append(3)\nque.append(2)\nque.append(5)\nque.append(4)\n\n# \u6700\u521d\u306e\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9\nfront: int = que[0]\n\n# \u8981\u7d20\u3092\u30c7\u30ad\u30e5\u30fc\npop: int = que.popleft()\n\n# \u30ad\u30e5\u30fc\u306e\u9577\u3055\u3092\u53d6\u5f97\nsize: int = len(que)\n\n# \u30ad\u30e5\u30fc\u304c\u7a7a\u304b\u3069\u3046\u304b\u30c1\u30a7\u30c3\u30af\nis_empty: bool = len(que) == 0\n</code></pre> queue.cpp<pre><code>/* \u30ad\u30e5\u30fc\u3092\u521d\u671f\u5316 */\nqueue&lt;int&gt; queue;\n\n/* \u8981\u7d20\u3092\u30a8\u30f3\u30ad\u30e5\u30fc */\nqueue.push(1);\nqueue.push(3);\nqueue.push(2);\nqueue.push(5);\nqueue.push(4);\n\n/* \u6700\u521d\u306e\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\nint front = queue.front();\n\n/* \u8981\u7d20\u3092\u30c7\u30ad\u30e5\u30fc */\nqueue.pop();\n\n/* \u30ad\u30e5\u30fc\u306e\u9577\u3055\u3092\u53d6\u5f97 */\nint size = queue.size();\n\n/* \u30ad\u30e5\u30fc\u304c\u7a7a\u304b\u3069\u3046\u304b\u30c1\u30a7\u30c3\u30af */\nbool empty = queue.empty();\n</code></pre> queue.java<pre><code>/* \u30ad\u30e5\u30fc\u3092\u521d\u671f\u5316 */\nQueue&lt;Integer&gt; queue = new LinkedList&lt;&gt;();\n\n/* \u8981\u7d20\u3092\u30a8\u30f3\u30ad\u30e5\u30fc */\nqueue.offer(1);\nqueue.offer(3);\nqueue.offer(2);\nqueue.offer(5);\nqueue.offer(4);\n\n/* \u6700\u521d\u306e\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\nint peek = queue.peek();\n\n/* \u8981\u7d20\u3092\u30c7\u30ad\u30e5\u30fc */\nint pop = queue.poll();\n\n/* \u30ad\u30e5\u30fc\u306e\u9577\u3055\u3092\u53d6\u5f97 */\nint size = queue.size();\n\n/* \u30ad\u30e5\u30fc\u304c\u7a7a\u304b\u3069\u3046\u304b\u30c1\u30a7\u30c3\u30af */\nboolean isEmpty = queue.isEmpty();\n</code></pre> queue.cs<pre><code>/* \u30ad\u30e5\u30fc\u3092\u521d\u671f\u5316 */\nQueue&lt;int&gt; queue = new();\n\n/* \u8981\u7d20\u3092\u30a8\u30f3\u30ad\u30e5\u30fc */\nqueue.Enqueue(1);\nqueue.Enqueue(3);\nqueue.Enqueue(2);\nqueue.Enqueue(5);\nqueue.Enqueue(4);\n\n/* \u6700\u521d\u306e\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\nint peek = queue.Peek();\n\n/* \u8981\u7d20\u3092\u30c7\u30ad\u30e5\u30fc */\nint pop = queue.Dequeue();\n\n/* \u30ad\u30e5\u30fc\u306e\u9577\u3055\u3092\u53d6\u5f97 */\nint size = queue.Count;\n\n/* \u30ad\u30e5\u30fc\u304c\u7a7a\u304b\u3069\u3046\u304b\u30c1\u30a7\u30c3\u30af */\nbool isEmpty = queue.Count == 0;\n</code></pre> queue_test.go<pre><code>/* \u30ad\u30e5\u30fc\u3092\u521d\u671f\u5316 */\n// Go\u3067\u306f\u3001list\u3092\u30ad\u30e5\u30fc\u3068\u3057\u3066\u4f7f\u7528\nqueue := list.New()\n\n/* \u8981\u7d20\u3092\u30a8\u30f3\u30ad\u30e5\u30fc */\nqueue.PushBack(1)\nqueue.PushBack(3)\nqueue.PushBack(2)\nqueue.PushBack(5)\nqueue.PushBack(4)\n\n/* \u6700\u521d\u306e\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\npeek := queue.Front()\n\n/* \u8981\u7d20\u3092\u30c7\u30ad\u30e5\u30fc */\npop := queue.Front()\nqueue.Remove(pop)\n\n/* \u30ad\u30e5\u30fc\u306e\u9577\u3055\u3092\u53d6\u5f97 */\nsize := queue.Len()\n\n/* \u30ad\u30e5\u30fc\u304c\u7a7a\u304b\u3069\u3046\u304b\u30c1\u30a7\u30c3\u30af */\nisEmpty := queue.Len() == 0\n</code></pre> queue.swift<pre><code>/* \u30ad\u30e5\u30fc\u3092\u521d\u671f\u5316 */\n// Swift\u306b\u306f\u7d44\u307f\u8fbc\u307f\u306e\u30ad\u30e5\u30fc\u30af\u30e9\u30b9\u304c\u306a\u3044\u305f\u3081\u3001Array\u3092\u30ad\u30e5\u30fc\u3068\u3057\u3066\u4f7f\u7528\nvar queue: [Int] = []\n\n/* \u8981\u7d20\u3092\u30a8\u30f3\u30ad\u30e5\u30fc */\nqueue.append(1)\nqueue.append(3)\nqueue.append(2)\nqueue.append(5)\nqueue.append(4)\n\n/* \u6700\u521d\u306e\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\nlet peek = queue.first!\n\n/* \u8981\u7d20\u3092\u30c7\u30ad\u30e5\u30fc */\n// \u914d\u5217\u306a\u306e\u3067\u3001removeFirst\u306e\u8a08\u7b97\u91cf\u306fO(n)\nlet pool = queue.removeFirst()\n\n/* \u30ad\u30e5\u30fc\u306e\u9577\u3055\u3092\u53d6\u5f97 */\nlet size = queue.count\n\n/* \u30ad\u30e5\u30fc\u304c\u7a7a\u304b\u3069\u3046\u304b\u30c1\u30a7\u30c3\u30af */\nlet isEmpty = queue.isEmpty\n</code></pre> queue.js<pre><code>/* \u30ad\u30e5\u30fc\u3092\u521d\u671f\u5316 */\n// JavaScript\u306b\u306f\u7d44\u307f\u8fbc\u307f\u306e\u30ad\u30e5\u30fc\u304c\u306a\u3044\u305f\u3081\u3001Array\u3092\u30ad\u30e5\u30fc\u3068\u3057\u3066\u4f7f\u7528\nconst queue = [];\n\n/* \u8981\u7d20\u3092\u30a8\u30f3\u30ad\u30e5\u30fc */\nqueue.push(1);\nqueue.push(3);\nqueue.push(2);\nqueue.push(5);\nqueue.push(4);\n\n/* \u6700\u521d\u306e\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\nconst peek = queue[0];\n\n/* \u8981\u7d20\u3092\u30c7\u30ad\u30e5\u30fc */\n// \u57fa\u790e\u69cb\u9020\u304c\u914d\u5217\u306a\u306e\u3067\u3001shift()\u30e1\u30bd\u30c3\u30c9\u306e\u6642\u9593\u8a08\u7b97\u91cf\u306fO(n)\nconst pop = queue.shift();\n\n/* \u30ad\u30e5\u30fc\u306e\u9577\u3055\u3092\u53d6\u5f97 */\nconst size = queue.length;\n\n/* \u30ad\u30e5\u30fc\u304c\u7a7a\u304b\u3069\u3046\u304b\u30c1\u30a7\u30c3\u30af */\nconst empty = queue.length === 0;\n</code></pre> queue.ts<pre><code>/* \u30ad\u30e5\u30fc\u3092\u521d\u671f\u5316 */\n// TypeScript\u306b\u306f\u7d44\u307f\u8fbc\u307f\u306e\u30ad\u30e5\u30fc\u304c\u306a\u3044\u305f\u3081\u3001Array\u3092\u30ad\u30e5\u30fc\u3068\u3057\u3066\u4f7f\u7528\nconst queue: number[] = [];\n\n/* \u8981\u7d20\u3092\u30a8\u30f3\u30ad\u30e5\u30fc */\nqueue.push(1);\nqueue.push(3);\nqueue.push(2);\nqueue.push(5);\nqueue.push(4);\n\n/* \u6700\u521d\u306e\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\nconst peek = queue[0];\n\n/* \u8981\u7d20\u3092\u30c7\u30ad\u30e5\u30fc */\n// \u57fa\u790e\u69cb\u9020\u304c\u914d\u5217\u306a\u306e\u3067\u3001shift()\u30e1\u30bd\u30c3\u30c9\u306e\u6642\u9593\u8a08\u7b97\u91cf\u306fO(n)\nconst pop = queue.shift();\n\n/* \u30ad\u30e5\u30fc\u306e\u9577\u3055\u3092\u53d6\u5f97 */\nconst size = queue.length;\n\n/* \u30ad\u30e5\u30fc\u304c\u7a7a\u304b\u3069\u3046\u304b\u30c1\u30a7\u30c3\u30af */\nconst empty = queue.length === 0;\n</code></pre> queue.dart<pre><code>/* \u30ad\u30e5\u30fc\u3092\u521d\u671f\u5316 */\n// Dart\u306eQueue\u30af\u30e9\u30b9\u306f\u53cc\u65b9\u5411\u30ad\u30e5\u30fc\u3067\u3059\u304c\u3001\u30ad\u30e5\u30fc\u3068\u3057\u3066\u4f7f\u7528\u3067\u304d\u307e\u3059\nQueue&lt;int&gt; queue = Queue();\n\n/* \u8981\u7d20\u3092\u30a8\u30f3\u30ad\u30e5\u30fc */\nqueue.add(1);\nqueue.add(3);\nqueue.add(2);\nqueue.add(5);\nqueue.add(4);\n\n/* \u6700\u521d\u306e\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\nint peek = queue.first;\n\n/* \u8981\u7d20\u3092\u30c7\u30ad\u30e5\u30fc */\nint pop = queue.removeFirst();\n\n/* \u30ad\u30e5\u30fc\u306e\u9577\u3055\u3092\u53d6\u5f97 */\nint size = queue.length;\n\n/* \u30ad\u30e5\u30fc\u304c\u7a7a\u304b\u3069\u3046\u304b\u30c1\u30a7\u30c3\u30af */\nbool isEmpty = queue.isEmpty;\n</code></pre> queue.rs<pre><code>/* \u53cc\u65b9\u5411\u30ad\u30e5\u30fc\u3092\u521d\u671f\u5316 */\n// Rust\u3067\u306f\u3001\u53cc\u65b9\u5411\u30ad\u30e5\u30fc\u3092\u901a\u5e38\u306e\u30ad\u30e5\u30fc\u3068\u3057\u3066\u4f7f\u7528\nlet mut deque: VecDeque&lt;u32&gt; = VecDeque::new();\n\n/* \u8981\u7d20\u3092\u30a8\u30f3\u30ad\u30e5\u30fc */\ndeque.push_back(1);\ndeque.push_back(3);\ndeque.push_back(2);\ndeque.push_back(5);\ndeque.push_back(4);\n\n/* \u6700\u521d\u306e\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\nif let Some(front) = deque.front() {\n}\n\n/* \u8981\u7d20\u3092\u30c7\u30ad\u30e5\u30fc */\nif let Some(pop) = deque.pop_front() {\n}\n\n/* \u30ad\u30e5\u30fc\u306e\u9577\u3055\u3092\u53d6\u5f97 */\nlet size = deque.len();\n\n/* \u30ad\u30e5\u30fc\u304c\u7a7a\u304b\u3069\u3046\u304b\u30c1\u30a7\u30c3\u30af */\nlet is_empty = deque.is_empty();\n</code></pre> queue.c<pre><code>// C\u306f\u7d44\u307f\u8fbc\u307f\u306e\u30ad\u30e5\u30fc\u3092\u63d0\u4f9b\u3057\u3066\u3044\u307e\u305b\u3093\n</code></pre> queue.kt<pre><code>\n</code></pre> queue.zig<pre><code>\n</code></pre>"},{"location":"chapter_stack_and_queue/queue/#522","title":"5.2.2 \u00a0 \u30ad\u30e5\u30fc\u306e\u5b9f\u88c5","text":"<p>\u30ad\u30e5\u30fc\u3092\u5b9f\u88c5\u3059\u308b\u306b\u306f\u3001\u4e00\u65b9\u306e\u7aef\u3067\u8981\u7d20\u3092\u8ffd\u52a0\u3057\u3001\u3082\u3046\u4e00\u65b9\u306e\u7aef\u3067\u8981\u7d20\u3092\u524a\u9664\u3067\u304d\u308b\u30c7\u30fc\u30bf\u69cb\u9020\u304c\u5fc5\u8981\u3067\u3059\u3002\u9023\u7d50\u30ea\u30b9\u30c8\u3068\u914d\u5217\u306e\u4e21\u65b9\u304c\u3053\u306e\u8981\u4ef6\u3092\u6e80\u305f\u3057\u307e\u3059\u3002</p>"},{"location":"chapter_stack_and_queue/queue/#1","title":"1. \u00a0 \u9023\u7d50\u30ea\u30b9\u30c8\u30d9\u30fc\u30b9\u306e\u5b9f\u88c5","text":"<p>\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u306e\u300c\u30d8\u30c3\u30c9\u30ce\u30fc\u30c9\u300d\u3068\u300c\u30c6\u30fc\u30eb\u30ce\u30fc\u30c9\u300d\u3092\u305d\u308c\u305e\u308c\u30ad\u30e5\u30fc\u306e\u300c\u30d5\u30ed\u30f3\u30c8\u300d\u3068\u300c\u30ea\u30a2\u300d\u3068\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u30ce\u30fc\u30c9\u306f\u5f8c\u308d\u3067\u306e\u307f\u8ffd\u52a0\u3067\u304d\u3001\u524d\u3067\u306e\u307f\u524a\u9664\u3067\u304d\u308b\u3088\u3046\u306b\u898f\u5b9a\u3055\u308c\u3066\u3044\u307e\u3059\u3002</p> LinkedListQueuepush()pop() <p></p> <p></p> <p></p> <p> \u56f3 5-5 \u00a0 \u9023\u7d50\u30ea\u30b9\u30c8\u306b\u3088\u308b\u30ad\u30e5\u30fc\u5b9f\u88c5\u306e\u30a8\u30f3\u30ad\u30e5\u30fc\u3068\u30c7\u30ad\u30e5\u30fc\u64cd\u4f5c </p> <p>\u4ee5\u4e0b\u306f\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u3092\u4f7f\u7528\u3057\u3066\u30ad\u30e5\u30fc\u3092\u5b9f\u88c5\u3059\u308b\u30b3\u30fc\u30c9\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig linkedlist_queue.py<pre><code>class LinkedListQueue:\n    \"\"\"\u9023\u7d50\u30ea\u30b9\u30c8\u30d9\u30fc\u30b9\u306e\u30ad\u30e5\u30fc\u30af\u30e9\u30b9\"\"\"\n\n    def __init__(self):\n        \"\"\"\u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf\"\"\"\n        self._front: ListNode | None = None  # \u30d8\u30c3\u30c9\u30ce\u30fc\u30c9 front\n        self._rear: ListNode | None = None  # \u30c6\u30fc\u30eb\u30ce\u30fc\u30c9 rear\n        self._size: int = 0\n\n    def size(self) -&gt; int:\n        \"\"\"\u30ad\u30e5\u30fc\u306e\u9577\u3055\u3092\u53d6\u5f97\"\"\"\n        return self._size\n\n    def is_empty(self) -&gt; bool:\n        \"\"\"\u30ad\u30e5\u30fc\u304c\u7a7a\u304b\u3069\u3046\u304b\u3092\u5224\u5b9a\"\"\"\n        return self._size == 0\n\n    def push(self, num: int):\n        \"\"\"\u30a8\u30f3\u30ad\u30e5\u30fc\"\"\"\n        # \u30c6\u30fc\u30eb\u30ce\u30fc\u30c9\u306e\u5f8c\u308d\u306b num \u3092\u8ffd\u52a0\n        node = ListNode(num)\n        # \u30ad\u30e5\u30fc\u304c\u7a7a\u306e\u5834\u5408\u3001\u30d8\u30c3\u30c9\u3068\u30c6\u30fc\u30eb\u30ce\u30fc\u30c9\u306e\u4e21\u65b9\u3092\u305d\u306e\u30ce\u30fc\u30c9\u306b\u5411\u3051\u308b\n        if self._front is None:\n            self._front = node\n            self._rear = node\n        # \u30ad\u30e5\u30fc\u304c\u7a7a\u3067\u306a\u3044\u5834\u5408\u3001\u305d\u306e\u30ce\u30fc\u30c9\u3092\u30c6\u30fc\u30eb\u30ce\u30fc\u30c9\u306e\u5f8c\u308d\u306b\u8ffd\u52a0\n        else:\n            self._rear.next = node\n            self._rear = node\n        self._size += 1\n\n    def pop(self) -&gt; int:\n        \"\"\"\u30c7\u30ad\u30e5\u30fc\"\"\"\n        num = self.peek()\n        # \u30d8\u30c3\u30c9\u30ce\u30fc\u30c9\u3092\u524a\u9664\n        self._front = self._front.next\n        self._size -= 1\n        return num\n\n    def peek(self) -&gt; int:\n        \"\"\"\u30d5\u30ed\u30f3\u30c8\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9\"\"\"\n        if self.is_empty():\n            raise IndexError(\"Queue is empty\")\n        return self._front.val\n\n    def to_list(self) -&gt; list[int]:\n        \"\"\"\u51fa\u529b\u7528\u306e\u30ea\u30b9\u30c8\u306b\u5909\u63db\"\"\"\n        queue = []\n        temp = self._front\n        while temp:\n            queue.append(temp.val)\n            temp = temp.next\n        return queue\n</code></pre> linkedlist_queue.cpp<pre><code>/* \u9023\u7d50\u30ea\u30b9\u30c8\u306b\u57fa\u3065\u304f\u30ad\u30e5\u30fc\u30af\u30e9\u30b9 */\nclass LinkedListQueue {\n  private:\n    ListNode *front, *rear; // \u5148\u982d\u30ce\u30fc\u30c9front\u3001\u672b\u5c3e\u30ce\u30fc\u30c9rear\n    int queSize;\n\n  public:\n    LinkedListQueue() {\n        front = nullptr;\n        rear = nullptr;\n        queSize = 0;\n    }\n\n    ~LinkedListQueue() {\n        // \u9023\u7d50\u30ea\u30b9\u30c8\u3092\u8d70\u67fb\u3001\u30ce\u30fc\u30c9\u3092\u524a\u9664\u3001\u30e1\u30e2\u30ea\u3092\u89e3\u653e\n        freeMemoryLinkedList(front);\n    }\n\n    /* \u30ad\u30e5\u30fc\u306e\u9577\u3055\u3092\u53d6\u5f97 */\n    int size() {\n        return queSize;\n    }\n\n    /* \u30ad\u30e5\u30fc\u304c\u7a7a\u304b\u3069\u3046\u304b\u3092\u5224\u5b9a */\n    bool isEmpty() {\n        return queSize == 0;\n    }\n\n    /* \u30a8\u30f3\u30ad\u30e5\u30fc */\n    void push(int num) {\n        // \u672b\u5c3e\u30ce\u30fc\u30c9\u306e\u5f8c\u308d\u306bnum\u3092\u8ffd\u52a0\n        ListNode *node = new ListNode(num);\n        // \u30ad\u30e5\u30fc\u304c\u7a7a\u306e\u5834\u5408\u3001\u5148\u982d\u3068\u672b\u5c3e\u30ce\u30fc\u30c9\u306e\u4e21\u65b9\u3092\u305d\u306e\u30ce\u30fc\u30c9\u306b\u5411\u3051\u308b\n        if (front == nullptr) {\n            front = node;\n            rear = node;\n        }\n        // \u30ad\u30e5\u30fc\u304c\u7a7a\u3067\u306a\u3044\u5834\u5408\u3001\u305d\u306e\u30ce\u30fc\u30c9\u3092\u672b\u5c3e\u30ce\u30fc\u30c9\u306e\u5f8c\u308d\u306b\u8ffd\u52a0\n        else {\n            rear-&gt;next = node;\n            rear = node;\n        }\n        queSize++;\n    }\n\n    /* \u30c7\u30ad\u30e5\u30fc */\n    int pop() {\n        int num = peek();\n        // \u5148\u982d\u30ce\u30fc\u30c9\u3092\u524a\u9664\n        ListNode *tmp = front;\n        front = front-&gt;next;\n        // \u30e1\u30e2\u30ea\u3092\u89e3\u653e\n        delete tmp;\n        queSize--;\n        return num;\n    }\n\n    /* \u5148\u982d\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\n    int peek() {\n        if (size() == 0)\n            throw out_of_range(\"Queue is empty\");\n        return front-&gt;val;\n    }\n\n    /* \u9023\u7d50\u30ea\u30b9\u30c8\u3092Vector\u306b\u5909\u63db\u3057\u3066\u8fd4\u5374 */\n    vector&lt;int&gt; toVector() {\n        ListNode *node = front;\n        vector&lt;int&gt; res(size());\n        for (int i = 0; i &lt; res.size(); i++) {\n            res[i] = node-&gt;val;\n            node = node-&gt;next;\n        }\n        return res;\n    }\n};\n</code></pre> linkedlist_queue.java<pre><code>/* \u9023\u7d50\u30ea\u30b9\u30c8\u306b\u57fa\u3065\u304f\u30ad\u30e5\u30fc\u30af\u30e9\u30b9 */\nclass LinkedListQueue {\n    private ListNode front, rear; // \u5148\u982d\u30ce\u30fc\u30c9 front\u3001\u672b\u5c3e\u30ce\u30fc\u30c9 rear\n    private int queSize = 0;\n\n    public LinkedListQueue() {\n        front = null;\n        rear = null;\n    }\n\n    /* \u30ad\u30e5\u30fc\u306e\u9577\u3055\u3092\u53d6\u5f97 */\n    public int size() {\n        return queSize;\n    }\n\n    /* \u30ad\u30e5\u30fc\u304c\u7a7a\u304b\u3069\u3046\u304b\u3092\u5224\u5b9a */\n    public boolean isEmpty() {\n        return size() == 0;\n    }\n\n    /* \u30a8\u30f3\u30ad\u30e5\u30fc */\n    public void push(int num) {\n        // \u672b\u5c3e\u30ce\u30fc\u30c9\u306e\u5f8c\u308d\u306b num \u3092\u8ffd\u52a0\n        ListNode node = new ListNode(num);\n        // \u30ad\u30e5\u30fc\u304c\u7a7a\u306e\u5834\u5408\u3001\u5148\u982d\u3068\u672b\u5c3e\u30ce\u30fc\u30c9\u306e\u4e21\u65b9\u3092\u305d\u306e\u30ce\u30fc\u30c9\u306b\u30dd\u30a4\u30f3\u30c8\n        if (front == null) {\n            front = node;\n            rear = node;\n        // \u30ad\u30e5\u30fc\u304c\u7a7a\u3067\u306a\u3044\u5834\u5408\u3001\u305d\u306e\u30ce\u30fc\u30c9\u3092\u672b\u5c3e\u30ce\u30fc\u30c9\u306e\u5f8c\u308d\u306b\u8ffd\u52a0\n        } else {\n            rear.next = node;\n            rear = node;\n        }\n        queSize++;\n    }\n\n    /* \u30c7\u30ad\u30e5\u30fc */\n    public int pop() {\n        int num = peek();\n        // \u5148\u982d\u30ce\u30fc\u30c9\u3092\u524a\u9664\n        front = front.next;\n        queSize--;\n        return num;\n    }\n\n    /* \u5148\u982d\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\n    public int peek() {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        return front.val;\n    }\n\n    /* \u9023\u7d50\u30ea\u30b9\u30c8\u3092\u914d\u5217\u306b\u5909\u63db\u3057\u3066\u8fd4\u3059 */\n    public int[] toArray() {\n        ListNode node = front;\n        int[] res = new int[size()];\n        for (int i = 0; i &lt; res.length; i++) {\n            res[i] = node.val;\n            node = node.next;\n        }\n        return res;\n    }\n}\n</code></pre> linkedlist_queue.cs<pre><code>[class]{LinkedListQueue}-[func]{}\n</code></pre> linkedlist_queue.go<pre><code>[class]{linkedListQueue}-[func]{}\n</code></pre> linkedlist_queue.swift<pre><code>[class]{LinkedListQueue}-[func]{}\n</code></pre> linkedlist_queue.js<pre><code>[class]{LinkedListQueue}-[func]{}\n</code></pre> linkedlist_queue.ts<pre><code>[class]{LinkedListQueue}-[func]{}\n</code></pre> linkedlist_queue.dart<pre><code>[class]{LinkedListQueue}-[func]{}\n</code></pre> linkedlist_queue.rs<pre><code>[class]{LinkedListQueue}-[func]{}\n</code></pre> linkedlist_queue.c<pre><code>[class]{LinkedListQueue}-[func]{}\n</code></pre> linkedlist_queue.kt<pre><code>[class]{LinkedListQueue}-[func]{}\n</code></pre> linkedlist_queue.rb<pre><code>[class]{LinkedListQueue}-[func]{}\n</code></pre> linkedlist_queue.zig<pre><code>[class]{LinkedListQueue}-[func]{}\n</code></pre>"},{"location":"chapter_stack_and_queue/queue/#2","title":"2. \u00a0 \u914d\u5217\u30d9\u30fc\u30b9\u306e\u5b9f\u88c5","text":"<p>\u914d\u5217\u306e\u6700\u521d\u306e\u8981\u7d20\u3092\u524a\u9664\u3059\u308b\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O(n)\\)\u3067\u3001\u30c7\u30ad\u30e5\u30fc\u64cd\u4f5c\u304c\u975e\u52b9\u7387\u306b\u306a\u308a\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u3053\u306e\u554f\u984c\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u5de7\u5999\u306b\u56de\u907f\u3067\u304d\u307e\u3059\u3002</p> <p>\u5909\u6570<code>front</code>\u3092\u4f7f\u7528\u3057\u3066\u30d5\u30ed\u30f3\u30c8\u8981\u7d20\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u793a\u3057\u3001\u5909\u6570<code>size</code>\u3092\u7dad\u6301\u3057\u3066\u30ad\u30e5\u30fc\u306e\u9577\u3055\u3092\u8a18\u9332\u3057\u307e\u3059\u3002<code>rear = front + size</code>\u3092\u5b9a\u7fa9\u3057\u3001\u3053\u308c\u306f\u30c6\u30fc\u30eb\u8981\u7d20\u306e\u76f4\u5f8c\u306e\u4f4d\u7f6e\u3092\u6307\u3057\u307e\u3059\u3002</p> <p>\u3053\u306e\u8a2d\u8a08\u306b\u3088\u308a\u3001\u914d\u5217\u5185\u306e\u8981\u7d20\u306e\u6709\u52b9\u306a\u9593\u9694\u306f<code>[front, rear - 1]</code>\u3067\u3059\u3002\u5404\u64cd\u4f5c\u306e\u5b9f\u88c5\u65b9\u6cd5\u3092\u4e0b\u56f3\u306b\u793a\u3057\u307e\u3059\u3002</p> <ul> <li>\u30a8\u30f3\u30ad\u30e5\u30fc\u64cd\u4f5c\uff1a\u5165\u529b\u8981\u7d20\u3092<code>rear</code>\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306b\u5272\u308a\u5f53\u3066\u3001<code>size</code>\u30921\u5897\u52a0\u3055\u305b\u307e\u3059\u3002</li> <li>\u30c7\u30ad\u30e5\u30fc\u64cd\u4f5c\uff1a\u5358\u306b<code>front</code>\u30921\u5897\u52a0\u3055\u305b\u3001<code>size</code>\u30921\u6e1b\u5c11\u3055\u305b\u307e\u3059\u3002</li> </ul> <p>\u30a8\u30f3\u30ad\u30e5\u30fc\u3068\u30c7\u30ad\u30e5\u30fc\u64cd\u4f5c\u306f\u4e21\u65b9\u3068\u3082\u5358\u4e00\u306e\u64cd\u4f5c\u306e\u307f\u3092\u5fc5\u8981\u3068\u3057\u3001\u305d\u308c\u305e\u308c\u306e\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O(1)\\)\u3067\u3059\u3002</p> ArrayQueuepush()pop() <p></p> <p></p> <p></p> <p> \u56f3 5-6 \u00a0 \u914d\u5217\u306b\u3088\u308b\u30ad\u30e5\u30fc\u5b9f\u88c5\u306e\u30a8\u30f3\u30ad\u30e5\u30fc\u3068\u30c7\u30ad\u30e5\u30fc\u64cd\u4f5c </p> <p>\u554f\u984c\u306b\u6c17\u3065\u304f\u304b\u3082\u3057\u308c\u307e\u305b\u3093\uff1a\u30a8\u30f3\u30ad\u30e5\u30fc\u3068\u30c7\u30ad\u30e5\u30fc\u64cd\u4f5c\u304c\u7d99\u7d9a\u7684\u306b\u5b9f\u884c\u3055\u308c\u308b\u3068\u3001<code>front</code>\u3068<code>rear</code>\u306e\u4e21\u65b9\u304c\u53f3\u306b\u79fb\u52d5\u3057\u3001\u6700\u7d42\u7684\u306b\u914d\u5217\u306e\u672b\u5c3e\u306b\u5230\u9054\u3057\u3066\u305d\u308c\u4ee5\u4e0a\u79fb\u52d5\u3067\u304d\u306a\u304f\u306a\u308a\u307e\u3059\u3002\u3053\u308c\u3092\u89e3\u6c7a\u3059\u308b\u305f\u3081\u306b\u3001\u914d\u5217\u3092\u300c\u5faa\u74b0\u914d\u5217\u300d\u3068\u3057\u3066\u6271\u3044\u3001\u914d\u5217\u306e\u672b\u5c3e\u3092\u5148\u982d\u306b\u63a5\u7d9a\u3057\u307e\u3059\u3002</p> <p>\u5faa\u74b0\u914d\u5217\u3067\u306f\u3001<code>front</code>\u307e\u305f\u306f<code>rear</code>\u304c\u672b\u5c3e\u306b\u5230\u9054\u3059\u308b\u3068\u3001\u914d\u5217\u306e\u5148\u982d\u306b\u30eb\u30fc\u30d7\u30d0\u30c3\u30af\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u5faa\u74b0\u30d1\u30bf\u30fc\u30f3\u306f\u3001\u4ee5\u4e0b\u306e\u30b3\u30fc\u30c9\u306b\u793a\u3059\u3088\u3046\u306b\u300c\u5270\u4f59\u6f14\u7b97\u300d\u3067\u5b9f\u73fe\u3067\u304d\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig array_queue.py<pre><code>class ArrayQueue:\n    \"\"\"\u5faa\u74b0\u914d\u5217\u30d9\u30fc\u30b9\u306e\u30ad\u30e5\u30fc\u30af\u30e9\u30b9\"\"\"\n\n    def __init__(self, size: int):\n        \"\"\"\u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf\"\"\"\n        self._nums: list[int] = [0] * size  # \u30ad\u30e5\u30fc\u8981\u7d20\u3092\u683c\u7d0d\u3059\u308b\u914d\u5217\n        self._front: int = 0  # \u30d5\u30ed\u30f3\u30c8\u30dd\u30a4\u30f3\u30bf\u3001\u30d5\u30ed\u30f3\u30c8\u8981\u7d20\u3092\u6307\u3059\n        self._size: int = 0  # \u30ad\u30e5\u30fc\u306e\u9577\u3055\n\n    def capacity(self) -&gt; int:\n        \"\"\"\u30ad\u30e5\u30fc\u306e\u5bb9\u91cf\u3092\u53d6\u5f97\"\"\"\n        return len(self._nums)\n\n    def size(self) -&gt; int:\n        \"\"\"\u30ad\u30e5\u30fc\u306e\u9577\u3055\u3092\u53d6\u5f97\"\"\"\n        return self._size\n\n    def is_empty(self) -&gt; bool:\n        \"\"\"\u30ad\u30e5\u30fc\u304c\u7a7a\u304b\u3069\u3046\u304b\u3092\u5224\u5b9a\"\"\"\n        return self._size == 0\n\n    def push(self, num: int):\n        \"\"\"\u30a8\u30f3\u30ad\u30e5\u30fc\"\"\"\n        if self._size == self.capacity():\n            raise IndexError(\"Queue is full\")\n        # \u30ea\u30a2\u30dd\u30a4\u30f3\u30bf\u3092\u8a08\u7b97\u3001\u30ea\u30a2\u30a4\u30f3\u30c7\u30c3\u30af\u30b9 + 1 \u3092\u6307\u3059\n        # \u30e2\u30b8\u30e5\u30ed\u6f14\u7b97\u3092\u4f7f\u7528\u3057\u3066\u30ea\u30a2\u30dd\u30a4\u30f3\u30bf\u3092\u914d\u5217\u306e\u672b\u5c3e\u304b\u3089\u5148\u982d\u306b\u623b\u3059\n        rear: int = (self._front + self._size) % self.capacity()\n        # num \u3092\u30ea\u30a2\u306b\u8ffd\u52a0\n        self._nums[rear] = num\n        self._size += 1\n\n    def pop(self) -&gt; int:\n        \"\"\"\u30c7\u30ad\u30e5\u30fc\"\"\"\n        num: int = self.peek()\n        # \u30d5\u30ed\u30f3\u30c8\u30dd\u30a4\u30f3\u30bf\u30921\u3064\u5f8c\u308d\u306b\u79fb\u52d5\u3001\u672b\u5c3e\u3092\u8d85\u3048\u305f\u5834\u5408\u306f\u914d\u5217\u306e\u5148\u982d\u306b\u623b\u308b\n        self._front = (self._front + 1) % self.capacity()\n        self._size -= 1\n        return num\n\n    def peek(self) -&gt; int:\n        \"\"\"\u30d5\u30ed\u30f3\u30c8\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9\"\"\"\n        if self.is_empty():\n            raise IndexError(\"Queue is empty\")\n        return self._nums[self._front]\n\n    def to_list(self) -&gt; list[int]:\n        \"\"\"\u51fa\u529b\u7528\u306e\u914d\u5217\u3092\u8fd4\u3059\"\"\"\n        res = [0] * self.size()\n        j: int = self._front\n        for i in range(self.size()):\n            res[i] = self._nums[(j % self.capacity())]\n            j += 1\n        return res\n</code></pre> array_queue.cpp<pre><code>/* \u5faa\u74b0\u914d\u5217\u306b\u57fa\u3065\u304f\u30ad\u30e5\u30fc\u30af\u30e9\u30b9 */\nclass ArrayQueue {\n  private:\n    int *nums;       // \u30ad\u30e5\u30fc\u8981\u7d20\u3092\u683c\u7d0d\u3059\u308b\u914d\u5217\n    int front;       // \u5148\u982d\u30dd\u30a4\u30f3\u30bf\u3001\u5148\u982d\u8981\u7d20\u3092\u6307\u3059\n    int queSize;     // \u30ad\u30e5\u30fc\u306e\u9577\u3055\n    int queCapacity; // \u30ad\u30e5\u30fc\u306e\u5bb9\u91cf\n\n  public:\n    ArrayQueue(int capacity) {\n        // \u914d\u5217\u3092\u521d\u671f\u5316\n        nums = new int[capacity];\n        queCapacity = capacity;\n        front = queSize = 0;\n    }\n\n    ~ArrayQueue() {\n        delete[] nums;\n    }\n\n    /* \u30ad\u30e5\u30fc\u306e\u5bb9\u91cf\u3092\u53d6\u5f97 */\n    int capacity() {\n        return queCapacity;\n    }\n\n    /* \u30ad\u30e5\u30fc\u306e\u9577\u3055\u3092\u53d6\u5f97 */\n    int size() {\n        return queSize;\n    }\n\n    /* \u30ad\u30e5\u30fc\u304c\u7a7a\u304b\u3069\u3046\u304b\u3092\u5224\u5b9a */\n    bool isEmpty() {\n        return size() == 0;\n    }\n\n    /* \u30a8\u30f3\u30ad\u30e5\u30fc */\n    void push(int num) {\n        if (queSize == queCapacity) {\n            cout &lt;&lt; \"Queue is full\" &lt;&lt; endl;\n            return;\n        }\n        // \u672b\u5c3e\u30dd\u30a4\u30f3\u30bf\u3092\u8a08\u7b97\u3001\u672b\u5c3e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9 + 1\u3092\u6307\u3059\n        // \u5270\u4f59\u6f14\u7b97\u3092\u4f7f\u7528\u3057\u3066\u672b\u5c3e\u30dd\u30a4\u30f3\u30bf\u304c\u914d\u5217\u306e\u672b\u5c3e\u304b\u3089\u5148\u982d\u306b\u623b\u308b\u3088\u3046\u306b\u30e9\u30c3\u30d7\n        int rear = (front + queSize) % queCapacity;\n        // num\u3092\u672b\u5c3e\u306b\u8ffd\u52a0\n        nums[rear] = num;\n        queSize++;\n    }\n\n    /* \u30c7\u30ad\u30e5\u30fc */\n    int pop() {\n        int num = peek();\n        // \u5148\u982d\u30dd\u30a4\u30f3\u30bf\u30921\u3064\u5f8c\u308d\u306b\u79fb\u52d5\u3001\u672b\u5c3e\u3092\u8d85\u3048\u305f\u5834\u5408\u306f\u914d\u5217\u306e\u5148\u982d\u306b\u623b\u308b\n        front = (front + 1) % queCapacity;\n        queSize--;\n        return num;\n    }\n\n    /* \u5148\u982d\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\n    int peek() {\n        if (isEmpty())\n            throw out_of_range(\"Queue is empty\");\n        return nums[front];\n    }\n\n    /* \u914d\u5217\u3092Vector\u306b\u5909\u63db\u3057\u3066\u8fd4\u5374 */\n    vector&lt;int&gt; toVector() {\n        // \u6709\u52b9\u306a\u9577\u3055\u7bc4\u56f2\u5185\u306e\u8981\u7d20\u306e\u307f\u3092\u5909\u63db\n        vector&lt;int&gt; arr(queSize);\n        for (int i = 0, j = front; i &lt; queSize; i++, j++) {\n            arr[i] = nums[j % queCapacity];\n        }\n        return arr;\n    }\n};\n</code></pre> array_queue.java<pre><code>/* \u914d\u5217\u306b\u57fa\u3065\u304f\u30ad\u30e5\u30fc\u30af\u30e9\u30b9 */\nclass ArrayQueue {\n    private int[] nums; // \u8981\u7d20\u3092\u683c\u7d0d\u3059\u308b\u914d\u5217\n    private int front; // \u30ad\u30e5\u30fc\u30d8\u30c3\u30c9\u30dd\u30a4\u30f3\u30bf\u3001\u6700\u521d\u306e\u8981\u7d20\u3092\u6307\u3059\n    private int queSize; // \u30ad\u30e5\u30fc\u306e\u9577\u3055\n\n    public ArrayQueue(int capacity) {\n        nums = new int[capacity];\n        front = queSize = 0;\n    }\n\n    /* \u30ad\u30e5\u30fc\u306e\u5bb9\u91cf\u3092\u53d6\u5f97 */\n    public int capacity() {\n        return nums.length;\n    }\n\n    /* \u30ad\u30e5\u30fc\u306e\u9577\u3055\u3092\u53d6\u5f97 */\n    public int size() {\n        return queSize;\n    }\n\n    /* \u30ad\u30e5\u30fc\u304c\u7a7a\u304b\u3069\u3046\u304b\u3092\u5224\u5b9a */\n    public boolean isEmpty() {\n        return queSize == 0;\n    }\n\n    /* \u30a8\u30f3\u30ad\u30e5\u30fc */\n    public void push(int num) {\n        if (queSize == capacity()) {\n            System.out.println(\"\u30ad\u30e5\u30fc\u304c\u6e80\u676f\u3067\u3059\");\n            return;\n        }\n        // \u30ea\u30a2\u30dd\u30a4\u30f3\u30bf\u3092\u8a08\u7b97\uff1afront + queSize\n        // \u30e2\u30b8\u30e5\u30ed\u64cd\u4f5c\u306b\u3088\u308a rear \u304c\u914d\u5217\u306e\u9577\u3055\u3092\u8d85\u3048\u308b\u3053\u3068\u3092\u56de\u907f\n        int rear = (front + queSize) % capacity();\n        // \u8981\u7d20\u3092\u30ad\u30e5\u30fc\u30ea\u30a2\u306b\u8ffd\u52a0\n        nums[rear] = num;\n        queSize++;\n    }\n\n    /* \u30c7\u30ad\u30e5\u30fc */\n    public int pop() {\n        int num = peek();\n        // \u30ad\u30e5\u30fc\u30d8\u30c3\u30c9\u30dd\u30a4\u30f3\u30bf\u3092\u5f8c\u308d\u306b1\u3064\u79fb\u52d5\u3001\u30e2\u30b8\u30e5\u30ed\u64cd\u4f5c\u306b\u3088\u308a\u7bc4\u56f2\u3092\u8d85\u3048\u308b\u3053\u3068\u3092\u56de\u907f\n        front = (front + 1) % capacity();\n        queSize--;\n        return num;\n    }\n\n    /* \u30ad\u30e5\u30fc\u30d8\u30c3\u30c9\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\n    public int peek() {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        return nums[front];\n    }\n\n    /* \u914d\u5217\u3092\u8fd4\u3059 */\n    public int[] toArray() {\n        // front \u304b\u3089\u958b\u59cb\u3057\u3066 queSize \u500b\u306e\u8981\u7d20\u306e\u307f\u3092\u30b3\u30d4\u30fc\n        int[] res = new int[queSize];\n        for (int i = 0, j = front; i &lt; queSize; i++, j++) {\n            res[i] = nums[j % capacity()];\n        }\n        return res;\n    }\n}\n</code></pre> array_queue.cs<pre><code>[class]{ArrayQueue}-[func]{}\n</code></pre> array_queue.go<pre><code>[class]{arrayQueue}-[func]{}\n</code></pre> array_queue.swift<pre><code>[class]{ArrayQueue}-[func]{}\n</code></pre> array_queue.js<pre><code>[class]{ArrayQueue}-[func]{}\n</code></pre> array_queue.ts<pre><code>[class]{ArrayQueue}-[func]{}\n</code></pre> array_queue.dart<pre><code>[class]{ArrayQueue}-[func]{}\n</code></pre> array_queue.rs<pre><code>[class]{ArrayQueue}-[func]{}\n</code></pre> array_queue.c<pre><code>[class]{ArrayQueue}-[func]{}\n</code></pre> array_queue.kt<pre><code>[class]{ArrayQueue}-[func]{}\n</code></pre> array_queue.rb<pre><code>[class]{ArrayQueue}-[func]{}\n</code></pre> array_queue.zig<pre><code>[class]{ArrayQueue}-[func]{}\n</code></pre> <p>\u4e0a\u8a18\u306e\u30ad\u30e5\u30fc\u5b9f\u88c5\u306b\u306f\u307e\u3060\u5236\u9650\u304c\u3042\u308a\u307e\u3059\uff1a\u9577\u3055\u304c\u56fa\u5b9a\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u3053\u306e\u554f\u984c\u306f\u89e3\u6c7a\u304c\u56f0\u96e3\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u914d\u5217\u3092\u5fc5\u8981\u306b\u5fdc\u3058\u3066\u81ea\u52d5\u62e1\u5f35\u3067\u304d\u308b\u52d5\u7684\u914d\u5217\u306b\u7f6e\u304d\u63db\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u8208\u5473\u306e\u3042\u308b\u8aad\u8005\u306f\u81ea\u5206\u3067\u5b9f\u88c5\u3057\u3066\u307f\u3066\u304f\u3060\u3055\u3044\u3002</p> <p>2\u3064\u306e\u5b9f\u88c5\u306e\u6bd4\u8f03\u306f\u30b9\u30bf\u30c3\u30af\u306e\u5834\u5408\u3068\u4e00\u8cab\u3057\u3066\u304a\u308a\u3001\u3053\u3053\u3067\u306f\u7e70\u308a\u8fd4\u3057\u307e\u305b\u3093\u3002</p>"},{"location":"chapter_stack_and_queue/queue/#523","title":"5.2.3 \u00a0 \u30ad\u30e5\u30fc\u306e\u5178\u578b\u7684\u306a\u5fdc\u7528","text":"<ul> <li>Amazon\u306e\u6ce8\u6587\uff1a\u8cb7\u3044\u7269\u5ba2\u304c\u6ce8\u6587\u3092\u884c\u3063\u305f\u5f8c\u3001\u3053\u308c\u3089\u306e\u6ce8\u6587\u306f\u30ad\u30e5\u30fc\u306b\u53c2\u52a0\u3057\u3001\u30b7\u30b9\u30c6\u30e0\u306f\u9806\u756a\u306b\u51e6\u7406\u3057\u307e\u3059\u3002\u72ec\u8eab\u306e\u65e5\u306a\u3069\u306e\u30a4\u30d9\u30f3\u30c8\u4e2d\u306f\u3001\u77ed\u6642\u9593\u3067\u5927\u91cf\u306e\u6ce8\u6587\u304c\u751f\u6210\u3055\u308c\u3001\u9ad8\u3044\u540c\u6642\u5b9f\u884c\u6027\u304c\u30a8\u30f3\u30b8\u30cb\u30a2\u306b\u3068\u3063\u3066\u91cd\u8981\u306a\u8ab2\u984c\u3068\u306a\u308a\u307e\u3059\u3002</li> <li>\u69d8\u3005\u306aToDo\u30ea\u30b9\u30c8\uff1a\u300c\u5148\u7740\u9806\u300d\u6a5f\u80fd\u304c\u5fc5\u8981\u306a\u30b7\u30ca\u30ea\u30aa\u3001\u4f8b\u3048\u3070\u30d7\u30ea\u30f3\u30bf\u30fc\u306e\u30bf\u30b9\u30af\u30ad\u30e5\u30fc\u3084\u30ec\u30b9\u30c8\u30e9\u30f3\u306e\u914d\u9054\u30ad\u30e5\u30fc\u306a\u3069\u3001\u30ad\u30e5\u30fc\u3067\u51e6\u7406\u9806\u5e8f\u3092\u52b9\u679c\u7684\u306b\u7dad\u6301\u3067\u304d\u307e\u3059\u3002</li> </ul>"},{"location":"chapter_stack_and_queue/stack/","title":"5.1 \u00a0 \u30b9\u30bf\u30c3\u30af","text":"<p>\u30b9\u30bf\u30c3\u30af\u306f\u3001\u5f8c\u5165\u5148\u51fa\uff08LIFO\uff09\u306e\u539f\u5247\u306b\u5f93\u3046\u7dda\u5f62\u30c7\u30fc\u30bf\u69cb\u9020\u3067\u3059\u3002</p> <p>\u30b9\u30bf\u30c3\u30af\u3092\u30c6\u30fc\u30d6\u30eb\u4e0a\u306e\u76bf\u306e\u5c71\u306b\u4f8b\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u5e95\u306e\u76bf\u306b\u30a2\u30af\u30bb\u30b9\u3059\u308b\u306b\u306f\u3001\u307e\u305a\u4e0a\u306e\u76bf\u3092\u53d6\u308a\u9664\u304f\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u76bf\u3092\u69d8\u3005\u306a\u7a2e\u985e\u306e\u8981\u7d20\uff08\u6574\u6570\u3001\u6587\u5b57\u3001\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u306a\u3069\uff09\u306b\u7f6e\u304d\u63db\u3048\u308b\u3053\u3068\u3067\u3001\u30b9\u30bf\u30c3\u30af\u3068\u547c\u3070\u308c\u308b\u30c7\u30fc\u30bf\u69cb\u9020\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002</p> <p>\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u8981\u7d20\u306e\u5c71\u306e\u4e0a\u90e8\u3092\u300c\u30b9\u30bf\u30c3\u30af\u306e\u30c8\u30c3\u30d7\u300d\u3001\u4e0b\u90e8\u3092\u300c\u30b9\u30bf\u30c3\u30af\u306e\u30dc\u30c8\u30e0\u300d\u3068\u547c\u3073\u307e\u3059\u3002\u30b9\u30bf\u30c3\u30af\u306e\u30c8\u30c3\u30d7\u306b\u8981\u7d20\u3092\u8ffd\u52a0\u3059\u308b\u64cd\u4f5c\u3092\u300c\u30d7\u30c3\u30b7\u30e5\u300d\u3001\u30c8\u30c3\u30d7\u8981\u7d20\u3092\u524a\u9664\u3059\u308b\u64cd\u4f5c\u3092\u300c\u30dd\u30c3\u30d7\u300d\u3068\u547c\u3073\u307e\u3059\u3002</p> <p></p> <p> \u56f3 5-1 \u00a0 \u30b9\u30bf\u30c3\u30af\u306e\u5f8c\u5165\u5148\u51fa\u30eb\u30fc\u30eb </p>"},{"location":"chapter_stack_and_queue/stack/#511","title":"5.1.1 \u00a0 \u30b9\u30bf\u30c3\u30af\u306e\u4e00\u822c\u7684\u306a\u64cd\u4f5c","text":"<p>\u30b9\u30bf\u30c3\u30af\u306e\u4e00\u822c\u7684\u306a\u64cd\u4f5c\u3092\u4e0b\u8868\u306b\u793a\u3057\u307e\u3059\u3002\u5177\u4f53\u7684\u306a\u30e1\u30bd\u30c3\u30c9\u540d\u306f\u4f7f\u7528\u3059\u308b\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u306b\u3088\u3063\u3066\u7570\u306a\u308a\u307e\u3059\u3002\u3053\u3053\u3067\u306f\u3001\u4f8b\u3068\u3057\u3066<code>push()</code>\u3001<code>pop()</code>\u3001<code>peek()</code>\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002</p> <p> \u8868 5-1 \u00a0 \u30b9\u30bf\u30c3\u30af\u64cd\u4f5c\u306e\u52b9\u7387 </p> \u30e1\u30bd\u30c3\u30c9 \u8aac\u660e \u6642\u9593\u8a08\u7b97\u91cf <code>push()</code> \u8981\u7d20\u3092\u30b9\u30bf\u30c3\u30af\u306b\u30d7\u30c3\u30b7\u30e5\uff08\u30c8\u30c3\u30d7\u306b\u8ffd\u52a0\uff09 \\(O(1)\\) <code>pop()</code> \u30b9\u30bf\u30c3\u30af\u304b\u3089\u30c8\u30c3\u30d7\u8981\u7d20\u3092\u30dd\u30c3\u30d7 \\(O(1)\\) <code>peek()</code> \u30b9\u30bf\u30c3\u30af\u306e\u30c8\u30c3\u30d7\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 \\(O(1)\\) <p>\u901a\u5e38\u3001\u30d7\u30ed\u30b0\u30e9\u30df\u30f3\u30b0\u8a00\u8a9e\u306b\u7d44\u307f\u8fbc\u307e\u308c\u3066\u3044\u308b\u30b9\u30bf\u30c3\u30af\u30af\u30e9\u30b9\u3092\u76f4\u63a5\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002\u305f\u3060\u3057\u3001\u4e00\u90e8\u306e\u8a00\u8a9e\u3067\u306f\u5177\u4f53\u7684\u306b\u30b9\u30bf\u30c3\u30af\u30af\u30e9\u30b9\u3092\u63d0\u4f9b\u3057\u3066\u3044\u306a\u3044\u5834\u5408\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u5834\u5408\u3001\u8a00\u8a9e\u306e\u300c\u914d\u5217\u300d\u307e\u305f\u306f\u300c\u9023\u7d50\u30ea\u30b9\u30c8\u300d\u3092\u30b9\u30bf\u30c3\u30af\u3068\u3057\u3066\u4f7f\u7528\u3057\u3001\u30d7\u30ed\u30b0\u30e9\u30e0\u3067\u30b9\u30bf\u30c3\u30af\u30ed\u30b8\u30c3\u30af\u306b\u95a2\u9023\u3057\u306a\u3044\u64cd\u4f5c\u3092\u7121\u8996\u3067\u304d\u307e\u3059\u3002</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinZig stack.py<pre><code># \u30b9\u30bf\u30c3\u30af\u3092\u521d\u671f\u5316\n# Python\u306b\u306f\u7d44\u307f\u8fbc\u307f\u306e\u30b9\u30bf\u30c3\u30af\u30af\u30e9\u30b9\u304c\u306a\u3044\u305f\u3081\u3001list\u3092\u30b9\u30bf\u30c3\u30af\u3068\u3057\u3066\u4f7f\u7528\nstack: list[int] = []\n\n# \u8981\u7d20\u3092\u30b9\u30bf\u30c3\u30af\u306b\u30d7\u30c3\u30b7\u30e5\nstack.append(1)\nstack.append(3)\nstack.append(2)\nstack.append(5)\nstack.append(4)\n\n# \u30b9\u30bf\u30c3\u30af\u306e\u30c8\u30c3\u30d7\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9\npeek: int = stack[-1]\n\n# \u30b9\u30bf\u30c3\u30af\u304b\u3089\u8981\u7d20\u3092\u30dd\u30c3\u30d7\npop: int = stack.pop()\n\n# \u30b9\u30bf\u30c3\u30af\u306e\u9577\u3055\u3092\u53d6\u5f97\nsize: int = len(stack)\n\n# \u30b9\u30bf\u30c3\u30af\u304c\u7a7a\u304b\u3069\u3046\u304b\u30c1\u30a7\u30c3\u30af\nis_empty: bool = len(stack) == 0\n</code></pre> stack.cpp<pre><code>/* \u30b9\u30bf\u30c3\u30af\u3092\u521d\u671f\u5316 */\nstack&lt;int&gt; stack;\n\n/* \u8981\u7d20\u3092\u30b9\u30bf\u30c3\u30af\u306b\u30d7\u30c3\u30b7\u30e5 */\nstack.push(1);\nstack.push(3);\nstack.push(2);\nstack.push(5);\nstack.push(4);\n\n/* \u30b9\u30bf\u30c3\u30af\u306e\u30c8\u30c3\u30d7\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\nint top = stack.top();\n\n/* \u30b9\u30bf\u30c3\u30af\u304b\u3089\u8981\u7d20\u3092\u30dd\u30c3\u30d7 */\nstack.pop(); // \u623b\u308a\u5024\u306a\u3057\n\n/* \u30b9\u30bf\u30c3\u30af\u306e\u9577\u3055\u3092\u53d6\u5f97 */\nint size = stack.size();\n\n/* \u30b9\u30bf\u30c3\u30af\u304c\u7a7a\u304b\u3069\u3046\u304b\u30c1\u30a7\u30c3\u30af */\nbool empty = stack.empty();\n</code></pre> stack.java<pre><code>/* \u30b9\u30bf\u30c3\u30af\u3092\u521d\u671f\u5316 */\nStack&lt;Integer&gt; stack = new Stack&lt;&gt;();\n\n/* \u8981\u7d20\u3092\u30b9\u30bf\u30c3\u30af\u306b\u30d7\u30c3\u30b7\u30e5 */\nstack.push(1);\nstack.push(3);\nstack.push(2);\nstack.push(5);\nstack.push(4);\n\n/* \u30b9\u30bf\u30c3\u30af\u306e\u30c8\u30c3\u30d7\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\nint peek = stack.peek();\n\n/* \u30b9\u30bf\u30c3\u30af\u304b\u3089\u8981\u7d20\u3092\u30dd\u30c3\u30d7 */\nint pop = stack.pop();\n\n/* \u30b9\u30bf\u30c3\u30af\u306e\u9577\u3055\u3092\u53d6\u5f97 */\nint size = stack.size();\n\n/* \u30b9\u30bf\u30c3\u30af\u304c\u7a7a\u304b\u3069\u3046\u304b\u30c1\u30a7\u30c3\u30af */\nboolean isEmpty = stack.isEmpty();\n</code></pre> stack.cs<pre><code>/* \u30b9\u30bf\u30c3\u30af\u3092\u521d\u671f\u5316 */\nStack&lt;int&gt; stack = new();\n\n/* \u8981\u7d20\u3092\u30b9\u30bf\u30c3\u30af\u306b\u30d7\u30c3\u30b7\u30e5 */\nstack.Push(1);\nstack.Push(3);\nstack.Push(2);\nstack.Push(5);\nstack.Push(4);\n\n/* \u30b9\u30bf\u30c3\u30af\u306e\u30c8\u30c3\u30d7\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\nint peek = stack.Peek();\n\n/* \u30b9\u30bf\u30c3\u30af\u304b\u3089\u8981\u7d20\u3092\u30dd\u30c3\u30d7 */\nint pop = stack.Pop();\n\n/* \u30b9\u30bf\u30c3\u30af\u306e\u9577\u3055\u3092\u53d6\u5f97 */\nint size = stack.Count;\n\n/* \u30b9\u30bf\u30c3\u30af\u304c\u7a7a\u304b\u3069\u3046\u304b\u30c1\u30a7\u30c3\u30af */\nbool isEmpty = stack.Count == 0;\n</code></pre> stack_test.go<pre><code>/* \u30b9\u30bf\u30c3\u30af\u3092\u521d\u671f\u5316 */\n// Go\u3067\u306f\u3001Slice\u3092\u30b9\u30bf\u30c3\u30af\u3068\u3057\u3066\u4f7f\u7528\u3059\u308b\u3053\u3068\u304c\u63a8\u5968\u3055\u308c\u307e\u3059\nvar stack []int\n\n/* \u8981\u7d20\u3092\u30b9\u30bf\u30c3\u30af\u306b\u30d7\u30c3\u30b7\u30e5 */\nstack = append(stack, 1)\nstack = append(stack, 3)\nstack = append(stack, 2)\nstack = append(stack, 5)\nstack = append(stack, 4)\n\n/* \u30b9\u30bf\u30c3\u30af\u306e\u30c8\u30c3\u30d7\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\npeek := stack[len(stack)-1]\n\n/* \u30b9\u30bf\u30c3\u30af\u304b\u3089\u8981\u7d20\u3092\u30dd\u30c3\u30d7 */\npop := stack[len(stack)-1]\nstack = stack[:len(stack)-1]\n\n/* \u30b9\u30bf\u30c3\u30af\u306e\u9577\u3055\u3092\u53d6\u5f97 */\nsize := len(stack)\n\n/* \u30b9\u30bf\u30c3\u30af\u304c\u7a7a\u304b\u3069\u3046\u304b\u30c1\u30a7\u30c3\u30af */\nisEmpty := len(stack) == 0\n</code></pre> stack.swift<pre><code>/* \u30b9\u30bf\u30c3\u30af\u3092\u521d\u671f\u5316 */\n// Swift\u306b\u306f\u7d44\u307f\u8fbc\u307f\u306e\u30b9\u30bf\u30c3\u30af\u30af\u30e9\u30b9\u304c\u306a\u3044\u305f\u3081\u3001Array\u3092\u30b9\u30bf\u30c3\u30af\u3068\u3057\u3066\u4f7f\u7528\nvar stack: [Int] = []\n\n/* \u8981\u7d20\u3092\u30b9\u30bf\u30c3\u30af\u306b\u30d7\u30c3\u30b7\u30e5 */\nstack.append(1)\nstack.append(3)\nstack.append(2)\nstack.append(5)\nstack.append(4)\n\n/* \u30b9\u30bf\u30c3\u30af\u306e\u30c8\u30c3\u30d7\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\nlet peek = stack.last!\n\n/* \u30b9\u30bf\u30c3\u30af\u304b\u3089\u8981\u7d20\u3092\u30dd\u30c3\u30d7 */\nlet pop = stack.removeLast()\n\n/* \u30b9\u30bf\u30c3\u30af\u306e\u9577\u3055\u3092\u53d6\u5f97 */\nlet size = stack.count\n\n/* \u30b9\u30bf\u30c3\u30af\u304c\u7a7a\u304b\u3069\u3046\u304b\u30c1\u30a7\u30c3\u30af */\nlet isEmpty = stack.isEmpty\n</code></pre> stack.js<pre><code>/* \u30b9\u30bf\u30c3\u30af\u3092\u521d\u671f\u5316 */\n// JavaScript\u306b\u306f\u7d44\u307f\u8fbc\u307f\u306e\u30b9\u30bf\u30c3\u30af\u30af\u30e9\u30b9\u304c\u306a\u3044\u305f\u3081\u3001Array\u3092\u30b9\u30bf\u30c3\u30af\u3068\u3057\u3066\u4f7f\u7528\nconst stack = [];\n\n/* \u8981\u7d20\u3092\u30b9\u30bf\u30c3\u30af\u306b\u30d7\u30c3\u30b7\u30e5 */\nstack.push(1);\nstack.push(3);\nstack.push(2);\nstack.push(5);\nstack.push(4);\n\n/* \u30b9\u30bf\u30c3\u30af\u306e\u30c8\u30c3\u30d7\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\nconst peek = stack[stack.length-1];\n\n/* \u30b9\u30bf\u30c3\u30af\u304b\u3089\u8981\u7d20\u3092\u30dd\u30c3\u30d7 */\nconst pop = stack.pop();\n\n/* \u30b9\u30bf\u30c3\u30af\u306e\u9577\u3055\u3092\u53d6\u5f97 */\nconst size = stack.length;\n\n/* \u30b9\u30bf\u30c3\u30af\u304c\u7a7a\u304b\u3069\u3046\u304b\u30c1\u30a7\u30c3\u30af */\nconst is_empty = stack.length === 0;\n</code></pre> stack.ts<pre><code>/* \u30b9\u30bf\u30c3\u30af\u3092\u521d\u671f\u5316 */\n// TypeScript\u306b\u306f\u7d44\u307f\u8fbc\u307f\u306e\u30b9\u30bf\u30c3\u30af\u30af\u30e9\u30b9\u304c\u306a\u3044\u305f\u3081\u3001Array\u3092\u30b9\u30bf\u30c3\u30af\u3068\u3057\u3066\u4f7f\u7528\nconst stack: number[] = [];\n\n/* \u8981\u7d20\u3092\u30b9\u30bf\u30c3\u30af\u306b\u30d7\u30c3\u30b7\u30e5 */\nstack.push(1);\nstack.push(3);\nstack.push(2);\nstack.push(5);\nstack.push(4);\n\n/* \u30b9\u30bf\u30c3\u30af\u306e\u30c8\u30c3\u30d7\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\nconst peek = stack[stack.length - 1];\n\n/* \u30b9\u30bf\u30c3\u30af\u304b\u3089\u8981\u7d20\u3092\u30dd\u30c3\u30d7 */\nconst pop = stack.pop();\n\n/* \u30b9\u30bf\u30c3\u30af\u306e\u9577\u3055\u3092\u53d6\u5f97 */\nconst size = stack.length;\n\n/* \u30b9\u30bf\u30c3\u30af\u304c\u7a7a\u304b\u3069\u3046\u304b\u30c1\u30a7\u30c3\u30af */\nconst is_empty = stack.length === 0;\n</code></pre> stack.dart<pre><code>/* \u30b9\u30bf\u30c3\u30af\u3092\u521d\u671f\u5316 */\n// Dart\u306b\u306f\u7d44\u307f\u8fbc\u307f\u306e\u30b9\u30bf\u30c3\u30af\u30af\u30e9\u30b9\u304c\u306a\u3044\u305f\u3081\u3001List\u3092\u30b9\u30bf\u30c3\u30af\u3068\u3057\u3066\u4f7f\u7528\nList&lt;int&gt; stack = [];\n\n/* \u8981\u7d20\u3092\u30b9\u30bf\u30c3\u30af\u306b\u30d7\u30c3\u30b7\u30e5 */\nstack.add(1);\nstack.add(3);\nstack.add(2);\nstack.add(5);\nstack.add(4);\n\n/* \u30b9\u30bf\u30c3\u30af\u306e\u30c8\u30c3\u30d7\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\nint peek = stack.last;\n\n/* \u30b9\u30bf\u30c3\u30af\u304b\u3089\u8981\u7d20\u3092\u30dd\u30c3\u30d7 */\nint pop = stack.removeLast();\n\n/* \u30b9\u30bf\u30c3\u30af\u306e\u9577\u3055\u3092\u53d6\u5f97 */\nint size = stack.length;\n\n/* \u30b9\u30bf\u30c3\u30af\u304c\u7a7a\u304b\u3069\u3046\u304b\u30c1\u30a7\u30c3\u30af */\nbool isEmpty = stack.isEmpty;\n</code></pre> stack.rs<pre><code>/* \u30b9\u30bf\u30c3\u30af\u3092\u521d\u671f\u5316 */\n// Vec\u3092\u30b9\u30bf\u30c3\u30af\u3068\u3057\u3066\u4f7f\u7528\nlet mut stack: Vec&lt;i32&gt; = Vec::new();\n\n/* \u8981\u7d20\u3092\u30b9\u30bf\u30c3\u30af\u306b\u30d7\u30c3\u30b7\u30e5 */\nstack.push(1);\nstack.push(3);\nstack.push(2);\nstack.push(5);\nstack.push(4);\n\n/* \u30b9\u30bf\u30c3\u30af\u306e\u30c8\u30c3\u30d7\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\nlet top = stack.last().unwrap();\n\n/* \u30b9\u30bf\u30c3\u30af\u304b\u3089\u8981\u7d20\u3092\u30dd\u30c3\u30d7 */\nlet pop = stack.pop().unwrap();\n\n/* \u30b9\u30bf\u30c3\u30af\u306e\u9577\u3055\u3092\u53d6\u5f97 */\nlet size = stack.len();\n\n/* \u30b9\u30bf\u30c3\u30af\u304c\u7a7a\u304b\u3069\u3046\u304b\u30c1\u30a7\u30c3\u30af */\nlet is_empty = stack.is_empty();\n</code></pre> stack.c<pre><code>// C\u306f\u7d44\u307f\u8fbc\u307f\u306e\u30b9\u30bf\u30c3\u30af\u3092\u63d0\u4f9b\u3057\u3066\u3044\u307e\u305b\u3093\n</code></pre> stack.kt<pre><code>\n</code></pre> stack.zig<pre><code>\n</code></pre>"},{"location":"chapter_stack_and_queue/stack/#512","title":"5.1.2 \u00a0 \u30b9\u30bf\u30c3\u30af\u306e\u5b9f\u88c5","text":"<p>\u30b9\u30bf\u30c3\u30af\u304c\u3069\u306e\u3088\u3046\u306b\u52d5\u4f5c\u3059\u308b\u304b\u3092\u3088\u308a\u6df1\u304f\u7406\u89e3\u3059\u308b\u305f\u3081\u306b\u3001\u81ea\u5206\u3067\u30b9\u30bf\u30c3\u30af\u30af\u30e9\u30b9\u3092\u5b9f\u88c5\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002</p> <p>\u30b9\u30bf\u30c3\u30af\u306f\u5f8c\u5165\u5148\u51fa\u306e\u539f\u5247\u306b\u5f93\u3046\u305f\u3081\u3001\u30b9\u30bf\u30c3\u30af\u306e\u30c8\u30c3\u30d7\u3067\u306e\u307f\u8981\u7d20\u3092\u8ffd\u52a0\u307e\u305f\u306f\u524a\u9664\u3067\u304d\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u914d\u5217\u3068\u9023\u7d50\u30ea\u30b9\u30c8\u306e\u4e21\u65b9\u306f\u4efb\u610f\u306e\u4f4d\u7f6e\u3067\u8981\u7d20\u3092\u8ffd\u52a0\u30fb\u524a\u9664\u3067\u304d\u308b\u305f\u3081\u3001\u30b9\u30bf\u30c3\u30af\u306f\u5236\u9650\u3055\u308c\u305f\u914d\u5217\u307e\u305f\u306f\u9023\u7d50\u30ea\u30b9\u30c8\u3068\u898b\u306a\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u8a00\u3044\u63db\u3048\u308c\u3070\u3001\u914d\u5217\u3084\u9023\u7d50\u30ea\u30b9\u30c8\u306e\u7279\u5b9a\u306e\u7121\u95a2\u4fc2\u306a\u64cd\u4f5c\u3092\u300c\u906e\u853d\u300d\u3057\u3066\u3001\u5916\u90e8\u306e\u52d5\u4f5c\u3092\u30b9\u30bf\u30c3\u30af\u306e\u7279\u6027\u306b\u5408\u308f\u305b\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002</p>"},{"location":"chapter_stack_and_queue/stack/#1","title":"1. \u00a0 \u9023\u7d50\u30ea\u30b9\u30c8\u30d9\u30fc\u30b9\u306e\u5b9f\u88c5","text":"<p>\u9023\u7d50\u30ea\u30b9\u30c8\u3092\u4f7f\u7528\u3057\u3066\u30b9\u30bf\u30c3\u30af\u3092\u5b9f\u88c5\u3059\u308b\u5834\u5408\u3001\u30ea\u30b9\u30c8\u306e\u30d8\u30c3\u30c9\u30ce\u30fc\u30c9\u3092\u30b9\u30bf\u30c3\u30af\u306e\u30c8\u30c3\u30d7\u3001\u30c6\u30fc\u30eb\u30ce\u30fc\u30c9\u3092\u30b9\u30bf\u30c3\u30af\u306e\u30dc\u30c8\u30e0\u3068\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002</p> <p>\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u30d7\u30c3\u30b7\u30e5\u64cd\u4f5c\u3067\u306f\u3001\u5358\u306b\u9023\u7d50\u30ea\u30b9\u30c8\u306e\u30d8\u30c3\u30c9\u306b\u8981\u7d20\u3092\u633f\u5165\u3057\u307e\u3059\u3002\u3053\u306e\u30ce\u30fc\u30c9\u633f\u5165\u65b9\u6cd5\u306f\u300c\u30d8\u30c3\u30c9\u633f\u5165\u300d\u3068\u3057\u3066\u77e5\u3089\u308c\u3066\u3044\u307e\u3059\u3002\u30dd\u30c3\u30d7\u64cd\u4f5c\u3067\u306f\u3001\u30ea\u30b9\u30c8\u304b\u3089\u30d8\u30c3\u30c9\u30ce\u30fc\u30c9\u3092\u524a\u9664\u3059\u308b\u3060\u3051\u3067\u3059\u3002</p> LinkedListStackpush()pop() <p></p> <p></p> <p></p> <p> \u56f3 5-2 \u00a0 \u9023\u7d50\u30ea\u30b9\u30c8\u306b\u3088\u308b\u30b9\u30bf\u30c3\u30af\u5b9f\u88c5\u306e\u30d7\u30c3\u30b7\u30e5\u3068\u30dd\u30c3\u30d7\u64cd\u4f5c </p> <p>\u4ee5\u4e0b\u306f\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u306b\u57fa\u3065\u304f\u30b9\u30bf\u30c3\u30af\u5b9f\u88c5\u306e\u30b5\u30f3\u30d7\u30eb\u30b3\u30fc\u30c9\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig linkedlist_stack.py<pre><code>class LinkedListStack:\n    \"\"\"\u9023\u7d50\u30ea\u30b9\u30c8\u30d9\u30fc\u30b9\u306e\u30b9\u30bf\u30c3\u30af\u30af\u30e9\u30b9\"\"\"\n\n    def __init__(self):\n        \"\"\"\u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf\"\"\"\n        self._peek: ListNode | None = None\n        self._size: int = 0\n\n    def size(self) -&gt; int:\n        \"\"\"\u30b9\u30bf\u30c3\u30af\u306e\u9577\u3055\u3092\u53d6\u5f97\"\"\"\n        return self._size\n\n    def is_empty(self) -&gt; bool:\n        \"\"\"\u30b9\u30bf\u30c3\u30af\u304c\u7a7a\u304b\u3069\u3046\u304b\u3092\u5224\u5b9a\"\"\"\n        return self._size == 0\n\n    def push(self, val: int):\n        \"\"\"\u30d7\u30c3\u30b7\u30e5\"\"\"\n        node = ListNode(val)\n        node.next = self._peek\n        self._peek = node\n        self._size += 1\n\n    def pop(self) -&gt; int:\n        \"\"\"\u30dd\u30c3\u30d7\"\"\"\n        num = self.peek()\n        self._peek = self._peek.next\n        self._size -= 1\n        return num\n\n    def peek(self) -&gt; int:\n        \"\"\"\u30b9\u30bf\u30c3\u30af\u30c8\u30c3\u30d7\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9\"\"\"\n        if self.is_empty():\n            raise IndexError(\"Stack is empty\")\n        return self._peek.val\n\n    def to_list(self) -&gt; list[int]:\n        \"\"\"\u51fa\u529b\u7528\u306e\u30ea\u30b9\u30c8\u306b\u5909\u63db\"\"\"\n        arr = []\n        node = self._peek\n        while node:\n            arr.append(node.val)\n            node = node.next\n        arr.reverse()\n        return arr\n</code></pre> linkedlist_stack.cpp<pre><code>/* \u9023\u7d50\u30ea\u30b9\u30c8\u306b\u57fa\u3065\u304f\u30b9\u30bf\u30c3\u30af\u30af\u30e9\u30b9 */\nclass LinkedListStack {\n  private:\n    ListNode *stackTop; // \u5148\u982d\u30ce\u30fc\u30c9\u3092\u30b9\u30bf\u30c3\u30af\u30c8\u30c3\u30d7\u3068\u3057\u3066\u4f7f\u7528\n    int stkSize;        // \u30b9\u30bf\u30c3\u30af\u306e\u9577\u3055\n\n  public:\n    LinkedListStack() {\n        stackTop = nullptr;\n        stkSize = 0;\n    }\n\n    ~LinkedListStack() {\n        // \u9023\u7d50\u30ea\u30b9\u30c8\u3092\u8d70\u67fb\u3001\u30ce\u30fc\u30c9\u3092\u524a\u9664\u3001\u30e1\u30e2\u30ea\u3092\u89e3\u653e\n        freeMemoryLinkedList(stackTop);\n    }\n\n    /* \u30b9\u30bf\u30c3\u30af\u306e\u9577\u3055\u3092\u53d6\u5f97 */\n    int size() {\n        return stkSize;\n    }\n\n    /* \u30b9\u30bf\u30c3\u30af\u304c\u7a7a\u304b\u3069\u3046\u304b\u3092\u5224\u5b9a */\n    bool isEmpty() {\n        return size() == 0;\n    }\n\n    /* \u30d7\u30c3\u30b7\u30e5 */\n    void push(int num) {\n        ListNode *node = new ListNode(num);\n        node-&gt;next = stackTop;\n        stackTop = node;\n        stkSize++;\n    }\n\n    /* \u30dd\u30c3\u30d7 */\n    int pop() {\n        int num = top();\n        ListNode *tmp = stackTop;\n        stackTop = stackTop-&gt;next;\n        // \u30e1\u30e2\u30ea\u3092\u89e3\u653e\n        delete tmp;\n        stkSize--;\n        return num;\n    }\n\n    /* \u30b9\u30bf\u30c3\u30af\u30c8\u30c3\u30d7\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\n    int top() {\n        if (isEmpty())\n            throw out_of_range(\"Stack is empty\");\n        return stackTop-&gt;val;\n    }\n\n    /* \u30ea\u30b9\u30c8\u3092\u914d\u5217\u306b\u5909\u63db\u3057\u3066\u8fd4\u5374 */\n    vector&lt;int&gt; toVector() {\n        ListNode *node = stackTop;\n        vector&lt;int&gt; res(size());\n        for (int i = res.size() - 1; i &gt;= 0; i--) {\n            res[i] = node-&gt;val;\n            node = node-&gt;next;\n        }\n        return res;\n    }\n};\n</code></pre> linkedlist_stack.java<pre><code>/* \u9023\u7d50\u30ea\u30b9\u30c8\u306b\u57fa\u3065\u304f\u30b9\u30bf\u30c3\u30af\u30af\u30e9\u30b9 */\nclass LinkedListStack {\n    private ListNode stackPeek; // \u30d8\u30c3\u30c9\u30ce\u30fc\u30c9\u3092\u30b9\u30bf\u30c3\u30af\u30c8\u30c3\u30d7\u3068\u3057\u3066\u4f7f\u7528\n    private int stkSize = 0; // \u30b9\u30bf\u30c3\u30af\u306e\u9577\u3055\n\n    public LinkedListStack() {\n        stackPeek = null;\n    }\n\n    /* \u30b9\u30bf\u30c3\u30af\u306e\u9577\u3055\u3092\u53d6\u5f97 */\n    public int size() {\n        return stkSize;\n    }\n\n    /* \u30b9\u30bf\u30c3\u30af\u304c\u7a7a\u304b\u3069\u3046\u304b\u3092\u5224\u5b9a */\n    public boolean isEmpty() {\n        return size() == 0;\n    }\n\n    /* \u30d7\u30c3\u30b7\u30e5 */\n    public void push(int num) {\n        ListNode node = new ListNode(num);\n        node.next = stackPeek;\n        stackPeek = node;\n        stkSize++;\n    }\n\n    /* \u30dd\u30c3\u30d7 */\n    public int pop() {\n        int num = peek();\n        stackPeek = stackPeek.next;\n        stkSize--;\n        return num;\n    }\n\n    /* \u30b9\u30bf\u30c3\u30af\u30c8\u30c3\u30d7\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\n    public int peek() {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        return stackPeek.val;\n    }\n\n    /* List \u3092 Array \u306b\u5909\u63db\u3057\u3066\u8fd4\u3059 */\n    public int[] toArray() {\n        ListNode node = stackPeek;\n        int[] res = new int[size()];\n        for (int i = res.length - 1; i &gt;= 0; i--) {\n            res[i] = node.val;\n            node = node.next;\n        }\n        return res;\n    }\n}\n</code></pre> linkedlist_stack.cs<pre><code>[class]{LinkedListStack}-[func]{}\n</code></pre> linkedlist_stack.go<pre><code>[class]{linkedListStack}-[func]{}\n</code></pre> linkedlist_stack.swift<pre><code>[class]{LinkedListStack}-[func]{}\n</code></pre> linkedlist_stack.js<pre><code>[class]{LinkedListStack}-[func]{}\n</code></pre> linkedlist_stack.ts<pre><code>[class]{LinkedListStack}-[func]{}\n</code></pre> linkedlist_stack.dart<pre><code>[class]{LinkedListStack}-[func]{}\n</code></pre> linkedlist_stack.rs<pre><code>[class]{LinkedListStack}-[func]{}\n</code></pre> linkedlist_stack.c<pre><code>[class]{LinkedListStack}-[func]{}\n</code></pre> linkedlist_stack.kt<pre><code>[class]{LinkedListStack}-[func]{}\n</code></pre> linkedlist_stack.rb<pre><code>[class]{LinkedListStack}-[func]{}\n</code></pre> linkedlist_stack.zig<pre><code>[class]{LinkedListStack}-[func]{}\n</code></pre>"},{"location":"chapter_stack_and_queue/stack/#2","title":"2. \u00a0 \u914d\u5217\u30d9\u30fc\u30b9\u306e\u5b9f\u88c5","text":"<p>\u914d\u5217\u3092\u4f7f\u7528\u3057\u3066\u30b9\u30bf\u30c3\u30af\u3092\u5b9f\u88c5\u3059\u308b\u5834\u5408\u3001\u914d\u5217\u306e\u672b\u5c3e\u3092\u30b9\u30bf\u30c3\u30af\u306e\u30c8\u30c3\u30d7\u3068\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u30d7\u30c3\u30b7\u30e5\u3068\u30dd\u30c3\u30d7\u64cd\u4f5c\u306f\u3001\u305d\u308c\u305e\u308c\u914d\u5217\u306e\u672b\u5c3e\u3067\u306e\u8981\u7d20\u306e\u8ffd\u52a0\u3068\u524a\u9664\u306b\u5bfe\u5fdc\u3057\u3001\u3069\u3061\u3089\u3082\u6642\u9593\u8a08\u7b97\u91cf\\(O(1)\\)\u3067\u3059\u3002</p> ArrayStackpush()pop() <p></p> <p></p> <p></p> <p> \u56f3 5-3 \u00a0 \u914d\u5217\u306b\u3088\u308b\u30b9\u30bf\u30c3\u30af\u5b9f\u88c5\u306e\u30d7\u30c3\u30b7\u30e5\u3068\u30dd\u30c3\u30d7\u64cd\u4f5c </p> <p>\u30b9\u30bf\u30c3\u30af\u306b\u30d7\u30c3\u30b7\u30e5\u3055\u308c\u308b\u8981\u7d20\u304c\u7d99\u7d9a\u7684\u306b\u5897\u52a0\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308b\u305f\u3081\u3001\u52d5\u7684\u914d\u5217\u3092\u4f7f\u7528\u3067\u304d\u3001\u914d\u5217\u62e1\u5f35\u3092\u81ea\u5206\u3067\u51e6\u7406\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u305b\u3093\u3002\u4ee5\u4e0b\u306f\u30b5\u30f3\u30d7\u30eb\u30b3\u30fc\u30c9\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig array_stack.py<pre><code>class ArrayStack:\n    \"\"\"\u914d\u5217\u30d9\u30fc\u30b9\u306e\u30b9\u30bf\u30c3\u30af\u30af\u30e9\u30b9\"\"\"\n\n    def __init__(self):\n        \"\"\"\u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf\"\"\"\n        self._stack: list[int] = []\n\n    def size(self) -&gt; int:\n        \"\"\"\u30b9\u30bf\u30c3\u30af\u306e\u9577\u3055\u3092\u53d6\u5f97\"\"\"\n        return len(self._stack)\n\n    def is_empty(self) -&gt; bool:\n        \"\"\"\u30b9\u30bf\u30c3\u30af\u304c\u7a7a\u304b\u3069\u3046\u304b\u3092\u5224\u5b9a\"\"\"\n        return self.size() == 0\n\n    def push(self, item: int):\n        \"\"\"\u30d7\u30c3\u30b7\u30e5\"\"\"\n        self._stack.append(item)\n\n    def pop(self) -&gt; int:\n        \"\"\"\u30dd\u30c3\u30d7\"\"\"\n        if self.is_empty():\n            raise IndexError(\"Stack is empty\")\n        return self._stack.pop()\n\n    def peek(self) -&gt; int:\n        \"\"\"\u30b9\u30bf\u30c3\u30af\u30c8\u30c3\u30d7\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9\"\"\"\n        if self.is_empty():\n            raise IndexError(\"Stack is empty\")\n        return self._stack[-1]\n\n    def to_list(self) -&gt; list[int]:\n        \"\"\"\u51fa\u529b\u7528\u306e\u914d\u5217\u3092\u8fd4\u3059\"\"\"\n        return self._stack\n</code></pre> array_stack.cpp<pre><code>/* \u914d\u5217\u306b\u57fa\u3065\u304f\u30b9\u30bf\u30c3\u30af\u30af\u30e9\u30b9 */\nclass ArrayStack {\n  private:\n    vector&lt;int&gt; stack;\n\n  public:\n    /* \u30b9\u30bf\u30c3\u30af\u306e\u9577\u3055\u3092\u53d6\u5f97 */\n    int size() {\n        return stack.size();\n    }\n\n    /* \u30b9\u30bf\u30c3\u30af\u304c\u7a7a\u304b\u3069\u3046\u304b\u3092\u5224\u5b9a */\n    bool isEmpty() {\n        return stack.size() == 0;\n    }\n\n    /* \u30d7\u30c3\u30b7\u30e5 */\n    void push(int num) {\n        stack.push_back(num);\n    }\n\n    /* \u30dd\u30c3\u30d7 */\n    int pop() {\n        int num = top();\n        stack.pop_back();\n        return num;\n    }\n\n    /* \u30b9\u30bf\u30c3\u30af\u30c8\u30c3\u30d7\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\n    int top() {\n        if (isEmpty())\n            throw out_of_range(\"Stack is empty\");\n        return stack.back();\n    }\n\n    /* Vector\u3092\u8fd4\u5374 */\n    vector&lt;int&gt; toVector() {\n        return stack;\n    }\n};\n</code></pre> array_stack.java<pre><code>/* \u914d\u5217\u306b\u57fa\u3065\u304f\u30b9\u30bf\u30c3\u30af\u30af\u30e9\u30b9 */\nclass ArrayStack {\n    private ArrayList&lt;Integer&gt; stack;\n\n    public ArrayStack() {\n        // \u30ea\u30b9\u30c8\uff08\u52d5\u7684\u914d\u5217\uff09\u3092\u521d\u671f\u5316\n        stack = new ArrayList&lt;&gt;();\n    }\n\n    /* \u30b9\u30bf\u30c3\u30af\u306e\u9577\u3055\u3092\u53d6\u5f97 */\n    public int size() {\n        return stack.size();\n    }\n\n    /* \u30b9\u30bf\u30c3\u30af\u304c\u7a7a\u304b\u3069\u3046\u304b\u3092\u5224\u5b9a */\n    public boolean isEmpty() {\n        return size() == 0;\n    }\n\n    /* \u30d7\u30c3\u30b7\u30e5 */\n    public void push(int num) {\n        stack.add(num);\n    }\n\n    /* \u30dd\u30c3\u30d7 */\n    public int pop() {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        return stack.remove(size() - 1);\n    }\n\n    /* \u30b9\u30bf\u30c3\u30af\u30c8\u30c3\u30d7\u8981\u7d20\u306b\u30a2\u30af\u30bb\u30b9 */\n    public int peek() {\n        if (isEmpty())\n            throw new IndexOutOfBoundsException();\n        return stack.get(size() - 1);\n    }\n\n    /* List \u3092 Array \u306b\u5909\u63db\u3057\u3066\u8fd4\u3059 */\n    public Object[] toArray() {\n        return stack.toArray();\n    }\n}\n</code></pre> array_stack.cs<pre><code>[class]{ArrayStack}-[func]{}\n</code></pre> array_stack.go<pre><code>[class]{arrayStack}-[func]{}\n</code></pre> array_stack.swift<pre><code>[class]{ArrayStack}-[func]{}\n</code></pre> array_stack.js<pre><code>[class]{ArrayStack}-[func]{}\n</code></pre> array_stack.ts<pre><code>[class]{ArrayStack}-[func]{}\n</code></pre> array_stack.dart<pre><code>[class]{ArrayStack}-[func]{}\n</code></pre> array_stack.rs<pre><code>[class]{ArrayStack}-[func]{}\n</code></pre> array_stack.c<pre><code>[class]{ArrayStack}-[func]{}\n</code></pre> array_stack.kt<pre><code>[class]{ArrayStack}-[func]{}\n</code></pre> array_stack.rb<pre><code>[class]{ArrayStack}-[func]{}\n</code></pre> array_stack.zig<pre><code>[class]{ArrayStack}-[func]{}\n</code></pre>"},{"location":"chapter_stack_and_queue/stack/#513-2","title":"5.1.3 \u00a0 2\u3064\u306e\u5b9f\u88c5\u306e\u6bd4\u8f03","text":"<p>\u30b5\u30dd\u30fc\u30c8\u3055\u308c\u308b\u64cd\u4f5c</p> <p>\u4e21\u65b9\u306e\u5b9f\u88c5\u306f\u3001\u30b9\u30bf\u30c3\u30af\u3067\u5b9a\u7fa9\u3055\u308c\u305f\u3059\u3079\u3066\u306e\u64cd\u4f5c\u3092\u30b5\u30dd\u30fc\u30c8\u3057\u307e\u3059\u3002\u914d\u5217\u5b9f\u88c5\u306f\u3055\u3089\u306b\u30e9\u30f3\u30c0\u30e0\u30a2\u30af\u30bb\u30b9\u3092\u30b5\u30dd\u30fc\u30c8\u3057\u307e\u3059\u304c\u3001\u3053\u308c\u306f\u30b9\u30bf\u30c3\u30af\u5b9a\u7fa9\u306e\u7bc4\u56f2\u3092\u8d85\u3048\u3066\u304a\u308a\u3001\u4e00\u822c\u7684\u306b\u306f\u4f7f\u7528\u3055\u308c\u307e\u305b\u3093\u3002</p> <p>\u6642\u9593\u52b9\u7387</p> <p>\u914d\u5217\u30d9\u30fc\u30b9\u306e\u5b9f\u88c5\u3067\u306f\u3001\u30d7\u30c3\u30b7\u30e5\u3068\u30dd\u30c3\u30d7\u64cd\u4f5c\u306e\u4e21\u65b9\u304c\u4e8b\u524d\u306b\u5272\u308a\u5f53\u3066\u3089\u308c\u305f\u9023\u7d9a\u30e1\u30e2\u30ea\u3067\u767a\u751f\u3057\u3001\u826f\u597d\u306a\u30ad\u30e3\u30c3\u30b7\u30e5\u5c40\u6240\u6027\u304c\u3042\u308b\u305f\u3081\u52b9\u7387\u304c\u9ad8\u304f\u306a\u308a\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u30d7\u30c3\u30b7\u30e5\u64cd\u4f5c\u304c\u914d\u5217\u5bb9\u91cf\u3092\u8d85\u3048\u308b\u5834\u5408\u3001\u30ea\u30b5\u30a4\u30ba\u30e1\u30ab\u30cb\u30ba\u30e0\u304c\u30c8\u30ea\u30ac\u30fc\u3055\u308c\u3001\u305d\u306e\u30d7\u30c3\u30b7\u30e5\u64cd\u4f5c\u306e\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O(n)\\)\u306b\u306a\u308a\u307e\u3059\u3002</p> <p>\u9023\u7d50\u30ea\u30b9\u30c8\u5b9f\u88c5\u3067\u306f\u3001\u30ea\u30b9\u30c8\u62e1\u5f35\u306f\u975e\u5e38\u306b\u67d4\u8edf\u3067\u3001\u914d\u5217\u62e1\u5f35\u306e\u3088\u3046\u306a\u52b9\u7387\u4f4e\u4e0b\u306e\u554f\u984c\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u3057\u304b\u3057\u3001\u30d7\u30c3\u30b7\u30e5\u64cd\u4f5c\u306b\u306f\u30ce\u30fc\u30c9\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u306e\u521d\u671f\u5316\u3068\u30dd\u30a4\u30f3\u30bf\u306e\u5909\u66f4\u304c\u5fc5\u8981\u306a\u305f\u3081\u3001\u52b9\u7387\u306f\u6bd4\u8f03\u7684\u4f4e\u304f\u306a\u308a\u307e\u3059\u3002\u30d7\u30c3\u30b7\u30e5\u3055\u308c\u308b\u8981\u7d20\u304c\u3059\u3067\u306b\u30ce\u30fc\u30c9\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u306e\u5834\u5408\u3001\u521d\u671f\u5316\u30b9\u30c6\u30c3\u30d7\u3092\u30b9\u30ad\u30c3\u30d7\u3067\u304d\u3001\u52b9\u7387\u304c\u5411\u4e0a\u3057\u307e\u3059\u3002</p> <p>\u3057\u305f\u304c\u3063\u3066\u3001\u30d7\u30c3\u30b7\u30e5\u3068\u30dd\u30c3\u30d7\u64cd\u4f5c\u306e\u8981\u7d20\u304c<code>int</code>\u3084<code>double</code>\u306a\u3069\u306e\u57fa\u672c\u30c7\u30fc\u30bf\u578b\u306e\u5834\u5408\u3001\u4ee5\u4e0b\u306e\u7d50\u8ad6\u3092\u5c0e\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\uff1a</p> <ul> <li>\u914d\u5217\u30d9\u30fc\u30b9\u306e\u30b9\u30bf\u30c3\u30af\u5b9f\u88c5\u306f\u62e1\u5f35\u6642\u306b\u52b9\u7387\u304c\u4f4e\u4e0b\u3057\u307e\u3059\u304c\u3001\u62e1\u5f35\u306f\u4f4e\u983b\u5ea6\u64cd\u4f5c\u3067\u3042\u308b\u305f\u3081\u3001\u5e73\u5747\u52b9\u7387\u306f\u9ad8\u304f\u306a\u308a\u307e\u3059\u3002</li> <li>\u9023\u7d50\u30ea\u30b9\u30c8\u30d9\u30fc\u30b9\u306e\u30b9\u30bf\u30c3\u30af\u5b9f\u88c5\u306f\u3088\u308a\u5b89\u5b9a\u3057\u305f\u52b9\u7387\u30d1\u30d5\u30a9\u30fc\u30de\u30f3\u30b9\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002</li> </ul> <p>\u7a7a\u9593\u52b9\u7387</p> <p>\u30ea\u30b9\u30c8\u3092\u521d\u671f\u5316\u3059\u308b\u969b\u3001\u30b7\u30b9\u30c6\u30e0\u306f\u300c\u521d\u671f\u5bb9\u91cf\u300d\u3092\u5272\u308a\u5f53\u3066\u307e\u3059\u304c\u3001\u3053\u308c\u306f\u5b9f\u969b\u306e\u5fc5\u8981\u91cf\u3092\u8d85\u3048\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002\u3055\u3089\u306b\u3001\u62e1\u5f35\u30e1\u30ab\u30cb\u30ba\u30e0\u306f\u901a\u5e38\u3001\u7279\u5b9a\u306e\u4fc2\u6570\uff082\u500d\u306a\u3069\uff09\u3067\u5bb9\u91cf\u3092\u5897\u52a0\u3055\u305b\u3001\u3053\u308c\u3082\u5b9f\u969b\u306e\u5fc5\u8981\u91cf\u3092\u8d85\u3048\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u914d\u5217\u30d9\u30fc\u30b9\u306e\u30b9\u30bf\u30c3\u30af\u306f\u4e00\u90e8\u306e\u7a7a\u9593\u3092\u7121\u99c4\u306b\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002</p> <p>\u3057\u304b\u3057\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u30ce\u30fc\u30c9\u306f\u30dd\u30a4\u30f3\u30bf\u3092\u683c\u7d0d\u3059\u308b\u305f\u3081\u306e\u8ffd\u52a0\u7a7a\u9593\u304c\u5fc5\u8981\u306a\u305f\u3081\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u30ce\u30fc\u30c9\u304c\u5360\u6709\u3059\u308b\u7a7a\u9593\u306f\u6bd4\u8f03\u7684\u5927\u304d\u304f\u306a\u308a\u307e\u3059\u3002</p> <p>\u307e\u3068\u3081\u308b\u3068\u3001\u3069\u3061\u3089\u306e\u5b9f\u88c5\u304c\u3088\u308a\u30e1\u30e2\u30ea\u52b9\u7387\u7684\u304b\u3092\u5358\u7d14\u306b\u5224\u65ad\u3059\u308b\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093\u3002\u7279\u5b9a\u306e\u72b6\u6cc1\u306b\u57fa\u3065\u304f\u5206\u6790\u304c\u5fc5\u8981\u3067\u3059\u3002</p>"},{"location":"chapter_stack_and_queue/stack/#514","title":"5.1.4 \u00a0 \u30b9\u30bf\u30c3\u30af\u306e\u5178\u578b\u7684\u306a\u5fdc\u7528","text":"<ul> <li>\u30d6\u30e9\u30a6\u30b6\u306e\u623b\u308b\u3068\u9032\u3080\u3001\u30bd\u30d5\u30c8\u30a6\u30a7\u30a2\u306e\u5143\u306b\u623b\u3059\u3068\u3084\u308a\u76f4\u3057\u3002\u65b0\u3057\u3044Web\u30da\u30fc\u30b8\u3092\u958b\u304f\u305f\u3073\u306b\u3001\u30d6\u30e9\u30a6\u30b6\u306f\u524d\u306e\u30da\u30fc\u30b8\u3092\u30b9\u30bf\u30c3\u30af\u306b\u30d7\u30c3\u30b7\u30e5\u3057\u3001\u623b\u308b\u64cd\u4f5c\uff08\u672c\u8cea\u7684\u306b\u306f\u30dd\u30c3\u30d7\u64cd\u4f5c\uff09\u3092\u901a\u3058\u3066\u524d\u306e\u30da\u30fc\u30b8\u306b\u623b\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u623b\u308b\u3068\u9032\u3080\u306e\u4e21\u65b9\u3092\u30b5\u30dd\u30fc\u30c8\u3059\u308b\u306b\u306f\u30012\u3064\u306e\u30b9\u30bf\u30c3\u30af\u304c\u9023\u643a\u3057\u3066\u52d5\u4f5c\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002</li> <li>\u30d7\u30ed\u30b0\u30e9\u30e0\u306e\u30e1\u30e2\u30ea\u7ba1\u7406\u3002\u95a2\u6570\u304c\u547c\u3073\u51fa\u3055\u308c\u308b\u305f\u3073\u306b\u3001\u30b7\u30b9\u30c6\u30e0\u306f\u30b9\u30bf\u30c3\u30af\u306e\u30c8\u30c3\u30d7\u306b\u30b9\u30bf\u30c3\u30af\u30d5\u30ec\u30fc\u30e0\u3092\u8ffd\u52a0\u3057\u3066\u95a2\u6570\u306e\u30b3\u30f3\u30c6\u30ad\u30b9\u30c8\u60c5\u5831\u3092\u8a18\u9332\u3057\u307e\u3059\u3002\u518d\u5e30\u95a2\u6570\u3067\u306f\u3001\u4e0b\u65b9\u5411\u306e\u518d\u5e30\u30d5\u30a7\u30fc\u30ba\u306f\u30b9\u30bf\u30c3\u30af\u3078\u306e\u30d7\u30c3\u30b7\u30e5\u3092\u7d9a\u3051\u3001\u4e0a\u65b9\u5411\u306e\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30ad\u30f3\u30b0\u30d5\u30a7\u30fc\u30ba\u306f\u30b9\u30bf\u30c3\u30af\u304b\u3089\u306e\u30dd\u30c3\u30d7\u3092\u7d9a\u3051\u307e\u3059\u3002</li> </ul>"},{"location":"chapter_stack_and_queue/summary/","title":"5.4 \u00a0 \u307e\u3068\u3081","text":""},{"location":"chapter_stack_and_queue/summary/#1","title":"1. \u00a0 \u91cd\u8981\u306a\u30dd\u30a4\u30f3\u30c8","text":"<ul> <li>\u30b9\u30bf\u30c3\u30af\u306f\u5f8c\u5165\u308c\u5148\u51fa\u3057\uff08LIFO\uff09\u306e\u539f\u5247\u306b\u5f93\u3046\u30c7\u30fc\u30bf\u69cb\u9020\u3067\u3001\u914d\u5217\u307e\u305f\u306f\u9023\u7d50\u30ea\u30b9\u30c8\u3092\u4f7f\u3063\u3066\u5b9f\u88c5\u3067\u304d\u307e\u3059\u3002</li> <li>\u6642\u9593\u52b9\u7387\u306e\u89b3\u70b9\u3067\u306f\u3001\u30b9\u30bf\u30c3\u30af\u306e\u914d\u5217\u5b9f\u88c5\u306e\u65b9\u304c\u5e73\u5747\u7684\u306a\u52b9\u7387\u304c\u9ad8\u3044\u3067\u3059\u3002\u305f\u3060\u3057\u3001\u62e1\u5f35\u6642\u306b\u306f\u5358\u4e00\u306e\u30d7\u30c3\u30b7\u30e5\u64cd\u4f5c\u306e\u6642\u9593\u8a08\u7b97\u91cf\u304c\\(O(n)\\)\u306b\u60aa\u5316\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002\u5bfe\u7167\u7684\u306b\u3001\u30b9\u30bf\u30c3\u30af\u306e\u9023\u7d50\u30ea\u30b9\u30c8\u5b9f\u88c5\u306f\u3088\u308a\u5b89\u5b9a\u3057\u305f\u52b9\u7387\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002</li> <li>\u7a7a\u9593\u52b9\u7387\u306b\u95a2\u3057\u3066\u306f\u3001\u30b9\u30bf\u30c3\u30af\u306e\u914d\u5217\u5b9f\u88c5\u306f\u4e00\u5b9a\u7a0b\u5ea6\u306e\u7a7a\u9593\u306e\u7121\u99c4\u306b\u3064\u306a\u304c\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002\u305f\u3060\u3057\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u306e\u30ce\u30fc\u30c9\u304c\u5360\u6709\u3059\u308b\u30e1\u30e2\u30ea\u7a7a\u9593\u306f\u4e00\u822c\u7684\u306b\u914d\u5217\u306e\u8981\u7d20\u3088\u308a\u3082\u5927\u304d\u3044\u3053\u3068\u306b\u6ce8\u610f\u3059\u308b\u3053\u3068\u304c\u91cd\u8981\u3067\u3059\u3002</li> <li>\u30ad\u30e5\u30fc\u306f\u5148\u5165\u308c\u5148\u51fa\u3057\uff08FIFO\uff09\u306e\u539f\u5247\u306b\u5f93\u3046\u30c7\u30fc\u30bf\u69cb\u9020\u3067\u3001\u540c\u69d8\u306b\u914d\u5217\u307e\u305f\u306f\u9023\u7d50\u30ea\u30b9\u30c8\u3092\u4f7f\u3063\u3066\u5b9f\u88c5\u3067\u304d\u307e\u3059\u3002\u30ad\u30e5\u30fc\u306e\u6642\u9593\u3068\u7a7a\u9593\u52b9\u7387\u306b\u95a2\u3059\u308b\u7d50\u8ad6\u306f\u3001\u30b9\u30bf\u30c3\u30af\u3068\u4f3c\u3066\u3044\u307e\u3059\u3002</li> <li>\u4e21\u7aef\u30ad\u30e5\u30fc\uff08deque\uff09\u306f\u3088\u308a\u67d4\u8edf\u306a\u30ad\u30e5\u30fc\u306e\u7a2e\u985e\u3067\u3001\u4e21\u7aef\u3067\u306e\u8981\u7d20\u306e\u8ffd\u52a0\u3068\u524a\u9664\u3092\u53ef\u80fd\u306b\u3057\u307e\u3059\u3002</li> </ul>"},{"location":"chapter_stack_and_queue/summary/#2-q-a","title":"2. \u00a0 Q &amp; A","text":"<p>Q: \u30d6\u30e9\u30a6\u30b6\u306e\u9032\u3080\u30fb\u623b\u308b\u6a5f\u80fd\u306f\u53cc\u65b9\u5411\u9023\u7d50\u30ea\u30b9\u30c8\u3067\u5b9f\u88c5\u3055\u308c\u3066\u3044\u308b\u306e\u3067\u3059\u304b\uff1f</p> <p>\u30d6\u30e9\u30a6\u30b6\u306e\u9032\u3080\u30fb\u623b\u308b\u30ca\u30d3\u30b2\u30fc\u30b7\u30e7\u30f3\u306f\u672c\u8cea\u7684\u306b\u300c\u30b9\u30bf\u30c3\u30af\u300d\u6982\u5ff5\u306e\u73fe\u308c\u3067\u3059\u3002\u30e6\u30fc\u30b6\u30fc\u304c\u65b0\u3057\u3044\u30da\u30fc\u30b8\u3092\u8a2a\u554f\u3059\u308b\u3068\u3001\u305d\u306e\u30da\u30fc\u30b8\u304c\u30b9\u30bf\u30c3\u30af\u306e\u5148\u982d\u306b\u8ffd\u52a0\u3055\u308c\u307e\u3059\u3002\u623b\u308b\u30dc\u30bf\u30f3\u3092\u30af\u30ea\u30c3\u30af\u3059\u308b\u3068\u3001\u30da\u30fc\u30b8\u304c\u30b9\u30bf\u30c3\u30af\u306e\u5148\u982d\u304b\u3089\u30dd\u30c3\u30d7\u3055\u308c\u307e\u3059\u3002\u4e21\u7aef\u30ad\u30e5\u30fc\uff08deque\uff09\u306f\u3001\u300c\u4e21\u7aef\u30ad\u30e5\u30fc\u300d\u306e\u7ae0\u3067\u8ff0\u3079\u305f\u3088\u3046\u306b\u3001\u3044\u304f\u3064\u304b\u306e\u8ffd\u52a0\u64cd\u4f5c\u3092\u4fbf\u5229\u306b\u5b9f\u88c5\u3067\u304d\u307e\u3059\u3002</p> <p>Q: \u30b9\u30bf\u30c3\u30af\u304b\u3089\u30dd\u30c3\u30d7\u3057\u305f\u5f8c\u3001\u30dd\u30c3\u30d7\u3055\u308c\u305f\u30ce\u30fc\u30c9\u306e\u30e1\u30e2\u30ea\u3092\u89e3\u653e\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u304b\uff1f</p> <p>\u30dd\u30c3\u30d7\u3055\u308c\u305f\u30ce\u30fc\u30c9\u304c\u5f8c\u3067\u4f7f\u7528\u3055\u308c\u308b\u5834\u5408\u306f\u3001\u305d\u306e\u30e1\u30e2\u30ea\u3092\u89e3\u653e\u3059\u308b\u5fc5\u8981\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u81ea\u52d5\u30ac\u30d9\u30fc\u30b8\u30b3\u30ec\u30af\u30b7\u30e7\u30f3\u3092\u6301\u3064Java\u3084Python\u306a\u3069\u306e\u8a00\u8a9e\u3067\u306f\u3001\u624b\u52d5\u306e\u30e1\u30e2\u30ea\u89e3\u653e\u306f\u5fc5\u8981\u3042\u308a\u307e\u305b\u3093\u3002C\u3084C++\u3067\u306f\u3001\u624b\u52d5\u306e\u30e1\u30e2\u30ea\u89e3\u653e\u304c\u5fc5\u8981\u3067\u3059\u3002</p> <p>Q: \u4e21\u7aef\u30ad\u30e5\u30fc\u306f2\u3064\u306e\u30b9\u30bf\u30c3\u30af\u3092\u7d50\u5408\u3057\u305f\u3082\u306e\u306e\u3088\u3046\u306b\u898b\u3048\u307e\u3059\u3002\u305d\u306e\u7528\u9014\u306f\u4f55\u3067\u3059\u304b\uff1f</p> <p>\u4e21\u7aef\u30ad\u30e5\u30fc\u306f\u3001\u30b9\u30bf\u30c3\u30af\u3068\u30ad\u30e5\u30fc\u306e\u7d44\u307f\u5408\u308f\u305b\u307e\u305f\u306f2\u3064\u306e\u30b9\u30bf\u30c3\u30af\u3092\u7d50\u5408\u3057\u305f\u3082\u306e\u3067\u3001\u30b9\u30bf\u30c3\u30af\u3068\u30ad\u30e5\u30fc\u306e\u4e21\u65b9\u306e\u30ed\u30b8\u30c3\u30af\u3092\u793a\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u30b9\u30bf\u30c3\u30af\u3068\u30ad\u30e5\u30fc\u306e\u3059\u3079\u3066\u306e\u30a2\u30d7\u30ea\u30b1\u30fc\u30b7\u30e7\u30f3\u3092\u5b9f\u88c5\u3067\u304d\u3001\u3088\u308a\u5927\u304d\u306a\u67d4\u8edf\u6027\u3092\u63d0\u4f9b\u3057\u307e\u3059\u3002</p> <p>Q: \u5143\u306b\u623b\u3059\u3068\u3084\u308a\u76f4\u3057\u306f\u5177\u4f53\u7684\u306b\u3069\u306e\u3088\u3046\u306b\u5b9f\u88c5\u3055\u308c\u308b\u306e\u3067\u3059\u304b\uff1f</p> <p>\u5143\u306b\u623b\u3059\u3068\u3084\u308a\u76f4\u3057\u306e\u64cd\u4f5c\u306f2\u3064\u306e\u30b9\u30bf\u30c3\u30af\u3092\u4f7f\u3063\u3066\u5b9f\u88c5\u3055\u308c\u307e\u3059\uff1a\u5143\u306b\u623b\u3059\u7528\u306e\u30b9\u30bf\u30c3\u30af<code>A</code>\u3068\u3084\u308a\u76f4\u3057\u7528\u306e\u30b9\u30bf\u30c3\u30af<code>B</code>\u3067\u3059\u3002</p> <ol> <li>\u30e6\u30fc\u30b6\u30fc\u304c\u64cd\u4f5c\u3092\u5b9f\u884c\u3059\u308b\u305f\u3073\u306b\u3001\u305d\u308c\u304c\u30b9\u30bf\u30c3\u30af<code>A</code>\u306b\u30d7\u30c3\u30b7\u30e5\u3055\u308c\u3001\u30b9\u30bf\u30c3\u30af<code>B</code>\u304c\u30af\u30ea\u30a2\u3055\u308c\u307e\u3059\u3002</li> <li>\u30e6\u30fc\u30b6\u30fc\u304c\u300c\u5143\u306b\u623b\u3059\u300d\u3092\u5b9f\u884c\u3059\u308b\u3068\u3001\u6700\u65b0\u306e\u64cd\u4f5c\u304c\u30b9\u30bf\u30c3\u30af<code>A</code>\u304b\u3089\u30dd\u30c3\u30d7\u3055\u308c\u3001\u30b9\u30bf\u30c3\u30af<code>B</code>\u306b\u30d7\u30c3\u30b7\u30e5\u3055\u308c\u307e\u3059\u3002</li> <li>\u30e6\u30fc\u30b6\u30fc\u304c\u300c\u3084\u308a\u76f4\u3057\u300d\u3092\u5b9f\u884c\u3059\u308b\u3068\u3001\u6700\u65b0\u306e\u64cd\u4f5c\u304c\u30b9\u30bf\u30c3\u30af<code>B</code>\u304b\u3089\u30dd\u30c3\u30d7\u3055\u308c\u3001\u30b9\u30bf\u30c3\u30af<code>A</code>\u306b\u623b\u3055\u308c\u307e\u3059\u3002</li> </ol>"},{"location":"chapter_tree/","title":"\u7b2c 7 \u7ae0 \u00a0 \u6728","text":"<p>Abstract</p> <p>\u305d\u3073\u3048\u7acb\u3064\u6728\u306f\u6d3b\u529b\u306b\u6e80\u3061\u305f\u672c\u8cea\u3092\u653e\u3061\u3001\u6df1\u3044\u6839\u3068\u8c4a\u304b\u306a\u8449\u3092\u8a87\u308a\u306a\u304c\u3089\u3082\u3001\u305d\u306e\u679d\u306f\u758e\u3089\u306b\u6563\u3089\u3070\u308a\u3001\u5e7d\u7384\u306a\u96f0\u56f2\u6c17\u3092\u91b8\u3057\u51fa\u3057\u3066\u3044\u307e\u3059\u3002</p> <p>\u305d\u308c\u306f\u30c7\u30fc\u30bf\u306b\u304a\u3051\u308b\u5206\u5272\u7d71\u6cbb\u306e\u9bae\u3084\u304b\u306a\u5f62\u3092\u79c1\u305f\u3061\u306b\u793a\u3057\u3066\u3044\u307e\u3059\u3002</p>"},{"location":"chapter_tree/#_1","title":"\u7ae0\u306e\u5185\u5bb9","text":"<ul> <li>7.1 \u00a0 \u4e8c\u5206\u6728</li> <li>7.2 \u00a0 \u4e8c\u5206\u6728\u306e\u8d70\u67fb</li> <li>7.3 \u00a0 \u6728\u306e\u914d\u5217\u8868\u73fe</li> <li>7.4 \u00a0 \u4e8c\u5206\u63a2\u7d22\u6728</li> <li>7.5 \u00a0 AVL\u6728 *</li> <li>7.6 \u00a0 \u307e\u3068\u3081</li> </ul>"},{"location":"chapter_tree/array_representation_of_tree/","title":"7.3 \u00a0 \u4e8c\u5206\u6728\u306e\u914d\u5217\u8868\u73fe","text":"<p>\u9023\u7d50\u30ea\u30b9\u30c8\u8868\u73fe\u3067\u306f\u3001\u4e8c\u5206\u6728\u306e\u683c\u7d0d\u5358\u4f4d\u306f\u30ce\u30fc\u30c9<code>TreeNode</code>\u3067\u3042\u308a\u3001\u30ce\u30fc\u30c9\u306f\u30dd\u30a4\u30f3\u30bf\u306b\u3088\u3063\u3066\u63a5\u7d9a\u3055\u308c\u307e\u3059\u3002\u9023\u7d50\u30ea\u30b9\u30c8\u8868\u73fe\u3067\u306e\u4e8c\u5206\u6728\u306e\u57fa\u672c\u64cd\u4f5c\u306b\u3064\u3044\u3066\u306f\u524d\u306e\u7bc0\u3067\u7d39\u4ecb\u3057\u307e\u3057\u305f\u3002</p> <p>\u3067\u306f\u3001\u914d\u5217\u3092\u4f7f\u3063\u3066\u4e8c\u5206\u6728\u3092\u8868\u73fe\u3059\u308b\u3053\u3068\u306f\u3067\u304d\u308b\u3067\u3057\u3087\u3046\u304b\uff1f\u7b54\u3048\u306f\u30a4\u30a8\u30b9\u3067\u3059\u3002</p>"},{"location":"chapter_tree/array_representation_of_tree/#731","title":"7.3.1 \u00a0 \u5b8c\u5168\u4e8c\u5206\u6728\u306e\u8868\u73fe","text":"<p>\u307e\u305a\u7c21\u5358\u306a\u30b1\u30fc\u30b9\u304b\u3089\u5206\u6790\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u5b8c\u5168\u4e8c\u5206\u6728\u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u304d\u3001\u30ec\u30d9\u30eb\u9806\u63a2\u7d22\u306e\u9806\u5e8f\u306b\u5f93\u3063\u3066\u3059\u3079\u3066\u306e\u30ce\u30fc\u30c9\u3092\u914d\u5217\u306b\u683c\u7d0d\u3057\u3001\u5404\u30ce\u30fc\u30c9\u306f\u4e00\u610f\u306e\u914d\u5217\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002</p> <p>\u30ec\u30d9\u30eb\u9806\u63a2\u7d22\u306e\u7279\u6027\u306b\u57fa\u3065\u3044\u3066\u3001\u89aa\u30ce\u30fc\u30c9\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3068\u305d\u306e\u5b50\u30ce\u30fc\u30c9\u306e\u9593\u306e\u300c\u30de\u30c3\u30d4\u30f3\u30b0\u516c\u5f0f\u300d\u3092\u5c0e\u304d\u51fa\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\uff1a\u30ce\u30fc\u30c9\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u304c\\(i\\)\u306e\u5834\u5408\u3001\u305d\u306e\u5de6\u306e\u5b50\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306f\\(2i + 1\\)\u3001\u53f3\u306e\u5b50\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u306f\\(2i + 2\\)\u3067\u3059\u3002\u4e0b\u56f3\u306f\u3001\u3055\u307e\u3056\u307e\u306a\u30ce\u30fc\u30c9\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u9593\u306e\u30de\u30c3\u30d4\u30f3\u30b0\u95a2\u4fc2\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002</p> <p></p> <p> \u56f3 7-12 \u00a0 \u5b8c\u5168\u4e8c\u5206\u6728\u306e\u914d\u5217\u8868\u73fe </p> <p>\u30de\u30c3\u30d4\u30f3\u30b0\u516c\u5f0f\u306f\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u306e\u30ce\u30fc\u30c9\u53c2\u7167\uff08\u30dd\u30a4\u30f3\u30bf\uff09\u3068\u540c\u69d8\u306e\u5f79\u5272\u3092\u679c\u305f\u3057\u307e\u3059\u3002\u914d\u5217\u5185\u306e\u4efb\u610f\u306e\u30ce\u30fc\u30c9\u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u304d\u3001\u30de\u30c3\u30d4\u30f3\u30b0\u516c\u5f0f\u3092\u4f7f\u7528\u3057\u3066\u305d\u306e\u5de6\uff08\u53f3\uff09\u306e\u5b50\u30ce\u30fc\u30c9\u306b\u30a2\u30af\u30bb\u30b9\u3067\u304d\u307e\u3059\u3002</p>"},{"location":"chapter_tree/array_representation_of_tree/#732","title":"7.3.2 \u00a0 \u4efb\u610f\u306e\u4e8c\u5206\u6728\u306e\u8868\u73fe","text":"<p>\u5b8c\u5168\u4e8c\u5206\u6728\u306f\u7279\u5225\u306a\u30b1\u30fc\u30b9\u3067\u3059\u3002\u4e8c\u5206\u6728\u306e\u4e2d\u9593\u30ec\u30d9\u30eb\u306b\u306f\u591a\u304f\u306e<code>None</code>\u5024\u304c\u5b58\u5728\u3059\u308b\u3053\u3068\u304c\u3088\u304f\u3042\u308a\u307e\u3059\u3002\u30ec\u30d9\u30eb\u9806\u63a2\u7d22\u306e\u30b7\u30fc\u30b1\u30f3\u30b9\u306b\u306f\u3053\u308c\u3089\u306e<code>None</code>\u5024\u304c\u542b\u307e\u308c\u306a\u3044\u305f\u3081\u3001\u3053\u306e\u30b7\u30fc\u30b1\u30f3\u30b9\u3060\u3051\u306b\u4f9d\u5b58\u3057\u3066<code>None</code>\u5024\u306e\u6570\u3068\u5206\u5e03\u3092\u63a8\u6e2c\u3059\u308b\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093\u3002\u3064\u307e\u308a\u3001\u8907\u6570\u306e\u4e8c\u5206\u6728\u69cb\u9020\u304c\u540c\u3058\u30ec\u30d9\u30eb\u9806\u63a2\u7d22\u30b7\u30fc\u30b1\u30f3\u30b9\u3068\u4e00\u81f4\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u307e\u3059\u3002</p> <p>\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u5b8c\u5168\u3067\u306a\u3044\u4e8c\u5206\u6728\u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408\u3001\u4e0a\u8a18\u306e\u914d\u5217\u8868\u73fe\u65b9\u6cd5\u306f\u5931\u6557\u3057\u307e\u3059\u3002</p> <p></p> <p> \u56f3 7-13 \u00a0 \u30ec\u30d9\u30eb\u9806\u63a2\u7d22\u30b7\u30fc\u30b1\u30f3\u30b9\u304c\u8907\u6570\u306e\u4e8c\u5206\u6728\u306e\u53ef\u80fd\u6027\u306b\u5bfe\u5fdc </p> <p>\u3053\u306e\u554f\u984c\u3092\u89e3\u6c7a\u3059\u308b\u305f\u3081\u306b\u3001\u30ec\u30d9\u30eb\u9806\u63a2\u7d22\u30b7\u30fc\u30b1\u30f3\u30b9\u3067\u3059\u3079\u3066\u306e<code>None</code>\u5024\u3092\u660e\u793a\u7684\u306b\u66f8\u304d\u51fa\u3059\u3053\u3068\u3092\u691c\u8a0e\u3067\u304d\u307e\u3059\u3002\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u3053\u306e\u51e6\u7406\u5f8c\u3001\u30ec\u30d9\u30eb\u9806\u63a2\u7d22\u30b7\u30fc\u30b1\u30f3\u30b9\u306f\u4e8c\u5206\u6728\u3092\u4e00\u610f\u306b\u8868\u73fe\u3067\u304d\u307e\u3059\u3002\u30b5\u30f3\u30d7\u30eb\u30b3\u30fc\u30c9\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig <pre><code># \u4e8c\u5206\u6728\u306e\u914d\u5217\u8868\u73fe\n# None\u3092\u4f7f\u7528\u3057\u3066\u7a7a\u306e\u30b9\u30ed\u30c3\u30c8\u3092\u8868\u73fe\ntree = [1, 2, 3, 4, None, 6, 7, 8, 9, None, None, 12, None, None, 15]\n</code></pre> <pre><code>/* \u4e8c\u5206\u6728\u306e\u914d\u5217\u8868\u73fe */\n// \u6700\u5927\u6574\u6570\u5024INT_MAX\u3092\u4f7f\u7528\u3057\u3066\u7a7a\u306e\u30b9\u30ed\u30c3\u30c8\u3092\u30de\u30fc\u30af\nvector&lt;int&gt; tree = {1, 2, 3, 4, INT_MAX, 6, 7, 8, 9, INT_MAX, INT_MAX, 12, INT_MAX, INT_MAX, 15};\n</code></pre> <pre><code>/* \u4e8c\u5206\u6728\u306e\u914d\u5217\u8868\u73fe */\n// Integer\u30e9\u30c3\u30d1\u30fc\u30af\u30e9\u30b9\u3092\u4f7f\u7528\u3057\u3066null\u3067\u7a7a\u306e\u30b9\u30ed\u30c3\u30c8\u3092\u30de\u30fc\u30af\nInteger[] tree = { 1, 2, 3, 4, null, 6, 7, 8, 9, null, null, 12, null, null, 15 };\n</code></pre> <pre><code>/* \u4e8c\u5206\u6728\u306e\u914d\u5217\u8868\u73fe */\n// nullable int (int?)\u3092\u4f7f\u7528\u3057\u3066null\u3067\u7a7a\u306e\u30b9\u30ed\u30c3\u30c8\u3092\u30de\u30fc\u30af\nint?[] tree = [1, 2, 3, 4, null, 6, 7, 8, 9, null, null, 12, null, null, 15];\n</code></pre> <pre><code>/* \u4e8c\u5206\u6728\u306e\u914d\u5217\u8868\u73fe */\n// any\u578b\u30b9\u30e9\u30a4\u30b9\u3092\u4f7f\u7528\u3057\u3066nil\u3067\u7a7a\u306e\u30b9\u30ed\u30c3\u30c8\u3092\u30de\u30fc\u30af\ntree := []any{1, 2, 3, 4, nil, 6, 7, 8, 9, nil, nil, 12, nil, nil, 15}\n</code></pre> <pre><code>/* \u4e8c\u5206\u6728\u306e\u914d\u5217\u8868\u73fe */\n// optional Int (Int?)\u3092\u4f7f\u7528\u3057\u3066nil\u3067\u7a7a\u306e\u30b9\u30ed\u30c3\u30c8\u3092\u30de\u30fc\u30af\nlet tree: [Int?] = [1, 2, 3, 4, nil, 6, 7, 8, 9, nil, nil, 12, nil, nil, 15]\n</code></pre> <pre><code>/* \u4e8c\u5206\u6728\u306e\u914d\u5217\u8868\u73fe */\n// null\u3092\u4f7f\u7528\u3057\u3066\u7a7a\u306e\u30b9\u30ed\u30c3\u30c8\u3092\u8868\u73fe\nlet tree = [1, 2, 3, 4, null, 6, 7, 8, 9, null, null, 12, null, null, 15];\n</code></pre> <pre><code>/* \u4e8c\u5206\u6728\u306e\u914d\u5217\u8868\u73fe */\n// null\u3092\u4f7f\u7528\u3057\u3066\u7a7a\u306e\u30b9\u30ed\u30c3\u30c8\u3092\u8868\u73fe\nlet tree: (number | null)[] = [1, 2, 3, 4, null, 6, 7, 8, 9, null, null, 12, null, null, 15];\n</code></pre> <pre><code>/* \u4e8c\u5206\u6728\u306e\u914d\u5217\u8868\u73fe */\n// nullable int (int?)\u3092\u4f7f\u7528\u3057\u3066null\u3067\u7a7a\u306e\u30b9\u30ed\u30c3\u30c8\u3092\u30de\u30fc\u30af\nList&lt;int?&gt; tree = [1, 2, 3, 4, null, 6, 7, 8, 9, null, null, 12, null, null, 15];\n</code></pre> <pre><code>/* \u4e8c\u5206\u6728\u306e\u914d\u5217\u8868\u73fe */\n// None\u3092\u4f7f\u7528\u3057\u3066\u7a7a\u306e\u30b9\u30ed\u30c3\u30c8\u3092\u30de\u30fc\u30af\nlet tree = [Some(1), Some(2), Some(3), Some(4), None, Some(6), Some(7), Some(8), Some(9), None, None, Some(12), None, None, Some(15)];\n</code></pre> <pre><code>/* \u4e8c\u5206\u6728\u306e\u914d\u5217\u8868\u73fe */\n// \u6700\u5927int\u5024\u3092\u4f7f\u7528\u3057\u3066\u7a7a\u306e\u30b9\u30ed\u30c3\u30c8\u3092\u30de\u30fc\u30af\u3001\u3057\u305f\u304c\u3063\u3066\u30ce\u30fc\u30c9\u5024\u306fINT_MAX\u3067\u3042\u3063\u3066\u306f\u306a\u3089\u306a\u3044\nint tree[] = {1, 2, 3, 4, INT_MAX, 6, 7, 8, 9, INT_MAX, INT_MAX, 12, INT_MAX, INT_MAX, 15};\n</code></pre> <pre><code>/* \u4e8c\u5206\u6728\u306e\u914d\u5217\u8868\u73fe */\n// null\u3092\u4f7f\u7528\u3057\u3066\u7a7a\u306e\u30b9\u30ed\u30c3\u30c8\u3092\u8868\u73fe\nval tree = mutableListOf( 1, 2, 3, 4, null, 6, 7, 8, 9, null, null, 12, null, null, 15 )\n</code></pre> <pre><code>\n</code></pre> <pre><code>\n</code></pre> <p></p> <p> \u56f3 7-14 \u00a0 \u4efb\u610f\u306e\u7a2e\u985e\u306e\u4e8c\u5206\u6728\u306e\u914d\u5217\u8868\u73fe </p> <p>\u6ce8\u76ee\u3059\u3079\u304d\u306f\u3001\u5b8c\u5099\u4e8c\u5206\u6728\u306f\u914d\u5217\u8868\u73fe\u306b\u975e\u5e38\u306b\u9069\u3057\u3066\u3044\u308b**\u3068\u3044\u3046\u3053\u3068\u3067\u3059\u3002\u5b8c\u5099\u4e8c\u5206\u6728\u306e\u5b9a\u7fa9\u3092\u601d\u3044\u51fa\u3059\u3068\u3001<code>None</code>\u306f\u6700\u4e0b\u4f4d\u30ec\u30d9\u30eb\u3067\u306e\u307f\u3001\u304b\u3064\u53f3\u5074\u306b\u5411\u304b\u3063\u3066\u73fe\u308c\u307e\u3059\u3002**\u3064\u307e\u308a\u3001\u3059\u3079\u3066\u306e<code>None</code>\u5024\u306f\u78ba\u5b9f\u306b\u30ec\u30d9\u30eb\u9806\u63a2\u7d22\u30b7\u30fc\u30b1\u30f3\u30b9\u306e\u6700\u5f8c\u306b\u73fe\u308c\u307e\u3059\u3002</p> <p>\u3053\u308c\u306f\u3001\u914d\u5217\u3092\u4f7f\u7528\u3057\u3066\u5b8c\u5099\u4e8c\u5206\u6728\u3092\u8868\u73fe\u3059\u308b\u969b\u3001\u3059\u3079\u3066\u306e<code>None</code>\u5024\u306e\u683c\u7d0d\u3092\u7701\u7565\u3067\u304d\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u3001\u975e\u5e38\u306b\u4fbf\u5229\u3067\u3059\u3002\u4e0b\u56f3\u306b\u4f8b\u3092\u793a\u3057\u307e\u3059\u3002</p> <p></p> <p> \u56f3 7-15 \u00a0 \u5b8c\u5099\u4e8c\u5206\u6728\u306e\u914d\u5217\u8868\u73fe </p> <p>\u4ee5\u4e0b\u306e\u30b3\u30fc\u30c9\u306f\u3001\u914d\u5217\u8868\u73fe\u306b\u57fa\u3065\u304f\u4e8c\u5206\u6728\u3092\u5b9f\u88c5\u3057\u3001\u6b21\u306e\u64cd\u4f5c\u3092\u542b\u307f\u307e\u3059\uff1a</p> <ul> <li>\u30ce\u30fc\u30c9\u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u304d\u3001\u305d\u306e\u5024\u3001\u5de6\uff08\u53f3\uff09\u306e\u5b50\u30ce\u30fc\u30c9\u3001\u304a\u3088\u3073\u89aa\u30ce\u30fc\u30c9\u3092\u53d6\u5f97\u3059\u308b\u3002</li> <li>\u524d\u9806\u3001\u4e2d\u9806\u3001\u5f8c\u9806\u3001\u304a\u3088\u3073\u30ec\u30d9\u30eb\u9806\u63a2\u7d22\u30b7\u30fc\u30b1\u30f3\u30b9\u3092\u53d6\u5f97\u3059\u308b\u3002</li> </ul> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig array_binary_tree.py<pre><code>class ArrayBinaryTree:\n    \"\"\"\u914d\u5217\u30d9\u30fc\u30b9\u306e\u4e8c\u5206\u6728\u30af\u30e9\u30b9\"\"\"\n\n    def __init__(self, arr: list[int | None]):\n        \"\"\"\u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf\"\"\"\n        self._tree = list(arr)\n\n    def size(self):\n        \"\"\"\u30ea\u30b9\u30c8\u306e\u5bb9\u91cf\"\"\"\n        return len(self._tree)\n\n    def val(self, i: int) -&gt; int | None:\n        \"\"\"\u30a4\u30f3\u30c7\u30c3\u30af\u30b9i\u306e\u30ce\u30fc\u30c9\u306e\u5024\u3092\u53d6\u5f97\"\"\"\n        # \u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u304c\u7bc4\u56f2\u5916\u306e\u5834\u5408\u3001None\u3092\u8fd4\u3057\u3001\u7a7a\u5e2d\u3092\u8868\u3059\n        if i &lt; 0 or i &gt;= self.size():\n            return None\n        return self._tree[i]\n\n    def left(self, i: int) -&gt; int | None:\n        \"\"\"\u30a4\u30f3\u30c7\u30c3\u30af\u30b9i\u306e\u30ce\u30fc\u30c9\u306e\u5de6\u306e\u5b50\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u53d6\u5f97\"\"\"\n        return 2 * i + 1\n\n    def right(self, i: int) -&gt; int | None:\n        \"\"\"\u30a4\u30f3\u30c7\u30c3\u30af\u30b9i\u306e\u30ce\u30fc\u30c9\u306e\u53f3\u306e\u5b50\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u53d6\u5f97\"\"\"\n        return 2 * i + 2\n\n    def parent(self, i: int) -&gt; int | None:\n        \"\"\"\u30a4\u30f3\u30c7\u30c3\u30af\u30b9i\u306e\u30ce\u30fc\u30c9\u306e\u89aa\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u53d6\u5f97\"\"\"\n        return (i - 1) // 2\n\n    def level_order(self) -&gt; list[int]:\n        \"\"\"\u30ec\u30d9\u30eb\u9806\u8d70\u67fb\"\"\"\n        self.res = []\n        # \u914d\u5217\u3092\u8d70\u67fb\n        for i in range(self.size()):\n            if self.val(i) is not None:\n                self.res.append(self.val(i))\n        return self.res\n\n    def dfs(self, i: int, order: str):\n        \"\"\"\u6df1\u3055\u512a\u5148\u8d70\u67fb\"\"\"\n        if self.val(i) is None:\n            return\n        # \u524d\u9806\u8d70\u67fb\n        if order == \"pre\":\n            self.res.append(self.val(i))\n        self.dfs(self.left(i), order)\n        # \u4e2d\u9806\u8d70\u67fb\n        if order == \"in\":\n            self.res.append(self.val(i))\n        self.dfs(self.right(i), order)\n        # \u5f8c\u9806\u8d70\u67fb\n        if order == \"post\":\n            self.res.append(self.val(i))\n\n    def pre_order(self) -&gt; list[int]:\n        \"\"\"\u524d\u9806\u8d70\u67fb\"\"\"\n        self.res = []\n        self.dfs(0, order=\"pre\")\n        return self.res\n\n    def in_order(self) -&gt; list[int]:\n        \"\"\"\u4e2d\u9806\u8d70\u67fb\"\"\"\n        self.res = []\n        self.dfs(0, order=\"in\")\n        return self.res\n\n    def post_order(self) -&gt; list[int]:\n        \"\"\"\u5f8c\u9806\u8d70\u67fb\"\"\"\n        self.res = []\n        self.dfs(0, order=\"post\")\n        return self.res\n</code></pre> array_binary_tree.cpp<pre><code>/* \u914d\u5217\u30d9\u30fc\u30b9\u306e\u4e8c\u5206\u6728\u30af\u30e9\u30b9 */\nclass ArrayBinaryTree {\n  public:\n    /* \u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf */\n    ArrayBinaryTree(vector&lt;int&gt; arr) {\n        tree = arr;\n    }\n\n    /* \u30ea\u30b9\u30c8\u306e\u5bb9\u91cf */\n    int size() {\n        return tree.size();\n    }\n\n    /* \u30a4\u30f3\u30c7\u30c3\u30af\u30b9 i \u306e\u30ce\u30fc\u30c9\u306e\u5024\u3092\u53d6\u5f97 */\n    int val(int i) {\n        // \u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u304c\u7bc4\u56f2\u5916\u306e\u5834\u5408\u3001INT_MAX \u3092\u8fd4\u3059\uff08null \u3092\u8868\u3059\uff09\n        if (i &lt; 0 || i &gt;= size())\n            return INT_MAX;\n        return tree[i];\n    }\n\n    /* \u30a4\u30f3\u30c7\u30c3\u30af\u30b9 i \u306e\u30ce\u30fc\u30c9\u306e\u5de6\u306e\u5b50\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u53d6\u5f97 */\n    int left(int i) {\n        return 2 * i + 1;\n    }\n\n    /* \u30a4\u30f3\u30c7\u30c3\u30af\u30b9 i \u306e\u30ce\u30fc\u30c9\u306e\u53f3\u306e\u5b50\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u53d6\u5f97 */\n    int right(int i) {\n        return 2 * i + 2;\n    }\n\n    /* \u30a4\u30f3\u30c7\u30c3\u30af\u30b9 i \u306e\u30ce\u30fc\u30c9\u306e\u89aa\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u53d6\u5f97 */\n    int parent(int i) {\n        return (i - 1) / 2;\n    }\n\n    /* \u30ec\u30d9\u30eb\u9806\u8d70\u67fb */\n    vector&lt;int&gt; levelOrder() {\n        vector&lt;int&gt; res;\n        // \u914d\u5217\u3092\u8d70\u67fb\n        for (int i = 0; i &lt; size(); i++) {\n            if (val(i) != INT_MAX)\n                res.push_back(val(i));\n        }\n        return res;\n    }\n\n    /* \u524d\u9806\u8d70\u67fb */\n    vector&lt;int&gt; preOrder() {\n        vector&lt;int&gt; res;\n        dfs(0, \"pre\", res);\n        return res;\n    }\n\n    /* \u4e2d\u9806\u8d70\u67fb */\n    vector&lt;int&gt; inOrder() {\n        vector&lt;int&gt; res;\n        dfs(0, \"in\", res);\n        return res;\n    }\n\n    /* \u5f8c\u9806\u8d70\u67fb */\n    vector&lt;int&gt; postOrder() {\n        vector&lt;int&gt; res;\n        dfs(0, \"post\", res);\n        return res;\n    }\n\n  private:\n    vector&lt;int&gt; tree;\n\n    /* \u6df1\u3055\u512a\u5148\u8d70\u67fb */\n    void dfs(int i, string order, vector&lt;int&gt; &amp;res) {\n        // \u7a7a\u306e\u4f4d\u7f6e\u306e\u5834\u5408\u3001\u623b\u308b\n        if (val(i) == INT_MAX)\n            return;\n        // \u524d\u9806\u8d70\u67fb\n        if (order == \"pre\")\n            res.push_back(val(i));\n        dfs(left(i), order, res);\n        // \u4e2d\u9806\u8d70\u67fb\n        if (order == \"in\")\n            res.push_back(val(i));\n        dfs(right(i), order, res);\n        // \u5f8c\u9806\u8d70\u67fb\n        if (order == \"post\")\n            res.push_back(val(i));\n    }\n};\n</code></pre> array_binary_tree.java<pre><code>/* \u914d\u5217\u30d9\u30fc\u30b9\u306e\u4e8c\u5206\u6728\u30af\u30e9\u30b9 */\nclass ArrayBinaryTree {\n    private List&lt;Integer&gt; tree;\n\n    /* \u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf */\n    public ArrayBinaryTree(List&lt;Integer&gt; arr) {\n        tree = new ArrayList&lt;&gt;(arr);\n    }\n\n    /* \u30ea\u30b9\u30c8\u306e\u5bb9\u91cf */\n    public int size() {\n        return tree.size();\n    }\n\n    /* \u30a4\u30f3\u30c7\u30c3\u30af\u30b9 i \u306e\u30ce\u30fc\u30c9\u306e\u5024\u3092\u53d6\u5f97 */\n    public Integer val(int i) {\n        // \u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u304c\u7bc4\u56f2\u5916\u306e\u5834\u5408\u3001null \u3092\u8fd4\u3059\uff08\u7a7a\u306e\u4f4d\u7f6e\u3092\u8868\u3059\uff09\n        if (i &lt; 0 || i &gt;= size())\n            return null;\n        return tree.get(i);\n    }\n\n    /* \u30a4\u30f3\u30c7\u30c3\u30af\u30b9 i \u306e\u30ce\u30fc\u30c9\u306e\u5de6\u306e\u5b50\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u53d6\u5f97 */\n    public Integer left(int i) {\n        return 2 * i + 1;\n    }\n\n    /* \u30a4\u30f3\u30c7\u30c3\u30af\u30b9 i \u306e\u30ce\u30fc\u30c9\u306e\u53f3\u306e\u5b50\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u53d6\u5f97 */\n    public Integer right(int i) {\n        return 2 * i + 2;\n    }\n\n    /* \u30a4\u30f3\u30c7\u30c3\u30af\u30b9 i \u306e\u30ce\u30fc\u30c9\u306e\u89aa\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3092\u53d6\u5f97 */\n    public Integer parent(int i) {\n        return (i - 1) / 2;\n    }\n\n    /* \u30ec\u30d9\u30eb\u9806\u8d70\u67fb */\n    public List&lt;Integer&gt; levelOrder() {\n        List&lt;Integer&gt; res = new ArrayList&lt;&gt;();\n        // \u914d\u5217\u3092\u8d70\u67fb\n        for (int i = 0; i &lt; size(); i++) {\n            if (val(i) != null)\n                res.add(val(i));\n        }\n        return res;\n    }\n\n    /* \u6df1\u3055\u512a\u5148\u8d70\u67fb */\n    private void dfs(Integer i, String order, List&lt;Integer&gt; res) {\n        // \u7a7a\u306e\u4f4d\u7f6e\u306e\u5834\u5408\u3001\u623b\u308b\n        if (val(i) == null)\n            return;\n        // \u524d\u9806\u8d70\u67fb\n        if (\"pre\".equals(order))\n            res.add(val(i));\n        dfs(left(i), order, res);\n        // \u4e2d\u9806\u8d70\u67fb\n        if (\"in\".equals(order))\n            res.add(val(i));\n        dfs(right(i), order, res);\n        // \u5f8c\u9806\u8d70\u67fb\n        if (\"post\".equals(order))\n            res.add(val(i));\n    }\n\n    /* \u524d\u9806\u8d70\u67fb */\n    public List&lt;Integer&gt; preOrder() {\n        List&lt;Integer&gt; res = new ArrayList&lt;&gt;();\n        dfs(0, \"pre\", res);\n        return res;\n    }\n\n    /* \u4e2d\u9806\u8d70\u67fb */\n    public List&lt;Integer&gt; inOrder() {\n        List&lt;Integer&gt; res = new ArrayList&lt;&gt;();\n        dfs(0, \"in\", res);\n        return res;\n    }\n\n    /* \u5f8c\u9806\u8d70\u67fb */\n    public List&lt;Integer&gt; postOrder() {\n        List&lt;Integer&gt; res = new ArrayList&lt;&gt;();\n        dfs(0, \"post\", res);\n        return res;\n    }\n}\n</code></pre> array_binary_tree.cs<pre><code>[class]{ArrayBinaryTree}-[func]{}\n</code></pre> array_binary_tree.go<pre><code>[class]{arrayBinaryTree}-[func]{}\n</code></pre> array_binary_tree.swift<pre><code>[class]{ArrayBinaryTree}-[func]{}\n</code></pre> array_binary_tree.js<pre><code>[class]{ArrayBinaryTree}-[func]{}\n</code></pre> array_binary_tree.ts<pre><code>[class]{ArrayBinaryTree}-[func]{}\n</code></pre> array_binary_tree.dart<pre><code>[class]{ArrayBinaryTree}-[func]{}\n</code></pre> array_binary_tree.rs<pre><code>[class]{ArrayBinaryTree}-[func]{}\n</code></pre> array_binary_tree.c<pre><code>[class]{ArrayBinaryTree}-[func]{}\n</code></pre> array_binary_tree.kt<pre><code>[class]{ArrayBinaryTree}-[func]{}\n</code></pre> array_binary_tree.rb<pre><code>[class]{ArrayBinaryTree}-[func]{}\n</code></pre> array_binary_tree.zig<pre><code>[class]{ArrayBinaryTree}-[func]{}\n</code></pre>"},{"location":"chapter_tree/array_representation_of_tree/#733","title":"7.3.3 \u00a0 \u5229\u70b9\u3068\u5236\u9650","text":"<p>\u4e8c\u5206\u6728\u306e\u914d\u5217\u8868\u73fe\u306b\u306f\u4ee5\u4e0b\u306e\u5229\u70b9\u304c\u3042\u308a\u307e\u3059\uff1a</p> <ul> <li>\u914d\u5217\u306f\u9023\u7d9a\u3057\u305f\u30e1\u30e2\u30ea\u7a7a\u9593\u306b\u683c\u7d0d\u3055\u308c\u308b\u305f\u3081\u3001\u30ad\u30e3\u30c3\u30b7\u30e5\u30d5\u30ec\u30f3\u30c9\u30ea\u30fc\u3067\u3001\u3088\u308a\u9ad8\u901f\u306a\u30a2\u30af\u30bb\u30b9\u3068\u63a2\u7d22\u304c\u53ef\u80fd\u3067\u3059\u3002</li> <li>\u30dd\u30a4\u30f3\u30bf\u3092\u683c\u7d0d\u3059\u308b\u5fc5\u8981\u304c\u306a\u3044\u305f\u3081\u3001\u30b9\u30da\u30fc\u30b9\u3092\u7bc0\u7d04\u3067\u304d\u307e\u3059\u3002</li> <li>\u30ce\u30fc\u30c9\u3078\u306e\u30e9\u30f3\u30c0\u30e0\u30a2\u30af\u30bb\u30b9\u304c\u53ef\u80fd\u3067\u3059\u3002</li> </ul> <p>\u3057\u304b\u3057\u3001\u914d\u5217\u8868\u73fe\u306b\u306f\u3044\u304f\u3064\u304b\u306e\u5236\u9650\u3082\u3042\u308a\u307e\u3059\uff1a</p> <ul> <li>\u914d\u5217\u683c\u7d0d\u306b\u306f\u9023\u7d9a\u3057\u305f\u30e1\u30e2\u30ea\u7a7a\u9593\u304c\u5fc5\u8981\u306a\u305f\u3081\u3001\u5927\u91cf\u306e\u30c7\u30fc\u30bf\u3092\u6301\u3064\u6728\u306e\u683c\u7d0d\u306b\u306f\u9069\u3057\u3066\u3044\u307e\u305b\u3093\u3002</li> <li>\u30ce\u30fc\u30c9\u306e\u8ffd\u52a0\u3084\u524a\u9664\u306b\u306f\u914d\u5217\u306e\u633f\u5165\u3084\u524a\u9664\u64cd\u4f5c\u304c\u5fc5\u8981\u3067\u3001\u52b9\u7387\u304c\u4f4e\u304f\u306a\u308a\u307e\u3059\u3002</li> <li>\u4e8c\u5206\u6728\u306b\u591a\u304f\u306e<code>None</code>\u5024\u304c\u3042\u308b\u5834\u5408\u3001\u914d\u5217\u306b\u542b\u307e\u308c\u308b\u30ce\u30fc\u30c9\u30c7\u30fc\u30bf\u306e\u5272\u5408\u304c\u4f4e\u304f\u306a\u308a\u3001\u7a7a\u9593\u5229\u7528\u7387\u304c\u4f4e\u4e0b\u3057\u307e\u3059\u3002</li> </ul>"},{"location":"chapter_tree/avl_tree/","title":"7.5 \u00a0 AVL\u6728 *","text":"<p>\u300c\u4e8c\u5206\u63a2\u7d22\u6728\u300d\u306e\u7bc0\u3067\u306f\u3001\u8907\u6570\u306e\u633f\u5165\u3068\u524a\u9664\u306e\u5f8c\u3001\u4e8c\u5206\u63a2\u7d22\u6728\u304c\u9023\u7d50\u30ea\u30b9\u30c8\u306b\u9000\u5316\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308b\u3053\u3068\u3092\u8ff0\u3079\u307e\u3057\u305f\u3002\u3053\u306e\u3088\u3046\u306a\u5834\u5408\u3001\u3059\u3079\u3066\u306e\u64cd\u4f5c\u306e\u6642\u9593\u8a08\u7b97\u91cf\u304c\\(O(\\log n)\\)\u304b\u3089\\(O(n)\\)\u306b\u60aa\u5316\u3057\u307e\u3059\u3002</p> <p>\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u30012\u3064\u306e\u30ce\u30fc\u30c9\u524a\u9664\u64cd\u4f5c\u306e\u5f8c\u3001\u3053\u306e\u4e8c\u5206\u63a2\u7d22\u6728\u306f\u9023\u7d50\u30ea\u30b9\u30c8\u306b\u9000\u5316\u3057\u307e\u3059\u3002</p> <p></p> <p> \u56f3 7-24 \u00a0 \u30ce\u30fc\u30c9\u524a\u9664\u5f8c\u306eAVL\u6728\u306e\u9000\u5316 </p> <p>\u4f8b\u3048\u3070\u3001\u4e0b\u56f3\u306b\u793a\u3059\u5b8c\u5168\u4e8c\u5206\u6728\u3067\u306f\u30012\u3064\u306e\u30ce\u30fc\u30c9\u3092\u633f\u5165\u3057\u305f\u5f8c\u3001\u6728\u304c\u5de6\u306b\u5927\u304d\u304f\u50be\u304d\u3001\u691c\u7d22\u64cd\u4f5c\u306e\u6642\u9593\u8a08\u7b97\u91cf\u3082\u60aa\u5316\u3057\u307e\u3059\u3002</p> <p></p> <p> \u56f3 7-25 \u00a0 \u30ce\u30fc\u30c9\u633f\u5165\u5f8c\u306eAVL\u6728\u306e\u9000\u5316 </p> <p>1962\u5e74\u3001G. M. Adelson-Velsky\u3068E. M. Landis\u304c\u8ad6\u6587\u300cAn algorithm for the organization of information\u300d\u3067AVL\u6728\u3092\u63d0\u6848\u3057\u307e\u3057\u305f\u3002\u3053\u306e\u8ad6\u6587\u3067\u306f\u3001\u30ce\u30fc\u30c9\u306e\u7d99\u7d9a\u7684\u306a\u8ffd\u52a0\u3068\u524a\u9664\u306e\u5f8c\u3082AVL\u6728\u304c\u9000\u5316\u3057\u306a\u3044\u3053\u3068\u3092\u4fdd\u8a3c\u3059\u308b\u4e00\u9023\u306e\u64cd\u4f5c\u306b\u3064\u3044\u3066\u8a73\u8ff0\u3057\u3001\u3055\u307e\u3056\u307e\u306a\u64cd\u4f5c\u306e\u6642\u9593\u8a08\u7b97\u91cf\u3092\\(O(\\log n)\\)\u30ec\u30d9\u30eb\u306b\u7dad\u6301\u3057\u307e\u3057\u305f\u3002\u3064\u307e\u308a\u3001\u983b\u7e41\u306a\u8ffd\u52a0\u3001\u524a\u9664\u3001\u691c\u7d22\u3001\u5909\u66f4\u304c\u5fc5\u8981\u306a\u30b7\u30ca\u30ea\u30aa\u3067\u3001AVL\u6728\u306f\u5e38\u306b\u52b9\u7387\u7684\u306a\u30c7\u30fc\u30bf\u64cd\u4f5c\u6027\u80fd\u3092\u7dad\u6301\u3067\u304d\u3001\u5927\u304d\u306a\u5fdc\u7528\u4fa1\u5024\u304c\u3042\u308a\u307e\u3059\u3002</p>"},{"location":"chapter_tree/avl_tree/#751-avl","title":"7.5.1 \u00a0 AVL\u6728\u306e\u4e00\u822c\u7684\u306a\u7528\u8a9e","text":"<p>AVL\u6728\u306f\u4e8c\u5206\u63a2\u7d22\u6728\u3067\u3042\u308a\u304b\u3064\u5e73\u8861\u4e8c\u5206\u6728\u3067\u3082\u3042\u308a\u3001\u3053\u308c\u30892\u3064\u306e\u7a2e\u985e\u306e\u4e8c\u5206\u6728\u306e\u3059\u3079\u3066\u306e\u6027\u8cea\u3092\u6e80\u305f\u3057\u3066\u3044\u308b\u305f\u3081\u3001\u5e73\u8861\u4e8c\u5206\u63a2\u7d22\u6728\u3067\u3059\u3002</p>"},{"location":"chapter_tree/avl_tree/#1","title":"1. \u00a0 \u30ce\u30fc\u30c9\u306e\u9ad8\u3055","text":"<p>AVL\u6728\u306b\u95a2\u9023\u3059\u308b\u64cd\u4f5c\u3067\u306f\u30ce\u30fc\u30c9\u306e\u9ad8\u3055\u3092\u53d6\u5f97\u3059\u308b\u5fc5\u8981\u304c\u3042\u308b\u305f\u3081\u3001\u30ce\u30fc\u30c9\u30af\u30e9\u30b9\u306b<code>height</code>\u5909\u6570\u3092\u8ffd\u52a0\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig <pre><code>class TreeNode:\n    \"\"\"AVL\u6728\u30ce\u30fc\u30c9\"\"\"\n    def __init__(self, val: int):\n        self.val: int = val                 # \u30ce\u30fc\u30c9\u5024\n        self.height: int = 0                # \u30ce\u30fc\u30c9\u306e\u9ad8\u3055\n        self.left: TreeNode | None = None   # \u5de6\u306e\u5b50\u3078\u306e\u53c2\u7167\n        self.right: TreeNode | None = None  # \u53f3\u306e\u5b50\u3078\u306e\u53c2\u7167\n</code></pre> <pre><code>/* AVL\u6728\u30ce\u30fc\u30c9 */\nstruct TreeNode {\n    int val{};          // \u30ce\u30fc\u30c9\u5024\n    int height = 0;     // \u30ce\u30fc\u30c9\u306e\u9ad8\u3055\n    TreeNode *left{};   // \u5de6\u306e\u5b50\n    TreeNode *right{};  // \u53f3\u306e\u5b50\n    TreeNode() = default;\n    explicit TreeNode(int x) : val(x){}\n};\n</code></pre> <pre><code>/* AVL\u6728\u30ce\u30fc\u30c9 */\nclass TreeNode {\n    public int val;        // \u30ce\u30fc\u30c9\u5024\n    public int height;     // \u30ce\u30fc\u30c9\u306e\u9ad8\u3055\n    public TreeNode left;  // \u5de6\u306e\u5b50\n    public TreeNode right; // \u53f3\u306e\u5b50\n    public TreeNode(int x) { val = x; }\n}\n</code></pre> <pre><code>/* AVL\u6728\u30ce\u30fc\u30c9 */\nclass TreeNode(int? x) {\n    public int? val = x;    // \u30ce\u30fc\u30c9\u5024\n    public int height;      // \u30ce\u30fc\u30c9\u306e\u9ad8\u3055\n    public TreeNode? left;  // \u5de6\u306e\u5b50\u3078\u306e\u53c2\u7167\n    public TreeNode? right; // \u53f3\u306e\u5b50\u3078\u306e\u53c2\u7167\n}\n</code></pre> <pre><code>/* AVL\u6728\u30ce\u30fc\u30c9 */\ntype TreeNode struct {\n    Val    int       // \u30ce\u30fc\u30c9\u5024\n    Height int       // \u30ce\u30fc\u30c9\u306e\u9ad8\u3055\n    Left   *TreeNode // \u5de6\u306e\u5b50\u3078\u306e\u53c2\u7167\n    Right  *TreeNode // \u53f3\u306e\u5b50\u3078\u306e\u53c2\u7167\n}\n</code></pre> <pre><code>/* AVL\u6728\u30ce\u30fc\u30c9 */\nclass TreeNode {\n    var val: Int // \u30ce\u30fc\u30c9\u5024\n    var height: Int // \u30ce\u30fc\u30c9\u306e\u9ad8\u3055\n    var left: TreeNode? // \u5de6\u306e\u5b50\n    var right: TreeNode? // \u53f3\u306e\u5b50\n\n    init(x: Int) {\n        val = x\n        height = 0\n    }\n}\n</code></pre> <pre><code>/* AVL\u6728\u30ce\u30fc\u30c9 */\nclass TreeNode {\n    val; // \u30ce\u30fc\u30c9\u5024\n    height; // \u30ce\u30fc\u30c9\u306e\u9ad8\u3055\n    left; // \u5de6\u306e\u5b50\u30dd\u30a4\u30f3\u30bf\n    right; // \u53f3\u306e\u5b50\u30dd\u30a4\u30f3\u30bf\n    constructor(val, left, right, height) {\n        this.val = val === undefined ? 0 : val;\n        this.height = height === undefined ? 0 : height;\n        this.left = left === undefined ? null : left;\n        this.right = right === undefined ? null : right;\n    }\n}\n</code></pre> <pre><code>/* AVL\u6728\u30ce\u30fc\u30c9 */\nclass TreeNode {\n    val: number;            // \u30ce\u30fc\u30c9\u5024\n    height: number;         // \u30ce\u30fc\u30c9\u306e\u9ad8\u3055\n    left: TreeNode | null;  // \u5de6\u306e\u5b50\u30dd\u30a4\u30f3\u30bf\n    right: TreeNode | null; // \u53f3\u306e\u5b50\u30dd\u30a4\u30f3\u30bf\n    constructor(val?: number, height?: number, left?: TreeNode | null, right?: TreeNode | null) {\n        this.val = val === undefined ? 0 : val;\n        this.height = height === undefined ? 0 : height;\n        this.left = left === undefined ? null : left;\n        this.right = right === undefined ? null : right;\n    }\n}\n</code></pre> <pre><code>/* AVL\u6728\u30ce\u30fc\u30c9 */\nclass TreeNode {\n  int val;         // \u30ce\u30fc\u30c9\u5024\n  int height;      // \u30ce\u30fc\u30c9\u306e\u9ad8\u3055\n  TreeNode? left;  // \u5de6\u306e\u5b50\n  TreeNode? right; // \u53f3\u306e\u5b50\n  TreeNode(this.val, [this.height = 0, this.left, this.right]);\n}\n</code></pre> <pre><code>use std::rc::Rc;\nuse std::cell::RefCell;\n\n/* AVL\u6728\u30ce\u30fc\u30c9 */\nstruct TreeNode {\n    val: i32,                               // \u30ce\u30fc\u30c9\u5024\n    height: i32,                            // \u30ce\u30fc\u30c9\u306e\u9ad8\u3055\n    left: Option&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;,    // \u5de6\u306e\u5b50\n    right: Option&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;,   // \u53f3\u306e\u5b50\n}\n\nimpl TreeNode {\n    /* \u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf */\n    fn new(val: i32) -&gt; Rc&lt;RefCell&lt;Self&gt;&gt; {\n        Rc::new(RefCell::new(Self {\n            val,\n            height: 0,\n            left: None,\n            right: None\n        }))\n    }\n}\n</code></pre> <pre><code>/* AVL\u6728\u30ce\u30fc\u30c9 */\nTreeNode struct TreeNode {\n    int val;\n    int height;\n    struct TreeNode *left;\n    struct TreeNode *right;\n} TreeNode;\n\n/* \u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf */\nTreeNode *newTreeNode(int val) {\n    TreeNode *node;\n\n    node = (TreeNode *)malloc(sizeof(TreeNode));\n    node-&gt;val = val;\n    node-&gt;height = 0;\n    node-&gt;left = NULL;\n    node-&gt;right = NULL;\n    return node;\n}\n</code></pre> <pre><code>/* AVL\u6728\u30ce\u30fc\u30c9 */\nclass TreeNode(val _val: Int) {  // \u30ce\u30fc\u30c9\u5024\n    val height: Int = 0          // \u30ce\u30fc\u30c9\u306e\u9ad8\u3055\n    val left: TreeNode? = null   // \u5de6\u306e\u5b50\n    val right: TreeNode? = null  // \u53f3\u306e\u5b50\n}\n</code></pre> <pre><code>\n</code></pre> <pre><code>\n</code></pre> <p>\u300c\u30ce\u30fc\u30c9\u306e\u9ad8\u3055\u300d\u3068\u306f\u3001\u305d\u306e\u30ce\u30fc\u30c9\u304b\u3089\u6700\u3082\u9060\u3044\u8449\u30ce\u30fc\u30c9\u307e\u3067\u306e\u8ddd\u96e2\u3001\u3064\u307e\u308a\u901a\u904e\u3059\u308b\u300c\u8fba\u300d\u306e\u6570\u3092\u6307\u3057\u307e\u3059\u3002\u91cd\u8981\u306a\u306e\u306f\u3001\u8449\u30ce\u30fc\u30c9\u306e\u9ad8\u3055\u306f\\(0\\)\u3067\u3001null\u30ce\u30fc\u30c9\u306e\u9ad8\u3055\u306f\\(-1\\)\u3067\u3042\u308b\u3053\u3068\u3067\u3059\u3002\u30ce\u30fc\u30c9\u306e\u9ad8\u3055\u3092\u53d6\u5f97\u3057\u3001\u66f4\u65b0\u3059\u308b\u305f\u3081\u306e2\u3064\u306e\u30e6\u30fc\u30c6\u30a3\u30ea\u30c6\u30a3\u95a2\u6570\u3092\u4f5c\u6210\u3057\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig avl_tree.py<pre><code>def height(self, node: TreeNode | None) -&gt; int:\n    \"\"\"\u30ce\u30fc\u30c9\u306e\u9ad8\u3055\u3092\u53d6\u5f97\"\"\"\n    # \u7a7a\u30ce\u30fc\u30c9\u306e\u9ad8\u3055\u306f-1\u3001\u8449\u30ce\u30fc\u30c9\u306e\u9ad8\u3055\u306f0\n    if node is not None:\n        return node.height\n    return -1\n\ndef update_height(self, node: TreeNode | None):\n    \"\"\"\u30ce\u30fc\u30c9\u306e\u9ad8\u3055\u3092\u66f4\u65b0\"\"\"\n    # \u30ce\u30fc\u30c9\u306e\u9ad8\u3055 = \u6700\u3082\u9ad8\u3044\u90e8\u5206\u6728\u306e\u9ad8\u3055 + 1\n    node.height = max([self.height(node.left), self.height(node.right)]) + 1\n</code></pre> avl_tree.cpp<pre><code>/* \u30ce\u30fc\u30c9\u306e\u9ad8\u3055\u3092\u53d6\u5f97 */\nint height(TreeNode *node) {\n    // \u7a7a\u30ce\u30fc\u30c9\u306e\u9ad8\u3055\u306f-1\u3001\u8449\u30ce\u30fc\u30c9\u306e\u9ad8\u3055\u306f0\n    return node == nullptr ? -1 : node-&gt;height;\n}\n\n/* \u30ce\u30fc\u30c9\u306e\u9ad8\u3055\u3092\u66f4\u65b0 */\nvoid updateHeight(TreeNode *node) {\n    // \u30ce\u30fc\u30c9\u306e\u9ad8\u3055 = \u6700\u3082\u9ad8\u3044\u90e8\u5206\u6728\u306e\u9ad8\u3055 + 1\n    node-&gt;height = max(height(node-&gt;left), height(node-&gt;right)) + 1;\n}\n</code></pre> avl_tree.java<pre><code>/* \u30ce\u30fc\u30c9\u306e\u9ad8\u3055\u3092\u53d6\u5f97 */\nint height(TreeNode node) {\n    // \u7a7a\u30ce\u30fc\u30c9\u306e\u9ad8\u3055\u306f -1\u3001\u8449\u30ce\u30fc\u30c9\u306e\u9ad8\u3055\u306f 0\n    return node == null ? -1 : node.height;\n}\n\n/* \u30ce\u30fc\u30c9\u306e\u9ad8\u3055\u3092\u66f4\u65b0 */\nvoid updateHeight(TreeNode node) {\n    // \u30ce\u30fc\u30c9\u306e\u9ad8\u3055\u306f\u6700\u3082\u9ad8\u3044\u90e8\u5206\u6728\u306e\u9ad8\u3055 + 1\n    node.height = Math.max(height(node.left), height(node.right)) + 1;\n}\n</code></pre> avl_tree.cs<pre><code>[class]{AVLTree}-[func]{Height}\n\n[class]{AVLTree}-[func]{UpdateHeight}\n</code></pre> avl_tree.go<pre><code>[class]{aVLTree}-[func]{height}\n\n[class]{aVLTree}-[func]{updateHeight}\n</code></pre> avl_tree.swift<pre><code>[class]{AVLTree}-[func]{height}\n\n[class]{AVLTree}-[func]{updateHeight}\n</code></pre> avl_tree.js<pre><code>[class]{AVLTree}-[func]{height}\n\n[class]{AVLTree}-[func]{updateHeight}\n</code></pre> avl_tree.ts<pre><code>[class]{AVLTree}-[func]{height}\n\n[class]{AVLTree}-[func]{updateHeight}\n</code></pre> avl_tree.dart<pre><code>[class]{AVLTree}-[func]{height}\n\n[class]{AVLTree}-[func]{updateHeight}\n</code></pre> avl_tree.rs<pre><code>[class]{AVLTree}-[func]{height}\n\n[class]{AVLTree}-[func]{update_height}\n</code></pre> avl_tree.c<pre><code>[class]{}-[func]{height}\n\n[class]{}-[func]{updateHeight}\n</code></pre> avl_tree.kt<pre><code>[class]{AVLTree}-[func]{height}\n\n[class]{AVLTree}-[func]{updateHeight}\n</code></pre> avl_tree.rb<pre><code>[class]{AVLTree}-[func]{height}\n\n[class]{AVLTree}-[func]{update_height}\n</code></pre> avl_tree.zig<pre><code>[class]{AVLTree}-[func]{height}\n\n[class]{AVLTree}-[func]{updateHeight}\n</code></pre>"},{"location":"chapter_tree/avl_tree/#2","title":"2. \u00a0 \u30ce\u30fc\u30c9\u306e\u5e73\u8861\u56e0\u5b50","text":"<p>\u30ce\u30fc\u30c9\u306e\u5e73\u8861\u56e0\u5b50\u306f\u3001\u305d\u306e\u30ce\u30fc\u30c9\u306e\u5de6\u90e8\u5206\u6728\u306e\u9ad8\u3055\u304b\u3089\u53f3\u90e8\u5206\u6728\u306e\u9ad8\u3055\u3092\u5f15\u3044\u305f\u5024\u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u3001null\u30ce\u30fc\u30c9\u306e\u5e73\u8861\u56e0\u5b50\u306f\\(0\\)\u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u307e\u3059\u3002\u5f8c\u3067\u4f7f\u3044\u3084\u3059\u304f\u3059\u308b\u305f\u3081\u3001\u30ce\u30fc\u30c9\u306e\u5e73\u8861\u56e0\u5b50\u3092\u53d6\u5f97\u3059\u308b\u6a5f\u80fd\u3082\u95a2\u6570\u306b\u30ab\u30d7\u30bb\u30eb\u5316\u3057\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig avl_tree.py<pre><code>def balance_factor(self, node: TreeNode | None) -&gt; int:\n    \"\"\"\u30d0\u30e9\u30f3\u30b9\u56e0\u5b50\u3092\u53d6\u5f97\"\"\"\n    # \u7a7a\u30ce\u30fc\u30c9\u306e\u30d0\u30e9\u30f3\u30b9\u56e0\u5b50\u306f0\n    if node is None:\n        return 0\n    # \u30ce\u30fc\u30c9\u306e\u30d0\u30e9\u30f3\u30b9\u56e0\u5b50 = \u5de6\u90e8\u5206\u6728\u306e\u9ad8\u3055 - \u53f3\u90e8\u5206\u6728\u306e\u9ad8\u3055\n    return self.height(node.left) - self.height(node.right)\n</code></pre> avl_tree.cpp<pre><code>/* \u5e73\u8861\u56e0\u5b50\u3092\u53d6\u5f97 */\nint balanceFactor(TreeNode *node) {\n    // \u7a7a\u30ce\u30fc\u30c9\u306e\u5e73\u8861\u56e0\u5b50\u306f0\n    if (node == nullptr)\n        return 0;\n    // \u30ce\u30fc\u30c9\u306e\u5e73\u8861\u56e0\u5b50 = \u5de6\u90e8\u5206\u6728\u306e\u9ad8\u3055 - \u53f3\u90e8\u5206\u6728\u306e\u9ad8\u3055\n    return height(node-&gt;left) - height(node-&gt;right);\n}\n</code></pre> avl_tree.java<pre><code>/* \u5e73\u8861\u56e0\u5b50\u3092\u53d6\u5f97 */\nint balanceFactor(TreeNode node) {\n    // \u7a7a\u30ce\u30fc\u30c9\u306e\u5e73\u8861\u56e0\u5b50\u306f 0\n    if (node == null)\n        return 0;\n    // \u30ce\u30fc\u30c9\u306e\u5e73\u8861\u56e0\u5b50 = \u5de6\u90e8\u5206\u6728\u306e\u9ad8\u3055 - \u53f3\u90e8\u5206\u6728\u306e\u9ad8\u3055\n    return height(node.left) - height(node.right);\n}\n</code></pre> avl_tree.cs<pre><code>[class]{AVLTree}-[func]{BalanceFactor}\n</code></pre> avl_tree.go<pre><code>[class]{aVLTree}-[func]{balanceFactor}\n</code></pre> avl_tree.swift<pre><code>[class]{AVLTree}-[func]{balanceFactor}\n</code></pre> avl_tree.js<pre><code>[class]{AVLTree}-[func]{balanceFactor}\n</code></pre> avl_tree.ts<pre><code>[class]{AVLTree}-[func]{balanceFactor}\n</code></pre> avl_tree.dart<pre><code>[class]{AVLTree}-[func]{balanceFactor}\n</code></pre> avl_tree.rs<pre><code>[class]{AVLTree}-[func]{balance_factor}\n</code></pre> avl_tree.c<pre><code>[class]{}-[func]{balanceFactor}\n</code></pre> avl_tree.kt<pre><code>[class]{AVLTree}-[func]{balanceFactor}\n</code></pre> avl_tree.rb<pre><code>[class]{AVLTree}-[func]{balance_factor}\n</code></pre> avl_tree.zig<pre><code>[class]{AVLTree}-[func]{balanceFactor}\n</code></pre> <p>Tip</p> <p>\u5e73\u8861\u56e0\u5b50\u3092\\(f\\)\u3068\u3059\u308b\u3068\u3001AVL\u6728\u306e\u4efb\u610f\u306e\u30ce\u30fc\u30c9\u306e\u5e73\u8861\u56e0\u5b50\u306f\\(-1 \\le f \\le 1\\)\u3092\u6e80\u305f\u3057\u307e\u3059\u3002</p>"},{"location":"chapter_tree/avl_tree/#752-avl","title":"7.5.2 \u00a0 AVL\u6728\u306e\u56de\u8ee2","text":"<p>AVL\u6728\u306e\u7279\u5fb4\u7684\u306a\u6a5f\u80fd\u306f\u300c\u56de\u8ee2\u300d\u64cd\u4f5c\u3067\u3001\u3053\u308c\u306f\u4e8c\u5206\u6728\u306e\u4e2d\u9806\u63a2\u7d22\u30b7\u30fc\u30b1\u30f3\u30b9\u306b\u5f71\u97ff\u3092\u4e0e\u3048\u308b\u3053\u3068\u306a\u304f\u3001\u4e0d\u5e73\u8861\u306a\u30ce\u30fc\u30c9\u306e\u30d0\u30e9\u30f3\u30b9\u3092\u56de\u5fa9\u3067\u304d\u307e\u3059\u3002\u3064\u307e\u308a\u3001\u56de\u8ee2\u64cd\u4f5c\u306f\u300c\u4e8c\u5206\u63a2\u7d22\u6728\u300d\u306e\u6027\u8cea\u3092\u7dad\u6301\u3057\u306a\u304c\u3089\u3001\u6728\u3092\u300c\u5e73\u8861\u4e8c\u5206\u6728\u300d\u306b\u623b\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002</p> <p>\u7d76\u5bfe\u5e73\u8861\u56e0\u5b50\u304c\\(&gt; 1\\)\u306e\u30ce\u30fc\u30c9\u3092\u300c\u4e0d\u5e73\u8861\u30ce\u30fc\u30c9\u300d\u3068\u547c\u3073\u307e\u3059\u3002\u4e0d\u5e73\u8861\u306e\u30bf\u30a4\u30d7\u306b\u5fdc\u3058\u3066\u30014\u7a2e\u985e\u306e\u56de\u8ee2\u304c\u3042\u308a\u307e\u3059\uff1a\u53f3\u56de\u8ee2\u3001\u5de6\u56de\u8ee2\u3001\u53f3\u5de6\u56de\u8ee2\u3001\u5de6\u53f3\u56de\u8ee2\u3067\u3059\u3002\u4ee5\u4e0b\u3001\u3053\u308c\u3089\u306e\u56de\u8ee2\u64cd\u4f5c\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u8aac\u660e\u3057\u307e\u3059\u3002</p>"},{"location":"chapter_tree/avl_tree/#1_1","title":"1. \u00a0 \u53f3\u56de\u8ee2","text":"<p>\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u4e8c\u5206\u6728\u3067\u4e0b\u304b\u3089\u4e0a\u3078\u306e\u6700\u521d\u306e\u4e0d\u5e73\u8861\u30ce\u30fc\u30c9\u306f\u300c\u30ce\u30fc\u30c93\u300d\u3067\u3059\u3002\u3053\u306e\u4e0d\u5e73\u8861\u30ce\u30fc\u30c9\u3092\u6839\u3068\u3059\u308b\u90e8\u5206\u6728\u306b\u7126\u70b9\u3092\u5f53\u3066\u3001\u3053\u308c\u3092<code>node</code>\u3068\u3057\u3001\u305d\u306e\u5de6\u306e\u5b50\u3092<code>child</code>\u3068\u3057\u3066\u3001\u300c\u53f3\u56de\u8ee2\u300d\u3092\u5b9f\u884c\u3057\u307e\u3059\u3002\u53f3\u56de\u8ee2\u5f8c\u3001\u90e8\u5206\u6728\u306f\u518d\u3073\u30d0\u30e9\u30f3\u30b9\u304c\u53d6\u308c\u3001\u540c\u6642\u306b\u4e8c\u5206\u63a2\u7d22\u6728\u306e\u6027\u8cea\u3082\u7dad\u6301\u3055\u308c\u307e\u3059\u3002</p> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt; <p></p> <p></p> <p></p> <p></p> <p> \u56f3 7-26 \u00a0 \u53f3\u56de\u8ee2\u306e\u624b\u9806 </p> <p>\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001<code>child</code>\u30ce\u30fc\u30c9\u306b\u53f3\u306e\u5b50\uff08<code>grand_child</code>\u3068\u8868\u8a18\uff09\u304c\u3042\u308b\u5834\u5408\u3001\u53f3\u56de\u8ee2\u3067\u624b\u9806\u3092\u8ffd\u52a0\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\uff1a<code>grand_child</code>\u3092<code>node</code>\u306e\u5de6\u306e\u5b50\u306b\u8a2d\u5b9a\u3057\u307e\u3059\u3002</p> <p></p> <p> \u56f3 7-27 \u00a0 grand_child\u304c\u3042\u308b\u53f3\u56de\u8ee2 </p> <p>\u300c\u53f3\u56de\u8ee2\u300d\u306f\u6bd4\u55a9\u7684\u306a\u7528\u8a9e\u3067\u3001\u5b9f\u969b\u306b\u306f\u30ce\u30fc\u30c9\u30dd\u30a4\u30f3\u30bf\u3092\u5909\u66f4\u3059\u308b\u3053\u3068\u3067\u5b9f\u73fe\u3055\u308c\u307e\u3059\u3002\u4ee5\u4e0b\u306e\u30b3\u30fc\u30c9\u3067\u793a\u3055\u308c\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig avl_tree.py<pre><code>def right_rotate(self, node: TreeNode | None) -&gt; TreeNode | None:\n    \"\"\"\u53f3\u56de\u8ee2\u64cd\u4f5c\"\"\"\n    child = node.left\n    grand_child = child.right\n    # child\u3092\u4e2d\u5fc3\u306bnode\u3092\u53f3\u306b\u56de\u8ee2\n    child.right = node\n    node.left = grand_child\n    # \u30ce\u30fc\u30c9\u306e\u9ad8\u3055\u3092\u66f4\u65b0\n    self.update_height(node)\n    self.update_height(child)\n    # \u56de\u8ee2\u5f8c\u306e\u90e8\u5206\u6728\u306e\u30eb\u30fc\u30c8\u3092\u8fd4\u3059\n    return child\n</code></pre> avl_tree.cpp<pre><code>/* \u53f3\u56de\u8ee2\u64cd\u4f5c */\nTreeNode *rightRotate(TreeNode *node) {\n    TreeNode *child = node-&gt;left;\n    TreeNode *grandChild = child-&gt;right;\n    // child\u3092\u4e2d\u5fc3\u306bnode\u3092\u53f3\u306b\u56de\u8ee2\n    child-&gt;right = node;\n    node-&gt;left = grandChild;\n    // \u30ce\u30fc\u30c9\u306e\u9ad8\u3055\u3092\u66f4\u65b0\n    updateHeight(node);\n    updateHeight(child);\n    // \u56de\u8ee2\u5f8c\u306e\u90e8\u5206\u6728\u306e\u30eb\u30fc\u30c8\u3092\u8fd4\u3059\n    return child;\n}\n</code></pre> avl_tree.java<pre><code>/* \u53f3\u56de\u8ee2\u64cd\u4f5c */\nTreeNode rightRotate(TreeNode node) {\n    TreeNode child = node.left;\n    TreeNode grandChild = child.right;\n    // child \u3092\u8ef8\u3068\u3057\u3066 node \u3092\u53f3\u306b\u56de\u8ee2\n    child.right = node;\n    node.left = grandChild;\n    // \u30ce\u30fc\u30c9\u306e\u9ad8\u3055\u3092\u66f4\u65b0\n    updateHeight(node);\n    updateHeight(child);\n    // \u56de\u8ee2\u5f8c\u306e\u90e8\u5206\u6728\u306e\u6839\u3092\u8fd4\u3059\n    return child;\n}\n</code></pre> avl_tree.cs<pre><code>[class]{AVLTree}-[func]{RightRotate}\n</code></pre> avl_tree.go<pre><code>[class]{aVLTree}-[func]{rightRotate}\n</code></pre> avl_tree.swift<pre><code>[class]{AVLTree}-[func]{rightRotate}\n</code></pre> avl_tree.js<pre><code>[class]{AVLTree}-[func]{rightRotate}\n</code></pre> avl_tree.ts<pre><code>[class]{AVLTree}-[func]{rightRotate}\n</code></pre> avl_tree.dart<pre><code>[class]{AVLTree}-[func]{rightRotate}\n</code></pre> avl_tree.rs<pre><code>[class]{AVLTree}-[func]{right_rotate}\n</code></pre> avl_tree.c<pre><code>[class]{}-[func]{rightRotate}\n</code></pre> avl_tree.kt<pre><code>[class]{AVLTree}-[func]{rightRotate}\n</code></pre> avl_tree.rb<pre><code>[class]{AVLTree}-[func]{right_rotate}\n</code></pre> avl_tree.zig<pre><code>[class]{AVLTree}-[func]{rightRotate}\n</code></pre>"},{"location":"chapter_tree/avl_tree/#2_1","title":"2. \u00a0 \u5de6\u56de\u8ee2","text":"<p>\u5bfe\u5fdc\u3057\u3066\u3001\u4e0a\u8a18\u306e\u4e0d\u5e73\u8861\u4e8c\u5206\u6728\u306e\u300c\u93e1\u50cf\u300d\u3092\u8003\u616e\u3059\u308b\u3068\u3001\u4e0b\u56f3\u306b\u793a\u3059\u300c\u5de6\u56de\u8ee2\u300d\u64cd\u4f5c\u3092\u5b9f\u884c\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002</p> <p></p> <p> \u56f3 7-28 \u00a0 \u5de6\u56de\u8ee2\u64cd\u4f5c </p> <p>\u540c\u69d8\u306b\u3001\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001<code>child</code>\u30ce\u30fc\u30c9\u306b\u5de6\u306e\u5b50\uff08<code>grand_child</code>\u3068\u8868\u8a18\uff09\u304c\u3042\u308b\u5834\u5408\u3001\u5de6\u56de\u8ee2\u3067\u624b\u9806\u3092\u8ffd\u52a0\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\uff1a<code>grand_child</code>\u3092<code>node</code>\u306e\u53f3\u306e\u5b50\u306b\u8a2d\u5b9a\u3057\u307e\u3059\u3002</p> <p></p> <p> \u56f3 7-29 \u00a0 grand_child\u304c\u3042\u308b\u5de6\u56de\u8ee2 </p> <p>**\u53f3\u56de\u8ee2\u3068\u5de6\u56de\u8ee2\u306e\u64cd\u4f5c\u306f\u8ad6\u7406\u7684\u306b\u5bfe\u79f0\u3067\u3042\u308a\u30012\u3064\u306e\u5bfe\u79f0\u7684\u306a\u4e0d\u5e73\u8861\u30bf\u30a4\u30d7\u3092\u89e3\u6c7a\u3057\u307e\u3059**\u3053\u3068\u304c\u89b3\u5bdf\u3067\u304d\u307e\u3059\u3002\u5bfe\u79f0\u6027\u306b\u57fa\u3065\u3044\u3066\u3001\u53f3\u56de\u8ee2\u306e\u5b9f\u88c5\u30b3\u30fc\u30c9\u3067\u3059\u3079\u3066\u306e<code>left</code>\u3092<code>right</code>\u306b\u3001\u3059\u3079\u3066\u306e<code>right</code>\u3092<code>left</code>\u306b\u7f6e\u304d\u63db\u3048\u308b\u3053\u3068\u3067\u3001\u5de6\u56de\u8ee2\u306e\u5b9f\u88c5\u30b3\u30fc\u30c9\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig avl_tree.py<pre><code>def left_rotate(self, node: TreeNode | None) -&gt; TreeNode | None:\n    \"\"\"\u5de6\u56de\u8ee2\u64cd\u4f5c\"\"\"\n    child = node.right\n    grand_child = child.left\n    # child\u3092\u4e2d\u5fc3\u306bnode\u3092\u5de6\u306b\u56de\u8ee2\n    child.left = node\n    node.right = grand_child\n    # \u30ce\u30fc\u30c9\u306e\u9ad8\u3055\u3092\u66f4\u65b0\n    self.update_height(node)\n    self.update_height(child)\n    # \u56de\u8ee2\u5f8c\u306e\u90e8\u5206\u6728\u306e\u30eb\u30fc\u30c8\u3092\u8fd4\u3059\n    return child\n</code></pre> avl_tree.cpp<pre><code>/* \u5de6\u56de\u8ee2\u64cd\u4f5c */\nTreeNode *leftRotate(TreeNode *node) {\n    TreeNode *child = node-&gt;right;\n    TreeNode *grandChild = child-&gt;left;\n    // child\u3092\u4e2d\u5fc3\u306bnode\u3092\u5de6\u306b\u56de\u8ee2\n    child-&gt;left = node;\n    node-&gt;right = grandChild;\n    // \u30ce\u30fc\u30c9\u306e\u9ad8\u3055\u3092\u66f4\u65b0\n    updateHeight(node);\n    updateHeight(child);\n    // \u56de\u8ee2\u5f8c\u306e\u90e8\u5206\u6728\u306e\u30eb\u30fc\u30c8\u3092\u8fd4\u3059\n    return child;\n}\n</code></pre> avl_tree.java<pre><code>/* \u5de6\u56de\u8ee2\u64cd\u4f5c */\nTreeNode leftRotate(TreeNode node) {\n    TreeNode child = node.right;\n    TreeNode grandChild = child.left;\n    // child \u3092\u8ef8\u3068\u3057\u3066 node \u3092\u5de6\u306b\u56de\u8ee2\n    child.left = node;\n    node.right = grandChild;\n    // \u30ce\u30fc\u30c9\u306e\u9ad8\u3055\u3092\u66f4\u65b0\n    updateHeight(node);\n    updateHeight(child);\n    // \u56de\u8ee2\u5f8c\u306e\u90e8\u5206\u6728\u306e\u6839\u3092\u8fd4\u3059\n    return child;\n}\n</code></pre> avl_tree.cs<pre><code>[class]{AVLTree}-[func]{LeftRotate}\n</code></pre> avl_tree.go<pre><code>[class]{aVLTree}-[func]{leftRotate}\n</code></pre> avl_tree.swift<pre><code>[class]{AVLTree}-[func]{leftRotate}\n</code></pre> avl_tree.js<pre><code>[class]{AVLTree}-[func]{leftRotate}\n</code></pre> avl_tree.ts<pre><code>[class]{AVLTree}-[func]{leftRotate}\n</code></pre> avl_tree.dart<pre><code>[class]{AVLTree}-[func]{leftRotate}\n</code></pre> avl_tree.rs<pre><code>[class]{AVLTree}-[func]{left_rotate}\n</code></pre> avl_tree.c<pre><code>[class]{}-[func]{leftRotate}\n</code></pre> avl_tree.kt<pre><code>[class]{AVLTree}-[func]{leftRotate}\n</code></pre> avl_tree.rb<pre><code>[class]{AVLTree}-[func]{left_rotate}\n</code></pre> avl_tree.zig<pre><code>[class]{AVLTree}-[func]{leftRotate}\n</code></pre>"},{"location":"chapter_tree/avl_tree/#3","title":"3. \u00a0 \u5de6\u53f3\u56de\u8ee2","text":"<p>\u4e0b\u56f3\u306b\u793a\u3059\u4e0d\u5e73\u8861\u30ce\u30fc\u30c93\u306e\u5834\u5408\u3001\u5de6\u56de\u8ee2\u307e\u305f\u306f\u53f3\u56de\u8ee2\u306e\u3044\u305a\u308c\u304b\u3060\u3051\u3067\u306f\u90e8\u5206\u6728\u306e\u30d0\u30e9\u30f3\u30b9\u3092\u56de\u5fa9\u3067\u304d\u307e\u305b\u3093\u3002\u3053\u306e\u5834\u5408\u3001\u307e\u305a<code>child</code>\u306b\u5bfe\u3057\u3066\u300c\u5de6\u56de\u8ee2\u300d\u3092\u5b9f\u884c\u3057\u3001\u6b21\u306b<code>node</code>\u306b\u5bfe\u3057\u3066\u300c\u53f3\u56de\u8ee2\u300d\u3092\u5b9f\u884c\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002</p> <p></p> <p> \u56f3 7-30 \u00a0 \u5de6\u53f3\u56de\u8ee2 </p>"},{"location":"chapter_tree/avl_tree/#4","title":"4. \u00a0 \u53f3\u5de6\u56de\u8ee2","text":"<p>\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u4e0a\u8a18\u306e\u4e0d\u5e73\u8861\u4e8c\u5206\u6728\u306e\u93e1\u50cf\u30b1\u30fc\u30b9\u3067\u306f\u3001\u307e\u305a<code>child</code>\u306b\u5bfe\u3057\u3066\u300c\u53f3\u56de\u8ee2\u300d\u3092\u5b9f\u884c\u3057\u3001\u6b21\u306b<code>node</code>\u306b\u5bfe\u3057\u3066\u300c\u5de6\u56de\u8ee2\u300d\u3092\u5b9f\u884c\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002</p> <p></p> <p> \u56f3 7-31 \u00a0 \u53f3\u5de6\u56de\u8ee2 </p>"},{"location":"chapter_tree/avl_tree/#5","title":"5. \u00a0 \u56de\u8ee2\u306e\u9078\u629e","text":"<p>\u4e0b\u56f3\u306b\u793a\u30594\u7a2e\u985e\u306e\u4e0d\u5e73\u8861\u306f\u3001\u305d\u308c\u305e\u308c\u4e0a\u8a18\u3067\u8aac\u660e\u3057\u305f\u30b1\u30fc\u30b9\u306b\u5bfe\u5fdc\u3057\u3001\u53f3\u56de\u8ee2\u3001\u5de6\u53f3\u56de\u8ee2\u3001\u53f3\u5de6\u56de\u8ee2\u3001\u5de6\u56de\u8ee2\u304c\u5fc5\u8981\u3067\u3059\u3002</p> <p></p> <p> \u56f3 7-32 \u00a0 AVL\u6728\u306e4\u3064\u306e\u56de\u8ee2\u30b1\u30fc\u30b9 </p> <p>\u4e0b\u8868\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u4e0d\u5e73\u8861\u30ce\u30fc\u30c9\u306e\u5e73\u8861\u56e0\u5b50\u3068\u305d\u306e\u9ad8\u3044\u5074\u306e\u5b50\u306e\u5e73\u8861\u56e0\u5b50\u306e\u7b26\u53f7\u3092\u5224\u65ad\u3059\u308b\u3053\u3068\u3067\u3001\u4e0d\u5e73\u8861\u30ce\u30fc\u30c9\u304c\u4e0a\u8a18\u306e\u3069\u306e\u30b1\u30fc\u30b9\u306b\u5c5e\u3059\u308b\u304b\u3092\u6c7a\u5b9a\u3057\u307e\u3059\u3002</p> <p> \u8868 7-3 \u00a0 4\u3064\u306e\u56de\u8ee2\u30b1\u30fc\u30b9\u306e\u9078\u629e\u6761\u4ef6 </p> \u4e0d\u5e73\u8861\u30ce\u30fc\u30c9\u306e\u5e73\u8861\u56e0\u5b50 \u5b50\u30ce\u30fc\u30c9\u306e\u5e73\u8861\u56e0\u5b50 \u4f7f\u7528\u3059\u308b\u56de\u8ee2\u65b9\u6cd5 \\(&gt; 1\\)\uff08\u5de6\u306b\u50be\u3044\u305f\u6728\uff09 \\(\\geq 0\\) \u53f3\u56de\u8ee2 \\(&gt; 1\\)\uff08\u5de6\u306b\u50be\u3044\u305f\u6728\uff09 \\(&lt;0\\) \u5de6\u56de\u8ee2\u3057\u3066\u304b\u3089\u53f3\u56de\u8ee2 \\(&lt; -1\\)\uff08\u53f3\u306b\u50be\u3044\u305f\u6728\uff09 \\(\\leq 0\\) \u5de6\u56de\u8ee2 \\(&lt; -1\\)\uff08\u53f3\u306b\u50be\u3044\u305f\u6728\uff09 \\(&gt;0\\) \u53f3\u56de\u8ee2\u3057\u3066\u304b\u3089\u5de6\u56de\u8ee2 <p>\u4fbf\u5b9c\u4e0a\u3001\u56de\u8ee2\u64cd\u4f5c\u3092\u95a2\u6570\u306b\u30ab\u30d7\u30bb\u30eb\u5316\u3057\u307e\u3059\u3002\u3053\u306e\u95a2\u6570\u306b\u3088\u308a\u3001\u3055\u307e\u3056\u307e\u306a\u7a2e\u985e\u306e\u4e0d\u5e73\u8861\u306b\u5bfe\u3057\u3066\u56de\u8ee2\u3092\u5b9f\u884c\u3057\u3001\u4e0d\u5e73\u8861\u30ce\u30fc\u30c9\u306e\u30d0\u30e9\u30f3\u30b9\u3092\u56de\u5fa9\u3067\u304d\u307e\u3059\u3002\u30b3\u30fc\u30c9\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig avl_tree.py<pre><code>def rotate(self, node: TreeNode | None) -&gt; TreeNode | None:\n    \"\"\"\u56de\u8ee2\u64cd\u4f5c\u3092\u5b9f\u884c\u3057\u3066\u90e8\u5206\u6728\u306e\u30d0\u30e9\u30f3\u30b9\u3092\u5fa9\u5143\"\"\"\n    # node\u306e\u30d0\u30e9\u30f3\u30b9\u56e0\u5b50\u3092\u53d6\u5f97\n    balance_factor = self.balance_factor(node)\n    # \u5de6\u504f\u308a\u6728\n    if balance_factor &gt; 1:\n        if self.balance_factor(node.left) &gt;= 0:\n            # \u53f3\u56de\u8ee2\n            return self.right_rotate(node)\n        else:\n            # \u5de6\u56de\u8ee2\u3057\u3066\u304b\u3089\u53f3\u56de\u8ee2\n            node.left = self.left_rotate(node.left)\n            return self.right_rotate(node)\n    # \u53f3\u504f\u308a\u6728\n    elif balance_factor &lt; -1:\n        if self.balance_factor(node.right) &lt;= 0:\n            # \u5de6\u56de\u8ee2\n            return self.left_rotate(node)\n        else:\n            # \u53f3\u56de\u8ee2\u3057\u3066\u304b\u3089\u5de6\u56de\u8ee2\n            node.right = self.right_rotate(node.right)\n            return self.left_rotate(node)\n    # \u30d0\u30e9\u30f3\u30b9\u306e\u53d6\u308c\u305f\u6728\u3001\u56de\u8ee2\u4e0d\u8981\u3001\u623b\u308b\n    return node\n</code></pre> avl_tree.cpp<pre><code>/* \u56de\u8ee2\u64cd\u4f5c\u3092\u5b9f\u884c\u3057\u3066\u90e8\u5206\u6728\u306e\u5e73\u8861\u3092\u56de\u5fa9 */\nTreeNode *rotate(TreeNode *node) {\n    // node\u306e\u5e73\u8861\u56e0\u5b50\u3092\u53d6\u5f97\n    int _balanceFactor = balanceFactor(node);\n    // \u5de6\u306b\u50be\u3044\u305f\u6728\n    if (_balanceFactor &gt; 1) {\n        if (balanceFactor(node-&gt;left) &gt;= 0) {\n            // \u53f3\u56de\u8ee2\n            return rightRotate(node);\n        } else {\n            // \u5148\u306b\u5de6\u56de\u8ee2\u3001\u305d\u306e\u5f8c\u53f3\u56de\u8ee2\n            node-&gt;left = leftRotate(node-&gt;left);\n            return rightRotate(node);\n        }\n    }\n    // \u53f3\u306b\u50be\u3044\u305f\u6728\n    if (_balanceFactor &lt; -1) {\n        if (balanceFactor(node-&gt;right) &lt;= 0) {\n            // \u5de6\u56de\u8ee2\n            return leftRotate(node);\n        } else {\n            // \u5148\u306b\u53f3\u56de\u8ee2\u3001\u305d\u306e\u5f8c\u5de6\u56de\u8ee2\n            node-&gt;right = rightRotate(node-&gt;right);\n            return leftRotate(node);\n        }\n    }\n    // \u5e73\u8861\u306a\u6728\u3001\u56de\u8ee2\u4e0d\u8981\u3001\u305d\u306e\u307e\u307e\u623b\u308b\n    return node;\n}\n</code></pre> avl_tree.java<pre><code>/* \u56de\u8ee2\u64cd\u4f5c\u3092\u5b9f\u884c\u3057\u3066\u90e8\u5206\u6728\u306e\u5e73\u8861\u3092\u56de\u5fa9 */\nTreeNode rotate(TreeNode node) {\n    // node \u306e\u5e73\u8861\u56e0\u5b50\u3092\u53d6\u5f97\n    int balanceFactor = balanceFactor(node);\n    // \u5de6\u50be\u659c\u306e\u6728\n    if (balanceFactor &gt; 1) {\n        if (balanceFactor(node.left) &gt;= 0) {\n            // \u53f3\u56de\u8ee2\n            return rightRotate(node);\n        } else {\n            // \u5148\u306b\u5de6\u56de\u8ee2\u3001\u305d\u306e\u5f8c\u53f3\u56de\u8ee2\n            node.left = leftRotate(node.left);\n            return rightRotate(node);\n        }\n    }\n    // \u53f3\u50be\u659c\u306e\u6728\n    if (balanceFactor &lt; -1) {\n        if (balanceFactor(node.right) &lt;= 0) {\n            // \u5de6\u56de\u8ee2\n            return leftRotate(node);\n        } else {\n            // \u5148\u306b\u53f3\u56de\u8ee2\u3001\u305d\u306e\u5f8c\u5de6\u56de\u8ee2\n            node.right = rightRotate(node.right);\n            return leftRotate(node);\n        }\n    }\n    // \u5e73\u8861\u6728\u3001\u56de\u8ee2\u306f\u4e0d\u8981\u3001\u623b\u308b\n    return node;\n}\n</code></pre> avl_tree.cs<pre><code>[class]{AVLTree}-[func]{Rotate}\n</code></pre> avl_tree.go<pre><code>[class]{aVLTree}-[func]{rotate}\n</code></pre> avl_tree.swift<pre><code>[class]{AVLTree}-[func]{rotate}\n</code></pre> avl_tree.js<pre><code>[class]{AVLTree}-[func]{rotate}\n</code></pre> avl_tree.ts<pre><code>[class]{AVLTree}-[func]{rotate}\n</code></pre> avl_tree.dart<pre><code>[class]{AVLTree}-[func]{rotate}\n</code></pre> avl_tree.rs<pre><code>[class]{AVLTree}-[func]{rotate}\n</code></pre> avl_tree.c<pre><code>[class]{}-[func]{rotate}\n</code></pre> avl_tree.kt<pre><code>[class]{AVLTree}-[func]{rotate}\n</code></pre> avl_tree.rb<pre><code>[class]{AVLTree}-[func]{rotate}\n</code></pre> avl_tree.zig<pre><code>[class]{AVLTree}-[func]{rotate}\n</code></pre>"},{"location":"chapter_tree/avl_tree/#753-avl","title":"7.5.3 \u00a0 AVL\u6728\u306e\u4e00\u822c\u7684\u306a\u64cd\u4f5c","text":""},{"location":"chapter_tree/avl_tree/#1_2","title":"1. \u00a0 \u30ce\u30fc\u30c9\u306e\u633f\u5165","text":"<p>AVL\u6728\u306e\u30ce\u30fc\u30c9\u633f\u5165\u64cd\u4f5c\u306f\u4e8c\u5206\u63a2\u7d22\u6728\u306e\u305d\u308c\u3068\u4f3c\u3066\u3044\u307e\u3059\u3002\u552f\u4e00\u306e\u9055\u3044\u306f\u3001AVL\u6728\u3067\u30ce\u30fc\u30c9\u3092\u633f\u5165\u3057\u305f\u5f8c\u3001\u305d\u306e\u30ce\u30fc\u30c9\u304b\u3089\u6839\u30ce\u30fc\u30c9\u307e\u3067\u306e\u30d1\u30b9\u4e0a\u306b\u4e00\u9023\u306e\u4e0d\u5e73\u8861\u30ce\u30fc\u30c9\u304c\u73fe\u308c\u308b\u53ef\u80fd\u6027\u304c\u3042\u308b\u3053\u3068\u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u3053\u306e\u30ce\u30fc\u30c9\u304b\u3089\u59cb\u3081\u3066\u4e0a\u5411\u304d\u306b\u56de\u8ee2\u64cd\u4f5c\u3092\u5b9f\u884c\u3057\u3001\u3059\u3079\u3066\u306e\u4e0d\u5e73\u8861\u30ce\u30fc\u30c9\u306e\u30d0\u30e9\u30f3\u30b9\u3092\u56de\u5fa9\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u30b3\u30fc\u30c9\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig avl_tree.py<pre><code>def insert(self, val):\n    \"\"\"\u30ce\u30fc\u30c9\u3092\u633f\u5165\"\"\"\n    self._root = self.insert_helper(self._root, val)\n\ndef insert_helper(self, node: TreeNode | None, val: int) -&gt; TreeNode:\n    \"\"\"\u518d\u5e30\u7684\u306b\u30ce\u30fc\u30c9\u3092\u633f\u5165\uff08\u30d8\u30eb\u30d1\u30fc\u30e1\u30bd\u30c3\u30c9\uff09\"\"\"\n    if node is None:\n        return TreeNode(val)\n    # 1. \u633f\u5165\u4f4d\u7f6e\u3092\u898b\u3064\u3051\u3066\u30ce\u30fc\u30c9\u3092\u633f\u5165\n    if val &lt; node.val:\n        node.left = self.insert_helper(node.left, val)\n    elif val &gt; node.val:\n        node.right = self.insert_helper(node.right, val)\n    else:\n        # \u91cd\u8907\u30ce\u30fc\u30c9\u306f\u633f\u5165\u3057\u306a\u3044\u3001\u623b\u308b\n        return node\n    # \u30ce\u30fc\u30c9\u306e\u9ad8\u3055\u3092\u66f4\u65b0\n    self.update_height(node)\n    # 2. \u56de\u8ee2\u64cd\u4f5c\u3092\u5b9f\u884c\u3057\u3066\u90e8\u5206\u6728\u306e\u30d0\u30e9\u30f3\u30b9\u3092\u5fa9\u5143\n    return self.rotate(node)\n</code></pre> avl_tree.cpp<pre><code>/* \u30ce\u30fc\u30c9\u3092\u633f\u5165 */\nvoid insert(int val) {\n    root = insertHelper(root, val);\n}\n\n/* \u30ce\u30fc\u30c9\u3092\u518d\u5e30\u7684\u306b\u633f\u5165\uff08\u30d8\u30eb\u30d1\u30fc\u30e1\u30bd\u30c3\u30c9\uff09 */\nTreeNode *insertHelper(TreeNode *node, int val) {\n    if (node == nullptr)\n        return new TreeNode(val);\n    /* 1. \u633f\u5165\u4f4d\u7f6e\u3092\u898b\u3064\u3051\u3066\u30ce\u30fc\u30c9\u3092\u633f\u5165 */\n    if (val &lt; node-&gt;val)\n        node-&gt;left = insertHelper(node-&gt;left, val);\n    else if (val &gt; node-&gt;val)\n        node-&gt;right = insertHelper(node-&gt;right, val);\n    else\n        return node;    // \u91cd\u8907\u30ce\u30fc\u30c9\u306f\u633f\u5165\u3057\u306a\u3044\u3001\u305d\u306e\u307e\u307e\u623b\u308b\n    updateHeight(node); // \u30ce\u30fc\u30c9\u306e\u9ad8\u3055\u3092\u66f4\u65b0\n    /* 2. \u56de\u8ee2\u64cd\u4f5c\u3092\u5b9f\u884c\u3057\u3066\u90e8\u5206\u6728\u306e\u5e73\u8861\u3092\u56de\u5fa9 */\n    node = rotate(node);\n    // \u90e8\u5206\u6728\u306e\u30eb\u30fc\u30c8\u30ce\u30fc\u30c9\u3092\u8fd4\u3059\n    return node;\n}\n</code></pre> avl_tree.java<pre><code>/* \u30ce\u30fc\u30c9\u3092\u633f\u5165 */\nvoid insert(int val) {\n    root = insertHelper(root, val);\n}\n\n/* \u518d\u5e30\u7684\u306b\u30ce\u30fc\u30c9\u3092\u633f\u5165\uff08\u88dc\u52a9\u30e1\u30bd\u30c3\u30c9\uff09 */\nTreeNode insertHelper(TreeNode node, int val) {\n    if (node == null)\n        return new TreeNode(val);\n    /* 1. \u633f\u5165\u4f4d\u7f6e\u3092\u898b\u3064\u3051\u3066\u30ce\u30fc\u30c9\u3092\u633f\u5165 */\n    if (val &lt; node.val)\n        node.left = insertHelper(node.left, val);\n    else if (val &gt; node.val)\n        node.right = insertHelper(node.right, val);\n    else\n        return node; // \u91cd\u8907\u30ce\u30fc\u30c9\u306f\u633f\u5165\u3057\u306a\u3044\u3001\u623b\u308b\n    updateHeight(node); // \u30ce\u30fc\u30c9\u306e\u9ad8\u3055\u3092\u66f4\u65b0\n    /* 2. \u56de\u8ee2\u64cd\u4f5c\u3092\u5b9f\u884c\u3057\u3066\u90e8\u5206\u6728\u306e\u5e73\u8861\u3092\u56de\u5fa9 */\n    node = rotate(node);\n    // \u90e8\u5206\u6728\u306e\u6839\u30ce\u30fc\u30c9\u3092\u8fd4\u3059\n    return node;\n}\n</code></pre> avl_tree.cs<pre><code>[class]{AVLTree}-[func]{Insert}\n\n[class]{AVLTree}-[func]{InsertHelper}\n</code></pre> avl_tree.go<pre><code>[class]{aVLTree}-[func]{insert}\n\n[class]{aVLTree}-[func]{insertHelper}\n</code></pre> avl_tree.swift<pre><code>[class]{AVLTree}-[func]{insert}\n\n[class]{AVLTree}-[func]{insertHelper}\n</code></pre> avl_tree.js<pre><code>[class]{AVLTree}-[func]{insert}\n\n[class]{AVLTree}-[func]{insertHelper}\n</code></pre> avl_tree.ts<pre><code>[class]{AVLTree}-[func]{insert}\n\n[class]{AVLTree}-[func]{insertHelper}\n</code></pre> avl_tree.dart<pre><code>[class]{AVLTree}-[func]{insert}\n\n[class]{AVLTree}-[func]{insertHelper}\n</code></pre> avl_tree.rs<pre><code>[class]{AVLTree}-[func]{insert}\n\n[class]{AVLTree}-[func]{insert_helper}\n</code></pre> avl_tree.c<pre><code>[class]{AVLTree}-[func]{insert}\n\n[class]{}-[func]{insertHelper}\n</code></pre> avl_tree.kt<pre><code>[class]{AVLTree}-[func]{insert}\n\n[class]{AVLTree}-[func]{insertHelper}\n</code></pre> avl_tree.rb<pre><code>[class]{AVLTree}-[func]{insert}\n\n[class]{AVLTree}-[func]{insert_helper}\n</code></pre> avl_tree.zig<pre><code>[class]{AVLTree}-[func]{insert}\n\n[class]{AVLTree}-[func]{insertHelper}\n</code></pre>"},{"location":"chapter_tree/avl_tree/#2_2","title":"2. \u00a0 \u30ce\u30fc\u30c9\u306e\u524a\u9664","text":"<p>\u540c\u69d8\u306b\u3001\u4e8c\u5206\u63a2\u7d22\u6728\u3067\u306e\u30ce\u30fc\u30c9\u524a\u9664\u65b9\u6cd5\u306b\u57fa\u3065\u3044\u3066\u3001\u4e0b\u304b\u3089\u4e0a\u3078\u56de\u8ee2\u64cd\u4f5c\u3092\u5b9f\u884c\u3057\u3066\u3059\u3079\u3066\u306e\u4e0d\u5e73\u8861\u30ce\u30fc\u30c9\u306e\u30d0\u30e9\u30f3\u30b9\u3092\u56de\u5fa9\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u30b3\u30fc\u30c9\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig avl_tree.py<pre><code>def remove(self, val: int):\n    \"\"\"\u30ce\u30fc\u30c9\u3092\u524a\u9664\"\"\"\n    self._root = self.remove_helper(self._root, val)\n\ndef remove_helper(self, node: TreeNode | None, val: int) -&gt; TreeNode | None:\n    \"\"\"\u518d\u5e30\u7684\u306b\u30ce\u30fc\u30c9\u3092\u524a\u9664\uff08\u30d8\u30eb\u30d1\u30fc\u30e1\u30bd\u30c3\u30c9\uff09\"\"\"\n    if node is None:\n        return None\n    # 1. \u30ce\u30fc\u30c9\u3092\u898b\u3064\u3051\u3066\u524a\u9664\n    if val &lt; node.val:\n        node.left = self.remove_helper(node.left, val)\n    elif val &gt; node.val:\n        node.right = self.remove_helper(node.right, val)\n    else:\n        if node.left is None or node.right is None:\n            child = node.left or node.right\n            # \u5b50\u30ce\u30fc\u30c9\u6570 = 0\u3001\u30ce\u30fc\u30c9\u3092\u524a\u9664\u3057\u3066\u623b\u308b\n            if child is None:\n                return None\n            # \u5b50\u30ce\u30fc\u30c9\u6570 = 1\u3001\u30ce\u30fc\u30c9\u3092\u524a\u9664\n            else:\n                node = child\n        else:\n            # \u5b50\u30ce\u30fc\u30c9\u6570 = 2\u3001\u4e2d\u9806\u8d70\u67fb\u306e\u6b21\u306e\u30ce\u30fc\u30c9\u3092\u524a\u9664\u3057\u3001\u305d\u308c\u3067\u73fe\u5728\u306e\u30ce\u30fc\u30c9\u3092\u7f6e\u304d\u63db\u3048\n            temp = node.right\n            while temp.left is not None:\n                temp = temp.left\n            node.right = self.remove_helper(node.right, temp.val)\n            node.val = temp.val\n    # \u30ce\u30fc\u30c9\u306e\u9ad8\u3055\u3092\u66f4\u65b0\n    self.update_height(node)\n    # 2. \u56de\u8ee2\u64cd\u4f5c\u3092\u5b9f\u884c\u3057\u3066\u90e8\u5206\u6728\u306e\u30d0\u30e9\u30f3\u30b9\u3092\u5fa9\u5143\n    return self.rotate(node)\n</code></pre> avl_tree.cpp<pre><code>/* \u30ce\u30fc\u30c9\u3092\u524a\u9664 */\nvoid remove(int val) {\n    root = removeHelper(root, val);\n}\n\n/* \u30ce\u30fc\u30c9\u3092\u518d\u5e30\u7684\u306b\u524a\u9664\uff08\u30d8\u30eb\u30d1\u30fc\u30e1\u30bd\u30c3\u30c9\uff09 */\nTreeNode *removeHelper(TreeNode *node, int val) {\n    if (node == nullptr)\n        return nullptr;\n    /* 1. \u30ce\u30fc\u30c9\u3092\u898b\u3064\u3051\u3066\u524a\u9664 */\n    if (val &lt; node-&gt;val)\n        node-&gt;left = removeHelper(node-&gt;left, val);\n    else if (val &gt; node-&gt;val)\n        node-&gt;right = removeHelper(node-&gt;right, val);\n    else {\n        if (node-&gt;left == nullptr || node-&gt;right == nullptr) {\n            TreeNode *child = node-&gt;left != nullptr ? node-&gt;left : node-&gt;right;\n            // \u5b50\u30ce\u30fc\u30c9\u6570 = 0\u3001\u30ce\u30fc\u30c9\u3092\u524a\u9664\u3057\u3066\u623b\u308b\n            if (child == nullptr) {\n                delete node;\n                return nullptr;\n            }\n            // \u5b50\u30ce\u30fc\u30c9\u6570 = 1\u3001\u30ce\u30fc\u30c9\u3092\u524a\u9664\n            else {\n                delete node;\n                node = child;\n            }\n        } else {\n            // \u5b50\u30ce\u30fc\u30c9\u6570 = 2\u3001\u4e2d\u9806\u8d70\u67fb\u306e\u6b21\u306e\u30ce\u30fc\u30c9\u3092\u524a\u9664\u3057\u3001\u73fe\u5728\u306e\u30ce\u30fc\u30c9\u3068\u7f6e\u304d\u63db\u3048\u308b\n            TreeNode *temp = node-&gt;right;\n            while (temp-&gt;left != nullptr) {\n                temp = temp-&gt;left;\n            }\n            int tempVal = temp-&gt;val;\n            node-&gt;right = removeHelper(node-&gt;right, temp-&gt;val);\n            node-&gt;val = tempVal;\n        }\n    }\n    updateHeight(node); // \u30ce\u30fc\u30c9\u306e\u9ad8\u3055\u3092\u66f4\u65b0\n    /* 2. \u56de\u8ee2\u64cd\u4f5c\u3092\u5b9f\u884c\u3057\u3066\u90e8\u5206\u6728\u306e\u5e73\u8861\u3092\u56de\u5fa9 */\n    node = rotate(node);\n    // \u90e8\u5206\u6728\u306e\u30eb\u30fc\u30c8\u30ce\u30fc\u30c9\u3092\u8fd4\u3059\n    return node;\n}\n</code></pre> avl_tree.java<pre><code>/* \u30ce\u30fc\u30c9\u3092\u524a\u9664 */\nvoid remove(int val) {\n    root = removeHelper(root, val);\n}\n\n/* \u518d\u5e30\u7684\u306b\u30ce\u30fc\u30c9\u3092\u524a\u9664\uff08\u88dc\u52a9\u30e1\u30bd\u30c3\u30c9\uff09 */\nTreeNode removeHelper(TreeNode node, int val) {\n    if (node == null)\n        return null;\n    /* 1. \u30ce\u30fc\u30c9\u3092\u898b\u3064\u3051\u3066\u524a\u9664 */\n    if (val &lt; node.val)\n        node.left = removeHelper(node.left, val);\n    else if (val &gt; node.val)\n        node.right = removeHelper(node.right, val);\n    else {\n        if (node.left == null || node.right == null) {\n            TreeNode child = node.left != null ? node.left : node.right;\n            // \u5b50\u30ce\u30fc\u30c9\u6570 = 0\u3001\u30ce\u30fc\u30c9\u3092\u524a\u9664\u3057\u3066\u623b\u308b\n            if (child == null)\n                return null;\n            // \u5b50\u30ce\u30fc\u30c9\u6570 = 1\u3001\u30ce\u30fc\u30c9\u3092\u524a\u9664\n            else\n                node = child;\n        } else {\n            // \u5b50\u30ce\u30fc\u30c9\u6570 = 2\u3001\u4e2d\u9806\u8d70\u67fb\u306e\u6b21\u306e\u30ce\u30fc\u30c9\u3092\u524a\u9664\u3057\u3001\u73fe\u5728\u306e\u30ce\u30fc\u30c9\u3092\u305d\u308c\u3067\u7f6e\u304d\u63db\u3048\u308b\n            TreeNode temp = node.right;\n            while (temp.left != null) {\n                temp = temp.left;\n            }\n            node.right = removeHelper(node.right, temp.val);\n            node.val = temp.val;\n        }\n    }\n    updateHeight(node); // \u30ce\u30fc\u30c9\u306e\u9ad8\u3055\u3092\u66f4\u65b0\n    /* 2. \u56de\u8ee2\u64cd\u4f5c\u3092\u5b9f\u884c\u3057\u3066\u90e8\u5206\u6728\u306e\u5e73\u8861\u3092\u56de\u5fa9 */\n    node = rotate(node);\n    // \u90e8\u5206\u6728\u306e\u6839\u30ce\u30fc\u30c9\u3092\u8fd4\u3059\n    return node;\n}\n</code></pre> avl_tree.cs<pre><code>[class]{AVLTree}-[func]{Remove}\n\n[class]{AVLTree}-[func]{RemoveHelper}\n</code></pre> avl_tree.go<pre><code>[class]{aVLTree}-[func]{remove}\n\n[class]{aVLTree}-[func]{removeHelper}\n</code></pre> avl_tree.swift<pre><code>[class]{AVLTree}-[func]{remove}\n\n[class]{AVLTree}-[func]{removeHelper}\n</code></pre> avl_tree.js<pre><code>[class]{AVLTree}-[func]{remove}\n\n[class]{AVLTree}-[func]{removeHelper}\n</code></pre> avl_tree.ts<pre><code>[class]{AVLTree}-[func]{remove}\n\n[class]{AVLTree}-[func]{removeHelper}\n</code></pre> avl_tree.dart<pre><code>[class]{AVLTree}-[func]{remove}\n\n[class]{AVLTree}-[func]{removeHelper}\n</code></pre> avl_tree.rs<pre><code>[class]{AVLTree}-[func]{remove}\n\n[class]{AVLTree}-[func]{remove_helper}\n</code></pre> avl_tree.c<pre><code>[class]{AVLTree}-[func]{removeItem}\n\n[class]{}-[func]{removeHelper}\n</code></pre> avl_tree.kt<pre><code>[class]{AVLTree}-[func]{remove}\n\n[class]{AVLTree}-[func]{removeHelper}\n</code></pre> avl_tree.rb<pre><code>[class]{AVLTree}-[func]{remove}\n\n[class]{AVLTree}-[func]{remove_helper}\n</code></pre> avl_tree.zig<pre><code>[class]{AVLTree}-[func]{remove}\n\n[class]{AVLTree}-[func]{removeHelper}\n</code></pre>"},{"location":"chapter_tree/avl_tree/#3_1","title":"3. \u00a0 \u30ce\u30fc\u30c9\u306e\u691c\u7d22","text":"<p>AVL\u6728\u3067\u306e\u30ce\u30fc\u30c9\u691c\u7d22\u64cd\u4f5c\u306f\u4e8c\u5206\u63a2\u7d22\u6728\u306e\u305d\u308c\u3068\u4e00\u81f4\u3057\u3066\u304a\u308a\u3001\u3053\u3053\u3067\u306f\u8a73\u8ff0\u3057\u307e\u305b\u3093\u3002</p>"},{"location":"chapter_tree/avl_tree/#754-avl","title":"7.5.4 \u00a0 AVL\u6728\u306e\u5178\u578b\u7684\u306a\u5fdc\u7528","text":"<ul> <li>\u5927\u91cf\u306e\u30c7\u30fc\u30bf\u306e\u6574\u7406\u3068\u683c\u7d0d\u306b\u4f7f\u7528\u3055\u308c\u3001\u691c\u7d22\u983b\u5ea6\u304c\u9ad8\u304f\u3001\u633f\u5165\u3068\u524a\u9664\u306e\u983b\u5ea6\u304c\u4f4e\u3044\u30b7\u30ca\u30ea\u30aa\u306b\u9069\u3057\u3066\u3044\u307e\u3059\u3002</li> <li>\u30c7\u30fc\u30bf\u30d9\u30fc\u30b9\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u30b7\u30b9\u30c6\u30e0\u306e\u69cb\u7bc9\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002</li> <li>\u8d64\u9ed2\u6728\u3082\u4e00\u822c\u7684\u306a\u5e73\u8861\u4e8c\u5206\u63a2\u7d22\u6728\u306e\u4e00\u7a2e\u3067\u3059\u3002AVL\u6728\u3068\u6bd4\u8f03\u3057\u3066\u3001\u8d64\u9ed2\u6728\u306f\u3088\u308a\u7de9\u3044\u5e73\u8861\u6761\u4ef6\u3092\u6301\u3061\u3001\u30ce\u30fc\u30c9\u306e\u633f\u5165\u3068\u524a\u9664\u306b\u304b\u304b\u308b\u56de\u8ee2\u6570\u304c\u5c11\u306a\u304f\u3001\u30ce\u30fc\u30c9\u306e\u8ffd\u52a0\u3068\u524a\u9664\u64cd\u4f5c\u306e\u5e73\u5747\u52b9\u7387\u304c\u9ad8\u304f\u306a\u308a\u307e\u3059\u3002</li> </ul>"},{"location":"chapter_tree/binary_search_tree/","title":"7.4 \u00a0 \u4e8c\u5206\u63a2\u7d22\u6728","text":"<p>\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u4e8c\u5206\u63a2\u7d22\u6728\u306f\u4ee5\u4e0b\u306e\u6761\u4ef6\u3092\u6e80\u305f\u3057\u307e\u3059\u3002</p> <ol> <li>\u6839\u30ce\u30fc\u30c9\u306b\u3064\u3044\u3066\u3001\u5de6\u90e8\u5206\u6728\u306e\u3059\u3079\u3066\u306e\u30ce\u30fc\u30c9\u306e\u5024 \\(&lt;\\) \u6839\u30ce\u30fc\u30c9\u306e\u5024 \\(&lt;\\) \u53f3\u90e8\u5206\u6728\u306e\u3059\u3079\u3066\u306e\u30ce\u30fc\u30c9\u306e\u5024\u3002</li> <li>\u4efb\u610f\u306e\u30ce\u30fc\u30c9\u306e\u5de6\u3068\u53f3\u306e\u90e8\u5206\u6728\u3082\u4e8c\u5206\u63a2\u7d22\u6728\u3067\u3059\u3002\u3064\u307e\u308a\u3001\u6761\u4ef6<code>1.</code>\u3082\u6e80\u305f\u3057\u307e\u3059\u3002</li> </ol> <p></p> <p> \u56f3 7-16 \u00a0 \u4e8c\u5206\u63a2\u7d22\u6728 </p>"},{"location":"chapter_tree/binary_search_tree/#741","title":"7.4.1 \u00a0 \u4e8c\u5206\u63a2\u7d22\u6728\u306e\u64cd\u4f5c","text":"<p>\u4e8c\u5206\u63a2\u7d22\u6728\u3092\u30af\u30e9\u30b9<code>BinarySearchTree</code>\u3068\u3057\u3066\u30ab\u30d7\u30bb\u30eb\u5316\u3057\u3001\u6728\u306e\u6839\u30ce\u30fc\u30c9\u3092\u6307\u3059\u30e1\u30f3\u30d0\u30fc\u5909\u6570<code>root</code>\u3092\u5ba3\u8a00\u3057\u307e\u3059\u3002</p>"},{"location":"chapter_tree/binary_search_tree/#1","title":"1. \u00a0 \u30ce\u30fc\u30c9\u306e\u691c\u7d22","text":"<p>\u30bf\u30fc\u30b2\u30c3\u30c8\u30ce\u30fc\u30c9\u5024<code>num</code>\u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408\u3001\u4e8c\u5206\u63a2\u7d22\u6728\u306e\u6027\u8cea\u306b\u5f93\u3063\u3066\u691c\u7d22\u3067\u304d\u307e\u3059\u3002\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u30ce\u30fc\u30c9<code>cur</code>\u3092\u5ba3\u8a00\u3057\u3001\u4e8c\u5206\u6728\u306e\u6839\u30ce\u30fc\u30c9<code>root</code>\u304b\u3089\u958b\u59cb\u3057\u3001\u30ce\u30fc\u30c9\u5024<code>cur.val</code>\u3068<code>num</code>\u306e\u30b5\u30a4\u30ba\u3092\u6bd4\u8f03\u3059\u308b\u30eb\u30fc\u30d7\u3092\u884c\u3044\u307e\u3059\u3002</p> <ul> <li><code>cur.val &lt; num</code>\u306e\u5834\u5408\u3001\u30bf\u30fc\u30b2\u30c3\u30c8\u30ce\u30fc\u30c9\u306f<code>cur</code>\u306e\u53f3\u90e8\u5206\u6728\u306b\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3059\u308b\u305f\u3081\u3001<code>cur = cur.right</code>\u3092\u5b9f\u884c\u3057\u307e\u3059\u3002</li> <li><code>cur.val &gt; num</code>\u306e\u5834\u5408\u3001\u30bf\u30fc\u30b2\u30c3\u30c8\u30ce\u30fc\u30c9\u306f<code>cur</code>\u306e\u5de6\u90e8\u5206\u6728\u306b\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3059\u308b\u305f\u3081\u3001<code>cur = cur.left</code>\u3092\u5b9f\u884c\u3057\u307e\u3059\u3002</li> <li><code>cur.val = num</code>\u306e\u5834\u5408\u3001\u30bf\u30fc\u30b2\u30c3\u30c8\u30ce\u30fc\u30c9\u304c\u898b\u3064\u304b\u3063\u305f\u3053\u3068\u3092\u610f\u5473\u3059\u308b\u305f\u3081\u3001\u30eb\u30fc\u30d7\u3092\u7d42\u4e86\u3057\u3066\u30ce\u30fc\u30c9\u3092\u8fd4\u3057\u307e\u3059\u3002</li> </ul> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt; <p></p> <p></p> <p></p> <p></p> <p> \u56f3 7-17 \u00a0 \u4e8c\u5206\u63a2\u7d22\u6728\u3067\u306e\u30ce\u30fc\u30c9\u691c\u7d22\u4f8b </p> <p>\u4e8c\u5206\u63a2\u7d22\u6728\u3067\u306e\u691c\u7d22\u64cd\u4f5c\u306f\u4e8c\u5206\u63a2\u7d22\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3068\u540c\u3058\u539f\u7406\u3067\u52d5\u4f5c\u3057\u3001\u5404\u30e9\u30a6\u30f3\u30c9\u3067\u30b1\u30fc\u30b9\u306e\u534a\u5206\u3092\u6392\u9664\u3057\u307e\u3059\u3002\u30eb\u30fc\u30d7\u6570\u306f\u6700\u5927\u3067\u4e8c\u5206\u6728\u306e\u9ad8\u3055\u3067\u3059\u3002\u4e8c\u5206\u6728\u304c\u5e73\u8861\u3057\u3066\u3044\u308b\u5834\u5408\u3001\\(O(\\log n)\\)\u306e\u6642\u9593\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002\u30b3\u30fc\u30c9\u4f8b\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig binary_search_tree.py<pre><code>def search(self, num: int) -&gt; TreeNode | None:\n    \"\"\"\u30ce\u30fc\u30c9\u3092\u63a2\u7d22\"\"\"\n    cur = self._root\n    # \u30eb\u30fc\u30d7\u3067\u63a2\u7d22\u3001\u8449\u30ce\u30fc\u30c9\u3092\u901a\u904e\u3057\u305f\u5f8c\u306b\u30d6\u30ec\u30fc\u30af\n    while cur is not None:\n        # \u30bf\u30fc\u30b2\u30c3\u30c8\u30ce\u30fc\u30c9\u306fcur\u306e\u53f3\u90e8\u5206\u6728\u306b\u3042\u308b\n        if cur.val &lt; num:\n            cur = cur.right\n        # \u30bf\u30fc\u30b2\u30c3\u30c8\u30ce\u30fc\u30c9\u306fcur\u306e\u5de6\u90e8\u5206\u6728\u306b\u3042\u308b\n        elif cur.val &gt; num:\n            cur = cur.left\n        # \u30bf\u30fc\u30b2\u30c3\u30c8\u30ce\u30fc\u30c9\u3092\u767a\u898b\u3001\u30eb\u30fc\u30d7\u3092\u30d6\u30ec\u30fc\u30af\n        else:\n            break\n    return cur\n</code></pre> binary_search_tree.cpp<pre><code>/* \u30ce\u30fc\u30c9\u3092\u691c\u7d22 */\nTreeNode *search(int num) {\n    TreeNode *cur = root;\n    // \u30eb\u30fc\u30d7\u3067\u691c\u7d22\u3001\u8449\u30ce\u30fc\u30c9\u3092\u901a\u308a\u904e\u304e\u305f\u3089\u7d42\u4e86\n    while (cur != nullptr) {\n        // \u76ee\u6a19\u30ce\u30fc\u30c9\u306fcur\u306e\u53f3\u90e8\u5206\u6728\u306b\u3042\u308b\n        if (cur-&gt;val &lt; num)\n            cur = cur-&gt;right;\n        // \u76ee\u6a19\u30ce\u30fc\u30c9\u306fcur\u306e\u5de6\u90e8\u5206\u6728\u306b\u3042\u308b\n        else if (cur-&gt;val &gt; num)\n            cur = cur-&gt;left;\n        // \u76ee\u6a19\u30ce\u30fc\u30c9\u3092\u898b\u3064\u3051\u305f\u3001\u30eb\u30fc\u30d7\u3092\u629c\u3051\u308b\n        else\n            break;\n    }\n    // \u76ee\u6a19\u30ce\u30fc\u30c9\u3092\u8fd4\u3059\n    return cur;\n}\n</code></pre> binary_search_tree.java<pre><code>/* \u30ce\u30fc\u30c9\u3092\u691c\u7d22 */\nTreeNode search(int num) {\n    TreeNode cur = root;\n    // \u30eb\u30fc\u30d7\u3067\u691c\u7d22\u3001\u8449\u30ce\u30fc\u30c9\u3092\u901a\u904e\u5f8c\u306b\u7d42\u4e86\n    while (cur != null) {\n        // \u5bfe\u8c61\u30ce\u30fc\u30c9\u306f cur \u306e\u53f3\u90e8\u5206\u6728\u306b\u3042\u308b\n        if (cur.val &lt; num)\n            cur = cur.right;\n        // \u5bfe\u8c61\u30ce\u30fc\u30c9\u306f cur \u306e\u5de6\u90e8\u5206\u6728\u306b\u3042\u308b\n        else if (cur.val &gt; num)\n            cur = cur.left;\n        // \u5bfe\u8c61\u30ce\u30fc\u30c9\u3092\u898b\u3064\u3051\u305f\u3001\u30eb\u30fc\u30d7\u3092\u7d42\u4e86\n        else\n            break;\n    }\n    // \u5bfe\u8c61\u30ce\u30fc\u30c9\u3092\u8fd4\u3059\n    return cur;\n}\n</code></pre> binary_search_tree.cs<pre><code>[class]{BinarySearchTree}-[func]{Search}\n</code></pre> binary_search_tree.go<pre><code>[class]{binarySearchTree}-[func]{search}\n</code></pre> binary_search_tree.swift<pre><code>[class]{BinarySearchTree}-[func]{search}\n</code></pre> binary_search_tree.js<pre><code>[class]{BinarySearchTree}-[func]{search}\n</code></pre> binary_search_tree.ts<pre><code>[class]{BinarySearchTree}-[func]{search}\n</code></pre> binary_search_tree.dart<pre><code>[class]{BinarySearchTree}-[func]{search}\n</code></pre> binary_search_tree.rs<pre><code>[class]{BinarySearchTree}-[func]{search}\n</code></pre> binary_search_tree.c<pre><code>[class]{BinarySearchTree}-[func]{search}\n</code></pre> binary_search_tree.kt<pre><code>[class]{BinarySearchTree}-[func]{search}\n</code></pre> binary_search_tree.rb<pre><code>[class]{BinarySearchTree}-[func]{search}\n</code></pre> binary_search_tree.zig<pre><code>[class]{BinarySearchTree}-[func]{search}\n</code></pre>"},{"location":"chapter_tree/binary_search_tree/#2","title":"2. \u00a0 \u30ce\u30fc\u30c9\u306e\u633f\u5165","text":"<p>\u633f\u5165\u3059\u308b\u8981\u7d20<code>num</code>\u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408\u3001\u4e8c\u5206\u63a2\u7d22\u6728\u306e\u6027\u8cea\u300c\u5de6\u90e8\u5206\u6728 &lt; \u6839\u30ce\u30fc\u30c9 &lt; \u53f3\u90e8\u5206\u6728\u300d\u3092\u7dad\u6301\u3059\u308b\u305f\u3081\u3001\u633f\u5165\u64cd\u4f5c\u306f\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u9032\u884c\u3057\u307e\u3059\u3002</p> <ol> <li>\u633f\u5165\u4f4d\u7f6e\u3092\u898b\u3064\u3051\u308b: \u691c\u7d22\u64cd\u4f5c\u3068\u540c\u69d8\u306b\u3001\u6839\u30ce\u30fc\u30c9\u304b\u3089\u958b\u59cb\u3057\u3001\u73fe\u5728\u306e\u30ce\u30fc\u30c9\u5024\u3068<code>num</code>\u306e\u30b5\u30a4\u30ba\u95a2\u4fc2\u306b\u5f93\u3063\u3066\u4e0b\u5411\u304d\u306b\u30eb\u30fc\u30d7\u3057\u3001\u8449\u30ce\u30fc\u30c9\u3092\u901a\u904e\uff08<code>None</code>\u306b\u8d70\u67fb\uff09\u3059\u308b\u307e\u3067\u3001\u30eb\u30fc\u30d7\u3092\u7d42\u4e86\u3057\u307e\u3059\u3002</li> <li>\u3053\u306e\u4f4d\u7f6e\u306b\u30ce\u30fc\u30c9\u3092\u633f\u5165: \u30ce\u30fc\u30c9<code>num</code>\u3092\u521d\u671f\u5316\u3057\u3001<code>None</code>\u304c\u3042\u3063\u305f\u5834\u6240\u306b\u914d\u7f6e\u3057\u307e\u3059\u3002</li> </ol> <p></p> <p> \u56f3 7-18 \u00a0 \u4e8c\u5206\u63a2\u7d22\u6728\u3078\u306e\u30ce\u30fc\u30c9\u633f\u5165 </p> <p>\u30b3\u30fc\u30c9\u5b9f\u88c5\u3067\u306f\u3001\u4ee5\u4e0b\u306e2\u70b9\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002</p> <ul> <li>\u4e8c\u5206\u63a2\u7d22\u6728\u306f\u91cd\u8907\u30ce\u30fc\u30c9\u306e\u5b58\u5728\u3092\u8a31\u53ef\u3057\u307e\u305b\u3093\u3002\u305d\u3046\u3067\u306a\u3051\u308c\u3070\u3001\u305d\u306e\u5b9a\u7fa9\u306b\u9055\u53cd\u3057\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u633f\u5165\u3059\u308b\u30ce\u30fc\u30c9\u304c\u65e2\u306b\u6728\u306b\u5b58\u5728\u3059\u308b\u5834\u5408\u3001\u633f\u5165\u306f\u5b9f\u884c\u3055\u308c\u305a\u3001\u30ce\u30fc\u30c9\u306f\u76f4\u63a5\u623b\u308a\u307e\u3059\u3002</li> <li>\u633f\u5165\u64cd\u4f5c\u3092\u5b9f\u884c\u3059\u308b\u306b\u306f\u3001\u524d\u306e\u30eb\u30fc\u30d7\u304b\u3089\u306e\u30ce\u30fc\u30c9\u3092\u4fdd\u5b58\u3059\u308b\u305f\u3081\u306b\u30ce\u30fc\u30c9<code>pre</code>\u3092\u4f7f\u7528\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u3088\u3046\u306b\u3057\u3066\u3001<code>None</code>\u306b\u8d70\u67fb\u3057\u305f\u3068\u304d\u306b\u3001\u305d\u306e\u89aa\u30ce\u30fc\u30c9\u3092\u53d6\u5f97\u3067\u304d\u3001\u30ce\u30fc\u30c9\u633f\u5165\u64cd\u4f5c\u3092\u5b8c\u4e86\u3067\u304d\u307e\u3059\u3002</li> </ul> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig binary_search_tree.py<pre><code>def insert(self, num: int):\n    \"\"\"\u30ce\u30fc\u30c9\u3092\u633f\u5165\"\"\"\n    # \u6728\u304c\u7a7a\u306e\u5834\u5408\u3001\u30eb\u30fc\u30c8\u30ce\u30fc\u30c9\u3092\u521d\u671f\u5316\n    if self._root is None:\n        self._root = TreeNode(num)\n        return\n    # \u30eb\u30fc\u30d7\u3067\u63a2\u7d22\u3001\u8449\u30ce\u30fc\u30c9\u3092\u901a\u904e\u3057\u305f\u5f8c\u306b\u30d6\u30ec\u30fc\u30af\n    cur, pre = self._root, None\n    while cur is not None:\n        # \u91cd\u8907\u30ce\u30fc\u30c9\u3092\u767a\u898b\u3057\u305f\u305f\u3081\u3001\u623b\u308b\n        if cur.val == num:\n            return\n        pre = cur\n        # \u633f\u5165\u4f4d\u7f6e\u306fcur\u306e\u53f3\u90e8\u5206\u6728\u306b\u3042\u308b\n        if cur.val &lt; num:\n            cur = cur.right\n        # \u633f\u5165\u4f4d\u7f6e\u306fcur\u306e\u5de6\u90e8\u5206\u6728\u306b\u3042\u308b\n        else:\n            cur = cur.left\n    # \u30ce\u30fc\u30c9\u3092\u633f\u5165\n    node = TreeNode(num)\n    if pre.val &lt; num:\n        pre.right = node\n    else:\n        pre.left = node\n</code></pre> binary_search_tree.cpp<pre><code>/* \u30ce\u30fc\u30c9\u3092\u633f\u5165 */\nvoid insert(int num) {\n    // \u6728\u304c\u7a7a\u306e\u5834\u5408\u3001\u30eb\u30fc\u30c8\u30ce\u30fc\u30c9\u3092\u521d\u671f\u5316\n    if (root == nullptr) {\n        root = new TreeNode(num);\n        return;\n    }\n    TreeNode *cur = root, *pre = nullptr;\n    // \u30eb\u30fc\u30d7\u3067\u691c\u7d22\u3001\u8449\u30ce\u30fc\u30c9\u3092\u901a\u308a\u904e\u304e\u305f\u3089\u7d42\u4e86\n    while (cur != nullptr) {\n        // \u91cd\u8907\u30ce\u30fc\u30c9\u3092\u898b\u3064\u3051\u305f\u5834\u5408\u3001\u623b\u308b\n        if (cur-&gt;val == num)\n            return;\n        pre = cur;\n        // \u633f\u5165\u4f4d\u7f6e\u306fcur\u306e\u53f3\u90e8\u5206\u6728\u306b\u3042\u308b\n        if (cur-&gt;val &lt; num)\n            cur = cur-&gt;right;\n        // \u633f\u5165\u4f4d\u7f6e\u306fcur\u306e\u5de6\u90e8\u5206\u6728\u306b\u3042\u308b\n        else\n            cur = cur-&gt;left;\n    }\n    // \u30ce\u30fc\u30c9\u3092\u633f\u5165\n    TreeNode *node = new TreeNode(num);\n    if (pre-&gt;val &lt; num)\n        pre-&gt;right = node;\n    else\n        pre-&gt;left = node;\n}\n</code></pre> binary_search_tree.java<pre><code>/* \u30ce\u30fc\u30c9\u3092\u633f\u5165 */\nvoid insert(int num) {\n    // \u6728\u304c\u7a7a\u306e\u5834\u5408\u3001\u6839\u30ce\u30fc\u30c9\u3092\u521d\u671f\u5316\n    if (root == null) {\n        root = new TreeNode(num);\n        return;\n    }\n    TreeNode cur = root, pre = null;\n    // \u30eb\u30fc\u30d7\u3067\u691c\u7d22\u3001\u8449\u30ce\u30fc\u30c9\u3092\u901a\u904e\u5f8c\u306b\u7d42\u4e86\n    while (cur != null) {\n        // \u91cd\u8907\u30ce\u30fc\u30c9\u3092\u898b\u3064\u3051\u305f\u5834\u5408\u3001\u623b\u308b\n        if (cur.val == num)\n            return;\n        pre = cur;\n        // \u633f\u5165\u4f4d\u7f6e\u306f cur \u306e\u53f3\u90e8\u5206\u6728\u306b\u3042\u308b\n        if (cur.val &lt; num)\n            cur = cur.right;\n        // \u633f\u5165\u4f4d\u7f6e\u306f cur \u306e\u5de6\u90e8\u5206\u6728\u306b\u3042\u308b\n        else\n            cur = cur.left;\n    }\n    // \u30ce\u30fc\u30c9\u3092\u633f\u5165\n    TreeNode node = new TreeNode(num);\n    if (pre.val &lt; num)\n        pre.right = node;\n    else\n        pre.left = node;\n}\n</code></pre> binary_search_tree.cs<pre><code>[class]{BinarySearchTree}-[func]{Insert}\n</code></pre> binary_search_tree.go<pre><code>[class]{binarySearchTree}-[func]{insert}\n</code></pre> binary_search_tree.swift<pre><code>[class]{BinarySearchTree}-[func]{insert}\n</code></pre> binary_search_tree.js<pre><code>[class]{BinarySearchTree}-[func]{insert}\n</code></pre> binary_search_tree.ts<pre><code>[class]{BinarySearchTree}-[func]{insert}\n</code></pre> binary_search_tree.dart<pre><code>[class]{BinarySearchTree}-[func]{insert}\n</code></pre> binary_search_tree.rs<pre><code>[class]{BinarySearchTree}-[func]{insert}\n</code></pre> binary_search_tree.c<pre><code>[class]{BinarySearchTree}-[func]{insert}\n</code></pre> binary_search_tree.kt<pre><code>[class]{BinarySearchTree}-[func]{insert}\n</code></pre> binary_search_tree.rb<pre><code>[class]{BinarySearchTree}-[func]{insert}\n</code></pre> binary_search_tree.zig<pre><code>[class]{BinarySearchTree}-[func]{insert}\n</code></pre> <p>\u30ce\u30fc\u30c9\u306e\u691c\u7d22\u3068\u540c\u69d8\u306b\u3001\u30ce\u30fc\u30c9\u306e\u633f\u5165\u306b\u306f\\(O(\\log n)\\)\u306e\u6642\u9593\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002</p>"},{"location":"chapter_tree/binary_search_tree/#3","title":"3. \u00a0 \u30ce\u30fc\u30c9\u306e\u524a\u9664","text":"<p>\u307e\u305a\u3001\u4e8c\u5206\u6728\u3067\u30bf\u30fc\u30b2\u30c3\u30c8\u30ce\u30fc\u30c9\u3092\u898b\u3064\u3051\u3001\u305d\u308c\u3092\u524a\u9664\u3057\u307e\u3059\u3002\u30ce\u30fc\u30c9\u306e\u633f\u5165\u3068\u540c\u69d8\u306b\u3001\u524a\u9664\u64cd\u4f5c\u304c\u5b8c\u4e86\u3057\u305f\u5f8c\u3082\u3001\u4e8c\u5206\u63a2\u7d22\u6728\u306e\u6027\u8cea\u300c\u5de6\u90e8\u5206\u6728 &lt; \u6839\u30ce\u30fc\u30c9 &lt; \u53f3\u90e8\u5206\u6728\u300d\u304c\u6e80\u305f\u3055\u308c\u308b\u3053\u3068\u3092\u4fdd\u8a3c\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u30bf\u30fc\u30b2\u30c3\u30c8\u30ce\u30fc\u30c9\u306e\u5b50\u30ce\u30fc\u30c9\u6570\u306b\u57fa\u3065\u3044\u3066\u30010\u30011\u30012\u306e3\u3064\u306e\u30b1\u30fc\u30b9\u306b\u5206\u3051\u3001\u5bfe\u5fdc\u3059\u308b\u30ce\u30fc\u30c9\u524a\u9664\u64cd\u4f5c\u3092\u5b9f\u884c\u3057\u307e\u3059\u3002</p> <p>\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u524a\u9664\u3059\u308b\u30ce\u30fc\u30c9\u306e\u6b21\u6570\u304c\\(0\\)\u306e\u5834\u5408\u3001\u305d\u306e\u30ce\u30fc\u30c9\u306f\u8449\u30ce\u30fc\u30c9\u3067\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u3001\u76f4\u63a5\u524a\u9664\u3067\u304d\u307e\u3059\u3002</p> <p></p> <p> \u56f3 7-19 \u00a0 \u4e8c\u5206\u63a2\u7d22\u6728\u3067\u306e\u30ce\u30fc\u30c9\u524a\u9664\uff08\u6b21\u65700\uff09 </p> <p>\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u524a\u9664\u3059\u308b\u30ce\u30fc\u30c9\u306e\u6b21\u6570\u304c\\(1\\)\u306e\u5834\u5408\u3001\u524a\u9664\u3059\u308b\u30ce\u30fc\u30c9\u3092\u305d\u306e\u5b50\u30ce\u30fc\u30c9\u3067\u7f6e\u304d\u63db\u3048\u308b\u3060\u3051\u3067\u5341\u5206\u3067\u3059\u3002</p> <p></p> <p> \u56f3 7-20 \u00a0 \u4e8c\u5206\u63a2\u7d22\u6728\u3067\u306e\u30ce\u30fc\u30c9\u524a\u9664\uff08\u6b21\u65701\uff09 </p> <p>\u524a\u9664\u3059\u308b\u30ce\u30fc\u30c9\u306e\u6b21\u6570\u304c\\(2\\)\u306e\u5834\u5408\u3001\u76f4\u63a5\u524a\u9664\u3059\u308b\u3053\u3068\u306f\u3067\u304d\u307e\u305b\u3093\u304c\u3001\u30ce\u30fc\u30c9\u3092\u4f7f\u7528\u3057\u3066\u7f6e\u304d\u63db\u3048\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u4e8c\u5206\u63a2\u7d22\u6728\u306e\u6027\u8cea\u300c\u5de6\u90e8\u5206\u6728 \\(&lt;\\) \u6839\u30ce\u30fc\u30c9 \\(&lt;\\) \u53f3\u90e8\u5206\u6728\u300d\u3092\u7dad\u6301\u3059\u308b\u305f\u3081\u3001\u3053\u306e\u30ce\u30fc\u30c9\u306f\u53f3\u90e8\u5206\u6728\u306e\u6700\u5c0f\u30ce\u30fc\u30c9\u307e\u305f\u306f\u5de6\u90e8\u5206\u6728\u306e\u6700\u5927\u30ce\u30fc\u30c9\u306e\u3044\u305a\u308c\u304b\u3067\u3059\u3002</p> <p>\u53f3\u90e8\u5206\u6728\u306e\u6700\u5c0f\u30ce\u30fc\u30c9\uff08\u4e2d\u9806\u8d70\u67fb\u3067\u306e\u6b21\u306e\u30ce\u30fc\u30c9\uff09\u3092\u9078\u629e\u3059\u308b\u3068\u4eee\u5b9a\u3059\u308b\u3068\u3001\u524a\u9664\u64cd\u4f5c\u306f\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u9032\u884c\u3057\u307e\u3059\u3002</p> <ol> <li>\u524a\u9664\u3059\u308b\u30ce\u30fc\u30c9\u306e\u300c\u4e2d\u9806\u8d70\u67fb\u30b7\u30fc\u30b1\u30f3\u30b9\u300d\u3067\u306e\u6b21\u306e\u30ce\u30fc\u30c9\u3092\u898b\u3064\u3051\u3001<code>tmp</code>\u3068\u3057\u3066\u793a\u3057\u307e\u3059\u3002</li> <li>\u524a\u9664\u3059\u308b\u30ce\u30fc\u30c9\u306e\u5024\u3092<code>tmp</code>\u306e\u5024\u3067\u7f6e\u304d\u63db\u3048\u3001\u6728\u5185\u3067\u30ce\u30fc\u30c9<code>tmp</code>\u3092\u518d\u5e30\u7684\u306b\u524a\u9664\u3057\u307e\u3059\u3002</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt; <p></p> <p></p> <p></p> <p></p> <p> \u56f3 7-21 \u00a0 \u4e8c\u5206\u63a2\u7d22\u6728\u3067\u306e\u30ce\u30fc\u30c9\u524a\u9664\uff08\u6b21\u65702\uff09 </p> <p>\u30ce\u30fc\u30c9\u3092\u524a\u9664\u3059\u308b\u64cd\u4f5c\u3082\\(O(\\log n)\\)\u306e\u6642\u9593\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002\u524a\u9664\u3059\u308b\u30ce\u30fc\u30c9\u3092\u898b\u3064\u3051\u308b\u306e\u306b\\(O(\\log n)\\)\u306e\u6642\u9593\u304c\u5fc5\u8981\u3067\u3001\u4e2d\u9806\u8d70\u67fb\u306e\u5f8c\u7d99\u30ce\u30fc\u30c9\u3092\u53d6\u5f97\u3059\u308b\u306e\u306b\\(O(\\log n)\\)\u306e\u6642\u9593\u304c\u5fc5\u8981\u3067\u3059\u3002\u30b3\u30fc\u30c9\u4f8b\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig binary_search_tree.py<pre><code>def remove(self, num: int):\n    \"\"\"\u30ce\u30fc\u30c9\u3092\u524a\u9664\"\"\"\n    # \u6728\u304c\u7a7a\u306e\u5834\u5408\u3001\u623b\u308b\n    if self._root is None:\n        return\n    # \u30eb\u30fc\u30d7\u3067\u63a2\u7d22\u3001\u8449\u30ce\u30fc\u30c9\u3092\u901a\u904e\u3057\u305f\u5f8c\u306b\u30d6\u30ec\u30fc\u30af\n    cur, pre = self._root, None\n    while cur is not None:\n        # \u524a\u9664\u3059\u308b\u30ce\u30fc\u30c9\u3092\u767a\u898b\u3001\u30eb\u30fc\u30d7\u3092\u30d6\u30ec\u30fc\u30af\n        if cur.val == num:\n            break\n        pre = cur\n        # \u524a\u9664\u3059\u308b\u30ce\u30fc\u30c9\u306fcur\u306e\u53f3\u90e8\u5206\u6728\u306b\u3042\u308b\n        if cur.val &lt; num:\n            cur = cur.right\n        # \u524a\u9664\u3059\u308b\u30ce\u30fc\u30c9\u306fcur\u306e\u5de6\u90e8\u5206\u6728\u306b\u3042\u308b\n        else:\n            cur = cur.left\n    # \u524a\u9664\u3059\u308b\u30ce\u30fc\u30c9\u304c\u5b58\u5728\u3057\u306a\u3044\u5834\u5408\u3001\u623b\u308b\n    if cur is None:\n        return\n\n    # \u5b50\u30ce\u30fc\u30c9\u6570 = 0 \u307e\u305f\u306f 1\n    if cur.left is None or cur.right is None:\n        # \u5b50\u30ce\u30fc\u30c9\u6570 = 0/1\u306e\u5834\u5408\u3001child = null/\u305d\u306e\u5b50\u30ce\u30fc\u30c9\n        child = cur.left or cur.right\n        # \u30ce\u30fc\u30c9cur\u3092\u524a\u9664\n        if cur != self._root:\n            if pre.left == cur:\n                pre.left = child\n            else:\n                pre.right = child\n        else:\n            # \u524a\u9664\u3055\u308c\u308b\u30ce\u30fc\u30c9\u304c\u30eb\u30fc\u30c8\u306e\u5834\u5408\u3001\u30eb\u30fc\u30c8\u3092\u518d\u5272\u308a\u5f53\u3066\n            self._root = child\n    # \u5b50\u30ce\u30fc\u30c9\u6570 = 2\n    else:\n        # cur\u306e\u4e2d\u9806\u8d70\u67fb\u306e\u6b21\u306e\u30ce\u30fc\u30c9\u3092\u53d6\u5f97\n        tmp: TreeNode = cur.right\n        while tmp.left is not None:\n            tmp = tmp.left\n        # \u518d\u5e30\u7684\u306b\u30ce\u30fc\u30c9tmp\u3092\u524a\u9664\n        self.remove(tmp.val)\n        # cur\u3092tmp\u3067\u7f6e\u304d\u63db\u3048\n        cur.val = tmp.val\n</code></pre> binary_search_tree.cpp<pre><code>/* \u30ce\u30fc\u30c9\u3092\u524a\u9664 */\nvoid remove(int num) {\n    // \u6728\u304c\u7a7a\u306e\u5834\u5408\u3001\u623b\u308b\n    if (root == nullptr)\n        return;\n    TreeNode *cur = root, *pre = nullptr;\n    // \u30eb\u30fc\u30d7\u3067\u691c\u7d22\u3001\u8449\u30ce\u30fc\u30c9\u3092\u901a\u308a\u904e\u304e\u305f\u3089\u7d42\u4e86\n    while (cur != nullptr) {\n        // \u524a\u9664\u3059\u308b\u30ce\u30fc\u30c9\u3092\u898b\u3064\u3051\u305f\u3001\u30eb\u30fc\u30d7\u3092\u629c\u3051\u308b\n        if (cur-&gt;val == num)\n            break;\n        pre = cur;\n        // \u524a\u9664\u3059\u308b\u30ce\u30fc\u30c9\u306fcur\u306e\u53f3\u90e8\u5206\u6728\u306b\u3042\u308b\n        if (cur-&gt;val &lt; num)\n            cur = cur-&gt;right;\n        // \u524a\u9664\u3059\u308b\u30ce\u30fc\u30c9\u306fcur\u306e\u5de6\u90e8\u5206\u6728\u306b\u3042\u308b\n        else\n            cur = cur-&gt;left;\n    }\n    // \u524a\u9664\u3059\u308b\u30ce\u30fc\u30c9\u304c\u306a\u3044\u5834\u5408\u3001\u623b\u308b\n    if (cur == nullptr)\n        return;\n    // \u5b50\u30ce\u30fc\u30c9\u6570 = 0 \u307e\u305f\u306f 1\n    if (cur-&gt;left == nullptr || cur-&gt;right == nullptr) {\n        // \u5b50\u30ce\u30fc\u30c9\u6570 = 0 / 1\u306e\u5834\u5408\u3001child = nullptr / \u305d\u306e\u5b50\u30ce\u30fc\u30c9\n        TreeNode *child = cur-&gt;left != nullptr ? cur-&gt;left : cur-&gt;right;\n        // \u30ce\u30fc\u30c9cur\u3092\u524a\u9664\n        if (cur != root) {\n            if (pre-&gt;left == cur)\n                pre-&gt;left = child;\n            else\n                pre-&gt;right = child;\n        } else {\n            // \u524a\u9664\u3055\u308c\u308b\u30ce\u30fc\u30c9\u304c\u30eb\u30fc\u30c8\u306e\u5834\u5408\u3001\u30eb\u30fc\u30c8\u3092\u518d\u5272\u308a\u5f53\u3066\n            root = child;\n        }\n        // \u30e1\u30e2\u30ea\u3092\u89e3\u653e\n        delete cur;\n    }\n    // \u5b50\u30ce\u30fc\u30c9\u6570 = 2\n    else {\n        // cur\u306e\u4e2d\u9806\u8d70\u67fb\u306e\u6b21\u306e\u30ce\u30fc\u30c9\u3092\u53d6\u5f97\n        TreeNode *tmp = cur-&gt;right;\n        while (tmp-&gt;left != nullptr) {\n            tmp = tmp-&gt;left;\n        }\n        int tmpVal = tmp-&gt;val;\n        // \u30ce\u30fc\u30c9tmp\u3092\u518d\u5e30\u7684\u306b\u524a\u9664\n        remove(tmp-&gt;val);\n        // cur\u3092tmp\u3067\u7f6e\u304d\u63db\u3048\n        cur-&gt;val = tmpVal;\n    }\n}\n</code></pre> binary_search_tree.java<pre><code>/* \u30ce\u30fc\u30c9\u3092\u524a\u9664 */\nvoid remove(int num) {\n    // \u6728\u304c\u7a7a\u306e\u5834\u5408\u3001\u623b\u308b\n    if (root == null)\n        return;\n    TreeNode cur = root, pre = null;\n    // \u30eb\u30fc\u30d7\u3067\u691c\u7d22\u3001\u8449\u30ce\u30fc\u30c9\u3092\u901a\u904e\u5f8c\u306b\u7d42\u4e86\n    while (cur != null) {\n        // \u524a\u9664\u3059\u308b\u30ce\u30fc\u30c9\u3092\u898b\u3064\u3051\u305f\u3001\u30eb\u30fc\u30d7\u3092\u7d42\u4e86\n        if (cur.val == num)\n            break;\n        pre = cur;\n        // \u524a\u9664\u3059\u308b\u30ce\u30fc\u30c9\u306f cur \u306e\u53f3\u90e8\u5206\u6728\u306b\u3042\u308b\n        if (cur.val &lt; num)\n            cur = cur.right;\n        // \u524a\u9664\u3059\u308b\u30ce\u30fc\u30c9\u306f cur \u306e\u5de6\u90e8\u5206\u6728\u306b\u3042\u308b\n        else\n            cur = cur.left;\n    }\n    // \u524a\u9664\u3059\u308b\u30ce\u30fc\u30c9\u304c\u306a\u3044\u5834\u5408\u3001\u623b\u308b\n    if (cur == null)\n        return;\n    // \u5b50\u30ce\u30fc\u30c9\u6570 = 0 \u307e\u305f\u306f 1\n    if (cur.left == null || cur.right == null) {\n        // \u5b50\u30ce\u30fc\u30c9\u6570 = 0/1 \u306e\u5834\u5408\u3001child = null/\u305d\u306e\u5b50\u30ce\u30fc\u30c9\n        TreeNode child = cur.left != null ? cur.left : cur.right;\n        // \u30ce\u30fc\u30c9 cur \u3092\u524a\u9664\n        if (cur != root) {\n            if (pre.left == cur)\n                pre.left = child;\n            else\n                pre.right = child;\n        } else {\n            // \u524a\u9664\u3055\u308c\u308b\u30ce\u30fc\u30c9\u304c\u6839\u306e\u5834\u5408\u3001\u6839\u3092\u518d\u5272\u308a\u5f53\u3066\n            root = child;\n        }\n    }\n    // \u5b50\u30ce\u30fc\u30c9\u6570 = 2\n    else {\n        // cur \u306e\u4e2d\u9806\u8d70\u67fb\u306e\u6b21\u306e\u30ce\u30fc\u30c9\u3092\u53d6\u5f97\n        TreeNode tmp = cur.right;\n        while (tmp.left != null) {\n            tmp = tmp.left;\n        }\n        // \u518d\u5e30\u7684\u306b\u30ce\u30fc\u30c9 tmp \u3092\u524a\u9664\n        remove(tmp.val);\n        // cur \u3092 tmp \u3067\u7f6e\u304d\u63db\u3048\u308b\n        cur.val = tmp.val;\n    }\n}\n</code></pre> binary_search_tree.cs<pre><code>[class]{BinarySearchTree}-[func]{Remove}\n</code></pre> binary_search_tree.go<pre><code>[class]{binarySearchTree}-[func]{remove}\n</code></pre> binary_search_tree.swift<pre><code>[class]{BinarySearchTree}-[func]{remove}\n</code></pre> binary_search_tree.js<pre><code>[class]{BinarySearchTree}-[func]{remove}\n</code></pre> binary_search_tree.ts<pre><code>[class]{BinarySearchTree}-[func]{remove}\n</code></pre> binary_search_tree.dart<pre><code>[class]{BinarySearchTree}-[func]{remove}\n</code></pre> binary_search_tree.rs<pre><code>[class]{BinarySearchTree}-[func]{remove}\n</code></pre> binary_search_tree.c<pre><code>[class]{BinarySearchTree}-[func]{removeItem}\n</code></pre> binary_search_tree.kt<pre><code>[class]{BinarySearchTree}-[func]{remove}\n</code></pre> binary_search_tree.rb<pre><code>[class]{BinarySearchTree}-[func]{remove}\n</code></pre> binary_search_tree.zig<pre><code>[class]{BinarySearchTree}-[func]{remove}\n</code></pre>"},{"location":"chapter_tree/binary_search_tree/#4","title":"4. \u00a0 \u4e2d\u9806\u8d70\u67fb\u306f\u9806\u5e8f\u4ed8\u3051\u3055\u308c\u3066\u3044\u308b","text":"<p>\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u4e8c\u5206\u6728\u306e\u4e2d\u9806\u8d70\u67fb\u306f\u300c\u5de6 \\(\\rightarrow\\) \u6839 \\(\\rightarrow\\) \u53f3\u300d\u306e\u8d70\u67fb\u9806\u5e8f\u306b\u5f93\u3044\u3001\u4e8c\u5206\u63a2\u7d22\u6728\u306f\u300c\u5de6\u5b50\u30ce\u30fc\u30c9 \\(&lt;\\) \u6839\u30ce\u30fc\u30c9 \\(&lt;\\) \u53f3\u5b50\u30ce\u30fc\u30c9\u300d\u306e\u30b5\u30a4\u30ba\u95a2\u4fc2\u3092\u6e80\u305f\u3057\u307e\u3059\u3002</p> <p>\u3053\u308c\u306f\u3001\u4e8c\u5206\u63a2\u7d22\u6728\u3067\u4e2d\u9806\u8d70\u67fb\u3092\u5b9f\u884c\u3059\u308b\u3068\u304d\u306b\u3001\u5e38\u306b\u6b21\u306b\u5c0f\u3055\u3044\u30ce\u30fc\u30c9\u304c\u6700\u521d\u306b\u8d70\u67fb\u3055\u308c\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u3001\u91cd\u8981\u306a\u6027\u8cea\u306b\u3064\u306a\u304c\u308a\u307e\u3059\uff1a\u4e8c\u5206\u63a2\u7d22\u6728\u306e\u4e2d\u9806\u8d70\u67fb\u306e\u30b7\u30fc\u30b1\u30f3\u30b9\u306f\u6607\u9806\u3067\u3059\u3002</p> <p>\u4e2d\u9806\u8d70\u67fb\u306e\u6607\u9806\u6027\u8cea\u3092\u4f7f\u7528\u3057\u3066\u3001\u4e8c\u5206\u63a2\u7d22\u6728\u3067\u9806\u5e8f\u4ed8\u3051\u3055\u308c\u305f\u30c7\u30fc\u30bf\u3092\u53d6\u5f97\u3059\u308b\u306b\u306f\\(O(n)\\)\u306e\u6642\u9593\u306e\u307f\u304c\u5fc5\u8981\u3067\u3001\u8ffd\u52a0\u306e\u30bd\u30fc\u30c8\u64cd\u4f5c\u306f\u4e0d\u8981\u3067\u3042\u308a\u3001\u975e\u5e38\u306b\u52b9\u7387\u7684\u3067\u3059\u3002</p> <p></p> <p> \u56f3 7-22 \u00a0 \u4e8c\u5206\u63a2\u7d22\u6728\u306e\u4e2d\u9806\u8d70\u67fb\u30b7\u30fc\u30b1\u30f3\u30b9 </p>"},{"location":"chapter_tree/binary_search_tree/#742","title":"7.4.2 \u00a0 \u4e8c\u5206\u63a2\u7d22\u6728\u306e\u52b9\u7387","text":"<p>\u30c7\u30fc\u30bf\u306e\u30bb\u30c3\u30c8\u304c\u4e0e\u3048\u3089\u308c\u305f\u5834\u5408\u3001\u914d\u5217\u307e\u305f\u306f\u4e8c\u5206\u63a2\u7d22\u6728\u3092\u4f7f\u7528\u3057\u3066\u683c\u7d0d\u3059\u308b\u3053\u3068\u3092\u691c\u8a0e\u3057\u307e\u3059\u3002\u4e0b\u306e\u8868\u3092\u89b3\u5bdf\u3059\u308b\u3068\u3001\u4e8c\u5206\u63a2\u7d22\u6728\u306e\u3059\u3079\u3066\u306e\u64cd\u4f5c\u306f\u5bfe\u6570\u6642\u9593\u8a08\u7b97\u91cf\u3092\u6301\u3061\u3001\u5b89\u5b9a\u3057\u3066\u52b9\u7387\u7684\u3067\u3059\u3002\u914d\u5217\u306f\u3001\u983b\u7e41\u306a\u8ffd\u52a0\u3068\u691c\u7d22\u3084\u524a\u9664\u306e\u983b\u5ea6\u304c\u5c11\u306a\u3044\u30b7\u30ca\u30ea\u30aa\u3067\u306e\u307f\u3001\u4e8c\u5206\u63a2\u7d22\u6728\u3088\u308a\u3082\u52b9\u7387\u7684\u3067\u3059\u3002</p> <p> \u8868 7-2 \u00a0 \u914d\u5217\u3068\u63a2\u7d22\u6728\u306e\u52b9\u7387\u6bd4\u8f03 </p> \u672a\u30bd\u30fc\u30c8\u914d\u5217 \u4e8c\u5206\u63a2\u7d22\u6728 \u8981\u7d20\u306e\u691c\u7d22 \\(O(n)\\) \\(O(\\log n)\\) \u8981\u7d20\u306e\u633f\u5165 \\(O(1)\\) \\(O(\\log n)\\) \u8981\u7d20\u306e\u524a\u9664 \\(O(n)\\) \\(O(\\log n)\\) <p>\u7406\u60f3\u7684\u306b\u306f\u3001\u4e8c\u5206\u63a2\u7d22\u6728\u306f\u300c\u5e73\u8861\u300d\u3057\u3066\u304a\u308a\u3001\u4efb\u610f\u306e\u30ce\u30fc\u30c9\u3092\\(\\log n\\)\u30eb\u30fc\u30d7\u5185\u3067\u898b\u3064\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002</p> <p>\u3057\u304b\u3057\u3001\u4e8c\u5206\u63a2\u7d22\u6728\u3067\u7d99\u7d9a\u7684\u306b\u30ce\u30fc\u30c9\u3092\u633f\u5165\u304a\u3088\u3073\u524a\u9664\u3059\u308b\u3068\u3001\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u9023\u7d50\u30ea\u30b9\u30c8\u306b\u9000\u5316\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u3001\u3055\u307e\u3056\u307e\u306a\u64cd\u4f5c\u306e\u6642\u9593\u8a08\u7b97\u91cf\u3082\\(O(n)\\)\u306b\u60aa\u5316\u3057\u307e\u3059\u3002</p> <p></p> <p> \u56f3 7-23 \u00a0 \u4e8c\u5206\u63a2\u7d22\u6728\u306e\u9000\u5316 </p>"},{"location":"chapter_tree/binary_search_tree/#743","title":"7.4.3 \u00a0 \u4e8c\u5206\u63a2\u7d22\u6728\u306e\u4e00\u822c\u7684\u306a\u5fdc\u7528","text":"<ul> <li>\u30b7\u30b9\u30c6\u30e0\u3067\u306e\u591a\u30ec\u30d9\u30eb\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u3068\u3057\u3066\u4f7f\u7528\u3055\u308c\u3001\u52b9\u7387\u7684\u306a\u691c\u7d22\u3001\u633f\u5165\u3001\u524a\u9664\u64cd\u4f5c\u3092\u5b9f\u88c5\u3057\u307e\u3059\u3002</li> <li>\u7279\u5b9a\u306e\u691c\u7d22\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u57fa\u76e4\u3068\u306a\u308b\u30c7\u30fc\u30bf\u69cb\u9020\u3068\u3057\u3066\u6a5f\u80fd\u3057\u307e\u3059\u3002</li> <li>\u30c7\u30fc\u30bf\u30b9\u30c8\u30ea\u30fc\u30e0\u3092\u683c\u7d0d\u3057\u3066\u3001\u305d\u306e\u9806\u5e8f\u4ed8\u3051\u3055\u308c\u305f\u72b6\u614b\u3092\u7dad\u6301\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002</li> </ul>"},{"location":"chapter_tree/binary_tree/","title":"7.1 \u00a0 \u4e8c\u5206\u6728","text":"<p>\u4e8c\u5206\u6728\u306f\u3001\u7956\u5148\u3068\u5b50\u5b6b\u306e\u9593\u306e\u968e\u5c64\u95a2\u4fc2\u3092\u8868\u73fe\u3057\u3001\u300c\u4e8c\u3064\u306b\u5206\u5272\u3059\u308b\u300d\u5206\u5272\u7d71\u6cbb\u6cd5\u306e\u8ad6\u7406\u3092\u4f53\u73fe\u3059\u308b\u975e\u7dda\u5f62\u30c7\u30fc\u30bf\u69cb\u9020\u3067\u3059\u3002\u9023\u7d50\u30ea\u30b9\u30c8\u3068\u540c\u69d8\u306b\u3001\u4e8c\u5206\u6728\u306e\u57fa\u672c\u5358\u4f4d\u306f\u30ce\u30fc\u30c9\u3067\u3042\u308a\u3001\u5404\u30ce\u30fc\u30c9\u306f\u5024\u3001\u5de6\u306e\u5b50\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\u3001\u53f3\u306e\u5b50\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\u3092\u542b\u307f\u307e\u3059\u3002</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig <pre><code>class TreeNode:\n    \"\"\"\u4e8c\u5206\u6728\u30ce\u30fc\u30c9\"\"\"\n    def __init__(self, val: int):\n        self.val: int = val                # \u30ce\u30fc\u30c9\u5024\n        self.left: TreeNode | None = None  # \u5de6\u306e\u5b50\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\n        self.right: TreeNode | None = None # \u53f3\u306e\u5b50\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\n</code></pre> <pre><code>/* \u4e8c\u5206\u6728\u30ce\u30fc\u30c9 */\nstruct TreeNode {\n    int val;          // \u30ce\u30fc\u30c9\u5024\n    TreeNode *left;   // \u5de6\u306e\u5b50\u30ce\u30fc\u30c9\u3078\u306e\u30dd\u30a4\u30f3\u30bf\n    TreeNode *right;  // \u53f3\u306e\u5b50\u30ce\u30fc\u30c9\u3078\u306e\u30dd\u30a4\u30f3\u30bf\n    TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}\n};\n</code></pre> <pre><code>/* \u4e8c\u5206\u6728\u30ce\u30fc\u30c9 */\nclass TreeNode {\n    int val;         // \u30ce\u30fc\u30c9\u5024\n    TreeNode left;   // \u5de6\u306e\u5b50\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\n    TreeNode right;  // \u53f3\u306e\u5b50\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\n    TreeNode(int x) { val = x; }\n}\n</code></pre> <pre><code>/* \u4e8c\u5206\u6728\u30ce\u30fc\u30c9 */\nclass TreeNode(int? x) {\n    public int? val = x;    // \u30ce\u30fc\u30c9\u5024\n    public TreeNode? left;  // \u5de6\u306e\u5b50\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\n    public TreeNode? right; // \u53f3\u306e\u5b50\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\n}\n</code></pre> <pre><code>/* \u4e8c\u5206\u6728\u30ce\u30fc\u30c9 */\ntype TreeNode struct {\n    Val   int\n    Left  *TreeNode\n    Right *TreeNode\n}\n/* \u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf */\nfunc NewTreeNode(v int) *TreeNode {\n    return &amp;TreeNode{\n        Left:  nil, // \u5de6\u306e\u5b50\u30ce\u30fc\u30c9\u3078\u306e\u30dd\u30a4\u30f3\u30bf\n        Right: nil, // \u53f3\u306e\u5b50\u30ce\u30fc\u30c9\u3078\u306e\u30dd\u30a4\u30f3\u30bf\n        Val:   v,   // \u30ce\u30fc\u30c9\u5024\n    }\n}\n</code></pre> <pre><code>/* \u4e8c\u5206\u6728\u30ce\u30fc\u30c9 */\nclass TreeNode {\n    var val: Int // \u30ce\u30fc\u30c9\u5024\n    var left: TreeNode? // \u5de6\u306e\u5b50\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\n    var right: TreeNode? // \u53f3\u306e\u5b50\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\n\n    init(x: Int) {\n        val = x\n    }\n}\n</code></pre> <pre><code>/* \u4e8c\u5206\u6728\u30ce\u30fc\u30c9 */\nclass TreeNode {\n    val; // \u30ce\u30fc\u30c9\u5024\n    left; // \u5de6\u306e\u5b50\u30ce\u30fc\u30c9\u3078\u306e\u30dd\u30a4\u30f3\u30bf\n    right; // \u53f3\u306e\u5b50\u30ce\u30fc\u30c9\u3078\u306e\u30dd\u30a4\u30f3\u30bf\n    constructor(val, left, right) {\n        this.val = val === undefined ? 0 : val;\n        this.left = left === undefined ? null : left;\n        this.right = right === undefined ? null : right;\n    }\n}\n</code></pre> <pre><code>/* \u4e8c\u5206\u6728\u30ce\u30fc\u30c9 */\nclass TreeNode {\n    val: number;\n    left: TreeNode | null;\n    right: TreeNode | null;\n\n    constructor(val?: number, left?: TreeNode | null, right?: TreeNode | null) {\n        this.val = val === undefined ? 0 : val; // \u30ce\u30fc\u30c9\u5024\n        this.left = left === undefined ? null : left; // \u5de6\u306e\u5b50\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\n        this.right = right === undefined ? null : right; // \u53f3\u306e\u5b50\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\n    }\n}\n</code></pre> <pre><code>/* \u4e8c\u5206\u6728\u30ce\u30fc\u30c9 */\nclass TreeNode {\n  int val;         // \u30ce\u30fc\u30c9\u5024\n  TreeNode? left;  // \u5de6\u306e\u5b50\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\n  TreeNode? right; // \u53f3\u306e\u5b50\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\n  TreeNode(this.val, [this.left, this.right]);\n}\n</code></pre> <pre><code>use std::rc::Rc;\nuse std::cell::RefCell;\n\n/* \u4e8c\u5206\u6728\u30ce\u30fc\u30c9 */\nstruct TreeNode {\n    val: i32,                               // \u30ce\u30fc\u30c9\u5024\n    left: Option&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;,    // \u5de6\u306e\u5b50\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\n    right: Option&lt;Rc&lt;RefCell&lt;TreeNode&gt;&gt;&gt;,   // \u53f3\u306e\u5b50\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\n}\n\nimpl TreeNode {\n    /* \u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf */\n    fn new(val: i32) -&gt; Rc&lt;RefCell&lt;Self&gt;&gt; {\n        Rc::new(RefCell::new(Self {\n            val,\n            left: None,\n            right: None\n        }))\n    }\n}\n</code></pre> <pre><code>/* \u4e8c\u5206\u6728\u30ce\u30fc\u30c9 */\ntypedef struct TreeNode {\n    int val;                // \u30ce\u30fc\u30c9\u5024\n    int height;             // \u30ce\u30fc\u30c9\u306e\u9ad8\u3055\n    struct TreeNode *left;  // \u5de6\u306e\u5b50\u30ce\u30fc\u30c9\u3078\u306e\u30dd\u30a4\u30f3\u30bf\n    struct TreeNode *right; // \u53f3\u306e\u5b50\u30ce\u30fc\u30c9\u3078\u306e\u30dd\u30a4\u30f3\u30bf\n} TreeNode;\n\n/* \u30b3\u30f3\u30b9\u30c8\u30e9\u30af\u30bf */\nTreeNode *newTreeNode(int val) {\n    TreeNode *node;\n\n    node = (TreeNode *)malloc(sizeof(TreeNode));\n    node-&gt;val = val;\n    node-&gt;height = 0;\n    node-&gt;left = NULL;\n    node-&gt;right = NULL;\n    return node;\n}\n</code></pre> <pre><code>/* \u4e8c\u5206\u6728\u30ce\u30fc\u30c9 */\nclass TreeNode(val _val: Int) {  // \u30ce\u30fc\u30c9\u5024\n    val left: TreeNode? = null   // \u5de6\u306e\u5b50\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\n    val right: TreeNode? = null  // \u53f3\u306e\u5b50\u30ce\u30fc\u30c9\u3078\u306e\u53c2\u7167\n}\n</code></pre> <pre><code>\n</code></pre> <pre><code>\n</code></pre> <p>\u5404\u30ce\u30fc\u30c9\u306f2\u3064\u306e\u53c2\u7167\uff08\u30dd\u30a4\u30f3\u30bf\uff09\u3092\u6301\u3061\u3001\u305d\u308c\u305e\u308c\u5de6\u306e\u5b50\u30ce\u30fc\u30c9\u3068\u53f3\u306e\u5b50\u30ce\u30fc\u30c9\u3092\u6307\u3057\u3066\u3044\u307e\u3059\u3002\u3053\u306e\u30ce\u30fc\u30c9\u306f\u3001\u3053\u308c\u30892\u3064\u306e\u5b50\u30ce\u30fc\u30c9\u306e\u89aa\u30ce\u30fc\u30c9\u3068\u547c\u3070\u308c\u307e\u3059\u3002\u4e8c\u5206\u6728\u306e\u30ce\u30fc\u30c9\u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u304d\u3001\u3053\u306e\u30ce\u30fc\u30c9\u306e\u5de6\u306e\u5b50\u3068\u305d\u306e\u4e0b\u306b\u3042\u308b\u3059\u3079\u3066\u306e\u30ce\u30fc\u30c9\u3067\u5f62\u6210\u3055\u308c\u308b\u6728\u3092\u3001\u3053\u306e\u30ce\u30fc\u30c9\u306e\u5de6\u90e8\u5206\u6728\u3068\u547c\u3073\u307e\u3059\u3002\u540c\u69d8\u306b\u3001\u53f3\u90e8\u5206\u6728\u3082\u5b9a\u7fa9\u3067\u304d\u307e\u3059\u3002</p> <p>\u4e8c\u5206\u6728\u3067\u306f\u3001\u8449\u30ce\u30fc\u30c9\u3092\u9664\u3044\u3066\u3001\u4ed6\u306e\u3059\u3079\u3066\u306e\u30ce\u30fc\u30c9\u306f\u5b50\u30ce\u30fc\u30c9\u3068\u7a7a\u3067\u306a\u3044\u90e8\u5206\u6728\u3092\u542b\u307f\u307e\u3059\u3002 \u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u300c\u30ce\u30fc\u30c92\u300d\u3092\u89aa\u30ce\u30fc\u30c9\u3068\u3057\u3066\u898b\u308b\u3068\u3001\u305d\u306e\u5de6\u3068\u53f3\u306e\u5b50\u30ce\u30fc\u30c9\u306f\u305d\u308c\u305e\u308c\u300c\u30ce\u30fc\u30c94\u300d\u3068\u300c\u30ce\u30fc\u30c95\u300d\u3067\u3059\u3002\u5de6\u90e8\u5206\u6728\u306f\u300c\u30ce\u30fc\u30c94\u300d\u3068\u305d\u306e\u4e0b\u306b\u3042\u308b\u3059\u3079\u3066\u306e\u30ce\u30fc\u30c9\u3067\u5f62\u6210\u3055\u308c\u3001\u53f3\u90e8\u5206\u6728\u306f\u300c\u30ce\u30fc\u30c95\u300d\u3068\u305d\u306e\u4e0b\u306b\u3042\u308b\u3059\u3079\u3066\u306e\u30ce\u30fc\u30c9\u3067\u5f62\u6210\u3055\u308c\u307e\u3059\u3002</p> <p></p> <p> \u56f3 7-1 \u00a0 \u89aa\u30ce\u30fc\u30c9\u3001\u5b50\u30ce\u30fc\u30c9\u3001\u90e8\u5206\u6728 </p>"},{"location":"chapter_tree/binary_tree/#711","title":"7.1.1 \u00a0 \u4e8c\u5206\u6728\u306e\u4e00\u822c\u7684\u306a\u7528\u8a9e","text":"<p>\u4e8c\u5206\u6728\u3067\u3088\u304f\u4f7f\u7528\u3055\u308c\u308b\u7528\u8a9e\u3092\u4e0b\u56f3\u306b\u793a\u3057\u307e\u3059\u3002</p> <ul> <li>\u6839\u30ce\u30fc\u30c9\uff1a\u4e8c\u5206\u6728\u306e\u6700\u4e0a\u4f4d\u30ec\u30d9\u30eb\u306b\u3042\u308b\u30ce\u30fc\u30c9\u3067\u3001\u89aa\u30ce\u30fc\u30c9\u3092\u6301\u3061\u307e\u305b\u3093\u3002</li> <li>\u8449\u30ce\u30fc\u30c9\uff1a\u5b50\u30ce\u30fc\u30c9\u3092\u6301\u305f\u306a\u3044\u30ce\u30fc\u30c9\u3067\u3001\u4e21\u65b9\u306e\u30dd\u30a4\u30f3\u30bf\u304c<code>None</code>\u3092\u6307\u3057\u3066\u3044\u307e\u3059\u3002</li> <li>\u8fba\uff1a2\u3064\u306e\u30ce\u30fc\u30c9\u3092\u7d50\u3076\u7dda\u5206\u3067\u3001\u30ce\u30fc\u30c9\u9593\u306e\u53c2\u7167\uff08\u30dd\u30a4\u30f3\u30bf\uff09\u3092\u8868\u73fe\u3057\u307e\u3059\u3002</li> <li>\u30ce\u30fc\u30c9\u306e\u30ec\u30d9\u30eb\uff1a\u4e0a\u304b\u3089\u4e0b\u306b\u5411\u304b\u3063\u3066\u5897\u52a0\u3057\u3001\u6839\u30ce\u30fc\u30c9\u304c\u30ec\u30d9\u30eb1\u3067\u3059\u3002</li> <li>\u30ce\u30fc\u30c9\u306e\u6b21\u6570\uff1a\u30ce\u30fc\u30c9\u304c\u6301\u3064\u5b50\u30ce\u30fc\u30c9\u306e\u6570\u3067\u3059\u3002\u4e8c\u5206\u6728\u3067\u306f\u3001\u6b21\u6570\u306f0\u30011\u3001\u307e\u305f\u306f2\u306b\u306a\u308a\u307e\u3059\u3002</li> <li>\u4e8c\u5206\u6728\u306e\u9ad8\u3055\uff1a\u6839\u30ce\u30fc\u30c9\u304b\u3089\u6700\u3082\u9060\u3044\u8449\u30ce\u30fc\u30c9\u307e\u3067\u306e\u8fba\u306e\u6570\u3067\u3059\u3002</li> <li>\u30ce\u30fc\u30c9\u306e\u6df1\u3055\uff1a\u6839\u30ce\u30fc\u30c9\u304b\u3089\u305d\u306e\u30ce\u30fc\u30c9\u307e\u3067\u306e\u8fba\u306e\u6570\u3067\u3059\u3002</li> <li>\u30ce\u30fc\u30c9\u306e\u9ad8\u3055\uff1a\u6700\u3082\u9060\u3044\u8449\u30ce\u30fc\u30c9\u304b\u3089\u305d\u306e\u30ce\u30fc\u30c9\u307e\u3067\u306e\u8fba\u306e\u6570\u3067\u3059\u3002</li> </ul> <p></p> <p> \u56f3 7-2 \u00a0 \u4e8c\u5206\u6728\u306e\u4e00\u822c\u7684\u306a\u7528\u8a9e </p> <p>Tip</p> <p>\u300c\u9ad8\u3055\u300d\u3068\u300c\u6df1\u3055\u300d\u306f\u901a\u5e38\u300c\u901a\u904e\u3059\u308b\u8fba\u306e\u6570\u300d\u3068\u3057\u3066\u5b9a\u7fa9\u3057\u307e\u3059\u304c\u3001\u4e00\u90e8\u306e\u554f\u984c\u3084\u6559\u79d1\u66f8\u3067\u306f\u300c\u901a\u904e\u3059\u308b\u30ce\u30fc\u30c9\u306e\u6570\u300d\u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u308b\u3053\u3068\u304c\u3042\u308a\u307e\u3059\u3002\u3053\u306e\u5834\u5408\u3001\u9ad8\u3055\u3068\u6df1\u3055\u306e\u4e21\u65b9\u30921\u3060\u3051\u5897\u3084\u3059\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002</p>"},{"location":"chapter_tree/binary_tree/#712","title":"7.1.2 \u00a0 \u4e8c\u5206\u6728\u306e\u57fa\u672c\u64cd\u4f5c","text":""},{"location":"chapter_tree/binary_tree/#1","title":"1. \u00a0 \u4e8c\u5206\u6728\u306e\u521d\u671f\u5316","text":"<p>\u9023\u7d50\u30ea\u30b9\u30c8\u3068\u540c\u69d8\u306b\u3001\u4e8c\u5206\u6728\u306e\u521d\u671f\u5316\u3067\u306f\u3001\u307e\u305a\u30ce\u30fc\u30c9\u3092\u4f5c\u6210\u3057\u3001\u6b21\u306b\u305d\u308c\u3089\u306e\u9593\u306e\u53c2\u7167\uff08\u30dd\u30a4\u30f3\u30bf\uff09\u3092\u78ba\u7acb\u3057\u307e\u3059\u3002</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig binary_tree.py<pre><code># \u4e8c\u5206\u6728\u306e\u521d\u671f\u5316\n# \u30ce\u30fc\u30c9\u306e\u521d\u671f\u5316\nn1 = TreeNode(val=1)\nn2 = TreeNode(val=2)\nn3 = TreeNode(val=3)\nn4 = TreeNode(val=4)\nn5 = TreeNode(val=5)\n# \u30ce\u30fc\u30c9\u9593\u306e\u53c2\u7167\uff08\u30dd\u30a4\u30f3\u30bf\uff09\u3092\u7d50\u3076\nn1.left = n2\nn1.right = n3\nn2.left = n4\nn2.right = n5\n</code></pre> binary_tree.cpp<pre><code>/* \u4e8c\u5206\u6728\u306e\u521d\u671f\u5316 */\n// \u30ce\u30fc\u30c9\u306e\u521d\u671f\u5316\nTreeNode* n1 = new TreeNode(1);\nTreeNode* n2 = new TreeNode(2);\nTreeNode* n3 = new TreeNode(3);\nTreeNode* n4 = new TreeNode(4);\nTreeNode* n5 = new TreeNode(5);\n// \u30ce\u30fc\u30c9\u9593\u306e\u53c2\u7167\uff08\u30dd\u30a4\u30f3\u30bf\uff09\u3092\u7d50\u3076\nn1-&gt;left = n2;\nn1-&gt;right = n3;\nn2-&gt;left = n4;\nn2-&gt;right = n5;\n</code></pre> binary_tree.java<pre><code>// \u30ce\u30fc\u30c9\u306e\u521d\u671f\u5316\nTreeNode n1 = new TreeNode(1);\nTreeNode n2 = new TreeNode(2);\nTreeNode n3 = new TreeNode(3);\nTreeNode n4 = new TreeNode(4);\nTreeNode n5 = new TreeNode(5);\n// \u30ce\u30fc\u30c9\u9593\u306e\u53c2\u7167\uff08\u30dd\u30a4\u30f3\u30bf\uff09\u3092\u7d50\u3076\nn1.left = n2;\nn1.right = n3;\nn2.left = n4;\nn2.right = n5;\n</code></pre> binary_tree.cs<pre><code>/* \u4e8c\u5206\u6728\u306e\u521d\u671f\u5316 */\n// \u30ce\u30fc\u30c9\u306e\u521d\u671f\u5316\nTreeNode n1 = new(1);\nTreeNode n2 = new(2);\nTreeNode n3 = new(3);\nTreeNode n4 = new(4);\nTreeNode n5 = new(5);\n// \u30ce\u30fc\u30c9\u9593\u306e\u53c2\u7167\uff08\u30dd\u30a4\u30f3\u30bf\uff09\u3092\u7d50\u3076\nn1.left = n2;\nn1.right = n3;\nn2.left = n4;\nn2.right = n5;\n</code></pre> binary_tree.go<pre><code>/* \u4e8c\u5206\u6728\u306e\u521d\u671f\u5316 */\n// \u30ce\u30fc\u30c9\u306e\u521d\u671f\u5316\nn1 := NewTreeNode(1)\nn2 := NewTreeNode(2)\nn3 := NewTreeNode(3)\nn4 := NewTreeNode(4)\nn5 := NewTreeNode(5)\n// \u30ce\u30fc\u30c9\u9593\u306e\u53c2\u7167\uff08\u30dd\u30a4\u30f3\u30bf\uff09\u3092\u7d50\u3076\nn1.Left = n2\nn1.Right = n3\nn2.Left = n4\nn2.Right = n5\n</code></pre> binary_tree.swift<pre><code>// \u30ce\u30fc\u30c9\u306e\u521d\u671f\u5316\nlet n1 = TreeNode(x: 1)\nlet n2 = TreeNode(x: 2)\nlet n3 = TreeNode(x: 3)\nlet n4 = TreeNode(x: 4)\nlet n5 = TreeNode(x: 5)\n// \u30ce\u30fc\u30c9\u9593\u306e\u53c2\u7167\uff08\u30dd\u30a4\u30f3\u30bf\uff09\u3092\u7d50\u3076\nn1.left = n2\nn1.right = n3\nn2.left = n4\nn2.right = n5\n</code></pre> binary_tree.js<pre><code>/* \u4e8c\u5206\u6728\u306e\u521d\u671f\u5316 */\n// \u30ce\u30fc\u30c9\u306e\u521d\u671f\u5316\nlet n1 = new TreeNode(1),\n    n2 = new TreeNode(2),\n    n3 = new TreeNode(3),\n    n4 = new TreeNode(4),\n    n5 = new TreeNode(5);\n// \u30ce\u30fc\u30c9\u9593\u306e\u53c2\u7167\uff08\u30dd\u30a4\u30f3\u30bf\uff09\u3092\u7d50\u3076\nn1.left = n2;\nn1.right = n3;\nn2.left = n4;\nn2.right = n5;\n</code></pre> binary_tree.ts<pre><code>/* \u4e8c\u5206\u6728\u306e\u521d\u671f\u5316 */\n// \u30ce\u30fc\u30c9\u306e\u521d\u671f\u5316\nlet n1 = new TreeNode(1),\n    n2 = new TreeNode(2),\n    n3 = new TreeNode(3),\n    n4 = new TreeNode(4),\n    n5 = new TreeNode(5);\n// \u30ce\u30fc\u30c9\u9593\u306e\u53c2\u7167\uff08\u30dd\u30a4\u30f3\u30bf\uff09\u3092\u7d50\u3076\nn1.left = n2;\nn1.right = n3;\nn2.left = n4;\nn2.right = n5;\n</code></pre> binary_tree.dart<pre><code>/* \u4e8c\u5206\u6728\u306e\u521d\u671f\u5316 */\n// \u30ce\u30fc\u30c9\u306e\u521d\u671f\u5316\nTreeNode n1 = new TreeNode(1);\nTreeNode n2 = new TreeNode(2);\nTreeNode n3 = new TreeNode(3);\nTreeNode n4 = new TreeNode(4);\nTreeNode n5 = new TreeNode(5);\n// \u30ce\u30fc\u30c9\u9593\u306e\u53c2\u7167\uff08\u30dd\u30a4\u30f3\u30bf\uff09\u3092\u7d50\u3076\nn1.left = n2;\nn1.right = n3;\nn2.left = n4;\nn2.right = n5;\n</code></pre> binary_tree.rs<pre><code>// \u30ce\u30fc\u30c9\u306e\u521d\u671f\u5316\nlet n1 = TreeNode::new(1);\nlet n2 = TreeNode::new(2);\nlet n3 = TreeNode::new(3);\nlet n4 = TreeNode::new(4);\nlet n5 = TreeNode::new(5);\n// \u30ce\u30fc\u30c9\u9593\u306e\u53c2\u7167\uff08\u30dd\u30a4\u30f3\u30bf\uff09\u3092\u7d50\u3076\nn1.borrow_mut().left = Some(n2.clone());\nn1.borrow_mut().right = Some(n3);\nn2.borrow_mut().left = Some(n4);\nn2.borrow_mut().right = Some(n5);\n</code></pre> binary_tree.c<pre><code>/* \u4e8c\u5206\u6728\u306e\u521d\u671f\u5316 */\n// \u30ce\u30fc\u30c9\u306e\u521d\u671f\u5316\nTreeNode *n1 = newTreeNode(1);\nTreeNode *n2 = newTreeNode(2);\nTreeNode *n3 = newTreeNode(3);\nTreeNode *n4 = newTreeNode(4);\nTreeNode *n5 = newTreeNode(5);\n// \u30ce\u30fc\u30c9\u9593\u306e\u53c2\u7167\uff08\u30dd\u30a4\u30f3\u30bf\uff09\u3092\u7d50\u3076\nn1-&gt;left = n2;\nn1-&gt;right = n3;\nn2-&gt;left = n4;\nn2-&gt;right = n5;\n</code></pre> binary_tree.kt<pre><code>// \u30ce\u30fc\u30c9\u306e\u521d\u671f\u5316\nval n1 = TreeNode(1)\nval n2 = TreeNode(2)\nval n3 = TreeNode(3)\nval n4 = TreeNode(4)\nval n5 = TreeNode(5)\n// \u30ce\u30fc\u30c9\u9593\u306e\u53c2\u7167\uff08\u30dd\u30a4\u30f3\u30bf\uff09\u3092\u7d50\u3076\nn1.left = n2\nn1.right = n3\nn2.left = n4\nn2.right = n5\n</code></pre> binary_tree.rb<pre><code>\n</code></pre> binary_tree.zig<pre><code>\n</code></pre>"},{"location":"chapter_tree/binary_tree/#2","title":"2. \u00a0 \u30ce\u30fc\u30c9\u306e\u633f\u5165\u3068\u524a\u9664","text":"<p>\u9023\u7d50\u30ea\u30b9\u30c8\u3068\u540c\u69d8\u306b\u3001\u4e8c\u5206\u6728\u3067\u306e\u30ce\u30fc\u30c9\u306e\u633f\u5165\u3068\u524a\u9664\u306f\u30dd\u30a4\u30f3\u30bf\u3092\u5909\u66f4\u3059\u308b\u3053\u3068\u3067\u5b9f\u73fe\u3067\u304d\u307e\u3059\u3002\u4e0b\u56f3\u306b\u4f8b\u3092\u793a\u3057\u307e\u3059\u3002</p> <p></p> <p> \u56f3 7-3 \u00a0 \u4e8c\u5206\u6728\u3067\u306e\u30ce\u30fc\u30c9\u306e\u633f\u5165\u3068\u524a\u9664 </p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig binary_tree.py<pre><code># \u30ce\u30fc\u30c9\u306e\u633f\u5165\u3068\u524a\u9664\np = TreeNode(0)\n# n1 -&gt; n2\u306e\u9593\u306b\u30ce\u30fc\u30c9P\u3092\u633f\u5165\nn1.left = p\np.left = n2\n# \u30ce\u30fc\u30c9P\u3092\u524a\u9664\nn1.left = n2\n</code></pre> binary_tree.cpp<pre><code>/* \u30ce\u30fc\u30c9\u306e\u633f\u5165\u3068\u524a\u9664 */\nTreeNode* P = new TreeNode(0);\n// n1\u3068n2\u306e\u9593\u306b\u30ce\u30fc\u30c9P\u3092\u633f\u5165\nn1-&gt;left = P;\nP-&gt;left = n2;\n// \u30ce\u30fc\u30c9P\u3092\u524a\u9664\nn1-&gt;left = n2;\n</code></pre> binary_tree.java<pre><code>TreeNode P = new TreeNode(0);\n// n1\u3068n2\u306e\u9593\u306b\u30ce\u30fc\u30c9P\u3092\u633f\u5165\nn1.left = P;\nP.left = n2;\n// \u30ce\u30fc\u30c9P\u3092\u524a\u9664\nn1.left = n2;\n</code></pre> binary_tree.cs<pre><code>/* \u30ce\u30fc\u30c9\u306e\u633f\u5165\u3068\u524a\u9664 */\nTreeNode P = new(0);\n// n1\u3068n2\u306e\u9593\u306b\u30ce\u30fc\u30c9P\u3092\u633f\u5165\nn1.left = P;\nP.left = n2;\n// \u30ce\u30fc\u30c9P\u3092\u524a\u9664\nn1.left = n2;\n</code></pre> binary_tree.go<pre><code>/* \u30ce\u30fc\u30c9\u306e\u633f\u5165\u3068\u524a\u9664 */\n// n1\u3068n2\u306e\u9593\u306b\u30ce\u30fc\u30c9P\u3092\u633f\u5165\np := NewTreeNode(0)\nn1.Left = p\np.Left = n2\n// \u30ce\u30fc\u30c9P\u3092\u524a\u9664\nn1.Left = n2\n</code></pre> binary_tree.swift<pre><code>let P = TreeNode(x: 0)\n// n1\u3068n2\u306e\u9593\u306b\u30ce\u30fc\u30c9P\u3092\u633f\u5165\nn1.left = P\nP.left = n2\n// \u30ce\u30fc\u30c9P\u3092\u524a\u9664\nn1.left = n2\n</code></pre> binary_tree.js<pre><code>/* \u30ce\u30fc\u30c9\u306e\u633f\u5165\u3068\u524a\u9664 */\nlet P = new TreeNode(0);\n// n1\u3068n2\u306e\u9593\u306b\u30ce\u30fc\u30c9P\u3092\u633f\u5165\nn1.left = P;\nP.left = n2;\n// \u30ce\u30fc\u30c9P\u3092\u524a\u9664\nn1.left = n2;\n</code></pre> binary_tree.ts<pre><code>/* \u30ce\u30fc\u30c9\u306e\u633f\u5165\u3068\u524a\u9664 */\nconst P = new TreeNode(0);\n// n1\u3068n2\u306e\u9593\u306b\u30ce\u30fc\u30c9P\u3092\u633f\u5165\nn1.left = P;\nP.left = n2;\n// \u30ce\u30fc\u30c9P\u3092\u524a\u9664\nn1.left = n2;\n</code></pre> binary_tree.dart<pre><code>/* \u30ce\u30fc\u30c9\u306e\u633f\u5165\u3068\u524a\u9664 */\nTreeNode P = new TreeNode(0);\n// n1\u3068n2\u306e\u9593\u306b\u30ce\u30fc\u30c9P\u3092\u633f\u5165\nn1.left = P;\nP.left = n2;\n// \u30ce\u30fc\u30c9P\u3092\u524a\u9664\nn1.left = n2;\n</code></pre> binary_tree.rs<pre><code>let p = TreeNode::new(0);\n// n1\u3068n2\u306e\u9593\u306b\u30ce\u30fc\u30c9P\u3092\u633f\u5165\nn1.borrow_mut().left = Some(p.clone());\np.borrow_mut().left = Some(n2.clone());\n// \u30ce\u30fc\u30c9P\u3092\u524a\u9664\nn1.borrow_mut().left = Some(n2);\n</code></pre> binary_tree.c<pre><code>/* \u30ce\u30fc\u30c9\u306e\u633f\u5165\u3068\u524a\u9664 */\nTreeNode *P = newTreeNode(0);\n// n1\u3068n2\u306e\u9593\u306b\u30ce\u30fc\u30c9P\u3092\u633f\u5165\nn1-&gt;left = P;\nP-&gt;left = n2;\n// \u30ce\u30fc\u30c9P\u3092\u524a\u9664\nn1-&gt;left = n2;\n</code></pre> binary_tree.kt<pre><code>val P = TreeNode(0)\n// n1\u3068n2\u306e\u9593\u306b\u30ce\u30fc\u30c9P\u3092\u633f\u5165\nn1.left = P\nP.left = n2\n// \u30ce\u30fc\u30c9P\u3092\u524a\u9664\nn1.left = n2\n</code></pre> binary_tree.rb<pre><code>\n</code></pre> binary_tree.zig<pre><code>\n</code></pre> <p>Tip</p> <p>\u30ce\u30fc\u30c9\u306e\u633f\u5165\u306f\u4e8c\u5206\u6728\u306e\u5143\u306e\u8ad6\u7406\u69cb\u9020\u3092\u5909\u66f4\u3059\u308b\u53ef\u80fd\u6027\u304c\u3042\u308a\u3001\u30ce\u30fc\u30c9\u306e\u524a\u9664\u306f\u901a\u5e38\u305d\u306e\u30ce\u30fc\u30c9\u3068\u305d\u306e\u3059\u3079\u3066\u306e\u90e8\u5206\u6728\u3092\u524a\u9664\u3059\u308b\u3053\u3068\u306b\u306a\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u4e8c\u5206\u6728\u3067\u306f\u3001\u633f\u5165\u3068\u524a\u9664\u306f\u901a\u5e38\u4e00\u9023\u306e\u64cd\u4f5c\u3092\u901a\u3058\u3066\u5b9f\u884c\u3055\u308c\u3001\u610f\u5473\u306e\u3042\u308b\u7d50\u679c\u3092\u5f97\u307e\u3059\u3002</p>"},{"location":"chapter_tree/binary_tree/#713","title":"7.1.3 \u00a0 \u4e8c\u5206\u6728\u306e\u4e00\u822c\u7684\u306a\u7a2e\u985e","text":""},{"location":"chapter_tree/binary_tree/#1_1","title":"1. \u00a0 \u5b8c\u5168\u4e8c\u5206\u6728","text":"<p>\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u5b8c\u5168\u4e8c\u5206\u6728\u3067\u306f\u3001\u3059\u3079\u3066\u306e\u30ec\u30d9\u30eb\u304c\u30ce\u30fc\u30c9\u3067\u5b8c\u5168\u306b\u57cb\u3081\u3089\u308c\u3066\u3044\u307e\u3059\u3002\u5b8c\u5168\u4e8c\u5206\u6728\u3067\u306f\u3001\u8449\u30ce\u30fc\u30c9\u306e\u6b21\u6570\u306f\\(0\\)\u3067\u3001\u4ed6\u306e\u3059\u3079\u3066\u306e\u30ce\u30fc\u30c9\u306e\u6b21\u6570\u306f\\(2\\)\u3067\u3059\u3002\u30ce\u30fc\u30c9\u306e\u7dcf\u6570\u306f\\(2^{h+1} - 1\\)\u3068\u3057\u3066\u8a08\u7b97\u3067\u304d\u3001\u3053\u3053\u3067\\(h\\)\u306f\u6728\u306e\u9ad8\u3055\u3067\u3059\u3002\u3053\u308c\u306f\u6a19\u6e96\u7684\u306a\u6307\u6570\u95a2\u4fc2\u3092\u793a\u3057\u3001\u81ea\u7136\u754c\u306e\u7d30\u80de\u5206\u88c2\u306e\u4e00\u822c\u7684\u306a\u73fe\u8c61\u3092\u53cd\u6620\u3057\u3066\u3044\u307e\u3059\u3002</p> <p>Tip</p> <p>\u4e2d\u56fd\u8a9e\u570f\u3067\u306f\u3001\u5b8c\u5168\u4e8c\u5206\u6728\u306f\u3057\u3070\u3057\u3070\u6e80\u4e8c\u5206\u6728\u3068\u547c\u3070\u308c\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002</p> <p></p> <p> \u56f3 7-4 \u00a0 \u5b8c\u5168\u4e8c\u5206\u6728 </p>"},{"location":"chapter_tree/binary_tree/#2_1","title":"2. \u00a0 \u5b8c\u5099\u4e8c\u5206\u6728","text":"<p>\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u5b8c\u5099\u4e8c\u5206\u6728\u306f\u3001\u6700\u4e0b\u4f4d\u30ec\u30d9\u30eb\u306e\u307f\u304c\u5b8c\u5168\u306b\u57cb\u3081\u3089\u308c\u3066\u3044\u306a\u3044\u53ef\u80fd\u6027\u304c\u3042\u308b\u4e8c\u5206\u6728\u3067\u3001\u6700\u4e0b\u4f4d\u30ec\u30d9\u30eb\u306e\u30ce\u30fc\u30c9\u306f\u5de6\u304b\u3089\u53f3\u306b\u9023\u7d9a\u3057\u3066\u57cb\u3081\u3089\u308c\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u5b8c\u5168\u4e8c\u5206\u6728\u306f\u5b8c\u5099\u4e8c\u5206\u6728\u3067\u3082\u3042\u308b\u3053\u3068\u306b\u6ce8\u610f\u3057\u3066\u304f\u3060\u3055\u3044\u3002</p> <p></p> <p> \u56f3 7-5 \u00a0 \u5b8c\u5099\u4e8c\u5206\u6728 </p>"},{"location":"chapter_tree/binary_tree/#3","title":"3. \u00a0 \u6e80\u4e8c\u5206\u6728","text":"<p>\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u6e80\u4e8c\u5206\u6728\u3067\u306f\u3001\u8449\u30ce\u30fc\u30c9\u3092\u9664\u3044\u3066\u3001\u4ed6\u306e\u3059\u3079\u3066\u306e\u30ce\u30fc\u30c9\u304c2\u3064\u306e\u5b50\u30ce\u30fc\u30c9\u3092\u6301\u3061\u307e\u3059\u3002</p> <p></p> <p> \u56f3 7-6 \u00a0 \u6e80\u4e8c\u5206\u6728 </p>"},{"location":"chapter_tree/binary_tree/#4","title":"4. \u00a0 \u5e73\u8861\u4e8c\u5206\u6728","text":"<p>\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u5e73\u8861\u4e8c\u5206\u6728\u3067\u306f\u3001\u4efb\u610f\u306e\u30ce\u30fc\u30c9\u306e\u5de6\u3068\u53f3\u306e\u90e8\u5206\u6728\u306e\u9ad8\u3055\u306e\u7d76\u5bfe\u5dee\u304c1\u3092\u8d85\u3048\u307e\u305b\u3093\u3002</p> <p></p> <p> \u56f3 7-7 \u00a0 \u5e73\u8861\u4e8c\u5206\u6728 </p>"},{"location":"chapter_tree/binary_tree/#714","title":"7.1.4 \u00a0 \u4e8c\u5206\u6728\u306e\u9000\u5316","text":"<p>\u4e0b\u56f3\u306f\u3001\u4e8c\u5206\u6728\u306e\u7406\u60f3\u7684\u306a\u69cb\u9020\u3068\u9000\u5316\u3057\u305f\u69cb\u9020\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002\u4e8c\u5206\u6728\u306f\u3001\u3059\u3079\u3066\u306e\u30ec\u30d9\u30eb\u304c\u57cb\u3081\u3089\u308c\u3066\u3044\u308b\u3068\u304d\u306b\u300c\u5b8c\u5168\u4e8c\u5206\u6728\u300d\u306b\u306a\u308a\u3001\u3059\u3079\u3066\u306e\u30ce\u30fc\u30c9\u304c\u4e00\u65b9\u306b\u504f\u3063\u3066\u3044\u308b\u3068\u304d\u306b\u300c\u9023\u7d50\u30ea\u30b9\u30c8\u300d\u306b\u9000\u5316\u3057\u307e\u3059\u3002</p> <ul> <li>\u5b8c\u5168\u4e8c\u5206\u6728\u306f\u3001\u4e8c\u5206\u6728\u306e\u300c\u5206\u5272\u7d71\u6cbb\u6cd5\u300d\u306e\u5229\u70b9\u3092\u5341\u5206\u306b\u6d3b\u7528\u3067\u304d\u308b\u7406\u60f3\u7684\u306a\u30b7\u30ca\u30ea\u30aa\u3067\u3059\u3002</li> <li>\u4e00\u65b9\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u306f\u5225\u306e\u6975\u7aef\u3092\u8868\u3057\u3001\u3059\u3079\u3066\u306e\u64cd\u4f5c\u304c\u7dda\u5f62\u306b\u306a\u308a\u3001\u6642\u9593\u8a08\u7b97\u91cf\u304c\\(O(n)\\)\u306b\u306a\u308a\u307e\u3059\u3002</li> </ul> <p></p> <p> \u56f3 7-8 \u00a0 \u4e8c\u5206\u6728\u306e\u6700\u826f\u3068\u6700\u60aa\u306e\u69cb\u9020 </p> <p>\u4e0b\u8868\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u6700\u826f\u3068\u6700\u60aa\u306e\u69cb\u9020\u3067\u306f\u3001\u4e8c\u5206\u6728\u306f\u8449\u30ce\u30fc\u30c9\u6570\u3001\u7dcf\u30ce\u30fc\u30c9\u6570\u3001\u9ad8\u3055\u306e\u6700\u5927\u5024\u307e\u305f\u306f\u6700\u5c0f\u5024\u3092\u9054\u6210\u3057\u307e\u3059\u3002</p> <p> \u8868 7-1 \u00a0 \u4e8c\u5206\u6728\u306e\u6700\u826f\u3068\u6700\u60aa\u306e\u69cb\u9020 </p> \u5b8c\u5168\u4e8c\u5206\u6728 \u9023\u7d50\u30ea\u30b9\u30c8 \u30ec\u30d9\u30eb\\(i\\)\u306e\u30ce\u30fc\u30c9\u6570 \\(2^{i-1}\\) \\(1\\) \u9ad8\u3055\\(h\\)\u306e\u6728\u306e\u8449\u30ce\u30fc\u30c9\u6570 \\(2^h\\) \\(1\\) \u9ad8\u3055\\(h\\)\u306e\u6728\u306e\u7dcf\u30ce\u30fc\u30c9\u6570 \\(2^{h+1} - 1\\) \\(h + 1\\) \u7dcf\u30ce\u30fc\u30c9\u6570\\(n\\)\u306e\u6728\u306e\u9ad8\u3055 \\(\\log_2 (n+1) - 1\\) \\(n - 1\\)"},{"location":"chapter_tree/binary_tree_traversal/","title":"7.2 \u00a0 \u4e8c\u5206\u6728\u306e\u8d70\u67fb","text":"<p>\u7269\u7406\u7684\u69cb\u9020\u306e\u89b3\u70b9\u304b\u3089\u898b\u308b\u3068\u3001\u6728\u306f\u9023\u7d50\u30ea\u30b9\u30c8\u306b\u57fa\u3065\u304f\u30c7\u30fc\u30bf\u69cb\u9020\u3067\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u305d\u306e\u8d70\u67fb\u65b9\u6cd5\u306f\u30dd\u30a4\u30f3\u30bf\u3092\u901a\u3057\u3066\u30ce\u30fc\u30c9\u306b\u4e00\u3064\u305a\u3064\u30a2\u30af\u30bb\u30b9\u3059\u308b\u3053\u3068\u3092\u542b\u307f\u307e\u3059\u3002\u3057\u304b\u3057\u3001\u6728\u306f\u975e\u7dda\u5f62\u30c7\u30fc\u30bf\u69cb\u9020\u3067\u3042\u308b\u305f\u3081\u3001\u6728\u306e\u8d70\u67fb\u306f\u9023\u7d50\u30ea\u30b9\u30c8\u306e\u8d70\u67fb\u3088\u308a\u3082\u8907\u96d1\u3067\u3001\u691c\u7d22\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u306e\u652f\u63f4\u304c\u5fc5\u8981\u3067\u3059\u3002</p> <p>\u4e8c\u5206\u6728\u306e\u4e00\u822c\u7684\u306a\u8d70\u67fb\u65b9\u6cd5\u306b\u306f\u3001\u30ec\u30d9\u30eb\u9806\u8d70\u67fb\u3001\u524d\u9806\u8d70\u67fb\u3001\u4e2d\u9806\u8d70\u67fb\u3001\u5f8c\u9806\u8d70\u67fb\u304c\u3042\u308a\u307e\u3059\u3002</p>"},{"location":"chapter_tree/binary_tree_traversal/#721","title":"7.2.1 \u00a0 \u30ec\u30d9\u30eb\u9806\u8d70\u67fb","text":"<p>\u4e0b\u56f3\u306b\u793a\u3059\u3088\u3046\u306b\u3001\u30ec\u30d9\u30eb\u9806\u8d70\u67fb\u306f\u4e8c\u5206\u6728\u3092\u4e0a\u304b\u3089\u4e0b\u3078\u3001\u5c64\u3054\u3068\u306b\u8d70\u67fb\u3057\u307e\u3059\u3002\u5404\u30ec\u30d9\u30eb\u5185\u3067\u306f\u3001\u5de6\u304b\u3089\u53f3\u3078\u30ce\u30fc\u30c9\u3092\u8a2a\u554f\u3057\u307e\u3059\u3002</p> <p>\u30ec\u30d9\u30eb\u9806\u8d70\u67fb\u306f\u672c\u8cea\u7684\u306b\u5e45\u512a\u5148\u8d70\u67fb\u306e\u4e00\u7a2e\u3067\u3001\u5e45\u512a\u5148\u63a2\u7d22\uff08BFS\uff09\u3068\u3082\u547c\u3070\u308c\u3001\u300c\u5468\u56f2\u306b\u5411\u304b\u3063\u3066\u5916\u5411\u304d\u306b\u62e1\u5f35\u3059\u308b\u300d\u5c64\u3054\u3068\u306e\u8d70\u67fb\u65b9\u6cd5\u3092\u4f53\u73fe\u3057\u3066\u3044\u307e\u3059\u3002</p> <p></p> <p> \u56f3 7-9 \u00a0 \u4e8c\u5206\u6728\u306e\u30ec\u30d9\u30eb\u9806\u8d70\u67fb </p>"},{"location":"chapter_tree/binary_tree_traversal/#1","title":"1. \u00a0 \u30b3\u30fc\u30c9\u5b9f\u88c5","text":"<p>\u5e45\u512a\u5148\u8d70\u67fb\u306f\u901a\u5e38\u300c\u30ad\u30e5\u30fc\u300d\u306e\u52a9\u3051\u3092\u501f\u308a\u3066\u5b9f\u88c5\u3055\u308c\u307e\u3059\u3002\u30ad\u30e5\u30fc\u306f\u300c\u5148\u5165\u308c\u5148\u51fa\u3057\u300d\u306e\u898f\u5247\u306b\u5f93\u3044\u3001\u5e45\u512a\u5148\u8d70\u67fb\u306f\u300c\u5c64\u3054\u3068\u306e\u9032\u884c\u300d\u898f\u5247\u306b\u5f93\u3044\u307e\u3059\u3002\u4e21\u8005\u306e\u57fa\u672c\u7684\u306a\u8003\u3048\u65b9\u306f\u4e00\u81f4\u3057\u3066\u3044\u307e\u3059\u3002\u5b9f\u88c5\u30b3\u30fc\u30c9\u306f\u4ee5\u4e0b\u306e\u901a\u308a\u3067\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig binary_tree_bfs.py<pre><code>def level_order(root: TreeNode | None) -&gt; list[int]:\n    \"\"\"\u30ec\u30d9\u30eb\u9806\u8d70\u67fb\"\"\"\n    # \u30ad\u30e5\u30fc\u3092\u521d\u671f\u5316\u3057\u3001\u30eb\u30fc\u30c8\u30ce\u30fc\u30c9\u3092\u8ffd\u52a0\n    queue: deque[TreeNode] = deque()\n    queue.append(root)\n    # \u8d70\u67fb\u30b7\u30fc\u30b1\u30f3\u30b9\u3092\u683c\u7d0d\u3059\u308b\u30ea\u30b9\u30c8\u3092\u521d\u671f\u5316\n    res = []\n    while queue:\n        node: TreeNode = queue.popleft()  # \u30ad\u30e5\u30fc\u304b\u3089\u30c7\u30ad\u30e5\u30fc\n        res.append(node.val)  # \u30ce\u30fc\u30c9\u306e\u5024\u3092\u4fdd\u5b58\n        if node.left is not None:\n            queue.append(node.left)  # \u5de6\u306e\u5b50\u30ce\u30fc\u30c9\u3092\u30a8\u30f3\u30ad\u30e5\u30fc\n        if node.right is not None:\n            queue.append(node.right)  # \u53f3\u306e\u5b50\u30ce\u30fc\u30c9\u3092\u30a8\u30f3\u30ad\u30e5\u30fc\n    return res\n</code></pre> binary_tree_bfs.cpp<pre><code>/* \u30ec\u30d9\u30eb\u9806\u8d70\u67fb */\nvector&lt;int&gt; levelOrder(TreeNode *root) {\n    // \u30ad\u30e5\u30fc\u3092\u521d\u671f\u5316\u3001\u30eb\u30fc\u30c8\u30ce\u30fc\u30c9\u3092\u8ffd\u52a0\n    queue&lt;TreeNode *&gt; queue;\n    queue.push(root);\n    // \u8d70\u67fb\u9806\u5e8f\u3092\u4fdd\u5b58\u3059\u308b\u30ea\u30b9\u30c8\u3092\u521d\u671f\u5316\n    vector&lt;int&gt; vec;\n    while (!queue.empty()) {\n        TreeNode *node = queue.front();\n        queue.pop();              // \u30ad\u30e5\u30fc\u304b\u3089\u30c7\u30ad\u30e5\u30fc\n        vec.push_back(node-&gt;val); // \u30ce\u30fc\u30c9\u5024\u3092\u4fdd\u5b58\n        if (node-&gt;left != nullptr)\n            queue.push(node-&gt;left); // \u5de6\u306e\u5b50\u30ce\u30fc\u30c9\u3092\u30a8\u30f3\u30ad\u30e5\u30fc\n        if (node-&gt;right != nullptr)\n            queue.push(node-&gt;right); // \u53f3\u306e\u5b50\u30ce\u30fc\u30c9\u3092\u30a8\u30f3\u30ad\u30e5\u30fc\n    }\n    return vec;\n}\n</code></pre> binary_tree_bfs.java<pre><code>/* \u30ec\u30d9\u30eb\u9806\u8d70\u67fb */\nList&lt;Integer&gt; levelOrder(TreeNode root) {\n    // \u30ad\u30e5\u30fc\u3092\u521d\u671f\u5316\u3057\u3001\u6839\u30ce\u30fc\u30c9\u3092\u8ffd\u52a0\n    Queue&lt;TreeNode&gt; queue = new LinkedList&lt;&gt;();\n    queue.add(root);\n    // \u8d70\u67fb\u9806\u5e8f\u3092\u683c\u7d0d\u3059\u308b\u30ea\u30b9\u30c8\u3092\u521d\u671f\u5316\n    List&lt;Integer&gt; list = new ArrayList&lt;&gt;();\n    while (!queue.isEmpty()) {\n        TreeNode node = queue.poll(); // \u30ad\u30e5\u30fc\u306e\u30c7\u30ad\u30e5\u30fc\n        list.add(node.val);           // \u30ce\u30fc\u30c9\u306e\u5024\u3092\u4fdd\u5b58\n        if (node.left != null)\n            queue.offer(node.left);   // \u5de6\u306e\u5b50\u30ce\u30fc\u30c9\u3092\u30a8\u30f3\u30ad\u30e5\u30fc\n        if (node.right != null)\n            queue.offer(node.right);  // \u53f3\u306e\u5b50\u30ce\u30fc\u30c9\u3092\u30a8\u30f3\u30ad\u30e5\u30fc\n    }\n    return list;\n}\n</code></pre> binary_tree_bfs.cs<pre><code>[class]{binary_tree_bfs}-[func]{LevelOrder}\n</code></pre> binary_tree_bfs.go<pre><code>[class]{}-[func]{levelOrder}\n</code></pre> binary_tree_bfs.swift<pre><code>[class]{}-[func]{levelOrder}\n</code></pre> binary_tree_bfs.js<pre><code>[class]{}-[func]{levelOrder}\n</code></pre> binary_tree_bfs.ts<pre><code>[class]{}-[func]{levelOrder}\n</code></pre> binary_tree_bfs.dart<pre><code>[class]{}-[func]{levelOrder}\n</code></pre> binary_tree_bfs.rs<pre><code>[class]{}-[func]{level_order}\n</code></pre> binary_tree_bfs.c<pre><code>[class]{}-[func]{levelOrder}\n</code></pre> binary_tree_bfs.kt<pre><code>[class]{}-[func]{levelOrder}\n</code></pre> binary_tree_bfs.rb<pre><code>[class]{}-[func]{level_order}\n</code></pre> binary_tree_bfs.zig<pre><code>[class]{}-[func]{levelOrder}\n</code></pre>"},{"location":"chapter_tree/binary_tree_traversal/#2","title":"2. \u00a0 \u8a08\u7b97\u91cf\u5206\u6790","text":"<ul> <li>\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O(n)\\): \u3059\u3079\u3066\u306e\u30ce\u30fc\u30c9\u304c\u4e00\u5ea6\u305a\u3064\u8a2a\u554f\u3055\u308c\u3001\\(O(n)\\)\u306e\u6642\u9593\u304c\u304b\u304b\u308a\u307e\u3059\u3002\u3053\u3053\u3067\\(n\\)\u306f\u30ce\u30fc\u30c9\u6570\u3067\u3059\u3002</li> <li>\u7a7a\u9593\u8a08\u7b97\u91cf\u306f\\(O(n)\\): \u6700\u60aa\u306e\u5834\u5408\u3001\u3064\u307e\u308a\u5b8c\u5168\u4e8c\u5206\u6728\u306e\u5834\u5408\u3001\u6700\u4e0b\u4f4d\u30ec\u30d9\u30eb\u306b\u8d70\u67fb\u3059\u308b\u524d\u306b\u3001\u30ad\u30e5\u30fc\u306f\u6700\u5927\\((n + 1) / 2\\)\u500b\u306e\u30ce\u30fc\u30c9\u3092\u540c\u6642\u306b\u542b\u3080\u3053\u3068\u304c\u3067\u304d\u3001\\(O(n)\\)\u306e\u7a7a\u9593\u3092\u5360\u6709\u3057\u307e\u3059\u3002</li> </ul>"},{"location":"chapter_tree/binary_tree_traversal/#722","title":"7.2.2 \u00a0 \u524d\u9806\u3001\u4e2d\u9806\u3001\u5f8c\u9806\u8d70\u67fb","text":"<p>\u5bfe\u5fdc\u3057\u3066\u3001\u524d\u9806\u3001\u4e2d\u9806\u3001\u5f8c\u9806\u8d70\u67fb\u306f\u3059\u3079\u3066\u6df1\u5ea6\u512a\u5148\u8d70\u67fb\u306b\u5c5e\u3057\u3001\u6df1\u5ea6\u512a\u5148\u63a2\u7d22\uff08DFS\uff09\u3068\u3082\u547c\u3070\u308c\u3001\u300c\u307e\u305a\u6700\u5f8c\u307e\u3067\u9032\u307f\u3001\u305d\u306e\u5f8c\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30af\u3057\u3066\u7d9a\u884c\u3059\u308b\u300d\u8d70\u67fb\u65b9\u6cd5\u3092\u4f53\u73fe\u3057\u3066\u3044\u307e\u3059\u3002</p> <p>\u4e0b\u56f3\u306f\u4e8c\u5206\u6728\u306b\u5bfe\u3057\u3066\u6df1\u5ea6\u512a\u5148\u8d70\u67fb\u3092\u5b9f\u884c\u3059\u308b\u52d5\u4f5c\u539f\u7406\u3092\u793a\u3057\u3066\u3044\u307e\u3059\u3002\u6df1\u5ea6\u512a\u5148\u8d70\u67fb\u306f\u4e8c\u5206\u6728\u5168\u4f53\u3092\u300c\u6b69\u304d\u56de\u308b\u300d\u3088\u3046\u306a\u3082\u306e\u3067\u3001\u5404\u30ce\u30fc\u30c9\u30673\u3064\u306e\u4f4d\u7f6e\u306b\u906d\u9047\u3057\u3001\u305d\u308c\u3089\u306f\u524d\u9806\u3001\u4e2d\u9806\u3001\u5f8c\u9806\u8d70\u67fb\u306b\u5bfe\u5fdc\u3057\u3066\u3044\u307e\u3059\u3002</p> <p></p> <p> \u56f3 7-10 \u00a0 \u4e8c\u5206\u63a2\u7d22\u6728\u306e\u524d\u9806\u3001\u4e2d\u9806\u3001\u5f8c\u9806\u8d70\u67fb </p>"},{"location":"chapter_tree/binary_tree_traversal/#1_1","title":"1. \u00a0 \u30b3\u30fc\u30c9\u5b9f\u88c5","text":"<p>\u6df1\u5ea6\u512a\u5148\u63a2\u7d22\u306f\u901a\u5e38\u518d\u5e30\u306b\u57fa\u3065\u3044\u3066\u5b9f\u88c5\u3055\u308c\u307e\u3059\uff1a</p> PythonC++JavaC#GoSwiftJSTSDartRustCKotlinRubyZig binary_tree_dfs.py<pre><code>def pre_order(root: TreeNode | None):\n    \"\"\"\u524d\u9806\u8d70\u67fb\"\"\"\n    if root is None:\n        return\n    # \u8a2a\u554f\u9806\u5e8f: \u30eb\u30fc\u30c8\u30ce\u30fc\u30c9 -&gt; \u5de6\u90e8\u5206\u6728 -&gt; \u53f3\u90e8\u5206\u6728\n    res.append(root.val)\n    pre_order(root=root.left)\n    pre_order(root=root.right)\n\ndef in_order(root: TreeNode | None):\n    \"\"\"\u4e2d\u9806\u8d70\u67fb\"\"\"\n    if root is None:\n        return\n    # \u8a2a\u554f\u9806\u5e8f: \u5de6\u90e8\u5206\u6728 -&gt; \u30eb\u30fc\u30c8\u30ce\u30fc\u30c9 -&gt; \u53f3\u90e8\u5206\u6728\n    in_order(root=root.left)\n    res.append(root.val)\n    in_order(root=root.right)\n\ndef post_order(root: TreeNode | None):\n    \"\"\"\u5f8c\u9806\u8d70\u67fb\"\"\"\n    if root is None:\n        return\n    # \u8a2a\u554f\u9806\u5e8f: \u5de6\u90e8\u5206\u6728 -&gt; \u53f3\u90e8\u5206\u6728 -&gt; \u30eb\u30fc\u30c8\u30ce\u30fc\u30c9\n    post_order(root=root.left)\n    post_order(root=root.right)\n    res.append(root.val)\n</code></pre> binary_tree_dfs.cpp<pre><code>/* \u524d\u9806\u8d70\u67fb */\nvoid preOrder(TreeNode *root) {\n    if (root == nullptr)\n        return;\n    // \u8a2a\u554f\u512a\u5148\u5ea6\uff1a\u30eb\u30fc\u30c8\u30ce\u30fc\u30c9 -&gt; \u5de6\u90e8\u5206\u6728 -&gt; \u53f3\u90e8\u5206\u6728\n    vec.push_back(root-&gt;val);\n    preOrder(root-&gt;left);\n    preOrder(root-&gt;right);\n}\n\n/* \u4e2d\u9806\u8d70\u67fb */\nvoid inOrder(TreeNode *root) {\n    if (root == nullptr)\n        return;\n    // \u8a2a\u554f\u512a\u5148\u5ea6\uff1a\u5de6\u90e8\u5206\u6728 -&gt; \u30eb\u30fc\u30c8\u30ce\u30fc\u30c9 -&gt; \u53f3\u90e8\u5206\u6728\n    inOrder(root-&gt;left);\n    vec.push_back(root-&gt;val);\n    inOrder(root-&gt;right);\n}\n\n/* \u5f8c\u9806\u8d70\u67fb */\nvoid postOrder(TreeNode *root) {\n    if (root == nullptr)\n        return;\n    // \u8a2a\u554f\u512a\u5148\u5ea6\uff1a\u5de6\u90e8\u5206\u6728 -&gt; \u53f3\u90e8\u5206\u6728 -&gt; \u30eb\u30fc\u30c8\u30ce\u30fc\u30c9\n    postOrder(root-&gt;left);\n    postOrder(root-&gt;right);\n    vec.push_back(root-&gt;val);\n}\n</code></pre> binary_tree_dfs.java<pre><code>/* \u524d\u9806\u8d70\u67fb */\nvoid preOrder(TreeNode root) {\n    if (root == null)\n        return;\n    // \u8a2a\u554f\u512a\u5148\u5ea6: \u6839\u30ce\u30fc\u30c9 -&gt; \u5de6\u90e8\u5206\u6728 -&gt; \u53f3\u90e8\u5206\u6728\n    list.add(root.val);\n    preOrder(root.left);\n    preOrder(root.right);\n}\n\n/* \u4e2d\u9806\u8d70\u67fb */\nvoid inOrder(TreeNode root) {\n    if (root == null)\n        return;\n    // \u8a2a\u554f\u512a\u5148\u5ea6: \u5de6\u90e8\u5206\u6728 -&gt; \u6839\u30ce\u30fc\u30c9 -&gt; \u53f3\u90e8\u5206\u6728\n    inOrder(root.left);\n    list.add(root.val);\n    inOrder(root.right);\n}\n\n/* \u5f8c\u9806\u8d70\u67fb */\nvoid postOrder(TreeNode root) {\n    if (root == null)\n        return;\n    // \u8a2a\u554f\u512a\u5148\u5ea6: \u5de6\u90e8\u5206\u6728 -&gt; \u53f3\u90e8\u5206\u6728 -&gt; \u6839\u30ce\u30fc\u30c9\n    postOrder(root.left);\n    postOrder(root.right);\n    list.add(root.val);\n}\n</code></pre> binary_tree_dfs.cs<pre><code>[class]{binary_tree_dfs}-[func]{PreOrder}\n\n[class]{binary_tree_dfs}-[func]{InOrder}\n\n[class]{binary_tree_dfs}-[func]{PostOrder}\n</code></pre> binary_tree_dfs.go<pre><code>[class]{}-[func]{preOrder}\n\n[class]{}-[func]{inOrder}\n\n[class]{}-[func]{postOrder}\n</code></pre> binary_tree_dfs.swift<pre><code>[class]{}-[func]{preOrder}\n\n[class]{}-[func]{inOrder}\n\n[class]{}-[func]{postOrder}\n</code></pre> binary_tree_dfs.js<pre><code>[class]{}-[func]{preOrder}\n\n[class]{}-[func]{inOrder}\n\n[class]{}-[func]{postOrder}\n</code></pre> binary_tree_dfs.ts<pre><code>[class]{}-[func]{preOrder}\n\n[class]{}-[func]{inOrder}\n\n[class]{}-[func]{postOrder}\n</code></pre> binary_tree_dfs.dart<pre><code>[class]{}-[func]{preOrder}\n\n[class]{}-[func]{inOrder}\n\n[class]{}-[func]{postOrder}\n</code></pre> binary_tree_dfs.rs<pre><code>[class]{}-[func]{pre_order}\n\n[class]{}-[func]{in_order}\n\n[class]{}-[func]{post_order}\n</code></pre> binary_tree_dfs.c<pre><code>[class]{}-[func]{preOrder}\n\n[class]{}-[func]{inOrder}\n\n[class]{}-[func]{postOrder}\n</code></pre> binary_tree_dfs.kt<pre><code>[class]{}-[func]{preOrder}\n\n[class]{}-[func]{inOrder}\n\n[class]{}-[func]{postOrder}\n</code></pre> binary_tree_dfs.rb<pre><code>[class]{}-[func]{pre_order}\n\n[class]{}-[func]{in_order}\n\n[class]{}-[func]{post_order}\n</code></pre> binary_tree_dfs.zig<pre><code>[class]{}-[func]{preOrder}\n\n[class]{}-[func]{inOrder}\n\n[class]{}-[func]{postOrder}\n</code></pre> <p>Tip</p> <p>\u6df1\u5ea6\u512a\u5148\u63a2\u7d22\u306f\u53cd\u5fa9\u306b\u57fa\u3065\u3044\u3066\u3082\u5b9f\u88c5\u3067\u304d\u307e\u3059\u3002\u8208\u5473\u306e\u3042\u308b\u8aad\u8005\u306f\u81ea\u5206\u3067\u5b66\u7fd2\u3057\u3066\u304f\u3060\u3055\u3044\u3002</p> <p>\u4e0b\u56f3\u306f\u4e8c\u5206\u6728\u306e\u524d\u9806\u8d70\u67fb\u306e\u518d\u5e30\u30d7\u30ed\u30bb\u30b9\u3092\u793a\u3057\u3066\u304a\u308a\u3001\u3053\u308c\u306f\u300c\u518d\u5e30\u300d\u3068\u300c\u5fa9\u5e30\u300d\u3068\u3044\u30462\u3064\u306e\u53cd\u5bfe\u306e\u90e8\u5206\u306b\u5206\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002</p> <ol> <li>\u300c\u518d\u5e30\u300d\u306f\u65b0\u3057\u3044\u30e1\u30bd\u30c3\u30c9\u3092\u958b\u59cb\u3059\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u3001\u30d7\u30ed\u30b0\u30e9\u30e0\u306f\u3053\u306e\u30d7\u30ed\u30bb\u30b9\u3067\u6b21\u306e\u30ce\u30fc\u30c9\u306b\u30a2\u30af\u30bb\u30b9\u3057\u307e\u3059\u3002</li> <li>\u300c\u5fa9\u5e30\u300d\u306f\u95a2\u6570\u304c\u623b\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u3001\u73fe\u5728\u306e\u30ce\u30fc\u30c9\u304c\u5b8c\u5168\u306b\u30a2\u30af\u30bb\u30b9\u3055\u308c\u305f\u3053\u3068\u3092\u793a\u3057\u307e\u3059\u3002</li> </ol> &lt;1&gt;&lt;2&gt;&lt;3&gt;&lt;4&gt;&lt;5&gt;&lt;6&gt;&lt;7&gt;&lt;8&gt;&lt;9&gt;&lt;10&gt;&lt;11&gt; <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p></p> <p> \u56f3 7-11 \u00a0 \u524d\u9806\u8d70\u67fb\u306e\u518d\u5e30\u30d7\u30ed\u30bb\u30b9 </p>"},{"location":"chapter_tree/binary_tree_traversal/#2_1","title":"2. \u00a0 \u8a08\u7b97\u91cf\u5206\u6790","text":"<ul> <li>\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O(n)\\): \u3059\u3079\u3066\u306e\u30ce\u30fc\u30c9\u304c\u4e00\u5ea6\u305a\u3064\u8a2a\u554f\u3055\u308c\u3001\\(O(n)\\)\u306e\u6642\u9593\u3092\u4f7f\u7528\u3057\u307e\u3059\u3002</li> <li>\u7a7a\u9593\u8a08\u7b97\u91cf\u306f\\(O(n)\\): \u6700\u60aa\u306e\u5834\u5408\u3001\u3064\u307e\u308a\u6728\u304c\u9023\u7d50\u30ea\u30b9\u30c8\u306b\u9000\u5316\u3057\u305f\u5834\u5408\u3001\u518d\u5e30\u306e\u6df1\u3055\u306f\\(n\\)\u306b\u9054\u3057\u3001\u30b7\u30b9\u30c6\u30e0\u306f\\(O(n)\\)\u306e\u30b9\u30bf\u30c3\u30af\u30d5\u30ec\u30fc\u30e0\u7a7a\u9593\u3092\u5360\u6709\u3057\u307e\u3059\u3002</li> </ul>"},{"location":"chapter_tree/summary/","title":"7.6 \u00a0 \u307e\u3068\u3081","text":""},{"location":"chapter_tree/summary/#1","title":"1. \u00a0 \u91cd\u8981\u306a\u30dd\u30a4\u30f3\u30c8","text":"<ul> <li>\u4e8c\u5206\u6728\u306f\u975e\u7dda\u5f62\u30c7\u30fc\u30bf\u69cb\u9020\u3067\u3001\u300c\u4e00\u3064\u3092\u4e8c\u3064\u306b\u5206\u3051\u308b\u300d\u5206\u5272\u7d71\u6cbb\u306e\u30ed\u30b8\u30c3\u30af\u3092\u53cd\u6620\u3057\u3066\u3044\u307e\u3059\u3002\u5404\u4e8c\u5206\u6728\u30ce\u30fc\u30c9\u306b\u306f\u5024\u30682\u3064\u306e\u30dd\u30a4\u30f3\u30bf\u304c\u542b\u307e\u308c\u3001\u305d\u308c\u305e\u308c\u5de6\u3068\u53f3\u306e\u5b50\u30ce\u30fc\u30c9\u3092\u6307\u3057\u307e\u3059\u3002</li> <li>\u4e8c\u5206\u6728\u306e\u30ce\u30fc\u30c9\u306b\u3064\u3044\u3066\u3001\u305d\u306e\u5de6\uff08\u53f3\uff09\u5b50\u30ce\u30fc\u30c9\u3068\u305d\u306e\u4e0b\u306b\u5f62\u6210\u3055\u308c\u308b\u6728\u306f\u3001\u307e\u3068\u3081\u3066\u305d\u306e\u30ce\u30fc\u30c9\u306e\u5de6\uff08\u53f3\uff09\u90e8\u5206\u6728\u3068\u547c\u3070\u308c\u307e\u3059\u3002</li> <li>\u4e8c\u5206\u6728\u306b\u95a2\u9023\u3059\u308b\u7528\u8a9e\u306b\u306f\u3001\u6839\u30ce\u30fc\u30c9\u3001\u8449\u30ce\u30fc\u30c9\u3001\u30ec\u30d9\u30eb\u3001\u6b21\u6570\u3001\u30a8\u30c3\u30b8\u3001\u9ad8\u3055\u3001\u6df1\u3055\u304c\u3042\u308a\u307e\u3059\u3002</li> <li>\u4e8c\u5206\u6728\u306e\u521d\u671f\u5316\u3001\u30ce\u30fc\u30c9\u306e\u633f\u5165\u3001\u30ce\u30fc\u30c9\u306e\u524a\u9664\u306e\u64cd\u4f5c\u306f\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u306e\u64cd\u4f5c\u3068\u4f3c\u3066\u3044\u307e\u3059\u3002</li> <li>\u4e00\u822c\u7684\u306a\u4e8c\u5206\u6728\u306e\u7a2e\u985e\u306b\u306f\u3001\u5b8c\u5168\u4e8c\u5206\u6728\u3001\u5b8c\u5099\u4e8c\u5206\u6728\u3001\u6e80\u4e8c\u5206\u6728\u3001\u5e73\u8861\u4e8c\u5206\u6728\u304c\u3042\u308a\u307e\u3059\u3002\u5b8c\u5168\u4e8c\u5206\u6728\u306f\u7406\u60f3\u7684\u306a\u72b6\u614b\u3092\u8868\u3057\u3001\u9023\u7d50\u30ea\u30b9\u30c8\u306f\u9000\u5316\u5f8c\u306e\u6700\u60aa\u306e\u72b6\u614b\u3067\u3059\u3002</li> <li>\u4e8c\u5206\u6728\u306f\u3001\u30ce\u30fc\u30c9\u5024\u3068\u7a7a\u304d\u30b9\u30ed\u30c3\u30c8\u3092\u30ec\u30d9\u30eb\u9806\u8d70\u67fb\u30b7\u30fc\u30b1\u30f3\u30b9\u3067\u914d\u7f6e\u3057\u3001\u89aa\u30ce\u30fc\u30c9\u3068\u5b50\u30ce\u30fc\u30c9\u9593\u306e\u30a4\u30f3\u30c7\u30c3\u30af\u30b9\u30de\u30c3\u30d4\u30f3\u30b0\u95a2\u4fc2\u306b\u57fa\u3065\u3044\u3066\u30dd\u30a4\u30f3\u30bf\u3092\u5b9f\u88c5\u3059\u308b\u3053\u3068\u3067\u3001\u914d\u5217\u3092\u4f7f\u7528\u3057\u3066\u8868\u73fe\u3067\u304d\u307e\u3059\u3002</li> <li>\u4e8c\u5206\u6728\u306e\u30ec\u30d9\u30eb\u9806\u8d70\u67fb\u306f\u5e45\u512a\u5148\u63a2\u7d22\u624b\u6cd5\u3067\u3001\u300c\u5186\u3092\u62e1\u5927\u3057\u306a\u304c\u3089\u300d\u306e\u5c64\u3054\u3068\u306e\u8d70\u67fb\u65b9\u5f0f\u3092\u53cd\u6620\u3057\u3066\u3044\u307e\u3059\u3002\u901a\u5e38\u306f\u30ad\u30e5\u30fc\u3092\u4f7f\u7528\u3057\u3066\u5b9f\u88c5\u3055\u308c\u307e\u3059\u3002</li> <li>\u524d\u9806\u3001\u4e2d\u9806\u3001\u5f8c\u9806\u8d70\u67fb\u306f\u3059\u3079\u3066\u6df1\u5ea6\u512a\u5148\u63a2\u7d22\u624b\u6cd5\u3067\u3001\u300c\u307e\u305a\u6700\u5f8c\u307e\u3067\u884c\u304d\u3001\u305d\u306e\u5f8c\u30d0\u30c3\u30af\u30c8\u30e9\u30c3\u30af\u3057\u3066\u7d9a\u884c\u3059\u308b\u300d\u8d70\u67fb\u65b9\u5f0f\u3092\u53cd\u6620\u3057\u3066\u3044\u307e\u3059\u3002\u901a\u5e38\u306f\u518d\u5e30\u3092\u4f7f\u7528\u3057\u3066\u5b9f\u88c5\u3055\u308c\u307e\u3059\u3002</li> <li>\u4e8c\u5206\u63a2\u7d22\u6728\u306f\u8981\u7d20\u691c\u7d22\u306e\u305f\u3081\u306e\u52b9\u7387\u7684\u306a\u30c7\u30fc\u30bf\u69cb\u9020\u3067\u3001\u691c\u7d22\u3001\u633f\u5165\u3001\u524a\u9664\u64cd\u4f5c\u306e\u6642\u9593\u8a08\u7b97\u91cf\u306f\u3059\u3079\u3066\\(O(\\log n)\\)\u3067\u3059\u3002\u4e8c\u5206\u63a2\u7d22\u6728\u304c\u9023\u7d50\u30ea\u30b9\u30c8\u306b\u9000\u5316\u3059\u308b\u3068\u3001\u3053\u308c\u3089\u306e\u6642\u9593\u8a08\u7b97\u91cf\u306f\\(O(n)\\)\u306b\u60aa\u5316\u3057\u307e\u3059\u3002</li> <li>AVL\u6728\u306f\u5e73\u8861\u4e8c\u5206\u63a2\u7d22\u6728\u3068\u3082\u547c\u3070\u308c\u3001\u56de\u8ee2\u64cd\u4f5c\u3092\u901a\u3057\u3066\u7d99\u7d9a\u7684\u306a\u30ce\u30fc\u30c9\u633f\u5165\u3068\u524a\u9664\u5f8c\u3082\u6728\u304c\u5e73\u8861\u3092\u4fdd\u3064\u3053\u3068\u3092\u4fdd\u8a3c\u3057\u307e\u3059\u3002</li> <li>AVL\u6728\u306e\u56de\u8ee2\u64cd\u4f5c\u306b\u306f\u3001\u53f3\u56de\u8ee2\u3001\u5de6\u56de\u8ee2\u3001\u53f3\u5de6\u56de\u8ee2\u3001\u5de6\u53f3\u56de\u8ee2\u304c\u3042\u308a\u307e\u3059\u3002\u30ce\u30fc\u30c9\u306e\u633f\u5165\u307e\u305f\u306f\u524a\u9664\u5f8c\u3001AVL\u6728\u306f\u30dc\u30c8\u30e0\u30a2\u30c3\u30d7\u65b9\u5f0f\u3067\u3053\u308c\u3089\u306e\u56de\u8ee2\u3092\u5b9f\u884c\u3057\u3066\u81ea\u5df1\u5e73\u8861\u3092\u53d6\u308a\u307e\u3059\u3002</li> </ul>"},{"location":"chapter_tree/summary/#2-q-a","title":"2. \u00a0 Q &amp; A","text":"<p>Q: \u4e00\u3064\u306e\u30ce\u30fc\u30c9\u306e\u307f\u3092\u6301\u3064\u4e8c\u5206\u6728\u306b\u3064\u3044\u3066\u3001\u6728\u306e\u9ad8\u3055\u3068\u6839\u30ce\u30fc\u30c9\u306e\u6df1\u3055\u306e\u4e21\u65b9\u304c\\(0\\)\u3067\u3059\u304b\uff1f</p> <p>\u306f\u3044\u3001\u9ad8\u3055\u3068\u6df1\u3055\u306f\u901a\u5e38\u300c\u901a\u904e\u3057\u305f\u30a8\u30c3\u30b8\u306e\u6570\u300d\u3068\u3057\u3066\u5b9a\u7fa9\u3055\u308c\u308b\u305f\u3081\u3067\u3059\u3002</p> <p>Q: \u4e8c\u5206\u6728\u306b\u304a\u3051\u308b\u633f\u5165\u3068\u524a\u9664\u306f\u4e00\u822c\u7684\u306b\u4e00\u9023\u306e\u64cd\u4f5c\u306b\u3088\u3063\u3066\u9054\u6210\u3055\u308c\u307e\u3059\u3002\u3053\u3053\u3067\u306e\u300c\u4e00\u9023\u306e\u64cd\u4f5c\u300d\u3068\u306f\u4f55\u3092\u6307\u3057\u307e\u3059\u304b\uff1f\u5b50\u30ce\u30fc\u30c9\u306e\u30ea\u30bd\u30fc\u30b9\u3092\u89e3\u653e\u3059\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u304b\uff1f</p> <p>\u4e8c\u5206\u63a2\u7d22\u6728\u3092\u4f8b\u306b\u53d6\u308b\u3068\u3001\u30ce\u30fc\u30c9\u3092\u524a\u9664\u3059\u308b\u64cd\u4f5c\u306f3\u3064\u306e\u7570\u306a\u308b\u30b7\u30ca\u30ea\u30aa\u3067\u51e6\u7406\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u3001\u305d\u308c\u305e\u308c\u8907\u6570\u30b9\u30c6\u30c3\u30d7\u306e\u30ce\u30fc\u30c9\u64cd\u4f5c\u304c\u5fc5\u8981\u3067\u3059\u3002</p> <p>Q: \u4e8c\u5206\u6728\u306eDFS\u8d70\u67fb\u3067\u524d\u9806\u3001\u4e2d\u9806\u3001\u5f8c\u9806\u306e3\u3064\u306e\u30b7\u30fc\u30b1\u30f3\u30b9\u304c\u3042\u308b\u306e\u306f\u306a\u305c\u3067\u3059\u304b\uff1f\u305d\u306e\u7528\u9014\u306f\u4f55\u3067\u3059\u304b\uff1f</p> <p>\u914d\u5217\u306e\u9806\u6b21\u304a\u3088\u3073\u9006\u9806\u8d70\u67fb\u3068\u540c\u69d8\u306b\u3001\u524d\u9806\u3001\u4e2d\u9806\u3001\u5f8c\u9806\u8d70\u67fb\u306f\u4e8c\u5206\u6728\u3092\u8d70\u67fb\u3059\u308b3\u3064\u306e\u65b9\u6cd5\u3067\u3042\u308a\u3001\u7279\u5b9a\u306e\u9806\u5e8f\u3067\u8d70\u67fb\u7d50\u679c\u3092\u53d6\u5f97\u3067\u304d\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u4e8c\u5206\u63a2\u7d22\u6728\u3067\u306f\u3001\u30ce\u30fc\u30c9\u30b5\u30a4\u30ba\u304c\u300c\u5de6\u5b50\u30ce\u30fc\u30c9\u5024 &lt; \u6839\u30ce\u30fc\u30c9\u5024 &lt; \u53f3\u5b50\u30ce\u30fc\u30c9\u5024\u300d\u3092\u6e80\u305f\u3059\u305f\u3081\u3001\u300c\u5de6 \\(\\rightarrow\\) \u6839 \\(\\rightarrow\\) \u53f3\u300d\u306e\u512a\u5148\u9806\u4f4d\u3067\u6728\u3092\u8d70\u67fb\u3059\u308b\u3053\u3068\u3067\u3001\u9806\u5e8f\u4ed8\u3051\u3089\u308c\u305f\u30ce\u30fc\u30c9\u30b7\u30fc\u30b1\u30f3\u30b9\u3092\u53d6\u5f97\u3067\u304d\u307e\u3059\u3002</p> <p>Q: \u4e0d\u5e73\u8861\u30ce\u30fc\u30c9<code>node</code>\u3001<code>child</code>\u3001<code>grand_child</code>\u9593\u306e\u95a2\u4fc2\u3092\u51e6\u7406\u3059\u308b\u53f3\u56de\u8ee2\u64cd\u4f5c\u306b\u304a\u3044\u3066\u3001\u53f3\u56de\u8ee2\u5f8c\u306b<code>node</code>\u3068\u305d\u306e\u89aa\u30ce\u30fc\u30c9\u9593\u306e\u63a5\u7d9a\u3068<code>node</code>\u306e\u5143\u306e\u30ea\u30f3\u30af\u304c\u5931\u308f\u308c\u308b\u306e\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u304b\uff1f</p> <p>\u3053\u306e\u554f\u984c\u3092\u518d\u5e30\u7684\u306a\u89b3\u70b9\u304b\u3089\u898b\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002<code>right_rotate(root)</code>\u64cd\u4f5c\u306f\u90e8\u5206\u6728\u306e\u6839\u30ce\u30fc\u30c9\u3092\u6e21\u3057\u3001\u6700\u7d42\u7684\u306b<code>return child</code>\u3067\u56de\u8ee2\u3055\u308c\u305f\u90e8\u5206\u6728\u306e\u6839\u30ce\u30fc\u30c9\u3092\u8fd4\u3057\u307e\u3059\u3002\u90e8\u5206\u6728\u306e\u6839\u30ce\u30fc\u30c9\u3068\u305d\u306e\u89aa\u30ce\u30fc\u30c9\u9593\u306e\u63a5\u7d9a\u306f\u3001\u3053\u306e\u95a2\u6570\u304c\u623b\u3063\u305f\u5f8c\u306b\u78ba\u7acb\u3055\u308c\u3001\u3053\u308c\u306f\u53f3\u56de\u8ee2\u64cd\u4f5c\u306e\u4fdd\u5b88\u7bc4\u56f2\u5916\u3067\u3059\u3002</p> <p>Q: C++\u3067\u306f\u3001\u95a2\u6570\u306f<code>private</code>\u3068<code>public</code>\u30bb\u30af\u30b7\u30e7\u30f3\u306b\u5206\u304b\u308c\u3066\u3044\u307e\u3059\u3002\u3053\u308c\u306b\u306f\u3069\u306e\u3088\u3046\u306a\u8003\u616e\u4e8b\u9805\u304c\u3042\u308a\u307e\u3059\u304b\uff1f\u306a\u305c<code>height()</code>\u95a2\u6570\u3068<code>updateHeight()</code>\u95a2\u6570\u304c\u305d\u308c\u305e\u308c<code>public</code>\u3068<code>private</code>\u306b\u914d\u7f6e\u3055\u308c\u3066\u3044\u308b\u306e\u3067\u3059\u304b\uff1f</p> <p>\u3053\u308c\u306f\u30e1\u30bd\u30c3\u30c9\u306e\u4f7f\u7528\u7bc4\u56f2\u306b\u3088\u308a\u307e\u3059\u3002\u30e1\u30bd\u30c3\u30c9\u304c\u30af\u30e9\u30b9\u5185\u3067\u306e\u307f\u4f7f\u7528\u3055\u308c\u308b\u5834\u5408\u3001<code>private</code>\u306b\u8a2d\u8a08\u3055\u308c\u307e\u3059\u3002\u4f8b\u3048\u3070\u3001\u30e6\u30fc\u30b6\u30fc\u304c\u72ec\u81ea\u306b<code>updateHeight()</code>\u3092\u547c\u3073\u51fa\u3059\u3053\u3068\u306f\u610f\u5473\u304c\u3042\u308a\u307e\u305b\u3093\u3002\u3053\u308c\u306f\u633f\u5165\u307e\u305f\u306f\u524a\u9664\u64cd\u4f5c\u306e\u4e00\u30b9\u30c6\u30c3\u30d7\u306b\u904e\u304e\u306a\u3044\u304b\u3089\u3067\u3059\u3002\u3057\u304b\u3057\u3001<code>height()</code>\u306f\u30ce\u30fc\u30c9\u306e\u9ad8\u3055\u306b\u30a2\u30af\u30bb\u30b9\u3059\u308b\u305f\u3081\u306e\u3082\u306e\u3067\u3001<code>vector.size()</code>\u3068\u540c\u69d8\u3067\u3042\u308b\u305f\u3081\u3001\u4f7f\u7528\u306e\u305f\u3081\u306b<code>public</code>\u306b\u8a2d\u5b9a\u3055\u308c\u3066\u3044\u307e\u3059\u3002</p> <p>Q: \u5165\u529b\u30c7\u30fc\u30bf\u306e\u30bb\u30c3\u30c8\u304b\u3089\u4e8c\u5206\u63a2\u7d22\u6728\u3092\u3069\u306e\u3088\u3046\u306b\u69cb\u7bc9\u3057\u307e\u3059\u304b\uff1f\u6839\u30ce\u30fc\u30c9\u306e\u9078\u629e\u306f\u975e\u5e38\u306b\u91cd\u8981\u3067\u3059\u304b\uff1f</p> <p>\u306f\u3044\u3001\u6728\u3092\u69cb\u7bc9\u3059\u308b\u65b9\u6cd5\u306f\u4e8c\u5206\u63a2\u7d22\u6728\u30b3\u30fc\u30c9\u306e<code>build_tree()</code>\u30e1\u30bd\u30c3\u30c9\u3067\u63d0\u4f9b\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u6839\u30ce\u30fc\u30c9\u306e\u9078\u629e\u306b\u3064\u3044\u3066\u306f\u3001\u901a\u5e38\u5165\u529b\u30c7\u30fc\u30bf\u3092\u30bd\u30fc\u30c8\u3057\u3001\u4e2d\u592e\u306e\u8981\u7d20\u3092\u6839\u30ce\u30fc\u30c9\u3068\u3057\u3066\u9078\u629e\u3057\u3001\u518d\u5e30\u7684\u306b\u5de6\u3068\u53f3\u306e\u90e8\u5206\u6728\u3092\u69cb\u7bc9\u3057\u307e\u3059\u3002\u3053\u306e\u30a2\u30d7\u30ed\u30fc\u30c1\u306f\u6728\u306e\u5e73\u8861\u3092\u6700\u5927\u5316\u3057\u307e\u3059\u3002</p> <p>Q: Java\u3067\u306f\u3001\u6587\u5b57\u5217\u6bd4\u8f03\u306b\u5e38\u306b<code>equals()</code>\u30e1\u30bd\u30c3\u30c9\u3092\u4f7f\u7528\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u304b\uff1f</p> <p>Java\u3067\u306f\u3001\u30d7\u30ea\u30df\u30c6\u30a3\u30d6\u30c7\u30fc\u30bf\u578b\u306e\u5834\u5408\u3001<code>==</code>\u306f2\u3064\u306e\u5909\u6570\u306e\u5024\u304c\u7b49\u3057\u3044\u304b\u3069\u3046\u304b\u3092\u6bd4\u8f03\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002\u53c2\u7167\u578b\u306e\u5834\u5408\u30012\u3064\u306e\u30b7\u30f3\u30dc\u30eb\u306e\u52d5\u4f5c\u539f\u7406\u306f\u7570\u306a\u308a\u307e\u3059\u3002</p> <ul> <li><code>==</code>: 2\u3064\u306e\u5909\u6570\u304c\u540c\u3058\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u3092\u6307\u3057\u3066\u3044\u308b\u304b\u3069\u3046\u304b\u3001\u3064\u307e\u308a\u30e1\u30e2\u30ea\u5185\u306e\u4f4d\u7f6e\u304c\u540c\u3058\u304b\u3069\u3046\u304b\u3092\u6bd4\u8f03\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002</li> <li><code>equals()</code>: 2\u3064\u306e\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u306e\u5024\u304c\u7b49\u3057\u3044\u304b\u3069\u3046\u304b\u3092\u6bd4\u8f03\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002</li> </ul> <p>\u3057\u305f\u304c\u3063\u3066\u3001\u5024\u3092\u6bd4\u8f03\u3059\u308b\u306b\u306f<code>equals()</code>\u3092\u4f7f\u7528\u3059\u3079\u304d\u3067\u3059\u3002\u305f\u3060\u3057\u3001<code>String a = \"hi\"; String b = \"hi\";</code>\u3067\u521d\u671f\u5316\u3055\u308c\u305f\u6587\u5b57\u5217\u306f\u6587\u5b57\u5217\u5b9a\u6570\u30d7\u30fc\u30eb\u306b\u683c\u7d0d\u3055\u308c\u3001\u540c\u3058\u30aa\u30d6\u30b8\u30a7\u30af\u30c8\u3092\u6307\u3059\u305f\u3081\u3001<code>a == b</code>\u30822\u3064\u306e\u6587\u5b57\u5217\u306e\u5185\u5bb9\u3092\u6bd4\u8f03\u3059\u308b\u305f\u3081\u306b\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002</p> <p>Q: \u6700\u4e0b\u4f4d\u30ec\u30d9\u30eb\u306b\u5230\u9054\u3059\u308b\u524d\u306b\u3001\u5e45\u512a\u5148\u8d70\u67fb\u3067\u30ad\u30e5\u30fc\u5185\u306e\u30ce\u30fc\u30c9\u6570\u306f\\(2^h\\)\u3067\u3059\u304b\uff1f</p> <p>\u306f\u3044\u3001\u4f8b\u3048\u3070\u9ad8\u3055\\(h = 2\\)\u306e\u6e80\u4e8c\u5206\u6728\u306f\u5408\u8a08\\(n = 7\\)\u500b\u306e\u30ce\u30fc\u30c9\u3092\u6301\u3061\u3001\u6700\u4e0b\u4f4d\u30ec\u30d9\u30eb\u306b\u306f\\(4 = 2^h = (n + 1) / 2\\)\u500b\u306e\u30ce\u30fc\u30c9\u304c\u3042\u308a\u307e\u3059\u3002</p>"}]}
\ No newline at end of file
diff --git a/ja/sitemap.xml b/ja/sitemap.xml
new file mode 100644
index 000000000..359a132c5
--- /dev/null
+++ b/ja/sitemap.xml
@@ -0,0 +1,528 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<urlset xmlns="http://www.sitemaps.org/schemas/sitemap/0.9">
+    <url>
+         <loc>https://www.hello-algo.com/ja/</loc>
+         <lastmod>2025-10-16</lastmod>
+         <changefreq>daily</changefreq>
+    </url>
+    <url>
+         <loc>https://www.hello-algo.com/ja/chapter_appendix/</loc>
+         <lastmod>2025-10-16</lastmod>
+         <changefreq>daily</changefreq>
+    </url>
+    <url>
+         <loc>https://www.hello-algo.com/ja/chapter_appendix/contribution/</loc>
+         <lastmod>2025-10-16</lastmod>
+         <changefreq>daily</changefreq>
+    </url>
+    <url>
+         <loc>https://www.hello-algo.com/ja/chapter_appendix/installation/</loc>
+         <lastmod>2025-10-16</lastmod>
+         <changefreq>daily</changefreq>
+    </url>
+    <url>
+         <loc>https://www.hello-algo.com/ja/chapter_appendix/terminology/</loc>
+         <lastmod>2025-10-16</lastmod>
+         <changefreq>daily</changefreq>
+    </url>
+    <url>
+         <loc>https://www.hello-algo.com/ja/chapter_array_and_linkedlist/</loc>
+         <lastmod>2025-10-16</lastmod>
+         <changefreq>daily</changefreq>
+    </url>
+    <url>
+         <loc>https://www.hello-algo.com/ja/chapter_array_and_linkedlist/array/</loc>
+         <lastmod>2025-10-16</lastmod>
+         <changefreq>daily</changefreq>
+    </url>
+    <url>
+         <loc>https://www.hello-algo.com/ja/chapter_array_and_linkedlist/linked_list/</loc>
+         <lastmod>2025-10-16</lastmod>
+         <changefreq>daily</changefreq>
+    </url>
+    <url>
+         <loc>https://www.hello-algo.com/ja/chapter_array_and_linkedlist/list/</loc>
+         <lastmod>2025-10-16</lastmod>
+         <changefreq>daily</changefreq>
+    </url>
+    <url>
+         <loc>https://www.hello-algo.com/ja/chapter_array_and_linkedlist/ram_and_cache/</loc>
+         <lastmod>2025-10-16</lastmod>
+         <changefreq>daily</changefreq>
+    </url>
+    <url>
+         <loc>https://www.hello-algo.com/ja/chapter_array_and_linkedlist/summary/</loc>
+         <lastmod>2025-10-16</lastmod>
+         <changefreq>daily</changefreq>
+    </url>
+    <url>
+         <loc>https://www.hello-algo.com/ja/chapter_backtracking/</loc>
+         <lastmod>2025-10-16</lastmod>
+         <changefreq>daily</changefreq>
+    </url>
+    <url>
+         <loc>https://www.hello-algo.com/ja/chapter_backtracking/backtracking_algorithm/</loc>
+         <lastmod>2025-10-16</lastmod>
+         <changefreq>daily</changefreq>
+    </url>
+    <url>
+         <loc>https://www.hello-algo.com/ja/chapter_backtracking/n_queens_problem/</loc>
+         <lastmod>2025-10-16</lastmod>
+         <changefreq>daily</changefreq>
+    </url>
+    <url>
+         <loc>https://www.hello-algo.com/ja/chapter_backtracking/permutations_problem/</loc>
+         <lastmod>2025-10-16</lastmod>
+         <changefreq>daily</changefreq>
+    </url>
+    <url>
+         <loc>https://www.hello-algo.com/ja/chapter_backtracking/subset_sum_problem/</loc>
+         <lastmod>2025-10-16</lastmod>
+         <changefreq>daily</changefreq>
+    </url>
+    <url>
+         <loc>https://www.hello-algo.com/ja/chapter_backtracking/summary/</loc>
+         <lastmod>2025-10-16</lastmod>
+         <changefreq>daily</changefreq>
+    </url>
+    <url>
+         <loc>https://www.hello-algo.com/ja/chapter_computational_complexity/</loc>
+         <lastmod>2025-10-16</lastmod>
+         <changefreq>daily</changefreq>
+    </url>
+    <url>
+         <loc>https://www.hello-algo.com/ja/chapter_computational_complexity/iteration_and_recursion/</loc>
+         <lastmod>2025-10-16</lastmod>
+         <changefreq>daily</changefreq>
+    </url>
+    <url>
+         <loc>https://www.hello-algo.com/ja/chapter_computational_complexity/performance_evaluation/</loc>
+         <lastmod>2025-10-16</lastmod>
+         <changefreq>daily</changefreq>
+    </url>
+    <url>
+         <loc>https://www.hello-algo.com/ja/chapter_computational_complexity/space_complexity/</loc>
+         <lastmod>2025-10-16</lastmod>
+         <changefreq>daily</changefreq>
+    </url>
+    <url>
+         <loc>https://www.hello-algo.com/ja/chapter_computational_complexity/summary/</loc>
+         <lastmod>2025-10-16</lastmod>
+         <changefreq>daily</changefreq>
+    </url>
+    <url>
+         <loc>https://www.hello-algo.com/ja/chapter_computational_complexity/time_complexity/</loc>
+         <lastmod>2025-10-16</lastmod>
+         <changefreq>daily</changefreq>
+    </url>
+    <url>
+         <loc>https://www.hello-algo.com/ja/chapter_data_structure/</loc>
+         <lastmod>2025-10-16</lastmod>
+         <changefreq>daily</changefreq>
+    </url>
+    <url>
+         <loc>https://www.hello-algo.com/ja/chapter_data_structure/basic_data_types/</loc>
+         <lastmod>2025-10-16</lastmod>
+         <changefreq>daily</changefreq>
+    </url>
+    <url>
+         <loc>https://www.hello-algo.com/ja/chapter_data_structure/character_encoding/</loc>
+         <lastmod>2025-10-16</lastmod>
+         <changefreq>daily</changefreq>
+    </url>
+    <url>
+         <loc>https://www.hello-algo.com/ja/chapter_data_structure/classification_of_data_structure/</loc>
+         <lastmod>2025-10-16</lastmod>
+         <changefreq>daily</changefreq>
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+}
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+[data-md-color-scheme="slate"] {
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+  --md-body-bg-color: #22272e;
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+  --md-code-fg-color: #adbac7;
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+  --md-admonition-fg-color: #adbac7;
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+  --md-footer-fg-color: #adbac7;
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+  --md-typeset-color: #adbac7;
+  --md-typeset-a-color: #52bbb1;
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+  --md-typeset-btn-color: #52bbb1;
+  --md-typeset-btn-hover-color: #55aea6;
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+  --md-admonition-pythontutor-color: #30363f;
+}
+
+[data-md-color-scheme="slate"][data-md-color-primary="black"],
+[data-md-color-scheme="slate"][data-md-color-primary="white"] {
+  --md-typeset-a-color: #52bbb1;
+}
+
+[data-md-color-primary="black"] .md-header {
+  background-color: var(--md-header-bg-color);
+}
+
+.md-header--shadow,
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+  box-shadow: none;
+  transition: none;
+  backdrop-filter: saturate(180%) blur(20px);
+  /* Gaussian blur */
+  -webkit-backdrop-filter: saturate(180%) blur(20px);
+  /* Safari */
+  background-color: var(--md-header-bg-color);
+}
+
+/* https://github.com/squidfunk/mkdocs-material/issues/4832#issuecomment-1374891676 */
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+  color: var(--md-default-fg-color) !important;
+}
+
+/* Figure class */
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+  border-radius: 0.3rem;
+  display: block;
+  margin: 0 auto;
+  box-shadow: var(--md-shadow-z2);
+}
+
+/* Cover image class */
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+  width: 28rem;
+  height: auto;
+  border-radius: 0.3rem;
+  display: block;
+  margin: 0 auto;
+  box-shadow: var(--md-shadow-z2);
+}
+
+/* Center Markdown Tables (requires md_in_html extension) */
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+  text-align: center;
+}
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+/* Reset alignment for table cells */
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+}
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+/* Font size */
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+}
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+}
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+/* Markdown Header */
+/* https://github.com/squidfunk/mkdocs-material/blob/dcab57dd1cced4b77875c1aa1b53467c62709d31/src/assets/stylesheets/main/_typeset.scss */
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+  color: var(--md-default-fg-color);
+}
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+}
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+}
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+}
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+}
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+  font-weight: normal;
+}
+
+/* font-family setting for Win10 */
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+  --md-text-font-family: -apple-system, BlinkMacSystemFont,
+    var(--md-text-font, _), Helvetica, Arial, sans-serif;
+  --md-code-font-family: var(--md-code-font, _), SFMono-Regular, Consolas, Menlo,
+    -apple-system, BlinkMacSystemFont, var(--md-text-font, _), monospace;
+}
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+/* max height of code block */
+/* https://github.com/squidfunk/mkdocs-material/issues/3444 */
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+  max-height: 25rem;
+}
+
+/* Make the picture not glare in dark theme */
+[data-md-color-scheme="slate"] .md-typeset img,
+[data-md-color-scheme="slate"] .md-typeset svg,
+[data-md-color-scheme="slate"] .md-typeset video {
+  filter: brightness(0.85) invert(0.05);
+}
+
+/* landing page */
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+  display: flex;
+  align-items: center;
+  justify-content: center;
+  margin: 0 auto;
+  width: 100%;
+  /* Default to full width */
+}
+
+/* Admonition for python tutor */
+.md-typeset .admonition.pythontutor,
+.md-typeset details.pythontutor {
+  border-color: var(--md-default-fg-color--lightest);
+  margin-top: 0;
+  margin-bottom: 1.5625em;
+}
+
+.md-typeset .admonition:focus-within,
+.md-typeset details:focus-within {
+  box-shadow: var(--md-shadow-z1);
+}
+
+.md-typeset .pythontutor>.admonition-title,
+.md-typeset .pythontutor>summary {
+  background-color: var(--md-code-bg-color);
+}
+
+.md-typeset .pythontutor>.admonition-title::before,
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+  -webkit-mask-image: var(--md-admonition-icon--pythontutor);
+  mask-image: var(--md-admonition-icon--pythontutor);
+}
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+  width: 1.25em;
+}
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+  padding: .78125em 1.0em .625em;
+}
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+/* header banner */
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+  background-color: var(--md-code-bg-color);
+  color: var(--md-default-fg-color);
+  font-size: 0.75rem;
+}
+
+.md-banner .banner-svg svg {
+  margin-right: 0.3rem;
+  height: 0.63rem;
+  fill: var(--md-default-fg-color);
+}
+
+.pythontutor-iframe {
+  width: 125%;
+  height: 125%;
+  max-width: 125% !important;
+  max-height: 125% !important;
+  transform: scale(0.8);
+  transform-origin: top left;
+  border: none;
+}
+
+/* landing page container */
+.home-div {
+  width: 100%;
+  height: auto;
+  display: flex;
+  justify-content: center;
+  align-items: center;
+  background-color: var(--md-default-bg-color);
+  color: var(--md-default-fg-color);
+  font-size: 0.9rem;
+  padding: 3em 2em;
+  text-align: center;
+}
+
+.section-content {
+  width: 100%;
+  height: auto;
+  max-width: 70vw;
+}
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+/* rounded button */
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+  display: inline-flex;
+  align-items: center;
+  justify-content: center;
+  border-radius: 10em;
+  margin: 0 0.1em;
+  padding: 0.6em 1.3em;
+  border: none;
+  background-color: var(--md-typeset-btn-color);
+  color: var(--md-primary-fg-color) !important;
+  text-align: center;
+  text-decoration: none;
+  cursor: pointer;
+}
+
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+  background-color: var(--md-typeset-btn-hover-color);
+}
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+  margin: 0;
+  margin-bottom: 0.07em;
+  white-space: nowrap;
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+  fill: var(--md-primary-fg-color);
+  width: auto;
+  height: 1.2em;
+  margin-right: 0.5em;
+}
+
+/* device image */
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+  width: auto;
+  transition: transform 0.3s ease-in-out, filter 0.3s ease-in-out;
+}
+
+a:hover .device-on-hover {
+  filter: drop-shadow(0 0 0.2rem rgba(0, 0, 0, 0.15));
+  transform: scale(1.01);
+}
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+/* text button */
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+  display: flex;
+  justify-content: center;
+  align-items: flex-end;
+  height: 32vw;
+}
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+  height: 100%;
+  margin: 0 0.2em;
+}
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+  color: var(--md-typeset-btn-color);
+  text-decoration: none;
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+  margin: 2.7em auto;
+}
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+  width: auto;
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+  background-size: cover;
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+  margin-left: 0.15em;
+}
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+a:hover .text-button span {
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+}
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+/* hero image */
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+  width: min(112vh, 100vw);
+  margin: 0 auto;
+  margin-top: -2.4rem;
+  padding: 0;
+  position: relative;
+  font-size: min(1.8vh, 2.5vw);
+  font-weight: normal;
+}
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+  height: 100%;
+  width: 100%;
+  object-fit: cover;
+  position: absolute;
+}
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+/* hover on the planets */
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+  width: auto;
+  position: absolute;
+  transition: transform 0.3s ease-in-out, filter 0.3s ease-in-out;
+}
+
+.hero-div>a>span {
+  margin: 0;
+  position: absolute;
+  transform: translateX(-50%) translateY(-50%);
+  white-space: nowrap;
+  /* prevent line breaks */
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+}
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+  transform: scale(1.03);
+}
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+  text-decoration: underline;
+  color: var(--md-typeset-btn-color);
+}
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+  width: 100%;
+  position: absolute;
+  transform: translateX(-50%);
+  left: 50%;
+  bottom: min(2vh, 3vw);
+  pointer-events: none;
+  color: #fff;
+}
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+/* code badge */
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+  width: 100%;
+  height: auto;
+  margin: 1em auto;
+}
+
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+  height: 1.07em;
+  width: auto;
+}
+
+/* brief intro */
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+  display: flex;
+  align-items: center;
+  margin: 2em auto;
+}
+
+.intro-image {
+  flex-shrink: 0;
+  flex-grow: 0;
+  width: 50%;
+  border-radius: 0.5em;
+  box-shadow: var(--md-shadow-z2);
+}
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+.intro-text {
+  flex-grow: 1;
+  /* fill the space */
+  display: flex;
+  flex-direction: column;
+  justify-content: center;
+  text-align: left;
+  align-items: flex-start;
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+  margin: 2em;
+}
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+  width: auto;
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+}
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+}
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+  .reading-media {
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+  .contrib-image {
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+}
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+  .hero-div {
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+  .intro-container {
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+  .intro-text {
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+  .endor-text {
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+  .intro-image {
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+  .text-button {
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+}
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+}
+/*! update cache: 20251017053011 */
diff --git a/javascripts/katex.js b/javascripts/katex.js
index a85bdad90..f9f62254f 100644
--- a/javascripts/katex.js
+++ b/javascripts/katex.js
@@ -8,4 +8,4 @@ document$.subscribe(({ body }) => {
     ],
   });
 });
-/*! update cache: 20251007160224 */
+/*! update cache: 20251017052948 */
diff --git a/javascripts/mathjax.js b/javascripts/mathjax.js
index 137d7ad97..e69f0bb4e 100644
--- a/javascripts/mathjax.js
+++ b/javascripts/mathjax.js
@@ -15,4 +15,4 @@ window.MathJax = {
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index e3826badb..4f7a3909e 100644
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diff --git a/stylesheets/extra.css b/stylesheets/extra.css
index cf0c6c4c0..a1f2e24ba 100644
--- a/stylesheets/extra.css
+++ b/stylesheets/extra.css
@@ -552,4 +552,4 @@ a:hover .text-button span {
   width: 100%;
   height: 100%;
 }
-/*! update cache: 20251007160224 */
+/*! update cache: 20251017052948 */
diff --git a/zh-hant/404.html b/zh-hant/404.html
index 8b9cb5337..1e4af6bad 100644
--- a/zh-hant/404.html
+++ b/zh-hant/404.html
@@ -188,6 +188,12 @@
             </a>
           </li>
         
+          <li class="md-select__item">
+            <a href="/ja/" hreflang="ja" class="md-select__link">
+              日本語
+            </a>
+          </li>
+        
       </ul>
     </div>
   </div>
diff --git a/zh-hant/assets/javascripts/bundle.c18c5fb9.min.js b/zh-hant/assets/javascripts/bundle.c18c5fb9.min.js
index 989d4998d..9f95955bb 100644
--- a/zh-hant/assets/javascripts/bundle.c18c5fb9.min.js
+++ b/zh-hant/assets/javascripts/bundle.c18c5fb9.min.js
@@ -27,4 +27,4 @@ PERFORMANCE OF THIS SOFTWARE.
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circle{fill:var(--md-mermaid-label-bg-color)}.actor{fill:var(--md-mermaid-sequence-actor-bg-color);stroke:var(--md-mermaid-sequence-actor-border-color)}text.actor>tspan{fill:var(--md-mermaid-sequence-actor-fg-color);font-family:var(--md-mermaid-font-family)}line{stroke:var(--md-mermaid-sequence-actor-line-color)}.actor-man circle,.actor-man line{fill:var(--md-mermaid-sequence-actorman-bg-color);stroke:var(--md-mermaid-sequence-actorman-line-color)}.messageLine0,.messageLine1{stroke:var(--md-mermaid-sequence-message-line-color)}.note{fill:var(--md-mermaid-sequence-note-bg-color);stroke:var(--md-mermaid-sequence-note-border-color)}.loopText,.loopText>tspan,.messageText,.noteText>tspan{stroke:none;font-family:var(--md-mermaid-font-family)!important}.messageText{fill:var(--md-mermaid-sequence-message-fg-color)}.loopText,.loopText>tspan{fill:var(--md-mermaid-sequence-loop-fg-color)}.noteText>tspan{fill:var(--md-mermaid-sequence-note-fg-color)}#arrowhead 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Hn(e,{viewport$:t,target$:r,print$:o}){return T(...R(".annotate:not(.highlight)",e).map(n=>wn(n,{target$:r,print$:o})),...R("pre:not(.mermaid) > code",e).map(n=>On(n,{target$:r,print$:o})),...R("pre.mermaid",e).map(n=>_n(n)),...R("table:not([class])",e).map(n=>Cn(n)),...R("details",e).map(n=>Mn(n,{target$:r,print$:o})),...R("[data-tabs]",e).map(n=>kn(n,{viewport$:t,target$:r})),...R("[title]",e).filter(()=>G("content.tooltips")).map(n=>Ge(n)))}function Ra(e,{alert$:t}){return t.pipe(b(r=>T($(!0),$(!1).pipe(Ye(2e3))).pipe(m(o=>({message:r,active:o})))))}function $n(e,t){let r=P(".md-typeset",e);return H(()=>{let o=new v;return o.subscribe(({message:n,active:i})=>{e.classList.toggle("md-dialog--active",i),r.textContent=n}),Ra(e,t).pipe(y(n=>o.next(n)),_(()=>o.complete()),m(n=>F({ref:e},n)))})}function Pa({viewport$:e}){if(!G("header.autohide"))return $(!1);let 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$(...e).pipe(re(o=>d(o,"change").pipe(m(()=>o))),q(e[r]),m(o=>({index:e.indexOf(o),color:{media:o.getAttribute("data-md-color-media"),scheme:o.getAttribute("data-md-color-scheme"),primary:o.getAttribute("data-md-color-primary"),accent:o.getAttribute("data-md-color-accent")}})),B(1))}function jn(e){let t=R("input",e),r=E("meta",{name:"theme-color"});document.head.appendChild(r);let o=E("meta",{name:"color-scheme"});document.head.appendChild(o);let n=At("(prefers-color-scheme: light)");return H(()=>{let i=new v;return i.subscribe(s=>{if(document.body.setAttribute("data-md-color-switching",""),s.color.media==="(prefers-color-scheme)"){let a=matchMedia("(prefers-color-scheme: light)"),c=document.querySelector(a.matches?"[data-md-color-media='(prefers-color-scheme: light)']":"[data-md-color-media='(prefers-color-scheme: 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Q([t,r.pipe(q(ve()),g(o=>!!o.searchParams.get("h")))]).pipe(m(([o,n])=>Yn(o.config)(n.searchParams.get("h"))),m(o=>{var s;let n=new Map,i=document.createNodeIterator(e,NodeFilter.SHOW_TEXT);for(let a=i.nextNode();a;a=i.nextNode())if((s=a.parentElement)!=null&&s.offsetHeight){let c=a.textContent,p=o(c);p.length>c.length&&n.set(a,p)}for(let[a,c]of n){let{childNodes:p}=E("span",null,c);a.replaceWith(...Array.from(p))}return{ref:e,nodes:n}}))}function Ya(e,{viewport$:t,main$:r}){let o=e.closest(".md-grid"),n=o.offsetTop-o.parentElement.offsetTop;return Q([r,t]).pipe(m(([{offset:i,height:s},{offset:{y:a}}])=>(s=s+Math.min(n,Math.max(0,a-i))-n,{height:s,locked:a>=i+n})),Y((i,s)=>i.height===s.height&&i.locked===s.locked))}function Qr(e,o){var n=o,{header$:t}=n,r=to(n,["header$"]);let i=P(".md-sidebar__scrollwrap",e),{y:s}=Ue(i);return H(()=>{let a=new v,c=a.pipe(ee(),oe(!0)),p=a.pipe(Me(0,de));return p.pipe(ae(t)).subscribe({next([{height:l},{height:f}]){i.style.height=`${l-2*s}px`,e.style.top=`${f}px`},complete(){i.style.height="",e.style.top=""}}),p.pipe(He()).subscribe(()=>{for(let l of R(".md-nav__link--active[href]",e)){if(!l.clientHeight)continue;let f=l.closest(".md-sidebar__scrollwrap");if(typeof f!="undefined"){let u=l.offsetTop-f.offsetTop,{height:h}=pe(f);f.scrollTo({top:u-h/2})}}}),fe(R("label[tabindex]",e)).pipe(re(l=>d(l,"click").pipe(Oe(ie),m(()=>l),U(c)))).subscribe(l=>{let f=P(`[id="${l.htmlFor}"]`);P(`[aria-labelledby="${l.id}"]`).setAttribute("aria-expanded",`${f.checked}`)}),Ya(e,r).pipe(y(l=>a.next(l)),_(()=>a.complete()),m(l=>F({ref:e},l)))})}function oi(e,t){if(typeof t!="undefined"){let r=`https://api.github.com/repos/${e}/${t}`;return Lt(De(`${r}/releases/latest`).pipe(he(()=>L),m(o=>({version:o.tag_name})),Qe({})),De(r).pipe(he(()=>L),m(o=>({stars:o.stargazers_count,forks:o.forks_count})),Qe({}))).pipe(m(([o,n])=>F(F({},o),n)))}else{let r=`https://api.github.com/users/${e}`;return De(r).pipe(m(o=>({repositories:o.public_repos})),Qe({}))}}function ni(e,t){let r=`https://${e}/api/v4/projects/${encodeURIComponent(t)}`;return De(r).pipe(he(()=>L),m(({star_count:o,forks_count:n})=>({stars:o,forks:n})),Qe({}))}function ii(e){let t=e.match(/^.+github\.com\/([^/]+)\/?([^/]+)?/i);if(t){let[,r,o]=t;return oi(r,o)}if(t=e.match(/^.+?([^/]*gitlab[^/]+)\/(.+?)\/?$/i),t){let[,r,o]=t;return ni(r,o)}return L}var Ba;function Ga(e){return Ba||(Ba=H(()=>{let t=__md_get("__source",sessionStorage);if(t)return $(t);if(ne("consent").length){let o=__md_get("__consent");if(!(o&&o.github))return L}return ii(e.href).pipe(y(o=>__md_set("__source",o,sessionStorage)))}).pipe(he(()=>L),g(t=>Object.keys(t).length>0),m(t=>({facts:t})),B(1)))}function ai(e){let t=P(":scope > :last-child",e);return H(()=>{let r=new v;return 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$([...o].reduce((p,[l,f])=>{for(;c.length&&o.get(c[c.length-1]).tagName>=f.tagName;)c.pop();let u=f.offsetTop;for(;!u&&f.parentElement;)f=f.parentElement,u=f.offsetTop;let h=f.offsetParent;for(;h;h=h.offsetParent)u+=h.offsetTop;return p.set([...c=[...c,l]].reverse(),u)},new Map))}).pipe(m(c=>new Map([...c].sort(([,p],[,l])=>p-l))),je(i),b(([c,p])=>t.pipe(Rr(([l,f],{offset:{y:u},size:h})=>{let w=u+h.height>=Math.floor(a.height);for(;f.length;){let[,A]=f[0];if(A-p<u||w)l=[...l,f.shift()];else break}for(;l.length;){let[,A]=l[l.length-1];if(A-p>=u&&!w)f=[l.pop(),...f];else break}return[l,f]},[[],[...c]]),Y((l,f)=>l[0]===f[0]&&l[1]===f[1])))))).pipe(m(([a,c])=>({prev:a.map(([p])=>p),next:c.map(([p])=>p)})),q({prev:[],next:[]}),Ke(2,1),m(([a,c])=>a.prev.length<c.prev.length?{prev:c.prev.slice(Math.max(0,a.prev.length-1),c.prev.length),next:[]}:{prev:c.prev.slice(-1),next:c.next.slice(0,c.next.length-a.next.length)}))}function ci(e,{viewport$:t,header$:r,main$:o,target$:n}){return H(()=>{let i=new v,s=i.pipe(ee(),oe(!0));if(i.subscribe(({prev:a,next:c})=>{for(let[p]of c)p.classList.remove("md-nav__link--passed"),p.classList.remove("md-nav__link--active");for(let[p,[l]]of a.entries())l.classList.add("md-nav__link--passed"),l.classList.toggle("md-nav__link--active",p===a.length-1)}),G("toc.follow")){let a=T(t.pipe(be(1),m(()=>{})),t.pipe(be(250),m(()=>"smooth")));i.pipe(g(({prev:c})=>c.length>0),je(o.pipe(Oe(ie))),ae(a)).subscribe(([[{prev:c}],p])=>{let[l]=c[c.length-1];if(l.offsetHeight){let f=sr(l);if(typeof f!="undefined"){let u=l.offsetTop-f.offsetTop,{height:h}=pe(f);f.scrollTo({top:u-h/2,behavior:p})}}})}return G("navigation.tracking")&&t.pipe(U(s),X("offset"),be(250),Le(1),U(n.pipe(Le(1))),at({delay:250}),ae(i)).subscribe(([,{prev:a}])=>{let c=ve(),p=a[a.length-1];if(p&&p.length){let[l]=p,{hash:f}=new URL(l.href);c.hash!==f&&(c.hash=f,history.replaceState({},"",`${c}`))}else 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diff --git a/zh-hant/assets/javascripts/glightbox.min.js b/zh-hant/assets/javascripts/glightbox.min.js
index 4b8341a23..1995a7b62 100644
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t=this;e.touches.length<2&&(this.multipointEnd.dispatch(e,this.element),this.sx2=this.sy2=null),this.x2&&Math.abs(this.x1-this.x2)>30||this.y2&&Math.abs(this.y1-this.y2)>30?(e.direction=this._swipeDirection(this.x1,this.x2,this.y1,this.y2),this.swipeTimeout=setTimeout((function(){t.swipe.dispatch(e,t.element)}),0)):(this.tapTimeout=setTimeout((function(){t._preventTap||t.tap.dispatch(e,t.element),t.isDoubleTap&&(t.doubleTap.dispatch(e,t.element),t.isDoubleTap=!1)}),0),t.isDoubleTap||(t.singleTapTimeout=setTimeout((function(){t.singleTap.dispatch(e,t.element)}),250))),this.touchEnd.dispatch(e,this.element),this.preV.x=0,this.preV.y=0,this.zoom=1,this.pinchStartLen=null,this.x1=this.x2=this.y1=this.y2=null}}},{key:"cancelAll",value:function(){this._preventTap=!0,clearTimeout(this.singleTapTimeout),clearTimeout(this.tapTimeout),clearTimeout(this.longTapTimeout),clearTimeout(this.swipeTimeout)}},{key:"cancel",value:function(e){this.cancelAll(),this.touchCancel.dispatch(e,this.element)}},{key:"_cancelLongTap",value:function(){clearTimeout(this.longTapTimeout)}},{key:"_cancelSingleTap",value:function(){clearTimeout(this.singleTapTimeout)}},{key:"_swipeDirection",value:function(e,t,i,n){return 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this.singleTapTimeout&&clearTimeout(this.singleTapTimeout),this.tapTimeout&&clearTimeout(this.tapTimeout),this.longTapTimeout&&clearTimeout(this.longTapTimeout),this.swipeTimeout&&clearTimeout(this.swipeTimeout),this.element.removeEventListener("touchstart",this.start),this.element.removeEventListener("touchmove",this.move),this.element.removeEventListener("touchend",this.end),this.element.removeEventListener("touchcancel",this.cancel),this.rotate.del(),this.touchStart.del(),this.multipointStart.del(),this.multipointEnd.del(),this.pinch.del(),this.swipe.del(),this.tap.del(),this.doubleTap.del(),this.longTap.del(),this.singleTap.del(),this.pressMove.del(),this.twoFingerPressMove.del(),this.touchMove.del(),this.touchEnd.del(),this.touchCancel.del(),this.preV=this.pinchStartLen=this.zoom=this.isDoubleTap=this.delta=this.last=this.now=this.tapTimeout=this.singleTapTimeout=this.longTapTimeout=this.swipeTimeout=this.x1=this.x2=this.y1=this.y2=this.preTapPosition=this.rotate=this.touchStart=this.multipointStart=this.multipointEnd=this.pinch=this.swipe=this.tap=this.doubleTap=this.longTap=this.singleTap=this.pressMove=this.touchMove=this.touchEnd=this.touchCancel=this.twoFingerPressMove=null,window.removeEventListener("scroll",this._cancelAllHandler),null}}]),e}();function W(e){var t=function(){var e,t=document.createElement("fakeelement"),i={transition:"transitionend",OTransition:"oTransitionEnd",MozTransition:"transitionend",WebkitTransition:"webkitTransitionEnd"};for(e in i)if(void 0!==t.style[e])return i[e]}(),i=window.innerWidth||document.documentElement.clientWidth||document.body.clientWidth,n=c(e,"gslide-media")?e:e.querySelector(".gslide-media"),s=u(n,".ginner-container"),l=e.querySelector(".gslide-description");i>769&&(n=s),h(n,"greset"),v(n,"translate3d(0, 0, 0)"),a(t,{onElement:n,once:!0,withCallback:function(e,t){d(n,"greset")}}),n.style.opacity="",l&&(l.style.opacity="")}function B(e){if(e.events.hasOwnProperty("touch"))return!1;var t,i,n,s=y(),l=s.width,o=s.height,r=!1,a=null,g=null,f=null,p=!1,m=1,x=1,b=!1,S=!1,w=null,T=null,C=null,k=null,E=0,A=0,L=!1,I=!1,O={},P={},M=0,z=0,X=document.getElementById("glightbox-slider"),Y=document.querySelector(".goverlay"),q=new _(X,{touchStart:function(t){if(r=!0,(c(t.targetTouches[0].target,"ginner-container")||u(t.targetTouches[0].target,".gslide-desc")||"a"==t.targetTouches[0].target.nodeName.toLowerCase())&&(r=!1),u(t.targetTouches[0].target,".gslide-inline")&&!c(t.targetTouches[0].target.parentNode,"gslide-inline")&&(r=!1),r){if(P=t.targetTouches[0],O.pageX=t.targetTouches[0].pageX,O.pageY=t.targetTouches[0].pageY,M=t.targetTouches[0].clientX,z=t.targetTouches[0].clientY,a=e.activeSlide,g=a.querySelector(".gslide-media"),n=a.querySelector(".gslide-inline"),f=null,c(g,"gslide-image")&&(f=g.querySelector("img")),(window.innerWidth||document.documentElement.clientWidth||document.body.clientWidth)>769&&(g=a.querySelector(".ginner-container")),d(Y,"greset"),t.pageX>20&&t.pageX<window.innerWidth-20)return;t.preventDefault()}},touchMove:function(s){if(r&&(P=s.targetTouches[0],!b&&!S)){if(n&&n.offsetHeight>o){var a=O.pageX-P.pageX;if(Math.abs(a)<=13)return!1}p=!0;var h,d=s.targetTouches[0].clientX,c=s.targetTouches[0].clientY,u=M-d,m=z-c;if(Math.abs(u)>Math.abs(m)?(L=!1,I=!0):(I=!1,L=!0),t=P.pageX-O.pageX,E=100*t/l,i=P.pageY-O.pageY,A=100*i/o,L&&f&&(h=1-Math.abs(i)/o,Y.style.opacity=h,e.settings.touchFollowAxis&&(E=0)),I&&(h=1-Math.abs(t)/l,g.style.opacity=h,e.settings.touchFollowAxis&&(A=0)),!f)return v(g,"translate3d(".concat(E,"%, 0, 0)"));v(g,"translate3d(".concat(E,"%, ").concat(A,"%, 0)"))}},touchEnd:function(){if(r){if(p=!1,S||b)return C=w,void(k=T);var t=Math.abs(parseInt(A)),i=Math.abs(parseInt(E));if(!(t>29&&f))return t<29&&i<25?(h(Y,"greset"),Y.style.opacity=1,W(g)):void 0;e.close()}},multipointEnd:function(){setTimeout((function(){b=!1}),50)},multipointStart:function(){b=!0,m=x||1},pinch:function(e){if(!f||p)return!1;b=!0,f.scaleX=f.scaleY=m*e.zoom;var t=m*e.zoom;if(S=!0,t<=1)return S=!1,t=1,k=null,C=null,w=null,T=null,void f.setAttribute("style","");t>4.5&&(t=4.5),f.style.transform="scale3d(".concat(t,", ").concat(t,", 1)"),x=t},pressMove:function(e){if(S&&!b){var t=P.pageX-O.pageX,i=P.pageY-O.pageY;C&&(t+=C),k&&(i+=k),w=t,T=i;var n="translate3d(".concat(t,"px, ").concat(i,"px, 0)");x&&(n+=" scale3d(".concat(x,", ").concat(x,", 1)")),v(f,n)}},swipe:function(t){if(!S)if(b)b=!1;else{if("Left"==t.direction){if(e.index==e.elements.length-1)return W(g);e.nextSlide()}if("Right"==t.direction){if(0==e.index)return W(g);e.prevSlide()}}}});e.events.touch=q}var H=function(){function e(i,n){var s=this,l=arguments.length>2&&void 0!==arguments[2]?arguments[2]:null;if(t(this,e),this.img=i,this.slide=n,this.onclose=l,this.img.setZoomEvents)return!1;this.active=!1,this.zoomedIn=!1,this.dragging=!1,this.currentX=null,this.currentY=null,this.initialX=null,this.initialY=null,this.xOffset=0,this.yOffset=0,this.img.addEventListener("mousedown",(function(e){return s.dragStart(e)}),!1),this.img.addEventListener("mouseup",(function(e){return s.dragEnd(e)}),!1),this.img.addEventListener("mousemove",(function(e){return s.drag(e)}),!1),this.img.addEventListener("click",(function(e){return s.slide.classList.contains("dragging-nav")?(s.zoomOut(),!1):s.zoomedIn?void(s.zoomedIn&&!s.dragging&&s.zoomOut()):s.zoomIn()}),!1),this.img.setZoomEvents=!0}return n(e,[{key:"zoomIn",value:function(){var e=this.widowWidth();if(!(this.zoomedIn||e<=768)){var t=this.img;if(t.setAttribute("data-style",t.getAttribute("style")),t.style.maxWidth=t.naturalWidth+"px",t.style.maxHeight=t.naturalHeight+"px",t.naturalWidth>e){var i=e/2-t.naturalWidth/2;this.setTranslate(this.img.parentNode,i,0)}this.slide.classList.add("zoomed"),this.zoomedIn=!0}}},{key:"zoomOut",value:function(){this.img.parentNode.setAttribute("style",""),this.img.setAttribute("style",this.img.getAttribute("data-style")),this.slide.classList.remove("zoomed"),this.zoomedIn=!1,this.currentX=null,this.currentY=null,this.initialX=null,this.initialY=null,this.xOffset=0,this.yOffset=0,this.onclose&&"function"==typeof this.onclose&&this.onclose()}},{key:"dragStart",value:function(e){e.preventDefault(),this.zoomedIn?("touchstart"===e.type?(this.initialX=e.touches[0].clientX-this.xOffset,this.initialY=e.touches[0].clientY-this.yOffset):(this.initialX=e.clientX-this.xOffset,this.initialY=e.clientY-this.yOffset),e.target===this.img&&(this.active=!0,this.img.classList.add("dragging"))):this.active=!1}},{key:"dragEnd",value:function(e){var t=this;e.preventDefault(),this.initialX=this.currentX,this.initialY=this.currentY,this.active=!1,setTimeout((function(){t.dragging=!1,t.img.isDragging=!1,t.img.classList.remove("dragging")}),100)}},{key:"drag",value:function(e){this.active&&(e.preventDefault(),"touchmove"===e.type?(this.currentX=e.touches[0].clientX-this.initialX,this.currentY=e.touches[0].clientY-this.initialY):(this.currentX=e.clientX-this.initialX,this.currentY=e.clientY-this.initialY),this.xOffset=this.currentX,this.yOffset=this.currentY,this.img.isDragging=!0,this.dragging=!0,this.setTranslate(this.img,this.currentX,this.currentY))}},{key:"onMove",value:function(e){if(this.zoomedIn){var t=e.clientX-this.img.naturalWidth/2,i=e.clientY-this.img.naturalHeight/2;this.setTranslate(this.img,t,i)}}},{key:"setTranslate",value:function(e,t,i){e.style.transform="translate3d("+t+"px, "+i+"px, 0)"}},{key:"widowWidth",value:function(){return window.innerWidth||document.documentElement.clientWidth||document.body.clientWidth}}]),e}(),V=function(){function e(){var i=this,n=arguments.length>0&&void 0!==arguments[0]?arguments[0]:{};t(this,e);var s=n.dragEl,l=n.toleranceX,o=void 0===l?40:l,r=n.toleranceY,a=void 0===r?65:r,h=n.slide,d=void 0===h?null:h,c=n.instance,u=void 0===c?null:c;this.el=s,this.active=!1,this.dragging=!1,this.currentX=null,this.currentY=null,this.initialX=null,this.initialY=null,this.xOffset=0,this.yOffset=0,this.direction=null,this.lastDirection=null,this.toleranceX=o,this.toleranceY=a,this.toleranceReached=!1,this.dragContainer=this.el,this.slide=d,this.instance=u,this.el.addEventListener("mousedown",(function(e){return i.dragStart(e)}),!1),this.el.addEventListener("mouseup",(function(e){return i.dragEnd(e)}),!1),this.el.addEventListener("mousemove",(function(e){return i.drag(e)}),!1)}return n(e,[{key:"dragStart",value:function(e){if(this.slide.classList.contains("zoomed"))this.active=!1;else{"touchstart"===e.type?(this.initialX=e.touches[0].clientX-this.xOffset,this.initialY=e.touches[0].clientY-this.yOffset):(this.initialX=e.clientX-this.xOffset,this.initialY=e.clientY-this.yOffset);var t=e.target.nodeName.toLowerCase();e.target.classList.contains("nodrag")||u(e.target,".nodrag")||-1!==["input","select","textarea","button","a"].indexOf(t)?this.active=!1:(e.preventDefault(),(e.target===this.el||"img"!==t&&u(e.target,".gslide-inline"))&&(this.active=!0,this.el.classList.add("dragging"),this.dragContainer=u(e.target,".ginner-container")))}}},{key:"dragEnd",value:function(e){var t=this;e&&e.preventDefault(),this.initialX=0,this.initialY=0,this.currentX=null,this.currentY=null,this.initialX=null,this.initialY=null,this.xOffset=0,this.yOffset=0,this.active=!1,this.doSlideChange&&(this.instance.preventOutsideClick=!0,"right"==this.doSlideChange&&this.instance.prevSlide(),"left"==this.doSlideChange&&this.instance.nextSlide()),this.doSlideClose&&this.instance.close(),this.toleranceReached||this.setTranslate(this.dragContainer,0,0,!0),setTimeout((function(){t.instance.preventOutsideClick=!1,t.toleranceReached=!1,t.lastDirection=null,t.dragging=!1,t.el.isDragging=!1,t.el.classList.remove("dragging"),t.slide.classList.remove("dragging-nav"),t.dragContainer.style.transform="",t.dragContainer.style.transition=""}),100)}},{key:"drag",value:function(e){if(this.active){e.preventDefault(),this.slide.classList.add("dragging-nav"),"touchmove"===e.type?(this.currentX=e.touches[0].clientX-this.initialX,this.currentY=e.touches[0].clientY-this.initialY):(this.currentX=e.clientX-this.initialX,this.currentY=e.clientY-this.initialY),this.xOffset=this.currentX,this.yOffset=this.currentY,this.el.isDragging=!0,this.dragging=!0,this.doSlideChange=!1,this.doSlideClose=!1;var t=Math.abs(this.currentX),i=Math.abs(this.currentY);if(t>0&&t>=Math.abs(this.currentY)&&(!this.lastDirection||"x"==this.lastDirection)){this.yOffset=0,this.lastDirection="x",this.setTranslate(this.dragContainer,this.currentX,0);var n=this.shouldChange();if(!this.instance.settings.dragAutoSnap&&n&&(this.doSlideChange=n),this.instance.settings.dragAutoSnap&&n)return this.instance.preventOutsideClick=!0,this.toleranceReached=!0,this.active=!1,this.instance.preventOutsideClick=!0,this.dragEnd(null),"right"==n&&this.instance.prevSlide(),void("left"==n&&this.instance.nextSlide())}if(this.toleranceY>0&&i>0&&i>=t&&(!this.lastDirection||"y"==this.lastDirection)){this.xOffset=0,this.lastDirection="y",this.setTranslate(this.dragContainer,0,this.currentY);var s=this.shouldClose();return!this.instance.settings.dragAutoSnap&&s&&(this.doSlideClose=!0),void(this.instance.settings.dragAutoSnap&&s&&this.instance.close())}}}},{key:"shouldChange",value:function(){var e=!1;if(Math.abs(this.currentX)>=this.toleranceX){var t=this.currentX>0?"right":"left";("left"==t&&this.slide!==this.slide.parentNode.lastChild||"right"==t&&this.slide!==this.slide.parentNode.firstChild)&&(e=t)}return e}},{key:"shouldClose",value:function(){var e=!1;return Math.abs(this.currentY)>=this.toleranceY&&(e=!0),e}},{key:"setTranslate",value:function(e,t,i){var n=arguments.length>3&&void 0!==arguments[3]&&arguments[3];e.style.transition=n?"all .2s ease":"",e.style.transform="translate3d(".concat(t,"px, ").concat(i,"px, 0)")}}]),e}();function j(e,t,i,n){var s=e.querySelector(".gslide-media"),l=new Image,o="gSlideTitle_"+i,r="gSlideDesc_"+i;l.addEventListener("load",(function(){T(n)&&n()}),!1),l.src=t.href,""!=t.sizes&&""!=t.srcset&&(l.sizes=t.sizes,l.srcset=t.srcset),l.alt="",I(t.alt)||""===t.alt||(l.alt=t.alt),""!==t.title&&l.setAttribute("aria-labelledby",o),""!==t.description&&l.setAttribute("aria-describedby",r),t.hasOwnProperty("_hasCustomWidth")&&t._hasCustomWidth&&(l.style.width=t.width),t.hasOwnProperty("_hasCustomHeight")&&t._hasCustomHeight&&(l.style.height=t.height),s.insertBefore(l,s.firstChild)}function F(e,t,i,n){var s=this,l=e.querySelector(".ginner-container"),o="gvideo"+i,r=e.querySelector(".gslide-media"),a=this.getAllPlayers();h(l,"gvideo-container"),r.insertBefore(m('<div class="gvideo-wrapper"></div>'),r.firstChild);var d=e.querySelector(".gvideo-wrapper");S(this.settings.plyr.css,"Plyr");var c=t.href,u=location.protocol.replace(":",""),g="",v="",f=!1;"file"==u&&(u="http"),r.style.maxWidth=t.width,S(this.settings.plyr.js,"Plyr",(function(){if(c.match(/vimeo\.com\/([0-9]*)/)){var l=/vimeo.*\/(\d+)/i.exec(c);g="vimeo",v=l[1]}if(c.match(/(youtube\.com|youtube-nocookie\.com)\/watch\?v=([a-zA-Z0-9\-_]+)/)||c.match(/youtu\.be\/([a-zA-Z0-9\-_]+)/)||c.match(/(youtube\.com|youtube-nocookie\.com)\/embed\/([a-zA-Z0-9\-_]+)/)){var r=function(e){var t="";t=void 0!==(e=e.replace(/(>|<)/gi,"").split(/(vi\/|v=|\/v\/|youtu\.be\/|\/embed\/)/))[2]?(t=e[2].split(/[^0-9a-z_\-]/i))[0]:e;return t}(c);g="youtube",v=r}if(null!==c.match(/\.(mp4|ogg|webm|mov)$/)){g="local";var u='<video id="'+o+'" ';u+='style="background:#000; max-width: '.concat(t.width,';" '),u+='preload="metadata" ',u+='x-webkit-airplay="allow" ',u+="playsinline ",u+="controls ",u+='class="gvideo-local">';var p=c.toLowerCase().split(".").pop(),y={mp4:"",ogg:"",webm:""};for(var x in y[p="mov"==p?"mp4":p]=c,y)if(y.hasOwnProperty(x)){var S=y[x];t.hasOwnProperty(x)&&(S=t[x]),""!==S&&(u+='<source src="'.concat(S,'" type="video/').concat(x,'">'))}f=m(u+="</video>")}var w=f||m('<div id="'.concat(o,'" data-plyr-provider="').concat(g,'" data-plyr-embed-id="').concat(v,'"></div>'));h(d,"".concat(g,"-video gvideo")),d.appendChild(w),d.setAttribute("data-id",o),d.setAttribute("data-index",i);var C=O(s.settings.plyr,"config")?s.settings.plyr.config:{},k=new Plyr("#"+o,C);k.on("ready",(function(e){var t=e.detail.plyr;a[o]=t,T(n)&&n()})),b((function(){return e.querySelector("iframe")&&"true"==e.querySelector("iframe").dataset.ready}),(function(){s.resize(e)})),k.on("enterfullscreen",R),k.on("exitfullscreen",R)}))}function R(e){var t=u(e.target,".gslide-media");"enterfullscreen"==e.type&&h(t,"fullscreen"),"exitfullscreen"==e.type&&d(t,"fullscreen")}function G(e,t,i,n){var s,l=this,o=e.querySelector(".gslide-media"),r=!(!O(t,"href")||!t.href)&&t.href.split("#").pop().trim(),d=!(!O(t,"content")||!t.content)&&t.content;if(d&&(C(d)&&(s=m('<div class="ginlined-content">'.concat(d,"</div>"))),k(d))){"none"==d.style.display&&(d.style.display="block");var c=document.createElement("div");c.className="ginlined-content",c.appendChild(d),s=c}if(r){var u=document.getElementById(r);if(!u)return!1;var g=u.cloneNode(!0);g.style.height=t.height,g.style.maxWidth=t.width,h(g,"ginlined-content"),s=g}if(!s)return console.error("Unable to append inline slide content",t),!1;o.style.height=t.height,o.style.width=t.width,o.appendChild(s),this.events["inlineclose"+r]=a("click",{onElement:o.querySelectorAll(".gtrigger-close"),withCallback:function(e){e.preventDefault(),l.close()}}),T(n)&&n()}function Z(e,t,i,n){var s=e.querySelector(".gslide-media"),l=function(e){var t=e.url,i=e.allow,n=e.callback,s=e.appendTo,l=document.createElement("iframe");return l.className="vimeo-video 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t=e;if(null!==(e=e.toLowerCase()).match(/\.(jpeg|jpg|jpe|gif|png|apn|webp|avif|svg)/))return"image";if(e.match(/(youtube\.com|youtube-nocookie\.com)\/watch\?v=([a-zA-Z0-9\-_]+)/)||e.match(/youtu\.be\/([a-zA-Z0-9\-_]+)/)||e.match(/(youtube\.com|youtube-nocookie\.com)\/embed\/([a-zA-Z0-9\-_]+)/))return"video";if(e.match(/vimeo\.com\/([0-9]*)/))return"video";if(null!==e.match(/\.(mp4|ogg|webm|mov)/))return"video";if(null!==e.match(/\.(mp3|wav|wma|aac|ogg)/))return"audio";if(e.indexOf("#")>-1&&""!==t.split("#").pop().trim())return"inline";return e.indexOf("goajax=true")>-1?"ajax":"external"}},{key:"parseConfig",value:function(e,t){var i=this,n=l({descPosition:t.descPosition},this.defaults);if(L(e)&&!k(e)){O(e,"type")||(O(e,"content")&&e.content?e.type="inline":O(e,"href")&&(e.type=this.sourceType(e.href)));var s=l(n,e);return this.setSize(s,t),s}var r="",a=e.getAttribute("data-glightbox"),h=e.nodeName.toLowerCase();if("a"===h&&(r=e.href),"img"===h&&(r=e.src,n.alt=e.alt),n.href=r,o(n,(function(s,l){O(t,l)&&"width"!==l&&(n[l]=t[l]);var o=e.dataset[l];I(o)||(n[l]=i.sanitizeValue(o))})),n.content&&(n.type="inline"),!n.type&&r&&(n.type=this.sourceType(r)),I(a)){if(!n.title&&"a"==h){var d=e.title;I(d)||""===d||(n.title=d)}if(!n.title&&"img"==h){var c=e.alt;I(c)||""===c||(n.title=c)}}else{var u=[];o(n,(function(e,t){u.push(";\\s?"+t)})),u=u.join("\\s?:|"),""!==a.trim()&&o(n,(function(e,t){var s=a,l=new RegExp("s?"+t+"s?:s?(.*?)("+u+"s?:|$)"),o=s.match(l);if(o&&o.length&&o[1]){var r=o[1].trim().replace(/;\s*$/,"");n[t]=i.sanitizeValue(r)}}))}if(n.description&&"."===n.description.substring(0,1)){var g;try{g=document.querySelector(n.description).innerHTML}catch(e){if(!(e instanceof DOMException))throw e}g&&(n.description=g)}if(!n.description){var v=e.querySelector(".glightbox-desc");v&&(n.description=v.innerHTML)}return this.setSize(n,t,e),this.slideConfig=n,n}},{key:"setSize",value:function(e,t){var i=arguments.length>2&&void 0!==arguments[2]?arguments[2]:null,n="video"==e.type?this.checkSize(t.videosWidth):this.checkSize(t.width),s=this.checkSize(t.height);return e.width=O(e,"width")&&""!==e.width?this.checkSize(e.width):n,e.height=O(e,"height")&&""!==e.height?this.checkSize(e.height):s,i&&"image"==e.type&&(e._hasCustomWidth=!!i.dataset.width,e._hasCustomHeight=!!i.dataset.height),e}},{key:"checkSize",value:function(e){return M(e)?"".concat(e,"px"):e}},{key:"sanitizeValue",value:function(e){return"true"!==e&&"false"!==e?e:"true"===e}}]),e}(),U=function(){function e(i,n,s){t(this,e),this.element=i,this.instance=n,this.index=s}return n(e,[{key:"setContent",value:function(){var e=this,t=arguments.length>0&&void 0!==arguments[0]?arguments[0]:null,i=arguments.length>1&&void 0!==arguments[1]&&arguments[1];if(c(t,"loaded"))return!1;var n=this.instance.settings,s=this.slideConfig,l=w();T(n.beforeSlideLoad)&&n.beforeSlideLoad({index:this.index,slide:t,player:!1});var o=s.type,r=s.descPosition,a=t.querySelector(".gslide-media"),d=t.querySelector(".gslide-title"),u=t.querySelector(".gslide-desc"),g=t.querySelector(".gdesc-inner"),v=i,f="gSlideTitle_"+this.index,p="gSlideDesc_"+this.index;if(T(n.afterSlideLoad)&&(v=function(){T(i)&&i(),n.afterSlideLoad({index:e.index,slide:t,player:e.instance.getSlidePlayerInstance(e.index)})}),""==s.title&&""==s.description?g&&g.parentNode.parentNode.removeChild(g.parentNode):(d&&""!==s.title?(d.id=f,d.innerHTML=s.title):d.parentNode.removeChild(d),u&&""!==s.description?(u.id=p,l&&n.moreLength>0?(s.smallDescription=this.slideShortDesc(s.description,n.moreLength,n.moreText),u.innerHTML=s.smallDescription,this.descriptionEvents(u,s)):u.innerHTML=s.description):u.parentNode.removeChild(u),h(a.parentNode,"desc-".concat(r)),h(g.parentNode,"description-".concat(r))),h(a,"gslide-".concat(o)),h(t,"loaded"),"video"!==o){if("external"!==o)return"inline"===o?(G.apply(this.instance,[t,s,this.index,v]),void(s.draggable&&new V({dragEl:t.querySelector(".gslide-inline"),toleranceX:n.dragToleranceX,toleranceY:n.dragToleranceY,slide:t,instance:this.instance}))):void("image"!==o?T(v)&&v():j(t,s,this.index,(function(){var i=t.querySelector("img");s.draggable&&new V({dragEl:i,toleranceX:n.dragToleranceX,toleranceY:n.dragToleranceY,slide:t,instance:e.instance}),s.zoomable&&i.naturalWidth>i.offsetWidth&&(h(i,"zoomable"),new H(i,t,(function(){e.instance.resize()}))),T(v)&&v()})));Z.apply(this,[t,s,this.index,v])}else F.apply(this.instance,[t,s,this.index,v])}},{key:"slideShortDesc",value:function(e){var t=arguments.length>1&&void 0!==arguments[1]?arguments[1]:50,i=arguments.length>2&&void 0!==arguments[2]&&arguments[2],n=document.createElement("div");n.innerHTML=e;var s=n.innerText,l=i;if((e=s.trim()).length<=t)return e;var o=e.substr(0,t-1);return l?(n=null,o+'... <a href="#" class="desc-more">'+i+"</a>"):o}},{key:"descriptionEvents",value:function(e,t){var i=this,n=e.querySelector(".desc-more");if(!n)return!1;a("click",{onElement:n,withCallback:function(e,n){e.preventDefault();var s=document.body,l=u(n,".gslide-desc");if(!l)return!1;l.innerHTML=t.description,h(s,"gdesc-open");var o=a("click",{onElement:[s,u(l,".gslide-description")],withCallback:function(e,n){"a"!==e.target.nodeName.toLowerCase()&&(d(s,"gdesc-open"),h(s,"gdesc-closed"),l.innerHTML=t.smallDescription,i.descriptionEvents(l,t),setTimeout((function(){d(s,"gdesc-closed")}),400),o.destroy())}})}})}},{key:"create",value:function(){return m(this.instance.settings.slideHTML)}},{key:"getConfig",value:function(){k(this.element)||this.element.hasOwnProperty("draggable")||(this.element.draggable=this.instance.settings.draggable);var e=new $(this.instance.settings.slideExtraAttributes);return this.slideConfig=e.parseConfig(this.element,this.instance.settings),this.slideConfig}}]),e}(),J=w(),K=null!==w()||void 0!==document.createTouch||"ontouchstart"in window||"onmsgesturechange"in window||navigator.msMaxTouchPoints,Q=document.getElementsByTagName("html")[0],ee={selector:".glightbox",elements:null,skin:"clean",theme:"clean",closeButton:!0,startAt:null,autoplayVideos:!0,autofocusVideos:!0,descPosition:"bottom",width:"900px",height:"506px",videosWidth:"960px",beforeSlideChange:null,afterSlideChange:null,beforeSlideLoad:null,afterSlideLoad:null,slideInserted:null,slideRemoved:null,slideExtraAttributes:null,onOpen:null,onClose:null,loop:!1,zoomable:!0,draggable:!0,dragAutoSnap:!1,dragToleranceX:40,dragToleranceY:65,preload:!0,oneSlidePerOpen:!1,touchNavigation:!0,touchFollowAxis:!0,keyboardNavigation:!0,closeOnOutsideClick:!0,plugins:!1,plyr:{css:"https://cdn.plyr.io/3.6.8/plyr.css",js:"https://cdn.plyr.io/3.6.8/plyr.js",config:{ratio:"16:9",fullscreen:{enabled:!0,iosNative:!0},youtube:{noCookie:!0,rel:0,showinfo:0,iv_load_policy:3},vimeo:{byline:!1,portrait:!1,title:!1,transparent:!1}}},openEffect:"zoom",closeEffect:"zoom",slideEffect:"slide",moreText:"See more",moreLength:60,cssEfects:{fade:{in:"fadeIn",out:"fadeOut"},zoom:{in:"zoomIn",out:"zoomOut"},slide:{in:"slideInRight",out:"slideOutLeft"},slideBack:{in:"slideInLeft",out:"slideOutRight"},none:{in:"none",out:"none"}},svg:{close:'<svg version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" x="0px" y="0px" viewBox="0 0 512 512" xml:space="preserve"><g><g><path d="M505.943,6.058c-8.077-8.077-21.172-8.077-29.249,0L6.058,476.693c-8.077,8.077-8.077,21.172,0,29.249C10.096,509.982,15.39,512,20.683,512c5.293,0,10.586-2.019,14.625-6.059L505.943,35.306C514.019,27.23,514.019,14.135,505.943,6.058z"/></g></g><g><g><path d="M505.942,476.694L35.306,6.059c-8.076-8.077-21.172-8.077-29.248,0c-8.077,8.076-8.077,21.171,0,29.248l470.636,470.636c4.038,4.039,9.332,6.058,14.625,6.058c5.293,0,10.587-2.019,14.624-6.057C514.018,497.866,514.018,484.771,505.942,476.694z"/></g></g></svg>',next:'<svg version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" x="0px" y="0px" viewBox="0 0 477.175 477.175" xml:space="preserve"> <g><path d="M360.731,229.075l-225.1-225.1c-5.3-5.3-13.8-5.3-19.1,0s-5.3,13.8,0,19.1l215.5,215.5l-215.5,215.5c-5.3,5.3-5.3,13.8,0,19.1c2.6,2.6,6.1,4,9.5,4c3.4,0,6.9-1.3,9.5-4l225.1-225.1C365.931,242.875,365.931,234.275,360.731,229.075z"/></g></svg>',prev:'<svg version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" x="0px" y="0px" viewBox="0 0 477.175 477.175" xml:space="preserve"><g><path d="M145.188,238.575l215.5-215.5c5.3-5.3,5.3-13.8,0-19.1s-13.8-5.3-19.1,0l-225.1,225.1c-5.3,5.3-5.3,13.8,0,19.1l225.1,225c2.6,2.6,6.1,4,9.5,4s6.9-1.3,9.5-4c5.3-5.3,5.3-13.8,0-19.1L145.188,238.575z"/></g></svg>'},slideHTML:'<div class="gslide">\n    <div class="gslide-inner-content">\n        <div class="ginner-container">\n            <div class="gslide-media">\n            </div>\n            <div class="gslide-description">\n                <div class="gdesc-inner">\n                    <h4 class="gslide-title"></h4>\n                    <div class="gslide-desc"></div>\n                </div>\n            </div>\n        </div>\n    </div>\n</div>',lightboxHTML:'<div id="glightbox-body" class="glightbox-container" tabindex="-1" role="dialog" aria-hidden="false">\n    <div class="gloader visible"></div>\n    <div class="goverlay"></div>\n    <div class="gcontainer">\n    <div id="glightbox-slider" class="gslider"></div>\n    <button class="gclose gbtn" aria-label="Close" data-taborder="3">{closeSVG}</button>\n    <button class="gprev gbtn" aria-label="Previous" data-taborder="2">{prevSVG}</button>\n    <button class="gnext gbtn" aria-label="Next" data-taborder="1">{nextSVG}</button>\n</div>\n</div>'},te=function(){function e(){var i=arguments.length>0&&void 0!==arguments[0]?arguments[0]:{};t(this,e),this.customOptions=i,this.settings=l(ee,i),this.effectsClasses=this.getAnimationClasses(),this.videoPlayers={},this.apiEvents=[],this.fullElementsList=!1}return n(e,[{key:"init",value:function(){var e=this,t=this.getSelector();t&&(this.baseEvents=a("click",{onElement:t,withCallback:function(t,i){t.preventDefault(),e.open(i)}})),this.elements=this.getElements()}},{key:"open",value:function(){var e=arguments.length>0&&void 0!==arguments[0]?arguments[0]:null,t=arguments.length>1&&void 0!==arguments[1]?arguments[1]:null;if(0==this.elements.length)return!1;this.activeSlide=null,this.prevActiveSlideIndex=null,this.prevActiveSlide=null;var i=M(t)?t:this.settings.startAt;if(k(e)){var n=e.getAttribute("data-gallery");n&&(this.fullElementsList=this.elements,this.elements=this.getGalleryElements(this.elements,n)),I(i)&&(i=this.getElementIndex(e))<0&&(i=0)}M(i)||(i=0),this.build(),g(this.overlay,"none"==this.settings.openEffect?"none":this.settings.cssEfects.fade.in);var s=document.body,l=window.innerWidth-document.documentElement.clientWidth;if(l>0){var o=document.createElement("style");o.type="text/css",o.className="gcss-styles",o.innerText=".gscrollbar-fixer {margin-right: ".concat(l,"px}"),document.head.appendChild(o),h(s,"gscrollbar-fixer")}h(s,"glightbox-open"),h(Q,"glightbox-open"),J&&(h(document.body,"glightbox-mobile"),this.settings.slideEffect="slide"),this.showSlide(i,!0),1==this.elements.length?(h(this.prevButton,"glightbox-button-hidden"),h(this.nextButton,"glightbox-button-hidden")):(d(this.prevButton,"glightbox-button-hidden"),d(this.nextButton,"glightbox-button-hidden")),this.lightboxOpen=!0,this.trigger("open"),T(this.settings.onOpen)&&this.settings.onOpen(),K&&this.settings.touchNavigation&&B(this),this.settings.keyboardNavigation&&X(this)}},{key:"openAt",value:function(){var e=arguments.length>0&&void 0!==arguments[0]?arguments[0]:0;this.open(null,e)}},{key:"showSlide",value:function(){var e=this,t=arguments.length>0&&void 0!==arguments[0]?arguments[0]:0,i=arguments.length>1&&void 0!==arguments[1]&&arguments[1];f(this.loader),this.index=parseInt(t);var n=this.slidesContainer.querySelector(".current");n&&d(n,"current"),this.slideAnimateOut();var s=this.slidesContainer.querySelectorAll(".gslide")[t];if(c(s,"loaded"))this.slideAnimateIn(s,i),p(this.loader);else{f(this.loader);var l=this.elements[t],o={index:this.index,slide:s,slideNode:s,slideConfig:l.slideConfig,slideIndex:this.index,trigger:l.node,player:null};this.trigger("slide_before_load",o),l.instance.setContent(s,(function(){p(e.loader),e.resize(),e.slideAnimateIn(s,i),e.trigger("slide_after_load",o)}))}this.slideDescription=s.querySelector(".gslide-description"),this.slideDescriptionContained=this.slideDescription&&c(this.slideDescription.parentNode,"gslide-media"),this.settings.preload&&(this.preloadSlide(t+1),this.preloadSlide(t-1)),this.updateNavigationClasses(),this.activeSlide=s}},{key:"preloadSlide",value:function(e){var t=this;if(e<0||e>this.elements.length-1)return!1;if(I(this.elements[e]))return!1;var i=this.slidesContainer.querySelectorAll(".gslide")[e];if(c(i,"loaded"))return!1;var n=this.elements[e],s=n.type,l={index:e,slide:i,slideNode:i,slideConfig:n.slideConfig,slideIndex:e,trigger:n.node,player:null};this.trigger("slide_before_load",l),"video"==s||"external"==s?setTimeout((function(){n.instance.setContent(i,(function(){t.trigger("slide_after_load",l)}))}),200):n.instance.setContent(i,(function(){t.trigger("slide_after_load",l)}))}},{key:"prevSlide",value:function(){this.goToSlide(this.index-1)}},{key:"nextSlide",value:function(){this.goToSlide(this.index+1)}},{key:"goToSlide",value:function(){var e=arguments.length>0&&void 0!==arguments[0]&&arguments[0];if(this.prevActiveSlide=this.activeSlide,this.prevActiveSlideIndex=this.index,!this.loop()&&(e<0||e>this.elements.length-1))return!1;e<0?e=this.elements.length-1:e>=this.elements.length&&(e=0),this.showSlide(e)}},{key:"insertSlide",value:function(){var e=arguments.length>0&&void 0!==arguments[0]?arguments[0]:{},t=arguments.length>1&&void 0!==arguments[1]?arguments[1]:-1;t<0&&(t=this.elements.length);var i=new U(e,this,t),n=i.getConfig(),s=l({},n),o=i.create(),r=this.elements.length-1;s.index=t,s.node=!1,s.instance=i,s.slideConfig=n,this.elements.splice(t,0,s);var a=null,h=null;if(this.slidesContainer){if(t>r)this.slidesContainer.appendChild(o);else{var d=this.slidesContainer.querySelectorAll(".gslide")[t];this.slidesContainer.insertBefore(o,d)}(this.settings.preload&&0==this.index&&0==t||this.index-1==t||this.index+1==t)&&this.preloadSlide(t),0==this.index&&0==t&&(this.index=1),this.updateNavigationClasses(),a=this.slidesContainer.querySelectorAll(".gslide")[t],h=this.getSlidePlayerInstance(t),s.slideNode=a}this.trigger("slide_inserted",{index:t,slide:a,slideNode:a,slideConfig:n,slideIndex:t,trigger:null,player:h}),T(this.settings.slideInserted)&&this.settings.slideInserted({index:t,slide:a,player:h})}},{key:"removeSlide",value:function(){var e=arguments.length>0&&void 0!==arguments[0]?arguments[0]:-1;if(e<0||e>this.elements.length-1)return!1;var t=this.slidesContainer&&this.slidesContainer.querySelectorAll(".gslide")[e];t&&(this.getActiveSlideIndex()==e&&(e==this.elements.length-1?this.prevSlide():this.nextSlide()),t.parentNode.removeChild(t)),this.elements.splice(e,1),this.trigger("slide_removed",e),T(this.settings.slideRemoved)&&this.settings.slideRemoved(e)}},{key:"slideAnimateIn",value:function(e,t){var i=this,n=e.querySelector(".gslide-media"),s=e.querySelector(".gslide-description"),l={index:this.prevActiveSlideIndex,slide:this.prevActiveSlide,slideNode:this.prevActiveSlide,slideIndex:this.prevActiveSlide,slideConfig:I(this.prevActiveSlideIndex)?null:this.elements[this.prevActiveSlideIndex].slideConfig,trigger:I(this.prevActiveSlideIndex)?null:this.elements[this.prevActiveSlideIndex].node,player:this.getSlidePlayerInstance(this.prevActiveSlideIndex)},o={index:this.index,slide:this.activeSlide,slideNode:this.activeSlide,slideConfig:this.elements[this.index].slideConfig,slideIndex:this.index,trigger:this.elements[this.index].node,player:this.getSlidePlayerInstance(this.index)};if(n.offsetWidth>0&&s&&(p(s),s.style.display=""),d(e,this.effectsClasses),t)g(e,this.settings.cssEfects[this.settings.openEffect].in,(function(){i.settings.autoplayVideos&&i.slidePlayerPlay(e),i.trigger("slide_changed",{prev:l,current:o}),T(i.settings.afterSlideChange)&&i.settings.afterSlideChange.apply(i,[l,o])}));else{var r=this.settings.slideEffect,a="none"!==r?this.settings.cssEfects[r].in:r;this.prevActiveSlideIndex>this.index&&"slide"==this.settings.slideEffect&&(a=this.settings.cssEfects.slideBack.in),g(e,a,(function(){i.settings.autoplayVideos&&i.slidePlayerPlay(e),i.trigger("slide_changed",{prev:l,current:o}),T(i.settings.afterSlideChange)&&i.settings.afterSlideChange.apply(i,[l,o])}))}setTimeout((function(){i.resize(e)}),100),h(e,"current")}},{key:"slideAnimateOut",value:function(){if(!this.prevActiveSlide)return!1;var e=this.prevActiveSlide;d(e,this.effectsClasses),h(e,"prev");var t=this.settings.slideEffect,i="none"!==t?this.settings.cssEfects[t].out:t;this.slidePlayerPause(e),this.trigger("slide_before_change",{prev:{index:this.prevActiveSlideIndex,slide:this.prevActiveSlide,slideNode:this.prevActiveSlide,slideIndex:this.prevActiveSlideIndex,slideConfig:I(this.prevActiveSlideIndex)?null:this.elements[this.prevActiveSlideIndex].slideConfig,trigger:I(this.prevActiveSlideIndex)?null:this.elements[this.prevActiveSlideIndex].node,player:this.getSlidePlayerInstance(this.prevActiveSlideIndex)},current:{index:this.index,slide:this.activeSlide,slideNode:this.activeSlide,slideIndex:this.index,slideConfig:this.elements[this.index].slideConfig,trigger:this.elements[this.index].node,player:this.getSlidePlayerInstance(this.index)}}),T(this.settings.beforeSlideChange)&&this.settings.beforeSlideChange.apply(this,[{index:this.prevActiveSlideIndex,slide:this.prevActiveSlide,player:this.getSlidePlayerInstance(this.prevActiveSlideIndex)},{index:this.index,slide:this.activeSlide,player:this.getSlidePlayerInstance(this.index)}]),this.prevActiveSlideIndex>this.index&&"slide"==this.settings.slideEffect&&(i=this.settings.cssEfects.slideBack.out),g(e,i,(function(){var t=e.querySelector(".ginner-container"),i=e.querySelector(".gslide-media"),n=e.querySelector(".gslide-description");t.style.transform="",i.style.transform="",d(i,"greset"),i.style.opacity="",n&&(n.style.opacity=""),d(e,"prev")}))}},{key:"getAllPlayers",value:function(){return this.videoPlayers}},{key:"getSlidePlayerInstance",value:function(e){var t="gvideo"+e,i=this.getAllPlayers();return!(!O(i,t)||!i[t])&&i[t]}},{key:"stopSlideVideo",value:function(e){if(k(e)){var t=e.querySelector(".gvideo-wrapper");t&&(e=t.getAttribute("data-index"))}console.log("stopSlideVideo is deprecated, use slidePlayerPause");var i=this.getSlidePlayerInstance(e);i&&i.playing&&i.pause()}},{key:"slidePlayerPause",value:function(e){if(k(e)){var t=e.querySelector(".gvideo-wrapper");t&&(e=t.getAttribute("data-index"))}var i=this.getSlidePlayerInstance(e);i&&i.playing&&i.pause()}},{key:"playSlideVideo",value:function(e){if(k(e)){var t=e.querySelector(".gvideo-wrapper");t&&(e=t.getAttribute("data-index"))}console.log("playSlideVideo is deprecated, use slidePlayerPlay");var i=this.getSlidePlayerInstance(e);i&&!i.playing&&i.play()}},{key:"slidePlayerPlay",value:function(e){if(k(e)){var t=e.querySelector(".gvideo-wrapper");t&&(e=t.getAttribute("data-index"))}var i=this.getSlidePlayerInstance(e);i&&!i.playing&&(i.play(),this.settings.autofocusVideos&&i.elements.container.focus())}},{key:"setElements",value:function(e){var t=this;this.settings.elements=!1;var i=[];e&&e.length&&o(e,(function(e,n){var s=new U(e,t,n),o=s.getConfig(),r=l({},o);r.slideConfig=o,r.instance=s,r.index=n,i.push(r)})),this.elements=i,this.lightboxOpen&&(this.slidesContainer.innerHTML="",this.elements.length&&(o(this.elements,(function(){var e=m(t.settings.slideHTML);t.slidesContainer.appendChild(e)})),this.showSlide(0,!0)))}},{key:"getElementIndex",value:function(e){var t=!1;return o(this.elements,(function(i,n){if(O(i,"node")&&i.node==e)return t=n,!0})),t}},{key:"getElements",value:function(){var e=this,t=[];this.elements=this.elements?this.elements:[],!I(this.settings.elements)&&E(this.settings.elements)&&this.settings.elements.length&&o(this.settings.elements,(function(i,n){var s=new U(i,e,n),o=s.getConfig(),r=l({},o);r.node=!1,r.index=n,r.instance=s,r.slideConfig=o,t.push(r)}));var i=!1;return this.getSelector()&&(i=document.querySelectorAll(this.getSelector())),i?(o(i,(function(i,n){var s=new U(i,e,n),o=s.getConfig(),r=l({},o);r.node=i,r.index=n,r.instance=s,r.slideConfig=o,r.gallery=i.getAttribute("data-gallery"),t.push(r)})),t):t}},{key:"getGalleryElements",value:function(e,t){return e.filter((function(e){return e.gallery==t}))}},{key:"getSelector",value:function(){return!this.settings.elements&&(this.settings.selector&&"data-"==this.settings.selector.substring(0,5)?"*[".concat(this.settings.selector,"]"):this.settings.selector)}},{key:"getActiveSlide",value:function(){return 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d=document.getElementById("glightbox-body");this.modal=d;var g=d.querySelector(".gclose");this.prevButton=d.querySelector(".gprev"),this.nextButton=d.querySelector(".gnext"),this.overlay=d.querySelector(".goverlay"),this.loader=d.querySelector(".gloader"),this.slidesContainer=document.getElementById("glightbox-slider"),this.bodyHiddenChildElms=i,this.events={},h(this.modal,"glightbox-"+this.settings.skin),this.settings.closeButton&&g&&(this.events.close=a("click",{onElement:g,withCallback:function(t,i){t.preventDefault(),e.close()}})),g&&!this.settings.closeButton&&g.parentNode.removeChild(g),this.nextButton&&(this.events.next=a("click",{onElement:this.nextButton,withCallback:function(t,i){t.preventDefault(),e.nextSlide()}})),this.prevButton&&(this.events.prev=a("click",{onElement:this.prevButton,withCallback:function(t,i){t.preventDefault(),e.prevSlide()}})),this.settings.closeOnOutsideClick&&(this.events.outClose=a("click",{onElement:d,withCallback:function(t,i){e.preventOutsideClick||c(document.body,"glightbox-mobile")||u(t.target,".ginner-container")||u(t.target,".gbtn")||c(t.target,"gnext")||c(t.target,"gprev")||e.close()}})),o(this.elements,(function(t,i){e.slidesContainer.appendChild(t.instance.create()),t.slideNode=e.slidesContainer.querySelectorAll(".gslide")[i]})),K&&h(document.body,"glightbox-touch"),this.events.resize=a("resize",{onElement:window,withCallback:function(){e.resize()}}),this.built=!0}},{key:"resize",value:function(){var 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m=g.split(":"),x=this.settings.videosWidth,b=this.settings.videosWidth,S=(b=M(x)||-1!==x.indexOf("px")?parseInt(x):-1!==x.indexOf("vw")?l*parseInt(x)/100:-1!==x.indexOf("vh")?o*parseInt(x)/100:-1!==x.indexOf("%")?l*parseInt(x)/100:parseInt(i.clientWidth))/(parseInt(m[0])/parseInt(m[1]));if(S=Math.floor(S),r&&(o-=s.offsetHeight),b>l||S>o||o<S&&l>b){var w=i.offsetWidth,T=i.offsetHeight,C=o/T,k={width:w*C,height:T*C};i.parentNode.setAttribute("style","max-width: ".concat(k.width,"px")),r&&s.setAttribute("style","max-width: ".concat(k.width,"px;"))}else i.parentNode.style.maxWidth="".concat(x),r&&s.setAttribute("style","max-width: ".concat(x,";"))}}}}},{key:"reload",value:function(){this.init()}},{key:"updateNavigationClasses",value:function(){var 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this.events)this.events.hasOwnProperty(t)&&this.events[t].destroy();this.events=null}return!1}if(this.closing)return!1;this.closing=!0,this.slidePlayerPause(this.activeSlide),this.fullElementsList&&(this.elements=this.fullElementsList),this.bodyHiddenChildElms.length&&o(this.bodyHiddenChildElms,(function(e){e.removeAttribute("aria-hidden")})),h(this.modal,"glightbox-closing"),g(this.overlay,"none"==this.settings.openEffect?"none":this.settings.cssEfects.fade.out),g(this.activeSlide,this.settings.cssEfects[this.settings.closeEffect].out,(function(){if(e.activeSlide=null,e.prevActiveSlideIndex=null,e.prevActiveSlide=null,e.built=!1,e.events){for(var t in e.events)e.events.hasOwnProperty(t)&&e.events[t].destroy();e.events=null}var i=document.body;d(Q,"glightbox-open"),d(i,"glightbox-open touching gdesc-open glightbox-touch glightbox-mobile gscrollbar-fixer"),e.modal.parentNode.removeChild(e.modal),e.trigger("close"),T(e.settings.onClose)&&e.settings.onClose();var 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+/*! update cache: 20251017053000 */
diff --git a/zh-hant/assets/stylesheets/glightbox.min.css b/zh-hant/assets/stylesheets/glightbox.min.css
index fad29fb3d..1319b226b 100644
--- a/zh-hant/assets/stylesheets/glightbox.min.css
+++ b/zh-hant/assets/stylesheets/glightbox.min.css
@@ -1,2 +1,2 @@
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diff --git a/zh-hant/assets/stylesheets/palette.06af60db.min.css b/zh-hant/assets/stylesheets/palette.06af60db.min.css
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+++ b/zh-hant/assets/stylesheets/palette.06af60db.min.css
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diff --git a/zh-hant/stylesheets/extra.css b/zh-hant/stylesheets/extra.css
index fb0a7633a..7166967b6 100644
--- a/zh-hant/stylesheets/extra.css
+++ b/zh-hant/stylesheets/extra.css
@@ -552,4 +552,4 @@ a:hover .text-button span {
   width: 100%;
   height: 100%;
 }
-/*! update cache: 20251007160237 */
+/*! update cache: 20251017053000 */